Answer:
Step-by-step explanation:
5
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.
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A start-up news company is looking to expand their audience and is interested in studying the how many adults regularly use social media as a source of news. According to the Pew Research Center, 62% of adults get their news from social media, but researchers want to determine of this proportion is actually greater than 62% in region they plan on advertising on.
They take a random sample of 200 adults in the region they are interested in advertising in and what they use to typically get their news. A total of 137 adults reported regularly getting their news from social media.
The point estimate for this problem is: (report your answer to 3 decimal places)
Checking Conditions: We are told that the sample was randomly selected. Are the other conditions met to perform a hypothesis test for p?
A) Yes, the sample size is greater than 30.
B) Yes, there are at least 10 adults saying they get their news from social media and at least 10 that do not.
C) Yes, the population standard deviation is known.
D) No, the population mean is unknown.
Answer:
Step-by-step explanation:
The point estimate is the sample proportion.
Considering the sample,
Sample proportion, p = x/n
Where
x = number of success = 137
n = number of samples = 200
p = 137/200 = 0.685
From the information given,
Population proportion = 62% = 62/100 = 0.62
The correct options are
A) Yes, the sample size is greater than 30.
B) Yes, there are at least 10 adults saying they get their news from social media and at least 10 that do not.
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
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 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
Triangle XYZ is translated so that X’ is that (4,-2) which rule defines this translation?
Answer: y
Step-by-step explanation:
The market and Stock J have the following probability distributions:
Probability rM rJ
0.3 14% 22%
0.4 10 4
0.3 19 12
1. Calculate the expected rate of return for the market. Round your answer to two decimal places.%
2. Calculate the expected rate of return for Stock J. Round your answer to two decimal places.%
3. Calculate the standard deviation for the market. Round your answer to two decimal places.%
4. Calculate the standard deviation for Stock J. Round your answer to two decimal places.%
Answer:
1) [tex] E(M) = 14*0.3 + 10*0.4 + 19*0.3 = 13.9 \%[/tex]
2) [tex]E(J)= 22*0.3 + 4*0.4 + 12*0.3 = 11.8 \%[/tex]
3) [tex] E(M^2) = 14^2*0.3 + 10^2*0.4 + 19^2*0.3 = 207.1 [/tex]
And the variance would be given by:
[tex]Var (M)= E(M^2) -[E(M)]^2 = 207.1 -(13.9^2)= 13.89[/tex]
And the deviation would be:
[tex] Sd(M) = \sqrt{13.89}= 3.73[/tex]
4) [tex] E(J^2) = 22^2*0.3 + 4^2*0.4 + 12^2*0.3 =194.8 [/tex]
And the variance would be given by:
[tex]Var (J)= E(J^2) -[E(J)]^2 = 194.8 -(11.8^2)= 55.56[/tex]
And the deviation would be:
[tex] Sd(M) = \sqrt{55.56}= 7.45[/tex]
Step-by-step explanation:
For this case we have the following distributions given:
Probability M J
0.3 14% 22%
0.4 10% 4%
0.3 19% 12%
Part 1
The expected value is given by this formula:
[tex] E(X)=\sum_{i=1}^n X_i P(X_i)[/tex]
And replacing we got:
[tex] E(M) = 14*0.3 + 10*0.4 + 19*0.3 = 13.9 \%[/tex]
Part 2
[tex]E(J)= 22*0.3 + 4*0.4 + 12*0.3 = 11.8 \%[/tex]
Part 3
We can calculate the second moment first with the following formula:
[tex] E(M^2) = 14^2*0.3 + 10^2*0.4 + 19^2*0.3 = 207.1 [/tex]
And the variance would be given by:
[tex]Var (M)= E(M^2) -[E(M)]^2 = 207.1 -(13.9^2)= 13.89[/tex]
And the deviation would be:
[tex] Sd(M) = \sqrt{13.89}= 3.73[/tex]
Part 4
We can calculate the second moment first with the following formula:
[tex] E(J^2) = 22^2*0.3 + 4^2*0.4 + 12^2*0.3 =194.8 [/tex]
And the variance would be given by:
[tex]Var (J)= E(J^2) -[E(J)]^2 = 194.8 -(11.8^2)= 55.56[/tex]
And the deviation would be:
[tex] Sd(M) = \sqrt{55.56}= 7.45[/tex]
On Sunday, a local hamburger shop sold a combined of 572 hamburger and cheeseburger. The number of cheeseburgers sold was three times the number of hamburger sold. How many hamburger were sold on Sunday
Among 25- to 30-year-olds, 29% say they have used a computer while under the influence of alcohol. Suppose five 25- to 30-year-olds are selected at random. Complete parts (a) through (d) below. (a) What is the probability that all five have used a computer while under the influence of alcohol? (Round to four decimal places as needed.) (b) What is the probability that at least one has not used a computer while under the influence of alcohol? (Round to four decimal places as needed.) (c) What is the probability that none of the five have used a computer while under the influence of alcohol? (Round to four decimal places as needed.) (d) What is the probability that at least one has used a computer while under the influence of alcohol? (Round to four decimal places as needed.)
Answer:
(a) The probability that all five have used a computer while under the influence of alcohol is 0.0021.
(b) The probability that at least one has not used a computer while under the influence of alcohol is 0.9979.
(c) The probability that none of the five have used a computer while under the influence of alcohol is 0.1804.
(d) The probability that at least one has used a computer while under the influence of alcohol is 0.8196.
Step-by-step explanation:
We are given that among 25- to 30-year-olds, 29% say they have used a computer while under the influence of alcohol.
Suppose five 25- to 30-year-olds are selected at random.
The above situation can be represented through the binomial distribution;
[tex]P(X = x) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r} ; x = 0,1,2,3,.........[/tex]
where, n = number of trials (samples) taken = Five 25- to 30-year-olds
r = number of success
p = probability of success which in our question is probability that
people used a computer while under the influence of alcohol,
i.e. p = 29%.
Let X = Number of people who used computer while under the influence of alcohol.
So, X ~ Binom(n = 5, p = 0.29)
(a) The probability that all five have used a computer while under the influence of alcohol is given by = P(X = 5)
P(X = 5) = [tex]\binom{5}{5}\times 0.29^{5} \times (1-0.29)^{5-5}[/tex]
= [tex]1 \times 0.29^{5} \times 0.71^{0}[/tex]
= 0.0021
(b) The probability that at least one has not used a computer while under the influence of alcohol is given by = P(X [tex]\geq[/tex] 1)
Here, the probability of success (p) will change because now the success for us is that people have not used a computer while under the influence of alcohol = 1 - 0.29 = 0.71
SO, now X ~ Binom(n = 5, p = 0.71)
P(X [tex]\geq[/tex] 1) = 1 - P(X = 0)
= [tex]1-\binom{5}{0}\times 0.71^{0} \times (1-0.71)^{5-0}[/tex]
= [tex]1 -(1 \times 1 \times 0.29^{5})[/tex]
= 1 - 0.0021 = 0.9979.
(c) The probability that none of the five have used a computer while under the influence of alcohol is given by = P(X = 0)
P(X = 0) = [tex]\binom{5}{0}\times 0.29^{0} \times (1-0.29)^{5-0}[/tex]
= [tex]1 \times 1 \times 0.71^{5}[/tex]
= 0.1804
(d) The probability that at least one has used a computer while under the influence of alcohol is given by = P(X [tex]\geq[/tex] 1)
P(X [tex]\geq[/tex] 1) = 1 - P(X = 0)
= [tex]1-\binom{5}{0}\times 0.29^{0} \times (1-0.29)^{5-0}[/tex]
= [tex]1 -(1 \times 1 \times 0.71^{5})[/tex]
= 1 - 0.1804 = 0.8196
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.
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
What’s the correct answer for this?
Answer:
(2,-2)
Step-by-step explanation:
In the attached file
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
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
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.)
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.
