The tables show the amount earned by James and Paco working at the same store.

James's Hours Amount Earned
3 $35.40
5 $59.00
8 $94.40

Paco's Hours Amount Earned
2 $24.00
4 $48.00
7 $84.00
What are the two equations that can represent James and Paco's hourly wages, where h is the number of hours worked and d is the amount of money earned?

Compare the equations to determine if there is any difference between what James and Paco make each hour.

ntObserve the graph carefully.

It is evident that each square of the grid has a side of 1 unit.

The x-coordinate is defined as the horizontal distance of the point from the origin. While y-coordinate is defined as the vertical distance of the point from the origin.

Point F

Consider that point F lies at 4 units right and 1 unit downwards from the origin. So the corresponding coordinates of the point F will be (4,-1).

Point H

Consider that point H lies at 1 unit right and 4 units upwards from the origin. So the corresponding coordinates of the point F will be (1,4).

Point A

Consider that point A lies at 2 units left and 3 units upwards from the origin. So the corresponding coordinates of point A will be (-2,3).

Point K

Consider that point K lies on the x-axis so its vertical distance from the origin will be zero. Also, K lies at 2 units left of the origin. Then the coordinates of point K will be (-2,0).

Point C

Consider that point C lies at 3 units left and 2 units downwards from the origin. So the corresponding coordinates of point C will be (-3,-2).

Thus, the required set of coordinates are obtained as,

Since the division is 15 by 4, the the fraction would be 15/4 and the decimal it's 0.266

Answer:

Dilation changes (x,y) values not the grid or coordinate plane. Basically, dilating a graph or a coordinate grid means the original coordinates you may have had will be changed with the dilation.  For example, a triangle plotted had its original area of 26 dilated to an area of 58.

Answer:

2/3

Step-by-step explanation:

use point slope formula: \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)to find the slope.

3-1=2

8-5=3

your slope is 2/3

Answer:

2/3

Step-by-step explanation:

The formula for slope is y2 - y1 over x2 - x1.

If we plug our numbers in we get 3-1=2

and.

8-5= 3

so the answer is 2/3.

The probability that X is greater than or equal to 9 is approximately  0.9825

Probability can be defined as the ratio of favorable outcomes to the total number of events.

To find the probability for X greater than or equal to 9 using the normal approximation to the binomial, we can use the standard normal distribution and calculate the z-score. The formula for the z-score is:

z = (X - np) / (√(np(1-p)))

For X = 9, n = 11, and p = 0.5:

z = (9 - 11 × 0.5) / (√(11 × 0.5 × 0.5))
z = (9 - 5.5) / 1.66
z = 2.11

Next, we use a standard normal table or calculator to find the cumulative probability for this z-value. Since we want the probability for X greater than or equal to 9, we need to find the cumulative probability from 9 to 11.

P(X > 9) = P(Z < 2.11) = 0.9825

Rounding to 4 decimal places, the final answer is P(X >= 9) =  0.9825

So, the probability that X is greater than or equal to 9 is approximately  0.9825.

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Answer:

x=3

Step-by-step explanation:

2x-6=0

2x=0+6

2x=6

2x/2=6/2

x=3

Answer:

-1/6

Step-by-step explanation:

= 1/3 (-1-1) x -1/4 (-1)

= 1/3 (-2) x 1/4

= -2/3 x 1/4

= -2\12

2 and 12 can cancel out each other.

so the answer will be.

= -1/6.

Answer:

D. $10,909.09

Step-by-step explanation:

The class recovery period for residential rental property each year = 27.5 years

The cost basis for the residential property = $300,000

The amount he will be able to depreciate

= Cost basis/ Number of years

= $300000/ 27.5 years

=$10, 909.090909

Approximately ≈ $10,909.09

The amount he will be able to depreciate  using the class recovery period for residential rental property each year is: D. $10,909.09.

Using this formula

Depreciation=Rental unit amount/ MACRS residential rental property recovery period

Where:

Rental unit amount=$300,000

MACRS Residential rental property recovery period=27.5 years

Let plug in the formula

Depreciation=$300,000/27.5

Depreciation=$10,909.09

Inconclusion the amount he will be able to depreciate  using the class recovery period for residential rental property each year is: D. $10,909.09.

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Answer:

(2, -8)

Step-by-step explanation:

y=6x-20

y=-4x

since the bottom equation shows us that y=-4x, we can substitute 4x in place of y in the first equation and solve:

-4x=6x-20

-10x=-20

x=2

since the bottom equation shows y=-4x, and we already know that x=2:

y=-4(2)

y=-8

(2, -8)

Answer:

a) [-9,8)

b) [-5,5]

c) (-4,0), (1,6)

d) [-9,-4), (6,8)

e) [0,1]

f) just the y-value: 5;  as a point: (-8,5)

g) just the y-value: -5;  as a point: (-4,-5)

Step-by-step explanation:

a) Domain is all of the x-values that are defined in the function. The smallest x-value in the graph is -9, and the largest is 8. And all values in between are defined (have corresponding y-values). But notice that there's an open dot on (8,0).

b) Range is found the same way as Domain, but with the y-values. The smallest y-value of this function is -5, and the largest is 5.

For c-e, notice where the graph changes direction and draw a vertical line from the x-axis through the turning point. These lines are the boundaries between intervals of increasing/decreasing/constant. You should have vertical lines at x=-4, x=0, x=1, and x=6.

c) Interval(s) on which f(x) is increasing: Reading the graph from Left To Right, between which vertical lines is the graph going up?

d) Interval(s) on which f(x) is decreasing: Reading the graph from Left To Right, between which vertical lines is the graph going down?

e) Interval(s) on which f(x) is constant: Reading the graph from Left To Right, between which vertical lines is the graph staying flat?

f) Look for the highest non-infinity point on the graph

g) Look for the lowest non-infinity point on the graph

Answer:

48/13

Step-by-step explanation:

To make this into an improper fraction, convert the integer into a fraction using the denominator of the fraction

3 * 13/13 = 39/13

Then add it to the rest of the fraction

39/13 + 9/13

= 48/13

Answer: 48/13

Step-by-step explanation: first multiply 3 x 13 to get 39. do this because you get the fraction for the whole number, 3. then, add 39 to the numerator (9). you will get 48/13. you do this because you are adding the whole number (3) to the fraction so that way it is an improper fraction.

Answer: 329.55

Step-by-step explanation: multiple 8.45 by 39 which is 329.55

8.45 * 39 = 329.55

This function represents a downward-opening parabola with a vertical shift of 6 units upward.

The given function is Ƒ(t) = –1/(2t²) + 2t + 6.

This is a quadratic function in terms of t. The general form of a quadratic function is f(t) = at² + bt + c, where a, b, and c are constants.

Comparing the given function Ƒ(t) = –1/(2t²) + 2t + 6 with the general form, we can see that a = -1/2, b = 2, and c = 6.

So, the function Ƒ(t) can be written as:

Ƒ(t) = (-1/2)t² + 2t + 6

This function represents a downward-opening parabola with a vertical shift of 6 units upward.

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Answer:

First option, (4, -6)

Step-by-step explanation:

Scaled by 2. Multiply each coordinate of point C by 2.

(2*2, -3*2) = (4, -6)

The surface areas are 110 in², 87.6 mm² and 49 m².

Given that are solid figure, we need to find the surface area of them,

1) Triangular prism = perimeter × length + 2 × base area

= (5 + 5 + 6) × 5 + 2(3×5) = 110 in²

2) Triangular pyramid = base area + perimeter × slant height / 2

= 1/2 × 5.2 × 6 + 3 × 6 × 8/2

= 87.6 mm²

3) Cube = 4side²

= 4 × (3 1/2)²

= 4 × 3.5²

= 49 m²

Hence the surface areas are 110 in², 87.6 mm² and 49 m².

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The ratio of the given distribution of  pants to shirts is; 5:3

The ratio of shirts to pants can be expressed by putting the number of shirts and pants in the following way;

Number of shirts       :        Number of pants

20                               :                   12

Then we will have to reduce this ratio to the lowest term by dividing by the highest common factor of both numbers.

The highest common factor of 12 and 20 is 4 and as such when divided by 4 we get:

20/4 : 12/4

= 5 : 3

This represents the ratio.

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Answer:

see photo

Step-by-step explanation:

see photo for answer

sometimes when there is a fraction in the question it's a good idea to keep things as fractions and not decimals

The sine equation for the object's height is given as follows:

d = -5sin(0.24t).

The standard definition of the sine function is given as follows:

y = Asin(Bx) + C.

The parameters are given as follows:

The amplitude for this problem is of 5 inches, hence:

A = 5.

The period is of 1.5 seconds, hence the coefficient B is given as follows:

2π/B = 1.5

B = 1.5/2π

B = 0.24.

The function starts moving down, hence it is negative, so:

d = -5sin(0.24t).

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Answer:

4x + 3y = - 6

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 )

• Parallel lines have equal slopes

calculate the slope of the line using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (3, - 1) ← 2 points on the line

m = \(\frac{-1-3}{3-0}\) = \(\frac{-4}{3}\) = - \(\frac{4}{3}\) , then

y = - \(\frac{4}{3}\) x + c ← is the partial equation

to find c substitute (- 3, 2 ) into the partial equation

2 = 4 + c ⇒ c = 2 - 4 = - 2

y = - \(\frac{4}{3}\) x - 2 ← equation in slope- intercept form

multiply through by 3 to clear the fraction

3y = - 4x - 6 ( add 4x to both sides )

4x + 3y = - 6 ← in standard form

The probability that an antigen test comes back positive is approximately 0.05225, or about 5.225%.

We have,

To find the probability that an antigen test comes back positive, we need to consider both the true positive rate (probability of a positive test given that the person is infected) and the false positive rate.

Now,

Prevalence of coronavirus in California: 3 out of 1000

False positive rate of the antigen test: 0.05 (5 out of 100)

Let's calculate the probability of a positive test result.

The true positive rate can be calculated as 1 minus the false negative rate (probability of a negative test given that the person is infected):

True positive rate = 1 - 0.2 = 0.8 (or 80 out of 100)

The probability of a positive test result can be calculated using Bayes' theorem:

P(Positive test) = P(Positive test | Infected) x P(Infected) + P(Positive test | Not Infected) x P(Not Infected)

P(Positive test) = (0.8 x 3/1000) + (0.05 x 997/1000)

P(Positive test) = 0.0024 + 0.04985

P(Positive test) = 0.05225

Therefore,

The probability that an antigen test comes back positive is approximately 0.05225, or about 5.225%.

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The types of discontinuities are: removable discontinuity at x = -3 and vertical asymptotes at x = 0 and x = 3.

A. To find f(x) + g(x), we add the two functions together:

f(x) + g(x) = (x + 2)/(x^2 - 9) + 11/(x^2 + 3x)

To add these fractions, we need a common denominator. The common denominator in this case is (x^2 - 9)(x^2 + 3x). So, we rewrite the fractions with the common denominator:

f(x) + g(x) = [(x + 2)(x^2 + 3x) + 11(x^2 - 9)] / [(x^2 - 9)(x^2 + 3x)]

Simplifying the numerator:

f(x) + g(x) = (x^3 + 3x^2 + 2x^2 + 6x + 11x^2 - 99) / [(x^2 - 9)(x^2 + 3x)]

Combining like terms:

f(x) + g(x) = (x^3 + 16x^2 + 6x - 99) / [(x^2 - 9)(x^2 + 3x)]

B. To find the excluded values, we look for values of x that would make the denominators zero, as division by zero is undefined. In this case, the excluded values occur when:

(x^2 - 9) = 0  --> x = -3, 3

(x^2 + 3x) = 0 --> x = 0, -3

So, the excluded values are x = -3, 0, and 3.

C. To classify each type of discontinuity, we examine the excluded values and the behavior of the function around these points.

At x = -3, we have a removable discontinuity or hole since the denominator approaches zero but the numerator doesn't. The function can be simplified and defined at this point.

At x = 0 and x = 3, we have vertical asymptotes. The function approaches positive or negative infinity as x approaches these points, indicating a vertical asymptote.

Therefore, the types of discontinuities are: removable discontinuity at x = -3 and vertical asymptotes at x = 0 and x = 3.

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Answer:

DEEZNUUTZZZ

Step-by-step explanation:

Answer: D

Step-by-step explanation:

Hope it helps

Answer:

4c/2a 60 degrees 3bf 2ad

Answer:

f=120

b=40

d=140

e=120

c=30

a=30

The original equation formed after factoring out \($-\frac{1}{2}$\) is \($$(x-0)^2 - 2x - 8 = 0$$\).

What is meant by factor?

In mathematics, a factor is a number or expression that divides another number or expression evenly without a remainder. Factoring is the process of finding the factors of a number or expression. In algebra, factoring is used to simplify expressions, solve equations, and find zeros of functions. By factoring, we can rewrite a complex expression or equation as a product of simpler expressions or factors.

To factor out \($-\frac{1}{2}$\) from the equation \($-\frac{1}{2}(x-0)^2+x+4=0$\), we can divide both sides of the equation by \(-\frac{1}{2}$:\)

\($-\frac{1}{2}(x-0)^2 \div -\frac{1}{2} + x \div -\frac{1}{2} + 4 \div -\frac{1}{2} = 0 \div -\frac{1}{2}$$\)

Simplifying each term, we get:

\($$(x-0)^2 - 2x - 8 = 0$$\)

This is the factored form of the original equation, after factoring out \(-\frac{1}{2}$.\)

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Answer:

growth rate: 4

y-value: 19

equation: y=4x+19

Step-by-step explanation:

Growth Rate:
The growth rate of a linear function is constant. This means that the function will increase or decrease by the same amount for every unit increase in x.
This can be found by dividing the change in y-values by the change in x-values.

For the question:
The change in y-values is 11-7=4,

and the change in x-values is +1.

Therefore, the growth rate is 4.

\(\hrulefill\)

Initial Value: The initial value of a linear function is the value of the function when x is 0.

In this case, the initial value is 19.

This can be found by looking at the y-value of the point where x is 0.

In this case, the y-value is 19.

\(\hrulefill\)Equation: The equation of a linear function is y = mx + b, where m is the slope and b is the y-intercept.

Using the table you provided, we can find the slope by using two points on the line.

Let’s use (-3, 7) and (1, 23).

The slope is (y2-y1)/(x2-x1)=(23-7)(1-(-3)=16/4=4

Now,

Taking 1 point (-3,7) and slope 4.

we can find the equation by using formula:

y-y1=m(x-x1)

y-7=4(x+3)

y=4x+12+7

y=4x+19

Therefore, the equation of the given table is y=4x+19\(\hrulefill\)

Answer:

Growth rate:  4

Initial value:  19

Equation:  y = 4x + 19

Step-by-step explanation:

The slope of a linear function represents its growth rate.

Therefore, the growth rate of a linear function can be found using the slope formula.

Substitute two (x, y) points from the table into the slope formula, and solve for m.  Substituting points (0, 19) and (1, 23):

\(\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{23-19}{1-0}=\dfrac{4}{1}=4\)

Therefore, the growth rate of the linear function is 4.

The initial value of a linear function refers to the y-intercept, which is the value of the y when x = 0.

From inspection of the given table, y = 19 when x = 0.

Therefore, the initial value of the linear function is 19.

To write a linear equation given the growth rate (slope) and initial value (y-intercept), we can use the slope-intercept formula, which is y = mx + b. The slope is represented by the variable m, and the y-intercept is represented by the variable b.

As the growth rate of the given linear function is 4, and the initial value is 19, substitute m = 4 and b = 19 into the slope-intercept formula to create the equation of the linear function represented by the given table:

\(\boxed{y=4x+19}\)

Answer:

1.75

Step-by-step explanation:

Finding average rate of change :

The average rate of change for P between 1992 and 2000 is -1.025.

The average rate at which one quantity changes in relation to another is known as the average rate of change function.

It can be determined by dividing the amount of one quantity's change by the amount of another quantity's change.

Average rate of change for a function 'f' in the interval [a, b] is,

A = f(b) - f(a) / (b-a)

So, the Average rate of change

= P(2000) - P(1992) / (2000 - 1992)

= (34.5 - 42.7) /(2000 - 1992)

= -8.2 / 8

= -1.025

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If y varies directly as x, we can write the following equation:

When x = 3, we have y = 6, so:

Now, using x = 9, we have:

Therefore the answer is y = 18.

Answer:

86/3

Step-by-step explanation:

28.6