in how many ways can 8 hearts be chosen if 11 cards are chosen from a well-shuffled deck of 52 playing cards?

The calculation \((9.04-8.23+21.954+81.0) \times 3.1416\) would have 4 significant figures.



To determine the number of significant figures in a calculation, we follow the rules for significant figures:

1. Addition and subtraction: The result should have the same number of decimal places as the measurement with the fewest decimal places.
2. Multiplication and division: The result should have the same number of significant figures as the measurement with the fewest significant figures.

Let's break down the calculation step by step:
\(9.04-8.23+21.954+81.0\) yields \(104.764\).

Now, multiplying this result by \(3.1416\) gives \(329.5719744\).

The measurement with the fewest significant figures in the calculation is \(3.1416\), which has 5 significant figures.

According to the rule for multiplication and division, the result should have the same number of significant figures as the measurement with the fewest significant figures. Hence, the result, \(329.5719744\), will be rounded to 4 significant figures.

Therefore, the calculation \((9.04-8.23+21.954+81.0) \times 3.1416\) would have 4 significant figures.

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Harold had originally 100 pencils.

Let X be the number of pencils Harold had originally. After giving 17 to his friend Carl, he had X-17 left. Then, after giving 35 to his teacher, he had X-17-35 left, which is equal to 48.

Therefore, we can set up an equation: X-17-35=48. Solving for X, we get X=100 pencils.

Thus, Harold originally had 100 pencils. To check, we can verify that after giving 17 to Carl and 35 to his teacher, he is left with 48, which matches the information given in the problem.

This problem can also be solved by using algebraic equations, but since there are only two steps involved, we can use simple arithmetic to arrive at the answer.

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The rate of change of volume is 418.6  inch³/s .

Rate of increase of radius with time is ( dr/dt ) = 5

rate of decrease of height with time is (dh/dt ) = -3

volume of a cone is given by (V) =  \(\frac{1}{3} \pi r^{2}h\)

Now the rate of change of volume  with respect to time is given by dV/dt

∴ dV/dt = d( \(\frac{1}{3} \pi r^{2}h\)) / dt

dV/dt =  \(\frac{1}{3} \pi (2rh\frac{dr}{dt} + r^{2}\frac{dh}{dt} )\)

value of radius and height when volume is changing are :

r = 20 inches

h = 40 inches

dV/dt = \(\frac{1}{3} \pi (\) 2×20×40 ×5 - \(20^{2}\)×3 )

dV/dt = \(\frac{1}{3} \pi\)(1600 - 1200)

dV/dt = (400/3) 3.14

dV/dt = 418.66 inch³/s

So the rate of change of the volume is 418.66 inch³/s.

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The minimum number amount of light energy that can exist in Hasbrouck 20 is zero due to the divisibility of light.

According to quantum theory, light is composed of particles called photons. Each photon carries a certain amount of energy, which is directly proportional to its frequency.

However, the size of the lecture hall being 9 m across does not impose any constraints on the minimum amount of light energy. In the quantum realm, light can be continuously divided, and there is no lower limit to the amount of light energy that can exist.

Therefore, the minimum amount of light energy in Hasbrouck 20 is considered to be zero.

This implies that arbitrarily small quantities of light can exist, and the division of light energy can continue indefinitely.

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Answer:

Step-by-step explanation:

3-6x should be the same as -6x+3

1. The period of the function is π

2. The period of the function is 6

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

The graphs

By definition, the period of the function is calculated as

Period = Difference between cycles or the length of one complete cycle

Graph 1

Using the above as a guide, we have the following:

Period = 2π - π

Evaluate

Period = π

Graph 2

Using the above as a guide, we have the following:

Period = 9 - 3

Evaluate

Period = 6

Hence, the period of the functions are π and 6

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The equation that can be used to find the distance Rin rides each evening is: 5(1.5x) = 25

In this equation, x represents the distance she rides each evening. Since Rin rides 1.5 miles to school and then rides home in the afternoon for a total of 2 trips, multiplying the distance she rides each evening by 5 (the number of school days in the week) will give us the total distance of 25 miles that she rides over the 5 school days.

what is distance?

