Anwar selects a playing card at random from the following 6 cards:
{9 of hearts, 5 of spades, 6 of hearts, 2 of spades, 4 of hearts, 7 of hearts}
Let A be the event that Anwar selects an even-numbered card and B be
the event that she chooses a heart.
Which
of the following statements are true?
at apply:
Choose all answers that a
P(A|B) = P(A), the conditional probability that Anwar selects
an even-numbered card given that she has chosen a heart is equal to
the probability that Anwar selects an even-numbered card.
P(BA) = P(B), the conditional probability that Anwar selects
a heart given that she has chosen an even-numbered card is equal to
the probability that Anwar selects a heart.
Events A and B are independent events.
The outcome of events A and B are dependent on each other.
P(A and B)=P(A) - P(B). the probability that Anwar selects
a card that is even-numbered and a heart is equal to the probability
that Anwar selects an even-numbered card multiplied by the
probability that she selects a heart.
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The correct statement is; Pentagon M’N’P’Q’R is smaller than pentagon MNPQR because the scale factor is smaller than 1.

The ratio between comparable measurements of an item and a representation of that thing is known as a scale factor in arithmetic.

If a polygon is dilated by a scale factor = k

Rule to be followed as;

(x, y) → (kx, ky)

Here, k = Scale factor

If 0 < k < 1, size of the image will be reduced.

Similarly, k > 1, size of the image will be enlarged.

We are given that Pentagon MNPQR is dilated with the origin as the center of dilation to form an image M'N'P'Q'R'.

Rule used for the transformation,

(x, y) → (1/4x, 1/4y)

Here, the scale factor through which MNPQR has been dilated is 1/4.

Since, scale factor is between zero and 1/4, size of M'N'P'Q'R' will be reduced.

Therefore, the size of pentagon M'N'P'Q'R' will be 1/4 smaller than pentagon MNPQR.

Option (2) is the answer.

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The complete question is: Pentagon MNPQR is shown on the coordinate grid. Pentagon MNPQR is dilated with the origin as the center of dilation using the rule (x, y)→(1/4x, 1/4y) to create pentagon M'N'P'Q'R'.

Which statement is true?

a. Pentagon M'N'P'Q'R' is larger than pentagon MNPQR, because the scale factor is greater than 1.

b. Pentagon M'N'P'Q'R' is smaller than pentagon MNPQR, because the scale factor is less than 1.

c. Pentagon M'N'P'Q'R' is larger than pentagon MNPQR, because the scale factor is less than 1.

d. Pentagon M'N'P'Q'R' is smaller than pentagon MNPQR, because the scale factor is greater than 1.

Answer:

7 to 8 months / most probably 8 months

7.5 months to be exact

Step-by-step explanation:

Hi there!! Let's work!

So lets Break it down,

Given: $40 every month

Prove: How many months till he has in total $300

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400 x (months) = $300 / (or how much ever we get)

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We have 2 final equations because we don't have a straight forward answer. (Refer to explanation below)

40 x 7 = 280

and

40 x 8 = 320

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So in problems like these we have to think like we would in real life, if you have an option you can write 7 to 8 months or you should write 8 instead of seven since they may be asking for a specific amount of months and after 8 months Gage will reach (surpass) his goal of $300 by $20.

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Answer:

To simplify the expression (a÷b)³×(b÷c)×(c÷a)³ when a=3, b=a², c=a³, we can substitute the given values and perform the calculations.

Substituting the values of a, b, and c:

a = 3

b = a² = 3² = 9

c = a³ = 3³ = 27

Now let's simplify the expression:

(a÷b)³×(b÷c)×(c÷a)³

(3÷9)³×(9÷27)×(27÷3)³

Simplifying each term:

(3÷9) = 1/3

(9÷27) = 1/3

(27÷3) = 9

Now we can substitute the simplified values back into the expression:

(1/3)³×(1/3)×9

Simplifying further:

(1/27)×(1/3)×9

1/9

Therefore, the simplified expression is 1/9.

