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Question 13 (Essay Worth 12 points)
(Constant of Proportionality, Graphing Proportional Relationships, Real-World Proportional Problems HC)

An ice cream shop serves chocolate milkshakes that are made with ice cream and milk. There is a proportional relationship between the number of scoops of ice cream and the amount of milk needed to make them. For every 1 scoop of ice cream, one-half cup of milk is needed, and for every 5 scoops of ice cream, two and one-half cups of milk are needed.

Part A: Find the constant of proportionality. Show every step of your work. (4 points)

Part B: Write an equation that represents the relationship. Show every step of your work. (2 points)

Part C: Describe how you would graph the relationship. Use complete sentences. (4 points)

Part D: How many cups of milk are needed for 18 scoops of ice cream? (2 points)

Formula used to calculate the grades to a student is as follows:

F=G−((1−w)×C))/w.

You may determine the grade you need on the final exam to get your desired course grade if you know your present grade and the final test's weight.

The explanation for the given formula, F = Final exam grade

G = Grade you want for the class

w = Weight of the final exam, divided by 100 (put weight in decimal form vs. percentage form)

C = Your current grade.

Being able to keep track of your class grades is a really valuable ability. You may keep track of your progress and see whether you need to work more to achieve the grade you want. In order to figure out how much you need to raise your grade with a point system. Compare that number against the point count for the work you have not yet done. Thus this is the way to calculate grades.

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The amount of interest in 7 years will be $126.

To calculate the interest earned by Buddy after 7 years, we can use the formula for simple interest, which is given by:

I = Prt

Where I is the interest earned, P is the principal (initial investment), r is the annual interest rate as a decimal, and t is the time period in years.

We are given that Buddy invests $600 in a savings account that pays 3% interest, which means that the annual interest rate r is 0.03. Therefore, we can plug these values into the formula and solve for I:

I = 600 x  0.03 x 7

I = $126

Therefore, Buddy will earn $126 in interest after 7 years.

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The cruise ship traveled 78 miles.

Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.

Given:

A cruise ship traveled at a constant rate of 16 mph for 3 hours.

Then it traveled for 2 hours at a constant rate of 15 mph.

The total traveled distance,

= distance at the rate of 16 mph for 3 hours + distance of 15 mph for 2 hours.

= 16 x 3 + 15 x 2

= 48 + 30

= 78 miles.

Therefore, the total distance is 78 miles.

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The measure of asymmetry, also known as skewness, is a statistical measure that describes the degree of asymmetry in a distribution of data.

It provides information on the shape of the distribution and the deviation of the data from a normal distribution. In a symmetrical distribution, the mean, median, and mode are all equal, and the distribution is said to have zero skewness. A distribution that is skewed to the right, or positively skewed, has a tail that extends to the right, and the mean is larger than the median. A distribution that is skewed to the left, or negatively skewed, has a tail that extends to the left, and the mean is smaller than the median.

Skewness is calculated by taking the third standardized moment of the distribution, which is the average cubed deviation from the mean, and dividing it by the cube of the standard deviation. This gives a measure of the degree of asymmetry of the distribution.

Skewness is an important measure in many fields, including finance, economics, and biology, as it can indicate whether a distribution is likely to produce extreme values, and can help identify outliers in the data. It is also important in hypothesis testing, as many tests assume that the data are normally distributed, and skewed data can affect the validity of the results.

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Step-by-step explanation:

Is there more to this question? I feel like the 2021 federal income tax bracket is missing

The corresponding values of y so that each ordered pair is a solution of the equation y = 0.2x – 2 is,

Input    (x)    -6        -1       1  

Output (y)     -3.2  -2.2   -1.8

Function rule is the rule of writing the relationship between the two variables, one is dependent and another is independent.

The table given in the problem is;

Input    (x)    -6        -1       1  

Output (y)

We have given the equation as;

y = 0.2x – 2

Complete the table using the above function rule;

At (x) equal to -6,

y = 0.2x – 2

y = 0.2(-6) – 2

y = -3.2

At (x) equal to -1,

y = 0.2x – 2

y = 0.2(-1) – 2

y = -2.2

At (x) equal to 1,

y = 0.2x – 2

y = 0.2(1) – 2

y = -1.8

Hence,

Input    (x)    -6        -1       1  

Output (y)     -3.2  -2.2   -1.8

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

If AB║DC,

∴∡BAC=∡ACD(ALTERNATE  aNGLES)

AB=DC

AC=AC (COMMON SIDE)

∡BAC=∡ACD (PROVED)

∴ ΔABC≡ΔACD(S.A.S)

∴EF=FG

If the current selling price, variable costs, and fixed costs are the same as last year, the expected net income in the current year is $162,105.

Net income can be computes as follows:

Net income = total revenue - total cost

Total cost consists of two costs, fixed cost and total variable cost.

Total cost = fixed cost + total variable cost

Fixed cost does not depend on the produced quantity, while total variable cost is a function of produced quantity.

Let q = produced quantity, then:

Total variable cost = variable cost per unit x q.

Let's assume that the sold quantity = produced quantity. Hence,

Total revenue = selling price x q

Information from last year:

Total revenue = $475,000

475,000 = selling price x q

Here, q = the product quantity sold last year.

Let r = the product quantity sold in the current year. Since the selling price is the same, we have:

500,000 = selling price x r

Comparing with last year, we have:

selling price = 475,000/q = 500,000/r

Hence,

r = (500,000/475,000) q

r = (20/19) q

Hence, the quantity sold this year is 20/19 higher than last year.

Total variable cost this year = variable cost per unit x r.

Substitute r = (20/19) q:

Total variable cost this year = variable cost per unit x (20/19) q

Total variable cost this year = (20/19) x variable cost per unit x q

Total variable cost this year = (20/19) x Total variable cost last year

Total variable cost this year = (20/19) x 150,000 = 157,895

Therefore,

Net income this year = total revenue - fixed cost - total variable cost

                                   = 500,000 - 180,000 - 157,895

                                   = 162,105

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Answer: A sorry if i got it wrong

Step-by-step explanation:

Answer:

The last choice

Step-by-step explanation:

Since 3/8 is smaller than 1/2(=4/8) and 1/4 is also smaller than 1/2(=2/4), she has enough water to make her snacks.

I hope this makes sense to you. I am generally good with following up with additional questions. Feel free to leave a comment if you have any questions or you can also message me as well!

Answer:

Step-by-step explanation:

A 1 standard deviation increase means that a data point has increased by one unit of standard deviation from the mean of a dataset. In a normal distribution, the standard deviation is a measure of the spread of the data around the mean. Approximately 68% of the data falls within 1 standard deviation of the mean, so a 1 standard deviation increase means that the data point has moved farther away from the mean, but still falls within the range of the typical values.

For example, if the mean of a dataset is 100 and the standard deviation is 10, a data point with a value of 110 would be 1 standard deviation above the mean. This means that it is one standard deviation unit away from the mean, in the direction of higher values. Similarly, a data point with a value of 90 would be 1 standard deviation below the mean, meaning it is one standard deviation unit away from the mean in the direction of lower values.

It's worth noting that standard deviation is a relative measure, so a 1 standard deviation increase or decrease in one dataset may have a different absolute effect than in another dataset with a different mean and standard deviation.

The solution is, √27xy × √3xy² = 9xy√y

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

here, we have,

here, we have,

√27xy × √3xy²

=√27×3× xy × xy²

=√9×3×3×xy × xy²

=9xy√y

Hence, The solution is, √27xy × √3xy² = 9xy√y

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The measure of the missing side b is 12 unit.

A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.

The triangle is right angled so we have;

opposite = side opposite the angle 42° = 20

adjacent = b

hypotenuse = 20

b^2 + 16^2 = 20^2

b^2 = 400 - 256

b^2 = 144

b = 12 unit

Approximately to the nearest whole number, b = 12

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The 50th term is 290.

It is a sequence where there is a common difference between each consecutive term.

Example:

12, 14, 16, 18, 20 is an arithmetic sequence.

We have,

-4, 2, 8, 14,

This is an arithmetic sequence.

First term = a = - 4

Common difference.

d = 2 - (-4) = 6

d = 8 - 2 = 6

Now,

The nth term = a + (n -1)d

So,

n = 50

a = -4

d = 6

50th term.

= -4 + (50 - 1) 6

= - 4 + 49 x 6

= - 4 + 294

= 290

Thus,

The 50th term is 290.

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The complete question:

What is the 50th term of the sequence that begins −4, 2, 8, 14, ...?

the length of BC is 11.9 cm.

A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.

Given a right triangle ABC with hypotenuse AC and the foot angle of 58-degree.

Using the sine ratio in the right triangle

sin58° = (Opposite side)/(hypotenuse)

In our case,

opposite side = height

opposite side = BC

hypotenuse = AC

hypotenuse = 14(given)

So,

Multiply both sides by 14

14 × sin58° = BC, thus

BC ≈ 11.9 cm

Therefore, the height of the given right angle triangle will be 11.9 cm(Approx.).

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Complete question:

Answer:

i think 18

Step-by-step explanation:

The constant of proportionality from the number of sweaters to the total profit is 17 dollars and cents.

Proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.

Here,
It can be seen from the equation p = 17s, where p is the profit and s is the number of sweaters. The constant 17 represents the profit per sweater. So, The constant of proportionality from the number of sweaters to the total profit is 17 dollars and cents.

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Area of semicircle is (πr²)/2 and perimeter is  (πr) + 2r

The area and perimeter of a semicircle can be calculated using the formulas for the area and circumference of a full circle, and then dividing by 2.

The formula for the area of a full circle is A = πr², where r is the radius of the circle. So the area of a semicircle would be A = (πr²)/2.

The formula for the circumference of a full circle is C = 2πr, where r is the radius of the circle. The perimeter of a semicircle would be half of the circumference, plus the diameter (which is 2r). So the perimeter of a semicircle would be P = (πr) + 2r.

So, to find the area and perimeter of a semicircle, you would need to know the radius of the semicircle, and then plug it into the formulas above.

For example, if the radius of the semicircle is 4, the area would be A = (π(4²))/2 = 8π, and the perimeter would be P = (π(4)) + (2(4)) = 4π + 8.

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The minimum and maximum side lengths to complete a triangle with two side lengths of 18 cm and 21 cm are 3 cm and 39 cm, respectively.

A triangle is a closed two-dimensional shape with three straight sides and three angles. It is one of the basic shapes in geometry and is formed by connecting three non-collinear points. The three sides and three angles of a triangle are interconnected by various geometrical principles and formulas, such as the Pythagorean theorem, trigonometric ratios, and the Law of Cosines. Triangles are commonly classified based on their side lengths and angles, including equilateral, isosceles, scalene, acute, right, and obtuse triangles. Triangles are also used in various real-life applications, such as in architecture, engineering, and physics.

To complete a triangle with side lengths 18 cm and 21 cm, the length of the third side must be such that it satisfies the triangle inequality. The triangle inequality states that the sum of any two sides of a triangle must be greater than the third side.

Let x be the length of the third side. Then we have:

18 + 21 > x

18 + x > 21

21 + x > 18

Simplifying each inequality, we get:

x < 39

x > 3

x > -3 (since length cannot be negative)

The minimum value of x is 3 cm (when the two sides form a degenerate triangle), and the maximum value of x is 39 cm (when the three sides form an equilateral triangle). Therefore, the minimum and maximum side lengths to complete a triangle with two side lengths of 18 cm and 21 cm are 3 cm and 39 cm, respectively.

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An equation of the line that is perpendicular to y = 4x + 6 and passes through the point (8, -4) is y = -x/4 - 2

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

In Mathematics, a condition that must be met for two lines to be perpendicular is given by:

m₁ × m₂ = -1

4 × m₂ = -1

m₂ = -1/4

At point (8, -4), an equation of the line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-4) = -1/4(x - 8)

y + 4 = -1/4(x - 8)

y = -x/4 + 2 - 4

y = -x/4 - 2

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Answer:

The width of the television is 23 in.

What is rectangle?

A rectangle is a closed 2-D shape, having 4 sides, 4 corners, and 4 right angles. The opposite sides of a rectangle are equal and parallel.

Given that, A television's length is 3 inches more than twice its width the perimeter of the television is 144 inches

Perimeter of a rectangle = 2(length+width)

According to question,

l = 3+2w

Therefore,

Perimeter = 2(w + 3+2w) = 144

3w + 3 = 72

3w = 69

w = 23

Hence, The width of the television is 23 in.

Answer:

The width of the television is 23 in.What is rectangle?A rectangle is a closed 2-D shape, having 4 sides, 4 corners, and 4 right angles. The opposite sides of a rectangle are equal and parallel.Given that, A television's length is 3 inches more than twice its width the perimeter of the television is 144 inchesPerimeter of a rectangle = 2(length+width)According to question,l = 3+2wTherefore,Perimeter = 2(w + 3+2w) = 1443w + 3 = 723w = 69w = 23

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

12

Answer:

x = 5

y = -4

Step-by-step explanation:

 3x + 4y = -1 -----------(I)

-2x - 5y = 10 -----(II)

Multiply equation (I) by 2 and equation (II) by 3 and then add. Doing so, x will be eliminated, and we can find the value of 'y'.

