Answer:
D. (2, 3, 4)
Step-by-step explanation:
The range is the y values. The y values, in numerical order, range from 2 to 4. The 2s do not need to be repeated.
Please answer this correctly
Answer:
Look at the money bags below!!! (but I'll give you the answer)
Step-by-step explanation:
John F: 7 full bags - 1 half
Juan A: 9 full bags
Jason A: 3 full bags
Nick J: 3 full bags- 1 half
Alfonso S: 8 full bags
Hope this helped and wasn't confusing!!! xx - Asia
Little Equipment for Hire is a subsidiary in the Giant Machinery and currently under the liquidation plan due to the severe contraction of operation due to corona virus. The company plans to pay total dividend of $2.5 million now and $ 7.5 million one year from now as a liquidating dividend. The required rate of return for shareholders is 12%. Calculate the current value of the firm’s equity in total and per share if the firm has 1.5 million shares outstanding. (4 marks)
Complete Question:
The Giant Machinery has the current capital structure of 65% equity and 35% debt. Its net income in the current year is $250 000. The company is planning to launch a project that will requires an investment of $175 000 next year. Currently the share of Giant machinery is $25/share. Required: a. How much dividend Giant Machinery can pay its shareholders this year and what is dividend payout ratio of the company. Assume the Residual Dividend Payout Policy applies? b. If the company is paying a dividend of $2.50/share and tomorrow the stock will go ex-dividend. Calculate the ex-dividend price tomorrow morning. Assuming the tax on dividend is 15%? c. Little Equipment for Hire is a subsidiary in the Giant Machinery and currently under the liquidation plan due to the severe contraction of operation due to corona virus. The company plans to pay total dividend of $2.5 million now and $ 7.5 million one year from now as a liquidating dividend. The required rate of return for shareholders is 12%. Calculate the current value of the firm’s equity in total and per share if the firm has 1.5 million shares outstanding?
Answer:
a) Total dividend for the current year = $136,250
Dividend Payout Ratio = 0.545
b) Ex-dividend price = $22.875
c) Total current value = $9,196,428.57
Current value per share = $6.13
Step-by-step explanation:
a) Equity = 65%
Debt = 35%
Net Income for year 0 = $250,000
proposed Investment for year 1= $175,000
Current price = $25/share
Tax on dividend = 15%
Total dividend for year 0 = 250000 - (65% of 175000)
Total dividend for year 0= 250000 - 113750
Total dividend for the current year = $136,250
Dividend Payout Ratio = total dividends/ total earning
Dividend Payout Ratio = 136250/250000
Dividend Payout Ratio = 0.545
b) Dividend = $2.5/ share
Ex-dividend price = current price - Dividend * (1-tax on dividend)
Substituting the appropriate values:
Ex-dividend price = 25 - 2.5 * (1-15%)
Ex-dividend price = 25 - 2.125
Ex-dividend price = $22.875
c) Current value of the firm = Dividend paid in year 0 + (Dividend to be paid in year 1/discount rate)
Dividend paid in year 0 = $2,500,000
Dividend to be paid in year 1 = $7,500,000
Discount rate = 12%
Total current value = 2,500,000 + (7,500,000 / 1.12)
Total current value = $9,196,428.57
Numbe of shares = 1,500,000
Current value per share = Total current value / number of shares
Current value per share = 9,196,428.57/1,500,000
Current value per share = $6.13
45 units and is centered at
A circle has a radius of
(-2.4, -4.8).
What is the equation of this circle?
The correct question is:
A circle has a radius of 45 units and is centered at (-2.4, -4.8).
What is the equation of this circle?
Answer:
Equation of the circle is;
(x + 2.4)² + (y + 4.8)² = 2304
Step-by-step explanation:
The standard equation of a circle is;
(x - a)² + (y - b)² = r²
where;
(a,b) is the center of the circle and r is the radius of the circle
Now, from the question, the circle is centered at (-2.4, -4.8) and the radius is 45
Thus, plugging those values into the standard form of equation of a circle, we have;
(x - (-2.4))² + (y - (-4.8))² = 48²
This gives;
(x + 2.4)² + (y + 4.8)² = 2304
A street performer earns 40% of all his daily earnings at the barclays center subway station.He earns about $60 at that station. Assuming he works everyday and earns the same amount, how much does he earn in two weeks?
