Hullan's age is two times Thomas's age. The sum of their ages is 21. What is Thomas's age?

Answer:

C

Step-by-step explanation:

multiply by 2 to be 2x-6

Answer:

x=8//

Step-by-step explanation:

2(x- 3)

or,2x-6

or,X=6+2

hence,X=8//

Answer: The complex conjugate has a very special property. Consider what happens when we multiply a complex number by its complex conjugate. We find that the answer is a purely real number  it has no imaginary part. This always happens when a complex number is multiplied by its conjugate the result is real number.

Real numbers can be positive or negative, and include the number zero. They are called real numbers because they are not imaginary, which is a different system of numbers

Step-by-step explanation: Every complex number has a complex conjugate. The complex conjugate of a + bi is a - bi. For example, the conjugate of 3 + 15i is 3 - 15i, and the conjugate of 5 - 6i is 5 + 6i.

Answer:

for every 5 roses there's 1 plant(s)

Step-by-step explanation:

All values of y are not restriction on the variable for the rational expression 2y² + 2 - 5y + y - 5

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

2y² + 2 - 5y + y - 5

The rational expression given is 2y² + 2 - 5y + y - 5.

A restriction on the variable in a rational expression is any value of the variable that would make the denominator of the expression equal to zero i.e. the values not in the domain

For this expression, the expression has no denominator, there is no restriction on the variable y.

Therefore, all values of y are allowed and there are no restrictions on the variable y.

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Answer:

Answer is -1, 0, -5, & 1.

A, B, C, & D.

The predicted outcome of the game, or the strategy profile played in the game, would then depend on the remaining strategies.

1. A strategy is considered strictly dominant for a player if it always leads to a higher payoff than any other strategy, regardless of the choices made by the other player. In this game, for player 1 to have a strictly dominant strategy, the payoff for strategy U must be strictly higher than the payoffs for strategies M and D, regardless of the choices made by player 2.

2. For player 2 to have a strictly dominant strategy, the payoff for strategy R must be strictly higher than the payoffs for strategies L and any other possible strategy that player 2 can choose.

3. To determine if any player has a strictly dominant strategy, we need to compare the payoffs for each strategy for both players. In this specific example, using the given values (a=2, b=3, c=4, x=5, y=5, z=2, and w=3),

4. The order in which strategies are deleted does matter when using iterative deletion of weakly dominated strategies. In the given example, when we delete the weakly dominated strategy M for player 1, we are left with a 2x2 game.

(c) In the original game of part (4), when we note that U is a weakly dominated strategy for player 1, we can look for a strategy that weakly dominates it. By comparing the payoffs, we can determine the weakly dominant strategy.

(d) After deleting U and noting that L is weakly dominated for player 2, we can delete it as well. The predicted outcome of the game, or the strategy profile played in the game, would then depend on the remaining strategies.

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The angle between the tangents at the ends of the radii is 180 - 110 = 70 degrees.

The angle between the tangents at the ends of the radii of a circle,

when the angle between the radii is 110 degrees, can be determined using the property of the tangents being perpendicular to the radii at the points of contact.

Let's consider a circle with two radii originating from the center of the circle.

The angle between the radii is given as 110 degrees.

Since the tangents are perpendicular to the radii,

we can visualize a quadrilateral formed by the two radii and the two tangents.

In this quadrilateral,

the sum of all angles is 360 degrees.

The opposite angles in a quadrilateral are supplementary,

meaning they add up to 180 degrees.

The angle between the tangents at the ends of the radii can be found by subtracting the given angle between the radii from 180 degrees.

