The value of X is 42.5 and Y is 90.98.
How to solve equations?
To solve an equation, you need to perform the same operation on both sides of the equation until you isolate the variable on one side and have a numerical value on the other side. The process of solving an equation generally involves the following steps:
Simplify both sides of the equation by combining like terms and following the order of operations.
Add or subtract the same value from both sides of the equation to isolate the variable term.
Multiply or divide both sides of the equation by the same non-zero value to isolate the variable term.
Check your solution by plugging it back into the original equation and verifying that it satisfies the equation.
Solving the given equations :
To solve for X, we can use inverse operations to isolate the variable. Since 10 is multiplied by X, we can use the inverse operation of division by 10 to isolate X. So, dividing both sides of the equation by 10 gives:
[tex]10x/10 = 425/10[/tex]
Simplifying the left side of the equation gives:
[tex]x = 42.5[/tex]
Therefore, X is 42.5.
To solve for Y, we can use similar steps. Since 81729 is divided by Y, we can use the inverse operation of multiplication by Y to isolate Y. So, multiplying both sides of the equation by Y gives:
[tex]81729 = 898.12 \times Y[/tex]
Simplifying the right side of the equation gives:
[tex]Y = 81729 / 898.12[/tex]
[tex]Y = 90.98[/tex]
Therefore, Y is 90.98.
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An avid gardener wants to know which of two brands of fertilizer is best for her tomatoes. The two brands of fertilizer are A and B. She plants five pairs of tomato plants in two rectangular planters and places them beside one another. She gives each set of tomato plants the same amount of water each day, only she gives one set of plants fertilizer A and the other set of plants fertilizer B. At the end of the growing season, she counts the number of tomatoes each plant has yielded. Assume that all conditions for inference have been met. The rectangular planters are lined up so that plant 1 is beside plant 6, and plant 2 is beside plant 7, and so on. The yield for the five pairs of tomato plants are given. Plant 1 2 3 4 5 Yield with Fertilizer A 7 6 5 8 10 Plant 6 7 8 9 10 Yield with Fertilizer B 4 7 6 5 3 The gardener believes that fertilizer A enhances the yield of her tomatoes more than fertilizer B. She uses the following order of subtraction when determining the difference in the yields for the two brands: A- B (a) We would like to carry out a t test for the population mean difference. Calculate the point estimate. (b) Calculate the standard deviation of the differences. (Round your answer to three decimal places.) (c) Calculate the test statistic. (Round your answer to two decimal places.)
(a) Point estimate (mean difference): 2.2 tomatoes. (b) The standard deviation of differences: Approximately 3.47. (c) The test statistic: Approximately 1.38.
To perform a t-test for the population mean difference, follow these steps:
(a) Calculate the point estimate (mean difference): The point estimate is the mean difference between the yields of fertilizer A and fertilizer B.
Mean difference = (Sum of differences) / Number of pairs
Using the given data gives:
Mean difference = ((7-4) + (6-7) + (5-6) + (8-5) + (10-3)) / 5
Subtracting gives:
Mean difference = (3 - 1 - 1 + 3 + 7) / 5
Solving gives:
Mean difference = 11 / 5
Dividing gives:
Mean difference = 2.2
(b) Calculate the standard deviation of the differences:
To calculate the standard deviation of the differences, we need to calculate the squared differences, find their sum, divide by (n-1), and then take the square root.
Squared differences:[tex](3 - 2.2)^2, (-1 - 2.2)^2, (-1 - 2.2)^2, (3 - 2.2)^2, (7 - 2.2)^2[/tex]
Solving gives:
Sum of squared differences = (0.64 + 12.96 + 12.96 + 0.64 + 21.16)
Solving gives:
The sum of squared differences = 48.36
The standard deviation of the differences [tex]= \sqrt{48.36 / 4}[/tex]
Solving gives:
The standard deviation of the differences [tex]= \sqrt{2.09}[/tex]
Rounded to three decimal places
The standard deviation of the differences ≈ 3.47
c) Calculate the test statistic:
The test statistic (t) = (Point estimate - Null hypothesis value) / (Standard deviation /√(sample size))
Let's assume the null hypothesis is that there is no difference between the two fertilizers
(i.e., mean difference = 0).
[tex]t = (2.2 - 0) / (3.47 / \sqrt5)[/tex]
Substituting [tex]\sqrt 5 = 2.236[/tex]
t = 2.2 / (3.47 / 2.236)
Rounded to two decimal places
t ≈ 1.378
So, the test statistic is approximately 1.378.
The gardener can compare this test statistic to critical values from the t-distribution to determine whether the difference between the two fertilizers is statistically significant at a certain significance level. If the calculated test statistic is greater than the critical value, she ma
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Fractions of money question
1/6 + 1/4= 10/24 (5/12 simplified)
2.50× 12= 30
This is the total sum of money shared.
