1 point
What is 3V45 expressed in simplest radical form?
a. 615
b. 2715
c. 9/5
d. 515
b
Ο Ο Ο Ο
d
Answers
Answer:
The simplest radical form is \(9\sqrt{5}\) ⇒ (c)
Step-by-step explanation:
To simplify any square root;
Factorize the number under the root using prime numbersTake out the root any number repeated twice as one numberExamples:
1. Simplify \(\sqrt{8}\)
factorize 8 using prime numbers
8 = 2 × 2 × 2, then \(\sqrt{8}=\sqrt{(2)(2)(2)}\)
Take two of 2 out the root, then \(\sqrt{8}=2\sqrt{2}\)
2. Simplify \(\sqrt{18}\)
factorize 18 using prime numbers
18 = 2 × 3 × 3, then \(\sqrt{18}=\sqrt{(2)(3)(3)}\)
Take the two 3 out the root, then \(\sqrt{18}=3\sqrt{2}\)
Let us simplify \(3\sqrt{45}\)
∵ 45 = 3 × 3 × 5
∴ \(3\sqrt{45}=3\sqrt{(3)(3)(5)}\)
→ Take the two 3 out by one 3
∴ \(3\sqrt{45}=3(3)\sqrt{5}\)
→ Multiply the numbers out the root
∴ \(3\sqrt{45}=9\sqrt{5}\)
∴ The simplest radical form is \(9\sqrt{5}\)
Related Questions
2:6 and 24:72 are equal ratios. True OR False?
Answers
True
Explanation:
2/6 = 1/3
24/72 = 12/36 = 2/6 = 1/3
What equation matches this situation?
—John wants to buy an MP3 Player that costs $30. How much change did he receive
if he gives the cashier $40–
Answers
30 + c = 40
Suppose each license plate in a certain state has three digits followed by three letters. The digits 4 and 5 are not used. So, there are 26 letters and 8 digits that are used. Assume that the letters and digits can be repeated. How many license plates can be generated using this format?
Answers
The required, there are 8998912 possible license plates that can be generated using this format.
Here, we have,
There are 8 digits that can be used for each of the three digits on the license plate, with two digits (4 and 5) that cannot be used.
Therefore, there are 8 choices for each of the three digits,
giving us 8 x 8 x 8 = 512 possible combinations for the digits.
Similarly, there are 26 letters that can be used for each of the three letters on the license plate.
Therefore, there are 26 choices for each of the three letters, giving us 26 x 26 x 26 = 17576 possible combinations for the letters.
Total number of license plates = number of choices for the digits x number of choices for the letters
= 512 x 17576
= 8998912
Therefore, there are 8998912 possible license plates that can be generated using this format.
Learn more about combination here:
brainly.com/question/13387529
#SPJ1
For a two-sample hypothesis which tests for differences in population parameters (1) and (2), a two-tailed test seeks evidence that population parameter:
Answers
The two-tailed test seeks evidence that the population parameter
(1) is not equal to the population parameter (2).
What is the purpose of conducting a two-tailed test for a two-sample hypothesis?In a two-sample hypothesis test, a two-tailed test is employed to determine if there is evidence that the population parameter (1) differs from the population parameter (2).
This test is useful when we want to examine whether the two populations have significantly different means, proportions, or other relevant parameters.
The two-tailed test considers two possible alternative hypotheses: the population parameter (1) is either greater than the population parameter (2), or it is smaller than the population parameter (2). By considering both directions of the difference, we can evaluate the possibility of a significant difference in either direction.
In a two-tailed test, the null hypothesis assumes that the population parameters (1) and (2) are equal. The alternative hypothesis, on the other hand, states that there is a significant difference between the two population parameters. By conducting the test, we gather evidence to either support or reject the null hypothesis.
To perform a two-tailed test, we follow a standardized process. We calculate the test statistic, such as the t-statistic or z-statistic, and compare it to the critical value(s) from the appropriate distribution. If the test statistic falls in the rejection region, we reject the null hypothesis and conclude that there is evidence of a significant difference between the population parameters.
Hypothesis testing, specifically two-sample hypothesis testing, can provide a deeper understanding of statistical analysis. By exploring the various types of tests, their assumptions, and applications, researchers and analysts can make informed decisions based on reliable evidence. Additionally, understanding the nuances of hypothesis testing contributes to the development of robust experimental designs and accurate interpretation of results.
Learn more about Null Hypothesis
brainly.com/question/30484892
#SPJ11
A system of equations is given.
−5y = 10 − 5x
−2y = 8 − 4x
Solve for (x, y) using the elimination method. Write your solution in (x,y) form.
Answers
Answer:
(2, 0 )
Step-by-step explanation:
- 5y = 10 - 5x → (1)
- 2y = 8 - 4x → (2)
multiplying (1) by - 2 and (2) by 5 and adding will eliminate y
10y = - - 20 + 10x → (3)
- 10y = 40 - 20x → (4)
add (3) and (4) term by term to eliminate y
0 = 20 - 10x ( add 10x to both sides )
10x = 20 ( divide both sides by 10 )
x = 2
substitute x = 2 into either of the 2 equations and solve for y
substituting into (1)
- 5y = 10 - 5(2)
- 5y = 10 - 10 = 0 , then
y = 0
solution is (2, 0 )
This vector function removes an item from a vector. A) remove_item B) delete_item C) erase D) pop_back
Answers
This vector function removes an item from a vector is erase (option c).
The vector function that removes an item from a vector in most programming languages, including C++, is typically called "erase." The erase function is used to remove elements from a vector based on a specified position or range.
The erase function can take different forms depending on the programming language and vector implementation. For example, in C++, the erase function is a member function of the vector class and can be used in the following ways:
vector.erase(position) - Removes the element at the specified position.
vector.erase(first, last) - Removes elements in the range defined by the iterators 'first' and 'last'.
Using the erase function allows you to remove elements from a vector and adjust the size of the vector accordingly. The correct option is c.
To know more about vector:
https://brainly.com/question/24256726
#SPJ4
maximum likelihood estimate (mle) is a very general method that can be applied to both continuous and discrete distributions. in this problem, we assume we have a training data that are drawn from a poisson distribution, with probability mass function (pmf) we want to use mle to fit the parameter with the training data. to do so, we first compute the log likelihood of our training data, or in other words, log of the probability of obtaining the sample given the model and where are independent. the log likelihood is...unansweredin the next step, we maximize this log likelihood function by taking the derivative. what is the resulting estimate for ?unansweredis it in accordance with the definition of in poisson distribution? (there is no answer box for this question.)
Answers
In this case, the likelihood function is the product of the Poisson probability mass function evaluated at each data point in the training data. To compute the log-likelihood, we take the natural logarithm of this product. To maximize the log-likelihood function, we take the derivative of it with respect to the parameter and set it equal to zero. Solving for the parameter gives us the maximum likelihood estimate.
To help you with your question, let's go through the process of using maximum likelihood estimation (MLE) for a Poisson distribution step by step.
1. Given training data drawn from a Poisson distribution, we have the probability mass function (PMF) as:
P(X=k) = (λ^k * e^(-λ)) / k!, where k is a non-negative integer and λ is the parameter we want to estimate.
2. The likelihood function, which is the joint probability of obtaining the sample given the model, is the product of individual probabilities:
L(λ) = Π P(X_i=k_i), for i = 1 to n, where n is the number of data points.
3. For MLE, we compute the log-likelihood function, which is the natural logarithm of the likelihood function:
log(L(λ)) = Σ log(P(X_i=k_i)), for i = 1 to n.
4. Plugging in the PMF, the log-likelihood becomes:
log(L(λ)) = Σ [k_i * log(λ) - λ - log(k_i!)], for i = 1 to n.
5. To maximize the log-likelihood function, we take its derivative with respect to λ and set it to 0:
d(log(L(λ))) / dλ = Σ [k_i/λ - 1] = 0.
6. Solve for the MLE estimate of λ:
λ_MLE = Σ k_i / n, where n is the number of data points.
The resulting estimate for λ, λ_MLE, is in accordance with the definition of λ in a Poisson distribution, as it represents the average number of events in the sample. The resulting estimate for the Poisson distribution parameter is the sample mean of the training data. This is in accordance with the definition of the Poisson distribution, where the mean and variance are equal to the parameter lambda.
Learn more about log-likelihood:
brainly.com/question/29646733
#SPJ11
which of the following is (are) time series data? i. weekly receipts at a clothing boutique ii. monthly demand for an automotive part iii. quarterly sales of automobiles
Answers
i. weekly receipts at a clothing boutique
ii. monthly demand for an automotive part
Which data sets represent time series data?Time series data refers to information collected and recorded at regular intervals over a specific period. In the case of i. weekly receipts at a clothing boutique and ii. monthly demand for an automotive part, both data sets are examples of time series data.
Time series data consists of observations recorded over regular intervals, allowing for the analysis of patterns and trends over time. In i. weekly receipts at a clothing boutique, the data is collected on a weekly basis, providing insights into the boutique's revenue fluctuations over different weeks. Similarly, ii. monthly demand for an automotive part captures the demand for the part on a monthly basis, enabling analysis of monthly variations and seasonal patterns.
On the other hand, iii. quarterly sales of automobiles do not fall under time series data. While it represents sales data, the intervals between measurements are not consistent enough to qualify as time series. Quarterly intervals are less frequent and may not capture shorter-term trends or variations as effectively as weekly or monthly intervals.
Learn more about automobiles
brainly.com/question/17326089
#SPJ11
WILL GIVE BRAINLIST TO BEST ANSWER AND EXTRA POINTS
Kyle is running from his house to his grandmother’s house. His distance, in feet, from his grandmother’s house can be found by using the expression below, where m represents the number of minutes Kyle has been running.
1500 - 110m
What does the value 110 in the expression represent?
The distance between Kyle's house and his grandmother's house.
Kyle's speed.
The distance Kyle has covered in m minutes.
Kyle's speed in feet per minute.
Answers
Kyle's speed in feet per minute. That has to be what it is; if it's not, I am sorry. I hope this is the correct answer. Good luck.
whats is 4x 1/10 ? ... lol i am dumb
Answers
Answer:
4 x 1/10 = 4/10
Step-by-step explanation
One way to think about it is you turn 4 to a fraction which would be 4/1. then you multiply the numerators(the top numbers) and the denominators(bottom numbers) and that's that. so 4 x 1 = 4. and 1 x 10 = 10. then put 4 over 10.
\(\large\color{lime}\boxed{\colorbox{black}{Answer : - }}\)
\(4 \times \frac{ 1 }{ 10 }\)
\(Multiply \: 4 \: and \: \frac{1}{10} \: to \: get \: \frac{4}{10}.\)
\(\frac{4}{10} \)
\(Reduce \: the \: fraction \: \frac{4}{10} \: to \: lowest \\ \: terms \: by \: extracting \: and \\ canceling \: out \: 2.\)
\( \color{red}\frac{2}{5} = 0.4\)
Write an equation in slope intercept form of the line that passes through the points (1,−6) and (5,−6).
Answers
slope intercept form = y=mx+b
m= slope
b= y-intercept
the slope is rise over run, so if the points are (1, -6) and (5, -6), the slope is 0
the y intercept is -6
y = 0x-6
or
y = -6
The absolute value of (2−7)=
Answers
That because anything in the absolute value that is a negative answer it will always be positive. Like 2-7 which supposed to equal to -5 but when it come in a absolute value the answer will be positive 5.
The absolute value is:
5Work/explanation:
First, we will evaluate 2-7.
It evaluates to -5.
Now, let's find the absolute value of -5 by using these rules:
\(\sf{\mid a\mid=a}\)
\(\sf{\mid-a \mid=a}\)
Similarly, the absolute value of -5 is:
\(\sf{\mid-5\mid=5}\)
Hence, 5 is the answer.consider the vectors x and a and the symmetric matrix a. i. what is the first derivative of at x with respect to x? ii. what is the first derivative of xt ax with respect to x? what is the second derivative?
Answers
The first derivative of at x with respect to x is simply the transpose of the matrix a.The first derivative of xt ax with respect to x is 2ax, since taking the derivative of the product of two vectors involves multiplying one of the vectors by the derivative of the other vector, and in this case the derivative of x is the identity matrix (since x is a vector and not a matrix).The second derivative of xt ax with respect to x is simply the matrix 2a, since the second derivative involves taking the derivative of the first derivative.1. Given the vector x and the symmetric matrix A.
2. We need to find the first and second derivatives of the following expressions:
i. A * x
ii. x^T * A * x
The question involves vectors, symmetric matrices, and derivatives. Let's break it down step-by-step.
i. First derivative of A * x with respect to x:
To find the derivative of A * x with respect to x, we treat A as a constant matrix. The first derivative is simply the matrix A itself.
Answer: The first derivative of A * x with respect to x is A.
ii. First derivative of x^T * A * x with respect to x:
To find the first derivative of this expression, we'll use the following formula for the derivative of a quadratic form:
d/dx (x^T * A * x) = (A + A^T) * x
Since A is a symmetric matrix, A = A^T. Therefore, the formula becomes:
d/dx (x^T * A * x) = 2 * A * x
Answer: The first derivative of x^T * A * x with respect to x is 2 * A * x.
iii. Second derivative of x^T * A * x with respect to x:
The second derivative of x^T * A * x with respect to x is the derivative of the first derivative (2 * A * x) with respect to x. Since A is a constant matrix, the second derivative is zero.
Answer: The second derivative of x^T * A * x with respect to x is 0.
To learn more about derivative : brainly.com/question/25324584
#SPJ11
If a leinear system has more unknowns equations then it must hav einfinitely many solutions.
a. true
b. false
Answers
If a linear system has more unknown equations then it must have infinitely many solutions, which is true.
What is a linear equation?A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
If there is only one equation with more than one parameter, then the number of the solution will be infinite.
If a linear system has more unknown equations then it must have infinitely many solutions, which is true.
More about the linear equation link is given below.
https://brainly.com/question/11897796
#SPJ4
The perimeter of a rectangle is 168 m. Its length is five times its width. Find the length and width.
Answers
Answer:
Length of rectangle = 63 mWidth of rectangle = 21 mStep-by-step explanation:
Given:
Perimeter of rectangle = 168 mLength of rectangle is five times the widthTo Find:
Length and WidthSolution:
Let's assume width of rectangle x m and length of rectangle be 3x m. To calculate the dimensions of the rectangle we will use the formula of Perimeter of the rectangle
Perimeter of rectangle = 2(L + B)
Substituting the required values:
→ 168 = 2(3x + x)
→ 168 = 2(4x)
→ 168/2 = 4x
→ 84 = 4x
→ 84/4 = x
→ 21 = x
Hence,
Length of the Rectangle = 3x = 3(21) = 63 mWdith of the rectangle = x = 21 mAnswer:
Length = 70 metreWidth = 14 metre⠀
Step-by-step explanation :
⠀
As, it is given that, the perimeter of a rectangle is 168 m and its length is five times its width and we are to find the length and width of the rectangle. So,
⠀
Let us assume the width of the rectangle as w metre and therefore, the length will be 5w metre .
⠀
Now, According to the Question :
⠀
\({\longrightarrow \qquad { \pmb{\frak {2 ( Length + Breadth )= Perimeter_{(Rectangle)} }}}}\)
⠀
\({\longrightarrow \qquad { {\sf{2 (5 w + w )= 168 }}}}\)
⠀
\({\longrightarrow \qquad { {\sf{2 (6 w )= 168 }}}}\)
⠀
\({\longrightarrow \qquad { {\sf{12 w = 168 }}}}\)
⠀
\({\longrightarrow \qquad { {\sf \: w = \dfrac{168}{12} }}}\)
⠀
\({\longrightarrow \qquad { \underline{ \boxed{ \pmb {\frak{ w = 14 }}}}}} \: \: \bigstar\)
⠀
Therefore,
The width of the rectangle 14 metre .⠀
Now, we are to find the length of the rectangle :
⠀
\({\longrightarrow \qquad { { { \pmb {\frak{ Length = 5w }}}}}} \: \: \)
⠀
\({\longrightarrow \qquad { { { \pmb {\frak{ Length = 5 \times 14 }}}}}} \: \: \)
⠀
\({\longrightarrow \qquad { \underline{ \boxed{ \pmb {\frak{ Length = 70 }}}}}} \: \: \bigstar\)
⠀
Therefore,
The length of the rectangle is 70 metreA car traveled 150 miles on 5 gallons of gas. Find the unit rate.
Answers
Answer:
30m per gallon
Step-by-step explanation:
150m/5g= 30m/g
Lance used two gallons of paint to pain 785 square feet. How many gallons will he need to purchase to cover 2,500 square feet?
Answers
Answer:
7 gallon
Step-by-step explanation:
Divide the space that needs paints by how much space has been painted
2500/785 = 3.18
Then double that because it takes 2 gallons to paint every 785 square feet
3.18 x 2 = 6.36
You would need 6.36 gallons of paint, which would round up to 7 because you cannot buy 0.36 of a gallon
18 i
Use the given information to find the amount A in the account earning compound interest after 6 years when the principal is $3500.
r=1. 83%, compounded daily
Answers
When the principal is $3500 and the annual interest rate is 1.83%, compounded daily, the balance in the account receiving compound interest after 6 years is $4,036.32.