Answer:

The input is x−2, therefore

Step-by-step explanation:

f(x−2)=(x−2)2−3(x−2)+1

Answer:

Step-by-step explanation:

Let x = base side length

y = side height

volume V = x²y

y = V/x²

surface area

A = x² + 4xy

A = x² + 4x(V/x²)

A = x² + 4V/x

Solving for volume

V = (A - x²)(x/4)

V = ¼(Ax - x³)

a maximum will occur when the derivative equals zero

V' = ¼(A - 3x²)

0 = ¼(A - 3x²)

0 = A - 3x²

3x² = A

3x² = 1100

x² = (1100 / 3)

x = √(1100/3)

V = (A - x²)(x/4)

V = (1100 - √(1100/3))²(√(1100/3)/4)

V = 3,510.56606...

V = 3510.6 cm³

The box height will be half of the base side length.

y = ½√(1100/3)

Step-by-step explanation:

We can use the Pythagorean theorem to find the height of the cone, h. The slant height, s, and radius, r, of the cone form a right triangle where s is the hypotenuse. Therefore, we can write:

s^2 = r^2 + h^2

Substituting the given values, we get:

12^2 = 7^2 + h^2

Simplifying and solving for h, we get:

144 - 49 = h^2

95 = h^2

h = sqrt(95)

h ≈ 9.7

Therefore, the height of the cone is approximately 9.7 inches when rounded to the nearest tenth.

Answer:

9.7

Step-by-step explanation:

have a great day and thx for your inquiry :)

Using a linear regression calculator, the best fit line, initial velocity and the velocity of the car after 15 seconds is :

Using technology, the linear regression equation obtained by fitting the data is :

The approximate velocity at time = 0 ; x = 0 :

y = 3.64(0) + 5.7

y = 0 + 5.7

y = 5.7 m/s

3.) Velocity after 15 seconds :

At time, x = 15 seconds

y = 3.64(15) + 5.7

y = 60.3 m/s

Therefore, the velocity of the car after 15 seconds is 60.3 m/s

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Answer:

4 1/2

Step-by-step explanation:Because 2x2 =4 and 2x1/4 = 1/2 so it is 4 1/2

An increasing linear function results in a graph that slants upward from left to right and has a positive slope. A decreasing linear function results in a graph that slants downward from left to right and has a negative slope. A constant linear function results in a graph that is a horizontal line.

Inequality: 6(x+30) > 27

solve : 6(x+30) > 27

6x + 180 > 27

-180 -180

6x > -153

Divide by 6

x > -25.5

Answer:

Step-by-step explanation:

Let the sum = x

x/3 = 24

x/3 * 3 = 24 * 3

x = 72

The sum of the three numbers is 72

By analyzing the graph and evaluating the objective function at each vertex of the feasible region, we can find the optimal solution, which is the vertex that maximizes the objective function z = 3x + y.

To find the optimal solution of the given problem using the graphical method, we need to plot the feasible region determined by the given constraints and then identify the point within that region that maximizes the objective function.

Let's start by graphing the constraints:

1. Plot the line 2x - y = 5. To do this, find two points on the line by setting x = 0 and solving for y, and setting y = 0 and solving for x. Connect the two points to draw the line.

2. Plot the line -x + 3y = 6 using a similar process.

3. The x-axis and y-axis represent the constraints x ≥ 0 and y ≥ 0, respectively.

Next, identify the feasible region, which is the region where all the constraints are satisfied. This region will be the intersection of the shaded regions determined by each constraint.

Finally, we need to identify the point within the feasible region that maximizes the objective function z = 3x + y. The optimal solution will be the vertex of the feasible region that gives the highest value for the objective function. This can be determined by evaluating the objective function at each vertex and comparing the values.

Note: Without a specific graph or additional information, it is not possible to provide the precise coordinates of the optimal solution in this case.

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Answer:

An amortization schedule is a complete table of periodic loan payments, showing the amount of principal and the amount of interest that comprise each payment until the loan is paid off at the end of its term.

