A club swimming pool is 22 ft wide and 44 ft long. The club
members want an exposed aggregate border in a strip of
uniform width around the pool. They have enough material for
432 ft squared. How wide can the strip be?

Answer:

Letters as in the attached image.
Triangles ABC and ADC are congruent by SSS. From that, corresponding angles are congruent, in parcicualre B and D, both measuring 94°.
Final angle is obtained by difference. The internal angles of a quadrilater add to 360, so the remaining is 360-90-94-94 =82°

Answer:

-5, -1, 4, 10, 13

Step-by-step explanation:

the larger the negative, the smaller the number

Answer:

  has its vertex below the x-axis

Step-by-step explanation:

In the vertex form equation for a parabola, the parameter k is the y-coordinate of the vertex.

__

When k is negative, the parabola has its vertex located below the x-axis.

To find the measure of Angle A, we'll need to use a trigonometric function.

Remember: SOH-CAH-TOA

Looking from Angle A, we know the opposite side and the hypotenuse. Therefore, we should use the sine function.

sin(A) = 9 / 18

---To solve for A, you'll need to use the inverse sin function on your calculator. It should look like so: sin^-1()

The inverse sin of 1/2 = 30

Answer: first option, 30 degrees

Hope this helps!

Answer:

>

Step-by-step explanation:

This is the greater than symbol. Think of it like an alligator mouth that wants to eat the larger number. 3.2 is larger than -99.

Answer:

3.2 > -99

Step-by-step explanation:

3.2 ? -99

3.2 (positive number)

-99 (negative number)

Positive numbers are always bigger than negative numbers

3.2 ? -99

3.2 > -99

Hope this helps!

Using the normal distribution, it is found that there is a 0.383 = 38.3% probability that the sample proportion is between 18% and 22%.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem, the proportion and the sample size are of p = 0.2 and n = 100, respectively, hence:

[tex]\mu = p = 0.2[/tex]

[tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.2(0.8)}{100}} = 0.04[/tex]

The probability that in a random sample of 100 M&M candies, there are between 18% and 22% orange candies is the p-value of Z when X = 0.22 subtracted by the p-value of Z when X = 0.18, hence:

X = 0.22:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.22 - 0.2}{0.04}[/tex]

Z = 0.5

Z = 0.5 has a p-value of 0.6915.

X = 0.18:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.18 - 0.2}{0.04}[/tex]

Z = -0.5

Z = -0.5 has a p-value of 0.3085.

0.6915 - 0.3085 = 0.383.

0.383 = 38.3% probability that the sample proportion is between 18% and 22%.

To learn more about the normal distribution and the central limit theorem, you can check https://brainly.com/question/24663213

Answer:

b.520 units

Step-by-step explanation:

find the area of the bigger triangle the base is 20 which is 10×2 while the height is 28. 1/2×20×28=280units find the area of the smaller triangle. the base is also 20 while the height is 24. 1/2×20×24=240. sum the areas of the two triangles. 280+240=520units

Answer:

A. About 47.5π

B. About 149.1

Answer:

12,39,21,18,24,17,12,25

Step-by-step explanation:

Answer:

In y = 2x the value of y is twice the value of x, and in y = x + 2 the value of y is two more than the value of x.

Same for the y=4x and y=x+4, just plug the numbers into the sentence.

Step-by-step explanation:

Answer:

[tex]\huge\boxed{\sf h = 6.75 \ in.}[/tex]

Step-by-step explanation:

Given Data:

Base area = [tex]A_{B}[/tex] = 108 in.²

Volume = V  = 729 in.³

Required:

Height = h = ?

Formula:

[tex]V=A_{B}h[/tex]

Solution:

For h, rearranging formula:

[tex]\displaystyle h = \frac{V}{A_{B}} \\\\h =\frac{729 \ in.^3}{108 \ in.^2} \\\\h = 6.75 \ in.\\\\\rule[225]{225}{2}[/tex]

Answer:

0.47 pounds

Step-by-step explanation:

Simple subtraction!

Total pounds = pounds of onions + pounds of potatoes + pounds of hamburger

Setting the pounds of onions to [tex]x[/tex] we get:

[tex]6.4 = x + 1.18 + 4.75[/tex]

[tex]x=0.47[/tex]

So we get 0.47 pounds of onions!

Answer:

Hopefully, this helps you!!

:3

Here's a graph!

Have a great day!!

[tex]Sokkachan[/tex]

Answer:

Point W

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

Let the probability of picking an orange = P(O), and the probability of picking a strawberry = P(S),

Based on the question, he picked an orange first and the probability of picking that is

P(O) = 12/50

Then he picked a strawberry on the second pick, the probability of picking the strawberry is P(S) and we'll find that later.

The probability of picking orange then strawberry with replacement is

P(O) × P(S) = 9/125

Substitute the P(O)=12/50,

12/50 × P(S) = 9/125

P(S) = 3/10

Then by finding the number of strawberry candies, we'll just have to multiply P(S) with the total number of candies, i.e.

Number of strawberry candy

= 3/10 × 50

= 15

[tex]\textbf{a)}\\\\6x^2 -3x = 3x(2x-1)\\\\\textbf{b)}\\\\x^2+3x -28 \\\\=x^2 +7x-4x-28\\\\=x(x+7)-4(x+7)\\\\=(x-4)(x+7)\\\\\textbf{c)}\\\\4au+24av-5bu-30bv\\\\=4a(u+6v)-5b(u+6v)\\\\=(u+6v)(4a-5b)[/tex]

Step-by-step explanation:

A.6x^2-3x

3x(2x-1)

B.x^2+3x-28

product= -28x^2 sum= +3x factors= +7x, -4x

(x^+7x)(-4x-28)

x(x+7)-4(x+7)

(x-4)(x+7)

C.4au + 24av -5bu - 30bv

4a(u+6v)-5b(u+6v)

(4a-5b)(u+6v)

Answer:

1) f(-6) = 8

2) f(3) = -2

3) f(x) = -5 when x = 4

Answer:

x+50+4x=90(being complementary angle)

5x+50=90

5x=90_50

5x=40

x=40÷5

x=8

first we add those both numbers, x+4x=5x and we divide it with 40(40÷5) and the solution comes.

Answer:

B

Step-by-step explanation:

B is the best answer because it's a lot of students and unbiased

Answer:

x = -6          or   x = -2

Step-by-step explanation:

|3x-4(x+1)|=2

Simplify inside the absolute value by distributing

|3x-4x-4|=2

Combine like terms

|-x-4|=2

Now separate into two equations, one positive and one negative

-x-4 = 2   or -x-4 = -2

Add 4 to each side

-x-4+4 = 2+4     or -x-4 = -2+4

-x = 6                  or -x =2

Multiply by -1

x = -6          or   x = -2

Answer: 5 + 5 = 10

Reason: Imagine that you have 5 pencils in one hand, then you add another 5 pencils into that hand, and you would have 10 pencils. Thus 5 + 5 in this case is 10

Hope that helps!

Answer:

Step-by-step explanation:

First box: (3/4)*b

Second box (3/4 * -8)

third box (3/4b)

fourth box: -6

5th box: 12

The profit generated in terms of x is  −0.9x²+61.2x - 500

Given the following parameters

Revenue generated by a company = R=−0.9x²+90.2x

The cost to produce the mowers C(x) =  29x + 500

Determine the profit function

p(x) = R(x) - C(x)

P(x) = −0.9x²+90.2x  - (29x + 500)

P(x) = −0.9x²+90.2x - 29x - 500
P(x) = −0.9x²+61.2x - 500

Hence the profit generated in terms of x is  −0.9x²+61.2x - 500

Learn more on profit function here: https://brainly.com/question/25638609

Answer:

Step-by-step explanation:

Hello:

an equation   for the line is : y =mx +b    (m: is a slope )

perpendicular to the line described by : y = 4/3 x

So : product for two slopes = -1   means : m×4/3=-1

m = -3/4

now : y = -3/4 x+b

but this line :

through the point (4,2) : 2 =(-3/4)(4)+b....... b=5

conclusion :

the equation is : y = -3/4x +5

Answer:

The answer would be The answer would be 26 meters squared.

Step-by-step explanation:

1. Identify three rectangles
(The ones I identified were 5 by 2 [twice!] and 3 by 2)
2. Do 5x2 (10)
3. Do 5x2 again (10)
4. Do 3x2 (6)
5. Add 10, 10, and 6, to get 26
6. Label to get 26 meters squared. I hope this helps! :)

The amount of mg required per kg for the patient is 2,438.1mg/kg

Proportions are ratios of two integers.

Given the medication with a strength 125mg/5ml which has been ordered at 25 mg/kg.

For a patient that weighs 215lb, the weight in kg will be 97.5224kg

Since 25mg = 1 kg

x = 97.5224kg
x = 25 * 97.5224
x = 2,438.06

Hence the amount of mg required per kg for the patient is 2,438.06mg/kg

Learn more on ratio and proportion here: https://brainly.com/question/19994681

Answer:

If two sides in one triangle are congruent to two sides of a second triangle, and also if the included angles are congruent, then the triangles are congruent. Using labels: If in triangles ABC and DEF, AB = DE, AC = DF, and angle A = angle D, then triangle ABC is congruent to triangle DEF  

Step-by-step explanation:

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