The cuboid ABCDEFGH has sides AB = 3 cm, BC = 4 cm and CG = 5 cm.



What is the length AG? Give your answer in cm correct to 3 significant figures.

Answer:

Radius is 2 centimeters

Step-by-step explanation:

4π is the area of a circle

Area of a circle = πr^2

4π / π = πr^2 / π

sqrt(4) = sqrt(r^2)

2 = r

Answer:  Radius is 2 centimeters

84 sq. ft of the wall has to be covered with paint or wallpaper.

Step-by-step explanation:

Area of the wall = 8 × 16 = 128 ft²

Area of the window = 18/12 × 14 = 1.5 × 14 = 21 ft² (since 1 ft = 12 in)

Area of the fireplace = 5 × 3 = 15 ft²

Area of the mirror = 4 × 2 = 8 ft²

Area of the wall to be covered with paint or wallpaper = 128 - (21 + 15 + 8)

                              = 128 - 44

                              = 84 ft²

Answer:

84 ft²

Step-by-step explanation:

Step 1: Find the area of the wall.

The wall is 8 ft high and  16 ft wide

A = LW

A = (16)(8)

A = 128 ft²

Step 2: Find the area of the window, fireplace, and mirror.

Window: The window measures 18 in wide  and 14 ft high

18 in = 1.5 ft

A = LW

A = (14)(1.5)

A = 21 ft²

Fireplace: The fireplace is 5 ft wide and 3 ft high

A = LW

A = (3)(5)

A = 15 ft²

Mirror: The mirror above the fireplace is 4 ft wide and 2 ft high

A = LW

A = (2)(4)

A = 8 ft²

Step 3: Add all the areas of the three objects (window, fireplace, and mirror)

A = 21 + 15 + 8

A = 36 + 8

A = 44 ft²

Step 4: Subtract the total area of the objects from the area of the wall.

A = 128 ft² - 44 ft²

A = 84 ft²

Will this help?

Answers:

1. $8 left

2. 4 minutes

3. 9 balloons

Questions

1. Craig has a twenty dollar bill. He buys six squirt guns

for $2 each. How much money did Craig have left?

2. Lauren and Gina's mother told her daughters they can

swim in the pool for 20 minutes. First, they swam laps in

the pool for 7 minutes. Then they swam underwater for

one minute. Then they played water polo for 8 minutes.

How much longer can they stay in the pool?

3. Maria invited 4 of her friends over for a water balloon fight in

the backyard. At the start of the game, Maria gave each of

her friends 2 water balloons. She had one water balloon for

herself. How many water balloons did they have altogether?

Answer:

1)P = 2 x(L+l) = 2 x (25+L)

2) Maintaing L= 25 cm

P= 2x (25+45) = 140 cm²

P= 2x (25+0,25m) =2x(25+25)= 100 cm²

P= 2x (25+650 mm) =2x(25+65)= 180 cm²

d) ambigous

P= 2x (25+3dm) = 2x (25+30)=110 cm²

Step-by-step explanation:

The solutions are £5575, £312.5 and £345 respectively.

Step-by-step explanation:

£1 = 11.15 kr

⇒ £500 = 500 × 11.15 = £5575

£1 = 1.25 CHF

⇒ £250 = 250 × 1.25 = £312.5

£1 = 1.18 euros

⇒ 407.10 euros = 407.10/1.18 = £345

A triangle has sides with lengths of 4 meters, 5 meters, and 7 meters. It is a right triangle because the square of the largest side length is not equal to the sum of the square of the other two small side lengths and it can be determined by using the properties of the right triangle.

A triangle has sides with lengths of 4 meters, 5 meters, and 7 meters. ​

Is it a right triangle?

To determine the right triangle following all the steps given below.

A triangle has sides with lengths of 4 meters, 5 meters, and 7 meters. ​

The square of the largest side length is not equal to the sum of the square of the other two small side lengths then it is called the right triangle.

Then,

[tex]= (4)^2+(5)^2 = 7^2\\\\= 16 +25 = 49\\\\=41\neq 49[/tex]

Hence, Yes it is a right triangle because the square of the largest side length is not equal to the sum of the square of the other two small sides lengths.

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The unit rate at which the group of rangers plants trees is 5/8 of an acre per week, which is found by calculating the daily acreage planted and then multiplying by the number of workdays in a week.

To determine the unit rate per week of the group of rangers planting trees, we need to calculate how much of an acre they can plant in a standard work week. As it takes them 4 days to plant trees on 1/2 acre, they will plant 1/2 acre in every 4 days of work. Since they work 5 days per week, we can adjust the ratio to calculate the weekly rate:

Therefore, the unit rate at which the group of rangers plants trees is 5/8 of an acre per week.

the volume of cube with edge length 11 m is [tex]Volume = 1331m^3[/tex] .

Step-by-step explanation:

Here  we have a side length of a cube as 11 m . We need to find the volume of cube . Let's find out:

We know that every side of a cube is identical and equal . And volume of cube is given by formula :

⇒ [tex]Volume = (side)^3[/tex]   ...........(1)

According to question we have following parameters as

[tex]side = 11m[/tex]

Putting this in (1)

⇒ [tex]Volume = (11m)^3[/tex]

⇒ [tex]Volume = 11(11)(11)m^3[/tex]

⇒ [tex]Volume = (121)(11)m^3[/tex]

⇒ [tex]Volume = 1331m^3[/tex]

Therefore , the volume of cube with edge length 11 m is [tex]Volume = 1331m^3[/tex] .

The volume of the cube is 1331 m³

Explanation:

Given:

side of the cube, a = 11m

Volume of the cube, v = ?

we know:

Volume of the cube = (a)³

V = (11m)³

V = 1331 m³

Therefore, the volume of the cube is 1331 m³

Answer:

1/2

Step-by-step explanation:

there is two side of a coin, so there is a 1/2 chance that you will head heads.

A coin has two sides, one side is heads, and the other is tails. Since there are 2 sides the probability of getting either heads or tails is 1/2. Therefore, the probability of flipping a coin and getting heads is C) 1/2.

Best of Luck!

Answer:

n=-3

Step-by-step explanation:

2-2n=3n+17

Add 2n to each side

2-2n+2n=3n+2n+17

2 = 5n+17

Subtract 17 from each side

2-17 = 5n+17-17

-15 = 5n

Divide by 5

-15/5 = 5n/5

-3 =n

Answer:

n = -3

Step-by-step explanation:

2 - 2n = 3n + 17

Collect the like terms

-2n - 3n = 17 - 2

-5n = 15

Divide both sides by -5

n = 15/-5

n = -3

Final answer:

The value of (f•g)(2), given f(7)=12 and g(2)=7, is 12. This is found by first applying g to 2 to get 7, and then applying f to get f(7), which equals 12.

Explanation:

The question pertains to the composition of functions and the use of the chain rule in calculus. Given that f(7)=12 and g(2)=7, we need to find the value of (f•g)(2). The notation (f•g)(x) means we first apply g to x, and then apply f to the result of g(x). Therefore, to find (f•g)(2), we first find g(2), which is 7, and then find f(g(2)) which is f(7). Since we know that f(7)=12, the value of (f•g)(2) is therefore 12.

Area of the larger circle is 9/4 πx²

Step-by-step explanation:

⇒ 1/4 πx² = πr²

⇒ x²/4 = r²

∴ r = x/2

Area of the larger circle = πr² = π × (3x/2)²

                                        = 9/4 πx²

Answer:

$355

Explanation:

See the photo attached :)

The theoretical probability of drawing an 'A' from the word 'ALABAMA' is 0.57. This result arrives from dividing the number of 'A's (4) by the total number of letters in 'ALABAMA' (7).

The question deals with a probability problem related to the selection of letters from the word 'ALABAMA'. The word 'ALABAMA' has 7 letters out of which 4 are 'A's. The theoretical probability is calculated as the number of successful outcomes divided by the total number of outcomes. Since we are interested in drawing an 'A', the successful outcomes are the number of 'A's which is 4, and the total outcomes are the total number of letters which is 7.

To calculate theoretical probability, you divide the number of successful outcomes by the total number of outcomes. In this case, the calculation will be 4 / 7 = 0.57 (rounded to the nearest hundredth).

So, the theoretical probability of drawing an A from the word 'ALABAMA' in decimal form, rounded to the nearest hundredth, is 0.57.

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The given function is even.

