500 people are enrolled in at least two of these three classes: art, drama, and piano. 170 are enrolled in both art and drama, 150 are enrolled in both piano and drama, and 300 are enrolled in art and piano. How many of the 500 people are enrolled in all three?

Answer:

  (x, y) = (-3 5/8, 1 5/16)

Step-by-step explanation:

Add y+14 to the second equation to get ...

  3.5x +14 = y

Substitute this for y in the first equation:

  2.5x -3(3.5x +14) = -13

  2.5x -10.5x -42 = -13

  -8x = 29

  x = -29/8 = -3 5/8

Using this in the formula for y, we get ...

  3.5(-29/8) +14 = y

  -203/16 +14 = y = 21/16 = 1 5/16

Answer : The value of x and y is, 4 and 27 respectively.

Step-by-step explanation :

The given equations are:

[tex]2.5x-3y=-13[/tex]       ...........(1)

[tex]3.25x-y=-14[/tex]      .........(2)

or,

[tex]y=3.25x+14[/tex]     ..........(3)

Now put equation 3 in 1, we get the value of 'x'.

[tex]2.5x-3y=-13[/tex]

[tex]2.5x-3(3.25x+14)=-13[/tex]

[tex]2.5x-9.75x-42=-13[/tex]

[tex]-7.25x=-13+42[/tex]

[tex]-7.25x=29[/tex]

[tex]x=-\frac{29}{7.25}[/tex]

[tex]x=-4[/tex]

Now put the value of 'x' in equation 3, we get the value of 'y'.

[tex]y=3.25x+14[/tex]

[tex]y=3.25(4)+14[/tex]

[tex]y=13+14[/tex]

[tex]y=27[/tex]

Therefore, the value of x and y is, 4 and 27 respectively.

Answer:

B & E.

Step-by-step explanation:

$25 is the y value, because she has to pay the fee no matter what.

Integers can be less than or equal to 8 because 65(8) + 25 is equal to 545, which does not exceed the budget.

Hope this helps!

Answer:

y equals one fourth times x minus 16

y = 4x − 16

Step-by-step explanation:

this is because you're taking the time it took to get there minus 16 because of the delay

Answer:

Answer is three because it is one fourth of the time don't listen to the other person's.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

For a function to be true, there cannot be any same x value for two different y value. Therefore, B, there is the same x value for 4 but with 2 different ys, 4 and 1.

Answer:

B.

Step-by-step explanation:

It is B because it contains a one-to-many relation.

4 maps to 4 and also 4 maps to 1.

The productivity of labor increases by 5% would cause the firm to increase hiring capital and decrease hiring of labor

Step-by-step explanation:

A company can convert input data to output data. So, it gets divided the data into broad categories called production factors. Productivity variations, or more precisely the marginal products of labour, work in the same way as differences in real wages. Remember that marginal prices depend on both - real wages and the productivity.

If in case, productivity increases, perhaps because the company has increased its capital base, thereby marginal costs will decrease. Companies will produce more products and employ more employees. Conversely, if productivity drops, companies will produce less and destroy jobs.

When a firm faces union demands for higher wages, they may increase hiring of capital and decrease hiring of labor. This can result in increased labor productivity. In the United States in the 1970s, firms shifted towards more capital and less labor due to union demands for higher wages.

When a firm is confronted with union demands for higher wages, they may choose to increase hiring of capital and decrease hiring of labor. This is because using more physical capital and less labor can result in increased labor productivity.

For example, if the cost of machines increases relative to labor, the firm may shift towards using less capital and more labor to minimize costs. In this situation, the firm would hire more capital and decrease hiring of labor.

In the United States in the 1970s, this situation occurred where firms faced union demands for higher wages, causing a shift towards more capital and less labor in production methods.

The highest point for the dollhouse will be 3.12 feet

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

His house is 28 feet wide and 36 feet tall at the highest point of the roof.

And, The dollhouse will be 2.5 feet wide.

