You don't need to explain if you don't want.

Answer:

total distance = 654.5

Total gas used = 27.5

Distance per gallon = 654.5 ÷ 27.5 = 23.8

We drove 23.8 miles for each gallon of gas

Solution

Solution

The final answer

253.75 gallons remain in the tank when the depth of oil is 3.5 ft

Answer:

24° , 60° , 96°

Step-by-step explanation:

sum the parts of the ratio, 2 + 8 + 5 = 15 parts

divide the sum of the angles in a triangle by 15 to find the value of one part of the ratio.

180° ÷ 15 = 12° , then

2 parts = 2 × 12° = 24°

5 parts = 5 × 12° = 60°

8 parts = 8 × 12° = 96°

the 3 angles in the triangle are 24° , 60° , 96°

Answer:

28°

Step-by-step explanation:

AB and CD are straight lines, all angles in a straight line add up to 180

Answer:

That is my own idea and I hope it is very helpful

Table A shows a proportional relationship

What is proportional relationship?

When the value of independent variable changes the value of dependent variable changes. that means if the value independent variables is increase the value of dependent variable will also be increased.

In the figure we are given 2 tables

We plot both the curve on the graph we get

Table A shows a linear relationship where are Table b Does not shows a proportional relationship

Hence Table A shows a proportional relationship

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Answer:

Step-by-step explanation:

The values x = 0, y = 0.03 and z = 0.039 for the three events A,B and C with their associated probabilities.

The following are axioms of probability for the purpose of answering the given question:

Two events are said to be mutually exclusive if the probability of their intersection is zero.

Two events are said to be independent if the probability of their intersection is equal to the product of their respective probability

From the question, the probability of the event A alone occurring=0.10

the probability of the event B alone occurring=0.30

the probability of the event C alone occurring=0.39

Given that B and C are mutually exclusive events;

x = probability of the intersection of B and C=0

A and C are said to be independent so; z = probability of the intersection of A and C = 0.10×0.39

probability of the intersection of A and C = 0.039

If A and B are not mutually exclusive events and are independent then;

y = probability of the intersection of A and B

probability of the intersection of A and B = 0.10×0.30

probability of the intersection of A and B = 0.03.

Hence, the values of x,y and z are 0, 0.03 and 0.039 respectively for the events A,B and C with their associated probabilities.

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We are asked to determine the degree of the polynomial given its graph. To do that we can count the number of bumps in the graph. We notice that it has 4 bumps:

This type of behavior is usual of polynomials of degree 5.

EXPLANATION

Since the vertex is at (-1, -3), the only appropriate option is to translate the function one unit to the left, and again translating 3 units down, with the following form:

g(x) = |x+1| - 3

Therefore, the solution is the last option.

The solution is x = √ 14, it is irrational

The closest integer approximation to the solution is 4

From the information given, we have that;

42 equals 3 x squared

This is represented as;

3x² = 42

Let's take the following steps to determine the value of x

Divide both sides by the coefficient of x²

x² = 42/3

x² = 14

Take the square root of both sides, we have;

x = √ 14

The solution is an irrational number

An irrational number is described as a number that cannot be expressed in a fractional form.

They are real numbers that expressed as quotients

Examples of irrational numbers are;

√5, √7, √11, √13

Now, let's find the square root, we have

= 3. 74

Take '7' as 1 and add to the whole number 3, we get;

= 4 ; to the closest integer

Hence, the value is 4

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The resulting sample space of the given situation is S = {PQ, QP, PR, RP, QR, RQ}

Sample space:

Sample space refers the collection or a set of possible outcomes of a random experiment. The sample space is represented using the symbol, “S”.

Given,

Patty, Quinlan, and Rashad want to be club officers. The teacher who directs the club will place their names in a hat and choose two without looking. The student whose name is chosen first will be president and the student whose name is chosen second will be vice president.

Here we need to find the sample space for the event.

Let us consider,

P represents Patty

Q represents Quinlan

R  represents Rashad

And through the question we have know that, the teacher drawn two card at a time,

So we have consider that the teacher is going to draw out of the hat one first, without replacement, and then draw another one.  

The first chosen one will be the president, and that could be P, Q or R, Now, the chosen second one is the Vice president, and already one has already being drawn, that could only be two fellows.

Therefore, the total of likely outcomes is PQ,QP, PR, RP, QR, RQ, one paired up with either of the two remaining in the hat.

So, the resulting sample space is

S = {PQ, QP, PR, RP, QR, RQ}

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Answer:Answer: number 2 is correct

The measure of ∠C in the given triangle is 58°.

According to the question,

We have the following information:

ACD is a triangle where we have BD as an altitude on the side AC.

Now, we know that the altitude on any side makes an angle of 90° or in other words, it can be said that it makes a right angle.

Now, we have two right-angled triangle: ABD and CBD.

We have ∠ADB = 32°.

Now, ∠CDB will also be equal to 32° because the altitude bisects the angle (in two equal parts).

We know that the sum of the three angles in a triangle is 180°.

In ΔCBD, we have:

∠B + ∠C + ∠CDB = 180°

90° + ∠C + 32° = 180°

∠C + 122° = 180°

∠C = (180-122)°

(Moving 122 from the left hand side to right hand side will result in the change of sign.)

∠C = 58°

Hence, the measurement of ∠C in the given triangle is 58°.

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-( ( 7 - u )( u - 2 ) ) is the factorized form of the polynomial -7u² + 12u + 4, using the AC method.

Given the polynomial in the question;

-7u² + 12u + 4

Factor out -1 out of the polynomial

-1( 7u² - 12u - 4 )

Compare to the form ax² + bx + c

To factor, compare to the form ax² + bx + c and rewrite the middle term as a sum of two terms whose product is;

a × c = 7 × -4 = -28

and whose sum is;

b = -12

Now, factor -12 out of -12x

-1( 7u² - 12(u) - 4 )

We know that -13 is the same as 2 plus -14

-1( 7u² - ( 2 - 14 )u - 4 )

Apply distributive property

-1( 7u² - 2u - 14u - 4 )

Group the terms

-1( u(7u - 2) - 2(7u - 2 ) )

-1( (7-u)(u-2) )

-( (7-u)(u-2) )

Therefore, the factorized form of the polynomial is -( ( 7 - u )( u - 2 ) ).

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-(7u+2)(u-2) is the factorized form of expression -7u²+12u+4.

An expression is combination of variables, numbers and operators.

The given expression is -7u²+12u+4.

We need to find the factors of this expression.

-7u²+12u+4.

This can be written as

-7u^2+14u-2u+4.

Take 7u from first two terms and 2 from last two terms in the expression.

-7u(u-2)-2(u-2)

(-7u-2)(u-2)

-(7u+2)(u-2)

Hence -(7u+2)(u-2) is the factorized form of -7u^2+12u+4.

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The number that you can square to give an answer bigger than 500 but bigger than 600 = 25.

The square of a number is defined as the ability to multiple the given number by itself to give a perfect whole number.

For example the square of 2, which is written as 2² = 2×2 = 4

From the given scenario, the number that would be squared to give an answer bigger than 500 but bigger than 600 = 25

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Answer: 31

Step-by-step explanation:

The numbers are increasing by 1, then 2, then 3, ...

In other words, the second difference is 1.

So, the next number is likely [tex]24+7=31[/tex].

The slopes formed by each of the pairs of points are given as follows:

The slope is equivalent to the rate of change, hence, given two points, the slope is calculated as the change in y, also called rise, of these two points divided by the change in x, also called run.

For the first case, the points are:

(2, 11.9) and (4, 10.5)

Hence:

The slope is:

m = -1.4/2 = -0.7.

The other slopes are calculated as follows:

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To find the number we can create the following equation and solve for x:

Let x be the missing number, use inverse operations to solve the equation:

The number is 40.

The Solution:

Given the graph of f(x), we are required to determine whether the degree of the function is ODD or EVEN, and also to determine whether the function itself is ODD.

An odd function is defined as a function that has f(–x) = –f(x) for any value of x. The opposite input gives the opposite output.

From the given graph of f(x), the function f(x) is ODD.

The degree of the function f(x) is odd since the f(x) itself is odd.

Answer:

Step-by-step explanation:

12 times 2 =24 60 into 10 so i think it will be 6

Answer:

92 over 100

Step-by-step explanation:

Proportion = 0.2119

P (X is less than or equal to 0.18) = P [(X-μ)/ sigma is less than or equal to (0.18-0.22)/ 0.05] = P(Z is less than or equal to -0.80). Using z-table proportion = 0.2119

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Firstly, let's draw a picture of the distribution:

Graphically, we want to calculate the blue area. To put it differently, we want to calculate

To do this, we need to find the z-score associated with 6. We can calculate it by

Now, we must check our favorite z-score table and look for the probability associated with the z-score we just found. It's 0.0018.

The probability that a randomly selected TV will have a warranty of less than 6 years is 0.0018.

The rates of changes of the given function for the corresponding intervals are:  [-5, -1] = -8, [-4, -1] = -7, [-3, -1] = -6, [-2, -1] = -5.

What is function?

A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.

This means that a function f will map an object x to exactly one object f(x) in the set of potential outputs if the object x is in the set of inputs (referred to as the domain) (called the codomain).

The rate of change of a function can be calculate using the formula:

[tex]R = \frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]

Putting the value from the question:

given [x₁, x₂] = [-5, -1]

f(-5) = 35 , f(-1) = 3

Putting these value in formula:

[tex]R = \frac{3-35}{-1 -(-5)}[/tex]

R = -32/4

R = -8

given [x₁, x₂] = [-4, -1]

f(-4) = 24, f(-1) = 3

Putting these value in formula:

[tex]R = \frac{3-24}{-1 -(-4)}[/tex]

R = -21/3

R = -7

given [x₁, x₂] = [-3, -1]

f(-3) = 15, f(-1) = 3

Putting these value in formula:

[tex]R = \frac{3-15}{-1 -(-3)}[/tex]

R = -12/2

R = -6

given [x₁, x₂] = [-2, -1]

f(-2) = 8, f(-1) = 3

Putting these value in formula:

[tex]R = \frac{3-8}{-1 -(-2)}[/tex]

R = -5/1

R = -5

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It takes 1190 minutes for Allie to drive to the store and then to the car wash.

According to the question,

We have the following information:

Time taken by Allie to drive to the store = 456 minutes

Time taken by Allie to drive to the car wash from the store = 734 minutes

Now, we have to find the total time in minutes. So, we will add the total time taken by Allie to drive to the store and then to the car wash.

(Note that the time asked in the question is in minutes. So, we do not need to change the units of given time.)

Now,

The total time taken by Allie to drive to the store and then to the car wash = Time taken by Allie to drive to the store + Time taken by Allie to drive to the car wash from the store

The total time taken by Allie to drive to the store and then to the car wash = (456 + 734) minutes

The total time taken by Allie to drive to the store and then to the car wash = 1190 minutes

Hence, the total time taken by Allie to drive to the store and then to the car wash is 1190 minutes.

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Answer:

x³ + 4x² + 3x + 1

Step-by-step explanation:

fg(x) + f(x)

= x³ + 4x² + 3x + 1

Line c is also perpendicular to line a.

Suppose that c and b are perpendicular. This implies that:

option 1) b and a are the same line or,

option 2) b is parallel to a

Since we know that a and b are different lines, hence, the option 2 is the correct.

consider

note that the letter g is common to all the numbers in the equation, so we take the lowest power of g and make a common factor, that is:

so the correct answer is

g(5g - 4)

Answer: 9g

Step-by-step explanation:

3g^2 + 2g^2 - 4g

you simplify the exponents first, because of P.E.M.D.A.S.:

9g + 4g - 4g combine like terms

Answer: 9g

So, as shown at the function

f(x) is constant at the middle interval (10 , 15)

at which f(x) = 2 and the digit 2 is constant

so, the answer is (10 , 15)