A local middle school adopted a policy for school uniforms. Students can wear black pants or tan pants. They can wear a yellow shirt, a red shirt, a green shirt, or a white shirt. The tree diagram shows the possible outfit choices.

The exact volume of the composite figure with a cylinder of height and diameter 3.5 feet and a hemisphere on top is 49.92 cubic feet.

To find the volume of the composite figure, we need to add the volumes of the cylinder and the hemisphere on top of it.

The formula for the volume of a cylinder is:

V_cylinder = π\(r^2\)h

where r is the radius of the cylinder and h is its height.

The formula for the volume of a hemisphere is:

V_hemisphere = (2/3)π\(r^3\)

where r is the radius of the hemisphere.

In this case, the diameter of the cylinder is given as 3.5 feet, so the radius is half of that, or 1.75 feet. The height of the cylinder is also given as 3.5 feet. Therefore, the volume of the cylinder is:

V_cylinder = π(1.75\()^2\)(3.5) ≈ 32.67 cubic feet

To find the volume of the hemisphere, we need to first find its radius. Since the diameter of the cylinder is also the diameter of the hemisphere, the radius of the hemisphere is also 1.75 feet. Therefore, the volume of the hemisphere is:

V_hemisphere = (2/3)π(1.75\()^3\) ≈ 17.25 cubic feet

Finally, we add the volumes of the cylinder and hemisphere to get the total volume of the composite figure:

V_total = V_cylinder + V_hemisphere

≈ 32.67 + 17.25

= 49.92 cubic feet

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We are 96% confident that the percentage of all students at this particular college who are left-handed is between 4.7% and 13.3%.

Using the given information, we can find the point estimate for the percentage of all students at this particular college who are left-handed by dividing the number of left-handed students in the sample by the total number of students in the sample: 45/500 = 0.09.

Since the sample size is greater than 30, we can assume a normal population distribution. We can also use a 1-Proportion Z-Interval to find the confidence interval. The formula for this is:

point estimate ± z* (standard error)

Where z* is the z-score corresponding to the desired level of confidence (96% in this case), and the standard error is calculated as:

√((phat * (1-p-hat)) / n)

Where that is the point estimate, and n is the sample size.

Using the values we have, we can find:

z* = 1.750
phat = 0.09
n = 500

Plugging these values into the standard error formula, we get:

√((0.09 * 0.91) / 500) ≈ 0.022

Now we can plug everything into the confidence interval formula:

0.09 ± 1.750 * 0.022

Which gives us the interval (0.047, 0.133).

Therefore, we are 96% confident that the percentage of all students at this particular college who are left-handed is between 4.7% and 13.3%.

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Answer:

Step-by-step explanation:

To solve an algebraic expression in simplest form, you can follow these steps:

1. Use the order of operations (PEMDAS) to simplify any arithmetic in the expression (parentheses, exponents, multiplication and division, addition and subtraction).

2. Combine like terms by adding or subtracting any coefficients in front of similar variables.

3. Divide or multiply both sides of the equation by the same non-zero number to solve for the variable.

4. If possible, factor the expression to make it simpler.

5. If the expression is a fraction, check for a common denominator and then simplify by canceling any common factors in the numerator and denominator.

6. If the expression is a radical, check for a perfect square and simplify by taking the square root of the number inside the radical.

7. Use the properties of exponents and logarithms to simplify the expression.

8. Evaluate the expression by plugging in the values of any known variables.

It's important to keep in mind that there may be multiple ways to simplify an algebraic expression and the solution that is in simplest form may not always be obvious.

Answer:

\(\displaystyle y=-\frac{5}{4}x-3\)

Step-by-step explanation:

Recall that perpendicular lines form a 90-degree angle, so the slope of the line perpendicular to the given equation will be the opposite reciprocal.

Hence, the equation of the line that will intersect at a 90-degree angle is \(\displaystyle y=-\frac{5}{4}x-3\)

Answer:

The answer to your problem is, D. $13,564.80

Step-by-step explanation:

We know it took her 4 years to pay this amount. Let's solve for the total amount she paid including the interest.

