Ethanol fuel mixtures have "E" numbers that indicate the percentage of ethanol in the mixture by volume. For example, E10 is a mixture of 10% ethanol and 90% gasoline. How much E7 should be mixed with 4000 gal of E10 to make an E9 mixture?

Answer: 2.5, 5.4

Step-by-step explanation:

[tex]-16t^2 +126t=213\\ \\ 16t^2 -126t+213=0\\\\t=\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(213)}}{2(16)}\\\\t \approx 2.5, 5.4[/tex]

The answer to the inequality is P> 5

What is Inequality?

Inequality in mathematics, the relationship between two values that are not equal

To solve the inequality we follow the steps;

P+5 > 10

Subtract 5 from both sides

P + 5-5 > 10-5

P>5

Therefore, the answer to the inequality is P> 5

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The rate of change of the company Water's Edge rafts is greater than Ryan’s Rafts.

The slope is the ratio of rising or falling and running. The difference between the ordinate is called rise or fall and the difference between the abscissa is called run.

From the graph, the two points are taken as (0, 0) and (1, 6). Then the slope of the Water's edge rafts will be given as,

⇒ (6 - 0) / (1 - 0)

⇒ $6 per hour

From the table, the two points are taken as (1, 15) and (5, 24). Then the slope of Ryan's rafts will be given as,

⇒ (24 - 15) / (5 - 1)

⇒ 9 / 4

⇒ $2.25 per hour

The rate of change of the company Water's Edge rafts is greater than Ryan’s Rafts.

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Answer:

Rides cost $4

Games cost $2.50

Step-by-step explanation:

Let g = cost of games

Let r = cost of rides

6g + 3r = 27

2g + 9r = 41  Multiple this through by -3 and then add to the equation above.

-3(2g + 9r) = (41) -3

-6g - 27r = - 123

6g + 3r = 27

       -24r = -96  Divide both sides by -24

r = 4  This is the cost of the rides.

Plug is 4 for r in either of the two original equations to solve for g

6g + 3r = 27

6g + 3(4) = 27

6g + 12 = 27  Subtract 12 from both sides

6g = 15  Divide both sides by 6

g = 2.5  This is the cost of the games.

in this problem we have that

y+20=x+15 -------> by vertical angles

isolate variable y

y=x+15-20

y=x-5 ------> equation A

and

(3x+5)+(x+15)=180 ------> by form a linear pair (sipplementary angles)

solve for x

4x+20=180

4x=160

x=40

substitute the value of x in equation A

y=40-5

y=35

therefore

x=40 and y=35

1.

What do you know?

the troposphere extends 8 to 20 km above the Earth's surface. The surface temperature is 15°C and decreases at a rate of 6.5°C per kilometer away.

What do you want to find out?

The temperature at any point of the troposphere

What kind of answer do you expect?

Any value below 15°C

2. Define variables,

T is for temperature, and

d is the distance away from the surface

3. What is the b -value

b = 15

which is the Earth's surface temperature or the initial temperature for our problem

4. What is the slope

the slope 'm' equals -6.5

which means that the temperature decreases 6.5°C per km

5. write the equation

the general form for this equations is y = b + mx

thus, for our problem, the equation is: T = 15 - 6.5*d

6.

a) the slope represents the rate of change of temperature with respect to distance, since m = -6.5 °C/km , this means the troposphere is getting 6.5 °C colder per km away from Earth's surface

b) the y-intercept represents the Earth's surface temperature

Graph:

7. identify 3 points

when d = 0 then T = 15, so our first point is (0,15)

when d = 1 then T = 15 - 6.5 = 8.5 , so our second point is (1,8.5)

when d = 2 then T = 15 - 13 = 2 so our third point is (2,2)

8. calculate the slope

let's use this equation and this set of points,

let's replace and solve

We can see that it does match the slope from our model, which is -6.5

9. graph the line and the points,

10. Complete the sentence

... ends between 8 km and 20 km above Earth.

11. temperature at the farthest point

when d = 20 then,

... the temperature is -115°C

12. Temperature range,

from... 15 °C to -115 °C

The compound inequality for the graph shown above is :

The number of Screamers when Runners are 6 is 4,

and the number of Runners when Screamers are 10 is 15.

It is basically the measurement of two numbers and it compares by how much one quantity is bigger than another.

When two ratios are equal, they are usually said to be in proportion.

