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Triangle DEF has vertices at D(−3, 5), E(−10, 4), and F(−2, 2). Triangle D′E′F′ is the image of triangle DEF after a reflection. Determine the line of reflection if F′ is located at (2, 2).

x = 2
y = 1
y-axis
x-axis

Answers

Answer 1

Answer:

Step-by-step explanation:To determine the line of reflection, we need to find the equation of the line that is equidistant from each vertex of the original triangle and the corresponding vertex of the reflected triangle.

First, let's find the coordinates of the image of each vertex under the reflection. Since F' is given as (2, 2), we can reflect F across the unknown line of reflection to find the image of D and E. The line of reflection must be equidistant from each of these pairs of corresponding points.

To reflect F across a vertical line, the x-coordinate of F' must be the same as that of F but with the opposite sign. The x-coordinate of F is -2, so the x-coordinate of its image F' must be 2. Similarly, the y-coordinate of F' is 2, which means that the line of reflection must pass through the point (2, 2).

To reflect D across the same line, we can draw a perpendicular bisector between D and its image D', which must intersect the line of reflection at a right angle. The midpoint of DD' lies on the line of reflection, and it is equidistant from D and D'. Using the midpoint formula, we find the midpoint of DD' to be ((-3+2)/2, (5+2)/2) = (-0.5, 3.5). Since this point lies on the line of reflection, we can use the point-slope form of a line to find the equation of the line passing through (2, 2) and (-0.5, 3.5):

(y - 2) = m(x - 2) (where m is the slope of the line of reflection)

Simplifying:

y - 2 = m(x - 2)

y = mx - 2m + 2

To find the value of m, we can use the fact that the midpoint of DE lies on the line of reflection as well. The midpoint of DE is ((-3-10)/2, (5+4)/2) = (-6.5, 4.5). Substituting these values into the equation of the line, we get:

4.5 = m(-6.5) - 2m + 2

2.5 = -8.5m

m = -0.294

Therefore, the equation of the line of reflection is:

y = -0.294x + 2.588

This line is not the x-axis, y-axis or the line y=x. Therefore, the line of reflection is neither the x-axis nor the y-axis, and it is not the line y = x.

Answer 2

Answer:

X-axis

Step-by-step explanation:

I am in the middle of taking the quiz and this is the answer I think would be correct!


Related Questions

a die is rolled and a coin is tossed. find the probability that the die shows an odd number and the coin shows a head.
a. 1/2
b. 1/3
c. 1/4
d. 1/5

Answers

The probability of rolling an odd number on a die and getting a head on a coin toss is 1/4. Therefore, the correct answer is (c) 1/4.

The probability of two independent events occurring simultaneously: rolling an odd number on a die and getting a head on a coin toss. To find the probability, we'll multiply the probabilities of each event.

1. Probability of rolling an odd number on a die:
There are 3 odd numbers (1, 3, 5) and 6 possible outcomes (1, 2, 3, 4, 5, 6). So the probability is 3/6, which simplifies to 1/2.

2. Probability of getting a head on a coin toss:
There are 2 possible outcomes (heads or tails), and 1 of them is heads. So the probability is 1/2.

Now, we'll multiply the probabilities: (1/2) * (1/2) = 1/4.

So the probability of rolling an odd number on a die and getting a head on a coin toss is 1/4. Therefore, the correct answer is (c) 1/4.

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Find a power series representation for the function. Determine the radius of convergence, R. (Give your power series representation centered at x = 0.)
f(x) = ln(2 − x)

Answers

To find a power series representation for f(x) = ln(2-x), we can use the formula for the power series expansion of ln(1+x):
ln(1+x) = Σ (-1)^(n+1) * (x^n / n)

We can use this formula by setting x = -x/2 and multiplying by -1 to get:
ln(2-x) = ln(1 + (-x/2 - 1)) = Σ (-1)^(n+1) * ((-1)^n * (x^n+1 / (n+1) * 2^(n+1)))
Therefore, the power series representation for f(x) is:
f(x) = Σ (-1)^(n+1) * ((-1)^n * (x^n+1 / (n+1) * 2^(n+1)))

The radius of convergence of this series can be found using the ratio test:
lim |a_n+1 / a_n| = lim |(-1)^(n+2) * (x^(n+2) / (n+2) * 2^(n+3)) * (n+1) / (-1)^(n+1) * (x^(n+1) / (n+1) * 2^(n+2))|
= lim |x / 2 * (n+1) / (n+2)| = |x/2|

Therefore, the radius of convergence is R = 2. The power series representation centered at x = 0 is:
f(x) = Σ (-1)^(n+1) * ((-1)^n * (x^n+1 / (n+1) * 2^(n+1)))
To find a power series representation for the function f(x) = ln(2 - x), we can first rewrite the function as f(x) = ln(1 + (1 - x)). Now, we'll use the Taylor series formula for ln(1 + u) centered at x = 0:

ln(1 + u) = u - (1/2)u^2 + (1/3)u^3 - (1/4)u^4 + ... + (-1)^n(1/n)u^n + ...
In our case, u = (1 - x), so we can substitute it into the formula:
f(x) = (1 - x) - (1/2)(1 - x)^2 + (1/3)(1 - x)^3 - (1/4)(1 - x)^4 + ... + (-1)^n(1/n)(1 - x)^n + ...

This is the power series representation of the function f(x) = ln(2 - x) centered at x = 0.
Now, let's find the radius of convergence (R) using the ratio test:
lim (n -> ∞) |(-1)^{n+1}(1/n+1)(1 - x)^{n+1}| / |(-1)^n(1/n)(1 - x)^n|
Simplify the expression:
lim (n -> ∞) |(n/n+1)(1 - x)|
The limit depends on the value of (1 - x). To ensure convergence, the limit should be less than 1:
|(1 - x)| < 1

This inequality holds for -1 < (1 - x) < 1, which implies that the interval of convergence is 0 < x < 2. Therefore, the radius of convergence, R, is 1.

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Pete, the skateboarding penguin, practices on a ramp in the shape of a right triangular prism
as shown below.

Answers

Answer:

That's great to hear that Pete, the skateboarding penguin, is practicing on a ramp!

Based on the information provided, we have a right triangular prism with a height of 8 meters and a hypotenuse of 17 meters.

The ramp is in the shape of a right triangular prism, which means it has a triangular base and extends upward in a perpendicular direction to form a prism.

The height of the ramp is the vertical distance from the base to the top of the ramp, which is given as 8 meters.

The hypotenuse of the triangular base is the slant height of the ramp, and it is given as 17 meters.

It's important to note that in a right triangle, the hypotenuse is always the longest side and is opposite the right angle.

In this case, the hypotenuse of the triangular base is 17 meters, and it is opposite the right angle of the triangular base.

Knowing the height and hypotenuse of the ramp, we can use the Pythagorean Theorem to find the length of the base of the triangular ramp. The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).

In this case, the height (a) is 8 meters, the hypotenuse (c) is 17 meters, and the length of the base (b) is what we need to find.

We can use the Pythagorean Theorem to solve for

b:a^2 + b^2 = c^2

8^2 + b^2 = 17^2

64 + b^2 = 289

b^2 = 289 - 64

b^2 = 225

b = sqrt(225)

b = 15

So, the length of the base of the triangular ramp is 15 meters.

Step-by-step explanation:

Q-6: [5 marks] Determine the area of the largest rectangle that can be inscribed in a circle of radius 1.

Answers

The largest rectangle inscribed in a circle of radius 1 has an area of 2√2 units.

Draw the circle of radius 1 and sketch the rectangle inscribed in it. Let the length of the rectangle be 2x and the width be 2y. By symmetry, we know that the diagonals of the rectangle will pass through the center of the circle.

The length of the diagonal is equal to the diameter of the circle, which is 2. Using the Pythagorean theorem, we can write an equation relating the side lengths of the rectangle and the diameter of the circle

(2x)² + (2y)² = 2²

Simplifying, we get

4x² + 4y² = 4

Dividing both sides by 4, we get

x² + y² = 1

We want to maximize the area of the rectangle, which is given by A = 4xy.

We can use the equation from step 5 to solve for y in terms of x

y² = 1 - x²

y = √(1 - x²)

Substituting this into the area formula, we get

A = 4x*√(1 - x²)

To maximize this function, we can take the derivative with respect to x and set it equal to zero

dA/dx = 4(1 - x²)^(-1/2) - 4x²(1 - x²)^(-3/2) = 0

Solving for x, we get x = 1/√(2) or x = -1/√(2).

We can discard the negative solution since we are looking for a positive length.

