A math class consists of 10 girls and 8 boys. The teacher wants to choose 2 girls and 2 boys to go on a trip. How many different groups could the teacher choose?


A. 5040

B. 3060

C. 1260

D. 73

The simplified form of the provided expression of 2 startroot 18 endroot +3 startroot 2 endroot startroot +162 endroot is 18√2.

The simplified form of an equation is the simplest way of expressing the equation, by applying the required operations of mathematics.

The equation provided in the problem is,

[tex]2\sqrt{18}+3\sqrt{2}+\sqrt{162}[/tex]

Let the simplified form of the above expression is n. Thus,

[tex]n=2\sqrt{18}+3\sqrt{2}+\sqrt{162}[/tex]

Rewrite the equation to solve it further as,

[tex]n=2\sqrt{3\times3\times2}+3\sqrt{2}+\sqrt{9\times9\times2}\\n=2\sqrt{3^2\times2}+3\sqrt{2}+\sqrt{9^2\times2}[/tex]

The square of the term cancel out the square root of it. Thus,

[tex]n=2\times3\sqrt{2}+3\sqrt{2}+9\sqrt{2}\\n=6\sqrt{2}+3\sqrt{2}+9\sqrt{2}\\n=(6+3+9)\sqrt{2}\\n=18\sqrt{2}[/tex]

Thus, the simplified form of the provided expression of 2 startroot 18 endroot +3 startroot 2 endroot startroot +162 endroot is 18√2.

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The equivalent statement is "if m∠A = 60°, then Δ ABC is an equilateral triangle. (Option C).

Equivalent Statements refer to statements that when written differently, retain their logical equivalence. another way to know if a set of statements are equivalent is if they can be proven by one another.

An example of equivalent statement besides the one given already is:

A cat is an animal.

A pet is an animal you own.

Therefore owning a cat is the same as owning a pet.

Therefore:

If Jake owns a cat then he owns a pet.

If Jake doesn't own a pet then he doesn't own a cat.

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Answer:

a)  0.905 (3 dp)

Step-by-step explanation:

Binomial distribution X ~ B(n, p)

where n is the the number of trials and p is the probability of success

Binomial formula:

[tex]P(X=x)=\left(\left\begin{array}{cc}n\\x\end{array}\right) \cdot p^x \cdot (1-p)^{n-x}[/tex]

Given:  X ~ B(100, 0.001)

Therefore, n = 100 and p = 0.001

Substituting these values into the binomial formula and solving for x = 0:

[tex]\implies P(X=0)=\dfrac{100!}{0!100!} \cdot 0.001^0 \cdot (1-0.001)^{100-0}[/tex]

[tex]\implies P(X=0)=1 \cdot 1 \cdot 0.999^{100}[/tex]

[tex]\implies P(X=0)=0.9047921471...[/tex]

[tex]\implies P(X=0)=0.905 \ \sf(3 \ dp)[/tex]

The perimeter and area of a regular hexagon with side length of 8 and apothem of 9 are 48 units and 216 units² respectively.

A regular hexagon is a polygon with 6 sides and the angles are congruent.

The perimeter of the hexagon is the sum of the whole sides. Therefore,

side length = 8 units

apothem = 9 units

perimeter = 8 × 6 = 48 cm

The area of the hexagon can be calculated as follows:

area = 1 / 2 pa

where

p  =perimeter

a = apothem

Therefore,

area = 1  / 2 × 48 × 9

area = 432 / 2

area = 216 units²

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

∠ABD is the complementary angle to ∠BDC.

Two angles are complementary when they add up to 90°

Answer:

A = 3x² - x - 10

Step-by-step explanation:

the area (A) of a rectangle is calculated as

A = length × width , then

A = (3x + 5)(x - 2)

each term in the second factor is multiplied by each term in the first factor.

A = 3x(x - 2) + 5(x - 2) ← distribute parenthesis

   = 3x² - 6x + 5x - 10 ← collect like terms

   = 3x² - x - 10

Answer:

A = 3x² - x - 10

Step-by-step explanation:

A = length × width

A = (3x + 5)(x - 2)

A = 3x(x - 2) + 5(x - 2)

A = 3x² - 6x + 5x - 10

A = 3x² - x - 10

Answer:

101828.833333

Step-by-step explanation:

you have to multiply the two numbers then divide by 12

Answer:

  x = 43°

Step-by-step explanation:

The three angles to the right of the diagonal line add up to give the angle measure of the line:

  x +90° +47° = 180°

  x = 43° . . . . . . . . . . . . . subtract 137° from both sides

Answer:

36 feet

Step-by-step explanation:

Hello!

Recall that the formula for the area of a triangle is [tex]\frac12b*h[/tex]

That means the equations is 144 = 0.5(8 * h)

Solve:

The height is 36, but since the units are feet, it is 36 feet.

In the question it is given that a triangular garden has an area of 144 ft² and measure of its base is 8ft. So we would be simply using the formula of calculating the area of rectangle.

Here,

To calculate :

We have :

Putting the values in formula :

[tex] \implies \: \sf{144 = \: \dfrac{1}{2} \times l \times 8 } \\ \\ \implies \: \sf{144 = \: \dfrac{1}{ \cancel2} \times l \times \cancel8 } \\ \\ \implies \: \sf{144 = \: \dfrac{1}{1} \times l \times 4 } \\ \\ \implies \: \sf{144 = \: l \times 4 } \\ \\ \implies \: \sf{ l \: = \: \dfrac{144}{4} } \\ \\ \implies \: \sf{ l \: = \: \cancel\dfrac{144}{4} } \\ \\ \implies \: \sf{ l \: = \: \dfrac{72}{2} } \\ \\ \implies \: \sf{ l \: = \: \cancel\dfrac{72}{2} } \\ \\ \implies \: \sf{ l \: = \: \dfrac{36}{1} } \\ \\ \implies \: \red{\underline{\underline{\bf{ l \: = \: 36 }}}}[/tex]

Henceforth,

Check the picture below.

Answer:

g is 50 degrees

g is a supplement of 130 so they add up to 180

Answer:

The angel G:
= 50 degrees

A straight line is 180 degrees. The is already an angel has shown that takes up the majority of the line which is 130 degrees.

180 degrees - 130 degrees = 50 degrees

Step-by-step explanation:

Have a great rest of your day
#TheWizzer

Answer:

The mass of the ring is 12 grams.

Step-by-step explanation:

Total 20 parts

Gold 3/4 total mass (15/20)

3/4=9g

1/4=3g

4/4=12g

Answer:

mass of the ring = 12 g

Step-by-step explanation:

Given ratio

gold : palladium : nickel : zinc = 15 : 2 : 2 : 1

Add the ratios:  15 + 2 + 2 + 1 = 20

Therefore, as a fraction, gold is [tex]\sf \dfrac{15}{20}=\dfrac34[/tex] of the total mass of the ring.

Let the mass of the ring = x

As the ring containts 9 g of gold

[tex]\sf \implies \dfrac34x=9[/tex]

[tex]\sf \implies x=9 \cdot \dfrac43[/tex]

[tex]\sf \implies x=12[/tex]

Therefore, the mass of the ring is 12 g

comprising 9 g of gold, 1.2 g of palladium, 1.2 g of nickel and 0.6 g of zinc.

Answer:

Just substitute the values in!
(-5/9) + (-4/3) - 2/3 = - 5/9 - 12/9 - 6/9 = -23/9.

This refers to the tax paid to a governing body for the sales of certain goods and services.

In  Williamson County, the sales tax rate is 9.75% = 9.75% × $1,000 = $1,097.5

In Davidson County , the sales tax rate is 9.25% =  9.25%  × $1,000 = $1,092.5

The amount saved will therefore be $1,097.5 - $1,092.5 = $5.

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Answer:

x = 3 , x = 7

Step-by-step explanation:

3(x - 5)² - 17 = - 5 ( add 17 to both sides )

3(x - 5)² = 12 ( divide both sides by 3 )

(x - 5)² = 4 ( take square root of both sides )

x - 5 = ± [tex]\sqrt{4}[/tex] = ± 2 ( add 5 to both sides )

x = 5 ± 2

then

x = 5 - 2 = 3

x = 5 + 2 = 7

Answer:

 2a2 • (a + 1) • (a - 3)

Step-by-step explanation:

Answer:

a₁₂ = - 4194304

Step-by-step explanation:

the nth term of a geometric sequence is

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

here a₁ = 1 and r = [tex]\frac{-4}{1}[/tex] = - 4 , then

a₁₂ = 1 × [tex](-4)^{11}[/tex] = - 4194304

Answer: 31

Step-by-step explanation:

25+6 which equals the answer 31!

Answer:

4.8 ounces

Step-by-step explanation:

X= number of ounces for the $3.00 mixture of seasoning

$3.00/OZ + $1.75/ OZ = $2.00/ OZ We are adding the seasonings together to produce the 24 OZ mixture

X + 24-X = 24OZ To get the missing term we will subtract what we have from X

100 [(3.00)(X) + (1.75)(24-X)] = [(2.00)(24)] 100 to get rid of the decimals multiply both sides by 100

(300)(X) + (175)(24-X) = (200)(24) Multiply on each side, removing the parenthesis

300X + 4,200 - 175x = 4,800 Get all of the X's on one side of the equation remember to change the sign of 4,200

300X - 175X = 4,800 - 4,200 Combine Like Terms

125X = 600 Get X alone

125 125 To get X, we will divide both sides by 125

X = 4.8 OZ

The chef used 4.8 ounces of the $3.00 seasoning

Answer: Look at the screenshot

Step-by-step explanation:

Ive added a screenshot of what this graph should look like

Answer:

*View attached graph*

Step-by-step explanation:

I graphed 6 points, so you are able to choose the ones you want :)

*View attached graph*

Hope this helps!

Answer:

8.16, 8.2, 8.245, 8.25

Step-by-step explanation:

8 1/6 = 8.16

41/5 = 8.2

Answer:

y:  13, 22, 25, 28

ordered pairs: (3, 13)  (6, 22)  (7, 25)  (8, 28)

Step-by-step explanation:

Given:

To find the y-values, substitute the x-values into the function and solve.

when x = 3

y = 3(3) + 4

  = 9 + 4

  = 13

when x = 6

y = 3(6) + 4

   = 18 + 4

   = 22

when x = 7

y = 3(7) + 4

   = 21 + 4

   = 25

when x = 8

y = 3(8) + 4

  = 24 + 4

  = 28

Therefore, the ordered pairs are;  (3, 13)  (6, 22)  (7, 25)  (8, 28)

Answer:270

Step-by-step explanation:

Length:

U = 3 inches

W = 7 inches

Y = 8 inches

Add them up: 18 inches all together.

Width:

V = 4 inches

X = 7 inches
Z = 4 inches

Add them up: 15

A= L x W —>  15 x 18 = 270

Based on the amount that London deposited every month and the number of years involved, London would have $57,515.16.

The amount that London deposits every month is an annuity because it is a fixed amount.

The value in 11 years is therefore the future value of an annuity which can be found as:

= Amount x ( (1 + rate) ^ number of periods - 1) / rate

The number of periods is:

= 11 years x 12 months

= 132 months

Future value is:
= 320 x ( ( 1 + 0.45%)¹³² - 1) / 0.45%

= $57,515.16

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Answer:

[tex]x < -3\quad \mathrm{or}\quad \:x > 3[/tex]

Step-by-step explanation:

Given:

[tex]9-x^2 < \:0[/tex]

Solve:

[tex]\mathrm{Subtract\:}9\mathrm{\:from\:both\:sides}[/tex]

[tex]9-x^2-9 < 0-9[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]-x^2 < -9[/tex]

[tex]Multiply\:both\:sides\:by\:-1\:[/tex]

[tex]\left(-x^2\right)\left(-1\right) > \left(-9\right)\left(-1\right)[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]x^2 > 9[/tex]

[tex]\mathrm{For\:}u^n\: > \:a\mathrm{,\:if\:}n\:\mathrm{is\:even}\mathrm{\:then\:}u\: < \:-\sqrt[n]{a}\:or\:u\: > \:\sqrt[n]{a}[/tex]

[tex]x < -\sqrt{9}\quad \mathrm{or}\quad \:x > \sqrt{9}[/tex]

[tex]\sqrt{9}=3[/tex]

[tex]x < -3\quad \mathrm{or}\quad \:x > 3[/tex]

~lenvy~

Answer: c-3

Step-by-step explanation:

it is wanting you to take c minus 3

Answer:

angle 1=angle 4 ( vertical opposite angle)

Answer:

x=0

Step-by-step explanation:

because you divide by x^12

x^n=x^0

x=0

Step-by-step explanation:

input is C and D and output is A and B