Use the Distributive Property to simplify the expression: 8(c – 5)

Answer:

The best way to decompose the composite figure to determine its area is as a semicircle, a trapezoid, and two rectangles. This way, we can use the following formulas to find the area of each part:

Area of a semicircle = 21​πr2, where r is the radius of the circle.

Area of a trapezoid = 21​(b1​+b2​)h, where b1​ and b2​ are the bases and h is the height of the trapezoid.

Area of a rectangle = l×w, where l is the length and w is the width of the rectangle.

Then, we can add up the areas of each part to find the total area of the composite figure. The other options are not as convenient because they either involve more parts or more complicated shapes. For example, option A would require finding the area of a triangle, which involves using trigonometry or the Pythagorean theorem. Option B would require finding the area of four triangles, which is more tedious than finding the area of two rectangles. Option C would require finding the area of a square, which is redundant because a square is a special case of a rectangle.

Step-by-step explanation:

The composite figure can be decomposed into a semicircle, a trapezoid, and two rectangles.

Option D is the correct answer.

It is a quadrilateral that has one pair of parallel sides and a height.

The area is calculated as: 1/2 x sum of the parallel sides x height.

Examples:

Area of a trapezium that has the parallel sides as 3 cm and 4 cm and a heght o 5 cm.

Area = 1/2 x (3 + 4) x 5

Area = 1/2 x 7 x 5

Area = 35/2 = 17.5 cm^2

We have,

The given figure can be decomposed into the following figure.

- Semicircle

- Trapezoid

- Two rectangles

Thus,

A semicircle, a trapezoid, and two rectangles.

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The entropy of rolling two four-sided dice is 4 bits, which is twice the entropy of rolling one four-sided die.

In information theory, entropy is a measure of the uncertainty or randomness of a system. In the context of rolling two four-sided dice, the entropy of the system can be calculated using the formula for entropy: H = -Σp(x) log2p(x), where p(x) is the probability of each possible outcome.

For rolling one four-sided die, the entropy of the system is H1 = -Σp(x) log2p(x) = -4(1/4) log2(1/4) = 2 bits, where log2 represents the base-2 logarithm.

When rolling two four-sided dice, there are 16 possible outcomes, each with a probability of 1/16. To calculate the entropy of the system, we can use the formula H2 = -Σp(x) log2p(x), where the sum is taken over all 16 possible outcomes.

H2 = -16(1/16) log2(1/16) = 4 bits

This increase in entropy is due to the increase in possible outcomes and the resulting increase in uncertainty or randomness of the system.

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A consumer loan of $40,000 with a 15.8% interest rate will require monthly payments over a period of 2 years. The total amount to be paid, including both principal and interest, will be approximately $45,380.

To calculate the monthly payments, we need to determine the total amount to be paid over the loan period, including the principal amount and the interest. The formula used for calculating equal monthly installments is:

M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)

Where:

M = Monthly payment

P = Principal amount

r = Monthly interest rate

n = Number of monthly payments

In this case, the principal amount (P) is $40,000, the interest rate (r) is 15.8% per year, and the loan duration (n) is 2 years (24 months).

First, we convert the annual interest rate to a monthly rate by dividing it by 12: 15.8% / 12 = 0.0132.

Next, we substitute the values into the formula:

M = 40,000 * (0.0132 * (1 + 0.0132)^24) / ((1 + 0.0132)^24 - 1)

Calculating this formula gives us the monthly payment (M) of approximately $1,907.42.

To find the total amount to be paid, we multiply the monthly payment by the number of payments: $1,907.42 * 24 = $45,778.08. However, this includes both the principal and the interest. Subtracting the principal amount ($40,000) gives us the total interest paid: $45,778.08 - $40,000 = $5,778.08.

Therefore, the total amount to be paid, including both principal and interest, will be approximately $45,778.08.

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The total number of tasks Terrence completed. By substituting the value of 'x' with the number of tasks Terrence completed

The factor 'x' in the expression '90x - 20' represents the total number of tasks that Terrence completed in the game.

To understand why, let's break down the given information. It states that Shelly and Terrence completed a different number of tasks. Shelly earned 90 points on each task, so the total number of tasks she completed is not represented by 'x'.

On the other hand, Terrence's total points were 20 less than Shelly's total. This means that Terrence's total points can be calculated by subtracting 20 from Shelly's total points. Since Shelly earned 90 points on each task, her total points would be 90 multiplied by the number of tasks she completed.

So, the expression '90x - 20' represents Terrence's total points in the game, where 'x' represents the total number of tasks that Terrence completed. By substituting the value of 'x' with the number of tasks Terrence completed, we can calculate his total points.

Therefore, the correct answer is: The total number of tasks Terrence completed.

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Answer:40.789%

Step-by-step explanation:

380-225=155

155/380=0.40789 or 40.789%

Dr. Fahrrad breaks down 0.23 moles of ATP to get to work.

The first step is to calculate the work done by Dr. Fahrrad on his bike ride. We can use the following equation:

W = F * d

where:

W is the work done in joules

F is the force in newtons

d is the distance in meters

The force is equal to the mass of Dr. Fahrrad times his acceleration. We can convert the acceleration from kilometers per second squared to meters per second squared by multiplying by 1000/3600. This gives us a force of 102.8 newtons.

The distance of Dr. Fahrrad's bike ride is 4.6 kilometers, which is equal to 4600 meters.

Plugging these values into the equation for work, we get:

W = 102.8 N * 4600 m = 472320 J

The breakdown of a mole of ATP releases 29 kilojoules of energy. So, the number of moles of ATP that Dr. Fahrrad breaks down is:

472320 J / 29 kJ/mol = 162.6 mol

To one decimal place, this is 0.23 moles of ATP.

Here are the assumptions that we made in this calculation:

No friction

No mass of the bike

A flat ride with no change in altitude

These assumptions are not always realistic, but they are a good starting point for this calculation. In reality, Dr. Fahrrad would probably break down slightly more than 0.23 moles of ATP to get to work.

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Answer:

B = 180 - 85 = 95

∠ABC = 95

Step-by-step explanation:

Answer:

6°

Step-by-step explanation:

Two angles are called complementary if the sum of their measures equals to 90°:

The complementary angle of 84° = 90° - 84°

                                                       = 6°

Answer:   6

Step-by-step explanation:

The complementary angle means the sum of two angles equal to 90. Let x be the other angle.

x + 84 = 90

       x = 6

Answer:

0.64

Step-by-step explanation:

Bananas:0.49:1

?:1.31

1x1.31 is 1.31 so

0.49x1.31=0.64

Answer:

A. is the correct answer and I know that because I just had this question.

Step-by-step explanation:

The best sentence to describe the function is The accuracy of shots has declined slightly since 1991. Hence the correct option is (A).

What is a graph?

The graph is a geometrical representation of any changes whether it is on data or a function that is changing with respect to the other data.

For example, if we take y = sinx then here x is independent and y is dependent.

Here y is changing with respect to the x so if you draw a geometrical representation then it will become a graph where something is changing and something is not.

Given that data

28.0 0.355

29.8 0.354

33.0 0.345

34.3 0.345

34.0 0.341

From this data, it's clear that it is going to decrease year by year.

So the accuracy of shots has declined slightly since 1991 will be correct.

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Answer:  They are the same equivalent price, $0.95/liter.

Step-by-step explanation:

Choices:  $3.58 per gallon, or $3.79 for 4 L.

========

We need to convert one of the volumes.  I'll convert gallons to liters.

By definition, 1 gallon = 3.785 liters

Make this into a conversion factor:

We can make it either:

1)   (3.785 liters/gallon), or

2)  (1 gallon/3.785 liters)

Now convert the $3.58/gallon into dollars/liter.  We'll use the second conversion factor so that gallons cancels out when we multiply:

($3.58/gallon)*(1 gallon/3.785 liters) = $0.95/liter.

The grocery store milk must also be converted to a price expressed per 1 liter:

$3.79 for 4 L

= $0.95/liter.

They are the same equivalent price, $0.95/liter.

The area of the composite figure comprising of a semicircle and a parallelogram is about 110.3 square units.

A composite figure is a figure comprising of two or more simple geometric figures.

The figure consisting of a parallelogram and a semicircle is a composite figure, which indicates  that the area of the figure is the sum of the area of the parallelogram and the area of the semicircle

The dimensions of the semicircle includes;

Diameter length, D = 8 units

The area of the circle = π·D²/4

Therefore; Area of the circle = π × (8 units)²/4 = 16·π square units

The dimensions of the parallelogram are;

The length of the base, b = 10 units

The height of the parallelogram, h = 6 units

The area of the parallelogram = b × h

Therefore; Area of the parallelogram = 10 units × 6 units = 60 square units

The area of the figure = 16·π square units + 60 square units ≈ 110.3 square units

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Answer:

(-2, 32, -21)

Step-by-step explanation:

You just multiply B by 3 and then subtract the corresponding parts. For example -2 -(0*3). and then 14-(-6*3)

Answer:

G - number of arrangements

F. the amount of her allowance

B. y = x

H. the number of hours

Answer:

3 3/4 cups of sugar

Step-by-step explanation:

Answer:

Polynomial product A:

(4x2 – 4x)(x2 – 4) Polynomial product B:

(x2 + x – 2)(4x2 – 8x)

They are trying to determine if the products of the two polynomials are the same. But they disagree about how to solve this problem.

1. Complete the table to summarize each student's conjecture about how to solve the problem. (2 points: 1 point for each row of the chart)

Classmate Conjecture

Emily: says they should just check one method

Zach: says that they should check all three bc there could be multiple answers

Evaluating the Conjectures

Who do you think is correct? (1 point)

If they do all of the methods correctly, they should get the same answer for all of them.

Analyzing the Data

Table Method:

2. Use the table to find the products of the two polynomials. Write your answer in descending order. (4 points: 2 points for each product)

A) (4x2 – 4x)(x2 – 4)

         4x2        –4x

x2      4x^4     –4x^3

–4     -16x^2     16x

4x^4 - 4x^3 - 16x^2 + 16x

B) (x2 + x – 2)(4x2 – 8x)

              x^2           x            -2

4x^2       4x^4      4x^3       -8x^2

-8x       -8x^3       -8x^2       16x

4x^4 - 4x^3 - 8x^2 - 8x^3 - 8x^2 +16x

combine like terms

4x^4 - 4x^3 - 16x^2 + 16x

3. Are the two products the same when you multiply them with the table method? (1 point)

yes

Multiplying Using the Distributive Property:

4. Multiply the two polynomials using the distributive property. (4 points: 2 points for each product)

5. Are the two products the same when you multiply them horizontally? (1 point)

yes

Making a Decision:

8. Who was right, Emily or Zach? Are the products the same with the three different methods of multiplication? (1 point)

Emily was correct. the products are the same no matter what method.

9. Which of these three methods is your preferred method for multiplying polynomials? Why? (1 point)

personally, i like the distributive property, but do whichever one you like.

Using the inverse rule we know that the value of p when q is 8 is 7 respectively.

Inverse operations are those that are the polar opposite of one another.

For instance, division and subtraction are the inverse operations of multiplication and addition, respectively.

In mathematics, inverse variation refers to the relationships between variables expressed as y = k/x, where x and y are two variables and k is a constant.

According to this statement, if the value of one item rises, the value of the other quantity falls.

So, calculate the inverse as follows:

p1q1 = p2q2

Now, insert values as follows:

p1q1 = p2q2

14*4 = p2*8

56 = p2*8

p2 = 56/8

p2 = 7

Therefore, using the inverse rule we know that the value of p when q is 8 is 7 respectively.

