if we remove all of the queens and jacks from a 52-card deck, how many unique four card hand combinations can we create?

The probability value for P(B) is obtained to be, Option (c) : 0.83.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

We can use the formula: P(A È B) = P(A) + P(B) - P(A Ç B) to find P(B).

Rearranging the terms, we get -

P(B) = P(A È B) - P(A) + P(A Ç B)

Substituting the given values, we get -

P(B) = 0.72 - 0.55 + 0.66

P(B) = 0.83

The probability of an event A occurring is denoted by P(A) and is a number between 0 and 1, inclusive.

If A and B are two events, then P(A È B) denotes the probability that at least one of A or B occurs.

P(A Ç B) denotes the probability that both A and B occur simultaneously.

The formula used to find P(B) in terms of P(A), P(A È B), and P(A Ç B) is known as the addition rule of probability.

Therefore, the answer is 0.83.

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Answer:

A- the slope is -4 and y-intercept is 3

Step-by-step explanation:

The standard form is y=mx+c (for straight line graph) while m is slope(gradient) and c is y-intercept.

So, slope is -4 and y-intercept is 3

======================================================

Explanation:

Plug in x = 1

f(x) = 17-x^2

f(1) = 17-1^2

f(1) = 17-1

f(1) = 16

Repeat for x = 5 to find that f(5) = -8

Now we'll use the formula below to find the average rate of change from x = a to x = b.

\(m = \frac{f(b)-f(a)}{b-a}\\\\m = \frac{f(5)-f(1)}{5-1}\\\\m = \frac{-8-16}{4}\\\\m = \frac{-24}{4}\\\\m = -6\\\\\)

The average rate of change is -6

The formula is basically the slope formula, more or less. So that's why I used 'm' to represent the average rate of change.

The average rate of change on the interval [1,5] is the same as finding the slope through the lines (1, 16) and (5, -8)

Answer:

A. $11.75

B. $1.75x + $1.00y = c (cost)

Step-by-step explanation:

A. Because apples cost $1.75 each you could multiply the amount of apples you intent to buy by $1.75 which in this case the amount of apples wanted is  3. $1.75 x 5 = $8.75. You would do the same thing for the peaches except the amount per peach is different. $1.00 x 3 = $3. Then you would add the two amounts together to get the amount Brooklyn and her friend would have to pay. $8.75 + $3 = 11.75

B. Because you multiply the amount of items you intend to get by the cost per item the equation you would follow if the amount of items changed would be. $1.75x + $1.00y = c (cost)

Hope this helps!

Please tell me if I am incorrect I enjoy learning from my mistakes!

Good luck!!

Answer:

64.3738

Step-by-step explanation:

Answer:

64

Step-by-step explanation:

5 miles is = to 8km, so, since it takes 5 times to get to 40 using 8, it would be 8x8(km). 8x8=64. If using a speed calculator, it makes some wierd numbers, just round.

Options B, C and D will satisfy the given inequality by putting the values in the given inequality.

let's first try to understand what are inequalities.

An inequality in algebra is a mathematical statement that employs the inequality symbol to show how two expressions relate to one another. The phrases on either side of an inequality symbol are not equal. The phrase on the left should be larger or smaller than the expression on the right, or vice versa, according to this symbol. Relationships between two algebraic expressions that are represented by inequality symbols are referred to as literal inequalities.

If the symbols ">,"< ">=," "<=,"  are used to connect two real numbers or algebraic expressions, that relationship is referred to as an inequality.

We put Given values in inequality and then see whether inequality is true or not.

Inequality is 3x+y < = 6

first x = 4 y =3

3x+y <= 6

3*4 + 3 <= 6

15 <= 6 this is not true because 15 is greater than 6.

second x = -2 y =4

3x+y <= 6

3*-2 + 4 <= 6

-2 <= 6 this is true because -2 is less than 6.

third x = -5, y =-3

3x+y <= 6

3*-5 + -3 <= 6

-15 <= 6 this is true because -15 is less than 6.

fourth x = 3, y = -3

3x+y <= 6

3*3 - 3 <= 6

6 <= 6 this is true because 6 is equal to  6.

Given Question is incomplete Complete the Question here:

How do you determine ordered pairs are part of the solution set of inequalities ex: #3x+y<=6#

for A(4,3), B(-2,4), C(-5,-3), D(3,-3)?

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Answer:

h > 24

Step-by-step explanation:

h/3 > 8

so basially you move the number three from the left side to the right side

so from division to multiplication

h > 8 x 3
h > 24
Solved !

Hope it helped ! Have a nice day !

The equation of the line in standard form is x + 2y = -16

Linear equations are the set of equations that have constant slopes or  gradient

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

y+4=-1/2(x+8)

Rewrite the above equation properly

So, we have the following representation

y + 4 = -1/2(x + 8)

Multiply through the equation by -2

So, we have the following equation

-2(y + 4) = -1/2(x + 8) * -2

Evaluate the products

-2y - 8 = x + 8

To rewrite as standard form is to make the variable stand alone

So, we have

-x -2y = 8 + 8

Evaluate the like terms

So, we have the following representation

-x -2y = 16

Multiply through by -1

x + 2y = -16

Hence, the equation is x + 2y = -16

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Possible question

consider the equation y+4=-1/2(x+8)

Put the equation of a line into standard form

The rate of change for the function is 15

From the information given, we have the function as;

f(x) = x² + 4x - 2

With an interval of -8≤x 3

Now, substitute the value of x as 8 in the function, we have;

f(8) = (8)² + 4(8) - 2

expand the bracket, we have;

f(8) = 64 + 32 - 2

add the values

f(8) = 96 - 2

f(8) = 94

Substitute for the value of 3

f(3) = (3)² + 4(3) - 2

expand the bracket

f(3) = 9 + 12 -2

f(3) 19

Then, the rate of change;

= 94 - 19/8 - 3

= 75/5

= 15

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Answer:

{-2,3,4,2}

Domain is basically the x values

Answer:

domain = {-2,3,4,2}

Step-by-step explanation:

domain is related to x coordinate of the point

To create an ellipse with a semi-major axis of 5 AU (astronomical units) and eccentricity of 0.5, we can follow these steps:

1. Find the semi-minor axis b by using the formula:

b = a * sqrt(1 - e^2)

where a is the semi-major axis and e is the eccentricity.

b = 5 * sqrt(1 - 0.5^2) = 3.6515 AU (rounded to four decimal places)

2. Determine the center of the ellipse, which is the point (h, k) on the Cartesian plane. Since the eccentricity is less than 1, the center is at the origin (0,0).

3. Sketch the ellipse using the semi-major axis a, semi-minor axis b, and the center (0,0) as a reference point.

To plot points on the ellipse, we can use the parametric equations for an ellipse in standard position:

x = a * cos(t)

y = b * sin(t)

where t is the angle in radians measured from the positive x-axis. We can choose values of t and plug them into these equations to get the corresponding x and y coordinates.

For example, when t = 0, we have:

x = 5 * cos(0) = 5

y = 3.6515 * sin(0) = 0

So the point (5, 0) is on the ellipse.

We can repeat this process for different values of t to plot more points on the ellipse. Finally, we can connect the points to create the ellipse.

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To create an ellipse with a semi-major axis of 5 AU (astronomical units) and eccentricity of 0.5, we can follow these steps:

1. Find the semi-minor axis b by using the formula:

b = a * sqrt(1 - e^2)

where a is the semi-major axis and e is the eccentricity.

b = 5 * sqrt(1 - 0.5^2) = 3.6515 AU (rounded to four decimal places)

2. Determine the center of the ellipse, which is the point (h, k) on the Cartesian plane. Since the eccentricity is less than 1, the center is at the origin (0,0).

3. Sketch the ellipse using the semi-major axis a, semi-minor axis b, and the center (0,0) as a reference point.

To plot points on the ellipse, we can use the parametric equations for an ellipse in standard position:

x = a * cos(t)

y = b * sin(t)

where t is the angle in radians measured from the positive x-axis. We can choose values of t and plug them into these equations to get the corresponding x and y coordinates.

For example, when t = 0, we have:

x = 5 * cos(0) = 5

y = 3.6515 * sin(0) = 0

So the point (5, 0) is on the ellipse.

We can repeat this process for different values of t to plot more points on the ellipse. Finally, we can connect the points to create the ellipse.

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The part of the function over the interval (-2,2) is nonlinear and decreasing.

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The length of the diagonal YW of rectangle WXYZ is; 5 units.

The diagonals of a rectangle are congruent and so;

YW ≅ XZ

Thus; YW = XZ = b

Now, given the three sides of right triangle XWZ, we can solve for XZ using Pythagorean Theorem:

(XW)² + (WZ)² = (XZ)²

Plugging in the relevant values gives;

3² + 4² = b²

9 + 16 = b²

25 = b²

b = √25

b = 5

Thus, we can conclude that the length of the diagonal YW is 5 units.

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We as we see this question is quite simple

first we find the vocabulary which is in simple text slang and convert it formally to english...

Next we find that this question makes no sense so g'day

The y intercept is the point at which the line/curve cuts the y axis

The curve cuts the y axis at point (0 , 22) so the y intercept is therefore

(0 , 22)

Therefore, it will take approximately 0.34 years for the substance to decay to half of its original amount, rounded to the nearest hundredth year.

A function is a rule that assigns to each input value (or argument) from a set called the domain, a unique output value (or result) from a set called the range. The function is usually denoted by a symbol such as f(x), where "f" is the name of the function and "x" is the input value.

A function can be visualized as a mapping between two sets, where each element of the domain is paired with exactly one element of the range. This mapping can be represented graphically by a plot of the function, which shows how the output values change as the input values vary.

The amount of a radioactive substance at a given time t is given by the function \(A(t) = A_{0} e^{(-kt)}\), where A₀ is the initial amount and k is the decay constant. In this case, we are given A₀ = 500 and k = 2.04.

To find the time it takes for the substance to decay to half of its original amount, we need to solve the equation:

\(A(t) = 0.5A_{0}\)

Substituting the given values, we get:

\(0.5A_{0} = 500e^{(-2.04t)}\)

Dividing both sides by 500, we get:

\(e^{(-2.04t)} = 0.5\)

Taking the natural logarithm of both sides, we get:

\(-2.04t = ln(0.5)\)

Solving for t, we get:

\(t = -ln(0.5)/2.04\)

Using a calculator, we get:

t ≈ 0.34

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The equation that shows the product of a square matrix A and its identity matrix as A is A * I = A.

In matrix multiplication, when a matrix is multiplied by an identity matrix, the resulting matrix is the same as the original matrix. An identity matrix is a square matrix with ones on the diagonal and zeros elsewhere. The size of the identity matrix is determined by the size of the original matrix.

By multiplying a square matrix A by the identity matrix I, each element of A is multiplied by the corresponding element of I, which is 1 if the positions are on the diagonal and 0 otherwise. Since multiplying any number by 1 gives the same number, the resulting matrix will be equal to the original matrix A. Therefore, the equation A * I = A expresses this relationship.


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Answer:

Width: 20 in

Length: 25 in

Explanation:

We can represent the situation with the following figure

Where x is the width of the rectangular piece of metal, (x + 5) is the length of the rectangular because it is 5 in longer than its wide, and the corners have squares of side 1 in.

Therefore, the volume of the box will be equal to

Volume = Length · Width · Height

Volume = (x + 5 - 1 - 1) · (x - 1 - 1) · (1)

Volume = (x + 3)(x - 2)(1)

Volume = (x + 3)(x - 2)

Because the length of the box will be the length of the rectangle less the length of the squares and the width of the box will be the length of the rectangle less the width of the squares.

The volume is 414 in³, so we need to solve the following equation:

414 = (x + 3)(x - 2)

414 = x² + 3x - 2x + 3(-2)

414 = x² + x - 6

414 - 414 = x² + x - 6 - 414

0 = x² + x - 420

Factorizing x² + x - 420, we get:

(x + 21)(x - 20) = 0

Then

x + 21 = 0

x + 21 - 21 = 0 - 21

x = -21

or

x - 20 = 0

x - 20 + 20 = 0 + 20

x = 20

Since x = -21 doesn't have sense, the width is x = 20 and the length is:

x + 5 = 20 + 5 = 25 in.

So, the original width is 20 in and the original length is 25 in

Answer:

1. (2,5) 2. (-1,0) 3. (-3.5,-3.5)

Step-by-step explanation:

to solve these you need to take the x and y of each point and find the number in-between for example number 1 the x value is 3, and 1, the number in-between is 2. The way I like to do these is with a graph, place both points on the graph and connect them with a line find the middle of the line and that's your midpoint.

Answer:

the answer is Y = -1.5x + 36

Answer:

17

Step-by-step explanation:

Given quardratic polynomial is 3x^2+(2k-5)x-7

On Comparing this with the standard quadratic Polynomial ax^2+bx+c

a = 3

b=2k-5

c = -7

Given zeroes α and -α

sum of the zeroes α +(-α) = -b/a

⇛ α +(-α) = -(2k-5)/3

⇛ 0 = -(2k-5)/3

⇛ 0×3 = -(2k-5)

⇛0 = -(2k-5)

⇛-2K+5 = 0

⇛ -2k = -5

⇛ 2k = 5

⇛ k = 5/2

Answer:- The value of k is 5/2.

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the mass of the rod is 673.8 kg.To find the mass of the rod, we need to integrate the density function over the interval [1, 4].

The mass of the rod (m) can be calculated using the formula:

m = ∫(1 to 4) p(x) dx,

where p(x) represents the density function.

Substituting the given density function p(x) = 4 + 3x^4 into the integral, we have:

m = ∫(1 to 4) (4 + 3x^4) dx.

Evaluating this integral will give us the mass of the rod in kilograms. To calculate the integral, we can find the antiderivative of the integrand and evaluate it at the upper and lower limits of integration.

Performing the integration, we have:

m = [4x + (3/5)x^5] evaluated from 1 to 4.

Substituting the upper and lower limits, we get:

m = (4(4) + (3/5)(4^5)) - (4(1) + (3/5)(1^5)).

Simplifying further:

m = 64 + (3/5)(1024) - 4 - (3/5).

Combining like terms and simplifying, we find the mass of the rod:

m = 64 + 614.4 - 4 - 0.6 = 673.8 kg.

Therefore, the mass of the rod is 673.8 kg.



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The number of cups of vinegar that Mike used lies between the whole numbers 2 and 4

If Mike used one cup of vinegar for each salad dressing recipe, then he used a total of 3 cups of vinegar (1 cup x 3 recipes = 3 cups).

However, the question states that he used "a cup of vinegar" in each recipe, which could mean that he used slightly less than one cup, exactly one cup, or slightly more than one cup.

Assuming that Mike used at least 3/4 cup of vinegar in each recipe (which is still close to "a cup"), then he used a minimum of 2 and 1/4 cups of vinegar in total (3/4 cup x 3 recipes = 2 and 1/4 cups).

Assuming that Mike used at most 1 and 1/4 cups of vinegar in each recipe (which is still close to "a cup"), then he used a maximum of 3 and 3/4 cups of vinegar in total (1 and 1/4 cups x 3 recipes = 3 and 3/4 cups).

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without knowing the distance between mile marker 195 and the mouth of the river, we cannot calculate the gradient along the same stretch of the Sacramento River.

The gradient along the same stretch of the Sacramento River can be calculated by finding the change in elevation divided by the distance.
Given that the interval is 115 ft and the distance is from mile marker 195 to the mouth of the river at sea level, we need to determine the total distance in miles.
To do this, we need to know the distance between mile marker 195 and the mouth of the river. Unfortunately, this information is not provided in the question.

Without knowing the specific distance, we cannot accurately calculate the gradient. Therefore, the answer cannot be determined with the information given.

In conclusion, without knowing the distance between mile marker 195 and the mouth of the river, we cannot calculate the gradient along the same stretch of the Sacramento River.

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the required probability is 0.5668

Given that the distribution of the time it takes for the first goal to be scored in a hockey game is known to be extremely right-skewed with population mean 12 minutes and population standard deviation 8 minutes.

We need to find the probability

that in a random sample of 36 games, the mean time to the first goal is more than 15 minutes.To find this probability, we will use the z-score formula.z = (x - μ) / (σ / √n)wherez is the z-scorex is the sample meanμ is the population meanσ is the population standard deviationn

is the sample sizeGiven that n = 36, μ = 12, σ = 8, and x = 15, we havez = (15 - 12) / (8 / √36)z = 1.5Therefore, the probability that in a random sample of 36 games, the mean time to the first goal is more than 15 minutes is P(z > 1.5).We can find this probability using a standard normal table or a calculator.Using a standard normal table, we can find the area to the right of the z-score of 1.5. This is equivalent to finding the area between z = 0 and z = 1.5 and subtracting it from 1.P(z > 1.5) = 1 - P(0 < z < 1.5)Using a standard normal table, we find thatP(0 < z < 1.5) = 0.4332Therefore,P(z > 1.5) = 1 - 0.4332 = 0.5668Therefore, the probability that in a random sample of 3games, the mean time to the first goal is more than 15 minutes is 0.5668 (rounded to four decimal places).

Hence, the required probability is 0.5668.

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The probability that in a random sample of 36 games, the mean time to the first goal is more than 15 minutes is approximately 0.0122 or 1.22%.

The probability that in a random sample of 36 games, the mean time to the first goal is more than 15 minutes can be determined using the Central Limit Theorem (CLT).

According to the CLT, the distribution of sample means from a large enough sample follows a normal distribution, even if the population distribution is not normal. In this case, since the sample size is 36 (which is considered large), we can assume that the sample mean follows a normal distribution.

To find the probability, we need to standardize the sample mean using the population mean and standard deviation.

First, we calculate the standard error of the mean, which is the population standard deviation divided by the square root of the sample size. In this case, it would be 8 / √36 = 8 / 6 = 4/3 = 1.3333.

Next, we calculate the z-score, which is the difference between the sample mean and the population mean divided by the standard error of the mean. In this case, it would be (15 - 12) / 1.3333 = 2.2501.

Finally, we use the z-table or a calculator to find the probability associated with a z-score of 2.2501. The probability is the area under the standard normal curve to the right of the z-score.

Using a z-table, we find that the probability is approximately 0.0122. This means that there is a 1.22% chance that the mean time to the first goal in a random sample of 36 games is more than 15 minutes.

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The probability of x taking on a value between 75 to 90 is 0.25.

Given that x is a continuous random variable uniformly distributed between 65 and 85.To find the probability that x lies between 75 and 90, we need to find the area under the curve between the values 75 and 85, and add to that the area under the curve between 85 and 90.

The curve represents a rectangular shape, the height of which is the maximum probability. So, the height is given by the formula height of the curve = 1/ (b-a) = 1/ (85-65) = 1/20.Area under the curve between 75 and 85 is = (85-75) * (1/20) = (10/20) = 0.5Area under the curve between 85 and 90 is = (90-85) * (1/20) = (5/20) = 0.25.

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Answer: 946 ml

Step-by-step explanation: 1 pint= 473.2

2*

473.2= 946.4

=946 ml

Answer:

The original data set would be:

57, 58, 61, 66, 71, 77, 82, 91, 95, 100, 102, 105

So to find the range you would do:

105 - 57 which equals 48.

So the range for the original data set would be 48.

The new data set adding 80.8:

57, 58, 61, 66, 71, 77, 80.8, 82, 91, 95, 100, 102, 105

So to find the range for the new data set you would do:

105 - 57 which would still equal 48.

So the range for the new data set would be 48.

The range for the original and new data set stayed the same.

Step-by-step explanation:

You're welcome.

Answer:

The original data set would be:57, 58, 61, 66, 71, 77, 82, 91, 95, 100, 102, 105So to find the range you would do:105 - 57 which equals 48.So the range for the original data set would be 48.The new data set adding 80.8:57, 58, 61, 66, 71, 77, 80.8, 82, 91, 95, 100, 102, 105So to find the range for the new data set you would do:105 - 57 which would still equal 48.So the range for the new data set would be 48.The range for the original and new data set stayed the same.

Step-by-step explanation: hi everybodyyy!!