A. Dilate triangle ABC using center p and scale factor 3/2.
B. What do properties of dilations tell you about B'? (please answer B)

Using the exponential function given y = 7.1(1.03)ˣ, the amount produced in 2006 was 7.8 billion pounds and the estimated amount in 2014 is 9.8 billion pounds

An exponential function is a function of form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

In the function given;

y = 7.1(1.03)ˣ

a) What is the estimated number in 2006

We can find the value of x in 2006 as

2006 - 2003 = 3

x = 3

Let's substitute the values into the formula above;

y = 7.1(1.03)³

y = 7.76 ≅ 7.8 billion pounds

b)

The cheese produced in 2014

x = 2014 - 2003 = 11

Plug in the value

y = 7.1(1.03)¹¹

y = 9.83 ≅ 9.8 billion pounds

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The estimate of the total cheese production in 2006 is 7.8 billions of pounds.

The estimate of the total cheese production in 2014 is 9.8 billions of pounds.

[tex]y =7 .1( {1.03})^{x} [/tex]

Where,

The total cheese production in 2006;

x = 3 years

[tex]y =7 .1( {1.03})^{x} [/tex]

[tex]y =7 .1( {1.03})^{3} [/tex]

[tex]y =7 .1(1.092727)[/tex]

y = 7.7583617 billions of pounds

Approximately,

y = 7.8 billions of pounds

The total amount of cheese produced in 2014;

x = 11

[tex]y =7 .1( {1.03})^{x} [/tex]

[tex]y =7 .1( {1.03})^{11} [/tex]

[tex]y =7 .1(1.3842338707244)[/tex]

y = 9.8280604821435

y = 9.8 billions of pounds

In conclusion, the estimated production of cheese in 2006 and 2014 are 7.8 and 9.8 billions of pounds respectively.

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We get the flawless quarte trinomial, finish the quadrilateral is (q+5/12)² we can say as a quadratic equation is q²+ 5/6q+---.

Given that,

The equation is q²+ 5/6q+---

We have to find to create a flawless quarte trinomial, finish the quadrilateral.

We know that,

Take the equation

q²+ 5/6q+---

By adding some thing we get the quadratic equation.

The missing term we add is 5/2×6

We get

q²+ 5/6q+(5/6×2)²

q²+ 5/6q+(5/12)²

We can write as

(q+5/12)²

Therefore, we get the flawless quarte trinomial, finish the quadrilateral is (q+5/12)² we can say as a quadratic equation is q²+ 5/6q+---.

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Answer:

Step-by-step explanation: 20% to 50%

In the samples, the percent of students that bike to school varies from 20% to 50%.

In the data plot, 10 is the minimum and 25 is the maximum so 10/50= 0.2 or 20%. 25/50= 0.5 or 50%. Meaning it should vary from 20% to 50%.

The simplified expression of the radical expression ∛54 is 3∛3

Expression:

Expression is also known as equation is the combination of number, variable and the mathematical operator.

Given,

Here we have the radical expression ∛54.

Now, we have to simplify the expression and to find the simplest form of it.

Here we have to radical expression

=> ∛54.

Now, we have to expand this equation, then we get,

=> ∛(27 x 3)

We know that the value of ∛27 = 3,

Therefore, when we apply these on the expression, then we get,

=> 3∛3.

Therefore, the simplified expression is 3∛3.

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The correct mapping (an isomorphism) between the sets of vertices of the two graphs is f(u1) = v1, f(u2) = v2, f(u3) = v4, f(u4) = v5, and f(u5) = v3

The two given graphs are isomorphic in nature

In the firsts graph, the serial order is u1, u2, u3, u4, u5

wherease in the second graph the order is v1, v2, v4, v5, v3

Upon analysis, it can be seen that  the correct mapping (an isomorphism) between the sets of vertices of the two graphs is

f(u1) = v1, f(u2) = v2, f(u3) = v4, f(u4) = v5, and f(u5) = v3

Then the correct mapping (an isomorphism) between the sets of vertices of the two graphs is f(u1) = v1, f(u2) = v2, f(u3) = v4, f(u4) = v5, and f(u5) = v3.

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Answer:

13 - 6(2)

Step-by-step explanation:

I found this out because, since you have to subtract the 6 from the 13, the 13 will go first:

13 -

Then, you figure out what the 6 and two times means. It means 6 x 2, or 6(2):

13 - 6(2).

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Answer:

Step-by-step explanation:

The answer is D

By using the cross multiplication, we can determine the solutions to the equation  w=2 , w=6.