Now,

Let the highest point for the dollhouse = x

So, By definition of proportion, we get;

⇒ 28 / 36 = 2.5 / x

Solve for x as;

⇒ x = 2.5 × 36/28

⇒ x = 3.12 feet

Thus, The highest point for the dollhouse = 3.12 feet

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Answer:

minutes spent on phone (t) is directly proportional to the phone calls routed (p)  with equation [tex]t =26+2p[/tex].

Step-by-step explanation:

Given:

Number of minutes already spent = 26 minutes

Number of minutes expected to spend on each call = 2

Let number of calls routed be 'p'

Also Let number of minutes on the phone be 't'.

We need to find the relationship between phone calls routed and mins spend on the phone.

Solution:

Now we know that;

Total minutes spent on phone is equal to Number of minutes already spent plus Number of minutes expected to spend on each call routes multiplied by number of calls routed.

framing in equation form we get;

[tex]t =26+2p[/tex]

From above we can see that whenever p increases the value of t will increase too .

Hence we can say that minutes spent on phone (t) is directly proportional to the phone calls routed (p)  with equation [tex]t =26+2p[/tex].

Answer:

C

Step-by-step explanation:

We need to find the length of the red dotted line.

It is divided into 3 parts: the top, the middle slant, and the bottom

The top

Goes from y = 50 to y = 120, the length is:

120 - 50 = 70 units

The bottom

Goes from x = 60 to x = 120, the length is:

120 - 60 = 60 units

The middle slant

This is hypotenuse of the right triangle shown.

We will use Pythagorean Theorem to solve for this length, let it be x.

The theorem is:

Leg^2 + Another Leg^2 = x^2

One leg goes from x = 20 to x = 60, the length is 60 - 20 = 40

Another leg goes from y = 20 to y = 50, the lenth is 50 - 20 = 30

So, we have:

[tex]30^2+40^2=x^2\\2500=x^2\\x=\sqrt{2500}\\x=50[/tex]

THe slant length is 50 units

TOtal fencing is:  70 + 60 + 50 = 180 units

1 unit is 3 feet, so

180 units * 3 = 540 feet

C is the correct answer

Answer: the height in inches, of the pile after 3 weeks is 34 11/12 inches

Step-by-step explanation:

Each consecutive week for the next 5 weeks the height of pile increase by 8 7/12 inches. Converting 8 7/12 inches to improper fraction, it becomes 103/12 inches. The height is increasing in an arithmetic progression. The formula for determining the nth term of an arithmetic sequence is expressed as

Tn = a + (n - 1)d

Where

a represents the first term of the sequence.

d represents the common difference.

n represents the number of terms in the sequence.

From the information given,

a = 17 3/4= 71/4 inches

d = 103/12 inches

n = 3 weeks

the height in inches, of the pile after 3 weeks, T3. Therefore,

T3 = 71/4 + (3 - 1)103/12

T3 = 71/4 + 2 × 103/12 = 71/4 + 103/6

T3 = 419/12 inches = 34 11/12 inches

Answer:

∆AKM is a right triangle for it is inscribed in semicircle O.

AM = diameter of semi-circle O = 2R = 2(2) = 4

%22AK%22%2F%22AM%22=cos%2833%5Eo%29

AK+=+AM%2Acos%2833%5Eo%29

AK+=+4cos%2833%5Eo%29

%22KM%22%2F%22AM%22=sin%2833%5Eo%29

KM+=+AM%2Asin%2833%5Eo%29

KM+=+4sin%2833%5Eo%29

The perimeter of a triangle is the sum of the three sides.

perimeter=AK%2BKM%2BAM

perimeter=4cos%2833%5Eo%29%2B4sin%2833%5Eo%29%2B4

Approximately 9.533238412

Step-by-step explanation:

Answer:

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Step-by-step explanation:

The question is incomplete. Here is the complete question:

Two roads that cross at right angles are used as coordinate axes for a map. A library is  located at point L.

Use the drop-down menus to complete the statements about the location of the library.

(a) The library is located at point (_,_).

(b) The library is __  miles from Road X and __  miles from Road Y.

Answer:

(a) The library is located at point (3.25, -1.5).

(b) The library is 1.5 miles from Road X and 3.25 miles from Road Y

Step-by-step explanation:

Given:

The roads are at right angles to each other. Point 'L' is the location of the library.

(a)

From the graph, we can conclude that,

The length of each square in the graph is 0.5 miles. So,

The coordinates of point L are (3.25, -1.5).

The 'x' value is 3.25 and the 'y' value is -1.5.

Since the point 'L' is the location of library, therefore, the library is located at point (3.25,-1.5).

(b)

The distance of point L from road X is obtained by moving vertically up from point L till we reach the road X. In other words, the perpendicular distance between point L and horizontal x axis is the required distance.

The perpendicular distance is the absolute value of the y-coordinate of point L. The absolute value of 'y' of point L is |-1.5| = 1.5 miles.

Hence, the library is 1.5 miles from road X.

Similarly, the distance of point L from road Y is the perpendicular distance of point L to the road Y.

The perpendicular distance is the absolute value of the x-coordinate of point L. The absolute value of 'x' of point L is |3.25| = 3.25 miles.

Therefore, the library is 3.25 miles from road Y.

So, the library is 1.5 miles from Road X and 3.25 miles from Road Y

Final answer:

To calculate the percent error, subtract the actual attendance from the predicted attendance, take the absolute value, divide by the actual attendance, and multiply by 100%. Sheila's prediction has a percent error of 37.14%.

Explanation:

The question is asking for the calculation of the percent error between Sheila's prediction for concert attendance and the actual attendance. To find the percent error, you subtract the actual value from the predicted value, take the absolute value of the difference, divide by the actual value, and then multiply by 100 to convert it to a percentage.

Steps to Calculate Percent Error

The percent error in Sheila's prediction is 37.14%.

Answer:

Part a) [tex]M=6\frac{2}{3}\ min[/tex]

Part b) [tex]M=9\frac{1}{3}\ min[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, M, and N, represent a proportional variation if it can be expressed in the form [tex]k=\frac{N}{M}[/tex] or [tex]N=kM[/tex]

In this problem, the relationship between the number of photos N to the number of minutes M represent a proportional variation

we have that

For M=2, N=3

Find the the constant of proportionality k

[tex]k=\frac{N}{M}[/tex]

substitute the value of N and M

[tex]k=\frac{3}{2}[/tex]

so

[tex]N=\frac{3}{2}M[/tex]

Part a) How long will it take to print 10 photos?

For N=10

substitute in the linear equation

[tex]10=\frac{3}{2}M[/tex]

solve for M

[tex]M=\frac{10*2}{3}[/tex]

[tex]M=\frac{20}{3}\ min[/tex]

Convert to mixed number

[tex]M=\frac{20}{3}\ min=\frac{18}{3}+\frac{2}{3}=6\frac{2}{3}\ min[/tex]

Part b) How long will it take to print 14 photos?

For N=14

substitute in the linear equation

[tex]14=\frac{3}{2}M[/tex]

solve for M

[tex]M=\frac{14*2}{3}[/tex]

[tex]M=\frac{28}{3}\ min[/tex]

Convert to mixed number

[tex]M=\frac{28}{3}\ min=\frac{27}{3}+\frac{1}{3}=9\frac{1}{3}\ min[/tex]

Answer:

AE = 70

Step-by-step explanation:

Given that ACE is a triangle and B , D , F are mid-points of AC, CE, AE respectively.

⇒ BF, FD, BD are mid-segments.

Mid-segment is a line segment joining mid points of two sides of a triangle,

And it as two properties :

1) mid-segment is always parallel to the third side

2) mid-segment is half in length of the third side

⇒ Here, BD is the mid-segment and is parallel to third side AE

And also BD is half of AE

⇒ AE = 2×BD = 2×35

⇒ AE = 70.    

Final answer:

It takes 30 minutes for the moon's shadow to travel 1150 miles during a solar eclipse based on the speed of 2300 miles per hour.

Explanation:

The question asks us to calculate the amount of time it takes the moon's shadow to travel a certain distance during a solar eclipse, based on given speeds and distances. We know that the shadow travels 2300 miles in one hour, so the speed of the shadow is 2300 miles per hour. In the first 20 minutes, the shadow traveled 766 ⅓ miles. To find the time it takes the shadow to reach 1150 miles, we set up a proportion since the motion of the shadow is at a constant speed.

First, let's convert the 20-minute travel time to hours by dividing by 60, which is ⅓ of an hour (20 / 60 = ⅓). Then we can set up the proportion as follows:

766 ⅓ miles is to ⅓ hour, as 1150 miles is to T hours. Which gives us:

(766 ⅓ / 2300) = (⅓ / 1)

(1150 / 2300) = (T / 1)

Now, we solve for T:

⅓ = 1150 / 2300

T = ⅓

So, T is ⅓ of an hour, which means that it takes ⅓ of an hour for the shadow to reach 1150 miles. We can convert ⅓ of an hour to minutes by multiplying by 60, thus:

T = ⅓ × 60

T = 30 minutes

Therefore, it takes 30 minutes for the shadow to reach 1150 miles.

Answer:

B. [tex]\displaystyle y = -2x + 7[/tex]

Step-by-step explanation:

The y-intercept is given to us, which is [tex]\displaystyle [0, 7],[/tex]and Parallel Lines have SIMILAR RATE OF CHANGES [SLOPES], so −2 remains the way it is.

I am joyous to assist you anytime.

Answer:

$32,000

Step-by-step explanation:

Yearly investment = $3,000

Number of years = 20

Investments earned an average of 8 percent a year.

Total invested amount = $3,000 × 20 = $60,000

Current value of investment = $92,000.

We need to find the total earnings on the investment.

Earnings = Current value of investment - Total invested amount

Earnings = $92,000 - $60,000

Earnings = $32,000

Therefore, the total earnings is $32,000.

To find out how much was earned on the investments over a 20-year period, we subtract the total amount invested ($60,000) from the final value of the portfolio ($92,000), yielding $32,000 as the total earnings. However, this option is not offered in the question.

This type of question is typically encountered in personal finance or mathematics related to investment portfolios. The total amount invested over twenty years is calculated by multiplying the yearly investment by the number of years, so $3,000 * 20 years = $60,000. This is the amount you've put in from your own pocket. The value of the investment portfolio now is given as $92,000, which is the sum of your investment and the earnings. So to calculate your earnings alone, you subtract the total amount you invested from the current value of your portfolio: $92,000 (total value) - $60,000 (your total investment) = $32,000. So the amount you earned on your investments over this 20-year period is not given in the question as none of the options match our calculation of $32,000.

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Answer:

Step-by-step explanation:

The diameter equals the side length of the outer square. The radius of the circle is √2. The diameter of the circle would be

2 × radius = 2 × √2 = 2√2

The area of a square is expressed as length^2. This means that the area of the outer square would be

( 2√2)^2 = 4×2 = 8

The area of the circle is expressed as πr^2. Therefore, the area of the circle would be

π×√2^2 = 2π = 2×3.14 = 6.28

Looking at the inner square, to find the length of the base, we would apply Pythagoras theorem.

√2^2 = base^2 + 1^2

2 = base^2 + 1

base^2 = 2 -1 = 1

base = √1

Area of the inner square would be

√1^2 = 1

Total shaded area would be

6.28 - 1 = 5.28

The probability that the dart will land on the shaded area is

5.28/8 = 0.66

Answer:

Live preview

Step-by-step explanation:

Live preview

When looking for a font name live preview is the real time view of how a font looks. Software which provides a live preview allows the person to see their font as it would appear if published, updated live as they make changes

Moving the pointer over font names in the font list displays a preview of the different font choices.

As you move the pointer over font names in the font list, the text on the slide displays a preview of the different font choices. This allows you to see how the text will look with different fonts before making a selection. It helps in making a decision based on the visual appearance of the text.

