1. You begin working at Tasty Tacos with the payment schedule listed in the table below:


Write an equation that describes the relationship between the years (x) and the earnings per hour (y).

2. If this pattern continues, what would the earnings per hour be after working for 15 years?

3. If this pattern continues, after how many years of service would you earn $9.65 per hour?

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)

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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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:

10,172 women

Step-by-step explanation:

47093 / 50 = 941.86

So 941.86 lots of 50 women

941.86 x 10.8 = 10172.088 women

rounded to 10,172 women

( can't have part of a person

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.

[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 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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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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Answer: $110 but that may be wrong

Step-by-step explanation:

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

Answer:

10 and 11

or

-11 and -10

Step-by-step explanation:

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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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 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:

[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:

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: 2 real solutions

Step-by-step explanation:

The discriminant is [tex](-9)^2 -4(1)(3)=69[/tex].

Since the discriminant is positive, there are 2 real solutions.

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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{(-2,3),(-3,3),(-4,3)} Each member of the domain is assigned exactly one member of the range that defines the correct relation. The correct option is D.

The expression that established the relationship between the dependent variable and independent variable is referred to as a function. In the function as the value of the independent variable varies the value of the dependent variable also varies.

When one magnitude depends on another, the relationship between them is known as a mathematical function. So long as they are uniquely and solely connected.

Every mathematical function is the relationship between an element of group A and an element of group B. Consequently, the following algebraic expression can be used to represent this function:

Therefore, the {(-2,3),(-3,3),(-4,3)} Each member of the domain is assigned exactly one member of the range that defines the correct relation. The correct option is D.

The complete question is given below,

Which relation describes a function? What makes it a function?

A) {(-2,3),(-2,5),(-6,7)} Each member of the range is unique.

B) {(2,3),(3,3),(3,4)} Each member of the domain and range is positive.

C) {(2,3),(3,3),(3,4)} Each member of the domain and range is a real number.

D) {(-2,3),(-3,3),(-4,3)} Each member of the domain is assigned exactly one member of the range.

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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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Answer:

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

Step-by-step explanation:

Please see picture on how to do it

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 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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