Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval ≤ x ≤ 9.

Answer:

A

Step-by-step explanation:

There are two inputs for one output, which means the relation is not a function.

Answer:

A

Step-by-step explanation:

The melting point of element C is 41 degrees C

The question states "The melting point of a certain element is -5 times the melting point of the element C."

Multiply the melting point of Element C by -5 to get the melting point of the certain element

-5 * 41

Solution

-205

The five credit score tiers are listed in ascending order, starting with the lowest tier:

Deep Subprime < Subprime < near prime < prime < superprime

The ability of a consumer to get credit may be significantly influenced by their credit score. These interactive graphs demonstrate how lending behavior has changed for different credit score profiles of borrowers.

We concentrate on the following five commercially available credit score levels:

Subprime's credit scores is between 580 to 619.

Prime's credit score level is between 660 to 719.

The credit score level of deep subprime is below 580.

The credit score level of near prime is 620 - 659.

The credit score level of superprime is 720 or above.

Therefore, the five tires of credit scores from lowest to highest are:

Deep Subprime < Subprime < near prime < prime < superprime

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Answer:

The graph will have two lines which will never intersect

In probability , there are two events independent events and dependent events.

Independent Events :

Two events A and B are said to be independent if the fact that one event has occurred does not affect the probability that the other event will occur.

Example

. Choosing a marble from a jar AND landing on heads after tossing a coin.

Dependent Events :

If whether or not one event occurs does affect the probability that the other event will occur, then the two events are said to be dependent.

Example

Buying ten lottery tickets and winning the lottery.

The number of ways that the planning committee can be formed if there are 3 members from each group is 6545 ways.

Combinations are also referred to as selections. Combinations imply the selection of things from a given set of things. In this case, we intend to select the objects. This can be illustrated by ⁿCr

The combination formula is illustrated thus:

ⁿCr = n! / ((n – r)! r!)

n = the number of items.

r = how many items are taken at a time

The number of people will be:

= 10 + 16 + 9

= 35

The number of ways will be:

= ³⁵C₃

= 35! / (35 - 3)! 3!

= 35! / 32! 3!

= 35 × 34 × 33 / 3 × 2

= 6545 ways

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6545 ways can a planning committee be formed if there are 3 members from each group.

Combination is a way of selecting items from a collection where the order of selection does not matter.

The formula for combination is ⁿCr = n! / ((n – r)! r!)

Where n is total number of objects and r is number of objects we have to choose.

The committee has 10 administrators, 16 faculty members, and 9 staff members.

The total number of persons

10+16+9

35

Now we need to select 3 persons from 35 persons

n=35 and r=3

³⁵C3 = 35! / ((35 – 3)! 3!)

=35! / ((32)! 3!)

=35×34×33×32! / (32! 3!)

=35×34×33 /6

=6545 ways

Hence in 6545 ways can a planning committee be formed if there are 3 members from each group.

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We are given a rhombus shape.

The measure of angle ∠1 = 160°

Recall that in a rhombus, the oppsite angles are equal, this means ∠1 = ∠2

So, ∠2 = 160°

Recall that the sum of all four interior angles in a rhombus must be equal to 360°

The diagonal line divides the angles in half.

This means that angle 3 and angle x are equal.

Since we know that ∠3 and ∠x are equal then

∠3 = 10° and ∠x = 10°

Therefore,

∠2 = 160°

∠3 = 10°

Answer: ask ten students wearing football jerseys each day for a week

This sample wouldn't b representative because, the use of a footblla

In a right triangle, given an angle, the ratio between the opposite side of this angle by the hypotenuse is equal to the sine of the angle. Using this relation in our triangle, we have

ANSWER:

STEP-BY-STEP EXPLANATION:

We can determine the domain and range of the function, knowing that the domain is the interval of values in x and the range is the interval of values in y.

Therefore:

When a function is inverted, the domain and range are inverted, therefore:

Which means that the inverted function goes from -5 to 25/17 in x and from -5 to 5 in y.

In addition to this we must take into account that when the inverse function is done, in most cases a reflection is made in y = x.

The only graph that meets all of the above is graph A

For the cicle with intersecting chords the relation between the length of segments of chords is,

Substitute the values in the equation and solve for x.

So value of x is 4.

The equation for the length of chord KZ is,

Substitute the value of x in equation to determine the length of KZ.

So answer is 12.

Given that Tom invested $4500 in an investment paying 10% compounded quarterly for 3 years.

We have to find the interest for the given time period.

We know that the formula of amount on a principal P, rate r per annum, time t years where interest is compounding quarterly is:

Here, P = 4500, r = 0.1 and t = 3. So,

So, the amount we get is $6051.6.

Now, it is known that the interest is the difference between the amount and the principal. So,

Thus, the interest is $1551.6.

We know that

• The volume of one ball is 221 cubic centimeters.

Since the ball is spherical, we can find its radius with the following formula.

The diameter would be double than the radius, by definition.

Since there are three balls in the cylinder, the height would be

Now, we find the volume of the cylindrical package.

we have the system

-7y=-34-2x ------> equation A

2x+4y=10​ ------> equation B

In the equation A

Multiply by -1

-2x+7y=34------> new equation A

Adds new equation A and equation B

-2x+7y=34

2x+4y=10

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

7y+4y=34+10

11y=44

y=4

Find the value of x

Substitute the value of y in equation A or equation B

2x+4(4)=10​

solve for x

2x+16=10

2x=10-16

2x=-6

x=-3

therefore

Answer:

32

Step-by-step explanation:

Solution

If the total amount of hand lotion is available, then you have 128 ounces of hand lotion.

If 128 oz is put into a number of smaller containers (each one 4 oz) then you have

128/4 containers.

