Part A: greatest common factor: 4.
Part B: Factor of the expression are: x = 4, 1/2.
Part c: Check for the factors are found correct.
Explain about the greatest common factor?A group of numbers' greatest common factor (GCF) is the biggest factor each of the numbers have in common. The largest number that may divide evenly into two or more other numbers is known as the greatest common factor (GCF).The given expression is-
8x² + 28x - 16 = 0
Part A: The highest number that can be taken common is 4.
4(2x² + 7x - 4) = 0
Thus, greatest common factor: 4.
Part B: Factor of the expression.
4(2x² + 7x - 4) = 0
2x² + 7x - 4 = 0
2x² + 8x - x - 4 = 0
2x(x + 4) - (x + 4) = 0
(x + 4)(2x - 1) = 0
x = 4, 1/2
Thus, the Factor of the expression are: x = 4, 1/2.
Part C: Check:
x = 4, 1/2
8x² + 28x - 16
Put x = 4
= 8(4)² + 28(4) - 16
= 0 (satisfies)
Put x = 1/2
= 8(1/2)² + 28(1/2) - 16
= 0 (satisfies)
Thus, the check for the factors are found correct.
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PLease answer will give alot of points
Answer:
Step-by-step explanation:
1. Imagine a triangle with base side 36 feet and Kate at the right with the angle of elevation, 24 degrees. We can use tangent:
tan 24 = o/a ; tan(24) = o/36 ; 36(tan(24)) = o ; o = 16 feet
This is how tall the screen is.
2. We do a similar operation:
tan(74) = o/a ; tan(74) = 555/a ; a = 555/tan(74) ; a = 159.1 feet
Hope this helps!
What is a simplified value of the expression
The expression [tex]\frac{(\sqrt[3]{3})^{3/5} }{(\sqrt[3]{3})^{6/5}}[/tex] is equivalent to the expression [tex]\frac{1}{\sqrt[5]{3} }[/tex]. Then the correct option is B.
What is an equivalent?The equivalent is the expression that is in different forms but is equal to the same value.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expression is given below.
[tex]\rightarrow \dfrac{(\sqrt[3]{3})^{3/5} }{(\sqrt[3]{3})^{6/5}}[/tex]
Simplify the expression, then we have
[tex]\rightarrow \dfrac{(\sqrt[3]{3})^{3/5} }{(\sqrt[3]{3})^{6/5}}\\\\\rightarrow \dfrac{(3)^{1/5 }}{(3)^{2/5}}\\\\\rightarrow \dfrac{(3)^{1/5 }}{(9)^{1/5}}\\\\\rightarrow \dfrac{1}{\sqrt[5]{3} }\\[/tex]
The expression [tex]\frac{(\sqrt[3]{3})^{3/5} }{(\sqrt[3]{3})^{6/5}}[/tex] is equivalent to the expression [tex]\frac{1}{\sqrt[5]{3} }[/tex]. Then the correct option is B.
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What is the No information rate in statistics?
The No Information Rate (NIR) is a measure of the accuracy of a classification model that predicts the most frequent class as the outcome for all cases.
In statistics, the No Information Rate (NIR) is a measure of the accuracy of a classification model that predicts the most frequent class as the outcome for all cases. It represents the accuracy rate that can be achieved by simply guessing the most frequent outcome without using any predictive model or variable.
The NIR is commonly used as a benchmark for evaluating the performance of classification models, as any model that performs worse than the NIR is considered to be poorly performing. Conversely, a model that performs better than the NIR is considered to have some predictive power beyond simply guessing the most frequent outcome.
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2 years ago father was three times old as his son and two years hence twice his age will be equal to 5 times that of his son find their present age
Answer:
Step-by-step explanation:
PLEASE HELP!! WILL MARK YOU BRAINLIEST!!! LOTS OF LOVE!!! ♡♡
1) Andrea bought tacos from a food truck and left a 25% percent tip of $2.00
What was the price of Andrea's tacos, before tip?
2) Savanna had 40 iris blooms last year. This year, she had 15% more iris blooms.
How many more iris blooms did Savanna have this year?
1. Answer: The price of Andrea's tacos is $8.
Step-by-step explanation:
Hi, to answer this question we have to write an equation with the information given:
Tip amount: $2.0
Percentage: 25% = 0.25 (decimal form, 25/100=0.25)
So, if we multiply the taco's price (x) by the percentage (0.25) we will obtain the amount of the tip (2).
Mathematically speaking:
x (0.25) = 2
Solving for x
x = 2/0.25
x = 8
The price of Andrea's tacos is $8.
2. To solve this problem what you can do is the following rule of three:
40 iris blooms -----> 100%
x iris blooms -------> 115%
Clearing the value of x we have:
x = (115/100) * (40)
x = 46
Then, comparing with last year we have:
40-46 = 6
Answer:
Savanna had this year 6 more iris blooms than last year.
If 5 is subtracted from a number and this difference is tripled, the result is 3 more than the number. Find the number
The outcome is three more than the number, which is 9 if five is taken away from it and the difference is tripled.
What kinds of numbers are there in math?Whole Numbers: The collection of natural numbers that include the number 0. Integers are whole integers that are next to their counterparts (negative numbers). Real numbers would be any integers that can be stated as fractions. Any number that cannot be expressed as a fraction is irrational.
What are numbers and their many types?Many operations, like measuring, counting, and indexing, require the use of numbers. According to their characteristics, there are several sorts of numbers, including natural numbers, whole figures, rational or irrational numbers, integers, actual values, complex numbers, and even odd numbers, etc.
Let the number be y
5 is subtracted from the number. This can be written as:
y – 5
The difference is tripled. This can be written as:
3(y – 5)
The result of the difference tripled is 23 more than the number. This can be written as:
3(y – 5) = 3 + y
Thus, we can obtain the value of y as follow:
3(y – 5) = 3 + y
Clear bracket
3y – 15 = 3 + y
Collect like terms
3y – y = 3 + 15
2y = 18
y = 18 / 2
y = 9
Thus, the number is 9.
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What numbers that are less than 200 have the prime factors 3,5,and 13
The number that is less than 200 and have the prime factors 3, 5, and 13 is 195.
Prime factors are the prime numbers that divide a given positive integer exactly without leaving any remainder. In other words, prime factors are the building blocks of a number.
For example, the prime factors of the number 24 are 2 and 3, because 24 can be written as the product of these prime numbers: 2 × 2 × 2 × 3.
To find the numbers that have prime factors 3,5, and 13, multiply the prime factors together:
3 * 5 * 13 = 195
This is the only number less than 200 that has prime factors 3,5, and 13.
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How do you calculate orthogonal projection?
The vector "p" that represents "a's closest point" on the line "b" spans is the orthogonal projection of vector "a" onto vector "b."
So the vector "p" that represents "a's closest point" on the line "b" spans is the orthogonal projection of vector "a" onto vector "b." The following is the formula for projecting "a" orthogonally onto "b": CSS Copy: p = (dot(a, b) / dot(b, b)) * b, where "dot" stands for the dot product of the two vectors.
The procedures to determine the orthogonal projection of a vector "a" onto a vector "b" are as follows:
Identify the "a" and "b" dot product.
Add "b" to itself and calculate the dot product.
Divide the intersection of "a" and "b" by the intersection of "b" and itself.
Multiply the vector "b" by the step 3 result.
Here is a MATLAB sample that shows the orthogonal projection.
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A factory manufactures a metal piece in 32 minutes. New technology allowed the
factory to cut that time by 8%. Then another improvement cut the time by 5%.
How long does it take to manufacture the piece now? Round your answer to
the nearest minute.
Answer: The first improvement cut the time by 32 * 0.08 = 2.56 minutes.
So, the new time after the first improvement is 32 - 2.56 = 29.44 minutes.
The second improvement cut the time by 29.44 * 0.05 = 1.472 minutes.
So, the final time is 29.44 - 1.472 = 27.968 minutes.
Rounding to the nearest minute, it now takes 28 minutes to manufacture the piece.
Step-by-step explanation:
Kevin is 3 times as old as Daniel. 4 years ago, Kevin was 5 times as old as Daniel.
How old is Daniel now?
Answer:
Daniel is 8 years old now
Step-by-step explanation:
Let Kevin's age now be K and let Daniel's age now be D
"Kevin is 3 times as old as Daniel"
Translation: K = 3D
"4 years ago, Kevin was 5 times as old as Daniel"
4 years ago Kevin's age = K - 4
4 years ago Daniel's age = D - 4
4 years ago, Kevin was 5 times as old as Daniel.
