In every box of bubble gum there are 18 pieces, which describes a proportional relationship between the number of packages, x,
and the number of pieces, y. Choose the equation that expresses this relationship.
Ay=9x
B y = 18x
Cy=
Dy = kr
0 0 0 0 0 0 0 0 0 0 0 0 0 0
00069AVAVAVAVA 0 0 0 0 0 0 0 0 0 0 6
AVAVAVAVAVAVA0000000
2600960 69 69 690000000
696969696969090
AV A V A V A V A V A V A V0909090
0 0

If a and b are any odd integers, then a2 + b2 is even.

And the proof for that we can explain as,

 So we have a and b are any odd integers. By definition of odd integer,

           a = 2r + 1 and b = 2r + 1 for any integers r and s.

By definition of odd integer,

          a = 2r + 1 and b = 2s + 1 for some integers r and s.

By substitution and algebra,

      a2 + b2 = (2r + 1)2 + (2s + 1)2 = 2[2(r2 +52) + 2(r + s) + 1]. 2r2 + 2s2.

        Then k is an integer because sums and products of integers are integers. Let k = Thus, a2 + b2 = 2k, where k is an integer.

Proof: 1. Suppose a and b are any odd integers.

Proof:2. By definition of odd integer, a = 2r + 1 and b = 2r + 1 for any integers r and s.

Proof:3. By substitution and algebra, a2 + b2 = (2r + 1)2 + (2s + 1)2 = 2[2(r2 + s2) + 2(r + s) + 1].

Proof:4. Let k = 2(r2 + s2) + 2(r + s) + 1. Then k is an integer because sums and products of integers are integers.

Proof:5. Hence a2 + b2 is even by definition of even.

Proof:6. Thus, a2 + b2 = 2k, where k is an integer.

  Hence we proved that "If a and b are any odd integers, then a2 + b2 is even".

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Answer:

Quadrilateral as it is a four-sided ploygon, having 4 edges and corners

The equation of g(x) is 24 (3)ˣ when the graph is stretched vertically by a factor of 3 to form the graph g(x).

What is function?

For the parent function f(x) and a constant k >0,

then, the function given by  

g(x) = kf(x) can be sketched by vertically stretching f(x) by a factor of k if k>1 (or)

if 0 < k < 1 , then it is vertically shrinking f(x) by a factor of k

As per the given statement that the graph of f(x) is stretched vertically by a factor of 3 i.e

k = 3 >1

so, by definition

g(x) = 3 f(x) = 3 . 8(3)ˣ

= 8(3)ˣ⁺¹

= 24 (3)ˣ

Hence, the equation of g(x) is 24 (3)ˣ when the graph is stretched vertically by a factor of 3 to form the graph g(x).

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Answer:

(1.) 148 (2.) 42 (3.) $72?

Step-by-step explanation:

(1) 37 X 4 = 148

(2) 21 X 2 = 42

(3) it was confusing so i just added it all up

hope this helps and i hope i got number 3 right hehe

Answer:

Tyler's mom purchased a savings bond for Tyler. The value of the savings bond increases by 4% each year. One year after it was purchased, the value of the savings bond was $156.

Find the value of the bond when Tyler's mom purchased it. Explain your reasoning.

Step-by-step explanation:

Answer:

2/4 +6/8 =5/4

Step-by-step explanation:

(x + 2) is not a factor of the given polynomial f(x).

What is factor of polynomial?

A polynomial with coefficients in a specific field or in integers is expressed as the product of irreducible factors with coefficients in the same domain in mathematics and computer algebra, which is known as polynomial factorization.

Consider, the given polynomial

f(x)=2x^4-3x²-4x+1

We have to check that (x + 2) is a factor of polynomial or not.

Since, if (x - a) is a factor of polynomial then 'a' is a zero of polynomial.

Here if (x + 2) is a factor of f(x) then f(-2) = 0

Plug x = -2 in f(x).

⇒

f(-2) = 2(-2)^4 - 3(-2)^2 - 4(-2) + 1

      = 32 - 12 + 8 + 1

       = 20 + 9

f(-2) = 9

f(-2) ≠ 0

Hence, (x + 2) is not a factor of the given polynomial f(x).

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If x < 3, then the square root of  (x^2 - 6x + 9) can be simplified to (3-x).

