Small sample: During an economic downturn, companies were sampled and asked whether they were planning to increase their workforce. Only of the companies were planning to increase their workforce. Use the small-sample method to construct a confidence interval for the proportion of companies that are planning to increase their workforce. Round the answers to at least three decimal places. A confidence interval for the proportion of companies that are planning to increase their workforce is .
Answers
Complete Question
The complete question is shown on the first uploaded image
Answer:
The confidence level interval is [tex]0.016 \le C \le 0.404[/tex]
Step-by-step explanation:
The sample size is [tex]n = 20[/tex]
The number planning to increase workforce is [tex]x = 3[/tex]
The confidence level is [tex]c = 98[/tex]%
The value of proportion for a plus 4 method is
[tex]p = \frac{x+2}{n+4}[/tex]
substituting values
[tex]p = \frac{3+2}{20+4}[/tex]
[tex]p =0.21[/tex]
The z-critical value at confidence level of 98% is
[tex]z_{c}=z_{0.98} = 2.33[/tex]
This values is obtained from the standard normal table
The confidence level interval can be mathematically represented as
[tex]C =p \ \pm z_{c} * \sqrt{\frac{p(1-p)}{n+4} }[/tex]
substituting values
[tex]C = 0.21 \pm 2.33 * \sqrt{\frac{0.21(1- 0.21)}{20 +4} }[/tex]
[tex]C = 0.21 \pm 0.194[/tex]
=> [tex]0.016 \le C \le 0.404[/tex]
Related Questions
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answers
Answer:
D. Yes; the graph passes the vertical line test.
Step-by-step explanation:
→The vertical line test is when you hold something (like a pencil), straight up/vertically, and you move it from left-to-right to see if any two points repeat.
→The correct answer is "D. Yes; the graph passes the vertical line test," because the x-values can't repeat, not the y-values, if the graph were to show a function. In this case, the graph passes the vertical line test.
what is 2n+3n +1 +8n+4
Answers
If you need it simplified it would be 13n+5
Please tell me or you need it solved
Answer:
13n + 5
Step-by-step explanation:
2+3+8 = 13n
1+4 = 5
13n+5
Three spinners numbered 1 through 12 are spun. What is the probability of spinning a five on the first spinner, an even number on the second spinner, and a multiple of 4 on the third spinner?
1/96
1/72
7/12
5/6
Answers
Answer:
[tex]\frac{1}{96}[/tex]
Step-by-step explanation:
Spinning a 5 is [tex]\frac{1}{12}[/tex]
Spinning even is [tex]\frac{1}{2}[/tex]
Spinning multiple of 4 is [tex]\frac{1}{4}[/tex]
[tex]\frac{1}{12} *\frac{1}{2} *\frac{1}{4}[/tex][tex]=\frac{1}{96}[/tex]
Which value of k makes 5-k+12=16 a true statement? Choose 1 answer: Choice A) k=1 (Choice B) k=2 (Choice C) k=3 (Choice D) k=4
Answers
Answer:
A) k=1
Step-by-step explanation:
5-k+12=16
17-k=16
k=1
Answer:
k=1
Step-by-step explanation:
5-k+12=16
Combine like terms
17 - k = 16
Subtract 17 from each side
17-k-17 = 16-17
-k = -1
Divide by -1
k = 1
A powerful computer is purchased for $2000, but loses 20% of its value each year. How much will it be worth 4 years from now?
a. Growth or Decay?
b. What is your multiplier?
c. Is $2000 your zero term or first term? term
d. Write the equation. (do not use spaces in your response; example: f(x)=10.2(1.22)^x )
e. Solve
Answers
Answer:
(A)Decay
(b)0.8
(c)First Term
(d)[tex]f(t)=2000(0.8)^t[/tex]
(e)$819.20
Step-by-step explanation:
The exponential function for modelling growth or decay is given as:
[tex]A(t)=A_o(1\pm r)^t[/tex],
Where:
Plus indicates growth and minus indicates decay.
