Urgent!!! What is the volume of this rectangular prism? Picture provided.
A: 15/2x
B: 3x+12/2x+8
C: 15/2x+2
D: 15/8

Answer:

320,000 people / km²

Step-by-step explanation:

We need to find the area of the city first.

The area of a triangle is: [tex]A=\frac{1}{2} bh[/tex], where b is the base and h is the height.

Here, both b and h are the legs of the right triangle and they're equal to 25 km. So:

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

[tex]A=\frac{1}{2} *25*25=312.5[/tex] km²

Population density is simply (population) ÷ (area). Here, the population is 100,000,000 people and the area is 312.5 km², so:

100,000,000 ÷ 312.5 = 320,000 people / km²

Answer:

320,000 people per km²

Step-by-step explanation:

Since two angles are equal, their opposite lengths are also equal

Assuming it's a right ankle triangle,

Area = ½ × 25 × 25 = 312.5 km²

Population density:

100,000,000/312.5

320,000

Answer:

the correct volume is 120in.3

Step-by-step explanation:

he did his math wrong, 20 x 6 is not 26.

V = 5 x 4 x 6 = 20 x 6 = 120

Answer:

He added instead of multiplying 20 and 6. The correct answer is 120 cubic inches.

Step-by-step explanation:

on edg2020

Answer:

The solution for the system is the pair (6,1).

Step-by-step explanation:

The system has two equations and two variables, therefore i has only one solution. To solve it we will multiply the second equation by "-2". So we have:

2x-4y = 8

x + y = 7 *(-2)

2x - 4y = 8

-2x -2y = -14

We now sum boh equations:

2x -2x -4y -2y = 8 -14

-6y = -6

y = -6/-6 = 1

2x - 4(1) = 8

2x - 4 = 8

2x = 8 + 4

2x = 12

x = 12/2 = 6

The solution is the pair (6,1).

Answer:

The system has 2 solution .

Step-by-step explanation:

The equation is a simultaneous equation

2x - 4y=8 ............(i)

x + y=7................(ii)

make x the subject of the formula in equation (ii)

x = 7 - y

Substitute the value of x in equation(i)

2(7 - y) - 4y = 8

14 - 2y - 4y = 8

14 - 6y = 8

-6y =  8 - 14

-6y = -6

divide both sides by -6

y = 1

insert the value of  in equation (ii)

x + y = 7

x + 1 = 7

x = 7 - 1

x = 6

The system has 2 solution .

Answer:

6

Step-by-step explanation:

search up on quizizz

Answer:

-1.596

Step-by-step explanation:

4^(x + 3) = 7

log4 both sides

log4[4^(x + 3)] = log4(7)

(x + 3) × log4(4) = lg7/lg4

x + 3 = 1.403677461

x = -1.596322539

Answer:

19 meters

Step-by-step explanation:

The area of a circle is given as [tex]90.25\pi[/tex]

-A circle's area is calculated using the formula:

[tex]A=\pi r^2, r=0.5D, D=Diameter[/tex]

#We substitute for area in the equation and solve for D;

[tex]A=\pi (0.5D)^2\\\\90.25\pi=\pi (0.5D)^2\\\\\sqrt{90.25}=0.5D\\\\D=19[/tex]

Hence, the circle's diameter is 19 meters

Diameter of a circle = 19 meters

Circle is a rounded figure that consists of points that are equidistance from the center

Area of a circle is the area enclosed by the circle . The distance between the center to the circumference of circle is the radius.

Diameter is a straight line from one end of circle to the other end and it passes through the center of the circle

Given that area of the circle is 90.25 pi square meters

Area of the circle formula is

[tex]Area = \pi r^2\\90.25\pi =\pi r^2\\divide \; both \; sides \; by \; pi\\90.25=r^2\\take \; square \; root \; on \; both \; sides\\r=\sqrt{90.25}\\ r=9.5[/tex]

diameter of the circle = 2 times of the radius

Diameter = 2 times 9.5=19 meters

Diameter of a circle = 19 meters

Learn more information about 'Circle' here :

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Answer:

The height of Sydney opera house in the model is 2.13 feet.

Step-by-step explanation:

We are given the following in the question:

Height of Sydney opera house = 213 feet

Height in model =

[tex]\dfrac{1}{100}\text{ of the actual height}[/tex]

We have to evaluate the height of Sydney opera house in model.

Height in model =

[tex]=\dfrac{1}{100}\times 213\\\\=2.13\text{ feet}[/tex]

Thus, the height of Sydney opera house in the model is 2.13 feet.

