Answer:
a) 22.4 pounds.
b) 0.17 pounds.
c) 0.0127 = 1.27% approximate probability the sample mean weight will be less than 22.02.
d) c = 22.62
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 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.
Average 22.4 pounds with a standard deviation of 1.36 pounds.
This means that [tex]\mu = 22.4, \sigma = 1.36[/tex]
Consider the sample mean weight of 64 watermelons of this variety.
This means that [tex]n = 64, s = \frac{1.36}{\sqrt{64}} = 0.17[/tex]
a. What is the expected value of the sample mean weight?
By the Central Limit Theorem, 22.4 pounds.
b. What is the standard deviation of the sample mean weight?
By the Central Limit Theorem, 0.17 pounds.
c. What is the approximate probability the sample mean weight will be less than 22.02?
This is the p-value of Z when X = 22.02. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{22.02 - 22.4}{0.17}[/tex]
[tex]Z = -2.235[/tex]
[tex]Z = -2.235[/tex] has a p-value of 0.0127.
0.0127 = 1.27% approximate probability the sample mean weight will be less than 22.02.
d. What is the value c such that the approximate probability the sample mean will be less than c is 0.9?
This is the 90th percentile, that is, [tex]X = c[/tex] when z has a p-value of 0.9, so X when Z = 1.28.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]1.28 = \frac{c - 22.4}{0.17}[/tex]
[tex]c - 22.4 = 1.28*0.17[/tex]
[tex]c = 22.62[/tex]
need some help with math:)
From eq(1)
[tex]\\ \sf\longmapsto x=3-3y\dots(3)[/tex]
Putting the value in eq(2)
[tex]\\ \sf\longmapsto 3y-2(3-3y)=12[/tex]
[tex]\\ \sf\longmapsto 3y-6-6y=12[/tex]
[tex]\\ \sf\longmapsto -3y-6=12[/tex]
[tex]\\ \sf\longmapsto -3y=12+6[/tex]
[tex]\\ \sf\longmapsto -3y=18[/tex]
[tex]\\ \sf\longmapsto y=\dfrac{18}{-3}[/tex]
[tex]\\ \sf\longmapsto y=-6[/tex]
Putting value in eq(3)
[tex]\\ \sf\longmapsto x=3-3(-6)[/tex]
[tex]\\ \sf\longmapsto x=3+18[/tex]
[tex]\\ \sf\longmapsto x=21[/tex]
x,y=(21,-18)Answer:
x=-3 & y=2
Step-by-step explanation:
x+3y=3----(i)
3y-2x=12----(ii)
Solving eqn--(i)
x+3y=3
or, x=3-3y---(iii)
Substituting the value of x from eqn --(iii) in eqn (ii) ,we get
3y-2x=12
or, 3y-2(3-3y)=12
or, 3y-6+6y=12
or,9y=18
y=18/9=2
Substituting the value of x in eqn--(iii),
x=3-3y=3-3*2=3-6=-3
18. Solve the equation for X.
Answer:
Option a is the correct answer
look at the image below
Answer:
4.2 mi²
Step-by-step explanation:
Volume of a cone = (1/3)πr²h, where r = radius and h = height
(1/3)πr²h
= (1/3)×π×1²×4
= 4π/3
= 4.2 mi² (rounded to the nearest tenth)
A ball is thrown straight up from a rooftop 320 feet high. The formula below describes the ball's height above the ground, h, in feet, t seconds after it was thrown. The ball misses the rooftop on its way down and eventually strikes the ground. How long will it take for the ball to hit the ground? Use this information to provide tick marks with appropriate numbers along the horizontal axis in the figure shown.
h=-16t^2+16t+320
The ball hits the ground after____ seconds
Answer:
28 seconds ..............
