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1 year ago

15

A square countertop has a side length of 28 inches. Find the perimeter and area of the countertopusong the correct number of sig

nificant digits.

2 answers:

iren [92.7K]1 year ago

5 0

Perimeter is 14
area is 4

Juliette [100K]1 year ago

5 0

Answer:

$\text{Perimeter of counter-top}=112\text{ inches}$

$\text{Area of counter-top}=784\text{ inches}^2$

Step-by-step explanation:

We have been given that a square counter-top has a side length of 28 inches. We are asked to find the perimeter and area of the counter-top.

We know that perimeter of a square is 4 times its side length.

$\text{Perimeter of counter-top}=4\times 28\text{ inches}$

$\text{Perimeter of counter-top}=112\text{ inches}$

Therefore, the perimeter of the counter-top is 112 inches.

We know that area of square is square of side length of square.

$\text{Area of counter-top}=(28\text{ inches})^2$

$\text{Area of counter-top}=784\text{ inches}^2$

Therefore, the area of the counter-top is 784 square inches.

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Noah read 6 books in 9 months. What was his rate of reading in books per month?

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a quarter of a book a month

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The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 247.9 and a standard deviation of

labwork [276]

Answer:

A) Approximate percentage of women with platelet counts within 2 standard deviations of the mean, or between 118.5 and 377.3 = 95%

B) approximate percentage of women with platelet counts between 53.8 and 442.0 = 99.7%

Step-by-step explanation:

We are given;

mean;μ = 247.9

standard deviation;σ = 64.7

A) We want to find the approximate percentage of women with platelet counts within 2 standard deviations of the mean, or between 118.5 and 377.3.

Now, from the image attached, we can see that from the empirical curve, the probability of 1 standard deviation from the mean is (34% + 34%) = 68 %.

While probability of 2 standard deviations from the mean is (13.5% + 34% + 34% + 13.5%) = 95%

Thus, approximate percentage of women with platelet counts within 2 standard deviations of the mean, or between 118.5 and 377.3 = 95%

B) Now, we want to find the approximate percentage of women with platelet counts between 53.8 and 442.0.

53.8 and 442.0 represents 3 standard deviations from the mean.

Let's confirm that.

Since mean;μ = 247.9

standard deviation;σ = 64.7 ;

μ = 247.9

σ = 64.7

μ + 3σ = 247.9 + 3(64.7) = 442

Also;

μ - 3σ = 247.9 - 3(64.7) = 53.8

Again from the empirical curve attached, we cans that at 3 standard deviations from the mean, we have a percentage probability of;

(2.35% + 13.5% + 34% + 34% + 13.5% + 2.35%) = 99.7%

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1 year ago

What is the nearest ten thousand, the population of Vermont was estimated to be about 620,000 in 2008 . What might have been the

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Answer:

618,000 might be the exact population of Vermont in 2008

Step-by-step explanation:

* <em>Lets explain the rule of rounding to the nearest ten thousands</em>

- To round numbers to the nearest ten thousand, make the

numbers whose last four digits are 0001 through 4999 into the

next lower number that ends in 0000

- Ex: 83,525 rounded to the nearest ten thousand would be

80,000.

- Numbers that have the last four digits of 5000 or more should

be rounded up to the next even ten thousand

- Ex: The number 58,988 rounded to the nearest ten thousand

would be 60,000

* <em>Lets do that in the problem</em>

∵ The number is 620,000 after rounded to the nearest

ten thousands

∴ We can chose any number whose last four digits are 00001

through 4999 as 624,000 <em>OR</em> 5000 or more as 618,000

∴ 618,000 might be the exact population of Vermont in 2008

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1 year ago

In triangle XYZ, if angle X is congruent to angle Z, XY = 13x - 21, YZ = 8x - 6, & XZ = x + 4, find x & the measure of e

Naily [24]

Answer:

Given: In triangle XYZ, $\angle X \cong \angle Z$ , XY=13x-21 , YZ=8x-6 and XZ=x+4.

If two angles are congruent if and only if, they measure the same number of degrees.

therefore, from the given condition; $\angle X = \angle Z$ .

Isosceles Triangle : An triangle with two equal sides. The angles opposite the equal sides are also equal.

Therefore, the triangle XYZ is an isosceles triangle, as the base angle $\angle X$ and $\angle Z$ are equal and the sides opposite to these angles are also equal i.e, XY=YZ.

Since, we have XY=YZ ,

⇒ 13x-21 =8x-6 or

13x-8x=21-6 or

5x=15

Simplify:

x=3

Therefore, the sides of an isosceles triangle are:

XY = 13x-21 = $13\cdot 3 -21$ = 39-21 = 18 unit ,

YZ = 8x-6 = $8 \cdot3 -4$ = 24-6 =18 unit,

and XZ = x+4 = 3+4 =7 unit.

Since, the triangle is isosceles, we draw a line from an vertex angle Y of a triangle XYZ which is perpendicular (i.e, of 90 degree angle) to opposite side meets the opposite side at its midpoint i.e, say W.

As W is the midpoint(i.e, it divide the sides into two equal halves),

XW=WZ = $\frac{7}{2} =3.5$ unit

Now, use the Pythagorean theorem, to find the altitude WY.

⇒ $(WY)^2+(WZ)^2=(YZ)^2$

Substitute the value of WZ = 3.5 unit and YZ = 18 unit in above formula to calculate the length of WY;

⇒ $(WY)^2+(3.5)^2=(18)^2$

Simplify:

$(WY)^2=324-12.25=311.75$ or

$WY=\sqrt{311.75}$

On simplify we get;

WY=17.65 unit(approx.)

The vertex angle Y is split into two equal angles, we can find the vertex angle by finding the one of the base angle by using the fact; $Cosine = \frac{Base}{Hypotenuse}$ .

⇒ $\cos Z =\frac{3.5}{18}$

⇒ $\cos Z = 0.195$ (approx) or

$Z=\cos^{-1}(0.195)$

Therefore, the angle $\angle Z = 78.7^{\circ}$ .

The sum of the measure of the angle in the triangle is 180 degree.

In triangle XYZ.

$\angle X +\angle Y+\angle Z =180^{\circ}$

Since $\angle X=\angle Z =78.7^{\circ}$

then,

$78.7^{\circ}+\angle Y+78.7^{\circ}=180^{\circ}$

⇒ $157.4^{\circ}+\angle Y=180^{\circ}$

Simplify:

$\angle Y=22.6^{\circ}$ .

Therefore, the measure of each angle are: $\angle X=\angle Z=78.7^{\circ}$ and $\angle Y =22.6^{\circ}$

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1 year ago

Algebra. Find the variable in the equation 803 divided by 73=m

weeeeeb [17]

<u>Answer:</u>

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<u>Solution:</u>

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That means need to solve below expression to determine value of variable m.

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So let’s solve left hand side to get the value of m.

For sake of simplicity let’s do factorization of numerator and denominator and remove the common terms in numerator and denominator.

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1 year ago