Find the volume of the triangular prism.
4 ft
8 ft
37 ht

Answer:

x = sqroot(122)

Step-by-step explanation:

First find the line that goes thru the middle of the shape. It is the hypotenuse of the bottom/left triangle. Use the pythagorean thm.

9^2 + 5^2 = h^2

81 + 25 = h^2

sqroot106 = h

Now sqroot106 is a leg in the right triangle that is on the top/right in the image.

Use pythagorean thm again.

4^2 + (sqroot106)^2

= x^2

16 + 106 = x^2

122 = x^2

sqroot122 = x

[tex]\cfrac{6!}{3!}\implies \cfrac{6\cdot 5\cdot 4\cdot \qquad 3\cdot 2\cdot 1}{3\cdot 2\cdot 1}\implies \cfrac{6\cdot 5\cdot 4\cdot 3!}{3!}\implies 6\cdot 5\cdot 4\implies 120[/tex]

Answer:

Step-by-step explanation:

Use the factorials formula.

Factorials formula:

[tex]\Longrightarrow: \sf{\dfrac{n!}{(n-m)!}=n*(n-1)* (n-m+1),\:\quad \:n > \:m}[/tex]

→ 6!/3!=6*5*4

⇒ 6*5*4

Solve a order of operations.

PEMDAS stands for:

First, multiply.

→ 6*5*4

⇒ 6*5=30

⇒ 30*4=120

= 120

I hope this helps you! Let me know if my answer is wrong or not.

Answer:

61/112.

Step-by-step explanation:

For 5 lemon sweets to be in the bowl the 3 taken  must be from the 4 blackcurrent and/or 7 orange sweets.

First work out the probability of having a lemon in one of the 3 picks:

Prob (Taking 3  lemons) = 5/16 * 4/15* 3/14 =  60/3360 = 1/56.

Prob (Taking 2  lemons and 1 blackcurrent) = 5/16*4/15*4/14 =  1/42

There are 3 ways of doing this so Probab) = 3/42 = 1/14.

Prob (Taking 1  lemon and 2 blackcurrent) = 5/16*4/15*3/14 = 1/56.

There are 3 ways of doing this so Prob = 3/56.

Prob (Taking 2  lemons and orange) = 5/16*4/15*7/14 = 140/3360 = 1/24.

There are 3 ways of doing this so Prob) = 3/24 = 1/8.

Prob (Taking 1  lemon and 2 orange) = 5/16*7/15*6/14 =  1/16

There are 3 ways of doing this so Prob = 3/16.

Therefore the probability of have 1 or more lemons in one of the 3 picks

= 1/56 + 1/14 + 3/56 + 1/8 + 3/16

=  51/112

and the probability of NOT having a lemon in one of the 3 picks

= 1 - 51/112

=  61/112.

Answer:

yessir

Step-by-step explanation:

Answer:10.5

Step-by-step explanation: I hope this helps

The height, x, of the right trapezoidal prism is 10.5 ft.

Given that, the volume of this right trapezoidal prism is 341.25 ft³.

We need to find the height x, of the prism.

The formula to find the volume of this right trapezoidal prism is Volume=BH.

Where B=Area of the Base and H=Height.

Area of the Base(Trapezium)=1/2(a+b)×h

Where a and b are parallel sides of the trapezium and h= height of the trapezium.

Now, the area of the Base=1/2(8+5)×5=32.5 ft²

The volume of the right trapezoidal prism=32.5×x

⇒341.25=32.5×H

⇒x=10.5 ft

Therefore, the height, x, of the right trapezoidal prism is 10.5 ft.

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Answer: 7

Step-by-step explanation:

Answer:

A(0,1) B(0,4) C(1,2) D(3,2)

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

6 divided by 10 = 0.6

0.6 = 6/10

6/10 = 3/5

Answer:

One Kilogram

Step-by-step explanation:

1kg = 1000g

Answer:

Kilogram

Step-by-step explanation:

Hope it helps.

Do comment if you have any query.

Let's start off with  1. 3/10 * 5/7

3/10×5/7=?

For fraction multiplication, multiply the numerators and then multiply the denominators to get

(3×5) / (10×7) = 15 / 70

This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 15 and 70 using

GCF(15,70) = 5

(15÷5)/ (70÷5)=3/14

Therefore:

3/10×57=3/14

Now, #2. 7/10 * 2/4- We do the same process.

7/10×2/4=?

For fraction multiplication, multiply the numerators and then multiply the denominators to get

(7×2) / (10×4)=1440

This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 14 and 40 using

GCF(14,40) = 2

(14÷2) / (40÷2) = 7/20

Therefore:

7/10×2/4=7/20

Hope this helps!

Answer:

  c = 2√3 ≈ 3.464

Step-by-step explanation:

A 30°-60°-90° triangle is a "special" triangle that has sides in the ratios ...

  1 : √3 : 2 . . . . . shortest to longest.

Comparing those to the side measures you have, we see ...

  1 : √3 : 2 = b : 3 : c

Multiplying the basic ratios by √3 gives a value that matches the long side:

  √3 : 3 : 2√3 = b : 3 : c

Then the value of c is 2√3 ≈ 3.464.

_____

Additional comment

Side length b is √3 ≈ 1.732.

Answer:

They are increasing at the same rate.

Answer:

18 cups of lemonade

Step-by-step explanation:

so if it cost him $0.15 to make each cup of lemonade and he sold a cup for $0.35 then he sold 18 cups

One of the strategies that would eliminate a variable in the system of equations is by subtracting both equations to eliminate the variable "x"

System of equations consists of a different set of equations with unknown variables.

Given the system of equations

2x+3y=-5

2x-3y=10

Since the coefficient of x from both equations are the same, we will subtract both equations to eliminate the variable "x"

(2x-2x)+(3y+3y) = -5 + 10
6y  = 5

Hence we can conclude that one of the strategies that would eliminate a variable in the system of equations is by subtracting both equations to eliminate the variable "x"

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Answer: 4 committees

Hope this helps! :)

I need brainliest please.

Answer:

[tex]\sf -11+7\sqrt{2}[/tex]

Step-by-step explanation:

Given expression:

[tex]\sf \dfrac{3-\sqrt{32}}{1+\sqrt{2} }[/tex]

Rewrite 32 as 16 · 2:

[tex]\sf \implies \dfrac{3-\sqrt{16 \cdot 2}}{1+\sqrt{2} }[/tex]

Apply radical rule [tex]\sf \sqrt{a \cdot b}=\sqrt{a}\sqrt{b}[/tex]

[tex]\sf \implies \dfrac{3-\sqrt{16}\sqrt{2}}{1+\sqrt{2} }[/tex]

As [tex]\sf \sqrt{16}=4[/tex]:

[tex]\sf \implies \dfrac{3-4\sqrt{2}}{1+\sqrt{2} }[/tex]

Multiply by the conjugate:

[tex]\sf \implies \dfrac{3-4\sqrt{2}}{1+\sqrt{2} } \times \dfrac{1-\sqrt{2} }{1-\sqrt{2} }[/tex]

[tex]\sf \implies \dfrac{(3-4\sqrt{2})(1-\sqrt{2})}{(1+\sqrt{2})(1-\sqrt{2})}[/tex]

[tex]\sf \implies \dfrac{3-3\sqrt{2}-4\sqrt{2}+4\sqrt{2}\sqrt{2}}{1-\sqrt{2}+\sqrt{2}-\sqrt{2}\sqrt{2}}[/tex]

As [tex]\sf \sqrt{2}\sqrt{2}=\sqrt{4}=2[/tex]:

[tex]\sf \implies \dfrac{3-3\sqrt{2}-4\sqrt{2}+4 \cdot 2}{1-\sqrt{2}+\sqrt{2}-2}[/tex]

[tex]\sf \implies \dfrac{3-7\sqrt{2}+8}{1-2}[/tex]

[tex]\sf \implies \dfrac{11-7\sqrt{2}}{-1}[/tex]

[tex]\sf \implies -11+7\sqrt{2}[/tex]

Answer:

let the number be x.

(x+6)/10 = 3

x+6 = 30

x =24

Answer:

Leanne is correct. It is important that g(x) is subtracted from f(x).

Shiloh is incorrect. She subtracted f(x) from g(x), and subtraction isn't commutative.

*Just took the test, got the answer correct!! Hope this helps!

Answer:

? = 13.6

Step-by-step explanation:

the angle between a tangent and the diameter = 90°

Then the triangle is right with legs 2 × 6 = 12 and 6.4

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the legs , that is

? ² = 12² + 6.4² = 144 + 40.96 = 184.96 ( take square root of both sides )

? = [tex]\sqrt{184.96}[/tex] = 13.6

Answer:

b) 55 and 43

Step-by-step explanation:

I can tell by the first 3 or so numbers that the sequence is decreasing by 6 each time, so when you go from 61- blank - 49 it has to be 55 and same with the other one.

The mean of the data set can be used because it is not easily affected by extreme values.

A measure of central tendency is a measure that tries to describe an entire data set by using the central value of the data.

Mean is often used as a measure of central tendency when dealing with a large data such as tourism in the city because it is not easily affected by extreme values.

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Answer:  $19.50

Step-by-step explanation:

Answer: Trapezoid

Step-by-step explanation:

Answer:

No, the mayor cannot conclude that 90% of residents favor the expansion.

Step-by-step explanation:

The sample taken is from the employees that will work on the highway, but we need to know the resident's opinion. The workers will have a different opinion than the average person, so this is not an accurate conclusion.

Answer:

54√2

Step-by-step explanation:

6√3 × 3√6 =

( 6 × 3 ) × [tex]\sqrt{3*6}[/tex] =

18√18 = 18√(2×9) =

18 ( √2 × √9 ) =

(18 × 3)√2 = 54√2

The product of 6 square root 3 and 3 square root 6 in the simplest radical form will be 54 square root 2.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

It is given that the two terms are 6√3  and 3√6.

We have to find the product of the given terms,

Radical notation is the term for an expression that employs a root, such as the square or cube root.

=6√3 × 3√6

=( 6 × 3 )√( 6 × 3 )

=18√18

= 18√(2×9)

=18 ( √2 × √9 )

=(18 × 3)√2

= 54√2

54√2 is the term shown in the radical form.

Thus, the product of 6 square root 3 and 3 square root 6 in the simplest radical form will be square root 54.

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Answer:

m(C)<m(B)<m(A).

Step-by-step explanation:

1) according to the condition the shortest side is AB, the longest side is BC, the middle is AC. Then

2) the smallest angle is BCA (or C), the middle angle is ABC (or B), the largest angle is BAC (or A).

The list of the angles from smallest to largest are C, B and A.

Given that a triangle has side measurements represented in terms of the variable m, where m > 6.

AB = m - 2

BC = m + 4

AC = m

We need to list the angles from smallest to largest.

Since none of the sides are equal, therefore it is a scalene triangle.

Let us consider m = 6.

Then,

AB = m - 2

AB = 6 - 2

AB = 4

BC = m + 4

BC = 6+4

BC = 10

AC = m

AC = 6

It means that the longest side is BC, the medium side is AC and the shortest side is AB.

We know that the longest side of a triangle corresponds to the largest angle and vise versa.

Therefore,

The smallest angle is angle C.

The medium angle is angle B.

The largest angle is angle A

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