The function c (x) = .5x + 70 represent the cost c(in dollars) of renting a truck from a moving company where x is the number of miles you drive the truck

Remember that

the area of a triangle is equal to

we have

A=10.98 ft2

h=3.6 ft

substitute the given values

answer is 6.1 ft

In this problem we have a normal distribution with:

• μ = mean = 100,

• σ = standard deviation = 15.

(a) The z-score for a value x = 124 is:

(b) We must compute the probability that x is greater than 124, which is equivalent to the probability of having z greater than 1.6. Using a table of z-score, we find that:

Answer

• (a), z = 1.6

• (b), P(x > 124) = 0.0548

From the bar graph, we have:

Sales in first quarter (Jan - Mar) = $155,000

Sales in second quarter(Apr to JUn) = $232,500

Sales in third quarter (Jul to Sep) = $135,000

Sales in fourth quarter (Oct to Dec) = $160,000

Let's find the percent increase in sales from the first to second quarter.

To find the percent increase from first to second quarter, apply the formula:

Thus, we have:

Therefore, the percent increase from first to second quarter is 50 percent.

ANSWER:

50%

For the first solution, the error is adding 1 to 3 to get 4 instead of subtracting 1 from 3 to get 2.

It should have been

I-4x + 1I > 3

- 4x + 1 > 3

- 4x > 3 - 1

- 4x > 2

x < - 2/4

x < - 1/2

For the second solution, the error was omitting the negative sign in the final answer. It should have been

-4x + 1 > - 3

- 4x > 2

x < -1/2





Let

L ----> the length

W ----> the width

The perimeter is equal to

P=2(L+W)

we have that

P=30 m ----> given

L=1.6W ---> given

substitute in the formula of perimeter

30=2(1.6W+W)

solve for W

15=2.6W

W=5.77 m

L=1.6*5.77

L=9.23 m

therefore

the dimensions are

The slope of the line that passes through the points (x1, y1) and (x2, y2) is computed as follows:

The slope of the line that passes through (-4, -11) and (3, 3) is:

The slope of the line that passes through (5, -2) and (6, -9) is

Yes, lines m and n intersect because their slopes are different

3/4

First box:

number of pencils = 1

number of pens = 3

Probability of picking pen in the first box = number of pens /total number in the box

Total = 1 + 3 = 4

probability of picking pen in the 1st box = 3/4

2nd box:

number of color pencils = 2

number of crayons = 6

Total = 2 + 6 = 8

Probability of picking crayons in the 2nd box = number of crayons/total number in the box

Probability of picking crayons in the 2nd box = 6/8 = 3/4

Probability of picking a pen from the first box and a crayon from the second box = probability of picking pen in the 1st box × Probability of picking crayons in the 2nd box

Probability of picking a pen from the first box and a crayon from the second box = 3/4 × 3/4

Probability of picking a pen from the first box and a crayon from the second box = 9/16

We find the missing number as follows:

If we have that "blank" has a value of 14, then the equation would not make sense and therefore has no solutions.

To determine the distinguishable permutations of the given word, here are the steps.

1. Count the number of letters in the given word. In the word EFFECTIVE, there are 9 letters.

2. Calculate 9!.

3. Determine what are the letters found in the word effective and count how many times the letter occurred.

Letter E - 3 times

Letter F - 2 times

Letter C - 1 time

Letter T - 1 time

Letter I - 1 time

Letter V - 1 time

4. Get the product of the factorial of the letters that occurred more than once.

5. Divide the result of step 2 by the result of step 4.

Therefore, there are 30,240 different permutations of the word EFFECTIVE.

with the same base if we multiplicate this expression we sum the exponents

the result will be

the result is 9^13 the last option

1) Let's draw that to better understand this

The Bisector Theorem states that the angle bisected is equally divided

since the angle TRB = 86º . Besides that the m TR

To determine whether it does bisect let's set an equation in which x +27 = the half of 86º

x+27 =43

x=16

3x -5 =43

3x =48

x=16

So, RI bisects the angle TRB, for each angle is half of the measure of TRB.

To find the volume of water in the pool, we would find the area of the pool's surface and multiply it by the depth of the pool. The area of the pool's surface would be determined by the formula,

Area = pi x radius^2

From the information given,

diameter = 5

recall,

radius = diameter/2

Thus,

radius = 5/2 = 2.5

depth = 6 inches

We would convert from inches to feet

Recall,

12 inches = 1 foot

6 inches = 6/12 = 0.5 foot

Thus, depth = 0.5

pi = 3.14

Thus,

Area = 3.14 x 2.5^2 = 19.625

Volume = 19.625 x 0.5 = 9.8125

Volume of water in pool is 9.8 cubic feet to 1 decimal place

The expression :

gives the number of pages Eliza read in those three days. If r=357, then we have that:

She read 204 pages on those days. Therefore, the answer is B.

Answer:

• Domain: {-2, 1, 4}

• Range: (-4, 0}

Explanation:

The points on the graph of relation H are:

Domain of H

The domain of H is the set of all te xvalues of the relation.

Range of H

The range of H is the set of all the y-values of the relation.

Recall that the formula for determining the area of a parallelogram is

Given that the height is 0.4 yards, and the area is 8.2 square yards. Substitute the following values and we get

Therefore, the base of the parallelogram is equal to 20.5 yards.

Solution

Given the following:

when x is greater than 2

when y is less than 5

Therefore the best option is when x = 3 and y = 2

it is correct because 8 is greater than 6

Therefore the best option is (3, 2)

Hence the correct answer is Option C

For the given question, we will write the rules of the sign when multiplying or dividing the integers:

The same rules are correct when replacing the product sign with the divided sign

We want to find where x and y are equal in both equations.

First step: replacing the x value given by the second equation in the first

3x + 4y = 8

x = 16 - 4y​

↓

3(16 - 4y​) + 4y = 8

Distributing the parenthesis:

3 · 16 - 3 · 4y + 4y = 8

48 - 12y + 4y = 8

48 - 8y = 8

Rearranging the equation:

48 - 8y = 8

48 - 8 = 8y

40 = 8y

40/8 = y

5 = y

Second step: replacing the 5 = y value in one of the equations

We replace it in the second equation:

x = 16 - 4y​

x = 16 - 4 · 5

x = 16 - 20

x = -4

To answer this question, we have the next statement:

And

Then

This property can also be represented as follows, and has the following structure:

If a = b and b = c, then a = c

Using an analogy, we can say that:

• a = AB

• b = CD + EF

• c = GH

And we end up with the same statement written above:

• AB = CD + EF and CD + EF = GH, then AB = GH

This property is called the Transitive Property of Equality.

In summary, the answer to this question is option D: Transitive Property of Equality.

[The other options do not correspond to this answer.]

The value of the expression is;

Here, we want to make a fraction subtraction

To do this, we will have to convert the mixed fraction to improper fraction and then proceed to subtract

To make the fraction improper, we multiply the denominator by the stand-alone number and add the numerator;

so we have;

B ) S ={(2, 2), (4,-2)}

1) Setting the system:

y + 2 = (x-4)²

And adding the 2nd Equation to the System:

y+2 = (x-4)²

2x -y - 6 =0

2) Now let's solve it by using the Addition Method:

y+2 = (x-4)²

2x -y - 6 =0 x (-1)

y+2 = (x-4)²

-2x +y + 6 =0

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

-2x +8 = (x-4)²

-2x +8 = x² -8x +16

-x²+8x -16-2x +8 =0

-x² +6x -8 =0

x² -6x +8 = 0

Factoring it we have:

(x-2)(x-4) = 0 So the solution set i

x- 2 =0

x = 2

x-4= 0

x=4

3) Plug into the first equation x = 4:

y +2 = (x-4)²

y+2 =(4-4)²

y = -2

Finally, plugging x = 2 into the same equation:

y +2 = (x-4)²

y +2 = (2 -4)²

y+2 = (-2)²

y +2 = 4

y = 4-2

y= 2

So the answer is S ={(2, 2), (4,-2)} s

0

SOLUTION

Given the information and graph on the question tab;

Given that the general cosin function is expressed as

By comparing equations 1 and 2, we have

Thus, we have

We will address different properties that are applied to integers.

Commulative property:

The commulative property states that if you change the order of integers while applying the basic mathematical operations of ( Addition and Multiplication ) the answer will remain unchanged. We will illustrate this with help of an example as follows:

We tried changing the order of real numbers used in the two basic operations. We saw that the answer of each remain unchanged if we changed the order. Hence, Commulative property.

Associative property:

Refers to grouping of real number by adding paranthesis ( ) around a set of operations in a bigger chain of operations. So the property asserts that the choice of grouping the smaller sets does not affect the final answer. We will illustrate this with help of an example as follows:

We made three combinations for selecting a smaller operations within a larger chain operation of addition. We grouped a pair of real numbers using parenthesis and resolved the parenthesis first then applied the last operation in each of the 3 cases illustrated above.

Identity property:

This property is divided into properties of addition and multiplication, where the identity is a real number ( 0 or 1 ) respectively. Both types of identity property are illustrated below as follows:

Both the identity property leaves to the same conclusion i.e any "number" added to (0) is always the " number ". Any "number" multiplied with digit ( 1 ) is the "number" itself.

Multiplication property of zero:

This property states that any real or imaginary number multiplied with ( 0 ) always results in 0. Illustrated below:

we have two sides and a known angle, then we use the following formula for area

where a = 8. b = 12 and C = 62°, so

answer: 42.4 m^2

ANSWER

EXPLANATION

Given;

To find x, we add 8.91 to both side, hence we have

Now, 8.91 will cancel out aand then we have;

Answer:

• A) 3 pounds of chocolate.

• B) 7 Pounds of nuts.

Explanation:

• Let the number of pounds of chocolate he should use = c

• Let the number of pounds of nuts he should use = n

Colin is making a total of 10-lb bag of trail mix, therefore:

• Chocolates cost $2.00 per pound and mixed nuts cost $8.00.

• Colin has a budget of $6.20 per pound of trail mix

• He needs to make 10 pounds of trail-mix.

We solve the two equations simultaneously.

Recall that c=10-n.

Therefore, Colin should use (A) 3 pounds of chocolate; and (B) 7 Pounds of nuts.

Explanation

We are required to determine the correlation coefficient (r) of the data provided. This should be calculated with the formula:

The information can be represented in a table as:

From the table, we have:

Therefore, we can calculate the correlation coefficient as:

Hence, the answer is 0.88.

An arc is the path along the circumference of a circle.

When a circle is divided into two parts unevenly, there are two arcs, the shorter one and the longer one.

In our circle, there's arc AB and ADB and the shorter path is arc AB with angle 115 degrees, option C

Given,

The height of the shape is 18 inches.

The height of cuboidal part is 11 inches.

The height of pyramid part is 18- 11 = 7 inches.

The side of the cuboidal part is 3 inches.

The base of the pyramid part is also 3 inches.

The volume of the cuboidal part is,

The volume of pyramid part is,

Here, the value of a is 3 and h is 7 then,