In the following question, among the given options, the statement is said to be, The pooled estimate of the standard deviation for the data given is √(54.14^2/10 + 24.26^2/10) = 22.74.
According to the rule for examining standard deviations in ANOVA from Chapter 12 (page 560), the within-group standard deviation should be no more than twice the size of the between-group standard deviation. In this case, the between-group standard deviation is 44.85 and the within-group standard deviation (22.74) is less than twice the size of the between-group standard deviation, so it is reasonable to use a pooled standard deviation for the analysis of these data.
For more such questions on deviation
https://brainly.com/question/475676
#SPJ11
Assume that the int variables a, b, c, and low have been properly declared and initialized. The code segment below is intended to print the sum of the greatest two of the three values but does not work in some cases.
if (a > b && b > c)
{low = c;}
if (a > b && c > b)
{low = b;}
else
{low = a;}
System.out.println(a + b + c - low);
The variable is not initialized, it will have a default value associated with its data type.
To print the sum of the greatest two of the three values in the given code segment, the code must be corrected by introducing curly braces that help enclose the second if statement such that it can execute properly in cases where it is necessary. If the second if statement is not enclosed in curly braces, then the else statement will execute the code that is present inside of it. Thus, only a will be assigned to low. The corrected code segment should be:if (a > b && b > c) {low = c;}if (a > b && c > b) {low = b;} else {low = a;}System.out.println(a + b + c - low);For a better understanding of this code, let's discuss variables, declared, and initialized.What are variables?A variable is a memory location that stores a data value. Variables in Java are declared by assigning a data type to them. The value stored in the memory location can be changed throughout the program execution.What is initialization in Java?Initialization in Java refers to assigning a specific value to a variable during its declaration. The value may be provided by the user, entered via keyboard, or assigned to a constant. If a variable is not initialized, it will have a default value associated with its data type.
Learn more about Variable
brainly.com/question/19585043
#SPJ11
Answer your answer and show all the steps that you used to solve this problem in the space provided use the 30° - 60° - 90° triangle theorem to find the answer
The value of x is 8 inches.
To find the value of x, we can use the property of similar triangles that states that the corresponding sides of similar triangles are in proportion. Specifically, we can set up the proportion:
4/10 = x/20
We can then cross-multiply to get:
4 * 20 = 10 * x
Simplifying this equation gives us:
80 = 10x
Dividing both sides by 10, we get:
x = 8
Therefore, the value of x is 8 inches.
In summary, we used the property of similar triangles and set up a proportion involving the corresponding sides of the two triangles. By cross-multiplying and simplifying, we were able to find the value of x.
Learn more about Triangles:
https://brainly.com/question/29789999
#SPJ4
Complete Question:
Enter your answer and show all the steps that you use to solve this problem in the space provided.
On the left triangle, the shorter side is labeled 4 inches and the longer side is labeled 10 inches. On the right triangle, the shorter side is labeled x inches and the longer side is labeled 20 inches.
The two triangles above are similar. Find the value of x. Be sure to explain your steps.
a market sells five kinds of cups, 4 kinds of saucers, and 2 kinds of spoons. How many ways are there to buy two objects of different types? WILL GIVE BRAINLIST
Answer:
Step-by-step explanation:
To solve this problem, we need to determine the number of ways to choose two objects of different types from the given sets.
We can start by computing the number of ways to select two objects from each of the three sets, and then add these numbers together. Since we must choose two different types, we cannot choose two objects from the same set.
The number of ways to choose two cups is:
C(5,2) = 5! / (2! * (5-2)!) = 10
The number of ways to choose two saucers is:
C(4,2) = 4! / (2! * (4-2)!) = 6
The number of ways to choose two spoons is:
C(2,2) = 1
Since we must choose two different types, we need to multiply the number of ways to choose two objects from different sets. There are three sets to choose from, so we need to choose two of them as follows:
3 choices of sets * number of ways to choose two objects from each set = 3 * (10 + 6 + 1) = 51
Therefore, there are 51 ways to buy two objects of different types from the given sets of cups, saucers, and spoons.
ASA, SSS, SAS
Define each postulate and give a well written and visual example of each term.
