At the Queen of Peace Festival, you have 50 tickets to ride the Ferris Wheel and the roller coaster. If you ride 12
times, using 3 tickets for each Ferris Wheel ride and 5 tickets for each roller coaster ride, how many times did you go
on each ride?

2. Using proportion, the value of x = 38, the length of FC = 36 in.

3. Applying the angle bisection theorem, the value of x = 13. The length of CD = 39 cm.

The Angle Bisector Theorem states that in a triangle, an angle bisector divides the opposite side into segments that are proportional to the lengths of the other two sides of the triangle.

2. The proportion we would set up to find x is:

(x - 2) / 4 = 27 / 3

Solve for x:

3 * (x - 2) = 4 * 27

3x - 6 = 108

3x = 108 + 6

Simplifying:

3x = 114

x = 114 / 3

x = 38

Length of FC = x - 2 = 38 - 2

FC = 36 in.

3. The proportion we would set up to find x based on the angle bisector theorem is:

13 / 3x = 7 / (2x - 5)

Cross multiply:

13 * (2x - 5) = 7 * 3x

26x - 65 = 21x

26x - 21x - 65 = 0

5x - 65 = 0

5x = 65

x = 65 / 5

x = 13

Length of CD = 3x = 3(13)

CD = 39 cm

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The probability that a salesperson selected at random has above-average sales ability and has excellent potential for advancement is 0.27.

Probability simply means the likelihood that an event will occur.

In this case, the data for the 500 sampled salespeople are summarized in the table.

The probability that the person has above-average sales ability and has excellent potential for advancement will be:

= Number of people that above-average sales ability and has excellent potential for advancement / Total number of people

= 135 / 500

= 0.27

The probability is 0.27.

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Step-by-step explanation:

y+x(x-y)-5

substitute: -7+3(3+7)-5

-7+3(10)-5

-7+30-5

22

If this isn't correct, then use distributive property on 3(3+7)

If so then it would be -7+9+21-5

It would be the same answer, just a different way of finishing it

\(\huge\text{Hey there!}\)

\(\large\textsf{y + x(x - y) - 5}\)

\(\large\textsf{= 3 + (-7)(3 - (-7)) - 5}\)

\(\large\textsf{= 3 - 7(3 - (-7)) - 5}\)

\(\large\textsf{= 3 + (-7)(10) - 5}\)

\(\large\textsf{= 3 - 7(10) - 5}\)

\(\large\textsf{= 3 - 70 - 5}\)

\(\large\textsf{= -67 - 5}\)

\(\large\textsf{= -72}}\)

\(\huge\boxed{\textsf{Therefore, your answer is: \boxed{\mathsf{-72}}}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day! }\)

~\(\frak{Amphitrite1040:)}\)

Answer:

Step-by-step explanation:

The property of the triangle congruence state that a ≅ B then B ≅ A are:

The triangle is a polygon that has 3 edge and vertices. Triangle is one of the basic shape in the geometric. The area of the triangle is formulated as base of the triangle * height of triangle x 0,5. The value of three triangle edge degree is 180°.

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Answer:

b

Step-by-step explanation:

its a straigt line thats what linear means (line)

Answer:

It is usually an integer that is multiplied by the variable next to it.

Step-by-step explanation:

9514 1404 393

Answer:

  $82.28

Step-by-step explanation:

Being married puts Celeste on the right half of the table. Four allowances put her in the 5th section down, where 4 is in the left-most column. Her weekly wage of 1298 puts her wage between 923.30 and 2068.20, so on the second line in that section.

The table tells you to subtract $612.37 from Celeste's weekly wage, then multiply the result by 12% to find her withholding. Doing that, we find the withholding to be ...

  (1298.00 -612.37) × 0.12 = $82.28 . . . . rounded up to the nearest cent

The withholding tax applicable to Celeste's earnings is $82.28.

Answer:

(0,8)

Step-by-step explanation:

Therefore , the percentage of case 1 is 68% and percentage of case 2 is 47.4%

One percent (symbolized as 1%), being the hundredth component, is represented as 100 percent, while 200 percent signifies twice the amount specified. As an illustration, 1% of 1,000 chickens is equal to 1/100 of 1,000, or 10 birds, and 20% of the quantity is equal to 20% of 1,000, or 200.