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Step-by-step explanation:

Length of  automobile = 16 feet = 4.88 m

Length of truck = 28 feet = 8.53 m

Speed of truck = 30 mph = 48 km/h = 13.33 m/s

Time in which automobile to pass truck = 4 s

Distance traveled by truck in 4 seconds = 4 x 13.33 = 53.33 m

Distance which need to cover by automobile in 4 seconds to pass truck is the sum of length of  automobile, length of truck and distance traveled by truck in 4 seconds.

Distance which need to cover by automobile in 4 seconds = 4.88 + 8.53 + 53.33

Distance which need to cover by automobile in 4 seconds = 66.74 m

Distance = Speed x Time

66.74 = Speed x 4

Speed = 16.69 m/s = 60 km/h = 96 mph

Automobile must travel at 96 mph to pass the truck in 4 seconds.

Answer:

9 batches of tarts.

Step-by-step explanation:

This is  8 / (8/9)

= 8 * 9/8

= 9 batches of tarts.

Answer:

a) ΔL = 80mm

b) h = 600 - 10w mm

Step-by-step explanation:

a. From the time when 7 L have been removed to the time when 15 L have been removed, the change in the volume has been 8L and how the height of the water decreases 10mm per liter removed, then the acumulate change in the height of water has been (8lt)(10mm/lt) = 80 mm

b) If w liters have been removed, then the change in the height of water is (10mm/lt)(wlt) = 10w mm and thus the water's height at this precise point in time is 600 - 10w mm

Answer:

.006%

Step-by-step explanation:

Answer:

per person$15.71

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

Work Shown:

Through the inscribed angle theorem, we can say that 2 times the inscribed angle gets us the arc that the inscribed angle cuts off.

2*(inscribed angle) = arc measure

2*(2x+2) = 76

4x+4 = 76

4x+4-4 = 76-4 ... subtract 4 from both sides

4x = 72

4x/4 = 72/4 ... divide both sides by 4

x = 18

Answer:

Step-by-step explanation:

2 × inscribed angle = 76

2 × (2x + 2) = 76

Open bracket

4x + 4 = 76

Collect like terms

4x = 76 - 4

4x = 72

Divide both sides by 4

4x/4 = 72/4

X = 18

Therefore X is Equal to 18.

If you could elaborate on what this is, I would be gladly to assist you, but there is uncertainty going on here. I apologise.

Answer:

108 feet long

Step-by-step explanation:

You know that to find the perimeter you have to add up all the sides. A rectangle has 4 sides, so 30+30 is 60 and 24+24 is 48. Add 60 and 48 up and you get 108 as the perimeter. Since Madhu is hanging a string of flowers on the PERIMETER, the flower string will need to be 108 feet long.

Hope this Helped!

Answer:

The vertex is the point  [tex](4,11)[/tex]

Step-by-step explanation:

we know that

The equation of the absolute value in vertex form is equal to

[tex]y=a\left|x-h\right|+k[/tex]

where

a is a coefficient      

(h,k) is the vertex

In this problem we have

[tex]y=-2\left|x-4\right|+11[/tex]

so

[tex]a=-2[/tex] ---> the vertex represent a maximum

[tex]h=4[/tex]

[tex]k=11[/tex]

therefore

The vertex is the point  [tex](4,11)[/tex]            

Answer:

There are infinite such positive integers which can be written as a sum of cubes of two positive integers. Some of them are written below:

Hence it is not possible to write all such numbers which can be written in this format. Though some of them can be enlisted if the value of maximum integer "N" is given.

Answer:C) 4 feet and 12 feet

Step-by-step explanation:

The diagram of the first mural is shown. The formula for determining the perimeter of a rectangle is expressed as

Perimeter of rectangle = 2(L + W)

The length of the first mural is given as 8ft while the width of the first mural is given as 6 ft. The perimeter becomes

P = 2(8 + 6) = 2×14 = 28ft

The area of a rectangle is expressed as L×W

The area if the first mural would be

6 × 8 = 48ft^2

The second mural has the same area as the first mural but has a different perimeter. The side lengths of the second mural are

4 ft and 12ft

Area = 4×12 = 48 ft^2

Perimeter = 2(12+4) = 32ft

So area is the same and perimeter is different.