Which statements are correct about the average rate of change for the function given in the table? Select all correct answers. Select 2 correct answer(s) Question 3 options: The rate of change is 3 over the interval 1 ≤ x ≤ 2. The rate of change is 3 over the interval 1 ≤ x ≤ 3. The rate of change is 6 over the interval 1 ≤ x ≤ 4. The rate of change is 6 over the interval 2 ≤ x ≤ 4. The rate of change is 5 over the interval 2 ≤ x ≤ 3.

Answer:

2. $9.99

3. 45 tickets for $27

4. 20 cents

Step-by-step explanation:

2. 79.92/8 = 9.99

3. 27/45 0.6 and 15/20 = 0.75 and 60 cents is less than 75 cents

4. 6/30 = 20

Answer:

Step-by-step explanation:

79.92/8= 9.12 per cd

15/20= .75

27/45=.6 better deal because it is .60 cents per ticket

6/30= .20 per can

Answer: 3,020,000

Step-by-step explanation:

three million twenty thousand

Answer: 3,020,000

Step-by-step explanation: 3,000,000 + 20,000 = 3020000

The width and height are given to one decimal place, and we have multiplied them together, the answer should be rounded to one decimal place. Therefore, the area of the rectangle is 25.1 cm²

To calculate the area of a rectangle, we need to multiply its width by its height.

The size of a patch on a surface is determined by its area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina. Area can be interpreted as the quantity of material with a specific thickness required to create a model of the shape or as the quantity of paint required to completely cover the surface in a single coat.

Area = width x height

Substituting the given values, we get:

Area = 7.6 cm x 3.3 cm

Area = 25.08 cm²

Since the width and height are given to one decimal place, and we have multiplied them together, the answer should be rounded to one decimal place. Therefore, the area of the rectangle is 25.1 cm² (rounded to one decimal place).

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The required, we have proven that the sum of the measures of the angles in parallelogram ABCD is 360 degrees.

Given: ABCD is a parallelogram. To prove: mZA + mZB + mZC + mZD = 360 degrees

A parallelogram is a quadrilateral consisting of pairs of parallel sides.

Here,
The proof you provided is correct! Here's a step-by-step explanation of the proof:

By the definition of a parallelogram, AD // BC and AB/DC.

Using AD as a transversal, ZA and ZD are same-side interior angles, so they are supplementary (meaning their measures add up to 180 degrees).

Using side AB as a transversal, ZB and ZC are same-side interior angles, so they are supplementary as well.

By the definition of supplementary angles, mZA + mZD = 180 degrees and mZB + mZC = 180 degrees.
Adding the two equations together, we get:

mZA + mZD + mZB + mZC = 180 degrees + 180 degrees

Simplifying the right side of the equation, we get:

mZA + mZB + mZC + mZD = 360 degrees

Therefore, we have proven that the sum of the measures of the angles in parallelogram ABCD is 360 degrees.

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The slope of the line through each pair of points (11, 8), (- 13, 11) is -1/8.

The slope of a line is defined as the change in y- coordinate with respect to x - coordinate. The slope of a line represents the direction and steepness of a line. The formula for the slope of a line that passes through the points (x₁, y₁) and (x₂, y₂) is given by

Here we have

The pair of points (11, 8), (- 13, 11)  

By the given formula,

Slope (m) = [ y₂ - y₁]/ [x₂ - x₁]

The slope from (11, 8) to (- 13, 11) can be calculated as follows

Slope = [ 11 - 8 ]/ [ -13 -11 ] = 3/-24 = -1/8

Therefore,

The slope of the line through each pair of points (11, 8), (- 13, 11) is -1/8.    

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The amount of sales tax due on the entire purchase of a set of speakers and s songs is $2.89 plus $16.09 for each song purchased, rounded to the nearest hundredth.

What is an expression?

In mathematics, an expression is a combination of numbers, variables, and/or operators that represents a mathematical quantity or relationship. It can be a single number or variable, or a combination of multiple numbers, variables, and operators.

The given expression 0.0825(35+195s) represents the amount of sales tax due on the entire purchase of a set of speakers and s songs, where s is the number of songs purchased.

Expanding the expression, we get:

0.0825(35+195s) = 0.0825(35) + 0.0825(195s)

= 2.8875 + 16.0875s

Rounding this expression to the nearest hundredth, we get:

2.89 + 16.09s

Therefore, the amount of sales tax due on the entire purchase of a set of speakers and s songs is $2.89 plus $16.09 for each song purchased, rounded to the nearest hundredth.

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At a total price of $2720 for 4 Computers, retailer 2 delivers the best deal based on the listed specials.

Based on the stated sales, we need to figure out the entire cost of 4 computers at each retailer, accounting for any discounts or promotions, in order to determine which store will provide the lowest pricing for 4 Computers.

Let's use the following variables to symbolize the costs and special offers at each retailer:

P1: the price of a single computer in a store 1

P2: the price of a single computer in a store 2

P3: the price of a single computer in a store 3

P4: the price of a single computer in a store 4

D1: discount on one computer at store 1

D2: discount on one computer at store 2

D3: discount on one computer at store 3

D4: discount on one computer at store 4

Then, we may figure the total cost of four computers at each store using the following formulas:

Total cost at store 1 = 4(P1 - D1)

Total cost at store 2 = 4(P2 - D2)

Total cost at store 3 = 4(P3 - D3)

Total cost at store 4 = 4(P4 - D4)

The total cost at each store can then be calculated by plugging in the values from the table as follows:

Store 1: Total cost = 4(950 - 0.2*950) = 3040

Store 2: Total cost = 4(800 - 0.15*800) = 2720

Store 3: Total cost = 4(1100 - 0.25*1100) = 3300

Store 4: Total cost = 4(850 - 0.1*850) = 3060

Therefore, At a total price of $2720 for 4 Computers, retailer 2 delivers the best deal based on the listed specials.

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Answer:

1m/sec

Step-by-step explanation:

Mr. Hall spent 3 seconds to increase his speed to 3m/sec increasing 1m/sec, don't over think it.

Answer:

k = -6

Step-by-step explanation:

Expand by substituting -6:

(n+5) (n-6) = n^2 + 5n - 6n (-6×5)

Thus, (n+5)(n-6) = n^2 -1n -30

(In a facotrised form for quadratics, the numbers need to add to 'bx', in this case -1, and multiply to form 'c' (-30). So -6×5 = -30 and k= -6)

Answer:

1/24.

Step-by-step explanation:

There are 2 events here and they are independent, so the single probabilities are multiplied.

P(4 when die is rolled) = 1/6

P(A on the spinner) = 1/4

So, P(4 and A)

= 1/6 * 1/4

= 1/24.

Answer:

Step-by-step explanation:  (10)(A) Add and subtract polynomials of degree one and degree two. (10)(B) Multiply polynomials of degree one and degree two. (10)(C) Determine the quotient

Hope it helps =}

Answer:

b

Step-by-step explanation:

The indicated IQ score is given as 117.

The area under the curve is given as 0.1431

the area to the left of x = 1 - 0.1431

= 0.8569

for 0.8569 the z stat is 1.07

u = 100

sd = 15

x = u + z * sd

= 100 + 0.8569 * 15

= 116.05

approximately 117

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Find the indicated IQ score. The graph to the right depicts IQ scores of​ adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.

xx

0.1431

A symmetric bell-shaped curve is plotted over a horizontal scale. A vertical line runs from the scale to the curve at labeled coordinate x, which is to the right of the curve’s center and peak. The area under the curve to the right of the vertical line is shaded and labeled 0.1431.

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Answer:

Radius is 2√3 units

Center is (8,-4)

Step-by-step explanation:

Compared to the standard form equation of a circle, [tex](x-h)^2+(y-k)^2=r^2[/tex], then the radius would be [tex]r=\sqrt{12}=2\sqrt{3}[/tex] and the center would be [tex](h,k)\rightarrow(8,-4)[/tex].

The volume of the rectangular prism will be 1008 cubic inches and the volume of the pyramid is 504 cubic inches.

The volume of the rectangular prism is defined as the space in three-dimension covered by the rectangular prism having the sides Length, Width, and Height.

The volume of the rectangular prism will be the multiplication of the three parameters which are Length, Width, and Height of the prism.

The volume of the pyramid is the product of half of the area of the base and the height of the pyramid,

The volume of prism = 14 x 12 x 6

The volume of the prism = 1008 cubic inches

The volume of the pyramid,

Volume = 1/2 x Base area x H

Volume = 1/2 x 72 x 14

Volume = 504 cubic inches.

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Answer:

See below

Step-by-step explanation:

Sum of 18 and 6 = 24

1/4 of the sum of 18 and 6 is asking you what is the result of dividing 24 by 4

In  a way you can think of it as a fractional question but the answer is a whole number

[tex]\dfrac{1}{4} \cdot (18 + 6) = \dfrac{1}{4} \cdot 24 = \dfrac{24}{4} = 6\\[/tex]

The appropriate response will be (A). The first equation of motion gives the link between "velocity and time."

Equation: A statement that two variable or integer expressions are equal. In essence, equations are questions, and the motivation for the development of mathematics has been the systematic search for the answers to these questions.

An equation is a mathematical representation of two equal objects, one on each side of a "equals" sign. We can solve challenges in our daily lives with the aid of equations. Most of the time, we look for help with pre algebra to resolve problems in real life. Pre-algebra concepts contain the fundamentals of mathematics.

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True. The rule of thirds is a photography and visual arts guideline that involves dividing an image into thirds using two horizontal lines and two vertical lines, and then placing the image's most important elements at the intersection points or along the lines.

This aids in the creation of a balanced and visually appealing composition. This results in nine rectangular areas of equal size, with four intersection points where the lines cross.

The rule of thirds principle suggests that the points of intersection or the lines themselves are ideal places to position the composition's most important elements. The resulting image is more visually balanced and pleasing to the eye as important elements are placed in these areas.

It is important that, however, that the rule of thirds is not a hard and fast rule, and that there were times when breaking it can result in more dynamic and interesting compositions. The rule of thirds is merely a tool for artists and photographers to use in order to create more effective and engaging images.

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Boole. K-map stands for Karnaugh Map and is used to simplify and minimize the expression of logic in a similar form to algebra.

George Boole is the mathematician we honor for discovering ways to express and minimize logic through a new but similar form of algebra. The technique used to simplify and minimize these expressions is known as a Karnaugh Map, or K-map for short. A K-map is a visual representation of a Boolean expression using squares and circles to represent true or false variables in a table. By arranging the variables in the table, the same logic can be expressed in a simpler form with fewer variables. This allows for a simpler and more efficient form of logic expression. K-maps are used in many fields, such as digital logic design, where the efficiency of expression is important.

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Answer:

The solution is (x = 6, y = -3)

Step-by-step explanation:

[tex]\sf \frac{x}{y + 1} = - 3 \: \: ........(1) \\ \\ \sf \frac{y}{x - 3} = - 1 \: \: ........(2) \\ \\ - - - - - - - - - \\ \\ \sf x + 3y = - 3 \: ........(1) \\ \\ \sf x + y = 3 \: \: \: \: \: \: ........(2) \\ \\ - - - - - - - - - \\ \\ \: \: \: \sf x + 3y = - 3 \: \: \: \: \: | \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \sf x + y = 3 \: \: \: \:\: \: \: \: | \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

The amount of money Jamar will make in his 18th year working at this job is = $107,500

A salary is a form of periodic payment from an employer to an employee, which may be specified in an employment contract. It is contrasted with piece wages, where each job, hour or other unit is paid separately, rather than on a periodic basis.

here, we have,

Calculation of yearly salary outcome

The amount of money Jamar made in his first year= $48,000

The salary rise per year = $3,500

The amount of money he will make for the extra 17 years is

= 17 × $3,500

= $59,500

Therefore the amount he will receive as his salary in the 18th year working at this job = $48,000 + $59,500

= $107,500

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The proof is as shown below

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

If a² = b + c , b² = c + a and c² = a + b

We want to prove that 1/(a+1) + 1/(b+1) + 1/(c+1) = 1

Since a² = b + c

a²+a = a + b + c

a (a+1) = a + b + c

a+1 = (a + b + c)/a

Repeat the same process for b² = c + a and c² = a +b, we have:

1 + b= (a + b + c)/b

1 + c =(a + b + c)/c

Substitute the values 1+a, 1+b and 1+c into 1/(a+1) + 1/(b+1) + 1/(c+1):

1/(a+1) + 1/(b+1) + 1/(c+1) = a/(a+b+c) + b/(a+b+c) + c/(a+b+c)     (Taking LCM)

                                      = (a+b+c )/ (a+b+c ) = 1

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The shopping mall has 65,625 square feet of total leasable area. As stated in the problem, this indicates that the fitness club takes up 16% of the total leasable space.

According to the information provided, a fitness club occupies 10,500 square feet or 16% of the total leasable area at a sizable shopping mall. We can use the proportional and percentage approaches to determine the total leasable area.

Let's assume that the variable "x" stands for the whole amount of leasable space. Since we are aware that the area leased by the gym is 16% of the total leasable area, we can create the following equation:

10,500 = 0.16x

To solve for "x", we can divide both sides of the equation by 0.16:

10,500 / 0.16 = x

Simplifying this expression gives us:

x = 65,625

Therefore, The shopping mall has 65,625 square feet of total leasable area. As stated in the problem, this indicates that the fitness club takes up 16% of the total leasable space.

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The percentage increase of the gas would be 2.5%.

We can calculate the value of the percentage increase by the following formula,

percentage increase = (final value - initial value) / initial value × 100%

As per the given question, we have

initial value = $2.81 , and final value = $2.88

Substitute the values in the above formula, and we get

percentage increase= (2.88 - 2.81 ) / 2.81 × 100%

percentage increase = (0.07) / 2.81× 100%

percentage increase = 0.0249 × 100%

Apply the multiplication operation, and we get

percentage increase = 2.49%

Thus, the percentage increase of an item would be 2.5%.

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Answer:

a) y - 4 =3(x - 1)

b)  y + 2 = 4(x+ 1)

c) y = -(x - 3)

d) y = -5x

Step-by-step explanation:

You did not say which form, so I put them in the point-slope form of a line that follows the pattern:

y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex])

Answer:

see explanation

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

(a)

given m = 3 , then

y = 3x + c ← is the partial equation

to find c substitute (1, 4 ) into the partial equation

4 = 3(1) + c = 3 + c ( subtract 3 from both sides )

1 = c

y = 3x + 1 ← equation of line

(b)

given m = 4 , then

y = 4x + c ← is the partial equation

to find c substitute (- 1, - 2 ) into the partial equation

- 2 = 4(- 1) + c = - 4 + c ( add 4 to both sides )

2 = c

y = 4x + 2 ← equation of line

(c)

given m = - 1 , then

y = - x + c ← is the partial equation

to find c substitute (3, 0 ) into the partial equation

0 = - 3 + c ( add 3 to both sides )

3 = c

y = - x + 3 ← equation of line

(d)

given m = - 5 , then

y = - 5x + c ← is the partial equation

to find c substitute (0, 0 ) into the partial equation

0 = - 5(0) + c = 0 + c ⇒ c = 0

y = - 5x ← equation of line

The measure of ∠A is 53.

The measure of ∠B is 37.

An expression contains one variable or more than one variable with addition, subtraction, multiplication, and division.

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

We have,

∠A and ∠B are complementary.

This means,

∠A + ∠B = 90

Now,

∠A = 7x + 4

∠B = 4x + 9

7x + 4 + 4x + 9 = 90

11x + 13 = 90

11x = 90 - 13

11x = 77

x = 7

Now,

∠A = 7x + 4 = 7 x 7 + 4 = 49 + 4 = 53

∠B = 4x + 9 = 4 x 7 + 9 = 28 + 9 = 37

Thus,

∠A = 53

∠B = 37

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Answer: nope

Step-by-step explanation:

No, the 200$ marked down 20% would be 200 - 0.2 * 200 = 160$. Then, if it is increased by 20%, it would be 160 + 0.2 * 160 = 192$. So, 200$ is not equal to 192$.

Answer:

Step-by-step explanation:

the answer is 420 cuase the manufatcure of math is hard i wont give an explanation.

The number of ways the foreign language club can choose 4 movies from the available is [tex]nC4 = n! / 4!(n-4)![/tex].

To calculate the number of ways the foreign language club can choose four movies from the available subtitled movies, we need to use the combination formula, which is:

[tex]nCr = n! / r!(n-r)![/tex]

Where n is the total number of available subtitled movies and r is the number of movies to choose (in this case, r=4).

Assuming there are at least four subtitled movies available, the number of ways to choose four movies would be:

[tex]nC4 = n! / 4!(n-4)![/tex]

Simplifying the equation further, we have:

[tex]nC4 = (n * (n-1) * (n-2) * (n-3)) / 4 * 3 * 2 *1[/tex]

Therefore, the number of ways the foreign language club can choose four movies from the available subtitled movies is given by the formula nC4.

The formula calculates the number of possible combinations of four movies that can be selected from the total number of available subtitled movies, without regard to the order in which they are shown.

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The radius of the curved part of the track will be 37.3m.

Solution:

Given that

The length of straight parts = 80m each

The total length of the track = is 400m

So, the total length of curved parts = 400 - (80*2) = 240m

Therefore, the radius of the curved parts =

[tex]2\pi r = 240\\r = 240/2\pi \\[/tex]

Hence, r = 37.3m.

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