Here,

Given: Total number of freshman =500

mean =75 and standard deviation =7

a) the percentage of scores that fell between 68 and 82

340 is the number of freshman whose  scores that fell between 68 and 82

thus,

percentage = 340 /500 * 100

=> percentage = 68%

b)the percentage of scores that fell between 61 and 75

237 is the number of freshman whose  scores that fell between 61 and 75

thus,

percentage = 237/500 * 100

=> percentage = 47.4%

Therefore , the percentage of case 1 is 68% and percentage of case 2 is 47.4%

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The probability that 5 messages are received in 1 hour is is 0.1755 ,the probability that 10 messages are received in 1.5 hours is 0.0858 and the probability that less than 2 messages are received in 1/2 hour is 0.2873

Let X shows the number of messages received per hour. The pdf of X is

\(P(X=x)=\) \(\frac{e^{-5}\cdot 5^{x}}{x!},x=0,1,2,3,....\)

Therefore, the probability that 5 messages are received in a single hour is

\(P(X=5)=\frac{e^{-5}\cdot 5^{5}}{5!}=0.1755\)

(b) Number of message received in 1 hour is 5 so number of message received in 1.5 hour is 7.5. So the probability that 10 messages are received in 1.5 hours is

\(P(X=10)=\frac{e^{-7.5}\cdot 7.5^{10}}{10!}=0.0858\)

(c) Number of message received in 1 hour is 5 so number of message received in 1/2 hour is 2.5. So the probability that less than 2 messages are received in 1/2 hour is

\(P(X < 2)=\frac{e^{-2.5}\cdot 2.5^{0}}{0!}+\frac{e^{-2.5}\cdot 2.5^{1}}{1!}=0.2873\)

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10 - x ≤ 35

- x ≤ 35 - 10

- x ≤ 25

x ≥ - 25

true

a) To convert the second-order equation into a system of first-order equations, we introduce a new variable, say y, and its derivative y'. The original equation becomes:

x' = y

y' = (-c/m)x - (k/m)x

b) The behavior of the system depends on the values of m, c, and k.

- If m > 0, c = 0, and k > 0, we have an undamped system with no damping force. It exhibits simple harmonic motion.

- If m > 0, c > 0, and k > 0, we have a damped system with a damping force. The behavior depends on the damping ratio, which can be underdamped, critically damped, or overdamped.

- If m > 0, c = 0, and k = 0, we have a mass-spring system without any external forces. The behavior is characterized by free oscillations.

c) In this particular mass-spring system, we do not observe all possible behaviors because the equation assumes certain physical constraints. For example, the equation neglects external forces or nonlinearities, which can introduce additional behaviors like chaotic motion or limit cycles.

Exercise 3.5.2:

When P - λd11, where λ is a repeated eigenvalue and there is only one independent eigenvector, the solution exhibits degenerate behavior. Geometrically, this corresponds to a repeated eigenvalue with a single linearly independent eigenvector, which gives rise to a trajectory along a line in phase space.

Exercise 3.5.3:

When P is drawn, it represents a Jordan block in the matrix representation. In this case, the system exhibits a nontrivial generalized eigenvector behavior. The phase portrait may have a spiral or swirling pattern around an equilibrium point or a limit cycle, depending on the specific values in the Jordan block.

Exercise 3.5.4:

If P is diagonal, that is P = diag(a, b), the behaviors possible are decoupled or independent oscillations along the coordinate axes. Each component of the system evolves independently according to its respective eigenvalue, leading to distinct motions in different directions.

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Using the formula of area of a circle, about 226.08in² has been eaten

The diameter of the pizza is given as 24 inches. To calculate the area of the entire pizza, we need to use the formula for the area of a circle:

Area = π * r²

where π is approximately 3.14 and r is the radius of the circle.

Given that the diameter is 24 inches, the radius (r) would be half of the diameter, which is 12 inches.

Let's calculate the area of the entire pizza first:

Area = 3.14 * 12²

Area = 3.14 * 144

Area ≈ 452.16 square inches

Now, if half of the pizza is consumed, we need to calculate the area of half of the pizza. To do that, we divide the area of the entire pizza by 2:

Area of half of the pizza = 452.16 / 2

Area of half of the pizza ≈ 226.08 square inches

Therefore, if half of the pizza is consumed, approximately 226.08 square inches of pizza would be eaten.

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Answer:

Question 1 : B) (8 x 20) - (8 x 1)

Question 2 :  D) (2 x 9) + (2 x 3)

Step-by-step explanation:

Distributive Property is used in algebraic expressions, to divide the equation, to make it easier to solve. For question 1,  since it was 20, you must subtract 8 from that answer, because 20 is 1 more than 19. For question 2, (2 x 9) + (2 x 3) would be the same thing as 2(9+3).

-kiniwih426

Answer:

B) (8 x 20) - (8 x 1)

D) (2 x 9) + (2 x 3)

Step-by-step explanation:

Distributive Property: "The distributive property tells us how to solve expressions in the form of a(b + c)."

___________________

Step 1: 8 x 19 = 152

Using PEMDAS, you can see which order to solve the equations in.

PEMDAS tells us to solve whatever is within the parenthesis first but there are 2 parenthesis and both have multiplication so just solve the first parenthesis first;

8 x 20 = 160

Step 2: We now have to solve the second parenthesis;

8 x 1 = 8

Step 3: Using PEMDAS, we see that after we solve the parenthesis, we do subtraction. So subtract 8 from 160.

160 - 8 = 152

So your answer is B) (8 x 20) - (8 x 1).

___________________

Step 1: 2(9 + 3)

Using the Distributive property, we multiply 2 by 9 and 3;

2 x 9 = 18

2 x 3 = 6

Now you are left with 18 + 6.

18 + 6 = 24

So your answer is D) (2 x 9) + (2 x 3).

___________________

Hope this Helps! :)

Answer:

Step-by-step explanation:

Remark

It's a permutation question, Order does not matter.

Answer

Most people will try and tell you that the answer is 20 * 19. That would make a pure pure permutation question. The problem is that the actual answer is 20 * 20  because she can have 2 scoops are the same. I would still answer permutation but be prepared to get it incorrect.

Answer:

C

Step-by-step explanation:

Because in N(8)>2.N(5) there is 2 times N(5) in front of it. In the example N(g) means the numbers of students whose grade on the exam was g. so in this case N(8) means the numbers of students whose grade on the exam was 8 and N(5) means the numbers of students whose grade on the exam was 5. So when you turn this equation into words  it means The numbers of students whose grade was 8 is more than twice the number of students whose grade was 5.

Hence the equation 3(5x - 4) - 8x = 7x -12 has infinite number of solutions.

An equation is a statement of equality between two expressions consisting of variables, numbers and arithmetic operations.

Step-by-step explanation:

The equation 8x = 8(x - 1)+1 can be simplified as

8x=8x-8+1

0=-7( absurd)

This equation does not have any solution.

The equation 2x-5 = 2(x - 5) can be simplified as

2x-5=2x-10

-5=-10(absurd)

This equation does not have any solution.

The equation 22-6x = 2(3x - 11) can be simplified as

22-6x=6x-22

-6x-6x=-22-22

-12x=-44

x=44/12=11/3

This equation has only one solution.

The equation 3(5x - 4) - 8x = 7x -12 can be simplified as

15x-12-8x=7x-12

7x-12=7x-12

0=0, is an identity

This equation has infinite number of solutions.

Hence the equation 3(5x - 4) - 8x = 7x -12 has infinite number of solutions.

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Eli could travel 12 miles and 3/4x+2x>11 inequality matches the statement Three-fourths times x added to two times x is more than eleven

a relationship between two expressions or values that are not equal to each other is called 'inequality.

Given that a taxi charges a flat rate of $1.75 and an additional $0.65 per mile.

Eli has at most $10 to spend on the cab ride

We need to find how far could he travel

1.75+0.65x≤10

Subtract 1.75 on both sides

0.65x≤10-1.75

0.65x≤8.25

x≤8.25/0.65

x≤12.6

So he could travel 12 miles.

