The manager of an automobile dealership is considering a new bonus plan designed to increase sales volume. Currently, the mean sales volume is automobiles per month. The manager wants to conduct a research study to see whether the new bonus plan increases sales volume. To collect data on the plan, a sample of sales personnel will be allowed to sell under the new bonus plan for a one-month period. a. Which form of the null and alternative hypotheses most appropriate for this situation

Answer: y = 3x - 8

Step-by-step explanation: Given slope m = 3, and point x = 3, y = 1
y -1 = 3(x-3)
y = 3x - 9 + 1
y = 3x - 8

For a savings account with an initial deposit of $425.00, the account balance after 9 years if the account earns 2.7% simple interest annually is

The account balance is solved by adding the initial deposit to the simple interest.

The simple interest is solved using the simple interest formula

The formula is stated as

Simple interest = Principal *  time *  rate / 100

In the problem the give data include

principal = $425.00

rate= 2.7%

time = 9 years

plugging in the values

Simple interest = Principal *  time *  rate / 100

Simple interest = 425 * 9 * 2.7 / 100

Simple interest = 10327.5 / 100

Simple interest = 103.275

The account balance

=  initial deposit + simple interest

= 103.275 + 425

= $528.28

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Answer:

31.80

Step-by-step explanation:

20.53

× 1.55=

31.82

-.02

32.80

The common ratio for the sequence is 1/2.

Sets of numbers that adhere to a pattern or norm are known as number sequences. A geometric sequence is one where the rule is to multiply or divide by the same number each time.

Formula : [tex]a_n[/tex] = a[tex]r^{n-1[/tex]

where a is the first term, r is the common ratio.

Given:

Sequence: 14, 7, 7/2, 7/4

To calculate the common ratio = [tex]a_1/ a_2[/tex]

Now, the common ratio

= 7/14

= 1/2

Hence, the common ratio is 1/2.

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On solving the provided question, we can say that by the property of the triangle, if a line made from 2 mid points of a triangle the length of line of 2 mid points = 2 times the base ; AB = 80m

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

here,

by the property of the triangle, if a line made from 2 mid points of a triangle the length of line of 2 mid points = 2 times the base

so DC = 2*AB

AB = 80m

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The answers to each part is mentioned below..

The area of a square is -

Area = Side x Side

A = S²

Given is that the function {A} gives you the area in square inches of a square with side length {X} inches

We can complete the table as -

[x] :     0     1      2      3      4     5     6

A[x]  :  (0)²    (1)²   (2)²   (3)²  (4)²  (5)²  (6)²

A[x]  :   0       1       4      9     16    25   36

We can Represent the function A using the equation as -

A(x) = x²

The graph of the function is attached.

Therefore, the answers to each part is mentioned above.

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Answer: (-2,4) x (0,9)=36 simplified

y= 5/2x + 9 is the slope

Step-by-step explanation:

.

The function that represents how many more texts that were sent this week than last week is: B. (f − g)(x) = 3x + 16.

To find the value of a given functional expression, we have to apply the basic knowledge of how to solve algebraic expressions.

For example, if we are given that (f - g)(x), it means we are to subtract the function g(x) from f(x). That is (f - g)(x) = f(x) - g(x).

Given the following functions:

Number of texts sent this week is represented as the function, f(x) = 8x + 14

Number of texts sent last week is represented as the function, g(x) = 5x - 2.

Number of texts that were sent this week than last week = (f - g)(x)

(f - g)(x) = (8x + 14) - (5x - 2)

(f - g)(x) = 8x + 14 - 5x + 2

(f - g)(x) = 3x + 16

Therefore, the answer is: (f − g)(x) = 3x + 16.

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Therefore, the answer is: (f − g)(x) = 3x + 16.

Answer:

a = 3.31ft.

Step-by-step explanation:

The opposite is 3.31 feet.

Please let me know if this helped!!!

The differential of the function y - x² sin 8x with respect to x is dy/dx - 2x sin 8x + 8x² cos 8x

To find the differential of the function y = x² sin 8x, we can use the standard notation dy/dx which represents the rate of change of y with respect to x.

To calculate dy/dx, we need to use the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.

Let z be the given function,

z= y - x² sin 8x

The derivative of x² is 2x

The derivative of sin 8x is 8 cos 8x

So,

dz/dx= dy/dx - (2x)(sin 8x) + (x²)(8cos 8x)

= dy/dx- 2x sin 8x + 8x² cos 8x

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Answer:

So, Hypotenuse =  unit

Step-by-step explanation:

The function f(x)=⌊x⌋−3 in interval [−3,3] is represented by following graph:

The correct option is D.

The floor function floor(x) is defined as the function that gives the highest integer less than or equal to x.

Given function

f(x)=⌊x⌋−3 in interval [−3,3]

Above function is floor function.

f(x) = ⌊x⌋−3

f(3) = 3 - 3

f(3) = 0

f(2) = 2 - 3

f(2) = -1

f(1) = 1 - 3

f(1) = -2

f(0) = 0 - 3

f(0) = -3

f(-1) = -1 -3

f(-1) = -4

f(-2) = -2 -3

f(-2) = -5

f(-3) = -3 -3

f(-3) = -6

Plotting above points the graph we get is as follows:

Hence, Graph that represents the function f(x)=⌊x⌋−3 in interval  [−3,3] is below.

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Answer: Number 3 ( the one with the numbers added that are 4,13)

Step-by-step explanation:

There are 6 goats and 17 ducks present in the farmhouse

Let x represent the number of goats

Let y represent the number of ducks

x + y= 23....equation1

Goats have 4 legs and ducks have 2 legs

4x + 2y= 58.......equation 2

From equation 1

x + y= 23

x= 23-y

Substitute 23-y for x in equation 2

4(23-y) + 2y = 58

92- 4y + 2y= 58

92-2y= 58

-2y= 58-92

-2y= -34

y- 34/2

y= 17

Substitute 17 for y in equation 1

x + y= 23

x + 17= 23

x= 23-17

x= 6

Hence there are 6 goats and 17 ducks in the farmhouse shelter

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The value of x is given as follows:

x = 18.

Similar triangles are triangles that share these following two features:

The similar triangles for this problem are listed as follows:

ABD and EDC.

The proportional side lengths are given as follows:

Hence the value of x is obtained as follows:

x/6 = 12/4

x/6 = 3.

x = 18.

(using the proportional relationship for the equivalent side lengths of the similar triangles).

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Answer:

Step-by-step explanation:

d e e z n u t z

Therefore , algebraic solution is 55 is the total amount of money Peter earns raking lawns in August and September

The total amount of money Peter earns from raking lawns in August and September can be found by solving the equation 5 x 8 + 10 = m, where m represents the total money earned.

Here,

In this equation, 5 represents the number of lawns Peter raked in August, 8 represents the amount he earns for each lawn, and 10 represents the amount he earned from raking lawns in September.

When this equation is solved, the result is m = 55, meaning that Peter earned a total of $55 from raking lawns in August and September.

This can be seen by multiplying 5 times 8, which is 40, and then adding 10, which brings the total to 55.

Therefore, the total amount of money Peter earns from raking lawns in August and September is $55.

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Answer:

y is x - 5.

Step-by-step explanation:

x - y = 5
x = y + 5
we can isolate y by subtracting 5 from both sides of the equation:

x = y + 5
x - 5 = y

Therefore, the solution for y is x - 5.

Answer: The missing value is 86

Step-by-step explanation: The mean of a data set is the same as the average. The formula for mean is the sum of the data values/(the number of data values). Right now there are only 6 data values and we are looking for a seventh. If we sum the 6 current values and divide by 6, we get a data set with a mean of 96.5. We need a lower mean. The data set we need has 7 points so the sum of all 7 points should be 7(95) since if we divide 7(95) by the number of points which is 7, we get 95 which is the mean we want. 7(95) is 665. We can subtract the sum of the current 6 points from 665 to find the value we want.

On solving the provided question, we can say that expression is as follows r(m) . s(m) = [tex]241.^{-0.25} ]( 6 * 10^6) m^{ 0.2 }][/tex] = [tex]1.4446 X 10^9 m^{0.05}[/tex]

In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted. Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expression, all of which are separated by the arithmetic sign +.

expression is as follows

r(m) . s(m) = [tex]241.^{-0.25} ]( 6 * 10^6) m^{ 0.2 }][/tex] = [tex]1.4446 X 10^9 m^{0.05}[/tex]

the average number of lifetime heartbeats for a rhino with a mass of 2310 kilograms is [tex]1.7 X 10^8 KG[/tex]

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[tex]30 + 60[/tex]

I am pretty sure I'm wrong

[tex]30 \div 60[/tex]

[tex]30 \times 60[/tex]

[tex]30 - 60[/tex]

Answer: 806.59300

Step-by-step explanation:

The property of equality that was used to solve the equation is the division property of equality

From the question, we are to determine the property of equality that was used to solve the given equation

From the given information,

The equation is

-5x = 4

and

The solution is

(- 5x)/- 5 = 4/- 5

x = - 4/5

From the solution step, we can observe that both sides of the equation were divided by -5.

Thus,

The property of equality that was used is the division property of equality

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Answer:

2.14 rounded ............

The quotient when 2x² + 4x – 14 is divided by 2x is [tex]x + 2 - \frac{7}{x}[/tex] .  

When two numbers are divided by each other, the result is known as a quotient. For instance, when we divide 8 by 2, the result will be 2, where 2 is the quotient.

As we know division is a mathematical operation that involves dividing items into equal groups. It is represented by the symbol (÷). When we divide a number, the result we ultimately get is the quotient.

Here we have

2x² + 4x – 14 is divided by 2x  

=> [tex](2x^{2} + 4x - 14) \div {2x}[/tex]  

=>  [tex]\frac{(2x^{2} + 4x -14)}{2x}[/tex]  

Take 2x as common

=>  [tex]\frac{2x(x + 2 - \frac{7}{x} )}{2x}[/tex]    

=>  [tex]x + 2 - \frac{7}{x}[/tex]    

Therefore,

The quotient when 2x² + 4x – 14 is divided by 2x is [tex]x + 2 - \frac{7}{x}[/tex] .  

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The cost of the class would be $740 x 3 = $2220. If you were to work instead, at $10 per hour for 10 hours per week for 15 weeks, you would earn $1500. So, the net cost of the class would be $2220 - $1500 = $720.

In general, a college degree can lead to higher earning potential and greater career opportunities, so in most cases, it can be considered a worthwhile investment. However, the decision to take a particular class should be based on individual circumstances and goals. If the class is relevant to your future career aspirations and you can afford the cost, it may be a good investment. However, if the class is not directly related to your career goals, or you are not able to afford the cost, it may not be worth it.

The true statements are:

√(-1) is an imaginary number.

There are no real numbers that satisfy the equation  x = √-1.

A number that produces a negative square root is referred to as an imaginary number. An imaginary number, which has no real-world equivalent, is essentially the square root of a negative number.

Given:

We know that the value of √(-1) is i (iota) which is imaginary number.

So, √(-1) is an imaginary number.

Now, Negative numbers don't have real square roots since a square is either positive or 0.

So, x = √-1 have no real solution.

Now, x² = -1 again have no real solution because

x = √-1 and , Negative numbers don't have real square roots.

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Answer:

Triangle VWX and triangle IGH are congruent

Step-by-step explanation:

Answer:

1,000

Step-by-step explanation:

Formula: An=8/5x5(4)