Shawna is making smoothies. The recipe calls for 2 parts yogurt to 3 parts
blueberries. Shawna wants to make 10 cups of smoothie mix. How many cups of
yogurt and blueberries does Shawna need?

The most appropriate choice for equation of line in slope intercept form will be given by-

y = 2x - 8 is the required equation of line

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx + c

Where m is the slope of the line and c is the y intercept of the line.

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m = [tex]tan \theta[/tex]

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line

Here,

The given equation of line is y= 2x +3

Slope of this line = 2

Slope of the line parallel to this line = 2

The line passes through (-2, -12)

Equation of the required line = y - (-12) = 2(x - (-2))

                                                = y + 12 = 2x + 4

                                                = y = 2x + 4 - 12

                                                = y = 2x - 8

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Answer:

27 cubic feet

Explanation:

The volume of a cube with side length L is given by

Now in our case, L = 3 ft; therefore, the volume is

which simplifies to give

which is our answer!

Hence, the volume of the cube with the side length of 3 cm is 27 cubic cm.

To solve this problem, we will use the following graph as reference:

From the above graph, we get that the quadratic equation represents a vertical parabola that opens downwards with vertex:

The domain of the function consists of all real numbers, and the range consists of all numbers smaller or equal to 5.

Answer:

Maximum of 5, at x=3.

Vertex (3,5).

Domain:

Range:

Answer: 7040

Step-by-step explanation:

1
352

x20

——-

000
7040

+
———

7040

12x - 9y +12 =0

To find the slope and y intercept, we want to put the equation in slope intercept form

y = mx+b where m is the slope and b is the y intercept

Solve the equation for y

Add 9y to each side

12x - 9y+9y +12 =0+9y

12x+12 = 9y

Divide each side by 9

12x/9 +12/9 = 9y/9

4/3 x + 4/3 = y

Rewriting

y = 4/3x + 4/3

The slope is 4/3 and the y intercept is 4/3

Given that the triangles are similar, we can express a proportion between their sides. DE and XY are corresponding sides. EF and YZ are corresponding sides. Let's define the following proportion.

Now, we solve for x

Hello

We are given a log funtion to solve and see if it have a solution.

Step 1

we apply log rules

Step 2

Solve for x

From the calculation above, the solution of the set is 13; i.e x = 13

Given:

Adding a negativen number is the same as subtracting that number, so:

Since both denominators (bottom number ) are equal we can subtract the numerators ( top numbers)

Answer:

By the 65-95-99.7 rule,

By symmetry,

In our case,

Therefore,

Hence, 2.5 % of the values lie below 8

Step 1:

Cost of large cup = $5

Step 2:

Number of large David orders = 10 cups

A good plan to find the amount Jon spent is to find the number of large cups Jon orders from the number of large cups David orders.

Jon order 4 fewer large cups

Therefore,

Jon order = 6 cups

Step 3:

A good plan to find the amount Jon spent is to find the number of large cups Jon orders from the number of large cups David orders.

The amount Jon spent on coffee = 6 x $5 = $30

option B

The cost of renting per hour = $2

For 1 hour = $2

For each additional hour, it is $1

For 2 hours = First hour + 1(additional hour)

For 2 hours = $2 + $1(1) = 2+1 = $3

For 3 hours = $2 + $1 (2) = 2+2 = $4

For 4 hours = $2 + $1(3) = 2+3 = $5

The graph which shows this rental cost as 2, 3, 4, 5 is option B

Let be "x" Cilantro's earnings (in dollars) for the week.

According to the explained in the exercise, Cilantro makes $17.43 per hour and works a total of 27 hours per week.

With that information, you can set up the following proportion:

In order to find the value of "x", you need to solve for it. You can apply the Multiplication property of equality and multiply both sides of the equation by 27 hours.

Therefore, you get this result:

Then, Cilantro's earnings for the week will be $470.61

7 ( 1 + 3 )

Solve the sum inside the parentheses ( 1 + 3 = 4 )

7 ( 4 )

multiply

7*4 = 28

Since the sum must equal 28

7 + 21 = 28

Correct option = 7+21

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

Work Shown:

A = he eats pizza

B = he drinks cola

P(A) = 0.40

P(B) = 0.60

P(A and B) = 0.30

Then apply the conditional probability formula.

P(A given B) = P(A and B)/P(B)

P(A given B) = 0.30/0.60

P(A given B) = 0.5 exactly

P(A given B) = 50%

If we know for certain he drinks cola, then there's a 50% chance of him eating pizza.

Apply trigonometric functions:

Cos a = adjacent side / hypotenuse

Where:

a = angle = 59°

adjacent side = 34

Hypotenuse = x

Replacing:

Cos 59 = 34 / x

Solve for x:

x = 34 / cos 59

x = 66

`Answer:

h(x) = -x^2/2 - 4x + 32

Explanation:

The standard form of a quadratic equation is expresssed as

ax^2 + bx+c

Writing the given equation h(x)= -1/2 (x+4)^2 +10 in stabdard form will give;

h(x)= -1/2 (x+4)^2 +10

h(x)= -1/2 (x^2+8x+16)+40

h(x)= -x^2/2 - 4x - 8 + 40

h(x) = -x^2/2 - 4x + 32

Hence the equation in standard form is expressed as h(x) = -x^2/2 - 4x + 32

The number of rolls divided in the two groups so that the ratio is 3 to 5 is 27 and 45 respectively.

According to the question,

We have the following information:

Rolls are being prepared to go to grocery stores.

Now, we have to divide 72 rolls into 2 groups so the ratio is 3 to 5.

Now, let's take the number of rolls given to the first group to be 3x and the number of rolls given to the second group to be 5x.

So, we have the following expression:

3x+5x = 72

8x = 72

x = 72/8

x = 9

So, the number of rolls for the first group:

3x

3*9

27

Now, the number of rolls for the second group:

5x

5*9

45

Hence, the number of rolls divided in the given two group is 27 and 45.

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We will have the following:

First:

Since we have that sides a & c have the same length by theorem angles A & C are equal, so the following is true:

so, angles A & C have a measure of 77.5°.

*Second: We determine the measurement f the segment b, that is:

So we will have that the measurements are:

A = 77.5°

b = 10.8

C = 77.5°

[Option B]

Answer:

The 3 consecutive even numbers are 60, 62 and 64 and the value of the greatest is 64.

Explanation:

If the numbers are consecutive even numbers, it means that the next number will be 2 more than the previous one.

Let the 1st number be x, then other 2 consective numbers will be x + 2 and x + 4.

We're told that the sum of the 3 consecutive even numbers is equal to 186, our equation can then be written as shown below;

Let's go ahead and collect like terms and solve for x;

So our 1st number is 60.

Let's go ahead and find the other 2 numbers;

1st number: x + 2 = 60 + 2 = 62

2nd number: x + 4 = 60 + 4 = 64

So the 3 consecutive even numbers are 60, 62 and 64 and the value of the greatest is 64.

Part B

Remember that

z =(x - μ)/(σ/√n)

where

n=21

we have

μ=1,700

σ=200

For X=1,500

Find out the value of Z1

Z1=(1,500-1,700)/(200/√21)

Z1=-4.5826

For X=1,900

Z2=(1,900-1,700)//(200/√21)

Z2=4.5826

Using a z-score table value

P(1,500therefore

The answer is 21 out of 21

We can solve these values using the next triangle:

First, we need to label the sides using the angle of 30 degrees.

- The largest side is always the hypotenuse, h = 1.

- The opposite side is opposite to the angle, opp = 1/2.

- The adjacent side is between the angle of 30 degrees and the right angle,

adj = √3/2.

Now, we can solve the trigonometric expressions:

For sin:

sin θ = opposite side / hypotenuse

sin 30 = (1/2) / 1

sin 30 = 1/2

For cos:

cos θ = adjacent side / hypotenuse

cos 30 = (√3/2)/1

cos 30 =√3/2

For tan:

tan θ = opposite side / adjacent side

tan 30 =(1/2) / (√3/2)

Simplify the fractions:

tan 30 = 1/√3

Answer:

72

Explanation:

To choose a number between 49 and 95 that is a multiple of 3, 8, and 12, the first step is to find the lowest common multiple of the three numbers.

Begin by expressing them as a product of their prime factors:

Next, we find multiples of the L.C.M in between 49 and 95.

The only number that she could choose is 72.

First, we need to calculate the total earned during the three days, so we need to sum 20.56, 32.90, and 20.78 as:

So, the total earned is 74.24, then half of 74.24 is calculated as:

If he spends the half, he has left the half. Therefore, he has left 37.12

Answer: 37.12

From the problem, we have 3.25% to convert into fraction.

Note that percentage a% can be written as a/100

So 3.25% will be :

From here, we can multiply the numerator and the denominator by 100 to make 3.25 a whole number.

Next step is to simplify the fraction by getting the factors of the numerator and the denominator.

325 = 25 x 13

10000 = 25 x 400

Rewriting it again :

Cancel the common factor (25)

The answer is 13/400

The weight of the granite pyramid in tons is 1350 tons.

A pyramid is a three-dimensional shape.

The granite pyramid is 50 feet high and has a square base of 30 feet on a side.

Granit weighs 180 pounds per cubic foot.

Therefore, the weight in tons of the pyramid can be calculated as follows;

Hence,

volume of the granite pyramid = 1 / 3 b² h

Therefore,

volume of the granite pyramid = 1 / 3 × 30² × 50

volume of the granite pyramid = 45000 / 3

volume of the granite pyramid = 15000 ft³

Hence,

1 ft³ = 180 pounds

15000 ft³ = ?

weight = 2700000 pounds

1 pounds = 0.0005 tons

2700000 pounds = ?

Therefore,

weight of the pyramid granite in tons = 1350 tons

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To find the factors of a number, we can look for factors to divide it by subsequently.

It is easier to start with lower factors.

Let's start by "2".

Since "54" is even, it is divisable by "2":

So "2" is one of the factors.

Now, we have got 27. It is not even anymore, but it is divisable by "3":

So "3" is another factor.

Now we have got "9" and it is also divisable by "3":

So there is another "3" factor.

And since we have got now another "3", we know it is divisable by "3":

Now we have got to "1", so we found all the prime factors:

Now,, we need to combine them to find all possible combinations.

We will start from low to high.

"1" is always a factor.

There is "2" there, so it is also a factor.

Then we have "3" as another factor.

There is no need to combine "1" with another factor, so we will start b combining 2 and 3:

So, "6" is another factor.

We can combine 3 with 3:

"9" is another factor.

Now we start combining three of them:

So, "18" and "27" are factors.

And now we combine 4 of them, but this is get us back to "54" which is the last factor.

So, the factors of 54 are: 1, 2, 3, 6, 9, 18, 27, 54.

Answer:

Step-by-step explanation:

1 × 54 = 54, (1, 54) is a pair factor of 54.

2 × 27 = 54, (2, 27) is a pair factor of 54

3 × 18 = 54, (3, 18) is a pair factor of 54

6 × 9 = 54, (6, 9) is a pair factor of 54

Therefore, the positive pair factors are (1, 54), (2, 27),(3, 18) and (6, 9).

The time needed to look over the resumes depends on how many papers is the resume

But it is convenient to have a speed looking on each one

so, the answe will be 50 seconds

The number of quarts of each constituent she needs to produce 16 quarts of punch is; 12 quarts of fruit juice and 4 quarts of citrus soda.

It follows from the task content that the quantity of each constituent that is required to make 16 quarts of punch are to be determined.

Since it follows that 3 quarts of fruit juice are required to mix with every quart of citrus soda, it follows that the amount of punch made in this scenario is; 4 quarts of punch.

Hence, since there are 4 partitions of 4 quarts punch is 16 quarts punch, the amount of.each constituent needed by proportion are as follows;

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To find the number of page she read per minute

First let's chenge the 8 hours to minute

8 hours = 8 x 60 = 480 min

Since she read 600 pages

Number of pages read per min = 600/ 480

=1.25 pages