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Angelina read 30% of her book containing 360 pages. How many pages has she read so far
Answer:
108 pages
Step-by-step explanation:
Angelina read 30% of the book that contains 360 pages.
30% of 360 pages
"of" also means multiply, so we must multiply 30% and 360.
30% * 360
Convert 30% to a decimal. Divide 30 by 100, or move the decimal place 2 spots to the left.
30/100=0.30
or
30.0---> 3.0---> 0.30
Plug the decimal in for the percent.
0.30*360
Multiply the 2 numbers together
108
Angelina has read 108 pages so far.
if r is the radius of a circle and d is its diameter which of the following is an equivalent formula for the circumference c = 2 pie r
a C = pie d2
b C = pie rd
c C = pie d
d C = 2 pie d
Answer:
C
Step-by-step explanation:
C=2pier or pied
Answer:
a. C = 2πr
c. C= πd
both are correct
Listed below are head injury measurements from small cars that were tested in crashes. The measurements are in "hic," which is a measurement of a standard "head injury criterion," (lower "hic" values correspond to safer cars). The listed values correspond to cars A, B, C, D, E, F, and G, respectively. Find the
a. mean,
b. median,
c. midrange,
d. mode for the data.
Also complete parts e. and f. 514 541 302 400 507 406 369
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
Listed below are head injury measurements from small cars that were tested in crashes. The measurements are in "hic," which is a measurement of a standard "head injury criterion," (lower "hic" values correspond to safer cars). The listed values correspond to cars A, B, C, D, E, F, and G, respectively.
514 541 302 400 507 406 369
Find the
a. mean,
b. median,
c. midrange,
d. mode for the data.
Also complete parts e. and f.
e. Which car appears to be the safest?
f. Based on these limited results, do small cars appear to have about the same risk of head injury in a crash?
Answer:
a) Mean = 434.14
b) Median = 406
c) Midrange = 421.5
d) Mode = 0
e) Car C appears to be the safest
f) The small cars does not appear to have about the same risk of head injury in a crash.
Step-by-step explanation:
We are given the head injury measurements from small cars that were tested in crashes.
The measurements are in "hic," which is a measurement of a standard "head injury criterion.
The listed values are;
A = 514
B = 541
C = 302
D = 400
E = 507
F = 406
G = 369
a) Mean
The mean of the measurements is given by
Mean = Sum of measurements/ Number of measurements
Mean = (514 + 541 + 302 + 400 + 507 + 406 + 369)/7
Mean = 3039/7
Mean = 434.14
b) Median
Arrange the measurements in ascending order (low to high)
302, 369, 400, 406, 507, 514, 541
The median is given by
Median = (n + 1)/2
Median = (7 + 1)/2
Median = 8/2
Median = 4th
Therefore, the 4th measurement is the median that is 406
Median = 406
c) Mid-range
The midrange is given by
Midrange = (Max + Min)/2
The maximum measurement in the data set is 541
The minimum measurement in the data set is 302
Midrange = (541 + 302)/2
Midrange = 843/2
Midrange = 421.5
d) Mode for the data
The mode of the data set is the most repeated measurement.
302, 369, 400, 406, 507, 514, 541
In the given data set we don't have any repeated measurement therefore, there is no mode or we can say the mode of this data set is 0.
Mode = 0
e) Which car appears to be the safest?
Since we are given that the measurements are in "hic," which is a measurement of a standard "head injury criterion," (lower "hic" values correspond to safer cars)
The lowest hic value corresponds to car C that is 302
Therefore, car C appears to be the safest among other cars.
f) Based on these limited results, do small cars appear to have about the same risk of head injury in a crash?
302, 369, 400, 406, 507, 514, 541
As you can notice, the hic values differ a lot from each other therefore, we can conclude that the small cars does not appear to have about the same risk of head injury in a crash.
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
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.
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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]
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.
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
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)
what is the output from the following machine when the input is 4
Answer:
4 - 7 = -3
-3 / 3 = -1
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
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
: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.
