Answers
Explanation: since he cut two pieces and each piece is 4 1/4 you’re going to add 4 1/4 to 4 1/2 which makes it two pieces and the sum would be 8 1/2 then you’re going to 8 1/2 from the original length, 21 5/8 which is going to leave you with the remaining length being 13 1/8.
Hope it helps:)
Related Questions
1 thenth + 5 hundredths
Answers
Answer:
0.15
Step-by-step explanation:
el área de un rectángulo mide 15 unidades cuadradas. si un lado de rectángulo mide 3.75 unidades de largo cuánta unidad de mide el perímetro de rectángulo?
Answers
Translation from Google
the area of a rectangle measures 15 square units. if one side of a rectangle is 3.75 units long how much unit is the perimeter of the rectangle?
Answer:
15.5 unidades
Step-by-step explanation:
Area of rectangle is given by the product of its length and width and expressed as
A=lw
Where l is length, w is width and A is area.
Similarly, perimeter is given by
P=2(l+w)
Given that A=15 and w=3.75
15=3.75l
l=15÷3.75=4 unidades
Now perimeter will be
P=2(4+3.75)=2(7.75)=15.5 units
Assume that T is a linear transformation. Find the standard matrix of T. T: set of real numbers R cubedright arrowset of real numbers R squared, Upper T (Bold e 1 )equals(1,9), and Upper T (Bold e 2 )equals(negative 7,2), and Upper T (Bold e 3 )equals(9,negative 2), where Bold e 1, Bold e 2, and Bold e 3 are the columns of the 3times3 identity matrix.
Answers
The standard matrix of the transformation T, resulting from a composition of the reflection through the vertical x2-axis and the reflection through the line x2 = x1, is: [ 0 -1 ] [ 1 0 ].
Find the standard matrix of the transformation T.
To do this, we can break the transformation T down into two simpler transformations:
Reflection through the vertical x2-axis: This transformation negates the x1 coordinate of each point while leaving the x2 coordinate unchanged. The standard matrix for this transformation is:
[ -1 0 ]
[ 0 1 ]
Reflection through the line x2 = x1: This transformation swaps the x1 and x2 coordinates of each point. The standard matrix for this transformation is:
[ 0 1 ]
[ 1 0 ]
Since we are performing these transformations one after the other, we need to multiply the matrices together. The order of multiplication matters here, because matrix multiplication is not commutative. So, the standard matrix for the combined transformation T is:
[ 0 1 ] [ -1 0 ] = [ 0 -1 ]
[ 1 0 ] [ 0 1 ] [ 1 0 ]
Therefore, the standard matrix of the transformation T is:
[ 0 -1 ]
[ 1 0 ]
Complete question:
Assume that T is a linear transformation. Find the standard matrix of T.
T:
set of real numbers R squaredℝ2right arrow→set of real numbers R squaredℝ2
first reflects points through the
vertical x 2 dash axisvertical x2-axis
and then reflects points through the
line x 2 equals x 1line x2=x1
The standard matrix of the linear transformation reflects points through the vertical axis and the line[tex]\(x_2 = x_1\) is \([-1\ 1\ 0\ 0]\).[/tex]
To find the standard matrix of the linear transformation T , we need to determine the images of the standard basis vectors [tex]\( \mathbf{e}_1 \) and \( \mathbf{e}_2 \)[/tex] under T .
First, let's understand the transformation described:
1. Reflection through the vertical [tex]\( x_2 \)[/tex]axis:
This transformation replaces each point [tex]\( (x_1, x_2) \) with \( (-x_1, x_2) \).[/tex]
2. Reflection through the line [tex]\( x_2 = x_1 \):[/tex]
This transformation replaces each point [tex]\( (x_1, x_2) \) with \( (x_2, x_1) \).[/tex]
To find the images of the standard basis vectors under T :
- [tex]\( T(\mathbf{e}_1) \) is obtained by reflecting \( \mathbf{e}_1 = (1, 0) \) through the \( x_2 \) axis, resulting in \( (-1, 0) \).[/tex]
- [tex]\( T(\mathbf{e}_2) \) is obtained by reflecting \( \mathbf{e}_2 = (0, 1) \) through the line \( x_2 = x_1 \), resulting in \( (1, 0) \).[/tex]
Now, we can construct the standard matrix of T using the images of the standard basis vectors:
[tex]\[ [T] = \begin{bmatrix} -1 & 1 \\ 0 & 0 \end{bmatrix} \][/tex]
This matrix represents the transformation T as described.
The Complete Question:
Assume that T is a linear transformation. Find the standard matrix of T.
T: set of real numbers R squaredℝ2right arrow→set of real numbers R squaredℝ2
first reflects points through the
vertical x 2 dash axisvertical x2-axis
and then reflects points through the
line x 2 equals x 1line x2=x1
Solve Tan^2x/2-2 cos x = 1 for 0 < or equal to theta < greater or equal to 1.
Answers
Answer:
x = theta = 0°
Step-by-step explanation:
Given the trigonometry function
Tan²x/2-2 cos x = 1
Tan²x-4cosx = 2 ... 1
From trigonometry identity
Sec²x = tan²x+1
tan²x = sec²x-1 ... 2
Substituting 2 into 1, we have:
sec²x-1 -4cosx = 2
Note that secx = 1/cosx
1/cos²x - 1 - 4cosx = 2
Let cosx. = P
1/P² - 1 - 4P = 2
1-P²-4P³ = 2P²
4P³+2P²+P²-1 = 0
4P³+3P² = 1
P²(4P+3) = 1
P² = 1 and 4P+3 = 1
P = ±1 and P = -3/4
Since cosx = P
If P = 1
Cosx = 1
x = arccos1
x = 0°
If x = -1
cosx = -1
x = arccos(-1)
x = 180°
Since our angle must be between 0 and 1 therefore x = 0°
Please help me I need help
Answers
When sampling without replacement from a finite population of size N, the following formula is used to find the standard deviation of the population of sample means: σ = However, when the sample size n, is smaller than 5% of the population size, N, the finite population correction factor, , can be omitted. Explain in your own words why this is reasonable. For N = 200, find the values of the finite population correction factor when the sample size is 10%, 5%, 3%, 1% of the population, respectively. What do you notice?
Answers
Answer:
Check below for the required explanations
Step-by-step explanation:
The population correction factor is given by the formula :
PCF = [(N-n)/(N-1)]^1/2..........(1)
a) When the sample size is smaller than 5% of N. That is n < 0.05N
If n = 0.05N is substituted into the PCF formula, PCF will be approximately 1.
For a value of 1, PCF can be safely ignored.
b) N = 200
i) n = 10% N
n = 0.1 × 200 = 20
Substitute n = 20 into equation (1)
PCF = (200-20)/(200-1)]^1/2
PCF = 0.95
ii) n = 5% N
n = 0.05× 200 = 10
Substitute n = 20 into equation (1)
PCF = (200-10)/(200-1)]^1/2
PCF = 0.98
iii) i) n = 3% N
n = 0.03 × 200 = 6
Substitute n = 20 into equation (1)
PCF = (200-6)/(200-1)]^1/2
PCF = 0.99
iiii) n = 1% N
n = 0.01 × 200 = 2
Substitute n = 20 into equation (1)
PCF = (200-2)/(200-1)]^1/2
PCF = 0.998(approx. =1)
It is noticed that the smaller the sample size, the closer the population correction factor to unity. At 1% of the population, the population correction factor is negligible
For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. In a random sample of 502 judges, it was found that 283 were introverts. (a) Let p represent the proportion of all judges who are introverts. Find a point estimate for p. (Round your answer to four decimal places.)
Answers
Answer:
The point estimate for p is 0.5637.
Step-by-step explanation:
Point estimate for the proportion of all judges who are introverts.
We have a big sample.
So the proportion of the sample proportion of introverted judges can be used as the estimation of the population proportion.
In the sample:
502 judges
283 introverts.
So
p = 283/502 = 0.5637
The point estimate for p is 0.5637.
The point estimate for the proportion of judges who are introverts, denoted by p, is found by dividing the number of introverts (283) by the total number of judges in the sample (502), which gives a point estimate of 0.5637 when rounded to four decimal places.
Explanation:To estimate the proportion of judges who are introverts, we use the given data from the random sample. The point estimate for p, representing the proportion of all judges who are introverts, can be calculated by dividing the number of introverts in the sample by the total number of judges in the sample. The formula for the point estimate p' is:
p' = X / n
where:
X is the number of introverts in the sample (283).n is the total number of judges in the sample (502).Using the given data:
p' = 283 / 502
Calculating this gives us a point estimate for p' of 0.5637 after rounding to four decimal places.
This result represents the estimated proportion of the population of judges who are introverts based on the sample.
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A computer is inspected at the end of every hour. It is found to be either working (up) or failed (down). If the computer is found to be up, the probability of its remaining up for the next hour is 0.9. If it is down, the computer is repaired, which may require more than 1 hour. Whenever the computer is down (regardless of how long it has been down), the probability of its still being down 1 hour later is 0.75.a) Construct the (one-step) transition matrix for this Markov chain.
b) What is the long-term fraction of downtime of the computer?
c) If the computer is working right now, what is the probability that it will be down 10 hours from now?
Answers
Answer:
a) Transition matrix:
[tex]\left[\begin{array}{ccc}0.90&0.10\\0.25&0.75\end{array}\right][/tex]
b) The long-term fraction of downtime of the computer is 0.286 or 28.6%.
c) The probability of being down 10 hours from now is independent of the inital state and is equal to 0.286.
Step-by-step explanation:
We have two states for the computer: Up and Down.
The rows will represent the actual state and the column the next state, and the numbers within the matrix will be the probabilities of transition from the state of the row to the state of the column.
- If the computer is Up, there is a probability of 0.9 of being Up in the next hour. Then, there is a probability of 0.1 of being Down in the next hour.
- If the computer is Down, there is a probability of 0.75 of being Down in the next hour. Then, there is a probability of 0.25 of being Up in the next hour.
a) The transition matrix becomes:
[tex]\left[\begin{array}{ccc}&U&D\\U&0.90&0.10\\D&0.25&0.75\end{array}\right][/tex]
b) We can consider that we have a long-term state (stable) [πU, πD] when the fraction of each state does not change. This can be expressed as:
[tex]\left[\begin{array}{ccc}\pi_U&\pi_D\end{array}\right] *\left[\begin{array}{ccc}0.90&0.10\\0.25&0.75\end{array}\right]=\left[\begin{array}{ccc}\pi_U&\pi_D\end{array}\right][/tex]
If we develop this multiplication of matrix we get:
[tex]0.90\pi_U+0.25\pi_D=\pi_U\\\\0.10\pi_U+0.75\pi_D=\pi_D[/tex]
As this equations are linear combinations of each other, we need another equation to solve this.
We also know that the sum of the fractions of uptime and downtime is equal to one.
Solving these equation, we can calculate the long-term downtime fraction:
[tex]0.90\pi_U+0.25\pi_D=\pi_U\\\\0.25\pi_D=(1-0.90)\pi_U=0.10\pi_U\\\\\pi_U=(0.25/0.10)\pi_D=2.5\pi_D\\\\\\\pi_D+\pi_U=1\\\\\pi_D+2.5\pi_D=1\\\\3.5\pi_D=1\\\\\pi_D=1/3.5=0.286[/tex]
The long-term fraction of downtime of the computer is 0.286 or 28.6%.
c) To know what is the probability that it will be down 10 hours from now if the computer is now on, we have to compute the transition matrix for 10 hours. This is:
[tex]T^{10}=\left( \left[\begin{array}{ccc}0.90&0.10\\0.25&0.75\end{array}\right]\right)^{10}= \left[\begin{array}{ccc}0.714&0.286\\0.714&0.286\end{array}\right][/tex]
This is considered a steady state already.
If the computer is up, the actual state is [1, 0].
If we multiply this by the transition matrix, we get:
[tex]\left[\begin{array}{ccc}1&0\end{array}\right] *\left[\begin{array}{ccc}0.714&0.286\\0.714&0.286\end{array}\right]=\left[\begin{array}{ccc}0.714&0.286\end{array}\right][/tex]
The probability of being down 10 hours from now is independent of the inital state and is equal to 0.286.
A weight loss company wanted to predict how much weight a client would lose if they followed a prescribed exercise program in addition to the company's diet program. Volunteers were randomly divided into two groups, one group dieted but didn’t exercise, and the other group dieted and followed the exercise program. For the exercise group, they used linear regression with percent compliance with the exercise program as the explanatory variable and pounds lost in three months as the response variable. One of the clients was told that his residual was 5.5 pounds. What does this mean?
Answers
Options:
a. His predicted weight loss was 5.5 pounds higher than his actual weight loss.
b. His actual weight loss was 5.5 pounds higher than his predicted weight loss.
c. His actual weight loss was 5.5 pounds higher than it would have been if he didn’t exercise.
d. His predicted weight loss was 5.5 pounds higher than it would have been if he didn’t exercise.
Answer:
Option B. His actual weight loss was 5.5 pounds higher than his predicted weight loss.
Step-by-step explanation:
In regression analysis, the difference between the observed value of the dependent variable (y) and the predicted value (ŷ) is called the residual (e). Residual value= Observed value - Predicted value.i.e. e = y - ŷ
Since the residual weight of the client was 5.5 pounds, this means that His actual weight after compliance with the exercise program his 5.5 pounds higher than what he predicted.