What is the sum of the factors of the trinomial x^2-6x+5
Its a binomial
[tex]\\ \sf\longmapsto x^2-6x+5=0[/tex]
a=1b=-6c=5If zeros be alpha and beta
[tex]\\ \sf\longmapsto \alpha+\beta=\dfrac{-b}{a}[/tex]
[tex]\\ \sf\longmapsto \alpha+\beta=\dfrac{-(-6)}{1}[/tex]
[tex]\\ \sf\longmapsto \alpha+\beta=6[/tex]
the sum of the factors of the trinomial [tex]x^2-6x+5[/tex] is -6
Given :
A trinomial [tex]x^2-6x+5[/tex]
The given trinomial is in the form of [tex]ax^2+bx+c[/tex]
Compare the given trinomial with standard form and write the value of a,b,c
a=1, b=-6 and c=5
Sum of the factors of the trinomial is [tex]\frac{b}{a} =-\frac{-6}{1} =-6[/tex]
So, the sum of the factors of the trinomial is -6
Learn more : brainly.com/question/19800260
Find two consecutive whole numbers that ✓39 lies between.
Answer:
6 and 7
Step-by-step explanation:
6^2 = 36 which is less than 39
7^2 = 49 which is more than 39
So the two numbers you want are
x = 6
y = 7
Please Help!!!
In the following expression, both A and B are variables that can take positive values.
A+2/B
Which of these actions will cause the expression's value to increase?
Choose 2 Answers
A.
Keeping A constant and increasing B
B.
Keeping A constant and decreasing B
C.
Increasing A and keeping B constant
D.
Decreasing A and keeping B constant
Answer:
B
kepping a constant and decreasing
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The midpoint of AB is (1.2). The coordinates of A are (-3, 6) Find the coordinates of B.
Answer: coordinates of B are (5,-2)
Step-by-step explanation:
let B be (x2,y2)
x1 = -3 y1 = 6
x = 1
y = 2
so
x = (x2 + x1)/2
1 = (x2+(-3))/2
or, 2 = x2 - 3
so, x2 = 5
now
y = (y2+y1)/2
or, 2 = (y2 + 6)/2
or, 4 = y2 + 6
so, y2 = -2
The perimeter of Tamara's suitcase is 8x - 3 and the perimeter of Anna's suitcase is
3x + 2. Write an algebraic expression that represents
the difference between the perimeter of Tamara's suitcase
and the perimeter of Anna's suitcase?
Answer:
perimeter: 2
Step-by-step explanation:
8x-3 = 6x
8x – 6x = 3
2x = 3
x = 3/2
The required algebraic expression that represents the difference between the perimeter of Tamara's suitcase and the perimeter of Anna's suitcase is 5x - 5.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
The difference between the perimeter of Tamara's suitcase and Anna's suitcase can be found by subtracting the expression for the perimeter of Anna's suitcase from the expression for the perimeter of Tamara's suitcase:
(8x - 3) - (3x + 2)
Simplifying the expression by removing the parentheses and combining like terms, we get:
8x - 3 - 3x - 2
= 5x - 5
Therefore, the algebraic expression that represents the difference between the perimeter of Tamara's suitcase and the perimeter of Anna's suitcase is 5x - 5.
Learn more about models here:
https://brainly.com/question/22591166
#SPJ7
Maybe you have considered buying a term life insurance policy. The expected value of any term life insurance product yields a positive expected value for the insurance company and a negative expected value for you, meaning the insurance company will make profits by selling their insurance products. Would you still buy the term life insurance? Why or why not? Are there other examples other than insurance that uses this same concept?
Answer:
Yes one should consider to buy the policy as important to have insured plan that help at the time of need.
Step-by-step explanation:
Term of life insurance is a form of life insurance which guarantees the payment of the stated death benefit. If the person des during the plan the term expires. The policy has no value other than guarantee benefits. The term life insurance will make products by selling products and thus it's necessary to have insurance. Health, age, and life expectancy are some of the points that need to consider for buying plans.solve the following equations
Answer:
x=0,5/2
Step-by-step explanation:
不
Which line is horizontal?
O y=2
O y = 2x
O y = -2x
o y=x
Answer:
y=2
Step-by-step explanation:
A horizontal line has a slope of zero so the x term is zero
y = mx+b
y = b
y must equal a constant
What is the mapping for a reflection in the line y=-1
Answer:
0
Step-by-step explanation:
the key mapping for a reflection in the line y=-1 is 0
help help......................................................................................
Hey there! Is there more text to this? I would love to help, but there is no question.
Hey there, everyone!
I just wanted to shout out to all of those whom have helped me through my tortuous math homework and say thank you very much. XD
I manage to pass my very first year of high school without physically going to school.
It was a lot of twist and turns, I must say. But at least I managed to pass through!
Man, I'm gonna miss 2021 because now I'll have to ACTUALLY go to school. But when that day comes, I do hope you guys will continue helping me on!
In the mean time, stay safe everyone and thanks a lot!
But hold up! I got one more question!
I really want to delete my account so badly but I can't because I forgot my password and I'm using my school email unfortunately. Anyone got a solution to my issue? :(
Answer:
I don't know the answer please tell me
CAN SOMEONE PLEASE HELP ME!!!!!!!
Answer:
30.2
Step-by-step explanation:
We know that quadrilateral KLMN is larger than quadrilateral GHIJ by a scale factor. In order to figure out that scale factor, we must divide a value of a side of KLMN by the value of the side that it corresponds to on GHIJ. One said side is NM, because we know it corresponds to JI on GHIJ. The value of NM is 56, and the value of JI is 13, so to figure out the scale factor, we must divide 56 by 13. We have the scale factor as 56/13, so to figure out the measure of side NM, we must find the side it corresponds to on GHIJ. The side it corresponds to is side JG, which has a value of 7. To get the value of NK, we must multiply the scale factor by 7, and the scale factor is 56/13. 56/13 times 7 is equal to 392/13. Rounding to the nearest tenth, we have the answer as 30.2
The prices of paperbacks sold at a used bookstore are approximately Normally distributed, with a mean of $7.85 and a standard deviation of $1.25.
Use the z-table to answer the question.
If the probability that Joel randomly selects a book in the D dollars or less range is 56%, what is the value of D?
$4.46
$7.75
$8.04
$8.10
(C) 8.04
Answer:
The answer you want is indeed, (C).
8.04
ED2021
Answer:
C) 8.04
Step-by-step explanation:
edge 2023
tentukan himpinan penyelasaian dari plsv berikut. A:3x+=2x+12
Answer:
x=12
Step-by-step explanation:
3x=2x+12
3x-2x=12
x=12
Volunteering: The General Social Survey asked 1309 people whether they performed any volunteer work during the past year. A total of 518 people said they did. Part: 0 / 30 of 3 Parts Complete Part 1 of 3 (a) Find a point estimate for the population proportion of people who performed volunteer work in the past year. Round the answer to at least three decimal places. The point estimate for the proportion of people who performed volunteer work in the past year is .
Answer:
The point estimate for the population proportion of people who performed volunteer work in the past year is 0.396.
Step-by-step explanation:
Point estimate of a proportion:
Proportion is the number of desired outcomes divided by the number of total outcomes.
518 out of 1309 people performed volunteer work:
This means that:
[tex]p = \frac{518}{1309} = 0.396[/tex]
The point estimate for the population proportion of people who performed volunteer work in the past year is 0.396.
g Two different factories named A and B both produce an automobile part. If a part came from A, the probability that the part is defective is .04. If the part came from B, the probability that it is defective is .05. In a sample of 180 parts, 100 came from A and 80 came from B. (a) What is the probability that a part chosen at random (from the sample) was defective
Answer:
0.0444 = 4.44% probability that a part chosen at random (from the sample) was defective.
Step-by-step explanation:
Probability of a defective part:
0.04 of [tex]\frac{100}{180}[/tex], that is, coming from A.
0.05 of [tex]\frac{80}{180}[/tex], that is, coming from B. So
[tex]p = 0.04\frac{100}{180} + 0.05\frac{80}{180} = \frac{0.04*100 + 0.05*80}{180} = 0.0444[/tex]
0.0444 = 4.44% probability that a part chosen at random (from the sample) was defective.
Find the missing Side of the triangle
Answer:
2√15
Step-by-step explanation:
Use the Pythagorean theorem.
2² + x² = 8²
x² + 4 = 64
x² = 60
x² = 4 * 15
x = 2√15
is f(x)=e^-3x an exponential function?
Nicole took a taxi from her house to the airport. The taxi company charged a pick-up fee of $2.90 plus $1.75 per mile. The total fare was $44.90, not including the tip. Write and solve an equation which can be used to determine xx, the number of miles in the taxi ride.
