Answer:
16 - (4 x 3) + 7
Step-by-step explanation:
16 - (4 x 3) + 7
16 - 12 + 7
4 + 7
11
A cylindrical package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section) of 141 inches. Find the dimensions of the package of maximum volume that can be sent. (The cross section is circular.)
radius = ? in.
length = ? in.
Answer:
radius r = 47/π in
length l = 23.5 in
Step-by-step explanation:
Let us recall that:
Volume of a cylinder = [tex]\pi r^2 h[/tex] --- (1)
The girth g = [tex]2 \pi r + h[/tex] ----- (2)
Given that:
height (h) + girth (g) = 141
Then g = 141 - h ----- (3)
Equating equation (2) and (3), we have:
141 - h = 2πr + h
2h = 141 - 2πr
h = 70.5 - πr ------ (4)
From, here now, we can now replace the value of h into equation (1)
i.e.
V = πr²(70.5 - πr)
V = 70.5πr² - π²r³
Taking the differential of the above equation with respect to r, we have:
[tex]\dfrac{dv}{dr} = 141 \pi r- 3\pi ^2 r^2[/tex]
By further differentiation:
[tex]\dfrac{d^2v}{dr^2} = 141 \pi - 6\pi ^2 r[/tex]
Let set [tex]\dfrac{dv}{dr}= 0[/tex], Then:
141πr - 3π²r² = 0
141πr = 3π²r²
Divide both sides by πr
141 = 3πr
r = 141/3π
r = 47/π in
Replacing the value of r = 47/π into equation (4), we have:
h = 70.5 - πr
h = 70.5 - π(47/π)
h = 70.5 - 47
h = 23.5 in
From equation (3);
h + g = 141
23.5 + g = 141
g = 141 - 23.5
g = 117.5 in
Volume = πr²h
V = π × (47/π )² × 23.5
V = 16523.94 in³
As an avid golfer, you want to estimate your average score for 18 holes of golf. Suppose you know that the standard deviation of your score is 16.425 strokes and you want to find a sample mean that is within 5.947 strokes of your true average for all rounds of golf with 90% confidence. How many rounds would you need to play to determine this
Answer:
21
Step-by-step explanation:
Given that
The holes of golf is 18
The standard deviation of the score is 16.425 strokes
The sample mean is 5.947
And, there is 90% confidence
We need to find out the number of rounds
So,
At 90% confidence interval, the critical value is +/- 1.645
Margin of error = 5.947
Z_0.05 × SD/sqrt (n) = 5.947
1.645 × 16.425/sqrt (n) = 5.947
sqrt(n) = 1.645 × 16.425 ÷ 5.947
sqrt(n) = 4.54
= 21
A school psychologist wants to perform a study at a local elementary
school where 150 students that have long-term concentration issues. The purpose of the study would be to determine if doing jumping jacks for 5 minutes helps with long-term concentration compared to sitting still for 5 minutes.
Part A: Describe an appropriate design for the study. (5 points)
Part B: The hypotheses for this study are as follows:
H0: There is no difference in the mean improvement of long-term concentration for either treatment.
Ha: The mean improvement of long-term concentration is greater for the jumping jacks treatment.
The school will allow students to do jumping jacks during class if the null hypothesis is rejected. What are the possible Type I and II errors? Describe the consequences of each in the context of this study and discuss which type you think is more serious. (5 points)
Answer:
Kindly check explanation
Step-by-step explanation:
An appropriate research design which may be employed is to perform a random assignment of the 150 students into two groups whereby a certain group is made to perform the jumping exercise and the other group sitting still for 5 minutes, after this concentration level is measured in both groups in other to evaluate if there are differences in concentration levels between the two groups.
Given the hypothesis :
H0: There is no difference in the mean improvement of long-term concentration for either treatment.
Ha: The mean improvement of long-term concentration is greater for the jumping jacks treatment.
A type 1 error occurs when a true null is rejected ; this means that we conclude that The mean improvement of long-term concentration is greater for the jumping jacks treatment when this is actually not true. Hence, students will be allowed to do jumping jack in class but there won't be any improvement.
A type 11 error occurs when we fail to reject a false null hypothesis ; Hence, we conclude that There is no difference in the mean improvement of long-term concentration for either treatment when the jumping Jacks treatment actually does improve concentration level. Hence, the school will fail to allow students do jumping jack in class.
In my opinion, type 11 error is more serious in this scenario because, the school would have failed to identify and ignored a treatment which makes it's students attain a better level of concentration.
Sara
has
what
you can work out
she needs.
Saved & 75. This is 30% of
She needs. Explain how
Answer:
The question seems incomplete.
Step-by-step explanation:
Aaron participates in a walkathon for charity. He has a sponsor who has pledged a base donation of $2 for the first mile he walks and then a certain dollar amount for each additional mile he walks. Based on this pledge, if Aaron walks 8 miles, the sponsor will donate a total of $23 to the charity.
Write a formula that can be used to determine the amount of money this sponsor donates when Aaron walks n miles.
Explain how you determined your formula.
Answer:
2 + 3x(N-1) = Amount of money donated
Step-by-step explanation:
Since Aaron participates in a walkathon for charity, and he has a sponsor who has pledged a base donation of $ 2 for the first mile he walks and then a certain dollar amount for each additional mile he walks, and based on this pledge, if Aaron walks 8 miles, the sponsor will donate a total of $ 23 to the charity, to determine a formula that can be used to determine the amount of money this sponsor donates when Aaron walks N miles the following equation should be raised:
2 = fixed amount in the first mile
2 + ((23 - 2) / (8-1)) x (N-1) = Amount of money donated
2 + (21/7) x N = Amount of money donated
2 + 3x (N-1) = Amount of money donated
Thus, if N is 8, as in the example, the quantity is determined as follows:
2 + 3x (8-1) = X
2 + 3x7 = X
2 + 21 = X
23 = X
The following data set shows the times a product failed in a series of tests. What is the range of this data set? {16, 12, 19, 15, 12, 15, 14, 18, 11, 10, 19, 10}
A 9
B 10
C 15
D 19
Answer:
9
Step-by-step explanation:
Highest number is 19 lowest is 10. 19-10 is 9.
Which angles are supplementary to
∠4? Select all that apply.
∠2 ∠7
∠5 ∠6
∠1
Answer:
The supplementary angle are:
∠2
∠3
∠6
∠7
Please help the question is already on the pic and please explain
if a news paper costs 25p how much would 3 weeks . if the the paper is puplished six days each week
The best i could find out is 450p
In 2016, there were approximately 4.46 x 10° people in Asia. On average, a person takes 8.4 x 106 breaths
per year. Using this data, what was the number of breaths of all the people in Asia in 2016? Expressing your answer
in scientific notation in the form a x 10what are the values of a and b?
What is the value of a?
What is the value of b?
ANSWER PRONTO NEEDA ASAP !!!
Answer:
3.75 x 10^7
a = 3.745 (rounded) or 3.7464 (exact)
b = 7
Step-by-step explanation:
Assuming you meant "a person takes 8.4 x 10^6 breaths
per year" we would multiply the number of people 4.46 x 10° by the number of breaths each person takes 8.4 x 10^6 and we get 37464000 and in scientific notation it would be 3.75 x 10^7
Jack Wilson bought a tool chest and tools on the installment plan for a total cost $1600. He paid $200 down and the rest in monthly installments of $56 each. How many months will it take Jack to pay for the tool chest and tools?
Answer:
25 months
Step-by-step explanation:
quick math
Graph: - 4x + 4y > 20 & 4x + 4y < -12
please help !!!!!
Will mark Brainliest. So Im trying to calculate what I need to get on the final to keep an overall 80% for my semester grade. My math teacher said our final grade is 40% of 3st quarter & 40% of 4th quarter with our final weighing 20%. So what I was wondering was if i had a 85.29 in 3rd quarter and a 81.5 in 4th quarter what could i get on my final to keep an overall 80% average for my semester grade. ( my semester grade is currently at 83.39 )
Answer:
[tex]66.42\%[/tex]
Step-by-step explanation:
Hi there! We can establish the following inequality with the given weights provided in your question:
[tex]85.29\cdot 0.4+81.5\cdot 0.4 +\text{Final Exam Grade}\cdot0.2 \geq 80[/tex]
Solving, we get:
[tex]66.716+\text{Final Grade}\cdot 0.2\geq 80,\\\text{Final Exam Grade}\cdot 0.2\geq13.284,\\\text{Final Exam Grade}\geq\boxed{66.42\%}[/tex]
Thus, to maintain a final semester grade of 80% or higher, you must achieve a minimum of [tex]66.42\%[/tex] on your final exam!