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The mean, standard deviation, and the variance are respectively calculated as: a. μx = 2.96, σx ≈ 1.472; b. μy = 1.2, σy ≈ 0.693; c. μc = $8.88, σc² ≈ 29.97; d. μb = $8.00, σb² ≈ 2.40; e. μz = 4.16, σz² = 2.65; f. μw = $16.88, σw² = 32.37

To solve this problem, we'll use the given probability distributions and apply the formulas for mean and variance. Let's calculate each part step by step:

a. Compute the mean and standard deviation of x:

Mean of x (μx):

μx = ∑(x * p(x)) = (0 * 0.05) + (1 * 0.09) + (2 * 0.25) + (3 * 0.3) + (4 * 0.2) + (5 * 0.11) = 2.96

Variance of x (σx²):

σx² = ∑((x - μx)² * p(x)) = ((0 - 2.96)² * 0.05) + ((1 - 2.96)² * 0.09) + ((2 - 2.96)² * 0.25) + ((3 - 2.96)² * 0.3) + ((4 - 2.96)² * 0.2) + ((5 - 2.96)² * 0.11) ≈ 2.17

Standard deviation of x (σx):

σx = √(σx²) ≈ √(2.17) ≈ 1.472

b. Compute the mean and standard deviation of y:

Mean of y (μy):

μy = ∑(y * p(y)) = (0 * 0.4) + (1 * 0.2) + (2 * 0.4) = 1.2

Variance of y (σy²):

σy² = ∑((y - μy)² * p(y)) = ((0 - 1.2)² * 0.4) + ((1 - 1.2)² * 0.2) + ((2 - 1.2)² * 0.4) ≈ 0.48

Standard deviation of y (σy):

σy = √(σy²) ≈ √(0.48) ≈ 0.693

c. Compute the mean and variance of the total amount of money collected in tolls from cars:

Mean of cars toll (μc):

μc = ∑(x * $3 * p(x)) = (0 * $3 * 0.05) + (1 * $3 * 0.09) + (2 * $3 * 0.25) + (3 * $3 * 0.3) + (4 * $3 * 0.2) + (5 * $3 * 0.11) = $8.88

Variance of cars toll (σc²):

σc² = ∑(((x * $3) - μc)² * p(x)) = (((0 * $3) - $8.88)² * 0.05) + (((1 * $3) - $8.88)² * 0.09) + (((2 * $3) - $8.88)² * 0.25) + (((3 * $3) - $8.88)² * 0.3) + (((4 * $3) - $8.88)² * 0.2) + (((5 * $3) - $8.88)² * 0.11) ≈ 29.97

d. Compute the mean and variance of the total amount of money collected in tolls from buses:

Mean of buses toll (μb):

μb = ∑(y * $10 * p(y)) = (0 * $10 * 0.4) + (1 * $10 * 0.2) + (2 * $10 * 0.4) = $8.00

Variance of buses toll (σb²):

σb² = ∑(((y * $10) - μb)² * p(y)) = (((0 * $10) - $8.00)² * 0.4) + (((1 * $10) - $8.00)² * 0.2) + (((2 * $10) - $8.00)² * 0.4) ≈ 2.40

e. Compute the mean and variance of z = total number of vehicles (cars and buses) on the ferry:

Mean of z (μz):

μz = μx + μy = 2.96 + 1.2 = 4.16

Variance of z (σz²):

σz² = σx² + σy² = 2.17 + 0.48 = 2.65

f. Compute the mean and variance of w = total amount of money collected in tolls:

Mean of w (μw):

μw = μc + μb = $8.88 + $8.00 = $16.88

Variance of w (σw²):

σw² = σc² + σb² = 29.97 + 2.40 = 32.37

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False. To calculate a percent increase, the portion is not the missing element. The portion refers to the initial or original value, while the missing element is the final or increased value.

The formula for calculating a percent increase is:

Percent Increase = (Final Value - Initial Value) / Initial Value * 100

In this formula, the initial value is the portion that represents the starting or original value. The final value is the missing element, as it represents the increased or final value after the increase.

By subtracting the initial value from the final value, we obtain the difference between the two. Dividing this difference by the initial value gives us the relative increase as a decimal or fraction. Multiplying by 100 converts it into a percentage, representing the percent increase.

Therefore, the portion in calculating a percent increase is the known value or initial value, while the missing element is the final value that we are trying to determine or find.

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There are different consecutive ways that the flowers can be planted:

3,9,15,21 and so on.

Numbers that follow each other in a regular counting order or pattern are called consecutive numbers. They are written sequentially, where the difference between the numbers is fixed and no number in between is skipped.

Given that:

Roses plants in 1st, 2nd, row are:

3,9 ,.....

Since difference between consecutive terms is same:

It is an AP

We have to find number of row in the flower bed:

Lets assume there are n rows in the flowers bed.

We know that:

    aₙ = a + (n-1)d

and d = 9-3 = 6

Therefore, the next numbers can be:

3,9,15 ,21 ......

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Answer:

9 is the answer

Step-by-step explanation:

12*3/4

9

it may be helpful

Answer:

The area of the room is 432 square feet

Step-by-step explanation:

Let us use the ratio method to solve the question

∵ The scale drawing of the room is 1 inch: 3 feet

→ That means each 1 inch in the drawing represents 3 feet in real

∵ The drawing is 8 inches long by 6 inches wide

∴ The drawing length of the room = 8 inches

∴ The drawing width of the room = 6 inches

→ By using the ratio method

→  inches  :  feet

→  1            :  3

→  8           :  L

→  6           :  W

→ By using the cross multiplication

∵ 1 × L = 8 × 3

∴ L = 24

∴ The actual length of the room is 24 feet

∵ 1 × W = 6 × 3

∴ W = 18

∴ The actual width of the room is 18 feet

Use the formula of the area of the rectangle to find the area of the room

∵ Area of rectangle = length × width

∴ Area of the room = 24 × 18

∴ Area of the room = 432 feet²

∴ The area of the room is 432 square feet

Answer:

7/66

Step-by-step explanation:

Given problem,

→ (7/10) × (1/3) × (5/11)

Let's solve the given problem,

→ (7/10) × (1/3) × (5/11)

→ (7 × 1 × 5)/(10 × 3 × 11)

→ 35/330

→ 7/66

Hence, the answer is 7/66.

Answer:

solved graphically,

it's just the point where the two lines intersect

Answer:

\(V=90\)

Step-by-step explanation:

Step 1:  Find the volume of the cone

\(V = \frac{\pi *r^{2}*h}{3}\)

Plug in the values

\(V = \frac{\pi *3^{2}*10}{3}\)

Simplify and Solve

\(V = \frac{\pi *9*10}{3}\)

\(V = \frac{90\pi }{3}\)

\(V = \frac{90*3 }{3}\)

\(V=90\)

Answer:  \(V=90\)

The triple integral in spherical coordinates allows us to ev is option 3:\(\int\limits^{\frac{\pi}{2}}_0\int\limits^{\frac{\pi}{2}}_0\int\limits^5_2 {(\rho^2sin\phi) }d\phi d\theta d\rho\).

To evaluate the triple integral over the region D in spherical coordinates, we need to determine the limits of integration for each variable. In this case, we have two spheres defining the region: x² + y² + z² = 4 and x² + y² + z² = 25.

In spherical coordinates, the conversion formulas are:

x = ρsinφcosθ

y = ρsinφsinθ

z = ρcosφ

The first sphere, x² + y² + z² = 4, can be rewritten in spherical coordinates as:

(ρsinφcosθ)² + (ρsinφsinθ)² + (ρcosφ)² = 4

ρ²sin²φcos²θ + ρ²sin²φsin²θ + ρ²cos²φ = 4

ρ²(sin²φcos²θ + sin²φsin²θ + cos²φ) = 4

ρ²(sin²φ(cos²θ + sin²θ) + cos²φ) = 4

ρ²(sin²φ + cos²φ) = 4

ρ² = 4

ρ = 2

The second sphere, x² + y² + z² = 25, can be rewritten in spherical coordinates as:

ρ² = 25

ρ = 5

Since we are only interested in the region in the first octant, we have the following limits of integration:

0 ≤ θ ≤ π/2

0 ≤ φ ≤ π/2

2 ≤ ρ ≤ 5

Now, let's consider the given options for the triple integral and evaluate which one is correct.

