Answer:
0.0062 = 0.62% probability that the sample mean is less than $650.
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 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.
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.
Mean of $675 and a standard deviation of $80.
This means that [tex]\mu = 675, \sigma = 80[/tex]
A random sample of 64 families in this city paying for childcare is selected.
This means that [tex]n = 64, s = \frac{80}{\sqrt{64}} = 10[/tex]
Find the probability that the sample mean is less than $650.
This is the pvalue of Z when X = 650.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{650 - 675}{10}[/tex]
[tex]Z = -2.5[/tex]
[tex]Z = -2.5[/tex] has a pvalue of 0.0062
0.0062 = 0.62% probability that the sample mean is less than $650.
The probability that the sample mean is less than $650 is 0.62%.
The z score is given by:
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} } \\\\where\ x=raw\ score,\sigma=standard\ deviation,\mu=mean,n=sample\ size\\\\\\Given \ \mu=675,\sigma=80,n=84, hence:\\\\For\ x<650:\\\\z=\frac{650-675}{80/\sqrt{64} } =-2.5[/tex]
From the normal distribution table:
P(x < 650) = P(z < -2.5) = 0.0062 = 0.62%
The probability that the sample mean is less than $650 is 0.62%.
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a new optical illusion is posred on the internet. Write a recursive formula to describe the pattern. The, write the explicit formula that can be used to find the number of times the optical illusionis shared after eight hours.
Answer:
hope this helps
The solution is 3,27,680
The geometric progression is given by aₙ = a ( r )ⁿ⁻¹ , where r = 4 is the common ratio and after 8 hours a₈ = 3,27,680
What is Geometric Progression?A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.
The nth term of a GP is aₙ = arⁿ⁻¹
The general form of a GP is a, ar, ar2, ar3 and so on
Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )
Given data ,
Let the first term of the geometric sequence be a₁ = 20
Let the second term a₂ = 80
So , the common ratio r = second term / first term
On simplifying the equation , we get
Common ratio r = 80/20
Common ratio r = 4
Now , the explicit formula for the GP is
aₙ = a ( r )ⁿ⁻¹ , where n is the number of hours
aₙ = 20 ( 4 )ⁿ⁻¹
So , after 8 hours ,
Substitute the value of n = 8 in the equation , we get
a₈ = 20 ( 4 )ⁿ⁻¹
a₈ = 20 ( 4 )⁷
a₈ = 3,27,680
Therefore , the value of a₈ = 3,27,680
Hence , the equation is aₙ = 20 ( 4 )ⁿ⁻¹
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PLS HELP ME OUT WITH THIS
Student A: 78, 99, 80, 85, 95, 79, 85, 96
Student B: 100, 80, 79, 75, 92, 93, 75, 78, 84
Student A Mean:
Student A Mean Absolute Deviation:
Student B Mean:
Student B Mean Absolute Deviation:
Student A Mean:
(78 + 99 + 80 + 85 + 95 + 79 + 85 + 96)/8 = 87.125
Student A Mean Absolute Deviation: 7.15625
Student B Mean:
(100+ 80+ 79+75+92+ 93+75+ 78+ 84) / 9 = 84
Student B Mean Absolute Deviation: 7.33
HELP PLS MIGHT GIVE BRAINLIST BUT ONLY IF 2 PEOPLE ANSWER!
What are the coordinate points of A, B, C and D in quadrilateral ABCD? Refer to the image attached :)
Answer:
(-3,4),(5,4),(5,-4),(-3,-4)
Step-by-step explanation:
I mean its plotting
Three girls walked home together each day. They walked at a rate of 3 miles per hour. They left school each day at 3:35 pm. The first girl arrived home at 3:55 pm. The other two girls arrived home at 4:05 pm and 4:15 pm. What is the total number of miles walked by the three girls combined?
solved answer
Answer:
4.5
Step-by-step explanation:
first girl took 20 mins walking 1 mile
second girl took 30 mins walking 1.5 miles
third girl took 40 mins walking 2 miles
Pls help me with this one!! :>
Answer:
i dont see a picture?
Step-by-step explanation:
Step-by-step explanation:
the student who has the highest grades in a particular group of students and who gives the valedictory speech at a graduation ceremony compare salutatorian.
50 POINTS!
Match the symbols used in electric circuit diagrams to their functions.
Circuit Symbols Matching
1.
a device that converts electric energy into sound energy
2.
a device that provides energy to a circuit
3.
a device that glows when it receives current
4.
a device that starts or stops the flow of current
Answer:
im gussing sorry if its wrong :(
Step-by-step explanation:
1=a
2=d
3=b
4=c
PLz this is fr a quiz. There are forty - three walnut trees and thirty - four dogwood trees currently in the park. Park workers will plant more walnut trees today. When the workers are finished there will be sixty - five walnut trees in the park. How many walnut trees did the workers plant today ? explain in two sentence
mathematical literacy
Answer:
hope that help
Step-by-step explanation:
Mathematical literacy is defined as: "an individual's capacity to formulate, employ and interpret mathematics in a variety of contexts. It includes reasoning mathematically and using mathematical concepts, procedures, facts and tools to describe, explain and predict phenomena.
(02.01)Polygon ABCD slides 4 units left and 3 units up on the coordinate plane. If the original measure of angle A was 75 degrees, what is the measure of angle A'?
A-75 degrees
B-100 degrees
C-105 degrees
D-180 degrees
Morre Math HARDDDDDDDD
Answer:
the person above is right it's 4.5 units
give them the crown
Consider the polynomial function q(x)=-2x^8+5x^6-3x^5+50q(x)=−2x 8 +5x 6 −3x 5 +50q, left parenthesis, x, right parenthesis, equals, minus, 2, x, start superscript, 8, end superscript, plus, 5, x, start superscript, 6, end superscript, minus, 3, x, start superscript, 5, end superscript, plus, 50. What is the end behavior of the graph of q\q q, space? Choose 1 answer: Choose 1 answer:
Answer:
Step-by-step explanation:
The end behavior of the graph of q(x) is x → ∞, q(x) → -∞ and x → -∞, q(x) → -∞ option (C) is correct.
What is polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
The question is incomplete.
The complete question is in the picture, please refer to the attached picture
We have a polynomial shown in the picture:
q(x) = -2x⁸ + 5x⁶ - 3x⁵ + 50
The above polynomial is an eight-degree polynomial and the curve of the polynomial will be a curve graph.
After plotting the graph of a polynomial function we will see:
x → ∞
q(x) → -∞
x → -∞
q(x) → -∞
Thus, the end behavior of the graph of q(x) is x → ∞, q(x) → -∞ and x → -∞, q(x) → -∞ option (C) is correct.
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Find the area of the shape
A rectangle is 5 times as long as it is wide. The perimeter is 50 cm. Find the dimensions of the rectangle. Round to the nearest tenth if necessary.
Answer:
Dimensions = 21 centimeters by 4.2 centimeters.
Step-by-step explanation:
Let the length of the rectangle be L.
Let the width of the rectangle be W.
Given the following data;
Perimeter of rectangle = 50cm
Translating the word problem into an algebraic expression, we have;
L = 5W
To find the dimensions of the rectangle;
Perimeter of rectangle = 2L + 2W
50 = 2L + 2W
50 = 2(5W) + 2W
50 = 10W + 2W
50 = 12W
W = 50/12
W = 4.2 cm.
To find the length;
L = 5W
L = 5*4.2
L = 21 cm.
Solve 4c + 10 = 2. A. c = 2 B. c = -3 C. c = 3 D. c = -2
Answer:
d.c=-2
Step-by-step explanation:
Answer: A. c=-2
Step-by-step explanation:
4c + 10 = 2
4c = -8
c = -2
A cylindrical tank of radius 2.5 feet is being drained of water at a rate of `0.25\ ft^{3}/\sec`. How fast is the height of the water decreasing?
Answer:
DONT PRESS THAT LINK
Step-by-step explanation:
The height of the water decreases at a rate of 0.012 ft/sec if a cylindrical tank of a radius of 2.5 feet is being drained of water at a rate of 0.25 ft³/sec.
What is a cylinder?In geometry, it is defined as the three-dimensional shape having two circular shapes at a distance called the height of the cylinder.
We know the volume of the cylinder is given by:
[tex]\rm V = \pi r^2 h[/tex]
It is given that:
A cylindrical tank of a radius of 2.5 feet is being drained of water at a rate of 0.25 ft³/sec
As we know,
The volume of the cylinder is given by:
V = πr²h
Let V is the water draining rate
V = 0.25 ft³/sec
The radius r = 2.5 feet
0.25 ft³/sec = π(2.5 feet)²(h)
h = [0.25/(2.5²π)] [ft³/(sec×feet²]
h = 0.012 ft/sec
Thus, the height of the water decreases at a rate of 0.012 ft/sec if a cylindrical tank of a radius of 2.5 feet is being drained of water at a rate of 0.25 ft³/sec.
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I have an account. Why is your site not recognizing me.
Answer:
I don't know why that would be. I think you can contact they for customer support but I am not sure.
Step-by-step explanation:
The sum of three consecutive odd integers is -39. What is the largest integer?
Answer:
the sum of three consecutive odd number is less than 54.
Select the correct answer. Find the solution(s) for x in the equation below.
x2-9x+20=0
Step-by-step explanation:
Given
x² - 9x + 20 = 0
x² - ( 4 + 5) x + 20 = 0
x² - 4x - 5x + 20 = 0
x ( x - 4 ) - 5 (x - 4 ) = 0
(x - 4 ) ( x - 5 ) = 0
Either
x - 4 =0
x = 4
or
x - 5 =0
x = 5
x = 4 and 5
Hope it will help :)
[tex].)[/tex]
Answer: hope this helps. Check out the image.. and can u give me brainliest pls and I also have explanation
Step-by-step explanation:
A piece of ribbon is cut into three pieces that have length in the extended ratio of 7:8:9. The length of the ribbon is 96 centimeters. What is the length of each piece of ribbon?
Answer:
28:32:36
Step-by-step explanation:
you add the ratios up all together and divide your answer by 96 the answer you get there you multiply it with the ratios
Help meh with an explication
Answer:
[tex]\frac{6}{\sqrt 2}= 3\sqrt 2[/tex]
Step-by-step explanation:
Given
[tex]\frac{6}{\sqrt 2}[/tex]
Required
Rationalize
[tex]\frac{6}{\sqrt 2}[/tex]
To do this, we simply multiply by [tex]\frac{\sqrt 2}{\sqrt 2}[/tex]
[tex]\frac{6}{\sqrt 2} * \frac{\sqrt 2}{\sqrt 2}[/tex]
This gives:
[tex]\frac{6 * \sqrt 2}{\sqrt 2 * \sqrt 2}[/tex]
[tex]\frac{6 \sqrt 2}{2 }[/tex]
[tex]3\sqrt 2[/tex]
Hence:
[tex]\frac{6}{\sqrt 2}= 3\sqrt 2[/tex]
Susie can run 4 2/3 miles per hour. If she runs for 3/4 hours how far will she have run?
A box in the shape of a rectangular prism has the dimensions shown. What is the length of the interior diagonal of the box? Round to the nearest tenth. Enter your answer in the box.
A rectangular prism 60 centimeters wide, 80 centimeters long, and 100 centimeters tall.
Answer:
i think it is 141.4
Step-by-step explanation:
What's is 2+5 times 18 please answer fast
Free 100 points
Answer:
92
Step-by-step explanation:
5 times 18=90
90+2=92
you do times first because order of operations.
Answer:
92
Step-by-step explanation:
goodluck
The triangle below is isosceles. If ∠C≅∠B, then what is BC, in units?
Answer:
Step-by-step explanation:
If angles C and B have equal degrees then the side AC is also equal to side AB in length and you can make their equations equal as well and solve for X.
2x+16=7x+6
get X's all on same side and the constants all on the other side,
-2x +2x+16=7x+6+-2x
The X's on the left cancel out.
16=5x+6
-6+16=5x+6+-6
add -6 to each side. On the right the 6 is now cancelled out.
10=5X
divide each side by 5 to cancel out the 5
10/5= 5X/5
2=X . ANSWER
PLEASE HELP!
Find the area of each figure.
18 square units
9 square units
12 square units
24 square units
MATCH THE NUMBERS TO THE GRAPHS!!!!!
I do know the first figure is 24 square feet.
To get your answer,
Count the amount of the blocks stacked on top each other to make the length, in this case the first photo would be 3, and the width of the block, which is 8. To get the area, you would multiply the length and width together.
Image Form:
l x w = a
(length x width = area)
I hope this is a clear explanation!
Answer:
first one is 24
second one is 12
third one is 9
fourth one is 18
Step-by-step explanation:
John bought a car for $65.000. If the value depreciates by 8% each year,how much will the car be worth at the end of two years?
Answer:
$546000
Step-by-step explanation:
($65000×8%)(2)
- 4(x + 5) = 16 what does x equal?
Answer:x= 9
Step-by-step explanation:
-4(x+5) = 16
-4*x= -4x -4*5= -20
16 - -20= 36
-4x/-4= x 36/-4=9
PLEASE HELP ME 30 points!!!
Multiple Choice
Eighteen students in a class play baseball.
Seventeen students in the class play basketball.
Thirty students in the class play either or both sports
Select the Venn diagram that shows the number of students who play basketball and baseball.
Answer:
A
Step-by-step explanation:
its a bec count how many student are their an see if they add IP to 30
The Venn diagram which shows the number of students who play basketball and baseball is option A.
What is Venn Diagram?Venn diagram is a diagram denoting two or more sets which is drawn using circles inside a rectangle where the part where the two circle meet denotes the intersection of two sets.
Let A denotes the students playing baseball and B denotes the student playing basketball.
N(A) = 18
N(B) = 17
N(A ∪ B) = 30
We know,
N(A ∩ B) = N(A) + N(B) - N(A ∪ B)
= 18 + 17 - 30
= 35 - 30
= 5
Number of students who play both baseball and basketball = 5
Number of students who plays only baseball = 18 - 5 = 13
Number of students who plays only basketball = 17 - 5 = 12
This is shown in A.
Hence the correct option is A.
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The manager of a fast-food restaurant wants to be sure that, on average, customers are served within 4 minutes from the time the order is placed. He is particularly concerned about the staff working during the early morning shift. From a random sample of 41 orders, the mean time was 3.75 minutes with a standard deviation of 1.2 minutes.
(a) Is there convincing evidence at the a = 0.05 significance level that the true mean service time during the early morning shift is less than 4 minutes?
Answer:
There is not convincing evidence at the a = 0.05 significance level that the true mean service time during the early morning shift is less than 4 minutes
Step-by-step explanation:
The null hypothesis is:
[tex]H_{0} = 4[/tex]
The alternate hypothesis is:
[tex]H_{1} < 4[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
From a random sample of 41 orders, the mean time was 3.75 minutes with a standard deviation of 1.2 minutes.
This means that [tex]n = 41, \mu = 3.75, \sigma = 1.2[/tex]
The test-statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{3.75 - 4}{\frac{1.2}{\sqrt{41}}}[/tex]
[tex]z = -1.33[/tex]
[tex]z = -1.33[/tex] has a pvalue of 0.0918, looking at the z-table.
0.0918 > 0.05, which means that the null hypothesis is accepted, and that there is not convincing evidence at the a = 0.05 significance level that the true mean service time during the early morning shift is less than 4 minutes