A middle school took all of its 6th grade students on a field trip to see a ballet. The students filled 1898 seats, which was 73% of the total number of seats in the theater. How many total seats were in the theater?

Answer:

[tex]C = (2,-1)[/tex]

Step-by-step explanation:

Given

[tex]A = (-5,-1)[/tex]

[tex]B = (-5,3)[/tex]

[tex]D = (2,3)[/tex]

Required

The coordinate of the fourth point (C)

The given coordinates indicate the rectangle is vertical/horizontal because it has similar x and y values.

The coordinate of such rectangle can be represented as:

[tex]A = (x_1,y_1)[/tex]

[tex]B = (x_1,y_2)[/tex]

[tex]C = (x_2,y_1)[/tex]

[tex]D = (x_2,y_2)[/tex]

By comparing the general coordinates with the given coordinates, we have:

[tex]x_1 = -5[/tex] --- see A and B

[tex]y_1 = -1[/tex] --- see A and C

[tex]x_2 = 2[/tex] ---- see C and D

[tex]y_2 = 3[/tex] --- see B and D

So, we have:

[tex]C = (x_2,y_1)[/tex]

[tex]C = (2,-1)[/tex]

Answer:

C.  80%

Step-by-step explanation:

Answer:

1467 divided by 58 equals

25 with a remainder of 17

Step-by-step explanation:

Answer:

17

Step-by-step explanation:

Answer:

1.25p

Step-by-step explanation:

p = amount raised last year

amount raised this year = p +(25% of p)

=1 p+0.25p

=p(1+0.25)

=1.25p

Answer:

150658743

Step-by-step explanation:

(301 317 167+319)÷2=150658743

Answer :- 20/2.5 = 8

......

The total number of curtains that can be made is 8 if each curtain requires 2 and 1/2 meters

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

20 meters of cloth if each curtain requires 2 and 1/2 meters.

The total length of the cloth = 20 meters

Each curtain requires 2 and 1/2 meters

= 2 + 0.5

= 2.5 meters

Total number of curtains = 20/2.5

Total number of curtains = 8

Thus, the total number of curtains that can be made is 8 if each curtain requires 2 and 1/2 meters

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Answer:

1,123 is the absolute value because it is a positive integer hence it reaches the positive absolute value

Answer:

the correct answer is 1,123

Step-by-step explanation:

absolute value is the non-negative value of a real number, without regard to its sign. which means [1,123]= 1,123

Answer:

600 m²

Step-by-step explanation:

because the formula for surface area of a cube is 6a² in which a is the side length. so 10² is 100 multiplied by 6 which is 600

9514 1404 393

Answer:

  (d)

Step-by-step explanation:

The area of the semicircle is ...

  A = (1/2)πr²

  A = (1/2)(3.14)(4 m)² = 25.12 m²

The area of the triangle is ...

  A = 1/2bh

  A = 1/2(12 m)(8 m) = 48 m²

Then the total area of the composite figure is ...

  total area = semicircle area + triangle area

  = 25.12 m² + 48 m² = 73.12 m²

_____

Additional comment

The areas of choices A-C are too small. Choice A represents the area of the full circle. Choice B represents the area of the triangle only. Choice C is completely irrelevant. Choice D is the sum of the first two choices, inappropriately using the full circle area.

You should talk to your teacher about this question. None of the offered choices is correct.

Answer:

360 mi^3

Step-by-step explanation:

The figure is composed by two parallelepipeds. For find the volume we have to find the volume of both the solids and the added up the two values

solid  1

length = 11 - 4 = 7 mi

base area = length x width = 7 x 4 = 28 mi^2

V = base area x height = 28 x 6 = 168 mi^3

solid 2

base area = 8 x 4 = 32 mi^2

V = 32 x 6 = 192 mi^3

total volume: 168 + 192 = 360 mi^3

The volume of the figure is 360 mi³.

Volume of a three dimensional shape is the space occupied by the shape.

Given is a figure where two rectangular boxes are put on top of each other.

Volume of a rectangular prism = L × W × H

Here L is the length, W is the width and H is the height.

The dimensions of the rectangular prism are :

Larger one having L = 11 mi, W = 6 mi and H = 4 mi

Smaller one on top having L = 4 mi, W = 6 mi and H = 8 - 4 = 4 mi.

Volume of the figure = volume of larger box + Volume of smaller box

                                  = (11 × 6 × 4) + (4 × 6 × 4)

                                  = 264 + 96

                                  = 360 mi³

Hence the volume of the figure is 360 mi³.

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Answer:

392 ft²

Step-by-step explanation:

The composite figure can be divided into a rectangle, 2 triangles and a square

Area of rectangle = Length * width

Area of rectangle = 21 feets * 14 feets = 294 feet²

Area of triangle = 0.5 * base * height

Area of triangle = 0.5 * 7 * 7 = 24.5

AREA of square = a² = 7² = 49 feets²

Total area :

294 feets + (2 * 24.5) feets² + 49 feets²

294 + 49 + 49 = 392 ft²

Answer:

The required interest rate would be of 3.4% a year.

