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You may find the answer to this question in the statement of the problem, if the vehicles uses 1 gallon to travel 13 times, then it is traveling at a rate of 13 miles per gallon.

The graph of the proportional relationship is added as an attachment

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

Time = 3 minutes

Supply of water = 12 litres

Using the above parameters, we have the following ordered pairs

(0, 0) and (3, 12)

Rewrite the above points properly

So, we have the following ordered pairs

(x, y) = (0, 0) and (3, 12)

The gradient of the line is then calculated using the following slope equation

gradient = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (0, 0) and (3, 12)

Substitute the known values in the above equation

So, we have the following equation

gradient  = (12 - 0)/(4 - 0)

Evaluate

gradient  = 3

The equation of the line is then calculated as

y = gradient * x

Substitute the known values in the above equation

So, we have the following equation

y = 3 * x

Evaluate the products

y= 3x

Hence, the line equation is y= 3x

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tile will it take to cover the pedestal, including the bottom is 288 square feet

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Answer:

the football team sells 805,000 tickets each season

Step-by-step explanation:

average number of tickets sold per match=23,000

the average number of games played each session=35

the number of tickets sold on average each session = 23,000 x 35 which equals 805,000

so the average football club sells 805,000 tickets each season

A true proportion of the figure based on the triangle proportionality theorem is: A) i/j = h/k.

In Mathematics, a triangle can be defined as a two-dimensional (2D) geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.

The triangle proportionality theorem states that when any of the two (2) sides of a triangle is intersected by a straight line which is parallel to the third side of the triangle, then, the two (2) sides that are intersected would be divided proportionally and in the same ratio.

Since side TU is parallel to side QR, side TU will divide both sides QS and RS proportionally in accordance with the triangle proportionality theorem as follows;

RU/QT = SU/ST ≡ i/j = h/k

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Using the Leading Coefficient Test the end behavior of the given function f(x) = −x⁴ − 2x³ + 2x² − 5 is

The end behavior of function typically says the characteristics of the function at the ends

The given function is:

f(x) = −x⁴ − 2x³ + 2x² − 5

The end behavior is determined by the leading Coefficient =  −x⁴  and it is described as

x ⇒ ∞ f(x) ⇒ ∞

x ⇒ -∞ f(x) ⇒ -∞

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There are solutions when k = -1 and when k = -3

What is Linear Equation in One Variable?

A linear equation is a one-variable equation of a straight line. The variable's only power is 1. Linear equations in one variable have the form ax + b = 0 and are solved using simple algebraic techniques.

Solution:

|x + 3| - 2 = k

Removing the modulus sign

x + 3 - 2 = k -----(i) = x + 1 = k

-x - 3 - 2 = k -----(ii) -x - 5 = k

Putting k = -1

(i) x = -2 and (ii) x = -4

Putting k = -3

(i) x = -4 and (ii) x = -2

Since, x has solution on both the values of k

We can say that,

There are solutions when k = -1 and when k = -3

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Using the Central Limit Theorem, it is found that these conditions are required to avoid the high variability associated with small samples.

[tex]s=\sqrt{p(1-p)/n}[/tex]

[tex]p v=2*p(z < -0.531)=0.595[/tex]

1) Data given and notation

n=500 represent the random sample taken

X=380 represent the number of people with some characteristic

estimated proportion of adults that said that it is morally wrong to not report all income on tax returns

is the value that we want to test

represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

represent the p value (variable of interest)

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportion is 0.7 .:  

Null hypothesis:  

Alternative hypothesis:  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

(1)  The One-Sample Proportion Test is used to assess whether a population proportion  is significantly different from a hypothesized value Check for the assumptions that he sample must satisfy in order to apply the test

a)The random sample needs to be representative: On this case the problem no mention about it but we can assume it.

b) The sample needs to be large enough

3) Calculate the statistic  

[tex]z=\frac{0.76 - 0.77}{\sqrt{\frac{0.77(1-77)}{500} } =0.531}[/tex]

Since we have all the info requires we can replace in formula (1) like this:  

4) Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level provided [tex]\alpha =0.05[/tex]The next step would be calculate the p value for this test.  

Since is a bilateral test the p value would be:  

[tex]pv=2*p(z < -0.0531)=0.595[/tex]

If we compare the p value and using the significance level given  we have  so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion is not significantly different from 0.77.  

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Answer: 128 square centimeters

Step-by-step explanation:

If the perimeter is 48 cm, then the sum of the lengths of any two adjacent sides must be 24 cm.

Since the length of one of these sides is given to be 8 cm, it follows the length of the corresponding adjacent side is 16 cm.

Thus, using the formula for the area of a rectangle, the area is 128 square centimeters.

√5 km/h fast is the distance between the ships changing at 4:00 PM .

What is the Pythagorean theorem ?

The Pythagorean theorem states that the squares on the hypotenuse of a right triangle, which is the side that faces the right angle, are equal when added together.