Using x = 1/√(2), we can find the corresponding value of y

y = √(1 - x²) = √(1 - 1/2) = √(1/2)

Finally, we can calculate the area of the rectangle using these values

A = 4xy = 4(1/√(2))(√(1/2)) = 2(√(2))

Therefore, the area of the largest rectangle that can be inscribed in a circle of radius 1 is 2(√(2)).

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On average, Logan drinks 2/3 of a 6-ounce glass of water in 2 1/4 hours. How much water does he drink, in glasses per hour?

Answers

Logan drinks 8/3 glasses of water per hour on average.

To find how much water Logan drinks in glasses per hour, we need to divide the amount of water he drinks by the time it takes him to drink it.

First, let's convert 2/3 of a 6-ounce glass of water into ounces:

2/3 x 6 = 4 ounces

So Logan drinks 4 ounces of water in 2 1/4 hours. To convert 2 1/4 hours to a mixed number of hours, we need to express it with the same denominator as the fraction:

2 1/4 = 9/4

Now we can divide the amount of water (4 ounces) by the time (9/4 hours):

4 ÷ (9/4) = 16/9

So Logan drinks 16/9 ounces of water per hour. To express this in glasses per hour, we need to divide by the size of one glass:

6 ounces/glass

(16/9 ounces/hour) / (6 ounces/glass) = 8/3 glasses per hour.

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Seth bought a pair of shorts. The original cost was $21, but the store was having a sale of 25% off. Seth also had a coupon for 15% off any purchase at checkout. How much did Seth pay for the pair of shorts?

Answers

Answer:

13.65

Step-by-step explanation:

25% + 15% = 35%

35% of 21 = 7.35

21 - 7.35 = 13.65

hope this helps :)

Jon is buying some candy foe 19 cents. He has only dimes, nickles, and pennies in his pocket, list all the different combinations of dimes, nickels, and pennies he could use to pay for the cnady

Answers

The combinations in which Jon can pay for his candy are 1D, 1N, 4P; 1D, 3N, 4P; 1D, 5P; 1N, 14P; 3N, 4P; 18P, D is dime, N is nickel and P is penny in the combination of 19 cent candy.

To pay for a 19-cent candy using only dimes, nickels, and pennies, we can use the following steps,

1. Start with the largest coin, which is a dime. Jon can use at most one dime, which leaves 9 cents to pay for the candy.

2. If Jon uses a dime, he has 9 cents left. He can use at most one nickel, which leaves 4 cents to pay for the candy.

3. If Jon uses a dime and a nickel, he has 4 cents left. He can use at most four pennies to pay for the candy. Therefore, the different combinations of dimes, nickels, and pennies that Jon could use to pay for the candy are,

1 dime, 1 nickel, 4 pennies

1 dime, 3 nickels, 4 pennies

1 dime, 5 pennies

1 nickel, 14 pennies

3 nickels, 4 pennies

18 pennies

Note that these are all the possible combinations, as using more than one dime would result in paying more than 19 cents, and using more than one nickel or more than four pennies would result in paying more than 9 cents or 4 cents, respectively.

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Find the total surface area of the cylinder. Round to the nearest tenth.

Answers

Answer:

S = 2π(4^2) + 2π(4)(15) = 152π =

477.5 square centimeters

The closest answer is 477.3 square centimeters (3.14 was used for π).

Solving by elimination

5x+2y= -3

3x+3y=9

please help me solve x and y

Answers

After solving by elimination, the value of x and y are -3 and 6 respectively

Elimination refers to the process in which the variables are calculated by eliminating one of the variables.

Given the equations are:

5x + 2y = -3

3x + 3y = 9

For solving by elimination, we multiply the first equation by 3 and the second by 2.

15x + 6y = -9

6x + 6y = 18

Subtract both equations and we get

9x = -27

x = -3

Put the value in one of the given equation

5 (-3) + 2y = -3

-15 + 2y = -3

2y = -3 + 15

2y = 12

y = 6

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Which division problem is represented with this model?


1/6 ÷ 2

1/6÷7

1/2÷6

1/7÷2

Answers

A division problem that is represented with this model include the following: D. 1/7 ÷ 2.

What is a quotient?

In Mathematics, a quotient can be defined as a mathematical expression that is typically used for the representation of the division of a number by another number.

How to calculate the dividend?