Translation: K - 4 = 5(D - 4)
K - 4 = 5D - 20
Simplify this equation:
Add 4 to both sides:
K - 4 + 4 = 5D - 20 + 4
K = 5D - 16
Substitute K = #D:
3D = 5D - 16
Subtract 5D from both sides:
3D - 5D = - 16
-2D = -16
or
2D = 16 (multiply by - 1)
D = 16/2 = 8
and
K = 3D = 3 x 8 = 24
Now, Kevin is 24 years old and Daniel is 8 years old
Verify
If Kevin is 3x older than Daniel who is 8 now,
Kevin's age now = 3 x 8 = 24 Check
4 years ago, Daniel was 8 - 4 = 4 years
4 years ago, Kevin was 24 - 4 = 20
Kevin's age 4 years ago = 5 x 4 = 20 Check
Solve the problem pls
The original number in the word problem is 77.
How to find the numberLet's call the original two-digit number "x".
Information from the problem
the sum of the digits in x is 14.
So, we can write the number as x = 10a + b,
where a and b are the tens and ones digit, respectively, and a + b = 14.
Reversing and doubling the original number gives us 2(10b + a)
= 20b + 2a.
Adding the original number, x, and the doubled, reversed number, 2(10b + a),
we have 3x = 222.
Substituting x = 10a + b
3(10a + b) = 222
30a + 3b = 222
30a = 222 - 3b
Since the sum of the digits is 14, a + b = 14, so we can substitute for a in the equation:
30(14 - b) = 222 - 3b
420 - 30b = 222 - 3b
198 = 27b
Dividing both sides by 27, we find:
b = 7
So, the original number is x = 10a + b = 10(14 - 7) + 7 = 77.
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How do you find p-value from Z?
The p-value can be calculated from the Z-score of the observed result using the Z-table, which is a table of values for the standard normal distribution.
The p-value is the probability of getting a result at least as extreme as the one observed, given that the null hypothesis is true. It is calculated from the Z-score of the observed result, which is a measure of how many standard deviations away from the mean the observed result is. To calculate the p-value from a Z-score, you need to use the Z-table, which is a table of values for the standard normal distribution. The Z-table shows the probability of a given Z-score, or the area under the normal distribution curve to the left of the Z-score. To find the p-value associated with a given Z-score, you simply look up the probability in the Z-table, and subtract this probability from 1. This gives you the p-value, which is the probability of getting a result at least as extreme as the one observed, given that the null hypothesis is true.
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1) James and Sarah work at a restaurant wh
they make $6.25 an hour, plus tips. Last wook
James worked x number of hours and earned
$103.33 in tips Sarah worked y number of hours
and earned $139.45 in tips Sarah determined
that the expression
6.25x 103.356.25y + 139 62
will calculate the amount they earned together.
Which of the following expressions is equivalent
to Sarah's expression?
o 6.25(xy)+242.78
• 6.25r+y+242.78
o 6.25(x+y)+242.78
o 6.25x + 6.25y-242.78
Answer: The equivalent expression to Sarah's expression is:
6.25(x + y) + 242.78
This expression takes into account the total number of hours worked by James (x) and Sarah (y) and adds it to the sum of their tips, which is $242.78. The expression multiplies the total number of hours worked by 6.25, which is their hourly wage.
Step-by-step explanation:
Henry deposits $6000 into an account that pays simple Interest at an annual rate of 6%. He does not make any more deposits. He makes no withdrawals until
the end of 5 years when he withdraws all the money.
Answer the following questions. If necessary, refer to the list of financial formulas.
(a) How much total interest will Henry earn?
$
(b) What will the total amount in the account be (including interest)?
$
Answer:
1800
7800
Step-by-step explanation:
6000x0.06 = 360 x 5 for years since its annual then you get 1800 add that to the additional 6000 add those together and you get 7800.
Which expression represents the phrase, "half the sum of 10 and a number"?
○ ½x+10
○ ½(10+x)
01/2+10+x
○ 1⁄(10)+x
Answer: 1/2(10+x)
Step-by-step explanation:
"Half the sum of 10 and a number" means 1/2(10+x), where x is the unknown number.
Let A be an m×n matrix.
Suppose that the nullspace of A is a plane in R^3 and the range is spanned by a nonzero vector v in R^5. Determine m and n. Also, find the rank and nullity of A.
The rank (m) and the nullity (n) is the Matrix A is 5 and 3 respectively according to the planes given.
The maximum number of its linearly independent columns (or rows ) of a matrix is called the rank of a matrix. And the dimension of the null space of A, also called the kernel of A.
Given null space of [tex]L_{A}[/tex] is a plane in [tex]lR^{3}[/tex] .
So nullity of matrix A is A = 2
Since the dimensions of a plane in [tex]lR^{3}[/tex] is 2.
Also the range is spanned by non-vector V in [tex]R^{5}[/tex].
So rank of matrix A is A = 1
Clearly the linear transformation is from [tex]lR^{5}[/tex] to [tex]lR^{3}[/tex],
Then the Matrix A is a = 5x3 matrix.
Therefore, Rank of the matrix A (m)= 5 and Nullity of the matrix A (n) = 3.
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The price of a $250 coat decreased 10% last year. What is the price of the coat this year?
Answer: $225. If the price of the coat was $250 last year, then the coat costs $225 this year.
Step-by-step explanation:
Since the coat costed $250 last year, it is 100% of its original.
Now that it has decreased 10%, it is 100%-10%=90% of its original price.
The new price of the coat will be (90% ÷ 100%) × $250 = $225
i have a question....
The required proportional relationship used to evaluate the measure of segment LM is 9/LM = 6/4.5. Option D is correct.
What are Similar triangles?Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.
Here,
Since Triangle HJK is similar to triangle LMN.
The property of similar triangle states that the sides of both the triangle will be proportional to each other.
So,
9/6 = LM/4.5
Or
9/LM = 6/4.5
Thus, the required proportional relationship used to evaluate the measure of segment LM is 9/LM = 6/4.5. Option D is correct.
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Edward serves 4 cups of coffee every nine minutes how many cups of coffee does he serve every minute write an equation where y is the subject that represents this proportional relationship
The solution is, an equation where y is the subject that represents this proportional relationship is, y = 4x/9.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
given that,
Edward serves 4 cups of coffee every nine minutes
now, we have to find that,
how many cups of coffee does he serve every minute ,
i.e. we get,
in 9mint. cup = 4
so, in 1 mint cup = 4/9
now, an equation where y is the subject that represents this proportional relationship is,
y = 4x/9
where, x for the amount of minutes .
Hence, The solution is, an equation where y is the subject that represents this proportional relationship is, y = 4x/9.
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What is 156lbs to kg ?
From the given information, by using mass conversion, 156 lbs is equal to approximately 70.76 kg.
Mass conversion is the process of converting a given mass from one unit of measurement to another. It involves using a conversion factor to change the numerical value of the mass while keeping the physical quantity constant.
For example, converting a mass from pounds to kilograms involves using a conversion factor of 0.45359237 kg/lb.
To convert pounds to kilograms, you can use the following conversion formula:
1 lb = 0.45359237 kg
So, to convert 156 lbs to kg, you can multiply 156 by 0.45359237:
156 lbs × 0.45359237 kg/lb = 70.76 kg (rounded to two decimal places)
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A guy wire runs from the top of a cell tower to a metal stake in the ground. Grace places a 6-foot tall pole to support the guy wire. After placing the pole, Grace measures the distance from the stake to the pole to be 7 ft. She then measures the distance from the pole to the tower to be 19 ft. Find the length of the guy wire, to the nearest foot.
The length of the guy wire is 20 feet
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
We can use the Pythagorean theorem to find the length of the guy wire.
Let's call the length of the guy wire "g".
Then we have a right triangle with hypotenuse g, one leg of length 7 ft, and the other leg of length 19 ft.
Using the Pythagorean theorem, we have:
g² = 7² + 19²
g² = 49 + 361
g² = 410
Take square root on both sides
g = 20.24
Therefore, the length of the guy wire is 20 feet
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The figure is the net for a rectangular prism.
What is the surface area of the rectangular prism represented by the net?
The total surface area of the rectangular prism represented by the net is 174 inch²
What is a prism?A prism is a solid geometric shape with parallelograms for its sides and two comparable, equal, and parallel rectilinear figures for its ends.
Given:
Length of the base = 9 inch
Width of the base = 3inch
Height of the base = 5 inch
Area of the two rectangular base
= 2 x length x width
= 2 x 9 x 3
= 54 inch²
and, Area of lateral surfaces
= 2 lateral surfaces with length 9 inch + 2 lateral surfaces with width 3 inch
= 2 x 9 x 5+ 2 x 3 x 5
= 120 inch²
So, Total surface area = 54+120 = 174 inch²
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The surface area of the rectangular prism is,
⇒ SA = 174 Square units.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The figure is the net for a rectangular prism.
And, Length = 9 in.
Width = 3 in.
Height = 5 in.
