Assume that 2 cards are drawn from a standard 52-card deck. Find the following probabilities.
a) Assume the cards are drawn without replacement. Find the probability of drawing a club followed by a club.
b) Assume the cards are drawn with replacement. Find the probability of drawing a club followed by a club.
a. The probability of drawing a club followed by a club without replacement is
(Simplify your answer.)
b. The probability of drawing a club followed by a club with replacement is
(Simplify your answer.)

Answer:

90 stamps from Canada, 108 stamps from the United States, and 135 stamps from the Rest of the World

Step-by-step explanation:

Since this is a problem of proportion we can use the Rule of three to solve this. We do this by multiplying the diagonal available values and dividing by the third value in order to get the missing variable, which in this case would be the number of stamps in the other country. Like so...

1.5  <=====>  135 stamps

1.2  <=====>  x  stamps (United States)

(1.2 * 135) / 1.5 = 108 stamps (United States)

1.5  <=====>  135 stamps

1  <=====>  x  stamps (Canada)

(1 * 135) / 1.5 = 90 stamps (Canada)

Finally, we can see that Katie had 90 stamps from Canada, 108 stamps from the United States, and 135 stamps from the Rest of the World. All creating a ratio or 1:1.2:1.5

Answer:

Step-by-step explanation:

To get the remainder of (x-(-1)) we need to evaluate for -1,

\((-1)^{11}+101=-1+101=100\)

So if this is divided by x+1, it means that we can write

\(x^{11}+101=(x+1)P(x)+R\\\\so \ for \ x = -1\\\\(-1)^{11}+101=100=0*P(-1)+R=R\\\\\text{So the remainder is 100 !!}\)

thanks

a) Probability of occurrence of evant A is equals to the 7/10.

P(not getting a white or a blue shirt), P(Aᶜ ) is equals the 3/10.

Probability of occurrence of evant B is equal to the 1/2.

b) The events A and B are not mutually exclusive

c) Mike's preference is to getting a white shirt with his size L.

We have a probabality based problem. Probability is defined as chance of occurrence of an event or result. It can be calculate as favourable outcomes divided by total possible outcomes. There is total number of avaliabile shirts = 20 i.e., total possible outcomes = 20

Mike is interested in getting a white or a blue shirt in size L. Let us consider two events :

A : Getting a white or a blue shirt

B: Getting a shirt in size L

a) Number of favourable outcomes to getting white or a blue shirt = 9 white or 5 blues

Probability ( Getting a white or a blue shirt) , P(A)

= 9/20 + 5/20 + 0 = 14/20 = 7/10

P(not Getting a white or a blue shirt), P(Aᶜ )

= 1 - P(A) = 1 - 7/10 = 3/10

ii) The number of favourable outcomes for event B, n(B) = 10

So, Probability of getting a shirt in size L, P(B)

= 10/20 = 1/2

b) Mutually exclusive events are defined as the events that can't happen at the same time. In other words AnB = 0 . Here, we see there is total 14 shirts which are in white or blue colors and 10 are in size L , So there is possibility that shirt is white or blue in colour and in size L , i.e, An B ≠0

So, events A and B are not mutually exclusive.

c) Event ,n( A u B )= n(A) + n(B) - n(A n B)

On the basis of all details, we conclude that Mike's preference is to choose white shirt with size L .

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Answer: D

Step-by-step explanation:

To determine which ordered pair is a solution to the inequality, we can substitute the values of x and y into the inequality and check if it is true.

Let's start with ordered pair A (80, 6):

1/4x ≤ 7/3y + 2

1/4(80) ≤ 7/3(6) + 2

20 ≤ 14 + 2

20 ≤ 16

This is not true, so ordered pair A is not a solution to the inequality.

Now let's try ordered pair B (48, 9):

1/4x ≤ 7/3y + 2

1/4(48) ≤ 7/3(9) + 2

12 ≤ 21 + 2

12 ≤ 23

This is also not true, so ordered pair B is not a solution to the inequality.