Solution:

If f(-x) = f(x), then the function is even.

If f(-x) = -f(x), then the function is odd.

Given function:

[tex]f(x)=x^{6}-x^{4}[/tex]

Substitute x = -x

[tex]f(-x)=(-x)^{6}-(-x)^{4}[/tex]

          [tex]=x^{6}-x^{4}[/tex]

          = f(x)   (given)

   f(-x) = f(x)

From the definition, it is even.

Hence the given function is even.

Answer:

You need to provide the expressions you have to choose from.

Step-by-step explanation:

Step-by-step explanation:

By Geometric mean property:

[tex]x = \sqrt{5 \times 3} \\ = \sqrt{15} \\ = 3.87298335 \\ \huge\orange {\fbox{\therefore \: x \approx \: 3.9}} [/tex]

The diagram for this exercise is attached below. We have two linear functions [tex]f(x) \ and \ g(x)[/tex] and the following relationship:

[tex]g(x) = kf(x)[/tex]

From the graph, we know that:

[tex]f(-3)=1 \\ \\ g(-3)=-3[/tex]

Then, substituting into the relationship:

[tex]g(-3)=kf(-3) \\ \\ -3=k(1) \\ \\ \\ Finally: \\ \\ \boxed{k=-3}[/tex]

Answer:

Pamela is 20 years old

Jiris is 10 years old.

Step-by-step explanation:

The very first step is to identify your variables. Let's say that Pamela is 'P' and lets say Jiris is 'J.' The next step is to create an equation. 'The sum of their ages is 30' is something that we can use. So, P + J = 30. The next step is to see that Pamela is two times Jiris' age. So we can say that P = 2J. Now, in order to solve for one variable, we need to do some substitution. We know that P = 2J, so we can plug that into the first equation (P + J = 30). With this change, we now have, 2J + J = 30. With that, you combine like terms and solve for J to get an answer of J = 10. Now we can use that number and plug it into one of our previous equations, like P + J = 30. Now it is going to be P + 10 = 30. Solve for P and get an answer of 20 years old.

Answer:

D—

The histogram will have a horizontal or an x axis of time/minute intervals of the calls (5 minutes in each), and the vertical axis or y axis will be the number of calls made.

Answer:

d

Step-by-step explanation:

yo welcome

Answer:

[tex] { \cos}^{3} x[/tex]

Step-by-step explanation:

We want to simplify:

[tex] \frac{ \sin( \frac{\pi}{2} - x) }{ { \cot}^{2} ( \frac{\pi}{2} -1 ) + 1} [/tex]

Use the Pythagorean identity:

[tex] { \csc}^{2}x = { \cot}^{2}x + 1[/tex]

We apply this property to get:

[tex] \frac{ \sin( \frac{\pi}{2} - x) }{ { \csc}^{2} ( \frac{\pi}{2} -x) } [/tex]

This gives us:

[tex]\frac{ \sin( \frac{\pi}{2} - x) }{ \frac{1}{{ \sin}^{2} ( \frac{\pi}{2} -x)} } [/tex]

We simplify to get:

[tex]\sin^{3} ( \frac{\pi}{2} -x)[/tex]

[tex](\sin ( \frac{\pi}{2} -x))^{3}[/tex]

Apply the complementary identity;

[tex](\cos x)^{3} = { \cos}^{3} x[/tex]

Answer:

$6.00

Step-by-step explanation:

Let's look at our prices:

Sandwich = $3.50

Fruit cup = $1.50

Orange juice = $1.00

Now let's add them:

$3.50 + $1.50 = $5.00

$5.00 + $1.00 = $6.00

Tip: Adding money is like adding regular digits. You also regroup (like we did with 5 + 5) as normal.

Answer:

y=-6

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The high school boys vary in height more than the middle school boys.

middle school boys range = 169 − 164 = 5 cm

high school boys range = 183 − 175 = 8 cm

The range for both conditions is 5 cm and 8 cm respectively.

The difference between the highest and lowest value data points of the provided data is known as the range in mathematics.

In statistics, the mean is the product of all the values in a set of data divided by the total number of values in the data for a given set of observations.

The high school boys vary in height more than the middle school boys.

Middle school boys range = 169 − 164 = 5 cm

High school boys range = 183 − 175 = 8 cm.

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