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2 years ago

Question 1

2 answers:

8 0

#1) 4 weeks, $280
#2) (5, 38)
#3) (1, 3)
#4) Step 3
#5) (y+z=6)*-8
#6) 2x+2y=8

Explanation
#1) Setting them equal,
60x+40=50x+80

Subtract 50x from both sides:
60x+40-50x=50x+80-50x
10x+40=80

Subtract 40 from both sides:
10x+40-40=80-40
10x=40

Divide both sides by 10:
10x/10 = 40/10
x=4

Plugging this in to one of our equations,
60(4)+40=240+40=280

#2) Setting the equations equal to one another,
8x-2=9x-7

Subtract 8x from both sides:
8x-2-8x=9x-7-8x
-2=x-7

Add 7 to both sides:
-2+7=x-7+7
5=x

Plugging this in to the first equation,
8(5)-2=y
40-2=y
38=y

#3) Substituting our value from the second equation into the first one,
n-2+3n=10

Combining like terms,
4n-2=10

Add 2 to both sides:
4n-2+2=10+2
4n=12

Divide both sides by 4:
4n/4 = 12/4
n=3

Substitute this into the second equation:
m=3-2=1

#4) The mistake was made on Step 3; the 4 was left off when the equations were added.

#5) To eliminate y, we want the coefficients to be the same. To accomplish this, we will multiply the first equation by -8.

#6) In order to have infinitely many solutions, we want each coefficient as well as the constant to be a multiple of our equation. Multiplying the equation by 2, we get 2x+2y=8.

Usimov [2.4K]2 years ago

3 0

Question 1

Carly and Janiya put some money into their money boxes every week. The amounts of money (y), in dollars, in their money boxes after certain amounts of time (x), in weeks, are shown by the equations below:

Carly

y = 60x + 40

Janiya

y = 50x + 80

After how many weeks will Carly and Janiya have the same amount of money in their money boxes and what will that amount be?

5 weeks, $280

5 weeks, $340

4 weeks, $280

4 weeks, $340

Question 2

A system of equations is shown below:

y = 8x − 2

y = 9x − 7

What is the solution to the system of equations?

(−5, 38)

(−5, −38)

(5, 38)

(5, −38)

Question 3

Two equations are given below:

m + 3n = 10

m = n − 2

What is the solution to the set of equations in the form (m, n)?

(1, 3)

(2, 4)

(0, 2)

(4, 6)

Question 4

The work of a student to solve a set of equations is shown:

Equation 1: m = 8 + 2n

Equation 2: 3m = 4 + 4n

Step 1:

−3(m) =

−3(8 + 2n)

[Equation 1 is multiplied by −3.]

3m =

4 + 4n

[Equation 2]

Step 2:

−3m =

−24 − 6n

[Equation 1 in Step 1 is simplified.]

3m =

4 + 4n

[Equation 2]

Step 3:

−3m + 3m =

−24 − 6n + 4n

[Equations in Step 2 are added.]

Step 4:

0 =

−24 − 2n

Step 5:

n =

−12

In which step did the student first make an error?

Step 4

Step 3

Step 2

Step 1

Question 5

A student is trying to solve the system of two equations given below:

Equation P: y + z = 6

Equation Q: 8y + 7z = 1

Which of the following is a possible step used in eliminating the y-term?

(y + z = 6) ⋅ −8

(y + z = 6) ⋅ 7

(8y + 7z = 1) ⋅ 7

(8y + 7z = 1) ⋅ 8

Question 6

Line A is represented by the equation given below:

x + y = 4

What is most likely the equation for line B, so that the set of equations has infinitely many solutions?

4x + 4y = 4

4x + y = 4

2x + 2y = 8

x + y = 8

Report

by EvilEvie 10.05.2018

Answers

SamanthaBees · Beginner

Know the answer? Add it here!

MsEHolt Brainly Teacher

#1) 4 weeks, $280

#2) (5, 38)

#3) (1, 3)

#4) Step 3

#5) (y+z=6)*-8

#6) 2x+2y=8

Explanation

#1) Setting them equal,

60x+40=50x+80

Subtract 50x from both sides:

60x+40-50x=50x+80-50x

10x+40=80

Subtract 40 from both sides:

10x+40-40=80-40

10x=40

Divide both sides by 10:

10x/10 = 40/10

x=4

Plugging this in to one of our equations,

60(4)+40=240+40=280

#2) Setting the equations equal to one another,

8x-2=9x-7

Subtract 8x from both sides:

8x-2-8x=9x-7-8x

-2=x-7

Add 7 to both sides:

-2+7=x-7+7

5=x

Plugging this in to the first equation,

8(5)-2=y

40-2=y

38=y

#3) Substituting our value from the second equation into the first one,

n-2+3n=10

Combining like terms,

4n-2=10

Add 2 to both sides:

4n-2+2=10+2

4n=12

Divide both sides by 4:

4n/4 = 12/4

n=3

Substitute this into the second equation:

m=3-2=1

#4) The mistake was made on Step 3; the 4 was left off when the equations were added.

#5) To eliminate y, we want the coefficients to be the same. To accomplish this, we will multiply the first equation by -8.

#6) In order to have infinitely many solutions, we want each coefficient as well as the constant to be a multiple of our equation. Multiplying the equation by 2, we get 2x+2y=8.

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7 0

2 years ago

Critical Thinking: Empirical/Quantitative Skills

aliya0001 [1]

Answer:

1. 0.0910 = 9.10% probability that exactly 180 passengers show up for the flight.

2. 0.4522 = 45.22% probability that at most 180 passengers show up for the flight.

3. 0.5478 = 54.78% probability that more than 180 passengers show up for the flight.

Step-by-step explanation:

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.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

Assume that there is a 0.905 probability that a passenger with a ticket will show up for the flight.

This means that $p = 0.905$

Also assume that the airline sells 200 tickets

This means that $n = 200$

Question 1:

Exactly, so we can use the P(X = x) formula, to find P(X = 180).

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

$P(X = 180) = C_{200,180}.(0.905)^{180}.(0.095)^{20} = 0.0910$

0.0910 = 9.10% probability that exactly 180 passengers show up for the flight.

2. When 200 tickets are sold, calculate the probability that at most 180 passengers show up for the flight.

Now we have to use the approximation.

Mean and standard deviation:

$\mu = E(X) = np = 200*0.905 = 181$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{200*0.905*0.095} = 4.15$

Using continuity correction, this is $P(X \leq 180 + 0.5) = P(X \leq 180.5)$ , which is the p-value of Z when X = 180.5. Thus

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{180.5 - 181}{4.15}$

$Z = -0.12$

$Z = -0.12$ has a p-value of 0.4522.

0.4522 = 45.22% probability that at most 180 passengers show up for the flight.

3. When 200 tickets are sold, calculate the probability that more than 180 passengers show up for the flight.

Complementary event with at most 180 passengers showing up, which means that the sum of these probabilities is 1. So

$p + 0.4522 = 1$

$p = 1 - 0.4522 = 0.5478$

0.5478 = 54.78% probability that more than 180 passengers show up for the flight.

4 0

2 years ago

PLEASE HELP FAST!!! AND EXPLAIN YOUR WORK

fomenos

The drummers final position would be
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8 0

3 years ago

Determine the volume of the shaded area.

vovikov84 [41]

The shaded area in the image is 86.1 square inches.

<h3>How to get the shaded area?</h3>

Remember that for a circle of diameter D, the area is given by:

A = pi*(D/2)²

Where pi = 3.14, and here we have half-circles, so we need to add a factor 0.5

The area of the shaded figure, the area of the shaded figure will be the area of the half circle with diameter of 17in minus the area of the half circle with a diameter of 8.5 in, so the area is:

area = 0.5*3.14*(17in/2)² - 0.5*3.14*(8.5in/2)² = 86.1 in²

Learn more about area:

brainly.com/question/24487155

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4 0

11 months ago

Approximately what percentage of apple diameters is greater than the 66th percentile? 21. A. 3.4% B. 17% C. 66% D. 34%

astraxan [27]

Answer:

The correct option is D) 34%.

Step-by-step explanation:

Consider the provided information.

If it is given that you scored in the 66th percentile, that means you scored "as well as or better than" 66% of the group.

Here it is given that 66th percentile that means 66% of the data located below the 66th percentile.

That means 100%-66% = 34% of the data located above the 66th percentile,

Thus, the approximately 34% percentage of apple diameters is greater than the 66th percentile.

Therefore, the correct option is D) 34%.

5 0

3 years ago