2)

Why are the solutions to the proportions 40/8 = x/10 and x/40 = 10/8 the same?

romanna [79]

Answer:

Both proportions are equivalent.

Step-by-step explanation:

We have been given two proportions $\frac{40}{8}=\frac{x}{10}$ and $\frac{x}{40}=\frac{10}{8}$ . We are asked to find why the solutions to our given proportions are equal.

We can solve proportions by cross multiplying them.

After cross multiplying our both proportions we will get same equation that is:

$40*10=8*x$

$400=8x$

$8*x=40*10$

$8x=400$

Since we get same equation after cross multiplying both proportions, therefore, the solutions to the given proportions would be same.

4 0

3 years ago

Read 2 more answers

Because of staffing decisions, managers of the Gibson-Marion Hotel are interested in the variability in the number of rooms occu

olchik [2.2K]

Answer:

a) $s^2 =30^2 =900$

b) $\frac{(19)(30)^2}{30.144} \leq \sigma^2 \leq \frac{(19)(30)^2}{10.117}$

$567.28 \leq \sigma^2 \leq 1690.224$

c) $23.818 \leq \sigma \leq 41.112$

Step-by-step explanation:

Assuming the following question: Because of staffing decisions, managers of the Gibson-Marimont Hotel are interested in the variability in the number of rooms occupied per day during a particular season of the year. A sample of 20 days of operation shows a sample mean of 290 rooms occupied per day and a sample standard deviation of 30 rooms

Part a

For this case the best point of estimate for the population variance would be:

$s^2 =30^2 =900$

Part b

The confidence interval for the population variance is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

The degrees of freedom are given by:

$df=n-1=20-1=19$

Since the Confidence is 0.90 or 90%, the significance $\alpha=0.1$ and $\alpha/2 =0.05$ , the critical values for this case are:

$\chi^2_{\alpha/2}=30.144$

$\chi^2_{1- \alpha/2}=10.117$

And replacing into the formula for the interval we got:

$\frac{(19)(30)^2}{30.144} \leq \sigma^2 \leq \frac{(19)(30)^2}{10.117}$

$567.28 \leq \sigma^2 \leq 1690.224$

Part c

Now we just take square root on both sides of the interval and we got:

$23.818 \leq \sigma \leq 41.112$

5 0

3 years ago

A homeowner has a mortgage payment of $998.60, an annual property tax bill of $590, and an annual fire insurance premium of $280

grandymaker [24]

Answer:

the monthly payment is $134.72

Step-by-step explanation:

This is if the mortgage is annual also.

add all 3 which would equal 1,616.6.

But "why?" you ask is it so expensive.

it is still annual so divide it by 12 and you have 134.72

8 0

3 years ago

A spring stretches by 21.0 cm when a 135 n object is attached. what is the weight of a fish that would stretch the spring by 49

Akimi4 [234]

If the stretch is proportional to the weight, it will satisfy
weight/(49 cm) = (135 N)/(21 cm)
weight = (49/21)×135 N
weight = 315 N

The weight of the fish would be 315 N.

8 0

3 years ago

Jess is building a skateboarding ramp in the shape of a triangular prism with the dimensions shown. If Jess wants to cover all f

vredina [299]

The image showing the dimensions is missing, so i have attached it.

Answer:

A = 156 square feet

Step-by-step explanation:

To find how much plywood Jesse will need to cover all the surface simply means we are to find the surface area.

The surface area of the triangular prism is given by;

A = (2 * (Area of the base)) + (Perimeter of base x height)

Now, area of the base=bh/2

b = 3 ft

h = 4 ft

area of the base = 3*4/2 = 6 ft²

perimeter of the base = L + b + h = 4 + 3 + 5 = 12 ft

height of the prism;h = 12 ft

Thus;

surface area of the triangular prism;

A = (2 * 6) + (12*12)

A = 12 + 144

A = 156 ft²

8 0

3 years ago