Three-fourths times x added to two times x is more than eleven

3/4x+2x>11

Hence,  Eli could travel 12 miles and 3/4x+2x>11 inequality matches the statement Three-fourths times x added to two times x is more than eleven

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To find the probability that a 10-card hand from a 52-card deck has exactly 2 four-of-a-kinds (no 3-of-a-kinds and no pairs), we first need to calculate the total number of ways to choose a 10-card hand from a 52-card deck. This can be done using the formula for combinations:

52 choose 10 = 52! / (10! * (52-10)!) = 10,272,278,170

Next, we need to calculate the number of ways to choose exactly 2 four-of-a-kinds. There are 13 ranks in a deck of cards, and for each rank, there are 4 cards. So, the number of ways to choose 2 four-of-a-kinds is:

(13 choose 2) * (4 choose 4)^2 = 78

Next, we need to calculate the number of ways to choose the remaining 2 cards from the remaining 44 cards in the deck. Since we cannot have any pairs or 3-of-a-kinds, we need to choose 2 cards from 11 different ranks (since we already have 2 four-of-a-kinds). The number of ways to do this is:

(11 choose 2) * (4 choose 1)^2 * (4 choose 1)^2 = 16,384

So, the total number of ways to choose a 10-card hand with exactly 2 four-of-a-kinds (no 3-of-a-kinds or pairs) is:

78 * 16,384 = 1,279,232

Therefore, the probability of choosing a 10-card hand with exactly 2 four-of-a-kinds (no 3-of-a-kinds or pairs) is:

1,279,232 / 10,272,278,170 ≈ 0.0001245 or approximately 0.01245%.

To find the probability of a 10-card hand having exactly 2 four-of-a-kinds (and no 3-of-a-kinds or pairs) from a 52-card deck, you'll need to consider the combinations of cards.

First, there are 13 different ranks (2, 3, 4, ..., 10, J, Q, K, A) and 4 suits (hearts, diamonds, clubs, spades) in the deck. To have 2 four-of-a-kinds, you need to choose 2 different ranks. You can do this in C(13,2) ways, where C(n,r) is the number of combinations of choosing r items from a set of n items.

Next, you need to choose the remaining 2 cards. They must be of different ranks than the four-of-a-kinds and different from each other. There are 11 ranks left, so you can choose these 2 cards in C(11,2) ways.

For each of the two cards, you must choose one of the 4 suits. This can be done in C(4,1) ways for each card.

So, the number of desired 10-card hands is:
C(13,2) * C(11,2) * C(4,1) * C(4,1)

The total number of 10-card hands from a 52-card deck can be found using the combination formula as well:
C(52,10)

Now, to find the probability, divide the number of desired hands by the total number of possible hands:
P = (C(13,2) * C(11,2) * C(4,1) * C(4,1)) / C(52,10)

Calculating the combinations, you get:
P = (78 * 55 * 4 * 4) / 2,598,960

Simplifying this expression, the probability is approximately:
P ≈ 0.000454

So, the probability that a 10-card hand from a 52-card deck has exactly 2 four-of-a-kinds (with no 3-of-a-kinds or pairs) is approximately 0.000454 or 0.0454%.

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Answer:

6 Hours = 0.0357 Weeks

Rounding off o nearest hundredth we get
=> 0.36

All done!

Answer:

x = 3 +√43, x = 3 - √43

Step-by-step explanation:

x^2 - 6x - 34 = 0

move the 34 across

x^2 - 6x = 34

take -6 and divide by two, then square it

(-6/2)^2 = 9

add the product to your equation

x^2 - 6 + 9 = 34 + 9

solve

(x - 3)^2 = 43

x - 3 = ± √43

x = 3 ± √43

Answer:

x=19

Step-by-step explanation:

The perimeter of the right triangle is

P=9+12+15 =36

The perimeter of the left triangle is

P =x-7+ x-7+ x-7 = 3x-21

Set them equal

36 = 3x-21

Add 21 to each side

36+21 = 3x-21+21

57 = 3x

Divide each side by 3

57/3 = 3x/3

19 =x

Answer:

\(x=19\)

Step-by-step explanation:

The perimeter of a shape is the sum of all of its side lengths. Therefore, the perimeter of the first triangle is \(x-7+x-7+x-7=3x-21\) and the perimeter of the second triangle is \(9+15+12=36\).

We are given that the perimeters of the triangles are equal, so \(3x-21\) equals \(36\). As an equation, that would be \(3x-21=36\). Solving for \(x\), we get:

\(3x-21=36\)

\(3x=57\) (Add \(21\) to both sides of the equation to isolate \(x\))

\(x=19\) (Divide both sides of the equation by \(3\) to get rid of \(x\)'s coefficient)

Hope this helps!

Answer:

C

Step-by-step explanation:

the statement (y<1/2x -4) reads "y is LESS than 1/2 x -4."

to fulfil this statement, follow these steps.

1) graph the line 1/2x -4, there will be a yintercept at (0,-4). Also the slope will be increasing (left to right) because 1/2 has no negative sign before it.

2) recognize the inequality sign. In this situation, the solution does NOT INCLUDE THE LINE, rather it includes the area BELOW/LESS THAN the line. If this, < had a line under it, it would mean less than OR equal to.

3) know that if the line is not included, the line will be broken. If the line IS included, which it is not, it would be a solid line.

Answer:

C

Step-by-step explanation:

First, graph the equation:

The y-intercept is -4.

And the slope is 1/2, an upward sloping line.

So, our graph should be either A, B, or C.

D is not correct, so eliminate that.

So, our inequality is:

\(y<\frac{1}{2}x-4\)

Note that this inequality is strictly less than. There's no "or equal to" bar. Therefore, our line should be dotted.

Thus, eliminate A and B.

So, C is our answer

Further notes:

The inequality sign means that y is less than the equation. In other words, our shaded region should be below the line.

In C, the shaded area is indeed below the line.

So, C is indeed our answer :)

The line that is tangent to both parabolas at this point will have the slope 2x = 2 * 0 = 0 and y-intercept equal to 0, giving us the equation y = 0.

To graph the two parabolas y = x^2 and y = -x^2 + 2x - 5 in the same coordinate plane, we can use a tool such as a graphing calculator or plot the points of the parabolas by hand. The first parabola, y = x^2, will be a downward-facing parabola centered at the origin with a vertex at (0,0), while the second parabola, y = -x^2 + 2x - 5, will be an upward-facing parabola that is shifted to the right by 1 unit and downward by 5 units.

Next, we want to find the lines that are simultaneously tangent to both parabolas. To do this, we find the derivative of each parabolic function, which gives us the slope of the tangent line at any point on the graph.

For the first parabola, y = x^2, the derivative is 2x, so the slope of the tangent line at any point (x, x^2) is 2x.

For the second parabola, y = -x^2 + 2x - 5, the derivative is 2x - 2, so the slope of the tangent line at any point (x, -x^2 + 2x - 5) is 2x - 2.

To find the equations of the two lines simultaneously tangent to both parabolas, we set the slopes equal to each other and solve for x. This gives us the x-coordinate of the points of tangency on both parabolas, and from there we can use the original functions to find the y-coordinate.

For example, setting the slopes equal to each other, we get:

2x = 2x - 2

0 = -2

So, x = 0, and this point (0, 0) lies on both parabolas. Therefore, the line that is tangent to both parabolas at this point will have the slope 2x = 2 * 0 = 0 and y-intercept equal to 0, giving us the equation y = 0.

We can repeat this process to find the equation of the second tangent line.

Note: There may be other points of tangency that are not shown on the graph, and these can be found using the same process.

Therefore, the line that is tangent to both parabolas at this point will have the slope 2x = 2 * 0 = 0 and y-intercept equal to 0, giving us the equation y = 0.

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The probability that a minimum of seven adults enjoy superhero movies is P(X ≥ 7) = P(X = 7) + P(X = 8)

You can calculate the specific values using the formulas and then sum them up to find the probability that a minimum of seven adults enjoy superhero movies out of the random sample of eight adults.

To find the probability that a minimum of seven adults enjoy superhero movies out of a random sample of eight adults, we need to calculate the probability of different scenarios: exactly 7 adults, exactly 8 adults, and add them together.

First, let's calculate the probability that exactly 7 adults enjoy superhero movies. We can use the binomial probability formula:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

Where:

P(X = k) is the probability of getting exactly k successes,

C(n, k) is the combination formula (n choose k),

p is the probability of success (58% or 0.58 in decimal form),

n is the number of trials (8 in this case), and

k is the number of successes (7).

Using the formula, we can calculate:

P(X = 7) = C(8, 7) * 0.58^7 * (1 - 0.58)^(8 - 7)

Similarly, the probability that exactly 8 adults enjoy superhero movies is:

P(X = 8) = C(8, 8) * 0.58^8 * (1 - 0.58)^(8 - 8)

To find the probability of a minimum of seven adults enjoying superhero movies, we add these two probabilities together:

P(X ≥ 7) = P(X = 7) + P(X = 8)

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