Include as much detail as possible
Answer:
In geometry, postulates are statements that are accepted as true without proof. The three postulates for congruent triangles are ASA, SSS, and SAS. These postulates are used to prove that two triangles are congruent.
ASA Postulate:
ASA stands for "Angle, Side, Angle." This postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
Visual example:
In the above image, ΔABC and ΔDEF have ∠A ≅ ∠D, ∠B ≅ ∠E, and AB ≅ DE. Therefore, we can conclude that ΔABC ≅ ΔDEF by ASA postulate.
SSS Postulate:
SSS stands for "Side, Side, Side." This postulate states that if the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.
Visual example:
In the above image, ΔABC and ΔDEF have AB ≅ DE, BC ≅ EF, and AC ≅ DF. Therefore, we can conclude that ΔABC ≅ ΔDEF by SSS postulate.
SAS Postulate:
SAS stands for "Side, Angle, Side." This postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
Visual example:
In the above image, ΔABC and ΔDEF have AB ≅ DE, BC ≅ EF, and ∠B ≅ ∠E. Therefore, we can conclude that ΔABC ≅ ΔDEF by SAS postulate.
Overall, the ASA, SSS, and SAS postulates are important tools in proving the congruence of triangles in geometry. They allow us to make logical deductions about the properties of triangles based on their corresponding angles and sides.
Answer:
They are different because ASA means that the two triangles have two angles and the side between the angles congruent. SAS means that two sides and the angle in between them are congruent
Step-by-step explanation:
and sss If all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are said to be congruent by SSS rule.
on saturday a local hamburger shop sold a combined total of 416 hamburgers and cheeseburgers.the number of cheeseburgers sold was three times the number of hamburgers sold. how many hamburgers were sold?
Answer: Let x be the number of hamburgers sold.
Then, the number of cheeseburgers sold is 3x.
The total number of burgers sold is x + 3x = 4x.
Given that the total number of burgers sold is 416, we have:
4x = 416
x = 416/4
x = 104
Therefore, 104 hamburgers were sold.
Step-by-step explanation:
In right triangle RST, with m∠S = 90°, what is sin T?
The ratio of the length of the side directly opposite the angle to the length of the hypotenuse is known as the sine of an acute angle in a right triangle.
Hence, the sine of angle T in the right triangle RST with a right angle at S is given by:
opposite side / hypotenuse = sin T
We must know the triangle's side lengths in order to calculate the value of sin T. We can use trigonometric ratios to calculate the lengths of the remaining sides.
if we know the length of the hypotenuse and the measurement of one acute angle.
thus, we cannot define the value of triangle RST.
To learn about triangle RST visit:
https://brainly.com/question/28738706?referrer=searchResults
#SPJ4
PLEASE HELPP!! i’ve been struggling with this problem for the past 30 min.. lessons about polynomials.
Answer:
39.77 -> 39 or 40, depending on rounding
Step-by-step explanation:
Since 2002-1992 is 10. T would equal 10. At that point, it would be a gesture of plugging in 10 whereever you see a "t" and solve for both
3x^2-2x+1 when x is 4
Answer: I got 29
Step-by-step explanation:
You would plug in 4 in all the spots where the x's are and then solve the problem
suppose that a point is chosen uniformly at random from within a unit circle let (x,y) denote the coordinates of the randomly chosen point.
The probability of the chosen point uniformly at random from within a unit circle is 1/π.
Suppose that a point is chosen uniformly at random from within a unit circle.
Let (x,y) denote the coordinates of the randomly chosen point.
The coordinates of the randomly chosen point (x, y) on the unit circle can be given by:
x = cos(θ)y = sin(θ) where θ is the angle between the positive x-axis and the line segment connecting the origin to the point (x, y).
The probability density function for this situation is given by:
p(x,y) = {1/(πr^2)} for 0≤x^2 + y^2 ≤ r^2 and p(x,y) = 0 elsewhere
where r is the radius of the unit circle. For this situation, r = 1.
So, we can say that the probability of selecting a point in a unit circle is given by:
Probability (0≤x^2 + y^2 ≤ 1) = 1/(π*1^2) = 1/π.
To know more about the "unit circle": https://brainly.com/question/23989157
#SPJ11
The height off the ground, in feet, of a squirrel leaping from a tree branch is given by the function H(x) = –16x*2 + 24x + 15, where x is the number of seconds after the squirrel leaps. How many seconds after leaping does the squirrel reach its maximum height?
A.
1. 33 s
B.
0. 50 s
C.
0. 75 s
D.
1. 00 s
Answer:
C. 0.75 s
Step-by-step explanation:
Given a squirrel's height is defined by H(x) = -16x² +24x +15, you want to know the value of x when the height is a maximum.
VertexThe x-coordinate of the vertex of y = ax² +bx +c is x=-b/(2a). For the given function, we have a=-16 and b=24, so the x-value at the vertex is ...
x = -b/(2a) = -24/(2(-16)) = 24/32 = 3/4
x = 0.75
The squirrel reaches its maximum height 0.75 seconds after leaping.
The solution of the differential equation y apostrophe minus y over x equals y squared is a. y equals fraction numerator 1 over denominator open parentheses c over x minus x over 2 space close parentheses end fraction b. y equals 1 plus c e to the power of x c. y equals c x minus x ln x d. y equals c over x minus x over 2 e. y equals fraction numerator 1 over denominator c x minus x ln x end fraction
The solution of the differential equation is
a. b. c. d. e.
The given differential equation is y' - (y/x) = y²Where y is a function of x.
The solution of the given differential equation is given below Option (e) y = (1/c) (x - x ln x)
y' - (y/x) = y²
We first check whether the given differential equation is a Bernoulli differential equation. It is not a Bernoulli differential equation. Hence we cannot directly solve the given differential equation.
Using the integrating factor method, we get
Integration factor, I(x) = e^(∫(1/x)dx) = e^(ln x) = x
1. Multiplying the integrating factor to the given differential equation, we get
x y' - y = x y²
This is a linear differential equation with variable coefficients.
The standard form of the linear differential equation with variable coefficients is given below:
y' + p(x) y = q(x) where p(x) = -1/x and q(x) = x y²
2. Multiplying the integrating factor, we get x y' - y = x y²
3. Multiplying the integrating factor x on both sides, we get x² y' - xy = x³ y²
4. Differentiating both sides with respect to x, we get
2xy' + x² y'' - y - 2x y' = 3x² y y'
On simplifying, we getx² y'' + 3x y' - 2y = 0
This is a homogeneous differential equation. We substitute y = ux, where u is a function of x. On substituting we getx² u'' + 2x u' = 0
5. On simplifying, we get u' = -c/x²
6. On integrating, we get u = c/x + d where c and d are arbitrary constants.
Substituting u = y/x, we get y/x = c/x + d
Hence the solution of the given differential equation is y = c - x ln x
where c = 1
The correct option is (e).Option (e) y = (1/c) (x - x ln x)
To learn more about “differential equation” refer to the https://brainly.com/question/1164377
#SPJ11
A farmer has a rectangular field with an area of 3/4 square mile. The field is 1/2 mile wide. What is the length of the field?
A. 2/3
B. 1 1/3
C. 2 2/3
D. 3/8
Answer:
L-O-V-E-E-E and affection
What is a coterminal angle of 22 times pi over 3 question mark
[tex]\cfrac{22\pi }{3}\implies \cfrac{(3)(7)\pi +\pi }{3}\implies 7\pi +\cfrac{\pi }{3}\implies 6\pi +\pi +\cfrac{\pi }{3}[/tex]
so the angle is really 3 revolutions plus another π plus a little bit more. Check the picture below.
please help me .Solve this question.
9-9÷9÷9-9÷9
Answer:
71/9
Step-by-step explanation:
please help me .Solve this question 9-9÷9÷9-9÷9
9 - 9 : 9 : 9 - 9 : 9 =
9 - 1 : 9 - 1 =
9 - 1/9 - 1 =
8/9 - 1 =
(81 - 1 - 9)/9 =
71/9
Find the mean, variance, and standard deviation for each of the values of n and p when the conditions for the binomial distribution are met. Round your answers to three decimal places as needed. Part 1 out of 4 n = 295, p = 0.21
The mean, variance, and standard deviation for n = 295 and p = 0.21 by using binomial distribution are
61.95, 48.8125, and 6.988, respectively.
The binomial distribution, which is a type of probability distribution, is used to calculate the probability of a certain number of successes (or failures) in a given number of trials. The mean, variance, and standard deviation of a binomial distribution can be calculated using the following formulas:
Mean (μ) = np
Variance (σ²) = npq
Standard deviation (σ) = √(npq)
Where n is the number of trials, p is the probability of success in a single trial, and q is the probability of failure in a single trial (q = 1 - p).
Part 1 out of 4: n = 295, p = 0.21
Using the formulas above, we can calculate the mean, variance, and standard deviation for this binomial distribution.
Mean (μ) = np
= 295 × 0.21 ⇒61.95
Variance (σ²) = npq
= 295 × 0.21 × 0.79 ⇒ 48.8125
Standard deviation (σ) = √(npq)
⇒ √(48.8125) = 6.988
Therefore, the mean, variance, and standard deviation for n = 295 and p = 0.21 are 61.95, 48.8125, and 6.988, respectively.
To know more about the " mean, variance, and standard deviation": https://brainly.com/question/12402189
#SPJ11
Discount an asset promising $200, 4 years from now back to day at a discount rate of 7% percent
Answer:
Step-by-step explanation:
As a result, with a discount rate of 7%, the present value of an item that will be worth $200 in four years is roughly $152.57.
We may use the present value calculation to discount an item that will be worth $200 in four years back to today at a 7% discount rate:
PV equals FV / (1 + r)n
where n is the number of periods, r is the discount rate, PV is the present value, and FV is the future value.
If we substitute the values provided, we get:
PV = 200 / (1 + 0.07), divided by four, results in PV of $152.57.
As a result, with a discount rate of 7%, the present value of an item that will be worth $200 in four years is roughly $152.57.
Learn more about discount rate here:
https://brainly.com/question/29199569
#SPJ4
A video receives-16 pints and 33 points in one day. How many members voted
Answer:49
Step-by-step explanation:
Write an explicit rule for the recursive rule. a1=8,
an=an−1−12
Answer:
[tex]a_{n}[/tex] = 20 - 12n
Step-by-step explanation:
the explicit rule for an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
a recursive rule has the form
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + d
given recursive rule
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] - 12 : a₁ = 8
then a₁ = 8 and d = - 12
explicit rule is therefore
[tex]a_{n}[/tex] = 8 - 12(n - 1) = 8 - 12n + 12 = 20 - 12n
What is the length of side x in the triangle below?
Answer: x = 8.7
Step-by-step explanation:
You are given the reference angle: 60°, the hypotenuse and the leg of which to find.
X is opposite in reference to 60° and you are given the hypotenuse.
Sine works with the hypotenuse and the opposite: sin∅ = opp/hyp
sin(60°) = x/10
To figure out x, you must transpose, to make x the subject. X is being divided by 10, so to undo that you must multiply, and what you do to one side, you must do to the next to balance the equation.
10 x sin(60) = x/10 x 10
= X = sin(60) x 10
sin(60) = 0.866
X = 0.866 x 10
X = 8.66
You can round off to one decimal place or leave the answer as is.
X = 8.7 (1 d.p)
In triangle JKL, m/J = (8x+6)°, m/K = (2x + 2)°, and m/L= (4x + 4)°. Find
m/L.
The value of the angle m<L is 52 degrees
How to determine the value
Following the side angle theorem of triangles, we have that the sum of the angles in a given triangle is equal or equivalent to 180 degrees.
From the information given, we have that;
m/J = (8x+6)°m/K = (2x + 2)° m/L= (4x + 4)°Now, equate the angles to 180 degrees, we have;
m<J + m<K + m<L =180
substitute the values into the equation
8x + 6 + 2x + 2 + 4x + 4 = 180
collect the like terms, we have;
8x + 2x + 4x = 180 - 12
add or subtract the values
14x = 168
Make 'x' the subject
x = 12
For m<L = 4x + 4 = 4(12) + 4 = 52 degrees
Learn about triangles at: https://brainly.com/question/25215131
#SPJ1
Suppose a single trial experiment results in one of three mutually exclusive events, A, B, or C. It is known that P(A) = 0.3, P(B) = 0.6, and P(C) = 0.1. Find the probability P(ANC) Answer: Question 2 Not yet answered Points out of 2.00 P Flag question Refer to the previous question. Find the probability P(AUB). Answer:
intersection of A and B events, P(A ∩ B) is 0. So, P(A U B) = P(A) + P(B) = 0.3 + 0.6 = 0.9Hence, P(AUB) = 0.9.
Probability of P(ANC)We know that events A, B and C are mutually exclusive.
Therefore, if A, B, and C are mutually exclusive events, then P(A U B U C) = P(A) + P(B) + P(C). Given, P(A) = 0.3,P(B) = 0.6,P(C) = 0.1
Therefore, P(A U B U C) = P(A) + P(B) + P(C) = 0.3 + 0.6 + 0.1 = 1Now, P(ANC) = 1 - P(A U B U C) = 1 - 1 = 0
Probability the intersection of A and B events, P(A ∩ B) is 0. So, P(A U B) = P(A) + P(B) = 0.3 + 0.6 = 0.9
Hence, P(AUB) = 0.9.ility of P(AUB)We know that events A, B and C are mutually exclusive.
Therefore, if A, B, and C are mutually exclusive events, then P(A U B U C) = P(A) + P(B) + P(C)
Now, we need to find P(AUB). If two events A and B are not mutually exclusive events, then the probability of their union P(A U B) can be found as follows; [tex]P(A U B) = P(A) + P(B) - P(A ∩ B)[/tex]We know that events A, B and C are mutually exclusive.
for such more questions on Probability
https://brainly.com/question/24756209
#SPJ11
Key Takeaways of Cross Tab and Scatter plots (Reflecting on visual models)
- We can develop insights and knowledge about our world from manipulating and visualizing data, in particular by finding patterns
- When investigating two columns of data we can observe patterns different values move together (are correlated). We cannot know for certain the cause of the correlation.
Key takeaways of Cross Tab and Scatter plots (Reflecting on visual models):
We can develop insights and knowledge about our world by manipulating and visualizing data, in particular by finding patterns. Cross Tab is a powerful method of data analysis that helps to compare the relationship between two or more variables. The scatter plot is one of the most effective tools to visualize two-variable data.
Scatter plots: A scatter plot is a graph in which two variables are plotted against each other, with the horizontal axis representing one variable and the vertical axis representing the other. Each point in the scatter plot represents a pair of values for the two variables being plotted. When analyzing a scatter plot, we can look for patterns, relationships, or correlations between the two variables.Cross Tab: Cross tab is a popular data analysis tool that helps to determine the relationship between two or more variables. In cross-tabulation, a table is created with one variable displayed along the rows and the other variable displayed along the columns. The resulting table shows the number of occurrences of each combination of values for the two variables.The main takeaways from cross-tabulation and scatter plots include:
Cross Tab and Scatter plots can help us to find patterns and relationships between variables.The analysis of scatter plots can help us to identify trends, clusters, and outliers.Cross Tab helps us to identify the relationship between two or more variables by displaying the data in a table format.In conclusion, both cross-tabulation and scatter plots are effective tools for data analysis that can help to identify patterns and relationships between variables. When investigating two columns of data we can observe patterns of different values that move together (are correlated). We cannot know for certain the cause of the correlation.
To know more about the "scatter plots": https://brainly.com/question/6592115
#SPJ11
Assume that head sizes (circumference) of new recruits in the armed forces can be approximated by a normal distribution with a mean 22.8 inches and standard deviation of 1.1 inches. Suppose a recruit was found with a head size of 23 inches Find the approximate Z-score for this recruit. a. 0 -0.18 b. 0.18 c. 0.96 d. 476.73
The approximate Z-score for this recruit is b. 0.18.
The mean of the head sizes (circumference) of new recruits in the armed forces can be approximated by a normal distribution with a mean 22.8 inches and standard deviation of 1.1 inches. The head size of a recruit was found to be 23 inches.
The approximate Z-score for this recruit. The formula for Z-score is given by:
[tex]Z=\frac{X-\mu}{\sigma}[/tex]
where X is the head size of the recruit, μ is the mean head size of recruits, and σ is the standard deviation of head sizes of recruits. Substituting the given values in the above formula, we get,
Z=(23-22.8)(1.1)
Z=0.2/1.1
Z [tex]\approx[/tex] 0.18
Thus, the approximate Z-score for this recruit is b. 0.18.
To know more about mean: https://brainly.com/question/20118982
#SPJ11
Joseph paints ornaments for a school play. Each ornament is made up of two identical cylinders, as shown. All surfaces of each cylinder must be painted. How many cans of paint does he need to paint 75 ornaments?
PLEASE HELP ME BIG GRADE!!!!!!!!!
Number of cylindrical cans of paint does he need to paint 75 ornaments is 20.
What is the Surface Area of a Cylinder?The total area that the cylinder's curved surface and round bases enclose is referred to as its surface area. The cylinder's total surface area consists of the curving surface as well as the areas of the two bases, each of which is shaped like a circle. A cylinder is a 3D solid object made up of two circular bases connected by a curving face.
Surface Area of Cylinder = 2πrh+2πr²
where , r is radius of cylinder=4.6cm
H is height of cylinder=2*6.5cm=13cm
A=2×π×4.6×13+2×π×4.6²≈508.68668cm²
Total Number of cans of paint needed to paint 75 ornaments=75×508.68668
/1900=20.
To know more about circle, visit:
https://brainly.com/question/29142813
#SPJ1
Place the three sets of conditions in order. Begin with the set that gives the greatest number of triangles, and end with the set that gives the smallest number of triangles. Condition A: One side is 6 inches long, another side is 5 inches long, and the angle between them measures 50°. Condition B: One angle measures 50°, another angle measures 40°, and a third angle measures 90°. Condition C: One side is 4 inches long, another side is 9 inches long, and a third side measures 5 inches.
The order from the greatest number of triangles to the smallest is: Condition A, Condition B, Condition C.
What is triangle inequality theorem?According to the Triangle Inequality Theorem, any two triangle sides' sums must be bigger than the length of the third side.
The triangle inequality theorem can be used to determine the order of the greatest to smallest triangle.
Condition A: Under this condition, we have two sides with lengths 5 and 6, and their angle is 50°. Using these requirements, we may create two separate triangles since 5 + 6 = 11, which is more than the third side.
Condition B: This condition results in a right triangle with a third angle that is 90° and two sharp angles that measure 40° and 50°. According to the Pythagorean theorem, the triangle's two legs must be 30 and 40 inches long, respectively, meaning that the hypotenuse must be 50 inches long. We can only create one triangle as a result.
Condition C: This condition provides us with three sides that are 4, 5, and 9 lengths long. Any two sides must have a length total larger than the third side in order for a triangle to be formed. The three sides provided, however, do not satisfy this since 4 + 5 = 9. Hence, under these circumstances, a triangle cannot be formed.
Learn more about triangle inequality theorem here:
https://brainly.com/question/1163433
#SPJ1
11. Figure EFGH is a parallelogram. Find the length of Line FG.
The length οf line FG is 12 cm, If Figure EFGH is a parallelοgram.
What is parallelοgram?A parallelοgram is a type οf quadrilateral with twο pairs οf parallel sides. The οppοsite sides οf a parallelοgram are equal in length and parallel tο each οther.
Since EFGH is a parallelοgram, we knοw that the οppοsite sides are parallel and equal in length. Therefοre, the length οf line FG is equal tο the length οf line EH.
We can find the length οf EH by using the Pythagοrean theοrem οn right triangle EFG:
[tex]EF^2 + FG^2 = EG^2[/tex]
Since EF = 5 cm, EG = 13 cm, and angle FEG is a right angle (as οppοsite angles in a parallelοgram are equal), we can sοlve fοr FG:
[tex]FG^2 = EG^2 - EF^2[/tex]
[tex]FG^2 = 13^2 - 5^2[/tex]
[tex]FG^2 = 144[/tex]
[tex]FG = \sqrt{(144)[/tex]
[tex]FG = 12 cm[/tex]
Therefοre, the length οf line FG is 12 cm.
To learn more about parallelogram from the given link:
https://brainly.com/question/29147156
#SPJ1
write an equation of the line that passes through (1 3) and has a slope of 5/4
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{3})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{5}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{ \cfrac{5}{4}}(x-\stackrel{x_1}{1}) \\\\\\ y-3=\cfrac{5}{4}x-\cfrac{5}{4}\implies y=\cfrac{5}{4}x-\cfrac{5}{4}+3\implies {\Large \begin{array}{llll} y=\cfrac{5}{4}x+\cfrac{7}{4} \end{array}}[/tex]
Consider the decay function d(x)=850(0. 94)x. Describe the characteristics of the functions
The decay function d(x) is an exponential function with an initial value of 850, a decay factor of 0.94, and a rate of decay that increases as x increases. The function has a horizontal asymptote at y=0, and its domain is all real numbers while its range is (0, 850].
The decay function d(x) can be described by the following characteristics:Exponential Decay: The function d(x) is an exponential function because it has a constant base (0.94) raised to a variable exponent (x).
Initial Value: The initial value of the function d(x) is 850, which represents the value of the function when x=0.
Decay Factor: The decay factor of the function d(x) is 0.94, which is less than 1. This means that as x increases, the function decreases and approaches zero, but never reaches zero.
Rate of Decay: The rate of decay of the function d(x) is determined by the value of the decay factor, which is 0.94. The closer the decay factor is to 1, the slower the rate of decay. Conversely, the closer the decay factor is to 0, the faster the rate of decay.
Asymptote: The function d(x) has a horizontal asymptote at y=0. This means that as x becomes very large, the function approaches but never touches the x-axis.
Domain and Range: The domain of the function d(x) is all real numbers, and the range is (0, 850]. This means that the function outputs a positive value less than or equal to 850, but never outputs zero.
Learn more about decay function here
brainly.com/question/28640407
#SPJ4
The number of hours, x, Ryan rides his bike and the total number of miles, y, he rides is a lineadrelationship. Ryan has already ridden 5 miles, and he can ride at a constant rate of(12 miles per hour. Write an equation relating × hours and y miles. Then predict how many minutes will pass for Ryan to have traveled a total of 60 miles.
Answer: If x represents the number of hours that Ryan rides his bike, and y represents the total number of miles that he rides, we can write the equation relating x and y as:
y = 12x + 5
This is a linear equation in slope-intercept form, where the slope is 12 (the rate at which Ryan rides, in miles per hour) and the y-intercept is 5 (the number of miles Ryan has already ridden).
To predict how many minutes it will take for Ryan to ride a total of 60 miles, we can substitute y = 60 into the equation and solve for x:
60 = 12x + 5
55 = 12x
x = 55/12
To convert this to minutes, we need to multiply by 60, since there are 60 minutes in an hour:
x (in minutes) = (55/12) * 60
x (in minutes) ≈ 275
Therefore, it will take Ryan approximately 275 minutes (or 4 hours and 35 minutes) to ride a total of 60 miles.
Step-by-step explanation:
5. Find x and h.
x =
h =
Using pythagoras' theorem in the right-angled triangle
x = 3 andh = 3√3What is a right-angled triangle?A right-angled triangle is a polygon with 3 sides in which one angle is a right angle
Now, since we have 3 triangles, using Pythagoras' theorem in all three triangles, we have
h² + (12 - x)² = 12² - 6² (1)
Also, h² + x² = 6² (2)
So, h² + (12 - x)² = 12² - 6²
h² + (12 - x)² = 144 - 36
h² + (12 - x)² = 108 (3)
From equation (2), h² = 36 - x²
Substituting this into equation (3), we have that
h² + (12 - x)² = 108 (3)
36 - x² + (12 - x)² = 108 (3)
Expanding the brackets, we have that
36 - x² + 144 - 24x + x² = 108
36 + 144 - 24x = 108
180 - 24x = 108
-24x = 108 - 180
-24x = -72
x = -72/-24
x = 3
Since h² = 36 - x²
h = √(36 - x²)
So, substituting the value of x = 3 into the equation, we have that
h = √(36 - x²)
h = √(36 - 3²)
h = √(36 - 9)
h = √27
h = 3√3
So,
x = 3 andh = 3√3Learn more about right-angled triangle here:
https://brainly.com/question/2580674
#SPJ1