Can anyone help me with this?

Scorpion4ik [409]

You have the equations set up correctly. I will use r and b as the variables to make it easier to follow.

12r + 8b = 70
20r + 12b = 110

First let's solve one of the equations for one of the variables.

12r = 70 - 8b

$r = \frac{70-8b}{12}$

Now plug that in for r in the second equation.

$20( \frac{70-8b}{12})+12b = 110$

Simplify

$20(70-8b)+144b=1320$

$1400-160b+144b=1320$

$-16b = -80$

b = 5 grams

Now plug 5 in for b in one of the original equations to find r.

12r + 8(5) = 70

12r = 30

r = 2.5 grams

So the red marbles weigh 2.5 grams, and the blue marbles weigh 5 grams.

3 0

4 years ago

What is 2/3 divided by 5/6

Serjik [45]

4/5. 2/3 divided by 5/6 is equivalent to 2/3 multiplied by 6/5, so the answer is 4/5.

6 0

3 years ago

Two candidates face each other in an election. The Democratic candidate is supported by 46% of the population, and the Republica

7nadin3 [17]

Answer:

27.98% probability that less than half of them (3 or fewer) would support the Republican candidate

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they support the Republican candidate, or they do not. The people are chosen at random, which means that the probability of them supporting the republican candidate is independent from other people. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

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

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

And p is the probability of X happening.

In this problem we have that:

The Republican candidate is supported by 54%. This means that $p = 0.54$

Suppose you run a poll of 8 people (randomly choose 8 people). What is the probability that less than half of them (3 or fewer) would support the Republican candidate?

This is $P(X \leq 3)$ when $n = 8$ .

So

$P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{8,0}.(0.54)^{0}.(0.46)^{8} = 0.0020$

$P(X = 1) = C_{8,1}.(0.54)^{1}.(0.46)^{7} = 0.0188$

$P(X = 2) = C_{8,2}.(0.54)^{2}.(0.46)^{6} = 0.0774$

$P(X = 3) = C_{8,3}.(0.54)^{3}.(0.46)^{5} = 0.1816$

So

$P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0020 + 0.0188 + 0.0774 + 0.1816 = 0.2798$

27.98% probability that less than half of them (3 or fewer) would support the Republican candidate

3 0

4 years ago

The question is solve the standard algorithm

Delicious77 [7]

The standard algorithm is the way or steps to find an answer.

6 0

4 years ago

A block of stone measures 15 cm X 15 cm X 20 cm. What is the total surface area of the stone?(Hint: A block has six sides.)

BARSIC [14]

$Look\ at\ the\ picture.\\\\2\ sides:\ 15cm\times15cm\\\\Area:A_1=2\times(15cm\times15cm)=2\times225cm^2=450cm^2\\\\4\ sides:15cm\times20cm\\\\Area:A_2=4\times(15cm\times20cm)=4\times300cm^2=1200cm^2\\\\Area\ of\ the\ block:\\\\A=A_1+A_2\\\\\boxed{A=450cm^2+1200cm^2=1650cm^2}$

5 0

3 years ago