Answer:
c. 5.5 years, 0.51 years
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Mean of 5.5 years and a standard deviation of 2.1 years.
This means that, for the population, [tex]\mu = 5.5, \sigma = 2.1[/tex]
Random samples of size 17.
This means that [tex]n = 17[/tex]
Use the Central Limit Theorem to find the mean and standard error of the mean of the indicated sampling distribution.
The mean is the same as the mean for the population, that is, 5.5 years.
The standard deviation is:
[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{2.1}{\sqrt{17}} = 0.51[/tex]
This means that the correct answer is given by option c.
During three consecutive years, an employers salary is increased by 15%. If after three years his salary is 45,400, what was his salary before the raises?
Answer:
$29,851.24
Step-by-step explanation:
The salary started as x.
Each year it was increased 15%.
A full amount is 100% of the amount. When you add 15% to the amount, you now have 115% of the amount.
115% as a decimal is 1.15; that means that to increase an amount by 15%, multiply the amount by 1.15
For example, let's say you want to know what is a 15% increase on 100. Start with 100. 15% of 100 is 15, so if you add 15% to 100 you expect to get 115.
Now multiply 1.15 by 100. You also get 115 showing you that multiplying a number by 1.15 is the same as adding 15%.
Now let's get back to our problem.
The salary started as x.
Each year, the increase in salary was 15% of the previous salary.
After 1 year the salary is 1.15x.
After 2 years, the salary is 1.15(1.15x).
After 3 years, the salary is 1.15(1.15(1.15x)) = (1.15^3)x
We are told that the salary became $45,400 after the three 15% increases, so
(1.15)^3 * x = 45,400
Multiply out 1.15^3 as 1/15 * 1.15 * 1.15 = 1.520875
1.520875x = 45,400
Divide both sides by 1.520875.
x = 45,400/1.520875
x = 29,851.24
Answer: $29,851.24
Think of 5 positive integers that have a mean, median, mode, and range of 6.
Which equation can be simplified to find the inverse of
Answer:
x=y²-7hope it helps.
stay safe healthy and happy...The slope of diagonal OA IS__,
and its equation is__
Answer:
[tex](a)\ m = \frac{4}{3}[/tex] --- slope of OA
[tex](b)\ y = \frac{4}{3}x[/tex] --- the equation
Step-by-step explanation:
Given
The attached graph
Solving (a): Slope of OA
First, we identify two points on OA
[tex](x_1,y_1) = (0,0)[/tex]
[tex](x_2,y_2) = (3,4)[/tex]
So, the slope (m) is:
[tex]m = \frac{y_2 -y_1}{x_2 - x_1}[/tex]
This gives:
[tex]m = \frac{4-0}{3-0}[/tex]
[tex]m = \frac{4}{3}[/tex]
Solving (b): The equation
This is calculated as:
[tex]y = m(x - x_1) + y_1[/tex]
Recall that:
[tex](x_1,y_1) = (0,0)[/tex]
[tex]m = \frac{4}{3}[/tex]
So, we have:
[tex]y = \frac{4}{3}(x - 0) + 0[/tex]
[tex]y = \frac{4}{3}(x)[/tex]
[tex]y = \frac{4}{3}x[/tex]
Divide the following quantities in the following ratios £100 1:3
Geometry please someone help i cant fail this class
The time spent waiting in the line is approximately normally distributed. The mean waiting time is 6 minutes and the variance of the waiting time is 9. Find the probability that a person will wait for more than 9 minutes.
Answer:
0.1587 = 15.87% probability that a person will wait for more than 9 minutes.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The mean waiting time is 6 minutes and the variance of the waiting time is 9.
This means that [tex]\mu = 6, \sigma = \sqrt{9} = 3[/tex]
Find the probability that a person will wait for more than 9 minutes.
This is 1 subtracted by the p-value of Z when X = 9. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{9 - 6}{3}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a p-value of 0.8413.
1 - 0.8413 = 0.1587
0.1587 = 15.87% probability that a person will wait for more than 9 minutes.
An economic instructor at UCF is interested in the relationship between hours spent studying and total points earned in a course. Data collected on 11 students who took the course last semester follow:
# of observation(s) n = 30
# of independent variable(s) = 1
SSR = 1,297 SSE= 920
Required:
Find the F test statistic.
Answer:
[tex]F = 39.47[/tex]
Step-by-step explanation:
Given
[tex]n = 30[/tex] --- observations
[tex]p = 1[/tex] -- variables
[tex]SSR = 1,297[/tex]
[tex]SSE= 920[/tex]
Required
The F statistic
This is calculated using:
[tex]F = \frac{SSR}{p} \div \frac{SSE}{n - p -1}[/tex]
[tex]F = \frac{1297}{1} \div \frac{920}{30 - 1 -1}[/tex]
[tex]F = \frac{1297}{1} \div \frac{920}{28}[/tex]
[tex]F = 1297 \div \frac{920}{28}[/tex]
Rewrite as:
[tex]F = 1297 * \frac{28}{920}[/tex]
[tex]F = \frac{1297 *28}{920}[/tex]
[tex]F = \frac{36316}{920}[/tex]
[tex]F = 39.47[/tex]
8-6•4+10divided by 2 =
If the angles (4x + 4)° and (6x – 4)° are the supplementary angles, find the value of x.
Answer:
18
Step-by-step explanation:
Supplementary angles means sum of angles is 180.
4x + 4 + 6x - 4 = 180
4x + 6x + 4 - 4 = 180
10x = 180
x = 180 / 10
x = 18
Answer:
x=18 degree
Step-by-step explanation:
If they are supplementary angles, then their sum = 180 degree
4x+4 + 6x-4 =180
4x+6x + 4-4 = 180
10x = 180
x=180/10
x=18
Claim: Fewer than 94% of adults have a cell phone. In a reputable poll of 1004 adults, 86% said that they have a cell phone. Find the value of the test statistic.
Answer: The value of test statistic = -10.67
Step-by-step explanation:
Test statistic for proportion:
[tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}[/tex]
, where p= population proportion
n= sample size
[tex]\hat{p}[/tex] = sample proportion
AS per given,
p=0.94, n= 1004, [tex]\hat{p}=0.86[/tex]
[tex]z=\dfrac{0.86-0.94}{\sqrt{\dfrac{0.94(1-0.94)}{1004}}}\\\\=\dfrac{-0.08}{\sqrt{\dfrac{0.0564}{1004}}}\\\\=\dfrac{-0.08}{\sqrt{0.0000561752988048}}\\\\=\dfrac{-0.08}{0.00749501826581}\\\\=-10.673756509\approx-10.67[/tex]
i.e. the value of test statistic = -10.67
If the bearing of P and
Q is
145°. What is the bearing of
Q from P?
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Answer:
325°
Step-by-step explanation:
The bearing in the reverse direction is 180° more (or less) than the bearing in the forward direction.
145° +180° = 325°
The bearing of Q from P is 325°.
If the bearing of P and
Q is 145°
Soo,
the bearing of Q from P is 145+180=325°
Because it is reserve in the forward direction
[tex]\sf{ }[/tex] [tex]\sf{ }[/tex] [tex]\sf{ }[/tex]
What is 2225 rounded to the nearest thousand? Hurry please
Answer:
2000
Step-by-step explanation:
2225 to the nearest 100 is 2300 but 3
<5 so it is 2000
PLEASE HELP I WILL MARK YOUR ANSWER AS BRAINLIEST PLEASE BE CORRECT BEFORE ANSWERING
LOOK AT THE BOTTOM
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Answer:
y = 2
Step-by-step explanation:
The figure must be flipped top-to-bottom, so the line of reflection must be a horizontal line. Point B must be reflected to itself, so it is on the line of reflection. That means the line of reflection is y = 2.
__
You can draw the line of reflection using any two points that have y-coordinates of 2, for example, (0, 2) and (2, 2).
Please help !!!! will mark brainliest !!
Answer:
the first one
Step-by-step explanation:
Norm has $15,000 to deposit. His daughter is a junior in high school and plans to go to college. Recommend the best way for Norm to store his money. Note that the interest rates are expressed on an annual basis.
a.
A four-year CD paying 4.8% interest, with a substantial penalty for early withdrawal
b.
An online savings account offering 2.3% interest
c.
A money market account paying 3.5% interest, renewable for three-month commitments
d.
A checking account with no monthly fees
Answer:
A money market account paying 3.5% interest, renewable for three-month commitments.
SCALCET8 3.8.001.MI. A population of protozoa develops with a constant relative growth rate of 0.6137 per member per day. On day zero the population consists of two members. Find the population size after seven days. (Round your answer to the nearest whole number.) P(7)
Answer:
A population of protozoa develops with a constant relative growth rate of 0.6137 per member per day. On day zero the population · Q: For this discussion, you will work in groups to find the area and answer questions.
Step-by-step explanation:
The sum of four consecutive odd integers is –72. Write an equation to model this situation, and find the values of the four integers.
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Answer:
(x -3) +(x -1) +(x +1) +(x +3) = -72-21, -19, -17, -15Step-by-step explanation:
Let x represent the even integer between the middle two odd integers. Then the sum of the four odd integers is ...
(x -3) +(x -1) +(x +1) +(x +3) = -72
4x = -72
x = -18
The four integers are -21, -19, -17, -15.
_____
Additional comment
You could let x represent one of the integers. Often, people choose to let it represent the least of them. Then the equation becomes x +(x+2) +(x+4) +(x+6) = -72, so 4x = -84 and x = -21. This introduces a "subtract 12" step in the solution process that is unnecessary if x is chosen to be the average of the integers.
As the average, x is the sum divided by the number of them, so you know x=-72/4 = -18 immediately. Then you just have to find the nearest two odd integers below and above -18. You can do the whole problem mentally.
Is [0,2) is compact in R?
Answer:
no it is not compact in R
Solve the system of equations using the elimination method. 5x + 10y = 3 10x + 20y = 8
Answer:
Can not be solved
Step-by-step explanation:
5x+10y = 3............. Equation 1
10x+20y = 8 ............ Equation 2
From the equation above,
both equations can not be solved by elimination method, because both variables will be eliminated
the perimeter of a rectangle parking lot is 322M if the width of the parking lot is 74M what is its length
Step-by-step explanation:
Perimeter of rectangle = 2( l+b)
Ie, P = 2( L+B )
In substituting,
322 = 2( L + 74)
Ie, 322 = 2L + 148
Re - arrange
Hence,
2L = 322 - 148
2L = 174
Thus, L = 174/2
L = 87M
Test the claim that the proportion of men who own cats is significantly different than the proportion of women who own cats at the 0.2 significance level.
Answer:
Test the claim that the proportion of men who own cats is significantly different than the proportion of women who own cats at the 0.2 significance level.
The null and alternative hypothesis would be: H 0 : μ M = μ F H 1 : μ M < μ F H 0 : μ M = μ F H 1 : μ M > μ F H 0 : p M = p F H 1 : p M ≠ p F H 0 : p M = p F H 1 : p M < p F H 0 : p M = p F H 1 : p M > p F H 0 : μ M = μ F H 1 : μ M ≠ μ F
The test is:
right-tailed
left-tailed
two-tailed
Based on a sample of 40 men, 25%Based on a sample of 40 men, 25% owned cats
Based on a sample of 40 women, 40% owned cats
The test statistic is:
The p-value is:
Based on this we:
Reject the null hypothesis
Fail to reject the null hypothesis
What is the domain of the function f(x) =x+1/
X^2-6x+8?
Answer:
The domain of the function is all real values of x, except [tex]x = 4[/tex] and [tex]x = 2[/tex]
Step-by-step explanation:
We are given the following function:
[tex]f(x) = \frac{x+1}{x^2-6x+8}[/tex]
It's a fraction, so the domain is all the real values except those in which the denominator is 0.
Denominator:
Quadratic equation with [tex]a = 1, b = -6, c = 8[/tex]
Using bhaskara, the denominator is 0 for these following values of x:
[tex]\Delta = (-6)^2 - 4(1)(8) = 36-32 = 4[/tex]
[tex]x_{1} = \frac{-(-6) + \sqrt{4}}{2} = 4[/tex]
[tex]x_{2} = \frac{-(-6) - \sqrt{4}}{2} = 2[/tex]
The domain of the function is all real values of x, except [tex]x = 4[/tex] and [tex]x = 2[/tex]
I’ll mark u plz help
Answer:
D is the answer
Step-by-step explanation:
all sides and angles are equal
hope it helps!! let me know if it does
Diseases tend to spread according to the exponential growth model. In the early days of AIDS, the growth factor (i.e. common ratio; growth multiplier) was around 1.8. In 1983, about 1800 people in the U.S. died of AIDS. If the trend had continued unchecked, how many people would have died from AIDS in 2004?
Answer:
The people dies in 2004 by aids are 413042853.4
Step-by-step explanation:
growth factor = 1.8
People died in 1983 = 1800
Let the people dies in 2004 is P.
Time, t = 2004 - 1983 = 21
So,
[tex]P = 1800 \times (1.8)^{21}\\\\P = 413042853.4[/tex]
Hi, Friends,
please help me solve this problem.
Q. terms of a geometric sequence are found by the formula Tn = ar n-1 If a = 3 and r = 2 , find the 4 terms of the sequence.
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Answer:
3, 6, 12, 24
Step-by-step explanation:
It helps if the formula is properly written.
Tn = a·r^(n-1)
Fill in the given values for a, r, and use n = 1 to 4.
T1 = 3·2^(1-1) = 3
T2 = 3·2^(2-1) = 6
T3 = 3·2^(3 -1) = 12
T4 = 3·2^(4 -1) = 24
__
Additional comment
The value a=3 tells you the first term is 3. The value r=2 tells you each term is 2 times the previous one. Knowing this, you can write down the sequence based on your knowledge of multiplication tables (×2). You can use the formula as we did above, but it isn't necessary.
3, 6, 12, 24, ...
An angle with measure of 71° is bisect at what angle?
Answer:
A
Step-by-step explanation: just divide 71 into 2 which gives you 35.5 making a your answer.
Allen is looking through his weekly local grocery store newspaper ads he notices that Costco is advertising a pack of 60 eggs for $9.35 Safeway is advertising a dozen eggs for $4.79 and Trader Joe's is advertising a pack of 18 eggs for $6.18 which store is offering the better deal?
Answer:
Costco
Step-by-step explanation:
We find the cost per egg for each of the three stores.
Costco:
$9.35/(60 eggs) = $0.15583/egg
Safeway:
$4.79/(12 eggs) = $0.39917/egg
Trader Joe's:
$6.18/(18 eggs) = $0.34333/egg
The best deal is Costco.
Answer:
Costco
Step-by-step explanation:
[tex]\frac{60}{9.35}: \frac{1}{y}[/tex]
60 × y = 1 × 9.35
60y = 9.35
60y ÷ 60 = 9.35 ÷ 60
[tex]y=\frac{187}{1200}[/tex]
[tex]\frac{12}{4.79}: \frac{1}{y}[/tex]
12 × y = 1 × 4.79
12y = 4.79
12y ÷ 12 = 4.79 ÷ 12
[tex]y=\frac{479}{1200}[/tex]
[tex]\frac{18}{6.18}: \frac{1}{y}[/tex]
18 × y = 1 × 6.18
18y = 6.18
18y ÷ 18 = 6.18 ÷ 18
[tex]y=\frac{103}{300}=\frac{412}{1200}[/tex]
Solve by graphing. Round each answer to the nearest tenth.
6x2 = −19x − 15
a: −2, 1.7
b: −1.7, −1.5
c: −1.5, 1.5
d: −1.5, 1.7
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Answer:
b: -1.7, -1.5
Step-by-step explanation:
The graph is shown below. We have annotated the x-intercepts for the equivalent equation ...
6x^2 +19x +15 = 0
Is 237405 divisible by 11 Correct Answer = Brainliest
Answer:
Yes.
Step-by-step explanation:
.
