8. If APTS - APOR, find the value of x.5x + 13TP36306.r - 2R

The volume of a rectangular prism is given by the formula:

Given the length is 7 cm

Width is 3 cm

Height is 3 cm

Substituting into formula, we find the volume:

Using the combination formula, it is found that:

a) There are 210 distinct ways to choose the problems.

b) The probability is of 0.1667 = 16.67%.

c) The probability is of 0.3333 = 33.33%.

[tex]C_{n,x}[/tex] gives the number of different combinations of x objects from a set of n elements, according by the following formula, involving factorials.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The order in which the problems are chosen is not important, which is the reason for the use of the combination formula in this problem.

4 problems are chosen from a set of 10, hence the number of ways to choose the problems is given by:

[tex]C_{10,4} = \frac{10!}{4!6!} = 210[/tex]

The number of ways to choose 4 problems that she can solve is:

[tex]C_{7,4} = \frac{7!}{4!3!} = 35[/tex]

Hence the probability is:

p = 35/210 = 0.1667 = 16.67%.

For item c, the desired outcomes are as follows:

Hence the probability is:

p = (7 + 63)/210 = 70/210 = 0.3333.

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The property that completes the proof is the transitive property

From the question, we have the following parameters

The point C is the midpoint of AE

BC = CD

The above implies that

AC = CE

And it also means that:

The line segment BC and the line segment CD have equal lengths

According to the transitive property of equation, we have:

If A = B and B = C, then A = C

This can also be represented as

If A + B = C + D and C + D = E + F, then A  + B = E + F

Using the above as a guide, we have (in step 3)

AB + BC = AC

CD + DE = CE

This implies that

AB + BC = CD + DE

Hence, the statement that represents the reason 4 in the proof is (b) transitive property

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Answer:

-8x + 16y -15q - 30p

Step-by-step explanation:

your just expanding brackets here

Answer: -8x - 16y - 15q - 30p Is the correct answer

I hope this helps!

If a rectangular tabletop has an area of [tex]28\frac{1}{8}[/tex] square feet and the length of [tex]6\frac{1}{4}[/tex] feet, then the width of the tabletop is  [tex]4\frac{1}{2}[/tex] feet

The area of the tabletop =  [tex]28\frac{1}{8}[/tex] square feet

Convert the mixed fraction to simple fraction

[tex]28\frac{1}{8}[/tex] square feet = 225/8 square feet

The length of the tabletop =  [tex]6\frac{1}{4}[/tex] feet

Convert the mixed fraction to simple fraction

[tex]6\frac{1}{4}[/tex] feet = 25/4 feet

Area of the rectangle = Length ×  width

Width of the rectangle = Area of the rectangle ÷ Length of the rectangle

Substitute the values in the equation

Width of the rectangle = 225/8 ÷ 25/4

= 225/8 × 4/25

= 9/2 feet

Convert the simple fraction to mixed fraction

9/2 feet = [tex]4\frac{1}{2}[/tex] feet

Hence, if a rectangular tabletop has an area of [tex]28\frac{1}{8}[/tex] square feet and the length of [tex]6\frac{1}{4}[/tex] feet, then the width of the tabletop is  [tex]4\frac{1}{2}[/tex] feet

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The second term of the arithmetic sequence is:

a₂= -9

Here we have an arithmetic sequence, such the the recursive formula is:

aₙ = aₙ₋₁ + 4

So to get each term, we need to add 4 to the previous one.

We know that the first term is:

a₁ = -13

Then the second term will be:

a₂ = a₁ + 4 = -13 + 4 = -9

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To rotate the figure 90 degrees clockwise about a point, every point (x, y) will rotate to (y, -x):

The vertices of the triangle have the following coordinates:

Applying the transformation rule, we have the new coordinates to be:

The transformed image is shown below (the black triangle):

The solution of B(x) = 18 - 0.5x with x being -2, 0, 5 is 19, 18 and 15.5.

Given:

B(x) = 18-0.5x

x = -2, 0, 5

Putting the values of x to find the result of the function.

B(-2) = 18 - 0.5 × (-2) = 18 + 1 = 19

The required solution of the function at x = -2 is f(-2) = 19.

B(0) = 18 - 0.5 × (0) = 18

The required solution of the function at x = 0 is f(0) = 18.

B(5) = 18 - 0.5 × (5) = 18 - 2.5 = 15.5

Thus, the required solution of the function at x = 5 is f(5) = 15.5.

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The complete question is :"How do you solve B(x) = 18-0.5x with x being -2, 0, 5."

The area of the parallelogram is 240 feet.

A parallelogram's area is the area that it occupies in a two-dimensional plane. A parallelogram is a four-sided, two-dimensional form in geometry. This particular quadrilateral example has equal and parallel opposite sides. The space bounded by a parallelogram's four sides is known as its area. A parallelogram's area is determined by multiplying its length by its height. 

A quadrilateral's interior angles add up to 360 degrees.

The area of a parallelogram can thus be written as :

Area = Base × Height

In this diagram it is given that the Base = 20 feet and the height = 12 feet

Thus the area can be obtained by simply multiplying these two dimensions

So area = 20 × 12 = 240 feet .

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Answer:

42

Step-by-step explanation:

76-34

The percent change formula is:

In this case, the percent change is:

Finance charge = $93.00

The interest you'll pay on a loan is defined as a finance charge, and it's most commonly used in the context of credit card debt. A financing fee is computed by taking your annual percentage rate, or APR, the amount you owe, and the time period into account.

Given that,

Interest rate = 15.5%

Date: 1-3 (3 days)

Average daily balance = amount paid × days

                                      = $200 × 3 = $600  

Date: 4-20 (17 days)

Average daily balance = amount paid × days

                                      = $300 × 17 = $5100  

Date: 21-30 (10 days)

Average daily balance = amount paid × days

                                      = $150 × 10 = $1500  

So, total average daily balance for the month

= $(600+5100+1500)

= $7200

Now, the finance charge = $7200 × (15.5÷12)

                                         = $93.00

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Answer:

The best estimate for the correlation coefficient is .85.

The value of f'(x) at x = 1 is 1 for first order derivative of x^x^3.

A derivative in calculus is the rate of change of a quantity y with respect to another quantity x. It is also termed the differential coefficient of y with respect to x. Differentiation is the process of finding the derivative of a function.

Given that, x^x^3 and we have to find the first order derivative with respect to x and then find the value at x = 1.

Let's proceed to solve this question accordingly.

let f(x) = x^x^3

The first order derivative = f'(x) = d/dx(x^x^3)

First apply the generalized power rule, then we have

= x^x^3.d/dx(ln(x)x^3)

Applying the power rule, we get

= x^x^3 (d/dx(x^3).ln(x)+x^3.d/dx(ln(x)))

= x^x^3 (3x^2 ln(x) +x^3.1/x)

= x^x^3 (3x^2ln(x) +x^2)

On simplifying, we will get

= x^x^3+2(3ln(x)+1)

f'(x) = d/dx(x^x^3) = x^x^3+2(3ln(x)+1)

Now, at x = 1, we get

f'(x) = d/dx(x^x^3) = x^x^3+2(3ln(x)+1) = 1

Therefore, f'(x) = d/dx(x^x^3) = x^x^3+2(3ln(x)+1) = 1 is the required answer.

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According to the solving the given data the values of :

Range = 12

Variance= 25

Standard deviation= 5

Data points' deviations from the mean are quantified by their variance. Layman defines variance as the degree to which a set of data (numbers) deviates from the mean (average) value. Finding the predicted difference between the deviation from the actual value and the variation.

In statistics, range is the distinction between the most and least values in a set. Mathematics' interval, also known as range, is a collection of real numbers that contains all values that fall between any two other values.

Given data: 3, 3, 5, 9, 12, 13, 15

Range  = Highest value  - lowest value

            = 15 - 3

            = 12

Mean of the given data:

xi = 3, 3, 5, 9, 12, 13, 15

n = 7

S² = ∑(xi  - x)²/(n - 1)

    = (30.25 + 30.25 + .25+ 12.25 + 20.25 + 42.25 + 12.25)/6

   = 147.75/6

   = 24.6

     = 25

Finding the standard deviation:

√S² = 25

S = 5

According to the solving the given data the values of :

Range = 12

Variance= 25

Standard deviation= 5

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Solution:

Given a sphere of diameter, d, 2.5ft.

To find the volume, V, of the sphere, the formula to apply is

Where, the radius, r, is

Substitute for r into the formula to find the volume of a sphere above

Hence, the volume, V, of the given sphere is 8.2 ft³ (the nearest tenth)

Okay, here we have this:

Considering the provided rectangular pyramid, we are going to calculate the requested volume, so we obtain the following:

Then, we are going to use the following formula to find the volume of this rectangular pyramid:

V=(abH)/3

Replacing:

V=(abH)/3

V=(5cm*6cm*7cm)/3

V=(210cm^3)/3

V=70 cm^3

Finally we obtain that the volume of the rectangular prism is 70 cm^3.

Answer:

Step-by-step explanation:

13) 8 - 6 + 4 = 2 + 4 = 6

14) 16÷(4-2)-3 = 16÷2 - 3 = 8 - 3 = 5

15) 3x + 5 = 17

3x = 17 - 5

3x = 12

x = 4 ≠ 2

b. solution is incorrect

16)4y - 7 = 3y - 4

4y - 3y = -4 + 7

y = 3

a. solution is correct

17) 2m - 3 < 4

2m < 4 + 3

2m < 7

m < 3.5

2 < 2.5, so a. number is a solution

18 ) 5 + 2n ≥ 12

2n ≥ 12 - 5

2n ≥ 7

n ≥ 3.5

0 is not greater than equal to 3.5, so b. number is not a solution

Answer:

Area (A) = 42m²

Step-by-step explanation:

A = b·h = 6·7 = 42m²

3 is dividing on the right, then it will multiply on the left

B is multiplying on the right, then it will divide on the left

Answer: undefined, DNE

Step-by-step explanation:

This is a vertical line, so there is an undefined slope and no y-intercept.

)

2) So, let's begin with the lower-left product of matrices:

Now for the next pair of matrices in the middle:

Notice that each row is multiplied by each correspondent column.

And finally, the pair on the lower-right:

) Thus, the se are theanswers .

The money would Stella have to pay in a month in which she downloaded 40 songs is $59.

The amount that she has to pay if she downloaded ss songs is 9 + 1.25s.

From the information, Stella signed up for a streaming music service that costs $9 per month and the service allows Stella to listen to unlimited music, but if she wants to download songs for offline listening, the service charges $1.25 per song.

The money would Stella have to pay in a month in which she downloaded 40 songs is:

= 9 + 1.25s

where s = number of songs

= 9 + 1.25s

= 9 + 1.25(40)

= 9 + 50

= $59.

The amount that she has to pay if she downloaded s songs is:

= 9 + 1.25(s)

= 9 + 1.25s

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Answer: A and C

Sample Answer: Multiplication is a short way to write repeated addition. So 200 •12 means the same as 200 + 200 + . . . + 200.

Answer:

b

Step-by-step explanation:

Answer:

C) 0.1666

Step-by-step explanation:

The probability of selecting a calculator that is defective can be defined as: [tex]\frac{46}{46+26}[/tex]

The 46 in the numerator is the number of calculators that are defective in the group. The 46 + 26 represents the total amount of calculators since 46 are defective and 26 are not defective and assuming a calculator can only be defective or not defective then these are the total number of calculators in the group.

This gives you a probability of approximately: [tex]\frac{46}{72}[/tex] or approximately 0.638889

We can multiply independent events to find the combined probability of these events occurring. So we have to assume you put the calculator back into group after selecting one.

If this is the case we simply multiply 46/72 * 46/72 * 46/72 * 46/72 or (46/72)^4 to get an approximate probability of: 0.1666

The probability is 0.334 and the events are not disjoint​ events

The table of values represents the given parameters

The probability to calculate is given as

The probability of getting an order that is not accurate or is from Restaurant C

This can be represented as

P(Not accurate or Restaurant C)

This is calculated as

P(Not accurate or Restaurant C) = [n(Not accurate) + n(Restaurant C) - (Not accurate and Restaurant C)]/Total

So, we have

P(Not accurate or Restaurant C) = (37 + 52 + 34 + 19 +237 + 34 - 34)/(330 + 276 + 237 + 150 + 37 + 52 + 34 + 19)

Evaluate the sum and the difference

P(Not accurate or Restaurant C) = 379/1135

Evaluate the quotient

P(Not accurate or Restaurant C) = 0.334

Lastly, the events of selecting an order that is not accurate and selecting an order from Restaurant C are not disjoint​ events

This is so because it is possible to select an order from restaurant C that is not accurate

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Answer:

C , D

Step-by-step explanation:

The component form of a vector is given as < x, y >, where x describes how far right or left a vector is going and y describes how far up or down a vector is going.

The component form of vector C is <1, 5> and the component form of vector D is <8, 2>. The components represent the magnitudes of the vector's displacements in the x and y directions, respectively.

To write the component form of a vector, we simply list its components, which are the numerical values that represent the vector's magnitude and direction in each dimension. In this case, we have vector C with components C<1, 5> and vector D with components D<8, 2>.

The components of a vector represent its position or displacement along the coordinate axes. In a two-dimensional Cartesian coordinate system, the first component represents the displacement along the x-axis (horizontal direction), and the second component represents the displacement along the y-axis (vertical direction).

For vector C, the component form is written as <1, 5>, where the first component is 1 and the second component is 5. This means that vector C has a displacement of 1 unit in the x-direction and 5 units in the y-direction.

Similarly, for vector D, the component form is <8, 2>, indicating a displacement of 8 units in the x-direction and 2 units in the y-direction.

Therefore, the component form of vector C is <1, 5> and the component form of vector D is <8, 2>. The components represent the magnitudes of the vector's displacements in the x and y directions, respectively.

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f(g(x)) for the given equation f(x)=8x+1 and g(x)=4x-2 is 32x-15 using substitution method of solving the equation.

An equation is a mathematical statement that demonstrates the equality of two mathematical expressions. It is a formula that expresses the connection between two expressions on each side of a sign.

The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies.

given,

f(x)=8x+1

g(x)=4x-2

f(g(x))=8(4x-2)+1

=32x-16+1

f(g(x))=32x-15

Hence, this is required f(g(x)) for the given two equations.

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