Rectangular prism



Your cousin is building a sandbox for his daughter.



How much sand will he need to fill the box? Explain.


How much paint will he need to paint all six surfaces of the sandbox? Explain.


and dont forget to explain

A z-score of 2.14 indicates that Katie's score on the test is quite high and unusual, and places her in the top 2% of the scores in the population.

Katie scored a 93 on a test and her calculated z score was 2.14, that means that her score is 2.14 standard deviations above the mean of the test scores.

A z score represents the number of standard deviations a data point is from the mean of the data set.

A positive z score means that the data point is above the mean, while a negative z score means that the data point is below the mean.

The mean of the test scores was, 80 with a standard deviation of 5, then Katie's z score would be calculated as:

z = (x - μ) / σ

= (93 - 80) / 5

= 2.6

Z scores are useful for comparing data points from different data sets or for comparing data points within the same data set that are measured on different scales.

Katie's score is 2.6 standard deviations above the mean.

A z score of 2.14 would mean that Katie's score is slightly below this value, but still significantly above the mean.

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Answer:

Step-by-step explanation:

Angles ∠1 and ∠2 are

Picture 1

Picture 2

Answer: 185.7 miles

Step-by-step explanation:

To find the total distance, add the smaller distances together.

47.8 + 72 + 65.9 = 185.7

Answer:

2.8 pounds

Step-by-step explanation:

she spends on both types of bell peppers =

$2.56+$1.92=$4.48

$1.60 = 1 pound

$4.48 = ?

= 4.48/1.60

= 2.8 pounds

Answer: Double a number plus 16' .

Answer:

variable would be best modeled as discrete

Step-by-step explanation:

Since there are finite students and finite backpacks, so the weights will also be finite and hence countable, so the variable would be best modeled as discrete

pick a number = x

subtract 3 = x - 3

divide by 5 = (x-3)/5

multiply by 2 = [ (x-3)/5 ] * 2

Subctract the original number

[ (x-3)/5 ] * 2 - x

Answer:

The lowest is the cash price for other options, you have to pay more for a laptop and refrigerator. Then the suitable method is to save up and pay cash.

The process of making choice is by identifying the correct decision, gathering information, and assessing alternative solutions.

If someone were unable to pay cash right now then the suitable method will be

For laptop:

Rent to own payments will be

$150 each month for 12 months, then the total becomes

⇒ 150 × 12 = $1800

The installment plan will be

$100.83 each month for 12 months, then the total becomes

⇒ 100.83 × 12 = $1209.96

The cash price is $1000. So, the lowest is the cash price for other options you have to pay more.

For refrigerator:

Rent to own payments will be

$140 each month for 12 months, then the total becomes

⇒ 140 × 12 = $1680

The installment plan will be

$80.67 each month for 12 months, then the total becomes

⇒ 80.67 × 12 = $968.04

The cash price is $800. So, the lowest is the cash price for other options you have to pay more.

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Answer:

A 24

Step-by-step explanation:

The  answer to the multiple choice question is that a t distribution has slightly broader tails than the Z distribution. This is because the t distribution is based on smaller sample sizes and therefore has more variability, leading to wider tails.

Additionally, the explanation for the other options is as follows:
- A t distribution can be positively or negatively skewed depending on the sample size and distribution of the data.
- A t distribution does have a nonzero mean, just like any other distribution.
- As mentioned earlier, a t distribution has slightly broader tails than the Z distribution.
- A t distribution does have asymptotic tails, meaning they approach but never reach zero as the degrees of freedom increase.

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The equation of the plane that passes through the point (3, 4, 5) and contains the given line x = 5t, y = 3 + t, z = 4 - t is 2x - 8y + 2z = 16.

To obtain this equation, start by substituting the coordinates of the point into the line equation.

Then, you can use the point-normal form to determine the equation of the plane.

This form states that for a point (x0, y0, z0) and a normal vector (a, b, c) to a plane, the equation of the plane is: 

ax + by + cz = a x0 + b y0 + c z0.

For the given line and point, the normal vector to the plane is (2, -8, 2).

Substituting these values into the point-normal form and using the given point yields the equation of the plane:

 2x - 8y + 2z = 16.

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The equation also holds true for k+1. By mathematical induction, we have proved that the equation is true for all positive integers n.

To prove that 12−22+32−…+(−1)n−1n2=(−1)n−1n(n+1)2 whenever n is a positive integer using mathematical induction, we must first establish the base case.

When n=1, we have 1^2 = 1 and (-1)^(1-1) * 1 * (1+1) / 2 = 1. Therefore, the equation holds true for n=1.

Next, we assume that the equation holds true for some arbitrary positive integer k, meaning:

1^2 - 2^2 + 3^2 - ... + (-1)^(k-1) * k^2 = (-1)^(k-1) * k * (k+1) / 2

Now, we must prove that the equation also holds true for k+1:

1^2 - 2^2 + 3^2 - ... + (-1)^(k-1) * k^2 + (-1)^k * (k+1)^2 = (-1)^k * (k+1) * (k+2) / 2

Starting with the left side of the equation, we can substitute in the assumed equation for k:

(-1)^(k-1) * k * (k+1) / 2 + (-1)^k * (k+1)^2

Simplifying this expression:

(-1)^(k-1) * k * (k+1) / 2 - (k+1)^2 * (-1)^k

= (k+1) * [(-1)^(k-1) * k / 2 - (k+1) * (-1)^k]

= (k+1) * [(-1)^(k-1) * k / 2 + (k+1) * (-1)^{k+1}]

= (k+1) * [(-1)^(k-1) * k / 2 + (-1)^k * (k+1)]

= (k+1) * [(-1)^k * (k+1) / 2]

= (-1)^k * (k+1) * (k+2) / 2

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Answer:

4/100=2/50=1/25=0.04 .........

The number that best completes the sequence is 194,481

To find the number that best completes the sequence, let's analyze the pattern:

Looking at the sequence, it appears that every alternate number is the result of squaring the previous number.

3^2 = 9

4^2 = 16

5^2 = 25

20^2 = 400

21^2 = 441

So, based on this pattern, the next number in the sequence would be:

441^2 = 194,481.

Therefore, the number that best completes the sequence is 194,481.

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It should be noted that the cost of the package of cupcakes is 40 cents.

Akilah bought 1 package of cupcakes and 3 balloons, which were 75 cents each. This will be:

c + 3(0.75) = c + 2.25

Natalie bought 3 packages of cupcakes and a birthday candle that cost $1.45. This will be:

3c + 1.45

Therefore, we will equate both equations

c + 2.25 = 3c + 1.45

Collect like terms

3c - c = 2.25 - 1.45

2c = 0.80

Divide

c = 0.80 / 2

c = 0.40

Therefore, the should be noted that the cost of the package of cupcakes is 40 cents.

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Answer:

Step-by-step explanation: answer 1.25 per pound

To find the margin of error for a 95% confidence interval using the t-distribution, we first need to calculate the t-score with degrees of freedom (df) equal to the sample size minus 1 (n-1).

In this case, df = 9. Using a t-table or calculator, the t-score for a 95% confidence level and df = 9 is approximately 2.262. The margin of error can be calculated by multiplying the t-score by the standard error of the mean, which is equal to the standard deviation divided by the square root of the sample size.

In this case, the standard error of the mean is 206 / sqrt(10) = 65.20. Multiplying by the t-score, we get a margin of error of 2.262 * 65.20 = 147.54. To construct the 95% confidence interval, we can use the formula:
sample mean +/- (t-score * standard error of the mean)

Substituting in the values, we get:
$450.50 +/- (2.262 * $65.20) = $450.50 +/- $147.54

So, the 95% confidence interval for the population mean mu is $302.96 to $598.04.

Interpreting the results, we can say with 95% confidence that the true population mean full retail price of cell phones is between $302.96 and $598.04. The margin of error is the amount by which the sample mean may differ from the true population mean, and in this case it is +/- $147.54.


The 95% confidence interval for the population mean (µ) is ($304.1, $596.9), and the margin of error is $146.4. This means we can be 95% confident that the true population mean price of cell phones is between $304.1 and $596.9.

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Answer: here it is 14f-30-15e

Answer: c= 0.79p

Step-by-step explanation:

Divide each cost by the number of pens it have to find the constant change value.

3.95/5 = 0.79

7.90/10= 0 .79  

11.85/15 = 0.79

15.80 / 20 = 0.79

Since the constant change is 0.79  which means that for each pen it will cost you $0.79, then the equation will be  c= $0.79p  where c is the cost and p is the number of pens.