First we factorise the quadratic expression:

x^2 - 6x + 9 = (x - 3)^2 ..(i)

(Since the expression is a perfect square trinomial, it can be factored as the square of a binomial.)

Then we will simplify the square root:

√(x^2 - 6x + 9) = √((x - 3)^2).

Now, since x - 3 is squared, taking the square root will eliminate the square, resulting in the absolute value of x - 3.

Final simplified form: √((x - 3)^2) = |x - 3|.

Therefore, the simplified square root expression is |x - 3| when x < 3 which equals to 3-x.

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pakii Ayus po

Step-by-step explanation:

favsywuwinswyuqoqpwieygsbsnwjqkqkhzvshqjqkjwhegwy

Answer:

(0,10)

Step-by-step explanation:

-x + 2y = 20

2y = x +20

y = 1/2x + 10

This is slope-intercept form. The y-intercept is 10.

(0,10)

Answer:

(0, 10)

Step-by-step explanation:

Can be simplified to

2y = x+20 by adding x to both sides

then divide by 2 to get to slope intercept form: y = ax+b

b is the y-intercept

y = 1/2x + 10

so the answer is 10

Answer:

1.5 miles

Step-by-step explanation:

graph on desmos graphing calculator

(0.075t, 0.1t-5)  

The second runner will overtake after 1.5 miles.

An equation is a mathematical statement that is formed when two algebraic expressions are equated using an equal sign.

Let t represent the time taken at which both the joggers meet

Then the distance covered is given by

For jogger A = 0.075 t

For jogger B = 0.1 (t-5)

0.075 t = 0.1t - 0.5

0.025t = 0.5

t = 20 seconds

The distance at which they meet is

=0.075 * 20

= 1.5 miles

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The point (5, 10) has not been translated in the given figure.Hence this statement is false.

The graph shows five points.

A point has been translated right and up.

Now, the statements that are true based on the graph are as follows:

The point (9, D) has been translated right and up.Answer: False

There is no information given about point (9, D).

So, we cannot say anything about the translation of point (9, D).

The point (1, 8) has been translated right and up.Answer: True

As explained above, the point (1, 8) has been translated 7 units to the right and 2 units up to get the new point (8, 10). So, this statement is true.

The point (2, 9) has been translated right and up.Answer: False

The point (2, 9) has not been translated in the given figure.

So, this statement is false.

Statement 4: The point (8, B) has been translated right and up.Answer: True

The point (8, B) has been translated 1 unit up in the given figure. So, this statement is true.

The point (5, 10) has been translated right and up.Answer: False

The point (5, 10) has not been translated in the given figure.

So, this statement is false.

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Answer:

Step-by-step explanation:

ABC have sides: 5, 7 and 10

5^2 + 7^2 = 25+47 = 72 < 10^2

so triangle ABC is obtuse

JKL has sides: 12, 35 and 37

12^2 + 35^2 = 144 + 1225 = 1369 = 37^2

so triangle JKL is right-angled

PQR has sides 12, 10 and 16

12^2 + 10^2 = 144 + 100 = 244 > 16^2

so triangle PQR is acute

Answer:

Step-by-step explanation:

missing the Q: it asks 2 classify the triangles.

so the ans:

ABC - obtuse

JKL - right-angled

PQR - acute

Answer:

P=-5

Step-by-step explanation:

Answer:

f(5) = 10, but I didn't need to do synthetic division to get there.  So I may misunderstand the problem.

Step-by-step explanation:

f(x) = 3x^2 - 9x - 20

f(5) = 3 (5)^2 - 9*5 - 20

f(5) = 75 - 45 - 20

f(5) = 10

Answer:

0>32/3. no solution

Step-by-step explanation:

hopes this helps

(5x-3)(5x-3) is a product of two binomials, which can be expanded using the distributive property.

What is an example of distributive property?

A value is multiplied by a sum to leverage the distributive property of multiplication over addition. Take the case where you want to multiply 5 by the sum of 10 + 3. We frequently add the two sums when two terms are similar instead of multiplying by 5. However, the attribute states that you must first raise each addend by 5..

To expand, you would multiply each term in the first binomial (5x-3) by each term in the second binomial (5x-3) and then add the products.

(5x-3)(5x-3) = (5x)(5x) + (5x)(-3) + (-3)(5x) + (-3)(-3)

= 25x^2 - 15x + 15x - 9

= 25x^2 - 9

So the expanded form of (5x-3)(5x-3) is 25x^2 - 9.

