Evaluate the expression ab, for a = 4 and b = 7.

Answer:

driving home from a trip

Using a system of equations, it is found that:

------------------------

\(x + y = 108\)

Since \(x = 2y\)

\(2y + y = 108\)

\(3y = 108\)

\(y = \frac{108}{3}\)

\(y = 36\)

\(x = 2y = 2(36) = 72\)

Zoe is 36 inches tall.

Claire is 72 inches tall.

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We can begin by finding the x-intercept. This is the point at which the graph crosses the horizontal axis. This point is given when the y-value of the function is 0, then, we can solve the equation for y = 0 and find the value for x:

The x value of the x-intercept of the equation is approximately 4.67.

This is a linear equation, to build the graph we just need 2 points and join them with the line.

The x-intercept is the point (4.67, 0). Another easy point to find and build the graph can be the y-intercept, which is given when x = 0. Replacing in the equation:

With this, the other point we can use to graph the equation is (0, -2.33).

Drawing both points on a cartesian plane:

Both points (x and y-intercepts) are drawn in red.

35 is a reasonable prediction of the number of times he will select 2 yellow socks?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates that an event is impossible, and 1 indicates that an event is certain to occur. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

In probability theory, an event is a set of outcomes or a subset of a sample space. In simpler terms, an event is anything that can happen, or any possible outcome of an experiment or observation. An event can be a single outcome, or it can consist of multiple outcomes.

In the given question,

The theoretical probability of drawing two yellow socks with replacement from a bag containing equal numbers of red, yellow, green, blue, and purple socks is:

P(drawing two yellow socks) = P(yellow) * P(yellow) = (1/5) * (1/5) = 1/25

So, the probability of drawing two yellow socks from the bag in any given trial is 1/25.

To predict the number of times the child will select two yellow socks in 175 trials, we can use the formula for the expected value of a discrete random variable:

E(X) = n * p

where E(X) is the expected number of times the event occurs, n is the number of trials, and p is the probability of the event occurring in a single trial.

In this case, n = 175 and p = 1/25. So,

E(X) = 175 * (1/25) = 7

Therefore, a reasonable prediction of the number of times the child will select two yellow socks in 175 trials is 7. Since this prediction is not one of the answer choices, the closest option is 35, which is more than five times the expected value. However, this is within the range of possible outcomes due to the random nature of the experiment.

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Answer:

25/7.

Step-by-step explanation:

csc O = 1 /sin O

= 1/ 7 /25

= 25/7.

The mean number of movies that the students saw is 13.5 (rounded to the nearest tenth).

To find the mean number of movies the students saw, you need to calculate the average of the given data. Here are the reported numbers of movies seen by the 6 students: 14, 11, 15, 19, 12, 10.

To calculate the mean, you sum up all the reported numbers and divide by the total number of students. In this case, the total number of students is 6.

So, let's calculate the mean:

(14 + 11 + 15 + 19 + 12 + 10) / 6 = 81 / 6 = 13.5

Therefore, the mean number of movies that the students saw is 13.5 (rounded to the nearest tenth).

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Answer:

Option (C) will be the answer.

Step-by-step explanation:

Let the equation of the given line is,

y = mx + b

Where 'm' is the slope of the line and 'b' is the y-intercept

Slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is represented by,

Slope of the line (m) = \(\frac{y_2-y_1}{x_2-x_1}\)

For a line passing through (0, 6) and (4, 0)

Slope 'm' = \(\frac{6-0}{0-4}\)

           m = \(-\frac{3}{2}\)

y-intercept of the line 'b' = 6

Therefore, equation of the line will be,

y = \(-\frac{3}{2}x+6\)

2y = -3x + 12

3x + 2y = 12

Option (C) will be the answer.

Answer:

c is the answer

Step-by-step explanation:

3x+2y=12

Answer:

you have a 11/17 percent chance of getting an apple

Step-by-step explanation:

if there are 11 apples and 6 oranges. 11 out of 17 times you will get an apple

Hello there. To solve this question, we'll have to remember some properties about slope of a line.

In order to find the constant rate of change of the function represented in the table below, we first have to remember why does it means that the function is a line.

Knowing the instantaneous rate of change of a function f(x) is given by its derivative, i. e.

And say this rate of change is constant, that is

Integrating both sides of the equation with respect to x, we have that:

Where A and B are constants, therefore f(x) is the equation of a line.

In fact, this constant rate of change is the slope of the line, so we simply need to find it.

Given two points (x0, y0) and (x1, y1) from the equation of a line, we can find its slope m by using the following formula:

Taking two points from the table, say (-1, 7) and (3, -9), we plug in the formula to find:

Therefore the slope of this line, and constant rate of change of this function is equal to -4 and it is the answer contained in the option H.

Given the mathematical expression, it must be solved with the result \((\text{a} + \text{b})\)

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division.

We are given the expression:

\(\dfrac{(\text{x} + 100)}{(\text{x} - 100)} = \dfrac{(\text{a} + \text{b} + 100)}{(\text{a} + \text{b} - 100)}\)

The Denominators go to the other side of the equality by multiplying, so that we now have:

\((\text{x} + 100)(\text{a} + \text{b} - 100) = (\text{a} + \text{b} + 100)(\text{x} - 100)\)

The products of the binomials are developed by the trinomials.

\(\text{ax} + \text{bx} - 100\text{x} + 100\text{a} + 100\text{b} - 10000 = \text{ax} + \text{bx} + 100\text{x} - 100\text{a} - 100\text{b} - 10000\)

Like terms are removed.

\(100\text{a} + 100\text{b} - 100\text{x} = 100\text{x} - 100\text{a} - 100\text{b}\)

\(100\text{a} + 100\text{b} - 100\text{x} - 100\text{x} + 100\text{a} + 100\text{b}\)

\(200\text{a} + 200\text{b} - 200\text{x} =\)

Grouping.

\(200(\text{a} + \text{b})\)

Result.

\((\text{a} + \text{b})\)

Hence, the solution to the mathematical expression is \((\text{a} + \text{b})\)

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Answer:

\(y-2=3(x-4)\)

Step-by-step explanation:

We are given a line contains the point (4, 2).

We also know that the line is parallel to y= 3x - 7.

We want to write the equation of this line.

Parallel lines have the same slopes.

First, let's find the slope of y = 3x - 7.

3 is in the place of where m (the slope) is, so that means it is the slope of that line.

It is also the slope of the line whose equation we want to write.

The equation of the line can be written in three ways:

All of these ways are valid, but for this problem, let's write the equation in point-slope form, as it is the easiest.

Substitute 3 as m in \(y-y_1=m(x-x_1)\).

\(y-y_1=3(x-x_1)\)

Now, substitute 4 as \(x_1\) and 2 as \(y_1\).

\(y-2=3(x-4)\)

Topic: parallel and perpendicular lines

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Answer:  x = -3/2

Step-by-step explanation:

Answer:

Cost to pave the road = $4257

Step-by-step explanation:

Area of the pavement = Area of the outer circle - Area of the internal circle

Area of the outer circle = πr²

                                       = π(55)²

                                       = 3025π square feet

Area of the inner circle = π(33)²

                                       = 1089π square feet

Area of the pavement = 3025π - 1089π

                                     = 1936π

                                     = 6082.12 square feet

Cost of pavement = $0.70 per square feet

Therefore, cost of 6082.12 square feet = 6082.12 × 0.70

                                                                 = 4257.49

                                                                 ≈ $4257

Cost to pave the road = $4257                                    

Yes, there is an analogous ratio between 2:1 and 20:10.

We just cancel by a common factor. So 4:2=2:1 . The simplest representation of the ratio 4 to 2 is the ratio 2 to 1. Also, since each pair of numbers has the same relationship to one another, the ratios are equivalent.

By dividing the terms of each ratio by their greatest common factor, we may simplify both ratios to explain why.

As the greatest common factor for the ratio 2:1 is 1, additional simplification is not necessary.

The greatest common factor for the ratio 20:10 is 10. When we multiply both terms by 10, we get:

20 ÷ 10 : 10 ÷ 10

= 2 : 1

As a result, both ratios have the same reduced form, 2:1, making them equal.

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The coupon rate of the bonds by King of Diamonds Industries would be 7 %.

The formula for the bond price shows the coupon payment and so can be used to find the coupon rate:

= (Coupon payment  x ( 1 - ( 1 + r ) ^ ( - number of years till maturity ) ) ) / r + Face value /  (1  + rate )^ number of years

1,482.01 = (C x (1 - (1 + 0.07 )^ (- 14) ) ) / 0.07 + F / (1 + 0.07 ) ^ 14

103.7407 - 0.07 x (F / (1 + 0.07) ^14 ) = C x  (1 - ( 1 + 0.07) ^ ( - 14) )

Using a calculator, C is $ 70.

This means that the coupon rate is:

= 70 / 1, 000

= 7 %

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Answer:

1827

Step-by-step explanation:

Answer:

1827

Step-by-step explanation:

21% of 8700 = 1827

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Answer:

64x^3 + 996x^2 + 48x + 8

Step-by-step explanation:

Answer:

12x+6

Step-by-step explanation:

\((4x+2)3\)

Use the distributive property to multiply (4x+2) by 3:-

\(12x+6\)

Answer:

\(x = \frac{9}{ \sqrt{2} } = \frac{9 \sqrt{2} }{2} \)

The ratio of rainy days to total days written as a percent will be 75%.

Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

Ratio is used to compare two or more numbers. It is also used to indicate how big or small a quantity is when it is compared to another. It should be noted that in a ratio, two quantities are compared using division.

Since in the last 24 days, it rained 18 days.

Number of rainy days = 18.

Number of total days = 24

The ratio of rainy days to total days written as a percent will be:

= Number of rainy days / Total days × 100

= 18/24 × 100

= 3/4 × 100

= 75%

Therefore, the ratio is 3:4 which is 75%.

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A regression model is used to show the relationship between variables on a scatter plot

Using the Microsoft Office Excel, we have the following calculation summary

So, the regression equation is:

\(\^y = 28.2\^x- 27.9\)

This means that x = 6.0 and x = 8.5

When x = 6.0, we have:

\(\^y = 28.2 * 6.0- 27.9\)

\(\^y = 141.3\)

When x = 8.5, we have:

\(\^y = 28.2 * 8.5- 27.9\)

\(\^y = 211.8\)

Hence, the likely blood pressure for a patient with sodium intake of 6.0 and 8.5 are 141.3 and 211.8, respectively

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Answer:

Step-by-step explanation:

I= P*r*t

I = 12000* 7% *4

Total interest paid was $3360.

Answer: $3,360

Step-by-step explanation:

Consequently, when the equation is y = -2x + 6 and the constant is 2, the slope of the line is -2.

Slope is a mathematical term that describes how steep a path is. The character "m" is frequently used to denote it. The ratio of the vertical change (rise) to the horizontal change (run) between any two locations on a line is known as the slope of the line. In other terms, if there are two points on a line, (x1, y1) and (x2, y2), you can use the following formula to determine the slope of the line that passes through those points:

Depending on the orientation of the line, the slope can be positive, negative, zero, or undefinable. If the slope is positive, the line is ascending from left to right.

given

In the equation y = -2x + 6, the coefficient of x is -2. This is the slope of the line.

Consequently, when the equation is y = -2x + 6 and the constant is 2, the slope of the line is -2.

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Answer:

Step-by-step explanation:

Each of the given equations describes a line on a graph. There are numerous ways to find the values of x and y that will satisfy both equations at the same time. Two of them you have seen are "substitution" and "elimination." Here, "substitution" is easily accomplished by equating one expression for y to the other expression for y:

  y = y

  100 +65x = 40 +80x . . . substitute for y

  60 +65x = 80x . . . . . . . subtract 40 from both sides

  60 = 15x . . . . . . . . . . . . subtract 65x from both sides

  4 = x . . . . . . . . . . . . . . divide both sides by 15

  y = 40 +80x = 40 +80(4) = 360 . . . . find the value of y

The values of x and y that satisfy both equations are ...

  (x, y) = (4, 360)

__

The point (4, 360) is on both lines. That is the point where the lines intersect. It means 4 hours work will cost $360 in either shop.

__

The time of 4 hours that we found above is the "break-even" or "crossover" point in the cost equations. For times below that point, the lowest cost comes because of the lowest "service charge". For times above that point, the lowest cost comes because of the lowest per-hour charge.

3 hours is less than 4 hours, so the shop with the lowest service charge will have a lower cost. That is Amy's shop. Her price for 3 hours is ...

  40 +80(3) = 40 +240 = $280 . . . for 3 hours work in Amy's shop

__

If you want to make sure of that, you can find the cost in Mike's shop:

  y = 100 +65(3) = 100 +195 = $295 . . . for 3 hours in Mike's shop

ANSWER

1. 10

2. 5

EXPLANATION

We want to expand the expressions given:

1. 6 x 20 = 6 x 2 x ____

To do this, we have to divide 20 by 2, because 20 was expanded to give 2 x __.

20 divided by 2 is 10, so the answer is:

6 x 20 = 6 x 2 x 10

2. 5 x 100 = ___ x 10 x 10

This is straightforward, since 10 x 10 is 100.

The answer is:

5 x 100 = 5 x 10 x 10

Answer:

False

Step-by-step explanation:

1 + 2 (-4) = -7

1 - 8 = -7

-7 = -7

-4 (-4) = -1

16 = -1

The area of the figure in this problem is given as follows:

A. 30 in².

The area of a triangle is given by half the multiplication of the base length by the height of the triangle.

Applying the Pythagorean Theorem, we can obtain the missing side length, as follows:

4² + x² = 6²

x² = 36 - 16

x² = 20

x = square root of 20

x = 4.47.

For a right triangle, one side is considered the height of the other, hence the sides are:

Hence the area of the triangle is then obtained as follows:

Area = 0.5 x 4 x 12.47

Area = 25 in².

Which is closest to 30 in².

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Answer:

B

Step-by-step explanation:

B because it is the farthest away from 0.