  (I) * 2           6x + 8y = -2

 (II)* 3            -6x - 15y = 30  {Now add}

                            -7y   = 28

Divide both sides by (-7),

                               y = 28 ÷ (-7)

                               [tex]\boxed{y=(-4)}[/tex]

Plugin y = (-4) in equation (I),

            3x + 4*(-4) = -1

              3x - 16 = -1

                    3x = -1 +16

                     3x = 15

                       x = 15÷3

                        [tex]\boxed{x=5}[/tex]

Answer:

The given equation is:

√(x+10) - 9 = -7

Adding 9 to both sides of the equation, we get:

√(x+10) = 2

Squaring both sides of the equation, we get:

x + 10 = 4

Subtracting 10 from both sides, we get:

x = -6

Therefore, the solution of the equation √(x+10) - 9 = -7 is x = -6.

7A) The completion of the number line, based on the ratio of Dahlias to Sunflowers, is as follows:

Dahilas            0     4     8     12     16     10     24    28    32

Sunflowers      0     3     6      9     12     15      18    21     24

7B) When there are 33 sunflowers, there will be 44 Dahlias.

7C) The ratio of Dahlias to all flowers when there are 21 total flowers is 0.57:1 or 12:21.

7D) The ratio of Sunflowers to all flowers in a bouquet with 70 total flowers is 0.43:1 or 3:7.

The ratio is the relative size of one value compared to another.

The ratio is determined as the quotient or average of two relative values.

The number of Dahlias = 8

The number of Sunflowers = 6

Ratio of Dahlias to Sunflowers = 1.33:1 (8:6)

Ratio of Sunflowers to Dahlias = 0.75: 1 (6:8)

The sum of ratios = 14 (8 + 6)

B) When there are 33 sunflowers, there will be 44 Dahlias (33/0.75).

C) The ratio of Dahlias to all flowers:

The total flowers = 21

Dahlias = 12 (21 x 8/14)

The Ratio of Dahlias to all flowers = 12:21 = 0.57:1

The ratio of dahlias to Sunflowers = 12:9

D) The ratio of Sunflowers to all flowers:

The total flowers = 70

Sunflowers = 30 (70 x 6/14)

The ratio of Sunflowers to all flowers = 30:70 = 0.43:1

Ratio of sunflowers to dahlias = 30:40 = 3:4

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Answer:

need points srry

Step-by-step explanation:

Area of the scale drawing is 10 square inches. Area of the actual deck would be 160 square feet.

Area of the actual deck would be 16 times the area of the scale drawing.

Area of a two dimensional shape is the total region which is bounded by the object's shape.

Given scale drawing can be made into two squares.

One with a side length of 1 inch and other with side length of 3 inches.

Area of a square with side length 'a' = a²

Area of the given scale drawing = (1 inch)² + (3 inches)²

                                                     = 1 inch² + 9 inches²

                                                     = 10 inches²

If the scale is 1 inch = 4 feet,

Area of the actual deck = (1 × 4 feet)² + (3 × 4 feet)²

                                       = 4² [(1 feet)² + (3 feet)²]

                                       = 4² (10)

                                       = 160 feet²

Area of the actual deck = 160 feet²

                                        = 16 (Area of the scale drawing)

If the scale is 1 inch = k feet,

Area of the actual deck = k² ( Area of scale drawing)

                                        = 10 k² square feet

Hence the area of the actual deck would be 10k² if the scale is 1 inch = k feet.

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Answer:

It will take Ryan 59.6 years to break even on his purchase of 3 discount points (1% each) for a $520,000 loan with an APR of 4.15%. This break-even point was calculated by finding the difference in monthly payments between the loan with and without the discount points, and dividing the cost of the points by that difference.

Yes, the numbers of white and yellow flowers in Cara’s arrangements are proportional, the equation relates the number of white flowers, w, to the number of yellow flowers, y is y = 5w/3

Proportionality are relationships between two variables where their ratios are equivalent.

Given that, are two arrangements of flowers done by Cara and Hector,

We need to find whether the Cara’s arrangements proportional or not, and an equation relating the number of flowers,

The numbers of white flowers =  3, 6, 9, 12, 15

The numbers of yellow flowers = 5, 10, 15, 20, 25

A proportional relation given by =

y = kx

Put x = 5, and y = 3

3 = 5x

x = 3/5

Put x = 10, y = 6

6 = 10x

x = 3/5

Therefore, the relation is proportional, and the equation will be y = 5w/3

Hence, the numbers of white and yellow flowers in Cara’s arrangements are proportional, the equation relates the number of white flowers, w, to the number of yellow flowers, y is y = 5w/3

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The cost per hour for this recreational activity in the scenario which is also the unit rate is $2.5 per hour.

Number of hours= 2 hours

Total cost to roller skate = $5

Cost per hour of recreational activity= Total cost to roller skate / Number of hours

= $5 / 2 hours

= $2.5 per hour

In conclusion, it costs $2.5 per hour to roller skate.

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