if parallel lines are cut by transversal then there interior angles on the same side of the transversal are blank.

Based on the Federal Housing Administration's (FHA) total fixed payments-to-income ratio, Roberto would not qualify for the mortgage loan.

The Federal Housing Administration (FHA) allows 31% of a person's income to settle housing costs (as the front-end ratio) and 43% (as the back-end ratio) towards housing expenses and other long-term debt.

Monthly gross income = $3,500

Monthly payments for Housing:

Monthly mortgage = $1,000

Property taxes = $150

Homeowners insurance premium = $75

Mortgage insurance premium = $75

Total monthly housing costs = $1,300

Other monthly debts per month = $500

Total monthly payments = $1,800

Minimum front-end ratio = 31% = $1,085 ($3,500 x 31%)

Maximum back-end ratio = 43% = $1,505 ($3,500 x 43%)

Thus, using the FHA fixed payments-to-income ratio, Roberto would not qualify.

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Answer:

[tex]y=-\dfrac{1}{8}x^3[/tex]

Step-by-step explanation:

If a function is symmetrical about the origin, when y is replaced with (-y) and x is replaced with (-x), the resulting function will be equal to the original function.

Original function:

[tex]y=-\dfrac{1}{8}x^3[/tex]

Replace y with (-y) and x with (-x):

[tex]\implies -y=-\dfrac{1}{8}(-x)^3[/tex]

[tex]\implies -y=-\dfrac{1}{8}\cdot -x^3[/tex]

[tex]\implies -y=\dfrac{1}{8}x^3[/tex]

Multiply both sides by -1:

[tex]\implies y=-\dfrac{1}{8}x^3[/tex]

Therefore, as the function is equal to the original function, this function is symmetric with respect to the origin.

Answer:

10 and 11

or

-11 and -10

Step-by-step explanation:

Answer:

[tex] {2}^{ - 5} [/tex]

Step-by-step explanation:

Please see picture on how to do it

The Great Lakes are the world's largest group of freshwater lakes by total area and second-largest by total volume.

The Great Lakes, also known as the Great Lakes of North America or the Laurentian Great Lakes are a series of large interconnected freshwater lakes with sea-like characteristics in North America's mid-east region that connect to the Atlantic Ocean via the Saint Lawrence River.

Superior, Michigan, Huron, Erie, and Ontario are the names of five lakes that are located on or near the Canada-United States border. Lakes Michigan and Huron are joined hydrologically at the Straits of Mackinac. The Great Lakes Waterway allows for modern water travel.

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The number of subsets contained in Q if Q={x∣∣x is an even, positive integer and x < 27] is 13.

A subset implies a part of the mathematical concept that's referred to as the set. The set is the collection of the elements that are grouped in the curly braces.

In this case, since x is an even number and less than 27, this will be:

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, and 26.

Therefore, the numbers are 13.

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Answer:

a) -3x + y = 8

Step-by-step explanation:

Now we have to,

→ find which of these equations is linear.

Format of linear equation,

→ Ax + By = C

Then the linear equation is,

→ Ax + By = C

→ -3x + y = 8

Hence, answer is -3x + y = 8.

Answer:

A. -3x + y = 8

Step-by-step explanation:

Definition of a Linear Equation:

This is a linear equation as the highest power of its variables is one, and each variable is multiplied by a constant only.

This is not a linear equation as the highest power of the term in x is 2.

This is not a linear equation as the highest power of the term in x is 3.

This is not a linear equation as the x and y variables are multiplied by each other rather than by a constant.

Answer: (0,0)   (12,0)

Step-by-step explanation:

y=4x³-96x²+576x

Let y=0

Hence,

4x³-96x²+576x=0

Divide both parts of the equation by 4:

x³-24x²+144x=0

x(x²-24x+144x)=0

x=0

Thus, (0,0)

x²-24x+144=0

x²-2(x)(12)+12(12)=0

x²-2(x)(12)+12²=0

(x-12)²=0

x-12=0

x=12

Thus, (12,0)

Answer:

Step-by-step explanation:

The given steps describe constructing a parallel line using a compass and straightedge given line  and a point E that is not on line .

Step 1: Draw a line through point E that intersects line , and label the point of intersection, C.

Step 2: Place the point of the compass on C and draw an arc that crosses both lines.

Step 3: Without adjusting the compass width, move the compass to point E and draw an arc that has a similar orientation to the first arc drawn.

Step 4: Set the compass width to where the lower arc crosses the two lines.

Step 5: Move the compass point to the upper arc on the intersection of the arc and line .

Step 6: Draw an arc so it intersects the bottom of the arc. Label the intersection D.

Step 7: Use a straightedge to connect points E and D to form the parallel line .

so the answer is Place the point of the compass on C and draw an arc that crosses both lines

Answer:

39

Step-by-step explanation:

The given function to us is ,

[tex]\longrightarrow f(x) = 3x^3 + 1\\ [/tex]

We need to find the average rate of change between [tex] x=1 [/tex] and [tex] x=3[/tex] .

We can calculate the average rate of change as ,

[tex]\longrightarrow A(x) =\dfrac{f(b)-f(a)}{b-a} [/tex]

So that ,

[tex]\longrightarrow A(x) =\dfrac{f(3)-f(1)}{3-1}\\ [/tex]

[tex]\longrightarrow A(x) =\dfrac{ \{ 3(3)^3 +1 -(3(1)^3+1)\}}{2}\\ [/tex]

[tex]\longrightarrow A(x) = \dfrac{ 81 +1 - 3 -1 }{2}\\[/tex]

[tex]\longrightarrow A(x) = \dfrac{78}{2}\\ [/tex]

[tex]\longrightarrow\underline{\boxed{ A(x) = 39}} [/tex]

The solution to 4 divided by 3.48 is 0.87

Division in mathematics is the method of dividing large numbers into smaller numbers or par

Step 1: Rewrite the question in mathematical terms then

[tex]\frac{3.48}{4}[/tex]= 0.87

Therefore, answer to the division  is 0.87

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A model of the given expression on a number line is represented by a number line with open circle on point negative 11 over 2 (-11/2) and arrow shaded to the left.

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).

From the information provided, we have the following mathematical expression:

x = -3 - 2 1/2

x = -3 - 5/2

x = -11/2 or -5.5.

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[tex]4x+7=1+2(2x+3)[/tex]

⇒ Our goal is to solve for x. We can do this by moving everything else to the other side of the equation.

⇒ Open up the parentheses:

[tex]4x+7=1+4x+6[/tex]

⇒ Simplify:

[tex]4x+7=4x+7[/tex]

Because both sides are equal, we end up with x = x.

In this case, we can say that all values of x are true.

All values of x are true.

The number of tiles is 96

From the question, we have

The width of the room is 16 feet, 8 inches and the client has chosen a square tile that measures 4 inches on each side.

16 feet = 192 inches

Number of tiles = (192*8)/(4*4)

= 96 tiles

The number of tiles is 96.

Multiplication:

The product of two or more numbers is computed by mathematicians using multiplication. In everyday life, it is a basic mathematical operation that is frequently used. We employ multiplication when we must combine groups of like sizes. The operation of multiplication serves as a representation of the fundamental idea of adding the same number repeatedly. The product of two or more numbers is what is obtained when those numbers are multiplied, and the factors are the quantities that are multiplied. Multiplying the numbers simplifies the process of adding the same number repeated.

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The fraction in lowest terms or a decimal rounded to the nearest tenth is 0.0096.

Given that,

A normal 52-card deck is used to randomly select three cards.

We have to find the probability that a spade, a black card, and a ten will be dealt as the first, second, and third cards, respectively.

Three cards are drawn with replacement from a standard deck so for the first one i.e heart , probability is (13/52)=0.25

for 2nd one i.e red it is (26/52)=0.5

for 3rd one i.e queen  it is (4/52)=0.0769

thus, the answer is 0.25*0.5*0.0769=0.0096

Therefore, The fraction in lowest terms or a decimal rounded to the nearest tenth is 0.0096.

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The finance charge on the average daily balance for , this 1 month period is $3.45  .

In the question ,

it is given that ,

the daily balance over the period of 1 month = $145

The APR rate of interest = 28.5%

the monthly APR rate of interest = (28.5%)/12 = 2.375%

the finance charge for the 1 month period can be calculated using the formula .

finance charge = (daily average balance)×(monthly rate of interest)

Substituting the values , we get

finance charge = 145 × 2.375%

= 145 × 0.02375

= 3.44375

≈ 3.45

Therefore , The finance charge on the average daily balance for , this 1 month period is $3.45  .

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The two possible locations of L are (-2,-1) and (14/3, -5/3).

According to the question,

We have the following information:

JK has endpoints J(-10, 1) and K(2, -2). Point L divides JK into two parts with lengths in a ratio of 2:1.

We know that the following formulas are used to find the coordinates of a point:

x = [tex]\frac{(mx2+nx1)}{(m+n)}[/tex] and x = [tex]\frac{(mx2-nx1)}{(m+n)}[/tex]

y = [tex]\frac{(my2+ny1)}{(m+n)}[/tex] and y = [tex]\frac{(my2-ny1)}{(m+n)}[/tex]

In this case, we have the following values:

x1 = -10 and y1 = 1

x2 = 2 and y2 = -1

m = 2 and n = 1

So, we have:

x = {2*2+1*(-10)}/(2+1)

x = (4-10)/3

x = -6/3

x = -2

For the negative sign:

x = {2*2-1*(-10)}/3

x = (4+10)/3

x = 14/3

x = 4.67

The values of y:

y = {2*(-2)+1*1}/3

y = (-4+1)/3

y = -3/3

y = -1

For the negative sign:

y = {2*(-2)-1*1}/3

y = (-4-1)/3

y = -5/3

y = -1.67

Hence, the two possible locations of L are (-2,-1) and (14/3, -5/3).

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Answer:

Step-by-step explanation:

220.5-(12.8+20.25+18.2+25.5)

220.5-(76.25)

143.75 lbs of ice left

Answer:

7:43 or [tex]\frac{7}{43}[/tex]

Step-by-step explanation:

The total is 43     7 + 36

Answer:

7:43

Step-by-step explanation:

36+7 = 43

43 is the total amount of people that were polled

those who don't like shopping are 7, as stated in the question

the ratio is 7:43

The p-value of this sample proportion is equal to 0.0360.

At the 0.01 (1%) significance level, there isn't enough evidence to conclude that freshmen students study less than 2.5 hours per day, on an average.

For this statistical study, we would use a t-test statistic and the null and alternative hypotheses would be given by:

H₀: p ≥ 150 minutes

H₁: p < 150 minutes

Mathematically, the t-test statistic can be calculated by using this formula:

[tex]t=\frac{x\;-\;\mu}{\frac{\delta}{\sqrt{n} } }[/tex]

Where:

Substituting the given parameters into the formula, we have;

t-test, t = (135 - 150)/(44/√30)

t-test, t = (-15)/8.0333

t-test, t = -1.8672

From the t distribution table, the p-value is given by:

p-value = P(t < -1.8672)

p-value = 0.0360

Since the p-value (0.0360) is greater than the significance level (0.01), we fail to reject the null hypothesis because there is insufficient evidence to claim that the mean time of the freshman students is less than 2.5 hours per day.

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The number of revolutions = Total distance divided by its circumference

The radius of the tire is 1.167 yards.

A circle is a two-dimensional figure with a radius and circumference of
2πr.

The area of a circle is given as πr².

We have,

The number of revolutions = Total distance divided by its circumference

Total distance = 200 yards

Revolutions = 27.28

A tire is in the form of a circle.

So,

The circumference of the tire.

= 2πr

Now,

27.28 = 200 yards / 2πr

2πr = 200 yards / 27.28

r = 200/(27.28 x 2 x 3.14)

r = 200 / 171.32

r = 1.167 yards.

The radius of the tire is 1.167 yards.

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The value of the function when the value of x is 5 is 29.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

[tex]f(x)= \left \{ {{x^3 \;\;\;\;\;\; x < -3} \atop {2x^2-9\;\;\;-3\leq x < 4}} \atop {5x+4\;\;\;x > 4}}\right.[/tex]

As the value of the function is to be found when the value of x is 5.

So, we can write the function as,

f(5) = 5x + 4

f(5) = 5(5) + 4

f(5) = 29

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The error interval for m is 6.58 ≤ m < 6.59

Truncation is a process of dropping all decimal places after a certain point without rounding the number.

Given that, the mass, m, of the lorry is 6.58 tonnes truncated to 2 decimal places.

Since the number is truncated to two decimal places, the error interval is,

6.58 ≤ m < 6.59

Hence, the error interval for m is 6.58 ≤ m < 6.59.

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The probability that a teenager selected at random is female and their favourite hobby is watching films is 1/4.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

From the information given, there is a total of 32 teenagers. Of those, 8 are female with a favorite hobby of watching films.

Therefore, the probability will be:

= Female who watch films / Total teenagers

= 8/32

= 1/4.

The probability is 1/4.

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Complete question

A group of teenagers is asked about their favorite hobbies. The results are shown in the following table: Sports Playing video games Watching films Total

Male 9 2 3 14

Female 7 3 8 18

Total 16 5 11 32

Q6a. In fractions, what is the probability that a teenager selected at random is female and their favourite hobby is watching films? You can simplify this fraction if you wish.

Answer: $110 but that may be wrong

Step-by-step explanation: