Alona has some wood cutouts of two different shapes - square and triangle. Each square cutout is 6 mm thick and each triangular cutout is 8 mm thick. Both cutouts have the same area of cross-section. Alona makes an upright stack using 24 square cutouts. She is making an oblique stack using the triangular cutouts. How many triangular cutouts should she put in the oblique stack so that both stacks have the same volume?

Answer:

The answer is D: sin 11pi/6

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Step-by-step explanation:

The expression that is equivalent to the given expression is Sin(11π/6).

The given trigonometric expression is: [tex]Sin \frac{7\pi }{6}[/tex]

[tex]Sin\frac{7\pi }{6}[/tex] can be written as [tex]Sin(\pi +\frac{\pi }{6} )[/tex]

The value of [tex]Sin(\pi +\theta)[/tex] is [tex]-Sin\theta[/tex].

So, [tex]Sin(\pi +\frac{\pi }{6} )=-Sin\frac{\pi }{6}[/tex]

We know that

[tex]Sin(2\pi -\theta)=-Sin\theta[/tex]

Or, [tex]-Sin\theta=Sin(2\pi -\theta)[/tex]

So, [tex]-Sin\frac{\pi }{6} =Sin(2\pi -\frac{\pi }{6} )[/tex]

[tex]-Sin\frac{\pi }{6} =Sin\frac{11\pi }{6}[/tex]

So, the required expression is [tex]Sin\frac{11\pi }{6}[/tex].

Therefore, the expression that is equivalent to the given expression is Sin(11π/6).

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Answer: 12inches

Step-by-step explanation:

Area of a circle= 113.04square inches

Area of a circle =pir^2

Pi=3.14

R=?

So we are looking for the radius and from there we will get the diameter

Area=pir^2

113.04=3.14×r^2

R^2= 113.04/3.14

R^2=36

R=square root of 36

R= 6

Diameter =2r

Diameter = 2×6

Diameter = 12inches

Answer:

12 inches

Step-by-step explanation:

3.14 × r² = 113.04

r² = 36

r = 6

Diameter = 2r = 12

Answer:

A. 1256

Step-by-step explanation:

You have to find the radius of the shaded circle

So you can add 12 + 8 = 20

Or you can find the diameter of the two circles. The diameter of the first circle is 12 + 12 = 24 and the second circle is 8 + 8 = 16 + 20 + 40 is the diameter of the shaded circle. Since radius is half of diameter 40 ÷  2  = 20

So now since you know the radius of the shaded circle you can find the area

A = πr²

A = 3.14 x 20²

A = 3.14 x 400

A = 1256

The volume of the pyramid is  167.6 cube inch (approx).

Step-by-step explanation:

Given,

Each length (l) of the base of the pyramid = 8.3 in

Height(h) of the pyramid = 7.3 in

To find the volume of the pyramid.

Formula

Volume of the pyramid = [tex]\frac{1}{3}[/tex]×area of the base×height

Area of the base = l²

Now,

The volume of the pyramid =  [tex]\frac{1}{3}[/tex]×l²×h

=  [tex]\frac{1}{3}[/tex]×8.3²×7.3 cube inch = 167.6 cube inch (approx)

The volume of the pyramid is calculated using the formula for a pyramid's volume, V = (1/3)bh, with a base area of 68.89 in² and height of 7.3 in, which gives a volume of approximately 167.5 in³.

To find the volume of a pyramid with a square base, we can use the formula V = (1/3)bh, where b is the area of the base and h is the height of the pyramid. First, calculate the area of the square base by squaring the side length: b = s² = 8.3 in × 8.3 in = 68.89 in². Next, use this base area in the formula to get the volume: V = (1/3) × 68.89 in² × 7.3 in.

Doing the calculation, we find that V = (1/3) × 68.89 in² × 7.3 in = 167.4757 in³. To round to the nearest tenth, the volume of the pyramid is approximately 167.5 in³.

Answer: 900 square meters. 30x30

Step-by-step explanation: a square is the biggest area you can have, so 120 divided by 4 is 30, and then 30 times 30 is 900.

