Find the volume of the right pyramid shown below.

The set of -values that are appropriate in the given situation is known as the practical domain. Solution: F (x) = 2 x is the function's formula.

You are not accounting for or measuring any rainfall that occurred prior to the storm's onset, thus there is a total of 0 inches of precipitation at that time. Six and a half hours are spent in the storm.

Example :

Miami, Florida, experiences heavy rainfall due to a powerful hurricane. A 2 inch per hour downpour is occurring. In 6 and a half hours, the storm is over. The total amount of rain that has fallen throughout time should be modeled mathematically. The function is plotted. For this situation, identify the practical domain. The set of -values that are appropriate in the given situation is known as the practical domain.

Solution: Since there was no rain measured or included before the storm began, the function is as follows:

f(x)= 2x

There was 0 inches of rain at the moment the storm began. Six and a half hours are spent in the storm. f(6.5) = 2(6.5) = 13 inches of rain had been recorded at 6.5 hours, or so. It follows in words what the domain and range are:

Domain :

All real numbers between and including 0 and 6.5 hours.

Range :

All real numbers between and including 0 and 1.3 inches.

Domain and range can be expressed more easily with the help of some helpful notation, such as the following:

Domain { x∈R,0≤ x ≤ 6.5} [0,6.5]

Range { x∈R,0≤ x ≤ 6.13 [0,13].

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The number of people that attended the game in each cost category is Faculty: 7,000,Alumni: 18,000,Public: 18,000,Veterans: 4,000

To determine the number of people that attended the game in each cost category,  to consider the given information and set up a system of equations to solve for the unknowns. Let's break down the problem step by step.

Let's denote the number of people in each cost category as follows:

Faculty: F

Alumni: A

Public: P

Veterans: V

The number of alumni is 11,000 more than the faculty, so we have the equation:

A = F + 11,000

The number of public plus alumni together was 10 times the number of veterans, so  the equation:

P + A = 10V

The number of faculty plus alumni together was the same as the number of veterans, so we have the equation:

F + A = V

The total number of people attending the game is the sum of the people in each category, so  the equation:

F + A + P + V = 100,000

Now, use these equations to solve for the unknowns.

First, substitute equation 1 into equations 2 and 3:

P + (F + 11,000) = 10V

F + (F + 11,000) = V

Simplify these equations:

P + F + 11,000 = 10V

2F + 11,000 = V

Next, substitute these equations into equation 4:

F + (F + 11,000) + P + (2F + 11,000) = 100,000

Simplify and combine like terms:

4F + 22,000 + P = 100,000

Subtract 22,000 from both sides:

4F + P = 78,000

Now a system of two equations:

P + F + 11,000 = 10V

4F + P = 78,000

solve this system of equations to find the values of F, P, and V.

By solving the system,

F = 7,000

P = 18,000

V = 4,000

Finally, substitute these values back into equation 1 to find the value of A:

A = F + 11,000 = 7,000 + 11,000 = 18,000

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Answer:

Step-by-step explanation:

Since the length, i, of the rectangle is greater than its width, we can write:

i > w

The formula for the perimeter of a rectangle is:

P = 2(i + w)

We know the perimeter is at least 30 inches, so we can write:

2(i + w) ≥ 30

Simplifying the inequality, we get:

i + w ≥ 15

Now we can substitute i > w into the inequality:

w + w ≥ 15

2w ≥ 15

w ≥ 7.5

Therefore, the range of possible widths for the rectangle is:

w ≥ 7.5

This value represents the present worth below which the probability is 0.5, indicating a negative present worth.

To estimate the probability that the present worth is negative using the NORM.INV function in Excel,

we need to calculate the present worth of the project and then determine the corresponding probability using the normal distribution.

The present worth of the project can be calculated by finding the sum of the present values of the annual receipts over the 10-year period, minus the initial investment. The present value of each annual receipt can be calculated by discounting it back to the present using the minimum attractive rate of return (MARR).

