The constant of proportion is k = 2. An equation that represent the relation is y = 2x. A graph of the equation y = 2x will show 2 units of x values for y on the y–axis. 9 cups of milk are needed for 18 scoops of ice cream
How to evaluate for the solution of the proportionThe proportional relationship between the number of scoops of ice cream and the amount of milk can be expressed as:
1 scoop of ice cream = 1/2 cup of milk
we evaluate for k the constant of proportion as follows:
1 = k × 1/2
k = 2 {cross multiplication}
if we represent a scoop of ice cream with y and a cup of milk with x, then we can write the equation that represent the relation as:
y = 2x.
In the graph of y = 2x, for every value of x on the x–axis, there are 2 units of x for y on the y–axis, that is when x = 1, y = 2 or x = 3 then y = 6.
For 18 scoops of ice cream, we will evaluate for the amount of cup of milk as follows:
18 = 2x
x = 18/2 {divide through by 2}
x = 9.
In conclusion, he constant of proportion is k = 2. An equation that represent the relation is y = 2x. A graph of the equation y = 2x will show 2 units of x values for y on the y–axis. 9 cups of milk are needed for 18 scoops of ice cream
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I will give you brainy
A landscaper needs 3 1/5 pounds of fertilizer. He has 1 3/10 pounds in his truck, and another 1/5 pound at his shop.
How many more pounds of fertilizer does the landscaper need?
Enter your answer as a mixed number in simplest form by filling in the boxes.
help pleases
Answer:
1
Step-by-step explanation:
12
Last year, Terrific Copying had total revenue of $475 000, while operating at 60% of capacity. The total of its variable cost is $150 000. Fixed costs were $180 000. If the current selling price, variable costs, and fixed costs are the same as last year, what net income can be expected from revenue of $500 000 in the current year
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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Cara’s Flower Arrangements
White 3 6 9 12 15
Yellow 5 10 15 20 25
Hector’s Flower Arrangements
White 4 8 12 16 20
Yellow 6 10 14 18 22
Part A
Are the numbers of white and yellow flowers in Cara’s arrangements proportional?
Which equation relates the number of white flowers, w, to the number of yellow flowers, y?
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
What is proportionality?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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7. The ratio of dahlias to sunflowers is the same in all of the
flower arrangements at a banquet.
A. MTR Use Structure Complete the double number line to
show the ratios of dahlias to sunflowers in all the flower
arrangements at the banquet.
12
Dahlias 0
4
Sunflowers 0
8
16
6
a
15 18
B. How many dahlias will there be when there are 33 sunflowers?
C. What is the ratio of dahlias to all flowers when there are 21 total
flowers?
D. What is the ratio of sunflowers to all flowers in a bouquet with
70 total flowers?
20 24
12
21
32
8 dahlias
24
6 sunflo
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.
What is the ratio?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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A rectangular television's length is 3 inches more than twice its width. The
perimeter of the television is 144 inches. What is the width of the television
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:
Ryan wants to take out a $520,000 loan with an APR of 4.15% for 20 years. He purchased a discount point for 1% of his principal that will decrease his APR by 0.125%. If Ryan purchases 3 points, after how many months will he break even?
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.
solve the system of linear equations by elimination
3x+4y=-1
-2x-5y=10
Answer:
x = 5
y = -4
Step-by-step explanation:
Solving system of linear equations: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]
The proportional relationship between the number of sweaters a clothing store buys and sells, s, and the profit, in dollars and cents, that it makes off those sweaters, can be represented by the equation
�
=
17
�
p=17s. What is the constant of proportionality from the number of sweaters to the total profit, in dollars and cents?
The constant of proportionality from the number of sweaters to the total profit is 17 dollars and cents.
What is proportionality?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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Find the length of BC.
Give your answer to 1 decimal place.
the length of BC is 11.9 cm.
What is right-angle triangle?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:
1. What is the solution of the equation? (1 point)
•-6
•4
•14
•-8
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.
yº
20
b
20
16
zoom in
Solve the triangle by finding the missing sides
and angles. Round to 2 decimal points.
10.
11.
b=
12
Type a response
* REQUIRED
1
U
*REQUIRED 1
The measure of the missing side b is 12 unit.
What is a triangle?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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What is the measure of asymmetry?
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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What would be the 50th term than?
The 50th term is 290.
What is an arithmetic sequence?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, ...?
find the area of a sector with a central angle of 200 and a diameter of 7.5 cm round to the nearest tenth
Answer:
need points srry
Step-by-step explanation:
Lynn is making a snack. The recipes call for 38
cup of water for oats and 14
cup of water for dried fruit. She only has 1 cup of water. Does she have enough to make her snack? Explain.
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!
Scenario: It cost $5 to Roller Skate for 2 hours at Empire Roller Skating ring.
Identify the cost per hour for this recreational activity in the scenario
(Unit Rate)
The cost per hour for this recreational activity in the scenario which is also the unit rate is $2.5 per hour.
What is the cost per hour for the recreational activity?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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PLEASE HELP WILL GIVE BRAINLIEST
help with this proof please image attached
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
Blueprint
3 in
Deck
3 in
1 in
1 in
1 In
The area of the scale drawing is
square inches.
If the scale is 1 inch = 4 feet, the area of the actual deck would be
Numerically, the value of the area of the actual deck would be
Based on these results, if the scale is 1 inch = k feet, the area of the actual deck would be "
square feet.
times the value of the area of the scale drawing.
square feet
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.
What is Area?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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What does a 1 standard deviation increase mean?
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.
Need answer now! Please and thank you !!
Answer: A sorry if i got it wrong
Step-by-step explanation:
does anyone know how to do this?
Step-by-step explanation:
Is there more to this question? I feel like the 2021 federal income tax bracket is missing
a notebook is 8 inches tall and 10 inches wide what is its area?
Answer:
i think 18
Step-by-step explanation:
Three values of x are in the table. What are the corresponding values of y so that each ordered pair is a solution of the equation y = 0.2x – 2?
x y
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
What is the function rule?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:
Input (x) -6 -1 1 Output (y) -3.2 -2.2 -1.8Question 15(Multiple Choice Worth 4 points)
(02.04 MC)
What is the equation of the line that is perpendicular to y = 4x + 6 and passes through the point (8,-4)?
Oy=-x-2
Oy=-x+7
Oy=4x-36
Oy = 4x + 24
An equation of the line that is perpendicular to y = 4x + 6 and passes through the point (8, -4) is y = -x/4 - 2
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the points.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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Simplifying algebra radicals
Please help!!
The solution is, √27xy × √3xy² = 9xy√y
What is the algebraic expression?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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How do I calculate my grade calculator?
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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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. How many miles did the cruise ship traveled in all?
The cruise ship traveled 78 miles.
What is addition?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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What is the area and perimeter of semicircle?
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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Buddy invests $600 in a savings account that pays 3% interest. How much interest will he make after 7 years
The amount of interest in 7 years will be $126.
How to calculate the interest?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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what are the minimum and maximum side lengths to complete a triangle with two side lengths of 18 cm and 21 cm
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.
What is triangle?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.
According to given information :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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