Standard from 0.000000017

Chapter 5 Quiz<br>What is the sum of the two expressions?<br>(2/5x + 3)+(1/5x - 1)

larisa [96]

Answer:

1/5x+2

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Solve each problem. NO LINKS!!!!!

Sauron [17]

<h3>Answers:</h3>

Problem 10) There are 220 combinations
Problem 11) There are 126 combinations
Problem 12) There are 154,440 permutations
Problem 13) There are 300 different ways

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Explanations:

Problem 10

The order of the toppings doesn't matter. All that matter is the group itself. We'll use the combination formula nCr = (n!)/(r!*(n-r)!) where n = 12 and r = 3 in this case.

So,

nCr = (n!)/(r!*(n-r)!)

12C3 = (12!)/(3!*(12-3)!)

12C3 = (12!)/(3!*9!)

12C3 = (12*11*10*9!)/(3!*9!)

12C3 = (12*11*10)/(3*2*1)

12C3 = 1320/6

12C3 = 220

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Problem 11

Like with problem 10, the order doesn't matter. This is assuming that each member on any given team has the same rank as any other member.

If you used the nCr combination formula, with n = 9 and r = 5, you should get the answer 126

Here's another way to get that answer.

There are 9*8*7*6*5 = 15120 different permutations. If order mattered, then we'd go for this value instead of 126

Within any group of five people, there are 5! = 120 different ways to arrange them. So we must divide that 15120 figure by 120 to get the correct value of 126 combinations

15120/120 = 126

Note the connection between nCr and nPr, namely,

nCr = (nPr)/(r!)

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Problem 12

Now this is where order matters, because the positions in basketball are different (eg: a point guard differs from a center).

We have 13 choices for the first position, 12 for the second, and so on until we reach 13-r+1 = 13-5+1 = 9 as the number of choices for that last slot.

So we'll have 13*12*11*10*9 = 154,440 different permutations

Now if the condition that "each player can play any position" isn't the case, then the answer would very likely be different. This is because for the center position, for instance, we wouldn't have 13 choices but rather however many choices we have at center. To make the problem simpler however, your teacher is stating that any player can play at any slot. Realistically, the answer would be far less than 154,440

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Problem 13

We have 6 applications for the 2 math positions. Order doesn't matter. That means we'll have 6C2 = 15 different ways to pick the math people. Use the nCr formula mentioned in problem 10. Since we'll use this value later, let's make x = 15.

There are 2 people applying for the chemistry teaching position, meaning there are 2 ways to fill this slot. We could compute 2C1 = 2, but that's a bit overkill in my opinion. Let y = 2 so we can use it later.

Similarly, there are 10 applicants for the Spanish teacher position, leading to 10 ways to get this position filled. You could compute 10C1 = 10 if you wanted to. Let z = 10 so we can use it later.

Once we figured out those x,y,z values, we multiply them together to get our final answer: x*y*z = 15*2*10 = 30*10 = 300

There are 300 different ways to select 2 math teachers, a chemistry teacher, and a Spanish teacher from a pool of 6 math applicants, 2 chemistry applicants, and 10 Spanish teacher applicants.

7 0

3 years ago

Which expression represents the volume, in cubic units, of the composite figure?

Kipish [7]

The missing figure is attached

The expression represents the volume in cubic units of the composite figure is (Four-third)π(10)³ + π(10)²(28) ⇒ 1st answer

Step-by-step explanation:

The figure consists of

Two hemispheres
A cylinder

The volume of the hemisphere = $\frac{2}{3}\pi r^{3}$ , where r is its radius

The volume of the cylinder = πr²h, where r is its radius and h is its height

∵ The diameter of the hemisphere s and the cylinder is 20 units

∵ The radius = $\frac{1}{2}$ diameter

∴ The radius = $\frac{1}{2}$ × 20 = 10 units

∵ The volume of a hemisphere = $\frac{2}{3}$ πr³

∵ r = 10

- Substitute r by 10 in the rule

∴ The volume of a hemisphere = $\frac{2}{3}$ π(10)³

∵ The volume of the cylinder = πr²h

∵ h = 28 and r = 10

- Substitute h by 28 and r by 10 in the rule

∴ The volume of the cylinder = π(10)²(28)

∵ The volume of the figure = 2(volume of a hemisphere) +

volume of the cylinder

∴ The volume of the figure = 2( $\frac{2}{3}$ )π(10)³ + π(10)²(28)

∵ 2 × $\frac{2}{3}$ = $\frac{4}{3}$

∴ The volume of the figure = $\frac{4}{3}$ π(10)³ + π(10)²(28)

The expression represents the volume in cubic units of the composite figure is (Four-third)π(10)³ + π(10)²(28)

Learn more:

You can learn more about the volume of figures in brainly.com/question/12497249

#LearnwithBrainly

7 0

3 years ago

Read 2 more answers

The function P(x)equals0.35xnegative 76 models the relationship between the number of pretzels x that a certain vendor sells an

r-ruslan [8.4K]

Answer:

$P(X=700) =0.35*700 -76= 169$

Step-by-step explanation:

For this case we have the following profit function:

$P(X) = 0.35 X -76$

And we are interested on find the profit after selling 700 pretzels, so we just need to replace X=700 into the profit function like this:

$P(X=700) =0.35*700 -76= 169$

The profit function is on the figure attached. We see that for 0<X<217 we have negative profits, and for X>217 we will have positive values for the profit. And also we can see that for X=700 we have a profit of approximately 169.

3 0

4 years ago

Four brothers each bought two hot dogs and a bag of chips at the football concession stand. If the bag of chips was 1.25, and th

SSSSS [86.1K]

Answer:

$1.65

Step-by-step explanation:

If h is the price of a hot dog, then the total bill was ...

4(2h +1.25) = 18.20

2h +1.25 = 4.55 . . . . . . divide by 4

2h = 3.30 . . . . . . . . . . . subtract 1.25

h = 1.65 . . . . . . . . . . . . . divide by 2

The price of one hot dog was $1.65.

6 0

3 years ago