Answer:

27

Step-by-step explanation:

Answer:

[tex]\huge\boxed{\dfrac{2}{16}=12.5\%}[/tex]

Step-by-step explanation:

[tex]p\%=\dfrac{p}{100}\to p=p\cdot100\%\\\\\dfrac{2}{16}=\dfrac{2:2}{16:2}=\dfrac{1}{8}\\\\\dfrac{1}{8}=\dfrac{1}{8}\cdot100\%=\dfrac{100}{8}\%=12.5\%\\\\\text{Other method.}\\\\\dfrac{1}{8}=\dfrac{1\cdot125}{8\cdot125}=\dfrac{125}{1000}=\dfrac{125:10}{1000:10}=\dfrac{12.5}{100}=12.5\%[/tex]

Answer:

y = 40 degrees can i have branliest

Step-by-step explanation:

All angles in a triangle add up to 180

180 - 50 = 130

3y + 10 = 130

3y = 120

y = 40

Answer:

c

Step-by-step explanation:

Answer:

Step-by-step explanation:

When (i) is multiplied to itself it = -1

The number (i)is used for imaginary numbers.

Step-by-step explanation:

According to BODMAS

the first way to evaluate the expression is starting from brackets.,

=3 * 9 -27 / 9

= 3 * 9 - 3

= 27- 3

=24

Answer:

Parenthesis.

Step-by-step explanation:

Parenthesis

Exponent

Multiply or

Divide

Add or

Subtract

PEMDAS is the order to solve expressions like so.

sqrt(36/100) = +-6/10

You find the square root of the numerator and the denominator.

Answer:

399

Step-by-step explanation:

The only expression that does not equal 400 is c. 500 - 200.

From the question, we have the following parameters that can be used in our computation:

a. 2 * 200

b. 800/2

c. 500 - 200

d. 300 + 100

Evaluating each of the options, we have the following

a. 2 * 200 = 400

b. 800/2 = 400

c. 500 - 200 = 300

d. 300 + 100 = 400

Hence, the only option that does not equal 400 is c. 500 - 200.

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Question

Which is not equal to 400

a. 2 * 200

b. 800/2

c. 500 - 200

d. 300 + 100

The division problems 123.4/9.2 and 71.9/6.5 have an estimated quotient of 12 by considering 123.4 as 120, 9.2 as 10, 71.9 as 70, and 6.5 as 6.

The division problems with an estimated quotient of around 12 will be the ones where you divide a number close to 120 by 10. In this case, it comes to be 123.4/9.2 and 71.9/6.5. To estimate the quotient, you can consider 123.4 as approximately 120 and 9.2 as approximately 10. Similarly, 71.9 can be considered as approximately 70 and 6.5 as approximately 6. When you divide these estimate numbers, both quotients are close to 12.

Estimation is a useful skill in Mathematics that allows you to simplify complex problems and get close to the exact answer. It's particularly helpful in situations where you only need a rough estimate and not the exact figure.

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Answer:

65

Step-by-step explanation:

Use the formula: a²+b²=c²

63²=3969

16²=256

Add them = 4225 = c²

[tex]\sqrt{4225} = \sqrt{c^2}[/tex]

65 = c (or x in this case)

Answer:

17.96

Step-by-step explanation:

To find the hypotenuse we are will have to use Sine, since we are only given the degree and opposite leg. [tex]sin(degree)=\frac{Opposite}{Hypotenuse}[/tex]

[tex]sin(63)=\frac{16}{x}[/tex]

Let's cancel the x on the right side by multiplying both sides by x

sin(63)x = 16

Divide both sides by sin(63)  [Or 0.866, depending on the type of calculator you have]

sin(63)x ÷ sin(63) = 16 ÷ sin(63)

x = 17.9572198

Answer: hamburger $3.00

Coke $1.50

Step-by-step explanation:

2hamburgers & 3cokes= $10.50

4hamburgers & 4cokes= $18.00

Let hamburger represent H

And coke represent C

2H +3C= 10.50.......equation 1

4H+4C= 18.00.......equation 2

2H =10.50 -3C...........equation 3

The 4H can be rewriting as

2(2H) right

So substitute for the 4H

So we have,

2(2H) +4C= 18

Substitute for 2H

2(10.50 -3C) +4C =18

Open the bracket

21 -6C +4C= 18

21-2C= 18

-2C = 18-21

-2C = -3

Minus cancel minus

C= 3/2 = $1.5

Substitute for c in equation 1

2H+3C =10.50

2H+3(1.5)= 10.50

2H+4.5=10.5

2H= 10.5-4.5

2H =6

H= 6/2

H=$3

So

An hamburger cost $3.00

A coke cost $1.50

Answer:

Step-by-step explanation:

Answer:

The population will reach 20,400 after 6 years.