                      This is represented by the equation a2 + b2 = c2 in common algebraic notation.

Ship A is sailing 25 km/h east and Ship B is sailing 15 km north. They are giving us the time frame, which is 4 hours ( t = 4). Recall that Distance = Rate * time. Let us find the distance for each ship after 4 hours

Ship A Ship B

d=25*4 = 100 km d=15*4= 60 km

the Pythagorean theorem.

a2+b2=c2

(30)2+(60)2=c2

c=30√(5)

From the question, "How fast" is asking us for a rate. The rate on the hypotenuse side. We have to take the derivative of the pythagorean theorem with respect to time.

2a(da/dt) + 2b(db/dt) = 2c(dc/dt)

Solve for dc/dt

dc/dt = [a(da/dt) + b(db/dt)] / c

dc/dt = [30(-25) + 60(15)] / 30√5 ****Note: we have -25 as time increases, the distance is smaller

dc/dt = √5 km/h

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The correct match the following is shown below:

2x + 3 (x - 2) = 6 (x + 1) + x → x = -6

2x + 3 (x - 2) = 6 (x - 1) - x → All real numbers

2x + 3 (x - 2) = 6 (x - 1) + x → x = 0

2x + 3 (x - 1) = 6 (x - 1) - x → No solution.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given:

The equation is, 2x + 3 (x - 2) = 6 (x + 1) + x, 2x + 3 (x - 2) = 6 (x - 1) - x, 2x + 3 (x - 2) = 6 (x - 1) + x, and 2x + 3 (x - 1) = 6 (x - 1) - x

Solve the above equations as shown below,

2x + 3 (x - 2) = 6 (x + 1) + x

2x + 3x - 6 = 6x + 6 + x

5x - 6 = 7x + 6

7x - 5x = -6 - 6

x = -6

2x + 3 (x - 2) = 6 (x - 1) - x

2x + 3x - 6 = 6x - 6 - x

5x  - 6 = 5x - 6

Infinity solutions,

2x + 3 (x - 2) = 6 (x - 1) + x

2x + 3x - 6 = 6x - 6 + x

5x - 6 = 7x - 6

x = 0

2x + 3 (x - 1) = 6 (x - 1) - x

2x + 3x - 3 = 6x - 6 - x

5x - 3 = 5x - 6

Parallel line, hence, no solution.

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Answer:

B. Shape A can be matched to shape B by reflecting about the origin and then shifting –3 on the x-axis and 1 on the y-axis.

Step-by-step explanation:

Answer:

x^2-2x-48

Step-by-step explanation:

FOIL

Firsts = x*x = x^2

outside = x*-6 = -6x

inside = 8*x = 8x

lasts = 8*-6 = -48

add all together x^2-6x+8x-48 = x^2-2x-48

Answer:

x² + 2x - 48

Step-by-step explanation:

( x + 8 ) ( x - 6 )

=  x ( x - 6 ) + 8 ( x - 6 )

= x*x - 6*x + 8*x + 8*( - 6 )

= x² - 6x + 8x  - 48

= x² + 2x - 48

The area of the cylinder's base is 1÷4π.x² is the correct option

What is a cylinder?

A cylinder is a three-dimensional solid in mathematics that maintains, at a given distance, two parallel bases connected by a curving surface. These bases often have a circular form (like a circle), and a line segment known as the axis connects the centres of the two bases. The height of the cylinder is "h," while the radius of the cylinder is "r," measuring the distance from the axis to the outside surface.

The three-dimensional form of a cylinder is made up of two parallel circular bases connected by a curving surface. The right cylinder is created when the centres of the circular bases cross each other. The axis, which represents the height of the cylinder, is the line segment that connects the two centres.

The cylinder seems to be a rectangle from the side perspective and a circle from the top view.

Since a cylinder has a curved form and no straight lines, it lacks vertices in contrast to cones, cubes, and cuboid shapes. Two of its faces are round.

According to the question volume of the cylinder is

1. πr^2h = πr^3

h=r=x/2

2.

The radius of cylinder is

= x/2

3.

The area of the cylinder's base is

= πr^2

= (π x^2)/4

4.

The height of the cylinder is =

radius= height =x/2

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Answer:

[tex]P_t=5x+16[/tex]

Step-by-step explanation:

The perimeter of the triangle will be the sum of all the sides,

[tex]P_t=a+b+c[/tex]

For this problem, let a=x, b=3x+12, and c=4+x.  So,

[tex]P_t=(x)+(3x+12)+(4+x)\\P_t=x+3x+12+4+x\\P_t=x+3x+x+12+4\\P_t=5x+16[/tex]

Because both of its x-intercepts should be the same horizontal distance from the axis of symmetry at x = 5/2 or 2.5 according to symmetry, the vertex's x-coordinates are 5/2.

A pair of numbers that use the horizontal and vertical separations from the two reference axes to define a point's location on a coordinate plane. typically expressed by the x-value and y-value pair (x,y).

Here,

The parabola is symmetric around its vertex. This means that the roots are the same horizontal distance away from the vertex. Furthermore, we can apply the midpoint formula on the given roots to find the x coordinate of the vertex.

Find the midpoint of 2 and 3 to get

(2+3)/2 = 5/2

The x-coordinates of its vertex is 5/2 because by symmetry, both x-intercepts should be the same horizontal distance from the axis of symmetry at x = 5/2 or 2.5.

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Only the transitive relation is true for the provided relation for (x, y) R if x y defined on the set of positive integers.

Assuming (x, y), R

To determine whether or not a relation is transitive, symmetric, antisymmetric, reflexive, or a partial order:

If (x, x)R for all x R x x for all x R, which is false.

b. Symmetric: For all (x, y) R, if "x" and "y" are related, then "y" is also related to "x."

In this case, x y y x for all (x, y) R, which is false.

c. Antisymmetric: If "x" and "y" are related, then "x" equals "y" for all (x, y) R.

In this case, x y and y x x = y are false.

not in opposition.

c. Transitive: If "x" and "y" are related, then

For all values of x, y, and z R, 'x' is connected to 'z'.

For any x, y, and z R, x y, y z x z.

True.

Therefore, only the transitive relation for the given relation for (x, y) R if x y defined on the set of positive integers is true.

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The total years taken to double the money according to Compounding will be 12.5  years.

What is compound interest?

Compound interest is that the interest on savings calculated on each the initial principal and therefore the accumulated interest from previous periods.

Main body:

Given :

rate = 6%

amount = $900

Total amount = $1800

Compounded monthly,

so formula becomes,

Total amount = amount (1+r/1200)^12t

T = A[tex](1+r/1200)^{12t}[/tex]

1800 = 900 (1+6/1200)^12t

2 = (1+1/200)^12t

2 = 1.005^12t

taking log on both sides

log 2 = 12t *log 1.005

0.3/0.002 = 12t

t = 12.5 years

Hence the time taken to double the money is 12.5 years.

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a) The linear functions each cell phone provider are given as follows:

The graph with these functions is given by the image shown at the end of the answer.

b) The cheaper companies are given as follows:

The linear functions in this problem are defined in slope-intercept format as follows:

y = mx + b.

In which the coefficients and their meaning are given as follows:

Hence the cost functions for this problem are given as follows:

The functions intersect at x = 6.67, hence the cheaper plans are given as follows:

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The letters of "hyperbola" can be combined into 40,320 different nine-letter words by using each letter just once.

Combinations are the procedures used in mathematics to pick k things from n different items without replacement.

The following formula computes the combinations of k items from n:

(n, k) = n! / k!×(n-k)!

There are 8 letters in the word "hyperbola",

So, there are 8 choices for the first letter, 7 choices for the second letter, and so on, down to 1 choice for the last letter.

This means that there are :

⇒ 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320

Therefore, 40,320 possible nine-letter words can be formed from the letters of "hyperbola" using each letter once per word.

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The average class size of Newton middle school is 21.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that a decade ago, the average class size at Newton Middle School was 30 students. Now it is 30% smaller.

The average class size will be calculated as,

Average class size = 30 x (70%)

Average class size = 30 x 0.7

Average class size = 21

Therefore, the average class size at Newton middle school is 21.

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Answer:

f(x)=x/2-4

-f(x)=a

a=x/2-4

x=a/2-4

a/2-4=x /×2

a-8=2x

a=8+2x -> f^-1(x)=8+2x

Answer:

Infinitely many

Step-by-step explanation:

2x+y=1

4x+2y=2

Divide both sides of the second equation by 2.

2x + y = 1

This is the same as the first equations. Both equations are the same equation. Since you have only one equation and two variables, there is an infinite number of solutions.

Answer: Infinitely many

Answer:

---------------------------------

For the equation to have infinitely many solutions, the variables and constants should cancel and should end up with 0 = 0. It means for any value of the variable the equation is true, i.e. both sides are equal.

Given equation:

If we solve it for ? we'll get:

Answer:

Part A is 100

Part B is 50

Part C is 25

all of it goes down by 15 so just keep subtracting

Step-by-step explanation:

I used common since and a sheet of paper

Answer:75%

Step-by-step explanation:

The measure of angle B is (d)  114 degrees

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

B = 13x - 16

Exterior of B = 8x - 14

As a general rule, the sum of an angle and its exterior is 180 degrees

This means that

13x - 16 + 8x - 14 = 180

Evaluate the like terms

So, we have

21x = 210

Divide both sides

x = 10

Recall that

B = 13x - 16

So, we have

B = 13 x 10 - 16

Evaluate

B = 114

Hence, the measure is 114 degrees

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Answer:

The measure of angle B is (d)  114 degrees

Step-by-step explanation:

Answer: (fog)(x) = f(g(x)) = f(6x) = 5(6x) = 30x

So (fog)(x) = 30x, which is a polynomial in simplest form