Answer:
The probability that the mean daily precipitation will be of X inches or less for a random sample of n November days is the p-value of [tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex], in which [tex]\mu[/tex] is mean amount of inches of rain and [tex]\sigma[/tex] is the standard deviation.
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.
In this question:
Mean [tex]\mu[/tex], standard deviation [tex]\sigma[/tex]
n days:
This means that [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
Applying the Central Limit Theorem to the z-score formula.
[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
What is the probability that the mean daily precipitation will be of X inches or less for a random sample of November days?
The probability that the mean daily precipitation will be of X inches or less for a random sample of n November days is the p-value of [tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex], in which [tex]\mu[/tex] is mean amount of inches of rain and [tex]\sigma[/tex] is the standard deviation.
Quadrilateral
N
V
D
I
NVDI can be mapped onto Quadrilateral
F
L
S
W
FLSW by a reflection. If
m
∠
V
=
2
3
∘
m∠V=23
∘
and
m
∠
D
=
8
1
∘
m∠D=81
∘
, find
m
∠
S
m∠S.
9514 1404 393
Answer:
∠S = 81°
Step-by-step explanation:
Reflection does not change the angle measures.
The quadrilateral names tell you angle D corresponds with angle S. So, angle S has the same measure.
∠S = ∠D = 81°
The mean height of women in a country (ages 20-29) is 64 4 inches A random sample of 50 women in this age group is selected What is the probability that the mean height for the sample is greater than 65 inches? Assume o = 2.91 The probability that the mean height for the sample is greater than 65 inches is
Answer:
0.0721 = 7.21% probability that the mean height for the sample is greater than 65 inches.
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.
Mean of 64.4 inches, standard deviation of 2.91
This means that [tex]\mu = 64.4, \sigma = 2.91[/tex]
Sample of 50 women
This means that [tex]n = 50, s = \frac{2.91}{\sqrt{50}}[/tex]
What is the probability that the mean height for the sample is greater than 65 inches?
This is 1 subtracted by the p-value of Z when X = 65. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{65 - 64.4}{\frac{2.91}{\sqrt{50}}}[/tex]
[tex]Z = 1.46[/tex]
[tex]Z = 1.46[/tex] has a p-value of 0.9279
1 - 0.9279 = 0.0721
0.0721 = 7.21% probability that the mean height for the sample is greater than 65 inches.
You have savings of 30,000. You invest in a bond mutual fund that pays 3% simple interest. What are your total savings after 20 years?
Answer:
54,183.34
Step-by-step explanation:
a = 30,000(1.03)²⁰
a = 54,183.34
A and B are independent events. Use the following probabilities to answer the question. Round to 4 decimal places.
P(A) = 0.32, P(A and B) = 0.09, find P(B)
P(B) =
Answer:
.2813
Step-by-step explanation:
If two events are independent that means that
A*B= A and B
so
let p(b)= x
.09=.32*x
x= .28125
Round this to
.2813
Step-by-step explanation:
since p(a) and p(b) are independent events
p(a).p(b)= p(a and b)
0.32×p(b)=0.09
p(b)=0.09÷0.32
p(b)=0.28
two(2) color game dice were tossed together. make lists of possible outcomes, if each color game die has pink, red, orange, blue, green, and yellow side UseP for pink, R for red, O for orange, B for blue, G for green, and Y for yellow. write your answers in your notebook
How to solve and answer
Answer:
D. (-2, 0) and (3, 0).
Step-by-step explanation:
At the x -intercepts the function = 0, so
(2x + 4)(x - 3) = 0
2x + 4 = 0 and x - 3 = 0
x = -4/2 = -2 and x = 3.
So they are (-2, 0) and (3, 0).
x = 3 or x = -2
Step-by-step explanation:
f(x) = (2x + 4)(x - 3)
y = (2x + 4)(x - 3)
x - intercept occurs when y = 0
0 = (2x + 4)(x - 3)
0 = 2x² - 6x + 4x - 12
2x² - 2x - 12 = 0
(2x² - 2x - 12)/2 = 0/2
x² - x - 6 = 0
From the quadratic formula,
x = (-b +- √(b² - 4ac))/2a
x = (- ( -1 ) +- √(( -1)² - 4( 1 )( -6 )))/2( -1 )
x = (1 +- √(1 - ( -24)))/-2
x = (1 +- √25)/-2
x = (1 +- 5)/-2
x = 3 or x = -2
If this the graph of f(x), then which of the following could be the graph of f-1(x)
The graph (C) represents the inverse function of f(x) if the graph of a function f(x) is given option (C) is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have a graph of f(x) is shown in the picture.
As we know, if f(x) has ordered double (x, y)
Then inverse of function g(x) must have ordered double (y, x)
From the given options graph (C) satisfy the condition.
Thus, the graph (C) represents the inverse function of f(x) if the graph of a function f(x) is given option (C) is correct.
Learn more about the function here:
brainly.com/question/5245372
#SPJ1
Answer:
the answer would be option C
At a real estate agency, an agent sold a house for $367,000 The commission rate is
6.5% for the real estate agency and the commission rate for the agent is 25 % of the amount the real estate agency gets. How much did the agency make on the house? How much did the agent earn in commission?
The agency made $___ on the house.
Answer:
The agency makes 23855
The agent makes 5963.75
Step-by-step explanation:
First find the commission for the agency
367000 * 6.5%
367000*.065
23855
Now the agent gets 25% of this amount
23855 *25%
23855 *.25
5963.75
Answer:
Step-by-step explanation:
The agency made $24,440.00
The Agent made $6,110.00
what is a case control study
Answer:
A study that compares two groups of people: those with the disease or condition under study (cases) and a very similar group of people who do not have the disease or condition (controls). Researchers study the medical and lifestyle histories of the people in each group to learn what factors may be associated with the disease or condition. For example, one group may have been exposed to a particular substance that the other was not. Also called retrospective study.
Step-by-step explanation:
Answer:
A case-control study is designed to help determine if an exposure is associated with an outcome (i.e., disease or condition of interest).
Step-by-step explanation:
Use the following formula for compound interest. If P dollars is invested at an annual interest rate r (expressed as a decimal) compounded n times yearly, the amount A after t years is given by
A= P(1+ r/n)^nt
Required:
What rate of interest is required so that $1000 will yield $1900 after 5 years if the interest rate is compounded monthly?
Answer:
12.906%/year
Step-by-step explanation:
Given data
Principal= $1000
Final Amount= $1900
Time= 5 years
The compound interest formula is given as
A= P(1+ r/n)^nt
Solving for rate r as a decimal
r = n[(A/P)1/nt - 1]
r = 12 × [(1,900.00/1,000.00)1/(12)(5) - 1]
r = 0.12906
Then convert r to R as a percentage
R = r * 100
R = 0.12906 * 100
R = 12.906%/year
Savannah needs to buy a bag of dog food that will last for 2 weeks (14 days). She
estimates that a 20 lb bag will be enough. Is she correct?
Answer:
if it is a chihuahua, then it will be just fine with 20lb
Which of the following sets of data does not contain an outlier?
A.16, 17, 20, 19.48
B.59. 60. 61, 67.65
C.95.99.97.94.60
D.-1.2.1.0.5.16
Answer:
it is a letter b
Step-by-step explanation:
that does not contain an outlet
What are the zeros of the function y = 2x2 + 5x + 2?
A. x =
- 3x =
x = -2
B. X =
1
2
.X = 2
C. X =
3.x=-2
O D. x=-1.x = 2
Answer: not sure
but I need points
Step-by-step explanation:
JUST KIDDING It’s A I did this in school before and got it correct :)
Which choice describes symmetry?
A. When something is exactly the same on one side as it is on the
other side.
B. When something looks completely different on one side than
the other side.
C. When something has a spherical shape.
Answer: A. When something is exactly the same on one side as it is on the
other side
Step-by-step explanation: symmetry mean symmetrical: aka they look the same :) hope this helped!
anyone help me, let's prove
Answer:
In my opinion the limit is equal to 1 not 0, sorry.
Step-by-step explanation: 6 25 13 43
lim n ⇒∞ ((2n - 1)/2n)
lim n ⇒∞ (2n/2n) - 1)/2n) 2n/2n = 1 1/∞ = 0
= 1 - 0
= 1
when I graphed the function I also got 1
A filling machine fills bottles of nail polish with amounts that are normallydistributed with mean 18 mL and standard deviation 0.6 mL. A random sample of 12 bottles of this nail polish is selected for inspection.
Required:
a. What is the probability that one of the randomly selected bottles is filled with less than 17.5mL of nail polish?
b. What is the probability that the average fill of the twelve bottles is more than 17.5mL?
Answer:
a. 0.2033 = 20.33% probability that one of the randomly selected bottles is filled with less than 17.5mL of nail polish
b. 0.0019 = 0.19% probability that the average fill of the twelve bottles is more than 17.5mL
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.
Mean 18 mL and standard deviation 0.6 mL.
This means that [tex]\mu = 18, \sigma = 0.6[/tex]
a. What is the probability that one of the randomly selected bottles is filled with less than 17.5mL of nail polish?
This is the p-value of Z when X = 17.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{17.5 - 18}{0.6}[/tex]
[tex]Z = -0.83[/tex]
[tex]Z = -0.83[/tex] has a p-value of 0.2033
0.2033 = 20.33% probability that one of the randomly selected bottles is filled with less than 17.5mL of nail polish.
b. What is the probability that the average fill of the twelve bottles is more than 17.5mL?
Twelve bottles, so now [tex]n = 12, s = \frac{0.6}{\sqrt{12}}[/tex]
The probability is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{17.5 - 18}{\frac{0.6}{\sqrt{12}}}[/tex]
[tex]Z = -2.89[/tex]
[tex]Z = -2.89[/tex] has a p-value of 0.0019
0.0019 = 0.19% probability that the average fill of the twelve bottles is more than 17.5mL
PLEASE IM BEGGING ILL GIVE YOU BRAINIEST:
100 students are interviewed to see which of biology, chemistry or physics they prefer.
17 of the students are girls. 3 of the girls like biology best.
24 of the boys prefer physics.
8 out of the 28 who prefer chemistry are girls.
What percentage of the students prefer biology?
Answer:
32%
Step-by-step explanation:
3 girls like biology, 8 like chem and the rest prefer physics. 28 people like chemistry, and 24 boys like physics. This leaves 29 boys and 3 girls liking bio.
What type of number is 12/3
Choose all that apply.
Whole number
Integer
Rational
Irrational
Answer: Rational
Step-by-step explanation: bc
What are the solutions of the equation 3x2+6x−24=0
Answer:
x = -4, x = 2
Step-by-step explanation:
We can start by dividing both sides by 3, the GCF of the right side, in order to make the problem easier to solve:
3x^2 + 6x - 24 = 0
x^2 + 2x - 8 = 0
Now, we can factor this equation. We need to find two numbers that add to 2 and multiply to -8. These numbers are 4 and -2. Therefore, we can factor the equation as follows:
(x + 4)(x - 2) = 0
Using the zero product property we get two equations which we can solve:
x + 4 = 0
x = -4
x - 2 = 0
x = 2
Which polygon has
an interior angle sum of
1080°?
Answer:
OctagonStep-by-step explanation:
An octagon has eight sides, so the sum of the angles of the octagon is 180(8 – 2) = 180(6) = 1080 degrees.
Because the octagon is regular, all of its sides and angles are congruent
Answer:
It's an octagon. So should be the first one with 8 points.
Step-by-step explanation:
Suppose that from a group of 9 men, 1 will be randomly chosen for a dangerous assignment, and suppose that the chosen man will be killed during the assignment with a probability of 1/6. If Mark is one of the 9 men, what is the probability that he will be chosen for the assignment and killed during the assignment
Answer:
1/54
Step-by-step explanation:
1/9 x 1/6
(3√5 + 4√2)(√5 + √2）
Answer:
Step-by-step explanation:
3√5*√5+3√5*√2+ 4√2*√5+ 4√2*√2
15 +3√10 + 4√10 + 8
23+7√10
the fraction 6/10 is equivalent to which of the following? 12/24 or 24/40 or 3/6 or 16/20
Answer:
24/40
Step-by-step explanation:
You can multiply both the numerator and denominator by any number
Option #3: Lets multiply by 1/2 since when you multiply 6*1/2 it equals 3 and that is the same numerator as option #3 and so now let's do the same again to the denominator 10*1/2 equals 5 and that is NOT equal to 6 in the denominator for option #3 and you can't get 3 any other way than multiplying by 1/2 (same as *.5) and so it is wrong.
Now since we know how to do it I'll just do the math for the rest.
Option 1:
6/10
6*2/10*2
12/20 and that doesn't match so it's wrong.
Option 2:
6/10
6*4/10*4
=
24/40
It matches so it's correct let's try option 4 just to check.
Option 4:
6/10
6*2/10*2
12/20
that doesn't match so it's wrong (you could have tried multiplying by decimals by I doubt you are there to that kind of math yet.)
Answer: 24/40
The time to complete an exam is approximately Normal with a mean of 48 minutes and a standard deviation of 3 minutes. The bell curve below represents the distribution for testing times. The scale on the horizontal axis is equal to the standard deviation. Fill in the indicated boxes.
Answer:
This means the average amount of time is 48 minutes but many people will do it in 45 to 51
Hope This Helps!!!
Do the following lengths form a right triangle?
Answer:
Yes
Step-by-step explanation:
The lengths of this right angle triangle (6, 8, 10) proves that the polygon is indeed a right angle triangle. This is because there are certain ratios to prove that a right angle triangle is indeed a right angle triangle. These are called the Pythagorean Triples . Some examples include; (3, 4, 5), (7, 24, 25) and (28, 45, 53). The Pythagorean Triple 3, 4, 5 can be scaled up to provide the triple 6, 8, 10, where the scale factor is 2.
what is the midpoint with the line segments with end points (-4, 6) (2,-1)
Answer:
(-1, 5/2)
Step-by-step explanation:
Midpoint = (-4 + 2)/ 2 , (6 - 1)/2
= (-2/2), (5/2)
= (-1, 5/2)
Answer:
Step-by-step explanation:
The midpoints of two coordinate is = [tex]\frac{x2 + x1}{2}[/tex] , [tex]\frac{y2 +y1}{2}[/tex].
Let x2 = 2
x1 = -4
y2 = -1
y1 = 6
Solution:
[tex]\frac{2+-4}{2} , \frac{-1+6}{2} \\\\\\= (-1,\frac{5}{2})[/tex]
Differentiate the function, y = (2x - 5)^2 (5-x^5)^2?
Answer:
[tex]\displaystyle y' = 2(2x - 5)(x^5 - 5)(12x^5 - 25x^4 - 10)[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Algebra I
Terms/CoefficientsFactoringCalculus
Derivatives
Derivative Notation
Derivative of a constant is 0
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Rule [Product Rule]: [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
y = (2x - 5)²(5 - x⁵)²
Step 2: Differentiate
Derivative Rule [Product Rule]: [tex]\displaystyle y' = \frac{d}{dx}[(2x - 5)^2](5 - x^5)^2 + (2x - 5)^2\frac{d}{dx}[(5 - x^5)^2][/tex]Chain Rule [Basic Power Rule]: [tex]\displaystyle y' = [2(2x - 5)^{2-1} \cdot \frac{d}{dx}[2x]](5 - x^5)^2 + (2x - 5)^2[2(5 - x^5)^{2-1} \cdot \frac{d}{dx}[-x^5]][/tex]Simplify: [tex]\displaystyle y' = [2(2x - 5) \cdot \frac{d}{dx}[2x]](5 - x^5)^2 + (2x - 5)^2[2(5 - x^5) \cdot \frac{d}{dx}[-x^5]][/tex]Basic Power Rule: [tex]\displaystyle y' = [2(2x - 5) \cdot 1(2x^{1 - 1})](5 - x^5)^2 + (2x - 5)^2[2(5 - x^5) \cdot -5x^{5 - 1}][/tex]Simplify: [tex]\displaystyle y' = [2(2x - 5) \cdot 2](5 - x^5)^2 + (2x - 5)^2[2(5 - x^5) \cdot -5x^4][/tex]Multiply: [tex]\displaystyle y' = 4(2x - 5)(5 - x^5)^2 - 10x^4(2x - 5)^2(5 - x^5)[/tex]Factor: [tex]\displaystyle y' = 2(2x - 5)(5 - x^5)[2(5 - x^5) - 5x^4(2x - 5)][/tex][Distributive Property] Distribute 2: [tex]\displaystyle y' = 2(2x - 5)(5 - x^5)[10 - 2x^5 - 5x^4(2x - 5)][/tex][Distributive Property] Distribute 5x⁴: [tex]\displaystyle y' = 2(2x - 5)(5 - x^5)[10 - 2x^5 - 10x^5 + 25x^4][/tex][Addition] Combine like terms (x⁵): [tex]\displaystyle y' = 2(2x - 5)(5 - x^5)(10 - 12x^5 + 25x^4)[/tex]Rewrite: [tex]\displaystyle y' = 2(2x - 5)(x^5 - 5)(12x^5 - 25x^4 - 10)[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
solve the following
2(x-2)=8
Answer:
2
Step-by-step explanation:
2 (x-2)=8 equal to 2x-4=8, put -4 to the other side by subtracting 4 on both sides once you do you get 2x=4 so 4 divided by 2 equals 2.
Answer:
x = 6
Step-by-step explanation:
2(x - 2) = 8
2x - 4 = 8
2x = 12
x = 6
The line on the graph passes through the points A (1, 3) and B (7, 1).
YA
a) Calculate the gradient of line AB.
b) Find the gradient of a line perpendicular
to AB.
+
A
D
c) Find the equation of the line passing
through point (4, 2) and perpendicular
to AB.
Answer:
Step-by-step explanation:
a) gradient of AB
or
Slope of AB
[tex]Slope , m = \frac{y_B - y_A}{x_B - x_A}[/tex]
[tex]=\frac{1 - 3 }{7 - 1 } \\\\=\frac{-2}{6}\\\\=-\frac{1}{3}[/tex]
b)
when lines are perpendicular to each other, the product of their slope = - 1
That is ,
[tex]m_{AB} \times m_{perpendicular} = - 1 \\\\- \frac{1}{3} \times m_{perpendicular} = - 1\\\\m_{perpendicular} = - 1 \times \frac{-3}{1} = 3[/tex]
c) Equation of the line perpendicular to line AB and passing through ( 4 , 2 )
[tex]( y - y_1) = m_{perpendicular} ( x - x_1) \ where \ (x_1 , y_ 1 ) = ( 4 , 2 ) \\\\( y - 2 ) = 3(x - 4 ) \\\\y = 3x - 12 + 2\\\\y = 3x - 10[/tex]
There are currently 441 dairy cows at Dancing Dairy Farm. Due to some considerations, the number of dairy cows is decreasing at the rate of 13 cows per year. Currently, each cow produces an average of 1157 gallons of milk per year, and production of milk is increasing at the rate of 39 gallons per cow per year. Use the product rule to determine the rate at which milk production at Dancing Dairy Farm is currently changing.
Answer:
the production of milk at the Dancing Dairy Farm is increasing by 2158 gallons/year
Step-by-step explanation:
Given the data in the question;
Let us represent the number of cows at the farm with x and
each cow produces y gallons of milk
Total mil production will be T.
so
T = x × y
now, differentiating with respect to t
dT/dt = d( xy )/dt
dT/dt = xdy/dt + ydx/dt
given that;
x = 441
y = 1157
dx/dt = -13
dy/dt = 39
so we substitute
dT/dt = ( 441 )( 39 ) + ( 1157 )( -13 )
dT/dt = 17199 - 15041
dt/dT = 2158
Therefore, the production of milk at the Dancing Dairy Farm is increasing by 2158 gallons/year