7/12 is given to Farooq
7/12 of 30 is 17.5
answer= £17.5
Ray has 9 identical shoe boxes like the one shown. What is the total volume of all the shoe boxes?
Answer:
Step-by-step explanation:
You need to find the volume if one shoe box by doing:
Length x Width x Height
Of the shoe box
Then multiply by 30 to get the volume for all the shoe boxes
pls mark me brainliest
Verify that W is a subspace of V. Assume that V has the standard operations.
W is the set of all 3x2 matrices of the form [a,b;(a+b),0;0,c] and V=M[-subscript-(3,2)]
W satisfies all the three conditions of being a subspace of V. So, W is a subspace of V.
W is the set of all 3 x 2 matrices of the form [a,b; (a + b),0; 0,c]. It needs to be verified that W is a subspace of V, which has standard operations. Let us check whether W satisfies the three conditions to be a subspace of V or not:
Closure under addition: If X, Y are any two elements of W, then X + Y is also in
W.[a₁, b₁; (a₁ + b₁), 0; 0,c₁] + [a₂, b₂; (a₂ + b₂), 0; 0,c₂] = [a₁ + a₂, b₁ + b₂; (a₁ + b₁ + a₂ + b₂), 0; 0,c₁ + c₂]
The resulting matrix has the same form as W. So, W is closed under addition.
Closure under scalar multiplication: If X is any element of W and k is any scalar, then k
X is also in W.k[a, b; (a + b), 0; 0,c] = [ka, kb; k(a + b), 0; 0,kc]
This is of the same form as W. So, W is closed under scalar multiplication.
Contains zero vector: The zero vector is [0,0; 0,0; 0,0], which is of the same form as W. So, W contains the zero vector.
Therefore, W satisfies all the three conditions of being a subspace of V. So, W is a subspace of V.
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PART X: Lost at sea
Suddenly, during your race, a powerful thunderstorm strikes. A wave washes over your boat, shorting out your navigation devices. They wouldn't be much use anyhow, because the lightning is interfering with all communications in the area.
When the storm ends and the sea is calm, you're safe, because you observed all safety precautions, but you have no idea how far off course you are. However, you do know:
* The height of a nearby landmark, which you remember from the tourist center you visited yesterday.
> Mykonos: The light in the Armenistis Lighthouse is 604 feet above sea level.
* The length of your thumb - it's about 2 inches long.
* That you can estimate lengths of less than a foot pretty accurately (to the nearest inch).
1. First, you close one eye and hold your thumb up to block your view of the landmark. You move your thumb nearer and farther from your eye until it just covers the landmark.
Make a sketch showing overlapping triangles ΔEBT and ΔELH to illustrate this situation, where your eye is E, the base of your thumb is B, the tip of your thumb is T, the bottom of the landmark is L, and the top of the landmark is H.
2. Explain why ΔEBT~ΔELH
3. When your thumb covers the landmark, you estimate that it is 10 inches from your eye. Label your drawing with the known measurements.
4. Solve for EL, the distance from your eye to the landmark. Show all work and justify each step.
Answer: 1. Here is a sketch of the overlapping triangles ΔEBT and ΔELH:
H
/|
/ |
/ |
/ |
/ θ |
/____|L
E
|
|
|
|
T
|
|
|
|
B
2. ΔEBT~ΔELH because they have the same shape (both are right triangles with angle θ in common) and their corresponding sides are proportional. Specifically, angle θ is shared by both triangles, angle EBT is a right angle, and angle ELH is a right angle. Therefore, by the Angle-Angle Similarity Theorem, the two triangles are similar. Corresponding sides are proportional because EB/EL = BT/LH (by definition of similar triangles).
3. We are given that BT (the length of the thumb) is about 2 inches. We are also told that the distance from the eye to the landmark (EL) is unknown, but that the distance from the eye to the thumb (EB) is 10 inches (estimated by the person). We are given that LH (the height of the landmark) is 604 feet, or 604*12=7248 inches (since there are 12 inches in a foot). Therefore, we can label the diagram as follows:
7248
/|
/ |
/ | EL
/ |
/ θ |
/____|L
E
|10
|
|
|
T
| 2
|
|
|
|
B
4. To solve for EL, we use the fact that the triangles are similar: EB/EL = BT/LH. Substituting in the known values, we get:
10/EL = 2/7248
5. Multiplying both sides by EL and dividing both sides by 2, we get:
EL = 7248*5 = 36240 inches
Therefore, the distance from the eye to the landmark is 36240/12 = 3020 feet (rounded to the nearest foot).
