What are the values of the variables in the triangle below? if the answer is not an integer, leave it in simplest radical form. the diagram is not drawn to scale

Answer:

Refer to step-by-step.

Step-by-step explanation:

Fixed Cost Per Deck = Total Fixed Cost/Estimated Deck Sales

Fixed Cost Per Deck = 85000/13000

Fixed Cost Per Deck  = $7.08

Break Even Point in Units = Fixed Costs/ Sales Price per Unit - Variable Cost

Break Even Point in Units = 85000/11.95 - 3

Break Even Point in Units = 9497

Fixed Cost Per Deck = Total Fixed Cost/Estimated Deck Sales

Fixed Cost Per Deck = 85000/10000

Fixed Cost Per Deck  = $8.50

Break Even Point in Units = Fixed Costs/ Sales Price per Unit - Variable Cost

Break Even Point in Units = 85000/12.95 - 3

Break Even Point in Units = 8543

Break Even Point in Units = Fixed Costs/ Sales Price per Unit - Variable Cost

Break Even Point in Units = 85000/13.45 - 3

Break Even Point in Units = 8134

1.Total Cost = Variable Cost/unit x Units Produced + Fixed cost

Total Cost = (3 x 13000) + 85000

Total Cost = 39000 + 85000

Total Cost = $124000

2.Total Cost = Variable Cost/unit x Units Produced + Fixed cost

Total Cost = (3 x 10000) + 85000

Total Cost = 30000 + 85000

Total Cost = $115000

3. $12.95 and $13.45.

Because the total cost is greater than the revenue.

Let's try at $12.95:

Revenue  = 12.95 x 8000

Revenue = $103600

Total Cost = (3 x 8000) + 85000

Total Cost = 24000 + 85000

Total Cost = $109000

Profit = Revenue - Total Cost

Profit = 103600 - 109000

Profit = $-5400

Now at $13.45:

Revenue = 13.45 x 7000  

Revenue = $94150

Total Cost = (3 x 7000) + 85000

Total Cost = 21000 + 85000

Total Cost = $106000

Profit = Revenue - Total Cost

Profit = 94150 - 106000

Profit = $-11850

4. The fixed costs to produce $13.45 decks is so much greater than the fixed costs to produce 10.95 due to the estimated deck sales.

Answer:

The height of the cone is [tex]6.9\ units[/tex]

Step-by-step explanation:

we know that

The volume of the cone is equal to

[tex]V=\frac{1}{3}Bh[/tex]

where

B is the area of the circular base of the cone

h is the height of the cone

In this problem we have

[tex]V=29\ units^{3}[/tex]

[tex]r=2\ units[/tex]

Find the area of the base B

[tex]B=\pi r^{2}[/tex]

substitute the value of r

[tex]B=\pi (2)^{2}=4 \pi\ units^{2}[/tex]

Find the height of the cone

[tex]29=\frac{1}{3}(4 \pi)h[/tex]

[tex]h=29*3/(4 \pi)[/tex]

assume [tex]\pi=3.14[/tex]

[tex]h=29*3/(4*3.14)=6.9\ units[/tex]

Answer: first option

Step-by-step explanation:

As you can see in the figures shown in the image attached, the lenght of a side of the smaller figure is 2 inches and the the lenght of a side of the larger figure is 4 inches.

Therefore, you can find the ratio as following:

[tex]ratio=\frac{2in}{4in}[/tex]

Now, you must reduce the fraction. Therefore, you obtained that the ratio of the perimeters of the figures is:

 [tex]ratio=\frac{1}{2}[/tex]

Which can be written in the following form:

[tex]ratio=1:2[/tex]

Then, the answer is the first option.

Answer:

C)  We use csc = [tex]\frac{1}{sinx}[/tex] to verify.

Step-by-step explanation:

Given : [tex]\frac{sinx+ 1}{sinx}[/tex] = 1 +csc x.

To find : What basic trigonometric identity would you use to verify.

Solution : We have given that  [tex]\frac{sinx+ 1}{sinx}[/tex] = 1 +csc x.

To  verify we need to show left hand side equal to right hand side.

For right hand side

1 +csc x  

By csc = [tex]\frac{1}{sinx}[/tex].

Plug the value  csc = [tex]\frac{1}{sinx}[/tex].

1 +  [tex]\frac{1}{sinx}[/tex].

Taking least common multiple

[tex]\frac{sinx +1}{sinx}[/tex] = left hand side.

We can see this is equal to left hand side

Hence , left hand side = right hand side.

Therefore, C)  We use csc = [tex]\frac{1}{sinx}[/tex] to verify.

what are we supposed to evaluate, here? i dunno what your asking us to do

Answer:

[tex]304\dfrac{4}{7}\ milliliters[/tex]

Step-by-step explanation:

If there are 3 milliliters of compound A used for every 4 milliliters of compound B, then we can denote that we use 3x milliliters of compound A and 4x milliliters of compound B to get 533 milliliters of the drug. Thus,

[tex]3x+4x=533,\\ \\7x=533,\\ \\x=\dfrac{533}{7}\ milliliters.[/tex]

Hence, a chemist must take

[tex]4\cdot \dfrac{533}{7}=\dfrac{2132}{7}=304\dfrac{4}{7}\ milliliters[/tex]

of compound B.

Answer:

228.43 ml

Step-by-step explanation:

The ratio of compound A to compound B will be; 4: 3

4:3 is the same as 4x:3x where 4x is compound A and 3x is compound B.

We can solve for "x":

If amount of compound A is 4x  and compound B is 3x;

Then; 4x + 3x = 533

            7 x = 533

               x = 533/7

Then amount of compound B is 3x = 3(533/7)

                                                          = 228.43 ml

definition is valid since center is exactly 1radius away from any point on the outersurface.

other figures do not fit this defn

Answer:

Step-by-step explanation:

Her definition is valid because the sphere is basically defined by its radius, which is the equidistant points towards a center. If points are not equidistant, then that's not a sphere.

Also, Tabitha is considering "a set of points" referring to infinite points on the surface of the sphere. The single point she mentioned is the center.

Therefore, Tabitha's definition is valid because she's considering all elements that define a sphere.

Answer:

Part 1) The direct proportion is [tex]y=0.8x[/tex]. The graph is located on quadrants I and III

Part 2) The direct proportion is [tex]y=-0.4x[/tex]. The graph is located on quadrants II and IV

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y=kx[/tex]

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Part 1) we have

[tex]y=0.8x-1.6[/tex]

Remember that

If two lines are parallel, then their slopes are the same

In this problem, the slope of the given line is [tex]m=0.8[/tex]

therefore

The direct proportion is [tex]y=0.8x[/tex]

The graph is located on quadrants I and III

see the attached figure to better understand the problem

Part 2) we have

[tex]y=-0.4+1[/tex]

Remember that

If two lines are parallel, then their slopes are the same

In this problem, the slope of the given line is [tex]m=-0.4[/tex]

therefore

The direct proportion is [tex]y=-0.4x[/tex]

The graph is located on quadrants II and IV

see the attached figure to better understand the problem

Answer:

[tex]\large\boxed{x\in\mathbb{R}}[/tex]

Step-by-step explanation:

[tex]f(x)=(52)(47)^{x-4}[/tex]

It's an exponential function.

The domain of an exponential function is the set of all real numbers.

Answer:

58%

Step-by-step explanation:

This is a problem of conditional probability.

Let A represent the event that student has dark hair.

So P(A) = 55% = 0.55

Let B represents the event that student has blue eyes.

So, P(B) = 60% = 0.60

Probability that student has blue eyes and dark hairs = P(A and B) = 35% = 0.35

We are to find the probability that a randomly selected student will have dark hair, given that the student has blue eyes. Using the given formula and values, we get:

[tex]P(A|B)=\frac{P(A \cap B)}{P(B)}\\\\ P(A|B)=\frac{0.35}{0.60}\\\\ P(A|B)=0.58[/tex]

Therefore, there is 0.58 or 58% probability that the student will have dark hairs, given that the student has blue eyes.

Answer:

a.) 0.0825 years of age per year

Step-by-step explanation:

By the given table,

The median age at the time of first marriage on 1950 = 22.8 years,

While, the median age on 1990 = 26.1 years,

Hence, the average rate of change in median age per year from 1950 to 1990

[tex]=\frac{22.8 - 26.1}{1950 - 1990}[/tex]

[tex]=\frac{-3.3}{-40}[/tex]

[tex]=0.0825\text{ years of age per year}[/tex]

That is, OPTION a) is correct.

Answer:

It is D

Step-by-step explanation:

got it right on edge

To find the sales tax rate, you need to find what percentage of the base price the difference in cost is.

First, subtract 22.99 from 24.10:

24.1-22.99=1.11

Now, divide 1.11 by 22.99:

1.11/22.99=0.0483

Multiply 0.0483 by 100 to convert the decimal to a percentage:

0.0483*100=4.83

The sales tax rate was 4.83%.

Hope this helps!!

Answer:

[tex]A=2,002.9\ cm^{2}[/tex]

Step-by-step explanation:

we know that

The area of a regular polygon is equal to

[tex]A=\frac{1}{2}rP[/tex]

where

r is the apothem

P is the perimeter

step 1

Find the perimeter

The perimeter of a regular nonagon is

[tex]P=ns[/tex]

where

n is the number of sides (n=9)

s is the length side (s=18 cm)

substitute

[tex]P=9*18=162\ cm[/tex]

step 2

Find the apothem

The apothem in a regular polygon is equal to

[tex]r=\frac{1}{2}(s)cot(180\°/n)[/tex]

we have

[tex]s=18\ cm[/tex]

[tex]n=9[/tex]

substitute

[tex]r=\frac{1}{2}(18)cot(180\°/9)[/tex]

[tex]r=9cot(20\°)=24.73\ cm[/tex]

step 3

Find the area of the regular nonagon

[tex]A=\frac{1}{2}rP[/tex]

substitute

[tex]A=\frac{1}{2}(24.73)(162)=2,002.9\ cm^{2}[/tex]

[tex]24 \div 8 = 3 \: photos \: in \: 1 \: minute[/tex]

[tex]3 \: photos \: per \: 1 \: minute\: \times 3 \: minutes \: \\ = 9 \: photos \: per \: 3 \: minutes[/tex]

9 photos

Answer: 1.06

Step-by-step explanation:

This is the answer because the price of the shoes is s, and the tax is 0.06s. The total cost of the shoes with tax is s+0.06s= 1.06s

Answer:

Your answer is 1.06

Step-by-step explanation:

2x-4+50=100

2x-4=50

2x=54

x=27º

2x+4x=90

6x=90

x=15º

1. Simplify 100 = (2x - 4) + 50

x = 27

2. Complementary mean the angles equal 90 degrees when added, so

90  = 2x + 4x

x = 15

Answer:

the answer would be 6:30 pm

Step-by-step explanation:

if you left work at 5:15 and it took 1 1/4 min to get home

you would

find 1/4 witch would be 15 min because 60/4= 15  

then add 1:15 to 5:15

1:15 + 5:15 = 6:30 pm

you arrived home at 6:30 pm

Mr. Banks would get home at 6:30 PM after leaving work at 5:15 PM and driving for 1 hour and 15 minutes.

The student asked what time Mr. Banks would arrive home if he left work at 5:15 PM and took 1 and 1/4 hours to drive home. To solve this, we need to add the travel time to the departure time. Since 1 and 1/4 hours is the same as 1 hour and 15 minutes, we simply add this to 5:15 PM. Adding 1 hour to 5:15 PM, we get 6:15 PM. Then, adding the remaining 15 minutes, we get 6:30 PM. This means Mr. Banks would arrive home around 6:30 PM.

Answer:

left 3 units and up 6 units

Step-by-step explanation:

we know that

The rule of the translation is equal to

[tex](x,y)------> (x-3,y+6)[/tex]

That means

(x-3)-----> The figure is moved 3 units to the left, because the number is negative

(y+6)----> The figure is moved 6 units up because the number is positive

Answer:

left 3 units and up 6 units

Step-by-step explanation:

Answer:

B. None of these plants is yet producing actual widgets.

Step-by-step explanation:

As we can see in the graph, the number of days is on the x axis, and the number of widgets at y axis.

At 10 days, no line is above the '0' means no one is producing widgets at 10 days point.

Since the y axis represents number of widgets produced, this means none of the plants have produced more than 0 widgets yet.

So, option B is the answer.

Answer:

Calculate the Difference Quotient for f(x)=2x^2-3

Find f(x+h) and f(x), and plug these values into the difference quotient formula.

Answer:

1/3 of a pie.

Step-by-step explanation:

Givens

There are 3 pies

There are 9 people

Answer

Each person gets 3/9 or 1/3 of a pie

So each pie is cut into thirds.

A Polygon is shape with straight sides and must be closed. Polygon sides never touch and are classified according to the number of its sides. So:

If you have the coordinate plane, there are several ways to calculate the perimeter and area. If the polygon meaning that every side must have the same length and every angle must have the same measure, you just need the coordinates of two points and by using the distance formula you can calculate the length of that side. Then you must multiply the number of sides by that distance and this is the perimeter, but if the polygon is irregular you must calculate the length of each side of the polygon using the distance formula and then make the sum. To compute the area, you must divide the entire polygon in triangles, rectangles, parallelograms, etc, and then calculating the area of each figure using the formulas known for each type of figure.

If you don't have the coordinate plane, you need to have the length of each side to calculate the perimeter or each side should be calculated by using trigonometry and other mathematical skills. If the polygon is regular or is a known figure (trapezoid, parallelogram, triangle) you can use the formulas you know to compute the area of that figure. On the other hand, if the polygon is irregular you should divide the polygon in other simple figures and calculate each area and then making the sum.

_______________________

In conclusion, for both ways you need to have the length of each side to find the perimeter and can use well known formulas to find the area of the figure.

Answer:

30°

Step-by-step explanation:

Call the other end of the chord point B and the center of the circle point O. Then triangle AOB is an equilateral triangle, since OA = OB = AB.