Step-by-step explanation:

Exponential function:

[tex]y(t)=y_0(1+r)^t[/tex]

y(t)= Population after t years

[tex]y_0[/tex] = initial population

r= rate of grow

t= time.

A town has a population of 17,000 and grows at a rate 3% every year.

y(t)= 20,400, [tex]y_0[/tex] = 17,000, r=3%=0.03, t=?

[tex]20,400=17,000(1+0.03)^t[/tex]

[tex]\Rightarrow \frac{20,400}{17,000}=(1.03)^t[/tex]

[tex]\Rightarrow \frac{102}{85}=(1.03)^t[/tex]

Taking ln function both sides

[tex]\Rightarrow ln|\frac{102}{85}|=ln|(1.03)^t|[/tex]

[tex]\Rightarrow ln|\frac{102}{85}|=t\ ln|(1.03)|[/tex]

[tex]\Rightarrow t=\frac{ln|\frac{102}{85}|}{\ ln|(1.03)|}[/tex]

⇒ t = 6 year.

The population will reach 20,400 after 6 years.

Answer:

6

Step-by-step explanation:

deltamath

Answer:

f (-2)=(-2)-2

= -4

By putting value of x= -2 in f (x)

Answer:

$3.94

Step-by-step explanation:

You will need to use the compound interest formula for this.

[tex]P(1+\frac{r}{n} )^{nt}[/tex]

P = initial balance

r = interest rate

n = number of times compounded annually

t = time

Your equation will look like this:

[tex]3.31(1+\frac{.0088}{1} )^{20}[/tex] = 3.94

(6x-3)+(7x-7)

Hope I helped :d

Answer:

[tex]4x^{2} +x+2[/tex]

Answer:

400

Step-by-step explanation:

1 hour = 5 pieces • $2

1 hour = $10 bcas each piece you make is $2

40 hours = $400 because you get $10 per week

You earn $400 per week

Answer:

$400

Step-by-step explanation:

S x H  = (1 x 5 x 2) x 40

S x H  = (1 x 10)  x 40

S x H  = 10 x 40

S  =  400

S  = $400    H = 40

Answer:

75 gophers (about)

Step-by-step explanation:

We will use continuous compounding interest formula:

[tex]P(t)=P_0e^{rt}[/tex]

Where

P(t) is final value (at time t)

P_0 is initial value

r is the compounding rate

t is the time period

Given:

P(t) = 78

r is 1.5% or 1.5/100 = 0.015

t is 3

We solve for P_0, what we want, using algebra as shown below:

[tex]P(t)=P_0e^{rt}\\78=P_0e^{(0.015)(3)}\\78=P_0e^{0.045}\\\frac{78}{P_0}=e^{0.045}\\\frac{78}{P_0}=1.0460\\P_0=74.57[/tex]

So, the initial population was 75 gophers.

The 75 gophers were on the ranch at the beginning of the 3 years according to the exponential growth function.

To solve this problem, we can use the following exponential growth function:

P(t) = P_0 * e^(rt)

where:

P(t) is the population at time t

P_0 is the initial population

r is the annual growth rate

t is the time in years

We know that the population after 3 years is 78 gophers, and the annual growth rate is 1.5%. We want to find the initial population, P_0.

So, we can plug in the following values into the exponential growth function:

P(3) = 78 = P_0 * e^(0.015 * 3)

Dividing both sides by e^(0.015 * 3), we get:

P_0 = 78 / e^(0.015 * 3)

Using a calculator, we can evaluate P_0 to be approximately 75.0.

Rounding up to the nearest whole number, we get an initial population of 75 gophers.

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Answer:

3.5 feet

Step-by-step explanation:

Diameter = 7 feet

Radius = Diameter × [tex]\frac{1}{2}[/tex]

Radius = [tex]\frac{7}{2}[/tex] = 3.5 feet

Answer:

Last one

Step-by-step explanation:

f(x) = Asin(Bx) + C

C = 0

A = 5

B = 2pi/12 = pi/6

f(x) = 5 sin[(pi/6)x]

Answer:

3g

Step-by-step explanation:

Since 5p=3g

5p=x

So let's solve by cross multiplying

5px=3g×5p

5px=15gp

Divide both sides by 5p

x=3g

Therefore the final answer is 3g