7. (05.02 MC)
Luciana's laptop has 3,000 pictures. The size of the pictures is skewed to the right, with a mean of 3.7MB and a standard deviation of 0.78MB
Part A: Can you accurately calculate the probability that the mean picture size is more than 3.8MB for an SRS of 20 pictures? Explain.
Part B: If you take a random sample of 60 pictures instead of 20, explain how the Central Limit Theorem allows you to find the probability that the mean picture size is more than 3.8MB.

Answers

Answer 1

Considering the Central Limit Theorem, we have that:

a) The probability cannot be calculated, as the underlying distribution is not normal and the sample size is less than 30.

b) The probability can be calculated, as the sample size is greater than 30.

What does the Central Limit Theorem state?

It states that the sampling distribution of sample means of size n is approximately normal has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex], as long as the underlying distribution is normal or the sample size is greater than 30.

In this problem, the underlying distribution is skewed right, that is, not normal, hence:

For item a, the probability cannot be calculated, as the underlying distribution is not normal and the sample size is less than 30.For item b, the probability can be calculated, as the sample size is greater than 30.

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Related Questions

claire and martin are trying to determine the length of a slug. Claire has a mesuring stick whose markings are 1 cm apart, and Martin has a measuring stick whose markings are 0.1cm apart.

Answers

Claire's measuring stick would make a more precise measurement

How to determine the precise measurement?

The given parameters are:

Claire = 1 cm

Martin = 0.1 cm

The 0.1 cm marking would make a more accurate measurement.

This is so because the length of a slug would most likely be in decimal centimeters

However, this doesn't translate to a precise measurement.

Hence, Claire's measuring stick would make a more precise measurement

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Suppose you have $1500 in your savings account at the end of a certain period of time. You invested $1000 at a 2.71% simple annual interest rate. How long, in years, was your money invested? State your result to the nearest hundredth of a year.

Answers

The time taken in years for money invested to accumulate to $1500 is 18.45 years

Simple interestPrincipal = $1000Interest rate = 2.71% = 0.0271t = ?

Simple interest = Total savings - principal

= 1500 - 1000

= $500

Simple interest = principal × rate × time

500 = 1000 × 0.0271 × t

500 = 27.1 × t

500 = 27.1t

t = 18.4501845018450

Approximately,

t = 18.45 years

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suppose that fanf g are continuous functions,
12_(^28 f(x)dx=19, and 12 (^28 g(x)dx =35.
Find
12_ f^28 [kg(x)-2f(x)] dx, where the coefficient
k=7
those are intergral symbols with numbers on
top and bottom. please show work. thanks

Answers

The required result based on given continuous functions is: 207. See the explanation for same below.

What are continuous functions?


A continuous function in mathematics is one in which a continuous variation (that is, a change without a jump) of the argument causes a continuous variation of the function's value.

What is the calculation for the above solution?

Since G and F are continuous functions,

[tex]\int_{12}^{28}) \, f(x) dx[/tex] = 19

[tex]\int_{12}^{28}) \, f(x) dx[/tex] = 35

Therefore,

[tex]\int_{12}^{28}) \, [K g(x) - 2 f(x)] dx[/tex]

= K [tex]\int_{12}^{28}) \, g(x) dx -2 \int_{12}^{28}) \, f(x) dx[/tex]

So, given that K = 7, we have

7 x 35 - 2 x 19
= 245 - 38
= 207

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inverse function of f(x)=x-7/x+4

Answers

Final Answer: The inverse of f (x)=7x-4 is f^-1 (x)= (x+4)/7

Using the drawing what is the vertex of angle 4?

Answers

Answer: A

Step-by-step explanation:

Solve [tex]2 cosx=4cosx sin^2x[/tex]

Answers

There are four solutions for the trigonometric equation 2 · cos x = 4 · cos x · sin² x are x₁ = π/4 ± 2π · i, x₂ = 3π/4 ± 2π · i, x₃ = 5π/4 ± 2π · i and x₄ = 7π/4 ± 2π · i, [tex]i \in \mathbb{N}_{O}[/tex].