In Mathematics, dividend can be calculated by using this mathematical expression:

Dividend = divisor × quotient + residual

In this scenario, the division problem can be interpreted as a box that comprises 7 columns, in which one column is divided into equal halves (1/2) with a remainder of six. Therefore, the model represents the following division problem;

1/7 ÷ 2

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What is the value of x in the equation 4.76 - (23 x*51)-1(-33x+1):

Answers

The required value of x in the given equation is -0.00047.

Let's first simplify the expression inside the parentheses:

-33x+1 = 1-33x

Now, we can substitute this back into the original equation and use order of operations (PEMDAS) to simplify:

4.76 - (23 x 51)-1(-33x+1) = 4.76 - (23/51)(1-33x)

= 4.76 - (23/51) + (23/17)x

Now, we want to solve for x. We'll start by isolating the term with x on one side of the equation:

(23/17)x = 4.76 - (23/51)

x =-0.00047

Therefore, the value of x in the given equation is -0.00047.

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Kaveh and Jessa baked a blueberry pie. They each ate 2/8 of the pie. How much of the pie is left?

Answers

Answer:1/2

Step-by-step explanation:

If they both ate 2/8 of the pie, that means they ate 4/8 of the pie in total, which means that they ate 1/2 when simplified. If they ate one half of the pie, it also means there is 1/2 of the pie left.

What is the outlier for the data set?

A. 5

B. 9

C. 10

D. there is none

Answers

Answer:

The answer to your problem is, A. 5

Step-by-step explanation:

What is an outlier?

What just like it says an outlier it something “ away “ or “ out of civilization of its fellow numbers “

You can see that the hours of 8 - 10 they are all bunched up together

But you can see hour 5 seems a bit lonely

Which then we call he outlier

Thus the answer to your problem is, A. 5

An artist recreated a famous painting using a 4:1 scale. The dimensions of the scaled painting are 8 inches by 10 inches. What are the dimensions of the actual painting?

40 inches by 50 inches
32 inches by 40 inches
12 inches by 14 inches
2 inches by 2.5 inches

Answers

Answer:

To find the dimensions of the actual painting, we need to use the scale factor of 4:1. This means that the actual dimensions of the painting are four times larger than the scaled dimensions.

Let's start with the width of the actual painting:

8 inches (scaled width) × 4 = 32 inches (actual width)

Now, let's find the height of the actual painting:

10 inches (scaled height) × 4 = 40 inches (actual height)

Therefore, the dimensions of the actual painting are 32 inches by 40 inches.

(a) if is the subspace of m6(r) consisting of all symmetric matrices, then (b) if is the subspace of consisting of all diagonal matrices, then

Answers

(a) To show that the set of all symmetric matrices is a subspace of m6(r), we need to verify that it satisfies the three conditions for a subspace:


1. It contains the zero vector: The zero matrix is symmetric, so it is in the set.
2. It is closed under addition: If A and B are symmetric matrices, then A + B is also symmetric because (A + B)^T = A^T + B^T = A + B.
3. It is closed under scalar multiplication: If A is a symmetric matrix and c is a scalar, then cA is also symmetric because (cA)^T = cA^T = cA.

Therefore, the set of all symmetric matrices is a subspace of m6(r).

(b) To show that the set of all diagonal matrices is a subspace of m6(r), we again need to verify the three conditions:
1. It contains the zero vector: The zero matrix is diagonal, so it is in the set.
2. It is closed under addition: If A and B are diagonal matrices, then A + B is also diagonal because the sum of two diagonal entries is still a diagonal entry.
3. It is closed under scalar multiplication: If A is a diagonal matrix and c is a scalar, then cA is also diagonal because each diagonal entry is multiplied by c.

Therefore, the set of all diagonal matrices is a subspace of m6(r).

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The value of this function is positive or negative ?

Answers

Answer:  if a function's output values are all above the x-axis, then the function is positive

Step-by-step explanation:

3. Convert the given Infix expression "A+B* C + D" to Postfix expression using Stack. (2 marks)

Answers

The postfix expression for the given infix expression is "A B C * + D +".

To convert the infix expression "A+B*C+D" to postfix expression using a stack, we can follow these steps:

Create an empty stack and an empty output queue.

Process each symbol in the infix expression from left to right.

If the symbol is an operand (e.g. A, B, C, D), add it to the output queue.

If the symbol is an operator (e.g. +, *), then do the following:

a. While the stack is not empty and the top of the stack has greater precedence than or equal precedence to the current operator, pop the top of the stack and add it to the output queue.

b. Push the current operator onto the stack.

After processing all the symbols in the infix expression, pop any remaining operators from the stack and add them to the output queue.

Using this algorithm, we can convert the infix expression "A+B*C+D" to postfix expression as follows:

Symbol: A + B * C + D

Action: Push A Push + Push B Push * Push C Pop * Pop + Push D

Output: A B C * + D +

Therefore, the postfix expression for the given infix expression is "A B C * + D +".

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Three tennis balls are stored in a cylindrical container with a height of 8.2 inches and a radius of 1.32 inches. The circumference of a tennis ball is 8 inches. Find the amount of space within the cylinder not taken up by the tennis balls. Round your answer to the nearest hundredth.

Answers

The amount of space within the cylinder not taken up by the tennis balls is 18.9 [tex]inches^3[/tex]

The volume of a tennis ball:

The circumference of the tennis ball is 8 inches.

The tennis ball is the form of sphere whose circumference is given by formula [tex]2\pi r[/tex] , where r is the radius.

Thus, if r is the radius then according to condition,

[tex]2\pi r[/tex]  = 8 or

r = 8/2[tex]\pi[/tex] inches.

Now, the volume of the sphere of radius r is [tex]\frac{4}{3}\pi r^3[/tex] hence, find the volume of the given tennis ball by substituting r  = 8/2[tex]\pi[/tex] inches in [tex]\frac{4}{3}\pi r^3[/tex] and simplify:

Volume = [tex]\frac{4}{3} \pi[/tex] × [tex](\frac{8}{2\pi } )^3[/tex]

Volume = 8.65 [tex]inches^3[/tex]

Hence the required volume of the tennis ball is 8.65 [tex]inches^3[/tex]

The volume of three tennis balls is (3 × 8.65) [tex]inches^3[/tex]  = 25.96 [tex]inches^3[/tex]

Find the volume of the cylinder:

The volume of the cylinder with radius r units and height h units is given by  [tex]\pi r^2h[/tex] Hence the volume of the given cylinder with radius 1.32 inches , 8.2 height inches is:

[tex]\pi (1.32)^2[/tex] × 8.2

= 3.14 × [tex](1.32)^2[/tex] × 8.2

= 44.86 [tex]inches^3[/tex]

Hence the volume of the cylinder is 44.86 [tex]inches^3[/tex]

Find the amount of space within the cylinder not taken up by the tennis balls.

The required volume can be obtained by subtracting the volume three tennis balls from the volume of the cylinder as follows:

Volume of cylinder - volume of three tennis balls = (44.86 - 25.96) = 18.9 [tex]inches^3[/tex]

Hence, the amount of space within the cylinder not taken up by the tennis balls is 18.9 [tex]inches^3[/tex].

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What can you deduce about the height of a binary tree if you know that it has the following properties? (a) 26 leave nodes (b) 44 leave nodes(c) 64 leave nodes

Answers

The height of a binary tree depends on the number of nodes and the distribution of those nodes throughout the tree. However, knowing the number of leaf nodes in a binary tree can provide a lower bound on its height.

For a binary tree with 26 leaf nodes, the minimum height is 5, meaning the tree has at least 5 levels. For a binary tree with 44 leaf nodes, the minimum height is 6, and for a binary tree with 64 leaf nodes, the minimum height is 7.

This lower bound on height can be determined by recognizing that each level of a binary tree can contain at most twice as many nodes as the previous level. If a binary tree has L levels and K leaf nodes, then the number of nodes in the last level is at least K, and the number of nodes in the previous level is at least K/2. By repeating this reasoning, we can derive the minimum number of levels needed to accommodate a given number of leaf nodes.

Therefore, if a binary tree has a fixed number of leaf nodes, the minimum height is determined by the number of leaf nodes and the shape of the tree. However, it's important to note that this lower bound is not necessarily tight, as a binary tree with the same number of leaf nodes can have different heights depending on its structure.

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What is radical form (5x)½

Answers

Answer:

[tex] {(5x)}^{ \frac{1}{2} } = \sqrt{5x} [/tex]

Algebra 1 Ch 6 Lesson 2 Quadratic Functions in Vertex Form
Directions:How does the graph of each function compare to the graph of the parent function
f(x) = x2.. State the direction and units; then state if there was a change to the axis of symmetry.

