The table below shows that the number of miles driven by Lydia is directly
proportional to the number of gallons she used.
Gallons Used Miles Driven
42
47
50
1591.8
1781.3
1895
If m represents the number of miles driven for any number of gallons used, g,
write a proportional equation for m in terms of g that matches the context.

The equation of the linear function is y = 8x - 5.

What is a linear function?

Slope formula:

m = (y₂ - y₁) /  (x₂ - x₁)

Taking first two points from the given table

m = (3 + 5) / 1 - 0

m = 8

slope m = 8

Use one slope and one point formula to find the linear equation

y - y₁ = m (x - x₁)

y + 5 = 8 (x - 0)

     y = 8x - 5

Hence, the equation of the linear function is y = 8x - 5.

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Answer:

$10.79

Step-by-step explanation:

1) Make an equation

40x + 48.67 = 480.17

where x is hourly pay

2) Solve

40x + 48.67 = 480.17

40x + 48.67 - 48.67 = 480.17 - 48.67

40x = 431.50

40x / 40 = 431.50 / 40

x = 10.79

(a) There are 10 vertical rise per step.

(b) There are 58 steps needed to climb from road level to the 2nd floor.

What is angle of elevation?

The angle of elevation is the angle created between the line of sight and the horizontal. The angle created is an angle of elevation if the line of sight is upward from the horizontal line.

(a) First to find the vertical rise per step.

x = 13 x tan(37)

x = 9.80

x ≈ 10

Hence, there are 10 vertical rise per step.

(b) Now to find number of steps needed to climb from road level to the 2nd floor.

The total elevation = 24 + 24 = 48 feet

Vertical rise of each step = 10

To convert 48 feet into inches

⇒  48 x 12 = 576 inches

So, the number of steps = 576 / 10 = 57.6 ≈ 58

Hence, there are 58 steps needed to climb from road level to the 2nd floor.

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Answer:

Erin will pay a total of $21.196 in shipping and handling fees.

Step-by-step explanation:

To calculate the shipping and handling fees, we first need to find 20% of the price of the trampoline. Since 20% is the same as 0.20, we can multiply the price of the trampoline by 0.20 to find the shipping and handling fees. If the trampoline costs $105.98, then the shipping and handling fees would be $105.98 * 0.20 = $<<105.98*0.20=21.196>>21.196.

The we should use ANOVA instead of several t-tests to evaluate the differences in the mean of three or more groups.

A t- test is a measurable test that is utilized to look at the method for two gatherings. It is many times utilized in speculation testing to decide if a cycle or treatment really meaningfully affects the number of inhabitants in interest, or whether two gatherings are not quite the same as each other.

The ANOVA test permits an examination of multiple gatherings simultaneously to decide if a relationship exists between them.

We ought to utilize ANOVA rather than a few t-tests to assess the distinctions in the mean of at least three gatherings on the grounds that without fail, we direct a t-test (between two gatherings) there is some opportunity that a Kind I blunder is being made while doing the test.

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An apple cost $1.2 and the orange cost $1.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this situation, she bought 5 apples and 4 oranges for $10. This will be 5a + 4o = 10

The friend bought 5 apples and 5 oranges for $11. This will be 5a + 5o = 11

Equate the equations

5a + 4o = 10

5a + 5o = 11

Subtract

o = 1

The value of orange is $1

The value of apple will be:

5a + 4o = 10

5a + 4(1) = 10

5a + 4 = 10

Collect like terms

5a = 10 - 4

5a = 6

Divide

a = 6/5

a = 1.2

Apple cost $1.2

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Answer:$3.51

Step-by-step explanation:

$17.53 x 20% = 350.6

350.6/100 = 3.506

3.506 = $3.51

The domain of the function d(t) describing the Haru's journey to his friend is

In the graph, the input values is the time in hours, t while the output value is distance covered, d in kilometers

The domain is controlled by the input values. considering the time used for the journey as shown in the graph. The journey started from point 0 to the end point 2.1

The maximum time is at 2.1 hours. For the minimum, this is when the journey started which is 0

The domain starts from 0, with 0 not inclusive to 2.1 with 2.1 included

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Answer:

This equation does not have the same solution as the original equation.

In conclusion, equations 1 and 2 have the same solution as the original equation (2.3p – 10.1 = 6.5p – 4 – 0.01p). Equations 3, 4, and 5 do not have the same solution.

