A machine that drills holes for wells drilled to a depth of
72 feet in one day.

At this rate, how many hours will it take until the drill
reaches its final depth of -132 feet?

The composition function  for the given function f(x) and g(x) is,

f(g(x)) = 6x^2 - 10x - 21.

What is composition of function?

The mathematical operation known as "function composition" takes two functions, f and g, and creates a function, h = g o f, such that h(x) = g. This operation involves applying the function g to the outcome of applying the function f to x.

Given:

f(x) = 2x - 7

g(x) = 3x^2 - 5x - 7

We have to find the composition function f(g(x)).

[tex]f(g(x)) = f(3x^2- 5x - 7)[/tex]

Plug x = 3x^2 - 5x - 7 in f(x).

[tex]f(g(x)) = 2(3x^2 - 5x - 7) - 7\\f(g(x)) = 6x^2 - 10x - 14 - 7\\f(g(x)) = 6x^2 - 10x - 21[/tex]

Hence, the composition function  for the given function f(x) and g(x) is, f(g(x)) = 6x^2 - 10x - 21.

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Answer:

[tex]\huge\boxed{\sf c=\frac{ad}{e-b}}[/tex]

Step-by-step explanation:

[tex]\displaystyle b + \frac{ad}{c} = e[/tex]

Subtract b to both sides

[tex]\displaystyle \frac{ad}{c} = e-b[/tex]

Multiply c to both sides

[tex]ad=c(e-b)[/tex]

Divide (e - b) to both sides

[tex]\displaystyle \frac{ad}{e-b} = c\\\\\boxed{c=\frac{ad}{e-b} }[/tex]

[tex]\rule[225]{225}{2}[/tex]

Answer:

Step-by-step explanation:

what

Step-by-step explanation:

Using linear regression, you'd expect 50 people to sign up on day 7.

Answer:

x = 11

Explanation:

It looks like the total distance between points I and K is -3 + x. Since I to J and J to K is also the total distance, I to K is also equal to 6 + 2x - 20. You can represent this in an equation and solve for x.

-3 + x = 6 + 2x - 20

-3 + x = 2x - 14

- 3 = x - 14

11 = x

Answer:

7

Step-by-step explanation:

Answer: y= 1/2x+2

Step-by-step explanation:

Using the y=mx+b formula you simply find the slope between the two points considered on a graph

Hope this helps you

Answer:

R = 12

Step-by-step explanation:

1 + 12/R = 13

Answer:

B. For 5 students, the cost will be the same, and the cost will be $70

Step-by-step explanation:

Look at the graph and see where the two linear plots intersect.

This point of intersection is at the x value of 5 and y value of 70: (5, 70)

Since the x-axis represents the number of students and y axis the total cost, the answer is B

The best triangle congruent theorem for the image is Angle-Angle-Side (AAS)

Two triangles are congruent if they have exactly the same three sides and exactly the same three angles.

From triangle ABC,

<BAC is given

<ABC=90⁰

<BCA is not given

Also, in triangle ACD,

<ACD is given

<CDA =90⁰

<DAC is not given

Therefore <BAC=<ACD (given)

<CDA=<ABC=90

<DAC=<BCA (not given)

Therefore,  ΔABC=ΔACD (AAS)

In conclusion, The two triangles are congruent with SSA theorem.

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Coordinates of the point C after dilation with a scale factor of 5, centered at the origin will be: C'(10, 5)

Given that,

The point C

C(2, 1)

We have to find what are the coordinates of the point D after a dilation with a scale factor of 5, centered at the origin.

We know that,

The point C

The size of the coordinates of the picture of point P will be 5 times larger than the original coordinates of point C in a dilatation with a scale factor of 5.

The following is the scale factor 5 rule of dilation:

(x, y)  →  (5x, 5y)

C(2, 1)  →  (5x, 5y) = (5(2), 5(1)) = C'(10, 5)

Therefore, coordinates of the point C after dilation with a scale factor of 5, centered at the origin will be: C'(10, 5)

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a) Corey's percentage increase in pay per hour is 14.2%.

b) When Dele invests $6,000 for 4 years at 3% per annum compound interest, the value of his investment (future value) at the end of 4 years is $15,757.12.

c) The worth of the car at the end of 2020 is $11,812.50, depreciating by 14% per annum.

a. Corey's original pay per hour = £12.36

Corey's new pay per hour = $14.11

Increase in pay = £1.75 (£14.11 - £12.36)

Percentage increase in pay = 14.2% (£1.75/£12.36 x 100)

b. Principal investment = $14,000

Investment period = 4 years

Compound interest rate = 3%

Compounding terms = Annually

The future value (FV) in 4 years:

N (# of periods) = 4 years

I/Y (Interest per year) = 3%

PV (Present Value) = $14,000

PMT (Periodic Payment) = $0

Results:

FV = $15,757.12

Total Interest = $1,757.12

c. Value of a car at the end of 2017 = $17,500

Depreciation rate per annum = 14%

Depreciation period = 3 years (Dec. 31, 2017 - Dece. 2020)

Value of the car at the end of 2020 = $11,812.50 ($17,500 x 1.14⁻³)

Thus, the car will reduce (depreciate) in value every year by 14%, making its value to be $11,812.50 at the end of 2020.

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The statements that Adriano mixed 19/24 pound of butter with 3/16 pound of honey he ay that he ued 16/8 pound of butter than honey  is not reasonable.

A mixture is a substance made of two or more additional chemical compounds or substances that do not chemically combine. It is actually the physical blending of two or more substances so that they can still be distinguished from one another when combined as solutions, suspensions, or colloids. Physical means can be used to separate them. The different components in any mixture are not created through any sort of chemical transformation. As a result, each component's unique properties are unaltered.

A mixture's constituent parts also do not combine chemically to form new material, in contrast to a compound. Instead, they just combine while retaining their individual traits. because there are variable quantities of the components

Ratio 19/24 is nearby ¾

Ratio 3/16 is nearby ¼

And ratio 16/8 is nearby 2

So, that his statements is not reasonable.

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The break even point is at 500 baskets. The company must sell 500 baskets a month, at which point their revenue of $10,000 will cover their total costs of $10,000.

What is break even point?

In economics, business, and particularly cost accounting, the break-even point is the point at which total cost and total revenue are equal, or "even." Although opportunity costs have been paid and capital has received the risk-adjusted, expected return, there is no net loss or gain, and one has "broken even."

In this case we could probably solve the problem from the graph itself, but we can also solve it algebraically by setting the equations equal:

[tex]\begin{gathered}R(n)=C(n) \\20 n=6000+8 n\end{gathered}[/tex]

Subtract 8n from both sides:

[tex]12 n=6000[/tex]

Divide:[tex]n=\frac{6000}{12}=500[/tex]

Evaluate either function at this input: [tex]R(500)=C(500)=10,000[/tex]

The break even point is at 500 baskets. The company must sell 500 baskets a month, at which point their revenue of $10,000 will cover their total costs of $10,000.

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Equation that represents Jada’s take-home earnings in dollars E = 12.20(h)-7.15

The equation that represents the situation is h=6.82 hours.

An equation, a formula that is express the equality of two expressions. The equation is representing direct proportion is , by the commenting them with in the equal sign .

As per the given question

Pay hour = $12.20 per hour

Bus fare = $7.15

1.Equation:

Assume that

She has work for "h" hours

Total earning = E

So, E = 12.20(h) - 7.15

If, Total earning = E = $90.45

So, E = 12.20(h) - 7.15

90.45 = 12.20(h) - 7.15

h = 6.82 hours

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The total no: of pages needed are 18 pages

A fundamental idea behind the unitary method is using the value of one unit to determine the values of additional units. Study up on the unitary method. With an increase in units, the value of additional units rises.

The general unitary group, also known as the group of unitary similitudes, is simply the product of the unitary group and the group of all positive multiples of the identity matrix. It includes all matrices A such that AA is a nonzero multiple of the identity matrix.

According to the question:-

The no: of pages needed for 6 letters = 6

The no: of pages needed for the other 6 letters= 6*2

                                                                              =12

Total no: of pages are 18

Hence, the total no: of pages are 18

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Answer:

Step-by-step explanation:

if its asking how many people there are it would be 40,000

Mother, Father, 2 kids=4

4 x 10,000= 40,000

Answer:  A.( 2,10) B.(4,6) C(5,4)  D(6,2)

Step-by-step explanation:

The calculations for the slope-intercept forms of the equations are (1) m=-[tex]\frac{3}{4}[/tex],B=2  (2)m=1, B=5  (3) m=-1, B=6

How to use the Slope -intercept form?

Slope of a line is a number that describes both the direction and the steepness of the line.

The intercept of a line is defined as the point at which it intersects the y-axis in a graph.

The equation of a line is expressed as follows;

Y=MX+B

Where M=slope and B=intercept

From the equations:

(1) y<[tex]\frac{-3x}{4}[/tex]+2

Applying the equation of slope-intercept form,

m=[tex]\frac{-3}{4} , B=2[/tex]

(2) Y[tex]\leq 5[/tex]

Applying the equation: Y=MX+B

m=1,  B=5

(3) x+y>6

Applying the formula: Y=MX+B

Re-arrange the equation

y>-x+6(1)

⇒ m=-1, B=6

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Answer:

2x - 12

Hope this helps : )

Step-by-step explanation:

The equation for 12 less than twice a number is 2x-12. This is because "12 less than a number" means 12 is being subtracted from a number. The "number" is a variable which can be x. "Twice a number" is the variable being multiplied by 2. So the final equation would be 2x - 12.

C. size

because when things dilate they change in size but not shape, orientation or betweenness

Using the equation of the plane and the provided point (1,2,3) with the unit values perpendicular to the plane .The answer is [tex]\frac{x-1}{3.14} + \frac{y-2}{3.14} + \frac{z-3}{3.14} = 1[/tex]

A plane is a doubly ruled surface in two dimensions that is spanned by two linearly independent vectors. A hyperplane is a generalization of the plane to higher dimensions. The dihedral angle is the angle formed by two intersecting planes.

A normal in geometry is a piece of geometry that is perpendicular to another piece of geometry, such as a line, ray, or vector. For instance, the (infinite) line perpendicular to the tangent line to the curve at the point is the normal line to a plane curve at the point.

x1=1

y1=2

z1=3

[tex]\frac{x-x1}{\sqrt{x1^{2}+y1^{2}+z1^{2}}} + \frac{y-2}{\sqrt{x1^{2}+y1^{2}+z1^{2}}} + \frac{z-3}{\sqrt{x1^{2}+y1^{2}+z1^{2}}} = 1[/tex]

[tex]\frac{x-1}{3.14} + \frac{y-2}{3.14} + \frac{z-3}{3.14} = 1[/tex]

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Answer:

318.75 miles

Step-by-step explanation:

Postulates, corollaries, and common notions are the three main types of reasoning we will use for reasons in the right- hand of column.

A two-column geometric proof consists of a list of statements, and the reasons that we know those statements are true. The statements are listed in a column on the left, and the reasons for which the statements can be made are listed in the right column.

Postulates, corollaries, and common notions are the three main types of reasoning we will use for reasons in the right- hand of column.

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Answer:

A. (3,-1)

Step-by-step explanation:

A reflection of y = x would be:

[tex](x,y)\rightarrow(y,x)[/tex]

Therefore:

[tex](-1, 3) \rightarrow (3, -1)[/tex]

The correct option should be A.

Hope this helps.

The probability that the engineer has to test at least 5 computers in order to find 2 defective ones is 0.985.

Given :

A quality control engineer tests the quality of produced computers. suppose that 5% of computers have defects, and defects occur independently of each other.

So the probability of getting 0 defective computers out of 4 is :

= ( 1 - 0.05 )^4

= 0.95^4

= 0.814.

The probability of getting exactly 1 defective computer out of 4 is :

= 0.05 * ( 1 - 0.05 )^3 * 4! / ( 1! ( 4 - 1 )!)

= 0.05 * 0.95^3 * 24/ ( 1!3! )

= 0.05 * 0.857375 * 24/6

= 0.171.

So the probability of getting only 0 or 1 defective computers out of the 1st 4 is :

= 0.814 + 0.171

= 0.985

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Together, Tony and Ted caught 78.29 pounds + 59.36 pounds = 137.65 pounds of fish when they went fishing.

Addition is a mathematical process that combines two or more numbers or units to form a sum. One of the four fundamental operations of mathematics, along with addition, subtraction, multiplication, and division, it is generally represented by the plus sign (+). The fundamental idea of addition is one that is taught to children at a young age and is utilized frequently in both mathematics and daily life. For instance, when shopping, one may tally up the costs of several goods to get the overall expense. In algebra, adding is used to solve problems and make statements simpler. Finding side lengths and shape areas are both important aspects of geometry. In general, adding is flexible. for example,Tony and ted went fishing. and we got to calculate the total fishes caught by them.

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Answer: 12 pack.

Step-by-step explanation: 25.20 divided by 12 shows us that each gatorade costs 2.1 dollars. Now add the 3 gatorade worth to 25.2. You get 31.5 which is less than 33, showing that 12 pack is more worth as you pay less for 15 aswell.

$340 was invested in the 9% fund and 1660 was invested in the 2% profit fund.

Step-by-step explanation:

Let x be amount invested in 9% profit fund

let (2000-x) be the amount invested in the 2% profit fund

.09x+.02 times (2000-x)=89

.09x+40-.02x=89

0.07x=49

x=340

The amount invested in mutual fund A  and mutual fund B is $700 and $1300 respectively.

Profit margin is a measure of profitability. It is calculated by finding the profit as a percentage of the revenue. It is given by :

profit margin = (profit / revenue or return) × 100

Given here $ 2000 invested in two mutual funds

let the amount invested in A be x then the amount invested in B is $2000-x

now profit in dollars from the two mutual funds is equal to $89

therefore, 9% of x + 2% of $2000-x = $89

               0.09x + 0.02×(2000-x) = 89

                     0.09x + 40 - 0.02x = 89  

                                           0.07x = 49

                                                   x = $700

Hence  the amount invested in A is  $700 and amount invested in B is $1300.

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An arithmetic sequence is a sequence where the difference between each consecutive term is the same.

The sum of an arithmetic sequence is given as,

S(n) = a + d(n - 1)

The total number of books sold over the first 18 months is 7600.

It is a sequence where the difference between each consecutive term is the same.

Example:

2, 4, 6, 8, 10 is an arithmetic sequence.

We have,

In the first month, the author sold 2500 books, but the sales were declining steadily at 12% each month.

This means,

a = 2500

12% of 2500

12/100 x 2500

= 12 x 25

= 300

d = 300

Now,

The sum of an arithmetic sequence is given as,

S(n) = a + d(n - 1)

Now,

n = 18

a = 2500

d = 300

S(23):

= 2500 + 300(18 - 1)

= 2500 + 300 x 17

= 2500 + 5100
= 7600

Thus,

The total number of books sold over the first 18 months is 7600.

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