The 99% confidence interval for the true population mean textbook weight, based on the sample of 31 randomly selected textbooks, is estimated to be between 52.56 and 61.44 ounces.
To construct the confidence interval, we use the formula:Confidence Interval = sample mean ± (critical value * standard deviation / square root of sample size)Given that the sample mean weight is 57 ounces and the population standard deviation is 10.2 ounces, we can calculate the critical value using a t-distribution table for a 99% confidence level with 30 degrees of freedom (sample size minus 1). The critical value turns out to be approximately 2.750.
Plugging in the values into the formula, we get: Confidence Interval = 57 ± (2.750 * 10.2 / √31)Simplifying the calculation, we find the confidence interval to be: Confidence Interval = 57 ± 4.440Therefore, the 99% confidence interval for the true population mean textbook weight is 52.56 to 61.44 ounces. This means that if we were to repeat this study multiple times and construct confidence intervals, approximately 99% of the intervals would contain the true population mean textbook weight.
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A veterinarian says you should feed a 5-year-old beagle
2/3 cup of dog food twice a day. According to the veterinarian, how much food should the beagle eat in a 30 days?
Answer:
40 cups of food
Step-by-step explanation:
First, you would multiply 2/3 by 2, which gives you 4/3. That means the beagle will eat 1 and 1/3 of a cup a day. If you multiply that by 30, you get 40.
Donna made $357 for 17 hours of work. At the same rate, how many hours would she have to work to make $189?
Answer:
9 hours.
Step-by-step explanation:
$357 / 17 = $21. ($21 per hour.)
$189/$21 = 9. BOOM
Which of the following statements is not true if f(x) = 2x2 + x – 3 and g(x) = 2x3 + 3x2 – 2x – 3?
Answer:
Option 3 is not true for f(x) and g(x).
The incorrect statement will be;
⇒ f (x) × g(x) = 4x⁵ + 8x⁴ - 13x³ - 17x² + 3x + 9
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The function are,
⇒ f(x) = 2x² + x - 3
And , g(x) = 2x³ + 3x² - 2x - 3
Now,
Since, The function are,
⇒ f(x) = 2x² + x - 3
And , g(x) = 2x³ + 3x² - 2x - 3
Hence, We get;
⇒ f (x) + g(x) = 2x² + x - 3 + 2x³ + 3x² - 2x - 3
= 2x³ + 5x² - x - 6
⇒ g (x) - f (x) = (2x³ + 3x² - 2x - 3) - (2x² + x - 3)
= 2x³ + 3x² - 2x - 3 - 2x² - x + 3
= 2x³ + x² - 3x
⇒ f (x) × g(x) = (2x² + x - 3) (2x³ + 3x² - 2x - 3)
= 4x⁵ + 6x⁴ - 4x³ - 6x² + 2x⁴ + 3x³ - 2x² - 3x - 6x³ - 9x² + 6x +9
= 4x⁵ + 8x⁴ - 7x³ - 17x² + 3x + 9
Thus, The incorrect statement is,
⇒ f (x) × g(x) = 4x⁵ + 8x⁴ - 13x³ - 17x² + 3x + 9
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Are phone calls equally likely to occur any day of the week? The day of the week for each of 581 randomly selected phone calls was observed. The results are displayed in the table below. Use an a 0.10 significance level a. Complete the rest of the table by filling in the expected frequencies: Frequencies of Phone Calls for Each Day of the Week Outcome Frequency Expected Frequency Sunday 62 83 Monday 108 83 Tuesday 97 83 Wednesday 64 83 Thursday 77 83 3 To do: Mark as done b. What is the correct statistical test to use? Select an answer c. What are the null and alternative hypotheses? H: Phone calls and days of the week are dependent. The distribution of phone calls is uniform over the days of the week. The distribution of phone calls is not uniform over the days of the week. Phone calls and days of the week are independent H: The distribution of phone calls is uniform over the days of the week The distribution of phone calls is not uniform over the days of the week. Phone calls and days of the week are dependent. Phone calls and days of the week are independent. Phone calls and days of the week are dependent. O phone calls and days of the week are independent. d. The degrees of freedom - e. The test statistic for this data - (Please show your answer to three decimal places.) a 1. The p-value for this sample - (Please show your answer to four decimal places.) 8. The p-value is Select an answer h. Based on this, we should Select an answer 1. Thus, the final conclusion is... There is insufficient evidence to conclude that phone calls and days of the week are dependent. There is sufficient evidence to conclude that the distribution of phone calls is uniform over the days of the week. a 3. The p-value is Select an answer h. Based on this, we should Select an answer 1. Thus, the final conclusion is... O There is insufficient evidence to conclude that phone calls and days of the week are dependent. There is sufficient evidence to conclude that the distribution of phone calls is uniform over the days of the week. There is insufficient evidence to conclude that the distribution of phone calls is not uniform over the days of the week. There is sufficient evidence to conclude that phone calls and days of the week are dependent. There is sufficient evidence to conclude that the distribution of phone calls is not uniform over the days of the week.
Phone calls and days of the week are independent. There is insufficient evidence to conclude otherwise.
In the analysis of phone call frequencies for each day of the week, we need to determine if phone calls are equally likely to occur on any day. Using a significance level of 0.10, we can perform a chi-square goodness-of-fit test.
The null hypothesis (H₀) states that the distribution of phone calls is uniform over the days of the week, while the alternative hypothesis (H₁) suggests that the distribution is not uniform.
To calculate the expected frequencies, we divide the total number of phone calls (581) by the number of days (7), resulting in an expected frequency of 83 for each day.
The degrees of freedom for this test are (number of categories - 1), which in this case is 7 - 1 = 6.
Using the chi-square test statistic and the calculated expected frequencies, we can find the p-value associated with the test statistic. If the p-value is less than the significance level of 0.10, we reject the null hypothesis in favor of the alternative hypothesis. Otherwise, we fail to reject the null hypothesis.
Based on the analysis, the p-value is not provided, so we cannot draw a specific conclusion.
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help me asap plss school is done in 4 mins plsssss help me asap
Answer:
3(y +8) (d+e) /4
Step-by-step explanation:
I gotta get to class too soon so my explanation here is just to get this sent. hopefully it does. I tried my best. could be wrong
Soon Yee was putting together her notebook after the first day of
school. She bought a pack of 200 sheets of loose-leaf notebook
paper and some dividers. She wanted to put the same amount of
paper in each of the four sections for her core subjects: math,
history, English and science. She figured that herſtwaelective
courses (art and music) each only needed half bf the amount of
paper that a core subject needed. How many sheets of paper did
she put into the art section of her notebook?
Answer: Since her art and music sections each only had half the number of sheets of paper as a core subject, together the two sections had the same amount of paper as a core subject. Therefore, it is almost like her notebook had five core subjects, rather than four core subjects and two electives. If she divided the 200 sheets equally among the five core subjects, there would be 200 ÷ 5 = 40 sheets in each section. Now we can see that art would actually have half of this amount, or 20 sheets of paper.
1. 232 is 8 times the sum of Mark's and his sister's ages. His sister is 21. Find Mark's age.
2. George went to the store for a sale on designer socks. Each pair was $3 off. She bought 6 pairs for $31.20. How much was the original price of the socks?
Answer:
a. 8 years
b. $49.20
Step-by-step explanation:
The computation is shown below:
a. The mark age is
Given that
232 is 8 times of the sum of mark and his sister ages
And, his sister is 21
So,
Let us assume the mark age be x
now
8(x + 21) = 232
x + 21 = 29
x = 29 -21
x = 8
b. The original price of the socks is
As each pair get $3 off
And she bought 6 pairs for $31.20
= $31.20 + 6 × $3
= $31.20 + 18
= $49.20
Determine whether or not the following matrix A is diagonalizable. Be 5 00 sure to explain all of your reasoning. A= -2 2 1 0 0 2
Yes, the given matrix A is diagonalizable.
Let the matrix A be given by A = [−2 2 1 0 0 2].
To determine if this matrix is diagonalizable, we need to check whether A has enough linearly independent eigenvectors. If there are enough such eigenvectors, then A will be diagonalizable. Otherwise, A will not be diagonalizable.