Step-by-step explanation:

The amount of money earned in compound interest, after t years, is given by:

[tex]P(t) = P(0)(1+r)^t[/tex]

In which P(0) is the initial investment and r is the interest rate, as a decimal.

Peyton is going to invest $440 and leave it in an account for 5 years.

This means that [tex]P(0) = 440, t = 5[/tex]

So

[tex]P(t) = P(0)(1+r)^t[/tex]

[tex]P(t) = 440(1+r)^5[/tex]

What interest rate, to the nearest tenth of a percent, would be required in order for Peyton to end up with $520?

This is r for which P(t) = 520. So

[tex]P(t) = 440(1+r)^5[/tex]

[tex](1+r)^5 = \frac{520}{440}[/tex]

[tex]\sqrt[5]{(1+r)^5} = \sqrt[5]{\frac{52}{44}}[/tex]

[tex]1 + r = (\frac{52}{44})^{\frac{1}{5}}[/tex]

[tex]1 + r = 1.034[/tex]

Then

[tex]r = 1.034 - 1 = 0.034[/tex]

The required interest rate would be of 3.4% a year.

Answer:

The answer is b

Step-by-step explanation:

Answer:

25km/h

Step-by-step explanation:

It would be helpful to understand the 24 hour clock in this case so you don't get confused by the AM and PM. For reference, 5 AM is technically 17AM, since 5 + 12 = 17.

The ship departed at 9pm, subtract that from 17 and you'll get 8 hours.

17 - 9 = 8

We know that there are 8 hours total, and since the ship traveled 200km, we set up a fraction, which is 8hr/200km. Since we want the average speed, we'll go by km/hr. To do this, we need to set the hrs to 1.

8/x = 1

x = 8

200/8 = 25

Your answer is 25km/hr

Answer:

Let x be the variable for a t-shirt for $8.

Let y be the variable for shorts for $12.

Let z be the variable for the hats that cost $10 each.

We have the expression 1 below:

$464 = $8x + $12y + $10z

other expressions:

3z = x

2z =y

By substitution we can solve each variable:

464 = 8(3z) + 12(2z) + 10z

464 = 24z +24z +10z

464 = 58z

z = 8

Solve for x andy:

3z=x

3*8 = 24=x

2z=y

2*8 = 16 = y

The t-shirts are 24 pieces, the shorts are 16 pieces and hats are 8 pieces.

Step-by-step explanation:

Answer:

All three designs will hold he same amount of chocolate (60 cubic centimeters). So, the manager is wrong.

Step-by-step explanation:

Let's find the volume of each design.

For Design A, the cross section is a rectangle rectangle measured 3 cm by 2 cm.

Therefore, the area of the cross section is:

[tex]A_1=3(2)=6\text{ cm}^2[/tex]

Since the height is 10 cm, the total volume of Design A is:

[tex]V_1=10(6)=60\text{ cm}^2[/tex]

For Design B, the cross section is also a rectangle measuring 3 cm by 2 cm.

So, the area of the cross section is:

[tex]A_2=3(2)=6\text{ cm}^2[/tex]

And the height is still 10 cm. So, the total volume of Design B is:

[tex]V_2=6(10)=60\text{ cm}^3[/tex]

Note that we use the vertical height, and not the slant height. If this seems confusing, imagine each layer being a cracker. If 10 crackers were laid on top of each other perfectly, that is Design A. However, if we were to move each cracker to the right a bit, that is Design B. The volume of both cases are the same.

For Design C, the cross section is a triangle with a base length of 6 cm and a height of 2 cm.

So, the area of the cross section is:

[tex]\displaystyle A_3=\frac{1}{2}(2)(6)=6[/tex]

And since the height is 10 cm, the volume of Design C is:

[tex]V_3=6(10)=60\text{ cm}^3[/tex]

Therefore, as we can see, all three designs will hold he same amount of chocolate. So, the manager is wrong.

Answer:

99 units.

Step-by-step explanation:

The cost function for manufacturing x units of a certain product is:

[tex]C(x)=x^2-15x+34[/tex]

We want to find the number of units manufactured at a cost of $8350. Therefore:

[tex]8350=x^2-15x+34[/tex]

Subtract 8350 from both sides:

[tex]x^2-15x-8316=0[/tex]

This equation can be a bit difficult to factor, if even possible, so we can use the quadratic formula:

[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

In this case, a = 1, b = -15, and c = -8316. Thus:

[tex]\displaystyle x=\frac{-(-15)\pm\sqrt{(-15)^2-4(1)(-8316)}}{2(1)}[/tex]

Simplify:

[tex]\displaystyle x=\frac{15\pm\sqrt{33489}}{2}[/tex]

Evaluate:

[tex]\displaystyle x=\frac{15\pm183}{2}[/tex]

Therefore, our solutions are:

[tex]\displaystyle x=\frac{15+183}{2}=99\text{ and } x=\frac{15-183}{2}=-84[/tex]

We cannot produce negative items, so we can ignore the second answer.

Therefore, for a cost of $8350, 99 items are being produced.

Answer:

D) $5385.10

Step-by-step explanation:

Exponential equation of decay:

The exponential equation for the decay of an amount after t years is given by:

[tex]A(t) = A(0)(1-r)^t[/tex]

In which A(0) is the initial amount and r is the decay rate, as a decimal.

If you buy a motorcycle for $12,500 in 2015 and it depreciates (shrinks) in value by 15.5% every year

This means that [tex]A(0) = 12500, r = 0.155[/tex]

So

[tex]A(t) = A(0)(1-r)^t[/tex]

[tex]A(t) = 12500(1-0.155)^t[/tex]

[tex]A(t) = 12500(0.845)^t[/tex]

How much will it be worth in 2020?

2020 is 2020 - 2015 = 5 years after 2015, so this is A(5). So

[tex]A(5) = 12500(0.845)^5 = 5385.10[/tex]

The correct answer is given by option D.

Answer:

(2, - 1 )

Step-by-step explanation:

Given the 2 equations

2x - 5y = 9 → (1)

3x + 4y = 2 → (2)

Multiplying (1) by 4 and (2) by 5 and adding the result will eliminate the y- term

8x - 20y = 36 → (3)

15x + 20y = 10 → (4)

Add (3) and (4) term by term to eliminate y

23x + 0 = 46

23x = 46 ( divide both sides by 23 )

x = 2

Substitute x = 2 into either of the 2 equations and solve for y

Substituting into (2)

3(2) + 4y = 2

6 + 4y = 2 ( subtract 6 from both sides )

4y = - 4 ( divide both sides by 4 )

y = - 1

solution is (2, - 1 )

Answer:

basically, with each value of x, you replace it by x on the equation

Step-by-step explanation:

y=1/3(12)

y=4

--------

y=1/3(3)

y=1

--------

y=1/3(18)

y=6

-------

hope this helped!

Answer:

[tex]\bar x =29.7[/tex]

[tex]\sigma = 6.81[/tex]

[tex]Median = 30.5[/tex]

Step-by-step explanation:

Given

[tex]Data:20,38,24,39,27,40,28,37,29,35,30,31,32,19,33,18,34,21,36,23[/tex]

[tex]n = 20[/tex]

Solving (a): The sample mean

This is calculated as:

[tex]\bar x =\frac{\sum x}{n}[/tex]

[tex]\bar x =\frac{20+38+24+39+27+40+28+37+29+35+30+31+32+19+33+18+34+21+36+23}{20}[/tex]

[tex]\bar x =\frac{594}{20}[/tex]

[tex]\bar x =29.7[/tex]

Solving (b): The standard deviation

This is calculated as;

[tex]\sigma = \sqrt{\frac{\sum(x-\bar x)^2}{n}}[/tex]

So, we have:

[tex]\sigma = \sqrt{\frac{928.2}{20}}[/tex]

[tex]\sigma = \sqrt{46.41}[/tex]

[tex]\sigma = 6.81[/tex]

Solving (c): The median

First, sort the data in ascending order

[tex]Sorted:18,19,20,21,23,24,27,28,29,30,31,32,33,34,35,36,37,38,39,40[/tex]

The position of the median is calculated as:

[tex]Median = \frac{n+1}{2}[/tex]

[tex]Median = \frac{20+1}{2}[/tex]

[tex]Median = \frac{21}{2}[/tex]

[tex]Median = 10.5th[/tex]

The 10.5th item represents the mean of the 10th and 11th item.

So, median is:

[tex]Median = \frac{30+31}{2}[/tex]

[tex]Median = \frac{61}{2}[/tex]

[tex]Median = 30.5[/tex]

Answer:

[tex]A=440\ m^2[/tex]

Step-by-step explanation:

Given that,

The diameter of the cylinder, d = 10 m

Hight, h = 14 m

Radius, r = d/2 = 5 m

We need to find the lateral area of the cylinder. The formula for the lateral area of the cylinder is given by :

[tex]A=2\pi rh\\\\A=2\times \dfrac{22}{7} \times 5\times 14\\A=440\ m^2[/tex]

So, the lateral surface area of the cylinder is equal to [tex]440\ m^2[/tex].

Answer:

15$

Step-by-step explanation:

small car is 5 times smaller so we have to multiply the prise of the small car by 5.

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Answer:

13 + 3x = 34

Variables:

x = random number

Given:

The total revenue of this year = $14,600

This year revenue is 27% less than their total revenue in the previous year.

To find:

The total revenue in the previous year.

Solution:

Let x be the total revenue of the previous year.

This year revenue is 27% less than their total revenue the previous year.

Revenue in this year = Revenue in previous year - 27% of it

[tex]14600=x-\dfrac{27}{100}x[/tex]

[tex]14600=x-0.27x[/tex]

[tex]14600=0.73x[/tex]

Divide both sides by 0.73.

[tex]\dfrac{14600}{0.73}=x[/tex]

[tex]20,000=x[/tex]

Therefore, the total revenue in the previous year is $20,000.

Answer:

there is no attachment to look at

Step-by-step explanation:

Answer:

Divisors of 78 1,2,3,6,13,26,39,78