The total cost after tax to repair Deborah's computer is represented by0.08(50h)+50H, where h is the number of hours it takes to repair Deborah's computer. What part of the expression represents the amount of tax she has to pay? Explain

Answer:

y = - x - 2

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 )

Calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (2, - 4) and (x₂, y₂ ) = (- 1, - 1)

m = [tex]\frac{-1+4}{-1-2}[/tex] = [tex]\frac{3}{-3}[/tex] = - 1 , thus

y = - x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (- 1, - 1 ), then

- 1 = 1 + c ⇒ c = - 1 - 1 = - 2

y = - x - 2 ← equation of line

(4). If we break down this piecewise function, we have 3 main expressions to deal with, 'h(x) = 5 if {x ≥ 4}' (represented by the green graph) 'h(x) = x if {0 ≤ x ≤ 4}' (represented by the blue graph) and 'h(x) = 1 / 2x + 2 if {x < 0}' (represented by the red graph).

Take a look at the attachment below for your graph of these 3 functions / expressions.

(5). For this part we want to determine the average rate of change of the function f(x) = 4x² - 5x - 8 over the interval [- 2,3]. Remember that to calculate average rate of change between the 2 points we use the following formula...

f(b) - f(a) / b - a,

f(3) = 4(3)² - 5(3) - 8 = 4(9) - 15 - 8 = 36 - 15 - 8 = 13,

f(- 2) = 4(- 2)² - 5(- 2) - 8 = 4(4) + 10 - 8 = 16 + 10 - 8 = 18

13 - 18 / 3 - (- 2) = - 5 / 5 = - 1

Therefore the average rate of change of the function f(x) = 4x² - 5x - 8 over the interval [- 2,3] will be - 1.

Answer:

Both angles are right angles.

Step-by-step explanation:

Supplementary angles sum to 180°. Since we know that both angles are congruent, let's call them x and x. We can write the following equation:

x + x = 180

2x = 180

x = 90°

Therefore, we can conclude that both angles are right angles.

Answer:

Angles that are both congruent and supplementary each have a measurement that is equal to 90°.

Step-by-step explanation:

Answer:

  6

Step-by-step explanation:

Since you're familiar with your multiplication tables, you know that ...

  42 = 6 × 7

There are 6 tiles in each of the 7 rows.

Answer:

Step-by-step explanation:

You are given a graph and wish to determine whether or not it represents a function.  Draw a vertical line through this graph and count the number of times the vertical line intersects the graph.  

If exactly once, the graph passes the vertical line test and we say the graph represents a function.

If more than once, the graph fails the test and does not represent a function.

This is because a function assigns one and only one y value to any input value x in the domain.

Answer:

Step-by-step explanation:

vertical line test: a test that uses any kind of straight stuff (i.e line, pen, etc.) to go over the graph and check whether or not there are two points on one vertical line.

In a function, one domain (x value) can only have one range (y value).

NOTE: one range can have multiple domains

This means through vertical line test, if there are two points on one vertical line, it will not be a function.

The row of table reveals the x-intercept could be second ( -4, 0).

The x-intercept of a function of variable x ( y = f(x) ) form is an intersection fo the x-axis and the curve of the function.

The x-intercept for a function y = f(x) is a solution to the equation f(x) = 0 because at that value of x, the function f(x) lies on x-axis where y is 0.

Values of x-intercept for a function f(x) are also called roots or solution of f(x) = 0 equation.

We have to find Which row of table reveals the x-intercept.

Thus, We can conclude that the second row shows the unit rate.

Hence, the row of table reveals the x-intercept could be second ( -4, 0).

Learn more about x-intercept here:

https://brainly.com/question/14764115

#SPJ5

Answer:

12 feet

Step-by-step explanation:

For an inclined roof, the rise is the vertical distance from the roof rafter to the vertical top plate while the run is the distance from the edge of the wall to half of the center of the ridge.

The slope is the ratio of the rise to run. Given a rise to run ratio of 3 to 4. The house is 32 feet wide.

The run of the roof =  half of the width of the roof = 1/2 × 32 feet = 16 feet

Let the rise of the roof (height of the attic) be x, hence:

rise to run ratio = height of attic/ run of roof

3/4 = x/16

x = 3/4 × 16

x = 12 feet

The height of the attic is 12 feet

Answer:

A double integral can be written as:

[tex]\int\limits {f(x, y)} \, dx dy[/tex]

Now, to do this integral, we first can fix one of the variables, like in this case, we can fix x.

Now, with x fixed, this will be a function of only one variable, y, then we can do the integration over y.

Once the function is integrated over y, we can now do the integration over x.

Then the correct option will be:

" Varying the order variable y"

We keep x fixed, and integrate over the other variable.

Answer:

Option d (quantitative data) is the correct choice.

Step-by-step explanation:

The remaining three options do not apply to the specified scenario. Therefore the description made will serve as an example of quantitative data.

Answer:

0.3581<x<0.4429

Step-by-step explanation:

Using the formula for calculating the confidence interval of the population proportion p expressed as:

Confidence interval = p ± Z * √p(1-p)/n

p is the population proportion = x/n

p = 200/500

p = 0.4

Z is the z-score at 95% CI = 1.96

n is the sample size = 500

Substituting the given parameters into the formula we will have;

Confidence interval = 0.4 ± 1.96 * √p(1-p)/n

Confidence interval = 0.4 ± 1.96 * √0.4(0.6)/500

Confidence interval = 0.4 ± 1.96 * √0.24/500

Confidence interval = 0.4 ± 1.96 * √0.00048

Confidence interval = 0.4 ± 1.96 * 0.0219

Confidence interval = 0.4±0.04294

Confidence interval = (0.3571, 0.4429)

Hence the confidence interval of the population mean is 0.3581<x<0.4429

Answer:

4

Step-by-step explanation:

y = mx+b where m is slope so the slope is 4

Answer:

slope is 4

Step-by-step explanation:

The equation y=mx+b is the linear equation and m represents slope. In this case m is 4

Answer:

The value of n in this equation is -3/4

Step-by-step explanation:

5 - (n - 4) = 3 (n + 2)

Distribute the negative to (n - 4) and distribute 3 to (n + 2).

5 - n + 4 = 3n + 6

Add 4 to -5.

9 - n = 3n + 6

Subtract 9 from 6.

-n = 3n - 3

Subtract 3n from n.

4n = -3

Divide 4 by -3.

n = -3/4

Answer:

-7x+24

Step-by-step explanation:

(2*2-3x+7) - (-3*2+4x-7)

11-3x+13-4x

-7x+24

Answer:

-7x +24

Step-by-step explanation:

2*2-3x+7) - (-3*2+4x-7)

11-3x+13-4x

-7x+24

Answer:

x^2-6x+9  

Step-by-step explanation:

for f=x^2 subsititude x with g(x) = x-3 in which will give you (x-3)^2 using the perfect square formula ((a-b)^2=a^2-2ab+b^2)  in which a=x, b=3. you shall then get x^2 -2x · 3 + 3^2 to get x^2-6x+9  

Answer:

1

Step-by-step explanation:

[tex] \bigg(3 {w}^{4} {z}^{3} m \bigg) ^{0} \\ = {3}^{0} \times {w}^{4 \times 0} \times {z}^{3 \times 0} \times {m}^{0} \\ = {3}^{0} \times {w}^{0} \times {z}^{0} \times {m}^{0} \\ = 1 \times 1 \times 1 \times 1.. ( \because {a}^{0 } = 1) \\ = 1 \\ \therefore \: \bigg(3 {w}^{4} {z}^{3} m \bigg) ^{0} = 1[/tex]

Answer:

1

Step-by-step explanation:

whenever we have 0 in the exponent the term becomes equal to 1

(3w^4z^3m)^0

multiplying 0 with all terms inside the bracket

3^0 × w^4×0 × z^3×0 × m^1×0

solving the powers

3^0 × w^0 × z^0 × m^0

since we have 0 in the exponent so all the terms will become 1

1 × 1 × 1 × 1 = 1

The question is incomplete. Here is the complete question.

(a) How many three-digit numbers can be formed from the digits 0,1,2,3,4,5 and 6, if each digit can be used only once?

(b) How many of these are odd numbers?

(c) How many are greater than 330?

Answer: (a) 180

              (b) 75

               (c) 105

Step-by-step explanation:

(a) In the group, there are 7 digits. A three-digit number can not start with zero, otherwise, it will be a 2-digit number. So:

For the hundreds position, there are 6 choices.

For the tens position, since the digit can be used only once, there are 6 choices.

For the unit position, there are 5 choices.

The total three-digit number formed is: 6*6*5 = 180

(b) To form an odd number, the unit position must be an odd digit, then:

unit position has 3 choices;

hundreds position has 5 choices;

tens position has 5 remaining choices.

The total three-digit odd number is: 3*5*5 = 75

(c) The number formed must be greater than 330, so:

If the number start with a 3, to be greater, there are 3 other choices (4, 5 and 6), so Tens position has 3 choices and Unit position has 5 choices.

Total number is: 3*5 = 15

Another possibility is the number starts with a digit bigger than 3 and so,  there are 3 choices.

Tens position has 6 choices;

Unit position has 5 choices;

Total possibilities are: 3*6*5 = 90

The total number of ways a three-digit number is greater than 330 is:

90 + 15 = 105

Answer:

[tex]y=-4x+13[/tex]

Step-by-step explanation:

We are given the two points (3, 1) and (2, 5) and we want to find the equation of the line containing the given points.

First, find the slope of the line:

[tex]\displaystyle \begin{aligned} m &= \frac{\Delta y}{\Delta x} \\ \\ &= \frac{(5)-(1)}{(2)-(3)} \\ \\ &= \frac{4}{-1} \\ \\ &= -4 \end{aligned}[/tex]

Hence, the slope of the line is -4.

Since we know the slope and a point, we can consider using the point-slope form, given by:

[tex]y-y_1=m(x-x_1)[/tex]

Let's use (3, 1) as the chosen point, and we will substitute -4 for the slope m. This yields:

[tex]\displaystyle y-(1)=-4(x-(3))[/tex]

To convert into slope-intercept form, solve for y:

[tex]\displaystyle \begin{aligned} y - 1 &= -4 (x - 3) \\ y - 1 &= -4x + 12 \\ y &= -4x + 13 \end{aligned}[/tex]

In conclusion, the equation of the line is:

[tex]y=-4x+13[/tex]

Answer:

Step-by-step explanation:

Y=-4x+13

Answer:

x = 7

Step-by-step explanation:

First, put the x values on one side by subtracting 4x from each side:

5x + 11 = 4x + 18

x + 11 = 18

Subtract 11 from both sides to solve for x:

x = 7

Answer: The value of x is 7.

Step-by-step explanation:

Here's how I got my answer:

5x + 11 = 4x + 18

Isolate variables and combine like terms:

5x - 4x = 18 - 11

Simplify:

x = 7

That is the final answer.

Answer:

[tex] \boxed{\bold{\boxed{ \sf{1 \: , \: 2 \: , \: 3\: ,4 \: , \: 5 \: , \: 6 \: , \: 8 \: , \: 10 \: }}}}[/tex]

Option D is the correct option

Step-by-step explanation:

Let the sets be A and B.

A = { 1 , 2 , 3 , 4 , 5 }

B = { 2 , 4 , 6 , 8 , 10 }

Finding A union B ( A ∪ B )

The union of sets A and B is the set of all elements which belongs either A or B or both A and B

So, list them :

A ∪ B = { 1 , 2 , 3 , 4 , 5 , 6 , 8 , 10 }

Hope I helped!

Best regards! :D

Answer:

0.89736

Step-by-step explanation:

We solve this question using z score formula

Z score = x - μ/σ

x = raw score

μ = population mean

σ = population standard deviation

Hence,

x = 258, μ = 220, σ = 30

Z = 258 - 220/30

=1.26667

Probability value from Z-Table:

P(x<258) = 0.89736

Therefore, the probability that his weights is less than 258 kg is 0.89736

Answer:

34

Step-by-step explanation:

Order of Operations: BPEMDAS

Step 1: Write out equation

(b - 2a)² + bc

Step 2: Define variables

a = 6

b = 5

c = 3

Step 3: Plug in

(5 - 2(6))² + 5(-3)

Step 4: Multiply

(5 - 12)² - 15

Step 5: Parenthesis

(-7)² - 15

Step 6: Exponents

49 - 15

Step 7: Subtract

34

Answer:

4.472135955

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

-r^2+5ry+4y^2

= -(-2)^2+5(-2)(3)+4(3)^2

= -(4)+5(-6)+4(9)

= -4-30+36

= 36-30-4

= 36-34

= 2

Answer:

Simplify each radical, then combine.

3√8

Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

6 √ 2 = 3√8

Answer:

Hypotenuse is the longest side in a triangle.

a^2=b^2+c^2.

5^2=4^2+c^2.

c^2=25-16.

c^2=9.

c=√9.

c=3cm.

Answer:

-15/8 or -1 7/8, 1.875

Step-by-step explanation:

Answer:

Option A.

Step-by-step explanation:

Note: Let as consider, we have to find the total amount after 9 years.

It is given that,

Principal amount = $1000

Rate of compound (yearly) interest = 15% = 0.15

Time = 9 year

The formula for total amount is

[tex]M=P(1+i)^n[/tex]

where, P is principal, i is rate of interest and n is number of years.

Substituting P=1000, i=0.15 and n=9, we get

[tex]M=1000(1+0.15)^9[/tex]

[tex]M=1000(1.15)^9[/tex]

[tex]M=1000(3.5178763)[/tex]

[tex]M=3517.8763[/tex]

[tex]M\approx 3517.88[/tex]

So, the total amount after 9 years is $3517.88.

Therefore, the correct option is A.

Answer:

Solution: an Experimenter whats to estimate the average water consumption per family in the city

if individual families are used as the sampling united, a frame could be using censes data or atelephone book

if dwelling are used as the sampli units, aframe could be using Address book or city directory

If city blocks are used as the sampling units, aframe could been using is city directory

Step-by-step explanation:

Answer:

241.3 feet

Step-by-step explanation:

From the above question, we solve for this using the law of cosines

Law of cosines

a² = b² + c² -2bc Cos A

a =  √b² + c² -2bc Cos A

a = The distance between the bases in Little League =  60 feet

b = ???

c = The distance from home plate to the fence in dead center at the Oak Lawn Little League field =  280 feet

A = It makes an angle of 45°

This is because the distance 60 feet and 280 feet are perpendicular to each other and they meet at a point that divides a right angle 90° into equal parts.

a = √280² + 60² - 2 × 280 × 60  × Cos 45

a = 241.33216 feet

Approximately = 241.3 feet

How far is it from the fence in dead center to third base? 241.3 feet