The function y = f(x) is graphed below. Plot a line segment connecting the points
on f where x = -8 and x = -2. Use the line segment to determine the average
rate of change of the function f(x) on the interval -8 ≤ x ≤-2.

Answer:

f(5) = 16.5

Step-by-step explanation:

Substitute x = 2.5 into f(x) , that is

f(2.5) = 6(2.5) + 1.5 = 15 + 1.5 = 16.5

Answer:

16.5

Step-by-step explanation:

Answer:

17, -3, -13, -18, -23

Step-by-step explanation:

Plug in the x side into the equation so

g(-4) = -5(-4) -3

g(-4) = 20-3

g(-4) = 17

Therefore that answer is 17

Then you do that for all of them, I don't have the time to do them all but that's the concept for all of them. Hope this helps and hopefully it's not too late. Sorry!

Collin's gross salary, after the 7% raise, for each 2-week pay period, will be approximately $1,159.17.

To calculate Collin's gross salary after the 7% raise for each 2-week pay period, we need to find the raise amount and add it to his current gross salary.

Collin's current gross salary is $1,083.34.

To find the raise amount, we multiply his current gross salary by 7% (or 0.07):

Raise amount = $1,083.34 \(\times\) 0.07

= $75.8338 (rounded to two decimal places)

Now, we add the raise amount to his current gross salary to find the new gross salary:

New gross salary = $1,083.34 + $75.8338 = $1,159.1738 (rounded to two decimal places)

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Answer:

2

Step-by-step explanation:

2*3+3*4 x 1/3 power 2

6+12 x 1/9

18 x 1/9

2 x 1 (because 9 and 18 are cutted by each other)

2

2

To evaluate the expression (2b+3a)×(c^2) when a=4, b=3, and c=1/3, we substitute the given values into the expression and perform the indicated arithmetic operations:

(2b + 3a) × (c^2)

= (2(3) + 3(4)) × ((1/3)^2) (substitute a=4, b=3, c=1/3)

= (6 + 12) × (1/9) (evaluate 2(3) + 3(4) and (1/3)^2)

= 18/9

= 2

Therefore, when a=4, b=3, and c=1/3, the expression (2b+3a)×(c^2) equals 2.

Answer:

40,900   40,800   40,700   40,600   40,500

Step-by-step explanation:

The 4 will stay the same, it doesn't need to change because you are focusing on the number after it which is 1. a number has to be over 5 to round up the number. If we are trying to make a 1 , the previous number must be either a 5, a 6, a 7, an 8, or a 9

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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The perimeter of the polygon, with the specified coordinate points , found using Pythagorean Theorem  iis  approximately 16 units

The Pythagorean Theorem indicates that the square of the distance between points on the coordinate plans is the sum of the square of the horizontal and vertical distances between the  point.

The coordinates of the vertices of the polygon are;

(-3, 1), (-3, 3), (-1, 5), (2, 4), and (2, 1)

The length of the sides are therefore;

3 - 1 = 2,

√((-1 - (-3))² + (5 - 3)²) = 2·√2

√((2 - (-1))² + (4 - 5)²) = √(10)

4 - 1 = 3

2 - (-3) = 5

The perimeter is therefore;

2 + 2·√2 +  √(10) + 3 + 5  ≈ 16

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Answer:

Step-by-step explanation: b) 10

To make the fractions equivalent, we need to find the missing numerators that would make them equal. Let's fill in the missing numerators:

1/2 and __/8

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:

1/2 and 4/8

Now, the fractions are equivalent.

---

4/12 and __/60

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 5:

4/12 and 20/60

Now, the fractions are equivalent.

---

2/3 and __/12

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:

2/3 and 8/12

Now, the fractions are equivalent.

---

4/4 and __/8

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 2:

4/4 and 8/8

Now, the fractions are equivalent.

Answer:

3x²

Step-by-step explanation:

3x²

They would all reduce to 1, 2x^4, and -4x

We are given:

Horizontal distance of the point of observation from the building = 2 miles

Angle of elevation of the building = 5 degrees

Finding the height of the Building:

Let the height of the building be x miles

In the given case, the following right-angled triangle will be formed

We know that:  Tan(θ) = Opposite / Adjacent

So, Tan(5°) = x / 2

0.0875 = x/2                                   [since Tan(5°) = 0.0875 ]

x = 0.175                                         [Multiplying both sides by 2]

Height in Meters:

We know that 1 mile = 1609.344 meters

So, we can say that:

1609.344 meters / 1 mile  =  1

Multiplying the height of the building by 1

0.175 miles * 1

since 1 = 1609.344 meters / 1 mile:

0.175*1609.344 meters

\(0.175 miles * \frac{1609.344 meters}{1 mile}\)

Here, the 'miles' in the numerator and the denominator will cancel out

281.6 meters

Hence, the height of the Building is 281.6 m OR 0.175 miles

Answer:

by the way u typed in your answer I got -15n-12

Step-by-step explanation:

let me know If it is written another way

Answer:

its b

Step-by-step explanation:

Answer:

The correct answer is a.

Step-by-step explanation:

The sequence is: 2 3 E 4 5 I 6 8 We can notice that there are numbers and letters alternating in the sequence. The numbers are increasing, and the letters seem to be vowels in alphabetical order. So, the next value should be a letter (vowel) after I, which is O. The correct answer is a.

Explanation

We are asked to find the mean of the following numbers

Mean simply means to find the average

In our case, we have 15,9,12,5,15,12,4,8

So the total number will be: 8

The length of AE¯¯¯¯¯ is 5√2 cm.

Since quadrilateral ABCD is a square, all four sides are congruent. Let's denote the length of one side as s. Therefore, the length of BD¯¯¯¯¯ is equal to s.

Given that the length of BD¯¯¯¯¯ is 10 cm, we can conclude that s = 10 cm.

Now, we need to find the length of AE¯¯¯¯¯. Looking at the square, AE¯¯¯¯¯ is the diagonal connecting opposite corners.

In a square, the diagonal divides the square into two congruent right triangles. We can use the Pythagorean theorem to find the length of the diagonal.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the diagonal (the hypotenuse) is the same as the side length, s.

Applying the Pythagorean theorem:

s^2 = AE¯¯¯¯¯^2 + AE¯¯¯¯¯^2

10^2 = AE¯¯¯¯¯^2 + AE¯¯¯¯¯^2

100 = 2 * AE¯¯¯¯¯^2

AE¯¯¯¯¯^2 = 50

Taking the square root of both sides:

AE¯¯¯¯¯ = √50

Simplifying the square root:

AE¯¯¯¯¯ = √(25 * 2) = 5√2 cm

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Answer:

$3606.44

Step-by-step explanation:

The question asks us to calculate the principal amount that needs to be invested in order to earn an interest of $6180 in 28 years at an annual interest rate of 6.12%.

To do this, we need to use the formula for simple interest:

\(\boxed{I = \frac{P \times R \times T}{100}}\),

where:

I = interest earned

P = principal invested

R = annual interest rate

T = time

By substituting the known values into the formula above and then solving for P, we can calculate the amount that James needs to invest:

\(6180 = \frac{P \times 6.12 \times 28}{100}\)

⇒ \(6180 \times 100 = P \times 171.36\)     [Multiplying both sides by 100]

⇒ \(P = \frac{6180 \times 100}{171.36}\)    [Dividing both sides of the equation by 171.36]

⇒ \(P = \bf 3606.44\)

Therefore, James needs to invest $3606.44.

Answer:

4 answer

Step-by-step explanation:

The quotient 1 / (1 + √3) is (- 1 +√3) / 2.

Option D is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

1 / (1 +√3)

Rationalize the denominator.

1 / (1 +√3) x (1 -√3) / (1 -√3)

{ a² - b² = (a + b) (a - b) ]

(1 -√3) / (1 - 3)

(1 -√3) / -2

-(1 -√3) / 2

(- 1 +√3) / 2

Thus,

The final expression is (- 1 +√3) / 2

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Answer:

the answer to the question is 4

Full question attached

Answer:

UCL for x bar chart=7.145

LCL for x bar chart=4.874

Explanation:

Please find answer attached

Answer:

40

Step-by-step explanation:

8 muffins=1 cup of flour.

8 muffins × 5 cups = 40

In 5 cups of flour 40 muffins can be made.

The unitary technique involves first determining the value of a single unit,  followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

A recipe for 24 muffins needs 3 cups of flour.

So, in cup of flour the number of muffins can be made

= 24/3

= 8 muffins

and, In 5 cups of flour the number of muffins can be made

= 8 x 5

= 40 muffins

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We will call y to the Two Below price and x to the retail price.

We know that y (Two Below price) is always $2 below x (retail price).

Then, we can write the relation as:

This will be the equation of the line relating both prices.

Answer: B. y = x-2.

Use the steps given below to evaluate the expression formed.

Decide decision variable :

X₁ = Pounds of sausage Biscuits

X₂ = Pounds of Ham biscuits

Formulate objective function:

Maximize = 0.60X₁+0.50X₂

In linear programming, optimization issues are represented and resolved using objective functions, which are linear equations of the form Z = ax + by. Here, x and y are referred to as the choice variables, and this objective function is constrained by the terms x > 0 and y > 0.

Now set up constraints:

0.010X₁ + 0.024X₂ ≤ 6

0.10X₁ ≤ 30

0.15X₂ ≤ 30

0.04X₁ + 0.04X₂ ≤ 16

X₁ X₂ = 0

Now solve the formulated problem using excel solver and following the steps as shown below:

1. Open excel and enter data as shown in table.

2. Open solver by Excel<Data tab>Solver

3. Enter constraints and objective function in the solver dialog box

4. Choose simplex option

5. Click on solve.

Hence we get the required answer.

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It would take a total of 20 days to produce the batch of pens.

Let's calculate the work done by the 3 machines for the first 8 days:

Work done by 3 machines in 8 days = (3/12) * 8 = 2 days' worth of work

The remaining work that needs to be done by all 12 machines is:

Remaining work = 1 - (2/20) = 0.9

Now, we can use the work formula to find the total number of days needed to complete the remaining work with 12 machines:

Total work = 0.9

Work done by 12 machines in one day = 12/20 = 0.6

Total number of days needed = 0.9/0.6 = 1.5

Therefore, the total number of days needed to produce the batch of pens is:

8 (days with 3 machines) + 1.5 (days with 12 machines) = 9.5 days

However, we also need to add the 10.5 days it would take for all 12 machines to complete the batch from the beginning:

10.5 + 9.5 = 20 days

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Answer:

n = 17/3

or

(infinity, 17/3]

Step-by-step explanation:

3n + 8 < 25

-8 < -8

3n < 17

3n/3 < 17/3

No more than would actually be less than or equal to. because the sum has to be under 25.

Answer: \(\frac{17}{3}\)

\(\quad \begin{bmatrix}\mathrm{Solution:}\:&\:n<\frac{17}{3}\:\\ \:\mathrm{Decimal:}&\:n<5.66666\dots \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\frac{17}{3}\right)\end{bmatrix}\)

Step-by-step explanation:

The question is an Algebra type of question. Before I learned Algebra, I usually just did as the question asked, I thought about what it meant. However, we can easily find the number "n" by following it in Algebraic terms.

Step 1: Set up an equation

"the sum of three times a number n and 8 is no more than 25"

Three times a number, "n"

\(3n\)

The sum means addition, so;

\(3n\:+\)

And 8. Combine;

\(3n+8\)

No more than 25, which means that both of them combined would still not result in something greater than 25, so it is less than 25.

\(3n+8<25\)

The Equation to solving the problem is \(3n+8<25\). Now we just have to solve it.

Step 2: Solve the equation

\(3n+8<25\\:\:\:\:\:-8\:\:\:-8\)

Plus 8 minus 8 cancels out. So we are left with 25-8 = 17.

\(3n<17\)

\(\frac{3n}{3}<\frac{17}{3}\\\\n<\frac{17}{3}\)

Answer:

\(21.7 x 10^5\)

Step-by-step explanation:

(6.2 x 10²) x (3.5 x 10³)

First, multiply the coefficients: 6.2 x 3.5 = 21.7.

Then, add the exponents: 10² x 10³ = 10^(2+3) = 10^5.

Therefore, the result is 21.7 x 10^5.

Answer:

3286000

Step-by-step explanation:

Answer:

415 miles

Step-by-step explanation:

Start with the speed equation:

speed = distance/time

Now solve the speed equation for distance:

distance = speed × time

Apply the speed equation solved for distance to the two parts of the trip.

4 hours at 55 mph:

distance = 55 mph × 4 hours = 220 miles

3 hours at 65 mph:

distance = 65 mph × 3 hours = 195 miles

Add the two distances to find the total distance:

total distance = 220 miles + 195 miles = 415 miles

Answer: 415 miles

Answer:

415 miles

Step-by-step explanation:

Simon drove 55 miles per hour for 4 hours then 65 miles per hour for 3 hours.

How far did he drive?

d=rt

For the first part of the trip:

d = 55 * 4 = 220 miles

For the second part of the trip:

d = 65*3 =195 miles

Add the miles together

220+195 = 415 miles

Answer:

Step-by-step explanation:

To add the amounts of paint used, we need to have a common unit of measurement. One way to do this is to express both amounts in terms of a fraction of a gallon. Let's start by expressing 1 gallon as a fraction of a gallon using fraction strips.

We can use a fraction strip with 8 equal parts to represent 1 gallon, so each part represents 1/8 of a gallon.

 1 gallon = 8/8

 |-------|

 1/8     1/8

Now let's express the amount of tan paint Lindsey used in terms of this fraction. Since she used 1 gallon, which is the same as 8/8 of a gallon, we can represent this amount on the fraction strip as follows:

 1 gallon = 8/8

 |-------|

 8/8     0/8

Next, let's express the amount of green paint Lindsey used in terms of this same fraction. She used 43 gallons, so we can represent this amount on the fraction strip as follows:

 43 gallons = 344/8

 |----------------|

 8/8     8/8   ... 8/8  (43 times)

To add these two amounts, we can simply combine the fraction strips by stacking them on top of each other.

 1 gallon = 8/8

 |-------|

 8/8     0/8

 43 gallons = 344/8

 |----------------|

 8/8     8/8   ... 8/8  (43 times)

 Total = 352/8

       = 44

So Lindsey used a total of 44 gallons of paint.