The volume of the triangular prism is 54 cubic units.

A triangular prism with a volume of 54 cubic units is shown. The triangle has a base length of 4 and a height of x. The height of the prism is 3 x.

What is the value of x?

3
5
7
9

Step-by-step explanation:

Given radius = 30 in.

Circumference is given by 2πr

= 2 × π × 30

= 60π in

Answer:

Surface area of sphere = 1,344.8 m² (Approx)

Step-by-step explanation:

Given:

Volume of sphere = 1,476π m³

Find;

Surface area of sphere

Computation:

Volume of sphere = [4/3]πr³

1,476π = [4/3]πr³

1,476 = [4/3]r³

[1,476][3/4] = r³

1,107 = r³

r = 10.35 m (Approx.)

Surface area of sphere = 4πr²

Surface area of sphere = 4(3.14)(10.35)²

Surface area of sphere = 4(3.14)(107.1225)

Surface area of sphere = 1,345.45

Surface area of sphere = 1,344.8 m² (Approx)

Answer:

x<-3

Step-by-step explanation:

Answer:

Probability[Random choose marble is green] = 5 / 13

Step-by-step explanation:

Given:

Number of yellow marble in bag = 4

Number of white marble in bag = 4

Number of green marble in bag = 5

Find:

Probability[Random choose marble is green]

Computation:

Probability of an event = Number of favourable outcome / Number of total outcome

Probability[Random choose marble is green] = 5 / [4 + 4 + 5]

Probability[Random choose marble is green] = 5 / 13

Answer:

A

Step-by-step explanation:

basta letter A sagot dyan

Answer:

$2907.89

General Formulas and Concepts:

Symbols

Pre-Algebra

Order of Operations: BPEMDAS

Algebra i

Compounded Continuously Formula: [tex]\displaystyle A = Pe^{rt}[/tex]

Step-by-step explanation:

Step 1: Define

Identify variables

P = 930

t = 19

r = 6% = 0.06

Step 2: Find Interest

Answer:

optin d) 8

Step-by-step explanation:

           [tex]2 \times 2 \times 2 = 2^3[/tex] [tex]= 8[/tex]

Answer:

The series converges as any two consecutive elements of the sum are monotonically decreasing.

Step-by-step explanation:

The series converges since the consecutive element is monotonically decreasing. That is:

[tex]\forall\,i\in \mathbb{N}\,a_{i} > a_{i+1}[/tex] (1)

Where:

[tex]a_{i}[/tex] - The i-th component of the sum.

[tex]a_{i+1}[/tex] - The (i+1)-th component of the sum.

Answer:

where is the Venn diagram plz insert Venn diagram then I should solve

Answer:

Exact Length = 2*sqrt(30)

Approximate Length = 10.95445

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

Work Shown:

(tangent)^2 = (external secant)*(whole secant)

(CD)^2 = (CB)*(CA)

(CD)^2 = (CB)*(CB+BA)

x^2 = 5*(5+19)

x^2 = 120

x = sqrt(120)

x = sqrt(4*30)

x = sqrt(4)*sqrt(30)

x = 2*sqrt(30)  .......... exact length

x = 10.95445 ............. approximate length

The length of the tangent segment is; x = 10.95

From secant theorem, we know that;

Tangent ² = length of external secant × total length of secant.

From the image, we see that;

Length of tangent is x.

External secant = 5

Total length of secant = 19 + 5 = 24

Thus;

x² = 5 × 24

x² = 120

x = √120

x ≈ 10.95

Read more about length of tangent at;https://brainly.com/question/9132922

Answer: -3

Step-by-step explanation:

-l-7+4l = -l-3l = - 3

ll means anything inside there is positive, so for example if -3 was in there, l-3l = 3

Answer:

- 3

Step-by-step explanation:

-|-7 + 4|

Simplify inside the absolute values first( like parentheses)

-|-3|

Take the nonnegative value for the absolute value

- 3

Answer:

h=rt.96=4 rt.6

Step-by-step explanation:

r=2 inches

therefore 100= root over h + 4

          =>h=rt.96=4 rt.6

Answer:

so for this we do

39.42*1.08=42.5736

Hope This Helps!!!

Answer:

4.1 hours each day

Step-by-step explanation:

20.5 ÷ 5

= 4.1

Therefore 4.1 hours was spent on studying each day.

Answer:

[tex]\sqrt{77}[/tex] ft

Step-by-step explanation:

Hi there!

Notice how we can create a right triangle in the cone, where the base is 2 ft (4/2=2), the height is h and the hypotenuse is 9 ft.

Using these values, we can solve for h with the Pythagorean theorem: [tex]a^2+b^2=c^2[/tex] where a and b are the two legs of a right triangle and c is the hypotenuse.

Plug in 2 and h as a and b and 9 as c:

[tex]2^2+h^2=9^2\\4+h^2=81\\h^2=81-4\\h^2=77\\h=\sqrt{77}[/tex]

I hope this helps!