Now, We know that;
The surface area of a rectangular prism is given by,
⇒ SA = 2 (lh +wh + lw ) Square units.
Substitute all the values, we get;
⇒ SA = 2 (lh +wh + lw ) Square units.
⇒ SA = 2 (9×5 + 3×5 + 9×3 ) Square units.
⇒ SA = 2 (45 + 15 + 27) Square units.
⇒ SA = 2 × 87
⇒ SA = 174 Square units.
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help!!!!!!!!!!!!!!!!
Answer:
2 3/7
Step-by-step explanation:
Answer:
2^[tex]\frac{3}{2}[/tex]
Step-by-step explanation:
2^3·1/2 = 2^[tex]\frac{3}{2}[/tex]
the image you posted is very blurry, but it looks like the answer is the last choice
A large school district held a district-wide track meet for all high school students. For the 2-mile run, the population of female students participating had a mean running time of 8.8 minutes with standard deviation of 3.3 minutes, and the population of male students participating had a mean running time 7.3 minutes with standard deviation of 2.9 minutes. Suppose 8 female students and 8 male students who participated in the 2-mile run are selected at random from each population. Let īp represent the sample mean running time for the female students, and let M represent the sample mean running time for the male students. What are the mean and standard deviation of the sampling distribution of the difference in sample means īp - TM ? 8.8 +3 V 8 A The mean is 0.4, and the standard deviation is 7.3 B The mean is 0.4, and the standard deviation is 8,8ª 7.3° 8 8 3.3 2.9° The mean is 1.5, and the standard deviation is 8 8 3.3 V 8 D The mean is 1.5, and the standard deviation is 2.9 8 3.3ª 2.9º E The mean is 1.5, and the standard deviation is 8 8
The mean and standard deviation of the sampling distribution of the difference in sample means xF − xM is 1.5 minutes(mean) and 1.533 minutes(std. dev) approx The probability of getting a difference in sample means xF − xM that is less than 0 is 0.0239 approx.
Suppose that a random variable X is formed by n mutually independent and normally distributed random variables such that:
Xi = N(μi, σ²) ; i = 1, 2,......, n
And if
X = X1 + X2 +........+ Xₙ
Then, its distribution is given as:
X ≈ N (μ1 + μ2+........+ μₙ)
For this case, it's given that
Distribution of time taken for distance ran by lady is Normal distribution and had a mean handling time of = 8.8 minutes with standard divagation of = 3.3 minutes.
Distribution of time taken for distance ran by joker is Normal distribution and had a mean handling time of = 7.3 minutes with standard divagation of = 2.9 minutes.
Samples of size n = 8 are taken from both population.
Estimated sample mean = population mean
Estimated sample standard deviation = population std. dev / √n
where n = sample size
For sample of females, the distribution is
For sample of males, the distribution is
Also, if we take distribution of difference between sample means(, then it would be normal with mean = 8.8-7.3 = 1.5 minutes (as mean for will be -7.3 but same standard deviation) as factor gets squared for affecting standard deviation and variance)
and standard deviation is:
[tex]\sqrt{s^2f + s^2m } = \sqrt{3.3^2/8 + 2.9^2/8}[/tex]
≈ 1.553 minutes.
The distribution of difference between sample means is approximately
We need [tex]P(Xf - Xm < 0)[/tex]
Thus, the mean and standard deviation of the sampling distribution of the difference in sample means xF − xM is 1.5 minutes(mean) and 1.533 minutes(std. dev) approx The probability of getting a difference in sample means xF − xM that is less than 0 is 0.0239 approx.
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Pls helppppp its math and its pretty hard
A maintenance worker needs to wax a restaurant floor shaped like the image shown. A six-sided figure. There is a horizontal base of 35 feet then another horizontal base below it of 20 feet. The longest side is to the right and is 40 feet. The top is 30 feet. There is a perpendicular from the vertex of the top to the first base of 35 that is labeled 15 feet. If the wax cost $1.38 a square foot, how much will the wax cost to cover the floor? $1,224.75 $1,569.75 $2,104.50 $2,449.50
Note that the cost of wax that is required to cover the floor is given as = $1.677.39
To arrive at the correct answer, we had to deconstruct the complex shape in regular shapes comprising two rectangles and one right-angled triangle.
What is a Complex Shape in Math?
When disassembled, a composite form (or complex figure), also known as a compound shape, is made up of several separate regular shapes.
Note that the arrive at the correct answer, we need to deconstruct the complex shape in regular shapes comprising two rectangles and one right-angled triangle.
The objective is to add the area of all the shapes which comprise the irregular floor and multiply by the cost of wax per square foot. (See attached Image for Deconstructed Compound Shape.)
Step 1 - Find the area of the Right-Angled Triangle
Recall that the rea of a Right Angled Triangle = 1/2 B*H;
B = 15ft
H = 35ft
Area of Δ = 1/2 * 15 *35
Area of Triangle = 262.5ft
Step 2 - Find the area of the Two Rectangles
Dimensions of Rectangle a are: L = 30ft; B = 15ft
Area = L*B
Area = 30*15
Area of (a) = 450ft
Dimensions of Rectangle b are: L = 25ft: B= 20ft
Area (b) = 25* 20
Area (b) = 500ft
Step 3 - Find the area of the compound shape
Area of the compound shape = Sum of the area of the individual shapes =
262.5ft + 450ft + 500ft
= 1212.5 ft
Step 4 - Find the cost of waxing the floor (compound shape)
This is given as:
$1.38 * Area of Compound Shape
⇒ 1.38 * 1212.5
= $1.677.39
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See the images attached for the missing part of the question
2(5x + 2) = 10x - 4
what is the x
Answer:umm
There are no values of
x
that make the equation true.
No solution
Step-by-step explanation:
Watch help video
In circle D, m/EBC = 51°. Solve for x if mEC = (5x - 33)°. If necessary,
round your answer to the nearest tenth.
B
E
The measure of the value of x in the given circle is 27
What is an inscribed angle?In geometry, an inscribed angle is the angle formed in the interior of a circle when two chords intersect on the circle.
Given that a circle D, having an inscribed angle ∠ EBC measuring 51° and an arc covered by it is arc EC measuring 5x-33, we are to find the value of x,
We know that,
The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its intercepted arc.
Therefore,
m ∠ EBC = 2 arc EC
5x-33 = 2×51
5x-33 = 102
5x = 135
x = 27
Hence, the measure of the value of x in the given circle is 27
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The figure is not given, the question is solved for the attached figure.
Woof Chow Dog Food Company believes that it has a market share of 25 percent. It surveys n = 100 dog owners and ask whether or not Woof Chow is their regular brand of dog food, and 23 people say yes. Based upon this information, what is the critical value if the hypothesis is to be tested at the 0.05 level of significance?
The critical value for the 0.05 level of significance is k = 21.
To find the critical value, we can use the binomial distribution. The binomial distribution models the number of successes in n independent Bernoulli trials, each with probability p of success. In this case, the number of successes is the number of dog owners who say Woof Chow is their regular brand, and the number of trials is n = 100. The null hypothesis is that the true market share of Woof Chow is 25%, and the alternative hypothesis is that it is not 25%.
We can use the binomial cumulative distribution function (CDF) to find the critical value. The CDF gives the probability of getting k or fewer successes in n trials, given a probability of success p. The critical value is the smallest value of k such that the CDF at k is greater than or equal to 1 - alpha, where alpha is the level of significance. In this case, alpha = 0.05.
So, we want to find the smallest k such that:
P(X <= k) >= 1 - 0.05
where X is a random variable representing the number of dog owners who say Woof Chow is their regular brand. We can use a binomial calculator or a software package to calculate the binomial CDF, or we can use a table of critical values for the binomial distribution.
The critical value for the 0.05 level of significance is k = 21. This means that if the true market share of Woof Chow is 25%, then the probability of getting 23 or more dog owners who say Woof Chow is their regular brand is less than 0.05. Since the observed number of dog owners who say Woof Chow is their regular brand is 23, which is greater than 21, we can reject the null hypothesis that the true market share is 25%.
This means that based on the survey results, we cannot conclude that Woof Chow has a market share of 25%. The survey results suggest that Woof Chow may have a market share that is greater than 25%.
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Math!!! 100 points
circle all graphs that show a proportional relationship
Help, ASAP.............
The measure of angle number 1 is 69°.
How to find the measure of ∠1?We know that ∠1 + ∠2 = 180°
We also know that the sum of the interior angles of a triangle is always equal to 180°.
Then we can write simple linear equations to find the missing angles, for example we can write:
21° + 38° + ∠2 = 180°
∠2 = 180° - 21° - 38°
∠2 = 121°
Now we can replace that in the original equation ∠1 + ∠2 = 180°:
∠1 + 121° = 180°
∠1 = 180° - 121° = 69°
∠1 = 69°
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