31. Across a horizontal distance of 20 feet, a roller coaster has a steep drop. The height of the roller coaster at the bottom of the drop is-100 feet, compared to its height at the top of the drop. What is the average amount that the roller coasters height drops over each horizontal foot?

Answer:sales tax rate would be 0.1

using the formula

Sales tax rate = Sales tax percent / 100

For the given matrix the additive inverse property is shown.

What is additive inverse of matrix?

The matrix that is created by changing the sign of each matrix element is known as the additive inverse. -(-A)=A is the notation for the additive inverse of the matrix A.

Rows and columns serve as a measure of a matrix's dimensions. Given that it has three rows and three columns, for instance, the matrix below has a dimension of 3 x 3. Three by three can be read off as the matrix's dimension. We consequently obtain the additive inverse of the matrix

M = - M.

Consider the given matrix,

[tex]\left[\begin{array}{ccc}-6&15&-2\\9&0&-3\end{array}\right] + \left[\begin{array}{ccc}6&-15&2\\-9&0&3\end{array}\right] = \left[\begin{array}{ccc}0&0&0\\0&0&0\end{array}\right][/tex]

Here each element in first matrix is negative of the element of second matrix.

That is each element is inverse of the element in second matrix.

And the addition of elements is 0.

Hence, for the given matrix the additive inverse property is shown.

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When the costs of the two plans are equal, plan A will cost $37.81, whereas plan B will cost $25.65.

To find the number of calls at which the two plans cost the same, we need to set the costs equal to each other and solve for the number of minutes. The cost of plan A is $19 + $0.11 per minute, and the cost of plan B is $0.15 per minute. Setting these equal to each other, we get:

$19 + $0.11 per minute = $0.15 per minute

We can then solve for the number of minutes by dividing both sides by the per-minute cost:

$19 / $0.11 per minute = $0.15 per minute / $0.11 per minute

This simplifies to:

171 minutes = 135 minutes

Therefore, the two plans cost the same at 171 minutes of calling.

To find the cost at this point, we can substitute 171 minutes back into either of the original cost equations:

Plan A: $19 + $0.11 per minute × 171 minutes = $19 + $18.81 = $37.81

Plan B: $0.15 per minute × 171 minutes = $25.65

Thus, the cost when the two plans cost the same is $37.81 for plan A and $25.65 for plan B.

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Answer:

C is the answer

Step-by-step explanation:

Stem and leaf plots were also confusing to me at first, but once you understand they are actually easy!

Look at the first column where it says 2,3,4,5 and 6. Those are the tens place. The columns next to it with 2,3,8,9,etc are the ones place. For example, the first column has two, so we know that the number has a two in the tens place.

2_

Look at the numbers next to it, there's 2,3, and 8.

Since there's 3 numbers, that means that there are three numbers that have a two in the ones place. 2,3 and 8 are the numbers that go in the ones place.

So in the graph there is 22,23 and 28.

If you look at your choices, you can find all of them except 38, since on the row with the 3, next to it is the number 9 and not the number 8.

Step-by-step explanation:

[tex] - \frac{x}{2} - 1 = (y - 3) {}^{2} [/tex]

[tex] - 0.5(x + 2) = (y - 3) {}^{2} [/tex]

A parabola with a vertex (-2,3)

The set of scale factors that would produce a contraction under a dilation of the original image are:

B. -0.5

C. 0.5

A scale factor can be defined as the ratio of two corresponding length of sides or diameter in two similar geometric figures such as equilateral triangles, quadrilaterals, and other types of polygons.

In Mathematics, the following rules are applied to interpret and understand the dilation of a geometric figure:

For a contraction under a dilation of the original image, the scale factor (k) must either be negative or less than one (1). Therefore, the required values are -0.5 and 0.5 respectively.

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The rate of change of the function that is defined by the table:

X: 2 4 6 8 10

Y: 4 8 12 16 20

is r = 2

For a function with two known points (x₁, y₁) and (x₂, y₂), the rate of change between these two points is written as:

r = ( y₂ - y₁)/(x₂ - x₁)

Here we have the table that defines a function:

X: 2 4 6 8 10

Y: 4 8 12 16 20

Here we can use any pair of two points on the table, for example, if we use the first pair and last pair:

(2, 4) and (10, 20)

The rate is:

r = (20 - 4)/(10 - 2) = 16/8 = 2

If we use the first two pairs (2, 4) and (4, 8) we get:

r = (8 - 4)/(4 - 2) = 4/2 = 2

So the rate of change of the function is r = 2.

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Value of composite function (f∘g)(1) and (g∘f)(1) are 2 , 5 respectively.

What is composite function?

Function composition is associate operation ∘ that takes 2 performs f and g, and produces a perform h = g ∘ f such h(x) = g. during this operation, the perform g is applied to the results of applying the perform f to x

Main body:

according to question;

f(x) = 2x³

g(x) = 3x³ -2

we need to find composite function:

f o g (x) = 2(3x³-2)

{to find composite function , we replace one function as value of x in another}

f o g(x) = 6x³ -4

           = 6x³ -4

f o g(1) = 6*1 -

          = 2

g o f(x) = 3(2x³)-2

g o f(x) = 6x³ -2

           = 6x -2

g o f(1) = 6*1 -2

           = 5

Hence value of (f∘g)(1) and (g∘f)(1) are 2 , 5 respectively.

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The probability that a resident own a cat or a dog is 48%

From the question, we have the following parameters that can be used in our computation:

P(Own a cat) = 70%

P(Own a dog) = 59%

P(Own a cat and a dog) = 42%

The probability a resident own a cat or a dog is then calculated as

Probability a resident own a cat or a dog = P(Own a cat) + P(Own a dog) - P(Own a cat and a dog)  

Substitute the known values in the above equation, so, we have the following representation

Probability a resident own a cat or a dog = 70% + 59% - 42%

Evaluate the sum and the difference

Probability a resident own a cat or a dog = 48%

Hence, the probability is 48%

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Complete question

59% of all the town's residents own a dog and 70% own a cat. Of the dog owners 42% also own a cat. If a town resident is chosen at random find:

the probability a resident own a cat or a dog

(round to 4 decimal places where possible)

The ratio shows how many times one value is contained in another value.

The number of top dogs is 192.

The ratio shows how many times one value is contained in another value.

Example:

There are 3 apples and 2 oranges in a basket.

The ratio of apples to oranges is 3:2 or 3/2.

We have,

The ratio of top dogs to fat cats was 24 to 19.

if they were 152 fat cats.

This means,

Number of top dogs = 24x

Number of fat cats = 19x

Now,

Number of fat cats = 152

This means,

152 = 19x

x = 8

Now,

Number of top dogs = 24x

= 24x

= 24 x 8

= 192

Thus,

The number of top dogs is 192.

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By using the concept of unitary method, it can be calculated that

a) For 350 blocks of cement, [tex]8\frac{3}{4}[/tex] bags of mortar are required

b) For 50 blocks of cement, [tex]1\frac{1}{4}[/tex] bags of mortar are required

What is unitary method?

Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity

Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.

Here, unitary method will be used

The double number line has been shown below-

a) For 100 blocks of cement, [tex]2\frac{1}{2}[/tex] bags of mortar are required

   For 1 block of cement, [tex]\frac{5}{2} \times \frac{1}{100}[/tex] bags of mortar are required

   For 350 blocks of cement, [tex]\frac{5}{2} \times \frac{1}{100} \times 350[/tex] bags of mortar are required

   For 350 blocks of cement, [tex]\frac{35}{4}[/tex] bags of mortar are required

   For 350 blocks of cement, [tex]8\frac{3}{4}[/tex] bags of mortar are required

b)  For 100 blocks of cement, [tex]2\frac{1}{2}[/tex] bags of mortar are required

   For 1 block of cement, [tex]\frac{5}{2} \times \frac{1}{100}[/tex] bags of mortar are required

   For 50 blocks of cement, [tex]\frac{5}{2} \times \frac{1}{100} \times 50[/tex] bags of mortar are required

   For 50 blocks of cement, [tex]\frac{5}{4}[/tex] bags of mortar are required

   For 50 blocks of cement, [tex]1\frac{1}{4}[/tex] bags of mortar are required

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Answer:

-5

Step-by-step explanation:

The rate of change, also known as slope, would be -5.

Slope can be found with two points and the formula y minus y divided by x minus x or the change of y divided by the change in x.

To identify the slope on the equation is easy since this is slope-intercept form.

y=mx+b

where m is the slope

m in this case is -5, so -5 is your answer

The value of p pennies, n nickels and twice as many quarters as pennies is (51p + 5n) cents or  $(51p + 5n)/100.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Expressions have the following structure: (Number/variable, Math Operator, Number/variable).

Given that you have p number of coins of pennies, n number of coins of nickels and  twice as many quarters as pennies.

Thus the number of coins of quarters is 2p.

The value of penny, nickel, and quarter are

1 penny = 1 cent

1 nickel = 5 cents

1 quarter = 25 cents

The value of p number of pennies is p cents.

The value of n number of nickels is (n×5) =5n cents.

The value of 2p number of quarter is (2p × 25) = 50p cent.

The total value is p + 5n + 50p = (51p + 5n) cents

Divide 51p + 5n by 100 to convert it into dollar:

(51p + 5n) cents = $(51p + 5n)/100

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Answer: The expression a²+4b² can be factored in the following way:

a²+4b² = (a² + 2ab + 2ab + 4b²)

= (a+b)²

In general, the square of a binomial (a+b) can be written as (a+b)² = a² + 2ab + b². This is known as the "square of a sum" formula. In this case, we can apply this formula to the binomial a+b to obtain a² + 2ab + b² = (a+b)². We can then use the fact that the square of a binomial can be written as the square of each term plus twice the product of the two terms. This allows us to write the expression as (a+b)² = a² + 2ab + b² = a² + 2ab + 2ab + 4b² = (a² + 2ab + 2ab + 4b²) = (a²+4b²). Therefore, the fully factored form of a²+4b² is (a+b)².

1.6 seconds. The ball will hit the canopy after 1.58 seconds or -1.58 seconds. Since the time cannot be negative, the ball will hit the canopy after 1.58 seconds.

To find the time it takes for the ball to hit the canopy, we need to solve the equation h(t) = 12 for t.

The given equation for h(t) is h(t) = -16t^2 + 52, so we can substitute this into the equation h(t) = 12 to get:

12 = -16t^2 + 52

To solve this equation, we can move all the terms to one side of the equation to get:

-16t^2 + 40 = 0

We can then divide both sides of the equation by -16 to get:

t^2 - 2.5 = 0

We can then use the quadratic formula to solve for t:

t = +/- sqrt(2.5)

t = +/- 1.58

Thus, the ball will hit the canopy after 1.58 seconds or -1.58 seconds. Since the time cannot be negative, the ball will hit the canopy after 1.58 seconds.

Rounding this answer to the nearest tenth gives us 1.6 seconds, so the correct answer is 1.6 seconds.

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The probability that their mean pulse rate is less than 80 beats per minute is of:

0.7389 = 73.89%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

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

The parameters for this problem are given as follows:

[tex]\mu = 76, \sigma = 12.5, n = 4, s = \frac{12.5}{\sqrt{4}} = 6.25[/tex]

The probability that their mean pulse rate is less than 80 beats per minute is the p-value of Z when X = 80, hence:

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

By the Central Limit Theorem:

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

Z = (80 - 76)/6.25

Z = 0.64

Z = 0.64 has a p-value of 0.7389.

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Answer:

0,02

Step-by-step explanation:

i got it correct

We know that we need to sell out 53 candles to break even using mathematical operations.

The process of calculating a value using operands and a math operator is known as a mathematical "operation."

The provided operands or integers must follow certain established rules that are associated with the math operator's symbol.

PEMDAS stands for Parentheses, Exponents, Multiplication, Division, and Addition Subtraction (from left to right).

So, the total expense of the shop:

$100 + $32.50 = $132.50

No, the candle costs $2.50.

The selling price of a candle is $5.

Profit in each candle is: 5 - 2.50 = $2.50

A number of candles that we need to sell to break even are:

132.50/2.50

53

Therefore, we know that we need to sell out 53 candles to break even using mathematical operations.

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The mowing takes hours hence, the best rate is hours per lawn. Hence the correct option is option 1. It can be solved by rate of work.

The rate lawns per employee gives the lawns mowed by one employee.

The rate hours per lawn gives the number of hours required to mow one lawn.

The rate employee per lawn gives how many employees are required to mow one lawn.

The rate lawns per day gives the number of lawn mow in one day.

Since the mowing takes hours hence, the best rate is hours per lawn. Hence the correct option is option 1.

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Answer:

11/9

Step-by-step explanation:

If this is an addition question then this is your answer.

Answer:

8a + 3a^2 + 8

Answer:

it will take rahim 16 months

Step-by-step explanation:

6:4:2

3000÷12=250

1500:1000:500

20% 100

100×16=1600

The rate of change of the modelled equation is 3.5 and the initial value is 5.

Linear equation can be represented in different form such as slope intercept form, point slope form, general form and standard form.

Equation in slope intercept form is as follows:

y = mx + b

where

Therefore, Shirley has already jogged 5 miles. She continues to jog at an average rate of 3.5 miles per hour. This situation is modelled by the function y = 3.5x + 5 where y is the total miles jogged and x is the number of hours.

The equation is modelled in slope intercept form.

Therefore,

rate of change = 3.5

initial value  = 5

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Answer:

9.22 minutes

Step-by-step explanation:

You could use the form y=mx + b to find this equation

y will represent the total liters

x will represent the total number of minutes

b will represent the initial number of liters in the beginning

1. Plug 194 in for y, plug 9 in for m, put 111 in place of b

The equation should look be:  [tex]194 = 9x + 111[/tex]

2. Solve the equation

3. Subtract 111 on both sides. The equation would now be:  [tex]83 = 9x[/tex]

4. Divide both sides by 9 (to get x by itself). [tex]\frac{83}{9} = 9.22222222[/tex]

5. Round to the nearest hundredth place to get 9. 22 minutes

The area under the graph using the first two and then four rectangles = 0.221 unit square

According to the graphs given in the below figure,

Given in the question,

f(x) = [tex]x^{3}[/tex] when x = 0 and x = 1

The first rectangle of the first graph goes from 0 to 0 .6,

Width = 0.6

Height measured from the middle point = 0.3

f( 0.3) = [tex]( 0.3)^{3}[/tex]

f(0.3) = 0.027 units.

Area of first rectangle = 0.6 x 0.027 = 0.0162 unit square

Now taking the second rectangle of the first part,

It is going from 0.6 to 1.0,

Width = 0.4 units

height = 0.8 units

Height measured from the middle-

f(0.8) = [tex](0.8)^{3}[/tex] = 0.512

Area of the second part of the rectangle = 0.512 x 0.4

= 0.2048 unit square

Final area = 0.2048 + 0.0162 = 0.221 square units

Therefore, the same could be done with the second part rectangle of 4

For the given first part of four rectangles = width = 0.6 units and height = 0.1 unit

so f(0.1) = [tex]0.1^{3}[/tex]

= 0.001 units

Therefore, the area under the graph using the first two and then four rectangles = 0.221 unit square

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Answer:

0.39, 0.388, 38.38%, 3/8

Step-by-step explanation:

The probability that the sample's Republican percentage will be higher than 44% is 0.089.

Probability is a metric used to express the possibility or chance that a particular event will occur.

Probabilities can be expressed as fractions from 0 to 1, as well as percentages from 0% to 100%.

To determine the probability of a sample proportion, the normal probability is used as the z-test statistic of one sample proportion.

When the sample size is big, the z-test statistic, a normal test statistic, is employed.

So, the probability will be:

We know that the sample size is n = 488 and the proportion is p = 0.41.

Now, obtain P(p > 0.44) as follows:

[tex]\begin{aligned}& P(\hat{p} > 0.44)=1-P\left(\frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}} \leq \frac{0.44-p}{\sqrt{\frac{p(1-p)}{n}}}\right) \\& P(\hat{p} > 0.44)=1-P\left(Z \leq \frac{0.44-0.41}{\sqrt{\frac{0.41(1-0.41)}{488}}}\right) \\& P(\hat{p} > 0.44)=1-P(Z \leq 1.347)\end{aligned}[/tex]

Excel function for the p-value:

P(p > 0.44) = 1 - 0.911

P(p > 0.44) = 0.089

Therefore, the probability that the sample's Republican percentage will be higher than 44% is 0.089.

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Answer:

slope of line q = [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

calculate the slope of line p using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (8, 7 ) and (x₂, y₂ ) = (4, 4 )

m = [tex]\frac{4-7}{4-8}[/tex] = [tex]\frac{-3}{-4}[/tex] = [tex]\frac{3}{4}[/tex]

• Parallel lines have equal slopes

then slope of line q = [tex]\frac{3}{4}[/tex]