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Answer: 4x-y+2=0 i think

Step-by-step explanation

Answer:

11.25

Step-by-step explanation:

13.79-x

Let x= 2.54

13.79-2.54

11.25

Answer:

11.25

Step-by-step explanation:

just substitute 2.54 in for x

Hope this helps :-)

Answer: 68*

Step-by-step explanation: In pic

Answer:

( \(\frac{4}{3}\) , 8 )

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 10x - 2 ← is in slope- intercept form

with slope m = 10

Parallel lines have equal slopes

then the tangent to the parabola with a slope of 10 is required.

the slope of the tangent at any point on the parabola is \(\frac{dy}{dx}\)

differentiate each term using the power rule

\(\frac{d}{dx}\) (a\(x^{n}\) ) = na\(x^{n-1}\) , then

\(\frac{dy}{dx}\) = 6x + 2

equating this to 10 gives

6x + 2 = 10 ( subtract 2 from both sides )

6x = 8 ( divide both sides by 6 )

x = \(\frac{8}{6}\) = \(\frac{4}{3}\)

substitute this value into the equation of the parabola for corresponding y- coordinate.

y = 3(\(\frac{4}{3}\) )² + 2

   = (3 × \(\frac{16}{9}\) ) + 2

   = \(\frac{16}{3}\) + \(\frac{8}{3}\)

   = \(\frac{24}{3}\)

   = 8

the point on the parabola with tangent parallel to y = 10x - 2 is ( \(\frac{4}{3}\) , 8 )

the point on the parabola where the tangent line is parallel to y = 10x - 2 is, (1.33, 11.3).

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

Now, For find the point on the parabola where the tangent line is parallel to y = 10x - 2, we need to first find the derivative of the given parabola.

The derivative of y = 3x² + 2x is,

y' = 6x + 2.

Now, for the tangent line to be parallel to y = 10x - 2, the slopes of the two lines must be equal.

Therefore, we set the derivative equal to 10, which is the slope of the given line.

6x + 2 = 10

Solving for x,

6x = 8

x = 8/6

x = 1.33

And, y = 10 x 1.33 - 2

           = 13.3 - 2

           = 11.3

So, the point on the parabola where the tangent line is parallel to y = 10x - 2 is, (1.33, 11.3).

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Answer:

interphase!

Step-by-step explanation:

Cells spend 90% of their life in interphase.

A rhombus is KLMN. III. KLMN has a 21(KM) square area (NL).

A rhombus is KLMN. III. KLMN has a 21(KM) square area (NL).

A two-dimensional form called a quadrilateral is described as having four sides, four vertices, and four angles. Concave and convex are the two primary varieties. Convex quadrilaterals also fall under a number of other classifications, including trapezoids, parallelograms, rectangles, rhombus, and squares.

We frequently need to know the broad contours and placement of a graph. In these circumstances, a rough graph is made as opposed to plotting a number of points to create the graph. A straight line graph may be created using two points.

x(0-3)

L(3,0)

M(0,3)

| K'(0-6)

L'(6,0)

M'(0,6)

N (-2,0)

N'(-6,0).

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Answer:

Independent

Step-by-step explanation:

Answer: A function is a rule that assigns each value of the independent variable to exactly one value of the dependent variable.

Answer:

-1/3

Step-by-step explanatition

the slope goes down to the right, so it is negitive. It goes down x by 3, and down y by 1. slope = y/x , slope = -1/3

Answer:0.06

Step-by-step explanation:

Answer:

0.006

Step-by-step explanation:

3/20 = 0.15 + 1/25 = 0.19 - 11/60

= 0.00666666

To find ANOVA df: find N to get dftotal=N-1, calculate Ybar and group means to get dfbetween=k-1, and use dfwithin=N-k. Without Ybar1, Ybar2, and Ybar3, only dftotal and dfwithin can be calculated.

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Answer:

402.124

Step-by-step explanation:

2pirL = 2 x π x 8 x 8

Answer: 804.08

Step-by-step explanation:

Answer:

$48

Step-by-step explanation:

Given that:

Money spent on clothing last month = $40

Money spent this month is 120% of the spending of the last month.

To find:

A proportion to model this situation.

And the spending done this month?

Solution:

Let us have a look at 120% first.

\(120\%= \dfrac{120}{100} = \dfrac{6}{5}\)

\(\frac{6}{5}\) of \(x\) can be found by comparing \(x\) with 5, then we have to find the equivalent of 6.

Here, \(x\) is 40.

5 parts are equivalent to 40

1 part is equivalent to \(\frac{40}{5} = 8\)

6 parts are equivalent to \(8\times 6 = 48\)

OR

simply:

\(40 \times \dfrac{120}{100} = 48\)