Time (seconds)

2

3

4

5

6

Height (cm)

14

21

28

35

42

By contributing $207.50 each, Marci and Skylar will evenly distribute the costs and ensure that both parties contribute equally to the party expenses.

To split the costs evenly between Marci and Skylar, they should follow the following approach: First, let's calculate the total expenses incurred by Marci and Skylar. Marci spent $585 for catering and $50 for invitations, totaling $635. Skylar spent $35 on a cake and $75 to reserve the room, totaling $110. Therefore, the total expenses for the party amount to $745.

Next, let's consider the contributions received. Marci received $90 in checks made out to her, Skylar received $55 in checks made out to him, and there is one $20 check with the recipient entry blank. Additionally, there were $165 in cash contributions. The total contributions amount to $330.

To split the costs evenly, Marci and Skylar need to share the remaining expenses equally. The remaining expenses can be calculated by subtracting the contributions received from the total expenses: $745 - $330 = $415.

Since Marci and Skylar want to split the costs evenly, they should each contribute half of the remaining expenses. Half of $415 is $207.50. Therefore, Marci and Skylar should each contribute $207.50 to cover the remaining expenses.

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The probability of both having a pet and visiting a vet is 0.36 or 36%.

To find the probability of both having a pet and visiting a vet, we multiply the probability of having a pet by the probability of visiting a vet given that the person has a pet.

Let:

P(pet) = probability of having a pet = 40% = 0.40

P(vet | pet) = probability of visiting a vet given that the person has a pet = 90% = 0.90

The probability of having a pet and visiting a vet is given by:

P(pet and vet) = P(pet) * P(vet | pet)

P(pet and vet) = 0.40 * 0.90

P(pet and vet) = 0.36

Therefore, the probability of both having a pet and visiting a vet is 0.36 or 36%.

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To find the volume of the solid obtained by rotating the region bounded by the curves y = x³, y = 8, and x = 0 about the y-axis, we can use the method of cylindrical shells. The region between these curves will be rotated to form a solid.

The limits of integration will be from y = 0 to y = 8, as the region is bounded by these values of y. For each vertical strip at position y, the radius of the cylindrical shell will be x, which can be determined by solving the equation y = x³ for x. Hence, x = y^(1/3). The height of the strip will be the difference between the x-coordinate of the right curve (x = 0) and the left curve (x = y^(1/3)), which is 0 - y^(1/3) = -y^(1/3). The circumference of the shell is 2πx.

Using the cylindrical shell method, the volume can be calculated as:

V = 2π∫[0,8] (-y^(1/3)) (2πy^(1/3)) dy

Simplifying the expression, we get:

V = -4π²∫[0,8] y dy

Integrating this expression, we find the volume of the solid to be -128π.

Therefore, the volume of the solid obtained by rotating the region bounded by the curves y = x³, y = 8, and x = 0 about the y-axis is -128π cubic units.

To show that the volume of a sphere of radius r is (4/3)πr³, we can use the integral representation of the volume of a solid of revolution. By rotating the graph of a semicircle with radius r about its diameter, we obtain a sphere.

The equation of a semicircle of radius r can be written as y = √(r² - x²), where -r ≤ x ≤ r. The volume of the sphere can be found by rotating this semicircle about the x-axis.

Using the method of cylindrical shells, the volume can be calculated as:

V = 2π∫[-r,r] x √(r² - x²) dx

Simplifying the expression inside the integral, we get:

V = 2π∫[-r,r] x (√r) (√(r - x)(√(r + x)) dx

Integrating this expression, we find:

V = 2π(2/3)r^3

Simplifying further, we get:

V = (4/3)πr^3

Hence, we have shown that the volume of a sphere of radius r is indeed (4/3)πr³, which is a well-known result in geometry.

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Polonium-210 is a radioactive element that decays exponentially. Its half-life is 140 days, which means that after 140 days, the amount of Polonium-210 will be reduced by half. The rate of decay is proportional to the amount at time t, which means that the more Polonium-210 there is, the faster it will decay.

Now, if we start with 200mg of Polonium-210, we can calculate how much will remain after 12 weeks. To do this, we need to convert 12 weeks into days, since the half-life of Polonium-210 is measured in days.
12 weeks is equal to 84 days (12 x 7 = 84), so we need to find out how many half-lives occur in this time period.
84 days divided by 140 days (the half-life of Polonium-210) gives us approximately 0.6 half-lives.
To calculate how much Polonium-210 remains after 0.6 half-lives, we can use the formula:
Amount remaining = initial amount x (1/2)^(number of half-lives)
Plugging in the values, we get:
Amount remaining = 200mg x (1/2)^(0.6)
Amount remaining = 111.3mg
Therefore, after 12 weeks, approximately 111.3mg of Polonium-210 will remain out of the initial 200mg.

