jamilla is building a square sandbox with sides 8 1/2 feet long. she wants to put sand 2 1/2 feet deep in the box. how much sand should jamilla order?

Answer:

Step-by-step explanation:

they wrote the answer already^

Using the system of inequalities y ≥ 0, x ≥ 0, y ≤ -2x + 4 the minimum value of f(x,y) = 3x + y for the feasible region is d) 0.

We need to find the minimum value of the function

f(x,y) = 3x + y

we can use Lagrange multipliers method defining

F(x,y) = f(x,y) - λx g(x,y)  , where g(x,y) = x²+36 x y² - 1, such that

Fx(x,y) = fx(x,y) - λx gx(x,y) = 0

Fy(x,y) = fy(x,y) - λx gy(x,y) = 0

g(x,y)=0

where the sub-indices x and y represent the partial derivatives with respect to x and y, then

fx(x,y) - λx gx(x,y) = 3 - λx(2x) = 0 → x =3/(2xλ)

fy(x,y) - λx gy(x,y) = 1 - λx(36x2xy) = 0 → y =1/(72xλ)

x²+36xy² - 1 = 0 → [3/(2xλ)]²+36*[1/(72xλ)]² - 1 = 0

therefore, Using the system of inequalities y ≥ 0, x ≥ 0, y ≤ -2x + 4 the minimum value of f(x,y) = 3x + y for the feasible region is d) 0.

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To solve this expression, we can use the order of operations, also known as PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (performed left to right), and Addition and Subtraction (performed left to right).

Following this order, we first need to evaluate the exponent, which gives:

1000^3 = 1,000,000,000

Then, we can substitute this value back into the expression:

1000 + 1000^3 = 1000 + 1,000,000,000 = 1,000,000,000 + 1000 = 1,000,001,000

Therefore, 1000 + 1000^3 equals 1,000,001,000.

Answer: 8000000000

Step-by-step explanation:

The probability that a randomly selected region had exactly three hits is approximately 0.139.

In this problem, we can use the Poisson probability distribution formula to find the probability of a randomly selected region having exactly three hits.

The Poisson probability distribution formula is:

P(x) = (e^(-μ) * μ^x) / x!

Where:

P(x) is the probability of x occurrences of an event.

μ is the mean number of occurrences of the event in a given interval.

x is the number of occurrences of the event.

e is the mathematical constant e, approximately equal to 2.71828.

To apply this formula to the problem at hand, we need to determine the values of μ and x.

Since there were a total of 515 bombs that hit the 573 regions, we can calculate the average number of bombs that hit each region:

μ = total number of bombs / number of regions

μ = 515 bombs / 573 regions

μ = 0.8993

Therefore, the mean number of hits per region is 0.8993.

To find the probability that a randomly selected region had exactly three hits, we can plug in x = 3 into the Poisson probability distribution formula:

P(3) = (e^(-0.8993) * (0.8993)^3) / 3!

P(3) ≈ 0.139

Therefore, the probability that a randomly selected region had exactly three hits is approximately 0.139.

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Therefore, the angle V in parallelogram WXUV is 100 degrees. Therefore, the angle L in parallelogram LMJK is 98 degrees. Therefore, the length of side SP in parallelogram SRQP is 26 units. Therefore, the length of side FC in parallelogram FCDE is 12.6 units.

A parallelogram is a quadrilateral (a four-sided polygon) with two pairs of parallel sides. In other words, the opposite sides of a parallelogram are parallel and congruent (equal in length). The properties of a parallelogram include:

Opposite sides are parallel and congruent

Opposite angles are congruent (equal in measure)

Consecutive angles are supplementary (add up to 180 degrees)

Diagonals bisect each other (divide each other into two equal parts)

Some common examples of parallelograms include rectangles, rhombuses, and squares. A rectangle is a parallelogram with four right angles, a rhombus is a parallelogram with four congruent sides, and a square is a parallelogram with four congruent sides and four right angles.

Here,

1. In a parallelogram, opposite angles are equal. Therefore, if angle U is 80 degrees, then angle W must also be 80 degrees.

We know that the sum of the angles in a quadrilateral is 360 degrees, so the sum of the angles at vertices V and U is 360 - 2*80 = 200 degrees.

Since opposite angles in a parallelogram are equal, the angle at vertex V must also be 100 degrees.

2. In a parallelogram, opposite angles are equal. Therefore, if angle J is 98 degrees, then angle L must also be 98 degrees.

We know that the sum of the angles in a quadrilateral is 360 degrees, so the sum of the angles at vertices J and K is 360 - 2*98 = 164 degrees.

Since opposite angles in a parallelogram are equal, the angle at vertex M must also be 98 degrees.

3. In a parallelogram, opposite sides are equal in length. Therefore, if side RQ is 26 units, then side SP must also be 26 units.

This is because SRQP is a parallelogram, so side SR is equal in length to side PQ, and side RQ is equal in length to side SP.

4. In a parallelogram, opposite sides are equal in length. Therefore, if side DE is 12.6 units, then side FC must also be 12.6 units.

This is because FCDE is a parallelogram, so side FC is equal in length to side DE, and side DE is equal in length to side FC.

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Step-by-step explanation:

law of cosine :

c² = a² + b² - 2ab×cos(C)

c being the side opposite of the angle C. a and b are the other 2 sides.

a)

x² = 7² + 9² - 2×7×9×cos(102) = 49 + 81 - 126×cos(102) =

= 130 - 126×cos(102) = 156.196873...

x = 12.49787474... ≈ 12.5

b)

9² = 5² + 12² - 2×5×12×cos(theta)

81 = 25 + 144 - 120×cos(theta)

81 = 169 - 120×cos(theta)

120×cos(theta) = 88

cos(theta) = 88/120 = 11/15 = 0.733333333...

theta = 42.83342807...° ≈ 42.8°

The probability that the mean gain for the sample was between 400 and 800 is approximately 1 or 100%.

What is probability?

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

We can use the central limit theorem to approximate the sampling distribution of the sample mean as normal, with a mean of 651 and a standard deviation of (standard deviation of the population)/√(sample size) = 6/√(34) ≈ 1.03.

Then, we can standardize the values of 400 and 800 using the formula z = (x - μ) / σ, where x is the value of interest, μ is the mean of the sampling distribution, and σ is the standard deviation of the sampling distribution.

For 400:

z = (400 - 651) / 1.03 ≈ -241.75

For 800:

z = (800 - 651) / 1.03 ≈ 143.69

We want to find the probability that the sample mean falls between 400 and 800, which is the same as finding the probability that the standardized value falls between -241.75 and 143.69. We can use a standard normal distribution table or a calculator to find this probability:

P(-241.75 < z < 143.69) ≈ P(z < 143.69) - P(z < -241.75) ≈ 1 - 0 ≈ 1

Therefore, the probability that the mean gain for the sample was between 400 and 800 is approximately 1 or 100%.

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The future value οf the accοunt after 2 years is $1,830.28. If Alice depοsits $1,500 intο an accοunt with an interest rate οf 2.5 percent, cοmpοunded quarterly.

An algebraic expressiοn is a mathematical phrase that cοntains variables, cοnstants, and mathematical οperatiοns such as additiοn, subtractiοn, multiplicatiοn, and divisiοn.

Tο calculate the future value οf the accοunt after 2 years, we can use the fοrmula fοr cοmpοund interest:

[tex]FV = PV * (1 + r/n)^{(n*t)[/tex]

where:

FV is the future value οf the accοunt

PV is the present value (initial depοsit)

r is the annual interest rate (2.5%)

n is the number οf cοmpοunding periοds per year (4, since it is cοmpοunded quarterly)

t is the number οf years (2)

Plugging in the values, we get:

[tex]FV = 1,500 * (1 + 0.025/4)^{(4*2)[/tex]

[tex]FV = 1,500 * 1.02891^8[/tex]

FV = 1,500 * 1.22019

FV = 1,830.28

Therefοre, the future value οf the accοunt after 2 years is $1,830.28.

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Answer:

4,25

Step-by-step explanation:

[tex]3 \frac{5}{4} = \frac{17}{4} = 4 \frac{1}{4} = 4.25[/tex]

There are a total of 90 possible outcomes in this experiment involving three steps.

To find the total number of possible outcomes, you should multiply the number of outcomes for each step because each outcome for step 1 corresponds to each outcome for step 2 and so on. This experiment requires a sequence of three steps. First step can result in 5 possible outcomes, second step can result in 6 possible outcomes, third step can result in 3 possible outcomes. The total number of possible outcomes is the product of the possible outcomes of each step:

Total possible outcomes = 5 x 6 x 3

Total possible outcomes = 90

Therefore, the total number of possible outcomes in this experiment involving three steps is 90.

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Answer:A

Step-by-step explanation:

It would have the greatest chance to be the line on the graph