Next, let's try ordered pair C (40, 3):

1/4x ≤ 7/3y + 2

1/4(40) ≤ 7/3(3) + 2

10 ≤ 7 + 2

10 ≤ 9

This is false, so option C is not a solution to the inequality.

Finally, we have option D: (2, -6)

1/4(2) ≤ 7/3(-6) + 2

1/2 ≤ -14 + 2

1/2 ≤ -12

This is true, so option D is a solution to the inequality.

Therefore, the answer is D: (2, -6).

Answer:

count all of the weight on the right side, subtract 4 pounds from both sides, and divide it by 2.

Step-by-step explanation:

Answer:

y=2x-3 or B

Step-by-step explanation:

just shove into desmos graphing calculator

The probabilities in these cases are 0.125, 0.375, 0.58, 0.16, 0.5  and the only prime and even number is 2.

The probability is defined by the formula: specific outcome/ total possible outcomes. Based on this, let's calculate the probability in each case:

A prime number can be defined as a number that can be divided only by 1 and the number itself. On the opposite, a composite number can be divided by at least another number than 1 and itself.

The only prime and even number is 2.

Note: Here is the question in English:

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The center of mass for the system (x, y) is \(\left(\frac{a m+b M}{m+M}, 0\right)\).

What is center of mass?

The unique location where the weighted relative position of the scattered mass adds to zero is known as the center of mass in physics. Here is where a force may be applied to produce a linear acceleration without also producing an angular acceleration.

The center of mass is a position defined relative to an object or system of objects. It is the average position of all the parts of the system, weighted according to their masses.

Centre of mass is

\(x=\frac{m a+M b}{m+M}\)

and y=0

\((x, y)=\left(\frac{a m+b M}{m+M}, 0\right)\)

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h = hours till they're 58 miles apart

Check the picture below.

so they're travelling in opposite directions, however the combined distances is 58 miles at say "h" hours, by the time that happend Hopi has been walking "h" hours and Brittany has also being walking "h" hours too.

Since the combined distance is 58 miles than if Hopi has covered "m" miles then Brittany covered the slack of "58 - m".

\({\Large \begin{array}{llll} \underset{distance}{d}=\underset{rate}{r} \stackrel{time}{t} \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ Hopi&m&15&h\\ Brittany&58-m&14&h \end{array}\hspace{5em} \begin{cases} m=(15)(h)\\\\ 58-m=(14)(h) \end{cases} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{substituting on the 2nd equation}}{58-(\stackrel{m}{15h})=14h}\implies 58=29h\implies \cfrac{58}{29}=h\implies \boxed{2=h}\)

Answer:

I think the club made 3 pies.

Step-by-step explanation:

64 divided by 8 is 8. And 8 minus 5 is 3.

Answer: B)  False

Step-by-step explanation:

Detailed explanation:

F(x), when x=2, is 3x2-5x+1.

3(2)²-5(2)+1

3(4)-10+1

12-10+1

F(x)=3

hence false

Answer:

(3 × 10^4)+ (7 × 10^3) +(0 × 10^2) + (1 × 10^1) + (5 × 10^0) + (0 × 10^-1) + (8 × 10^-2)

Answer:

Step-by-step explanation:

We know that:

Work:

Hence, for a bag, it uses 7/8 yards of fabric.

If ABCD is dilated by a scale factor of 3, the coordinate of B' would be (-6, 6).

In Geometry, dilation simply refers to a type of transformation which typically changes the size of a geometric object, but not its shape.

This ultimately implies that, the size of the geometric shape would be increased (stretched or enlarged) or decreased (compressed or reduced) based on the scale factor applied.

Next, we would apply a dilation to the coordinates of the pre-image by using a scale factor of 3 centered at the origin as follows:

Ordered pair B (-2, 2) → Ordered pair B' (-2 × 3, 2 × 3) = Ordered pair B' (-6, 6).

