Rewrite the expression below.
-2a(a+b-5)+3(-5a + 2b) + b(6a+b-8)

#1. The coefficient of the a² term is..?

#2. The coefficient of the ab term is..?

#3. The coefficient of the b term is..?

The number of cups of vegetable oil used by Colin to make 8 cakes is given by A = 5 1/3 cups

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data,

Let the equation be represented as A

Now, the value of A is

Substituting the values in the equation, we get

Let the number of cups of vegetable oil used by Colin to make 8 cakes be represented as A

Now , the number of cups of vegetable oil used by Colin to make 1 cake is given by = ( 2/3 ) cups of oil

And , number of cups of vegetable oil used by Colin to make 8 cakes A =

A = 8 x number of cups of vegetable oil used by Colin to make 1 cake

On simplifying the equation, we get

[tex]\text{A} = 8 \times \huge \text{(} \dfrac{2}{3} \huge \text{)}= \dfrac{16}{3}[/tex]

[tex]\boxed{\bold{A = 5 \dfrac{1}{3} \ cups}}[/tex]

Therefore, the value of A is 5 1/3 cups

Hence, the number of cups of vegetable oil required is 5 1/3 cups

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Complete question is-

Colin uses 2/3 cup of vegetable oil in each cake that he makes for his father's bakery.

If Colin made 8 cakes, how much oil did Colin use in all?

A. 5 1/3 cups

B. 7 1/3 cups

C. 8 2/3 cups

D. 16 1/3 cups​

The ordered pairs for the equation y = -7x + 8 are (0, 8), (1, 1), and (-1, 15).

To find ordered pairs for the equation y = -7x + 8, we can substitute different values of x and solve for y.

Let's choose three values of x:

When x = 0, y = -7(0) + 8 = 8. So one ordered pair is (0, 8).

When x = 1, y = -7(1) + 8 = 1. So another ordered pair is (1, 1).

When x = -1, y = -7(-1) + 8 = 15. So another ordered pair is (-1, 15).

Therefore, the ordered pairs  are (0, 8), (1, 1), and (-1, 15).

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Answer:

On the first draw, there are 10 numerals out of 36 cards.

P(first card is a number) = 10/36 = 5/18

On the second draw, there are 9 numerals out of 35 cards.

P(second card is a number) = 9/35

The probability of both events is the product:

P(both cards are numbers) = P(first card is a number) x P(second card is a number)

= 5/18 x 9/35

= 1/2 x 1/7 (cancel a 5 and a 9).

= 1/14

The answer of the given question based on the circle is , Henry needs to purchase an additional 44 feet of fencing to enclose the new garden.

Circumference is distance around edge of  circular object. It is same as  perimeter of  circle. The circumference of a circle can be calculated using the radius of the circle, which is half the diameter.

The circumference of  circle with diameter d is given :

C = πd

Using the given diameter of 14 feet, the circumference of the original garden is:

C1 = πd1 = (22/7) * 14 = 44 feet

When the diameter is doubled to 28 feet, the circumference of the new garden is:

C2 = πd2 = (22/7) * 28 = 88 feet

To find how much more fencing Henry needs to purchase to enclose the new garden, we need to subtract the original circumference from the new circumference:

C2 - C1 = 88 - 44 = 44 feet

Therefore, Henry needs to purchase an additional 44 feet of fencing to enclose the new garden.

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Answer:

The surface area is 720 in^2

Answer:

The answer is ⁵√a²

Step-by-step explanation:

a⅖=⁵√a²

Answer:

[tex]y = \frac{5}{2} x[/tex]

[tex] \frac{y}{x} = \frac{5}{2} [/tex]

The constant of proportionality is the ratio of y to x. Here, the ratio of y to x is 5 to 2. We see that y is directly proportional to x.

well, let's say the regular price is "x", which oddly enough is the 100%, and we know the store is doing a 25% sale, that means the new prices are 100% - 25% = 75%, 75% of the regular price, so when buying item for "$x", the sale price will just be

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{75\% of x}}{\left( \cfrac{75}{100} \right)x}\implies \text{\LARGE 0.75}\cdot x[/tex]

The domain of the graph in this problem is given as follows:

C) -3 ≤ x ≤ 4.

To determine the domain of a graph, you need to identify the set of all possible input values (also known as the independent variable) that produce a valid output (also known as the dependent variable) on the graph.

On a graph, the input values are represented by the values of x of the graph.

On the graph in this problem, we have that it assumes values of x between -3 and 4, with closed intervals, hence the domain is given as follows:

-3 ≤ x ≤ 4.

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(1) The value of X is equal to 4  (2) The mean age is 3. (3) The probability of randomly selecting  a child under the age of 9  is approximately 0.83.  

The formula for calculating the average of given numbers is equal to the sum of all values ​​divided by the total number of values. There are three main types of averages: mean, median, and mode. All of these techniques work slightly differently and often give slightly different typical values.

(i). Given that there are a total of 42 children on the birthday, finding the value of x:

2x + 3x (4x-1) + x + (x-2) + (x-3) = 42

11x - 6 = 42

11x = 48

x = 4

Therefore, the value of x is equal to 4.

(ii). To find the average age, we need to calculate the sum of all the ages and divide by the total number of children:

Average age = (7 x 2 + 8 x 3 + 9 x (4-1) +10 x 4 +11 x (4-2) 12 x (4-3)) / 42

 = (14 + 24 + 27 + 40 + 22 +12) / 42

 = 139/42

 = 3.31

Rounded to the nearest whole number, the average age is 3.  

(iii). The probability of randomly selecting  a child under 9 is obtained by adding  the number of children aged 7, 8 or 9 (because we want children under 9) and  dividing by the total number of children:

Number of children under 9 years  = 2x + 3x + (4x-1)

Number of children under 9 years  = 9x - 1

Number of children under 9  = 9(4)–1

Number of children under 9 years  = 35

Probability of choosing a child under 9  = number of children under 9  / total number of children

Probability of choosing a child under 9 = 35/42

The probability of choosing a child under 9 years old is ≈ 0.83

Thus, the probability of randomly selecting  a child under the age of 9  is approximately 0.83.

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Answer: 8,336

Step-by-step explanation:

So 1 meter is equal to 100 centimeters. All you have to do is multiply 83.36 by 100.

83.36 * 100 = 8,336

Hope this helps!!! :)

Answer:

a. The circumference of the base is 2πr, where r is the radius of the cylinder. Therefore, the circumference of the base is:

2π(10) = 20π

So the circumference of the base is 20π.

b. The area of the base is πr^2, where r is the radius of the cylinder. Therefore, the area of the base is:

π(10)^2 = 100π

So the area of the base is 100π.

c. The lateral area of the cylinder is given by the formula 2πrh, where r is the radius of the cylinder and h is the height (or length) of the cylinder. Therefore, the lateral area of the cylinder is:

2π(10)(2) = 40π

So the lateral area of the cylinder is 40π.

d. The total surface area of the cylinder is the sum of the lateral area and the areas of the two bases. The area of each base is πr^2, which we already calculated to be 100π. Therefore, the total surface area of the cylinder is:

2(100π) + 40π = 240π

So the total surface area of the cylinder is 240π.

e. The volume of the cylinder is given by the formula πr^2h, where r is the radius of the cylinder and h is the height (or length) of the cylinder. Therefore, the volume of the cylinder is:

π(10)^2(2) = 200π

So the volume of the cylinder is 200π.

Answer:

5146

Explanation:

There are 5 nickels in a quarter,

5 - 1 = 4,

There are 4 sides in a quadrilateral,

and 6 would make the digital root 7.

5146 -> 5 + 1 + 4 + 6 = 16

16 -> 1 + 6 = 7

P (green, then yellow) = P(green) * P(yellow) = (4/20) * (3/20) = 0.03 or 3%.

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability is used in many areas of science, such as statistics, physics, and engineering, as well as in everyday life to make informed decisions based on the likelihood of various outcomes.

The probability of drawing a green block on the first draw is 4/20 (since there are 4 green blocks out of a total of 20 blocks in the bag).

Since the block is being replaced back into the bag after each draw, the probability of drawing a yellow block on the second draw is still 3/20.

Therefore, the probability of drawing a green block followed by a yellow block is:

P (green, then yellow) = P(green) * P(yellow) = (4/20) * (3/20) = 0.03 or 3%

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The scale factor is 1/3.

What is the scale factor?

The difference in scale between an original object's scale and a new object that is its representation but is larger or smaller is known as a scale factor. For instance, we can increase the size of a rectangle with sides of 2 cm and 4 cm by multiplying each side by, let's say, 2.

Here, we have

Given: Triangle D has been dilated to create triangle D′.

To find the scalar value, simply choose one side of D and one did of D’ and divide them to find the scalar. We can verify that we have the correct scalar by performing this division on each related edge. Below I will do D to D’ represented like D/D’:

4.8 / 1.6 = 3

4.2 / 1.4 = 3

2.7 / x = 3

Knowing that the scaling for each edge is 3, we can solve for x.

2.7 / 3 = x

0.9 = x

The edges for D are 4.8, 4.2, and 2.7 respectively to D’ scaled by 1/3. So we can determine that the edges for D’ are 1.6, 1.4, and 0.9 respectively to D scaled by 3.

So if we go D’ to D, we scale by 3. If we go D to D’, we scale by 1/3.

Hence, the scale factor is 1/3.

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Answer:

The correct answer is B: Saturday.

The relationship between Monday and Thursday is that they are two days apart in a typical Monday-to-Sunday week. Similarly, Friday is also two days apart from Tuesday in a typical week, so the relationship between Friday and Tuesday would be the same as the relationship between Monday and Thursday. Therefore, the correct answer is B: Saturday.

1/18  is the area of the mattress. none of these of the option.

What is a quick rectangle answer?

A quadrilateral of the kind represented by a square has equal sides that are equal to one another and four vertices that are equal to 90 degrees. The equiangular quadrilateral is hence another name for it. Since a rectangle's opposite sides are parallel and equal, a parallelogram is another word for a rectangle. With four sides, four corners, and four right angles (90°), a square form is a closed 2-D object. A square's opposing sides are comparable and equal.

Based on the given conditions, formulate = 1/2 * 1/1 + 2 * 1/2 * 2/1+2

                                      = [tex]\frac{2/3}{2 * 3 * 2}[/tex]

                    = [tex]\frac{2}{3} * \frac{2}{2 * 3 * 2}[/tex]

Cross out the common factor = 1/3 * 1/3 * 2

                              = 1/3 * 3 * 2

                             = 1/18

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The value of tan(R) is 2/3

What is the trigonometric ratio?

The trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others.

using tan (θ) = opposite/Adjacent

Here, tan (R) = opposite/Adjacent

Where: opposite side = 14

Adjacent Side = 21

tan (R) = 14/21  = 2/3

tan (R) = 2/3

Hence, the value of tan(R) is 2/3

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The complete question is in the attached figure:

What is tan(R) =?

The values accurate to two decimal places for -2  standard deviation, mean, and +2  standard deviation are 0.30, 0.40, and 0.49, respectively.

We can use the following formulas to calculate the mean and standard deviation of the sampling distribution:

Mean: μ = p = 0.40 (since the population proportion is 0.40)

Standard deviation: σ = √((p(1-p))/n)

σ = √((0.40(1-0.40))/165)

σ = 0.049

Now we can calculate the values for -2SD, mean, and +2SD as follows:

-2SD: μ - 2σ = 0.40 - 2(0.049) = 0.30

Mean: μ = 0.40

+2SD: μ + 2σ = 0.40 + 2(0.049) = 0.49

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The translation vector for the rectangle is described by T(x, y) = (- 3, - 6).

In this problem we must derive the translation vector between a rectangle and its image set on Cartesian plane (let assume that the origin is on the lower left corner of the square). The translation formula is:

B(x, y) = A(x, y) + T(x, y)

Where:

If we know that A(x, y) = (6, 9) and B(x, y) = (3, 3), then the translation vector is:

T(x, y) = B(x, y) - A(x, y)

T(x, y) = (3, 3) - (6, 9)

T(x, y) = (- 3, - 6)

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Answer:

We have supplementary angles.

123 + 3x = 180

3x = 57

x = 19

Answer:

x = 19

Step-by-step explanation:

Angle on a straight line add up to 180

123 + 3x = 180

3x = 180 - 123

3x = 57

3x/3 = 57/3

x = 19

all u got to do is subtract

0 and 1 are the numbers that do not represent the probabilities of complementary events.

Probability is a measure of the possibility or chance that an event will occur.It is a value between 0 and 1, with 0 indicating that the event will not happen and 1 indicating that the event will almost likely happen. The number of favourable outcomes divided by the total number of possible outcomes is the probability of an event. Probability is utilised extensively in a wide range of professions, including mathematics, statistics, science, economics, and engineering.

In probability theory, complementary events are two events that together encompass all possible outcomes, and their probabilities add up to 1. The complement of an event A is the absence of A, indicated by A'.  Therefore, the probability of the complement of A is 1 minus the probability of A, or P(A') = 1 - P(A).

In the given pair, 0 represents the probability of an impossible event, and 1 represents the probability of a certain event. These events are not complementary, as there is no other event that can occur apart from a certain event, and their probabilities do not add up to 1. Therefore, this pair does not represent the probabilities of complementary events.

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Answer: Michelle's income during 2014 was her base salary plus her commission.

Her commission was 3% of $500,000, which is 0.03 x $500,000 = $15,000.

So her total income for 2014 was $87,000 + $15,000 = $102,000.

Step-by-step explanation:

The average rate is given as 0.2895 gallons per hour

Gallons per hour (GPH) is a unit of measurement used to express the rate of flow of a liquid, typically fuel.

It represents the number of gallons of fuel that can flow through a particular system or device in one hour.

For example, the GPH of a car's fuel pump indicates how many gallons of fuel it can deliver to the engine in one hour. This unit is commonly used in the context of measuring the fuel efficiency of vehicles or other machinery.

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Answer:

9/16 of a square inch

Step-by-step explanation:

[tex] \frac{3}{4} \times \frac{3}{4} = \frac{9}{16} [/tex]

Answer:

9 /16 inches^2

Step-by-step explanation:

To find the area of the tile, multiply the length by the width

A = 3/4 * 3/4

A = 9 /16 inches^2

a)Por lo tanto, la ecuación lineal que representa la temperatura en función de la hora es T(h) = 4h + 29

b) Por lo tanto, la temperatura a las 11:15 am aproximadamente es de 75.3 grados Farenheit.

what is  aproximadamente ?

"Aproximadamente" is a Spanish word that means "approximately" or "roughly" in English. It is often used to indicate that a value or measurement is not exact, but rather an estimation or approximation.

In the given question,

a) La ecuación lineal que relaciona la temperatura con la hora en ese intervalo es:

T(h) = m*h + b

donde T es la temperatura en grados Farenheit, h es la hora en formato de 24 horas, m es la pendiente de la recta y b es el término independiente.

Primero encontramos la pendiente m:

m = (81 - 61) / (13 - 8) = 4

Luego, encontramos el término independiente b utilizando uno de los puntos:

61 = 4*8 + b

b = 29

Por lo tanto, la ecuación lineal que representa la temperatura en función de la hora es:

T(h) = 4h + 29

b) Para encontrar la temperatura a las 11:15 am, primero convertimos el tiempo a horas decimales:

11:15 am = 11 + 15/60 = 11.25 horas

Luego, sustituimos este valor en la ecuación lineal:

T(11.25) = 4(11.25) + 29 = 75.25

Por lo tanto, la temperatura a las 11:15 am aproximadamente es de 75.3 grados Farenheit.

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Answer:

The range is {-7, -4, -1, 2, 5}.