How to solve a trigonometric equation

In this problem we must simplify the trigonometric equation by both algebraic and trigonometric means and clear the variable x:

2 · cos x = 4 · cos x · sin² x

2 · sin² x = 1

sin² x = 1/2

sin x = ± √2 /2

There are several solutions:

x₁ = π/4 ± 2π · i, [tex]i \in \mathbb{N}_{O}[/tex]

x₂ = 3π/4 ± 2π · i, [tex]i \in \mathbb{N}_{O}[/tex]

x₃ = 5π/4 ± 2π · i, [tex]i \in \mathbb{N}_{O}[/tex]

x₄ = 7π/4 ± 2π · i, [tex]i \in \mathbb{N}_{O}[/tex]

There are four solutions for the trigonometric equation 2 · cos x = 4 · cos x · sin² x are x₁ = π/4 ± 2π · i, x₂ = 3π/4 ± 2π · i, x₃ = 5π/4 ± 2π · i and x₄ = 7π/4 ± 2π · i, [tex]i \in \mathbb{N}_{O}[/tex].

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Complete the equations to solve 1{,}860 \div61,860÷61, comma, 860, divided by, 6.
\phantom{=}\greenD{1{,}860}\div{\blueD6}=1,860÷6empty space, start color #1fab54, 1, comma, 860, end color #1fab54, divided by, start color #11accd, 6, end color #11accd
=(\greenD{1{,}800}\div\,=(1,800÷equals, left parenthesis, start color #1fab54, 1, comma, 800, end color #1fab54, divided by
) \, + \,(\greenD{60}\div\,)+(60÷right parenthesis, plus, left parenthesis, start color #1fab54, 60, end color #1fab54, divided by
))right parenthesis
= 300 +=300+equals, 300, plus
==equals

Answers

The division of the figure based on the information is 14.09.

How to illustrate the information?

It should be noted that the question is simply to divide 860 by 61.

The division based on the information will be illustrated thus:

= 860 ÷ 61

= 14.09

In conclusion, the correct option is 14.09.

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in triangle ABC, AC=13, BC=84, and AB=85. find the measure of angle C.

Answers

The sides all satisfy the Pythagorean Theorem so it is a right triangle. I attached an image of how the triangle should look like and as you can see, the angle is 90 degrees or pi/2 radians.

in triangle ABC, AC=13, BC=84, and AB=85.  the measure of angle is C.5.1 degrees,

How can the angle be found?

Using the The Law of Cosines in any triangle which can be expressed as;

[tex]c^2 = a^2 + b^2 - 2ab * cos(C)[/tex]

Then if we expressed the given sides in the cosine formula we have

[tex]13^2 = 85^2 + 84^2 - 2 * 85 * 84 * cos(C)[/tex]

Then we have [tex]169 = 7225 + 7056 - 14280 * cos(C)[/tex]

[tex]14280 * cosC = (7225 + 7056 - 169)[/tex]

[tex]cosC = \frac{14212}{ 14280}[/tex]

cos 0.9947

[tex]C = cos^-1(0.9947)[/tex]

C = 5.1 degrees

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Four students are simplifying the expression 5x(–3 – 7x).

Which student’s work is correct?

5x(–3 – 7x)
(5x)(–3) – 7x
–15x –7x
5x(–3 – 7x)
(5x)(–3) – (5x)(7x)
–15 – 35x
5x(–3 – 7x)
–3 + 5x – 7x
–3 – 2x
5x(–3 – 7x)
(5x)(–3) + (5x)(–7x)
–15x – 35x2

Answers

Answer:

So the questions isn't clear enough, but I could tell u that the nearest answer is the last answer, but without the multiplied 2

It's _15x_35xsquared

Answer:

5x(–3 – 7x)

(5x)(–3) + (5x)(–7x)

–15x – 35x2

Step-by-step explanation:

D

What is the volume of the cylinder?

