An aquarium holds 11.43 cubic feet of water, and is 2.6 feet long and 1.4 feet wide. What is its depth? Round your answer to the nearest whole number.

The standard deviation of the sampling distribution is approximately 0.3292.

The behaviour of the sampling distribution of the mean is described by the central limit theorem, a key conclusion in statistics. It asserts that regardless of how the population distribution is shaped, if a random sample of size n is taken from a population with mean and standard deviation, the distribution of sample means will tend towards a normal distribution as n increases.

Because it enables us to utilise the normal distribution to draw conclusions about the population mean based on sample means, the central limit theorem has significant practical ramifications. Additionally, it offers a foundation for confidence interval estimation and statistical hypothesis testing.

The standard deviation is given by the formula:

SD = σ/√(n)

Now, substituting the value of σ = 40, n = 147,400 we have:

SD = σ/√(n) = 40/√(147400) ≈ 0.3292

Hence, the standard deviation of the sampling distribution is approximately 0.3292.

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The calculated amount of money you have left over is $39,400

From the question, we have the following parameters that can be used in our computation:

Cost price in 2010 = $264,000

Selling price today = $389,000.

This means that the profit is

Profit = 389,000 - 264,000

Evaluate

Profit = 125000

You have purchased a new home for $428,000 at 20% deposit

So, we have amount left is

Amount = 125000 - 20% * 428,000

Evaluate

Amount = 39400

Hence, the amount of money you have left over is $39400

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Hello!

4 times the sum of x and y

4 * (x + y)

it's a mutliplication

the sum of 4x and y

= 4x + y

it's a sum

Answer:one is multiplying other is some.

Step-by-step explanation:

4xy and =4xy

these two are

Answer:

I will demonstrate the first two for you. The answer is 6, 30, 54, 78, 102.

The answer to the second question is -3, 21, 45, 63, 93.

Step-by-step explanation:

Pardon the messiness. I hope this clarifies how to do it from now on! If not, please let me know if you need more help! xoxo

Answer:

\(x = 20000000\)

Step-by-step explanation:

Recall the power property of logarithms which states:

\(log(a^n)=n\,\,log(a)\)

to re-write \(2\,log(4)=log(4^2)=log(16)\)

and then use the product and quotient rules of logarithms:

\(log (A*B)=log(A)+log(B)\)

and

\(log (\frac{A}{B} )=log(A)-log(B)\)

to rewrite the combination of logarithms on the left of the equal sign as a single logarithm:

\(log(x)+log(8)-2\,\,log(4)=7\\log(x)+log(8)-log(16)=7\\log(\frac{8\,x}{16}) =7\\log(\frac{x}{2}) =7\)

and now re-write this equation in exponent form to get rid of the logarithm:

\(10^7=\frac{x}{2} \\2\,\,\,10^7 = x\\x = 20000000\)

Answer:

0.288

Step-by-step explanation:

Given that :

Correlation (R) = 0.48

Slope of linear model which predicts Lifespan from years of education (m) = 0.8

To determine the value of slope of the model which predicts years of eductauoon from lifespan:

The square of the regression Coefficient is multiplied by the inverse of the slope of linear model which predicts Lifespan from years of education

Hence,

(R² * 1/m)

0.48² * 1/0.8

0.2304 * 1.25

= 0.288

9514 1404 393

Answer:

  (b)  He is correct. The tea will cool exponentially since it cools at a percentage rate every minute.

Step-by-step explanation:

Newton's Law of Cooling says the change in temperature is proportional to the temperature. This relation gives rise to an exponential function describing the temperature.

In this description, the temperature referred to is the difference between the temperature of the object and the temperature of the environment to/from which heat is being transferred.

Juan is only partially correct. The function is exponential, but the temperature that should be used in his equation is not the temperature of the tea, but the temperature difference between the tea and his desk.

__

The curve is not linear and not parabolic, excluding the other answer choices.

Answer: y = 3 or y=7

Step-by-step explanation:

\(y^{2} -10y+21\)

what 2 factors of 21 can equal 10 when added together (1*21- no 3*7- yes)

Factor

\((y-3)(y-7)\)

y-3=0

y=3

or y-7=0

y=7

Hello!

