Ava bought some markers for $2 each and some pencils for $1 each. She bought 3 more markers than pencils and spent a total of $12. How many pencils did ava buy?.

As for the second question, you haven't provided any information about the two samples that have been selected, so I'm unable to answer it. Please provide more details or rephrase the question if needed.

Sure, I'd be happy to help you! To answer your question, here are the steps to determine the upper-tail critical value for the x² test with 8 degrees of freedom for a = 0.01:

1. First, we need to determine the chi-square critical value using a chi-square distribution table. For this problem, we want to find the critical value for an upper-tailed test with a 0.01 level of significance and 8 degrees of freedom. According to the table, the chi-square critical value for this test is 20.090.

2. Therefore, the upper-tail critical value for the x² test with 8 degrees of freedom for a = 0.01 is 20.090.

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Answer:

A=85

B=58

Step-by-step explanation:

NO. OF 2 point basket⇒ A

NO. OF 3 point basket⇒B

A+B=89⇒ EQN 1

A=27+B

A-B=27⇒EQN 2

EQN 1 - EQN 2

2B=116

B=58

THEREFORE

 A=27+58

A=85

The expression that represents the volume of the cone is 6πa units^3. Option c is correct choice.

The volume of a cone is calculated using the formula V = (1/3) * pi * r^2 * h, where V is the volume, r is the radius, and h is the height. In this problem, we are given that the cone has a radius of 3, which means that r = 3. We are also given that the height of the cone is 2a, which means that h = 2a.

Substituting these values into the formula,

V = (1/3) * pi * 3^2 * 2a

Simplifying the expression inside the parentheses gives,

V = (1/3) * pi * 9 * 2a

V = 6 * pi * a
Option c is correct. This means that the volume of the cone is directly proportional to the value of a, since pi and 6 are constants. If a is doubled, for example, then the volume of the cone would also double.

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--The complete question is, A cone has a radius of 3 and a height given by the expression 2a. which expression represents the volume of the cone?

a. 2πa units^3

b. 4πa units^3
c. 6πa units^3

d. 24πa units^3--

Step-by-step explanation:

\(2 \pi4 ^{2} \times 7 + \pi \times 8 \times 7 \\ 219.94\)

Answer:

105

Step-by-step explanation:

2x17=34

17x2.5=42.5

1.5x17=25.5

1/2x2x2x1.5=3

34+42.5+25.5+3=105

Answer Po Ba Ay 11.33?

Step-by-step explanation:

Calc

After answering the prοvided questiοn, we can cοnclude that Therefοre, equatiοn the sοlutiοn tο the system is (x, y) = (5/13, 31/33).

In mathematics, an equatiοn is a declaratiοn that says the equality οf twο traits. An equatiοn cοnsists οf twο sides detached by an algebraic expressiοn (=). Fοr instance, the prοpοsitiοn "2x + 3 = 9" cοntends that the assertiοn "2x + 3" equals a value "9". The gοal οf sοlving equatiοns is tο find the value and values οf factοr(s) that will permit the calculatiοn tο be true. Fοrmulae can be simple οr cοmplicated, cοnsistent οr nοnlinear, and cοntain οne οr mοre variables. Fοr example, in the fοrmula "x² + 2x - 3 = 0," the variable x is raised tο the pοwer οf 2. Lines are used extensively in mathematics, including algebra, equatiοns, and geοmetry.

\($\begin{array}{l}{{\rm (x-3y)+(12x-3y)=-2+7}}\\ {{\rm 13x-60y=5}}\end{array}$\)

\($\begin{array}{l}{{\rm x=(5+6y)/13}}\\ {{\rm (5+6y)/13-3y=-2}}\end{array}$\)

\($\begin{array}{l}{\rm {5+6y-39y=-26}}\\ {{\rm -\,33y=-31}}\end{array}$\)

\($\begin{array}{l c r}{{\rm y=31/33}}\\ {{\rm x=(5+6(31/33))/13}}\\ {{\rm x = 5/13}}\end{array}$\)

Therefore, the solution to the system is (x, y) = (5/13, 31/33).

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Average cost per mile is $0.6

To calculate the average cost per mile that Kiara had to pay, we perform the following operations:

We add up all the payments Kiara made related to her car.

Later we divide the total value, in the number of miles traveled by Kiara

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Answer47.3%

Step-by-step explanation:

Answer:

47.3684211%

Step-by-step explanation:

caulculater

Example 1: Find the equation of the line passing through the points (–1, –2) and (2, 7).

Step 1: Find the slope of the line.

To find the slope of the line passing through these two points we need to use the slope

formula:

Step-by-step explanation:

use this on your problem

Answer:

3 and 18

Step-by-step explanation:

let x be the first number

let 6x be the second number

x + 6x = 21

7x=21

x=21/7

x=3

second number =6x

second number 6x3= 21

Answer: 7th Graders

Explanation:

Several people have gotten this question and 7th graders are the right choice

Answer:7th grade should be awarded !

Step-by-step explanation:

Answer:

For the first one, Noah's actions were accecptable. For the second one, Noah made a mistake.

Step-by-step explanation:

In the second equation, Noah failed to get x on one side of the equal sign. In his third step, he should have subtracted  2x from both sides instead of 10. Correct answer below:

2(5 + x ) - 1 = 3x + 9            original equation

10 + 2x -1 = 3x + 9               apply the distributive property

10 - 1 = x + 9                        subtract 2x from both sides

9 = x + 9                              subtract 1 from 10

0 = x                                   subtract 9 from both sides

In testing for differences between the means of two independent populations, the null hypothesis states that the difference between the two population means is not significantly different from zero or is H₀: µ₁ - µ₂ = 0  

Given: To state the null hypothesis between the difference of means for 2 independent populations.

What is a hypothesis?

A hypothesis is a proposed assumption or supposition which acts as an initial point for starting research work and it is based on just a few observations from the past that are based on a limited shred of evidence and is needed more evidence to prove to be true later in the future.

What is the null hypothesis?

In statistics, a null hypothesis is a proposition or explanation that says that for a given set of observations there is no significance or there is no difference for a certain characteristic of a population or a given data set under observation. It is denoted as H0

What is mean?

Mean is defined as the average for a given data set.

Hence in testing for differences between the means of two independent populations, the null hypothesis states that the difference between the two population means is not significantly different from zero or is H₀: µ₁ - µ₂ = 0  

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The Fredholm theory of integral equations of the second kind is a powerful tool that allows us to solve certain types of integral equations. In particular, it allows us to reduce the problem of solving an integral equation to that of solving a linear system of equations.

To begin with, let's take a closer look at the integral equation you've been given:

ϕ(x)=(x2−x4)+λ∫1−1(x4+5x3y)ϕ(y)dy

This is a second kind integral equation because the unknown function ϕ appears both inside and outside the integral sign. In general, solving such an equation directly can be quite difficult. However, the Fredholm theory provides us with a systematic method for approaching this type of problem.

The first step is to rewrite the integral equation in a more convenient form. To do this, we'll introduce a new function K(x,y) called the kernel of the integral equation, defined by:

K(x,y) = x^4 + 5x^3y

Using this kernel, we can write the integral equation as:

ϕ(x) = (x^2 - x^4) + λ∫[-1,1]K(x,y)ϕ(y)dy

Now, we can apply the Fredholm theory by considering the operator T defined by:

(Tϕ)(x) = (x^2 - x^4) + λ∫[-1,1]K(x,y)ϕ(y)dy

In other words, T takes a function ϕ(x) and maps it to another function given by the right-hand side of the integral equation. Our goal is to find a solution ϕ(x) such that Tϕ = ϕ.

To apply the Fredholm theory, we need to show that T is a compact operator, which means that it maps a bounded set of functions to a set of functions that is relatively compact. In this case, we can show that T is compact by applying the Arzelà-Ascoli theorem.

Once we have established that T is a compact operator, we can use the Fredholm alternative to solve the integral equation. This states that either:

1. There exists a non-trivial solution ϕ(x) such that Tϕ = ϕ.

2. The equation Tϕ = ϕ has only the trivial solution ϕ(x) = 0.

In the first case, we can find the solution ϕ(x) by solving the linear system of equations:

(λI - T)ϕ = 0

where I is the identity operator. This system can be solved using standard techniques from linear algebra.

In the second case, we can conclude that there is no non-trivial solution to the integral equation.

So, to summarize, the Fredholm theory allows us to solve certain types of integral equations by reducing them to linear systems of equations. In the case of second kind integral equations, we can use the Fredholm alternative to determine whether a non-trivial solution exists. If it does, we can find it by solving the corresponding linear system.

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The coordinates of p so that p partitions the segment of AB in the ratio 7 to 2 if A( -5,4) and B( -8,-2) is P(x, y) = [-22/3, -2/3].

In this scenario, line ratio would be used to determine the coordinates of the point P on the directed line segment that partitions the segment into a ratio of 1 to 4.