Answer:
He earns $2,100 in two weeks.
Step-by-step explanation:
We know that this street performers earn $60 per day at the Barclays center subway station, and that this earning represents 40% (or a proportion of 0.4) of his daily earnings. We can calculate his daily earnings as:
[tex]0.4D=\$\,60\\\\D=\dfrac{\$\,60}{0.4}=\$\,150[/tex]
If the daily earnings are $150, the earnings in 2 weeks (14 days) will be:
[tex]W=14\cdot\$\,150=\$\,2100[/tex]
Triangle XYZ is translated so that X’ is that (4,-2) which rule defines this translation?
Answer: y
Step-by-step explanation:
TWO PLANES INTERSECT IN A
A. point
B. Ray
C. Line
D. Line segments
Answer:
c. line
Step-by-step explanation:
the intersection of two planes is called a line
Answer:
Hello dear,
two planes intersect and forms line
so yaa your answer is C)
Hope I helped you ;)
please thank me !!!
satsriakal ji
Simplify the expression 4x^3 2x^3
Answer:
Step-by-step explanation:
2 3x6
the 3 is an exponet so supost to be smaller
the answer- 2^3 x^6
i think its right
An OSU senior is studying for exams in psychology and economics. The student has time to read 50 pages of psychology and 10 pages of economics. Or, in the same amount of time the student could read 30 pages of psychology and 70 pages of economics. How many pages of economics can the student read instead of reading just 1 page of psychology
Answer:
3 Pages
Step-by-step explanation:
Let the pages of economics read = eLet the pages of psychology read = pLet the total time taken on each instance=tIn the first instance, the student has time to read 50 pages of psychology and 10 pages of economics.
t=50p+10eThe student could read 30 pages of psychology and 70 pages of economics.
t=30p+70eSince the two situations take the same amount of time, we have:
50p+10e=30p+70e
Collect like terms
50p-30p=70e-10e
20p=60e
Divide both sides by 20
p=3e
Therefore, in the time it will take the student to read 1 page of psychology, the student can read 3 pages of economics.
Determine if two lines are parallel or perpendicular by comparing slopes
Question
Use slopes and y-intercepts to determine if the lines x = -1 and x = 0 are parallel.
Select the correct answer below:
Parallel
Not Parallel
Answer:
They are parallel because they are vertical lines, and all vertical lines are parallel.
Step-by-step explanation:
A parabola has a focus of (6,–6) and a directrix of y = –2. Which of the following could be the equation of the parabola?
Answer:
[tex]-8(y+4) =(x-6)^{2}[/tex]
Step-by-step explanation:
The standard form of a parabola is given by the following equation:
[tex](x-h)^{2} =4p(y-k)[/tex]
Where the focus is given by:
[tex]F(h,k+p)[/tex]
The vertex is:
[tex]V=(h,k)[/tex]
And the directrix is:
[tex]y-k+p=0[/tex]
Now, using the previous equations and the information provided by the problem, let's find the equation of the parabola.