To find the eigenvalues and eigenvectors of the matrix A, we solve the equation Ax = λx, where λ is a scalar (eigenvalue) and x is the corresponding eigenvector. This gives: (A - λI)x = 0, where I is the identity matrix.To solve for the eigenvalues, we need to find λ such that det(A - λI) = 0. This gives us the characteristic equation:
(−2 − λ)(2 − λ)(1 − λ) − 4(2 − λ) = 0, which simplifies to λ^3 − λ^2 − 10λ − 12 = 0.
To find the eigenvectors, we solve for x in the equation (A - λI)x = 0, using each eigenvalue λ obtained from the characteristic equation.To solve for λ, we need to solve the characteristic equation. Factoring it gives (λ - 4)(λ + 1)^2 = 0, which has eigenvalues λ1 = 4 and λ2 = −1 (multiplicity 2).
Since we have two distinct eigenvalues (λ1 = 4 and λ2 = −1), we know that A is diagonalizable if and only if it has two linearly independent eigenvectors corresponding to each eigenvalue.To find the eigenvectors corresponding to λ1 = 4, we need to solve the system (A - 4I)x = 0.
This gives the matrix equation:
[−6 2 1 0 0 −2][x1 x2 x3 x4 x5 x6] = [0 0 0 0 0 0]
Solving this system gives x1 = -x3/6 - x6/2, x2 = x2, and x4 = x4. We can choose any two of these variables (for example, x3 and x6) and solve for the other three variables in terms of them.
Doing so gives:
x1 = -1/6
x3 - x6/2x2 = x2x4 = x4x5 = 0
So, the eigenvectors corresponding to λ1 = 4 are of the form [x1 x2 x3 x4 x5 x6] = [−1/6t −2s t 0 0 −2t], where t and s are arbitrary constants.To find the eigenvectors corresponding to λ2 = −1, we need to solve the system (A + I)x = 0.
This gives the matrix equation: [−1 2 1 0 0 2][x1 x2 x3 x4 x5 x6] = [0 0 0 0 0 0]
Solving this system gives x1 = -x3 + 2x6, x2 = x2, and x4 = -2x6. We can choose any two of these variables (for example, x3 and x6) and solve for the other three variables in terms of them. Doing so gives: x1 = 2t - s, x2 = x2, x4 = -2t ,x5 = 0
So, the eigenvectors corresponding to λ2 = −1 are of the form [x1 x2 x3 x4 x5 x6] = [2t − s 0 t −2t 0], where t and s are arbitrary constants.Since we have four linearly independent eigenvectors (two corresponding to each eigenvalue), we can diagonalize the matrix A by forming the matrix P whose columns are these eigenvectors.
The matrix P is given by P = [−1/6 −2 2 0 0 2][0 1 0 0 0 0][1 −2 0 0 0 0][0 0 0 1 0 0][0 0 1 0 0 0][−2 0 0 0 0 1]
Hence A is diagonalizable.
Answer: Yes, the given matrix A is diagonalizable.
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Below is some information about the company Based on it, calculate what is requested and write down the result (answer with two decimals and use a point to separate the units)
Number of Clients in 2019
9539
Number of Clients in 2020
12504
Premium Clients of the Year 2020
1230
Number of stores in 2019
17
Number of stores in 2020
12
The client index of the company in 2020 compared to 2019 is
The client index of the company in 2020 compared to 2019 is 2.14.
To calculate the client index of the company in 2020 compared to 2019 we can use the formula below;
Client Index = (Number of clients in current year / Number of stores in current year) / (Number of clients in previous year / Number of stores in previous year)
The client index of the company in 2020 compared to 2019 is: 2.14 (rounded to 2 decimal places).
Clients in 2019 = 9539Clients in 2020 = 12504Premium Clients of the Year 2020 = 1230Stores in 2019 = 17Stores in 2020 = 12
To calculate the client index of the company in 2020 compared to 2019 we can use the formula below;
Client Index = (Number of clients in current year / Number of stores in current year) / (Number of clients in previous year / Number of stores in previous year)We can substitute the values into the formula and simplify it as follows;
Client Index = (12504 / 12) / (9539 / 17) = (1042 / 1) / (561 / 1) = 1042 / 561 = 1.85714285714 ≈ 2.14
Therefore, the client index of the company in 2020 compared to 2019 is 2.14 (rounded to 2 decimal places).
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Solve the following system of equations using addiction
Answer:
3x+y=13
+2x-y=12
SOlve it like what you would normally do
3x+2x=5x
y+(-y)=0
13+12=25
Basically
5x+0=25
Bring down all appropiate signs
Now solve that
5x=25
x=5
Now to find “y”
Plug in The “x”
3*5=15
15+y=13 now solve that and you’d get -2
If you plug it into the other one, it would be the same thing
2*5=10
10-y=12
-y=2
y= -2
x=5
y= -2
Can someone help me with this. Will Mark brainliest.
Answer:
1. True
2. True
3. True
what percentage of $15 is 75 cent
Answer: What percentage is 15 out of 75?
20
Percentage Calculator: 15 is what percent of 75? = 20.
Answer:
5%
Step-by-step explanation:
Which of the following is true?
A-9< -2
B-7 < -7
C-1 = -1
D-8 >-3
that's the correct answer!
Using the following returns, calculate the average returns, the variances, and the standard of deviations for X and Y.
Returns
Year X Z
1 21% 24%
2 -16 -3
3 9 26
4 18 -13
5 4 30
The variance is calculated as the average of the squared deviations from the average return. The standard deviation is the square root of the variance. For X, the standard deviation is √(130.24%) = 36.07%. For Y, the standard deviation is √(388.48%) = 62.35%.
First, calculate the average returns by summing up the returns for each year and dividing by the total number of years. For X, the average return is
(21% - 16% + 9% + 18% + 4%) / 5 = 7.2%.
For Y, the average return is
(24% - 3% + 26% - 13% + 30%) / 5 = 12.8%.
Next, calculate the variances. For X, subtract the average return from each year's return, square the result, and calculate the average of these squared deviations. The variance for X is
(6.2^2 + (-23.2)^2 + 1.8^2 + 10.8^2 + (-3.2)^2) / 5 = 130.24%.
Similarly, for Y, the variance is
(11.2^2 + (-15.8)^2 + 13.2^2 + (-25.8)^2 + 17.2^2) / 5 = 388.48%.
Finally, calculate the standard deviations by taking the square root of the variances. For X, the standard deviation is √(130.24%) = 36.07%. For Y, the standard deviation is √(388.48%) = 62.35%.
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Factor the expression: x^2 +10x+9
Answer:
(x+1)(x+9)
Step-by-step explanation:
Hope this helps!
Solve the linear congruence 2x + 6 = 4(mod 8).
The solution to the linear congruence 2x + 6 ≡ 4 (mod 8) is x ≡ 3 (mod 8).To solve the linear congruence 2x + 6 ≡ 4 (mod 8), we need to find the values of x that satisfy the congruence equation.
First, let's simplify the equation:
2x + 6 ≡ 4 (mod 8)
Subtracting 6 from both sides:
2x ≡ 4 - 6 (mod 8)
2x ≡ -2 (mod 8)
Next, we can simplify -2 (mod 8) by adding 8 to it:
-2 ≡ 6 (mod 8)
Now the congruence equation becomes:
2x ≡ 6 (mod 8)
To solve for x, we need to find the multiplicative inverse of 2 modulo 8. The multiplicative inverse of 2 is 4, as 2 * 4 ≡ 1 (mod 8).
Multiplying both sides of the congruence equation by 4:
4 * 2x ≡ 4 * 6 (mod 8)
8x ≡ 24 (mod 8)
Simplifying the equation:
8x ≡ 24 (mod 8)
x ≡ 3 (mod 8)
Therefore, the solution to the linear congruence 2x + 6 ≡ 4 (mod 8) is x ≡ 3 (mod 8).
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Sarah competes in a long jump competition.
Her first jump is 4.25 m.
I
Her best jump is 12% more than this.
However, her best jump is 15% lower than the winning jump.
Work out the length of the winning jump.
Answer:
4.046 m
Step-by-step explanation:
What is the slope of the line that
passes through these two points?
(-3, 1)
(3, 3)
slope =
Answer: M=1/3
Step-by-step explanation: We know how to find the slope by using the formula: y2-y1/x2-x1
Then we get 3-1/3--3=2/6=
1/3
A paint color is made using 4 drops of red and 5 drops of blue for each 5 gallons of paint. How many gallons of paint are being colored when 45 drops of color are used?
Questions are in the image above.
Answer:
hope this helps
you will find all answer in the photo i sent
May someone please help me with this :)
Answer: It would be option D :)
Step-by-step explanation: the formula for volume in a cylinder is π r squared times height. You plug those in and that’s your answer!
Help with question 4 please I’ll give brainlest
Answer: a
Step-by-step explanation: A plane is a 2d surface so if it ever intersects a 3d object the cross-section will be a 2d figure, in this case, a rectangle.
please tell me where to drag the numbers! thank you!
Answer:
1. 7
2. 3
3. 2 and 2
Step-by-step explanation:
first is 7
second is 3
third is 2 and 2
Please mark as brainliest
Have a great day, be safe and healthy
Thank u
XD
There were 442 students at Deerlake Middle School who voted on a theme for the spring
carnival. Those who voted represent 76% of the entire student population. About how many
students attend Deerlake Middle School?
581
590
600
580
Answer:
581
mark me as brainliest plz
PLEASE HELP ASAP!!!!!!!!!!!!!!!!!!!!
Answer:
Option A
Step-by-step explanation:
You're welcome.
HeLp I yEaH i HaVe AsKeD fOr LiKe 20 AnsWeRs BuT i NeEd ThEm AnSwErEd Or I fAiL AhAhA but please help even if you just answer one question
Answer:D
Step-by-step explanation:
What is 2.4 as a fraction in simplest for?
Answer:
2 2/5
Step-by-step explanation:
2.4 = 2 4/10 = 2 2/5 (all you had to do is divide by 2)
The answer would be 2 2/5 (could also be 1.2 as a decimal)
Hopefully this helps :3 sorry if wrong :( plz mark brainiest if correct :D Your bootiful/handsome! Have a great day luv <3
-Bee~
Step-by-step explanation:
The
2
is in the ones place, and the
4
is in the tenths place.
2.4
means two and four tenths. So in fraction form it is 2 4/10
Answer link
Convert: 76 ounces = _____ pounds _____ ounces
Answer:
4 pounds 12 ounces
Step-by-step explanation:
there are 16 ounces in 1 pound so 76/16 = 4.75 and .75 is equal to 12 ounces.
76 ounces is equal to 4 pounds and 12 ounces.
To convert 76 ounces to pounds and ounces, we need to consider that 1 pound is equal to 16 ounces.
Here's how to proceed:
Divide the total number of ounces by 16 to find the number of pounds:
76 ounces ÷ 16 ounces/pound = 4.75 pounds
Since 4 pounds = 4 x 16 pounce/ pound
= 64 ounces ,we subtract this amount from the total of 76 ounces to determine the remaining ounces:
= 76 ounces - 64 ounces
= 12 ounces
Therefore, 76 ounces is equal to 4 pounds and 12 ounces.
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Tank is a car salesman at EH Auto Dealer. The data below
shows how many cars he sold in each of the last nine
months.
29 30 29
29 31 28
28 31 28
Using this data, create a frequency table.
Number of cars sold
Number of months
28
29
30
Answer:
[tex]\begin{array}{cc}{Cars} & {Months} & {28} & {3} & {29} & {3} & {30} & {1} & {31} & {2} \ \end{array}[/tex]
Step-by-step explanation:
Given
Data:
[tex]29\ 30\ 29[/tex]
[tex]29\ 31\ 28[/tex]
[tex]28\ 31\ 28[/tex]
Required
Construct a frequency table
From the given data, we have:
28 occurs 3 times
29 occurs 3 times
30 occurs 1 time
31 occur 2 times
Hence, the frequency table is:
[tex]\begin{array}{cc}{Cars} & {Months} & {28} & {3} & {29} & {3} & {30} & {1} & {31} & {2} \ \end{array}[/tex]
Answer:
Hope it helps! follow me! brainliest! Peace out!
Step-by-step explanation:
Cars: months:
28 3
29 3
30 1
31 2
1 point
Ravi is shooting arrows at a target. The experimental probability that one
will hit a bull's eye is 12. If Ravi shoots 20 arrows, how many times can he
expect to hit a bull's eye?
O 10
O 20
Answer:
20
Step-by-step explanation: