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daser333 [38]
3 years ago
10

The yearly deductible for John's health care plan decreased from $1250 to $1000. What is the percent decrease?

Mathematics
1 answer:
sukhopar [10]3 years ago
6 0

Answer:

20%

Step-by-step explanation:

1. We assume, that the number 1250 is 100% - because it's the output value of the task.  

2. I assume, that x is the value we are looking for.  

3. If 100% equals 1250, so we can write it down as 100%=1250.  

4. We know, that x% equals 250 of the output value, so we can write it down as x%=250.  

5. Now we have two simple equations:

1) 100%=1250

2) x%=250

where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:

100%/x%=1250/250

6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 250 is what percent of 1250

100%/x%=1250/250

(100/x)*x=(1250/250)*x       - we multiply both sides of the equation by x

100=5*x       - we divide both sides of the equation by (5) to get x

100/5=x  

20=x  

x=20

now we have:  

250 is 20% of 1250


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3 years ago
Rent and other associated housing costs, such as utilities, are an important part of the estimated costs of attendance at colleg
zhenek [66]

Answer:

96% confidence interval estimate for the mean monthly rent of all unmarried BYU students in winter 2018 is  [335.89 , 356.10].

Step-by-step explanation:

We are given that a group of researchers at the BYU Off-Campus Housing department want to estimate the mean monthly rent that unmarried BYU students paid during winter 2018.

During March 2018, they randomly sampled 314 BYU students and found that on average, students paid $346 for rent with a standard deviation of $86.

So, the pivotal quantity for 95% confidence interval for the average age is given by;

           P.Q. = \frac{\bar X - \mu}{\frac{s}{\sqrt{n} } } ~ t_n_-_1

where, \bar X = average rent paid by 314 BYU students = $346

            s = sample standard deviation = $86

            n = sample of students = 314

            \mu = population mean monthly rent of all unmarried BYU students

So, 96% confidence interval for the population mean monthly rent, \mu is ;

P(-2.082 < t_3_1_3 < 2.082) = 0.96

P(-2.082 < \frac{\bar X - \mu}{\frac{s}{\sqrt{n} } } < 2.082) = 0.96

P( -2.082 \times {\frac{s}{\sqrt{n} } } < {\bar X - \mu} < 2.082 \times {\frac{s}{\sqrt{n} } } ) = 0.96

P( \bar X -2.082 \times {\frac{s}{\sqrt{n} } } < \mu < \bar X +2.082 \times {\frac{s}{\sqrt{n} } } ) = 0.96

96% confidence interval for \mu = [ \bar X -2.082 \times {\frac{s}{\sqrt{n} } } , \bar X +2.082 \times {\frac{s}{\sqrt{n} } } ]

                                                = [ 346 -2.082 \times {\frac{86}{\sqrt{314} } } , 346 +2.082 \times {\frac{86}{\sqrt{314} } } ]

                                                = [335.89 , 356.10]

Therefore, 96% confidence interval estimate for the mean monthly rent of all unmarried BYU students in winter 2018 is [335.89 , 356.10].

5 0
3 years ago
How do you solve 32 - 6x = 53?
katrin2010 [14]

\large\boxed{x=-\frac{7}{2}}

To solve for x, we need to isolate it on one side of the equation.

The most important part of this is knowing that whatever we do to one side of the equation, we must also do to the other.

Subtract 32 from both sides of the equation.

\begin{aligned}32-32-6x&=53-32\\-6x&=21\end{aligned}

Divide both sides of the equation by -6.

\begin{aligned}\frac{-6x}{-6}&=\frac{21}{-6}\\x&=\boxed{-\frac{7}{2}}\end{aligned}

7 0
2 years ago
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