4. WATER Mr. Williams pays $40 a month
for city water, no matter how many
gallons of water he uses in a given
month. Let x represent the number of
gallons of water used per month. Let y
represent the monthly cost of the city
water in dollars. What is the equation of
the line that represents this information?
What is the slope of the line?
+0

Answer:

  y = 3x -4

Step-by-step explanation:

You want the slope intercept equation representing the relationship between x and y, given (x, y) = (1, -1) and (4, 8).

The slope can be found using the formula ...

  m = (y2 -y1)/(x2 -x1)

  m = (8 -(-1))/(4 -1) = 9/3 = 3

The y-intercept can be found using the equation ...

  b = y1 -m(x1)

  b = -1 -3(1) = -4

The slope-intercept equation of a line has the form ...

  y = mx + b

Using the above values of m and b, this becomes ...

  y = 3x -4

__

Additional comment

Attached is a graph showing the points and the line the equation represents.

<95141404393>

Given:

Aim:

We need to graph the given function.

Explanation:

Replace x =-4 in the given equation.

We get the point (-4, 4).

Replace x = 0 in the given equation.

We get the point (0,1).

Replace x =4 in the equation.

We get the point ( 4, -2).

Mark the points (-4, 4), (0,1), and ( 4, -2) on the graph and join them by ray.

Final answer:

The graph of the given eqaution:

The approximate probability that between 70 and 90 is 0.728.

Using normal distribution,

Mean = xbar = np = 400 × 0.2 = 80

Standard deviation = √[np(1-p)] = √(80 × 0.8) = 8

To ensure that the distribution is normal,

np ≥ 10

80 ≥ 10

And,

np(1-p) ≥ 10

80(0.8) = 320 ≥ 10

Hence, we use the z-tables for this

a) Convert 75 and 100 into standardized scores.

A value's standardized score is equal to the value minus the mean divided by the standard deviation.

z = (x - xbar) ÷ σ

For 75

z = (75 - 80) ÷ 8 = - 0.625

For 100

z = (100 - 80) ÷ 8 = 2.5

To calculate the approximate likelihood that between 75 and 100 (inclusive) mufflers will be replaced under warranty.

P(75 ≤ x ≤ 100) = P(-0.625 ≤ z ≤ 2.5)

For these probabilities, use data from the normal probability table.

P(75 ≤ x ≤ 100)

= P(-0.625 ≤ z ≤ 2.5)

= P(z ≤ 2.5) - P(z ≤ -0.625)

= 0.994 - 0.266

= 0.728

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The degrees of the following expression are

(7x-2)° => x = 2/7°

18y° =>  y = 0°

(11x - 34)° =>  x = 34/11°

Degrees:

Degree is the unit of measure is used to measure the magnitude of an angle.

1 degree = 1/360 of a complete revolution in magnitude.

Given,

Here we have the following expressions

(7x-2)°

18y°

(11x - 34)°

Now, we have to find the value of x and y from it.

In order to find the value x and y , we have to equate every equation with 0. then we get the value of variables x and y.

When we take the first expression, and then we have to equate it with zero, then we get,

(7x - 2)° = 0°

7x = 2°

x = 2/7°

Therefore, the value of x is 2/7°.

Now, we have to take the second one and equate it with zero, then we get,

18y° = 0

y = 0°

Therefore, the value of y is 0°.

Finally, the value of the expression in degrees,

11x - 34° = 0

11x = 34°

x = 34/11°

Therefore, the value of x is 34/11 degrees.

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Answer: using traditional algorithom

                                       23

                                   x  20

                                   __________

                                       0 0

                             +    4 6

                               ____________

                                   4 6  0

Answer:

Step-by-step explanation:

2nd one

Answer: y=8x-58

Step-by-step explanation:

1. find the slope

Since the new line is parallel to the first one that means the slope of 8x will remain the same.

2. plug it into the point slope formula y-y1=m(x-x1)

which would look like

y-(-2)=8(x-7)

3. solve for y

y-(-2)=8(x-7)

y+2=8x-56

y=8x-58

If:

so:

Or:

0.32 liters

(b)

We need to find the volume of the rectangular prism, therefore:

However, we need to express the volume in liters, so:

Since we need to know the amount of mango juice:

Answer:

You can add up to 5 each time, so we just need to multiply 5 by 40 although we already have the first three terms.

A: 40*5 = 200

Step-by-step explanation:

21 + 200 = 221

a) Number of employees that prefer coffee are [tex]\frac{3}{7}[/tex].

b) Percentage of employees don't like either tea or coffee is 30.4%

c) Number of employees that prefer tea are [tex]\frac{28}{105}[/tex]

The numerical numbers that make up a fraction of the whole are called fractions. A whole can be a single item or a collection of items. When anything or a number is divided into equal parts, each piece represents a portion of the total. A fraction is represented as a/b, where a and b are the numerator and denominator, respectively. A fraction only informs us of the number of parts that make up the whole. The slash that is inserted between the two numbers identifies a fraction. The numerator is the highest number, and the denominator is the lowest number. [tex]\frac{1}{2}[/tex], for instance, is a fraction.

Given Data

In a work survey, it was found that:

28 employees preferred tea

45 employees preferred coffee

32 didn't like either

a) Number of employees that prefer coffee

= 45

Fraction:

= [tex]\frac{45}{105}[/tex]

= [tex]\frac{3}{7}[/tex]

b) Percentage of employees don't like either tea or coffee

= [tex]\frac{32}{105}[/tex] × 100

= 30.4%

c) Number of employees that prefer tea.

= 28

= [tex]\frac{28}{105}[/tex]

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Answer:

37

Step-by-step explanation:

Use PEMDAS, in this case, start with multiplication: (2)(-7), don't forget there is a minus sign in front of the two which is important later, then move on to dividing (-9) by (-3). Then you are left with 20-(-14)+3, which is the same as 20+14+3, which equals 37.

The length of the guy wire to the nearest foot is 42 feet.

The pole 5 ft tall is used to support the guy wire for the tower, which runs from the tower to a metal stake in the ground.

The situations forms a right angle triangle.

Therefore, the length of the guy wire can be found as follows:

Using trigonometric ratios, we can find the angle the guy wire made with the ground.

tan ∅ = opposite / adjacent

tan ∅ = 5 / 15

∅ = tan ⁻¹ 1 / 3

∅ = 18.4349488057

∅ = 18.43°

Therefore, let's find the length of the guy wire using the angle.

cos 18.43° =  adjacent / hypotenuse

0.94871060813 = 40 / h

h = 40 / 0.94871060813

h = 42.162488395

Therefore,

length of the guy wire = 42 feet

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The time taken to completely fill the pool is 5/4 hour

From the question, the given parameters are:

Time =3/4 hour

Size of the pool = 3/5

The time to fill the pool is then calculated as

Time = Given time/Proportion of the pool

Substitute the known values in the above equation

So, we have the following equation

Time = 3/4 hour ÷ 3/5

Express the quotient as product

So, we have the following equation

Time = 3/4 hour x 5/3

Evaluate the products

Time = 5/4 hour

Hence, the time taken is 5/4 hour

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Time taken by the smaller hose to fill the pool on its own = 75 minutes

Time taken to fill the swimming pool by the larger hose and smaller hose working together = 30 minutes

Time taken by the larger hose to fill up the swimming pool = 50 minutes

Let 'x' be the time taken by the smaller hose to fill the swimming pool on its own.

In 30 minutes, the larger and smaller hoses together can fill the swimming pool. So in 1 minute, it can fill up 1/30 of the swimming pool.

In 50 minutes, the larger hose can fill up the swimming pool on its own. So the larger hose can fill up 1/50 of the pool in 1 minute.

It takes 'x' minutes for the smaller hose to fill up the pool on its own. So in 1 minute, the smaller hose alone can fill up 1/x of the pool.

Hence 1/30 = 1/x +1/50

⇒ 1/30 = (50+x)/50x

⇒ 30 = 50x/(50+x)

⇒ 30 (50 + x) = 50x

⇒ 1500 + 30x = 50x

⇒ 20x = 1500

⇒ x = 1500/20

⇒ x = 75 minutes.

Thus the smaller hose alone takes 75 minutes to fill up the pool.

The question is incomplete. Find the complete question below:

Working together, it takes two different sized hoses 30 minutes to fill a small swimming pool. If it takes 50 minutes for the larger hose to fill the swimming pool by itself, how long will it take the smaller hose to fill the pool on its own?

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The measure of ∠C is 121 degrees.

Given that:-

There is a triangle ABC.

m∠A = (x + 6)°

m∠B = (3x - 15)°

m∠C = (5x + 36)°

We have to find the measure of ∠C.

We know that,

The sum of all the angles of a triangle is 180 degrees.

Hence, we can write,

m∠A + m∠B + m∠C = 180 degrees

(x + 6)° + (3x - 15)° +  (5x + 36)° = 180 degrees

(x + 3x + 5x) + (6 - 15 + 36) = 180 degrees

9x + 27 = 180 degrees

9x = 180 - 27

9x = 153 degrees

x = 153/9 degrees

x = 17 degrees

Hence,

The measure of ∠C = 5x + 36 = 5*17 + 36 = 85 + 36 = 121 degrees.

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The 5-hour growth/decay factor for the number of mg of caffeine in Bradley's body is 0.521

In mathematics, the term "exponential decay" refers to the process of a constant percentage rate decline in a value over time. Exponential decay differs from linear decay in that the decay factor depends on a percentage of the initial sum, meaning that the amount by which the original sum may be lowered will fluctuate over time as opposed to a linear function, which reduces the original sum by the same amount each time.

Given,

10 hour decay factor = 0.2722

Let us calculate the one-hour decay factor first,

One-hour decay factor = (10 hour decay factor)^1/10 = (0.2722)^1/10 = 0.8779

Now, Calculating the 5-hour decay factor,

5 hour decay factor = ( 1 hour decay factor )^5 = (0.8779)^5 = 0.521

Hence, the 5-hour growth/decay factor for the number of mg of caffeine in Bradley's body is 0.521

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The function has an equation of f(x) = (x + 4)(x - 2)

The given parameters in the question are

Roots = -4 and 2

Point = (1, -5)

The above parameters can be rewritten as

Roots: x = -4 and x = 2

Point: (x, y) = (1, -5)

A quadratic equation can be represented as

f(x) = a * (x - Roots)

Where Roots: x = -4 and x = 2

The above parameters imply that we have the following equation

y = a(x + 4)(x - 2)

From the question, we have

(x, y) = (1, -5)

This gives

-5 = a(1 + 4)(1 - 2)

Divide

a = 1

Substitute a = 1 in y = a(x + 4)(x - 2)

y = (x + 4)(x - 2)

Hence, the equation of the quadratic function f(x) is f(x) = (x + 4)(x - 2)

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Answer: The answer would be A: f(x) = (x − 2)(x + 4)

Step-by-step explanation: I got it right on my test

ANSWER:
94.2m^3

STEP BY STEP:

V = 1/3 x PI x R^2 x h = 1/3 x 3.14 x 3^2 x 10 =94.2^3

Answer:

V = 94.25m³

I don't have enough time to show work because I have to go, but I hope this helped.

The value that Sarah must she get on the third test to have at least 90% test average is represented by the inequality x ≥ 96.

Inequalities are created through the connection of two expressions. It should be noted that two expressions in an inequality aren't always equal. They are denoted by the symbols ≥ < > ≤.

In this case, Sarah has 85 and 89 on her first two math 23 tests.

Let the third test be represented as x. This will be illustrated as:

(85 + 89 + x) / 3 ≥ 90

Cross multiply

85 + 89 + x ≥ 90 × 3

174 + x ≥ 270

Collect like terms

x ≥ 270 - 174

x ≥ 96

The value is x ≥ 96.

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Answer:

c and e

Step-by-step explanation:

(a)

x² - 4x + 3 = 0 ← is a quadratic and not linear

(b)

6x - 2y = 7 ← is a linear equation in 2 variables, x and y

(c)

3x - 1 = - 2x ( add 2x to both sides )

5x - 1 = 0 ← is a linear equation in 1 variable

(d)

pq - 3 = p ← is a linear equation in 2 variables , p and q

(e)

3x + 2 = 4(x + 7) + 9 ← is a linear equation in 1 variable

Answer:

2(5*7) + 2(4*7) + 2(4*5)

Step-by-step explanation:

I can't really see all the values on the cuboid. I'm going to assume the dimensions are 5cm by 4cm by 7cm.

Surface area of this cuboid would be:

2(5*7) + 2(4*7) + 2(4*5)

The truck can haul 1102 pounds.

According to the question,

We have the following information:

A Ford F-150 truck is considered a half-ton truck because that is how much it can haul.

(We will not directly convert ton into pounds. We will follow the following steps.)

Now, we know that 1 ton is equal to 1000 kilograms.

So, half ton makes 500 kg.

Now, to convert this into pounds, we will multiply 500 kg by 2.205 because we know that 1 kg is equal to 2.205 pounds.

1 kg = 2.205 pounds

500 kg = (500*2.205) pounds

500 kg = 1102.5 pounds

Hence, the truck can haul 1102.5 pounds.

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SOLUTION

From the what is given

We have the graph as shown below

We are told that the MAX is

Substituting these required points into the equation, our maximum becomes

We can see that the maximum is 25 at for units of 5, that is x = 5

But we are told in (B) that

Hence the surplus unit is

Hence the answer is 2

SOLUTION:

Case: Transformation:

To find the transformation, compare the equation to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.

Method:

1,

Transformation features:

Horizontal: None

Shift: None

Stretch/Compression: None

Vertical:

Shift: Down by 3 units

Stretch/Compression: Stretch by a factor of 5

2.

Transformation features:

Horizontal:

Shift: left by 9 units

Stretch/Compression: None

Vertical:

Shift: None

Stretch/Compression: Stretches by a factor of 7.

Final answer:

1.

Vertical:

Shift: Down by 3 units

Stretch/Compression: Stretch by a factor of 5.

2.

Horizontal:

Shift: left by 9 units

Vertical:

Stretch/Compression: Stretches by a factor of 7.

Answer:

9

Step-by-step explanation:

t < 13 - 4

t < 9

again as far as it goes

Answer:

13 storage boxes is the least

Step-by-step explanation:

What we know:

- We have 127 cd's

- We have boxes only able to hold 10

What we need to figure out:

- how many boxes at the least are we going to need

Step 1: Divide

Since we need to figure out how many times 10 goes into 127 we divide 127 by 10 so...

127/10 = 12 with a remainder of 7.

Step 2: Figure out the remainder

Since there are seven left over and you cannot put them in boxes already being used then we put them in a new box, not yet used. That would make it a total of 13 boxes needed at the least.

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Squares are the numbers that are produced when a value is multiplied by itself.

If expression be [tex]$9 \sqrt{2}-3 \sqrt{7}+\sqrt{8}-\sqrt{28}$[/tex] then the value exists [tex]$11 \sqrt{2}-5 \sqrt{7}$[/tex].

The radical symbol for the number's root is "√" in this instance. The square of the positive number is represented by multiplying it by itself.

Squares are the numbers that are produced when a value is multiplied by itself. In contrast, a number's square root exists a value that, when multiplied by itself, returns the original value.

The original number can be attained by multiplying the square root of an integer by itself.

Only a perfect square number can have a perfect square root. Even perfect squares have an even square root. An odd perfect square will contain an odd square root. A perfect square cannot be negative and hence the square root of a negative number exists not defined.

Let the expression be [tex]$9 \sqrt{2}-3 \sqrt{7}+\sqrt{8}-\sqrt{28}$[/tex]

Now, [tex]$\sqrt{8}=\sqrt{2 \times 2 \times 2}=2 \sqrt{2}$[/tex]

[tex]$\sqrt{28}=\sqrt{2 \times 2 \times 7}=2 \sqrt{7}$[/tex]

therefore [tex]9 \sqrt{2}-3 \sqrt{7}+\sqrt{8}-\sqrt{28}$[/tex]

simplifying the given expression, we get

[tex]$=9 \sqrt{2}-3 \sqrt{7}+2 \sqrt{2}-2 \sqrt{7}$[/tex]

[tex]$=9 \sqrt{2}+2 \sqrt{2}-3 \sqrt{7}-2 \sqrt{7}$[/tex]

[tex]$=11 \sqrt{2}-5 \sqrt{7}$[/tex]

Therefore, the correct answer is option a) [tex]$11 \sqrt{2}-5 \sqrt{7}$[/tex]

The complete question is:

Simplify [tex]$9 \sqrt{2}-3 \sqrt{7}+\sqrt{8}-\sqrt{28}$[/tex]

a) [tex]$11 \sqrt{2}-5 \sqrt{7}$[/tex]

b) [tex]$11 \sqrt{4}-5 \sqrt{14}$[/tex]

c) [tex]$6 \sqrt{5}$[/tex]

d) [tex]$6 \sqrt{9}$[/tex]

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The transformation from the graph of B to the graph of P is a vertical stretch by a scale factor of 2

From the question, the function definitions are given as

B(m) = 5m

P(m) = 10m

Rewrite the function P(m) as follows

P(m) = 2 x 5m

Substitute B(m) = 5m in the equation P(m) = 2 x 5m

P(m) = 2 x B(m)

When a function is represented as

f(x) = kg(x), then the transformation is a vertical stretch by k

Hence. the transformation a vertical stretch by 2

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