The outside temperature decreases by 7°F in 3 hours. Part A How would you represent the temperature change as a unit rate? Express your answer as an integer. 3b.The outside temperature decreases by 7°F in 35 hours. Part B If the temperature continues to decrease at this rate, what will be the change in temperature after 5 hours?

The functions f and g are:

a. f(x) = 1/x

b. g(x) = x + 2

a) To find two functions f and g such that (fog)(x) = 1/(x + 2), we need to determine how the composition of the two functions f and g produces the given expression.

Let's start by assuming g(x) = x + a, where a is a constant. This means that g(x) adds the constant a to the input x.

Next, let's determine the function f(x) such that (fog)(x) results in the desired expression. We have:

(fog)(x) = f(g(x)) = f(x + a)

b) To simplify the expression 1/(x + 2) and make it match f(g(x)), we can consider f(x) = 1/x.

Substituting the expressions for f(x) and g(x) into (fog)(x), we have:

(fog)(x) = f(g(x)) = f(x + a) = 1/(x + a)

Comparing this with the desired expression 1/(x + 2), we see that a = 2. Therefore, the functions f and g are:

a. f(x) = 1/x

b. g(x) = x + 2

Using these functions, we can verify the composition (fog)(x):

(fog)(x) = f(g(x)) = f(x + 2) = 1/(x + 2)

Thus, (fog)(x) = 1/(x + 2), which matches the desired expression.

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The slope which shows  the cost per guest is $35 per guest

The given cost for 50 guests is $2150.

The cost for 75 guests is $3025.

It can also be represented as:

(Guest, Cost) =(50, $2150) & (75, $3025)

The slope can now be calculated as

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (50, $2150) & (75, $3025)

Substituting the given values in the equation as follows:

Slope = (3025 - 2150)/(75 - 50)

Slope = 35

Hence, the slope is $35 per guest.

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Answer: Its they second or last one but the second one sound more clear

Step-by-step explanation:

Answer:

43 becuase 8 3/5 times 5

Step-by-step explanation:

Step-by-step explanation:

Performance appraisal is the answer

Answer:

please see attached the annotated solution

Given data

p=20%= 0.2

n=15 companies

let x = 5 the number of companies that outsource to overseas consultants

The binomial  probability distribution is given as

P(x=λ)=nCx*P^x*q^n-x

we also know that q=1-p

Given:

Total earning = $70

He spends \(\dfrac{1}{5}\) of the total amount on movies.

He then spends \(\dfrac{1}{2}\) of the remaining money on school clothes.

To find:

The remaining money.

Solution:

We have,

Total earning = $70

He spends \(\dfrac{1}{5}\) of the total amount on movies.

Money spent on movie is

\(\$70\dfrac{1}{5}=\$14\)

Remining money after movie is

\(\$70-\$14=\$56\)

He then spends \(\dfrac{1}{2}\) of the remaining money on school clothes.

Money spent on school clothes is

\(\$56\times \dfrac{1}{2}=\$28\)

Remining money after movie and school clothes is

\(\$56-\$28=\$28\)

Therefore, the remaining money is $28.

Answer:

50/100 chance

Step-by-step explanation:

It would be a 50/50 chance, because the coin has two sides, so it's a 50/50 chance that it'll land on tails all 8 times.

Answer:

its 4.00%

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given the function f(x) = 8x³ − 12x² − 48x, the critical point of the function occurs at its turning point i,e at f'(x) = 0

First we have to differentiate the function as shown;

\(f'(x)= 3(8)x^{3-1}- 2(12)x^{2-1} - 48x^{1-1}\\ \\f'(x) = 24x^2 - 24x-48x^0\\\\f'(x) = 24x^2 - 24x-48\\\\At \ the\turning\ point\ f'(x)= 0\\24x^2 - 24x-48 = 0\\\\\\\)

\(Dividing \ through \ by \ 24\\\\x^2-x-2 = 0\\\\On \ factorizing\\\\x^2-2x+x-2 = 0\\\\x(x-2)+1(x-2) = 0\\\\(x-2)(x+1) = 0\\\\x-2 = 0 \ and \ x+1 = 0\\\\x = 2 \ and \ -1\)

Hence the critical numbers of the function are (2, -1)

Answer:

Length = 12cm

Width = 8cm

Step-by-step explanation:

Let the length be x

Let the width be 2/3x

Perimeter = 2 (l+b)

Length = 2 (x+2/3x) = 40

= x + 2/3x = 40/2

= x + 2/3x = 20

= x/1 + 2/3x = 20

LCM = 3

= 3x + 2x = 20

______

3

= 3x + 2x = 20 x 3

= 5x = 60

= x = 60/5

= x = 12

Width = 2/3 of 12

= 2/3 × 12

= 8

The exact value of cos theta if the terminal side of theta in standard position contains the point (6,-8) is, 3 / 5

We have to given that;

the terminal side of theta in standard position contains the point (6,-8)

Hence, For given condition we get;

The exact value of cos theta if the terminal side of theta in standard position contains the point (6,-8) is,

Here, x = 6, y = - 8

Hence, We get;

r = √x² + y²

r  = √6² + 8²

r = √36 + 64

r = √100

r = 10

So, The exact value of cos theta if the terminal side of theta in standard position contains the point (6,-8) is,

cos θ = x / r

cos θ = 6 / 10

cos θ =  3 / 5

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Answer:

9/35

Step-by-step explanation:

3/5 x 3/7

Answer:

v (E) = √(2E/m)

Step-by-step explanation:

From the question given:

E = ½mv²

E is the kinetic energy

m is the mass of object

v is the velocity.

To find a model v(E) for the velocity of the object, we simply make V the subject of the above equation.

This can be obtained as follow:

E = ½mv²

Cross multiply

mv² = 2E

Divide both side by m

v² = 2E/m

Take the square root of both side

v = √(2E/m)

Therefore, the model v(E) for the velocity of the object is given by:

v (E) = √(2E/m)

Answer:

11

Explanation:

I prefer to get paid in cash but you can pay me the way you want ;)

Answer:

-21√x + 32

Step-by-step explanation:

Let f(x) = 7x + 4  

g(x) = √x + 4

(-3)f(g(x)) = f (√x + 4)

= -3 [7(√x + 4) + 4]

= -3 [7√x + 28 + 4]

= = -21√x + 32

Even I find this complicated.

Hope its right tho.

Answer:

the second choice (-2,-3)

Step-by-step explanation:

Answer:

sin(100°) = 0.985

sin(-100°) = -0.985

Step-by-step explanation:

In a unit circle, each point (x, y) on the circumference corresponds to the coordinates (cos θ, sin θ), where θ represents the angle formed between the positive x-axis and the line segment connecting the origin to the point (x, y).

Therefore, sin(100°) equals the y-coordinate of the point (-0.174, 0.985), so:

\(\boxed{\sin(100^{\circ}) = 0.985}\)

Similarly, sin(-100°) equals the y-coordinate of the point (-0.174, -0.985), so:

\(\boxed{\sin(-100^{\circ}) = -0.985}\)

In the unit circle the value of sin (100) = 0.985 and the value of sin (-100) = -0.985, in three decimal places.

The value of the sine of the angles is calculated by applying the following formula as follows;

The value of sin (100) is calculated as follows;

sin(100°) corresponds to the y-coordinate of the point (-0.174, 0.985) as given on the coordinates of the unit circle.

sin (100) = 0.985

The value of sin (-100) is calculated as follows;

sin(100°) corresponds to the y-coordinate of the point (-0.174, -0.985), as given on the coordinates of the circle.

sin (-100) = -0.985

Thus, in the unit circle the value of sin (100) = 0.985 and the value of sin (-100) = -0.985, in three decimal places.

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Answer:

Initial amount: 934 g

After 80 years: 147 g

Step-by-step explanation:

\( A(t) = 934 (\dfrac{1}{2})^\frac{t}{30} \)

The initial amount occurs at t = 0.

\( A(0) = 934 (\dfrac{1}{2})^\frac{0}{30} \)

\( A(0) = 934 (\dfrac{1}{2})^0 \)

\( A(0) = 934 \times 1 \)

\( A(0) = 934 \)

After 80 years, t = 80.

\( A(80) = 934 (\dfrac{1}{2})^\frac{80}{30} \)

\( A(80) = 934 (\dfrac{1}{2})^\frac{8}{3} \)

\( A(80) = 934 (0.15749) \)

\( A(80) = 147 \)

Answer:

h = 16  ||    solution after squaring: \(x = -0.683\) or \(x = -7.32\)

steps by fieranswererft:

Given: \(x^2+8x+5=0\)

Take half of the x term and square it

The equations which show the total volume of the boxes Marcus shipped are as follows:

A. (20 × 10 × 7) + [2× (20 × 4 × 4)]

C. (20 × 10 × 7) + (20 × 4 × 4) + (20 × 4 × 4)

F. (200 × 7) + [2 × (80 × 4)]

Mathematically, the volume of a rectangular prism can be calculated by using this equation:

Volume = L × W × H

Where:

For rectangular prism 1, the volume is given by:

Volume 1 = L × W × H

Volume 1 = 20 × 7 × 10

Volume 1 = 200 × 7

Volume 1 = 1,400 cubic inches.

For rectangular prism 2, the volume is given by:

Volume 2 = L × W × H

Volume 2 = 20 × 4 × 4

Volume 2 = 80 × 4

Volume 2 = 320 cubic inches.

Since Marcus shipped 1 of the larger boxes and 2 of the smaller boxes, the total volume of the boxes Marcus shipped is given by these three (3) equations:

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To find f(g(x)), we substitute g(x) in place of x in the function f(x).

f(g(x)) = f(5x/(1-x)) = (5x/(1-x)) / (5 + (5x/(1-x))) = 5x / (1-x+5-5x) = 5x / 6 - 4x/6 = x/6

To find g(f(x)), we substitute f(x) in place of x in the function g(x).

g(f(x)) = g(x/(5+x)) = (5(x/(5+x))) / (1 - (x/(5+x))) = 5x / (5+x-x) = 5x/5 = x

Therefore, f(g(x)) = x/6 and g(f(x)) = x.

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Using proportional reasoning, we can predict that there will be 40 red candies in the large bag.

Using proportional reasoning, we can set up and solve the following equation to determine the number of red candies in the large bag:

P = Proportion of red candies in the large bag

R = Red candies in the small bag

R × (33/9) = P

12 × (33/9) = P

P = 40 red candies in the large bag

Therefore, using proportional reasoning, we can predict that there will be 40 red candies in the large bag.

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Answer:

≤ 4.3 gigabytes

Step-by-step explanation:

Flat fee + cost for x gigabytes = her budget

47 + 5 * x ≤ 68.50

5x = 68.50 - 47 ≤ 21.50

x ≤ 21.50/5 = 4.3 gigabytes

Micaela can use approximately 4.3 gigabytes of data while staying within her budget of $68.50 per month.

Let, "x" to represent the number of gigabytes of data Micaela can use while staying within her budget.

The total cost can be calculated by adding the flat cost of $47 to the cost based on the gigabytes used ($5 per gigabyte):

Total Cost = Flat Cost + (Cost per Gigabyte * Number of Gigabytes)

Given that Micaela wants to keep her bill at $68.50 per month, we can set up the equation:

68.50 = 47 + 5x

Now, solve for x:

68.50 - 47 = 5x

21.50 = 5x

Divide both sides by 5:

x = 21.50 / 5

x = 4.3

So, Micaela can use approximately 4.3 gigabytes of data while staying within her budget of $68.50 per month.

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The value of x that makes the line containing (1,2) and (5,3) perpendicular to the line containing (x,4) and (3,0) is x = 2.

To determine the value of x such that the line containing (1,2) and (5,3) is perpendicular to the line containing (x,4) and (3,0), we need to find the slope of both lines and apply the concept of perpendicular lines.

The slope of a line can be found using the formula:

slope = (change in y) / (change in x)

For the line containing (1,2) and (5,3), the slope is:

slope1 = (3 - 2) / (5 - 1) = 1 / 4

To find the slope of the line containing (x,4) and (3,0), we use the same formula:

slope2 = (0 - 4) / (3 - x) = -4 / (3 - x)

Perpendicular lines have slopes that are negative reciprocals of each other. In other words, if the slope of one line is m, then the slope of a line perpendicular to it is -1/m.

So, we can set up the equation:

-1 / (1/4) = -4 / (3 - x)

Simplifying this equation:

-4 = -4 / (3 - x)

To remove the fraction, we can multiply both sides by (3 - x):

-4(3 - x) = -4

Expanding and simplifying:

-12 + 4x = -4

Adding 12 to both sides:

4x = 8

Dividing both sides by 4:

x = 2

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Answer:

tan(θ)= dn/de

θ=arctan(dn/de)

Step-by-step explanation:

Answer:

80

Step-by-step explanation:

Objective: Supplementary Angles.

Supplementary Angles are Angles that add up to 180.

In the problem, Two angles add up to 180. We don't know Angle A and we know Angle B.

Let set up the equation

Let x represent the measure of Angle A and x+20 represent the measure of Angle B

\(x + x + 20 = 180\)

Combine Like Terms

\(2x + 20 = 180\)

Apply Basics Rules of Algebra

\(2x = 160\)

\(x = 80\)

This means angle A measure 80 degrees

answer would most likely be C