Answer:
Base Length of 84cmHeight of 42 cm.Step-by-step explanation:
Given a box with a square base and an open top which must have a volume of 296352 cubic centimetre. We want to minimize the amount of material used.
Step 1:
Let the side length of the base =x
Let the height of the box =h
Since the box has a square base
Volume, [tex]V=x^2h=296352[/tex]
[tex]h=\dfrac{296352}{x^2}[/tex]
Surface Area of the box = Base Area + Area of 4 sides
[tex]A(x,h)=x^2+4xh\\$Substitute h=\dfrac{296352}{x^2}\\A(x)=x^2+4x\left(\dfrac{296352}{x^2}\right)\\A(x)=\dfrac{x^3+1185408}{x}[/tex]
Step 2: Find the derivative of A(x)
[tex]If\:A(x)=\dfrac{x^3+1185408}{x}\\A'(x)=\dfrac{2x^3-1185408}{x^2}[/tex]
Step 3: Set A'(x)=0 and solve for x
[tex]A'(x)=\dfrac{2x^3-1185408}{x^2}=0\\2x^3-1185408=0\\2x^3=1185408\\$Divide both sides by 2\\x^3=592704\\$Take the cube root of both sides\\x=\sqrt[3]{592704}\\x=84[/tex]
Step 4: Verify that x=84 is a minimum value
We use the second derivative test
[tex]A''(x)=\dfrac{2x^3+2370816}{x^3}\\$When x=84$\\A''(x)=6[/tex]
Since the second derivative is positive at x=84, then it is a minimum point.
Recall:
[tex]h=\dfrac{296352}{x^2}=\dfrac{296352}{84^2}=42[/tex]
Therefore, the dimensions that minimizes the box surface area are:
Base Length of 84cmHeight of 42 cm.Ravi is 1 1/4 (mixed fraction).dinesh is 1 1/15 times as tall as Ravi .what is Dinesh's height
Let V be a vector space, and let v1, v2, v3 and v4 be linearly independent vectors in V . In parts (a) and (b) below, determine whether each of the given sets of vectors is linearly independent or linearly dependent. Prove your answers using the definition.
u1 = v1 − 7v3, u2 = v1, u3 = v3, u4 = v3 + v4.
Answer:
Step-by-step explanation:
[tex]u_3 = v_3[/tex] and [tex]u_2 = v_1[/tex]
[tex]u_1= v_1 -7 v_3[/tex]
Replace the first line to the second line, you have [tex]u_1= u_2-7u_3[/tex]
That shows [tex]\{u_1, u_2, u_3,u_4\}[/tex]
is not linear independent.
State the null and alternative hypotheses to test if the population represented by Sample 1 has a mean that is 2.0 units higher than the population represented by Sample 2. Let µd be the population mean of​ matched-pair differences for Sample 1 - Sample 2. State the null and alternative hypotheses.
Pair 1 2 3 4 5 6 7
Sample1 5 6 10 3 6 7 8
Sample2 4 4 3 5 5 5 3
Answer:
Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_A-\mu_B[/tex] = 2.0 units or [tex]\mu_D[/tex] = 2.0 units
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_A-\mu_B\neq[/tex] 2.0 units or [tex]\mu_D\neq[/tex] 2.0 units
Step-by-step explanation:
We are given the following data below and we have test if the population represented by Sample 1 has a mean that is 2.0 units higher than the population represented by Sample 2;
Pair : 1 2 3 4 5 6 7
Sample1 : 5 6 10 3 6 7 8
Sample2 : 4 4 3 5 5 5 3
Let [tex]\mu_A[/tex] = population mean represented by Sample 1
[tex]\mu_B[/tex] = population mean represented by Sample 2
[tex]\mu_D[/tex] = population mean matched-pair differences for Sample 1 - Sample 2
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_A-\mu_B[/tex] = 2.0 units or [tex]\mu_D[/tex] = 2.0 units
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_A-\mu_B\neq[/tex] 2.0 units or [tex]\mu_D\neq[/tex] 2.0 units
Here null hypothesis states that the population represented by Sample 1 has a mean that is 2.0 units higher than the population represented by Sample 2.
On the other hand, alternate hypothesis states that the population represented by Sample 1 has a mean that is not 2.0 units higher than the population represented by Sample 2.
What’s the correct answer for this question?
Answer:
D.
Step-by-step explanation:
For independent events
P(A and B) = P(A) × P(B)
FINDING P(B)
P(B) = P(A and B) /P(A)
P(B) = 0.6/0.8
P(B) = 0.75
The domain of the function is all
The range of the function is all
The domain of a function is the set of all the x terms of the function and the range of a function is the set of all the y terms of a function.
For example, take a look below.
The domain is the set of all x terms in each ordered pair and the
range will be the set of all the y terms in each ordered pair.
Which symbol should go into the box to make the statement true?
|17| ? 17.
A.< B.> C.equal sign with a line through it D. =
Answer:
the 3rd option is the right one
Diastolic blood pressures are assumed to follow a normal distribution with a mean of 85 and a standard deviation of 12. What proportion of people has diastolic blood pressures less than 80?
Answer:
0.3745
Step-by-step explanation:
We have to solve the problem by calculating the z-score value that has the following formula:
z <(x - m) / sd
x is the value to evaluate (<80), m is the mean (85) and the standard deviation is sd (12)
replacing:
p (x <80) = z <(80 - 85) / 12
z <-0.416, we look for this value in the normal distribution table and it corresponds to:
p (x <80) = 0.3745
Which means that the proportion of people is 0.3745
At 5:00 am, here's what we know about two airplanes: Airplane #1 has an elevation of 38520 ft and is descending at the rate of 750 ft/min. Airplane #2 has an elevation of 9400 ft and is climbing at the rate of 550 ft/min. (1) Let t represent the time in minutes since 5:00 am, and let E represent the elevation in feet. Write an equation for the elevation of each plane in terms of t . plane #1: E ( t ) = plane #2: E ( t ) =
Answer:
Plane 1
[tex]y_{1} = 38250\,ft - \left(750\,\frac{ft}{min}\right)\cdot t[/tex]
Plane 2
[tex]y_{2} = 9400\,ft + \left(550\,\frac{ft}{min}\right)\cdot t[/tex]
Step-by-step explanation:
As each plane is travelling at constant speed, each equation can be modelled after this expression:
[tex]y = y_{o} + \dot y \cdot t[/tex]
Where:
[tex]y_{o}[/tex] - Intial elevation of the airplane, measured in feet.
[tex]\dot y[/tex] - Climbing/Descending rate of the airplane, measured in feet per minute. (Positive - Climbing, Negative - Descending)
[tex]t[/tex] - Time, measured in minutes.
Equations are described below:
Plane 1
[tex]y_{1} = 38250\,ft - \left(750\,\frac{ft}{min}\right)\cdot t[/tex]
Plane 2
[tex]y_{2} = 9400\,ft + \left(550\,\frac{ft}{min}\right)\cdot t[/tex]
The required return on equity is:
A) It has nothing to do with market risk premium
B) generally less than post-tax debt costs.
C) A debt/capital ratio of 0.5 is smaller than WACC.
D) is directly related to the risk of the company's assets.
E) It is generally the reciprocal of inflation.
Answer:
D) is directly related to the risk of the company's assets.
Step-by-step explanation:
Equity which may be defined as what the difference between what your business worth minus what you owe in it.
It can also be put in a way as the remaining value of an owners interest in a particular company after all debt might have been cleared.
Equity= assets - liability
So equity has a lot to do in the risk management of a business or a particular company.
What is the completely factored form of polynomial 5X cubed +20 X squared plus 2X +8
Step-by-step explanation:
5x3 + 20x2 + 2x + 8
5x2 (x + 4) + 2(x + 4)
(5x2 + 2) (x + 4)
Directions:
Write and solve a proportion to answer the question.
1/5 is 40% of what number?
Answer:
20/40
Step-by-step explanation:
1/5=40/100*x
x=1/5*100/40
x=20/40 or 10/20 or 0.5
A DVD is on sale for $1.05 off. This is a 15% discount from the original price. Use an equation to find the origina
price
O $16.05
$15.75
$10.50
O $7.00
Answer:
D. $7.00
Step-by-step explanation:
I just did it.
Now, when you click ROLL, the simulator will keep track of the average of all rolls so far. For example, if you roll 2 and then 4, the average will be 3. ROLL sides What is the average after 10 rolls
Step-by-step explanation:
Suppose the results obtained are numbers from 1 to 10, then after 10 rolls, the average is
(1+2+3+4+5+6+7+8+9+10)/10
= 55/10
= 5.5
Answer:
5 , 3 , 3.5 C) The average would approach a set value.
Step-by-step explanation:
The first three numbers don't matter it could be anyone 1-6.
The last answer is C
What is the surface area of the figure shown?
Answer:
90 square feet.
Step-by-step explanation:
Let's set up an equation!
SA= 2(xy)+2(xz)+2(yz).
Lets say that x=3 y=6 and z=3
We plug it in.
2(18)+2(9)+2(18)= SA
36+18+36=SA
72+18=SA
90=SA
90 square feet = Surface area.
3. Barbara was asked to create a set of numbers that contained only integers. Which of the sets does
NOT contain only integers?
А
12
B
-3, -4,600,
9, 100, - 4, 12, -6, 5
5. 3, -6, -14, 3.5, 7
с
24
12
D 22, -12.0, 9, -14, 28, 4
Answer:
C (5.3, -6, -14, 3.5, 7)
Step-by-step explanation:
Integers are the sets of positive and negative whole numbers including zero.
In set notation, we denote the set of integers using the letter [tex]\mattbb{Z}[/tex].
From the given options:
In Option C (5. 3, -6, -14, 3.5, 7), we have the number 3.5 and 5.3 which are not whole numbers. Therefore 3.5 and 5.3 are not integers.
Option C is the set which does not contain only integers.
A password for a website must have 4 different digits. What is the probability a password chosen at random is 7654?
Please show work thanks
The 1st digit is 1 out of 10 numbers
The 2nd digit is 1 out of 9 numbers
The 3rd digit is 1 out of 8 numbers
The 4th digit is 1 out of 1 numbers.
Total combinations are 10 x 9 x 8 x 7 = 5040
Since the combination 7654 is one out of the total the probability would be 1/5040
At a carnival, an individual can win a prize by choosing a rubber duck from a pond with "Win" written on the underside of the duck. There are a total of eight ducks with "Win" written on the underside of the duck, and there are 17 ducks with "Lose" written on the underside of the duck. After each pick, if a prize is won, the duck is replaced in the pond. If a prize is not won, then the duck is again placed back into the pond. If an individual makes four picks, what is the probability the individual will win a prize exactly one time?
Step-by-step explanation:
The probability of success = 8/(8 + 17) = 8/25 = 0.32.
Let X be the random variable denoting the number of successes (number of times the individual won a prize) in four picks.
Hence, X ~ Bin(4, 0.32).
Thus, P(X = 1) = [tex]4C_1=(0.32)(1-0.68)^{4-1}=4C_1(0.32)(0.68)^3[/tex]
The probability the individual will win a prize exactly one time is
C(4, 1)(0.32)¹ (0.68)³ if the total of eight ducks with “Win” written on the underside of the duck.
What is probability?It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have:
There are a total of eight ducks with “Win” written on the underside of the duck, and there are 17 ducks with “Lose” written on the underside of the duck.
The probability of success
P = 8/(8 + 17)
P = 8/25
P = 0.32
Let's suppose the X is the random variable denoting the number of the individual won a prize in four picks.
So,
X ~ Bin(4, 0.32).
Thus, P(X = 1) = C(4, 1)(0.32)(1 0.32)⁴⁻¹
= C(4, 1)(0.32)¹ (0.68)³
Thus, the probability the individual will win a prize exactly one time is
C(4, 1)(0.32)¹ (0.68)³ if the total of eight ducks with “Win” written on the underside of the duck.
