What is the ratio 3:11

Solve the equation for x 2/3x-1/9x + 5 = 20

Nady [450]

$\bold{Answer}$

$\boxed{\bold{X \ = \ 27}}$

$\bold{Explanation}$

$\bold{Solve: \ \frac{2}{3}x-\frac{1}{9}x+5=20}$

$\bold{--------------------------}$

$\bold{Subtract \ 5 \ From \ Both \ Sides}$

$\bold{\frac{2}{3}x-\frac{1}{9}x+5-5=20-5}$

$\bold{Simplify}$

$\bold{\frac{2}{3}x-\frac{1}{9}x=15}$

$\bold{Multiply \ By \ LCM: \ LCM \ = \ 9}$

$\bold{\frac{2}{3}x\cdot \:9-\frac{1}{9}x\cdot \:9=15\cdot \:9}$

$\bold{Simplify}$

$\bold{6x-x=135}$

$\bold{5x=135}$

$\bold{Divide \ Both \ Sides \ By \ 5}$

$\bold{\frac{5x}{5}=\frac{135}{5}}$

$\bold{Simplify}$

$\bold{X \ = \ 27}$

$\boxed{\bold{Eclipsed}}$

8 0

3 years ago

Read 2 more answers

A bank is trying to determine which model of safe to install. The bank manager believes that each model is equally resistant to

alexandr402 [8]

Answer:

So on this case the 95% confidence interval would be given by (-1.152;5.152).

$-1.152 < \mu_{safe1}-\mu_{safe2}$

Should we conclude that the average time it takes experts to crack the safes does not differ by model at the 5% significance level?

A) Yes, the 95% confidence interval for ?D contains 0.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Solution

Let put some notation

x=value for Safe 1 , y = value for Safe 2

x: 103, 90, 64, 120, 104, 92, 145, 106, 76

y: 101, 94, 58, 112, 103, 90, 140, 110, 74

The first step is calculate the difference $d_i=x_i-y_i$ and we obtain this:

d: 2, -4, 6, 8, 1, 2, 5, -4, 2

The second step is calculate the mean difference

$\bar d= \frac{\sum_{i=1}^n d_i}{n}= \frac{18}{9}=2$

The third step would be calculate the standard deviation for the differences, and we got:

$s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1} =4.093$

The next step is calculate the degrees of freedom given by:

$df=n-1=9-1=8$

Now we need to calculate the critical value on the t distribution with 8 degrees of freedom. The value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , so we need a quantile that accumulates on each tail of the t distribution 0.025 of the area.

We can use the following excel code to find it:"=T.INV(0.025;8)" or "=T.INV(1-0.025;8)". And we got $t_{\alpha/2}=\pm 2.31$

The confidence interval for the mean is given by the following formula:

$\bar d \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

Now we have everything in order to replace into formula (1):

$2-2.31\frac{4.093}{\sqrt{9}}=-1.152$

$2+2.31\frac{4.093}{\sqrt{9}}=5.152$

So on this case the 95% confidence interval would be given by (-1.152;5.152).

$-1.152 < \mu_{safe1}-\mu_{safe2}$

Should we conclude that the average time it takes experts to crack the safes does not differ by model at the 5% significance level?

A) Yes, the 95% confidence interval for D contains 0.

5 0

3 years ago

A 279-foot rope is cut into three pieces. The second piece is twice as long as the first. The third piece is as long as the seco

777dan777 [17]

Step-by-step explanation:

Let's say x is the length of the first piece.

The second piece is 2x.

The third piece is 2x.

So the total length is:

x + 2x + 2x = 279

5x = 279

x = 55.8

That means 2x = 111.6.

So the first piece is 55.8 feet, the second piece is 111.6 feet, and the third piece is also 111.6 feet.

5 0

4 years ago

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36. Salma has a salary of 6.2 x 10 to the power of 4 dollars per year. Carter has a salary of

ElenaW [278]

Carter's salary is $1.1138⁶ more than Salma's salary.

<h3>How much larger is Carter's salary than Salma's?</h3>

To perform the difference, we need to be able to take a common factor.

We know that Salma's salary is $6.2×10⁴

While Carter's salary is $1.2×10⁶

To get the same common factor, 10⁴, we can divide and multiply Carter's salary by 100, so we get:

$1.2*10^6*\frac{100}{100} = (1.2*100)*(10^6/100) = 120*10^4$

Then Carter's salary is $120*10⁴

The difference between Carter's and Salma's salaries is:

$120*10⁴ - $6.2×10⁴ = $113.8*10⁴

If we return to the scientific notation, we get:

$113.8*10⁴ = $1.1138⁶

This means that Carter's salary is $1.1138⁶ more than Salma's salary.

If you want to learn more about scientific notation:

brainly.com/question/5756316

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3 0

2 years ago

Arrange the quantities in order from smallest to largest.<br> 2.6 km, 109,000 mm, 41.7 hm

Aleksandr-060686 [28]

The order of the values using the basic unit of meters from smallest to largest. is: 109000 mm < 2.6 km < 41.7 hm

What are the units of measurement of distance or length?

Distance is the gap between any two points under consideration.

The basic unit for measuring distance is the meter.

There are larger as well as smaller units for measuring length or distance which are based on the unit of meter.

The units are as follows:

millimeter, mm = 0.001 m

centimeter, cm = 0.01 m

decimeters, dm = 0.1 m

meter, m = 1 m

kilometer, km = 1000 m

hectometer, hm = 100 m

Now to compare the given quantities making the units same as two quantities can only be compared only when there units are same :

Considering the given values;

2.6 km = 2600 m

109,000 mm = 109 m

41.7 hm = 4170 m

Therefore, after comparison arranging the quantities in order from smallest to largest is 109000 mm < 2.6 km < 41.7 hm

Learn more about quantities at:

brainly.com/question/13421174

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4 0

1 year ago