128 / 4 = 32.

You can make 32 containers each one holding 4 ounces. The question uses division to solve.

We have the following information:'

We want to calculate the following probability:

then, using the information that we are given, we havE:

since:

we have the following:

therefore, the probability of selecting a score greater than 44 is 15.87%

We have to use the formula of the slope

Where,

Replacing all these values, we have

Now, we solve for m

Given the following systems of linear equations,

6x + 20y = -62 (Equation 1)

3x - 9y = -12 (Equation 2)

Step 1 : Solve 6x+20y=−62 for x:

6x + 20y + (−20y) = −62 + (−20y) (Add -20y to both sides)

6x = −20y −62

6x/6 = (−20y −62)/6 (Divide both sides by 6)

x = (-10y/3) + (-31/3)

Substitute to Equation 2:

3x−9y=−12

3[(-10y/3) + (-31/3)] - 9y = -12

−19y−31=−12 (Simplify both sides of the equation)

−19y−31+31=−12+31 (Add 31 to both sides)

−19y=19

-19y/-19 = 19/-19 (Divide both sides by -19)

y= −1

Step 2: Substitute −1 for y in x =(-10y/3) + (-31/3)

x =(-10(-1)/3) + (-31/3)

x = -7

Answer:

x=−7 and y=−1

To solve the system by substitution, isolate one variable from one equation and substitute the expression obtained for that variable into the other equation.

Isolate x from the first equation:

Substitute x=y-2 into the second equation:

Solve for y:

Substitute y=4 into the expression of x to find its value:

Therefore, the solution to the given system is:

The length of rectangle is : 6ft .

Width of rectangle is : 5.5ft .

The area of rectangle is :

A = l × w

Here given,

length is 5ft less than twice the width,

So the equation can be represented in terms of length as,

l = 2w - 5

Given area = 33sqft

By substituting value of length,

33 = (2w - 5) × w

By applying distributive property,

33 = 2w² - 5w

= 2w² - 5w - 33

By factoring the equation:

(2w - 11)(w + 3) = 0

To find value of zeros,

2w - 11 = 0

2w = 11

w = 5.5

Similarly,

w + 3 = 0

w = -3

Since width cannot be negative , the width will be:

the width = 5.5 ft.

Also find length by substituting value of width in equation,

33 = 5.5l

33/5.5 = l

l = 6 ft.

∴ The  length = 6ft, and width = 5.5ft.

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The explicit and recursive equations of the sequence 2, 12, 72, 432 are f(n) = 2 · 6ⁿ⁻¹ and f(n) = 6 · f(n - 1).

In this problem we find an example of a geometric progression, whose explicit and recursive forms are defined below:

Explicit form

f(n) = a · rⁿ⁻¹

Recursive form

f(1) = 2, f(n) = r · f(n - 1)

Where:

If we know that a = 2 and r = 6, then we find the explicit and recursive equations below:

Explicit form

f(n) = 2 · 6ⁿ⁻¹

Recursive form

f(n) = 6 · f(n - 1)

The first four elements of the sequence are 2, 12, 72, 432.

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The Pythagoras rule states that the square hypotenuse is equal to the sum of the squares of the other two sides

In this case, we are given both sides' measures and are asked about the hypotenuse. We leave the hypotenuse on the left side alone by applying the square root on both sides

L = √64+36

L= √100

L = 10

The answer is yes, the equation represents a proportional relationship.

The reason is that a proportional relationship is best described as that in which the value of one variable depends on what happens to the other variable. Just like having one more child every year would mean spending more money on education, etc.

In a proportiona; relationship as shown in this question, y is the total cost of a pizza and each x (each topping) would determine how much is y. So requesting for 5 more toppings would result in 1.5 multiplied by 5, and requesting 10 more would result in 1.5 multiplied by 10. So as the amount of toppings (x variable) increases, the total cost (y variable) likewise would increase.

As x increases or decreases, the value of y would likewise increase or decrease. That makes this equation a proportional relationship

We have to convert the number into scientific notation.

The number is 0.00098.

We start by expressing it as a fraction.

If we divide it by 10, we can express it as:

Dividing by 10 is not enough. In the same way, we have to look a numerator that is multiple of 10 that gives us a numerator that is 9.8.

We would get:

Now we have the numerator we need.

We now express the denominator 10,000 as a power of 10 and we get the number in scientific notation as:

Answer: 0.00098 = 9.8 * 10^(-5)

Using the DuPont analysis the return on equity is 5.46%.

Return on equity is the ratio of net income to average total equity. Return on equity is an example of a profitability ratio. Profitability ratios measure the ability of a firm to generate profits using available resources.

Return on equity = net income / average total equity

Using the Dupont formula, return on equity can be determined using:

Return on equity = total margin x asset turnover x equity multiplier

Return on equity = (Net income / Sales) x (Sales/Total Assets) x (total asset / common equity)

3.9% x 0.5 x 2.8 = 5.46%

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The median is the value of the data set that separates the sample in halves.

To determine the median of a determined data set, you have to calculate its position.

The given sample has n=7 elements, to determine the position of the median given that the data set is odd, you have to use the following formula:

Replace it with n=7

This result indicates that the media is the fourth observation of the data set.

Next, you have to order the data set from least to greatest:

Original data set: 4, 7, 9, 10, 5, 12, 6​

Ordered from least to greatest: 4, 5, 6, 7, 9, 10, 12

Once the data set is ordered, you have to count starting from the left until you reach the fourth observation:

O4, 5, 6, 7, 9, 10, 1

The fourth value of the data set is 7, which means that the median of the data set is 7.

Median=7

2

Since this situation can be represented by a right triangle, we can use the pythagorean theorem. Doing so, we have: