Four cards are randomly drawn from a standard deck of 52 cards. Answer the questions below: How many 4-card groups are possible? Find the probability of selecting 1 ace and 3 kings?

Answer:

115°

Step-by-step explanation:

hope this helps

The sample consists of three scores: 7, 8, and 9. The mean is 8, the median is 8, there is no mode, and the range is 2.

In statistics and probability, a sample refers to a subset of a population that is used to make inferences or draw conclusions about the entire population. In this case, the sample consists of the scores you obtained in 5 quizzes. The scores are as follows: 7, 8, and 9.
To analyze this sample, there are several key measures that can be calculated:
1. Mean: The mean, also known as the average, is calculated by summing up all the scores and dividing it by the number of scores. In this case, the mean can be calculated as (7 + 8 + 9) / 3 = 8.
2. Median: The median is the middle value when the scores are arranged in ascending order. In this case, since there are three scores, the median is the middle score, which is 8.
3. Mode: The mode is the score that appears most frequently in the sample. In this case, none of the scores repeat, so there is no mode.
4. Range: The range is the difference between the highest and lowest scores in the sample. In this case, the highest score is 9 and the lowest score is 7, so the range is 9 - 7 = 2.
5. Standard Deviation: The standard deviation is a measure of how spread out the scores are from the mean. It quantifies the amount of variation or dispersion in the sample. To calculate the standard deviation, you would need the full set of scores, not just the three provided.

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Answer:

Confidence Interval - "P" values  

(0.4433 , 0.5444 )

~~~~~~~~~~~~~~~~~~~~~~~

\(\mathrm{Expand\:}\left(x+4y\right)^3:\quad x^3+12x^2y+48xy^2+64y^3\)

in you image it is the last on "D"

Step-by-step explanation:

Confidence Level - "P" values  

99% 2.58

Confidence Interval - "P" values  

(0.4433 , 0.5444 )  

Answer:

9% per year

Step-by-step explanation:

True. The Span(S) equals the intersection of all subspaces of V that contain S.

The span of a set S of vectors in a vector space V is the smallest subspace of V that contains S. On the other hand, the intersection of all subspaces of V that contain S is the largest subspace of V that contains S. These two concepts are complementary to each other.

To see that span(S) equals the intersection of all subspaces of V that contain S, we need to show that each set is a subset of the other.

The span(S) is a subset of the intersection of all subspaces of V that contain S. This is because every subspace that contains S must contain all linear combinations of the vectors in S, which is precisely the span of S. Span(S) is contained in every subspace of V that contains S, and therefore, it is also contained in their intersection.

The intersection of all subspaces of V that contain S is a subset of span(S). This is because the span of S is a subspace of V that contains S, so it is also one of the subspaces that intersect to form the intersection of all subspaces of V that contain S.

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Maximize: Profit = 150C + 750T

Subject to:

5C + 3T ≤ 240 (Labor constraint)

4C + 20T ≤ 700 (Material constraint)

C ≥ 0

T ≥ 0

To determine the optimal production quantity of tables and the maximum profit, we can set up a linear programming problem based on the given information.

Let's define the decision variables:

Let C represent the number of chairs produced.

Let T represent the number of tables produced.

Objective function:

The objective is to maximize profit. The profit for each chair is $150, and the profit for each table is $750. Therefore, the objective function can be expressed as:

Profit = 150C + 750T

Constraints:

Labor constraint: The total labor hours available is 240, and each chair requires 5 hours, while each table requires 3 hours. So the labor constraint can be represented as:

5C + 3T ≤ 240

Material constraint: The warehouse has 700 linear feet of rich mahogany available, and each chair requires 4 linear feet, while each table requires 20 linear feet. Therefore, the material constraint can be expressed as:

4C + 20T ≤ 700

Non-negativity constraint: Since we cannot produce a negative quantity of chairs or tables, both C and T should be greater than or equal to zero:

C ≥ 0

T ≥ 0

Now, we can solve the linear programming problem to find the optimal solution:

Maximize: Profit = 150C + 750T

Subject to:

5C + 3T ≤ 240 (Labor constraint)

4C + 20T ≤ 700 (Material constraint)

C ≥ 0

T ≥ 0

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Answer:

The correct option is;

With the compass point on G, construct an arc that intersect GD←→

Step-by-step explanation:

The steps for constructing a parallel line to a given point is as follows;

1) With the straightedge, a transversal is drawn intersecting the giving line and passing through point G

2) Copy the angle formed between the transversal and the given line and the to the point G starting by constructing an arc with the compass on point G to intersect GD←→ then with the compass opening still the same, place the compass on the point of intersection of the arc constructed from point G on GD and construct another arc to intersect the arc previous arc from G to GD

3) The line drawn from the intersection through is a parallel line to EF

Therefore, the correct option is that with the compass point on G, construct an arc that intersect GD←→.

Answer:

A.  With the compass on point D , construct an arc that intersects EF¯¯¯¯¯ and GD←→.

Step-by-step explanation:

I just took the test!

The chi-square test for goodness of fit will produce a large value for chi-square under the circumstances where the observed frequencies significantly deviate from the expected frequencies based on the null hypothesis.

The chi-square test for goodness of fit is used to determine if there is a significant difference between the observed frequencies in a sample and the expected frequencies based on a specified distribution.

The test compares the observed frequencies in different categories or groups with the expected frequencies under the null hypothesis.

A large value for chi-square indicates a significant discrepancy between the observed and expected frequencies, suggesting that the null hypothesis is not supported.

This can occur in several circumstances.

First, if the sample size is large, even small differences between observed and expected frequencies can lead to a significant chi-square value.

Second, if there are substantial deviations between the observed and expected frequencies in one or more categories, the chi-square value will be large. This could indicate a lack of fit between the observed data and the expected distribution.

Additionally, if the assumptions of the chi-square test are violated, such as independence of observations or expected frequencies being sufficiently large, it can lead to inflated chi-square values.

These violations can distort the results and lead to a larger chi-square value.

In summary, the chi-square test for goodness of fit produces a large chi-square value when the observed frequencies significantly deviate from the expected frequencies, indicating a lack of fit between the observed data and the expected distribution.

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Answer:

Chart:

x           y

-6         11

3           5

15         -3

-12        15

Step-by-step explanation:

The only things you can plug in are the domain {-12, -6, 3, 15}

Plug in the domain into equation to find y.

-6 :

y = -2/3 (-6) +7

y = +47

y=11

(-6,11)

3:

y = -2/3 (3) +7

y = -2 +7

y = 5

(3, 5)

15:

y = -2/3 (15) +7

y =  -10 +7

y = -3

(15 , -3)

-12:

y = -2/3 (-12) +7

y = 8 + 7

y= 15

(-12,15)

Answer:

1) 11

2) 3

3) -3

4) -12

Step-by-step explanation:

eq(1):

\(y = \frac{-2}{3} x + 7\\\\y - 7 = \frac{-2}{3} x\\\\x = (y - 7)\frac{-3}{2} \\\\x = (7-y)\frac{3}{2} ---eq(2)\)

1) x = -6

sub in eq(1)

\(y = \frac{-2}{3} (-6) + 7\\\\y = \frac{12}{3} + 7\\\\y = 4+7\\\\y = 11\)

2) y = 5

sub in eq(2)

\(x = (7-5)\frac{3}{2} \\\\x = 3\)

3) x = 15

sub in eq(1)

\(y = \frac{-2}{3} 15 + 7\\\\y = \frac{-30}{3} +7\\\\y = -10 + 7\\\\y = -3\)

4)

sub in eq(2)

\(x = (7-15)\frac{3}{2} \\\\x = -8\frac{3}{2}\\ \\x = -12\)

Answer:

hope this helps.

Step-by-step explanation:

The solution of the quadratic equation is x = 2. Therefore, \(\frac{4+\sqrt{-4^{2}-4(1)(4) } }{2(1)}\)  or \(\frac{4-\sqrt{-4^{2}-4(1)(4) } }{2(1)}\)

The quadratic formula can be use to solve the quadratic equation as follows:

x² - 4x + 4 = 0

Modelling it to quadratic equation, ax² + bx + c

Hence,

using quadratic formula,

\(\frac{-b+\sqrt{b^{2}-4ac } }{2a}\) or \(\frac{-b-\sqrt{b^{2}-4ac } }{2a}\)

where

Hence,

a = 1

b = -4

c = 4

Therefore,

\(\frac{4+\sqrt{-4^{2}-4(1)(4) } }{2(1)}\) or \(\frac{4-\sqrt{-4^{2}-4(1)(4) } }{2(1)}\)

Finally

x = 2

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a) The probability of getting exactly 5 successes is  0.1029.

b)The  probability of getting 6 or more successes is 0.8497510126.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

Here, p = 0.7, q = 0.3 and n = 10

a) The probability of getting exactly 5 successes

P (x= 5) = C(10, 5) (0.7)⁵ (0.3)⁵

             = 10!/ 5! 5! x 0.16807 x 0.00243

             = 0.1029

b)The  probability of getting 6 or more successes

P(X≥6) = 1 - P(X<6)

           = 1 - P(X = 0, 1,2, 3, 4, 5)

           = 1 - [ P(0) + P(1)  P(2) + P(3) + P(4) + P(5)]

           = 1 - [C(10, 0) \((0.3)^{10\) + C(10, 1) (0.7) \((0.3)^{9\) +  C(10, 2) (0.7)² \((0.3)^{8\)

                     + C(10, 3) (0.7)³ \((0.3)^{7\) + C(10, 4) \((0.7)^4\)\((0.3)^{6\)  + C(10, 4) \((0.7)^5\)

                                                                                                    \((0.3)^{5\)  ]

          = 1 - [ 0.0000059049 + 0.000137781 + 0.0014467005 +

                    0.009001692 + 0.036756909 +  0.1029]

          = 1 - 0.1502489874

          = 0.8497510126

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Answer:

3.14 or pi

Step-by-step explanation:

the area of a circle = \(pi * r^{2}\) where r is the radius of the circle

this is 1/4 of the circle, so it would be 1/4 (pi * r²)

it shows that the radius is 2, so you have

1/4 ( pi * 2²)

= 1/4 ( pi * 4 )

= 1/4 (3.14 * 4)

= 3.14 units²

Using the formula to calculate the length of arcs, the approximate length of boundary ABCD is 23.1

The arc length is defined as the interspace between the two points along a section of a curve.

The formula for calculating arc length is :\(2\pi r*\frac{theta}{360}\)

DC = 5

AB = 5

AD = \(2*\frac{22}{7} *5*\frac{30}{360} = 2.619\)

BC = \(2*\frac{22}{7} *5*\frac{120}{360} = 10.4762\)

Length of ABCD = AB + BC +CD + AD = 23.1

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Answer:

6x-18

Step-by-step explanation:

(2x-6) + 4(x-3)

(2x-6) + (4x-12)

2x - 6 + 4x - 12

6x-18

Answer:

6x-18 (simplified)

Step-by-step explanation:

After encountering each statement in a computer program, the value of x when x=2 is  a) x = 3, b) x remains 2, c) x = 3, d) x = 3, e) x = 3.

Let's analyze each statement in the computer program and determine the value of x after encountering them, assuming x = 2 before each statement:

a) if x + 2 = 4 then x := x + 1

The condition x + 2 = 4 evaluates to true because 2 + 2 = 4.

Therefore, the statement x := x + 1 is executed.

After executing the statement, x becomes 3.

b) if (x + 1 = 4) OR (2x + 2 = 3) then x := x + 1

The condition (x + 1 = 4) OR (2x + 2 = 3) evaluates to false because both sub-conditions are false.

Since the condition is false, the statement x := x + 1 is not executed.

The value of x remains 2.

c) if (2x + 3 = 7) AND (3x + 4 = 10) then x := x + 1

The condition (2x + 3 = 7) AND (3x + 4 = 10) evaluates to true because both sub-conditions are true (2 * 2 + 3 = 7 and 3 * 2 + 4 = 10).

Therefore, the statement x := x + 1 is executed.

After executing the statement, x becomes 3.

d) if (x + 1 = 2) XOR (x + 2 = 4) then x := x + 1

The condition (x + 1 = 2) XOR (x + 2 = 4) evaluates to true because only one of the sub-conditions is true (x + 2 = 4 is true).

Therefore, the statement x := x + 1 is executed.

After executing the statement, x becomes 3.

e) if x < 3 then x := x + 1

The condition x < 3 evaluates to true because 2 is less than 3.

Therefore, the statement x := x + 1 is executed.

After executing the statement, x becomes 3.

Please note that the values of x depend on the execution of the program based on the conditions. The values provided are based on the given conditions and the initial value of x.

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Answer:

The answer is A.

Step by step explanation

x²-1

Where

Roots (-1,0) (1,0)

Domain x€R

Range f(x)€ [-1,+infinity]

Minimum (0,-1)

Vertical intercept (0,-1)

A random sample is a representative subset of individuals selected from the larger population in such a way that each member of the population has an equal chance of being chosen.

The purpose of a random sample is to obtain a sample that is unbiased and reflects the characteristics of the entire population.

By giving every individual an equal opportunity to be included in the sample, random sampling helps minimize selection bias and ensures that the sample is more likely to be representative of the population as a whole. This allows researchers to make valid inferences and generalizations about the population based on the characteristics observed in the random sample.

Random sampling is widely used in various fields, including research, surveys, and statistical analysis, to draw reliable conclusions about a larger population based on a smaller subset of individuals.

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Answer:

first blank: 15

second blank: 90

Step-by-step explanation:

Obviously, sin and cos are related, but they are not the same thing. In order for them to be equal:

sin(____) = cos(75)

the angles have to add up to 90 (complementary)

What + 75 is 90?

Do a tiny calc:

90 - 75 is 15

The second question is stating the rule generically.

x + (90 - x) is 90

The value of is 1.645. This is derived from the area under the normal curve between 0 and 1.645 being equal to 0.25, which is one-fourth of the total area under the entire curve.

To calculate this, we must first understand the concept of the Standard Normal Distribution. The Standard Normal Distribution is a normal distribution with a mean of 0 and a standard deviation of 1. This is the basis of the calculation.

Next, we need to understand the concept of the cumulative probability density function. This is a function that gives the probability that a variable will take a value that is less than or equal to a given value.

For our calculation, we will use the cumulative probability density function for the Standard Normal Distribution.

Now, to calculate the value of , we can use the cumulative probability density function. We will set the cumulative probability density function equal to 0.25.

This is the probability that a variable will take a value that is less than or equal to . Solving for, we get 1.645. This is the value of.

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9514 1404 393

Answer:

  80%

Step-by-step explanation:

To convert a fraction or any number to a percentage, multiply by 100%.

  4/5 × 100% = 80%

80% of the movies are sold out.

Answer:

outfit costs 81 dollars

Step-by-step explanation:

Answer: Yes, she received $40 and the total cost of the outfit would be $38.98.

Answer: Yes

Step-by-step explanation:

Remember, a fraction with a negative sign anywhere is a negative fraction; in other words, it represents a negative quantity. As long as you write only one negative sign, it doesn't matter whether you put it before the denominator, before the numerator or before the entire fraction

Answer:

b

Step-by-step explanation:

(-12/25) (-10/16) = 0.3

3/10 = 0.3

\( - \frac{12}{25} \times - \frac{10}{16} = \frac{3}{5} \times \frac{2}{4} = \\ \)

\( \frac{3}{5} \times \frac{1}{2} = \frac{3}{10} \\ \)

Thus B is the correct answer...

♥️♥️♥️♥️♥️

a) The chance of drawing no court cards (J, Q, K, A) in a hand of 13 cards randomly drawn from a pack of 52 is approximately 0.294. b) The chance of drawing at least one ace but no other court cards in a hand of 13 cards is approximately 0.089. c) The chance of drawing at most one kind of court card (J, Q, K, A) in a hand of 13 cards is approximately 0.633.

a) To find the chance of drawing no court cards, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes. In this case, there are 36 non-court cards (52 cards - 16 court cards), and we want to draw 13 cards without any court cards. The probability can be calculated using the formula:

Probability = (number of favorable outcomes) / (total number of possible outcomes)

The number of favorable outcomes is the number of ways to choose 13 cards from the 36 non-court cards, which can be calculated using combinations. Thus, the probability is:

Probability = C(36, 13) / C(52, 13) ≈ 0.2936

b) To find the chance of drawing at least one ace but no other court cards, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes. There are 4 aces in the deck, and we want to draw at least one of them along with 12 non-court cards (36 non-court cards - 4 aces).

The probability can be calculated using the formula:

Probability = (number of favorable outcomes) / (total number of possible outcomes)

For drawing two aces, there are C(4, 2) ways to choose two aces and C(36, 11) ways to choose the remaining non-court cards.

Thus, the probability is:

Probability = [C(4, 1) * C(36, 12) + C(4, 2) * C(36, 11)] / C(52, 13) ≈ 0.0892

c) To find the chance of drawing at most one kind of court card, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes. There are 4 court cards of each kind (J, Q, K, A), and we want to draw at most one kind of court card.

The probability can be calculated using the formula:

Probability = (number of favorable outcomes) / (total number of possible outcomes)

The number of favorable outcomes is the sum of three cases: drawing no court cards, drawing only one kind of court card, and drawing one court card of each kind. We have already calculated the probability of drawing no court cards in part (a).

Thus, the probability is:

Probability = [C(36, 13) + 4 * C(36, 13) + 4 * C(36, 12)] / C

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To find the chances in a hand of 13 cards drawn randomly from a pack of 52, we can use probability. The chance of no court cards can be calculated using combinations. The probability of at least one ace but no other court cards can be found by subtracting the probability of no aces from the probability of no court cards. The probability of at most one kind of court card can be calculated by finding the probability of having zero court cards and one court card.

To find the chances in a hand of 13 cards drawn randomly from a pack of 52, we can use probability.

There are 12 court cards (J, Q, K, A) in a deck of 52 cards. So, to have no court cards in a hand, we need to select all 13 cards from the remaining 40 non-court cards. The probability can be calculated as 40C13/52C13.

To find this probability, we need to subtract the probability of having no aces from the probability of having no court cards. The probability of having no aces is 48C13/52C13, and the probability of having no court cards is 40C13/52C13. The result is the difference between these two probabilities.

To find the probability of having at most one kind of court card, we can calculate the probability of having zero court cards or one court card. The probability of having zero court cards can be calculated as 40C13/52C13, and the probability of having one court card can be calculated as 12C1 * 40C12/52C13. The sum of these two probabilities gives the probability of having at most one kind of court card.

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15 friends pay £6 each for hall practice with inverse proportion

Friends  = 5

Each pays = £18

Total payments = 5*18

                          = 90

Friends = 15

Each pays = 90/15

                 = 6

Hence, 15 friends pay £6 each for hall practice with inverse proportion.

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The maximum profit is 6 and it is obtained when we mix 0.6 kg of type A, 0 kg of type B, and 0.4 kg of type C.

The optimal mix for the maximum profit can be found as follows:

The company mixes three types of toffees, A, B, and C. Let the weights of type A, B, and C be a, b, and c kg, respectively. Let us assume that we are making 1kg of toffee pack. Therefore, the weight of type C should be 1 - (a + b) kg. Also, the mixture must contain at least 300 gms of type A i.e a >= 0.3 kg

Also, the weight of the first two types (A and B) must be at least equal to the weight of type C, i.e a + b >= c. This condition can also be written as a + b - c >= 0

Let us now calculate the total cost of making 1kg of toffee pack.

Cost = 20a + 10b + 5c

If the pack is sold at Rs. 17, then the profit per 1kg of toffee pack is by

Profit = Selling Price - Cost = 17 - (20a + 10b + 5c)

Now we have the following linear programming problem:

Maximize P = 17 - (20a + 10b + 5c)

Subject to constraints: a + b + c = 1 (since we are making 1kg of toffee pack)

a >= 0.3a + b - c >= 0a, b, c >= 0

We can use the simplex method to solve this linear programming problem. However, to save time, we can solve it graphically. The feasible region is as follows:

We can see that the corner points of the feasible region are: (0.3, 0, 0.7), (0.6, 0, 0.4), (0, 0.5, 0.5), and (0, 1, 0).

Let us calculate the profit at each of these corner points. For example, at the point (0.3, 0, 0.7), we have a = 0.3, b = 0, and c = 0.7. Therefore, the profit is

P = 17 - (20(0.3) + 10(0) + 5(0.7)) = 3.5

Similarly, we can calculate the profit at the other corner points as well. The corner point (0.3, 0, 0.7) gives a profit of 3.5

Corner point (0.6, 0, 0.4) result in a profit of 6

Corner point (0, 0.5, 0.5) results in a profit of 5

Corner point (0, 1, 0) gives a profit of 3

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Answer:

D. 4

Step-by-step explanation:

Without actually solving the equation, recall that for \(a=|b|\), there are two cases:

\(\begin{cases}a=b, \\a=-b\end{cases}\)

In the given equation \(|x-2|^{10x^2-1}=|x-2|^{3x}\), there are two pairs of absolute value symbols.

Since each has two cases, there must be a total of \(2\cdot 2=\boxed{4}\) different equations created.

All four cases are:

\(\begin{cases}(x-2)^{10x^2-1}=(x-2)^{3x},\\(-x+2)^{10x^2-1}=(x-2)^{3x},\\(x-2)^{10x^2-1}=(-x+2)^{3x},\\(-x+2)^{10x^2-1}=(-x+2)^{3x}\end{cases}\)

Exponents differ, hence clearly there are four possible solutions to this equation.

You can solve for all four values of \(x\) by taking the log of both sides and using a bit of algebra to verify you have four solutions.