All categories

2 years ago

What is 7x − one over two (8x + 2) = 6

Mathematics

1 answer:

lesya692 [45]2 years ago

3 0

Answer:

The correct justifications Kelsey used to solve this equation is:

1. distributive property

2. combine like terms

3. addition property of equality

4. division property of equality

Step-by-step explanation:

Given that,

Kelsey solved the following equation:

Step 1:

By distributive property,

a(b + c) = ab + bc

Therefore,

Step 2:

Combine the like terms

7x - 4x - 1 = 6

3x - 1 = 6

Step 3:

Addition property of equality

The property means that when we add the same number to both sides of an equation, the sides remain equal

3x - 1 = 6

Add 1 on both sides

3x - 1 + 1 = 6 + 1

3x = 7

Step 4:

Division property of equality

The Division Property of Equality means that when we divide both sides of an equation by the same non zero number, the sides remain equal

3x = 7

Divide both sides by 3

Thus the correct justifications Kelsey used to solve this equation is:

1. distributive property. 2. combine like terms. 3. addition property of equality. 4. division property of equality

Please vote for Brainliest and I hope this helps!

You might be interested in

the pie chart shows the information about the favourite ice cream flavour of each student in a school there are 720 students in

kirill115 [55]

Answer:

chocolate= 180 students

vanilla= 120

strawberry= 210

mango= 210

Step-by-step explanation:

The chocolate section of the pie chart is at a right angle (90 degrees), which means a quarter of the students prefer chocolate

720/4= 180

The vanilla section is 60 degrees which is 2/3 of 90

180/3=60

60x2=120

the mango and strawberry sections represent whats left which is 420 students. The sections are equal to each other so they're each 210 students

7 0

3 years ago

When we toss a coin, there are two possible outcomes: a head or a tail. Suppose that we toss a coin 100 times. Estimate the appr

marin [14]

Answer:

96.42% probability that the number of tails is between 40 and 60.

Step-by-step explanation:

I am going to use the binomial approximation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

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 samples 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 $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

100 tosses, so $n = 100$

Two outcomes, both equally as likely. So $p = \frac{1}{2} = 0.5$

$E(X) = np = 100*0.5 = 50$

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100*0.5*0.5} = 5$

Estimate the approximate probability that the number of tails is between 40 and 60.

Using continuity correction.

$P(40 - 0.5 \leq X \leq 60 + 0.5) = P(39.5 \leq X \leq 60.5)$

This is the pvalue of Z when X = 60.5 subtracted by the pvalue of Z when X = 39.5. So

X = 60.5

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

$Z = \frac{60.5 - 50}{5}$

$Z = 2.1$

$Z = 2.1$ has a pvalue of 0.9821

X = 39.5

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

$Z = \frac{39.5 - 50}{5}$

$Z = -2.1$

$Z = -2.1$ has a pvalue of 0.0179

0.9821 - 0.0179 = 0.9642

96.42% probability that the number of tails is between 40 and 60.

8 0

3 years ago

I am arranging my dog's collars on a 6 hanger coat rack on the wall. If she has six collars, how many ways can I arrange the col

Irina18 [472]

Answer:

720 ways to arrange

Step-by-step explanation:

Use the factorial of 6 to find this solution. Namely, 6!

This means 6*5*4*3*2*1 which equals 720

It seems like a huge number, right? But think of it like this: For the first option, you have 6 collars. After you fill the first spot with one of the 6, you have 5 left that will fill the second spot. After the first 2 spots are filled and you used 2 of the 6 collars, there are 4 possibilities that can fill the next spot, etc.

7 0

3 years ago

Read 2 more answers

10×10×10×10×10×10×10 with an exponent

Free_Kalibri [48]

There are 7 tens, so i want to say 10^7
10 to the seventh power

6 0

3 years ago

Read 2 more answers

How far did Eddie travel after his break? (The break is the part with only the straight line!)

densk [106]

The break ended at 4pm when he was at 15 km.