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3 years ago

The perimeter of a rectangle is 48 in. If the length is twice the width, what is the length of the rectangle?

1 answer:

7 0

Step one: We need to find the formula for perimeter. And we can't just say "count all the sides". How can we express it? It's length + length + width + width, right? Let's size that down a little bit. 2*length 2*width. We'll use w to express "width" and 2w to express "length".
2(w)+2(2w)=48.
6w=48.
w=8.
Since length is twice the width, 8*2 is 16. Length=16.

You can check it by substituting the different values for length and width into the equation 2w+2l=perimeter.
2(8)+2(16)=48. Is this true? Yep! So you know you're right.

You might be interested in

Each employee in a company is either right-handed or left-handed.

PtichkaEL [24]

Answer:

Right handed 41

Right handed male 18

Right handed female 23

Male employees 22

Female employees 32

Left handed 13

Left handed male 4

Left handed female 9

4 0

3 years ago

suppose that a restaurant chain claims that its bottles of ketchup contain 24 ounces of ketchup on average, with a standard devi

ivann1987 [24]

Answer:

The 96% confidence interval for the mean number of ounces of ketchup per bottle in the sample is 24 ± 0.029

Step-by-step explanation:

Given

Mean, x = 24 ounces

Standard deviation, σ = 0.2 ounces

Sample Size, n = 49 bottles of ketchup

Confidence Interval of 95% (0.95)

To calculate the confidence at this level, the following steps are to be followed;

1. Calculating degree of freedom:

Degree of freedom (df) is calculated by subtracting 1 from the sample size.

df = n - 1

df = 49 - 1

df = 48

2. Subtract the confidence level from 1, then divide by two.

α = (1 – .95) / 2 = 0.025

3. Look up the answers to (1) and (2) in the t-distribution table.

For 48 degrees of freedom (df) and α = 0.025,

We get 2.0106

4. Divide sample standard deviation by the square root of sample size.

i.e σ/√n

= 0.2/√49

= 0.2/7

= 0.02857

= 0.029

5. Finally, the 95% confidence interval is calculated using the following illustration.

X ± result in step 5

Where x = 24

So, we have

24 ± 0.029

8 0

3 years ago

Read 2 more answers

A four-quart container holds 128 ounces of water. How much water does a one-quart container hold?

Licemer1 [7]

Answer:

32 oz

Step-by-step explanation:

4 quart -----------> hold 128 oz

1 quart -------------> holds 128 ÷ 4 oz = 32 oz

5 0

3 years ago

Read 2 more answers

Trevor is analyzing a circle, y2 + x2 = 100, and a linear function g(x). Will they intersect?

lakkis [162]

Given a circle described by the equation:
$y^2+x^2=100$
and a function g(x) given by the table
$\begin{center}
\begin{tabular}{ |c |c |c }
 x & g(x) \\
 -1 & -22 \\
 0 & -20 \\
1 & -18 
\end{tabular}
\end{center}$

The function g(x) describes a straight line with the equation:
$\frac{y-y_1}{x-x_1} = \frac{y_2-y_1}{x_2-x_1} \\ \\ \frac{y-(-22)}{x-(-1)} = \frac{-20-(-22)}{0-(-1)} \\ \\ \frac{y+22}{x+1} = \frac{-20+22}{0+1} = \frac{2}{1} \\ \\ y+22=2(x+1)=2x+2 \\ \\ y=2x-20$

To check if the circle and the line intersects, we substitute the equation of the line into the equation of the circle to see if we have a real solution.
i.e.
$y^2+x^2=100 \\ \\ (2x-20)^2+x^2=100 \\ \\ 4x^2-80x+400+x^2=100 \\ \\ 5x^2-80x+300=0 \\ \\ x^2-16x+60=0 \\ \\ (x-6)(x-10)=0 \\ \\ x-6=0 \ or \ x-10=0 \\ \\ x=6 \ or \ x=10$

When x = 6, y = 2(6) - 20 = 12 - 20 = -8 and when x = 10, y = 2(10) - 20 = 20 - 20 = 0

Therefore, the circle and the line intersect at the points (6, -8) and (10, 0).

8 0

3 years ago

Read 2 more answers

A man swims for 30 mins at a speed of 109 m/min. How far does he swim?

Law Incorporation [45]

The distance is meters per minute so you would multiply the distance per minute by total minutes:

109 x 30 = 3.270 total meters.

1 km = 1000 meters

3,270 meter/ 1000 meters per km = 3.27 km

They swam 3.27 km

8 0

2 years ago