Angle OAB is the internal angle of that triangle, so is 60°. Since OA is perpendicular to the tangent line (makes an angle of 90°), The angle between the tangent line and the chord must be ...

90° - 60° = 30°

___

The other way you know this is that central angle AOB is 60°, and the tangent-to-chord angle is half that, or 30°.

_____

One way to remember the angle relationship between a tangent line and a chord is this:

Consider a point C on long arc AB. The measure of inscribed angle ACB is half the measure of central angle AOB, no matter where C is on the circle. (If C happens to be on the short arc AB, then central angle AOB is a reflex angle, but the relationship still holds.) Consider what happens when C approaches A. The angle at vertex C is still the same: 1/2 the measure of central angle AOB. This remains true even in the limit when points A and C become coincident and line AC is a tangent at point A.

perpendicular slopes are those that are flipped and opposite signs to the original slope

Equation: y= mx + b

y = -3x +5

Graph the y intercept first.

Go down three times on the y axis.

Go across one because of -3/1 .

The equation of the line is y = -3x + 5. To graph the equation, plot the y-intercept and use the slope to find additional points on the line.

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is -3 and the y-intercept is 5, so the equation of the line is y = -3x + 5. To graph the equation, start by plotting the y-intercept of (0, 5). Then use the slope to find additional points on the line. For every increase of 1 on the x-axis, the y-value decreases by 3. You can use this pattern to plot more points and draw a straight line connecting them.

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Answer:

2 spoonfuls of sugar in each coffee.

Step-by-step explanation:

If there are 10 spoonfuls of sugar in 5 coffees, simply divide 10 by 5. Then you find that for every 1 coffee, she puts 2 spoonfuls.

Answer:

Ava puts two spoons of sugar in each coffee.

Step-by-step explanation:

We can find this by dividing the total number of spoons of sugar by the total number of coffees.

10 spoons/5 coffees = 2 spoons per coffee

Answer: 36 toy cars

Step-by-step explanation: If Lori bought gifts for her 3 brothers and 6 cousins then she bought gifts for 9 people (3+6). Since she bought 4 toy cars for each of them she bought 36, which is calculated by multiplying 9 x 4.

9 x 4 = 36

Lori bought a total of 36 gifts for her three brothers and six cousins since she bought four gifts for each of them. This was calculated by multiplying the total number of recipients (3+6) by the number of grants each person got (4).

The question is asking how many gifts Lori bought in total. Since Lori bought four toy cars for each of her three brothers and six cousins, we need to multiply the total number of recipients by the number of gifts per person. This gives us (3 brothers + 6 cousins) * 4 skills = 36. So, Lori bought a total of 36 grants.

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Answer:

[tex]cos(0\°)=-\frac{\sqrt{85}}{11}[/tex]

[tex]tan(0\°) = -\frac{6}{\sqrt{85}}\\\\[/tex]

Step-by-step explanation:

We know by definition that:

[tex]cos ^ 2(x) = 1-sin ^2(x)[/tex]

We also know that:

[tex]tan(x) = \frac{sin(x)}{cos(x)}[/tex]

[tex]sec(x) = \frac{1}{cos(x)}[/tex]

Then we can use these identities to solve the problem

if [tex]sin(0\°) = \frac{6}{11}[/tex] then [tex]cos^2(0\°) = 1-(\frac{6}{11})^2[/tex]

[tex]cos(0\°) = \±\sqrt{\frac{85}{121}}\\\\cos(0\°)=\±\frac{\sqrt{85}}{11}[/tex]

As [tex]sec(x) <0[/tex] then [tex]cos(x) <0[/tex]. Therefore we take the negative root:

[tex]cos(0\°)=-\frac{\sqrt{85}}{11}[/tex]

Now that we know [tex]sin(0\°)[/tex] and [tex]cos(0\°)[/tex] we can find [tex]tan(0\°)[/tex]

[tex]tan(0\°) = \frac{sin(0\°)}{cos(0\°)}\\\\tan(0\°) = \frac{\frac{6}{11}}{\frac{-\sqrt{85}}{11} }\\\\tan(0\°) = -\frac{6}{\sqrt{85}}\\\\[/tex]

Answer:

The area is 48 cm^2

Step-by-step explanation:

The formula for area of a triangle is

A = 1/2 b*h

A = 1/2 * 8cm*12cm

A = 1/2 *96cm^2

A = 48 cm^2

The area is 48 cm^2

Answer:

A = 48 cm^2

Step-by-step explanation:

k12

Answer: 5%

Step-by-step explanation: In order to calculate the sales tax rate you divide the amount of the sales tax by the purchase price.

$2/40 = .05 = 5%

The interest rate is 5%.