If the focus is (-6,6):
[tex]F=(h,k+p)=(6,-6)[/tex]
Hence:
[tex]h=6\\\\k+p=-6\hspace{10}(1)[/tex]
And if the directrix is [tex]y=-2[/tex] :
[tex]-2-k+p=0\\\\k-p=-2\hspace{10}(2)[/tex]
Using (1) and (2) we can build a 2x2 system of equations:
[tex]k+p=-6\hspace{10}(1)\\k-p=-2\hspace{10}(2)[/tex]
Using elimination method:
(1)+(2)
[tex]k+p+k-p=-6+(-2)\\\\2k=-8\\\\k=-\frac{8}{2}=-4\hspace{10}(3)[/tex]
Replacing (3) into (1):
[tex]-4+p=-6\\\\p=-6+4\\\\p=-2[/tex]
Therefore:
[tex](x-6)^{2} =4(-2)(y-(-4)) \\\\(x-6)^{2} =-8(y+4)[/tex]
So, the correct answer is:
Option 3
what is the solution set for the equation (x+3)(x-8)=0
Answer:
x = -3 x=8
Step-by-step explanation:
(x+3)(x-8)=0
Using the zero product property
x+3 =0 x -8 = 0
x = -3 x=8
A bank is investigating ways to entice customers to charge more on their credit cards. (Banks earn a fee from the merchant on each purchase, and hope to collect interest from the customers, as well.) A bank selects a random group of customers who are told their "cash back" will increase from 1% to 2% for all charges above a certain dollar amount each month. Of the 500 customers who were told the increase applied to charges above $1000 each month, the average increase in spending was $527 with a standard deviation of $225. Of the 500 customers who were told the increase applied to charges above $2000 each month, the average increase in spending was $439 with a standard deviation of $189. A level C = 95% confidence interval for \mu_1\:-\:\mu_2μ 1 − μ 2 is approximated by Group of answer choices (62.2, 113.8) (86.2, 120.5) (10.3, 23.8) (55.6, 67.8)
Answer:
[tex]CI = (\bar{x_{1} } - \bar{x_{2}} ) \pm MoE\\\\[/tex]
[tex]CI = (527 - 439) \pm 25.75\\\\CI = 88 \pm 25.75\\\\CI = 88 - 25.75 \:\: and \:\: 88 + 25.75\\\\CI = (62.2 \: ,\: 113.8 )[/tex]
The correct answer choice is a. (62.2, 113.8)
Step-by-step explanation:
Of the 500 customers who were told the increase applied to charges above $1000 each month, the average increase in spending was $527 with a standard deviation of $225.
Sample size = n₁ = 500
Sample mean = x₁ = $527
Standard deviation = s₁ = $225
Of the 500 customers who were told the increase applied to charges above $2000 each month, the average increase in spending was $439 with a standard deviation of $189
Sample size = n₂ = 500
Sample mean = x₂ = $439
Standard deviation = s₂ = $189
We are asked to find the 95% confidence interval for the difference between two means.
The given group of answer choices are
a. (62.2, 113.8)
b. (86.2, 120.5)
c. (10.3, 23.8)
d. (55.6, 67.8)
The confidence interval for the difference between two means is given by
[tex]CI = (\bar{x_{1} } - \bar{x_{2}} ) \pm MoE\\\\[/tex]
Where [tex]\bar{x_{1} }[/tex] and [tex]\bar{x_{2} }[/tex] are the given sample means and margin of error is given by
[tex]$ MoE = z_{\alpha/2} \cdot \sqrt{\frac{s_{1}^2}{n_1} + \frac{s_{2}^2}{n_2}} $[/tex]
The z-score corresponding to 95% confidence level is given by
Significance level = α = 1 - 0.95 = 0.05/2 = 0.025
From the z-table at α = 0.025 the z-score is 1.96
[tex]$ MoE = 1.96 \cdot \sqrt{\frac{225^2}{500} + \frac{189^2}{500}} $[/tex]
[tex]MoE = 1.96 \cdot 13.14[/tex]
[tex]MoE = 25.75[/tex]
Finally,
[tex]CI = (\bar{x_{1} } - \bar{x_{2}} ) \pm MoE\\\\[/tex]
[tex]CI = (527 - 439) \pm 25.75\\\\CI = 88 \pm 25.75\\\\CI = 88 - 25.75 \:\: and \:\: 88 + 25.75\\\\CI = (62.2 \: ,\: 113.8 )[/tex]
Therefore, the correct answer choice is a. (62.2, 113.8)
How to use z-table?
In the z-table find the probability of 0.025
Note down the value of that row, it would be 1.9.
Note down the value of that column, it would be 0.06.
Add the two numbers together.
