For each lawn mowing job, Marcus charges a fee for his equipment plus an hourly rate. The graph shows how he calculates his fee for providing mowing services. Which linear function, in the form of y = mx + b, best represent this situation? YA 20 13 17 15 A) y = x +5 B) y = x +5 C) y = 5x + D) y = 5x + 14 Total Cost ($) 0 1 2 3 4 5 6 8 10 11 12 14 15 16 17 18 19 20 Time (hours) A В Ос OD

Answer:

4

Step-by-step explanation: Its  4 becuase you plug in the zero like this'

f(x)=4-5(0)

f(0)=4-0

f(0)=4

So it will (0,4)

Using the equations, it is seen that if the trip is 100 miles long, it would cost the same amount to rent a car from either company.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

Let's assume the length of the trip in miles is represented by x.

The equation for total cost for Company A would be -

CA = 0.4x + 80

The equation for total cost for Company B would be -

CB = 0.2x + 100

To find the length of the trip where the price is the same for both companies, we can set CA equal to CB and solve for x -

0.4x + 80 = 0.2x + 100

0.2x = 20

x = 100

So, for a trip of 100 miles, the total cost for both companies would be the same -

CA = 0.4(100) + 80 = $120

CB = 0.2(100) + 100 = $120

Therefore, the distance value for cost being same is 100 miles.

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Answer:

See below :)

Step-by-step explanation:

Given ordered pairs :

( 2 , 3 ) , ( - 2 , 4 ) , ( 4 , 8 ) , ( - 2 , 5 )

Domain is the set of all x -coordinates in the set of ordered pairs.

( 2 , 3 ) , ( -2 , 4 ) , ( 4 , 8 ) , ( -2 , 5 )

List them :

Domain = { - 2 , 2 , 4 )

Range is the set of all y - coordinates in the set of ordered pairs.

( 2 , 3 ) , ( - 2 , 4 ) , ( 4 , 8 ) , ( - 2 , 5 )

List them :

Range = { 3 , 4 , 5 , 8 }

Hope I helped !

Best regards!!

Answer:

161.98

Step-by-step explanation:

do 159.99 - 15 which is 144.99. then add 16.99 + 149.99. which is 161.98

Answer:

No, the Normal/large sample condition is not met. A confidence interval assumes that the underlying population follows a normal distribution and that the sample size should be at least 30. Since the sample size in this case is only 10, the Normal/Large Sample condition is not met and the conditions for constructing a confidence interval are not met.

Answer:

78.1777777778

Step-by-step explanation:

5 is not correct, as well as 87, and 74 r 4. so the 3rd answer is correct.

The value of y is 18

Similar triangles have the same corresponding angle measures and proportional side lengths. The angles of the two triangle must be equal and it not necessary they have equal sides.

Therefore the corresponding angles of similar triangles are congruent and the ratio of corresponding sides of similar triangles are equal.

Therefore;

14/21 = 12/y

14y = 21 × 12

14y = 252

divide both sides by 14

y = 252/14

y = 18

Therefore the value of y is 18.

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Answer:

x=3

Step-by-step explanation:

Hey there!

In order to solve this equation, we must first distribute the 3

3x + 9 = -4x + 30

Now we combine like terms

7x = 21

Then we divide both sides by 7 to get x by itself

x = 21/7

x = 3

Answer: x=3

Step-by-step explanation:

To solve the given equation, it means to find the value of x. We want to use inverse properties to isolate x. The inverse properties are add/subtract and multiply/divide. Be sure to use the corresponding inverse operation.

3(x+3)=-4x+30                 [distribute]

3x+9=-4x+30                    [add both sides by 4x]

7x+9=30                            [subtract both sides by 9]

7x=21                                 [divide both sides by 7]

x=3

Therefore, we get x=3.

Considering the sum of the internal angles of a triangle, it is found that the correct student is Paige.

The sum of the three internal angles of a triangle is of 180º, and none of the angles can be zero.

Hence, a triangle can have at most one right angle(angle of 90º), and researching the question on the internet, the student who states this is Paige.

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Answer:

4

simplied=2

Step-by-step explanation:

10²=8²+x²

10²=8²-x²

20=16-x²

x²=4

Simplied=2

Answer:

the first option

Step-by-step explanation:

Answer:

18m+20

Step-by-step explanation:

Hope this helps ya

Answer:

150 canicas en total.....

Answer: 362,365 copies

Step-by-step explanation: Using proportions, I set it up like 33700/? (total copies)= 9.3/100. I multiplied 33700 and 100 to get 3370000 and divided by 9.3 and rounded.

here is the answer 1,000,700

The standard form of "one million seven hundred" is 1,000,700.

The standard form of a number refers to the representation of a number using digits and place value notation. It is also known as the decimal form or the base-10 form.

We have,

"one million seven hundred"

In standard form, numbers are written using place value notation, where each digit is assigned a position based on its place value.

In the case of "one million seven hundred," the digit 1 represents one million, the digit 7 represents seven hundred, and the remaining zeroes represent placeholders for the tens, ones, and smaller place values.

So, by combining the place values, we can express "one million seven hundred" in standard form as 1,000,700, where the 1 represents one million, the 0s serve as placeholders for the smaller place values, and the 7 represents seven hundred.

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Answer:

626.71 cm^2

Step-by-step explanation:

Area of figure = area of half circle + Area of half circle + area of a rectangle

here, diameter=15 cm

radius = 15/2=7.5 cm

length=30cm

breadth=15cm

Now

Area of figure = 1/2*π*radius^2+ 1/2*π*radius^2+length*breadth

=1/2* 1/2*π*7.5^2+1/2* 1/2*π*7.5^2+30*15

=626.71 cm^2

Answer:

\(\huge\boxed{\sf x = 9}\)

Step-by-step explanation:

3(x + 4) - 11 = 28

3(x + 4) = 28 + 11

3(x + 4) = 39

3x + 12 = 39

3x = 39 - 12

3x = 27

x = 27/3

\(\rule[225]{225}{2}\)

Answer:A

Step-by-step explanation:

the correct choice is: B. The numbers in the pattern are odd.

To determine if the numbers in the pattern are even, odd, or alternate between even and odd, let's examine the first few numbers in the pattern:

First number: 41

Second number: 41 - 4 = 37

Third number: 37 - 4 = 33

Fourth number: 33 - 4 = 29

As we can see, the numbers in the pattern are decreasing by 4 in each step. The first number (41) is odd, and subsequently, each number is decreasing by an even value (4). Therefore, all the numbers in the pattern will be odd.

So, the correct choice is:

B. The numbers in the pattern are odd.

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a) -32.06 (To the nearest hundredth)

b) -37.7 (To the nearest tenth)

c) 3.1 (To the nearest tenth)

d) 5.86  (To the nearest hundredth)

f) -4.33  (To the nearest hundredth)

g) 11.44  (To the nearest hundredth)

h) 62x + 45 = 38x + 79

i) 46y - 18 = -37y

An equation is a mathematical statement that asserts the equality of two expressions. It consists of two expressions separated by an equal sign (=), and shows the relationship between the variables present in the equation. Equations are used to model real-world problems and find solutions to various mathematical problems.

They can be solved for a specific variable by using various mathematical methods and techniques.

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Answer:

the answer is 7,348,000

Step-by-step explanation:

Answer:

c(x)=(3/4)^x

(3/4)^-2= 16/9

(3/4)^-1 =4/3

(3/4)^0=1

(3/4)^1 = 3/4

(3/4)^2= 9/16

The sale price (p) is $1,518.00 in $2530 dining room set.

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that Price = 2530

The Final Sale Price = 40% of 2530 or % of Price

The Final Price = Price - % off

Final Price = ( 2530 ) - ( 40/100 × 2530 )

Final Price = 2530 - 1012

Final Price = $1,518.00

Hence, the sale price (p) is $1,518.00 in $2530 dining room set.

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Value of an exterior angle of a triangle is equal to the sum of values of two opposite interior angles of a triangle.

\(\qquad\displaystyle \tt \dashrightarrow \: 5x + 10 = 40 + 70\)

\(\qquad\displaystyle \tt \dashrightarrow \: 5x = 110 - 10\)

\(\qquad\displaystyle \tt \dashrightarrow \: 5x = 100\)

\(\qquad\displaystyle \tt \dashrightarrow \: x = 100 \div 5\)

\(\qquad\displaystyle \tt \dashrightarrow \: x = 20\)

Value of x = 20°

Hey! there . Thanks for your question :)

Answer:

Step-by-step explanation:

In this question we are given with two interior angles of the triangle that are 40° and 70° , also we are given an exterior angle that is (5x + 10)°. And we are asked to find the value of angle x.

Solution :-

For finding the value of angle x , we have to use exterior angle property of triangle which states that sum of opposite interior angles of triangle is equal to the given exterior angle. So :

Step 1: Making equation :

\( \longmapsto \: \sf{40 {}^{°} + 70 {}^{°} = (5x + 10) {}^{°} }\)

Solving :

\( \longmapsto \: \sf{110 {}{°} = (5x) {}^{°} +10 {}^{°} }\)

Step 2: Subtracting 10 on both sides :

\( \longmapsto \sf{ 110 {}^{°} - 10 {}^{°} = 5x + \cancel{10 {}^{°}} - \cancel{10 {}^{°} } }\)

We get ,

\( \longmapsto \sf{(5x ){}^{°} = 100 {}^{°} }\)

Step 3: Dividing both sides by 5 :

\( \longmapsto \dfrac{ \cancel{5}x {}^{°} }{ \cancel{5}} = \dfrac{ \: \: \: \: \cancel{ 100} {°}^{} }{ \cancel{5} }\)

On cancelling , we get :

\( \longmapsto \underline{\boxed{\red{\sf{ \bold{ x = 20 {}^{°} }}}}} \: \: \bigstar\)

Verification :-

For verifying sum of both the interior angles is equal to given exterior angles. As we get the value of x as 20 we need to substitute it's value in place x and then L.H.S must be equal to R.H.S :

Therefore , our answer is correct .

The correct statement is that the theoretical probability of swimming, P(swimming), is one half, but the experimental probability is 16 over 40.

We know that there are 40 students at summer camp who are divided into two groups for either swimming or hiking. Each camper flips a coin, where heads represents swimming and tails represents hiking. The outcome frequency for swimming is 16 and for hiking is 24.
To compare the probabilities, we need to first understand the difference between theoretical probability and experimental probability. Theoretical probability is the expected probability of an event occurring based on mathematical calculations and assumptions, whereas experimental probability is the actual observed probability of an event occurring based on data from experiments or observations.
Option 1 states that the theoretical probability of swimming is one half, but the experimental probability is 24 over 40. This statement is incorrect because the theoretical probability of swimming is actually 50%, which is equal to one half, and the experimental probability of swimming is also 40%, which is equal to 16 over 40. Therefore, this option is false.
Option 2 states that the theoretical probability of swimming is one half, but the experimental probability is 16 over 40. This statement is correct because the theoretical probability of swimming is 50%, which is equal to one half, and the experimental probability of swimming is also 40%, which is equal to 16 over 40. Therefore, this option is true.
Option 3 states that the theoretical probability of swimming is 16 over 24, but the experimental probability is one half. This statement is incorrect because the theoretical probability of swimming is actually 50%, which is not equal to 16 over 24, and the experimental probability of swimming is also 40%, which is not equal to one half. Therefore, this option is false.
Option 4 states that the theoretical probability of swimming is 24 over 40, but the experimental probability is one half. This statement is incorrect because the theoretical probability of swimming is actually 50%, which is not equal to 24 over 40, and the experimental probability of swimming is also 40%, which is not equal to one half. Therefore, this option is false.
In conclusion, the correct statement is that the theoretical probability of swimming, P(swimming), is one half, but the experimental probability is 16 over 40.

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Answer: a. 0.4 × 0.15 = 0.060

Step-by-step explanation: Probability of the complement of an event is the one that is not part of the event.

For P(A):

P(A') = 1 - 0.6

P(A') = 0.4

For P(B):

P(B') = 1 - 0.85

P(B') = 0.15

To determine probability of A' and B':

P(A' and B') = P(A')*P(B')

P(A' and B') = 0.4*0.15

P(A' and B') = 0.06

Probability of the complement of the event is 0.060

The conclusion of the hypothesis testing is that; there is not enough evidence to support the claim that the mineral changes a person’s cholesterol level.

Hypothesis testing is defined as the method that is used to find the probability of the hypothesis to be proved in the future on the basis of the small population sample.

Let us first define the hypothesis in this problem;

Null Hypothesis; H₀: μ_d = 0

Alternative Hypothesis; Hₐ: μ_d ≠ 0 (Claim)

The degree of freedom is;

DF = n - 1

DF = 6 - 1

DF = 5

At a significance level of α = 0.10, with a DF of 5, the critical values are ±2.015.

Using a computer software, we can calculate the mean from the attached table as;

D' = ∑d/n

D' = 100/6 = 16.7

Similarly, the standard deviation is calculated from the formula;

S_d = √(n∑d² - (∑d)²)/(n(n - 1))

s_d = √(6.489 - 100²)/(6(6 - 1))

s_d = 25.4

The test statistic is gotten from the formula;

t = (D' - μ_d)/(s_d/√n)

t = (16.7 - 0)/(25.4/√6)

t = 1.610

This is less than the critical value and we fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim that the mineral changes a person’s cholesterol level.

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For the graphed function:

The domain is [-3, 3]

The range is [-3, -3]

For a function y = f(x), we define the domain as the set of the inputs and the range as the set of the outputs.

To identify the domain we need to look at the horizontal axis, we can see that the minimum value is at x = -3 and the maximum value is at x = 3, then the domain is: [-3, 3]

In the case of the range we have a single value (because the line is an horizontal line at y = -3) then the range is just R: {-3}

Or [-3, -3]

In interval notation.

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Answer:

G. 6 months

Step-by-step explanation:

1. 495-165 to remove the one-time payment = 330

2. 330/55 to find the number of months = 6

Barbara receive 6 months of dance lessons from Dance Unlimited

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, Barbara signed up for dance lessons at Dance Unlimited. She was charged $55 per month for lessons and a one-time recital fee of $165.

Let m be the no of months and f(m) is the total cost.

∴ f(m) = 55m + 165.

The equation represents the $495 total cost,

∴ 495 =  55m + 165.

55m = 330.

m = 330/55.

m = 6.

Barbara receives 6 months of dance lessons from Dance Unlimited.

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Answer:

52.5 inch square

Step-by-step explanation:

Area of pentagon: A = 1/2 × p × a;

where 'p' is the perimeter of the pentagon and 'a' is the apothem of the pentagon.

A = 1/2 x (6 x 5) x 3.5 = 1/2 x 30 x 3.5 = 15 x 3.5 = 52.5

The area of the regular pentagon with apothem 3.5 and side 6 is 52.5

In Mathematics, a pentagon is a polygon with 5 sides. A pentagon can be classified as a regular pentagon and irregular pentagon. When all the sides and the angles of a pentagon are of equal measure, then it is called a regular pentagon.

Given the question, we need to find the area of the regular pentagon with apothem 3.5 and side 6.

In order to find the area, the formula to calculate the area of the regular pentagon is given by:

\(\text{Area of pentagon} =\sf \huge \text(\dfrac{5}{2}\huge \text) \times s \times a\)

Now,

\(\text{Area of pentagon} =\sf \huge \text(\dfrac{5}{2}\huge \text) \times s \times a\)

\(\text{Area of pentagon} =\sf \huge \text(\dfrac{5}{2}\huge \text) \times 6 \times 3.5\)

\(\text{Area of pentagon} =52.5\)

Therefore, the area of the regular pentagon with apothem 3.5 and side 6 is 52.5

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