By multiplying the numerator of one side by the denominator of other side and equating the resulting two products, cross multiplying can be used to solve a fractional equation when each side has a fraction with a single denominator.

Given the expression [tex]\frac{w}{2w-4} = \frac{4}{w}[/tex]

By using cross multiplication, we have

[tex]w^{2} = 4(2w-3)\\ w^{2} = 8w-12\\w^{2}-8w+12=0\\(w-2)(w-6)=0\\w=2 and w=6[/tex]

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Jason's down payment is calculated to be 41250 if he bought the house for 275,000

Down payment is a term used to describe an initial payment made when something is bought on credit.

The original price of the house that Jason Aldeen bought is 275,000. Jason made a down payment of 15%. This means Jason Aldeen paid 15% of the original cost of the house. Therefore,

Jason's down payment is 15% of $275000

Down payment = 15% × 275,000

Down payment = 15/100 × 275000

Down payment = 0.15×275000

Down payment = 41250

Therefore; the down payment on the house bought by Jason Aldeen is calculated to be 41250

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The container's dimensions and maximum volume are 4/3 and 2/3 when the lateral side of a cylindrical container will be formed from a rectangular sheet of metal with a perimeter of 4 meters.

Given that,

The lateral side of a cylindrical container will be formed from a rectangular sheet of metal with a perimeter of 4 meters.

We have to find identify the container's dimensions and maximum volume.

We know that,

2(x+y)=4

x+y=2

Now,

Volume is π(x/2)²y

=π(x²/4)(2-x)

=π(f(x))

Now, volume will be maximum when f(x) will be max,

f(x)=x²/4(2-x)

f'(x)=2x(2-x)-x²

f'(x)=4x-3x²

We get,

f'(x)=0

4x-3x²=0

x(4-3x)=0

x=0, 4-3x=0

x=4/3

y value is 2-4/3=6-4/3=2/3

Therefore, The container's dimensions and maximum volume are 4/3 and 2/3 when the lateral side of a cylindrical container will be formed from a rectangular sheet of metal with a perimeter of 4 meters.

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Answer:

f-(9-2)

f-7

Step-by-step explanation:

It is proven that m∠LKG = 120°, and the corrected statement 6 is In a parallelogram opposite angles are equal i.e m∠JKG = m∠GHJ = 60°.  

A quadrilateral that has two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.

Here we have proof of Parallelogram

To get correct statement 6 let's rewrite the whole process from the start

Given that GHIK is a parallelogram, m ∠GHJ = 60° and JKL is a line

Here we need to prove m∠LKG = 120°  

   Statement                                  - Reason

1. GHIK is a parallelogram              -  Given  

2. m ∠GHJ = 60°                             -  Given

3. JKL is a line                                 -  Given

4. m ∠JKL = m∠LKG + m∠JKG       -  On line-segment, ∠JKL is equal to the

                                                           the sum of Non-overlapping parts

                                                            m∠LKG and m∠JKG  

5. m ∠JKL = 180°                            - Angle formed by a straight line is 180°  

6. 180°= m∠LKG + 60°                   - In a parallelogram opposite angles are

                                                         equal i.e m∠JKG = m∠GHJ = 60°

7. m∠JKG = m∠GHJ                       - Transitive/ Substitution

9. m∠LKG =  180° - 60°      

10. m∠LKG =  120°                          - from statement 6

Therefore,

It is proven that m∠LKG = 120°, and the corrected statement 6 is In a parallelogram opposite angles are equal i.e m∠JKG = m∠GHJ = 60°.    

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10 units is the length of the line segment

Given that: the graph of the line segment from negative 6 comma negative 5 to 0 comma 3. Thus:

point 1 (-6, -5) => x1 = -6, y1 = -5

point 2 (0, 3) => x2 = 0, y2 = 3

Length of x-axis (x): x2 -x1 = 0-(-6) = 6

Length of y-axis (y): y2 -y1 = 3-(-5) = 8

Let the length of the line segment be L

Using Pythagorean Theorem:

L² = x² + y²

L² = 6² + 8²

L² = 36 + 64

L² = 100

L = √100 = 10 units

Therefore, the length of the line segment is 10 units. The 3rd option is the answer

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The standard deviation of X is about 2.38.

Suppose X is normally distributed with mean of 5. If P (X ≤ 3) = 0.2

We need to find the standard deviation of X

We can use a z-table or a graphing calculator to find the z-value that is associated with a probability to 0.20 (you should get a z-value of about z = -0.84). Then use the z-value formula

z = (x−μ) /σ

−0.84 = (3−5) /σ

−0.84 = −2/σ

σ = -2/-0.84

σ  = 2.38

Solving for the standard deviation ( σ ) you should get a value of about 2.38. Therefore, the standard deviation of X is about 2.38.