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Answer:

X= -3

Step-by-step explanation:

(4+5)-1/3(40-4)=X

X=9- 1/3(36)

X=9-12

The addition property of equality is used when we add 9 to both sides

6x-9 = 45

6x-9+9 = 45+9

6x = 54

The next step would be to divide both sides by 6 using the division property of equality

6x = 54

6x/6 = 54/6

x = 9

Answer:

C. 4.6

Step-by-step explanation:

If you subtract 3.0 from 1.4 you get 1.6, which is the can be added to 3.0 to find the missing value.

Answer:

d does not have an inverse image

Step-by-step explanation:

From the question we are told that

    The  first set is    A (10, 11, 12, 13 )

     The  second set is     B (a, b, c, d)

      The function that from A to B is  f(10, a), (11,a), (12, b), (13,b))

Generally for a function defined by (x,y), y is the image of x while x is the inverse image  of  y

Now considering the function we are given and the value d we see that and inverse image is not defined for d in the function

hence d does not have an inverse image  

what you mean but heres the points on the map u were talking about

Answer: The slope m = 3/5

Step-by-step explanation:

The slope can be found by using the formula: m = y2 - y1 / x2-x1

Where m is the slope and (x1, y1) and (x2, y2) are the two points on the line.

x1 = 2  , y1 = 1

x2 = -3 , y2 = -2

Substituting the values from the points in the problem gives :

m = -2-1 / -3-2

m = 3/5

Hence, the slope that passes through (2, 1) and (-3, -2) is 3/5.

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100 feet of caution tape is required for the store.

Given that a police officer must run caution tape around a store where a crime occurred. The store is 30 feet long and 20 feet wide and asked to find the tape  required for the store.

According to given measurements, we assume the store be in rectangular shape .To find the tape required, calculate the perimeter of the rectangle.

Perimeter of the rectangle=2 ( length + width )

Given length = 30 feet and width = 20 feet

Perimeter of the rectangle = 2 ( 30 feet + 20 feet )

Perimeter of the rectangle = 2 ( 50 feet )

Perimeter of the rectangle = 100 feet

Therefore 100 feet of caution tape is required for the store.

Hence , caution tape of 100 feet is required for the store.

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We have that theses  Can affect the price if grape indirectly

From the question we are told

Name at least two independent variables that could result in a change in the price of a basket of grape fruits

Generally Independent variables are variables that are not dependent on the price of grape fruits directly

Therefore

We have that

People Can affect the price if grape indirectly

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y≤−5x−10 and y>x+2 The shaded region satisfies both inequalities and represents the solution to the system of linear inequalities.

To graphically solve this system of linear inequalities, we can start by graphing each inequality on the same coordinate system:

First, let's graph the inequality y ≤ -5x - 10. We can start by graphing the line y = -5x - 10, which is the boundary line of the inequality. We can plot two points on this line, say (-2,0) and (0,-10), and draw a straight line passing through them.

Next, we need to determine which side of the line satisfies the inequality y ≤ -5x - 10. We can choose any point on one side of the line, say (0,0), and test it in the inequality. If y ≤ -5x - 10 is true for (0,0), then that side of the line satisfies the inequality. Otherwise, the other side satisfies the inequality. Testing (0,0), we have:

0 ≤ -5(0) - 10

0 ≤ -10

This is false, so the side of the line containing the origin does not satisfy the inequality. The other side of the line does.

Now, let's graph the inequality y > x + 2. We can start by graphing the line y = x + 2, which is the boundary line of the inequality. We can plot two points on this line, say (-2,0) and (0,2), and draw a straight line passing through them.

Next, we need to determine which side of the line satisfies the inequality y > x + 2. We can choose any point on one side of the line, say (0,0), and test it in the inequality. If y > x + 2 is true for (0,0), then that side of the line satisfies the inequality. Otherwise, the other side satisfies the inequality. Testing (0,0), we have:

0 > 0 + 2

This is false, so the side of the line containing the origin does not satisfy the inequality. The other side of the line does.

Now, we can shade the region that satisfies both inequalities. The shaded region is the region that is below the line y = -5x - 10 (including the line itself) and above the line y = x + 2 (excluding the line itself).

The shaded region is shown below:

Graph of y≤−5x−10 and y>x+2

The shaded region satisfies both inequalities and represents the solution to the system of linear inequalities.

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A. The following are sets A and B:

A = {2, 3, 5, 7, 11}

B = {1, 2, 3, 4, 6, 12}

C. Elements not in A or A' = ∅

B. The Venn diagram is attached

A universal set is a set which consists of all elements related to the given sets. It is denoted by U.

A. Set A:

A = {2, 3, 5, 7, 11}

Set B:

B = {1, 2, 3, 4, 6, 12}

U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

A' = {1, 4, 6, 8, 9, 10, 12}

C. Elements not in A or A' = ∅

Complement of set A is refers to a set that contains the elements present in the universal set but not in set A.

Hence, the Venn diagram of sets A, B and U has been attached.

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The solution to the nonlinear system of equations is (x, y) = (-3, -2) and (x, y) = (1, 6). These points represent the coordinates where the two equations intersect and satisfy both equations simultaneously.

To solve the nonlinear system of equations:

Equation 1: \(y = -x^2 + 7\)

Equation 2: y = 2x + 4

We can equate the right sides of both equations since they both represent y.

\(-x^2 + 7 = 2x + 4\)

To simplify the equation, we can rearrange it to be in the standard quadratic form:

\(x^2 + 2x - 3 = 0\)

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, let's use factoring:

(x + 3)(x - 1) = 0

From this equation, we get two possible solutions:

x + 3 = 0 => x = -3

x - 1 = 0 => x = 1

Now, we substitute these x-values back into either equation to find the corresponding y-values.

For x = -3:

y = 2(-3) + 4

y = -6 + 4

y = -2

For x = 1:

y = 2(1) + 4

y = 2 + 4

y = 6

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The length of the rectangle is twice its width. If its perimeter is 7 1/3 cm, its length will be 22/9 cm, and the width is 11/9 cm.

Let's assume the width of the rectangle is "b" cm.

According to the given information, the length of the rectangle is twice its width, so the length would be "2b" cm.

The formula for the perimeter of a rectangle is given by:

Perimeter = 2 * (length + width)

Substituting the given perimeter value, we have:

7 1/3 cm = 2 * (2b + b)

To simplify the calculation, let's convert 7 1/3 to an improper fraction:

7 1/3 = (3*7 + 1)/3 = 22/3

Rewriting the equation:

22/3 = 2 * (3b)

Simplifying further:

22/3 = 6b

To solve for "b," we can divide both sides by 6:

b = (22/3) / 6 = 22/18 = 11/9 cm

Therefore, the width of the rectangle is 11/9 cm.

To find the length, we can substitute the width back into the equation:

Length = 2b = 2 * (11/9) = 22/9 cm

So, the length of the rectangle is 22/9 cm, and the width is 11/9 cm.

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3÷2 is the equation u would use to find out the amount for each.

The proportional equation to calculate the amount of flour needed is y= 3/2 x.

Constant of proportionality is the constant value of the ratio between two proportional quantities. Two varying quantities are said to be in a relation of proportionality when, either their ratio or their product yields a constant. The value of the constant of proportionality depends on the type of proportion between the two given quantities: Direct Variation and Inverse Variation.

Direct Variation: The equation for direct proportionality is y = kx,  which shows as x increases, y also increases at the same rate.

Example: The cost per item(y) is directly proportional to the number of items(x) purchased, expressed as y ∝ x

Inverse Variation: The equation for the indirect proportionality is y = k/x, which shows that as y increases, x decreases and vice-versa. Example: The speed of a moving vehicle (y) inversely varies as the time taken (x) to cover a certain distance, expressed as y ∝ 1/x

Given:

For 2 cake = 3 cups of flour used

So, For 1 cake = 3/2 cups of flour used

Now, let if we have make 7 cake then the flour used

=7 x 3/2

=21/2 cups

=10 1/2 cups of flour.

Hence, the proportion is y= 3/2x where y is cake and x is amount of flour.

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