5. Counting problems, leave answers as expressions, e.g., 10 npr 4, 8 nCr 3 or 35 [5 pts each part]
a) A club elects a steering committee of 5. Among these 5, a chair and secretary are chosen. How many different sets of committees (including officer selection) are possible if club has 15 members? Officers are not the same as the non-officer members, so this is hybrid permutation/combination problem.
b) At an event that drew 100 people where each attendee gets one raffle ticket, there are 6 raffle prizes worth $200, $100, $50, $25, $25, $25. How many different raffle ticket winner selections are possible? Be careful, the $25 prizes are equivalent, so this is hybrid permutation and combination problem.
c)If repeats are allowed but a code cannot begin with 0, how many six-digit PIN codes can be made?​

The bar diagram is attached and the equation is amount of trail mix in each bag = x/6

Let's say that Aarón has a total of "x" amount of trail mix.

To divide this equally into 6 bags, each bag will have "x/6" amount of trail mix.

We can illustrate this using a bar diagram as follows:

See attachment

Here, the total amount of trail mix "x" is divided equally into 6 parts, with each part representing "x/6" amount of trail mix.

The equation to represent this is:

x/6 = amount of trail mix in each bag.

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Answer:

Step-by-step explanation:

We will rationalize the denominator:

[tex]\frac{\sqrt{5} }{\sqrt{5} +2} =\frac{\sqrt{5} }{\sqrt{5} +2} \times \frac{\sqrt{5} -2}{\sqrt{5} -2}[/tex]

         [tex]=\frac{\sqrt{5} (\sqrt{5} -2)}{(\sqrt{5} +2)(\sqrt{5} -2)}[/tex]

         [tex]=\frac{5-2\sqrt{5} }{5-2\sqrt{5} +2\sqrt{5} -4}[/tex]

          [tex]=\frac{5-2\sqrt{5} }{1}[/tex]

          [tex]=5-2\sqrt{5}[/tex]

The probability that a customer Consumes both mayonnaise and ketchup at the same time is 0.55 or 55%.

To find the probability that a customer consumes both mayonnaise and ketchup at the same time, we need to use the concept of intersection in probability theory. The intersection represents the overlap or commonality between two events, in this case, the consumption of mayonnaise and ketchup.

Given that 80% of customers consume either mayonnaise or ketchup, we can assume that this includes the customers who consume both. Let's call the event of consuming mayonnaise "M" and the event of consuming ketchup "K". Therefore, we know that P(M U K) = 0.8.

To find the probability of consuming both, we can use the formula P(M ∩ K) = P(M) + P(K) - P(M U K), where ∩ represents the intersection. We can substitute the values we have been given to get:

P(M ∩ K) = 0.65 + 0.70 - 0.8 = 0.55

Therefore, the probability that a customer consumes both mayonnaise and ketchup at the same time is 0.55 or 55%. This means that more than half of the customers consume both, indicating that the chef could consider offering dishes that combine both sauces to cater to this preference.

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The experimental probability of the volcano erupting in 1 or 2 of the next 5 decades is 6/10 or 0.6.

We can do this by assigning a value of 1 to the numbers 1 and 2 (representing the volcano erupting) and a value of 0 to

the numbers 3, 4, and 5 (representing the volcano not erupting).

For each set of random numbers generated, we can count the number of times the volcano erupted (i.e. the sum of the

values assigned to the numbers 1 and 2).

Out of the 10 sets of random numbers generated, we might get results like this:
Set 1: 1 3 4 2 1 (2 eruptions)
Set 2: 2 1 5 4 3 (2 eruptions)
Set 3: 3 2 5 4 5 (1 eruption)
Set 4: 1 1 2 4 5 (3 eruptions)
Set 5: 4 4 4 4 4 (0 eruptions)
Set 6: 1 1 1 1 1 (5 eruptions)
Set 7: 3 3 3 3 3 (0 eruptions)
Set 8: 2 2 2 2 2 (0 eruptions)
Set 9: 1 2 1 2 1 (4 eruptions)
Set 10: 5 5 5 5 5 (0 eruptions)

Out of these 10 sets, we can see that there were 6 sets where the volcano erupted in 1 or 2 of the next 5 decades (sets

1, 2, 3, 4, 9, and 10). Therefore, the experimental probability of the volcano erupting in 1 or 2 of the next 5 decades is

6/10 or 0.6.

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We can use the formula for compound interest to calculate the amount of money we will have at the end of 3 years:

A = P(1 + r/n)^(nt)

Where:

A = the amount of money we will have at the end of 3 years

P = the principal (the initial amount we start with)

r = the interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

Plugging in the given values, we get:

A = 5000(1 + 0.045/12)^(12×3)

A = 5000(1.00375)^36

A ≈ $5,622.16

Therefore, we will have approximately $5,622.16 at the end of 3 years.