12,560 x 0.02 = 251.2 per year

251.2 x 4 = 1004.8 dollars for 4 years.

1004.8 + 12,560 = 13,564.8 dollars.

Thus the answer to your problem is, D. $13,564.80

The numerical  value of to the nearest tenth is 14.3.

From the diagram, we have a right angle triangle.

Using trig ratio, Tangent = Opposite / Adjacent.

Hence;

tan( Ф ) = Opposite / Adjacent

Plug in the given values and solve for x

tan( 40° ) = 12/ x

tan( 40° ) × x = 12

x = 12 / tan( 40° )

x = 12 / 0.8390996

x = 14.3

Therefore, the value of x is approximately 14.3.

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The elimination method is a technique used to solve a system of linear equations by eliminating one variable at a time.

If the coefficients of the variables are already the same, no multiplication is necessary and you can simply add or subtract the equations to eliminate the variable.

y = 9x - 23

y = x + 1

9x - y = 23

x - y = -1

8x = 24

x = 3

3 - y = -1

y = 4

x + y = 3

x - y = 7

2x = 10

x = 5

5 + y = 3

y = 3 - 5

y = -2

7x - 4y = -11

7x - 10y = 25

6y = -36

y = -6

7x - 4(-6) = -11

7x = -11 + 24

x = 13/7

4x - 2y= - 30 ---- x1

-x - 2y = 5 ----- x4

4x - 2y = -30

-4x - 8y = 20

-10y = -10

y = 1

4x - 2(1) = -30

x = -7

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There are 12,600 ways to choose 10 balls satisfying the given conditions of at least one red ball, at least two blue balls, and at least three green balls.

To calculate the number of ways to select the balls, we can use the concept of combinations.

Let's break down the selection criteria:

At least one red ball: This means we can select 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10 red balls.

At least two blue balls: This means we can select 2, 3, 4, 5, 6, 7, 8, 9, or 10 blue balls.

At least three green balls: This means we can select 3, 4, 5, 6, 7, 8, 9, or 10 green balls.

To find the total number of ways to select the balls, we need to consider all possible combinations of selecting the specified number of balls from each color category. We can calculate this by summing up the combinations for each case:

Number of ways = C(1, 10) × C(2, 9) × C(3, 7) = 10 × 36 × 35 = 12,600.

Therefore, there are 12,600 ways to select 10 balls satisfying the given conditions of at least one red ball, at least two blue balls, and at least three green balls.

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The exact value  of \(sin 2x\) is \(4√5/9.\)

Given that \(sec x = 3/2 and csc y = 3\)where x and y are in the 2x = 2 sin x quadrant, we need to find the exact value of sin 2x.

In the first quadrant, we have the following values of the trigonometric ratios:\(cos x = 2/3 and sin y = 3/5\)

Also, we know that sin \(2x = 2 sin x cos x.\)

Now, we need to find sin x.

Having sec x = 3/2, we can use the Pythagorean identity

\(^2x + 1 = sec^2xtan^2x + 1 = (3/2)^2tan^2x + 1 = 9/4tan^2x = 9/4 - 1 = 5/4tan x = ± √(5/4) = ± √5/2\)

As x is in the first quadrant, it lies between 0° and 90°.

Therefore, x cannot be negative.

Hence ,\(tan x = √5/2sin x = tan x cos x = √5/2 * 2/3 = √5/3\)

Now, we can find sin 2x by using the value of sin x and cos x derived above sin \(2x = 2 sin x cos xsin 2x = 2 (√5/3) (2/3)sin 2x = 4√5/9\)

Therefore, the exact value  of sin 2x is 4√5/9.

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Answer:

this is gonna be long so strap in

Step-by-step explanation:

l= -1.570796w^2+a/2w

All the given expressions are equivalent to 4x³ - 12x² + 20x - 60.

What is expressions?

An expression is made up of one or more integers or variables, as well as one or more operations.