As given in the above questions,

Screamers:Runners= 2:3

So, let the number of screamers in first case is x

Then, x:6 = 2:3

         x= 4

Hence , the number of screamers is 4.

In second case, let the number of runners is y

Then, 10:y = 2:3

          y= 15

Hence , the number of runners is 15.

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Answer:

Step-by-step explanation:

window*

Answer: I believe it is A.

Step-by-step explanation:let me start by saying that D and B aren't true because u is greater than 3 to the square root of 3, which is roughly 5.2. So were left with A and C. Then we realize that 3 to the square root of 3 is the same as 3 to the square root of 3, so it can't be C, so were left with A. (I could be wrong, I'm not the smartest in math, but I hope this helped and wish you luck)

Answer:

====================

Given is 30° × 60° × 90° triangle.

The matching choice is A

The equation is modelled as [tex]y\ = \frac{kx}{z^2}[/tex].

Given,

y varies directly with x

y varies inversely with square of z

According to given data the equation can be modelled as follows:

y varies directly with x, it can be written as [tex]y \ \alpha \ x[/tex]

and also y varies inversely with square of z, it can be written as [tex]y\ \alpha \ \frac{1}{z^2}[/tex]

Combining both, then we get,

[tex]y\ \alpha \ \frac{x}{z^2}\\\\y\ = \frac{kx}{z^2}[/tex]

Where, k is proportionality constant.

Thus, the combined equation is modelled as [tex]y\ = \frac{kx}{z^2}[/tex].

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Hello there. To solve this question, we'll find how many times George's grandpa is older than his grandson.

First, this is also called the ratio of the ages between George and his grandpa.

To find this, we divide their ages in the order Grandpa : Grandson as following:

Simplify the fraction by a factor of 8

This is how many times George's grandpa is older than him.

To find the price per ounce for each grocery store we have to divide the price by the size of the bottle:

Hawkin's Grocery:

$0.25 per ounce

MItchell's Store:

$0.32 per ounce

Selena's Market:

$0.30 per ounce

Teresa's Store:

$0.20 per ounce

We can see that Teresa's Store has the lowest price per ounce

S={5}

1) Evaluating x in this question

4x=20 Divide both sides by 4

4/4x=20/4

x=5

So x is equal to 5, in this equation 4x=20

S={5}

Answer:

the hat cost 18

Step-by-step explanation:

if the shirt is 24 half the price of the shirt is 12 so 21-12= 9 which is the price of the hat discounted.

The original price of the hat is 18 because 9 x 2 = 18

The fraction of 2 hrs 15 minutes to 1/4 of an hour is 1/9.

What is fraction?

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Since,

1 hour = 60 minutes.

2 hours = 120 minutes.

2 hours 15 minutes = 120 + 15 = 135 minutes.

1/4 of an hour = 60/4 = 15 minutes.

So, the fraction is,

[tex]\frac{15}{135} = \frac{1}{9}[/tex]

Therefore, the fraction of 2 hrs 15 minutes to 1/4 of an hour is 1/9.

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To answer this question, we need to find the unit rate for the steady speed. Then, we can proceed as follows:

Then, we have that the unit rate, in this case, is 2/3 miles per minute.

Hence, the car will travel in 34 minutes:

Thus, the car will travel 222/3 miles in 34 minutes.

The car will travel in one hour or 60 minutes:

Then, the car will travel 40 miles in one hour or 60 minutes.

The transformed equation of the parent function f(x) = x² will be g(x) = x²-27.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that, the transformed equation of the parent function f(x)=x² where g(x) has been translated 3 units right and reflected across the x-axis.

The function g(x) when the g(x) has been translated 3 units right is,

g(x) = x²-27

Thus, the transformed equation of the parent function f(x) = x² will be g(x) = x²-27.

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True about translations is they can help you see if two figures are congruent

What are translations?

In mathematics, a translation is an up, down, left, or right movement of a shape. Because the translated shapes appear to be exactly the same size as the original ones, they are consistent with one another. Just one or more directions have been altered. There is no change in the shape because it is simply being moved from one location to another.

Each point in a figure is moved the same distance in the same direction using a type of transformation known as translation.

Hence, they can help you see if two figures are congruent.

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The measures of the numbered angles in the rhombus ABCD if m∠ABC = 49° are m∠1 = 24.5°, m∠2 = 90°, m∠3 = 24.5° and m∠4 = 65.5°.

We are given:

A rhombus ABCD and m∠ABC = 49°.

The diagonal of the rhombus divides the angles into 2 equal parts. Therefore,

m∠1 = m∠ABC / 2 = 49 / 2 = 24.5°

The diagonal AC is perpendicular to the diagonal DB.

And we know that diagonals bisect each at right angles.

So, m∠2 = 90°.

Opposite angles of the rhombus are equal.

Therefore,

∠B = ∠D

multiply both sides by 1/2, we will get;

1/2 ∠B = 1/2 ∠D

m∠1 = m∠3 = 24.5°

Sum of angles in a quadrilateral = 360°

360 -  98 = 262°

∠A = ∠C = 262 / 2 = 131

Therefore,

m∠4 = 1 / 2 ∠C

m∠4 = 1 /2 * 131

m∠4 = 65.5°

Thus, the measures of the numbered angles in the rhombus ABCD if m∠ABC = 49° are m∠1 = 24.5°, m∠2 = 90°, m∠3 = 24.5° and m∠4 = 65.5°.

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The number of heavy equipment operators employed=16

The number of laborers employed=14

Assume

x=number of heavy equipment operators employed

30-x=number of laborers employed

From the question, we have

135x+97(30-x)=3518

135x+2910-97x=3518

38x=608

x=16

number of heavy equipment operators employed=16

number of laborers employed=14

Multiplication:

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.

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Answer:

The number of heavy equipment operators employed=16

The number of laborers employed=14

Assume

x=number of heavy equipment operators employed

30-x=number of laborers employed

From the question, we have

135x+97(30-x)=3518

135x+2910-97x=3518

38x=608

x=16

Step-by-step explanation:

Using conditional probability, it is found that there is a 0.83 = 83% almost 0.8403  probability that this student does spend more than $25 a week on gas, given that he/she does commute to school each day.

Probability: -

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%).

Conditional Probability :

Using conditional probability, it is found that there is a 0.83 = 83% = P( A∩ B) / P(A)

In which

In this problem:

Event A: Commute to school each day.

Event B: Spends more than $25 a week.

80% indicated that they commute to school each day. of those that commute to school each day, hence , P(A) = 0.8

Of those, 83% spend more than $25 a week on gasoline, hence .

                     P(B|A) = 0.83

Thus, 0.83 = 83% probability that this student does spend more than $25 a week on gas, given that he/she does commute to school each day.

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Let 'x' be the number of pounds of Yurly's package and let 'y' be the number of pounds of Anduray's package. Since the combined weight of both packages is 9 pounds, then:

now, we have that Yurly's package weights three pounds more than two times the weight of Anduray's, we can write this as:

thus, we have the following system of equations to represent this situation:

The relation is a function because (a) Yes, because every x-value corresponds with a single y-value.

From the question, we have the graph to represent the given parameters that can be used in our computation

We are to find out if the graph represents a function

For a graph to represent a function, the graph must pass the vertical line test

This means that a line drawn from the x-axis must touch the points at most once

In this case, the graph would pass the vertical line test because no two points have the same y coordinate

Hence, it is a function

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Answer:

B

Step-by-step explanation:

Answer:

Step-by-step explanation:

i think its B

Congruency is a term used to describe two objects with the same shape and size.

In this case, two triangles are congruent if they have exactly the same three sides and exactly the same three angles. The equal sides and angles may not be in the same position.

For instance,

these triangles are congruent. They have the same sides but in different position.

Another example is

In this case the congruency is about angles. These 2 triangles have the same angles and the same sides but in different positions.

Another instance is

They are the same triangles but in different positions.

From the first question we can see that both triangles are congruent.

This imply that they are the same but in different position:

We can note that angle C is equal to angle T, therefore

In the same way, angle U is equal to angle B, then we have

We can find angle A by noticing that the interior angles of a triangle add up 180, that is

Since angle V is equal to angle A, also V=66

Answer:

y=-11

Step-by-step explanation:

Step 1: Subtract 12 from both sides.

2y+12−12=−10−12

2y=−22

Step 2: Divide both sides by 2.

2y/2=-22/2

And would get you y=-11

Answer:

b

Step-by-step explanation:

just took the test yyyyyyyyyyyyyyyyyyyyyyyyy

The side opposite to 30 degree angle is 1/2. So,

The measure of side opposite to angle 60 degree is,

The measure of side x is,

The measure of hypotenuse is 2a. So,

So answers are,

and