Consider the expressions shown below.
A. -8x^2 - 3x + 4
B. 8x^2 - 3x + 8
C. 8x^2 + 3x - 4

Complete each of the following statements with the letter that represents the expression.
(3x^2 - 7x + 14) + (5x^2 + 4x - 6) is equivalent to expression
(2x^2 - 5x - 3) + (-10x^2 + 2x + 7) is equivalent to expression
(12x^2 - 2x - 13) + (-4x^2 + 5x +9) is equivalent to expression

the units of measurement for the composite function f(w(h)) are - furniture/weeks

function composition is an operation. that takes two functions f and g, and produces a function h = g . f such that h(x) = g. In this operation, the function g is applied to the result of applying the function f to x.

                               [tex]f(w(h)) = \frac{furniture}{hours} (\frac{hours}{week} )\\f(w(h)) = \frac{furniture}{week}[/tex]

The units of measurement for the composite function f(w(h)) is furniture/weeks.

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The system of inequalities that best describes this situation provided A represents the area in which the entire field exists:

[tex]$\left \{ {{A \geq x^{2} +10x+300} \atop {A \leq 1200}} \right.[/tex]

Word problems in mathematics exist methods we can utilize variables, algebra notations, and arithmetic operations to solve real-life cases.

We have a new addition to the current rectangular field,

Let that new addition to the current rectangular field be x

Length of the new addition = 10x

Twice the width of the new addition = 2x²

Original area of the field = 300

From the above information, we can derive a quadratic equation:

2x² + 10x + 300

Also, we exist given a constraint that the total area of the practice field should be no more than 1200.

It can be less than 1200 or equivalent to 1200.

Therefore, the system of inequalities that best describes this situation provided A represents the area in which the entire field exists:

[tex]$\left \{ {{A \geq x^{2} +10x+300} \atop {A \leq 1200}} \right.[/tex]

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Answer: x>8.

Step-by-step explanation:

[tex]14-2*(x+1) < -4\\ 14-2x-2 < -4\\12-2x < -4\\12-2x+4 < 0\\16-2x < 0\\16-2x+2x < 0+2x\\16 < 2x\\Divide \ both\ sides\ of \ the\ equation \ by \ 2:\\8 < x.[/tex]

From the table, the domain are all real numbers and they can be substituted for x to return a valid f(x) value:

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a Cartesian coordinate, which are the x-axis and y-axis.

By critically observing the table (see attachment), we can logically deduce that relationship between the amount of ink and the size of the sign is modeled by this function:

f(x) = x²

From the table, the domain are all real numbers and they can be substituted for x to return a valid f(x) value:

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Answer: 38 teachers.

Step-by-step explanation:

Let the share ratio be x.

So, quantity of teachers = 2x, quantity of male students = 17x,

quantity of female students = 18x.

17x+18x=665

35x=665

Divide the left and right sides of the equation by 35:

х=19.

2x=2*19

2x=38.

the volume of the oblique pyramid is 16 cubic units

The formula for finding the volume of a oblique pyramid is given as;

Volume = [tex]\frac{1}{3}[/tex] × base area/ height

Where

base area = area of a right triangle

From the lengths of the triangle given, we can deduce that the opposite side is 24unit and the adjacent side or the base is 10 unit

let's put in the values to the formula

Base area = 10 × 24

Base area = 240 units

height = 5 units

Since we have both the height and the base area, let's find the volume

Volume = [tex]\frac{1}{3}[/tex] × [tex]\frac{240}{5}[/tex]

Volume = [tex]\frac{1}{3}[/tex] × [tex]48[/tex]

Find the division

Volume = 16 cubic units

Thus, the volume of the oblique pyramid is 16 cubic units

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Using binomial distribution, the probability of

a. 5 will still be with the company after 1 year is 28%.

b. at most 6 will still be with the company after 1 year is 89%.

The probability of a new employee in a fast-food chain still being with the company at the end of the year is given to be 0.6, which can be taken as the success of the experiment, p.

We are finding probability for people, thus, our sample size, n = 8.

Thus, we can show the given experiment a binomial distribution, with n = 8, and p = 0.6.

(i) We are asked for the probability that 5 will still be with the company.

Thus, we take x = 5.

P(X = 5) = (8C5)(0.6⁵)((1 - 0.6)⁸⁻⁵),

or, P(X = 5) = (56)(0.07776)(0.064),

or, P(X = 5) = 0.27869184 ≈ 0.28 or 28%.

(ii) We are asked for the probability that at most 6 will still be with the company.

Thus, our x = 6, and we need to take all values below it also.

P(X ≤ 6)

= 1 - P(X > 6)

= 1 - P(X = 7) - P(X = 8)

= 1 - (8C7)(0.6)⁷((1 - 0.6)⁸⁻⁷) - (8C8)(0.6)⁸((1 - 0.6)⁸⁻⁸)

= 1 - 8*0.0279936*0.4 - 1*0.01679616*1

= 1 - 0.08957952 - 0.01679616

= 0.89362432 ≈ 0.89 or 89%.

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The provided question is incomplete. The complete question is:

If the probability of new employee in a fast-food chain still being with the company at the end of 1 year is 0.6, what is the probability that out of 8 newly hired people,

a. 5 will still be with the company after 1 year?

b. at most 6 will still be with the company after 1 year?

Answer:

B

Step-by-step explanation:

If x and y vary inversely, then as x increases, y decreases. That eliminates answers A, C, and D.

Answer: B

A sample statistic is a numerical descriptive measure of a sample.

Therefore, a  sample statistic is a numerical descriptive measure of a sample.

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The complete question is given below:

What is a sample statistic?

A _____descriptive measure of  a _____.

Give three examples. (Select all that apply.)

The height of the pyramid is [tex]16ft.[/tex]

The centroid of the base sits just above the right pyramid. Oblique pyramids are non-right pyramids. A right pyramid is typically assumed to be a regular pyramid because it has a regular polygon base.

To find the height of the pyramid:

l=the slant height of the right pyramid.

b=the length side of the square base of the right pyramid.

h=the height of the right pyramid.

Pythagorean Theorem: [tex]l^{2} =h^{2} +(\frac{b}{2} )^{2}[/tex]

Solve:h

[tex]h^{2} =l^{2} +(\frac{b}{2} )^{2}[/tex]

[tex]h^{2} =20^{2} -12^{2}[/tex]

[tex]h^{2} =256[/tex]

[tex]h=16ft[/tex]

Therefore, The height of the pyramid is [tex]16ft.[/tex]

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Answer:

The height of the pyramid is 16ft

Step-by-step explanation:

f(x) = -1/ 3x and f(x) = -z/xy are both examples of inverse variations. Option B

Inverse variation can be defined as the relationships between variables represented in the form of y = k/x

where;

From the options given, we can see that;

f(x) = -1/ 3x

f(x) = -z/xy

Both take the form of inverse variations

Thus, f(x) = -1/ 3x and f(x) = -z/xy are both examples of inverse variations. Option B

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The pair of triangles in option A, C and D are congruent triangles.

Pair of triangles are given.

Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.

A) In the given figure, two angles and one side of the one triangle is equal to two angles and one side of the other triangle

By AAS congruence, two triangles are congruent.

B) In the given figure, one angle and one side is equal

So, two triangles are not congruent

C) Here, two sides and one included angle of the one triangle is equal to two sides and one included angle of the other triangle

D) Here, two angles and one included side of the one triangle is equal to two angles and one included side of the other triangle.

Therefore, the pair of triangles in option A, C and D are congruent triangles.

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The parts of algebraic expressions related to polynomials are variables and coefficients.

The parts of algebraic expressions are;

Polynomials are algebraic expressions composed of variables, constants and exponents, that are combined using the mathematical operations such as addition, subtraction, and multiplication

Polynomials consists of variables and coefficients. The variables in polynomials are also called indeterminates. The coefficients also multiply this variables.

Thus, the parts of algebraic expressions related to polynomials are variables and coefficients.

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The solution of the given expression is:

(3*5)^6 = 11,390,625

Here we have an expression with an exponent, which is:

(3*5)^6

First, we can solve the thing inside the parenthesis is:

3*5 = 15

Replacing that we get:

(3*5)^6 = (15)^6

Now, the exponent 6 means that we need to multiply the number by itself 6 times, so we get:

(15)^6 = 15*15*15*15*15*15 = 11,390,625

Then we conclude that:

(3*5)^6 = 11,390,625

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Answer:I THINK IT IS 1,-3

Step-by-step explanation:

Answer:

y=2x+12

Step-by-step explanation:

Using the normal distribution, there is a 0.4826 = 48.26% probability that the sample mean is between 15 and 16 grams per day.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

For this problem, the parameters are given as follows:

[tex]\mu = 15, \sigma = 3, n = 40, s = \frac{3}{\sqrt{40}} = 0.4743[/tex]

The probability is the p-value of Z when X = 16 subtracted by the p-value of Z when X = 15, hence:

X = 16:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{16 - 15}{0.4743}[/tex]

Z = 2.11

Z = 2.11 has a p-value of 0.9826.

X = 15:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{15 - 15}{0.4743}[/tex]

Z = 0

Z = 0 has a p-value of 0.5.

0.9826 - 0.5 = 0.4826 = 48.26% probability that the sample mean is between 15 and 16 grams per day.

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Answer:

20

Step-by-step explanation:

To solve this you have to make a system of equations.

Since the father and son's age sum up to 60, the first equation will be:

f + s = 60

Secondly, since the father's age is 5 times the age of the son 6 years ago the equation will be:

6 - (5s) = f

Now, you have to solve the first equation to let it equal to s

f + s = 60

f = 60 - s

Plug in

6 - 5s = 60 - s

     +s          +s

6 - 4s = 60

-6         -6

---------------------

-4s = 54

-----   -----

 -4     -4

   s ≅ 14

14 + 6 = 20

Answer:

20.

Step-by-step explanation:

x = father's age and y = son's age,

x + y = 60

x - 6 = 5(y - 6)

x - 5y = -24

Subtract this from first equation:

6y = 84

y = 14

So the son's age is 14.

Six years time son will be 20.

The AD's length of 3m will enable the angle at B to be divided in half.

Angle Bisector Theorem: What is it?

The angle bisector of a triangle divides the opposing side into two portions that are proportional to the other two sides, according to the angle bisector theorem, in simpler words the angle bisector theorem is concerned with the relative lengths of the two segments that a triangle's side is divided into by a line that bisects the opposite angle. It equates their relative lengths to the relative lengths of the other two sides of the triangle.

The triangle has sides of 5, 7, and (x+4) m.

Angle B's angle bisector will only be the BD if

x/4 = 5/7

x = 5 *4 / 7

x = 20/7 = 2.85 ≈ 3m

Thus if AD has length of 3m then it will enable the angle at B to be divided in half.

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Answer:

AD = 3m

Hope this helps!

Step-by-step explanation:

Answer:

Its 50

Step-by-step explanation:

60 times 4 it gives you 240.

Now minus all the numbers on the table like this

240 - 55 - 70 - 65 which equals to 50

240 would be the miles

value of n could be 252 degree. Option 4

It is important to note that a decagon is a ten-sided polygon.

Since, a decagon has 10 sides

And we know that the angle made in one complete rotation is 360 degree.

Now find angle made in each rotation by the decagon is 360,

= 360/ 10

= 36 degrees

Now, we have to find possible values of n, and 'n' must be a multiple of 36

Apply hit and trial from given options.

We observe that from given options, only 252 degree is multiple of 36.

Therefore, value of n could be 252 degree. Option 4

The complete question is ;

A regular decagon is rotated n degrees about its center, carrying the decagon onto itself. The value of n could be:

1. 10 degrees

2. 150 degrees

3. 225 degrees

4. 252 degrees

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[tex]58.41 < f(x) < 150[/tex] inequality represents the range of the exponential function that models this situation

The exponential decay function is as follows:

[tex]y = a(1-r)^t[/tex]

Here,

y = final value

a = initial value

r = decay rate

t = time taken

Given that:

a = 150 mg

r = 9% = 0.09

Then the next hour the amount of caffeine in the body will be:

[tex]y = a (1-r)^t\\y = 150 \times (1-0.09)^2[/tex] = 136.5

Similarly, after 10 hours the amount of caffeine in the body will be:

[tex]y = 150 \times (1- 0.09)^{10} = 58.41[/tex]

Then the inequality representing the range of the exponential function that models this situation is:

58.41 < f(x) < 150

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The graph of the function has no asymptotes.

The function is given as:

c(t) = 5t - t² + 1

When t = 1, 2, 5, 10;

We have:

c(1) = 5(1) - 1² + 1 = 5

c(2) = 5(2) - 2² + 1 = 7

c(5) = 5(5) - 5² + 1 = 1

c(10) = 5(10) - 10² + 1 = -49

So, the table of values is

t        c(t)

1         5

2        7

5        1

10      -49

See attachment for the graph of the function

The domain

From the question, we understand that t represents time.

So, the domain is 0 ≤ t ≤ 5.2

The range

From the graph, the maximum of the graph is 7.25

So, the range is 0 ≤ f(t) ≤ 7.25

Asymptotes

From the graph, we can see that the graph has no asymptotes.

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Answer:

it's C. 2.26s

but you wrote 2.16s nearly

The soccer ball was in the air for approximately 2.31 seconds. Rounding to two decimal places, the answer is approximately 2.30 seconds,  option D.

To determine how long the soccer ball was in the air, we can use the vertical motion of the ball. When a projectile is launched at an angle, its vertical motion can be analyzed separately from its horizontal motion.

In this case, the initial velocity of the soccer ball can be divided into vertical and horizontal components. The initial velocity in the vertical direction can be calculated using the sine of the launch angle:

Vertical component (Vy) = initial speed (v) * sin(angle)

Vy = 16 m/s * sin(45°)

Vy = 11.31 m/s

Now, we can use the vertical motion equation to find the time the ball spends in the air:

Vertical displacement (y) = Vy * time - (1/2) * gravity * time^2

Since the ball reaches the same vertical position when it lands as when it was launched, the vertical displacement is 0. Therefore, we can set the equation equal to zero:

0 = (11.31 m/s) * time - (1/2) * 9.8 m/s^2 * time^2

Simplifying the equation:

4.9 * time^2 = 11.31 * time

Dividing both sides by time:

4.9 * time = 11.31

time = 11.31 / 4.9

time ≈ 2.31 seconds

Therefore, the soccer ball was in the air for approximately 2.31 seconds. Rounding to two decimal places, the answer is approximately 2.30 seconds, which corresponds to option D.

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a. The area of [tex]R[/tex] is given by the integral

[tex]\displaystyle \int_1^2 (x + 6) - 7\sin\left(\dfrac{\pi x}2\right) \, dx + \int_2^{22/7} (x+6) - 7(x-2)^2 \, dx \approx 9.36[/tex]

b. Use the shell method. Revolving [tex]R[/tex] about the [tex]x[/tex]-axis generates shells with height [tex]h=x+6-7\sin\left(\frac{\pi x}2\right)[/tex] when [tex]1\le x\le 2[/tex], and [tex]h=x+6-7(x-2)^2[/tex] when [tex]2\le x\le\frac{22}7[/tex]. With radius [tex]r=x[/tex], each shell of thickness [tex]\Delta x[/tex] contributes a volume of [tex]2\pi r h \Delta x[/tex], so that as the number of shells gets larger and their thickness gets smaller, the total sum of their volumes converges to the definite integral

[tex]\displaystyle 2\pi \int_1^2 x \left((x + 6) - 7\sin\left(\dfrac{\pi x}2\right)\right) \, dx + 2\pi \int_2^{22/7} x\left((x+6) - 7(x-2)^2\right) \, dx \approx 129.56[/tex]

c. Use the washer method. Revolving [tex]R[/tex] about the [tex]y[/tex]-axis generates washers with outer radius [tex]r_{\rm out} = x+6[/tex], and inner radius [tex]r_{\rm in}=7\sin\left(\frac{\pi x}2\right)[/tex] if [tex]1\le x\le2[/tex] or [tex]r_{\rm in} = 7(x-2)^2[/tex] if [tex]2\le x\le\frac{22}7[/tex]. With thickness [tex]\Delta x[/tex], each washer has volume [tex]\pi (r_{\rm out}^2 - r_{\rm in}^2) \Delta x[/tex]. As more and thinner washers get involved, the total volume converges to

[tex]\displaystyle \pi \int_1^2 (x+6)^2 - \left(7\sin\left(\frac{\pi x}2\right)\right)^2 \, dx + \pi \int_2^{22/7} (x+6)^2 - \left(7(x-2)^2\right)^2 \, dx \approx 304.16[/tex]

d. The side length of each square cross section is [tex]s=x+6 - 7\sin\left(\frac{\pi x}2\right)[/tex] when [tex]1\le x\le2[/tex], and [tex]s=x+6-7(x-2)^2[/tex] when [tex]2\le x\le\frac{22}7[/tex]. With thickness [tex]\Delta x[/tex], each cross section contributes a volume of [tex]s^2 \Delta x[/tex]. More and thinner sections lead to a total volume of

[tex]\displaystyle \int_1^2 \left(x+6-7\sin\left(\frac{\pi x}2\right)\right)^2 \, dx + \int_2^{22/7} \left(x+6-7(x-2)^2\right) ^2\, dx \approx 56.70[/tex]

r = 6
A=πr^2

A = 113.09734

Quarter circle formula = πr^2 / 4

113.09734 / 4 = 28.274335

113.09734 - 28.274335 = 84.824005 is the answer

The 5.25 m combined height of John, Jim, and Joe, the 12 cm height difference between John and Jim and the 0.09 m difference in height between Jim and Joe, indicates that solution to the word problem is Joe was 1.73  meters tall

A word problem is a presentation of a math problem using verbal description rather than numbers, variables and operators.

The combined height of John, Jim and Joe = 5.25 m

John's height = Jim's height - 12 cm = Jim's height - 0.12

Jim's height = Joe's height + 0.09 m

Let h represent Joe's height, we get;

Jim's height = h + 0.09

John's height = h + 0.09 - 0.12 = h - 0.03

John's height = h - 0.03

The sum of the heights is therefore; h + h + 0.09 + h - 0.03 = 3·h + 0.06

The sum of their heights = Their combined height = 5.25 meters

Therefore; 3·h + 0.06 = 5.25

h = (5.25 - 0.06)/3 = 1.73

Joe's height, h = 1.73 meters

Jim's height = 1.73 + 0.09 = 1.82

Jim's height = 1.82 meters

John's height = 1.73 - 0.03 = 1.7

John's height is 1.7 meters

Joe was 1,73 meters tall

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Answer:

E

Step-by-step explanation:

We can find the volume either by finding the scale factor between the two figures and multiplying the first cylinder's volume by it or simply finding the diameter of the second cylinder and doing the equation for volume of a cylinder.

I chose the second way to work out.

Since the two cylinders are similar, we can simply set up a proportion to find the diameter, d, of the second cylinder:

[tex]\frac{6}{d}=\frac{4.5}{6}\\ \\ 4.5d=36\\ d=8[/tex]

The formula for volume of a cylinder is [tex]V=\pi r^2h[/tex]

The radius is simply d/2 so the radius of the second cylinder is 8/2 or 4.

Thus, we have

[tex]V=\pi *4^2*6\\V=\pi *16*6\\V=96\pi \\V=301.59[/tex]