Answer: ABC = 70°, ACB = 70°

Step-by-step explanation:

I think the question asks the other two angles

ABC = (180 - 40)/2

ABC = 70

ABC = ACB since isosceles triangle

ACB = 70

a. The number of ways to select three people from the group of ten is 120.

b. The number of ways to select three Republicans from the group of six Republicans is 20.

c. The probability is 1/6.

What is probability?

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 essentially what probability means.

a. The number of ways to select three people from a group of ten is given by the combination formula:

C(10,3) = 10! / (3! * (10 - 3)!) = 120

Therefore, there are 120 ways to select three people from this group of ten.

b. The number of ways to select three Republicans from the six Republicans is given by the combination formula:

C(6,3) = 6! / (3! * (6 - 3)!) = 20

Therefore, there are 20 ways to select three Republicans from the six Republicans.

c. The probability of selecting all Republicans is the number of ways to select three Republicans divided by the total number of ways to select three people:

P(all Republicans) = C(6,3) / C(10,3) = 20/120 = 1/6

Therefore, the probability that the selected group will consist of all Republicans is 1/6.

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angles 1 and 7 are congruent corresponding angles because they are in corresponding positions on two parallel lines intersected by a transversal, and they have the same measure or size. Thus, option C is correct.

Angle 1 and angle 7 are corresponding angles because they are in the same position relative to the transversal and the parallel lines.

Specifically, they are in corresponding positions on the parallel lines, meaning that they are on the same side of the transversal.

in the same position relative to the intersection point of the transversal and the parallel lines, and they are both either interior m, or exterior angles. In this case, angles 1 and 7 are both interior angles.

Furthermore, angles 1 and 7 are congruent corresponding angles because they have the same measure or size.

Therefore, angles 1 and 7 are congruent corresponding angles because they are in corresponding positions on two parallel lines intersected by a transversal, and they have the same measure or size.

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Answer:

3yz^3 + 1

Step-by-step explanation:

let b = the binomial we are looking for.

divide and receive your answer

a) the probability of drawing a yellow marble than a blue marble is (1/3) x (4/9) = 4/27.

b) the probability of guessing a number less than 7 is 6/10 or 3/5.

c) the probability of drawing a white marble than a red marble is (2/9) x (6/17) = 4/51.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.

Since the marble is replaced after the first draw, the probability of drawing a yellow marble is 6/18 = 1/3.

Similarly, the probability of drawing a blue marble on the second draw is 8/18 = 4/9.

Therefore, the probability of drawing a yellow marble than a blue marble is (1/3) x (4/9) = 4/27.

There are 6 numbers less than 7 (1, 2, 3, 4, 5, 6) and 10 total numbers, so the probability of guessing a number less than 7 is 6/10 or 3/5.

Since the marble is not replaced after the first draw, the probability of drawing a white marble is 4/18 = 2/9.

The probability of drawing a red marble on the second draw, given that a white marble was drawn first, is 6/17.

Therefore, the probability of drawing a white marble than a red marble is (2/9) x (6/17) = 4/51.

Hence, a) the probability of drawing a yellow marble than a blue marble is (1/3) x (4/9) = 4/27.

b) the probability of guessing a number less than 7 is 6/10 or 3/5.

c) the probability of drawing a white marble than a red marble is (2/9) x (6/17) = 4/51.

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Let's assume that Terrell attends x number of classes in a month. Then, the total cost of the first membership plan would be:

Cost of the first membership plan = $30 + $1 * x

Similarly, the total cost of the second membership plan would be:

Cost of the second membership plan = $15 + $4 * x

As per the problem statement, both membership plans cost the same when Terrell attends a certain number of classes in a month. So, we can equate the above two expressions and solve for x:

$30 + $1 * x = $15 + $4 * x

$2 * x = $15

x = 7.5

Since the number of classes cannot be a fraction, we can round up to the nearest integer, which is 8. Therefore, Terrell needs to attend 8 classes per month to make both membership plans cost the same.

To find the total amount, we can substitute x = 8 in either of the above expressions:

Total amount = $30 + $1 * 8 = $38

Therefore, Terrell needs to attend 8 classes per month, and the total amount would be $38.

The statement can be read as "If the sky is clear, then the plane is not on time."

What is the conditional statement?

A conditional statement is a logical statement that has two parts: an antecedent (also called a hypothesis) and a consequent (also called a conclusion). The statement asserts that if the antecedent is true, then the consequent must also be true.