In Mathematics and Geometry, line ratio can be used to determine the coordinates of P and this is modeled by this mathematical equation:

P(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

By substituting the given parameters into the formula for line ratio, we have;

P(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

P(x, y) = [(7(-8) + 2(-5))/(7 + 2)],  [(7(-2) + 2(4))/(7 + 2)]

P(x, y) = [(-56 - 10)/(9)],  [(-14 + 8)/9]

P(x, y) = [-66/9],  [(-6)/(9)]

P(x, y) = [-22/3, -2/3]

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The equation of the given circle is

\((x - 3)^2 + (y + 7)^2 = 25\)

What is a circle?

Circle is a two dimensional round figure in which every point on the figure maintains a fixed distance from a point known as the center of the circle.

The fixed distance is called the radius of the circle.

Diameter of circle = 10 units

Radius of the circle = \(\frac{10}{2}\) = 5 units

Coordinates of center = (3, -7)

Equation of circle = \((x - 3)^2 + (y - (-7))^2 = 5^2\)

                                 \((x - 3)^2 + (y + 7)^2 = 25\)

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Answer:

30 mm

Step-by-step explanation:

1 centimeter (cm) is one hundredth of a meter

1 millimeter (mm) is one thousandth of a meter

Thus one cm is 10 times bigger, so 3cm = 30mm

Answer:

$36,529.26

Step-by-step explanation:

To find the answer, you need to use the formula to calculate the present value:

PV=FV/(1+i)^n, where:

PV= present value

FV= future value= $200,000

i= interest rate= 12%

n= number of periods of time= 15

Now, you have to replace the values in the formula:

PV=200,000/(1+0.12)^15

PV=200,000/(1.12)^15

PV=36,539.26

According to this, the answer is that you need $36,529.26 today.

The answer is B. 0.88, rounded to two decimal places.

In order to find P81, we need to use the z-score formula which is given by:z = (X - μ) / σwhere z is the z-score, X is the raw score, μ is the mean, and σ is the standard deviation. To find P81, we need to find the z-score corresponding to the score that separates the bottom 81% from the top 19%. We can do this by using a z-score table or a calculator that has the cumulative distribution function (CDF) for the standard normal distribution.Using a calculator, we can find that the z-score corresponding to the 81st percentile is approximately 0.88. Therefore, P81 is 0.88, which means that 81% of the scores on the test are below a score of 0.88 standard deviations above the mean, and 19% of the scores are above that score.

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Answer:

The surface area formula is 2πr (h + r) where r and h are the radius and height respectively. Since π = 3.14, r = 7, h = 15 the answer is:

2 * 3.14 * 7 * (15 + 7) = 43.96 * 22 = 967.6

Mr. jones now if the sum of their present age is 55 years is 41 years from the given information mr. jones was 4 times as old as his daughter 5 years ago and formulated linear equation..

Given that, Mr. Jones and their daughter are currently 55 years old.

Let Mr. Jones' age at this time be x years.

His daughter is currently y years old.

Since Mr. Jones's and his daughter's combined age as of right now is 55

Therefore, we can write linear equation x + y = 55.... I (i)

The current age of Mr. Jones is equal to (x - 5) years, and their ages prior to 5 years.

His daughter is currently (y - 5) years old.

Since Mr. Jones was four times as old as his daughter five years ago,

(x - 5) = 4 (y - 5), where x = 5 and y = 20 and 15, respectively. ... (ii) (ii)

When you solve for |(i) and (ii), you get y = 14.

And, x = 41

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Answer: one

Step-by-step explanation:

     When a system of equations is graphed the solutions are the point of intersections. Here, we only have one point of intersection since these are both linear equations. That means there is only one solution.

Step-by-step explanation:

the lengths OB, OC & BC together forms a isosceles triangle.

therefore,

OB=OC

3x+4=x+8

2x=4

x=2.

OB = 3x+4= 3.2+4=10cm.

OC= x+8= 2+8=10cm.

therefore, the diagonals are : 20cm each.

hope this helps you.

Answer:

∠ BAD = 80°

Step-by-step explanation:

∠ ACB = 90° ( angle in a semicircle )

∠ CAB = 180° - (90 + 30)° ← sum of angles in Δ ABC

∠ CAB = 180° - 120° = 60°

Then

∠ BAD = ∠ CAD - ∠ CAB = 140° - 60° = 80°

Answer:

80° is the answer

Step-by-step explanation:

I just took the test

Answer:

4

Step-by-step explanation:

m + 8 = 3m

8 = 2m

4 = m

Complete question is;

It took Priya 5 minutes to fill a cooler with 8 gallons of water from a faucet that was flowing at a steady rate. Let w be the number of gallons of water in the cooler after t minutes. Which of the following equations represent the relationship between w and t? Select all that apply

A) w = 1.6t

B) w = 0.625t

C) t = 1.6w

D) t = 0.625w

Answer:

Option A: w = 1.6t

& Option D: t = 0.625w

Step-by-step explanation:

We are told It took Priya 5 minutes to fill a cooler with 8 gallons of water at a steady rate.