Learn more about the probability here:
brainly.com/question/11234923
#SPJ5
Brainliest to whoever gets this correct , Describe the end behavior of the following function:
Answer:
graph starts high and ends high
When vector is added to vector , the resultant is vector such that . This resultant vector has components Rx=Ax+BxRx=Ax+Bx and Ry=Ay+ByRy=Ay+By. How do you determine the direction of , the angle the vector makes with the positive x-axis?
Answer:
a. When vector is added to vector , the resultant is vector such that its magnitude and direction is proportional to the resultant magnitude and direction of the component vectors.
b. ∅ = [tex]tan^{-1}[/tex](Rx/Ry)
Step-by-step explanation:
Vectors are used to express physical quantities with magnitude and direction. Vectors can be added by the parallelogram method or the triangular method of addition. the magnitude and direction of the resultant vector is usually proportional to the magnitude and direction of the component vectors.
The direction of the angle is found as
tan∅ = Rx/Ry
∅ = [tex]tan^{-1}[/tex](Rx/Ry)
Find cos angle∠ C
A. 5/13
B. 12/13
C. 12/5
D. 13/5
Answer:
The answer is A.
Step-by-step explanation:
Recall SohCahToa, which tells us that cosine is the ratio of the adjacent side to the hypotenuse. In other words:
[tex]\displaystyle \cos(x)=\frac{\text{adjacent}}{\text{hypotenuse}}[/tex]
The adjacent side to ∠C is 10 and the hypotenuse is 26.
Therefore:
[tex]\displaystyle \cos(C)=\frac{10}{26}=\frac{5}{13}[/tex]
Our answer is A.
If (x + 5) - 2(4x - 1) = 0, what is the value of x?
Answer:
x=1
Step-by-step explanation:
(x + 5) - 2(4x - 1) = 0
Distribute
x+5 - 8x +2 =0
Combine like terms
-7x +7 = 0
Add 7x to each side
-7x+7 +7x = 7x
7 = 7x
divide by 7
7/7 = 7x/7
1 =x
Amy's car holds at most 19 gallons of gas. Now it has 9 gallons. Use pencil and paper. Explain how to find the amount of gas she needs, in liters, to fill the gas tank.
Answer:
37.8541 litres.
Step-by-step explanation:
To find the amount of gas that she needs to fill her gas tank is 19 -9. She needs 10 gallons to fill her tank.
It says to state in litres, so convert.
1 gallon is about 3.78541 liters, so 10 gallons is 37.8541 litres
Hope that helped : )
rewrite the following without an exponent (-7)-1
Answer:
Step-by-step explanation:
-7-1=-8
In 2013, the average Girl Scout in New York City sold 96 boxes of cookies. The leader of Troop 5078 in New York City wants to know if the scouts in her troop sold more cookies than the average in New York City. She randomly samples 50 girls in Troop 5078 and records the number of boxes of cookies sold for each girl in the sample. The troop leader finds that her Girl Scouts each sold an average of 101.1 boxes of cookies with a standard deviation of 29.3. She analyzed her data using a t-test and obtained a p-value of 0.11. What conclusion can she draw from her data?
Answer:
We want to test if the scouts in her troop sold more cookies than the average in New York City (50), the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 50[/tex]
Alternative hypothesis:[tex]\mu > 50[/tex]
The statistic for this case is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
For this case we have also the p value calculated
[tex]p_v =0.11[/tex]
If we use any significance level lower than 10% we FAIL to reject the null hypothesis (pvalue>significance) and we can conclude that the true mean is not higher than the mean for New York otherwise if we use a significance level higher than 10% the conclusion would be the opposite.
Step-by-step explanation:
Information given
[tex]\bar X=101.1[/tex] represent the sample mean
[tex]s=29.3[/tex] represent the sample standard deviation
[tex]n=50[/tex] sample size
[tex]\mu_o =50[/tex] represent the value that we want to test
t would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We want to test if the scouts in her troop sold more cookies than the average in New York City (50), the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 50[/tex]
Alternative hypothesis:[tex]\mu > 50[/tex]
The statistic for this case is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
For this case we have also the p value calculated
[tex]p_v =0.11[/tex]
Conclusion
If we use any significance level lower than 10% we FAIL to reject the null hypothesis (pvalue>significance) and we can conclude that the true mean is not higher than the mean for New York otherwise if we use a significance level higher than 10% the conclusion would be the opposite.
Answer true or false to each statement concerning a confidence interval for a population mean.a) The length of a confidence interval can be determined if you know only the margin of error.b) The margin of error can be determined if you know only the length of the confidence interval.c) The confidence interval can be obtained if you know only the margin of error.d) The confidence interval can be obtained if you know only the margin of error and the sample mean.e) The margin of error can be determined if you know only the confidence level.f) The confidence level can be determined if you know only the margin of error.g) The margin of error can be determined if you know only the confidence level, population standard deviation, and sample size.h) The confidence level can be determined if you know only the margin of error, population standard deviation, and sample size.
Answer:
The true statements Include
A) The length of a confidence interval can be determined if you know only the margin of error.
B) The margin of error can be determined if you know only the length of the confidence interval.
D) The confidence interval can be obtained if you know only the margin of error and the sample mean.
G) The margin of error can be determined if you know only the confidence level, population standard deviation, and sample size.
F) The confidence level can be determined if you know only the margin of error, population standard deviation, and sample size.
The false statements include
C) The confidence interval can be obtained if you know only the margin of error.
E) The margin of error can be determined if you know only the confidence level.
F) The confidence level can be determined if you know only the margin of error.
Step-by-step explanation:
Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample mean) ± (Margin of error)
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error of the mean)
The critical value is obtained using the confidence level (and sample size for t-distributions).
Standard Error of the mean = (Standard deviation)/[√(sample size)]
Standard error of the mean = σₓ = (σ/√n)
Taking each of the statements one at a time
a) The length of a confidence interval can be determined if you know only the margin of error.
According to the mathematical expression of the confidence interval, the length of the confidence interval is 2 × Margin of error. Hence, the length of the confidence interval can be truly obtained from only the margin of error.
This statement is true.
b) The margin of error can be determined if you know only the length of the confidence interval.
This is another way of phrasing statement A. The margin of error is half of the length of the confidence interval.
Hence, this statement is also true.
c) The confidence interval can be obtained if you know only the margin of error.
The confidence interval can be obtained from an expression that involves the sample mean and margin of error.
Confidence Interval = (Sample mean) ± (Margin of error)
The confidence interval cannot be obtained from just the margin of error. Hence, this statement is false.
d) The confidence interval can be obtained if you know only the margin of error and the sample mean.
Like o stated in (c) above, the confidence interval can be obtained from an expression that involves the sample mean and margin of error.
Confidence Interval = (Sample mean) ± (Margin of error)
Hence, this statement is true.
e) The margin of error can be determined if you know only the confidence level.
To obtain the margin of error, if the confidence interval isn't used, an expression involving the critical value and the standard error of the mean is used.
Margin of Error = (Critical value) × (standard Error of the mean)
The critical value is obtained using the confidence level, but the margin of error cannot be obtained from just that, we still need the standard error of the mean.
Hence, this statement is false.
f) The confidence level can be determined if you know only the margin of error.
This is another way of phrasing statement E. Hence, this statement too is false.
g) The margin of error can be determined if you know only the confidence level, population standard deviation, and sample size.
This is true as these is all that is required to obtain the margin of error.
h) The confidence level can be determined if you know only the margin of error, population standard deviation, and sample size.
This can be a bit stressful to obtain, but it is true. It is easy to see this from all the explanation from the beginning to this point.
Hope this Helps!!!
In order to get promoted to the next grade, a student is required to score above 55 in the final test. Assume the scores to be normally distributed with a mean of 60 and a standard deviation of 5.5. Calculate the percentage of students who will be promoted to the next grade.
Answer:
[tex]P(X>55)=P(\frac{X-\mu}{\sigma}>\frac{55-\mu}{\sigma})=P(Z>\frac{55-60}{5.5})=P(z>-0.909)[/tex]
And we can find this probability with the complement rule:
[tex]P(z>-0.909)=1-P(z<-0.909)[/tex]
And we can use excel or the normal standard table and we got:
[tex]P(z>-0.909)=1-P(z<-0.909)=1-0.182= 0.818[/tex]
So then we expect about 81.8% of students that will be promoted
Step-by-step explanation:
Let X the random variable that represent the scores of promotion of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(60,5.5)[/tex]
Where [tex]\mu=60[/tex] and [tex]\sigma=5.5[/tex]
We want to find the following probability:
[tex]P(X>55)[/tex]
And we can use the z score formula given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Using the z score formula we got:
[tex]P(X>55)=P(\frac{X-\mu}{\sigma}>\frac{55-\mu}{\sigma})=P(Z>\frac{55-60}{5.5})=P(z>-0.909)[/tex]
And we can find this probability with the complement rule:
[tex]P(z>-0.909)=1-P(z<-0.909)[/tex]
And we can use excel or the normal standard table and we got:
[tex]P(z>-0.909)=1-P(z<-0.909)=1-0.182= 0.818[/tex]
So then we expect about 81.8% of students that will be promoted
Find the angle of least positive measure that is coterminal with 541 degrees
Answer: 181 degrees.
Step-by-step explanation:
If we have an angle A, between, then the angle B is coterminal to A if:
B = A + n*360°
where n can be any whole number (if n = 0, we have B = A)
Then, if we take our angle as A = 541°
we can take n = -1 and get:
B = 541° - 1*360° = 181°
Now, if we subtract again 360°, we will end with an angle of negative measure, so 181° is the least positive measure angle that is coterminal with 541°
Consider a sampling distribution with p equals 0.11 and samples of size n each. Using the appropriate formulas, find the mean and the standard deviation of the sampling distribution of the sample proportion. a. For a random sample of size n equals 5000. b. For a random sample of size n equals 1000. c. For a random sample of size n equals 250.
Answer:
a) Mean 0.11 and standard deviation 0.0044.
b) Mean 0.11 and standard deviation 0.0099.
c) Mean 0.11 and standard deviation 0.0198
Step-by-step explanation:
Central Limit Theorem:
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question:
[tex]p = 0.11[/tex]
a. For a random sample of size n equals 5000.
Mean:
[tex]\mu = p = 0.11[/tex]
Standard deviation:
[tex]s = \sqrt{\frac{0.11*0.89}{5000}} = 0.0044[/tex]
Mean 0.11 and standard deviation 0.0044.
b. For a random sample of size n equals 1000.
Mean:
[tex]\mu = p = 0.11[/tex]
Standard deviation:
[tex]s = \sqrt{\frac{0.11*0.89}{1000}} = 0.0044[/tex]
Mean 0.11 and standard deviation 0.0099.
c. For a random sample of size n equals 250.
Mean:
[tex]\mu = p = 0.11[/tex]
Standard deviation:
[tex]s = \sqrt{\frac{0.11*0.89}{250}} = 0.0198[/tex]
Mean 0.11 and standard deviation 0.0198
Can someone plz help me solved this problem I need help plz help me! Will mark you as brainiest!
Answer:
- 8b³+5ab²+7a²b
Step-by-step explanation:
(32ab³ - 20a²b² - 28a³b)/(-4a)= - 8b³+5ab²+7a²b
factorise fully 24x+16
Answer:
8(3x + 2)
Step-by-step explanation:
→To factorize this expression, you must take out the GCF (Greatest Common Factor). The GCF is the biggest number that you can take out of all the terms in the expression, meaning the number has to be able to be divide by 24x and 16.
→The GCF is 8:
8(3x + 2)
Answer:
8(3x+2)
Step-by-step explanation:
24x+16
8*3*x + 8*2
Factor out an 8
8(3x+2)