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Answer:

(−3)(+2)(3+2)

Step-by-step explanation:

Factor by grouping

Factor by grouping

Factor by grouping

Factor by grouping

(−3)(32+8+4)

Factor by grouping

Factor by grouping

Factor by grouping

Factor by grouping

(−3)(+2)(3+2)

Step-by-step explanation:

2/5 of marbles are blue

= 3/5 of marble are not blue.

Number of non-blue marbles = 500 * (3/5) = 300.

300 marbles are not blue.

Answer:

1 2/5

Step-by-step explanation:

The range of the random variable d is {-4, -2, 0, 2, 4}, so the correct answer is option b.

To find the range of the random variable d, we need to consider all possible outcomes of the experiment and calculate the value of d for each outcome.

In this experiment, a fair coin is flipped 4 times. Each flip can result in either a "heads" or "tails" outcome.

Let's consider the possible outcomes and calculate the corresponding values of d:

1. Four heads (HHHH): d = 4 - 0 = 4

2. Three heads and one tail (HHHT, HHTH, HTHH, THHH): d = 3 - 1 = 2

3. Two heads and two tails (HHTT, HTHH, THHH, TTHH, HTTH, HHTH): d = 2 - 2 = 0

4. Three tails and one head (TTTH, TTHT, THTT, HTTT): d = 1 - 3 = -2

5. Four tails (TTTT): d = 0 - 4 = -4

The range of d is the set of all possible values that d can take on, which is {-4, -2, 0, 2, 4}.

Therefore, the correct answer is option b. {-4, -2, 0, 2, 4}.

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Answer:

cos4θ=8cos^4θ−8cos^2θ+1

Step-by-step explanation:

Answer:

Step-by-step explanation:

17 is the answer:

9+3*4-1*4=

9+12-4=

21-4=17

Answer:

R0, 90°

R0, –270

Step-by-step explanation:

Answer:

A, E

Step-by-step explanation:

The regular price of a ticket to the game was $204.00.

We can use algebra to solve the problem. Let x be the regular price of a ticket to the game.

We know that the group rate saved Mason $5.75 per ticket, so the regular price of a ticket is x + $5.75.

We know that Mason bought 16 tickets and paid a total of $296.00, so we can set up the following equation:

x + $5.75 = (x + $5.75) * 16 = 16x + $92

So the regular price of a ticket is x = $296.00 - $92 = $204.00

Therefore, the regular price of a ticket to the game was $204.00.

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Answer:

 In order to change a rational number to a decimal, we just convert the number into the form of a fraction. We then divide the numerator with the denominator and find out the exact value of the division.

Step-by-step explanation:

25%×24 =6 jahdyheuxlfoodnxhydushgdys

6 more hours did Tremaine use the computer to play video games than to do research.

The percentage formula is used to calculate the amount or percentage of anything in terms of 100. Percentage indicates "per hundred" in its most basic form. The percentage formula is used to express a number between zero and one. It is a number that is expressed as a fraction of 100. It is represented by the sign% and is mostly used to compare and find ratios.

Given:

The percent for Video Game= 25%

and, percent for Research = 5%

So, 25% of  30 = 25 / 100 x 30 = 7.5

5% of 30 = 5/100 x 30 = 1.5

So, the the number of hour spend on more on Video game

= 7.5 - 1.5

= 6 hour

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If E and F are two events, P(E)= 0.6 and P(F|E)= 0.5. The value of P(E and F) will be 0.30.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

It is given that, E and F are two events and that P(E)= 0.6 and P(F|E)= 0.5

As we know,

P(F|E)=P(E and F) / P(E)

0.5 = P(E and F) / 0.6

P(E and F)=0.5×0.6

P(E and F)=0.30

Thus, if E and F are two events, P(E)= 0.6 and P(F|E)= 0.5. The value of P(E and F) will be 0.30.

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5 is the missing value of x.

From the intersecting of two chords theorem,

Given angle= 14x-1

Arcs are 13x+8, 65°

From the theorem,

14x-1 = (13x+8 + 65)/2

14x-1 = (13x+73)/2

28x-2=13x+73

15x=75

x= 5

Therefore, the value of x will be 5 for the given figure.

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Answer:

-6

Step-by-step explanation:

? - (-4) = -2

? + 4 = -2

-6 + 4 = -2

Your Answer will be -6

Hope that helps!

Answer:

-6

Step-by-step explanation:

because you are just doing basic math so just take 6-4 and you will get 2, except you put negitave signs so the answer is -6

Answer:

quadratic

Step-by-step explanation:

Answer: 40

Step-by-step explanation:

38+ 52=90

230-90=40

Since 80 out of 100 free throws were successful, the standard deviation of the success rate would be 8, and the standard deviation of a binomial distribution is the square root of (p*q)/n, where p is the probability of success, q is the probability of failure (1-p), and n is the total number of trials.

Standard deviation is calculated as follows:

p*q/n = 0.8*0.2/100 = 0.0016 = 0.04 = 8

Since 80% of 100 equals 80 successful free throws, the standard deviation of the successes from 100 free throws would be 8. The dispersion in a set of data is measured by standard deviation. A binomial distribution's standard deviation is equal to the square root of (p*q)/n, where p is the success probability, q is the failure probability (1-p), and n is the number of trials. Since the success rate in this instance is 80%, p = 0.8, q = 0.2, and n = 100. The standard deviation is then equal to the square root of (p*q/n): (0.8*0.2/100) = (0.0016) = (0.04), which equals 8. Therefore, the standard deviation of the successes from 100 free throws for a basketball player who makes 80% of them would be 8.

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Angle ∠C and angle ∠E are supplementary angles. Then the correct option is B.

The sum of the supplementary angle is 180 degrees.

The sum of two acute angles will be less than 180 degrees.

Similarly, the sum of two obtuse angles is more than 180 degrees.

The addition of angle ∠C and angle ∠E is calculated as,

∠C + ∠E = 61° + 119°

∠C + ∠E = 180°

The addition of angle ∠C and angle ∠E is 180°. Thus, the correct option is B.

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Answer:

1. y2-y1/x2-x2

2.y=mx+b

3.Ax+By=C

Step-by-step explanation:

According to the given matrix the determinant of the matrix [7 -1 3 2] is 17.

The given matrix is:
[7 -1]
[3  2]

To find the determinant of a 2x2 matrix, you can use the formula:
det [a b]
  [c d] = ad - bc

In this case, the determinant can be calculated as follows:
det [7 -1]
   [3  2] = (7 * 2) - (-1 * 3)

= 14 + 3
= 17

The determinant of the matrix [7 -1 3 2] is 17.

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To find the determinant of a 2x2 matrix, multiply the main diagonal values and subtract the product of the off-diagonal values. In this case, the determinant is 17.

The value of the determinant of the matrix [7 -1; 3 2] can be found using the formula for a 2x2 matrix.

To calculate the determinant, multiply the values on the main diagonal (top-left to bottom-right) and subtract the product of the values on the off-diagonal (top-right to bottom-left).

In this case, the main diagonal values are 7 and 2, while the off-diagonal values are -1 and 3.

So, the determinant is calculated as follows:

(7 * 2) - (-1 * 3) = 14 + 3 = 17.

Therefore, the value of det [7 -1; 3 2] is 17.

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Answer:

i hope my answer help you

Step-by-step explanation:

1st=8+4=12

2nd the answer is to the nearest 7.06

3rd =2+2³.7=2+13=15

4th=(36÷(4+5))+25=36÷9+25=4+25=29

5th=16÷16+8-3=1+8-3=9-3=6

6th=8-2.4=5.6

The standard deviation and the mean are 16.95 and 86.43 respectively.

Z at 75% ≈ 0.674.

Since the spending is more than $75, Z = -0.674

Z at 15% ≈ - 1.036.

Since the spending is more than $104, Z = 1.036

Now,

Z = (x-mean)/SD => Z*SD = x-mean

Therefore,

-0.674*SD = 75 - mean ------- (1)

1.036*SD = 104 -mean ------- (2)

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

(1) - (2)

-1.71SD = - 29 => SD = 75/1.71 = 16.95

Substituting SD in (1) => -0.674*43.8596 = 75 -mean => mean = 75+(0.674*43.8596) = 86.43.

Then,

SD = 16.95, mean = 86.43

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Step-by-step explanation:

one side.

as each tile is guaranteed an equilateral triangle, all sides are equally long. measuring 1 side clarifies therefore the overall size of the tile.

the angles are the same in any case, as every equilateral triangle (no matter its size) has only angles of 60°.

so, if any side has the same length as the side lengths of the other triangles, then the checked triangle is congruent with the others.

1) line segment MJ≅ Line segment MP

2) ∡OJP≅∡OML

3) line segment OM≅line segment MP

The below mentioned statements are true according to the figure , Option A, B and D is the correct answer.

A line that intersects the curve at a single point at 90 degree is called a tangent.

In the given figure it can be seen that the

Therefore , Option A , B and D is the correct answer

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The stream velocity has no influence on the amount of dissolved load it contains. The amount of dissolved material depends on erosion and deposition carried out in the watercourse. These are affected by factors such as the slope of the land, the resistance of the material to erosion, the size of the sediments transported, etc.

Stream velocity plays an important role in the transport of sediments and dissolved loads in a watercourse. It affects the erosion and deposition processes that occur in the watercourse, which in turn affect the amount of sediment and dissolved load that is carried by the stream. For example, faster stream velocities can cause more erosion of the stream bed, leading to more material being carried in the water.

Sediment is any particulate matter that is transported by a fluid, and it can come in many different forms. The three main types of sediment are:

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