Thus;

Rate of filling = 8 gallons/5 minutes = 1.6 gallons/minutes

Now, we are told that w is the number of gallons of water in the cooler after t minutes.

Thus, to find w, we will multiply the rate by t minutes.

w = 1.6 gallons/minutes × t minutes

w = 1.6t gallons

Or we can write as;

w/1.6 = t gallons

0.625w = t gallons

Therefore, options A & D are correct.

Answer:

a and d

Step-by-step explanation:

uhhhh just put a and d

Any 3 of those entries are equal to 0, the determinant will be 0, meaning the matrix is non-invertible.

The minimal number such that any 3-by-3 matrix with of its entries equal to zero is non-invertible is 3. This can be calculated by finding the determinant of the matrix. The determinant is the sum of the products of the entries in the matrix, each multiplied by its corresponding minor. If a 3-by-3 matrix has 3 of its entries equal to zero, the determinant will be equal to 0, which means the matrix is non-invertible. To calculate the determinant of a 3-by-3 matrix, use the formula.

Where a, b, c, d, e, f, g, h, i are the entries of the matrix. If any 3 of those entries are equal to 0, the any 3 of those entries are equal to 0, the determinant will be 0, meaning the matrix is non-invertible determinate will be 0, meaning the matrix is non-invertible.

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Answer:

.003   .03%

Step-by-step explanation:

45. 0 square units.

The area of the kite is 40.5 unit square.

The side of the kite inscribed in square is 9

We have to find the area of the kite

The area of a kite is,

\(A = (d_1d_2) / 2\)

Where \(d_1\) and \(d_2\) are the diagonals of the kite.

The kite is inscribed in the square, and the sides of the square are 9 units, the diagonals of the kite are both 9 units.

Therefore we get,

\(d_1 = 9 units\)

\(d_2 = 9 units\)

\(A = (9units \times 9units) / 2\)

\(A = 81units^2 / 2\)

\(A = 40.5 units^2\)

So the third option is correct .

Therefore ,The area of the kite is 40.5 unit square.

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The solution to the provided differential equation with the initial condition y(0) = 5 and u as a step change of unity is y = -2

The provided differential equation is: \(\[\frac{{dy}}{{dt}} = y + 2u\]\) with the initial condition: y(0) = 5 where u is a step change of unity.

To solve this differential equation, we can use the method of integrating factors.

First, let's rearrange the equation in the standard form:

\(\[\frac{{dy}}{{dt}} - y = 2u\]\)

Now, we can multiply both sides of the equation by the integrating factor, which is defined as the exponential of the integral of the coefficient of y with respect to t.

In this case, the coefficient of y is -1:

Integrating factor \(} = e^{\int -1 \, dt} = e^{-t}\)

Multiplying both sides of the equation by the integrating factor gives:

\(\[e^{-t}\frac{{dy}}{{dt}} - e^{-t}y = 2e^{-t}u\]\)

The left side of the equation can be rewritten using the product rule of differentiation:

\(\[\frac{{d}}{{dt}}(e^{-t}y) = 2e^{-t}u\]\)

Integrating both sides with respect to t gives:

\(\[e^{-t}y = 2\int e^{-t}u \, dt\]\)

Since u is a step change of unity, we can split the integral into two parts based on the step change:

\(\[e^{-t}y = 2\int_{{-\infty}}^{t} e^{-t} \, dt + 2\int_{t}^{{\infty}} 0 \, dt\]\)

Simplifying the integrals gives:

\(\[e^{-t}y = 2\int_{{-\infty}}^{t} e^{-t} \, dt + 0\]\)

\(\[e^{-t}y = 2\int_{{-\infty}}^{t} e^{-t} \, dt\]\)

Evaluating the integral on the right side gives:

\(\[e^{-t}y = 2[-e^{-t}]_{{-\infty}}^{t}\]\)

\(\[e^{-t}y = 2(-e^{-t} - (-e^{-\infty}))\]\)

Since \(\(e^{-\infty}\)\) approaches zero, the second term on the right side becomes zero:

\(\[e^{-t}y = 2(-e^{-t})\]\)

Dividing both sides by \(\(e^{-t}\)\) gives the solution: y = -2

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