We will go tu use the pythagorean theorem!

So:

BA² = BC² + AC²

AC² = BA² - BC²

AC² = 52² - 20²

AC² = 2304

AC = √2304

AC = 48

Answer:

The range of the function is: -∞≤y≤∞.

Consider the provided function.

The range of the function is the set of all values which a function can produce or the set of y values which a function can produce after substitute the possible values of x.

The range of a cubic root function is all real numbers.

Now consider the provided function.

The above function can be written as:

Taking cube on both sides.

The graph of the function is shown in figure 1:

For any value of x we can find different value of y.

Here, the cube root function can process negative values. Since, the function can produce any values, the range of the given function is  -∞≤y≤∞ .

Therefore, the range of the function is: -∞≤y≤∞ (A).

Answer:you need to show the diagram in order for me to

Step-by-step explanation:

From the question, we have that:

1. Chang had $10,000 to invest.

2. Let x the part Chang invested in an account that paid 5% simple interest per year.

3. Let y the part Chang invested in an account that paid 8% simple interest per year.

4. After one year, he received $740 in interest.

Then we can translate the situation as follows:

And we can solve this system using the substitution method to find x and y as follows:

6. We can multiply the first equation by 100 as follows:

7. Substituting y in terms of x, we have:

8. Using the distributive property, we have:

Therefore, x = $2000, and knowing that:

If we apply one of the above expressions, we have:

Therefore, in summary, Chang invested $2000 at 5% of simple interest, and $8000 at 8%. He invested

First account (5%) = $2000.

Second account (8%) = $8000.

Answer:

52$

Step-by-step explanation:

6 x 45 = 270

530 - 270 = 260

260/5 = 52

Answer:

A = $2,122.20

Step-by-step explanation:

A = P(1 + r/k)^kt

Where,

A = future amount

P = principal = $1,500

r = interest rate = 7%

k = number of periods compounded = 4

t = years = 5 years

A = P(1 + r/k)^kt

= 1,500 (1 + 0.07/4)^4*5

= 1,500 (1 + 0.0175)^20

= 1,500 (1.0175)^20

= 1,500 (1.4148)

= 2,122.20

A = $2,122.20

Answer:

p = 7

Step-by-step explanation:

trust me

Answer:

p = 7

Step-by-step explanation:

Given value of q = 4 so,

5p - 11 = 6 × 4

=> 5p = 24 + 11

=> 5p = 35

\( = > p = \frac{35}{5} \)

=> p = 7(Ans)

The correct option is

This corresponds to option B

Answer:

1/5

Step-by-step explanation:

just pretend 5 is 5/1 and then flip it, so 1/5

Option B

Hope it helps.

Do comment if you have any query.

Answer:

160 boxes = 384 pounds

Step-by-step explanation:

sgshshdhdjd

Answer:

The common difference in the given sequence is 5.

Step-by-step explanation:

The common difference in the sequence is 5 because they all add by 5 each time for example 5 + 5= 10 and 10+5=15

Answer:

Deductive reasoning

Step-by-step explanation:

Deductive reasoning

Answer:

24

Step-by-step explanation:

Remark

This can be done with a proportion which consists of 2 equal ratios. That's 4 parts total. If you know 3 of the parts, you can find the 4th.

Givens

Stars1  6

Moon1 4

Starts2 x

Moon2 16

Formula

stars1/moon1 = stars2/moon2

Solution

6/4 = x / 16         Multiply by 16

6 * 16/4 = x

Answer: 96/4 = 24

Equation (12x² - 6x)(4x - 2) simplifies to 12x(2x - 1)².

We can start by factoring out the greatest common factor from both terms, which is 6x:

(12x² - 6x)(4x - 2) = 6x(2x - 1)(4x - 2)

Next, we can simplify the expression by factoring out the common factor (4x - 2) from the remaining terms (2x - 1):

6x(2x - 1)(4x - 2) = 6x(2x - 1) × 2(2x - 1)

Now we have two factors that are the same, (2x - 1), so we can combine them by multiplying them together:

6x(2x - 1) × 2(2x - 1) = 12x(2x - 1)²

Therefore, (12x² - 6x)(4x - 2) simplifies to 12x(2x - 1)².

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Given question is incomplete, the complete question is below

Assuming that x ≠ 1/2, simplify (12x² - 6x)(4x - 2).

Answer:

1/100, 0.01, and shade one of the collums

Step-by-step explanation:

A. 0.1 or 10%

B. 0.01 or 1%

C. 0.0001 or 0.01%

D. 0.01 or 1%

Note: In textbooks like this, you should probably check the back of the book, they usually have detailed answers/rationales.

Answer:

maybe add the picture?

Step-by-step explanation:

Answer: Rhombus

Step-by-step explanation:

Answer:

f(4)=-2

Step-by-step explanation:

Plug in 4 into the equation. f(4)= 2(4)-10 then simplify the equation. Multiply 2 by 4, then subtract 10.

There will be approximately $594,311.34 in Nathan's daughter's RESP after 25 years of depositing $940 every 2 months with a 3.99% annual interest rate compounded quarterly.

To calculate the amount in Nathan's daughter's RESP after 25 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = Final amount (amount in the account after 25 years)

P = Principal amount (amount deposited every 2 months)

r = Annual interest rate (in decimal form)

n = Number of times the interest is compounded per year

t = Number of years

In this case, Nathan deposits $940 every 2 months, so the principal amount (P) is $940. The annual interest rate (r) is 3.99% or 0.0399 in decimal form. Since the interest is compounded quarterly, the compounding frequency (n) is 4. The number of years (t) is 25.

Since Nathan deposits every 2 months, we need to calculate the total number of deposits made over 25 years. There are 12 months in a year, so in 25 years, there will be 25 * 12 = 300 months. However, since Nathan deposits every 2 months, the number of deposits (m) is 300 / 2 = 150.

Now, we can substitute these values into the formula:

A = 940(1 + 0.0399/4)^(4*25)

Calculating the exponent first:

(1 + 0.0399/4)^(4*25) ≈ 2.703236

Now, substituting the calculated exponent and the number of deposits into the formula:

A = 940 * 2.703236 * 150 ≈ $594,311.34

Therefore, there will be approximately $594,311.34 in Nathan's daughter's RESP after 25 years of depositing $940 every 2 months with a 3.99% annual interest rate compounded quarterly.

It's important to note that this calculation assumes Nathan makes the same $940 deposit every 2 months consistently over the 25-year period and does not make any withdrawals from the account during that time. Additionally, the actual amount may vary slightly due to rounding and any potential changes in interest rates over the years.

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The order of the matrices of each product is given as follows:

AB is nonexistent, BA is nonexistent.

Multiplication of matrices is applied multiplying the rows of the first matrix by the columns of the second matrix, and hence the number of columns of the first matrix must be equal to the number of rows of the second matrix.

For the product AB, we have that:

Hence the product is nonexistent.

For the product BA, we have that:

Hence the product is nonexistent.

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The evaluation of the forms of the cubic polynomials, indicates that we get;

Question 1; C = -64

Question 2; The polynomial is; f(x) = x³ - 9·x² + 11·x + 21

A cubic polynomial is a polynomial of order three, and which can be expressed in the form; F(x) = A·x³ + B·x² + C·x + D

Question 1;

The specified polynomial can be presented as follows;

F(x) = A·x³ + B·x² + C·x + D

The zeros of the polynomial are;

x = 4, x = 8, and x = -8

Therefore, we get;

The polynomial is; f(x) = (x - 4) × (x - 8) × (x + 8) = x³ - 4·x² - 64·x + 256

Comparison of the polynomial with the function, F(x) = A·x³ + B·x² + C·x + D, indicates that we get;

A = 1, B = -4, C = -64, and D = 256

Therefore; C = -64

Question 2;

The polynomial form is; g(x) = A·x³ + B·x² + C··x + D
The zeros of the polynomial are; x = 3, x = 7, and x = -1

Therefore, we get; f(x) = (x - 3) × (x - 7) × (x + 1) = x³ - 9·x² + 11·x + 21

f(x) = x³ - 9·x² + 11·x + 21

Comparison indicates that we get;
A = 1, B = -9, C = 11, and D = 21

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