Using the given information, the present value of the initial investment is $10,000. The present value of each annual receipt is calculated by dividing the expected return of $1,800 by \((1+MARR)^t\),

where t is the year. We then sum up these present values for each year.

We can use the NORM.INV function in Excel to estimate the probability of a negative present worth. The function requires the probability value, mean, and standard deviation as inputs.

Since we have a mean and standard deviation for the present worth,

we can calculate the corresponding probability of a negative present worth using NORM.INV.

This value represents the present worth below which the probability is 0.5. By using the NORM.INV function,

we can estimate the probability that the present worth is negative based on the given data and assumptions.

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Answer:

Reflexive Property

(1) The significant figure will be 710.

Hence the correct option is (b).

(2) (a) The modulus of A and B are,

| A | = √62

| B | = √30

(b) The value of A + B = 7 i - 2 j + 9 k

(c) The value of A - B = -3 i - 4 j + 5 k

(3) (a) a ⋅ (b × c) is meaningful and result is a scalar.

(b) a × (b ⋅ c) is not meaningful.

(c) a × (b × c) is meaningful and result is a vector.

(d) (a ⋅ b) × c is not meaningful.

(e) (a ⋅ b) × (c ⋅ d) is not meaningful.

(f) (a × b) ⋅ (c × d) is meaningful and result is a scalar.

The not meaningful is because to conduct cross product we need two vectors.

(4) Given lines are parallel because the cross product of the vectors along that lines is zero vector.

(1) Given the multiplication is,

20.6 × 5.5 × 6.27

That gives the result,

20.6 × 5.5 × 6.27 = 710.391

Here significant figure will be 710.

So the correct option is (b).

(2) Given the vectors are,

A = 2 i - 3 j + 7 k

B = 5 i + j + 2 k

(a) The modulus of A and B are,

| A | = √[2² + (-3)² + 7²] = √62

| B | = √[5² + 1² + 2²] = √30

(b) The value of A + B vector is,

A + B = [2 i - 3 j + 7 k] + [5 i + j + 2 k] = 7 i - 2 j + 9 k

(c) The value of A - B vector is,

A - B = [2 i - 3 j + 7 k] - [5 i + j + 2 k] = -3 i - 4 j + 5 k

(3) We know that the cross product gives vector result and dot product gives scalar result.

The statements are,

(a) a ⋅ (b × c) is meaningful and result is a scalar.

(b) a × (b ⋅ c) is not meaningful.

(c) a × (b × c) is meaningful and result is a vector.

(d) (a ⋅ b) × c is not meaningful.

(e) (a ⋅ b) × (c ⋅ d) is not meaningful.

(f) (a × b) ⋅ (c × d) is meaningful and result is a scalar.

The not meaningful is because to conduct cross product we need two vectors.

(4) Here for first line vector is,

A = [(-2) - (-4)] i + [0 - (-6)] j + [(-3) - 1] k = 2 i + 6 j - 4 k

for second line vector is,

B = [5 - 10] i + [3 - 18] j + [14 - 4] k = -5 i - 15 j + 10 k

So now the cross product is,

A × B = \(\left[\begin{array}{ccc}i&j&k\\2&6&-4\\-5&-15&10\end{array}\right]\) = 0 i + 0 j + 0 k

So the cross vector is a zero vector so the initial vectors are parallel to each other.

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\(\huge \bf༆ Answer ༄\)

Let's simply ~

\({ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \: - 5 {x}^{2} (4x - 6 {x}^{2} - 3)\)

\({ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \:( - 5x {}^{2} \times 4x) - ( - 5 {x}^{2} \times 6 {x}^{2} ) - ( - 5 {x}^{2} \times 3)\)

\({ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \: - 20 {x}^{3} - ( - 30 {x}^{4} ) - ( - 15 {x}^{2} )\)

\({ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \: - 20 {x}^{3} + 30 {x}^{4} + 15 {x}^{2} \)

\({ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \:30 {x}^{4} - 20 {x}^{3} + 15 {x}^{2} \)

Answer:

It was correct for plato!

Step-by-step explanation:

Answer: I have put picture in there

Step-by-step explanation:

Answer:

61

Step-by-step explanation:

x+x+1+x+2 = 183

3x+3 = 183

3x = 180

x = 60

Second number = x+1 = 61

Answer:

Rectangle

Step-by-step explanation:

Plz Mark Brainliest Thanks

Answer:

9/40 or 0.225

Step-by-step explanation:

Answer:

Step-by-step explanation:

Numbers: HCF of 18 and 30

18: 2 * 3 * 3

30:2 * 3 * 5

HCF: 2 and 3 = 6

a: a * a and a.

HCF = a

b: b

c: c and c*c

HCF: C

Answer: 6*a*b*c(3a + 5*c)

Note: for this question one of the factors is the HCF and the other is what remains when the HCF is taken out.

The true statements are, Line A B and Line C G are parallel, Line C G and Line R S are perpendicular, Line A B and Line R S must intersect and Line segment C G lies in plane X.

Given that Planes X and Y intersect at a right angle. Line AB and CG are on plane X, while line RS is on plane Y. Therefore, line CG lies on plane X.

Since both line AB and CG lie on the same plane, they are parallel to each other.

Since plane X and plane Y are perpendicular to each other and line CG is on plane X while line RS is on plane Y, this means that Line CG and Line RS are perpendicular to each other.

Line AB and Line RS may or may not intersect. They could be skew lines, which do not intersect and are not parallel.

Line segment CG lies on plane X since it is contained within the plane that contains points C, G, and either A or B.

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The question is -

Which statements are true? Select three options.

a. Line A B and Line C G are parallel.

b. Line A B and Line R S are parallel.

c. Line C G and Line R S are perpendicular.

d. Line A B and Line R S must intersect.

e. Line segment C G lies in plane X.

f. Line segment R S lies in plane X.

Answer: ace

Step-by-step explanation:

The area of the puddle is 1810 cm^2.

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object. Take a pencil and draw a square on a piece of paper. It is a 2-D figure. The space the shape takes up on the paper is called its Area.

Area is a measure of how much space there is inside a shape. Calculating the area of a shape or surface can be useful in everyday life, for example you may need to know how much paint to buy to cover a wall or how much grass seed you need to sow a lawn.

It had rained for 4 hours with the hole in the roof (from 3am to 7am).

4 hours = 4×60 = 240 minutes.

Thus the radius of the puddle grew to

240×0.1 = 24 cm

therefore the area of the puddle was

pi×r² = pi×24² = 576pi = 1,809.557368... cm² ≈

≈ 1,810 cm²

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Because results has been normally distributed and every group of 100 people would have different heights .

The probability that Emma is interviewed first and Bob is interviewed second is 1/90 or 0.0111 (rounded to four decimal places).Hence, the correct option is A. 1/90.

Given:Six people, named Anna, Bob, Chandra, Darnell, Emma, and Francisco, will be interviewed for a job. The interviewer will choose two at random to interview on the first day.

To find:Probability that Emma is interviewed first and Bob is interviewed second.Solution:Total number of ways to choose 2 out of 6 people = 6C2 (using combination formula)

Number of ways Emma is interviewed first and Bob is interviewed second = 1 (since we are given that)Number of ways interviewer can choose 2 people out of remaining 4 = 4C2 (using combination formula)

Total number of ways = 6C2 × 4C2 = (6 × 5 / 2 × 1) × (4 × 3 / 2 × 1) = 15 × 6 = 90 ways

The probability of selecting two candidates, if there are six candidates available, is therefore, (2/6) * (1/5) = 1/15. (Probability of Emma being chosen on the first day multiplied by the probability of Bob being chosen on the second day)

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Answer:

2,169,490

Step-by-step explanation:

Answer:

80% are big dogs

Step-by-step explanation:

Answer:

Step-by-step explanation:

Both triangles are similar by SAS property,

that means corresponding sides are proportional,so,

5/6 = 15/N

= 6/5 = N/15

N = (6×15)/5

N = 6×3

N = 18

The given statement "The last indented line of a conditional proof sequence should always be the consequent of the conditional you are trying to prove" is True because this approach confirms that the consequent logically follows the antecedent and validates the conditional statement as true.