Step-by-step explanation:

Answer:

Step-by-step explanation:

An amortization schedule is a complete table of periodic loan payments, showing the amount of principal and the amount of interest that comprise each payment until the loan is paid off at the end of its term\

Answer:

\((\frac{1}{2}+\frac{\sqrt{3}}{2}i)^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

Step-by-step explanation:

Convert 1/2 + i√3/2 to rectangular form

\(\displaystyle z=a+bi=\frac{1}{2}+\frac{\sqrt{3}}{2}i\\\\r=\sqrt{a^2+b^2}=\sqrt{\biggr(\frac{1}{2}\biggr)^2+\biggr(\frac{\sqrt{3}}{2}\biggr)^2}=\sqrt{\frac{1}{4}+\frac{3}{4}}=\sqrt{1}=1\\\\\theta=\tan^{-1}\biggr(\frac{b}{a}\biggr)=\tan^{-1}\biggr(\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}\biggr)=\tan^{-1}(\sqrt{3})=\frac{\pi}{3}\\\\z=\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\)

Use DeMoivre's Theorem

\(\displaystyle z^n=r^n(\cos(n\theta)+i\sin(n\theta))\\\\z^5=1^5\biggr(\cos\biggr(\frac{5\pi}{3}\biggr)+i\sin\biggr(\frac{5\pi}{3}\biggr)\biggr)\\\\z^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

Since we are dealing with a right triangle, we can use the following trigonometric identities

Where θ is an inner angle (different than 90°) of the triangle, O is the opposite side to θ, A is the adjacent side to θ, and H is the hypotenuse.

a) In our case,

and

The answers are n=7 and m=7sqrt(3).

3) In a diagram, the problem states

Using the same trigonometric identities mentioned in part 1) (plus the tangent function), we get

The hypotenuse is equal to 36 ft, and the other leg is equal to 18sqrt(3) ft

The graph of an even function is symmetrical around the x-axis and the graph of an odd function is symmetrical around the origin.

The graph given does not fulfil neither of this conditions, hence we conclude that the function is neither even nor odd; therefore, the answer is C

Answer:

24 pints

Step-by-step explanation:

if 1 gallon is = to 8

then 3 gallons is 24

There are 24 pints in 3 gallons.

To determine how many pints are in 3 gallons, we can use the conversion factor provided: 1 gallon equals 8 pints.

Step 1: Calculate the number of pints in 1 gallon.

Since 1 gallon equals 8 pints, we can write this as 1 gallon = 8 pints.

Step 2: Multiply the number of pints in 1 gallon by the number of gallons.

To find the number of pints in 3 gallons, we multiply the number of pints in 1 gallon (8 pints) by 3 gallons:

3 gallons × 8 pints/gallon = 24 pints.

Therefore, there are 24 pints in 3 gallons.

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The equation of p(x) in vertex form is;

p(x) = 9.67(x + 1.04)² - 10.25

The closest answer choice is:

p(x) = 3(x - 1)²  - 2, which is not correct.

In the context of a quadratic function, the vertex is the highest or lowest point on the graph of the function. It is the point where the parabola changes direction. The vertex is also the point where the axis of symmetry intersects the parabola.

To find the vertex form of the quadratic function p(x), we need to first find the vertex, which is the point where the function reaches its maximum or minimum value.

To find the vertex, we can use the formula:

x = -b/2a, where a is the coefficient of the x²  term, b is the coefficient of the x term, and c is the constant term.

Using the table, we can see that the highest value of p(x) occurs at x = 5, and the value is 46.