Step-by-step explanation:
�
=
−
16
�
2
+
238
�
+
81
y=−16x
2
+238x+81
Answer:
7.44
Step-by-step explanation:
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I need help soon pls
The volume of the solid is 2160ft^3
Define the volume of cuboid?Volume of Cuboid is the multiplication of length breath and height.
We know that, Volume of Cuboid = l×b×h
put the given values from figure,
= 12×10×15
=1800ft^3
Volume of top = Area of triangle × length
= 1/2 × 4× 12× 15
=360ft^3
Total volume= 1800 + 360
= 2160ft^3
Therefore, the volume of the solid is 2160ft^3
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Cuboid: According to the question the volume of the solid is [tex]2160ft^3[/tex].
What is cuboid?A cuboid is a three-dimensional geometric shape which is composed of six rectangular faces. It has 12 edges and 8 vertices. It is also referred to as a rectangular prism. The three dimensions of a cuboid are its length, width, and height. The cuboid is a versatile shape that can be used in many different ways and can be seen in everyday objects such as boxes, desks, and bookshelves. It is also a common shape for mathematically-based problems such as calculating the volume of a cuboid.
We know that, Volume of Cuboid = l×b×h
put the given values from figure,
= 12×10×15
=[tex]1800ft^3[/tex]
Volume of top = Area of triangle × length
= 1/2 × 4× 12× 15
=[tex]360ft^3[/tex]
Total volume= 1800 + 360
= [tex]2160ft^3[/tex]
Therefore, the volume of the solid is [tex]2160ft^3[/tex]
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For each problem, select the best response (a) A x2 statistic provides strong evidence in favor of the alternative hypothesis if its value is A. a large positive number. OB. exactly 1.96 c. a large negative number. D. close to o E. close to 1. (b) A study was performed to examine the personal goals of children in elementary school. A random sample of students was selected and the sample was given a questionnaire regarding achieving personal goals. They were asked what they would most like to do at school: make good grades, be good at sports, or be popular. Each student's sex (boy or girl) was also recorded. If a contingency table for the data is evaluated with a chi-squared test, what are the hypotheses being tested? A. The null hypothesis that boys are more likely than girls to desire good grades vs. the alternative that girls are more likely than boys to desire good grades. OB. The null hypothesis that sex and personal goals are not related vs. the alternative hypothesis that sex and personal goals are related. C. The null hypothesis that there is no relationship between personal goals and sex vs. the alternative hypothesis that there is a positive, linear relationship. OD. The null hypothesis that the mean personal goal is the same for boys and girls vs. the alternative hypothesis is that the means differ. O E. None of the above. (C) The variables considered in a chi-squared test used to evaluate a contingency table A. are normally distributed. B. are categorical. C. can be averaged. OD. have small standard deviations. E. have rounding errors.
a) Option A, A x2 statistic provides strong evidence in favor alternative hypothesis if its value is a large positive number.
b) Option B, The null hypothesis that sex and personal goals are not related vs. the alternative hypothesis that sex and personal goals are related.
c) Option B, The variables considered in a chi-squared test used to evaluate a contingency table B. are categorical.
(a) A x2 statistic provides strong evidence in favor of the alternative hypothesis if its value is a large positive number. The x2 statistic is used in hypothesis testing to determine whether there is a significant difference between observed and expected frequencies. A large positive value indicates that the observed frequencies are significantly different from the expected frequencies, which supports the alternative hypothesis.
(b) The hypotheses being tested in a chi-squared test on a contingency table are the null hypothesis that sex and personal goals are not related vs. the alternative hypothesis that sex and personal goals are related. This test determines whether there is a significant association between two categorical variables.
(c) The variables considered in a chi-squared test used to evaluate a contingency table are categorical. These variables cannot be averaged or assumed to be normally distributed. The chi-squared test is used to analyze the relationship between two or more categorical variables, where each variable has a discrete set of categories.
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Q1 NEED HELP PLEASE HELP
Answer:
the maximum height is 2 meters
viola practices long-jumping. on average she has jumped 3.80 m so far. on the next jump she reaches 3.99 m and thus the mean increases to 3.81 m. how far does she have to jump on her next attempt in order to increase her mean to 3.82 m?
Viola needs to jump a distance of 0.04 m on her next attempt to increase her mean to 3.82 m
On average, she has jumped 3.80 m so far. Therefore, the sum of distances jumped so far by her is:
3.80 m × the total number of jumps taken so far.
On the next jump, she reaches 3.99 m. Therefore, after the next jump, the total distance jumped so far by her will be 3.80 m × total number of jumps taken so far + 3.99 m. The new mean is 3.81 m.
Therefore, (3.80 m × total number of jumps taken so far + 3.99 m)/(total number of jumps taken so far + 1) = 3.81.
The above equation can be simplified as 3.80 m × total number of jumps taken so far + 3.99 m = 3.81 m × (total number of jumps taken so far + 1).
This simplifies to 3.80 m × total number of jumps taken so far + 3.99 m = 3.81 m × total number of jumps taken so far + 3.81 m. Now, we need to solve the above equation to find out the distance she needs to jump on her next attempt to increase her mean to 3.82 m.
3.80 m × total number of jumps taken so far + 3.99 m = 3.81 m × total number of jumps taken so far + 3.81 m.
0.01 m = 0.01 m × total number of jumps taken so far.
1 = total number of jumps taken so far. Now, she needs to jump a distance of (3.82 m × (total number of jumps taken so far + 1)) - (3.80 m × total number of jumps taken so far)
= (3.82 m × (1 + 1)) - (3.80 m × 1)
= 3.82 m × 2 - 3.80 m
= 0.04 m
Therefore, she needs to jump a distance of 0.04 m on her next attempt to increase her mean to 3.82 m.
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Laura has done a two-factor factorial completely randomized design. From her experiment, Laura has constructed the following incomplete ANOVA display: Source SS DF MS F A 350.00 2 B 300.00 150 AB 200.00 50 Error 150.00 Total 1000.00 18 a. How many levels of factor B did she use in the experiment? b. How many degrees of freedom are associated with interaction? c. The error mean square is d. The mean square for factor A is e. How many replicates of the experiment were conducted? f. What are your conclusions about interaction and the two main effects? g. An estimate of the standard deviation of the response variable is h. If this experiment had been run in blocks (CRBD) there would have been degrees of freedom for blocks.
a. Two levels of factor B were used in the experiment.
b. The degrees of freedom associated with interaction are 50.
c. The error mean square is 6.00. d. The mean square for factor A is 175.00.e. The experiment was conducted with three replicates.f. The interaction is significant. Factor A is significant. Factor B is not significant.g. An estimate of the standard deviation of the response variable is 2.449. h. If the experiment had been run in blocks (CRBD) there would have been 12 degrees of freedom for blocks.Solution:Factorial design: A factorial design is an experimental design that consists of two or more factors, each with two or more levels, and each subject is assigned to one and only one level of each factor. The objective of a factorial experiment is to analyze the effect of each factor on the response variable and to examine if there is any interaction between factors.a. Two levels of factor B were used in the experiment.b. Interaction degrees of freedom = AB = 50.c.
Mean square for error: MSE = 150/10 = 15.d. Mean square for factor A: MS(A) =[tex]SSA/dfA = 350/2 = 175.e.\\[/tex] Three replicates were conducted (from the error df = 10).f. Interaction is significant. Factor A is significant. Factor B is not significant.g. Estimate of the standard deviation of the response variable: sqrt(15/2) = 2.449.h. If the experiment had been conducted in a CRBD, there would have been 12 degrees of freedom for the block.
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I need help with this
Therefore , the solution of the given problem of function comes out to be he function's average rate of change over the range 3 x 4 is 4.
Describe function.There will be questions on design, mathematics, each subject, and both real expression and imagined locations on the midterm exam. a list of the relationships between different elements that cooperate to create the same result. A service is composed of numerous distinctive components that cooperate to create distinctive results for each input. Every mailbox also has a specific address, which may be an enclave, a neighborhood.
Here,
Calculate the difference between the function values at
=> x = 4 and x = 3, then split by the difference in x-values,
which is 4 - 3 = 1, to determine the average rate of change of the function over the range 3 x 4.
We can see from the table that f(4) = -5 and f(3) = -9. As a result, the following function numbers are different:
=> f(4) - f(3) = (-5) - (-9) = 4
=> 4 - 3 = 1 represents the x-value disparity.
Therefore, the function's average rate of change over the period 3 x 4 is:
Average rate of change is equal to
=> (f(4)-f(3))/(4-3) = 4/1 = 4.
Consequently, the function's average rate of change over the range 3 x 4 is 4.
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the area of rectange is 297 sq cm if its length is increased by 3 cm and width decreases by 1 cm its area increased by 3 cm. sq. find the length and width of rectangle
The length and width of the rectangle is about 33cms and 9cms. This can be calculated with the help of the given area of the rectangle.
What is the width and length of rectangle?Let the original length and width of the rectangle be L and W respectively.
The given area of the rectangle is 297 square cm.
Area = L × B
297 = L × B
As per the question, the length is increased by 3 cm and the width is decreased by 1 cm.
Therefore, the new length and width are L + 3 and W - 1 respectively.
The new area is 3 square cm more than the original area.
So, (L + 3) × (W - 1) = 297 + 3
L×W -L +3W - 303 = 0
297 - L +3W - 303 = 0
-L + 3W - 6 = 0
-297/W + 3W = 6
-297 + 3W² = 6W
W² - 2W - 99 = 0
Using the quadratic formula, we get,
W = -2±[tex]\sqrt{ 2^2 - 4X1 X ( -99 ) ] ) / 2 X1 }[/tex]
[tex]W =\frac{-2±\sqrt{ (4+396)}}{2}[/tex]
[tex]W =\frac{-2±20}{2}[/tex]
Width can't be negative so, W = 9 cm
So, L 297/W
L = 297/9
L = 33cm
Therefore, the length and width of the rectangle are 33 cm and 9 cm respectively.
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10 is 30% of what number?
Solution:
Part:
whole
percent:
The number 10 is 30% of the following number: 33.33.
What is a percentage?In Mathematics, a percentage can be defined as any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.
How to calculate the percentage of a number?In order to determine the whole number which 10 is 30%, we would apply the following mathematical expression (formula);
Quantity = percent × number
Substituting the given parameters into the percentage and quantity formula, we have the following;
10 = 30/100 × number
10 = 0.3 × number
Number = 10/0.3
Number = 33.33.
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Arrange the steps in the correct order to find an inverse of a modulo m for each of the following pairs of relatively prime integers using the Euclidean algorithm. a = 55, m= 89 Rank the options below. The steps to find gcd(55, 89) using the Euclidean algorithm are listed below. 89 = 1.55 +34 55 = 1.34 +21 34 = 1.21 + 13 21 1 . 13 + 8 13 = 1.8+5 8 = 1.5+ 3 5 = 1.3+2 3 = 1.2+1 2 = 1.2 The Bézout coefficient of 55 is 34, and it is an inverse of 55 modulo 89. The Bézout coefficients of 55 and 89 are 34 and -21, respectively. -21, respectively. The ged in terms of 55 and 89 is written as 1 = 3-1.2 = 3-1. (5-1.3) = 2.3-1.5 = 2. (8-1.5) - 1.5 = 2.8-3.5 = 2.8-3. (13-1-8)= 5.8-3.13 = 5. (21-1.13) - 3.13 = 5.21-8. 13 = 5.21-8. (34-1.21) = 13.21-8.34 = 13. (55 - 1. 34)- 8. 34 = 13.55 - 21 34 = 13.55 - 21 - (89-1. 55) = 34.55 -21.89
The correct order of steps is 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.
To find the inverse of 55 modulo 89 using the Euclidean algorithm, the steps are:
1. 89 = 1.55 +34
2. 55 = 1.34 +21
3. 34 = 1.21 + 13
4. 21 = 1.13 + 8
5. 13 = 1.8 +5
6. 8 = 1.5 +3
7. 5 = 1.3 +2
8. 3 = 1.2 +1
9. 2 = 1.2
10. The Bézout coefficient of 55 is 34, and it is an inverse of 55 modulo 89.
11. The Bézout coefficients of 55 and 89 are 34 and -21, respectively.
12. The gcd in terms of 55 and 89 is written as 1 = 34-21.89 = 34-21. (55-1.34) = 13.34-21.55 = 13. (21-1.13) - 3.13 = 5.21-8. 13 = 5. (8-1.5) - 1.5 = 2.8-3.5 = 2. (3-1.2) = 2.3-1.5 = 2. (2-1) = 3-1.2 = 3-1. (1-0) = 34-21.89
The correct order of steps is 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.
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[LAST QUESTION, OFFERING BRAINLIEST]
??? PTS
Answer:
Step-by-step explanation:
Let h be the height of the trapezoid.
The area of a trapezoid is given by the formula:
Area = (1/2) × (sum of parallel sides) × (height)
In this case, we know that the area is 21 cm², one base length is 5 cm, and the other base length is 9 cm. So we can write:
21 = (1/2) × (5 + 9) × h
Simplifying this equation, we get:
21 = 7h
Dividing both sides by 7, we get:
h = 3
Therefore, the height of the trapezoid is 3 cm.
Answer:
Height of Trapezium is 3 cm.Step-by-step explanation:
Area of Trapezium is 21 cm². Parallel sides are 5 cm and 9 cm .
Shorter parallel side is 5 cm and the Longer Side is 9 cm.
As we know that formula of area of Trapezium is,
Area of Trapezium = ½ (a + b) hWhere,
a and b are Parallel sides and h is the height.On substituting the values of area and the two parallel sides in the above formula we will get the required Height.
Substituting the values,
21 = ½ (5 + 9)h
21 = ½ × 14 × h
21 = 7 × h
h = 21/7
h = 3 cm
Therefore, Height of the Trapezium will be 3 cm respectively.
Which of the following is the most appropriate inference procedure for the researchers to use to analyze the results? A. A one-sample zz-interval for a population proportionB. A one-sample tt-interval for a sample mean differenceC. A matched-pairs tt-interval for a population mean differenceD. A matched-pairs tt-interval for a sample mean differenceE. A two-sample tt-interval for a difference between means
The appropriate inference procedure for the researchers to analyze the results depends on the specific research question and the nature of the data.
A one-sample zz-interval for a population proportion is appropriate when the research question involves estimating the proportion of a population that has a particular characteristic or attribute.
A one-sample tt-interval for a sample mean difference is appropriate when the research question involves estimating the difference between a sample mean and a known population mean.
A matched-pairs tt-interval for a population mean difference is appropriate when the research question involves estimating the difference between two related population means.
A matched-pairs tt-interval for a sample mean difference is appropriate when the research question involves estimating the difference between two related sample means.
A two-sample tt-interval for a difference between means is appropriate when the research question involves estimating the difference between two independent sample means.
Therefore, without knowing the specifics of the research question and the data, it is impossible to determine the most appropriate inference procedure.
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you wish to compute the 90% confidence interval for the population proportion. how large a sample should you draw to ensure that the sample proportion does not deviate from the population proportion by more than 0.05? no prior estimate for the population proportion is available.
To compute the 90% confidence interval for the population proportion, large a sample should you draw to ensure that the sample proportion does not deviate from the population proportion by more than 0.05, 271 is the minimum sample
How do we find the minimum sample size?A confidence interval is a range of values where an unknown population parameter lies. The level of confidence is the likelihood of the interval containing the parameter.
The formula to calculate the sample size required to produce a specific margin of error with a known level of confidence for the estimation of a population proportion is given below: 95% confidence interval for population proportion using a sample size formula
[tex]\[n=\frac{z^{2}p(1-p)}{E^{2}}\][/tex]
Where
[tex]\[E\][/tex]is the margin of error[tex]\[p\][/tex] is the sample proportion.[tex]\[z\][/tex] is the z-score The formula is modified to calculate the sample size required to produce a specific margin of error with a known level of confidence as follows:
[tex]\[n=\frac{z^{2}}{4E^{2}}\][/tex]
Note: For this problem, the sample size needs to be large enough to ensure that the sample proportion does not deviate from the population proportion by more than 0.05.
Using a Z-score Table, the z-value that corresponds to 90% confidence interval is 1.645.
[tex]n=\frac{z^{2}}{4E^{2}}\ = \frac{1.645^{2}}{4(0.05)^{2}} = \frac{2.706225}{0.0100} = 270.6[/tex]
(rounded up to the next highest integer)Therefore, 271 is the minimum sample size required to compute a 90% confidence interval for the population proportion.
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Cheryl builds cylindrical pools according to measurements given by her customers. Cheryl uses the volume formula for a cylinder, V = pi R squared^2H to determine how big to build the pool If Cheryl is given the volume and height requirements, how would she rewrite the formula to determine the radius of the pool?
The radius of a cylindrical pool when given the volume and height is √{(V / (πh))}.
Cheryl can rewrite the volume formula for a cylinder in terms of the radius.
The volume formula for a cylinder is: V = πr²h
Where V is the volume of the cylinder,
r is the radius of the cylinder,
h is the height of the cylinder.
To determine the radius of the cylindrical pool, we can rearrange the formula for the volume of a cylinder,
V = πr²h, to solve for r.
Starting with the formula for the volume of a cylinder:
V = πr²h
Divide both sides by πh:
V / (πh) = r²
Take the square root of both sides:
√{(V / (πh))} = r
Therefore, the formula to determine the radius of the pool given the volume V and height h is:
r = √{(V / (πh))}
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Two of the integers {1,3,5} are chosen together (at the same time) at random, without replacement. Let X denote the maximum of the two integers
. (a) List all choices (Sample Space of the experiment) and the possible values of X. (
b) Find the probability mass function for all possible value of X.
(c) Find the expectation of X. (d) Find the variance of X.
(a) The possible choices are (1,3), (1,5), and (3,5), and the maximum of each pair is 3, 5, and 5, respectively.
(b) Since each pair has probability 1/3 of being chosen, the probability mass function for X is P(X=3) = 1/3 and P(X=5) = 2/3.
(c) The expectation of X is E(X) = 3(1/3) + 5(2/3) = 4.
(d) The variance of X can be calculated as Var(X) = E(X^2) - (E(X))^2 = (3^2)(1/3) + (5^2)(2/3) - 4^2 = 2/3.
(a) We can list all the possible choices of two integers from the set {1,3,5}: (1,3), (1,5), and (3,5). For each choice, we can determine the maximum of the two integers. These maximums are 3, 5, and 5, respectively.
(b) Since each pair has an equal probability of being chosen, the probability mass function for X can be calculated as the probability of getting 3 or 5. There is only one pair that results in X=3, which is (1,3). There are two pairs that result in X=5, which are (1,5) and (3,5). Thus, P(X=3) = 1/3 and P(X=5) = 2/3.
(c) To find the expectation of X, we multiply each possible value of X by its corresponding probability and sum the results. Thus, E(X) = 3(1/3) + 5(2/3) = 4.
(d) The variance of X can be calculated using the formula Var(X) = E(X^2) - (E(X))^2. We can calculate E(X^2) by multiplying each possible value of X squared by its corresponding probability and summing the results. Thus, E(X^2) = (3^2)(1/3) + (5^2)(2/3) = 16/3. Substituting E(X) = 4 and E(X^2) = 16/3 into the formula for variance gives Var(X) = 2/3.
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calculate the expected value, the variance, and the standard deviation of the given random variable x. (round all answers to two decimal places.) x is the number of red marbles that suzan has in her hand after she selects three marbles from a bag containing three red marbles and two green ones. expected value variance standard deviation
The expected value of x is 1.80, the variance is 0.72, and the standard deviation is 0.85.
Calculate the expected value, variance, and standard deviation of the random variable x as follows. Round all answers to two decimal places, and keep in mind that x is the number of red marbles that Suzan has in her hand after selecting three marbles from a bag containing three red marbles and two green ones.
Expected Value: Since there are 3 red marbles and 2 green marbles in the bag, the probability of drawing a red marble is: P(R) = 3/5The probability of drawing a green marble is P(G) = 2/5Therefore, the expected value of the random variable X is: E(X) = μ = np = 3/5 * 3 = 1.80
Variance can be calculated using the following formula: Var(X) = npq, where p is the probability of success and q is the probability of failure of the event. In this scenario, the probability of drawing a red marble is P(R) = 3/5, and the probability of drawing a green marble is P(G) = 2/5.
Therefore, Var(X) = npq Var(X) = (3/5)*(2/5)*3Var(X) = 1.80 * 0.4Var(X) = 0.72Standard Deviation: The square root of the variance is equal to the standard deviation. Hence, the formula for standard deviation is: S.D. = √Var(X)S.D. = √0.72S.D. = 0.85
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an ore sample weighs 18.5 n n in air. when the sample is suspended by a light cord and totally immersed in water, the tension in the cord is 11.8 n n .find the total volume and density of the sample
The total volume of the sample is 0.0067 m³ and the density of the sample is 2753.73 kg/m³.
An ore sample weighs 18.5 N in air. When the sample is suspended by a light cord and totally immersed in water, the tension in the cord is 11.8 N. When the ore sample is immersed in water, the tension in the cord is given as 11.8 N.
Thus, the buoyancy force experienced by the ore sample is given by the difference between the weight of the sample in the air and the tension in the cord.
Buoyancy force experienced by the ore sample = Weight of the sample in the air - Tension in the cord
Buoyancy force experienced by the ore sample = (18.5 N) - (11.8 N)
Buoyancy force experienced by the ore sample = 6.7 N
Also, we know that the weight of the ore sample in air is equal to the weight of the ore sample when immersed in water.
Weight of the ore sample = Weight of the displaced water
Weight of the ore sample = Buoyancy force experienced by the ore sample
Weight of the ore sample = 6.7 N
The density of the ore sample
Density is given by the formula Density = Mass/Volume
Where Density is measured in kg/m³
Mass is measured in kg
Volume is measured in m³
Also, the density of water is given as 1000 kg/m³.
The density of the ore sample = Mass/Volume
Mass = Density x Volume
Volume of the ore sample can be obtained from volume of the displaced water.
Volume of the displaced water = Weight of the ore sample/Density of water
Volume of the displaced water = (6.7 N)/(1000 kg/m³)
Volume of the displaced water = 0.0067 m³
Density of the ore sample = (18.5 N)/(0.0067 m³)
Density of the ore sample = 2753.73 kg/m³
Therefore, 0.0067 m³ is the sample's total volume and 2753.73 kg/m³ is the density of the sample.
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exponential law of heating and cooling
Answer:
A) k = 0.037
B) 186°F
Step-by-step explanation:
List initial (T₀) and air (Tₐ) temperature
[tex]T_0=280^\circ\\T_a=67^\circ\\[/tex]
Part A
[tex]T=T_a+(T_0-T_a)e^{-kt}\\193^\circ=67^\circ+(208^\circ-67^\circ)e^{-k(3)}\\193=67+141e^{-3k}\\126=141e^{-3k}\\\frac{126}{141}=e^{-3k}\\\ln(\frac{126}{141})=-3k\\-\frac{1}{3}\ln(\frac{126}{141})=k\\k\approx0.037[/tex]
Part B
[tex]T=T_a+(T_0-T_a)e^{-kt}\\T=67+(208-67)e^{-0.037(4.5)}\\T\approx186^\circ\text{F}[/tex]
write down the name of shape W
A hexagon with two lines
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I hope you are form India
Julio bought a fish tank shaped like a rectangular prism. The inside of the tank measures
24
24 inches in length,
10
10 inches in width, and
12
12 inches in height. The tank is filled with water to a height of
8
8 inches. How many more cubic inches of water are needed to fill the tank to the top?
The quantity of water are needed to fill the tank to the top is 960 cubic inches
The total volume of the tank is given by multiplying its length, width, and height
Volume of tank = 24 inches × 10 inches × 12 inches = 2,880 cubic inches
The volume of water in the tank is given by multiplying the filled height with the base area of the tank:
Volume of water = 8 inches × 24 inches × 10 inches = 1,920 cubic inches
To find how many more cubic inches of water are needed to fill the tank to the top, we need to subtract the volume of water in the tank from the total volume of the tank:
Volume of air space = Volume of tank - Volume of water
= 2,880 cubic inches - 1,920 cubic inches
= 960 cubic inches
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The given question is incomplete, the complete question is:
Julio bought a fish tank shaped like a rectangular prism. The inside of the tank measures
24 inches in length, 10 inches in width, and 12 inches in height. The tank is filled with water to a height of 8 inches. How many more cubic inches of water are needed to fill the tank to the top?
Multiply the polynomials.
(2x² + 6x+6)(3x - 2)
_____________
A. 6x³14x²2 + 6x + 12
B. 6x³ + 14x² + 6x + 12
Wan
C. 6x³22x² - 30x - 12
D. 6x³ + 14x² + 6x - 12
The ratio of shells to driftwood Gus found is shown on the ratio table. Complete the ratio table to make an equivalent ratio.
Shells 9 36
Driftwood 3 (blank)
Answer:
12
Step-by-step explanation:
Given the ratio [tex]9:36[/tex], we can say that the ratio of driftwood is divided by 3 for the number of shells.
[tex]\frac{9}{3} =3\\\frac{36}{3}=12[/tex]
So, to fill the blank and create an equivalent ratio, you need to input 12.
Which graph matches the equation y+6 = 3/4 (x + 4)
A graph that matches the equation include the following: A. graph A.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be determined by using this mathematical equation:
y - y₁ = m(x - x₁)
Where:
m represent the slope.x and y represent the points.Based on the information provided about the equation of this line, we can logically deduce the following parameters;
y + 6 = 3/4(x + 4)
y = 3x/4 + 3 - 6
y = 3x/4 - 3
Therefore, the slope, m is equal to 3/4 while the y-intercept is at point (0, 3).
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Determine the degree of the Maclaurin polynomial required for the error in the approximation of the function at the indicated value of x to be less than 0.001. f(x) = - " x+1' PA approximate f(0.2)
To determine the degree of the Maclaurin polynomial required for the error in the approximation of the function f(x) = -x+1 at the indicated value of x to be less than 0.001, we can use the formula: N ≥ ln(error)/ln(absolute value of x) + 1.
For our given function, the error is 0.001, and the value of x is 0.2. Plugging these values into the formula, we get: N ≥ ln(0.001)/ln(0.2) + 1, which is equivalent to N ≥ 6.64 + 1 = 7.64. Therefore, we need the degree of the Maclaurin polynomial to be 7.64 in order for the error in the approximation of the function at the indicated value of x to be less than 0.001.
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3 Charlie invests £4000 for 3 years in a savings
account.
She gets 2% per annum compound interest in
the first year, then x% for 2 years.
Charlie has £4228.20 at the end of 3 years,
work out the value of x.
Answer: The value of x is 3.45%
Step-by-step explanation:
We can solve the problem by using the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = final amount
P = principal (initial investment)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = time in years
In the first year, Charlie gets 2% interest, compounded annually. So, using the formula, we have:
A1 = 4000(1 + 0.02/1)^(1*1)
A1 = 4080
After the first year, Charlie has £4080 in her account. For the next two years, she gets x% interest, compounded annually. Using the formula again, we have:
A2 = 4080(1 + x/100/1)^(1*2)
A2 = 4080(1 + x/100)^2
Finally, after three years, Charlie has £4228.20 in her account. So, we can set up an equation:
A1 * A2 = 4000 * (1 + 0.02) * 4228.20
Substituting the values of A1 and A2, we get:
4080(1 + x/100)^2 = 4366.4496
Dividing both sides by 4080, we get:
(1 + x/100)^2 = 1.0694
Taking the square root of both sides, we get:
1 + x/100 = 1.0345
Subtracting 1 from both sides and multiplying by 100, we get:
x = 3.45
Therefore, the value of x is 3.45%.