Answers

The volume of a cylinder with a diameter of 16 feet and height of 10 feet is 2010.62 ft³

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

The volume of a cylinder with radius (r) and height (h) is:

Volume = πr²h

Given that h = 10 ft, r = 16/2 = 8 ft

The volume = π * 8² * 10 = 2010.62 ft³

The volume of a cylinder with a diameter of 16 feet and height of 10 feet is 2010.62 ft³

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6) Ron bought a car 8 years ago for $15,694. If the rate of depreciation is 4.75% per year, what is the value of
Ron's car now? Round answer to nearest cent.
O a.) $10,642.94
Ob.) $10,332.94
Oc.) $10,632.94
Od.) $10,662.94

Answers

It will be Od cause 10,662,94 is closer to and the biggest number you working with


Given the functions a(x) = 3x - 12 and b(x) = x-9, solve a[b(x)].

Oa[b(x)] = 3x²-21

O a[b(x)] = 3x² - 39

Oa[b(x)] = 3x - 21

Oa[b(x)] = 3x - 39

Answers

Answer:

Step-by-step explanation:

hello :

a(x) = 3x - 12 and b(x) = x-9, so

a[b(x)]=a(x-9) =3(x-9)-12

a[b(x)]=3x-9-12

a[b(x)]=3x+21

Hi I would like to know how I can solve this problem.

Answers

The [tex]n[/tex]-th term is

[tex]U_n = \dfrac14 n^2 (n+1)^2[/tex]

so the 39th term is

[tex]U_{39} = \dfrac14 39^2 40^2 = \boxed{608,400}[/tex]

Observe that

[tex]2^3 + 4^3 + 6^3 = 2^3 + 2^3\times2^3 + 2^3\times3^3 = 8\left(1^3+2^3+3^3)[/tex]

which suggests that

[tex]V_n = 8U_n = \boxed{2n^2(n+1)^2}[/tex]

will give brainly .Which statements are true regarding undefinable terms in geometry? Check all that apply.


A point has no length or width.

A point indicates a location in a coordinate plane.

A plane has one dimension, length.

A line has a definite beginning and end.

A plane consists of an infinite set of lines.

A line consists of an infinite set of points.

Answers

The true statements about terms in geometry that are undefinable are;

A point has no length or widthA point indicates a location on the coordinate planeA line consists of an infinite set of points.A plane consists of an infinite set of points.

How can the true statements be found?

Three undefinable terms in geometry are;

1) Point

2) Line

3) Plane

The above terms do not have a formal definition but they can be described based on their properties.

The other geometric terms are defined based on the above undefinable terms.

A point can be described as a location in space that is dimensionless and can be specified on the coordinate plane as an ordered pairs (x, y).

True statements about a point are therefore;

A point has no length or widthA point indicates a location on the coordinate plane

A line is infinitely long, that has no beginning or end. It has one dimension, with no thickness or height.

Given that a point is dimensionless, a line can be considered a set of points.

A true statement is therefore;

A line consists of an infinite set of points.

A plane is a two dimensional geometric figure that have infinite length and width.

An infinite set of lines that forms a two dimensional figure can be used to describe a plane.

The true statement with regards to a plane is therefore;

A plane consists of an infinite set of points.

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look at the pictures​

Answers

The key feature that the function of f(x) and g(x) has in common is the domain.

What is the domain and range of a function?

The domain of a function is the set of input or argument values for which the function is valid and well defined. The range is the set of the dependent variable for which a function is defined.

From the given information, we are to find the domain, range, x-intercept, and, y-intercept of the given equation:

[tex]\mathbf{f(x) = -4^x+5}[/tex]

[tex]\mathbf{g(x) = x^3 +x^2 -4x+5}[/tex]

For [tex]\mathbf{f(x) = -4^x+5}[/tex];

The domain of a function [tex]\mathbf{-4^x+5}[/tex] has no undefined points or constraints. Thus, the domain is -∞ < x < ∞.

The range f(x) < 5. The x-intercepts, when y is zero = [tex]\mathbf{(\dfrac{In(5)}{2In(2)},0)}[/tex]The y-intercepts; when x is zero = (0,4)

For [tex]\mathbf{g(x) = x^3 +x^2 -4x+5}[/tex]

The domain of a function [tex]\mathbf{g(x) = x^3 +x^2 -4x+5}[/tex] has no undefined points or constraints. Thus, the domain is -∞ < x < ∞.

The range  -∞ < f(x) < ∞. The x-intercepts, when y is zero = (-2.939, 0)The y-intercepts; when x is zero = (0,5)

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Find the exact solutions of x2 − 3x − 5 = 0 using the quadratic formula. Show all work! 75 points please help!!!!!

Answers

Answer:

[tex]x=\dfrac{3+ \sqrt{29}}{2}, \quad \dfrac{3- \sqrt{29}}{2}[/tex]

Step-by-step explanation:

Quadratic Formula

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]

Given quadratic equation:

[tex]x^2-3x-5=0[/tex]

Define the variables:

[tex]\implies a=1, \quad b=-3, \quad c=-5[/tex]

Substitute the defined variables into the quadratic formula and solve for x:

[tex]\implies x=\dfrac{-(-3) \pm \sqrt{(-3)^2-4(1)(-5)}}{2(1)}[/tex]

[tex]\implies x=\dfrac{3 \pm \sqrt{9+20}}{2}[/tex]

[tex]\implies x=\dfrac{3 \pm \sqrt{29}}{2}[/tex]

Therefore, the exact solutions to the given quadratic equation are:

[tex]x=\dfrac{3+ \sqrt{29}}{2}, \quad \dfrac{3- \sqrt{29}}{2}[/tex]

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Answer:

[tex]\boxed {\frac{3+\sqrt{29}}{2}} \boxed{\frac{3-\sqrt{29}}{2}}[/tex]

Step-by-step explanation:

Quadratic Formula :

[tex]\boxed {\frac{-b \pm \sqrt{b^{2}-4ac}}{2a}}[/tex]

We are given the equation x² - 3x - 5 = 0.

Here,

a = 1b = -3c = -5

Solving :

3 ± √3² - 4(1)(-5) / 2(1)3 ± √29 / 2

Hence, the solutions are :

[tex]\boxed {\frac{3+\sqrt{29}}{2}} \boxed{\frac{3-\sqrt{29}}{2}}[/tex]

Which expression is equivalent to
xay
8
700
8√√√x
y
8√√y
Mark this and return
128x56
√ 2x75
? Assume x > 0 and y> 0.
Save and Exit

Answers

The equivalent expression of [tex]\sqrt{\frac{128x^5y^6}{2x^7y^5}}[/tex] is [tex]\frac{8\sqrt y}{x}[/tex]

How to determine the equivalent expression?

The expression is given as:

[tex]\sqrt{\frac{128x^5y^6}{2x^7y^5}}[/tex]

Divide 128 by 2

[tex]\sqrt{\frac{64x^5y^6}{x^7y^5}}[/tex]

Apply the law of indices to the variables

[tex]\sqrt{\frac{64y^{6-5}}{x^{7-5}}}[/tex]

Evaluate the differences

[tex]\sqrt{\frac{64y}{x^2}}[/tex]

Take the square root of 64

[tex]8\sqrt{\frac{y}{x^2}}[/tex]

Take the square root of x^2

[tex]\frac{8\sqrt y}{x}[/tex]

Hence, the equivalent expression of [tex]\sqrt{\frac{128x^5y^6}{2x^7y^5}}[/tex] is [tex]\frac{8\sqrt y}{x}[/tex]

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Find the coordinates of the vertices of the triangle if it’s rotated 270° counterclockwise.

Answers

If these coordinates are rotated 270° counterclockwise, the resulting coordinates will be;

X' = (3, -1)

Y' = (2, -2)

Z' = (-1, -3)

Rotation of coordinates

If the coordinates (x, y) is rotated 270° counterclockwise, the resulting coordinate point will be;

(x, y) - > (y, -x)

From the given triangles, the coordinate points are expressed as

X = (1, 3)

Y = (2, 2)

Z = (3, -1)

If these coordinates are rotated 270° counterclockwise, the resulting coordinates will be;

X' = (3, -1)

Y' = (2, -2)

Z' = (-1, -3)

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Please look at the attachment and answer my question :(

Answers

Answer:

AB / BC = 2 / 3

A equals 9 and C = 13

AC = 13 - 9 = 4

AB + BC = 13

A) AB + BC = 4

B) AB / BC = 2/3   Therefore BC = AB / (2/3)  

B) BC = 1.5 AB  

A) BC = 4 - A/B

Multiplying equation A) by -1

A) -BC = -4 + AB then we add equation B)

B) BC = 1.5 AB then adding both equations

0 = 2.5 AB -4

2.5 AB = 4

AB = 1.6

Since A = 9 then the number at B is 9 + 1.6

equals 10.6

Step-by-step explanation:

Answer:

The number at B is 10.6

Step-by-step explanation:

Let the number at B be x.

We know that distance between two points on the number line is the absolute value of the difference of numbers at those points.

Then distances representing the lengths of segments AB and BC are:

AB = x - 9BC = 13 - x

We are given the ratio of segments:

AB/BC = 2/3

Substitute and solve for x:

(x - 9)/(13 - x) = 2/33(x - 9) = 2(13 - x)3x - 27 = 26 - 2x3x + 2x = 26 + 275x = 53x = 53/5x = 10.6

Suppose f(x) and g(x) are differentiable functions satisfying f(1) = f′(1) = 2. Let
h(x) = g(f(x)) − g(2x). Determine whether h′(1) > 1

Answers

Answer:

1777777777888876332222233

paulette spent 45.50 on concert tickets before fees. there was a service fee of 6% added on to her purchase.

Answers

The original price of concert tickets before the addition of service fee is 42.93

Percentage

Amount spent on tickets including service fee = 45.50Percentage if service fee = 6%Original cost before service fee = x

45.50 = x + (6% of x)

45.50 = x + (0.06 × x)

45.50 = x + 0.06x

45.50 = 1.06x

x = 45.50/1.06

x = 42.9245283018867

Approximately,

x = 42.93

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What is the solution to the following system of equations?
x-3y=6
2x + 2y = 4
(-1,3)
(3,-1)
(1, -3)
(-3,1)

Answers

Answer:

  (b)  (3,-1)

Step-by-step explanation:

One can determine the correct answer by checking to see if it satisfies the equations.

Checking

The first equation can be rewritten to ...

  x = 6 +3y . . . . . . . add 3y to both sides

This makes it easier to check answer choices:

  a) -1 = 6 +3(3) . . . . no

  b) 3 = 6 +3(-1) . . . . yes . . . . . (3, -1) is the solution

  c) 1 = 6 +3(-3) . . . . no

  d) -3 = 6 +3(1) . . . . no

__

Additional comment

We can further convince ourselves this is the correct choice by seeing if it satisfies the second equation:

  2x +2y = 4 . . . for (x, y) = (3, -1)

  2(3) +2(-1) = 4 . . . . yes

There are some 1-dollar bills, some 5-dollar bills, and a 20-dollar bill in an envelope. The number of 1-dollar bills is five times the number of the 5-dollar bills. We randomly pull a bill from the envelope. How many 1-dollar bills are in this envelope if the expected value of the bill pulled is $2.00?

Answers

Answer:

the number of 1 dollars bills was 5 si make 1 more 5 dollars so 8n total it is 10 dollars.

James has $20 in his wallet and makes $10 per hour. Kelly has $50 in her wallet but only makes $8 per hour.

How many hours of work will it take for these two people to have the same amount of money?

Answers

Answer:

At 15 hours of work they will be equal.

Step-by-step explanation:

James: y = 10x + 20

Kelly: y = 8X + 50

Set them equal to each other and solve

10x + 20 = 8x + 50  Subtract 8x from both sides of the equation

2x + 20 = 50  Subtract 20 from both sides of the equation

2x = 30  Divide both sides by 2

x =15

A random variable X has a gamma density function with parameters α= 8 and β = 2.
Without making any assumptions, derive the moment generating function of X and use to
determine the mean and variance of X.

Answers

I know you said "without making any assumptions," but this one is pretty important. Assuming you mean [tex]\alpha,\beta[/tex] are shape/rate parameters (as opposed to shape/scale), the PDF of [tex]X[/tex] is

[tex]f_X(x) = \dfrac{\beta^\alpha}{\Gamma(\alpha)} x^{\alpha - 1} e^{-\beta x} = \dfrac{2^8}{\Gamma(8)} x^7 e^{-2x}[/tex]

if [tex]x>0[/tex], and 0 otherwise.

