the 87 person team has 1/2 of a water cooler left, how much should each person get?

The critical value of the t-distribution, with a 98% confidence level and 27  df, is given as follows:

t* = 2.4727.

To obtain the critical value of the t-distribution, we must insert these following parameters into a two-tailed t-distribution calculator:

The parameters for this problem are given as follows:

Hence the critical value is given as follows:

t* = 2.4727.

Item b is incomplete, however a similar procedure to item a must be used to obtain the critical value.

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Answer: coupond 3 offers the best sale price of $60

Step-by-step explanation:

Answer:

B.) 3√15

Step-by-step explanation:

a^2 + b^2 = c^2

x^2 + 11^2 = 16^2

x^2 + 121 = 256

x^2 = 256 - 121

x^2 = 135

√x^2 = √135

√135 = √9 • √15

√9 = 3

√15 = √15

3√15

The ratios of their perimeters and the ratios of their areas are 1) 3:1 and 9:1 and 2) 7:4 and 49:16.

Given the scale factor of two similar polygons, we need to find the ratio of their perimeters and the ratios of their areas,

To find the ratio of the perimeters of two similar polygons, we can simply write the scale factor as it is because the ratio of the perimeter is equal to the ration of the corresponding lengths.

1) So, perimeter = 3:1

The ratio of areas between two similar polygons is equal to the square of the scale factor.

Since the scale factor is 3:1, the ratio of their areas is:

(Ratio of areas) = (Scale factor)² = 9/1 = 9:1

Similarly,

2) Perimeter = 7:4

Area = 49/16

Hence the ratios of their perimeters and the ratios of their areas are 1) 3:1 and 9:1 and 2) 7:4 and 49:16.

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Equations

Let's call:

x = time Stanley swam yesterday.

We know he ran for half an hour longer than he swam, thus the time he ran was:

x + 0.5 = time Stanley ran yesterday

We also know he biked for twice the time he ran, thus:

2(x + 0.5) = time Stanley biked yesterday.

The distance covered by Stanley when swimming is

2.5*x

The distance covered by Stanley when running is:

9*(x+0.5)

The distance covered by Stanley while biking is:

16*2*(x + 0.5) = 32(x + 0.5)

The total distance is 64 miles, thus:

2.5*x + 9*(x+0.5) + 32(x + 0.5) = 64

Operating:

2.5x + 9x + 4.5 + 32x + 16 = 64

Simplifying:

43.5x + 20.5 = 64

Subtracting 20.5:

43.5x = 43.5

Thus:

x = 1

Stanley swam for 1 hour, he ran for 1+0.5 = 1.5 hours and biked for 2*1.5=3 hours

Swam: 1 hour, Ran: 1.5 hours, Biked: 3 hours

Answer:

<U=70

Step-by-step explanation:

Straight line=180 degrees

180-120

=60

So, we have 2 angles.

60 and 50

180=60+50+x

180=110+x

70=x

So, U=70

Hope this helps! :)

To solve the equation (3/2)x = (3x)/8, we can start by cross-multiplying to eliminate the fractions:

8 * (3/2)x = 3x

Simplifying further, we have:

12x = 3x

Next, we can isolate the variable x by subtracting 3x from both sides:

12x - 3x = 0

Simplifying the left side of the equation, we get:

9x = 0

Finally, dividing both sides by 9 gives us the solution:

x = 0

Therefore, the solution to the equation (3/2)x = (3x)/8 is x = 0.

To solve the equation, we applied the cross-multiplication method to eliminate the fractions. Cross-multiplication involves multiplying the numerator of one fraction by the denominator of the other and vice versa. By multiplying both sides of the equation by the denominators (2 and 8) and cross-multiplying, we obtain an equation without fractions.

After cross-multiplying, we simplify the equation by performing arithmetic operations. In this case, we multiply 8 by (3/2)x to obtain 12x, and we multiply 3x by 2 to get 6x. Thus, the equation becomes 12x = 6x.

To isolate the variable x, we subtract 6x from both sides of the equation, resulting in 12x - 6x = 0. Combining like terms gives us 6x = 0.

Finally, we divide both sides of the equation by the coefficient of x, which is 6. This step yields the solution x = 0.

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Answer:

A

Step-by-step explanation:

I hope this is correct and have a great day

Answer:

Step-by-step explanation:

392/275 as a fraction

Answer:

a I believe sorry if I'm wrong

Answer:

I think its B: $56.26

Answer:  -12.4(13+19.3)

Step-by-step explanation: I took the quiz

The expression −12.4 (13) + (19.3) (−12.4) in the factored form will be (−12.4) and (32.3).

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

It is also known as the product. If the object n is given to m times then we just simply multiply them.

The expression is given below.

⇒ −12.4 (13) + (19.3) (−12.4)

Taking (−12.4) common from both terms. Then we have

⇒ (−12.4)(13 + 19.3)

⇒ (−12.4)(32.3)

The expression −12.4 (13) + (19.3) (−12.4) in the factored form will be (−12.4) and (32.3).

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The two consecutive integer numbers are 24 and 25.

We can write the two consecutive integers as x and x + 1, where the larger one is x + 1.

We know that 1/5 of the larger is 7 less than 1/2 of the lesser one, then we can write the linear equation:

1/5*(x + 1) = 1/2*x - 7

1/5*x + 1/5 = 1/2*x - 7

So we need to solve that for x:

1/5 + 7 = 1/2*x - 1/5*x

1/5 + 35/5 = 5/10*x - 2/10*x

36/5 = 3/10*x

(36/5)*(10/3) = x = 24

So the smaller is 24, and the larger is x + 1 = 25.

The two consecutive integer numbers are 24 and 25.

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Answer:

Angles 1 & 2 are adjacent

Step-by-step explanation:

Step-by-step explanation:

x² + 2x

x(x + 2)

OR

x² + 2x = 0

x(x + 2) = 0

x = 0 or x + 2 = 0

x = 0 or x = - 2

The statement "If the product of two integers is even, one of them has to be even" is true and can be proven.

It is known that an even number is any integer that is divisible by 2. So, if the product of two integers is even, then it must be divisible by 2. According to the fundamental theorem of arithmetic, every integer can be expressed uniquely as a product of prime numbers.

So, let's assume that the product of two integers is even and neither of them is even. This means that both integers must be odd and can be expressed in the form 2n + 1, where n is any integer. Thus, their product can be expressed as:(2n + 1)(2m + 1) = 4mn + 2m + 2n + 1 = 2(2mn + m + n) + 1This expression is odd because it cannot be divided by 2 without leaving a remainder. Therefore, the product of two odd integers is odd and not even.

Hence, it can be concluded that if the product of two integers is even, then at least one of them has to be even, as proven.

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Answer:

the answer is 5,746 = c

Step-by-step explanation:

Answer:

s = 6, r = 8 or s = 4, r = 7

Step-by-step explanation:

2r - s = 10

2r = 10 + s

r = 5 + s/2 --(1)

rs - s^2 = 12 --(2)

sub (1) into (2):

(5 + s/2)s - s^2 = 12

5s + 0.5s^2 - s^2 = 12

-0.5s^2 + 5s - 12 = 0

s^2 - 10s + 24 = 0

(s - 6)(s - 4) = 0

therefore s = 6 or s = 4

when s = 6, r = 8 and when s = 4, r = 7

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The expression for the area of the framed portrait in terms of w is: A = \(1.5w^{2}\) + 12w + 64.

Simplifying an expression means to write it in its simplest form by combining like terms and removing any redundant or unnecessary elements. There are several techniques you can use to simplify expressions, including:

Combining like terms: Like terms are terms that have the same variable raised to the same power. For example, 2x and 4x are like terms. To simplify an expression, you can add or subtract like terms.

Distributing: Distributing means multiplying a constant or variable by each term within a set of parentheses. For example, if you have the expression 2(x + 3), you can distribute the 2 to each term within the parentheses: 2x + 6.

Factoring: Factoring means finding a common factor among a set of terms and grouping them together. For example, if you have the expression \(x^{2}\) + 4x, you can factor out the x: x(x + 4).

Simplifying rational expressions: Rational expressions are expressions that have one fractional term. To simplify a rational expression, you can cancel out common factors in the numerator and denominator.

Let's call the width of the portrait w and the height h. We know that the height of the portrait is 1.5 times its width, so h = 1.5w.

The area of the portrait is the product of its width and height: A = w * h = w * 1.5w =  \(1.5w^{2}\).

The width of the frame is 4 inches all along its perimeter, so the total width of the framed portrait is w + 4 + 4 = w + 8.

The total height of the framed portrait is h + 4 + 4 = h + 8 = 1.5w + 8.

The area of the framed portrait is the product of its width and height: A = (w + 8) * (1.5w + 8) = (w + 8) * 1.5w + 8 * (w + 8) = 1.5w^2 + 12w + 64.

So, the expression for the area of the framed portrait in terms of w is: A = \(1.5w^{2}\) + 12w + 64.

This expression is already in standard form.

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Answer:

ede 5 years old er = wife 25 Ed 34

Answer:

6x^2-6x-6

Step-by-step explanation:

(x^2-3x+2)+(5x^2-3x-8)

x^2+5x^2-3x+(-3x)+2+(-8)

6x^2-3x-3x+2-8

6x^2-6x+2-8

6x^2-6x-6

Answer:

6.6 pints of white paint is used to paint the bedroom walls

Step-by-step explanation:

Pints of blue paint used to paint the bedroom walls = 8.8

Ratio of blue paint used = \(\frac{1}{4}\)

Therefore,

Ratio of white paint used = \(1-\frac{1}{4}=\frac{3}{4}\)

Pints of white paint used to paint the bedroom walls = \(\frac{3}{4}(8.8)=3(2.2)=6.6\)

Therefore,

6.6 pints of white paint is used to paint the bedroom walls.

Comparing the distances at 3 seconds (39 ft) and 4 seconds (51.96 ft), we can conclude that the distance between the person and the balloon is increasing after 4 seconds.

Let's analyze the situation using the given terms "person", "moving", and "distance".

At the 4-second mark:
1. The person has moved horizontally away from the balloon at a rate of 5 ft/sec.
2. The balloon has risen vertically at a rate of 12 ft/sec.

To determine if the distance between the person and the balloon is increasing or decreasing, we can use the Pythagoras Theorem to find the diagonal distance between them.

After 4 seconds:
- The person has moved 5 ft/sec × 4 sec = 20 ft horizontally.
- The balloon has risen 12 ft/sec × 4 sec = 48 ft vertically.

Now, we can use the Pythagorean theorem to find the distance between the person and the balloon:
distance² = horizontal distance² + vertical distance²

At 4 seconds:
distance² = (20 ft)² + (48 ft)²
distance² = 400 + 2304
distance² = 2704
distance = √2704 ≈ 51.96 ft

Now let's check the distance at 3 seconds:
- The person has moved 5 ft/sec × 3 sec = 15 ft horizontally.
- The balloon has risen 12 ft/sec × 3 sec = 36 ft vertically.

distance² = (15 ft)² + (36 ft)²
distance² = 225 + 1296
distance² = 1521
distance = √1521 = 39 ft

Comparing the distances at 3 seconds (39 ft) and 4 seconds (51.96 ft), we can conclude that the distance between the person and the balloon is increasing after 4 seconds.

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Answer:

-35x + 40

Step-by-step explanation:

I hope this helps!

Answer:

Step-by-step explanation:

I haven't done percentages in a while but the answer after I did it would 15 dollars from where I rounded it. You multiply 15 by 270% which is 2.7 and that's the closest to 40. So Kelly would have 15 dollars.

(Fact check me math people)

The probability that atleast one ball is red is 14/15.

Given that:-

Number of red balls = 4

Number of black balls = 2

One ball is randomly selected, without replacement, the second ball is selected.

We have to find the probability that atleast one ball is red.

There are four ways in which this can happen:-

RR, BR, RB, BB

Where R stands for Red ball and,

B stands for Black ball.

We know that,

Probability that no ball is red + Probability that atleast one ball is red = 1

Hence, we can write,

Probability that atleast one ball is red = 1 - Probability that no ball is red

P(BB) = (2/6)*(1/5) = 1/15

Hence,

Probability that atleast one ball is red = 1 - (1/15) = 14/15

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V = π [(3(\(\sqrt{18/2}\))³/1) - (2(\(\sqrt{18/2}\))⁵/15)] - π [0]

Simplifying this expression will give us the final volume of the solid.

, we need to evaluate the triple integral:

V = ∫₀²π ∫₀ᵣ ∫(18 - 2r²) r dz dr dθ

Integrating with respect to z first, we have:

V = ∫₀²π ∫₀ᵣ (18 - 2r²) r dr dθ

Integrating the volume with respect to r, we get:

V = ∫₀²π [(9r² - 2/3r⁴)]ᵣ₀ dθ

Simplifying the expression inside the brackets and evaluating the integral, we have:

V = ∫₀²π (9r² - 2/3r⁴) dθ

V = π [(9/3)r³ - (2/15)r⁵]ᵣ₀

V = π [(3r³/1) - (2r⁵/15)]ᵣ₀

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Answer:

720

Step-by-step explanation:

6*5*4*3*2=720