Answer:
a) 0.7088 = 70.88% probability that a randomly selected President was less than 60 years old on the day of their first inauguration.
b) The 75th percentile for the age of United States Presidents on the day of inauguration is 61.
c) 0.8643 = 86.43% probability that the average age on the day of their first inauguration for a random sample of 4 United States Presidents exceeds 60 years.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
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 zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes 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.
The age of United States Presidents on the day of their first inauguration follows a Normal distribution with mean 56 and standard deviation 7.3.
This means that [tex]\mu = 56, \sigma = 7.3[/tex]
(a) (5 points) Compute the probability that a randomly selected President was less than 60 years old on the day of their first inauguration.
This is the pvalue of Z when X = 60. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{60 - 56}{7.3}[/tex]
[tex]Z = 0.55[/tex]
[tex]Z = 0.55[/tex] has a pvalue of 0.7088
0.7088 = 70.88% probability that a randomly selected President was less than 60 years old on the day of their first inauguration.
(b) (5 points) Compute the 75th percentile for the age of United States Presidents on the day of inauguration.
This is X when Z has a pvalue of 0.75. So X when Z = 0.675.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.675 = \frac{X - 56}{7.3}[/tex]
[tex]X - 56 = 0.675*7.3[/tex]
[tex]X = 61[/tex]
The 75th percentile for the age of United States Presidents on the day of inauguration is 61.
(c) (5 points) Compute the probability that the average age on the day of their first inauguration for a random sample of 4 United States Presidents exceeds 60 years.
Now, by the Central Limit Theorem, we have that [tex]n = 4, s = \frac{7.3}{\sqrt{4}} = 3.65[/tex]
This is the pvalue of Z when X = 60. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{60 - 56}{3.65}[/tex]
[tex]Z = 1.1[/tex]
[tex]Z = 1.1[/tex] has a pvalue of 0.8643
0.8643 = 86.43% probability that the average age on the day of their first inauguration for a random sample of 4 United States Presidents exceeds 60 years.
what is -17 + 12 + 15?
Answer:
10
Step-by-step explanation:
I really need help! will give brainliest!!
Select whether the triangle is inscribed in the circle, circumscribed about the circle, or neither.
inscribed in the circle
circumscribed about the circle
neither
The correct answer is neither
Find the simplified product where sqrt 5x ( sqrt 8x^2 - 2 sqrt x)
Answer:
D is your answer
Step-by-step explanation:
Just did it and it was right : )
Also for anyone else who needs the other answers they are as follows:
1. D. [tex]6x^4[/tex] then C. [tex]3x^4[/tex]
2. B. [tex]-30x^2 \sqrt{2x}[/tex] then C. [tex]4x^4^3 \sqrt{2x^2}[/tex]
3. D. [tex]2x\sqrt{10x} - 2x \sqrt{5}[/tex]
4. B. [tex]32x^2 \sqrt[3]{2x} -8x^3[/tex]
5. A. [tex]-22[/tex] then C. [tex]4x^4 \sqrt{5} +2x^2 \sqrt{3x} + 4x^3 \sqrt{30} +6x \sqrt{2x}[/tex]
6. B. [tex]x^\frac{2}{12}* y^\frac{9}{12}[/tex] then C. [tex]\sqrt[12]{x^2*y^9}[/tex]
These answers are for!!!!NC Math 2 -22092x0
Multiplying Radicals
Assignment
Due March 11
Multiplying radicals with like indices.
The solution of the given equation will be 2√5x(√2-1).
What is an equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
The expression will be solved as below:-
= √5x ( √8x² - 2√x)
= √5x ( 2√2x - 2√x)
= √5x(√2-1)(2√x)
= 2√5x(√2-1).
Therefore the solution of the given equation will be 2√5x(√2-1).
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How much will it cost to mail one packet of compass boxes? 15 packets?
Answer:
7.50$
Step-by-step explanation:
The area of the triangle below is 8.91 square inches. What is the length of the base?
2.2 in is the height
Answer:
8.1 inches
Step-by-step explanation:
Area of a triangle = ½ × base × height = Area
Rearranged =
[tex] \frac{area}{ \frac{1}{2} \times height} [/tex]
Base is the length by the way.
[tex] \frac{8.91}{ \frac{1}{2} \times 2.2 } [/tex]
=8.1 inches
Answer:
Then answer is 8.1 inches ;)
pam ate 9 nuts in 6 minutes . if she continued eating at the same rate,how many would she eat in:
[tex]a)12min[/tex]
[tex]b)4min[/tex]
[tex]c)1 \: hour[/tex]
Answer:
18 nuts in 12 minutes, 13.5 nuts in 4 minutes and 90 nuts in one hour
Step-by-step explanation:
12 min :
12/6 = 2
2 x 9 = 18 nuts in 12 minuts
4 min:
6/4 = 1.5
1.5 x 9 = 13.5 nuts in 4 minutes
(round to 13 if whole nuts only)
1 hour:
1 hour = 60 mins
60/6 = 10
9 x 10 = 90 nuts in one hour
20/48 equals what as a percentage
Answer:
approx 41.6%
Step-by-step explanation:
Answer:
41.7%
Step-by-step explanation:
First, you will divide 20 by 48.
[tex]20/48=0.4167[/tex]
Secondly, you would multiply by 100%
[tex]0.4167* 100= 41.67%[/tex]%
If you round to the nearest whole number it would give you [tex]42[/tex]%. If it is rounded to the nearest tenth it would be [tex]41.7%[/tex]%
Translate the sentence into an inequality.
A number increased by 2 is greater than or equal to 19.
Answer:
X + 2 [tex]\geq \\[/tex] 19
Step-by-step explanation:
a number ur going to represent with a variable x and increased by 2 means + 2 so x + 2 and when it say greater than or equal to remember that it always opens to the lager number or x + 2 and has a line underneath to represent the or equal to.
I can't seem to factor out this equation.
40x squared -46x +12
A geometric sequence has a pattern of
multiplication. Previously we learned about
arithmetic sequences which have...
a pattern of division.
a pattern of addition.
no pattern.
Can someone help me with this question please :) (University)
Answer:
(-5 1 0 0) and (-3 0 1 0)
Step-by-step explanation:
Based on my memory, you can use the dot product to find orthogonality meaning
u1 . u2 = 0
In this case, we let u be the arbitrary vector represented by (x y z w)
u . (1 5 3 0) can be expressed as an equation given by:
{(x y z w) | x + 5y + 3z + 0w= 0}
We solve this equation letting y = s and z = t and x = -5s -3t
Reconstruct this according to their variable will give
(-5 1 0 0)s + (-3 0 1 0)t = 0
So the basis vectors are (-5 1 0 0) and (-3 0 1 0).
Let c1 and c2 be arbitrary constants:
if you solve for c1(-5 1 0 0) + c2(-3 0 1 0) = 0
c1 and c2 should have only trivial solution, which proves its
linear independence and so it forms a basis vector space.
A jeweler works with two kinds of metals, the first contains
72% silver and the second contains 87% silver.
If he wants to end up with a mixture of 50 grams that is
84% silver,
How many grams of the 72% silver metal should he use?
Answer:
The TI-84 Plus Silver Edition is powered by four AAA alkaline batteries (not included) , with an automatic shutoff to save energy.
Step-by-step explanation:
A carry out container is shown. The bottom base is a 4-inch square and the top base is a 4-inch by 6-inch rectangle. The height of the container is 5 inches. Find the volume of the food that it holds.
Answer: 100
Step-by-step explanation: I don't really have a step-by-step explaination, but I do know that the answer is 100.
which shape best describes the cross section cut at an angle to the base of a right rectangular prism
Answer:
Parallelogram
Step-by-step explanation:
sorry if it's wrong
What is the area of this shape?
https://www.savvasrealize.com/community/proxy/assessment/f36965b75bed44af919c75c94b34196a/images/6e1b6ba7-27ad-4449-a88c-9fa501708531
88 square inches
96 square inches
120 square inches
80 square inches
Answer: the link you posted is the area of the shape
Step-by-step explanation:
in ABC, what is the value of x?
Answer:
x = 16.2
Step-by-step explanation:
5/9 = 9/x
5x = 81
x = 16.2
Which set of measurements would not create a triangle?
A. 9 in., 8 in., 16 in.
B. 11 in., 12 in., 22 in.
C. 14 in., 6 in., 20 in.
D. 3 in., 8 in., 6 in.
7+12x=103 show how you checked it was right
Answer:
x=8. You plug 8 in for x.
7+12(8)=103
7+96=103
Step-by-step explanation:
7+12x=103
or 12x=103-7
x=96/12=8
to check it 8 is needed.
7+12×8=103
The action of coming to live permanently in a foreign country.
Answer:
Emigrate means to leave one's country to live in another. Immigrate is to come into another country to live permanently. Migrate is to move, like birds in the winter. The choice between emigrate, immigrate, and migrate depends on the sentence's point of view.
y varies directly as x.x= 1/2 and y= 5/4. Find x when y= 10.
x= ?
Answer:
X=4Step-by-step explanation:
x=1/2=2/4
y=5/4
y=2.5x
10/2.5=4
so x=4
Alyssa buys a carton of 12 eggs for $1.80. Which is the cost per egg?
A $0.015
B $0.15
C $1.50
D $15.00
Answer:
B is the answer
Cost of each egg= 1.80/12=$0.15
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
12 egg=$1.80 ,1 egg= $1.80÷12 =$0.15
Vanessa tried to prove that triangle KLM is congruent to triangle MNK. What is the first error Vanessa made in her proof?
Answer:
B. Vanessa only established some of the necessary conditions for a congruence criterion.
Step-by-step explanation:
The diagram does support the claim that \overline{KL}\cong\overline{MN}
KL
≅
MN
start overline, K, L, end overline, \cong, start overline, M, N, end overline because they both have two tick marks.
Step 1 is correct.
Step 2
The diagram does support the claim that \overline{LM}\cong\overline{NK}
LM
≅
NK
start overline, L, M, end overline, \cong, start overline, N, K, end overline because they both have a single tick mark.
Step 2 is correct.
Step 3
In this step, Vanessa claims that \triangle KLM\cong \triangle MNK△KLM≅△MNKtriangle, K, L, M, \cong, triangle, M, N, K using the side-side-side criterion. But Vanessa only established two pairs of congruent corresponding sides. To use this criterion, we must establish three pairs of congruent sides.
Vanessa would be able to use this criterion if she first established that \overline{MK}\cong\overline{KM}
MK
≅
KM
start overline, M, K, end overline, \cong, start overline, K, M, end overline (this can be done with the reason that line segments are congruent to themselves).
The first error Vanessa made in her proof was option B.
Vanessa only established two pairs of congruent corresponding sides
What is congruency?polygons are congruent if they may be identical in size and shape - that is, if their corresponding angles and sides are the same.
Congruent shapes are shapes that can be exactly equal. The corresponding facets are identical and the corresponding angles are equal.
⇒KL≅ MN 9K, L, end overline)
⇒LM≅ NK
⇒MNK△KLM≅△MNK (triangle, K, L, M)
Vanessa would be able to use this criterion if she first established that
⇒MK≅ KM
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Please answer this question!!! Thank you!
Answer:
your answer is b
Step-by-step explanation:
Select all order pairs that satisfy the function y = -2x + 5
(2,1)
(3,0)
(1, -7)
(-2,9)
(5, 5)
geometry: find the value of x. Round to the nearest tenth. How do I do this? screenshot attached
Answer:
[tex]\boxed {\boxed {\sf x \approx 105.3}}[/tex]
Step-by-step explanation:
To solve for x, remember the right triangle trigonometry ratios (soh-cah-toa).
sinθ= opposite/hypotenuse cosθ= adjacent/hypotenuse tanθ= opposite/adjacentIf we look at the angle given (θ), then we see that 36 is adjacent or next to the 70° angle. x is the hypotenuse because it is opposite the right angle. So, we have to use cosine (adjacent and hypotenuse).
[tex]cos (\theta)=\frac {adjacent}{hypotenuse}[/tex]
[tex]cos(70)=\frac{36}{x}[/tex]
Cross multiply. (Multiply the first numerator by the second denominator. Then, multiply the first denominator by the second numerator).
[tex]\frac{cos(70)}{1}=\frac{36}{x}[/tex]
[tex]cos(70)*x= 36[/tex]
Since we want to solve for x, we must isolate the variable. Divide both sides by the cosine of 70.
[tex]\frac{cos(70)*x}{cos(70)}=\frac{ 36}{cos(70)}\\x= 105.2569584[/tex]
Round to the nearest tenth. The 5 in the hundredth place tells us to round the 2 to a 3.
[tex]x \approx 105.3[/tex]
x is about 105.3
a clock strikes 2:00.what time will their needles form a right angle?
A) 1hr 26min 12s
B) 4hr 10min 32s
C) None of the answers are correct
D) 2hr 27min 16s
Answer:
C
Step-by-step explanation:
I really need help on this.
figure A :
step 1: multiply
3 x 4 x 4 x5=240m
figure B:
step 1: add
17+12+5+ 15=49cm
Steven purchases a bowl. The diameter of the bowl is 14 cm. What is the circumference of the bowl?
Answer:
14π
Step-by-step explanation:
C = 2πr
D=2r
D=14
14=2r
r=7
C=2π(7)
C=14π or 43.98
Meg pounded a stake into the ground. When she attached a leash to both the stake and her dog’s collar, the dog could reach 9 feet from the stake in any direction. Using 3.14 for pi, what is the approximate area of the lawn, in square feet, the dog could reach from the stake.
The dog is able to run around in a circle with a radius of9 ft.
The area of a circle is A = pi r^2
A = (3.14) (9)^2
A= (3.14)(81)
A= 254.34 sq ft