Answer:
0.0778 = 7.78% probability that the average age at death of these nine participants will exceed 68 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.
Approximately normal with mean equal to 66.3 years and standard deviation equal to 3.6 years.
This means that [tex]\mu = 66.3, \sigma = 3.6[/tex]
Sample of 9:
This means that [tex]n = 9, s = \frac{3.6}{\sqrt{9}} = 1.2[/tex]
What is the probability that the average age at death of these nine participants will exceed 68 years?
This is 1 subtracted by the pvalue of Z when X = 68. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{68 - 66.3}{1.2}[/tex]
[tex]Z = 1.42[/tex]
[tex]Z = 1.42[/tex] has a pvalue of 0.9222
1 - 0.9222 = 0.0778
0.0778 = 7.78% probability that the average age at death of these nine participants will exceed 68 years
--Please help, ill give 30 points and brainiest if your correct!!--
Lisa and Alice are playing a game. Each player either receives or has to pay play money based on the results of their spin. The table lists how much a player receives or pays for various spins. What color has the greatest amount?
Red
Pays $5
Blue
Receive $4
Yellow
Pay $1
Green
Receive $3
Orange
Pay $2
Answer:
The amount in table as positive negative numbers: -5, 4, -1, 3, -2.
The spinner lands on red the change to Lisa's amount of money is -$5.
Step-by-step explanation:
Consider the provided table.
Part(A)
The table list how much a player receives or pays for various.
Paying some money is represented by a negative sign while receiving money is represented by a positive sign.
For red they needs to pay $5 which can be written as -5.
For blue they received $4 which can be written as 4.
For yellow they needs to pay $1 which can be written as -1.
For green they received $3 which can be written as 3.
For orange they needs to pay $2 which can be written as -2.
So, the amount in table as positive negative numbers: -5, 4, -1, 3, -2.
Part(B)
Now, we need to describe the change to Lisa’s amount of money when the spinner lands on red.
If spinner lands on red then she needs to pay $5.
Thus, if the spinner lands on red the change to Lisa's amount of money is -$5.
Evaluate the following integral using trigonometric substitution
Integral underroot dx/ 9-x^2
Answer:
The result of the integral is:
[tex]\arcsin{(\frac{x}{3})} + C[/tex]
Step-by-step explanation:
We are given the following integral:
[tex]\int \frac{dx}{\sqrt{9-x^2}}[/tex]
Trigonometric substitution:
We have the term in the following format: [tex]a^2 - x^2[/tex], in which a = 3.
In this case, the substitution is given by:
[tex]x = a\sin{\theta}[/tex]
So
[tex]dx = a\cos{\theta}d\theta[/tex]
In this question:
[tex]a = 3[/tex]
[tex]x = 3\sin{\theta}[/tex]
[tex]dx = 3\cos{\theta}d\theta[/tex]
So
[tex]\int \frac{3\cos{\theta}d\theta}{\sqrt{9-(3\sin{\theta})^2}} = \int \frac{3\cos{\theta}d\theta}{\sqrt{9 - 9\sin^{2}{\theta}}} = \int \frac{3\cos{\theta}d\theta}{\sqrt{9(1 - \sin^{\theta})}}[/tex]
We have the following trigonometric identity:
[tex]\sin^{2}{\theta} + \cos^{2}{\theta} = 1[/tex]
So
[tex]1 - \sin^{2}{\theta} = \cos^{2}{\theta}[/tex]
Replacing into the integral:
[tex]\int \frac{3\cos{\theta}d\theta}{\sqrt{9(1 - \sin^{2}{\theta})}} = \int{\frac{3\cos{\theta}d\theta}{\sqrt{9\cos^{2}{\theta}}} = \int \frac{3\cos{\theta}d\theta}{3\cos{\theta}} = \int d\theta = \theta + C[/tex]
Coming back to x:
We have that:
[tex]x = 3\sin{\theta}[/tex]
So
[tex]\sin{\theta} = \frac{x}{3}[/tex]
Applying the arcsine(inverse sine) function to both sides, we get that:
[tex]\theta = \arcsin{(\frac{x}{3})}[/tex]
The result of the integral is:
[tex]\arcsin{(\frac{x}{3})} + C[/tex]
5/8÷1/3 do you now the answer
Answer:
15/8
Step-by-step explanation:
This is a fraction so when dividing fractions you can multiply by the reciprocal.
5/8*3/1= 5*3/8*1 = 15/8
Which inequality is true if p=3?
A. 3p <9
B. 13 < 4p
C. 5p > 15
D.8 > 2p
Answer:
D
Step-by-step explanation:
2×3 = 6 which is less than 8
A $24,000 car depreciates at a rate of 15% annually. What is that average rate of change from year 6 to year 10?
A sample of 5 integers selected is shown. Does this sample represent the general rule for picking an integer from 1 to 25 in the population of integers from 1 to 1,000? Explain.
Answer:
No
Step-by-step explanation:
The general rule for picking sample from a population at random ensures that all members of the population have equal chances of being selected.
Therefore to select 5 samples in the range 1 - 25 from a population of integers from 1 - 1000.
Firstly, befure we start selecting our samples directly from the population since we are not interested in all integers, we seperatw the integers belonging to our target samples from the population first, the we select 5 samples out of the sepwratwd integers between 1 - 25. This ensures that all our 5 samples will have integers between 1 - 25 becausw integers 1 - 25 is the range we want our specs to be within and not between 1 - 100.
However, from the trial samples recorded none of the samples have integer between 1 - 25 ; jnecw, the samples must have been chosen directly from the entire population of 1 - 1000
Liana is putting a border around a right triangle and needs to figure out the triangle's height. If the triangle has a base length of 9 cm and a total area of 27 cm², what is the height?
Answer:
6
Step-by-step explanation:
Three friends, Maria, Sarah, and Ruth, spend $356.50, $365.50, and $356.60,
respectively, at a shopping mall. Calculate who spent the most?
Answer:
Im guessing ruth...
Step-by-step explanation:
not very clear on question
use inductive reasoning to predict the next line in the sequence of computations.
1=1×1
1+7=2×4
1+7+13=3×7
Answer:
1 + (1+6) + (1+6+6) + (1+6+6+6) = 4 × n
Step-by-step explanation:
The computation of the next line in the sequence is shown below:
As we can see that there is an increase of 6 in the left side and on the right hand side there is an increase of one
So,
1 = 1 × n
1 + (1+6) = 2 × n
1 + (1+6) + (1+6+6) = 3 × n
So, the next line would be
1 + (1+6) + (1+6+6) + (1+6+6+6) = 4 × n
i.e.
1 + 7 + 13 + 19 = 4 × 10
As 1 + 7 + 13 + 19 = 40
And 40 = 4 × 10
Which is the equation of a line that has a slope of -7 and a Y intercept of 2
Answer:
y = -7x + 2
Step-by-step explanation:
Bill charges 20 dollars to come to your house. He also charges 12 dollars for each hour that he works there. If the total price of Bill’s visit is $116 how many hours was he there?
Answer:
He was there for 8 hours.
Step-by-step explanation:
Suppose that there are two types of tickets to a show: advance and same-day. The combined cost of one advance ticket and one same-day ticket is
$55
. For one performance,
40
advance tickets and
25
same-day tickets were sold. The total amount paid for the tickets was
$1900
. What was the price of each kind of ticket?
plz help me with this problem
Answer:
2/3 + 1/8 = 3/11 or 1-(2/3 + 1/8)=8/11
Step-by-step explanation:
To be honest addition or subtraction would be most used in theese types of problems so I think its 2/3 + 1/8 = 3/11 or either 1-(2/3 + 1/8)=8/11
5. Ms. Lee bought 8 tickets to the basketball game and spent a total of $30. She bought a combination of adult tickets for $5 and child tickets $3 each. Which system of equations below will determine the number of child tickets, c, and the number of adult tickets, a, she bought?
Answer:
she bought five children tickets and 3 adult tickets
whats 3/2 divided by 8/3 in fraction form
Answer:
9/16
Step-by-step explanation:
3/2 / 8/3 =
3/2 x 3/8 = 9/16
Hope that helps!
This que
Diners frequently add a 15% tip when charging a meal to a credit card. What is the price of the meal without the tip if the amount charged is $48.30? How much was the tip?
The price of the meal without tip is $
The amount of the tip is $
Enter your answer in each of the answer boxes.
.
Answer:sup
Step-by-step explanation:
The first five terms in a pattern of numbers are shown. 2.4, -3.4, -9.2, 15, -20.8, If the pattern continues, which expression can be used to find the n term? A 5.8 - 3n B -- 3 -- 5.8 C8.2 -- 5.8 D 5.8 - 8.2n
Answer: C, 8.2 - 5.8n
The expression for the nth term will be 8.2 - 5.8n. Then the correct option is C.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The first five terms in a pattern of numbers are shown. 2.4, -3.4, -9.2, -15, -20.8. Then the equation is given as,
At x = 1, y is 2.4.
2.4 = m + c ...1
At x = 2, y is -3.4.
-3.4 = 2m + c ...2
From equations 1 and 2, then we have
m = -3.4 - 2.4
m = - 5.8
Then the value of 'c' is given s,
2.4 = -5.8 + c
c = 8.2
Then the equation is given as,
y = 8.2 - 5.8x
If the pattern continues. Then the expression for the nth term is given as,
y = 8.2 - 5.8n
The expression for the nth term will be 8.2 - 5.8n. Then the correct option is C.
More about the linear equation link is given below.
https://brainly.com/question/11897796
#SPJ2
The exponential function h whose graph is given below, can be written as h(x)=a*b^x Complete the equation for h(x)
Answer:
h(x) = 3*2^xStep-by-step explanation:
Given
Equation h(x)=a*b^x and its graphTwo points given on the graph:
h(0) = 3 and h(1) = 6Substitute the coordinates and simplify:
ab^0 = 3 ⇒ a = 3ab^1 = 6 ⇒ ab = 6Divide the second equation by the first to find the value of b:
b = 6/3 = 2The equation is:
h(x) = 3*2^xAnswer:
h(x) = 3*2^x
Step-by-step explanation:
HELP ME PLEASEE!!!
A prize is divided between A and B in the ratio 5:2.
If A gets €165, find the total prize fund.
Answer:
231
Step-by-step explanation:
165 divided by 5 is 33
33 X 2= 66
165+66= 231
A consumer group studied two different manufacturers of cars, J and K, to investigate differences in gas
mileage for cars made by the two manufacturers. For a similar type of car, a random sample of 15 cars
from J and a random sample of 12 cars from K were selected, and the gas mileages, in miles per gallon
(mpg), were recorded. The difference in the sample mean gas mileages was used to construct the 90
percent confidence interval (3.5,5.7).
Assuming all conditions for inference were met, which of the following is a correct interpretation of the
interval?
А
The probability is 0.90 that the difference in sample means for gas mileage for the two
car manufacturers is between 3.5 mpg and 5.7 mpg
B
The probability is 0.90 that the population mean difference in gas mileage for the two car
manufacturers is between 3.5 mpg and 5.7 mpg
About 90 percent of the differences in gas mileage for the two car manufacturers are
between 3.5 mpg and 5.7 mpg.
D
We are 90 percent confident that the difference in sample means for gas mileage for the
two car manufacturers is between 3.5 mpg and 5.7 mpg.
E
We are 90 percent confident that the population mean difference of gas mileage for the
two car manufacturers is between 3.5 mpg and 5.7 mpg.
Answer:
E
Step-by-step explanation:
AP classroom said so
Note: Triangle may not be drawn to scale.
Suppose a = 10 and b = 2.
Find an exact value or give at least two decimal places:
sin(A) =
cos(A) =
tan(A) =
Answer:
Step-by-step explanation:
more info
Exact values are follows:
sin A = 0.98
cos A = 0.20
tan A = 5
What is Trigonometric function?In mathematics, the trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
What is Pythagorean theorem?In mathematics, the Pythagorean theorem, or Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle.
Given,
a = 10, b = 2
Draw the figure using the given data
Apply Pythagorean theorem to find the third side or hypotenuse
[tex]c^{2}=a^{2} +b^{2}[/tex]
[tex]c^{2}=10^{2}+2^{2}\\c^{2}=100+4\\ c^{2}=104\\ c=\sqrt{104}[/tex]
c = 10.19 units
We know sin θ = Opposite side / Hypotenuse
Sin A = [tex]\frac{10}{10.19}[/tex]
sin A = 0.98
cos θ = Adjacent side / Hypotenuse
cos A = [tex]\frac{2}{10.19}[/tex]
cos A =0.20
tan θ = Opposite side / Adjacent side
tan A = [tex]\frac{10}{2}[/tex]
tan A = 5
Hence, the Exact values are follows:
sin A = 0.98
cos A = 0.20
tan A = 5
Learn more about Trigonometric functions and Pythagorean theorem here
https://brainly.com/question/14669175
#SPJ2
The sum of 3 times the value of x and 2 is equal to less than 5 times the value of x. Which equation can be used to find the value of x?
A. 3x+2=4-5
B. 2x+3=4-5x
C. 3x+2=5x-4
D. None of these
sum is the answer to addition problem.
less than is subtraction and "times" is multiplication.
So we have
3x+2=5x-4
So the answer is C.
Also, i'm bored so imma solve it.
3x+2=5x-4
-2 -2
3x=5x-6
-5x -5x
-2x=-6
/-2 /-2
x=3
---
hope it helps
Complete the statement with the term that makes it true.
If there is no data for a value within the range, there still needs to be a
for that value in a frequency table.
O column
Orow
Otable
Answer is in the file below
tinyurl.com/wpazsebu
What is the value of the t in the following equation? t + 1/4 = 2 7/12 A. t = 3/7 B. t = 1 2/3 C. t = 2 1/3
D. t = 3 2/3
Answer: it’s C
Step-by-step explanation:
Answer:
its c
Step-by-step explanation:
The diameter of a circle is 100cm what is the circumference of the circle use 3.14 for
Given diameter (D) = 100
Radius = D/2 = 50
Circumference = πD
= 100π
= 314.15926535898
Which equation is true for the value b= 10? OA 2(b + 4) = 16 B. 2(b + 2) = 40 3(b - 2) = 24 OD 2(8 + b) = 42 o E. 31b-4) = 20
Answer:
OC
Step-by-step explanation:
3(b-2)
3(10-2)
3(8)
24
Samuel use the distributive property to simplify the expression -6(-2 - 10x) - 7x And came up with the answer 53X -12, which is wrong.
What was Samuels mistake
Answer:
-6 x -2 = 12
-6 x -10x = 60x
12 - 60x
60x - 7x = 53x
12 - 53x
He flipped it the wrong way its supposed to be 12 - 53x not 53x - 12.
Help??I have 4 questions and im confused on all of them
Who can solve this question?I will mark them as branlist.
Answer:
See below
Step-by-step explanation:
[tex] \overrightarrow a= \bigg(\frac{5}{\sqrt 34},\:\frac{3}{\sqrt 34}\bigg)[/tex]
We have to show that [tex] \overrightarrow a[/tex] is an unit vector.
To show this, we will find the modulus of [tex] \overrightarrow a[/tex] and if its value is 1, it will be a unit vector.
So,
[tex] | \overrightarrow a| = \sqrt{\bigg(\frac{5}{\sqrt 34} \bigg) ^{2}+\bigg(\frac{3}{\sqrt 34}\bigg)^{2} } \\ \\ | \overrightarrow a| = \sqrt{\frac{25}{ 34} +\frac{9}{ 34} } \\ \\ | \overrightarrow a| = \sqrt{\frac{25 + 9}{ 34} } \\ \\ | \overrightarrow a| = \sqrt{\frac{34}{ 34} } \\ \\ | \overrightarrow a| = \sqrt{1} \\ \\ | \overrightarrow a| = 1[/tex]
Thus, [tex] \overrightarrow a[/tex] is a unit vector.
Suppose two angles in a coordinate plane, one measuring 80° and the other measuring 160°, were both rotated 180° about the origin and then
translated 40 units down. Which of these would be a measure of one of the resulting angles? Select all that apply
Answer:
120 and 40
Step-by-step explanation:
Given
[tex]\angle 1 = 160[/tex]
[tex]\angle 2 = 80[/tex]
Rotation = 180 degrees
Translation = 40 units down
Required
A measure of the resulting angles
180 degrees rotation
Rotation only affects the positioning of angles and does not change the measure of the angles.
So, the measure of both angles remain unchanged.
40 units down translation
This will reduce the measure of both angles by 40 degrees.
So:
[tex]\angle 1 = 160 - 40 = 120[/tex]
[tex]\angle 2 = 80 - 40 = 40[/tex]