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1 month ago

A rectangle on a coordinate plane has vertices at (7,5), (-7,5), (-7,-2), and (7,-2). What is the perimeter of the rectangle?

2 answers:

8 0

Answer: 42 Step-by-step description: The rectangle situated on a coordinate plane has vertices at (7,5), (-7,5), (-7,-2), and (7,-2). The rectangle’s perimeter can be calculated using the formula 2(length) + 2(width). First, we determine the distance between the points (7,5) and (-7,5) since the y-values remain consistent; the distance is acquired by subtracting the x values for length. Next, for points (-7,5) and (-7,-2) where the x-values are consistent, we find the width by subtracting the y-values. Thus, the perimeter is then calculated as 2(length) + 2(width), resulting in 2(14) + 2(7) = 42 units.

lawyer [12.5K]1 month ago

7 0

For a rectangle, the perimeter can be calculated as P=2l+2w. Assuming the length is horizontal and the width is vertical, the span between the x coordinates will give the length, while the span between the y coordinates will determine the width. Once these measurements are obtained, you can apply them to the perimeter formula. |7 -(-7)| = 14 gives l = 14, |5-(-2)| = 7 gives w=7. Therefore, P=2(14)+2(7), which results in P= 28+14, thus, P= 42.

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Statistics can help decide the authorship of literary works. Sonnets by a certain Elizabethan poet are known to contain an avera

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Response:

It is inferred that the authors of the sonnets belong to a certain poet from the Elizabethan era.

Step-by-step breakdown:

The details provided in the question are as follows:

Population mean, μ = 8.9

Sample mean, $\bar{x}$ = 10.2

Sample size, n = 6

Alpha, α = 0.05

Population standard deviation, σ = 2.5

Initially, we formulate the null hypothesis and the alternative hypothesis

To conduct this test, we utilize the One-tailed z test.

a) Equation:

$z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }$

By substituting in all relevant values, we determine:

$z_{stat} = \displaystyle\frac{10.2 - 8.9}{\frac{2.5}{\sqrt{6}} } = 1.28$

Next, $z_{critical} \text{ at 0.05 level of significance } = 1.64$

b) The p-value is computed using the z-table.

P-value = 0.1003

The p-value surpasses the alpha of 0.05

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1 month ago

1 kilogram is equivalent to about 2.2 pounds. An orangutan weighs 142 pounds. What is its mass in kilograms? Round your answer t

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The weight of an orangutan is 64.5 kilograms

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It is stated that the orangutan's weight is 142 pounds

Additionally,

1 kilogram is approximately 2.2 pounds

We will now convert 142 pounds into kilograms

1 kilogram = 2.2 pounds

$\text{1 pound } = \frac{1}{2.2} \text{ kilograms }$

As a result, 142 pounds translates to

$142 \text{ pound } = \frac{1}{2.2} \times 142 \text{ kilogrmas }$

$\rightarrow \frac{1}{2.2} \times 142 = 64.545 \text{ kilograms }$

When rounding to the nearest tenth, we obtain 64.5 kilograms

Therefore the mass of the orangutan is 64.5 kilograms

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