Option 3 : \(\int\limits^{\frac{\pi}{2}}_0\int\limits^{\frac{\pi}{2}}_0\int\limits^5_2 {(\rho^2sin\phi) }d\phi d\theta d\rho\)

To determine the correct option, we need to consider the order of integration based on the limits of each variable.

In this case, the correct option is Option 3:

The integration order starts with φ, then θ, and finally ρ, which matches the limits we established for each variable.

You can now evaluate the triple integral using the limits 0 ≤ θ ≤ π/2, 0 ≤ φ ≤ π/2, and 2 ≤ ρ ≤ 5 in the integral expression based on Option 3.

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Answer: 60

Step-by-step explanation:

To find how much she rolls in 1 minute, you divide 18 by 12. This gets you 1.5. Multiply 1.5 by 40 and you get 60.

Based on the assumption of independence, the expected number of people in the box U.S. South and Plays Golf is 17.5.

What is number?

A number is a mathematical concept used to quantify and measure quantities. It represents a value or a magnitude in mathematics. Numbers can be used for counting, calculating, and comparing quantities.

To determine the expected number of people in the box U.S. South and Plays Golf under the assumption of independence between region and golf-playing, we need to calculate the expected value based on the row and column totals.

The expected value for a cell in a contingency table is calculated using the formula:

Expected Value = (Row Total * Column Total) / Overall Total

Let's apply this formula to the given table for the U.S. South and Plays Golf cell:

Row Total for U.S. South = 50 (from the row total)

Column Total for Plays Golf = 70 (from the column total)

Overall Total = 200 (from the total)

Expected Value = (50 * 70) / 200

Calculating this expression, we have:

Expected Value = 3500 / 200

Expected Value = 17.5

Therefore, based on the assumption of independence, the expected number of people in the box U.S. South and Plays Golf is 17.5.

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Answer:

\(x=25\)

Step-by-step explanation:

\(x-16=9\\x=9+16\\x=25\)

Hope it helps

Answer:

C

Step-by-step explanation:

Within the sentence, it explicitly states "the war was a vehicle for lasting social and economic gains." In other words, the war led to a better future in terms of social and economic gains for discriminated groups (discriminated groups were mentioned in the beginning of the sentence which gives us the who). Some may argue D is correct, but I strongly side with C instead because D emphasizes discrimination ended, while the sentence makes no such claim. The sentence only states discriminatory issues were improved, but still not completely absent. As for A, there is no mention of technology in the sentence. In terms of B, the sentence refers to the "gains" or improvement of discrimination and not the "plague" or worsening of discrimination. Hence, C fits best.

Answer:

Step-by-step explanation:

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Based on the information, the person traveled 117.8 feet by the Ferris wheel.

Circumference = π×diameter

Keep the values in formula and perform multiplication to find the circumference of the wheel

Circumference = 50π

On 1 complete revolution of 360 degrees, the distance covered = 50π

So, revolution of 270 degrees, the distance covered will be = (50π/360) × 270

Performing multiplication and division on Right Hand Side of the equation

The distance traveled = 117.8 feet

Hence, the person travelled 117.8 feet.

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Answer:

A

Step-by-step explanation:

I=PRN

=4500×(4.75/100)×3

=$641.25

Answer:

-2.5

Step-by-step explanation:

Here in this question, we are interested in calculating the z-score for a student that had a particular mark at the test

To calculate the z-score, we need to use a mathematical formula

Mathematically;

z-score = (x - mean)/SD

From the question;

x = 76

mean = 86

standard deviation SD = 4

Plugging these values in the equation, we have;

z-score = (76-86)/4 = -10/4 = -2.5

The volume of the solid generated by revolving the region bounded by the given curve and lines about the x-axis is V = 8π/3

The volume of a solid, given by the function f(x), over an interval between a and b, is given by:

\(V = \pi \int\limits^a_b {f(x)^2} \, dx\)

To find the area, integrate around that area. We're revolving around the x-axis so the area will be a circle;

V = ∫A(x)dx =  ∫(πr²)dr

Then we subtract them from each others.

