Reuben drove 243 miles using 12 gallons of gas. At this rate, how many miles would he drive using 16 gallons of gas?

Given data:

The number of red drops for first batch are r=100.

The number of blue drops for first batch are b=20.

The number of red drops for second batch are r'=75.

The number of blue drops for second batch are b'=15.

The expression for the red per blue drop for first batch is,

n=r/b

Substitute the given values in the above expression.

n=100/20

=5

The expression for the red drop per blue drop of the second batch is,

n'=r'/b'

Substitute the given values in the above expression.

n'=75/15

=5

Thus, yes the ratio of red to the blue drop is same for both batches.

The bottom of a 25 feet ladder is propped up against a wall, which is 7 feet away. When the ladder is 15 feet above the ground, 23.3 feet per second is the top of the ladder falling down the wall.

Given that,

The bottom of a 25 feet ladder is propped up against a wall, which is 7 feet away. A feet per second of the ladder's bottom begins to slide away from the wall.

We have to find when the ladder is 15 feet above the ground, how many feet per second is the top of the ladder falling down the wall.

Let us take x = height where the ladder hits the building

7 squared + x squared=25 squared

49+x squared=625

x squared=576

x=24 feet

Now,

If it slips 15 feet that 24-15=9 feet

Let x = distance from wall:

x² + 9² = 25²

x² + 81= 625

x² = 544

x = 23.3 feet

Therefore, when the ladder is 15 feet above the ground, 23.3 feet per second is the top of the ladder falling down the wall.

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Answer:

f(x)=x+2 Passes through

x-y=2 DOES NOT pass through

Step-by-step explanation:

Method- plug in x and see if the y matches the points. (1,3) (7,9)

f(x)=x+2

f(1)=1+2=3

f(7)=7+2=9

Matches!

x-y=2

1-y=2 --> y=-1

Does not match

The conditional probability that a degree is earned by a person whose race is white, given that it is an associate's degree, is 0.571.

The percentage of associate's degrees is 21%.

The percentage of degrees earned by people whose race is white is 58%.

The percentage of associate's degrees out of all degrees earned by people whose race is white is 12%.

Let the probability of earning an associate's degree be P(A).

P(A) = 0.21

Let the probability of earning a degree by the people whose race is white be P(B).

P(B) = 0.58

Let the probability of earning an associate's degree by the people whose race is white be P(C).

P(C) = 0.12

P(C) = P(A∩B)

We need to find the conditional probability that a degree is earned by a person whose race is white, given that it is an associate's degree.

P(B/A) = P(A∩B)/P(A)

P(B/A) = 0.12/0.21

P(B/A) = 0.571

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After evaluating the expression, the value of n is √(70/2C).

So, 2nCn = 70:

Now, solve for n as follows:

Therefore, after evaluating the expression, the value of n is √(70/2C).

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The curves are intersecting at (1, 1) and (-10, -4)

Nonlinear functions are the functions where the equations are not linear or the highest degree is more than 1. The following are some examples where the functions are not linear or non-linear. Ex. [tex]x^{2}[/tex] + 4x -1

In the above question, a graphical representation of non-linear system of equations is given

We need to find the solution of this non-linear system of equations based on the graphical representation

We can find the solutions from the graph, wherever the curves are intersecting, that intersection point is known as the solution of the non-linear system of equations

We can clearly see that, the curves are intersecting at

(1, 1) and (-10, -4)

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The curves are intersecting at (1, 1) and (-10, -4)

Nonlinear functions are the functions where the equations are not linear or the highest degree is more than 1. The following are some examples where the functions are not linear or non-linear. Ex. [tex]x^{2}[/tex] + 4x -1

In the above question, a graphical representation of non-linear system of equations is given

We need to find the solution of this non-linear system of equations based on the graphical representation

We can find the solutions from the graph, wherever the curves are intersecting, that intersection point is known as the solution of the non-linear system of equations

We can clearly see that, the curves are intersecting at

(1, 1) and (-10, -4)

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The slope of the line that is parallel to 8x + 9x = 3 is: -8/9.