Step-by-step explanation:

2.3p – 10.1 = 6.4p – 4

Using the commutative property of addition, we can rearrange the terms on the left-hand side of the equation to get:

-6.4p + 2.3p = -4 + 10.1

Combining like terms, we have:

-4.1p = 6.1

Dividing both sides by -4.1, we get:

p = -1.49

This equation has the same solution as the original equation.

2.3p – 10.1 = 6.49p – 4

Using the commutative property of addition, we can rearrange the terms on the left-hand side of the equation to get:

-6.49p + 2.3p = -4 + 10.1

Combining like terms, we have:

-4.19p = 6.1

Dividing both sides by -4.19, we get:

p = -1.46

This equation has the same solution as the original equation.

230p – 1010 = 650p – 400 – p

This equation does not have the same solution as the original equation.

23p – 101 = 65p – 40 – p

This equation does not have the same solution as the original equation.

2.3p – 14.1 = 6.4p – 4

Using the commutative property of addition, we can rearrange the terms on the left-hand side of the equation to get:

-6.4p + 2.3p = -4 + 14.1

Combining like terms, we have:

-4.1p = 10.1

Dividing both sides by -4.1, we get:

p = -2.47

Company A costs less for mileage than Company B, which can be represented by the inequality  0   ≤ m < 85 .

The parameters for the two companies are as follows:

For Company A, the initial cost is $55.

For Company B, the initial cost is $97.50.

The extra cost per mile is 20 cents.

Let us depict the overall fee for company A by C₁ and the total charge for company B by C₂, and we will obtain;

C₁ = 55 + 0.70 × m

C₂ =  97.50 + 0.20 × m

Where "m" stands for the amount of miles driven.

Therefore, the cost of Company A and Company B are the same or equal when have the following relation;

C₁ = C₂

Now we will solve the equation to find the value of m.

∴ 55 + 0.70 × m = 97.50 + 0.20 × m

0.70 × m - 0.20 × m = 97.50 - 55

0.5 × m = 42.5

m = 85

m = 85 miles is the number of miles driven for which both companies will charge the same amount.

As a result, given that Company A's initial fee is smaller than Company B's initial fee, we have;

As a result, Company A charges less than Company B for 0 miles m 85 miles.

Therefore the inequality to represent is given by: 0   ≤ m < 85

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The linear function (A) c(x) = 5.50 + 20.50x represents the total cost when x tickets are applied.

The term "linear function" in mathematics applies to two different but related ideas:

A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.

So, c ⇒ the overall expense.

The quantity (x) of tickets

The price of one ticket without a service charge.

The fact that:

108 = 5.50 + 5z

5z = 108 - 5.50

5z = 102.5

z = 102.5/5

z = $20.5

Equating the linear function is:

c(x) = 5.50 + 20.50x

Therefore, the linear function (A) c(x) = 5.50 + 20.50x represents the total cost when x tickets are applied.

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Correct question:
Tickets to a basketball game can be ordered online for a set price per ticket plus a $5.50 service fee. The total cost in dollars for ordering 5 tickets is $108.00. Which linear function represents c, the total cost, when x tickets are ordered? (A service fee is a single fee applied to the total, no matter the number of tickets purchased).

a c(x) = 5.50 + 20.50x

b c(x) = 5.50x + 20.50

c c(x) = 5.50 + 21.60x

d c(x) = 5.50x + 21.60

Answer:

The answer is $87.5

Step-by-step explanation:

350 × 25 ÷ 100

8750/100 = 87.5

Thus, Mr. Wright deposit $87.5

Answer:

1)  x=16

2) x=15

3) x=10

Step-by-step explanation:

1)  Since the triangles are similar and the ratio of the sides is 1 : 2, 1/2=(3x-4)/(10x-72). Cross multiplying, we get 6x-8=10x-72.

10x-72=6x-8 |+72

10x=6x+64 |-6x

4x=64  |/4

x=16

2) Angles HGJ and KLJ are corresponding (they are equal angles).

So, 5x-2=9x-62.

5x-2=9x-62  |+62

5x+60=9x  |-5x

60=4x |/4

x=15

3) If KM is a perpendicular bisector, KJ=KL.

So, 4x+9=11x-61.

4x+9=11x-61 |-4x

9=7x-61   |+61

70=7x  |/7

x=10

The difference between is 7-4 = 3

What are volume and area?

The area is the volume a flat, two-dimensional item occupies in a plane. The space occupied by a three-dimensional object is referred to as its volume. Area is measured in square units. Volume is measured in cubic units.

The volume formula is what.

The basic formula for volume is length, breadth, and height, as opposed to length, width, and height for the area of a rectangular shape. The calculation is unaffected by how you refer to the various dimensions; for instance, you can use "depth" instead of "height."

Given that :

Cube 1 has volume = 343 cubic feet

Volume = [tex]a^{3}[/tex]

[tex]a^{3}[/tex] = 343

a = 7

Cube 2 has volume = 64 cubic feet

Volume = [tex]a^{3}[/tex]

[tex]a^{3}[/tex] = 64

a = 4

Hence the difference between is 7-4 = 3

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The value of x that makes the expressions equivalent is 8

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

4(x-5)= 32-20

Distribute the 4

4x-20=12

4x= 12+20 = 32

x= 32/4 = 8

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On a test with a range of 110–410, these students received a mean score of 370 and a standard deviation of 50. What range would roughly 95% of the students' scores fall into, presuming a mound-shaped and symmetric distribution.

Any traits, figures, or amounts that may be gauged or counted are considered variables. Another name for a variable is a data item. Variables include things like age, sex, business income and expenses, birthplace, capital expenditures, class grades, eye color, and vehicle type.

A variable is a quality that may be measured and take on several values. A few examples of variables are height, age, income, province of birth, school grades, and kind of dwelling. Categorical and numeric variables are the two basic types of variables that can be categorized.

The relation that is able to model the decay is given as N = 690e^-0.04r. The quarterly rate of change is 0.21%.

We know that the term radioactivity has to do with the fact that the object is able to undergo the process of a spontaneous disintegration. The implication of this is that the element is going to be gradually be transformed into a different element and this is going to occur at a given rate which we have called the decay constant for the reaction.

We know that element X is a radioactive isotope such that its mass decreases by 4% every year then an experiment starts out with 690 grams of Element X.

It follows that;

Initial amount of X No = 690 g

Decay rate of X (r) = 0.04

Time taken for decay = t

Amount of X at time t = N

The model now becomes;

N = 690e^-0.04r

The  quarterly rate of change is obtained from;

A(t) = (1- 0.04)Ao

= 0.96 Ao

0.96Ao = Ao(1 - r)^30

0.94 = (1 - r)^30

30√0.94  = (1 - r)

r = -0.0021 or -0.21%

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the sum of squares of number of 6,7 and 8 is 149.

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

the product of three consecutive positive integers is 8 times thier sum.

So if 1st number is x

So the sum will be x+x+1+x+2 = 3x+3

and multiply will be x(x+1)(x+2)

according to question x(x+1)(x+2) = 24(x+1)

x³+3x²+2x = 24x+24

x = 6

So all the numbers will be 6,7 and 8

Hence the sum of their square is 36+49+64= 149

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The maximum height of the projectile will be 226 feet that is, as per question, the option c.

A quadratic equation , y = ax²+bx+c  (equation 1)

given, axis of symmetry is

x = [tex]\frac{b}{2a}[/tex]

As per the question:

The path of the projectile is modeled using the equation :

h(t) = -16t²+48t+190  (equation 2)

h(t) = height after t time.

comparing equation 1 and equation 2, we get

a = -16 and b = 48

further, t = [tex]\frac{48}{2(-16)}[/tex]

= [tex]\frac{48}{32}[/tex]

= 1.5sec

Substituting the found value in equation 2, we get

h(1.5) = -16(1.5)²+48(1.5)+190

h(1.5) = -36+72+190

h(1.5) = 226ft.

Thus, the maximum height of the projectile at 1.5 sec is, 226 feet.

Note that the full question is:

A projectile with an initial velocity of 48 feet per second is launched from a building 190 feet tall. The path of the projectile is modeled using the equation h(t) = –16t2 + 48t + 190.

What is the maximum height of the projectile?

A. 82 feet

B. 190 feet

C. 226 feet

D. 250 feet

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By using the fact that all the triangles are equilateral, we will see that AB = 32 units.

Here we have a figure made of equilateral triangles. Remember that all the sides of an equilateral triangle have the same measure.

Now we can see that FE = 16, then with that we can conclude that each segment of two consecutive vertices also measures 16 unints.

Now, we can write AB as:

AB = AD + DB

And we know that:

AD = 16 units

DB = 16 units.

Then:

AB = 16 + 16 = 32 units

That is the length of segment AB.

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Answer:

Step-by-step explanation:

15 (poles hight) divided by 6 (mans hight) is 2.5, so you would devide 45 by 2.5, and you get 18

A raw score is the actual number of correct answers a person gets on a test, without any adjustment for factors such as difficulty or time. For example, if a student takes a test with 10 questions and answers 8 correctly, their raw score would be 8 out of 10.

A raw score is the actual number of correct answers a person gets on a test, without any adjustment for factors such as difficulty or time. This means that the raw score is not adjusted or changed in any way.

For example, if a student takes a test with 10 questions and answers 8 correctly, their raw score would be 8 out of 10. This means that the student answered 8 out of the 10 questions correctly, without any adjustment for difficulty or time.

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The equation of a line that passes through [tex](-1,4)[/tex] and is parallel to the y-axis is [tex]x=-1[/tex]

The equation of the line passes through the point is [tex](-1,4)[/tex]

The line is parallel to the y-axis which means it cuts the x-axis at the point [tex](-1,0)[/tex]

The equation of the line parallel to the y-axis is [tex]x=-1[/tex]

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The equation y' = x + y + 1  is not seperable. Therefore the statement is false.

In mathematics, an ordinary differential equation (also known as an ODE) is an equation made up of one or more functions of a single independent variable and its derivatives. A function having one or more derivatives is a component of a differential equation.

Common differential equations are used in everyday life to compute the flow of electricity, the motion of an item back and forth like a pendulum, and to illustrate the principles of thermodynamics. Additionally, in medical terminology, they are employed to graphically monitor the progression of illnesses.

If you can express a differential equation as y′=f(x)g(y), where f(x) is only a function of x and g(y) is only a function of y, then the problem is separable. Here, it is not the situation.

But we are not limited to solving separable differential equations. We frequently use integrating factors to solve linear first-order differential equations, such as this one. Using the product rule, multiply your differential equation by an integrating factor—in this example, e—and you get (eyy)′=eyy+eyy′=eyx,

which you may integrate to get your differential equation's solution. Finding integrating factors for generic linear first-order differential equations of the type y′+p(x)y=q may be done in a general way (x).

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Yes, natural numbers are an example of closed under addition.

Natural numbers are closed under addition and also multiplication. The addition of two or more natural numbers results in always a natural number.  while for the case of subtraction and division, natural numbers don't obey the closure property, which means dividing or subtracting two natural numbers might not give a natural number. for example, considering two numbers 5 and 7, when we add both of them the result we come up with is 12, which is also a natural number.

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The product of -1.8 and = -1.8 x ?

3 more than a number = 3 + n

The product of -1.8 and 3 more than a number = -1.8(3 + n)

Is the same as 1/10 = equals (equal sign) 1/10

Full Equation: -1.8(3 + n) = 1/10

Steps to solve:

1. Divide both sides by -1.8 (or - 9/5)

(3 + n) = 1/10 x -5/9

3 + n = -5/90

2. Subtract 3 from both sides

n = -5/90 - 270/90

n = -30 5/9

Hope this helps!

Answer:

(-2^6) is 64, which is positive.

Step-by-step explanation:

To write -2^6 as repeated multiplication, we can write it as (-2)(-2)(-2)(-2)(-2)*(-2). To evaluate this expression, we can compute it as follows:

(-2)(-2)(-2)(-2)(-2)(-2)

= ((-2)(-2)(-2)(-2)(-2))(-2)

= ((((-2)(-2)(-2)(-2))(-2))(-2)

= (((((-2)(-2)(-2))(-2))(-2))(-2)

= (((((-2)(-2))(-2))(-2))(-2))(-2)

= (((((-2)(-2))(-2))(-2))(-2))(-2)

= (((-2)(-2)(-2))(-2))(-2)(-2)

= (((-2)(-2)(-2))(-2))(-2)(-2)

= ((-2)(-2))(-2)(-2)(-2)(-2)

= (-2)(-2)(-2)(-2)(-2)(-2)

= 64

Therefore, the result of (-2^6) is 64, which is positive.