Final answer:
The client's residual of 5.5 pounds means they lost 5.5 pounds more than predicted by the exercise program's linear regression model, indicating a discrepancy between the predicted and actual weight loss.
Explanation:
When a client has been told that his residual was 5.5 pounds in the context of a linear regression, it refers to the difference between the actual weight the client lost and the weight the regression model predicted they would lose based on their percent compliance with the exercise program. A residual of 5.5 pounds indicates that the client lost 5.5 pounds more than what the model predicted. Residuals are used to measure the accuracy of regression models; if they are small, it suggests that the model is accurately predicting outcomes. However, large or systematic residuals can indicate a problem with the model's fit to the data.
A 20 ft ladder is leaning up against a wall. The wall forms a 90 degree angle with the floor, which has recently been waxed and is very slippery. The base of the ladder begins to slide away from the wall causing the top of the ladder to slide down the wall toward the floor. When the base of the ladder slides to 12 ft away from the wall, the base is moving at a rate of 1 ft/sec away from the wall. How quickly is the top of the ladder moving toward the floor at that moment?
Answers
Answer: The top of the ladder is moving towards the floor at a rate of 0.75 ft/sec
Step-by-step explanation: Please see the attachments below
Consider the following sample of fat content (in percentage) of randomly selected hot dogs: (a) Assuming that these were selected from a normal population distribution, a 98 % confidence interval for the population mean fat content is (b) Find a 98 % prediction interval for the fat content of a single future hot dog.
Answers
Answer:
B is better option
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Bo had a container of flour that weighed 32 ounces. On Monday, he added 47 ounces of flour. During the week, he made cookies and waffles with some of the flour. At the end of the week, the container weighed 61 ounces. Estimate how many ounces of flour Bo used during the week
Answers
Answer:
~20 oz
Step-by-step explanation:
Originally, Bo had 32 ounces of flour, which is around 30 ounces. Then, he added in 47 ounces, which is about 50. So, now the new total is about 30 + 50 = 80 ounces.
During the week, he used up some of those ~80 ounces of flour. He used up enough so that at the end of the week, there was only 61 ounces, or approximately 60 oz, left. The difference between these two numbers must be how much Bo used:
80 - 60 = 20 ounces
Thus, the answer is about 20 ounces.
Hope this helps!
Bo started with 79 ounces of flour (32 ounces original and 47 ounces added), and ended with 61 ounces remaining, so he used an estimated 18 ounces of flour during the week.
Explanation:To determine how much flour Bo used during the week, we need to find out how much the total weight of flour was at the beginning of the week, and then subtract the weight of the flour that was left at the end of the week.
At first, Bo's container had 32 ounces of flour. On Monday, he added 47 more ounces. Therefore, the weight of the flour at the beginning of the week was 32 + 47 = 79 ounces.
At the end of the week, the leftover flour weighed 61 ounces. So, to estimate how much flour Bo used, we subtract the leftover weight from the original total weight: 79 ounces - 61 ounces = 18 ounces.
So, Bo used an estimated 18 ounces of flour during the week.
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Lupe sold 39 bags of cheese popcorn. She sold 3 times as many bags as Frances. How many bags did Frances sell?
Answers
Answer:
13
Step-by-step explanation:
Since Lupe is 3 times as many as Frances
39 ÷ 3= 13
Answer:
13
Step-by-step explanation:
Make an equation. Let x represent the bags that Frances sold. Since Lupe sold 3 times the popcorn Frances did, use multiplication.
[tex]39=3x[/tex]
Solve for x to find the amount Frances sold:
Divide both sides by 3:
[tex]\frac{39}{3}=\frac{3x}{3} \\\\13=x[/tex]
[tex]x=13[/tex]
Frances sold 13 bags.
For each reaction between a ketone and an amine, draw the curved arrow(s) to show the first step of the mechanism, then draw the final organic product. (If you accidentally changed the structures given in the problem, click on the red over/under arrows to remove any changes you have made.
Answers
The question deals with the mechanism of reactions between ketones and amines, acid-base reactions, and alkylation reactions. The primary step of a ketone-amine reaction involves the nitrogen attacking the carbonyl carbon to eventually form an imine or enamine. The acid-base reaction between acetic acid and ammonia results in the ammonium and acetate ions.
Explanation:The student's question is about organic reaction mechanisms, specifically the reactions between ketones and amines, and other related reactions such as acid-base reactions between acetic acid and ammonia. In the case of a ketone reacting with a primary or secondary amine, the first step typically involves nucleophilic attack by the nitrogen of the amine on the electrophilic carbonyl carbon of the ketone. This produces a tetrahedral intermediate which, after losing a water molecule, forms an imine or an enamine depending on whether a primary or secondary amine was used respectively.