All of the expressions are equivalent to 4x³ - 12x² + 20x - 60:

4x(x²-3x + 5) expands to 4x³ - 12x² + 20x

4(x-3)(x² + 5) expands to 4x³ - 12x² + 20x - 60

x³(x-3) +5(x-3) simplifies to x³ - 3x² + 5x - 15, which is equivalent to 4x³ - 12x² + 20x - 60

4(x³ - 3x² + 5x - 15) is already equivalent to 4x³ - 12x² + 20x - 60

4(x²(x-3) + 5(x-3)) simplifies to 4x³ - 12x² + 20x - 60

4(x²(x-3) - 5(x-3)) simplifies to 4x³ - 12x² + 20x - 60.

Therefore, All the given expressions are equivalent to 4x³ - 12x² + 20x - 60.

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Answer:

c = 6

Step-by-step explanation:

52 = 7 + 5(c = 3)

52 = 7 + 5c + 15

52 = 22 + 5c

-5c = 22 - 52

-5c = -30

c = \(\frac{-30}{-5}\)

c = 6

Answer:

C

Step-by-step explanation:

Add all percentages together, then divide by how many you added.

Answer:

C

Step-by-step explanation:

Answer:18

Step-by-step explanation: yes

20 is greater than 15 by 33.33%.

Percentage can be defined as a number or ratio that can be represented as a fraction of 100. In percentage numerator is the number and denominator is 100. To calculate percent of a number, we have to perform division on the given number by the whole number and then multiply by 100. Hence, the meaning of percentage is a part per hundred. The word per cent means per 100.

Given,

two numbers 20 and 15

Using subtraction operation,

20 - 15 = 5

20 is 5 greater than 15.

In percentage,

(5/15)× 100

= 0.3333 × 100

= 33.33%

Hence, 33.33% is 20 greater than 15.

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The function approaches the value 80 + √5 as x approaches 75 from the right. This is consistent with the algebraic limit in part (b), which was found to be 5 + √5.

Given the function g(x) = x + √5

To find the values of g at the points x = -2.2, -2.24, -2.236 and so on through successive decimal approximations of -5, we can use the following table:

| x | g(x) | |-22 | -22 + √5| |-2.24| -2.24 + √5| |-2.236 | -2.236 + √5| |-2.236 | -2.236 + √5| |-2.236 | -2.236 + √5| |-2.236 | -2.236 + √5| |-2.236 | -2.236 + √5| |-2.236 | -2.236 + √5| |-2.236 | -2.236 + √5| |-2.236 | -2.236 + √5| |-2.236 | -2.236 + √5| |-2.236 | -2.236 + √5| |-2.236 | -2.236 + √5| |-2.236 | -2.236 + √5| |

Limit x -> 5

The function g(x) = x + √5 is continuous everywhere.

So, we can find the limit algebraically.

Using the limit laws, we have:

lim x->5 g(x) = lim x->5 (x + √5)

= lim x->5 x + lim x->5 √5

= 5 + √5

Therefore, Lim x->5 g(x) = 5 + √5

To support the conclusion in part (a), we need to graph the function near c = 75 and use Zoom and Trace to estimate y values on the graph as x → 15.

We can use the following graph for this:

Graph of g(x) = x + √5As we can see from the graph, the function approaches the value 80 + √5 as x approaches 75 fr

the right.

This is consistent with the algebraic limit in part (b), which was found to be 5 + √5.

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Question:

Look at the picture of a scaffold used to support construction workers. The height of the scaffold can be changed by adjusting two slanting rods, one of which, labeled PR, is shown: Part A: What is the approximate length of rod PR? Round your answer to the nearest hundredth. Explain how you found your answer stating the theorem you used. Show all your work. (5 points)

B) The length of rod PR is adjusted to 16 feet. If width PQ remains the same, what is the approximate new height QR of the scaffold? Round your answer to the nearest hundredth.

Answer:

A) 16.64 Feets

B) 7.65 feets

Step-by-step explanation:

Given the following :

The question above can be solved by applying Pythagoras rule :

A^2 = B^2 + C^2

PR² = PQ² + QR²

PR² = 14² + 9²

PR² = 196 + 81

PR = √277

PR = 16.64feet

Now if PR is adjusted to 16 Feets, the New height of the scaffold will be:

QR² = PR² - PQ²

QR² = 16² - 14²

QR² = 256 - 196

QR² = 60

Take the Square root of both sides

QR = √60

QR = 7.7459666 Feets

Answer:

The water level will change at a rate of - 2 7/18 inches per year

Step-by-step explanation:

From the question, we have a change of -7 1/6 inch every 3 years

We now want to calculate the value of the change every year

Mathematically, that will be;

- 7 1/6 divided by 3

= -43/6 divided by 3

= -43/18 = - 2 7/18 inch per year

Answer:

He can buy 9 bagels

Step-by-step explanation:

6 divided by $0.65 gets you 9.230769230769231. We have to round this down so he can get 9 bagels.

Answer:

The first pic is for 2x +3y = 12 and the second is for x=7

The unit rate is 22 gal/min. So, you have

Then, you have

So, a minute and a half after 12 minutes, an additional 33 gallons will be pumped in. A total of 297 gallons

will have been pumped into the pool after 13 and a half minutes.

Answer:

Step-by-step explanation:

(x+8)(x−8)x2+13 is the answer

The given expression is:

x+8x+2⋅(x+2)(x−8)x2+13

To simplify this expression, you can start by simplifying the denominator:

2⋅(x+2)(x−8)x2+13 = 2(x2-6x-16)x2+13 = 2(x2-6x-16)x2 + 26x - 26x + 13

= 2(x2-6x-16)x2 + 26x + (-26x + 13)

Now you can rewrite the original expression as:

x+8x+(2(x2-6x-16)x2 + 26x + (-26x + 13))

= x(1 + 8x2(x2-6x-16)x2 + 26x + (-26x + 13))

x(2(x^2-6x-16)x^2 + 13)

We can simplify the expression inside the parenthesis first:

2(x^2-6x-16)x^2 = 2x^4 - 12x^3 - 32x^2

Substituting this back into the original expression, we get:

x(2x^4 - 12x^3 - 32x^2 + 13)

Multiplying out the brackets, we get:

2x^5 - 12x^4 - 32x^3 + 13x

Now, we can factor out a common factor of x:

x(2x^4 - 12x^3 - 32x^2 + 13)

= x(2x^4/x - 12x^3/x - 32x^2/x + 13/x)

= x(2x^3 - 12x^2 - 32x + 13/x)

Finally, we can factor the expression inside the brackets:

= x(2x^3 - 16x^2 + 4x^2 - 32x + 8x - 8 + 13/x)

= x(2x^2(x-8) + 4x(x-8) + 8(x-8) + 13/x)

= x(x-8)(2x^2+4x+8) + 13(x-8)/x

= (x-8)(x^3+2x^2+4x+13)/x

Now we can see that the expression can be written as:

(x-8)(x^3+2x^2+4x+13)/x

To simplify further, we can divide x into the numerator to get:

(x+8)(x−8)x^2+13

Therefore, the expression is equal to (x+8)(x−8)x2+13.

Answer:

B if two pdiwjsjwixjjsjsidff

Answer: x = 7/2

Step-by-step explanation: Isolate the factor by dividing each side by factors that don't contain a variable.

Answer: 13 and 5= coeeficients, x and y = variables,  -2 and 3 =constants

Step-by-step explanation:

Answer:

About 54.16 percent

Step-by-step explanation:

To turn a fraction into a percentage you must divide the numerator by the denominator.

Ex: 1/2 the percentage is  0.50 percent so its 50%

Step-by-step explanation:

16:35 plus 6 hours to account for them being 6 hours ahead is 22:35 off the bat. we then add 13.75 hours which goes to Friday at 12:20 pm.

The number of games that will be played in the first round will be 14 games.

It should be noted that the appropriate function to use in this scenario will be:

= (n - 1) × 2

where n = total number of people participating.

Therefore, this will be:

= (n - 1) × 2

= (8 - 1) × 2

= 7 × 2

= 14

Therefore, the number of games that will be played in the first round will be 14 games.

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Answer:

taking z as the reference angle XY becomes perpendicular and YX becomes base thus SIN Z= P/H

SIN Z = 30/50

therefore sin z= 0.6