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Answer:

1. \(\alpha=0.3838\)

2. \(\beta=0.6619\)

3. \(0.3381\)

Step-by-step explanation:

The detailed procedures are shown in the attached documents below (it is typed using the math editor for better clarity and presentation).

The probabilities for each value from 6 to 10 and summing them will give us the Type I error is P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10).

To calculate the values requested, we need to use the binomial distribution and perform some calculations based on the given information.

1. To calculate the Type I error (α), we assume that the null hypothesis is true. In this case, the null hypothesis is that the proportion (p) is equal to 0.41. We want to calculate the probability of rejecting the null hypothesis when it is actually true.

If the number of people in the sample that are visiting the area is anywhere from 6 to 10 (inclusive), we will not reject the null hypothesis. Therefore, the Type I error corresponds to the probability of rejecting the null hypothesis when the proportion falls within this range.

We can calculate the probability of observing 6 to 10 people visiting the area out of a sample of 17, assuming the true proportion is 0.41:

P(6 ≤ X ≤ 10) = P(X = 6) + P(X = 7) + ... + P(X = 10)

Using the binomial probability formula, where n is the sample size (17) and p is the assumed true proportion (0.41):

P(X = k) = (nCk) * (p^k) * ((1 - p)^(n - k))

Calculating the probabilities for each value from 6 to 10 and summing them will give us the Type I error:

α = P(6 ≤ X ≤ 10) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)

2. To calculate the Type II error (β), we assume an alternative hypothesis where the proportion (p) is different from 0.41. In this case, the alternative proportion is 0.49. We want to calculate the probability of failing to reject the null hypothesis when the alternative proportion is true.

We need to calculate the probability of observing fewer than 6 people or more than 10 people visiting the area out of a sample of 17, assuming the true proportion is 0.49:

P(X < 6 or X > 10) = P(X < 6) + P(X > 10)

Using the binomial probability formula, we can calculate the probabilities for each value and sum them:

β = P(X < 6) + P(X > 10)

3. The power of the test is equal to 1 minus the Type II error (β). It represents the probability of correctly rejecting the null hypothesis when the alternative hypothesis is true.

Power = 1 - β

Now, let's perform the calculations.

from scipy.stats import binom

1. Calculate Type I error (α)

p = 0.41

n = 17

alpha = sum(binom.pmf(k, n, p) for k in range(6, 11))

print("Type I error (α):", alpha)

2. Calculate Type II error (β) for p = 0.49

p_alt = 0.49

beta = binom.cdf(5, n, p_alt) + (1 - binom.cdf(10, n, p_alt))

print("Type II error (β):", beta)

3. Calculate the power of the test for p = 0.49

power = 1 - beta

print("Power of the test:", power)

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Answer:

Between 76 and 88

1 = False (6x6 = 36)

2 = True ( 6 + 5 = 11)

3 = True ( 6/2 = 3)

4 = True (17 - 6 = 11)

Answer:

false

true

true

true

Step-by-step explanation:

Line AB intersects line CD at point F. If m∠AFC = (9x − 3)° and m∠BFD = (6x + 9)°, then m∠AFC is 33 degrees.

What are the intersections of lines?

Two or more lines that share exactly one common point are called intersecting lines. This common point exists on all these lines and is called the point of intersection.

We can start by using the fact that the sum of the angles on one side of a transversal is 180 degrees. Since point F is the point where lines AB and CD intersect, we can write:

m∠AFC + m∠CFD = 180° (angles on one side of the transversal)

Similarly, for the other side of the transversal, we have:

m∠BFD + m∠CFD = 180° (angles on one side of the transversal)

We are given that m∠AFC = (9x - 3)° and m∠BFD = (6x + 9)°, so we can substitute these values into the equations above:

(9x - 3) + m∠CFD = 180°

(6x + 9) + m∠CFD = 180°

Simplifying these equations, we get:

m∠CFD = 183 - 9x

m∠CFD = 171 - 6x

Since both of these expressions are equal to m∠CFD, we can set them equal to each other and solve for x:

183 - 9x = 171 - 6x

3x = 12

x = 4

Now that we have found x, we can substitute it back into the expression for m∠AFC to find its value:

m∠AFC = 9x - 3

m∠AFC = 9(4) - 3

m∠AFC = 33

Therefore, Line AB intersects line CD at point F. If m∠AFC = (9x − 3)° and m∠BFD = (6x + 9)°, then m∠AFC is 33 degrees.

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Answer:

6:07

Step-by-step explanation:

8:22 minus 2 hours is 6:22, 1/4 an hour is 15 minutes so 22 minus 15 is 7, leading to the answer of 6:07 being your start time.

Answer:

  24π cm² ≈ 75.4 cm²

Step-by-step explanation:

The surface area of a cylinder can be found using the formula ...

  SA = 2πr(r +h) . . . . . radius r, height h

__

Your cylinder has a surface area of ...

  SA = 2π(2 cm)(2 cm +4 cm) = 24π cm² ≈ 75.4 cm²

Answer:

We are given a height and radius for a cylinder and we must determine what the surface area is.  Surface area is the area that is showing all around the shape.  So it would include the area of the top and bottom circles and also the entire strap around the cylinder.  Using the equation below we can find the surface area.

\(S = 2\pi rh+2\pi r^2\)

\(S = 2\pi (2\ cm)(4\ cm)+2\pi (2\ cm)^2\)

\(S = 16\ cm^2*\pi+8\ cm^2*\pi\)

\(S = 50.265\ cm^2+25.133\ cm^2\)

\(S = 75.398\ cm^2\)

In the end, after inputting all of the values and solving, we get that the surface area for this cylinder is \(75.398\ cm^2\)

Hope this helps!

The value of x using Pythagoras theorem is: x = √118 mi

Pythagoras Theorem is defined as the way in which you can find the missing length of a right angled triangle.

The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).

Pythagoras is in the form of;

a² + b² = c²

Thus:

x = √(12² - (√26)²)

x = √(144 - 26)

x = √118 mi

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Answer:

2

Step-by-step explanation:

Answer:

78

Step-by-step explanation:

To compute (f.g)(5.5) , first compute g(5.5) , then use that value in f(x) to compute the composite function value

g(5.5) = -12(5.5) - 6 = -66 - 6 = -72

Use this value for x in f(x) = -x + 6

f(g(5.5)) = f(-72) = -(-72) + 6 = 72 + 6 = 78

To graph a system of equations, you can first solve each equation for y, and then plot the solutions on the same coordinate plane.

For the first equation, 8x + 8y = 64, we can solve for y by subtracting 8x from both sides, which gives us 8y = 64 - 8x. Then we divide both sides by 8 to get y = (64 - 8x)/8.

For the second equation, 2x - 2y = -4, we can solve for y by adding 2x to both sides, which gives us 2y = 2x - 4.

So the solutions for y in the first equation are:

y = (64 - 8x)/8

and in the second equation are:

y = 2x - 4

We can now plot these two lines on the same coordinate plane. The point of intersection of these two lines will be the solution of the system of equations

Answer is attached in the graph.

Step by step

The easiest way to solve these is to graph on an internet or app graphing calculator.

To graph by hand you need to simplify them and arrange in slope intercept form y=mx + b

(#1)

8x + 8y = 64 all are divisible by 8

8/8x + 8/8y = 64/8

Simplify

x + y = 8

Arrange in slope intercept form

subtract x from both sides to isolate y

x - x + y = -x + 8

y = -x + 8

We plot the first point of y intercept of 8 (0,8) and plot the 2nd point by slope of -1/1 or

( 1, -1). Draw your line

(#2)

2x - 2y = -4 are all divisible by 2

2/2x - 2/2y = -4/2

Simplify

x - y = -2

Arrange in slope intercept form

subtract x from both sides to isolate y

x - x - y = -x -2

Simplify

-y = -x -2

Change the signs by multiplying all by -1

y= x +2

We plot the first point of y intercept

of 2 (0, 2) and plot the 2nd point by slope of 1/1 or ( 1, 1). Draw your line

Now you can find the solution is where the lines intersect. At (3, 5)

See my attached graph for your two line equations below

y = x + 2

y = -x + 8

Answer: -8xf-16xg

Step-by-step explanation:

Vertical lines have no slopes.

They have an undefined slope. So, no slope means that the line is vertical.

Answer:

Step-by-step explanation:

4(w +5) =3

→w+5=3/4