1. f(x) = x2 + 2

2. f(x) = ×2 - 6

3. f(x) = ×2 + 50

4. f(x) = (x - 6)?

5. f(x) = (x + 4)2

6. f(x) = (x - 7)2

Answers

Answer: I believe your answer is number one

Step-by-step explanation:

A study was conducted to explore the relationship between dietary anti-oxidant intake (Vitamin A and Vitamin E) and the risk of having colon cancer. 120,000 people, aged 20-70 years, were selected at random from the total population living in Melbourne in 1987 and invited to join the study. 110,700 of those invited agreed to participate. Participants were interviewed about their dietary intake using food frequency questionnaire so researchers can calculate the amount of anti-oxidant in the diet. Other health risk factors such as smoking, exercise and stress and demographics were also asked at start. Every two years thereafter participants were contacted and asked the same questionnaire. At the end of the study, 10 years later, study researchers were still in contact with 64% of the study population. Outcome data (cancer episode and site) were available for 97% of the original study population from the Victorian Cancer Registry. The study found that the risk of cancer was 2% lower among people with a higher intake of anti-oxidant vitamins, compared to those with lower intakes
What study design it is [2 marks]
What are the key points that led you to think that this is the design [2 marks]
What study design would be more efficient in terms of time and cost for asking the same research question? Explain no more than 100 words [2 marks]

Answers

The study design is a prospective cohort study.
The key points that led to this conclusion are:
- Participants were selected at random from the total population and followed up over a period of 10 years
- Information on dietary intake and other risk factors was collected at the beginning of the study
- Participants were contacted every two years to update their information
- Outcome data was collected from a cancer registry

A more efficient study design in terms of time and cost for asking the same research question could be a cross-sectional study. This would involve recruiting a larger sample of people at one time point and collecting data on their dietary intake and cancer status. However, this design would not allow for follow-up over time to assess changes in diet and cancer risk. In a case-control study, researchers would identify individuals with colon cancer (cases) and those without (controls), and then compare their dietary antioxidant intake. This design typically requires fewer participants and can be completed more quickly, as it doesn't involve following participants over an extended period of time.

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A system uses three components. Each component has probably 0.10 of toning, and the components that dependerity. What is the packability that we cre component works a. 0.001 b. 0.999 c. 0.900 d. 0.729

Answers

A system uses three components, with each component having a probability of 0.10 of toning, and the components have dependerity. To find the packability that at least one component works, we can use the following steps:

1. Calculate the probability that a component fails: 1 - probability of toning = 1 - 0.10 = 0.90
2. Since the components have dependerity, we can multiply the probability of failure for each component: 0.90 * 0.90 * 0.90 = 0.729
3. To find the packability that at least one component works, we can subtract the probability that all components fail from 1: 1 - 0.729 = 0.271

So, the packability that at least one component works is approximately 0.271, which is not listed in the given options.

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The following data shows the points scored by a basketball team during the first 13 games of the season.

{85, 94, 101, 118, 107, 110, 114, 96, 117, 105, 121, 88, 125}

Part A: Determine the best graphical representation to display the data. Explain why the type of graph you chose is an appropriate display for the data. (6 points)

Part B: Explain, in words, how to create the graphical display you chose in Part A. Be sure to include a title, axis label(s), scale for axis if needed, and a clear process of how to graph the data. (6 points)

Answers

Part A: A line graph is the leading graphical representation to show the given information. The line chart is an fitting show since it makes a difference in visualizing the drift of the team's execution over time. It too highlights any outliers and makes a difference in recognizing designs within the information.

How  can a  graphical display be created?

Part B: To make a line graph for the given information, take after the steps underneath:

Draw a even line for the x-axis and a vertical line for the y-axis.Name the x-axis as "Diversions" and the y-axis as "Focuses scored."Scale the x-axis to incorporate all the recreations from 1 to 13 and the y-axis to incorporate all the scores from 85 to 125, with suitable interims.Plot the focuses scored in each amusement on the chart by stamping a point at the comparing crossing point of the diversion number on the x-axis and the score on the y-axis.Interface the points with a line to imagine the slant of the team's execution over the primary 13 recreations of the season.Include a title to the chart, such as "Focuses scored by the ball group within the to begin with 13 diversions of the season."

The coming about line chart would appear the team's execution over the course of the primary 13 recreations, highlighting any patterns, crests, or plunges in their execution.

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Find an explicit formula for Fibonacci numbers, where the recurrence relation for In = {n-1 + fn-2, where fo = 0, fi = 1. 11. Solve the following recurrence relations (a) On=7an-1 -10am-2. (b) Qn=2

Answers

The solution to the recurrence relation is:

[tex]Qn = (1/2)(2^n) - (1/2)[/tex]

To find an explicit formula for the Fibonacci sequence, we first write out the first few terms:

[tex]f0 = 0[/tex]

[tex]f1 = 1[/tex]

[tex]f2 = 1[/tex]

[tex]f3 = 2[/tex]

[tex]f4 = 3[/tex]

[tex]f5 = 5[/tex]

[tex]f6 = 8[/tex]

...

We notice that each term is the sum of the two preceding terms. Therefore, we can write:

[tex]fn = fn-1 + fn-2[/tex]

Let's solve this recurrence relation to find an explicit formula for the nth term. First, we write out the first few terms in terms of f1 and f0:

[tex]f2 = f1 + f0[/tex]

[tex]f3 = f2 + f1 = f1 + f0 + f1 = 2f1 + f0[/tex]

[tex]f4 = f3 + f2 = 3f1 + 2f0[/tex]

[tex]f5 = f4 + f3 = 5f1 + 3f0[/tex]

[tex]f6 = f5 + f4 = 8f1 + 5f0[/tex]

We can see that the coefficients of f1 and f0 are the Fibonacci numbers themselves (1, 1, 2, 3, 5, 8, ...). Therefore, we can write the explicit formula:

[tex]fn = (1/√5) [(1+√5)/2]^n - (1/√5) [(1-√5)/2]^n[/tex]

(a) To solve the recurrence relation [tex]On = 7On-1 - 10On-2[/tex], we first find the roots of the characteristic equation:

[tex]r^2 = 7r - 10[/tex]

[tex]r = (7 ± √(7^2 + 40))/2[/tex]

[tex]r1 = 5, r2 = -2[/tex]

Therefore, the general solution to the recurrence relation is:

[tex]On = c1(5^n) + c2(-2^n)[/tex]

We can find the values of c1 and c2 by using the initial conditions:

[tex]O0 = 1, O1 = 5[/tex]

[tex]c1 + c2 = 1[/tex]

[tex]5c1 - 2c2 = 5[/tex]

Solving these equations, we get:

[tex]c1 = 1, c2 = -1/3[/tex]

Therefore, the solution to the recurrence relation is:

On = 5^n - (1/3)(-2)^n

(b) To solve the recurrence relation Qn [tex]= 2Qn-1 + 1[/tex], we first find the root of the characteristic equation:

[tex]r - 2 = 0[/tex]

[tex]r = 2[/tex]

Therefore, the general solution to the recurrence relation is:

Qn = c(2^n) + d

We can find the values of c and d using the initial conditions:

[tex]Q0 = 0, Q1 = 1[/tex]

[tex]c + d = 0[/tex]

[tex]2c + d = 1[/tex]

Solving these equations, we get:

[tex]c = 1/2, d = -1/2[/tex]

Therefore, the solution to the recurrence relation is:

Qn [tex]= (1/2)(2^n) - (1/2)[/tex]

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9
Find the missing side length of x of each triangle below. (Round answers to the nearest hundredth)

a.)

b.)

c.)

Answers

The missing side length of x of each triangle are

a) 9.2112

b) 17.82

c) 7.61

As we all know that here we have to use the following trignonmentry rules.

sin θ =opposite / hypotenuse.

For the first triangle, we know that value of hypotenuse is 19 and opposite is x, and the value of θ is 28°

Then the value of x is calculated as,

=> sin 28° = x/19

When we apply the value of sin 28° as 0.4848, then the value of x is

=> x = 0.4848 x 19 = 9.2112

For the second triangle, we have to use the rule,

cos θ = adjacent / hypotenuse.

Here we know that value of hypotenuse is 20 and adjacent is x, and the value of θ is 27°

Then the value of x is calculated as,

=> cos 27° = x/20

When we apply the value of cos 27° as 0.891, then the value of x is

=> x = 0.891 x 20 = 17.82

For the third triangle, we have to use the Pythagoras theorem,

That states that  in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

Based on this we have calculated the value of x as,

=> 3² + 7² = x²

=> x² = 58

=> x ≈ 7.61

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- Prices Shanes of company 9 of company on different days in a month were found to be 163 9163, 164, 164,1695, te 165, 169, 170, 171. Test whether the mean price of the shares in the moth is 165

Answers

Is not enough evidence to conclude that the mean price of the shares in the month is different from 165.

To test whether the mean price of the shares in the month is 165, we will perform a one-sample t-test.

The null hypothesis H0: μ = 165, where μ is the true population mean price of the shares in the month.

The alternative hypothesis Ha: μ ≠ 165.

We will use a significance level of α = 0.05.

First, we will calculate the sample mean and sample standard deviation:

sample mean (x) = (163 + 163 + 164 + 164 + 165 + 169 + 170 + 171) / 9 = 166.11

sample standard deviation (s) = √[((163-166.11)² + (163-166.11)² + (164-166.11)² + (164-166.11)² + (165-166.11)² + (169-166.11)² + (170-166.11)² + (171-166.11)²) / (9-1)] = 2.791

Next, we will calculate the t-statistic:

t = (x - μ) / (s / √n) = (166.11 - 165) / (2.791 / √9) = 1.441

Using a t-table or a calculator, we find that the p-value associated with a t-statistic of 1.441 and 8 degrees of freedom is approximately 0.186.

Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. There is not enough evidence to conclude that the mean price of the shares in the month is different from 165.

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10) How many distinguishable permutations are there for the word CONFERENCE

Answers

There are 151200 distinguishable permutations for the word CONFERENCE

How many distinguishable permutations are there for the word

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

CONFERENCE

In the above word, we have

Letters = 10

Repeated C = 2

Repeated N = 2

Repeated E = 3

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

The number of distinguishable permutations for the word is

Number = Letters!/Repeated letters!

This means that

Number = 10!/(2! * 2! * 3!)

Evaluate

Number = 151200

Hence, there are 151200 distinguishable permutations

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Q1 It is well known that any radiocarbon takes several decades to disintegrate. In an experiment, only 0.5 percent of thorium disappeared in 12 years. 1. What is the half-life of the thorium? 2. What percentage will disappear in 15 years?

Answers

The half-life of the thorium is approximately 311 years and 4.1 percent will have disappeared.  

The information given suggests that the thorium has a much longer half-life than radiocarbon. To find the half-life of the thorium, we can use the formula:

t1/2 = (ln 2) / k

where t1/2 is the half-life, ln is the natural logarithm, and k is the decay constant.

We know that after 12 years, only 0.5 percent of the thorium has disappeared, which means that 99.5 percent is still present. We can use this information to solve for the decay constant:

0.995 = e^(-k*12)

ln 0.995 = -k*12

k = 0.00223 per year

Now we can plug this value into the half-life formula:

t1/2 = (ln 2) / 0.00223

t1/2 = 311 years (rounded to the nearest year)

So the half-life of the thorium is approximately 311 years.

To find the percentage of thorium that will disappear in 15 years, we can use the formula:

N(t) / N(0) = e^(-kt)

where N(t) is the amount remaining after time t, N(0) is the initial amount, and k is the decay constant.

We know that after 12 years, only 0.5 percent of the thorium has disappeared, which means that 99.5 percent is still present. We can use this as the initial amount:

N(0) = 99.5

We want to find N(15), so we can solve for it:

N(15) / 99.5 = e^(-0.00223*15)

N(15) = 95.9

So after 15 years, approximately 95.9 percent of the thorium will still be present, and 4.1 percent will have disappeared.

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solve this problem and I will give u brainlist!

Answers

Answer:

32.16 degrees

Step-by-step explanation:

The angle of depression in these problems is always the same as the angle of elevation.

With that in mind, lets solve this problem.

So we are given 2 triangle lengths. The Hypotenuse is 898 ft, and the height of your triangle is 478 ft.

There are three trig functions, sine, cosine, and tangent, but we will be using sin for this triangle because he have the opposite side to the angle(see how the side labeled 478 ft is opposite to the angle of elevation?) and the hypotenuse.

Sin is defined as opposite/hypotenuse.

Now, we make our equation:

sin(478/898) = x

x is your answer, just plug it into a calculator.

You get 32.16 degrees

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