We can then use the formula to find the vertex:

x = -b/2a = -5/2a

Using the values from the table, we can set up two equations:

46 = a(5)² + b(5) + c

1 = a(0)²  + b(0) + c

Simplifying the second equation, we get:

1 = c

Substituting c = 1 into the first equation and solving for a and b, we get:

46 = 25a + 5b + 1

-20 = 5a + b

Solving for b, we get:

b = -20 - 5a

Substituting b = -20 - 5a into the first equation and solving for a, we get:

46 = 25a + 5(-20 - 5a) + 1

46 = 15a - 99

145 = 15a

a = 9.67

Substituting a = 9.67 and c = 1 into b = -20 - 5a, we get:

b = -20 - 5(9.67) = -71.35

Therefore, the equation of p(x) in vertex form is:

p(x) = 9.67(x - 5)²  + 1

Simplifying, we get:

p(x) = 9.67(x²  - 10x + 25) + 1

p(x) = 9.67x²  - 96.7x + 250.85 + 1

p(x) = 9.67x²  - 96.7x + 251.85

Rounding to the nearest hundredth, we get:

p(x) = 9.67(x - 5²  + 1 = 9.67(x + 1.04)²  - 10.25

Therefore, the answer is:

p(x) = 9.67(x + 1.04)² - 10.25

The closest answer choice is:

p(x) = 3(x - 1)²  - 2, which is not correct.

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Answer: x= 2

Step-by-step explanation:

X+3/2(-1/2x+5/3)+2=3x-1

= x - 3/4x + 15/6 +2 = 3x -1

= 1/4x + 15/6 + 2 = 3x -1

= 1/4x + 27/6 = 3x -1

= 1/4x + 33/6 = 3x

= 33/6 = 11/4 x

= x = 2

Answer:

6200

Step-by-step explanation:

first find how much she would make purely based on hours worked:

8x40 = 320 dollars

next subtract this from total on her paycheck so 692-320 is 372

we know that 372 is 6% of a number so...

\(\frac{6}{100}\) x = 372

\(\frac{6x}{100}\) = 372

6x= 37200(100)

x=6200 $ divide by 6

so she sold $6200 worth of merchandise to earn $372 of commission

Answer:

x=57

Step-by-step explanation:

To solve this problem we need to make an equation to use to solve x.

The sum of 88 and x will equal 145 so the equation will look like this, 88 + x = 145.

Whatever x is, it has to add with 88 to make 145 so we have to use reverse operations.

The opposite of addition is subtraction so we subtract 88 from 145 like so. 145 - 88 = 57, which means x = 57.

If you need me to explain further don’t hesitate to ask me and I hope I helped! :)

Answer:

7,647.4?

Step-by-step explanation:

Using linear function concepts, it is found that the correct option regarding the meaning of the slope is as follows:

d. the car traveled away from the marker at 19 miles per hour.

A linear function is modeled by:

\(y = mx + b\)

In which:

In this problem, the output is the distance in miles between two cars, while the input is the time, hence the slope would mean by how much the distance between the cars increased each hour, which means that option d is correct.

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In order to cater a holiday banquet, food service LLC agrees to buy one hundred pumpkin pies from great desserts inc. to be enforceable, the agreement must be in writing if the pies cost at least $500.

What is an Agreement?

This refers to the legally binding contract that exists between two or more entities where the terms of the contract have been drawn up and the terms have been agreed upon by all parties involved, subject to certain conditions before it can be enforceable.

Hence, we can see that in order to cater a holiday banquet, food service LLC agrees to buy one hundred pumpkin pies and because they are a limited liability company, there needs to be a minimum threshold and this can be done, if the cost of the pies is at least $500.

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Answer:

n=5

Step-by-step explanation:

Answer:

n=21

Step-by-step explanation:

A good practice to remember when adding transitions to a presentation is to ensure that they are purposeful, consistent, and enhance the overall flow of the presentation.

Purposeful: Use transitions to guide the audience through your key points and ideas, making sure they complement the content and contribute to the overall message.
Consistent: Maintain a consistent style of transitions throughout your presentation to maintain a cohesive look and feel. Avoid using too many different types of transitions, as this may be distracting.
Enhance flow: Transitions should help create a smooth flow between slides and ideas, making it easy for the audience to follow your presentation. Avoid using abrupt or overly flashy transitions that may interrupt the natural progression of your content.

finally, Test your presentation with the transitions to make sure they enhance the overall flow and comprehension of your message.

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