9514 1404 393
Answer:
24 miles
Step-by-step explanation:
The total fare is the sum of the pickup fee and the mileage charge. For xx miles, the mileage charge will be 1.75xx, so the total is ...
1.75xx +2.90 = 44.90 . . . equation for xx
1.75xx = 42.00 . . . . . subtract 2.90
xx = 24 . . . . . . . . . divide by 1.75
The number of miles in Nicole's taxi ride was 24.
Find the zeros of the function in the interval (-2 pie, 2 pie). f(x) = 3 cos x
Answer:
Roots are -π/2 and π/2
Step-by-step explanation:
[tex]{ \bf{f(x) = 3 \cos(x) }}[/tex]
when x is -2π:
[tex]{ \sf{f( - 2\pi) = 3 \cos( - 2\pi) }} \\ { \sf{ = 3}}[/tex]
hence -2π is not a zero of the function
when x is 2π:
[tex]{ \sf{f(2\pi) = 3 \cos(2\pi) }} \\ { \sf{ = 3}}[/tex]
hence 2π is not a zero of the function
when x is π/2:
[tex]{ \sf{f( \frac{\pi}{2}) = 3 \cos( \frac{\pi}{2} ) }} \\ { \sf{ = 0}}[/tex]
Hence ±π/2 is the zero of the function.
Answer the picture. X=450 BAC= 82 ABC=52
What’s the distance between A to C
Answer:
Hello,
Step-by-step explanation:
[tex]mes\ \widehat{C}=180^o-82^o - 52^o=46^o\\\\Using\ law\ of\ sinus:\\\dfrac{AB}{sin(C)}= \dfrac{AC}{sin(B)} \\\\\dfrac{450}{sin(46^o)}= \dfrac{AC}{sin(52^o)} \\\\AC=\dfrac{450*sin(52^o)}{sin(46^o)}= 492.9587..(ft)\approx{493(ft)}[/tex]
six times the sum of a number and 4 is 5
The sum of 6 times a number and 4 equals 5
The sum (+) of 6 times (multiply by 6) a number (x) and 4 equals (=) 5
6 times (multiply by 6) a number (x) + 4 = 5
6x + 4 = 5
6x = 5 - 4
6x = 1
x = 1/6
Answer:
6(x+4) = 5
=> 6x + 24 = 5
=> 6x= -19
=> x = -19/6
=> x = -3.16666
Lets subtitute the value of x for proof
6(x+4)
6(-3.16666+4)
-18.999996+24
= 5.00004~ 5.00
Kayla made two paper chains. The paper links on one represented the number of days until her birthday, and the other showed the days until summer vacation. Altogether, she made 135 links for her chains. The birthday chain had twice as many links as the vacation chain. How many links are on Kayla's birthday chain?
Answer:
90 days
Step-by-step explanation:
b= number of days til her birthday
s = number of days til summer
b+s =135
b = 2s
2s+s = 135
3s = 135
Divide by 3
3s/3 =135/3
s =45
b = 2s = 2(45) = 90
give 12 consecutive integers, in how many ways can three of these integers be selected to give a sum which divides by 4?
Answer:
55 waysStep-by-step explanation:
Out of 12 consecutive integers:
3 - divide by 4, so the remainder is 03- give remainder of 13- give remainder of 23 - give remainder of 3Sum of 3 integers will be divisible by 4 if the remainders are:
0 - 0 - 0 ⇒ 1 combination0 - 1 - 3 ⇒ 3*3 = 9 combinations0 - 3 - 1 ⇒ 3*3 = 9 combinations1 - 1 - 2 ⇒ 2*3 = 6 combinations1 - 2 - 1 ⇒ 2*3 = 6 combinations2 - 1 - 1 ⇒ 2*3 = 6 combinations3 - 0 - 1 ⇒ 3*3 = 9 combinations3 - 1 - 0 ⇒ 3*3 = 9 combinationsSo total number of combinations is:
1 + 4*9 + 3*6 = 55X-3y=-3; ( ,4), (12, ) complete each ordered pair
Answer:
(9,4) and (12,5)
Step-by-step explanation:
x-3y=-3
y=4, x-3*4=-3, x=9. (9,4)x=12, 12-3y=-3, y=5. (12,5)I need help with this balance mobile please:)
Answer:
blue 1
orange 5
green 3
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