The MGF of [tex]X[/tex] is given by

[tex]\displaystyle M_X(t) = \Bbb E\left[e^{tX}\right] = \int_{-\infty}^\infty e^{tx} f_X(x) \, dx = \frac{2^8}{\Gamma(8)} \int_0^\infty x^7 e^{(t-2) x} \, dx[/tex]

Note that the integral converges only when [tex]t<2[/tex].

Define

[tex]I_n = \displaystyle \int_0^\infty x^n e^{(t-2)x} \, dx[/tex]

Integrate by parts, with

[tex]u = x^n \implies du = nx^{n-1} \, dx[/tex]

[tex]dv = e^{(t-2)x} \, dx \implies v = \dfrac1{t-2} e^{(t-2)x}[/tex]

so that

[tex]\displaystyle I_n = uv\bigg|_{x=0}^{x\to\infty} - \int_0^\infty v\,du = -\frac n{t-2} \int_0^\infty x^{n-1} e^{(t-2)x} \, dx = -\frac n{t-2} I_{n-1}[/tex]

Note that

[tex]I_0 = \displaystyle \int_0^\infty e^{(t-2)}x \, dx = \frac1{t-2} e^{(t-2)x} \bigg|_{x=0}^{x\to\infty} = -\frac1{t-2}[/tex]

By substitution, we have

[tex]I_n = -\dfrac n{t-2} I_{n-1} = (-1)^2 \dfrac{n(n-1)}{(t-2)^2} I_{n-2} = (-1)^3 \dfrac{n(n-1)(n-2)}{(t-2)^3} I_{n-3}[/tex]

and so on, down to

[tex]I_n = (-1)^n \dfrac{n!}{(t-2)^n} I_0 = (-1)^{n+1} \dfrac{n!}{(t-2)^{n+1}}[/tex]

The integral of interest then evaluates to

[tex]\displaystyle I_7 = \int_0^\infty x^7 e^{(t-2) x} \, dx = (-1)^8 \frac{7!}{(t-2)^8} = \dfrac{\Gamma(8)}{(t-2)^8}[/tex]

so the MGF is

[tex]\displaystyle M_X(t) = \frac{2^8}{\Gamma(8)} I_7 = \dfrac{2^8}{(t-2)^8} = \left(\dfrac2{t-2}\right)^8 = \boxed{\dfrac1{\left(1-\frac t2\right)^8}}[/tex]

The first moment/expectation is given by the first derivative of [tex]M_X(t)[/tex] at [tex]t=0[/tex].

[tex]\Bbb E[X] = M_x'(0) = \dfrac{8\times\frac12}{\left(1-\frac t2\right)^9}\bigg|_{t=0} = \boxed{4}[/tex]

Variance is defined by

[tex]\Bbb V[X] = \Bbb E\left[(X - \Bbb E[X])^2\right] = \Bbb E[X^2] - \Bbb E[X]^2[/tex]

The second moment is given by the second derivative of the MGF at [tex]t=0[/tex].

[tex]\Bbb E[X^2] = M_x''(0) = \dfrac{8\times9\times\frac1{2^2}}{\left(1-\frac t2\right)^{10}} = 18[/tex]

Then the variance is

[tex]\Bbb V[X] = 18 - 4^2 = \boxed{2}[/tex]

Note that the power series expansion of the MGF is rather easy to find. Its Maclaurin series is

[tex]M_X(t) = \displaystyle \sum_{k=0}^\infty \dfrac{M_X^{(k)}(0)}{k!} t^k[/tex]

where [tex]M_X^{(k)}(0)[/tex] is the [tex]k[/tex]-derivative of the MGF evaluated at [tex]t=0[/tex]. This is also the [tex]k[/tex]-th moment of [tex]X[/tex].

