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2 years ago

Simplify the following expression:

1 answer:

5 0

Distributive property
a(b+c+d)=ab+ac+ad

-7(3e-2f+4)=-7(3e)-7(-2f)-7(4)=-21e+14f-28

now we have

-21e+14f-24+6e-2
group like terms
-21e+6e+14f-24-2
-15e+14f-26

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Misha used 1/4 of a carton of 12 eggs to make a omelet how many eggs did she use

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Answer: 3

Step-by-step explanation:

Multiply 1/4*12

Or divide 12 into 4 parts

Either way, you get 3

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2 years ago

The ratio of pink marbles to white marbles in Samara's bag is equal 1:5.What present of the bag contains pink marbles

Nat2105 [25]

Either 20% or a little bit less

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2 years ago

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The price of 600 grams of candy and 1.5 kg of cookies was 4 dollars and 62 cents. What is the price of one kg of cookies if it i

cupoosta [38]

Answer:

The price of the kilogram of cookies is $ 1.8

Step-by-step explanation:

Call x the price of the kilogram of candy and call y the price of kilogram of cookies

Then we know that

$0.600x + 1.5y = 4.62$

We also know that the price of kilogram of cookies is 1.40 dollars cheaper than the kilogram of candy

$y = x-1.40$

We solve this equation for x and then we substitute it in the first equation.

$x = y + 1.40$

$0.60 (y +1.40) + 1.5y = 4.62\\\\0.60y + 1.5y = 4.62 - 0.84\\\\2.1y = 3.78$

$y = \$1.8$

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2 years ago

A stack of cards consists of seven red and four blue cards. A second stack of cards consists of eleven red cards. A stack is sel

Ann [662]

Answer:

0.1733 = 17.33% probability the first stack was selected.

Step-by-step explanation:

To solve this question, it is needed to understand conditional probability, and the hypergeometric distribution.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

Conditional probability:

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

Probability of all red cards for the first stack:

For this, we use the hypergeometric distribution, as the cards all chosen without replacement.

7 + 4 = 11 cards, which means that $N = 11$ .

7 red, which means that $k = 7$

3 are chosen, which means that $n = 3$

We want all red, so we find P(X = 3).

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

$P(X = 3) = h(3,11,3,7) = \frac{C_{7,3}*C_{4,0}}{C_{11,3}} = 0.2121$

Conditional probability:

Event A: All red

Event B: From the first stack.

Probability of all red cards:

0.2121 of 50%(first stack)

1 of 50%(second stack). So

$P(A) = 0.2121*0.5 + 1*0.5 = 0.60605$

Probability of all red cards and from the first stack:

0.21 of 0.5. So

$P(A \cap B) = 0.21*0.5 = 0.105$

What is the probability the first stack was selected?

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.105}{0.60605} = 0.1733$

0.1733 = 17.33% probability the first stack was selected.

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2 years ago

Can you subtract 9 3/4in from 33ft

Gre4nikov [31]

Sure

first convert 33ft to inches

33 x 12 = 396 inches

then do 396-9.75 = 386.25in

to convert to ft, simply divide this answer by 12

32.1875 ft

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2 years ago

Read 2 more answers