A serving of crackers has 1.5 grams of fat.
How many grams of fat are in 3.75 servings?
O A. 3.90
B. 5.25
C. 5.305
D. 5.625
Can someone please answer?
Answer:
The answer is 24
Step-by-step explanation:
A classic data set for investigating categorical variables deals with the RMS Titanic. The Titanic sank in the North Atlantic Ocean on April 15, 1912. There were more than 2,000 passengers and crew on board and more than 1,500 did not survive. The data set titanic.jmp located with this homework contains data on 887 passengers. For each passenger, the variables Class (class of the passenger) and Survived (whether or not the passenger lived) were recorded. A main question of interest is whether there is an association between class and survival.
(a) Use JMP to obtain the distribution of the variable Survived. See the Categorical Data JMP guide for any additional help. This is the marginal distribution of Survived. Write down the marginal distribution below (give the categories of Survived and the proportions in each category).
(b) One variable that could be associated with the survival of a passenger is their Class. In studying this relationship, which variable is the explanatory variable? Circle the appropriate answer.
Class Survived
(c) Use JMP to obtain a contingency table and mosaic plot of the relationship between the Class of a passenger and whether or not they Survived. Change the contingency table so that it includes only the Count and Row % values. Print out the output and turn it in with this assignment. See the Categorical Data JMP guide for any additional help.
(d) Give the conditional distribution of Survived given that the passenger was in First class.
(e) Compare this conditional distribution to the overall marginal distribution of Survived from part (a). Are the two distributions similar to each other, or are they different? Explain.
(f) Based on the contingency table and mosaic plot, does it appear there is an association between Class and Survival?
Find the value of X in this circle.
Answer: 290
Step-by-step explanation: Because a circle area is 360 and if you subtract 70 from 360 you will get 290
And 290 + 70 = 360
How many times larger ?
Answer:
100,000
Step-by-step explanation:
So, when they say how many times larger 3x10^6 is than 3x10^1, they need you to divide 3x10^6 by 3x10^1.
When doing division and multiplcation with exponents, you subtract and add.
So, we have [tex]\frac{3*10^6}{3*10^1}[/tex]
The 3, that doesnt have a exponent on top or bottom, cancels out:
So now we have [tex]\frac{10^6}{10^1}[/tex]
Finally, since we are dividing 10^6 by 10^1, we are actually subtracting the exponents:
So we have [tex]10^5[/tex]
When you distrubute the ^5, you get:
100,000
So this is how many times bigger 3* [tex]10^6[/tex] is than 3*[tex]10^1[/tex]
HOpe this helps! :D
A certain computer microchip cannot be subjected to temperatures below 59° Fahrenheit. What is this in degrees Celsius?
Answer:
15°C
Step-by-step explanation:
Use the following formula to convert Fahrenheit to Celsius:
[tex]C=\frac{5}{9}(F-32)[/tex]
Substitute the value for the variable and solve for C.
[tex]C=\frac{5}{9}(59-32)\\C=\frac{5}{9}(27)\\C=15[/tex]
Therefore, 59°F is equivalent to 15°C.
If 3(x - 1) – 5(x – 3) = 3, find the value of 7x-5.
Answer:
36.5
Step-by-step explanation:
First solve for x
Factor:
3x-3-5x+15 = 3
Combine Like Terms:
-2x+12=3
-2x = -9
x = 4.5
PLug it in:
7(4.5)-5
31.5-5
36.5
[tex]{\boxed{\mathcal{\red{Step-by-step\:explanation:-}}}}[/tex]
[tex]3(x - 1) - 5(x - 3) = 3 \\ ⇝3x - 3 - 5x + 15 = 3 \\ ⇝ - 2x + 12 = 3 \\ ⇝ - 2x = 3 - 12 \\ ⇝x = \frac{ - 9}{ - 2} \\ x = 4.5[/tex]
To verify:
[tex]3(4.5 - 1) - 5(4.5 - 3) = 3 \\ ✒ \: 13.5 - 3 - 22.5 + 15 = 3 \\ ✒ \: 28.5 - 25.5 = 3\\✒\: 3 = 3[/tex]
✒ L. H. S. = R. H. S.
[tex]\sf\pink{Hence\:verified.}[/tex] ✔
Now,
7 [tex]x[/tex] - 5 = 7 x 4.5 - 5
= 31.5 - 5
= 26.5
[tex]\sf\purple{Therefore,\:the\:value\:of\:''7\:x-\:5''\:is\:26.5.}[/tex]
[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]
3
6
X =
04
06
O 12
please help !
Answer:
X=1
Step-by-step explanation:
I just did the math and boom but i think you should use this app https://www.tiger-algebra.com
HELP ASAP!! Will get fully ratedddd !!!!!!!!
Answer:
13. 4 sqrt(3)
14. sqrt(7)/2
Step-by-step explanation:
13. sqrt(2) * sqrt(3) * sqrt(8)
We know sqrt(a) * sqrt(b) = sqrt(ab)
sqrt(48)
Look for perfect squares
sqrt(16*3)
sqrt(16) sqrt(3)
4 sqrt(3)
14. sqrt(14)/ 2 sqrt(2)
We know sqrt(a) / sqrt(b) = sqrt(a/b)
sqrt(14/2) / 2
sqrt(7)/2
Hence, the Answer is
13. 4 sqrt(3)
14. sqrt(7)/2
Solution:
13. sqrt(2) * sqrt(3) * sqrt(8)
We know sqrt(a) * sqrt(b) = sqrt(ab)
sqrt(48)
Look for perfect squares
sqrt(16*3)
sqrt(16) sqrt(3)
4 sqrt(3)
14. sqrt(14)/ 2 sqrt(2)
We know sqrt(a) / sqrt(b) = sqrt(a/b)
sqrt(14/2) / 2
sqrt(7)/2
The sample survey showed that 67% of internet users said the internet has generally strengthened their relationship with family and friends. Develop a 95% confidence interval for the proportion of respondents who say the internet has strengthened their relationship with family and friends. (Round your answers to four decimal places.)
Answer:
The 95% confidence interval for the proportion of respondents who say the internet has strengthened their relationship with family and friends is [tex](0.67 - 1.96\sqrt{\frac{0.67*0.33}{n}}, 0.67 + 1.96\sqrt{\frac{0.67*0.33}{n}})[/tex], in which n is the size of the sample.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
67% of internet users said the internet has generally strengthened their relationship with family and friends.
This means that [tex]\pi = 0.67[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.67 - 1.96\sqrt{\frac{0.67*0.33}{n}}[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.67 + 1.96\sqrt{\frac{0.67*0.33}{n}}[/tex]
The 95% confidence interval for the proportion of respondents who say the internet has strengthened their relationship with family and friends is [tex](0.67 - 1.96\sqrt{\frac{0.67*0.33}{n}}, 0.67 + 1.96\sqrt{\frac{0.67*0.33}{n}})[/tex], in which n is the size of the sample.
Josh's bill for lunch at a restaurant was $49.59. He left an 18% tip. What was the amount
of the tip?
Round your answer to the nearest cent: $
what are the inputs of the function below
Please add an attachment/photo.
Answer:
There is no picture.
Find the distance from the point (1,4) to the line y = 1/3x - 3.
A) 4 units
B) 20 units
C) 4 units
OD) 20 units
Answer:
answer
is 6.325.............
Answer:
2√10
Step-by-step explanation:
I also got this question and it says I got it correct with this answer choice
Relationship in Figures
What are the first eight numbers in a Fibonacci sequence when N is equal to 1?
a. 1,2,3,4,5,6,7,8
b. 1,1,2,3,5,8,13,21
c. 3,0,2,3,2,5,5,7
d. 1,1,2,2,3,4,5,7
Please select the best answer from choices provided
Answer:
B. 1,1,2,3,5,8,13,21
Step-by-step explanation:
I calculated it logically
Given the quadratic equation x2 - 5x+ 10 = 0
Which of the following gives the value of the discriminant along with the
proper interpretation of it
The ages of students at a university are normally distributed with a mean of 21. What percentage of the student body is at least 21 years old? a. 50% b. It could be any value, depending on the magnitude of the standard deviation. c. 1.96% d. 21%
Answer:
50%
Step-by-step explanation:
Recall : When given a normal or Symmetric distribution, the mean of the distribution is at the centre with 0.5 or 50% of the distribution to either side (right and left) of the distribution.
Hence, if the mean = 21 ; then the percentage of student body with atleast 21 years is the percentage to the left of the distribution, which is 50%.
Therefore, P(x ≤ 21) = 0.5 = 50%
Question 1. Refer to the graph and write the inequality that satisfied the shaded region
Answer:
mexico
Step-by-step explanation: