Answer:
59.44
Step-by-step explanation:
Nine employees If an electronic company retired last year
The retirement ages are listed below
56, 65, 62, 53, 68, 58, 65, 52, 56
The mean retirement age can be calculated as follows
= 56+65+62+53+68+58+65+52+56/9
= 535/9
= 59.44
Hence the mean retirement age is 59.44
(10 points)Assume IQs of adults in a certain country are normally distributed with mean 100 and SD 15. Suppose a president, vice president, and secretary of state are chosen randomly from the adults in the country, with each adult having an equal chance to be assigned each of the 3 jobs. What is the probability that the president will have an IQ of at least 107.5 and that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130
Answer:
0.0139 = 1.39% probability that the president will have an IQ of at least 107.5 and that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.
Step-by-step explanation:
To solve this question, we need to use the binomial and the normal probability distributions.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
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.
Probability the president will have an IQ of at least 107.5
IQs of adults in a certain country are normally distributed with mean 100 and SD 15, which means that [tex]\mu = 100, \sigma = 15[/tex]
This probability is 1 subtracted by the p-value of Z when X = 107.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{107.5 - 100}{15}[/tex]
[tex]Z = 0.5[/tex]
[tex]Z = 0.5[/tex] has a p-value of 0.6915.
1 - 0.6915 = 0.3085
0.3085 probability that the president will have an IQ of at least 107.5.
Probability that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.
First, we find the probability of a single person having an IQ of at least 130, which is 1 subtracted by the p-value of Z when X = 130. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{130 - 100}{15}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a p-value of 0.9772.
1 - 0.9772 = 0.0228.
Now, we find the probability of at least one person, from a set of 2, having an IQ of at least 130, which is found using the binomial distribution, with p = 0.0228 and n = 2, and we want:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{2,0}.(0.9772)^{2}.(0.0228)^{0} = 0.9549[/tex]
[tex]P(X \geq 1) = 1 - P(X = 0) = 0.0451[/tex]
0.0451 probability that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.
What is the probability that the president will have an IQ of at least 107.5 and that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130?
0.3085 probability that the president will have an IQ of at least 107.5.
0.0451 probability that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.
Independent events, so we multiply the probabilities.
0.3082*0.0451 = 0.0139
0.0139 = 1.39% probability that the president will have an IQ of at least 107.5 and that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.
In a marketing survey, a random sample of 1020 supermarket shoppers revealed that 268 always stock up on an item when they find that item at a real bargain price.
a. Find a 95% confidence interval for p?
b. What is the margin of error based on a 95% confidence interval?
Answer:
a) 95% of the confidence intervals created using this method would include the true proportion of shoppers who stock up on bargains.
b) Margin of error = 0.0270.
Step-by-step explanation:
a)
[tex]\hat{p}[/tex] = point estimate of p [tex]= 268/1020 =0.2627[/tex]
[tex]\hat{q}= 1 - 0.2627 = 0.7373[/tex]
[tex]SE = \sqrt{\hat{p}\hat{q}/n}\\\\=\sqrt{0.2627\times 0.7373/1020}=0.0138\\\alpha = 0.05[/tex]
From Table, critical values of [tex]Z= \pm1.96[/tex] ,
Lower limit
[tex]= \hat{p} - Z SE\\ = 0.2627 - (1.96 X 0.0138) \\ = 0.2627 - 0.0276 \\ = 0.236[/tex]
upper limit = 0.2627 + 0.0276
= 0.2903
Correct option:
95% of the confidence intervals created using this method would include the true proportion of shoppers who stock up on bargains.
b) Margin of error =Z SE
= 1.96 X 0.0141
= 0.0270.
These two polygons are similar. In the spaces below, enter the values of a, b, m
Given:
The two polygons are similar.
To find:
The value of [tex]a,\ b,\ m\angle C,\ m\angle D[/tex].
Solution:
We know that the corresponding side of similar figures are proportional. So,
[tex]\dfrac{5}{4}=\dfrac{5.39}{a}[/tex]
[tex]1.25=\dfrac{5.39}{a}[/tex]
[tex]a=\dfrac{5.39}{1.25}[/tex]
[tex]a=4.312[/tex]
Similarly,
[tex]\dfrac{5}{4}=\dfrac{5.83}{b}[/tex]
[tex]1.25=\dfrac{5.83}{b}[/tex]
[tex]b=\dfrac{5.83}{1.25}[/tex]
[tex]b=4.664[/tex]
We know that the corresponding angles of similar figures are congruent and their measures are equal. So,
[tex]m\angle C=99.2^\circ[/tex]
[tex]m\angle D=149^\circ[/tex]
Therefore, [tex]a=4.312\text{ units},\ b=4.664\text{ units},\ m\angle C=99.2^\circ,\ m\angle D=149^\circ[/tex].
Write an equation for the line with passing through ( -2, 9) and ( 1, 0)
Answer:
[tex]y=-3x+3[/tex]
Step-by-step explanation:
We start by finding the slope of the line, which is given by the formula:
[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
The points (x1, y1) and (x2, y2) are represented by the pairs given: (-2, 9) and (1, 0). WE can substitute this in and simplify.
[tex]m=\frac{0-9}{1-(-2)} =\frac{-9}{1+2} =\frac{-9}{3} =-3[/tex]
Using the point-slope formula, [tex]y-y_{1} =m(x-x_{1} )[/tex], we can find the equation. We can substitute the point (-2, 9) for (x1, y1):
[tex]y-9=-3(x+2)\\y-9=-3x-6\\y=-3x+3[/tex]
A rectangular garden covers 80 yd?. The length is 7 yd longer than the width. Find the length and width.
Round your answers to the nearest tenth of a yard.
Answer:
The width of the rectangle is 6,105 yards, and the length of the rectangle is 13,105 yards.
Step-by-step explanation:
Given that a rectangular garden covers 80 square yards, and the length is 7 yd longer than the width, to find the length and width of the rectangle the following calculation must be performed, knowing that the area of a rectangle arises from multiplying its width by its length:
X x (X + 7) = 80
5 x 12 = 60
6 x 13 = 78
8 x 14 = 112
6.1 x 13.1 = 79.91
6,105 x 13,105 = 80
Therefore, the width of the rectangle is 6,105 yards, and the length of the rectangle is 13,105 yards.
what is the approximate surface area of a cylinder with a radius of 3 inches and a height of 10 inches?
1. 30in^2
2. 87in^2
3. 217in^2
4. 245in^2
Find the missing coordinates.
Answer:
1) (2, 1)
2) (2, -2)
3) (-1, -1)
4) (-5, -5)
Answer:
1. Pairs A(2, 5), B(6, 5), and C(6, 1)
missing coordinate is (2,1)
2. Pairs A(2, 3), B(7, 3), and C(7, -2)
missing coordinate is (2,-2)
3. Pairs A(-5, -1), B(1, -1), and C(1, -5)
missing coordinate is (-5,-5)
4. Pairs A(-1, 4), B(7, 4), and C(7, -1)
missing coordinate is (-1,-1)
Hope this is correct!! Have a nice day!!<3
Find the measure of theta to the nearest tenth helpppp pleaseeee
Answer:
54.3°
Step-by-step explanation:
sinθ=opposite/hypotenuse
sinθ=26/32
sinθ=0.8125
θ=54.3°
36 apples cost $6. How many apples can you buy for $1?
Answer: you can buy 6apples for$1
Step-by-step explanation: you divide 36 by 6 and get 6 so it’s 6apples.
Using the quadratic formula to solve x2 35-x, what are the values of x?
-12-121
-12-11
54.
12/19
51 21
2
Answer:
x = (-1 ± √21) / 2
The first choice
Step-by-step explanation:
x² = 5 - x
Put in standard form
x² + x - 5 = 0
Use quadratic equation
x = ( -b ± √( b² - 4ac) ) / (2a)
Plug in a = 1, b = 1 , c = -5
x = (-1 ± √( 1² - 4*1*(-5)) ) / 2
evaluate
x = (-1 ± √21) / 2
The measure of angle S is 65 degrees.
What is the measure of angle R?
RS
A
115°
B.
230°
с
65°
D
25°
Answer:
A. 115°
Step-by-step explanation:
180° - 65° = 115°
Study the adjoining figure and then explain why x = y
Answer:
Step-by-step explanation:
y is the remote exterior angle. The remote exterior angle has the strange property that it is equal to the two remote interior angle. The two remote interior angles are the two, neither of which is the supplement of the exterior angle
So y = x/2 + x/2 which are marked as being opposite equal angles.
1/2 x + 1/2 x = x
y by substitution is = x /2 + x/2
y = x
Cassie took 2 quizzes last week. She scored the same in each quiz.
Her score was -12 from being perfect. What was the difference
between Cassie's score and a perfect score on each quiz?
Help fastttt
Answer:
since her score was -12 from being perfect
if she had scored 12 more points her score would have been perfect .
that is difference between her score and the perfect score o each quiz was 12
Decide which project the most profitable is by:
(a) Determining the NPV at a discount rate of 6.5%. (8 marks)
(b) The IRR. ?
Answer:
Project A :
NPV : $703,888.64
IRR : 44.882%
Project B:
NPV : $5,241.26
IRR : 49.662%
Project B is more profitable
Step-by-step explanation:
The NPV gives the difference between the present value of cash inflow and cash outflow over a certain period of time.
The Internal rate of return is the discount rate which makes the NPV of an investment 0. It is used to estimate the potential return on an investment. Investments with higher IRR are said to be better than those with lower IRR value.
Using the net present value, (NPV) Calculator, the NPV for project A is : $703,888.64
The IRR of project A is : 44.882%
The NPV for Project B is : $5,241.26
The Internal rate of return (IRR) : 49.662%
From the Internal rate of return value obtained, we can conclude that, project B is more profitable as it has a higher IRR than project A.
Bro i dont know what the x is tbh
3. The simple interest on $6,000 for 4 years is $1,680. *
A news report suggested that an adult should drink a minimum of 4 pints of water per day.
Based on this report, determine the minimum amount of water an adult should drink,
in fluid ounces, per week.
9514 1404 393
Answer:
448
Step-by-step explanation:
(4 pt/da)×(7 da/wk)×(16 oz/pt) = 448 oz/wk
That would be 448 fluid ounces per week.
Find the volume V and surface area S of a
rectangular box with length 2 meters, width 6 meters,
and height 9 meters.
Answer:
Surface area add together all 6 sides = 24+36+108=168m^2
Volume L x W x D = 2 x 6 x 9 = 108 m ^3
Step-by-step explanation:
2 x 6 = 12
12 x 2 = 24 base and top
2 x 9 = 18
2 x 18 = 36 identical pair sides
6 x 9 = 54
2 x 54 = 108 identical pair sides
Surface area add together all 6 sides = 24+36+108=168m^2
Volume L x W x D = 2 x 6 x 9 = 108 m ^3
help please. I cant figure it out and it’s hard.
Answer:
The student is comparing the different heart rates due to the temperature. The independent variable is the Temperature and the dependent variable is the beats of the heart from the larva.
what is 1+544 please somone tell me or i wikl fail mah test qwq
Answer:555
Step-by-step explanation:
Answer:
545
Step-by-step explanation:
you are just adding one
544+1=
Plzzz help me please ??
A. 4/7 Answer:
B. 60/7 or (8 and 4/7)
Step-by-step explanation:
A. 4 divided by 7 is the same as 4/7
B. 4/7 • 15/1= 60/7
How to calculate raw score from standard score and percentile rank?
Answer:
Step-by-step explanation:
Suppose that $2000 is invested at a rate of 4%, compounded semiannually. Assuming that no withdrawals are made, find the total amount after 5 years. Do not round any intermediate computations, and round your answer to the nearest cent.
Answer:
Step-by-step explanation:
A = P(1+r/n)^ nt
A = 2000(1+.04/2)^(5*2)
A = [tex]2000(1.02)^{10}[/tex] = $2437.99
I need help with #1 . Please help. I have to show all work so please explain
Answer:C=10
Step-by-step explanation:
Follow along with the picture below
The formula for this type of problem is a^2+b^2=c^2
We know that 6=a and 8=b so we fill in the formula and square them
we then add the two values we got which get us to 100=c^2
we want to get rid of that square with we square root bothe sides and get c and the square root of 100 is 10.
So C=10
If a triangle has angles of X+2, 2x, and 55. What are the three angle
measurements?
Answer:
41, 43 and 82
Step-by-step explanation:
hope it may help you
Greg is installing a tile floor in a room that is 10 feet long by 15 feet wide. He will use 1-foot square tiles. He has two different types of tile: plain and hand-painted. Plain tiles cost $0.79 per tile. Hand-painted tiles cost $5.00 per tile. What is the maximum number of hand-painted tiles that Greg can use to keep the total cost under $200?
Answer:
The maximum number of hand-painted tiles that Greg can use to keep the total cost under $ 200 is 19.
Step-by-step explanation:
Since Greg is installing a tile floor in a room that is 10 feet long by 15 feet wide, and he will use 1-foot square tiles, and he has two different types of tile: plain and hand-painted, and plain tiles cost $ 0.79 per tile, while hand-painted tiles cost $ 5.00 per tile, to determine what is the maximum number of hand-painted tiles that Greg can use to keep the total cost under $ 200, the following calculation must be performed:
10 x 15 = 150
150 x 0.79 + 0 x 5 = 118.5
130 x 0.79 + 20 x 5 = 202.7
131 x 0.79 + 19 x 5 = 198.49
Therefore, the maximum number of hand-painted tiles that Greg can use to keep the total cost under $ 200 is 19.
If two standard, six-sided die were rolled and the numbers that turned up on each were added together, which of the following would be the probability their sum would be equal to 4?
Answer:
3/36 or 8.333
Step-by-step explanation:
the way you get it is write all the possibilities and that how you get 3/36
how to calculate surface area
9514 1404 393
Explanation:
Divide the figure into areas for which you have a surface area formula. Use the appropriate formula for each area, then add up the results.
Formulas are available for surface areas of a cone, cylinder, sphere, pyramid, rectangular prism, and for plane shapes that are circles, ellipses, triangles, rectangles, trapezoids, and regular polygons.
Most of the figures for which you are asked to find the area will decompose to some subset of these shapes. Take care to identify the relevant dimensions of each of the constituent parts of the area, and to make sure that all parts are accounted for. Do not allow your parts of the area to overlap, unless you intend to account for that overlap by subtracting the area that is counted more than once.
Also, use your common sense. A semicircle will have half the area of a circle, for example.
In some cases, it may be expedient to compute the area of a larger figure than the one you have, then subtract the part of that area that is missing from your figure.
For a rock concert a rectangular field of size 100 m by 50 m was reserved for the
audience.
The concert was completely sold out and the field was full with all the fans standing.
Which one of the following is likely to be the best estimate of the total number of people
attending the concert?
2000
5000
20000
50000
100000
Answer:
5000
Step-by-step explanation:
but this depends upon how much room each person needs
Given that events A and B are independent with P(A) = 0.55 and P(B) = 0.72,
determine the value of P(AB), rounding to the nearest thousandth, if necessary.
Answer:
Step-by-step explanation:
For independent events,
P(AB)=P(A)orP(B)
= P(A)uP(B)
=P(A)×P(B)
= 0.55×0.72
P(AB)=0.396