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3 years ago

What is 5√ ? Place a dot on the number line at the best approximation

1 answer:

7 0

You should place the square root of 5 between 2 and 3.

A square root is the number that get's multiplied by itself to get the given number. In this case, what 2 numbers multiply together to give 5.

It is an irrational number (never ending).
It is about 2.236

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A manufacturer of t-shirts marks a shirt as "irregular" when it has defects such as crooked seams, stains, rips, or holes. A sma

MaRussiya [10]

Answer:

The test statistic value is 1.474.

Step-by-step explanation:

In this case we need to determine whether the plant is making a higher than expected number of irregular t-shirts.

If more than 8% of the t-shirts manufactured at a plant are classified as irregular, the manager has to do an investigation to try to find the source of the increased mistakes in the manufacturing process..

The hypothesis for this test can be defined as follows:

H₀: The proportion of irregular t-shirts is 8%, i.e. p = 0.08.

Hₐ: The proportion of irregular t-shirts is more than 8%, i.e. p > 0.08.

The information provided is:

n = 100

X = number of irregular t-shirts = 12

Compute the sample proportion as follows:

$\hat p=\frac{X}{n}=\frac{12}{100}=0.12$

Compute the test statistic as follows:

$t=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}$

$=\frac{0.12-0.08}{\sqrt{\frac{0.08(1-0.08)}{100}}}\\\\=1.47441\\\\\approx 1.474$

Thus, the test statistic value is 1.474.

4 0

3 years ago

3х - 30 = у 7y - 6 = 3х

mars1129 [50]

Answer:

Step-by-step explanation:

This one is simple substitution... at least, substitution is the easiest method. The first equation is 3x – 30 = y and the second is 7y – 6 = 3x

As I look, I see 3 ways to use substitution to solve this:

substitute 7y – 6 for 3x
substitute 3x – 30 for y
solve 3x – 30 = y for 3x and make it equal to 7y – 6

We're going to only use 1 method for the sake of time. Try the other two on your own. Assuming you don't make any mistakes, they will work.

Method 1:

3x – 30 = y

7y – 6 = 3x — initial system of equations

7y – 6 – 30 = y — substitute 7y – 6 for 3x

7y – 6 – 30 = y — marking like terms, bold for constants, underlined for variables

7y – 36 = y — combining the constants and simplifying

Here, you could diverge into multiple paths: add 36 to both sides, subtract y from both sides, divide by 6 OR subtract 7y from both sides and divide by –6 . For the sake of time, I'm subtracting 7y, though I don't like dealing with negatives.

7y – 7y – 36 = y – 7y — subtract 7y from both sides

–36 = –6y — simplify

–36 ÷ –6 = –6y ÷ –6 — divide by –6 on both sides

y = 6 — simplify

Again, we can diverge here: substitute y into 3x – 30 = y or substitute y into 7y – 6 = 3x

I'm going to choose 3x – 30 = y but it will work either way, should you take the time (if you have it) to chase down every path this problem can take.

3x – 30 = y — initial equation

3x – 30 = 6 — substitute 6 for y

3x – 30 + 30 = 6 + 30 — add 30 to both sides to isolate 3x

3x = 36 — simplify the expression

3x ÷ 3 = 36 ÷ 3 — divide both sides by 3 to isolate x

x = 12 — simplify

So, we have x = 12 and y = 6 . We know they work for 3x – 30 = y but not if they work for 7y – 6 = 3x . Let's substitute those in to see if (12, 6) really is the solution point.

7y – 6 = 3x — original equation

7(6) – 6 ≟ 3(12) — substitute 6 for y and 12 for x

42 – 6 ≟ 36 — simplify by multiplying

36 = 36 ✔ — simplify by combining like terms on left side

Success! It works! We have found our solution!

I hope this helps increase your understanding of the concept. Have a great day!

8 0

3 years ago

Which is the side length of a cube with a volume of 2744 cm3? Please help

Elis [28]