Distance is a scalar quantity that measures the length between two points or the extent of space between two objects. It refers to the "how far" an object or a person has traveled from a starting point to a destination. Distance is typically measured in units such as meters (m), kilometers (km), feet (ft), miles (mi), or any other unit of length. It is a fundamental concept in mathematics, physics, and everyday life, used to quantify the spatial separation or interval between objects or locations.

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The number of possiblilities in which  n number teams can finish in (n-1)! or (n-1) factorial.

As given, there are n teams in the tournament, and each team will finish in a specific rank. We are needed to determine how many different orders the n teams can finish in.

In order to dtermine the last two teams in the tournament by the first match, which has two possible probabilities that  either the nth ranked team wins, or the (n-1)th ranked team wins. If the nth ranked team would  wins, they will play the (n-2)th ranked team in the next match, and if the (n-1)th ranked team wins, they will play the (n-3)th ranked team in the next match.

We can continue this process going on  until we get to the final match, where the winner of the second-to-last match plays the first-ranked team. Therefore, the number of possible and different orders the n teams can finish in depends on the outcome of each of these performed matches.

Let's again consider a specific example with n = 4 teams. In the first match, either the 4th ranked team wins and plays the 3rd ranked team, or the 3rd ranked team wins and plays the 2nd ranked team. If the 4th ranked team wins the first match, they will either beat the 3rd ranked team and play the 1st ranked team in the final match, or lose to the 3rd ranked team and finish in second place. Similarly, if the 3rd ranked team wins the first match, they will either beat the 2nd ranked team and play the 1st ranked team in the final match, or lose to the 2nd ranked team and finish in third place.

Therefore, the possible orders for the 4 teams are:

1st, 2nd, 3rd, 4th (if the 4th ranked team wins the first match and wins all subsequent matches)

1st, 2nd, 4th, 3rd (if the 4th ranked team wins the first match, beats the 3rd ranked team in the second match, but loses to the 1st ranked team in the final match)

1st, 3rd, 2nd, 4th (if the 4th ranked team loses the first match, but beats the 3rd ranked team in the second match and then loses to the 1st ranked team in the final match)

1st, 3rd, 4th, 2nd (if the 4th ranked team loses the first match and both subsequent matches)

1st, 4th, 2nd, 3rd (if the 3rd ranked team wins the first match, beats the 2nd ranked team in the second match, but loses to the 1st ranked team in the final match)

1st, 4th, 3rd, 2nd (if the 3rd ranked team wins the first match, but loses to the 2nd ranked team in the second match and then loses to the 1st ranked team in the final match)

Therefore, there are 6 different orders the 4 teams can finish in.

Henceforth, In general, it can be concluded that the number of different orders the n teams can finish in is equal to the number of ways to arrange the n-1 match winners, since the final match winner is determined by the second-to-last match winner. Therefore, the answer is (n-1)!, or (n-1) factorial.

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The ratios that could be the lengths of the two legs in a 30-60-90 triangle are √3:3 (option E) and 12√3 (option D).

In a 30-60-90 triangle, the angles are in the ratio of 1:2:3. The sides of this triangle are in a specific ratio that is consistent for all triangles with these angles. Let's analyze the given options to determine which ones could be the ratio between the lengths of the two legs.

A. √2:√2

The ratio √2:√2 simplifies to 1:1, which is not the correct ratio for a 30-60-90 triangle. Therefore, option A is not applicable.

B. 15

This is a specific value and not a ratio. Therefore, option B is not applicable.

C. √√√√5

The expression √√√√5 is not a well-defined mathematical operation. Therefore, option C is not applicable.

D. 12√3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which simplifies to √3:3. Therefore, option D is applicable.

E. √3:3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which is equivalent to √3:3. Therefore, option E is applicable.

F. √2:√5

This ratio does not match the ratio of the sides in a 30-60-90 triangle. Therefore, option F is not applicable. So, the correct option is D. 1 √2.

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The scale factor of the dilation is the ratio of the lengths of the corresponding sides of the two triangles. Since triangle ABC and triangle A'B'C' both have side lengths of AB, BC, and CA, the scale factor is 1.

1. Calculate the length of the sides of triangle ABC:

AB = length of side AB of triangle ABC

BC = length of side BC of triangle ABC

CA = length of side CA of triangle ABC

2. Calculate the length of the sides of triangle A'B'C':

A'B' = length of side A'B' of triangle A'B'C'

B'C' = length of side B'C' of triangle A'B'C'

C'A' = length of side C'A' of triangle A'B'C'

3. Calculate the scale factor of the dilation:

Scale factor = (AB/A'B') x (BC/B'C') x (CA/C'A')

= (length of side AB of triangle ABC / length of side A'B' of triangle A'B'C')

x (length of side BC of triangle ABC / length of side B'C' of triangle A'B'C')

x (length of side CA of triangle ABC / length of side C'A' of triangle A'B'C')

= 1 x 1 x 1

= 1

Therefore, the scale factor of the dilation is 1.

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Answer:

f = - \(\frac{12}{11}\)

Step-by-step explanation:

Given

- 5f - 8 = 2(3f + 2) ← distribute parenthesis

- 5f - 8 = 6f + 4 ( subtract 6f from both sides )

- 11f - 8 = 4 ( add 8 to both sides )

- 11f = 12 ( divide both sides by - 11 )

f = \(\frac{12}{-11}\) = - \(\frac{12}{11}\)

Answer:

f= -12/11

Step-by-step explanation:

-5f-8=6f+4

+5f +5f

-8=11f+4

-4 -4

-12=11f

÷11 ÷11

-12/11=f

Answer:

C. is the correct option

C. The student did not distribute 3 in * (2 ^ 3) ^ (x + 3) x + 3

and x = - 14

Step-by-step explanation:

8 ^ (x + 3) = 2 ^ (2x - 5)

Here is how the student solved the equation

8 ^ (x + 3) = 2 ^ (2x - 5)

8 ^ (x + 3) = 2 ^ (2x - 5)

(2 ^ 3) ^ (x + 3) = 2 ^ (2x - 5)

2 ^ (3x + 3) = 2 ^ (2x - 5) -----  This is where the student made the error.

The student did not distribute 3 in * (2 ^ 3) ^ (x + 3).

This is how to solve the equation

8 ^ (x + 3) = 2 ^ (2x - 5)

8 ^ (x + 3) = 2 ^ (2x - 5)

(2 ^ 3) ^ (x + 3) = 2 ^ (2x - 5)

Then, we will 3 distribute in  (2 ^ 3) ^ (x + 3), so that we get

2 ^ (3x +9) = 2 ^ (2x -5)

Since the bases on both sides of the equation are equal, we can equate the powers so that we get

(3x +9) = (2x -5)

Then we will collect like terms

3x - 2x = -5 -9

∴ x = -14

This solution could be better written in this format

\(8^{x+3} = 2^{2x-5} \\2^{3} ^{(x+3)} = 2^{2x-5}\\2^{(3x+9)} = 2^{2x-5}\\{(3x+9)} = {2x-5} \\3x-2x= -5-9\\x = -14\)

Total 4 dummy variables would be needed to include this categorical variable in a regression model.

A regression analysis serves as the foundation for many types of forecasting and determining the effects on target variables. When you hear about studies in the news about fuel efficiency, pollution causes, or the effects of screen time on learning, a regression model is frequently used to back up their claims.

A dummy variable (also known as an indicator variable or simply dummy) in regression analysis is one that takes the values 0 or 1 to indicate the absence or presence of some classification impact that may be predicted to shift the result.

Total 4 dummy variables would be needed to include this categorical variable in a regression model.

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Using the normal distribution, it is found that the probability that the association would observe 654 or less people who drink milk in the sample is of 0%.

The z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:

\(Z = \frac{X - \mu}{\sigma}\)

For the binomial distribution, the parameters are given as follows:

n = 800, p = 0.87.

Hence, the mean and the standard deviation of the approximation are given by:

The probability that the association would observe 654 or less people who drink milk in the sample, using continuity correction, is \(P(X \leq 654.5)\), which is the p-value of Z when X = 654.5, hence:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{654.5 - 696}{9.5121}\)

Z = -4.36

Z = -4.36 has a p-value of 0.

0% probability that the association would observe 654 or less people who drink milk in the sample.

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Option a. calculate a correlation coefficient is the right response because a correlation coefficient measures the strength and direction of the relationship between two interval level variables.

This is because a correlation coefficient measures the strength and direction of the relationship between two interval level variables. It provides a numerical value that ranges from -1 to 1, where -1 indicates a strong negative correlation, 0 indicates no correlation, and 1 indicates a strong positive correlation.

A scatter plot is also useful in visualizing the relationship between two variables, but it does not provide a numerical value like the correlation coefficient. A test of significance and variance calculation are not typically used as first steps in assessing the relationship between two variables.

Hence, option a. calculate a correlation coefficient is the correct answer.

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The possible first coordinate x with a slope of 3 is equal to -13/3.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided, we can logically deduce the following data points and slope on the line:

Substituting the given data points into the slope formula, we have the following;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

3 = (4 - 8)/(x + 3)

3x + 9 = -4

3x = -13

x = -13/3

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Given value of p: -2

Plug the value of "p" into the expression:

Simplify the expression obtained:

Therefore, the value of 3p + 1 when p = -2​, is -5.

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A stone arch can be twice as wide as a stone lintel because an arch distributes the weight of the structure vertically down its curve to the columns (piers) on either side while a lintel distributes the weight horizontally along the length of the stone.

A stone arch can be twice as wide as a stone lintel because an arch distributes the weight of the structure vertically down its curve to the columns (piers) on either side while a lintel distributes the weight horizontally along the length of the stone.

It requires only a small fraction of the arch's width to support itself while a lintel requires the full width of the structure that it spans. Thus, a stone arch can span a larger gap than a stone lintel and be twice as wide while using the same material.

For example, the Roman Colosseum uses an arch to span the entrances and exits while the walls supporting the upper levels use a series of stone lintels to support the structure.

Moreover, the arc prevents the need for a central support structure, which would be in the way of any events taking place in the structure. The technology of arches made them fundamental to ancient Roman architecture. For example, the arches were used to construct aqueducts, which provided a steady supply of water to the city of Rome.

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We have

the y-coordinate of A is 6

the y-coordinate of B is -8

B to A in y we need to add 14 units, therefore the translation rule that describes B -> A

Answer:

-9x+11y=-14

x= ( 13/4 +3/8y) + 11y+-4

y=2

x=13/4 + 3/8 x 2

x=4

Step-by-step explanation:

Triangle ABC

Apply rule of Cosin

If 12^ + 9^2 - 2•12•9 Cos X= 18^2

Then

144+ 81 - 216CosX = 324

CosX = (324 -225)/(-216) = 99/-216

CosX = -0.46

Then answer is YES, its a triangle because CosX only have values

between -1 and 1, and -0.46 is between them

Answer:

B

Step-by-step explanation:

Just read and you will see why i say that

The orthonormal basis for V is: {v1 = 1/√(2), v2 = (t - √(2)/2)/√(2), v3 = (√(3)/2)t^2 - (√(6)/2)t}. To produce an orthonormal basis for V, we need to find a set of vectors that are linearly independent and can span the space V. Since we are working with polynomials of degree less than 2, we can write them in the form:

p(t) = at^2 + bt + c

where a, b, and c are real coefficients.

To find the basis, we can start with the standard basis for V, which is {1, t, t^2}. We can then use the Gram-Schmidt process to produce an orthonormal basis.

Here are the steps:

1. Normalize the first vector in the basis, which is 1, to obtain:

v1 = 1/√(2)

2. Calculate the projection of t onto v1 and subtract it from t to obtain the second vector in the basis:

v2 = (t - (t, v1)v1)/∥(t - (t, v1)v1)∥

where (t, v1) is the inner product of t and v1.

Simplifying, we get:

v2 = (t - √(2)/2)/√(2)

3. Finally, calculate the projection of t^2 onto v1 and v2, and subtract these projections from t^2 to obtain the third vector in the basis:

v3 = (t^2 - (t^2, v1)v1 - (t^2, v2)v2)/∥(t^2 - (t^2, v1)v1 - (t^2, v2)v2)∥

where (t^2, v1) and (t^2, v2) are the inner products of t^2 with v1 and v2, respectively.

Simplifying, we get:

v3 = (√(3)/2)t^2 - (√(6)/2)t

Therefore, the orthonormal basis for V is:

{v1 = 1/√(2), v2 = (t - √(2)/2)/√(2), v3 = (√(3)/2)t^2 - (√(6)/2)t}

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Answer:

x = 25 degrees

Step-by-step explanation:

The sum of the angles of a triangle is always 180 degrees. Therefore, in a triangle with one angle measuring 130 degrees, the measures of the other two angles must add up to 180-130 = 50 degrees.

So, if the measures of the other two angles are x, the equation would be:

x + x = 50

This means that the measure of each angle is 50/2 = 25 degrees.

Therefore, in a triangle with one angle measuring 130 degrees, the measures of the other two angles are both 25 degrees.

Answer:

x+2y+z+80=360°

Step-by-step explanation:

the sum of the interior angles in a quadrilateral is 360°, so the answer is: x+2y+z+80=360°

Answer:

Option 4 - x+2y+z+80=360degrees is the correct answer.

Step-by-step explanation:

As given in the figure, it is a quadrilateral, and as all the angles in this quadrilateral are interior angles, the sum of the interior angles of a quadrilateral will be 360 degrees.

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Answer:

The number of doughnuts left over are 8 doughnuts

Step-by-step explanation:

The information given are;

The number of doughnuts fried per batch = 20 doughnuts

The number of doughnuts contained in a pack = 13 doughnuts

The number of doughnut batches just fried = 20 batches

The number of packs filled = 44 packs

The number of packs filled with the fried = 44 packs

The number of doughnuts per pack = 13 doughnuts

The number of doughnuts in the pack = The number of packs filled with the fried × The number of doughnuts per pack

The number of doughnuts in the pack = 44 × 13 = 572 doughnuts

Given that the number of batches of doughnuts fried = X batches and the amount of left over = Y doughnuts, where each batch contains 20 doughnuts, we have;

Number of doughnuts fried = Number of batches of doughnuts fried × Number of doughnuts per batch

Number of doughnuts fried = X × 20 =20×X doughnuts

Therefore we have;

Number of doughnuts fried = The number of doughnuts in the pack + The number of doughnuts left over

Which gives;

20×X = 572 + Y where Y < 20

Checking we have multiples of 20 are 560, 580

Given that 520 is the next multiple of 20 after 572, we have;

The number of doughnuts fried = 580 and the number of left over = 580 -  572 = 8 doughnuts.

By definition a parallelogram:

* Its opposite sides are equal in length

* Its opposite sides are parallel.

Since the figures ABCD and ABEC satisfy those properties, we can conclude that they are parallelograms

Answer:

The sequence can be continued by adding 7 to each number.

Step-by-step explanation:

15 + 7 = 22

22 + 7 = 29

29 + 7 = 36

36 + 7 =...... 43 would be your next number

Answer:

A is correct because you need to stop deleting my answers.