A conditional proof is a logical reasoning method used to establish the truth of a conditional statement (if P, then Q) by assuming the antecedent (P) and demonstrating that the consequent (Q) logically follows.

In conditional proof, you start by assuming the antecedent as a temporary hypothesis. Then, using valid inference rules and previously established premises, you deduce the consequent. If you can successfully derive the consequent, this shows that if the antecedent were true, the consequent would also be true. Thus, the conditional statement is proven to be true.

In summary, the last indented line of a conditional proof sequence should indeed be the consequent of the conditional you are trying to prove. This approach confirms that the consequent logically follows the antecedent and validates the conditional statement as true.

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The approximate angle of sunrise for February 3 at WPU, NJ, with an approximate latitude of 40 degrees north, would be around 66.5 degrees, and the approximate angle of sunset would be around 293.5 degrees.

To determine the approximate angle of sunrise and sunset for a specific location and date, we can use the knowledge that on the equinox, the sunrise and sunset angles are at their extremes. The equinox occurs around March 21 and September 21. Since we are looking for February 3, which is closer to the March equinox, we can use the values for the March equinox.

On the equinox, the sunrise and sunset angles are approximately 66.5 degrees and 293.5 degrees, respectively. These values correspond to the direction measured clockwise from due north.

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The concept of consumer surplus refers to the satisfaction that consumers get from purchasing a good or service for a price lower than their maximum willingness to pay. The difference between what they are willing to pay and what they actually pay is the consumer surplus.

Therefore, the consumer surplus that Frances gets for the iPhone she bought for $150 is $200, which means that her willingness to pay for an iPhone is $350. ($150 + $200 = $350)If Frances had bought the iPhone on sale for $100, her consumer surplus would have been $250. ($350 - $100 = $250)If the price of the iPhone had been $400, Frances would not have bought it because her willingness to pay is $350, and the price is more than that.

To summarize, Frances' willingness to pay for an iPhone is $350. If she had bought the iPhone on sale for $100, her consumer surplus would have been $250. If the price of the iPhone had been $400, her consumer surplus would have been zero because she would not have bought the iPhone.

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The area of square F in Figure 2 is D. 100 square units

The area of a shape simply means the total space that is taken by the shape. It simply expresses the extent of the region on a particular plane as well as a curved surface.

In Figure 1, the area of square A is 9 square units, the area of square B is 16 square units, and the area of square C is

25 square units and in Figure 2, the area of square D is 36 square units and the area of square E is 64 square units.

The area will be:= ✓8² ,+ √6²

= ✓100

Area = 10 × 10 = 100

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The length of time for one individual to be served at a cafeteria follows an exponential distribution with a mean of 4 minutes.

In an exponential distribution, the probability density function (PDF) is given by:

f(x) = (1/μ) * e^(-x/μ)

Where μ is the mean of the distribution. In this case, the mean is 4 minutes. Therefore, the PDF for the length of time for one individual to be served at the cafeteria can be expressed as:

f(x) = (1/4) * e^(-x/4)

The exponential distribution is commonly used to model the time between events in a Poisson process. In this case, it represents the time it takes for an individual to be served at the cafeteria, with an average of 4 minutes.

The exponential distribution is characterized by the property of memorylessness, which means that the probability of an event occurring in the next interval of time is independent of how much time has already elapsed. In the context of the cafeteria, this property implies that the probability of an individual being served in the next minute is the same, regardless of how much time has already passed.

It's important to note that the exponential distribution is only valid for non-negative values of x, as it represents a continuous random variable. The distribution is skewed to the right, with a longer tail on the positive side. The mean (μ) and standard deviation (σ) of the exponential distribution are equal and can be calculated as 1/λ, where λ is the rate parameter of the distribution.

In summary, the length of time for one individual to be served at the cafeteria follows an exponential distribution with a mean of 4 minutes. The probability density function (PDF) for this distribution is given by f(x) = (1/4) * e^(-x/4), where x represents the time in minutes.

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Answer:

6 7/8

Step-by-step explanation:

Answer:

A pound of jelly beans costs $4, and a pound of gummy worms costs $6

Step-by-step explanation:

Let

Cost of one pound of Jelly beans = x

Cost of one pound of Gummy worms = y

Making equations from the statements:

Lillian bought 4 pounds of jelly beans and 3 pounds of gummy worms for $34: \(4x+3y=34\)

Kelsey bought 5 pounds of jelly beans and 3 pounds of gummy worms for $38: \(5x+3y=38\)

Solving both equations we can found cost of candies.

Let:

\(4x+3y=34--eq(1)\\5x+3y=38--eq(2)\)

Subtracting both equations to find value of x

\(4x+3y=34\\5x+3y=38\\- \ \ \ - \ \ \ \ -\\------\\-x=-4\\x=4\)

So,we get value of x=4

Now putting value of x in eq(1) to find value of y

\(4x+3y=34\\4(4)+3y=34\\16+3y=34\\3y=34-16\\3y=18\\y=18/3\\y=6\)

We get value of y=6

Cost of one pound of Jelly beans = x = 4

Cost of one pound of Gummy worms = y = 6

A pound of jelly beans costs $4, and a pound of gummy worms costs $6

Answer:

true

Step-by-step explanation:

Let, x and y denotes the number of coin Deniel and Edwin had first. Then we have:

x + y = 500 .....(i)

Since Daniel spent 3/7 of his coins means he has 4/7 of his coins remaining and Edwin had spent its 7 coins so he has y-7 coins are remaining. Also given the ratio of the number of coins remaining is 3:2. Hence,

(4x/7):(y-7)  = 3:2

=> 8x/7 = 3y - 21

=> 8x/7 = 3( 500-x) - 21

=> 8x/7 = 1500 - 3x - 21

=> 29x = 1479*7

=> x = 357

So, the number of coins Daniel had at first is 357 coins.

Since Daniel’s remaining amount after spending some coins was 4/7 of its all coins and we know Daniel’s all coins were 20 cents coins. Hence, the money Daniel had in the end:Amount = (4/7)*357*0.20Amount = 40.8$

(a) The number of coins Daniel had at first:357

(b). The money Daniel had in the end:$40.8

Answer: Daniel had 134 coins at first.

All of Daniel's coins were 20-cent coins, he would have had 134 * 20 cents = $26.80 in the end.

Step-by-step explanation:

Let's solve the problem step by step:

(a) Let's assume Daniel had x coins at first. Edwin would have had 500 - x coins since they had a total of 500 coins.

After Daniel spent 3/7 of his coins, he would have (1 - 3/7)x = 4/7x coins left.

Edwin spent 7 coins, so he would have had (500 - x) - 7 = 493 - x coins left.

According to the given ratio, we have the equation:

(4/7x) / (493 - x) = 3/2

Cross-multiplying, we get:

2(4/7x) = 3(493 - x)

Simplifying, we have:

8/7x = 1479 - 3x

Combining like terms, we get:

11x = 1479

Dividing by 11, we find:

x = 1479/11 = 134

Therefore, Daniel had 134 coins at first.

(b) Since all of Daniel's coins were 20-cent coins, he would have had 134 * 20 cents = $26.80 in the end.

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