Recall that for [tex]|t|<1[/tex],

[tex]\displaystyle \frac1{1-t} = \sum_{k=0}^\infty t^k[/tex]

By differentiating both sides 7 times, we get

[tex]\displaystyle \frac{7!}{(1-t)^8} = \sum_{k=0}^\infty (k+1)(k+2)\cdots(k+7) t^k \implies \displaystyle \frac1{\left(1-\frac t2\right)^8} = \sum_{k=0}^\infty \frac{(k+7)!}{k!\,7!\,2^k} t^k[/tex]

Then the [tex]k[/tex]-th moment of [tex]X[/tex] is

[tex]M_X^{(k)}(0) = \dfrac{(k+7)!}{7!\,2^k}[/tex]

and we obtain the same results as before,

[tex]\Bbb E[X] = \dfrac{(k+7)!}{7!\,2^k}\bigg|_{k=1} = 4[/tex]

[tex]\Bbb E[X^2] = \dfrac{(k+7)!}{7!\,2^k}\bigg|_{k=2} = 18[/tex]

and the same variance follows.

A solid right square prism is cut into 5 equal pieces parallel to its bases. The volume of each piece is V = 1/5s2h.Solve the formula for s. help asap

Answers

The solution of the formula for s is:

[tex]s = \sqrt{\frac{5V}{h}}[/tex]

What is the symbolic equation?

The equation is:

[tex]V = \frac{1}{5}s^2h[/tex]

To solve for s, we isolate it, hence:

[tex]s^2 = \frac{5V}{h}[/tex]

[tex]s = \sqrt{\frac{5V}{h}}[/tex]

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What point is 2/3 of the distance from point A(3, 1) to point B(3, 19)?

What point is 2/3 of the distance from point A(3, 1) to point B(3, 19)?

(3, 13)

(9/3, 13)

(2, 12)

(3, 19)

Answers

Answer: (3, 13)

Step-by-step explanation:

If we let the point be P, then AP:BP=2:1.

[tex]P=\left(\frac{(2)(3)+(1)(3)}{2+1}, \frac{(2)(19)+(1)(1)}{2+1} \right)=(3, 13)[/tex]

To the nearest percent how much greater is 8 than 6

Answers

The percent greater of 8 than 6 to the nearest percent is 25%

Percentage

Percent greater = difference / higher chance value × 100

= 2/8 × 100

= 0.25 × 100

Percent greater = 25%

Therefore, the percent greater of 8 than 6 to the nearest percent is 25%

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a 300-acre farm produced 20,000 bushels of corn last year. what is the minimum rate of production, in bushels per acre, that is needed this year, so the farm's two-year production total will be at least 49,100 bushels of corn?

Answers

The minimum production rate of bushels per acre of corn needed this year is 97 for two year's production to reach the goal of 49,100.

How to calculate the minimum production rate?

To calculate the minimum production rate for this year, we must subtract the production rate of the previous year, with what is expected to be obtained this year.

49,100 - 20,000 = 29,100

Then we must divide the minimum that must be obtained by the total area, by the 300 acres that we have, to know how much corresponds to each acre.

29,100 ÷ 300 = 97

According to the above, each acre must produce 97 bushels of corn to reach the goal of 49,100 for both years.

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The total area of a picture and its frame can be represented by ^l + 2f h^w + 2f h, where l and w represent the length and width of the picture, respectively, and f represents the thickness of the frame.



a. Sketch a diagram to represent this scenario.



b. What binomial multiplication represents the area of an 8" # 12" picture and its frame?



c. Multiply the binomials from b., and combine like terms to simplify.



d. What is the total area of an 8" # 12" picture and its frame if the frame is 1.5" thick?

Answers

The answers to the question are

b. (l + 2f) (w + 2f)

c. f + 4, f + 6

d.  52.25

a. The diagram is an attachment.

B. How to solve for the binomial multiplication

The equation says

(l + 2f) (w + 2f)

We have the lengths of w and l as 8 and 12 respectively. Hence we have

(8 + 2f) (12 + 2f) as the area

c. (8 + 2f) (12 + 2f)

= 96 + 16f + 24f + 4f²

= 4f² + 40 f + 96

We have to factorize this using the quadratic equation calculator

f + 4, f + 6

= f = -4 and f = -6

d. If it is 1.25 thick we would have

1.25 x 2 = 2.5

12 - 2.5 = 9.5

8 - 2.5 = 5.5

Area = l * w

= 5.5 * 9.5

= 52.25

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