Answer:

N = 5/4 = 1.25

Altogether they eat 1.25 chocolate bar

Step-by-step explanation:

Dayle and his two brothers each eat 5/12 (five-twelfths) of a chocolate bar;

Three of them ate = 5/12 chocolate bar each

Total for the 3 of them N;

N = 3 × 5/12 = 15/12

N = 5/4 = 1.25

Altogether they eat 1.25 chocolate bar

Answer: ok so for 5 and 125 it is 65 and 25

for 1 and 9 it is 5 and 3 and for 4 and 9 it is 13/2 and 6

Answer:

C. 270

Step-by-step explanation:

If there are 10 millimeters in 1 centimeter, that means there is 10 times the number of millimeters in a centimeter. So, we would multiply 27 centimeters by 10 to find the number of millimeters.

12 bottles of paint does she need to paint 70 ornaments. Hence 12 is correct answer.

1. Calculate the surface area of one cone:
The surface area of a cone is the sum of the area of the base (a circle) and the lateral surface area. Since the cone is cut in half vertically, we only need to consider half of the base and lateral surface area.
Base area: The base is a circle with radius r. The area of a circle is πr². Since the cone is cut in half, the base area is πr² / 2.
Lateral surface area: The lateral surface area is a sector of a circle with radius r and arc length equal to the circumference of the base. The circumference of the base is 2πr. The area of a sector is (arc length × radius) / 2. In this case, area of sector is (2πr×r) / 2 = πr^2.
Therefore, total surface area of one cone is (πr²/ 2) + πr² = 3πr² / 2.
2. Calculate the surface area of one ornament:
Since each ornament is made up of two identical cones, the surface area of one ornament is twice the surface area of one cone. Therefore, the surface area of one ornament is 2×(3πr² / 2) = 3πr^2.
3. Calculate the total surface area of all ornaments:
If Donna needs to paint 70 ornaments, the total surface area she needs to cover is 70×3πr² = 210πr².
4. Convert the surface area to square meters:
However, if you provide the radius in meters, you can multiply the surface area you calculated in 3 by 1 to convert it to square meters.
5. Estimate the number of bottles of paint needed:
The total surface area in square meters, you can estimate the number of bottles of paint Donna needs by dividing the surface area by the coverage area of one bottle of paint. This information is typically available on the paint bottle itself. For example, if one bottle of paint covers 10 square meters, and the total surface area of the ornaments is 210 square meters, Donna would need approximately 210 square meters / 10 square meters/bottle = 21 bottles of paint.

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Answer: 57 child tickets were sold that day.

Step-by-step explanation:

Let x represent the number of child tickets that were sold.

Let y represent the number of adult tickets that were sold.

on Friday, 155 tickets were sold. It means that

x + y = 155

At the city museum, child admission is $5.70 and adult admission is $9.50. The ticket sales totaled $1255.90 on that day. It means that

5.7x + 9.5y = 1255.9- - - - - - - - - 1

Substituting x = 155 - y into equation 1, it becomes

5.7(155 - y) + 9.5y = 1255.9

883.5 - 5.7y + 9.5y = 1255.9

- 5.7y + 9.5y = 1255.9 - 883.5

3.8y = 372.4

y = 372.4/3.8

y = 98

x = 155 - y = 155 - 98

x = 57

Steps to simplify:

2x - 1 / x

~Convert to fraction

2xx/x - 1/x

~Combine the fractions

2xx-1/x

~Simplify

2x²-1/x

Best of Luck!

Answer:

The answer to your question is 4 times bigger.

Step-by-step explanation:

Data

radius = 5 cm

height = 16 cm

Cylinder 2, 4 times taller the radius is the same

Process

1.- Calculate the volume of the first cylinder

Volume 1 = πr²h

-Substitution

Volume = π(5)²(16)

-Simplification

Volume = 400π cm³

2.- Calculate the volume of the second cylinder

height = 4(16)

           = 64

-Substitution

Volume = π(5)²(64)

-Simplification

Volume 2 = 1600π cm³

3.- Find the relationship between the volume

Volume 2 / volume 1 = 1600π / 400π

                                   = 4

4.- The second cylinder is 4 times bigger than the first cylinder

Answer:

Area= (3x+4)×(x+3)

Step-by-step explanation:

(3x^2+10x+12)feet

Answer:

3x² + 13x + 12 ft²

Step-by-step explanation:

To work out the area of a rectangle you have to multiply the length and width together. In this case the length is 3x + 4 and the width is x + 3

So

( 3x + 4 ) × ( x + 3 )

Remember FOIL when expanding brackets

F = First two so 3x × x = 3x²

O = Outer two so 3x × 3 = 9x

I = Inner two so 4 × x = 4x

L = Last two so 4 × 3 = 12

but we aren't finished

3x² + 9x + 4x + 12 = 3x² + 13x + 12

Don't forget unit! ft²

Answer:

It is the first choice. (A)

Step-by-step explanation:

Red line: y = 2x + 1

Blue line: y = -4x + 7

To calculate the difference in area between two circular pizzas, first compute the area of each using the formula A = πr². After finding the areas, subtract the smaller area from the larger one to find the difference. The result is approximately 201 square inches.

The question involves calculating the area of two circles and finding the difference between the two. First, we need to find the radius of each pizza. Since the diameter is twice the radius, the large pizza has a radius of 10 inches (20 inches divided by 2), and the small pizza has a radius of 6 inches (12 inches divided by 2). The area of a circle is calculated using the formula A = πr², where π is approximately 3.14159, and r is the radius.

The area of the large pizza is A = π(10 inches)² = π * 100 inches² = 314.16 inches² (rounded to two decimal places). The area of the small pizza is A = π(6 inches)² = π * 36 inches² = 113.10 inches² (rounded to two decimal places). To find the difference, we subtract the area of the small pizza from the area of the large pizza, which gives us 314.16 inches² - 113.10 inches² = 201.06 inches², which is closest to 201 inches².

Answer:

1200 miles

Step-by-step explanation:

Miss Turner drove 900 miles in March.

We are told that she drove 3 times as many miles in March as she did in January. This means that to get the number of miles she drove in January, we divide the number of miles she drove in March by 3:

900 / 3 = 300 miles

We are also told that she drove 4 times as many miles in February than January. This means that to get the number of miles she drove in February, we multiply the number of miles she drove in January by 4:

300 * 4 = 1200 miles.

Hence, she drove 1200 miles in February.

Answer:

0.18

Step-by-step explanation:

Answer:

9/50

Step-by-step explanation:

0.1 is the equivalent of 1/10

You multiply:

[tex]\frac{3}{7} *\frac{1}{10}[/tex]

= [tex]\frac{3}{70}[/tex]

[tex]\frac{3}{70}[/tex]÷[tex]\frac{5}{21}[/tex]  is the equivalent of

[tex]\frac{3}{70}* \frac{21}{5}[/tex]

which equals [tex]\frac{63}{350}[/tex], or [tex]\frac{9}{50}[/tex] simplified (divide both sides by 7)

Answer:

0.083 is the required probability.

Step-by-step explanation:

We are given the following in the question:

Probability of captain hitting pirate's ship =

[tex]P(A) = \dfrac{1}{2}[/tex]

Probability of pirate hitting the captain's ship =

[tex]P(B) = \dfrac{1}{6}[/tex]

Probability that both the pirate and the Captain hit each other's ships:

[tex]P(A\cap B) = P(A)\times P(B)[/tex]

Putting values, we get,

[tex]P(A\cap B) =\dfrac{1}{2}\times \dfrac{1}{6} = \dfrac{1}{12} \\\\P(A\cap B) = 0 .083[/tex]

0.083 is the probability that both the pirate and the Captain hit each other's ships.

To solve the problem, use the concept of differential equations and solve for the rate of water leakage. Then, find the time at which the tank will be half empty and the volume of water after 4 days.

To solve this problem, we can use the concept of differential equations. Let's denote the volume of water in the tank at any time t as V(t). We are given that the rate at which water leaks is proportional to the square root of the remaining volume, so we can write the differential equation:

dV/dt = k * sqrt(V)

Where k is the proportionality constant. We also know that during the first day, 20 liters leak out, so we can find k:

dV/dt = k * sqrt(350) = -20

Now, we can solve this differential equation to find the time at which the tank will be half empty, and the volume of water after 4 days.

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The tank will be half empty (175 liters remaining) after approximately 3.6 days, and there will be about 135 liters of water remaining after 4 days. The problem involves solving differential equations relating to the leak rate being proportional to the square root of the remaining volume.

This problem involves solving a differential equation based on the rate at which water leaks out of a cylindrical tank. The leak rate is proportional to the square root of the volume of water remaining in the tank.

Differential Equation and Initial Conditions

Given:

Where k is a constant. To find k, we use the initial conditions:

At t = 1 day,

V = 350 - 20

= 330 liters.

∫dV/√V = [tex]-k\int_{V_0(350)}^{V(330)} dt \quad \text{from} \quad t=0 \quad \text{to} \quad t=1[/tex]

[tex]2\sqrt{V}\Bigg|_{350}^{330} = -kt\Bigg|_{0}^{1}[/tex]

2(√330 - √350) = -k(1)

k ≈ 2(√350 - √330)

Finding When the Tank is Half Empty

Half of the initial volume is 350/2 = 175 liters.

We need to find t when V = 175.

[tex]2\left(\sqrt{V}\Bigg|_{350}^{175}\right)[/tex] = -kt

2(√350 - √175) = kt

Substituting k, we get t ≈ 3.6 days.

Volume After 4 Days

[tex]2\left(\sqrt{V}\Bigg|_{350}^{V}\right)[/tex] = -k(4)

2√V = 2√350 - 4k

Solving for V, we find V ≈ 135 liters.PJ11

Answer:

m=8

Step-by-step explanation:

-40 divided by -5

Your answer is 8

Answer:

8m would be the answer

Step-by-step explanation:

-5m/-5  = -40/5 = positive 8

Answer:

C

Step-by-step explanation:

Since this is an indererminate form, use L'Hopital

d(sint)/dt = cos(t)

d[ln(2e^t) - 1] = (2e^t)/[2e^t - 1]

As t --> 0,

cos(0) = 1

(2e^t)/[2e^t - 1] = 2

1/2 is the limit

Answer:

△RST ~ △RYX by the SSS similarity theorem. Which ratio is also equal to RT/RX and RS/RY ?

A.XY/TS

B.SY/RY

C.RX/XT

D.ST/YX

Step-by-step explanation:

Check attachment for solution

Answer:

D

Step-by-step explanation:

Answer:

The student will have to save $404.2 minimum monthly

Step-by-step explanation:

Given that the total cost for the first year= $19,700

The grandparents paid half the amount = 1/2(19700)= $9850

The remaining balance to be paid is

19,700 - 9850=$9850

If an athlete paid $5000

The the remaining balance to be paid = 9850-5000=$4850

For the student to clear this amount in 12 months he must save

monthly 4850/12= $404.166

Hence the minimum amount to be saved per month is $404.2

Answer:

The student will have to save a minimum of $404.17 every month.

Step-by-step explanation:

The total cost of attending the sate university is $19, 700 for the first year alone.

Total cost for a year  = $19700

A student's grandparent will pay half of the cost . This means the grand parents will pay

1/2 of the total cost for a year

1/2 × 19700 = $9850

The grand parent will pay $9850

An athletic scholarship will pay $5000 . It will be 9850 - 5000 = 4850 . The remaining amount to pay is $4850 .

At the end of 12 months the minimum amount the student will save every month to be able to pay the remaining amount will be the amount payable divided by 12 month.

minimum amount to save every month = 4850/12

minimum amount to save every month = 404.16666667

minimum amount to save every month ≈ 404.17

Answer:

212

Step-by-step explanation:

47 goes into 99 2 times

Bring down the 5

47 goes into 56 1 time

Bring the 9

47 goes into 94 2 times

Answer:

Same length

24 ÷ 2=12

There is 12 inches in a foot

1 + 1= 2 ft

24 inches = 2 feet

Answer:

The length of the shelf will be less than 24 in feet. It will be 2 feet long.

Step-by-step explanation:

Inches are a smaller unit than feet, meaning that when something is measured in inches, the numerical amount of inches will be higher than the numerical amount of feet. The ratio is 12 inches to 1 foot, meaning that even though the length may be the exact same, inches represents the length with a higher numerical value and feet represent the length with a lower numerical value.

Answer:

Li Jing

Step-by-step explanation:

Given the sequence:

-5,-25,-125,-625,...

Mohamed's Formula is given as: [tex]g(n)=-5\cdot5^{\large{n}}[/tex]

Using Mohamed's formula:

[tex]When\: n=1,g(n)=-5\cdot5^{\large{n}}=-5\cdot5^{1}=-25\\When\: n=2,g(n)=-5\cdot5^{\large{n}}=-5\cdot5^{2}=-125\\[/tex]

Li Jing's Formula is given as: [tex]g(n)=-5\cdot5^{\large{n-1}}[/tex]

Using Mohamed's formula:

[tex]When\: n=1,g(n)=-5\cdot5^{\large{n-1}}=-5\cdot5^{1-1}=-5\\When\: n=2,g(n)=-5\cdot5^{\large{n-1}}=-5\cdot5^{\large{2-1}}=-25\\[/tex]

We can see that Li Jing's Formula produces the gien sequence.

Li Jing is Right.

Answer:

Only Li Jing

Step-by-step explanation:

This is because the formula −5 * 5 is worng as the first term is reapeated again so it is Li Jing

Answer:

f(-5)= -17

Step-by-step explanation:

We want to find at what value of f(x), or y, does x=-5

So, to find when x=-5, or f(-5), substitute -5 in for x

f(x)=3x-2

f(-5)=3(-5)-2

Multiply first (PEMDAS)

f(-5)=-15-2

Subtract

f(-5)= -17

Hope this helps! :)

Answer:

f(-5) = -17

Step-by-step explanation:

f(x) = 3x – 2        Substitute -5 for x

f(-5) = 3(-5) - 2      Multiply

f(-5) = -15 - 2         Subtract

f(-5) = -17

Answer:

1

Step-by-step explanation:

he cant earn 400 dollars because 8*40 is 320. if he cant work more than eight hours, theres no possible way he can earn 400 dollars ('least in a math equation).