which of these is an example of a proportional relationship

to facilitate the exercise we will draw the triangle

We start using the area

where A is the area, b the base and h the height

if we replace A=2312 and b=96 we can calculate the height(h)

now to calculate the measure of the angles we can solve the red triangle

first we find Y using trigonometric ratio of the sine

where alpha is the reference angle, O the opposite side from the angle and H the hypotenuse of the triangle

using Y like reference angle and replacing

simplify

and solve for y

value of angle y is 31.2°

Y and X are complementary because make a right line then if we add both numbers the solution is 180°

and solve for x

measure of the included angle is 148.8°

Given:

A line that passes the through the points (4, 0) and (0,-3).

Required:

Slope, y-intercept, and the equation of the given line.

Explanation:

As the line passes through the points (4, 0) and (0,-3), the slope is calculated as,

The y-intercept of the given line is the point through which the given line passes on the y-axis which is -3. Therefore the intercept of the given line is -3.

The equation of line in slope point form is given as,

Where m is the slope and c is the y-intercept. Therefore the equation of the line is given as,

Answer:

Thus the required equation of line is

We will have the following:

If there are 6 servings in a 2/3 pound package, we will divide the pounds by the number of servings, that is:

So, each serving has 1/9 of a pound.

***Explanation***

Since we have 6 servings and then the total value of pounds the package represents we will have that the weigth (in pounds) for each serving is given to us by dividing the total weight by the number of servings.

Now, in order to apply the division of a fraction by another fraction we rewrite the integer 6 as a fraction, and we know that 6 / 1 = 6 so, that is the fraction from for this number (At least the less complicated one) and we proceed with the "ear" opeation.

We can plot all that happened in the next graph:

This is the graph showing the inches of the snow on the ground over time using the data that Grayson collected.

Given the expression

To solve it for x, the first step is to calculate the term in parentheses, for this you have to apply the distributive property of multiplication.

Next order the alike terms toghether and calculate:

Subtract 20 to both sides of the equation:

And finally divide by 2 to reach the value of x:

For this equation x=4

Answer:

Explanation:

If an arc of a circle radius, r is subtended by a central angle, θ, then:

In Circle A:

• The central angle, θ = 40 degrees

• Radius = 6cm

Therefore, the length of arc CB:

The correct choice is C.

The coordinates of point A are (-2,3). A reflection across the y-axis is given by:

Applying this rule to point A we have:

Therefore, the image of point A is (2,3) and the correct option is B.

We have the relationship between inches and miles is:

1 inch to 5 miles.

The park has an actual area of:

Now, to make the conversion to inches, we need to consider that 1 inch represent 5 miles. Thus:

We squared this amounts, if 1 inch is 5 miles, 1 inch squared will be equal to 5 squared which is 25.

Now we divide 75 miles squared by 25, to know how many inches squared will the park represent on the map:

Answer: the area of the park on the map will be 3 inches squared.

Answer:

Given that,

In the diagram below the larger angle is four times bigger than the smaller angle

To find the larger angle.

Let x be smaller angle.

Then we get,

Larger angle is,

Larger angle and smaller angle are a linear pair.

Therefore we get,

Larger angle is,

The larger angle is 144 degrees.

She has cards that go from 9 to 21.

We assume she has one card with each number that goes from 9 to 21:

9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21.

If we want to calculate the probability she pulls a card lower than 17, we have to count how many cards are lower than 17 and then divide this number by the total amount of cards.

NOTE: each card is a possible event. We will calculate the probability as the quotient between the number of successful events (cards lower than 17) and the total possible events (number of cards available).

We have 17-9 = 8 cards that are lower than 17.

The total number is 22-9 = 13 cards (all the cards lower than 22).

Then, we can calculate the probability as:

Answer: The probabilty she pull a card lower than 17 is P=8/13

Answer:

Sam earns $15.25 per hour.

Explanation:

Sam works 40 hours in one week, and is paid $610

To know how much Sam earns per hour, we divide the amount earned by the number of hours worked.

This is:

Therefore, Sam earns $15.25 per hour.

Distributing over parentheses,

Adding r at both sides,

Adding 3 at both sides,

Dividing by -17 at both sides,

Step-by-step explanation:

We are given a two-way frequency table with some missing joint frequencies.

The frequencies in the total row and column are called "marginal frequencies"

The frequencies in the other rows and columns are called "joint frequencies"

Let us first find the joint frequency "Single Item and Tip"

So, the joint frequency "Single Item and Tip" is 90 (option B)

Now, let us find the joint frequency "Single Item and No Tip"

So, the joint frequency "Single Item and No Tip" is 270 (option D)

Now first we need to find the marginal frequency as below

Finally, now we can find the joint frequency "Multiple Items and No Tip"

So, the joint frequency "Multiple Items and No Tip" is 80 (option A)

Therefore, the missing joint frequencies are

Option A

Option B

Option D

EXPLANATION

Let's see the facts:

Purchase Price = $24,800

Depretiation = 12%/year

We should apply the formula for exponential decay wich is expressed as:

A = P(1-r)^t

A= value of the car after t years

t= number of years

P = Initial Value

r= rate of decay in decimal form

We have that A=unknown t=? P=24,800 r=0.12

Replacing terms:

A=24,800(1-0.12)^t

Now, the y-intercept is the value obtained when t=0, so substituting this on the equation give us the following result:

A=24,800(1-0.12)^0 = 24,800(0.88)^0= 24,800*1=24,800

The starting value is $24,800

Tell me if the inequalities are correct

x/4 + 7 < -1 2x - 1 >= 9

x/4 < -1 - 7 2x >= 9 + 1

x/4 < -8 2x >= 10

x < -32 x >= 10/2

x >= 5

The second option is the correct one

Part A

x= 0 y=8

x=1 y=13

x=2 y=18

x=3 y=23

y=4 y=28

x=5 y=33

y=6 y=28

y=7 y=43

Part B

Starting point (y-intercept) = 8

Part C.

slope is 5.

STEP - BY - STEP EXPLANATION

What to find?

• The values of y at x=0,1,2,3,4,5, 6 and 7

• Slope

• Y- intercept.

Given:

y=5x + 8

To determine the values of y at each point of x, substitute into the formula given and simplify.

That is;

At x = 0

At x = 1

At x = 2

At x = 3

At x = 4

At x = 5

At x = 6

At x=7

Hence,

x= 0 y=8

x=1 y=13

x=2 y=18

x=3 y=23

y=4 y=28

x=5 y=33

y=6 y=28

y=7 y=43

Part B

Starting point( y-intercept).

The y-intercept is the point at which x =0

Hence, from the values above, at x=0, y=8

Hence, the starting point (y-intercept) = 8

Part C

The changes in slope.

The slope is the changes in y-intercept, the y -values kept increasing by 5.

Hence, the slope is 5.

The line that describes this relationship goes from (0,0) to the point (6,11),we can draw it like this:

The surface area of a cone is given by the formula below:

Where r is the base radius and s is the slant height.

So, calculating the surface area of first cone, we have:

The surface area of the second cone is:

The surface area of the third cone is:

And the surface area of the fourth cone is:

600,000 (Six hundred thousand)

1) If we divide 600,000 by 100 we'll have 6000

So 600,000 is equal to 6000 hundreds.

The store's cost is php40

Let's call the store Cost = C

This means that this cost is elevated a 150% in order to get the price of php60

In an mathematical expression, this is:

C · 150% = php60

Then, let's convert the percentage to decimal. To do this, we just divide the percentage by 100:

150% ÷ 100 = 1.5

Now we can solve:

Then the store cost is C = php40

The empirical rule is an approximation that can be used sometimes if we have data in a normal distribution. If we know the mean and standard deviation, we can use the rule to approximate the percentage of the data that is 1, 2, and 3 standard deviations from the mean. The rules is:

In this case, the mean is 44. The receptionist who answered less than 44 phone calls are to the left of the mean, and to the right are the ones who answered more. Since we want to know the percentage of phone calls numbering between 36 and 52, we know that:

Thus, the lower bound is two standard deviations from the mean, and the upper bond is also 2 standard deviations from the mean.

Using the chart above, we can see that this corresponds to approximately 95% of the data.

The answer is approximately 95% of the data is numbering between 36 and 52

We will have the following:

*For 569:

For this number we would round to 600, thus the number of zeros the rounded number would be 2.

*For 983:

For this number, we would round to 1000, thus the number of zeros the rounded number would be 3.

The area of a rectangle can be calculated as the height times the wide.

But be careful, the problem asks it in square meters! So let's use meters instead of centimeters.

Remember that : 1 m = 100 cm ----> 1 cm = 0.01 m

Doing the multiplication

Therefore the area of the poster is 0.016 square meters

Answer:

12√3

Explanation:

First, we know that JL = 24.

Then, the triangle JKL is equilateral. It means that all the sides are equal, so JK is also equal to 24.

Finally, N is the midpoint of segment JK, so it divides the segment JK into two equal parts. Therefore, JN = 12.

Now, we have a right triangle JLN, where JL = 24 and JN = 12.

Then, we can use the Pythagorean theorem to find the third side of the triangle, so NL is equal to:

Because JL is the hypotenuse of the triangle and JN and NL are the legs.

So, solving for NL, we get:

Therefore, the length of NL is 12√3

Let:

Using the sine difference identity:

Answer:

In the given decimal inequality statements we can infer that only

9.07 > 9.008  is true.

The given statements are :

123.466 > 132.465

9.07 > 9.008

50.1 < 5.01

3.37 < 3.368

Let us take each statement and find out if it is true or false.

Statement 1: 123.466 > 132.465

Using the properties of decimals we see that 231<132 hence the statement is false.

Statement 2:

9.07 > 9.008

Here the second digit after decimal are 7 and 0. Since the first two significant digits are same , and 7>0 therefore 9.07>9.008 so it is true.

Statement 3:

50.1 < 5.01

Here 50 > 5 so the statement is false

Statement 4:

3.37 < 3.368

Here the first two significant digits are same. Again the digit in the hundredths place are 7 and 6, as 7>6, hence the statement is false.

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In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

8x² - x - 9 = (x + 1) ( ? )

Step 02:

We must find the missing root to solve the exercise.

x1 = - 1

x2 :

a = 8

b = -1

c = -9

x2 = 9 / 8

The answer is:

( x - 9/8)

8x² - x - 9 = (x + 1) ( x - 9/8 )