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The 5 positive integers are 3,3,4,4,16, for them mode is 3 and 4, a median is  4 and mean is 6.

The median is a middle number of sequence, more precisely when the series is shorted descending to ascending order the middle term is median.

Let the number 3 repeats m times,

The number 4 repeats n times,

and any other number is x,

Mean of series is 6, therefore,

(3m+4n+x)/5 = 6

3m+4n +x = 30

Since, mode of 5 number is 3 and 4

So, the value of m can be 2 and value of n can also be 2,

3(2) + 4(2) + x = 30

x = 30-14

x = 16

Therefore, the 5 numbers are 3,3,4,4,16

And median for this number is 4 and mean is 6.

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Answer:C

Step-by-step explanation:

The answer is c because of the following:

-5 + 7 = 2

so 3/x= 2

we can put two in x's place and x in 2 place and get 3/2= x

The solutions are,

1. True

2. False

3. True

4. False

For all the given statements the true or false are,

A, X and D are n X n matrices.

1. A is diagonalizable if A XDX⁻¹ for some diagonal matrix D and some invertible matrix X.

→ True

2. A is diagonalizable if and only if A has n eigenvalues, counting multiplicities.

→ False, It always has n eigenvalues, counting multiplicity.

3. If A is diagonalizable, then A is invertible.

→ True, In this case, we can construct a P which will be invertible. And a D.

4. If there exists a basis for R" consisting entirely of eigenvectors of A, then is diagonalizable.

→ False, It's invertible if it doesn't have zero an eigenvector but this doesn't affect diagonalizability.

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The half life for this radioactive substance is 40.76 years

As we know that radioactive decay is a first order reaction

For first order reaction, we can write

N = [tex]N^{0}[/tex][tex]e^{-kt}[/tex]

Where N = Amount of substance at time ‘t’

N0 = Initial amount of substance

K = rate constant for first order reaction

t = time in years

Now, as per the question,

This substance is decaying at a rate of 1.7% that means 98.3% will remain after decaying.

For time t = 1 years , N/[tex]N^{0}[/tex] = 0.983

Therefore, we have

N/[tex]N^{0}[/tex] = [tex]e^{-kt}[/tex]

0.983 = [tex]e^{-k }[/tex]

-k = ln(0.983)

-k = -0.017

K = 0.017 [tex]year^{-1}[/tex]

Now for half life, We can write N/[tex]N^{0}[/tex] = 0.5

Therefore, N/[tex]N^{0}[/tex] = [tex]e^{-kt}[/tex]

              0.5 = [tex]e^{-0.017t}[/tex]

ln(0.5) = -0.017t

-0.693 = -0.017t

t = 0.693/0.017 = 40.76 years

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There is a total of 190 ways to share apples between them.

What is a ball-and-urn method?

The ball-and-urn method often referred to as stars-and-bars, sticks-and-stones, or dots-and-dividers is a typical combinatorial method.

It is used to resolve issues of the following type: in how many different ways can one divide 'k' undifferentiable items into 'n' distinct bins?

Use the ball-and-urn method,  Let Alice get 'x' apples, Becky get 'y' apples, and Chris get 'z' apples.

⇒x + y + z = 24

We can manipulate this into an equation that can be solved using the ball-and-urn method

All of them get at least 2 apples, so we can subtract 2 from x, 2 from y, and 2 from z.

⇒(x - 2) + (y - 2) + (z - 2) = 18

Let x' = x - 2, y' = y - 2, z' = z - 2.

⇒ x' + y' + z' = 18

We can allow either of them to equal 0, hence this can be solved by the ball-and-urn method.

By the ball-and-urn method, we get

 [tex]$\binom{18 + 3 - 1}{3 - 1} = \binom{20}{2} = \ 190}$.[/tex]

Hence, there are 190 ways to split the apples among them.

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With a one-way ANOVA, you are comparing the T Statistic with the T critical value.

The Z test is a parametric procedure that is used on data that is dispersed in a normal fashion. For testing hypotheses, the z-test can be used on one sample, two samples, or proportions. When the population variance is known, it analyzes if the means of two big groups are dissimilar.

The critical value should be compared to the test statistic. The alternative hypothesis should be accepted in place of the null hypothesis if the test statistic is more extreme in the alternative's favor than the critical value. The null hypothesis should not be rejected if the test statistic is less extreme than the critical value.

Thus, with a one-way ANOVA, you are comparing the T Statistic with the T critical value.

The question is incomplete, the complete question is"

With a one-way ANOVA, you are comparing the _____ with the _____.

A. T Statistic with the T critical value

B. F Statistic with the F critical value

C. Correlation coefficient with the confidence interval

D. Outlier with the 4th quartile outer-most limit

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The value of m from the above expression  is  - 100

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In the given expression 1/4 m + 9 = -16, the m is equal to -100.

An algebraic expression is consists of variables, numbers with various mathematical operations,

The given expression is,

1/4 m + 9 = -16,

Simplify the expression to find the value of m,

1/4 m  = -16 - 9

1/4 m = -25

m = -100

The value of m for the given expression 1/4 m + 9 = -16, is -100.

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D'(5) is the expression that gives the rate of change at which the depth is changing at 5 minutes

A rate of change describes the rate at which one quantity changes in relation to another quantity.

Also, the derivative of a function can be found by determining the average rate of change of the function. Thus, these two terms are used interchangeably.

Given: The depth of a rain puddle D(t) is given in inches, and t is given in minutes.

The rate of change of D(t) is the derivative of D(t) which is written as D'(t).

Therefore, the expression that gives the rate of change at which the depth is changing at 5 minutes will be D'(5)

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Ratio is the relation between two amounts that shows the number of times one value contains within the other.

What is Ratio?

A ratio in mathematics illustrates how many times one number contains another. For example, if a dish of vegetables contains eight tomato and six carrots, the tomato-to-carrot ratio is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the proportion of carrots to tomato is 6:8 (or 3:4), while the proportion of tomato to overall fruit is 8:14. (or 4:7). A ratio's numbers can be any quantity, such as a count of persons or things, or measures of lengths, weights, time, and so forth. In most situations, both numbers must be positive.

Solution:

Ratio is the relation between two amounts that shows the number of times one value contains within the other.

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The combined thickness is 7/8 inches.

The installation over the pad indicates they are joined vertically. So, the combined thickness will be sum of individual thickness of carpet and pad. Hence, calculating the thickness now.

The thickness of the carpet and pad = thickness of carpet + thickness of pad

Keep the values in equation

The thickness of the carpet and pad = 3/8 + 1/2

Taking LCM on Right Hand Side, we get 8

Adding the fractions

The thickness of the carpet and pad = (3 + (1×4))/8

The thickness of the carpet and pad = (3 + 4)/8

The thickness of the carpet and pad = 7/8

Hence, the thickness of the carpet and pad is 7/8 inches.

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Answer:

Step-by-step explanation:

C=1.75m+10.50

Answer:

18/25

Step by step explanation:

Answer: 18 cents - 72%

The given expression 3x + 2.5 (4x + 2) is equivalent to 13x + 5.

The given question is a polynomial in one variable. Polynomials in one variable are algebraic expressions that depend on only one variable. The given expression is also dependent only on the variable, x.

In order to find its equivalent, we need to expand it. To expand it, we multiply the terms inside the bracket with the 2.5 outside. By doing so, we will get -

= 3x + (2.5*4x) + (2.5*2)

= 3x + 10x + 5

= 13x + 5

Hence, we find out that 3x + 2.5 (4x + 2) is equivalent to 13x+5.

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Answer: ∠1= 60° ∠2=120° ∠3=60° ∠4=60° ∠5=120° ∠6=120° ∠7=60°

Step-by-step explanation: hope this helps!

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Answer:

1. 60°

2. 120°

3. 60°

4. same as 1. 60°

5. same as 2. 120°

6. same as 2 and 5, and the angle given of 120°

7. same as 1. and 3. 60°

Step-by-step explanation:

You are given an angle of 120°

The lines are parallel, and the transversal gives you all the answers. All have to add up to 360°.

The value of x is 11

What is supplementary angle ?

Two angles are said to be supplementary if their sums total 180 degrees. A linear pair's two angles, like angles 1 and 2 in the illustration below, are always supplementary. But two angles don't have to be close to one another to be supplementary. In the following image, 3 and 4 are supplementary since their sums equal 180 degrees.

Angles ∠1 and ∠7 are alternate exterior angles where a transversal crosses parallel lines, so are congruent.

∠ 1 = ∠ 7

∴2x + 5 = 4x - 17

4x - 2x =17+5

 2x = 22

   x = [tex]\frac{22}{2}[/tex]

   x = 11

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