a. Write in your own words a definition of a complex numbers and Modulusof the complex number. Support your answers with examples. (4 marks) b.Find the modulus of + mi (10 marks) c. Write the complex number 2 = ((2+ m) + 3i)in polar form (13 marks) 100+m

The volume of cone is 2 cubic units.

In this image, we have :

The cylinder has a volume of 18 cubic units and a height of 3.

The cone has a congruent base and the same height.

We have to find the volume of the cone.

We know that:

Volume of the cylinder is :

Volume of cylinder = [tex]\pi r^{2} h[/tex]__(A)

18 = [tex]\pi r^2(3)[/tex]

[tex]\pi r^2= 6[/tex]

Now, Volume of cone = [tex](1/3)\pi r^{2} h[/tex]___(B)

and, The cone has a congruent base and the same height.

substitute equation A in equation B

Volume of cone = (1/3)volume of cylinder

Volume of cone = (1/3) × 6

Volume of cone = 2 units.

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The probability density function of Z is fZ(z) = (1/√(2π(4 + 2e^(-5)))) * e^(-z^2/(2(4 + 2e^(-5))))

Given that X(t) is a stationary Gaussian random process with mX(t) = 0 and RX(τ) = 2e^(-5|τ|).

We are interested in finding the probability density function (PDF) of Z = X(2) + X(3).

First, we need to find the mean and variance of Z:

E[Z] = E[X(2) + X(3)] = E[X(2)] + E[X(3)] = 0 + 0 = 0

Var(Z) = Var(X(2) + X(3)) = Var(X(2)) + Var(X(3)) + 2Cov(X(2), X(3))

Since X(t) is a stationary process, we have:

Var(X(2)) = Var(X(3)) = RX(0) = 2

Cov(X(2), X(3)) = RX(1) = 2e^(-5)

Therefore, Var(Z) = 2 + 2 + 2e^(-5) = 4 + 2e^(-5)

Now we can use the properties of Gaussian random variables to find the PDF of Z. Since Z is a linear combination of Gaussian random variables, it is also Gaussian with mean 0 and variance 4 + 2e^(-5).

Thus, fZ(z) = (1/√(2π(4 + 2e^(-5)))) * e^(-z^2/(2(4 + 2e^(-5)))).

Therefore, the probability density function of Z is fZ(z) = (1/√(2π(4 + 2e^(-5)))) * e^(-z^2/(2(4 + 2e^(-5))))

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For a list size of 1000, the sequential search would make about 500 key.

The sequential search algorithm searches a list item by item until the desired item is found or the end of the list is reached. On average, for a list size of 1000, the sequential search would make about 500 key comparisons. Therefore, the correct answer is 500.

Here's a concise description of the sequential search algorithm:

1.Start at the beginning of the list.

2.Compare the target value with the current element.

3.If they match, return the current position.

4.If they don't match, move to the next element.

5.Repeat steps 2-4 until the target is found or the end of the list is reached.

If the target is not found, return a designated value (e.g., -1) to indicate its absence.

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P(1) is true and assuming P(k) being true implies P(k+1) is true, we can conclude that the formula P(k) = (k-1) is true for all integers 1 ≤ k ≤ n by mathematical induction.

(a) To find the coefficient of x in (x+2)^11, we can expand the binomial using the binomial theorem. According to the binomial theorem, the expansion of (x+2)^11 can be written as:

(x+2)^11 = C(11,0) * x^11 * 2^0 + C(11,1) * x^10 * 2^1 + C(11,2) * x^9 * 2^2 + ... + C(11,11) * x^0 * 2^11

The coefficient of x is obtained from the term with x^10. Thus, the coefficient of x in (x+2)^11 is given by C(11,1) * 2^1 = 11 * 2 = 22.

Therefore, the coefficient of x in (x+2)^11 is 22.

(b) To show that the formula P(k) = (k-1) is true for all integers 1 ≤ k ≤ n using mathematical induction, we need to demonstrate two things:

Base case: Show that P(1) is true.

For k = 1, P(k) = (k-1) = (1-1) = 0. Therefore, P(1) is true.

Inductive step: Assume P(k) is true for some integer k ≥ 1, and prove that P(k+1) is true.

Assume P(k) = (k-1) is true.

We need to show that P(k+1) = ((k+1)-1) is also true.

P(k+1) = ((k+1)-1) = k

By assuming P(k) is true, we have shown that P(k+1) is also true.

Since P(1) is true and assuming P(k) being true implies P(k+1) is true, we can conclude that the formula P(k) = (k-1) is true for all integers 1 ≤ k ≤ n by mathematical induction.

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Answer:

The probability of selecting a pen from the first box is 3/4, and the probability of selecting a crayon from the second box is 5/10 or 1/2.

To find the probability of both events occurring together, we multiply the probabilities:

(3/4) × (1/2) = 3/8

Therefore, the probability of selecting a pen from the first box and a crayon from the second box is 3/8.

Step-by-step explanation:

Answer:

There are 4 items in the first box and 10 items in the second box, so there are 4 x 10 = 40 possible combinations of one item from each box.

The probability of selecting a pen from the first box is 3/4, since 3 of the 4 items in the first box are pens. The probability of selecting a crayon from the second box is 5/10 or 1/2, since there are 5 crayons in the second box out of 10 total items.

To find the probability of selecting a pen from the first box and a crayon from the second box, we need to multiply the probabilities of the two events:

P(pen from first box and crayon from second box) = P(pen from first box) * P(crayon from second box)

P(pen from first box and crayon from second box) = (3/4) * (1/2)

P(pen from first box and crayon from second box) = 3/8

Therefore, the probability that a pen from the first box and a crayon from the second box are selected is 3/8.

The mean life of the 25 items will be less than 5.9 years (rounded to one decimal place) 8% of the time.

We'll use the concepts of normal distribution, mean, standard deviation, and the z-score.

Step 1: Calculate the standard error of the mean. Standard error = (Standard deviation) / sqrt(Number of items) Standard error = 1.6 / sqrt(25) = 1.6 / 5 = 0.32 years

Step 2: Find the z-score corresponding to the 8% probability. We look for the z-score in a standard normal distribution table, which tells us that 8% of the time (0.08 probability), the z-score is approximately -1.4.

Step 3: Use the z-score formula to find the mean life (x) that corresponds to this probability. Z = (x - Mean) / Standard error -1.4 = (x - 6.3) / 0.32

Step 4: Solve for x. x - 6.3 = -1.4 * 0.32 x = 6.3 - (1.4 * 0.32) x ≈ 5.852

The mean life of the 25 items will be less than 5.9 years (rounded to one decimal place) 8% of the time.

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Given the rational function, f(x) = 1 + 3x, the value of f(-2) is -5, the value of f(0) is 1, and the value of f(2) is 7.

We will evaluate f(-2), f(0), and f(2) for the given rational function: f(x) = 1 + 3x.

To find the value of the function at specific points, you just need to replace x with the given values and calculate the result. Here's a step-by-step explanation for each case:

1. Evaluate f(-2):
f(x) = 1 + 3x
f(-2) = 1 + 3(-2)
f(-2) = 1 - 6
f(-2) = -5

2. Evaluate f(0):
f(x) = 1 + 3x
f(0) = 1 + 3(0)
f(0) = 1 + 0
f(0) = 1

3. Evaluate f(2):
f(x) = 1 + 3x
f(2) = 1 + 3(2)
f(2) = 1 + 6
f(2) = 7

So, the evaluated values for the given rational function are

f(-2) = -5, f(0) = 1, and f(2) = 7.

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(a) According to Chebyshev's theorem, at least 36% of the measurements lie between 122.7 mmHg and 145.5 mmHg. (b) According to Chebyshev's theorem, at least 56% measurements lie between 122.7 mmHg and 147.2. So, the correct option is 56%.

(a) Using Chebyshev's theorem to find how much data falls within a certain number of standard deviations from the mean.

Using k = 2,  to capture at least 75% of the data (which is 1 - 1/2^2 = 0.75).

Using k = 2, we can say that at least 75% of the data falls within the range of 134.1 - 2(5.7) = 122.7 mmHg and 134.1 + 2(5.7) = 145.5 mmHg.

The percentage of data that falls outside of this range is (1 - 0.75)/2 = 0.125, or 12.5%.

Therefore, at least 12.5% of the data falls in each, below 122.7 mmHg and above 145.5 mmHg. This means that at least 36% of the data falls within the range of 122.7 mmHg and 145.5 mmHg.

(b) We can use Chebyshev's theorem again, this time with k = 2.5, since we want to capture at least 56% of the data (which is 1 - 1/2.5^2 = 0.64).

Using the same calculations as in part (a), we find that at least 64% of the data falls within the range of 121.0 mmHg and 147.2 mmHg.

Therefore, we can say that at least 56% of the data falls within this range, since 56% is less than 64%.

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The value of the variable is 3

Proportion can be defined as a method of comparing numbers in mathematics such that one is made equal to another.

Note that a fraction is described as the part of a whole

From the information given, we have that;

×:8 = 9:24​

To determine the fraction, we divide the numerator by the denominator, we have;

x/8= 9/24

Now, cross multiply the values

24(x) =9(8)

multiply the values, we have;

24x = 72

Now, make 'x' the subject

Divide both sides by the coefficient

x = 3

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In this case, since the curve is not a cylindrical helix, there is no well-defined axis.

A cylindrical helix is a curve in 3D space that follows the path of a cylinder as it is unwrapped along a line. The curve is parameterized by a vector function α(t) = (x(t), y(t), z(t)), where x(t) = r cos(t), y(t) = r sin(t), and z(t) = ht, with r and h being the radius and height of the cylinder, respectively.

In this case, the parameterization of the curve is given by α(t) = (at, bt^2, t^3). To determine if it is a cylindrical helix, we need to check if it follows the path of a cylinder as it is unwrapped along a line.

First, let's look at the z-coordinate, which corresponds to the height of the curve. We see that it is a cubic function of t, which means that the curve is not a horizontal line and it does not lie in a plane. This suggests that the curve may be a helix.

Next, let's look at the x and y-coordinates. The x-coordinate is a linear function of t, which means that it varies uniformly along the curve. The y-coordinate, on the other hand, is a quadratic function of t, which means that it changes faster than the x-coordinate.

This indicates that the curve may be a spiral, which is a type of helix that has an additional circular motion in the x-y plane as it moves along the z-axis. To confirm that the curve is a spiral, we need to check that the radius of the circle traced out by the curve in the x-y plane is constant.

To find the radius, we can take the derivative of the x and y-coordinates with respect to t:

dx/dt = a

dy/dt = 2bt

The radius of the circle is given by:

r = sqrt(x^2 + y^2) = sqrt(a^2 + 4b^2t^2)

We can take the derivative of r with respect to t to see if it is constant:

dr/dt = 4bt/sqrt(a^2 + 4b^2t^2)

We see that dr/dt is not constant, which means that the radius of the circle traced out by the curve is changing as it moves along the z-axis. Therefore, the curve is not a spiral.

In summary, the necessary and sufficient conditions for the curve to be a cylindrical helix are:

The z-coordinate of the curve is a linear function of t, i.e., z(t) = ht.

The radius of the circle traced out by the curve in the x-y plane is constant.

In this case, the curve does not satisfy condition 2, which means that it is not a cylindrical helix.

The axis of the curve is the line along which the cylinder is unwrapped. In this case, since the curve is not a cylindrical helix, there is no well-defined axis.

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To determine the width of each class, we need to first find the range of the data set, which is the difference between the maximum value and the minimum value.

Max value = 77
Min value = 22
Range = 77 - 22 = 55

Next, we need to decide on the number of classes we want to use in the frequency table. For this data set, we can use between 5 and 8 classes.

Let's choose to use 5 classes for this example. To determine the width of each class, we divide the range by the number of classes:

Width of each class = Range/Number of classes
Width of each class = 55/5 = 11

So each class will have a width of 11.

Now we need to determine the boundaries of each class. We can start with the first class, which will start at the minimum value (22) and go up to the next multiple of the width (11), which is 33.

First class: [22 – 33]

For the second class, we start at the next value after the first class (39) and add the width (11) to get the upper bound of the second class:

Second class: (33 – 44]

We can continue this process to find the boundaries of the remaining classes.

Third class: (44 – 55]
Fourth class: (55 – 66]
Fifth class: (66 – 77]

From this, we can see that the fourth class is (55 – 66], which has a width of 11. Therefore, the answer is (c) 14 and (63 – 78].

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The probability of tossing 3 coins of uniform texture at the same time, and two of them happen to be heads up is [tex]\frac{3}{8}[/tex] or 0.375.

The probability of tossing 3 coins of uniform texture at the same time, and two of them happen to be heads up is as follows:

1. Each coin has 2 possible outcomes: heads (H) or tails (T).
2. Since there are 3 coins, there are [tex]2^3 = 8[/tex] total possible outcomes (HHH, HHT, HTH, THH, HTT, THT, TTH, TTT).
3. We're interested in the outcomes where 2 coins are heads up: HHT, HTH, THH.
4. There are 3 favorable outcomes out of 8 total outcomes.

So, the probability of tossing 3 coins of uniform texture at the same time, and two of them happen to be heads up is 3/8 or 0.375.

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To find the average number of bits required to encode this source using a Huffman code, we need to first construct the Huffman code for the given probabilities. The Huffman code assigns shorter codes to more probable values and longer codes to less probable values. We can start by listing the probabilities in descending order:

0.2, 0.15, 0.15, 0.15, 0.15, 0.1, 0.1

Next, we group the two least probable values and assign them a code of 0. We then repeat this process, grouping the next two least probable values and assigning them a code of 10. We continue until we have assigned codes to all values:

7: 0
1: 1000
2: 1001
3: 1010
4: 1011
5: 110
6: 111

We can see that the average number of bits required to encode this source using the Huffman code is:

(0.2 x 1) + (0.1 x 4) + (0.1 x 4) + (0.15 x 4) + (0.15 x 4) + (0.15 x 3) + (0.2 x 3) = 2.771 bits

Therefore, the correct answer is b) 2.771 bits.
To find the average number of bits required to encode this source using a Huffman code, follow these steps:

1. Arrange the probabilities in descending order: 0.2, 0.15, 0.15, 0.15, 0.15, 0.1, 0.1.

2. Build the Huffman tree:
- Combine the two smallest probabilities (0.1 and 0.1) into a single node with a probability of 0.2.
- Combine the next two smallest probabilities (0.15 and 0.15) into a single node with a probability of 0.3.
- Combine the next smallest probability (0.2) with the previously created 0.2 nodes to create a node with a probability of 0.4.
- Combine the remaining 0.3 and 0.4 nodes to create the root node with a probability of 0.7.

3. Assign binary codes to each value based on the Huffman tree:
- Value 1: 111
- Value 2: 110
- Value 3: 101
- Value 4: 100
- Value 5: 011
- Value 6: 010
- Value 7: 00

4. Calculate the average number of bits required to encode the source using the assigned binary codes and their probabilities:
- (3 * 0.1) + (3 * 0.1) + (3 * 0.15) + (3 * 0.15) + (3 * 0.15) + (3 * 0.15) + (2 * 0.2) = 0.9 + 0.9 + 1.35 + 1.35 + 0.4 = 2.771 bits

So, the average number of bits required to encode this source using a Huffman code is 2.771 bits, which corresponds to option (b).

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Answer:

Step-by-step explanation:

Let's start with the wording of the question. Since the sphere is tangential to the faces of the cube, if we draw our radius perpendicular (forming a right angle with the face), we can see it makes a direct connection to the cube face. This means that the diameter of the sphere is equal to the length of the cube.

Next, the question is asking for the volume outside the sphere and inside the cube. To find this, we need to take the volume of the sphere and subtract it from the volume of the cube.

The volume of a sphere is given as: 4/3*pi*(r)^3

The volume of a cube (or any rectangle) is given as: l*w*h

Now all that's left is to plug in the radius and sides of the cube (which we know is double the radius) and subtract.

(6)*(6)*(6)  -  4/3*pi*(3)^3

216 - 113.1 = 102.9

The question asks for standard units, but we aren't given any units so I'm a bit unclear about this. Either way, volumes are measured in cubics (m^3, ft^3, etc.) so it would be the unit of the radius cubed.

Hope I could help!

The volume contained outside the sphere and inside the cube is 216 - 36π cubic units, which is approximately 99.425 cubic units when rounded to three decimal places.

To find the volume contained outside the sphere and inside the cube, we need to calculate the volume of the cube and subtract the volume of the sphere.

The cube's side length is equal to twice the radius of the inscribed sphere. Therefore, the cube's side length is 2 * 3 = 6 units.

The volume of a cube is calculated by raising the side length to the power of 3. So, the volume of the cube is [tex]6^3 = 216[/tex] cubic units.

The volume of a sphere is given by the formula where r is the radius. Substituting the value, we have [tex](4/3) * π * 3^3 = (4/3) * π * 27[/tex]= 36π cubic units.

Now, to find the volume contained outside the sphere and inside the cube, we subtract the volume of the sphere from the  [tex](4/3) * π * r^3[/tex],volume of the cube: 216 - 36π.

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The probability of getting a fish taco (crunchy or soft) is 0.2.

Probability is identifiable as the measure of the probable likelihood or chance of a particular event manifesting itself. As a matter of mathematical fact, it serves to quantitatively assess and analyze uncertainty in occurrences ranging from gambling and random contests to atmospheric predictions and scientific breakthroughs.

Since there are 20 taco fish out of 100. The probability of getting a fish taco (crunchy or soft) is:

= 20 / 100

= 0.2.

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There are 20 taco fish out of 100. What is the probability of getting a fish taco (crunchy or soft) is 0.2.

Martina can run 4,920 more feet this year compared to last year.

Here, we have,

Martina can run 3 miles without stopping. Last year she could run 3,640 yards without stopping. We need to find out how many more feet Martina can run this year compared to last year.

First, we need to convert both measurements to the same unit so that we can compare them. We will convert both measurements to feet.

1 mile = 5,280 feet

1 yard = 3 feet

So, 3 miles = 3 x 5,280 feet = 15,840 feet

And, 3,640 yards = 3,640 x 3 feet = 10,920 feet

Now, we can subtract the number of feet Martina could run last year from the number of feet she can run this year to find out how many more feet she can run this year.

15,840 feet - 10,920 feet = 4,920 feet

Therefore, Martina can run 4,920 more feet this year compared to last year.

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complete question:

Martina can run 3 miles without stopping. Last year she could run 3,640 yards witho stopping. How many more feet can Martina

So, there are 20 possible outfits.

An outfit like t-shirts is a group of garments that have been specifically chosen or created to be worn together. A firm, organisation, or group that collaborates closely is referred to as an outfit. It may be used as a verb to signify to supply with the right tools.

The term outfit can be used to refer to coordinated clothing, such as a shirt and trousers that you usually wear to job interviews. From out- + fit (v.), "act of fitting out (a ship, etc.) for an expedition," 1769. The broader sense of "articles and equipment required for an expedition" is documented in American English from 1787.

To calculate the number of outfits possible, we need to multiply the number of options for each item.

Number of options for jeans = 2 pairs = 2

Number of options for t-shirts = 5

Number of options for shoes = 2 pairs = 2

Therefore, the total number of possible outfits is:

2 x 5 x 2 = 20

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When two fair dice are rolled,

(a) P(F) = 1/9

(b) P(F|E) = 1/5

a. To compute P(F), we need to find the probability that the total of two dice is five. There are four ways to obtain a total of five: (1,4), (2,3), (3,2), and (4,1). Since each die has six possible outcomes, there are 6x6=36 possible outcomes when two dice are rolled. Therefore, P(F) = 4/36 = 1/9.

b. To compute P(F|E), we need to find the probability that the total of two dice is five given that the total is odd. Since the sum of two odd numbers is always even, we know that if an odd total shows on the dice, then the sum must be either 3, 5, 7, 9, or 11. Out of these possibilities, only one yields a total of 5, which is (2,3). Therefore, P(F|E) = 1/5.

We would expect the probability of F to change when we condition on E because the occurrence of E affects the sample space. When we know that an odd total shows on the dice, we can eliminate some of the possible outcomes and reduce the sample space. This makes it more likely that the remaining outcomes will satisfy the condition for F, which increases the probability of F. Therefore, P(F|E) is greater than P(F) because E provides additional information that makes F more likely.

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Answer:

54

Step-by-step explanation:

Multiply each number by 3

The measure of the missing angle which is named ∠PQR = 84°

The first step to solving the problem is to identify the nature of the triangle.

Note that the information states that:

Side PQ and QR are equal,
This means that it is an isosceles triangle because only isosceles triangles have two equal sides.

Another property of isosceles triangles that will help determine the m∠PQR is that the angles at the base of those equal sides are always equal.

Since that is true, then,

∠PQR = 180 - (QPR x 2 )

We know ∠QPR is 48°, so


∠PQR = 180 - (48x 2 )

∠PQR = 180 - 96

Thus,

∠PQR = 84°

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Full Question:

Although part of your question is missing, you might be referring to this full question:

See attached image.

The amount of paper used for the label on the can of tune is 12.57 in²

Here, the shape of the can of can is cylindrical.

The area of the cured surface of cylinder is given by formula,

A = 2πrh

where r is the radius of the cylinder

and h is the height of the cylinder

Here, r = 2 in and h = 1 in

so, the area of the lateral surface of cylinder would be,

A = 2 × π × r × h

A = 2 × π × 2 × 1

A = 4 × π

A = 12.57 sq. in.

Therefore, the required amount of paper = 12.57 in²

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The standard deviation of the random variable B(400, 0.9) is 6 (option E).

To determine the standard deviation of the random variable B(400, 0.9), we need to use the formula for the standard deviation of a binomial distribution:

Standard deviation (σ) = √(n * p * (1 - p))

Here, n is the number of trials (400) and p is the probability of success (0.9). Now, let's calculate the standard deviation step by step:

1. Calculate the probability of failure (1 - p): 1 - 0.9 = 0.1
2. Multiply n, p, and the probability of failure: 400 * 0.9 * 0.1 = 36
3. Calculate the square root of the result: √36 = 6

So, the standard deviation of the random variable B(400, 0.9) is 6 (option E).

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31.25 g on the 5th day

no it will never by empty because even when it gets down to one singular piece of sugar you would technically just cut it in half, then that in half, yes it would get impossible, that's why you wouldn't actually do it, but if you typed it into a calculator it would just keep getting a smaller and smaller decimal.

In this regression analysis, the letter b in the equation y = a + bx represents the estimate of the cost for an additional customer visit. This means that for every additional customer visit to the store, the expected increase in monthly total costs is $2.08, according to the regression model.

The letter x in the regression equation represents the observed customer visits for a given month. This means that the regression model is predicting the monthly total costs based on the number of customer visits in that month.

The R2 value of 0.8681 means that 86.81% of the total variance in the monthly total costs can be explained by the regression equation, which indicates a strong relationship between the number of customer visits and the total costs. This can help managers of Brewsky's make informed decisions about how to allocate resources and improve profitability. However, it is important to note that other factors may also influence the costs, and the regression model may not capture all of these factors.

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The null hypothesis and conclude that the average number of months looking for jobs after graduation is different for GMU and University of Alaska students with 95% confidence.

H0: The average number of months looking for jobs after graduation is the same for GMU and University of Alaska students. Ha: The average number of months looking for jobs after graduation is different for GMU and University of Alaska students.

alpha = 0.05

df = ngmu + nua - 2 = 198 (degrees of freedom)

t* = t(0.025, 198) = 1.972 (from t-distribution table)

SE = sqrt[(sgmu^2/ngmu) + (sua^2/nua)] = sqrt[(2.1^2/100) + (2.3^2/100)] = 0.324

tobt = (xgmu - xua) / SE = (3.6 - 2.7) / 0.324 = 2.77

Since tobt (2.77) > t* (1.972), we reject the null hypothesis and conclude that the average number of months looking for jobs after graduation is different for GMU and University of Alaska students with 95% confidence.

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After the battery is fully charged, Car B can go further than Car A.  Car B, as compared to Car A, had lower variability measurements. After the battery is completely charged, Car B can go further than Car A since Car A has a lower mean and median. Option D is Correct.

The median splits the data in half. A lower median indicates that Car A has less mileage than Car B.

Two measurements exist.

The measure of centre reveals how closely or widely the data are dispersed around the centre.

The measurements of centre are mean, median, and mode.

Car A travelled less since it had a lower mean and median.

We can find out how data changes with a single value using the measure of variability. The data is denser at the mean when the MAD is less. The MAD in Car B is lower. Data that is closer to the centre of the data set has a smaller IQR.

IQR is lower in Car B.

Consequently, automobile B travelled steadily since its IQR and MAD were lower. Option D is Correct.

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Correct Question:

Annabel is comparing the distances that two electric cars can travel after the battery is fully charged. Car A (miles) Car B (miles) Mean 145 200 Median 142 196 IQR 8 4 MAD 6 2 Part A Use the measures of center to make an inference about the data. Use the drop-down menus to complete your answer. Car A can travel further than Car B after the battery is fully charged. Part B Based on the data, which car performs most consistently? Explain. A. Car A because the measures of center are smaller for Car A than for Car B. B. Car B because the measures of center are smaller for Car B than for Car A. C. Car A because the measures of variability are smaller for Car A than for Car B. D. Car B because the measures of variability are smaller for Car B than for Car A.

According to the figure of a circle, x is equal to 17

The total arc length in a circle is equal to 360 degrees

hence arc QR + arc RS + arc QS = 360 degrees

Where

arc QR = 120

arc RS = 2 * 67 = 134

arc QS = 5x + 20

plugging in the values

120 + 134 + 5x + 21 = 360

5x = 360 - 120 - 134 - 21

5x = 85

x = 17

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Answer:3 1/2 times 5= 15  1/10 - 7 1/4 = 8 6/40 or 8 3/20

Step-by-step explanation:

Answer:

3/4 or 0.75 tons

Step-by-step explanation:

The sum of the two months is 7 1/4 which is 29/4. For the first month, the company used 3 1/2 (7/2 or 14/4)

(29-14)/4=15/4.

Thus the second month you use 15/4.

Don’t simplify it yet-
15/4 divided by 5 is 3/4.