To find the amount A in the account earning compound interest after 6 years when the principal is $3500, we need to use the compound interest formula:
\(A = P(1 + \frac{r}{n})^{nt}\)
Where:
P = principal = $3500
r = annual interest rate = 1.83% = 0.0183 (as a decimal)
n = number of times the interest is compounded per year = 365 (daily compounding)
t = time in years = 6
Substituting these values into the formula, we get:
\(A = 3500(1 + \frac{0.0183}{365})^{(365*6)}\)
\(A = 3500(1.00005)^{2190}\)
A = $4,036.32
Therefore, the amount in the account earning compound interest after 6 years when the principal is $3500, with an annual interest rate of 1.83% compounded daily, is $4,036.32.
To learn more about compound interest refer to:
brainly.com/question/14295570
#SPJ4
help asap please! will give brainliest
Answers
Answer:
x= -3/2 or x=1.
Step-by-step explanation:
First, make the equation into a factorable form by subtracting 2 from each side to get 2x²+x-3=0. Then factor that into (2x+3)(x-1)=0. Then, you would do 2x+3=0, 2x=-3, x= -3/2. After that, do the second equation x-1=0, x=1.
(hope this helps :P)
In his free time, Gary spends 9 hours per week on the Internet and 12 hours per week playing video games. If Gary has five hours of free time per day, what percent of his free time is spent on the Internet and playing video games
Answers
Answer: 11.64%
Step-by-step explanation:
what is the precent increase from 72 to 81?
Answers
Given:
what is the percent increase from 72 to 81?
The difference between the numbers are =
\(81-72=9\)so, the percent increase =
\(\frac{9}{72}\cdot100=0.125\cdot100=12.5\%\)So, the answer is 12.5%
(1) what is the critical angle for light going from air (n = 1.0) into glass (n = 1.5) ?
Answers
The critical angle for light going from the air (n = 1.0) into the glass (n = 1.5) is 41.8 degrees.
When light travels from one medium to another, it changes its direction due to the change in the refractive index of the medium. The angle at which the light is refracted is determined by Snell's law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant for a given pair of media. At a certain angle of incidence, known as the critical angle, the refracted angle becomes 90 degrees, and the light is no longer refracted but reflected into the first medium.
This critical angle can be calculated using the formula sinθc = n2/n1, where θc is the critical angle, n1 is the refractive index of the first medium (in this case, air), and n2 is the refractive index of the second medium (in this case, glass).
In this case, substituting the values n1 = 1.0 and n2 = 1.5 into the formula, we get sin θc = 1.5/1.0 = 1.5. However, since the sine of any angle cannot be greater than 1, there is no critical angle for light going from glass to air. Thus, the critical angle for light going from air to glass is given by sin θc = 1/n2/n1 = 1/1.5/1.0 = 0.6667, and taking the inverse sine of this value gives us the critical angle of 41.8 degrees.
To learn more about the refractive index, visit:
https://brainly.com/question/83184
#SPJ11
Evaluate each expression for the given value.
a. a2 when a= 3/4
b. b3 when b = 1.1
Answers
Answer:
a. 9/16 or 0.5625
b. 1.331 or 1331/1000
Step-by-step explanation:
I’m assuming you meant a^2 and b^3
Derive the following cquation. β=
c
v
=
1−(
E
0
+K
E
0
)
2
Choose the best way to begin this derivation. We have E
2
=p
2
c
2
+E
0
2
=p
2
c
2
+m
2
c
4
. We have K+E=ε
0
=
1−β
2
.
E
. We have E=p
2
c
2
+E
0
=p
2
c
2
+mc
2
. We have K=E−E
0
=
1−rho
2
E
0
−E
0
. Rearrange to complete the proof. (Submit a file with a maximum size of 1 MB.)
Answers
We have derived the equation β = cv = 1 - (E₀ + KE₀)².
To derive the equation β = cv = 1 - (E₀ + KE₀)², we can begin with the given equations:
E² = p²c² + E₀²
K + E = ε₀ = 1 - β²
E = p²c² + E₀ = p²c² + mc²
K = E - E₀ = 1 - ρ²E₀² - E₀
We'll rearrange these equations to arrive at the desired equation.