[tex]A_o$ is the Initial Value\\r is the growth/decay rate\\t is the time period[/tex]
For a powerful computer that was purchased for $2000, but loses 20% of its value each year.
(a)Since it loses value, it is a decay.
(b)Multiplier
Its value decays by 20%.
Therefore, our multiplier(1-r) =(1-20&)=1-0.2
Multiplier =0.8
(c)$2000 is our First term (or Initial Value [tex]A_o[/tex])
(d)The function for this problem is therefore:
[tex]f(t)=f_o(1- r)^t\\f(t)=2000(1- 0.2)^t\\\\f(t)=2000(0.8)^t[/tex]
(e)Since we require the worth of the computer after 4 years,
t=4 years
[tex]f(4)=2000(0.8)^4\\f(4)=\$819.20[/tex]
Peggy had four times as many quarters as nickels. She had $2.10 in all. How many nickels and how many quarters did she have?
If the variable n represents the number of nickels, then which of the following expressions represents the number of quarters?
Answers
Answer:
2 nickels8 quartersStep-by-step explanation:
If n represents the number of nickels, and the number of quarters is 4 times the number of nickels, then the number of quarters is represented by 4n.
The total value of the coins in cents is ...
5(n) +25(4n) = 210
105n = 210 . . . . . . . . collect terms
n = 210/105 = 2 . . . . number of nickels
4n = 4(2) = 8 . . . . . . number of quarters
Peggy has 2 nickels and 8 quarters.
The city manager of Shinbone has received a complaint from the local union of firefighters to the effect that they are underpaid. Not having much time, the city manager gathers the records of a random sample of 27 firefighters and finds that their average salary is $38,073 with a standard deviation of $575. If she knows that the average salary nationally is $38,202, how can she respond to the complaint
Answers
Answer:
She can answer, after performing the hypothesis test, that there is not enough evidence to support the claim that the city firefighters salary is significantly lower than the national average.
Step-by-step explanation:
She can statistically test the claim of the firefighters to see if it has statistical evidence.
This is a hypothesis test for the population mean.
The claim is that the city firefighters salary is significantly lower than the national average.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=38202\\\\H_a:\mu< 38202[/tex]
The significance level is 0.1. Is less conservative than 0.05, for example, so if there is little evidence, the null hypothesis with be rejected.
The sample has a size n=27.
The sample mean is M=38073.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=575.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{575}{\sqrt{27}}=110.659[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{38073-38202}{110.659}=\dfrac{-129}{110.659}=-1.17[/tex]
The degrees of freedom for this sample size are:
df=n-1=27-1=26
This test is a left-tailed test, with 26 degrees of freedom and t=-1.17, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t<-1.17)=0.127[/tex]
As the P-value (0.127) is bigger than the significance level (0.1), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the city firefighters salary is significantly lower than the national average.
According to the Rational Root Theorem, Negative two-fifths is a potential rational root of which function?
f(x) = 4x4 – 7x2 + x + 25
f(x) = 9x4 – 7x2 + x + 10
f(x) = 10x4 – 7x2 + x + 9
f(x) = 25x4 – 7x2 + x + 4
Answers
Answer:
Neither expression satisfies the given rational root.Step-by-step explanation:
To find the right answer, we just need to replace the given root in each expression and see which one gives zero.
First expression.[tex]f(x)=4x^{4} -7x^{2} +x+25\\f(-\frac{2}{5})= 4(-\frac{2}{5})^{4} -7(-\frac{2}{5})^{2} +(-\frac{2}{5})+25=\frac{64}{625}-\frac{28}{25} -\frac{2}{5} +25 \approx 23.58[/tex]
Second expression.[tex]f(x)=9x^{4}-7x^{2} +x+10=9(-\frac{2}{5} )^{4} -7(-\frac{2}{5} )^{2} +\frac{2}{5} +10 \approx 9.5[/tex]
Third expression.[tex]f(x)=10x^{4}-7x^{2} +x+9=10(-\frac{2}{5} )^{4} -7(-\frac{2}{5})^{2} +(-\frac{2}{5})+9 \approx 7.7[/tex]
Fourth expression.[tex]f(x)=25x^{4}-7x^{2} +x+4=25(-\frac{2}{5} )^{4} -7(-\frac{2}{5})^{2} +(-\frac{2}{5})+4 \approx 3.12[/tex]
Therefore, neither expression satisfies the given rational root.
Answer:
D. f(x) = 25x^4 - 7x^2 + x + 4.
Step-by-step explanation:
The correct answer to your question is D.
The weight of an
object on Earth varies
directly as the weight
of that object on the
B moon. If a 150-1b
object would weigh
24 lbs on the moon,
how much would a 95-
lb object weigh on the
moon?
Answers
Answer:
15.2 lbs
Step-by-step explanation:
Make a ratio: 150 : 24 = 95 : x
[tex]\frac{75}{12}=\frac{95}{x}[/tex]
75x = 1140
x = 15.2
A bank wants to attract new customers for its credit card. The bank tries two different approaches in the marketing campaign. The first promises a cash back reward; the second promises low interest rates. A sample of 500 people is called the first brochure; of these, 100 get the credit card. A separate sample of 500 people is called the second brochure; 125 get the credit card. The bank wants to know if the two campaigns are equally attractive to customers. What is a 95% confidence interval for the difference in the two proportions
Answers
Answer:
Step-by-step explanation:
Confidence interval for the difference in the two proportions is written as
Difference in sample proportions ± margin of error
Sample proportion, p= x/n
Where x = number of success
n = number of samples
For the first brochure,
x = 100
n1 = 500
p1 = 100/500 = 0.2
For the second brochure
x = 125
n2 = 500
p2 = 125/500 = 0.25
Margin of error = z√[p1(1 - p1)/n1 + p2(1 - p2)/n2]
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.025 = 0.975
The z score corresponding to the area on the z table is 1.96. Thus, the z score for confidence level of 95% is 1.96
Margin of error = 1.96 × √[0.2(1 - 0.2)/500 + 0.25(1 - 0.25)/500]
= 1.96 × √0.000695
= 0.052
Confidence interval = (0.2 - 0.25) ± 0.052
= - 0.05 ± 0.052
Method 1: Long Division (x^2+3x-43) / (x+8
Answers
Answer:
x - 5 - (3/x+8)
Step-by-step explanation:
Answer:
Step-by-step explanation:
What’s the correct answer for this? Select two answers that, when combined, show that circles are similar
Answers
Answer:
A and F
Step-by-step explanation:
First we'll dilate it by a scale factor of 2. After that, we'll translate in 6 units left and 6 units up to map circle J onto circle K
A cell phone company is offering 2 different monthly plans. Each plan charges a monthly fee plus an additional cost per minute. Plan A: $ 40 fee plus $0.45 per minute Plan B: $70 fee plus $0.35 per minute a) Write an equation to represent the cost of Plan A b) Write an equation to represent the cost of Plan B c) Which plan would be least expensive for a total of 100 minutes?
*Please Show Work*
Answers
Answer:
Plan A would be the least expensive
Step-by-step explanation:
Plan A= $0.45x100= 45, 45+40=$85
Plan B= $0.35x100= 35, 35+70= %105
(Each plan is for 100 minutes)
what is Associative propert
Answers
Answer:
Associative property of multiplication is the grouping of numbers being multiplied can be changed without affecting the product.
here is an example!
Addison Rae work using the associative property:
(-8.5)(5)(-4) =
(-8.5)(-20) =
170
hope this helped it was from my FLVS schooling :)
What is the value of ¡97 - i?
Answers
Answer:
This is the answer
Step-by-step explanation:
Akmal, Bakri and Cadin share their mother medical expenses which cost RM4200. Cadin pays RM2100 while akmal pays three quarters of Bakri amount. Find the ratio of the expenses shared by Akmal to Bakri to Cadin
Answers
Answer:
The ratio of the expenses shared by Akmal to Bakri to Cadin is 7 : 4 : 3
Step-by-step explanation:
The 3 of them shares their mother medical expenses which cost RM4200 . There mother medical expenses is RM4200 in total. Cadin pays RM2100 which is half of their mother medical expenses. Then Akmal pays three quarters of Bakri amount.
Let
The amount Bakri pays = a
Akmal pays = 3/4 of a
Akmal pays = 3/4a
Therefore,
a + 3a/4 = 2100
4a + 3a/ 4 = 2100
7a/4 = 2100
cross multiply
7a = 8400
divide both sides by 7
a = 8400/7
a = 1200
Therefore,
Bakri pays =RM 1200
Akmal pays = 3/4 × 1200 =RM 900
The ratio of the expenses shared by AKmal to Bakri to Cadin is expressed as 2100 : 1200 : 900. Divide through by 300
7 : 4 : 3
What is the value of lifeee, and when do you think corona will stop! Will mark brainliest cuz why not
Answers
Answer:
LIFE: Your life purpose consists of the central motivating aims of your life—the reasons you get up in the morning. Purpose can guide life decisions, influence behavior, shape goals, offer a sense of direction, and create meaning. For some people, purpose is connected to vocation—meaningful, satisfying work. Also always be your self (:
Corona: I think corona depending on were you live will stop next year when they find a treatment for it.
Hope this helped!
Answer:
Your life is the most important thing. It shouldn't be worth 1 million dollars, or even 1 billion dollars, because it's worth everything.
Corona can't really stop. It's a matter of the government to try to contain the virus, so it won't spread even further. I think the right time to reopen the economy is when we find a vaccine. But of course, places all over the U.S. are already reopening which will cause a spike in cases, therefore making our "self-isolation" even longer.
Is 3/5 A.irrational, B.rational, C.natural and whole, or D.natural, whole integer and rational
Answers
Answer:
B
Step-by-step explanation:
3/5 is a fraction, meaning it isn't irrational, natural, whole or an integer, therefore the answer is rational (B).
Answer:
B.rational
Step-by-step explanation:
3/5 is written as a fraction so it is a rational number
It is not a whole number since it is a reduced fraction that is less than 1
Assume that when adults with smartphones are randomly selected, 53% use them in meetings or classes. If 7 adult smartphone users are randomly selected, find the probability that exactly 5 of them use their smartphones in meetings or classes.
Answers
Answer:
[tex]P(X=5)=(7C5)(0.53)^5 (1-0.53)^{7-5}=0.194[/tex]
Then the probability that exactly 5 of them use their smartphones in meetings or classes is 0.194
Step-by-step explanation:
Let X the random variable of interest "number of adults with smartphones", on this case we now that:
[tex]X \sim Binom(n=7, p=0.53)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
And we want to find this probability:
[tex] P(X=5)[/tex]
Using the probability mass function we got:
[tex]P(X=5)=(7C5)(0.53)^5 (1-0.53)^{7-5}=0.194[/tex]
Then the probability that exactly 5 of them use their smartphones in meetings or classes is 0.194
Leroy is 22 years old. His car averages 31 miles
per gallon. His car payments are $165.32 per
month, and he has 36 more payments to
make. How old will he be when he pays off his
car?
Answers
Answer:
he will be 25
Step-by-step explanation:
36 monthly payments left/12 payments a year = 3 years. 22 + 3 = 25
ps help me with this its urgent❤
Use the properties of exponents to simplify the expression. (photo attached)
Answers
Answer:
y^6/x^2
Step-by-step explanation:
(y^3/2x^-1/2)^4= y^(4*3/2)x^(-1/2*4)=y^6x^-2= y^6/x^2
Classify the triangle by its sides, and then by its angles.
7 m
7 m
9.9 m
Classified by its sides, the triangle is a(n)
▼
isosceles
scalene
equilateral
triangle.
Classified by its angles, the triangle is a(n)
▼
acute
right
obtuse
triangle.
Answers
Answer:
isosceles
Step-by-step explanation:
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answers
Answer:
G(x) = x^2 -10x +25
Step-by-step explanation:
To translate F(x) 5 units to the right, replace x with (x-5).
G(x) = F(x-5) = (x -5)^2
G(x) = x^2 -10x +25
A hot dog has about 1/4 the amount of protein as 3 ounces of hamburger. Together, they have about 25 grams of protein. How many grams of protein are in a 3 oz hamburger?
Answers
Answer:
(1) protein in hot dog = ¼ * protein in 3 ounces of hamburger
(2) protein in hot dog + protein in 3 ounces of hamburger = 25
So we need to re-arrange (1) and (2) to solve for the protein in 3 ounces of hamburger!
(re-arrange (1)): 4 * protein in hot dog = protein in 3 ounces of hamburger
(re-arrange (2)): protein in hot dog = 25 - protein in 3 ounces of hamburger
(plugging re-arranged (2) into re-arranged (1)):
4 * (25 - protein in 3 ounces of hamburger) = protein in 3 ounces of hamburger ( multiplying )
100- 4 protein in 3 ounces of hamburger = protein in 3 ounces of hamburger
solving for the protein in 3 ounces of hamburger:
5 * protein in 3 ounces of hamburger = 100
protein in 3 ounces of hamburger = 20 gram
Plz help me :(
Prove for any value of y the value of expression y^4−(y^2−9)(y^2+9) is divisible by 9.
Answers
PROOF:
[tex]y^4-(y^2-9)(y^2+9)\\=y^4 -(y^4-81)\\=y^4-y^4+81\\=81[/tex]
And 81 is ALWAYS divisible by 9
Answer:
Its 9*9
Step-by-step explanation:
The equation equals 81 and 9*9=81.
Have a great day! :)
Given fix) = 3x- 1 and g(x) = 2x-3, for which value of x does g(x) = f(2)?
X=
2
О
X= 2
NDI
X=
x=4
Answers
Answer:
The value of X would be 4.
Answer:
x=4
Step-by-step explanation:
f(2)=3*2-1=5
g(x)=2x-3=5
2x=8
x=4
I need help with all three :(
Answers
Answer:
1: Glide
2: Reflection
3: Reflection
Step-by-step explanation:
1): The first one is glide because you are just moving the triangle and not changing anything to the angle and the size.
2): The second one is a reflection because you are reflecting across an invisable line. Basicly think of it as a mirror. In the picture below, you can see the line of reflection.
3): The third one is also a reflection for the same reason as the second, (view attached image below for line of reflection.
Let uequalsleft angle 4 comma negative 3 right angle, vequalsleft angle negative 2 comma 5 right angle, and wequalsleft angle 0 comma negative 6 right angle. Express 7 Bold u minus 5 Bold v plus Bold w in the form left angle a comma b right angle.
Answers
Answer:
[tex]<38,52>[/tex]
Step-by-step explanation:
[tex]u=<4,-3>\\v=<-2,5>\\w=<0,-6>[/tex]
We are required to express 7u-5v+w in the form <a,b>.
[tex]7u-5v+w =7<4,-3>-5<-2,5>+<0,-6>\\=<28,-21>-<-10,25>+<0,-6>\\=<28-(-10)+0, -21-25-6>\\=<38,52>\\$Therefore:$\\7u-5v+w=<38,52>[/tex]
Sarah wants to refurbish her shop.
She is quoted £2500 for the refurbishment, with a 20% discount to be taken off.
What is the final cost of the refurbishment after the discount?
Answers
Answer:
2000
Step-by-step explanation:
2500 / 100 = 25 (1%)
25 X 20 =500 (20%)
2500 - 500 =2000
A loan of $8 000 was repaid in 2 years in
monthly payments of $400.00. The interest
on the loan, as e percentage, was?
Answers
Answer:
P = 8000
t = 2
I = p × r × t
400 = 8000 × r/100 × 2
r = 400/160 per year
r = 40/16 = 2.5 %