Please Help With problem 1

The required 7,000 gallons of gasoline which are 9% ethanol must be added to 2,000 gallons of gasoline with no ethanol to get a mixture that is 7% ethanol.

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

Here,
To solve the problem, we can use the following formula:

(amount of ethanol in the final mixture) / (total amount of gasoline in the final mixture) = 7%

To find the amount of ethanol in the 2,000 gallons of gasoline with no ethanol:

ethanol in 2,000 gallons of gasoline with no ethanol = 0 × 2,000 = 0 gallons

Then, find the amount of ethanol in the final mixture:

ethanol in final mixture = (0.09x + 0 * 2,000) / (x + 2,000)

Notice that we use 0 gallons for the ethanol in the 2,000 gallons of gasoline with no ethanol, since it contains no ethanol.

Ethanol in the final mixture / total amount of gasoline in the final mixture = 7%

(0.09x + 0) / (x + 2,000) = 0.07

0.09x + 0 = 0.07(x + 2,000)

0.09x = 0.07x + 140

0.02x = 140

x = 7,000

Therefore, 7,000 gallons of gasoline which is 9% ethanol must be added to 2,000 gallons of gasoline with no ethanol to get a mixture that is 7% ethanol.

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Answer:

Step-by-step explanation:

Cross out B and D, because angle D does not correspond with Y and Angle F does not correspond with X (order matters).

It comes down to either A or C, so look at the sides.

DF does not correspond to XY, again, the order it is displayed matters.

D is the first letter and F is the last, while X is the 2nd letter of the triangle, while it should be the first letter to correspond with D

Thus by Process of Elimination the answer is C.

(Also DF DOES correspond with WY)

Answer:

length = x + 1

Step-by-step explanation:

given area = x² - 6x - 7

factoring the area expression

= (x - 7)(x + 1)

area = width × length

with width = x - 7 and length = x + 1

Answer: Rounding Whole Numbers

Step-by-step explanation: There are many times in real life where numbers need to be made easier so that they can be quickly added or subtracted mentally. Adding or subtracting whole numbers is hard when the numbers are not simple. There is a lot of opportunity to make a mistake. It's easier to add 50 and 60 mentally than it is to add 54 and 67. Rounding helps to reduce the chance of making a mistake. So, what exactly is rounding whole numbers?

First, a whole number is any number that does not contain a decimal or a fraction and is positive. Basically, if it can be counted to, it's a whole number. Rounding is making a number simpler by changing it to the closest place value. Rounding whole numbers are all based on the place values of whole numbers. A good way to think about rounding as a concept is to think about the word around it. If your mom is somewhere on your property, but she doesn't say where an answer to where she is would be that she is around. Around is less specific than, she's in the kitchen, just like 50 is simpler and less specific than 57.

Before getting into the rules or processes of rounding, place value needs to be reviewed. Let's assume the whole number is 3593. There are 4 digits in this number and each one is in a specific place value column.

Ones - The ones place is the furthest digit to the right of a whole number. 3 is in the one's place.

Tens - The tens place is one digit to the left of the one's place and represents a group of 10 ones. The 9 is in the tens place.

Hundreds - The hundreds place is direct to the left of the tens and the 3rd digit from the left of the number. It represents a group of 100 ones or 10 tens. The 5 is in the hundreds place.

Thousands - The thousands place is the digit to the left of the hundreds and the 4th digit from the left. It represents a group of 1000 ones, 100 tens, and 10 hundred. The 3 is in the thousands place.

The process of rounding begins by focusing on place value. When a number is rounded, the very thing that must be known is which place value the number is being rounded to. In real life, the answer will depend on how accurate the numbers need to be. In a math problem, the place value to be rounded will be part of the question. It will say something like round to the nearest or round by.

Rounding is a step-by-step process. The following steps will outline the process of rounding whole numbers. For the steps, the number 473 will be used as an example.

Determine what place value the number is being rounded by. (The number will be rounded by tens)

Locate the place value and identify the digit in the column. (7 is in the tens place)

Move to the place value directly to the right of the place value being rounded by (Directly to the right of the tens is the ones. The digit in the ones is 3.)

If the digit is 1, 2, 3, or 4 then the number will be rounded down. If the digit is 5, 6, 7, 8, or 9 the number will be rounded up. (The digit is 3, so the number will be rounded down.)

If the number needs to be rounded down, then the digit in the place that is being rounded stays the same. If the number needs to be rounded up, the digit will increase by 1. (The digit in the ten is 7, so it will either stay at 7 or change to 8. The digit stays at 7 in the example.)

Change all the digits in the place values to the right of the place value being rounded by 0. (The number is rounded by tens, so the one digit changes to zero.)

The digits in the place values to the left of the place value being rounded will remain the same. (4 is in the hundreds place and stays the same.)

The result is then written down. (473 rounded by tens is 470)

If the steps are followed in the right order, rounding is a fairly simple task. There are some tips and rules that are important to note.

Answer:

8 1/8

Step-by-step explanation:

Multiple the first number by the second

Answer:

4 1/8

Step-by-step explanation:

dvdsfdsfdgfdsfdsfdsfdfdfdf a ss

9514 1404 393

Answer:

  c. 23.63

Step-by-step explanation:

"Time and a half" means each hour of overtime is paid at 1.5 times the regular pay rate. Hence, an hour of overtime earns ...

  1.5 × $15.75 = $23.625 ≈ $23.63

_____

Additional comment

The rounding of overtime pay will occur at the end of the computation. The first hour of overtime (and each odd hour) will earn $23.63, but the second hour (and each even hour) will earn only $23.62.

That is, total pay for 2 hours of overtime will not be 2 × $23.63 = $47.26, but will be 2 × $23.625 = $47.25.

Answer:

Step-by-step explanation:

To find the additional cost of making n candles compared to n ornaments, we need to subtract the cost of making n ornaments from the cost of making n candles.

The cost of making n candles is 9 + 7n, and the cost of making n ornaments is 5n + 4. Therefore, the additional cost of making n candles compared to n ornaments is:

additional cost = cost of making n candles - cost of making n ornaments

additional cost = (9 + 7n) - (5n + 4)

additional cost = 9 + 7n - 5n - 4

additional cost = 2n + 5

Therefore, the polynomial that represents the additional cost of making n candles compared to n ornaments is:

additional cost = 2n + 5

Answer:

To find the additional cost of making n candles compared to n ornaments, we need to subtract the cost of making n ornaments from the cost of making n candles.

The cost of making n candles is 9 + 7n.

The cost of making n ornaments is 5n + 4.

So, the additional cost of making n candles compared to n ornaments is:

(9 + 7n) - (5n + 4) = 7n - 5n + (9 - 4) = 2n + 5

Therefore, the polynomial that represents the additional cost of making n candles compared to n ornaments is:

2n + 5.

Answer:

IS the    radio² × π

Step-by-step explanation:

Calculating the area of a road involves considering the road's shape and cross-sectional profile. There are two common methods for calculating the area:

Cross-Sectional Area Method: This method involves measuring the width of the road at regular intervals along its length and taking elevation measurements. By dividing the road into sections and multiplying the width by the corresponding elevation difference, you can calculate the area of each section and sum them up to obtain the total road area.

Digital Terrain Model (DTM) Method: This method uses advanced surveying techniques to obtain a digital terrain model of the road surface. By applying surface area algorithms to the DTM, you can calculate the surface area of the road, considering the elevation data and interpolating the area between points.

The chosen method depends on available data, accuracy requirements, and project needs. It is essential to refer to engineering standards and guidelines specific to your region or project for accurate and appropriate road area calculations.

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Answer:

50 words per minute.

100 words per 2 minutes.

Step-by-step explanation:

Hope this helps!

North

North

North

South

Answer:

Select whether the advantage or strategy listed below was a Northern one or a Southern one.

Blockading ports            

✔ North

Having a bigger population      

✔ North

Controlling the Mississippi      

✔ North

Having stronger military leaders      

✔ South

Step-by-step explanation:

Answer:

√52

Step-by-step explanation:

6^2 = 36

4^2 = 16

   a.       b

√36 + √16 = c

c = √52

Step-by-step explanation:

2

\(2 \sqrt{13 } \)

Answer:

10 and 15 hours

Step-by-step explanation:

x+y =25 where x is the number of hours the first mechanic worked. y is the number of hours the second mechanic worked

75x+55y=1575

x+y =25 therefore y=25-x

We replace y in equation 75x+55y=1575 with 25-x

75x+55(25-x)=1575

now we solve for x

distribute 55 through the parentheses

75x+1375-55x=1575

combine like terms

20x+1375=1575

move the constant to the right-hand side and change its sign

20x=1575-1375

20x=200

divide each side by 20

x=10

If x is 10 then y has to be 15 since both worked a total of 25 hours.

To find the value of N, we need the future value of the retirement fund. If you provide the desired future value, I can calculate the exact value of N.

To find the value of N, we need to calculate the number of monthly deposits Sam made for his retirement fund over 20 years.

Sam deposited $1000 every month for 20 years, which is a total of 20 x 12 = 240 deposits. Each deposit has a compounded interest rate of 5% per year, compounded monthly.

The formula to calculate the future value of a series of monthly deposits is given by:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value of the investment,

P is the monthly deposit amount,

r is the monthly interest rate, and

n is the number of deposits.

In this case, P = $1000, r = 5% / 12 = 0.05 / 12 = 0.00417 (monthly interest rate), and FV is the value of the retirement fund after 20 years.

By rearranging the formula, we can solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Plugging in the values, we get:

n = log((FV * 0.00417) / (1000 * 0.00417 + FV)) / log(1 + 0.00417)

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Answer:

second choice is the answer

Step-by-step explanation:

Answer:

Pretty Sure its D!

Step-by-step explanation:

Answer:

Rectangle that measures 35 by 39.

Step-by-step explanation:

22/25=0.88

35/39=0.8974

0.8974>0.88

Hence, the dimensions of the 35 by 39 triangle are closer than the dimensions of the 22 by 25 rectangle.

Answer:

brown

Step-by-step explanation:

it might be brown because it compelled

Answer:

\(y=\frac{4}{3} x-9\)

Step-by-step explanation:

Here this is in standard form. Hope this helps!

Answer:

y=4/3x-9

Step-by-step explanation:

equasion for linear function is y=mx+b where y is m is slope and b is y intercept. just plug in your variables

Answer:

\(C = (2,-1)\)

Step-by-step explanation:

Given

\(A = (-5,-1)\)

\(B = (-5,3)\)

\(D = (2,3)\)

Required

The coordinate of the fourth point (C)

The given coordinates indicate the rectangle is vertical/horizontal because it has similar x and y values.

The coordinate of such rectangle can be represented as:

\(A = (x_1,y_1)\)

\(B = (x_1,y_2)\)

\(C = (x_2,y_1)\)

\(D = (x_2,y_2)\)

By comparing the general coordinates with the given coordinates, we have:

\(x_1 = -5\) --- see A and B

\(y_1 = -1\) --- see A and C

\(x_2 = 2\) ---- see C and D

\(y_2 = 3\) --- see B and D

So, we have:

\(C = (x_2,y_1)\)

\(C = (2,-1)\)

Answer: 597000000000000000000000000.00

Step-by-step explanation:

Since the exponent of the scientific notation is positive, move the decimal point 24 places to the right.

A point with a positive x-coordinate and a negative y-coordinate will lie in Quadrant IV.

option D is the correct answer.

The bottom right quadrant is the fourth quadrant, denoted as Quadrant IV. In this quadrant, the x-axis has positive numbers and the y-axis has negative numbers.

So for coordinate plane in which Quadrant 1 is the top right quadrant, quadrant 2 is the top left, quadrant 3 is the bottom left, and quadrant 4 is the bottom right, a point with a positive x-coordinate and a negative y-coordinate will lie in Quadrant IV.

Thus, Quadrant IV is the correct answer because the x-axis has positive numbers and the y-axis has negative numbers.

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In functions; translations are used to move lines, points or shapes across the graph (i.e. up, down, right or left).

The translation from \(y = (x - 5)^2 +5\) to \(y = (x - 0)^2 +0\) is to shift \(y = (x - 5)^2 +5\) to the left by 5 units and then downward by 5 units

The given parameters are:

\(y = (x - 5)^2 +5\)

\(y = (x - 0)^2 +0\)

Assume the first point is: \(y = (x - 5)^2 +5\)

While the second is: \(y = (x - 0)^2 +0\)

The first point is first shifted left by 5 units

The rule to this translation is: \((x,y) \to (x + 5,y)\)

So, we have:

\(y' = (x - 5 + 5)^2 + 5\)

\(y' = (x - 0)^2 + 5\)

Next, the resulting function is shifted down by 5 units.

The rule to this translation is: \((x,y) \to (x,y- 5)\)

So, we have:

\(y" = y' - 5\)

This gives:

\(y" = (x - 0)^2 + 5 - 5\)

\(y" = (x - 0)^2 + 0\)

Hence, the translation from \(y = (x - 5)^2 +5\) to \(y = (x - 0)^2 +0\) is to shift \(y = (x - 5)^2 +5\) to the left by 5 units and then downward by 5 units

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The ratio of the volumes of the two similar solids that have a scale factor of 5:3 is: 125:27.

If two solids that are similar to each other, have volumes A and B respectively, and have a scale factor of a:b, thus, the ratio of their volumes would be expressed as:

Volume of solid A/Volume of solid B = a³/b³

or

Volume of solid A : Volume of solid B = a³ : b³

Thus, the given similar solids have a scale factor of 5:3, therefore, the ratio of their volumes would be expressed as shown below:

5³ : 3³

125 : 27

Thus, the ratio of the volumes of the two similar solids that have a scale factor of 5:3 is: 125:27.

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Answer:

Step-by-step explanation:

1)  DE = 6/sin63 = 6.7

DF = 6/tan63 = 3.1

m∠E = 180 - 90 - 63 = 27°

2)  tan30 = 1/√3 = UV / (27√10)

UV = (27√10) / √3 · (√3/√3) = (27√30) / 3 = 9√30

3)  cosV = 3/8

cos⁻¹(3/8) = 68

m∠V = 68°

Answer:

B. linear

Step-by-step explanation:

x     y

0     9

1      9 + 8

2      9 + 2(8)

3      9 + 3(8)

4      9 + 4(8)

=> linear function

Answer:

It should be 128 cm

Step-by-step explanation:

Answer: 64

Step-by-step explanation:

Answer:64

Step-by-step explanation:

Answer:

The scatterplot that shows the strongest negative linear association would have the points on the plot in a downward slope from left to right. The closer the points are to forming a straight line going from the upper left to the lower right, the stronger the negative linear association is. The points on the scatterplot with the strongest negative linear association will be closely clustered along a line, indicating a clear and strong relationship between the two variables being plotted.