If two lines are parallel to each other, their slope values is equal to each other. This means the value of "m" in their equation expressed in slope-intercept form as y = mx + b, is the same.

Given the equation of a line in standard form as, 8x + 9y = 3, rewrite this in slope-intercept form:

8x + 9y = 3

8x + 9y - 8x = -8x + 3 [subtraction property of equality]

9y = -8x + 3

9y/9 = -8x/9 + 3/9 [division property of equality]

y = -8/9x + 1/3

The slope of the equation is -8/9. Therefore, the slope of the line that is parallel to the equation 8x + 9y = 3 will also be: -8/9.

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Using the angle of elevation, the height of the tree is 71.57 feet.

The angles of elevation to a nearby tree from a point on the ground is measured to be 54 degrees.

The distance from the tree to the point on the ground is 52 feet.

The height of the tree can be found as follows:

The situation can be modelled to a right triangle.

Therefore, the height of the tree is the opposite side of the right triangle formed.

Hence,

tan ∅ = opposite / adjacent

where

∅ = angle of elevation

tan 54 = h / 52

cross multiply

h = 52 tan 54

h = 52 × 1.37638192047

h = 71.5718598645

Therefore,

height of the tree = 71.57 feet.

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In plan B the price rises by 10%.

Thus the price rise is per week is $0.8

In plan A the price rise per week is $0.1

In plan C the price rise per week is

In plan D the price rise per week is $0.25

Considering all the plan the maximum price rise for each week is 0.8.

So the plan that would lead to $12 fastest is plan B.

The answer is plan B.

On the first line the distributive property was used. This property says that the product of a constant with a sum of two numbers is equal to the sum of the products.

On the third line the "associative" property was used. This property says that if you have the sum of three numbers the order at which you sum them doesn't affect the results.

Answer:

w = 35

Step-by-step explanation:

To solve this problem, you will need to undo it in reverse order. The first thing done to w is to multiply it by 17 and then add 29 to it. You need to undo the addition of 29 with subtraction first.

624-28=595

Next, you need to undo the multiplication by 17 with division.

[tex]\frac{595}{17} =35[/tex]

Therefore, your answer is 35

Answer:

y=9

Step-by-step explanation:

16y and 18y-18 are vertical angles. The definition of Vertical Angles states that both of the measures of the angles are equal to each other. Therefore,

18y-18=16y

2y-18=0

2y=18

y=9

Given data

Ammy has a piece of wood that measures 42 inches

Ammy cut from the 42-inch piece of wood is calculated as

Thus, Amy cut from the 42-inch piece of wood is 33 inches

Answer:

1st one- 4

2nd one- 1

3rd one- 5

4th one-6

5th one-3

6th one-2

The Probability that Robert randomly pulls out a black sock is 1/5  .

In the question ,

it is given that

Total number of socks in sock drawer = 30 socks

number of white socks in the drawer = 16 socks

number of black socks in the drawer = 6 socks

number of red socks in the drawer = 2 socks

number of yellow socks in the drawer = 6 socks

So , the probability that he randomly pulls out a black sock = (number of black socks in the drawer) / ( total number of socks in the drawer )

= 6 / 30

= 1/5

Therefore , The Probability that Robert randomly pulls out a black sock is 1/5  .

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Answer: C. Four loaves, with flour left over.

Step-by-step explanation:

7/2 simplifies to 3 1/2

Do the math,

3/4 + 3/4 = 1 1/2        2 loaves

1 1/2 + 3/4 = 2 1/4      3 loaves

2 1/4 + 3/4 = 3           4 loaves

Now when we add 3/4 to 3, we get more than 3 1/2. Which means we do not have enough flour for another loaf of bread. So, we can make four loaves and still have some four left over. The answer is C.

We will have the following:

Inferring from the information presented in the diagram we can conclude that the measurements will be:

Base: 3ft * 12ft = 36f t^2

Side1: 3ft * 2ft = 6 ft^2

Side 2: 12ft * 2ft = 24 ft^2

So, the values that would represent the dimension will be:

Length: 12 ft.

Width: 3 ft.

Height: 2 ft.

After simplification, 7h+(-9.1d)-13+6d-3.5h is 3.5h-3.1d-13.

According to the question,

We have the following expression:

7h+(-9.1d)-13+6d-3.5h

Now, we will simplify it by adding or subtracting the numbers or the numbers with the same variable together. For example, 3.5h can only be subtracted from 7h because both of them h as a variable. And 6d can be subtracted from 9.1d.

(More to know: when a positive and a negative number is multiplied then the result is always negative. In this case, we will multiply +1 into -9.1d.)

Now, let's simplify the given expression:

7h-3.5h-9.1d+6d-13

3.5h-3.1d-13

Hence, the expression obtained after solving the given expression is 3.5h-3.1d-13.

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Answer:

-20

Step-by-step explanation:

1- each of the two numbers are inside parenthesis and are beside each other which means they should be multiplied like this: -5.6 * 3.4

2- because 5.6 is negative, the rule in multiplying different signs would result to a negative number

3- and when you accurately multiply them, the answer is 19.04, and the options here are estimated so you should estimate the 19.04 too

4- 1 after it is 9 and nine is a great number, 1 turns to 2 and 9 turns into 0, which equals to 20, and DO NOT forget to add the sign, which is negative as i said previously

Answer:

2×10^7

Step-by-step explanation:

cuz 3:6 is 2 and 10^2÷10^-5 equals 10⁷

Answer:

2×10^7

Step-by-step explanation:

6×10²/3×10^5

6/3×10²-10^-5

2×10²-^(-5)

2×10²+^5

2×10^7

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The midpoints of the first and last parts are 4/5m units apart

The length of the line segment is given as

Length = m units

From the question, the number of partitions is given as

Partition = 5

So, the length of each partition is

Each partition = Length/Partition

This gives

Each partition = m/5

The midpoint of a partition is

Partition midpoint = m/5 x 1/2

Evaluate

Partition midpoint = m/10

The distance between the midpoints of the first and last segments is then calculated as

Distance = Length - 2 x Partition midpoint

So, we have

Distance = m - 2 x m/10

Evaluate

Distance = m - m/5

This gives

Distance = 4/5m

Hence, the distance is 4/5m units

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Answer: 48 is the smaller integer

Step-by-step explanation: 48+49=97 48 and 49 are the two integers, 48 is smaller than 49.

We will have that the relationship is proportional because each time he bought more sets they had the same cost, and the total cost added to the sum of the independent cost. And we have the following relationship for the 2 sets and 4 sets:

2 sets:

So, each individual set is $12.5.

4 sets:

So, each individual set is $12.5.

So, each individual set for each relationship has the same cost, therefore the relationship is proportional.

⇒Mathematically this means

[tex]\frac{1}{4} (r+10)= r-4\\\frac{r}{4} +\frac{10}{4} =r-4\\\frac{r}{4}(4) +\frac{10}{4} (4)=r(4)-4(4)\\r+10=4r-16\\r-4r=-16-10\\-3r=-26\\\frac{-3r}{-3} =\frac{-26}{-3} \\r=\frac{26}{3}[/tex]

Attached is the solution.

The formula written in symbols as T =UN. Solve the formula for U.​

we have

T=U*N

solve for U

so

isolate the variable U

step 1

divide by N both sides

T/N=U*N/N

T/N=U

therefore

In this kind of problem is better to work backwards. We have the number nine hundred twenty-eigh.

This means that the two last digits are a 2 and a 8, becasue we have a "twenty-eight" = 28

And then, we have "nine hundred" = 900

The number whole, then, is:

The volume of the cone is:

The volume of a cone is given by the formula:

Given radius, r = 8, and height, h = 4, we have: