Answer:
Step-by-step explanation:
a) For private colleges,
Mean = (52.8 + 30.6 + 43.2 + 45.8 + 45.0 + 37.8 + 33.3 + 50.5 + 44.0 + 42.0)/10 = 42.5
x1 = 42.5 × 1000 = 42500
Standard deviation = √(summation(x - mean)²/n
n = 10
Summation(x - mean)² = (52.8 - 42.5)^2 + (30.6 - 42.5)^2 + (43.2 - 42.5)^2 + (45.8 - 42.5)^2 + (45.0 - 52.5)^2 + (37.8 - 42.5)^2 + (33.3 - 42.5)^2 + (50.5 - 42.5)^2 + (44.0 - 42.5)^2 + (42.0 - 52.5)^2 = 598.56
standard deviation = √(598.56/10 = 7.74
s1 = 7.74 × 1000 = 7740
For public colleges,
Mean = (20.3 + 22.8 + 22.0 + 25.8 + 28.2 + 18.5 + 15.6 + 25.6 + 24.1 + 14.4 28.5 + 21.8)/12 = 22.3
x2 = 22.3 × 1000 = 22300
n2 = 12
Summation(x - mean)² = (20.3 - 22.3)^2 + (22.8 - 22.3)^2 + (22 - 22.3)^2 + (25.8 - 22.3)^2 + (28.2 - 22.3)^2 + (18.5 - 22.3)^2 + (15.6 - 22.3)^2 + (25.6 - 22.3)^2 + (24.1 - 22.3)^2 + (14.4 - 22.3)^2 + (28.5 - 22.3)^2 + (21.8 - 22.3)^2 = 225.96
standard deviation = √(225.96/12 = 4.34
s2 = 4.34 × 1000 = 4340
b) The point estimate is the difference between the sample means
Point estimate = 42500 - 22300 = 20200
The best guess for the difference in population mean annual cost of attending private and public colleges is $20200. The range of the value is determined by the margin of error.
c) Confidence interval = point estimate ± margin of error
Margin of error = z√(s²/n1 + s2²/n2)
Where z is the test score for 95% confidence level from the t distribution table. To find the test score, we would first find degree of freedom, df
df = (n1 - 1) + (n2 - 1) = (10 - 1) + (12 - 1) = 20
From the t distribution table,
z = 2.086
Margin of error = 2.086√(7.74²/10 + 4.34²/12) = 4.84
4.84 × 1000 = 4840
Confidence interval = 20200 ± 4840
Juanita wants to buy 12.5 pounds of stones to decorate her garden. The stone normally sells for $1.80 a pound. The salesman offers her a total price of $21.25. How much is she saving per pound with the salesman’s offer? Round to the nearest hundredth.
Answer:
She is saving 10 cents per pound
Step-by-step explanation:
First, we need to find how much she would pay without the sale:
12.5(1.8) = 22.5
Now, we can calculate how much she saved:
22.5 - 21.25 = 1.25
To find how much she's saving per pound, we divide the difference by the number of pounds:
1.25/12.5 = 0.1
She is saving 10 cents per pound
Answer:
A
Step-by-step explanation:
I took the test and got it right
In the morning, Marco sold 12 cups of lemonade for $3. By the end of the day, he had earned $9. How many cups of lemonade did he sell in all? Kaycee wrote the proportion 12/3=9/c for this situation identifly the error and give tow ways to write the proportion correctly
Answer:
36 cups
3/12 = 9/c
Step-by-step explanation
3 ÷ 12 = .25
each cup = 25 cents
9 ÷ .25 = 36
Marco sold 36 cups of lemonade.
3/12 = 9/c
Answer:
36 cups
Step-by-step explanation:
We can set up a proportion:
12/3=c/9
Cross multiply.
12*9=3*c
108=3c
Divide both sides by 3.
c=36
The error that the proportion Kaycee set up was
cups/price=price/cups
This is not proportionate.
Possible proportions include:
cups/price=cups/price
price/cups=price/cups
cups/cups=price/price
price/price=cups/cups
Which two equations are the equations of vertical asymptotes of the function y = 5∕3 tan(3∕4x)?
A) x-2pi/3 and x=-2pi/3
B) x=0 and x=2pi/3
C) x=4pi/3 and x =4pi/3
D) x=0 and x=4pi/3
I did not know how to paste the pi symbol so I used the letters (pi)
Answer:
A)x=2pi/3 and x=-2pi/3
Step-by-step explanation:
The function [tex]y=\frac{5}{3}tan(\frac{3}{4}x)[/tex] has vertical asymptotes in the values where the tan(a) has vertical asymptotes.
we know that tan(a) has vertical asymptotes in [tex]a=\frac{\pi }{2}[/tex] and [tex]a=\frac{-\pi }{2}[/tex], if we made [tex]a=\frac{3x}{4}[/tex] and solve for x, we get:
for [tex]a=\frac{\pi }{2}[/tex]
[tex]\frac{\pi }{2} =\frac{3x}{4}\\x = \frac{2\pi }{3}[/tex]
for [tex]a=\frac{-\pi }{2}[/tex]
[tex]\frac{-\pi }{2} =\frac{3x}{4}\\x = \frac{-2\pi }{3}[/tex]
Finally, the function [tex]y=\frac{5}{3}tan(\frac{3}{4}x)[/tex] has vertical asymptotes in the values x=2pi/3 and x=-2pi/3
Answer:
A
Step-by-step explanation:
The mayor of a town has proposed a plan for the construction of an adjoining community. A political study took a sample of 900 voters in the town and found that 45% of the residents favored construction. Using the data, a political strategist wants to test the claim that the percentage of residents who favor construction is over 42%. Determine the P-value of the test statistic. Round your answer to four decimal places.
Answer:
P-value = 0.0367
Step-by-step explanation:
This is a hypothesis test for a proportion.
The claim is that the percentage of residents who favor construction is significantly over 42%.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.42\\\\H_a:\pi>0.42[/tex]
The sample has a size n=900.
The sample proportion is p=0.45.
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.42*0.58}{900}}\\\\\\ \sigma_p=\sqrt{0.000271}=0.016[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.45-0.42-0.5/900}{0.016}=\dfrac{0.029}{0.016}=1.79[/tex]
This test is a right-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z>1.79)=0.0367[/tex]
what is the surface area of the prism shown to the left?
(idk the answer i guessed)
Answer:
828
Step-by-step explanation:
Missing leg of triangle:
√15²-12²= √225-144=√81=9
Triangle faces= 2*1/2*12*9= 108
Base= 20*9= 180
Front face= 20*15= 300
Back face= 20*12= 240
Total= 108+180+300+240= 828
Second choice
Given the equation A=250(1.1)t, you can determine that the interest is compounded annually and the interest rate is 10%. Suppose the interest rate were to change to being compounded quarterly. Rewrite the equation to find the new interest rate that would keep A and P the same. What is the approximate new interest rate? Convert your answer to a percentage, round it to the nearest tenth, and enter it in the space provided, like this: 42.53%
Answer:
[tex]r \approx 2.41\%[/tex]
Step-by-step explanation:
The computation of the approximate new interest rate is shown below:
As we know that there are four quarters in a year so
The new equation is
[tex]A = 250(1 + r)^{4t}[/tex]
Now to determine the value of interest rate,i.e r, so place this to the first equation.
So,
[tex]250(1.1)^{t} = 250(1 + r)^{4t}[/tex]
[tex]1.1^{t} = (1 + r)^{4t}[/tex]
1.1 = (1 + r)^4
[tex]\sqrt[4]{1.1} = 1 + r[/tex]
[tex]r = -1 + \sqrt[4]{1.1}[/tex]
[tex]r \approx 0.0241[/tex]
[tex]r \approx 2.41\%[/tex]
We simply applied the above formula so that the interest rate could come
i will give brainliest and 50 points pls help ASP
Answer:
Step-by-step explanation:
A trapezoid and two rectangulars are in the opening form of the geometric shapes and you should calculate their surface areas seperately which is:
12 cm and 30 cm first rectangular and its surface area is 12 x 30 = 360 cm^2second rectangular has 30 cm and 26 cm and 30 x 26 = 780 cm^2A trapezoid surface area is = [(24+29) /2] * 25 = 662.5 cm^2total surface area = 360 + 780 + 662.5 = 1802.5Answer:
Total surface area = 3744 cm^2
Step-by-step explanation:
All linear measurements are in cm
Surface area of BOTH bases
Ab = 2* (12+29)*24/2
= 984
Circumference of base
Cb = (25+12+26+29)
= 92
Height of prism
H = 30 (given)
Surface area of sides of prism
As= Cb*H
= 2760
Total Surface area of Prism
A = Ab + As
= 984 + 2760
= 3744 cm^2
Copy the diagram and oaloulate the sizes of
a bº and cº. What is the sum of the angles of
the triangle?
Answer:
sum of the angles of the triangle are 180°
Step-by-step explanation:
To find the sum of the interior angles, we use the formula( s-2*180), where s is the number of sides of the shape. If it is a pentagon, 5-2*180= 3*180= 540,
which shows that the sum of the interior angles of a pentagon is 540.
since, it is a triangle in the figure with 3 sides, 3-2*180=1*180=180.
The interior angles are unknown= a, b and c. we know that a+b+c=180 degrees and the exterior angles are mentioned. And we know that, opposite angles are equal. So, a is 40 degrees considering that 40 degrees is the opposite angle of a, b is 95 degrees whereas c is 45 degrees.
now, lets check if the angles indeed have a sum of 180 degrees,
40+95+45= 135+45 which gives 180 degrees.
Answer:
180°
Step-by-step explanation:
→ Angles in a triangles always add up to 180, we can prove this by calculating a, b and c so,
a = 40° (vertical angles are equal)
b = 95° (vertical angles are equal)
c = 45° (vertical angles are equal)
40 + 45 + 95 = 85 + 95 = 180°
Kurtis is a statistician who claims that the average salary of an employee in the city of Yarmouth is no more than $55,000 per year. Gina, his colleague, believes this to be incorrect, so she randomly selects 61 employees who work in Yarmouth and records their annual salaries. Gina calculates the sample mean income to be $56,500 per year with a sample standard deviation of 3,750. Using the alternative hypothesis Ha:μ>55,000, find the test statistic t and the p-value for the appropriate hypothesis test. Round the test statistic to two decimal places and the p-value to three decimal places.
Degrees of Freedom
0.0004 0.0014 0.0024 0.0034 0.0044 0.0054 0.0064
54 3.562 3.135 2.943 2.816 2.719 2.641 2.576
55 3.558 3.132 2.941 2.814 2.717 2.640 2.574
56 3.554 3.130 2.939 2.812 2.716 2.638 2.572
57 3.550 3.127 2.937 2.810 2.714 2.636 2.571
58 3.547 3.125 2.935 2.808 2.712 2.635 2.569
59 3.544 3.122 2.933 2.806 2.711 2.633 2.568
60 3.540 3.120 2.931 2.805 2.709 2.632 2.567
Answer:
Test statistic t = 3.12
P-value = 0.001
As the P-value (0.001) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the average salary of an employee in the city of Yarmouth is is significantly greater than $55,000 per year.
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the average salary of an employee in the city of Yarmouth is is significantly greater than $55,000 per year (Gina's claim).
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=55000\\\\H_a:\mu> 55000[/tex]
The significance level is 0.05.
The sample has a size n=61.
The sample mean is M=56500.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=3750.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{3750}{\sqrt{61}}=480.138[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{56500-55000}{480.138}=\dfrac{1500}{480.138}=3.12[/tex]
The degrees of freedom for this sample size are:
df=n-1=61-1=60
This test is a right-tailed test, with 60 degrees of freedom and t=3.12, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t>3.12)=0.001[/tex]
As the P-value (0.001) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the average salary of an employee in the city of Yarmouth is is significantly greater than $55,000 per year.
Find the value of x
Answer:
8
Step-by-step explanation:
the value of x is 8 because the sides are the same
Which of the following represents the ratio of the hypotenuse to the given side?
Answer:c
Step-by-step explanation:
hyp=6[tex]\sqrt{2}[/tex]
adj=6
hyp:adj=6[tex]\sqrt{2}[/tex] :2
hyp:adj=[tex]\frac{6\sqrt{2} }{6} \\[/tex]
[tex]=\frac{\sqrt{2} }{1} \\hyp:adj=\sqrt{2} :1[/tex]
Melvin has game and education apps on his tablet. He noticed that he has 3 game apps for every 2 education apps. Which of the following is another way to write this ratio? 1:2 2:1 2:3 3:2
3:3
Answer:
3: 2
Step-by-step explanation:
game Apps: education apps:
3: 2
Randomthing2143 help me please! Range of: 1, 2, 3, 1, 5, 2, 1, 8, 9, 7?
Answer:
8solution,
Highest score=9
lowest score=1
now,
range= highest score-lowest score
=9-1
=8
Hope this helps...
Answer:
8
Step-by-step explanation:
The range of the sequence is the largest number - the smallest number.
The largest number is 9.
The smallest number is 1.
9 - 1
= 8
The range of the sequence is 8.
helppppppppp hurryyyyyyyyyyyyyyyyyyyyyyyy
Answer:
2
Step-by-step explanation:
I would have to say it is two bc Everitt had 30% where Desery had 20%.
Look at the picture for the question ........................
Answer:
53/28
Step-by-step explanation:
100 g jam
19 g strawberries53 g blackberriesSugar= 100-(19+53)= 28 gBlackberry / sugar= 53/28
Answer:
53:28Solution,
Amount of sugar=100-(19+53)
=100-72
=28 gram
Ratio of blackberries to sugar=53/28
=53:28
Hope this helps..
Good luck on your assignment..
use the drop downs to identify the domain and range of the following relation.
{(-4, -7), (0, 6), (5, -3), (5, 2)}
Answer:Domain is x and range is y.For ex:-4 is domain and -7 is range.
Step-by-step explanatioFeel pleasure to help u:
Domain ( -4, 5) Range ( -7, 6)
The Domain includes the numbers between the least and the greatest x-values.
The range includes the numbers between the lowest and the highest y-values.
It is known that 10% of the calculators shipped from a particular factory are defective. What is the probability that exactly three of five chosen calculators are defective
Answer:0.0081 or 0.81%
Step-by-step explanation:
The required probability is P(3,5,0.1)= C5 3 * p^3*q^2, where
C5 3= 5!/3/2=4*5/2=10
p is the probability that one randomly selected calculator is defective= 10%=0.1
q is the probability that one randomly selected calculator is non-defective.
q=1-p=1-0.1=0.9
So P(3,5,0.1)= 10*0.1^3*0.9^2=0.01*0.81=0.0081
Sales personnel for Skillings Distributors submit weekly reports listing the customer contacts made during the week. A sample of 65 weekly reports showed a sample mean of 17.5 customer contacts per week. The sample standard deviation was 4.2.
Required:
Provide 90%90% and 95%95% confidence intervals for the population mean number of weekly customer contacts for the sales personnel.
Answer:
Since the Confidence is 0.90 or 90%, the value of [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and the critical value would be [tex]t_{\alpha/2}=1.669[/tex]
And replacing we got
[tex]17.5-1.669\frac{4.2}{\sqrt{65}}=16.63[/tex]
[tex]17.5+1.669\frac{4.2}{\sqrt{65}}=18.37[/tex]
For the 95% confidence the critical value is [tex]t_{\alpha/2}=1.998[/tex]
[tex]17.5-1.998\frac{4.2}{\sqrt{65}}=16.46[/tex]
[tex]17.5+1.998\frac{4.2}{\sqrt{65}}=18.54[/tex]
Step-by-step explanation:
Information given
[tex]\bar X¿ 17.5[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
s¿4.2 represent the sample standard deviation
n¿65 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom are given by:
[tex]df=n-1=65-1=64[/tex]
Since the Confidence is 0.90 or 90%, the value of [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and the critical value would be [tex]t_{\alpha/2}=1.669[/tex]
And replacing we got
[tex]17.5-1.669\frac{4.2}{\sqrt{65}}=16.63[/tex]
[tex]17.5+1.669\frac{4.2}{\sqrt{65}}=18.37[/tex]
For the 95% confidence the critical value is [tex]t_{\alpha/2}=1.998[/tex]
[tex]17.5-1.998\frac{4.2}{\sqrt{65}}=16.46[/tex]
[tex]17.5+1.998\frac{4.2}{\sqrt{65}}=18.54[/tex]
algebra ...........................
Answer:
see explanation
Step-by-step explanation:
Given that y is inversely proportional to x then the equation relating them is
y = [tex]\frac{k}{x}[/tex] ← k is the constant of proportion
(a)
To find k use the condition when y = 7 , x = 9, that is
7 = [tex]\frac{k}{9}[/tex] ( multiply both sides by 9 )
63 = k
y = [tex]\frac{63}{x}[/tex] ← equation of proportion
(b)
When x = 21, then
y = [tex]\frac{63}{21}[/tex] = 3
Select the correct answer. If g = 8, what is the value of the expression g/2+3 ? A. 8/5 B.11/2 C. 7 D. 19
Answer:
7Option C is the correct option
Step-by-step explanation:
g = 8 ( given )
Now,
[tex] \frac{g}{2} + 3[/tex]
Plugging the value of g
[tex] \frac{8}{2} + 3[/tex]
[tex] \frac{8 + 3 \times 2}{2} [/tex]
[tex] \frac{8 + 6}{2} [/tex]
[tex] \frac{14}{2} [/tex]
[tex]7[/tex]
Hope this helps...
Good luck on your assignment...
ALGEBRA Identify the similar triangles. Then find each measure.
FG
S
G
6
х
R
4
T
F
10
H
ARST - AFGHFG = 11
ARST - AFGHFG = 14
ARST - AFGH FG = 15
ARST- AFGH FG = 18
Answer:
fg t f h 10
Step-by-step explanation:
A department store chain is expanding into a new market, and is considering 13 different sites on which to locate 5 stores. Assuming that each site is equally likely to be chosen, in how many ways can the sites for the new stores be selected?
Answer:
Hope it helps you :)
And i hope you understand
For store 1, it can be placed on 16 sites. Store 2 can be placed on 15 sites( since store 1 is already on site 1). Store 3 can be placed on 14 sites and so on until store 5 which has 12 sites.
Therefore the number of way is
C= 16*15*14*13*12
c=524,160 possibilities
Which of the following statements is false regarding randomization?
Answer:b
Step-by-step explanation:
The graph of y = 1/2 x2 + 2x + 3 is shown. What are the solutions to the equation 1/2 x2 + 2x + 3 = x + 7?
Answer:
Step-by-step explanation:
Let's organise our information :
the function is (1/2)x²+2x+3we want to khow the value of x that gives us : (1/2)x²+2x+3=x+7
Now the trick is to write this expression as a quadratic equation with zero at one side :
(1/2)x²+2x+3=x+7 (1/2)x²+2x+3-x-7=0(1/2)x²+x-4=0Now let's solve this equation :
a= 1/2b= 1c= -4Δ=1²-4*(1/2)*(-4)
= 9
So we have two solutions :
[tex]\left \{ {{y=\frac{-1-3}{2*0.5} } \atop {x=\frac{-1+3}{2*0.5} }} \right.[/tex]y= -4x= 2So the solutions are -4 and 2
In a certain city, the true probability of a baby being a boy is 0.559. Among the next eight randomly selected births, find the probability that at least one of them is a boy. (round to three decimal places)
Answer:
99.86%
Step-by-step explanation:
What we have here is a binomial distribution, let x be the baby number among 8 births.
Binomial (n = 8, p = 0.559)
We want to find, P (X ≥ 1)
P (X ≥ 1) = 1 - P (X <1)
P (X ≥ 1) = 1 - P (X = 0)
P (X = 0) = 8C0 * (0.559) ^ 0 * (1 - 0.559) ^ (8-0)]
8C0 = 8! / (0! * (8-0)!) = 1
replacing we have:
P (X = 0) = 1 * 1 * 0.0014
P (X = 0) = 0.0014
P (X ≥ 1)) = 1 - 0.001 4
P (X ≥ 1) = 0.9986
Therefore the probability is 99.86%
Evaluate. Write your answer as a fraction or whole number without exponents. 3^–3 =
Answer:
The answer is 1/27
Step-by-step explanation:
According to the rules of indices
a^-b can be written as 1/a^b
So 3^- 3 can be written as 1/3³
And
1/3³ = 1/27
Hope this helps you
How do I calculate velocity?
Answer:
v = Δs/Δt
Step-by-step explanation:
Velocity is equal to the displacement/distance (delta symbol s) over the change of time (delta symbol t).
Could someone explain how to find square roots please?
Answer: graphing calculator!
Step-by-step explanation: if you’re looking for the square root of a # that isn’t a perfect square (ie. sqrt4, sqrt 36) then you have to use a calculator for that. however the idea behind square roots is just a # multiplied by itself to give the original #. just ask yourself “what can i multiply by itself to get the original number”. hope that helped !
Answer:
By multiplying the number by its power 2.
E.g= 4^2
A 6-digit number has at least one even digit in its record. How many such numbers are there? (0 is an even digit)
Answer:
884,375
Step-by-step explanation:
The first digit can't be 0, so there are 9×10⁵ = 900,000 possible six-digit numbers.
Of those, the number of six-digit numbers that have only odd digits is 5⁶ = 15,625.
Numbers with at least one even digit are all numbers that don't have only odd digits. So the number of six-digit numbers with at least one even digit is:
900,000 − 15,625 = 884,375
Quadrilaterals WXYZ and BADC are congruent. In addition, WX ≅ DC and XY ≅ BC.
If AD = 4 cm and AB = 6 cm, what is the perimeter of WXYZ?
18 cm
20 cm
22 cm
24 cm
Answer: 20 cm
If quadrilaterals WXYZ and BADC are congruent, then their corresponding sides are congruent.
Given that
WX≅DC,
XY≅BC,
you can state that
YZ≅AB,
WZ≅AD.
If AD = 4 cm and AB = 6 cm, then WZ = 4 cm and YZ = 6 cm. Opposite rectangle sides are congruent, then XY = 4 cm and WX = 6 cm.
The perimeter of WXYZ is
P = WX + XY + YZ + WZ = 6 + 4 + 6 + 4 = 20 cm.