An auto mechanic recommends that 3 ounces of isopropyl alcohol be mixed with a tankful of gas (14 gallons ) to increase the octane of the gasoline for better engine performance. At this rate, how many gallons of gas can be treated with a 16-ounce bottle of alcohol (You don’t need to translate or understand just solve the word problem please )

The distance, x, from one corner to another corner three corners away is 4. 70cm

The distance, y, from one corner to another corner two corners away is 4. 07cm

It is important to note that the image shown is a hexagon and each of the interior angles of a hexagon has a value of 120 degrees

Also note that the have the trigonometric identities;

Using the cosine identity, we have;

sin θ = adjacent/ hypotenuse

substitute the values

cos 60 = 2.35/x

cross multiply

x = 2. 35/cos 60

x = 2. 35/ 0. 5

x = 4. 7 cm

Then, we have,

sin 60 = y/ 4. 7

y = sin 60 × 4.7

y = 0. 8660 × 4. 7

y = 4. 07cm

Hence, the values are 4. 7cm and 4. 07cm

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Write the equation of this line in point-slope form: The line passes through (−2,22) and (4,-8).

step 1

Find the slope of the line

m=(-8-22)/(4+2)

m=-30/6

m=-5

step 2

Find the equation in point slope form

y-y1=m(x-x1)

substitute the given values

we have

m=-6

(x1,y1)=(4,-8)

substitute

only answer ;( c.

Step-by-step explanation:

so hope it help

Given the following set of data:

8 12 15 9 10 12 12 18 14 15 10 11 12 9 17

We will find the range of the data.

We need to find the maximum and the minimum

The maximum = 18

The minimum = 8

So, the range = maximum - minimum = 18 - 8 = 10

So, the answer will be The range = 10

The fractional portion of the whole graph is not represented by rent and savings? is 101/120.

From the information, there are 360° in a circle graph and 50° of the graph represents rent and 7" of the graph represents savings.

The part that isn't savings or rent will be:

= 360° - (7° + 50°)

= 360° - 57°

= 303°

Therefore, the fractional part will be:

= Part that isn't savings or rent / Entire degree

= 303/360

= 101 / 120

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Analyze the different intervals at which the function takes the values provided by the graph. Pay special attention on the circles, whether they are filled up or not.

From the graph, notice that the function takes the value of 3 when x is equal to -4, -2 or any number between them. Therefore, the condition is:

If x is greater (but not equal) than -2 and lower or equal to 3, the function takes the value of 5. Therefore:

Finally, the function takes the value of -3 whenever x is greater (but not equal) to 3 and less than or equal to 5. Then:

∠A + ∠B + ∠C = 180°

reason : Sum of all angle of triangle is 180°

72° + 86° + ∠C = 180°

158° + ∠C = 180°

∠C = 180° - 158°

∠C = 22°

hence the value of ∠3 is 22°

Now ,

∠3 =∠4

reason : Being vertically opposite angle

4 = 22°

hence the value of ∠4 is 22°

Again ,

∠C + ∠D + ∠E = 180°

reason : Sum of all angle of triangle is 180°

22° + ∠D + 70° = 180°

92° + ∠D = 180°

∠D = 180° - 92°

∠D = 88°

hence the value of ∠5 is 88°..

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hope it helps ....☘✨

Input data

75% = 0.75

format

y = kx

Procedure

The k factor would be equal to 0.25

The answer would be

In the equation y = 4x + 62, the increasing rate is 4

If the actual rate decreases at the rate they were expected to increase, then it is -4 instead of 4.

Then, the equation of the line is:

B) y = - 4x + 62

Let be "x" the amount of money (in dollars) you would save with the discount.

By definition, a percent can be converted to a Decimal number by dividing it by 100. Then, since the cake store is having 25% off sale on all cakes, this can be written as:

According to the information given in the exercise, the regular price of the cake you want is $9. Based on this, you can set up the following expression for price of the cake with the discount (in dollars):

Evaluating, you get:

Knowing this value, you can set up that:

Finally, evaluating, you get:

The answer is: You would save $2.25 with the discount.

Usually, to calculate the area of a solid we need to calculate the area of every face. Here we have a rectangle down, and four triangles. Our desired area (TA) will be the sum of those areas. Let's calculate those areas:

Area of the rectangle) The area of the rectangle (R) is

Area of the front triangle and the back tringle) Note that the front triangle and the back triangle are the "same". So the area of each of them is equal (this simplifies our work...). The area of each of them (FB) is

What is their high?

The triangle with red, blue, and green edges is a right triangle... Its hypotenuse is the blue edge. We know the red edge, its length is 6cm, but what is the length of the green edge? Because our solid is a rectangular pyramid, we can say that the green edge is half of the length of the rectangle. that is, 5cm (10cm/2). Now, we know the red and green edges; so we can apply The Pythagoras theorem to get

The amount for social security for all 3 months will $930 and the contribution for Medicare will be $217.5.

Given that the salary exists paid in US dollars, we can consider that Renae Walters falls under the social security and Medicare tax rates for the United States. These rates, as of 2020, fall at 6.2% for social security and 1.45% for Medicare.

Social security contribution = Social security tax rate × Income earned

January for example Social Security = 0.062 × $15,000 = $930    

Medicare contribution = Medicare tax rate × Income earned

January for example Medicare = 0.0145 × $15,000= $217.5

The above method will apply through the months without changes.

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First, we need to find out how many possible combinations of pizza toppings there would be.

To do this, we will use the formula for Combination.

Combination is all the possible arrangements of things in which order does not matter. In our example, this would mean that a pizza topped with spicy Italian sausage, banana pepper, and beef is the same as a pizza topped with banana pepper, beef, and Italian sausage.

The formula for combination is

From our given, n would be 17, since there are a total of 17 toppings (including spicy Italian sausage, banana peppers, and beef) and r would be 3 since there are three toppings that you chose.

Substituting it in the formula,

Now, since we know that there are a total of 680 combinations of pizza toppings, we can now solve the probability of the first winner selecting a pizza topped with Italian sausage, banana peppers, and beef.

Answer

• a) 8

• b) 4/8

• c) 4/8

Explanation

Given

• Blue cards: 4, {B1, B2, B3, B4}

• Red cards: 4 {R1, R2, R3, R4}

• A = card drawn is blue

• B = card drawn is odd-numbered {B1, R1, B3, R3}

Procedure

• a) elements in the sample space

There are: S = {B1, B2, B3, B4, R1, R2, R3, R4}

Thus, the number of elements in the sample space is n(S) = 8.

• b) P(A)

Can be calculated as follows:

• c) P(B)

Can be calculated as follows:

The value of the composite function is determined as: (g o f)(5) = 6.

To determine the value of a composite function, first evaluate the inner function by plugging in the value of x given, then use the output of the inner function as an input to evaluate the outer function.

Given the following:

f(x) = x² - 6x + 2

g(x) = -2x

Therefore:

(g o f)(5) = g(f(5))

Find f(5):

f(5) = (5)² - 6(5) + 2

f(5) = 25 - 30 + 2

f(5) = -3

Find g(f(5)) by substituting x = -3 into g(x) = -2x:

g(f(5)) = -2(-3)

g(f(5)) = 6

Therefore, (g o f)(5) = 6.

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By solving the equation 5x + 12 = -2, the value of x in is -2.8

Solution

5x = -2-12

5x = -14

We get -14

x = -14 ÷ 5

x = -2.8

Hence, by solving the equation 5x + 12 = -2, the value of x in is -2.8

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Answer:

3y=6-x

Explanation:

The slope-intercept form of a line is y=mx+b.

First, we determine the slope(m) of the line.

Since the y-intercept, b=2

The equation of the line is:

0.12

Probability is the likelihood or chance that an event will occur. It ca be expressed as:

where:

n(E) is the expected event

n(S) is the total sample space

If Mrs. Maria's Market buys 75% of eggs from farm A and the rest from farm B, the percentage amount of egg bought from B will be 25% (100-75)

n(S) = 25%

If 3% of the eggs from B are green, hence n(E) = 3%

Determine the required probability

Pr(egg is from farm B) = n(E)/n(S)

Pr(egg is from farm B) = 3/25 = 0.12

Hence the probability that the egg is from farm B is 0.12

To prove that p || r, we will complete the data in the given table

To determine the equation of the line you need to determine its slope first.

You know that the line 6y=x-12 is perpendicular to the line you have to determine, two lines that are perpendicular, their slopes are opposite reciprocals. For example, let "m" represent the slope of one of the lines and "n" represent the slope of the perpendicular line, you can express their relationship as follows:

To determine the slope of the given line, you have to write it in slope-intercept form:

Where

m represents the slope

b represents the y-intercept

Given the line:

-Divide both sides by 6

The slope of this line is the coefficient of the x-term, n=-1/6

Its opposite reciprocal is:

The slope of the line you have to determine is m=6

Now that you have the slope of the line, using the point-slope form, you can determine the equation of the line:

Where

m represents the slope of the line

(x₁,y₁) represent the coordinates of one point of the line

Replace the formula with m=6 and (x₁,y₁)=(4,-7)

The next step is to write the equation in slope-intercept form:

-Distribute the multiplication on the parentheses term:

-Pass "+7" to the right side of the equation by applying the opposite operation "-7" to both sides of it:

Finally, write the equation of the line using function notation:

The slope of the given equation is 0.075 and  y-intercept is 0.125

What is slope of line ?

Slope of line is the angle made by the line from positive x-axis in anticlockwise direction, it also denoted the steepness of the line.

The point with coordinate having same slope as with given coordinates can be plotted on the same line.

First writing the given equation in standard slope intercept form :

y = mx + c.........(1)

In which:

• m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

• c is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function

8y = 0.2(3x - 5)

8y = 0.6x - 1

y = 0.6/8x - 1/8

y = 0.075x - 0.125

Now, comparing it with equation (1) we get :

m = 0.075 and c = - 0.125

hence the slope of the given equation is 0.075 and  y-intercept is 0.125

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Answer:

379,001.

Explanation:

The population of the city grows by 4.25%.

This is a constant factor and models an exponential function.

An exponential population function is of the form:

From the given problem:

This then gives us:

The population after 12 years will be approximately 379,001.

Measure of each of the angles formed between ZAOB is 71° using angle bisector theorem.

In geometry, an angle bisector is a line that divides an angle into two equal angles. The term "bisector" refers to a device that divides an object or a shape into two equal halves. An angle bisector is a ray that divides an angle into two identical segments of the same length.

m(ZAOB)=142°

OX will bisect ZAOB in equal angel both side.

So m(ZAOX) is 71°

And also, m(ZAOB) is 71°

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Percentage of the wheat crop planted = 128/ 545 x 100

= 12800/545

= 23.4 percent

Since the growth rate is linear and constant over time, it means that the sequence formed is an arithmetic sequence. The formula for finding the nth term of an arithmetic sequence is expressed as

an = a1 + d(n - 1)

where

a1 is the first term of the sequence

n = number of terms

d = common difference

In this case, n would be t(number of years

From the information given,

a1 = 3

Since the first term is at t = 0 and it represents 2010, six years letter would be represented by t = 7. Thus, we would took for d given that a7 = 24

We have

24 = 3 + d(7 - 1)

24 = 3 + 6d

6d = 24 - 3 = 21

d = 21/6 = 3.5

The linear model would be

an = 3 + 3.5(t - 1)

Substituting H for an, the linear model is

H = 3 + 3.5(t - 1)

At 2020, t = 11

H = 3 + 3.5(11 - 1) = 3 + 35

H = 38

In order to find the value of h(x) when x=10, we replace the value of x along with the function by 10, however, since there are not any variables the function is constant for all variables

ANSWER

Quadrant II

EXPLANATION

• All angles between 0° and 90° are in the first quadrant.

• All angles between 90° and 180° are in the second quadrant.

• All angles between 180° and 270° are in the third quadrant.

• All angles between 270° and 360° are in the fourth quadrant.

115° is an angle measure that is between 90° and 180°. Therefore its terminal end is in the second quadrant.

Step 1: Problem

The area of a rectangular painting is 5568 cm².

If the width of the painting is 58 cm, what is its length?

Length of the painting:

Step 2: Concept

Area of a rectangle = Length x Width

Step 3: Method

Given data

Area = 5568 cm square

Width = 58 cm

Length = ?

Area of a rectangle = Length x Width

5568 = 58L

L = 5568/58

L = 96cm

Step 4: Final answer

Length of the painting = 96cm

Answer:

The amount of interest she will be paid in the first 3 years is;

Explanation:

Given that Lashonda deposits $500 into an account that pays simple interest at a rate of 6% per year. for the first 3 years;

Recall the simple interest formula;

substituting the given values;

Therefore, the amount of interest she will be paid in the first 3 years is;

Given:

The radius of the circiel is 4.2 in.

The value of π is 3.14.

The objective is to find the circumference of the circle.

The formula to find the circumference of the circle is,

Hence, the circumference of the circle is 26.376 inches.