2. (8 points) (See Example 4, page 467) An aquarium 2 m long, 1 m wide, and 1 m deep is full of water. Find the work needed to pump half of the water out of the aquarium. (Use the fact that the density of water is 1000 kg/m3.)

Answers:

a = 3

b = 3

c = -6

=====================================

Explanation:

The roots are x = 1 and x = -2. This leads to the factors x-1 and x+2 respectively.

This is because something like x = 1 becomes x-1 = 0 after subtracting 1 from both sides. For x = -2, we add 2 to both sides getting x+2 = 0.

The factorization is y = a(x-1)(x+2)

Plug in (x,y) = (2,12) and solve for 'a'

y = a(x-1)(x+2)

12 = a(2-1)(2+2)

12 = a(1)(4)

12 = 4a

12/4 = a

3 = a

a = 3

So we have y = a(x-1)(x+2) update to y = 3(x-1)(x+2)

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

The last thing we need to do is expand everything out (use the FOIL rule then distributive rule) to get the equation into standard form

y = 3(x-1)(x+2)

y = 3(x^2+2x-1x-2)

y = 3(x^2+x-2)

y = 3x^2+3x-6

Comparing this to y = ax^2+bx+c shows that:

a = 3

b = 3

c = -6

The graph is below.

The best description of the probability of drawing a king from the deck is 1 out of 13, or 1/13.

The probability of drawing a king from a standard deck of 52 playing cards can be determined by dividing the number of favorable outcomes (number of kings) by the total number of possible outcomes (total number of cards in the deck).

In a standard deck, there are 4 kings (one king for each suit: hearts, diamonds, clubs, and spades). Therefore, the number of favorable outcomes is 4.

The total number of possible outcomes is 52 (the total number of cards in the deck).

So, the probability of drawing a king is:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 4 / 52

Simplifying the fraction gives us:

Probability = 1 / 13

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Answer: $6.88

Step-by-step explanation:

Answer:

$7.52

Step-by-step explanation:

7.20×4.5%=32

7.20+32=$7.52

Answer:

Step-by-step

Math Symbols: 4 + y = -36

Subtract 4 from both sides.

y = -40

Answer:

-41

Step-by-step explanation:

(f∘g)(-5)

f(g(-5))

4(2(-5)) - 1

4(-10) - 1

-40 - 1

= -41

Answer:

-41.

Step-by-step explanation:

g(-5) = 2*-5 = -10

(f o g)(-5) =  4(-10) - 1

= -41.

16%

Step-by-step explanation:

500/100 = 1% = 5

80 / 5 = 16

Triangle ABC is the term used to refer to a triangle with the vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are discovered \(A^2 = B ^2 + c^2\)  => AC = \(\sqrt{115}\)

Given that it has three sides and three vertices, a triangle qualifies as a polygon. It belongs to the fundamental geometric shapes.

Triangles are polygons because they have three sides and three corners. The points where the three sides of the triangle converge are referred to as the triangle's corners. 180 degrees is obtained by multiplying three triangle angles.

Here, in this triangle by Pythagorean theorem

\(A^2 = B ^2 + c^2\)

AC = \(\sqrt{14^2- 9^2}\)

AC = \(\sqrt{196- 81}\)

Ac = \(\sqrt{115}\)

Therefore, We can state that this triangle conforms to the Pythagorean theorem after answering the offered question.

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Check the picture below.

The probability that the mean height of 64 dogs is between 27 and 28.5 inches is approximately 0.8531.

We can use the central limit theorem to approximate the distribution of the sample mean. The central limit theorem states that if we take a large enough sample from a population, the sample mean will be approximately normally distributed with mean equal to the population mean and standard deviation equal to the population standard deviation divided by the square root of the sample size. In this case, we have:

Population mean (μ) = 28 inches

Population standard deviation (σ) = 4 inches

Sample size (n) = 64

a) To find the probability that the mean height of 64 dogs is less than 27 inches, we need to standardize the sample mean and find the corresponding area under the standard normal distribution. We have:

z = (sample mean - population mean) / (population standard deviation / sqrt(sample size))

z = (27 - 28) / (4 / sqrt(64))

z = -2

Using a standard normal distribution table or calculator, we find that the probability of z being less than -2 is approximately 0.0228. Therefore, the probability that the mean height of 64 dogs is less than 27 inches is approximately 0.0228.

b) To find the probability that the mean height of 64 dogs is greater than 28.5 inches, we standardize the sample mean and find the area to the right of the standardized value. We have:

z = (sample mean - population mean) / (population standard deviation / sqrt(sample size))

z = (28.5 - 28) / (4 / sqrt(64))

z = 1

Using a standard normal distribution table or calculator, we find that the probability of z being greater than 1 is approximately 0.1587. Therefore, the probability that the mean height of 64 dogs is greater than 28.5 inches is approximately 0.1587.

c) To find the probability that the mean height of 64 dogs is between 27 and 28.5 inches, we need to find the area under the standard normal distribution between the two standardized values. We have:

z1 = (27 - 28) / (4 / sqrt(64))

z1 = -2

z2 = (28.5 - 28) / (4 / sqrt(64))

z2 = 1

Using a standard normal distribution table or calculator, we find that the probability of z being between -2 and 1 is approximately 0.8531. Therefore, the probability that the mean height of 64 dogs is between 27 and 28.5 inches is approximately 0.8531.

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Answer:

....

Step-by-step explanation:

Answer: y=0.5x+8

Step-by-step explanation:

Given:

f(0) = 2

So first of all, we let x = 2021, y = 0:

Then, F(2021) = 2021 + f(0)

Since f(0) = 2, then f(2021) = 2021 + 2 = 2023.

To add, the process that relates an input to an output is called a function.

There are always three main parts of a function, namely:

Input

The Relationship

The Output

The classic way of writing a function is "f(x) = ... ".

What goes into the function is put inside parentheses () after the name of the function: So, f(x) shows us the function is called "f", and "x" goes in.

What a function does with the input can be usually seen as:

f(x) = x2 reveals to us that function "f" takes "x" and squares it.

Answer: C

Step-by-step explanation:

\((2\pi)(6) \left(\frac{90}{360} \right) \approx \boxed{9.42}\)

for every 13 dogs, there are 25 cats. is the answer.

Answer:

56

Step-by-step explanation:

48 ounces would feed 6 people and if 16 oz is for two people than 8 oz is for one person. So, 48 plus 8 is 56.

If Mario will use all the rope as instructed right the number of 8 1/4 inch sections of  Mario that can come from the rope is: 6.

First step is to convert the 7 feet rope to inches

7 feet robes = 84 inches

Second step is to find the inches of rope left

Inches of rope left =84 inches - 34.5 inches

Inches of rope left = 49.5 inches

Now let find the number of 8 1/4 inch sections

Number of 8 1/4 inch sections =49.5 / 8.25

Number of 8 1/4 inch sections =6

Therefore 6 is the number of 8 1/4 inch sections .

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\(\huge \bf༆ Answer ༄\)

Total surface Area of the cuboid is ~

Surface area = 256 ft^2

Surface area (SA) = Total area on the Surface only

SA of cuboid = Area of rectangle (2 sides) + Area of square (2 sides) + Area of other rectangle (2 sides)

SA = 2(12x5) + 2(4x5) + 2(12x4)

SA = 120 + 40 + 96

SA = 256 ft^2

Answer:

i think the answer would be 24 im not to sure

Answer:

$327.00 (total interest)

Step-by-step explanation:

This is simple interest

Converting R percent to r a decimal

r = R/100 = 3%/100 = 0.03 per year.

A = 300[1 + (0.03 × 3)] = 327

A = $327.00

Answer: 27.82

Step-by-step explanation: Based on Principal Amount of $300, at an interest rate of 3%, over 3 year(s):

The temperature of exhaled air would also be around 37 degrees Celsius

The temperature of exhaled air is typically very close to the body's internal temperature, which is approximately 37 degrees Celsius (98.6 degrees Fahrenheit).

When we inhale air, it is warmed and humidified as it passes through our respiratory system, reaching a similar temperature to our body's internal temperature. This process helps to maintain the optimal conditions for various physiological processes in our body.

Therefore, the temperature of exhaled air would also be around 37 degrees Celsius (98.6 degrees Fahrenheit) under normal circumstances.

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Answer:

base x height the volume is 8

Step-by-step explanation:

base = 4 x 2

height is 1

so 8

Answer:

8 meter

Step-by-step explanation:

1:200

this equation means for every 1 cm on a map is 200 m in real life

4*200=800 which means equal 8 meter long

Answer:

I can help you for free if you want!

Step-by-step explanation:

I'm in 11th grade, so I know most 7th-grade math things.

Answer:

-8 is the answer, have a good day :)

Step-by-step explanation:

Hypothesis testing and confidence intervals are commonly used in health care research to make statistical inferences and draw conclusions about population parameters.

Hypothesis testing allows researchers to test specific claims or hypotheses, while confidence intervals provide a range of plausible values for a population parameter.

In health care, hypothesis testing can be used to investigate various research questions.

For example, a researcher may hypothesize that a new treatment is more effective than an existing treatment for a certain medical condition. By conducting a hypothesis test, the researcher can analyze data from a sample of patients and determine if there is sufficient evidence to support the hypothesis.

Confidence intervals, on the other hand, provide an estimate of the range within which a population parameter is likely to fall. In health care, confidence intervals are often used to estimate the true prevalence of a disease or the effectiveness of an intervention.

For instance, researchers may estimate the confidence interval for the proportion of individuals with a certain disease in a population based on a sample of patients. This interval provides a measure of uncertainty and helps researchers understand the precision of their estimates.

Both hypothesis testing and confidence intervals are valuable statistical tools in health care research, allowing researchers to make evidence-based decisions, draw meaningful conclusions, and contribute to advancements in medical knowledge and practice.

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Answer:

-1, 1, 3

Step-by-step explanation:

Let x equal the first odd integer.

The three consecutive odd integers would be represented by x, then x+2, then x+4.

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

Solve for x

3x + 2x + 8 = 4x + 8 -1

5x + 8 = 4x + 7

x = -1

Answer:

Below.

Step-by-step explanation:

What we know: 4 Shaded. 12 in total.

That means,

12 divided by 4=3.

1/3 of the shape is shaded.

Answer:

-3 < w < 8 or (-3, 8)

Step-by-step explanation:

Am i get it right?

Answer:

it is 8 -3 to the power of 5