The statement "Q -> ~P" is an example of a conditional statement in symbolic logic.

In this case, Q represents "The sky is clear" and ~P represents "The plane is not on time" (the tilde symbol ~ negates the truth value of P).

The arrow symbol -> means "implies" or "if...then". Therefore, the statement can be read as "If the sky is clear, then the plane is not on time."

In other words, the statement is saying that if the sky is clear, then it is not possible for the plane to be on time.

This is because the statement implies that the plane being on time is dependent on the sky not being clear. So if the sky is clear, it means that the conditions for the plane to be on time are not present, and therefore the plane is not on time.

It's worth noting that the statement does not say anything about what happens if the sky is not clear.

It's possible that the plane could still be on time even if the sky is not clear, according to this statement.

Hence, the statement can be read as "If the sky is clear, then the plane is not on time."

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For the given diameter d=20 cm, the radius is 10 cm.

What is radius?

Radius is a straight line segment that connects the center of a circle or sphere to any point on its circumference or surface respectively. It is a fundamental measurement used in geometry and is denoted by the letter "r". The radius is half the diameter of a circle or sphere, and it is used to calculate important properties of the circle or sphere, such as its circumference, area, and volume.

If d = 20 cm, then d represents the diameter of a circle.

To find the radius (r) of the circle, we divide the diameter by 2:

r = d/2 = 20 cm/2 = 10 cm

Therefore, for diameter d=20 cm, the radius of the circle is 10 cm.

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The length of the segment indicated in the circle is 12 units

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

The circle

Since the radius is perpendicular to the chord and intersects the chord at its midpoint, then the radius will divide the chord into two equal segments.

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

x = 12

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To convert 1/2% to a ratio, we first convert it to a decimal by dividing by 100:

1/2% = 1/2 ÷ 100 = 0.005

Then we express this decimal as a ratio by putting it in the form of x:y:

0.005 = x:y

To simplify this ratio, we can multiply both sides by a factor that will make x and y whole numbers. For example, we can multiply both sides by 100:

0.005 × 100 = x:y × 100

0.5 = x:y

So 1/2% as a ratio is 1:200.

1/2% is equivalent to 0.5% or 0.005 as a decimal.

To express 0.005 as a ratio, you can write it as a fraction with a numerator of 0.005 and a denominator of 1. Then, you can multiply both the numerator and denominator by 100 to get rid of the decimal and express it as a ratio.

0.005/1 = (0.005

Therefore, 1/2% is equivalent to the ratio 0.5:100 or 1:200.

1. x + 30 = 98 equation says that Jerome's total earnings y for the day is equal to his wages.

2. y = 68 + 30 equation says that Jerome's total earnings y for the day is equal to his wages.

A statement that affirms the equality of two expressions connected by the equals symbol "=" is known as an equation. For illustration, 2x - 5 = 13. 2x - 5 and 13 are expressions in this case. These two expressions are joined together by the sign "=".

There are different ways to represent this situation algebraically, but here are two possible equations:

1. Let x be the amount of money Jerome earns in wages, then the equation can be written as:

x + 30 = 98

This equation says that the sum of Jerome's wages x and his tips of $30 is equal to his total earnings of $98 for the day.

2. Alternatively, we can let y be the total amount of money Jerome makes for the day (including tips), then we can write:

y = 68 + 30

This equation says that Jerome's total earnings y for the day is equal to his wages of $68 plus his tips of $30.

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Thus, equation of line in slope intercept form: y = 5x + 3.

One approach to calculating the equation of a straight line is the slope-intercept form. The two point form, point-slope form, plus intercept form are the further approaches.

Passing points - (-2, -7)

slope m = 5

The standard slope intercept form for equation of line:

y = mx + c

m is the slope and c is the y-intercept.

Put the given values and find c.

-7 = 5(-2) + c

c = -7 + 10

c = 3

Thus, equation of line in slope intercept form:

y = 5x + 3

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the probability of selecting a tool produced by the old method on the first attempt and a tool produced by the new method on the second attempt is:

P(A and B) = P(A) * P(B | A) = 0.8305 * 0.1998 = 0.1660

How to solve the questions?

Part A:

Let A be the event that the first tool selected is acceptable and B be the event that the second tool selected is acceptable.

We need to find the probability of P(A and B), which can be calculated using the multiplication rule of probability as follows:

P(A and B) = P(A) * P(B | A)

where P(A) is the probability of selecting an acceptable tool on the first attempt and P(B | A) is the conditional probability of selecting an acceptable tool on the second attempt given that the first tool selected was acceptable.

P(A) = (1640 + 328) / (1640 + 328 + 23 + 9) = 0.985

P(B | A) = (1639 + 327) / (1640 + 328 + 23 + 9 - 1) = 0.985

Therefore, the probability of both selections being acceptable is:

P(A and B) = P(A) * P(B | A) = 0.985 * 0.985 = 0.9702

The events are dependent because the probability of selecting an acceptable tool on the second attempt depends on the result of the first attempt.

Part B:

Let A be the event that the first tool selected is produced by the old method and B be the event that the second tool selected is produced by the new method.

We need to find the probability of P(A and B), which can be calculated using the multiplication rule of probability as follows:

P(A and B) = P(A) * P(B | A)

where P(A) is the probability of selecting a tool produced by the old method on the first attempt and P(B | A) is the conditional probability of selecting a tool produced by the new method on the second attempt given that the first tool selected was produced by the old method.

P(A) = (1640 + 23) / (1640 + 328 + 23 + 9) = 0.8305

P(B | A) = 328 / (1640 + 328 + 23 + 9 - 1) = 0.1998

Therefore, the probability of selecting a tool produced by the old method on the first attempt and a tool produced by the new method on the second attempt is:

P(A and B) = P(A) * P(B | A) = 0.8305 * 0.1998 = 0.1660

The events are dependent because the probability of selecting a tool produced by the new method on the second attempt depends on the result of the first attempt.

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Answer:

$8.73 --> 8.73

Step-by-step explanation:

We need to add their costs together to find the total price of the three items.

The cost of Bagels is given as $2.17.

The cost of Cream Cheese is given as $2.82.

The cost of Raisins is given as $3.74.

Adding these three costs together gives us:

$2.17 + $2.82 + $3.74 = $8.73

Therefore, the total price of the three items is $8.73.

Answer:

17 - a

Step-by-step explanation:

1. Open parentheses: 25 - 2 x 4-a

2. Follow the Order of Operations to simplify:

-PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction):

- 25-2 x 4 - a

- 25 - 8 - a

- 17 - a

The answer of the given question based on the graph is  the coordinates of point B are (-8, 4).

A quadrant is one of four regions into which coordinate plane is divided by x-axis and y-axis. The x-axis is horizontal axis and the y-axis is vertical axis. The quadrants are labeled using Roman numerals, starting in upper right quadrant and moving counterclockwise.

Since point B is 11 units away from point A, we know that the distance between them is:

d = √((x2 - x1)² + (y2 - y1)²) = 11

where (x1, y1) = (-3, -5) are the coordinates of point A, and (x2, y2) are the coordinates of point B.

We also know that point B is located in quadrant 2, which means that its x-coordinate is negative and its y-coordinate is positive.

To find the coordinates of point B, we can use the distance formula and the fact that point B is in quadrant 2:

d = √((x2 - x1)² + (y2 - y1)²) => 11 = √((x2 - (-3))² + (y2 - (-5))²)

Since point B is in quadrant 2, its x-coordinate is negative and its y-coordinate is positive:

x2 < 0, y2 > 0

We can choose any values for x2 and y2 that satisfy these conditions and the distance formula equation. Let's choose x2 = -8 and y2 = 4:

11 = √((-8 - (-3))² + (4 - (-5))²)

11 = √(25 + 81)

11 = √106

Therefore, coordinates of point B is (-8, 4).

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Answer:

D. -7.2y - 49.5  is the correct answer.

Step-by-step explanation:

Distributing the 3 to the terms inside the parenthesis, we get:

3(-2.4y - 16.5) = -7.2y - 49.5

-2.4 x 3 = -7.2

16.5 x 3 = 49.5

so the expression that is equivalent to 3(-2.4y - 16.5) is -7.2y - 49.5

hope this helps

The sum of the given expression is equal to 3.

The process of numerical integration involves applying numerical techniques to approximate the value of a determined integral of a function across a specified interval. To approximate integrals that are challenging or impossible to solve analytically, it is employed in calculus.

Numerical integration works by breaking the integration interval into smaller subintervals, approximating the function over each subinterval with a simple function, and then summing the areas under the curve of the approximating function over each subinterval to estimate the integral.

Determine the value of f(xi):

f(x1) = (0-2)^3 = (-2)³ = -8

f(x2) = (1-2)^3 = (-1)³ = -1

f(x3) = (2-2)^3 = 0³ = 0

f(x4) = (3-2)^3 = 1³ = 1

f(x5) = (4-2)^3 = 2³ = 8

f(x6) = (5-2)^3 = 3³ = 27

Substituting the value in the given summation we have:

Σ i = 1 to 6 f(xi) Δ x = f(x1) Δ x + f(x2) Δ x + f(x3) Δ x + f(x4) Δ x + f(x5) Δ x + f(x6) Δ x

= (-8)(0.1) + (-1)(0.1) + (0)(0.1) + (1)(0.1) + (8)(0.1) + (27)(0.1)

= -0.5 + (-0.1) + 0 + 0.1

= 3

Hence, the sum is equal to 3.

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The angle measure of the triangle are;

m< A = 53 degrees

m<B = 90 degrees

m<C = 37 degrees

It is important to note that the sum of the angles in a triangle is equal to 180 degrees

From the diagram shown, we have that;

m< A = 4x + 1

m< B = 7x - 1

m< C = 3x - 2

Equate the angles, we have;

4x + 1 + 7x - 1 + 3x - 2 = 180

collect the like terms, we get

14x = 180 + 2

14x = 182

make 'x' the subject

x = 13

Then, m< A = 53 degrees

m<B = 90 degrees

m<C = 37 degrees

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Answer:

Step-by-step explanation:

You want the dimensions and volume of a cuboid that can be made from an 18 in square of cardboard when an x-inch square is cut from two adjacent corners, and an x-inch by 9-inch rectangle is cut from the other two corners.

The longest side of the cuboid will have length (18 -2x). The second longest side will have length (18 -9 -x) = (9 -x). The shortest side will have length x.

The volume of the cuboid is the product of these side lengths:

  V = (18 -2x)(9 -x)(x) = 2x(9 -x)²

The value of x that maximizes volume will be the value that makes the derivative with respect to x be zero.

  V' = 2(9 -x)² -4x(9 -x) = (9 -x)(2(9 -x) -4x) = 2(9 -x)(9 -3x)

  V' = 6(9 -x)(3 -x)

The derivative will be zero when its factors are zero, at x=9 and x=3. The value x=9 gives zero volume.

The value x=3 gives a volume of ...

  V = 2·3(9 -3)² = 6³ = 216 . . . . . cubic inches

The dimensions are ...

The dimensions for maximum volume are 3 inches by 6 inches by 12 inches. The maximum volume is 216 cubic inches.

Answer:

The answer is 4.5 miles.

Step-by-step explanation:

To solve this problem, we must remember that the shortest distance between two points lies along a straight line. In this case, this straight line is the hypotenuse of the triangle formed with the 2 mile and 4 mile legs. As a result, we can use the Pythagorean Theorem to find the distance between Lisa's house and the pool.

Pythagorean Theorem:

a² + b² = c²

2² + 4² = c²

c² = 4 + 16

c = √20

c = 4.5 miles (rounded to the nearest tenth)

Therefore, the shortest distance between Lisa's house and the pool is 4.5 miles.

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[tex]\blue{\huge {\mathrm{PYTHAGOREAN \; THEOREM}}}[/tex]

[tex]\\[/tex]

[tex]{===========================================}[/tex]

[tex]{\underline{\huge \mathbb{Q} {\large \mathrm {UESTION : }}}}[/tex]

[tex]{===========================================}[/tex]

[tex] {\underline{\huge \mathbb{A} {\large \mathrm {NSWER : }}}} [/tex]

*Please read and understand my solution. Don't just rely on my direct answer*

[tex]{===========================================}[/tex]

[tex]{\underline{\huge \mathbb{S} {\large \mathrm {OLUTION : }}}}[/tex]

We can use the Pythagorean theorem to find the shortest distance between Lisa's house and the pool.

Let's call the distance we're trying to find "d". We know that Lisa's school is 2 miles north of her house and the pool is 4 miles east of her school, so we can draw a triangle with the following sides:

Using the Pythagorean theorem, we can find d:

[tex]\qquad\qquad\qquad\begin{aligned}\sf c^2& =\sf a^2 + b^2\\\sf d^2& =\sf 2^2 + 4^2\\\sf d^2& =\sf 4 + 16\\\sf d^2& =\sf 20\\\sf d& =\sf \sqrt{20}\\\bold{d}& =\sf \boxed{\bold{\: 4.5\: miles\:}}\end{aligned}[/tex]

[tex]\\[/tex]

Therefore, the shortest distance between Lisa's house and the pool is 4.5 miles (rounded to the nearest tenth of a mile).

[tex]{===========================================}[/tex]

[tex]- \large\sf\copyright \: \large\tt{AriesLaveau}\large\qquad\qquad\qquad\tt 04/01/2023[/tex]

Answer:

e

Step-by-step explanation:

Answer:

the mean absolute deviation is 3