For the acid-base reaction between acetic acid (CH3CO2H) and ammonia (NH3), the mechanism begins with the lone pair on the nitrogen of ammonia attacking the hydrogen of acetic acid. This is shown with a curved arrow from the nitrogen to the hydrogen. This results in the formation of the ammonium ion (NH4+) and the acetate ion (CH3CO2-).
The alkylation reaction at the alpha-carbon of a ketone or aldehyde and the concept of kinetic versus thermodynamic control are also touched upon. In an alkylation reaction, the first step usually involves the generation of an enolate ion from the ketone or aldehyde, followed by its nucleophilic attack on an alkyl halide.
i need you to increase the number of customers you talk to daily by 20% i talk to an average of 8 customers per hour during an 8 hour shift so now i’ll need to talk to how many customers per day?
Answers
To increase the number of customers you talk to daily by 20%, you will need to calculate 20% of the current number of customers you talk to and add it to the original number.
Explanation:To increase the number of customers you talk to daily by 20%, you will need to calculate 20% of the current number of customers you talk to daily and add it to the original number. In this case, you talk to an average of 8 customers per hour during an 8-hour shift, which means you talk to 8 x 8 = 64 customers per day. To increase this number by 20%, you need to calculate 20% of 64, which is 0.20 x 64 = 12.8. Round this number to the nearest whole number to get an increase of 13 customers. Finally, add this increase to the original number of customers to find the new number of customers you need to talk to per day: 64 + 13 = 77 customers per day.
What is [4]{7^3} in exponential form?
Answers
Answer:
1.372 × 10^3
Step-by-step explanation:
Timmy and Tommy are two boys whose age add up to 23 Timmy is 5 year older than Tommy. how old are they
Answers
Answer:
Timmy is 18 and Tommy is 5.
Step-by-step explanation:
Step-by-step explanation:
So you have to find out tha ages which add up to 23 so if Tommy is 9 years old and when we add 5
So Timmy age = 9 + 5 = 14
Now if we add 14 and 9 the answer is 23
It means Timmy is 14 years old and Tommy is 9 years old
Bones Brothers & Associates prepare individual tax returns. Over prior years, Bones Brothers have maintained careful records regarding the time to prepare a return. The mean time to prepare a return is 90 minutes, and the population standard deviation of this distribution is 14 minutes. Suppose 49 returns from this year are selected and analyzed regarding the preparation time. What is the standard deviation of the sample mean? Select one: a. 14 minutes b. 2 minutes c. .28 minutes d. 98 minutes
Answers
Answer:
For this case we have the following info related to the time to prepare a return
[tex] \mu =90 , \sigma =14[/tex]
And we select a sample size =49>30 and we are interested in determine the standard deviation for the sample mean. From the central limit theorem we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:
[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]
And the standard deviation would be:
[tex]\sigma_{\bar X} =\frac{14}{\sqrt{49}}= 2[/tex]
And the best answer would be
b. 2 minutes
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".
Solution to the problem
For this case we have the following info related to the time to prepare a return
[tex] \mu =90 , \sigma =14[/tex]
And we select a sample size =49>30 and we are interested in determine the standard deviation for the sample mean. From the central limit theorem we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:
[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]
And the standard deviation would be:
[tex]\sigma_{\bar X} =\frac{14}{\sqrt{49}}= 2[/tex]
And the best answer would be
b. 2 minutes
A photoconductor film is manufactured at a nominal thickness of 25 mils. The product engineer wishes to increase the mean speed of the film, and believes that this can be achieved by reducing the thickness of the film to 20 mils. Eight samples of each film thickness are manufactured in a pilot production process, and the film speed (in microjoules per square inch) is measured. For the 25-mil film the sample data result is x1 = 1.17 and s1 = 0.11 , while for the 20-mil film, the data yield x2 = 1.04 and s2 = 0.09 . Note that an increase in film speed would lower the value of the observation in microjoules per square inch.
Do the data support the claim that reducing the film thickness increases the mean speed of the film? Use alpha=0.05
Answers
Answer:
[tex]t=\frac{1.17-1.04}{\sqrt{\frac{0.11^2}{8}+\frac{0.09^2}{8}}}}=2.587[/tex]
[tex]df=n_{1}+n_{2}-2=8+8-2=14[/tex]
Since is a one sided test the p value would be:
[tex]p_v =P(t_{(14)}>2.587)=0.0108[/tex]
If we compare the p value and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, we have enough evidence to reject the null hypothesis on this case and the 25 mil film have a mean greater than the 20 mil film so then the claim is not appropiate
Step-by-step explanation:
Data given and notation
[tex]\bar X_{1}=1.17[/tex] represent the mean for the sample 1 (25 mil film)
[tex]\bar X_{2}=1.04[/tex] represent the mean for the sample 2 (20 mil film)
[tex]s_{1}=0.11[/tex] represent the sample standard deviation for the sample 1
[tex]s_{2}=0.09[/tex] represent the sample standard deviation for the sample 2
[tex]n_{1}=8[/tex] sample size selected for 1
[tex]n_{2}=8[/tex] sample size selected for 2
[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if reducing the film thickness increases the mean speed of the film, the system of hypothesis would be:
Null hypothesis:[tex]\mu_{1} \leq \mu_{2}[/tex]
Alternative hypothesis:[tex]\mu_{1} > \mu_{2}[/tex]
If we analyze the size for the samples both are less than 30 so for this case is better apply a t test to compare means, and the statistic is given by:
[tex]t=\frac{\bar X_{1}-\bar X_{2}}{\sqrt{\frac{s^2_{1}}{n_{1}}+\frac{s^2_{2}}{n_{2}}}}[/tex] (1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other".
Calculate the statistic
We can replace in formula (1) the info given like this:
[tex]t=\frac{1.17-1.04}{\sqrt{\frac{0.11^2}{8}+\frac{0.09^2}{8}}}}=2.587[/tex]
P-value
The first step is calculate the degrees of freedom, on this case:
[tex]df=n_{1}+n_{2}-2=8+8-2=14[/tex]
Since is a one sided test the p value would be:
[tex]p_v =P(t_{(14)}>2.587)=0.0108[/tex]
If we compare the p value and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, we have enough evidence to reject the null hypothesis on this case and the 25 mil film have a mean greater than the 20 mil film so then the claim is not appropiate
An online clothing company decides to investigate whether offering their customers a coupon upon completion of their first purchase will encourage them to make a second purchase. To do so, the company programs the website to randomly select 100 first time customers. Sixty of these customers are randomly selected to receive a coupon for $5 off their next purchase, to be made in the next 30 days. The other 40 customers are not offered a coupon. The table below shows the number of customers in each group that made a second purchase within 30 days of their first purchase.
Based upon the table, is “yes, made a second purchase” independent of “yes, being sent a coupon”?
A) Yes, exactly half of the customers made a second purchase and half did not.
(B) Yes, the largest count in the table comes from those who were sent a coupon and made a second purchase within 30 days.
(C) No, the probability of making a second purchase is not equal to the probability of making a second purchase given that a coupon was sent.
(D) No, the probability of making a second purchase is the same whether or not a coupon was sent.
(E) It is impossible to draw a conclusion about independence because a coupon was not sent to exactly half of the customers.
Answers
Answer:
(C) No, the probability of making a second purchase is not equal to the probability of making a second purchase given that a coupon was sent.
Step-by-step explanation:
Let A = the customer makes a second purchase within 30 days and let B = customer is sent a coupon. Events A and B are independent if P(A) = P(A | B).
P(A) = P(the customer makes a second purchase within 30 days) = \frac{50}{100} = 0.5
100
50
=0.5
P(A | B) = P(the customer makes a second purchase within 30 days | customer is sent a coupon) = \frac{34}{60} = 0.567
60
34
=0.567
Because P(A) ≠ P(A | B) making a second purchase is not independent of being sent a coupon.
find an explicit formula for the arithmetic sequence 10, -10, -30, -50, ...
Answers
Step-by-step explanation:
The formula is subtracting by 20 you can count it so the next - 70
Answer:
10-20(n-1)
Step-by-step explanation:
Given the function g(x)=x^2+10x+23g(x)=x
2
+10x+23, determine the average rate of change of the function over the interval -8\le x \le -4−8≤x≤−4.
Answers
The average rate of change of the function g(x) over the interval from x = -8 to x = -4 is -2.
The average rate of change of a function over a certain interval is similar to finding the slope of the secant line that passes through the points on the graph of the function corresponding to the end points of the interval. In this case, for the function g(x) = x^2 + 10x + 23, we want to find the average rate of change over the interval from x = -8 to x = -4.
To do this, we calculate the change in g(x) divided by the change in x (\(\Delta x\)).
The value of the function at x = -8 is g(-8) = (-8)^2 + 10(-8) + 23 = 64 - 80 + 23 = 7.
The value of the function at x = -4 is g(-4) = (-4)^2 + 10(-4) + 23 = 16 - 40 + 23 = -1.
Now, the average rate of change is given by the formula:
Average rate of change = (g(-4) - g(-8)) / (-4 - (-8))
= (-1 - 7) / (-4 + 8) = -8 / 4 = -2
So, the average rate of change of the function g(x) over the interval from x = -8 to x = -4 is -2.
what more ounces our pounds?help if you see this please i will give you 25 points
Answers
Answer:
Ounces is smaller than lbs
Step-by-step explanation:
16 ounces = 1 lbs
Ounces is smaller than lbs
Answer:
An ounce is the smallest unit for measuring weight, a pound is a larger unit, and a ton is the largest unit
Step-by-step explanation:
Please give me brainliest
Tom makes a cake for a party. The recipe calls for 5/8 cup of orange juice and 5/12 cup of water. Can Tom use a one cup container to hold the orange juice and water at the same time? Explain.
Answers
Answer:
i am positive he can
Step-by-step explanation:
sorry if this is wrong...also can i pls have brainliest
Suppose the FAA weighed a random sample of 20 airline passengers during the summer and found their weights to have a sample mean of 180 pounds and sample standard deviation of 30 pounds. Assume the weight distribution is approximately normal.
a.) Find a one sided 95% confidence interval with an upper bound for the mean weight of all airline passengers during the summer. Show you work.
b.) Find a 95% prediction interval for the weight of another random selected airline passenger during the summer. Show you work.
Answers
Answer:
Step-by-step explanation:
Given Parameters
Mean, [tex]x[/tex] = 180
total samples, n = 20
Standard dev, [tex]\sigma[/tex] = 30
[tex]\alpha[/tex] = 1 - 0.95 = 0.05 at 95% confidence level
Df = n - 1 = 20 - 1 = 19
Critical Value, [tex]t_\alpha[/tex], is given by
[tex]t_{c}=t_{\alpha, df} = t_{0.05,19} = 1.729[/tex]
a).
Confidence Interval, [tex]\mu[/tex], is given by the formula
[tex]\mu = x +/- t_c \times \frac{s}{\sqrt{n} }[/tex]
[tex]\mu = 180 +/- 1.729 \times \frac{30}{\sqrt{20} }[/tex]
[tex]\mu = 180 +/-11.5985[/tex]
[tex]191.5985 > \mu > 168.4015[/tex]
b).
Critical Value, [tex]t_{\alpha/2}[/tex], is given by
[tex]t_{c}=t_{\alpha/2, df} = t_{0.05/2,19} = 2.093[/tex]
Confidence Interval, [tex]\mu[/tex], is given by
[tex]\mu = x +/- t_c \times \frac{s}{\sqrt{n} }[/tex]
[tex]\mu = 180 +/- 2.093 \times \frac{30}{\sqrt{20} }[/tex]
= 180 +/- 14.0403
= 165.9597 < [tex]\mu[/tex] < 194.0403
Tonisha has a lemonade stand. She has 34$ in expenses and wants to make at least 80$per day.
Answers
Tonisha must make $114 in daily sales to cover her $34 expenses and meet her $80 profit goal. This is a basic mathematics problem related to costs, revenues, and profits within a business context.
Explanation:The subject of Tonisha’s lemonade stand involves determining the required earnings to achieve a certain profit goal, which falls under the subject of Mathematics. Specifically, it involves basic arithmetic and understanding of costs and revenues within a business context. To calculate how much Tonisha needs to make in sales to achieve her goal of at least $80 per day, we must add the expenses of $34 to the desired profit of $80. Therefore, Tonisha needs to make $114 per day in sales to cover expenses and meet her profit goal.
a board is 77.47 centimeters long. How long is the board in inches. 1 inch is 2.54
Answers
Answer:
30.5 in
Step-by-step explanation:
Answer:
30.5 inches
Step-by-step explanation:
Since the board is 77.47 cm and 1 inch is 2.54 cm you have to divide 77.47 by 2.54.
Tammy picks apples at an orchard. She earns $3.10 for each hour she works and $2.30 for each bushel of apples she picks. Her goal is to earn at least $100 this week.
Write an inequality that will help Tammy determine the number of hours (h) and bushels (b) she needs to reach her goal.
Answers
Answer:
3.10h + 2.30b ≥ 100
Step-by-step explanation:
Tammy earns $3.10 for each hour,
Let h represents hour,
So total earning for h number of hours will be 3.10h
Tammy earns $2.30 for each bushel of apples
Let b represents bushel of apples,
So total earning for b number of bushels will be 2.30b
Tammy's goal is to earn at least $100 this week
Therefore, to reach her goal the inequality will be
3.10h + 2.30b ≥ 100
Where h is the number of hour and b is the number of bushels.