The z-score is 1.9 + 0.06 = 1.96
Evaluate each expression. 16 5/4 x 16 1/4 / (16 1/2)/2=
Answer: the answer is 4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
4 on edgunity 2020
Given cot ø = 4/3. Find the other two reciprocal trigonometic ratios. 1) scs 2) sec
Answer:
csc ø = 5/3 ; sec ø = 5/4
Step-by-step explanation:
cot ø = adj/opp
adj = 4
opp = 3
after that, we must find the hypotenuse by using phytagoras theorem
hpy² = adj² + opp²
hpy² = 4² + 3²
hpy² = 25
hpy = 5
now let's find the other
csc ø (not scs) = hyp/opp = 5/3
sec ø = hyp/adj = 5/4
If the figures below are similar, find the scale factor of Figure B to Figure A.
48
27
60
А
16
B
20
9
Answer:
The scale factor is 3.
Step-by-step explanation
Figure B has side measures 16, 20, and 9. Figure A has side measures 48, 27, and 60. The ratio of each of the corresponding sides is 1:3 (16:48, etc). Therefore, the scale factor of Figure B to Figure A is 3.
Please answer this correctly
Answer:
=3651 km^2
Step-by-step explanation:
The rectangle at the top is 11 km by 32 km
The area is 11*32 =352
The rectangle at the bottom is 9 km by 11 km
The area is 9*11 = 99
Add the two areas together
352+99 =451 km^2
What’s the correct answer for this?
Answer:
(2,-2)
Step-by-step explanation:
In the attached file
:4. In the Department of Natural Sciences, 14 faculty members have a PhD, and 30 faculty members do not have a PhD. In the Department, the number of female faculty who do not have a PhD is 10 more than the number of females who have a PhD. If a third of the male faculty in the Department have a PhD, then what is the number of female faculty in the Department with a PhD?
Answer:
The number of female faculty in the Department with a PhD is 8.
Step-by-step explanation:
There are 14 + 30 = 44 faculty members.
Of those, x are male and y are female.
Then
x + y = 44.
The number of female faculty who do not have a PhD is 10 more than the number of females who have a PhD.
y = z + w
z is the number of females with PhD.
w is the number of females without PhD.
w = z + 10
If a third of the male faculty in the Department have a PhD
[tex]\frac{x}{3} + z = 14[/tex]
Now, we can write all variables as functions of z, which is the number of female faculty in the Department with PhD.
The objective is:
To find z from the first equation, that is:
[tex]x + y = 44[/tex]
To do this, we have to write x and y as functions of z.
Writing x and y as functions z.
[tex]\frac{x}{3} + z = 14[/tex]
[tex]\frac{x}{3} = 14 - x[/tex]
[tex]x = 3(14 - z)[/tex]
[tex]x = 42 - 3z[/tex]
And
[tex]y = z + w[/tex]
In which
[tex]w = 10 + z[/tex]
So
[tex]y = z + 10 + z[/tex]
[tex]y = 2z + 10[/tex]
Replacing:
[tex]x + y = 44[/tex]
[tex]42 - 3z + 2z + 10 = 44[/tex]
[tex]-z + 52 = 44[/tex]
[tex]z = 52 - 44[/tex]
[tex]z = 8[/tex]
The number of female faculty in the Department with a PhD is 8.
The following data summarizes results from 1000 pre-employment drug screening tests. If one of the test subjects is randomly selected, find the probability that the subject had a positive test result or a negative test result.
Positive Test Result Negative Test Result
Subject Uses Drugs 76 6
Subject Is Not a Drug User 95 823
P (subject had a positive test result or a negative test result)= simplify your answer.
Answer:
P (subject had a positive test result or a negative test result) = 1
Step-by-step explanation:
Given
The table above
Required
P (subject had a positive test result or a negative test result)
This is calculated as follows;
P (subject had a positive test result or a negative test result) =
P (subject had a positive test result) + P (subject had a negative test result)
Calculating P (subject had a positive test result)
This can be calculated by number of subjects with positive results divided by 1000
Only data from the column of subjects with positive results will be considered.
Number of Subjects = Subjects that uses drugs + Subjects that do not use drugs
Number of subjects = 76 + 95
Number of Subjects = 171
P (Subject had a positive test Result) = 171/1000
Calculating P (subject had a negative test result)
This can be calculated by number of subjects with negative results divided by 1000
Only data from the column of subjects with negative results will be considered.
Number of Subjects = Subjects that uses drugs + Subjects that do not use drugs
Number of subjects = 6 + 823
Number of Subjects = 829
P (Subject had a negative test Result) = 829/1000
Hence, P (subject had a positive test result or a negative test result) =
P (subject had a positive test result) + P (subject had a negative test result) = 171/1000 + 829/1000
P (subject had a positive test result or a negative test result) = (171 + 829)/1000
P (subject had a positive test result or a negative test result) = 1000/1000
P (subject had a positive test result or a negative test result) = 1
According to a polling organization, 22% of adults in a large region consider themselves to be liberal. A survey asked 200 respondents to disclose their political philosophy: Conservative, Liberal, Moderate. Treat the results of the survey as a random sample of adults in this region. Do the survey results suggest the proportion is higher than that reported by the polling organization? Use an alphaequals0.01 level of significance.
Answer:
No. There is not enough evidence to support the claim that the proportion of liberals is higher than that reported by the polling organization (P-value = 0.0366).
Step-by-step explanation:
The question is incomplete: there is no information about the results of the survey. We will assume that 55 of the subjects answer "liberal", and test the claim.
This is a hypothesis test for a proportion.
The claim is that the proportion of liberals is higher than that reported by the polling organization.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.22\\\\H_a:\pi>0.22[/tex]
The significance level is 0.01.
The sample has a size n=200.
The sample proportion is p=0.275.
[tex]p=X/n=55/200=0.275[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.22*0.78}{200}}\\\\\\ \sigma_p=\sqrt{0.000858}=0.029[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.275-0.22-0.5/200}{0.029}=\dfrac{0.053}{0.029}=1.792[/tex]
This test is a right-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z>1.792)=0.0366[/tex]
As the P-value (0.0366) is greater than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the proportion of liberals is higher than that reported by the polling organization.
A study was conducted to determine if the salaries of librarians from two neighboring cities were equal. A sample of 15 librarians from each city was randomly selected. The mean from the first city was $28,900 with a standard deviation of $2300. The mean from the second city was $30,300 with a standard deviation of $2100. Construct a 95% confidence interval for u1 -u2.
a) (-4081, 597)
b) (-2054, 238)
c) (-2871, 567)
d) (-3125, 325)
Answer:
Step-by-step explanation:
The formula for determining the confidence interval for the difference of two population means is expressed as
Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)
Where
x1 = sample mean salary of city 1 librarians
x2 = sample mean salary of city 2 librarians
s1 = sample standard deviation for city 1
s2 = sample standard deviation for city 2
n1 = number of soles for city 1
n1 = number of soles for city 2
For a 95% confidence interval, we would determine the z score from the t distribution table because the number of samples are small
Degree of freedom =
(n1 - 1) + (n2 - 1) = (15 - 1) + (15 - 1) = 28
z = 2.048
x1 - x2 = 28,900 - 30,300 = - 1400
Margin of error = 2.048√(s1²/n1 + s2²/n2) = 2.036√(2300²/15 + 2100²/15)
= 1647
The upper boundary for the confidence interval is
- 1400 + 1647 = 247
The lower boundary for the confidence interval is
- 1400 - 1647 = - 3047
A car is driving at 75 kilometers per hour. How far, in meters, does it travel in 5 seconds?
75km convert to m 75x1000=75000m
converted I hour to seconds that is 3600seconds
If 75000m=3600seconds
? =5seconds
that id 75000x5=375000/3600
=104.26…metres
The distance will be 104.16 meters if the car is driving at 75 kilometers per hour.
What is the distance?Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.
It is given that:
A car is driving at 75 kilometers per hour.
Let x be the distance.
As we know from the distance time relation:
Distance = speed×time
Speed = 75 km/h
Speed = 75 km/(3600)seconds
Speed = 0.0208 km/s
x = 0.0208×5
x = 0.10416 km
in meters
x = 0.104x1000
x = 104.16 meters
Thus, the distance will be 104.16 meters if the car is driving at 75 kilometers per hour.
Learn more about the distance here:
brainly.com/question/26711747
#SPJ2
The breaking strength of a rivet has a mean of 10,000 psi and a standard deviation of 714.2857 psi. What is the probability that the sample mean breaking strength for a random sample of 49 rivets is between 9,832 and 10,200?
Answer:
[tex] z= \frac{9832- 10000}{\frac{714.2857}{\sqrt{49}}}= -1.646[/tex]
[tex] z= \frac{10200- 10000}{\frac{714.2857}{\sqrt{49}}}= 1.96[/tex]
And we can use the normal standard distribution table or excel and we can find the probability with this difference:
[tex] P(-1.646 <z< 1.96) =P(z<1.96) -P(z<-1.646) =0.975-0.0499= 0.9251[/tex]
Then the probability that the sample mean breaking strength for a random sample of 49 rivets is between 9,832 and 10,200 is 0.9251
Step-by-step explanation:
For this case we have the following info given:
[tex] \mu = 10000[/tex] represent the mean
[tex] \sigma = 714.2857[/tex] represent the deviation
[tex] n = 49[/tex] represent the sample size selected
For this case since the sample size is large enough n>30 we have enough evidence to use the central llmit theorem and the distribution for the sample mena would be given by:
[tex] \bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}}) [/tex]
And we want to find the following probability:
[tex] P(9832 < \bar X< 10200)[/tex]
And we can use the z score formula given by:
[tex] z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And if we use the z score formula for the limits given we got:
[tex] z= \frac{9832- 10000}{\frac{714.2857}{\sqrt{49}}}= -1.646[/tex]
[tex] z= \frac{10200- 10000}{\frac{714.2857}{\sqrt{49}}}= 1.96[/tex]
And we can use the normal standard distribution table or excel and we can find the probability with this difference:
[tex] P(-1.646 <z< 1.96) =P(z<1.96) -P(z<-1.646) =0.975-0.0499= 0.9251[/tex]
Then the probability that the sample mean breaking strength for a random sample of 49 rivets is between 9,832 and 10,200 is 0.9251
What is the distance between the following points?
Answer:
square root of 72
Step-by-step explanation:
Answer:
(c) square root of 72
Step-by-step explanation:
khan academy answer :)
Please answer this correctly
Answer:
2
Step-by-step explanation:
Set the height of the bar to 2 since there are 2 numbers between 21-40.
Answer:
2 people.
Step-by-step explanation:
34 minutes and 40 minutes were recorded.
Therefore, 2 people.
A sports physician conducts an observational study to learn the average amount of time that 3,000 swimmers in the town can hold their breath underwater. He uses 150 sampling of 60 people. The average of the means of all the samplings is 72.7, and the standard deviation is 0.92. This is a histogram of the sampling distribution of the sample mean
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
A sports physician conducts an observational study to learn the average amount of time that 3,000 swimmers in the town can hold their breath underwater. He uses 150 sampling of 60 people. The average of the means of all the samplings is 72.7, and the standard deviation is 0.92. This is a histogram of the sampling distribution of the sample mean. Based on this data, with a 95% confidence interval the researchers can determine that the actual average amount of time the entire population can hold their breath under water is?
Given Information:
sample mean time = 72.7
sample standard deviation = 0.92
Sampling size = n = 150
Confidence level = 95%
Required Information:
95% confidence interval = ?
Answer:
[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 72.7 \pm 0.14836\\\\\text {confidence interval} = 72.7 - 0.14836, \: 72.7 + 0.14836\\\\\text {confidence interval} = (72.552, \: 72.848)\\\\[/tex]
Step-by-step explanation:
The confidence interval is given by
[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\[/tex]
Where [tex]\bar{x}[/tex] is the sample mean time and Margin of error is given by
[tex]$ MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) $ \\\\[/tex]
Where n is the sampling size, s is the sample standard deviation, and [tex]t_{\alpha/2}[/tex] is the t-score corresponding to 95% confidence level.
The t-score corresponding to 95% confidence level is
Significance level = 1 - 0.95 = 0.05/2 = 0.025
Degree of freedom = n - 1 = 150 - 1 = 149
From the t-table at α = 0.025 and DoF = 149
t-score = 1.975
[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 1.975\cdot \frac{0.92}{\sqrt{150} } \\\\MoE = 1.96\cdot 0.07512\\\\MoE = 0.14836\\\\[/tex]
So the required 95% confidence interval is
[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 72.7 \pm 0.14836\\\\\text {confidence interval} = 72.7 - 0.14836, \: 72.7 + 0.14836\\\\\text {confidence interval} = (72.552, \: 72.848)\\\\[/tex]
Therefore, we are 95% confident that actual average amount of time the entire population can hold their breath under water is within the range of (72.552, 72.848)
In this diagram, BAC – EDF. If the
area of BAC = 24 in2, what is the
area of EDF?
Help please
If the area of ΔBAC = 24 in², the area of ΔEDF is 6 in².
What are similar triangles?If two triangles' angles are congruent and their corresponding sides are proportionate, they are considered similar. To put it another way, similar triangles are the same in shape but not necessarily in size. If ΔPQR and ΔMNO are two similar triangles, then we can write it as ΔPQR ∼ ΔMNO.
Statement:The square of the ratio of any pair of their respective sides is equal to the ratio of the areas of two similar triangles.
How to solve this problem?Since ΔBAC ∼ ΔEDF, we can use the above statement to find the area of ΔEDF. Let the area of ΔEDF be x in². Given that length of EF and BC is 2 in and 4 in respectively.
So, we have to solve this equation,
24/x = 4²/2²
Now, 24/x = 16/4
i.e. 24/x = 4
i.e. 4x = 24
i.e. x = 24/4 = 6
Therefore the area of ΔEDF is 6 in².
Learn more about similar triangles here -
https://brainly.com/question/16819417
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Find the area of a circle with radius, r = 6.89m.
Give your answer rounded to 2 DP (2 decimal points)
The photo is attached below
Answer:
149.14 [tex]m^{2}[/tex]
Step-by-step explanation:
Area of a circle = π[tex]r^{2}[/tex]
so A = π * 6.89^2 = 149.14 (to 2d.p.)
In ΔEFG, ∠E \cong≅∠G, GE = 7 and FG = 15. Find the length of EF.
Answer: EF = 15
Step-by-step explanation:
The given description is that of an isosceles triangle. The base angles are congruent, therefore the sides opposite of those angles are also congruent.
The base angles are ∠E and ∠G and the vertex angle is ∠F.
The sides opposite to the base angles are EF and FG.
Thus, EF ≡ FG.
Since FG = 15 and FG = EF, then 15 = EF.
Based on the definition of an isosceles triangle, the length of EF in the triangle is: 15 units.
What is an Isosceles Triangle?An isosceles triangle has two sides that are congruent. The angles opposite these congruent sides are also congruent.
ΔEFG is an isosceles triangle. The congruent sides are, FG and EF.
Therefore, EF = FG = 15 units.
Learn more about isosceles triangle on:
https://brainly.com/question/11884412
What’s the correct answer for this?
Answer:
1) Antonio's statement
2) <A = 123
Step-by-step explanation:
1) Antonio's statement is incorrect. This is because the opposite angles of a quadrilateral add up to 180°. Erin was incorrect because the opposite angles of this quadrilateral are unequal.
2) 2x+7+5x-2 = 180° (opposite angles of quadrilateral)
Now
7x+5 = 180
7x = 175
x = 25
<A = 5x-2
= 5(25)-2
= 125-2
= 123
