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2 years ago

The length of a rectangle is twice the with. If the perimeter of the rectangle is 60 units, find the area of the garden

Mathematics

1 answer:

Darya [45]2 years ago

4 0

w - width

2w - length

60 - perimeter

w + w + 2w + 2w = 6w - perimeter

The equation:

6w = 60 <em>divide both sides by 6</em>

w = 10 → 2w = 2 · 10 = 20

The area: A = width × length

A = (10)(20) = 200

<h3>Answer: The area of the garden is equal 200 square units.</h3>

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A sphere and a cylinder have the same radius and height. The volume of the cylinder is 27 pi feet cubed.

LenaWriter [7]

Answer:

C. V = two-thirds (27)

Step-by-step explanation:

Given

Solid Shapes: Cylinder and Sphere

Volume of Cylinder = 27π ft³

Required

Volume of the sphere.

From the question,

1. The volume of the sphere is the same as the volume of the cylinder

2. The height of the sphere is the same as the height of the cylinder.

From (2) above;

This means that the height of the cylinder equals the diameter of the sphere.

Let h represent the height of the sphere and d represent the diameter of sphere.

Mathematical, d = h

Recall that radius, r = $r = \frac{d}{2}$

Substitute h for d in the above expression

$r = \frac{h}{2}$ . ----- (take note of this)

Calculating the volume of a cylinder.

V = πr²h

Recall that V = 27; This gives us

27 = πr²h

Divide both sides by h

$\pi r^2 = \frac{27}{h}$

-------------------

Calculating the volume of a sphere

$V = \frac{4}{3}\pi r^3$

Expand the above expression

$V = \frac{4}{3}\pi r^2 * r$

Substitute $\pi r^2 = \frac{27}{h}$

$V = \frac{4}{3} * \frac{27}{h} * r$

Recall that $r = \frac{h}{2}$

So,

$V = \frac{4}{3} * \frac{27}{h} * \frac{h}{2}$

$V = \frac{4}{3} * \frac{27}{2}$

$V = \frac{2}{3} * 27$

$V = \frac{2}{3} (27)$

V = two-third (27)

4 0

2 years ago

Most college-bound students take either the SAT(Scholastic Assessment Test) or the ACT (which originally stood for American coll

Jlenok [28]

Answer:

Luis would need to have a SAT score of 574.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Nicole's z-score:

ACT scores have a mean of about 21 with a standard deviation of about 5, which means that $\mu = 21, \sigma = 5$