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Vera_Pavlovna [14]
3 years ago
15

This year, a small business has a total revenue of $63, 500. If this is 27% more than their total revenue the previous year, wha

t was their total revenue the previous year?
Mathematics
2 answers:
Andrew [12]3 years ago
8 0
Hey! Let me help you on this one.

Let's break this equation apart to better understand it!

We know that this year's revenue is $63,500, and we also know that this is 27% more than last year's revenue.

We don't know what was the last year's revenue, so let's mark this unknown variable as R.

Now, time for fun stuff! Let's form an equation.

R*1.27=63500

As you can see, 1.27 is a decimal form of 127% - this year's revenue compared to last year's revenue.

Let's solve this! First, we need to divide 1.27 from both sides.

R*(1.27/1.27) = 63500/1.27

Now, we need to simplify it. 

R = 50000

As we have mentioned before, R is the amount of money this company has received for the last year. 

Answer: Their total revenue for the previous year is $50,000.
hichkok12 [17]3 years ago
5 0
63.500 x 27% = 17.145   63.500 +17.145=$80.645
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The spinner for a board game has eight colors the arrow can land on. What are the degrees of freedom for a goodness-of-fit test
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Answer: Option 'c' is correct.

Step-by-step explanation:

Since we have given that

Number of colors that the arrow can land on = 8

We need to find the degrees of freedom for a goodness of fit test of the fairness of this spinner.

As we know that degree of freedom is 1 less than the size of sample.

So, Mathematically, it is expressed as below:

So, Degree of freedom would be

v=n-1\\\\v=8-1\\\\v=7

Hence, Option 'c' is correct.

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Two consecutive perfect squares have a difference of $99$. what is the value of the larger perfect square?
Fofino [41]

Answer:

2500

Step-by-step explanation:

Let the first square number be x^2 then the next square number is (x+1)^2.

The difference between these two consecutive numbers is 99.

This implies that:

(x+1)^2-x^2=99

We expand to get:

x^2+2x+1-x^2=99

Simplify:

2x=99-1

2x=98

Divide both sides by 2

x=49

Therefore the value of the larger perfect number is

(49+1)^2=50^2=2500.

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1. According to New Jersey Transit, the 8:00 a.m. weekday train from Princeton to New York
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Batteries produced by a manufacturing company have had a life expectancy of 135 hours. Because of an improved production process
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Answer:  c. z = 1.35; Reject the null hypothesis

Step-by-step explanation:

Let \mu be the average life expectancy of its batteries.

As per given , we have

Null hypothesis : H_0 : \mu =135

Alternative hypothesis : H_a : \mu >135

Since H_a is right-tailed and population standard deviation is also known, so we perform right-tailed z-test.

Test statistic : \dfrac{\overlien{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}

where, n= sample size

\overlien{x}= sample mean

\mu= Population mean

\sigma=population standard deviation

For n=42,\ \overline{x}=140\ \&\ \sigma=24, we have

z=\dfrac{140-135}{\dfrac{24}{\sqrt{42}}}=1.35015431217\approx1.35

Critical one-tailed test value for 0.10 significance level :

z_{0.1}=1.28

 Decision : Since critical z value (1.28) < test statistic (1.35), so we reject the null hypothesis .

[When critical value is less than the test statistic value , we reject the null hypothesis .]

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