Starting with equation 1, we have:
E² = p²c² + E₀²
From equation 3, we substitute E = p²c² + mc²:
(p²c² + mc²)² = p²c² + E₀²
Expanding and simplifying:
p⁴c⁴ + 2p²mc⁴ + m²c⁴ = p²c² + E₀²
Next, we focus on equation 4:
K = E - E₀ = 1 - ρ²E₀² - E₀
Substituting equation 1 into equation 4:
K = p²c² + E₀² - E₀ = 1 - ρ²E₀² - E₀
Now, we substitute equation 2 into equation 4:
K = 1 - β² - E₀
Substituting this value of K into our modified equation 4:
1 - β² - E₀ = p²c² + E₀² - E₀
Rearranging and simplifying:
β² = 1 - (E₀ + K E₀)²
Thus, we have derived the equation β = cv = 1 - (E₀ + KE₀)².
Learn more about equation
https://brainly.com/question/17145398
#SPJ11
( 2 points) Consider the following optimization problem: min∥a−x∥
2
2
subject to x∈C, where C is a convex set. Let x
⋆
be an optimal point. Write out a characterization of x
⋆
by applying the first-order optimality condition for convex optimization problems.
Answers
The first-order optimality condition for convex optimization problems can be applied to characterize the optimal point, x* in the given optimization problem.
The first-order optimality condition states that if x* is an optimal point for the given convex optimization problem, then there exists a vector v* such that:
∇f(x*) + v* = 0
Here, ∇f(x*) is the gradient of the objective function f(x) evaluated at x*, and v* is the Lagrange multiplier associated with the constraint x ∈ C.
In the given optimization problem, the objective function is ∥a−x∥², and the constraint set is C.
To apply the first-order optimality condition, we need to find the gradient of the objective function. The gradient of ∥a−x∥² is given by:
∇f(x) = 2(x - a)
Now, let's apply the first-order optimality condition to the given problem:
∇f(x*) + v* = 0
Substituting the gradient expression:
2(x* - a) + v* = 0
Rearranging the equation:
x* = a - (v*/2)
This equation provides a characterization of the optimal point x* in terms of the Lagrange multiplier v*. By solving the equation, we can find the optimal point x*.
It's important to note that the Lagrange multiplier v* depends on the constraint set C. The specific form of v* will vary depending on the nature of the constraint set. In some cases, it may be necessary to further analyze the specific properties of the constraint set C to fully characterize the optimal point x*.
To know more about optimization:
https://brainly.com/question/28587689
#SPJ11
You are taking a taxi from the airport to your hotel. The taxi charges a base fee of $5.25 and then $1.25 per mile. Your fare was $75. How many miles did you travel?
Answers
Answer:
54.75 is the answer I got
Step-by-step explanation:
first I calculated 75÷1.25 then subtracted the fare which is 5.25
A gallon of gasoline at the local gas station
cost $2.69. If you put 8 gallons of gasoline
in your car, how much will it cost you
Answers
Answer: $21.52
Step-by-step explanation: 2.69 times 8 = $21.52
HELP
15.Solve the equation, then choose the correct answer:
–4(x – 3) = –8
Answers
Answer:
x = 5
Step-by-step explanation:
-4 ( x - 3) = -8
-4x +12 = -8
-4x = -20
x = 5
-20
Explanation:
Distribute first
-4x + 12 = -8
Subtract 12 on both sides
-4x +12 = -8
-12 -12
-4x = -20
Divide by -4 on both sides
-4x = -20
/-4 /-4
x = 5
Hi please help I have no confidence or motivation at this point and I just don't wanna fail. Thank you.
1. To determine if "A" students tend to sit in a particular part of the classroom, a teacher recorded the locations of the students who received grades of A. He found that 17 sat in front, 9 sat in the middle, and 5 sat in the back of the classroom, when testing the assumption that the "A" students are distributed evenly throughout the room, he obtained the test statistic of x2 = 7.226. If using a 0.05 significance level, is there sufficient evidence to support the claim that the"A" students are not evenly distributed throughout the classroom? Then state the conclusion.
A. Fail to reject the null hypothesis; there is sufficient evidence to support the claim that the A" students are not evenly distributed throughout the classroom.
B. Fail to reject the null hypothesis; there is sufficient evidence to support the claim that the "A" students are evenly distributed throughout the classroom.
C. Reject the null hypothesis; there is sufficient evidence to support the claim that the "A" students are not evenly distributed throughout the classroom.
D. Reject the null hypothesis; there is sufficient evidence to support the claim that the "A students are evenly distributed throughout the classroom.
----
4. After getting several "flat tire" excuses for missed tests, a college instructor asked her 40 students to identify the tire they would select for their excuse and recorded the results in a frequency table with the following categories: left front, right front, left rear, and right rear. If you are using a 0.05 significance level to test a claim that the results fit a uniform distribution, what is the critical value for the goodness-of-fit test needed to test the claim?
A. 7.815
B. 55.758
C. 9.488
D. 43.773
----
7. An experiment is performed using 1000 trials to test a new scientific model. There are 10 different categories of outcomes. When testing the claim that the observed outcomes agree with the expected frequencies, a test statistic is found to be χ2 = 8.185. Use a 0.05 significance level to test the claim that the actual outcomes agree with the expected frequencies. State the conclusion.
A. Fail to reject the null hypothesis; there is sufficient evidence to warrant rejection of the claim that the observed outcomes agree with the expected frequencies.
B. Reject the null hypothesis; there is not sufficient evidence to warrant rejection of the claim that the observed outcomes agree with the expected frequencies.
C. Reject the null hypothesis; there is sufficient evidence to warrant rejection of the claim that the observed outcomes agree with the expected frequencies.
D. Fail to reject the null hypothesis; there is not sufficient evidence to warrant rejection of the claim that the observed outcomes agree with the expected frequencies.
----
8. A wedding caterer randomly selected clients from the past few years and recorded the months in which the wedding receptions were held. She was interested in testing a claim that weddings occur in different months with the same frequency. She found the test statistic to be χ2 = 10.600. Use a 0.05 significance level to find the critical value for the goodness-of-fit and test the claim that weddings occur in different months with the same frequency. Then state the conclusion.
A. 19.675; reject the null hypothesis
B. 21.026; reject the null hypothesis
C. 19.675; fail to reject the null hypothesis
D. 21.026; fail to reject the null hypothesis
----
10. A candy company claims that the colors of the candy in their packages are distributed with the (1 following percentages: 16% green, 20% orange, 14% yellow, 24% blue, 13% red, and 13% purple. If given a random sample of packages, using a 0.05 significance level, what is the critical value for the goodness-of-fit needed to test the claim?
A. 12.592
B. 15.822
C. 12.833
D. 11.071
Answers
Answer:
1) C. reject the null hypothesis; there is sufficient evidence to support the claim that “A” the students are NOT evenly distributed throughout the classroom
4) A. 7.815
7) D. fail to reject the null hypothesis; there is not sufficient evidence
i’m sorry my test doesn’t have questions 8 and 10 so i don’t know the answer
Step-by-step explanation:
i just took the test
in the land of maggiesville, a random sample of 2500 people were surveyed. if it is true that 8% of people in maggiesville are knitters, what is the probability that the sample proportion will be between 5% and 10%?
Answers
The probability that the sample proportion of knitters in a random sample of 2500 people from Maggiesville will be between 5% and 10% is approximately 0.9644, or 96.44%.
what is the probability that the sample proportion will be between 5% and 10%?To find the probability that the sample proportion of knitters will be between 5% and 10%, we can use the normal approximation to the binomial distribution.
The sample proportion can be modeled as a binomial distribution with parameters n (sample size) and p (true proportion). In this case, n = 2500 and p = 0.08.
To apply the normal approximation, we need to calculate the mean (μ) and the standard deviation (σ) of the sample proportion. The mean of a binomial distribution is μ = n * p, and the standard deviation is σ = √(n * p * (1-p)).
μ = 2500 * 0.08 = 200
σ = √(2500 * 0.08 * 0.92) ≈ 10.954
Next, we need to standardize the values of 5% and 10% using the z-score formula:
z1 = (0.05 - 0.08) / 0.010954 ≈ -2.741
z2 = (0.10 - 0.08) / 0.010954 ≈ 1.827
Now, we can use the standard normal distribution table or a calculator to find the probabilities associated with these z-scores.
P(5% ≤ sample proportion ≤ 10%) = P(-2.741 ≤ z ≤ 1.827)
By looking up the z-scores in the standard normal distribution table or using a calculator, we find:
P(-2.741 ≤ z ≤ 1.827) ≈ 0.9644
Therefore, the probability that the sample proportion of knitters will be between 5% and 10% is approximately 0.9644, or 96.44%.
Learn more on probability here;
https://brainly.com/question/251701
#SPJ4