Write a function that models y in terms of x. Round any coefficients to the nearest tenth. x 0 5 10 15 20
y 0 4.02 5.69 6.97 8.05

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:

need points srry

Step-by-step explanation:

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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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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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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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.

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.

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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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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Step-by-step explanation:

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

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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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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Answer:

i think 18

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!

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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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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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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Answer:

Step-by-step explanation:

Objective: Solve distance problems by creating and solving a linear

equation.

An application of linear equations can be found in distance problems. When

solving distance problems we will use the relationship rt = d or rate (speed) times

time equals distance. For example, if a person were to travel 30 mph for 4 hours.

To find the total distance we would multiply rate times time or (30)(4) = 120.

This person travel a distance of 120 miles. The problems we will be solving here

will be a few more steps than described above. So to keep the information in the

problem organized we will use a table. An example of the basic structure of the

table is blow:

Rate Time Distance

Person 1

Person 2

Table 1. Structure of Distance Problem

The third column, distance, will always be filled in by multiplying the rate and

time columns together. If we are given a total distance of both persons or trips we

will put this information below the distance column. We will now use this table to

set up and solve the following example

1

Example 1.

Two joggers start from opposite ends of an 8 mile course running towards each

other. One jogger is running at a rate of 4 mph, and the other is running at a

rate of 6 mph. After how long will the joggers meet?

Rate Time Distance

Jogger 1

Jogger 2

The basic table for the joggers, one and two

Rate Time Distance

Jogger 1 4

Jogger 2 6

We are given the rates for each jogger.

These are added to the table

Rate Time Distance

Jogger 1 4 t

Jogger 2 6 t

We only know they both start and end at the

same time. We use the variable tfor both times

Rate Time Distance

Jogger 1 4 t 4t

Jogger 2 6 t 6t

The distance column is filled in by multiplying

rate by time

8 We have total distance, 8 miles, under distance

4t + 6t = 8 The distance column gives equation by adding

10t = 8 Combine like terms, 4t + 6t

10 10 Divide both sides by 10

t =

4

5

Our solution fort, 4

5

hour(48 minutes)

As the example illustrates, once the table is filled in, the equation to solve is very

easy to find. This same process can be seen in the following example

Example 2.

Bob and Fred start from the same point and walk in opposite directions. Bob

walks 2 miles per hour faster than Fred. After 3 hours they are 30 miles apart.

How fast did each walk?

Rate Time Distance

Bob 3

Fred 3

The basic table with given times filled in

Both traveled 3 hours

2

Rate Time Distance

Bob r + 2 3

Fred r 3

Bob walks 2 mph faster than Fred

We know nothing about Fred,so use r for his rate

Bob is r + 2,showing 2 mph faster

Rate Time Distance

Bob r + 2 3 3r + 6

Fred r 3 3r

Distance column is filled in by multiplying rate by

Time.Be sure to distribute the 3(r +2)for Bob.

30 Total distance is put under distance

3r + 6+ 3r = 30 The distance columns is our equation, by adding

6r +6 = 30 Combine like terms 3r + 3r

− 6 − 6 Subtract 6 from both sides

6r = 24 The variable is multiplied by 6

6 6 Divide both sides by 6

r =4 Our solution for r

Rate

Bob 4+2 =6

Fred 4

To answer the question completely we plug 4 in for

r in the table.Bob traveled 6 miles per hour and

Fred traveled 4 mph

Some problems will require us to do a bit of work before we can just fill in the

cells. One example of this is if we are given a total time, rather than the individual times like we had in the previous example. If we are given total time we

will write this above the time column, use t for the first person’s time, and make

a subtraction problem, Total − t, for the second person’s time. This is shown in

the next example

Example 3.

Two campers left their campsite by canoe and paddled downstream at an average

speed of 12 mph. They turned around and paddled back upstream at an average

rate of 4 mph. The total trip took 1 hour. After how much time did the campers

turn around downstream?

Rate Time Distance

Down 12

Up 4

Basic table for down and upstream

Given rates are filled in

1 Total time is put above time column

Rate Time Distance

Down 12 t

Up 4 1 − t

As we have the total time, in the first time we have

t,the second time becomes the subtraction,

total − t

3

Rate Time Distance

Down 12 t 12t

Up 4 1 − t 4 − 4t

=

Distance column is found by multiplying rate

by time.Be sure to distribute 4(1 − t)for

upstream. As they cover the same distance,

= is put after the down distance

12t = 4 − 4t With equal sign, distance colum is equation

+ 4t + 4t Add4tto both sides so variableis onlyon one side

16t =4 Variable is multiplied by 16

16 16 Divide both sides by 16

t =

1

4

Our solution,turn around after 1

4

hr(15 min )

Another type of a distance problem where we do some work is when one person

catches up with another. Here a slower person has a head start and the faster

person is trying to catch up with him or her and we want to know how long it

will take the fast person to do this. Our startegy for this problem will be to use t

for the faster person’s time, and add amount of time the head start was to get the

slower person’s time. This is shown in the next example.

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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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

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:

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:

The length of the fishing pole is approximately 2.40 meters.

the equation is

The equation that relates the length of the fishing pole, the distance from the base of the pole to the wall, and the angle of elevation is:

cos (angle of elevation) = adjacent / hypotenuse

In this case, the hypotenuse side is the length of the fishing pole, x, and the adjacent side is the distance from the base of the pole to the wall, 0.5 meters. The angle of elevation is 78 degrees. Therefore:

cos (78) = 0.5 / x

x = 0.5 / cos (78)

x ≈ 2.40 meters

Therefore, the length of the fishing pole is approximately 2.40 meters.

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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 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 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:

Two membership options are available at a water park: unlimited use for $70 per month or $10 per month plus $5 per visit. 12 visits are the preferred schedule.

AQUAPARK THE BIGGEST IN THE NETHERLANDS! An incredible sight to behold a floating playground island that is 2,000 square meters in size and made up of various floating playsets. For anyone who like climbing, sliding, and jumping, this is a veritable wonderland. Malta's waters received a 96.6% outstanding rating in the assessment and are renowned for their clear waters and undeveloped coasts. Look no farther if you're searching for one of Europe's cleanest open-water locations. Siam Park is the place to go if you want a rush of adrenaline and fast-moving water rapids. While travelling with children, Aqualand is a great option if you're seeking for more family-friendly rides.

The cost of a $10 monthly charge plus $5 for each visit can be calculated as follows:

Cost = 10 + 5*v

where v denotes the monthly visits.

If both membership levels have the same price, then:

[tex]10 + 5*v = 70[/tex]

[tex]5*v = 70 - 10[/tex]

[tex]v = 60/5v = 12[/tex]

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Answer:

1

Step-by-step explanation:

12