Answer:91%

Step-by-step explanation:

Answer:

f(x) = x² - 3x - 10

Step-by-step explanation:

Given zeros x = - 2 and x = 5, then the corresponding factors are

(x + 2) and (x - 5) , so

f(x) = (x + 2)(x - 5) ← expand using FOIL

     = X² - 3X - 10

Answer:

f(x) = x² - 3x - 10

(option D)

Step-by-step explanation:

Answer:73825

Step-by-step explanation:

Shuts shield grid

Answer:

[tex]j=8[/tex]

Step-by-step explanation:

Special right triangles:

The sides of all 30-60-90 triangles are in the proportion [tex]x:x\sqrt{3}:2x[/tex], where [tex]2x[/tex] is the hypotenuse of the triangle and [tex]x[/tex] is the side directly opposite to the 30 degree angle.

Since the base of the triangle is directly opposite to the 30 degree angle, the hypotenuse, j, must be equal to [tex]4\cdot 2=\boxed{8}[/tex]

Basic trig:

[tex]\sin 30^{\circ}=\frac{4}{j},\\j=\frac{4}{\sin 30^{\circ}}=\boxed{8}[/tex]

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

Explanation:

Ignore the rows that are labeled "stock ABC" and "stock MNO".

We only focus on the top row (gains and losses) and the "stock JKL" row.

Multiply each gain or loss with its corresponding probability in decimal form. Use negative values to represent a loss

Add up those results to get the final answer: -3.75+3.25+9 = 8.50

-----------------------

Here's another way to get the answer.

Let's say you had a 10 by 10 grid of graph paper.

This can be thought of as like a dart board. Imagine throwing 1000 darts at this grid (maybe do so blindfolded to give each square an equal chance; if you land outside the grid then re-throw the dart). Theoretically, the probability of landing in the red area is 15/100 = 0.15, so we expect about 1000*0.15 = 150 darts will land there out of the 1000 thrown total. Each of those 150 darts in the red area represents a loss of $25. So we have a loss of 150*25 = 3750 dollars. We'll write this as -3750.

We also expect 0.65*1000 = 650 darts to have a gain of $5. That means 650*5 = 3250 is earned here. Furthermore, 0.20*1000 = 200 darts land in the green squares to get us $45 per attempt. So that's another 45*200 = 9000 dollars.

Overall, we would get -3750+3250+9000 = 8500 in profit.

Divide this over the 1000 dart throws and we end up with an expected value of 8500/1000 = 8.50

Keep in mind that this dart game or thought experiment is depending on theoretical probabilities. If you actually do this game, then your empirical probabilities will likely differ slightly from the theoretical values. However, the more trials you conduct, the closer your empirical probabilities should get to the theoretical ones.

Answer:

729167

Step-by-step explanation:

Now we can see that our fraction is 72.916666666667/100, which means that 35/48 as a percentage is 72.9167%.

Answer:

6√7=15.874507866387543=√252

Step-by-step explanation:

hope this is helpful

The expression that are equivalent to √252 are [tex]252^{\frac{1}{2} }[/tex] and 6√7.

Applying the surd rule,

√a = [tex]a^{\frac{1}{2} }[/tex]

Hence,

[tex]\sqrt{252}=252^{\frac{1}{2} }[/tex]

using surd rule, we can also decompose √252

Therefore,

√252 = √36 × 7 = 6√7

Hence, the equivalent expression of √252 are as follows:

learn more on expression here: https://brainly.com/question/27768447

#SPJ2

Answer:

x=-3×-5×-7

-3×-5=15

15×-7=-105

=-105

Answer:

77

Step-by-step explanation:

i took the test

Answer:

c

Step-by-step explanation:

OPTION C IS THE CORRECT ANSWER.

Answer:

y=-90

Step-by-step explanation:

y = kx

45 = k 3

k = 15

~~~~~~~~~~~~

y = 15*-6

y=-90

Answer:

36

We should write a formula for their relationship:

Y = x+42. <- this is what a direct varieation is I believe.

So, when x is -6, y is +42 aka 36

Answer:

5/6 hours

Step-by-step explanation:

Create a proportion where x is the number of hours it will take to walk 1/6 of a mile:

[tex]\frac{1/5}{1}[/tex] = [tex]\frac{1/6}{x}[/tex]

Cross multiply and solve for x:

1/5x = 1/6

x = 5/6

So, it will take the tortoise 5/6 hours to walk 1/6 of a mile

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

I found it easiest to draw arcs of radii AB and AC centered at A, and arcs of radii DB and DC centered at D. The intersection points of those arcs mark the points B' and C'. These are points B and C reflected across line AD.

Joining A, B', C', and D will make a figure symmetrical about AD.

If you meant to write [tex]\log_{b}(y) = x[/tex] then the statement is true.

As a more concrete example, something like [tex]\log_3(81) = 4[/tex] would be read out as "log base 3 of 81 is equal to 4".

Answer:

3 1/25

Step-by-step explanation:

3.04

Do the decimal part first

.04 = 4/100

Reduce - cancel out 4

1/25

Put back the whole number

3 1/25

Answer:

3 [tex]\frac{1}{25}[/tex]

Step-by-step explanation:

I agree with the previous answer :

You need to do it part by part.

0.04 is equal to [tex]\frac{4}{100}[/tex]

[tex]\frac{4}{100}[/tex] simplified (we divide by 4 with both the denomantor and the numerator.) =

[tex]\frac{1}{25}[/tex]

And we still have those 3 wholes that we had in the beginning.

Now we add.

3 + [tex]\frac{1}{25}[/tex] = 3 [tex]\frac{1}{25}[/tex]