The given equation, y = -1.7x + 8.5, is not in standard form with integer coefficients. The standard form of a linear equation is Ax + By = C, where A, B, and C are integers and A is positive.

To convert the given equation to standard form, we need to eliminate the decimal coefficient. We can do this by multiplying both sides of the equation by 10 to clear the decimal: 10y = -17x + 85 Next, we want the coefficient of x to be positive, so we can multiply both sides of the equation by -1: -10y = 17x - 85

Now, we can rearrange the terms to match the standard form: 17x - 10y = 85 So, the equation of the given line in standard form with integer coefficients is 17x - 10y = 85. To convert the given equation to standard form, we need to eliminate the decimal coefficient.

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Answer:

AB = ½XZ. XZ = 5*2=10. (The middle line of the triangle)

AC = ½YZ. YZ = 7*2=14. The middle line of the triangle)

XY+YZ+XZ=P. P=110+14+24.P=48

Step-by-step explanation:

The exponential function f with base b is defined by f(x) = bˣ, b > 0, and b ≠ 1. Using interval notation, the domain of this function is (-∞, ∞) and the range is (0, ∞).

As an exponential function is defined for all real numbers, its domain is all real numbers, which can be written as (-∞, ∞), in interval notation.

Yet, the range of an exponential function is never zero.

This is due to the fact that the outcome of raising any real number to a positive power, as the exponential function does, will always be greater than 0. As a result, the exponential function with base b has a range of (0, ∞).

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Answer:

Step-by-step explanation:

Answer:

1. maintain constant

2. decrease

3. increase

Monique can choose 20 different sets of 3 of the books

The set of books she can select from the library is an illustration of combination (or selection)

The expression that represents combination is represented as:

\(^nC_r = \frac{n!}{(n - r)!r!}\)

Where:

So, we have:

\(^6C_3 = \frac{6!}{(6 - 3)!3!}\)

Evaluate the differences

\(^6C_3 = \frac{6!}{3!3!}\)

Evaluate the factorials

\(^6C_3 = \frac{720}{6 \times 6}\)

Evaluate the products

\(^6C_3 = \frac{720}{36}\)

Divide 720 by 36

\(^6C_3 = 20\)

Hence, Monique can choose 20 different sets of 3 of the books

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Answer:

it is in fact 20 (for khan)

Step-by-step explanation:

credit goes to person above

Answer:

\(2\frac{1}{4}\)

Step-by-step explanation:

20 1/4 = 20.25

20.25/9 = 2.25

2.25 = \(2\frac{1}{4}\)

Each cake weighs 2.25 pounds.

The weight of each cake will be equal to 2(¹/₄).

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

A mixed expression, also known as a complex fraction, is a fraction that contains a fraction in the numerator, the denominator, or both the numerator and the denominator.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Nine identical cakes weigh a total of 20¼ pounds.

20(¹/₄) = 20.25

20.25/9 = 2.25

2.25 = 2(¹/₄).

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Answer:

a

Step-by-step explanation:

Answer:

Step-by-step explanation:

NOOOOOO FIGURE IT OUT YOUR SELF THATS WHY THEY TEACH YOU DUHHHHHHHHHHHHH

The result of multiplying 18 by 23 is 0.782608696. however, you would write 0.78 if you rounded your response to the nearest hundredth.

First things first, let's review the numerator and denominator of a fraction in case you don't know what they are:

18 (fraction)/23 (denominator)

The denominator, or a number of components, is represented by the numerator.

You can use the following trick to quickly change any fraction to a decimal: Subtract the numerator from the denominator as follows:

= 18/23

= 18 ÷ 23

= 0.78260869565217

You only need to divide 18 by 23. Since the hundredth is to the second decimal place, it is equal to 0.78260869565, which is 0.78 when rounded to the closest hundredth.

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The company's profits on June 1, 2002 is $4500 and the company's profits many years into the future is $1000 per month.

The equation f(t) = (t^2 + 9) / (t^2+2) provides the monthly profits, in thousands of dollar, where t refers to months after June 1, 2002.

The company’s profit on June 1, 2002 using the equation is when t = 0 months

f(0) = (0^2 + 9) / (0^2+2) = 9/2 = 4.5 or $4500.

The company’s profit on many years into the future using the equation is given by:

Limit(t→∞)((t^2+9)/(t^2+2))= Limit(t→∞)(2t/2t)=1

Hence the monthly profit is $1,000.

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