Thickness measurement ancient prehistoric Native American Pot Shards discovered in Hopi Village are approximately normally distributed with the mean of 5.1 millimeters and standard deviation of 0.9 millimeters. For a randomly found shard, What is the probability that the thickness is: a) Less than 3.0 millimeters b) More than 7.0 millimeters Present your answer in three decimal places. Present your answer: answer for "a",answer for "b" Group of answer choices
Answers
Answer:
a) [tex]P(X<3)=P(\frac{X-\mu}{\sigma}<\frac{3-\mu}{\sigma})=P(Z<\frac{3-5.1}{0.9})=P(z<-2.33)[/tex]
And we can find this probability using the normal standard table and we got:
[tex]P(z<-2.33)=0.010[/tex]
b) [tex]P(X>7)=P(\frac{X-\mu}{\sigma}>\frac{7-\mu}{\sigma})=P(Z>\frac{7-5.1}{0.9})=P(z>2.11)[/tex]
And we can find this probability using the complement rule and the normal standard table and we got:
[tex]P(z>2.11)=1-P(Z<2.11) = 1-0.983 = 0.017[/tex]
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(5.1,0.9)[/tex]
Where [tex]\mu=5.1[/tex] and [tex]\sigma=0.9[/tex]
Part a
We are interested on this probability
[tex]P(X<3)[/tex]
And the best way to solve this problem is using the normal standard distribution and the z score given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
If we apply this formula to our probability we got this:
[tex]P(X<3)=P(\frac{X-\mu}{\sigma}<\frac{3-\mu}{\sigma})=P(Z<\frac{3-5.1}{0.9})=P(z<-2.33)[/tex]
And we can find this probability using the normal standard table and we got:
[tex]P(z<-2.33)=0.010[/tex]
Part b
We are interested on this probability
[tex]P(X>7)[/tex]
And the best way to solve this problem is using the normal standard distribution and the z score given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
If we apply this formula to our probability we got this:
[tex]P(X>7)=P(\frac{X-\mu}{\sigma}>\frac{7-\mu}{\sigma})=P(Z>\frac{7-5.1}{0.9})=P(z>2.11)[/tex]
And we can find this probability using the complement rule and the normal standard table and we got:
[tex]P(z>2.11)=1-P(Z<2.11) = 1-0.983 = 0.017[/tex]
A consumer protection agency is testing a sample of cans of tomato soup from a company. If they find evidence that the average level of the chemical bisphenol A (BPA) in tomato soup from this company is greater than 100 ppb (parts per billion), they will recall all the soup and sue the company.
(a) State the null and alternative hypotheses.
(b) Using the context of the problem, what would a Type I Error be in this situation?
(c) Using the context of the problem, what would a Type II Error be in this situation?
Answers
(a) Null Hypothesis (H0): μ ≤ 100 ppb (The average level of BPA in the tomato soup is less than or equal to 100 ppb)
Alternative Hypothesis (H1): μ > 100 ppb (The average level of BPA in the tomato soup is greater than 100 ppb)
(b) A Type I Error would occur if the agency finds evidence that the average level of BPA is greater than 100 ppb (rejects H0) when, in fact, the true average level is less than or equal to 100 ppb.
(c) A Type II Error would occur if the agency fails to find evidence that the average level of BPA is greater than 100 ppb (fails to reject H0) when, in fact, the true average level is greater
(a) Null Hypothesis (H₀): The average level of BPA in the company's tomato soup is less than or equal to 100 ppb.
Mathematically: μ ≤ 100 ppb
Alternative Hypothesis (H₁):
The average level of BPA in the company's tomato soup is greater than 100 ppb.
Mathematically: μ > 100 ppb
(b) A Type I error occurs when we reject the null hypothesis when it is actually true. In this context, a Type I error would mean that the consumer protection agency concludes that the average BPA level is greater than 100 ppb and recalls the soup and sues the company, when in reality, the average BPA level is less than or equal to 100 ppb. This would result in unnecessary product recall and legal action against the company.
(c) A Type II error occurs when we fail to reject the null hypothesis when it is actually false. In this context, a Type II error would mean that the consumer protection agency concludes that the average BPA level is less than or equal to 100 ppb and does not recall the soup or sue the company, when in reality, the average BPA level is greater than 100 ppb. This would allow unsafe products to remain on the market, potentially harming consumers.