∫(πr₂² - πr₁²)dr

Now substitute the value and integrate;

∫(π(2)² - π(2x)²)dr

∫(4π - 4πx²)dr

4π∫(1 - x²)dr

Now integrate from 0 to 1 since that's where our boundary is.

V = 4π∫(1 - x²)dr = 8π/3

Therefore, The volume of the solid generated by revolving the region bounded by the given curve and lines about the x-axis is V = 8π/3

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Based on the given information, we have the mean concentration of sodium in the drinking water of a water system in Connecticut as 26.4 mg/l and the standard deviation as 6 mg/l.

The water department selects a simple random sample of 32 water specimens over the course of a year. To answer the question using the distributions tool, we need to set the mean and standard deviation parameters on the tool to the expected mean and standard error for the distribution of sample mean concentrations.

The expected mean for the distribution of sample mean concentrations is the same as the mean concentration of sodium in the drinking water, which is 26.4 mg/l.

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The water department in Connecticut is monitoring the concentration of sodium in their drinking water. By calculating the mean and standard error for the distribution of sample means, they can determine the probability of the mean concentration exceeding the notification level of 28 mg/l. If this probability is low, the water department will notify the public and recommend necessary actions.

In this scenario, the water department in Connecticut wants to monitor the concentration of sodium in their drinking water. They have set a notification level of 28 mg/l, meaning that if the mean concentration of sodium across a sample of 32 water specimens exceeds this level, they will notify the public.

To analyze this situation, we can use the distribution of sample means. The mean concentration of sodium in the drinking water of the water system is given as 26.4 mg/l, with a standard deviation of 6 mg/l.

To find the expected mean and standard error for the distribution of sample means, we can use the following formulas:

Expected mean of sample means = population mean

                                                        = 26.4 mg/l
Standard error of sample means = population standard deviation / square root of sample size

Using the given values, the standard error of sample means can be calculated as follows:
Standard error of sample means = 6 mg/l / square root of 32

                                                      ≈ 1.06 mg/l

Now, we can use a distributions tool to find the probability that the mean concentration of sodium in the sample of 32 water specimens exceeds 28 mg/l. We will set the mean parameter on the tool to 26.4 mg/l and the standard deviation parameter to 1.06 mg/l.

By entering these values into the distributions tool, we can find the probability of obtaining a mean concentration greater than 28 mg/l. If this probability is less than a certain threshold (e.g., 0.05), it indicates that the mean concentration exceeding 28 mg/l is unlikely to occur by chance alone. In such cases, the water department would notify the public and recommend that individuals on sodium-restricted diets inform their physicians of the sodium content in their drinking water.

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Answer:

Mean: 2.125

median: 2

range: 4

A line graph is used when an independent variable is a continuous quantitative variable. A line graph is a type of chart used to represent data over time with the help of lines connecting various data points.

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Using diagonals from a common vertex, 143 triangles could be formed from a13-gon. But there will be 47 distinct triangles in total.

If we choose a common vertex of an n-gon, we can form (n-2) triangles by drawing diagonals from that vertex to each of the other vertices of the polygon. This is because every vertex, except for the adjacent vertices, can be connected to the chosen vertex to form a triangle.

Therefore, for a 13-gon, we can choose any one of the 13 vertices as the common vertex and form (13-2) = 11 triangles using diagonals from that vertex. We can repeat this process for each of the 13 vertices to form a total of 13*11 = 143 triangles.

However, we need to be careful not to count the same triangle multiple times. In the process of forming triangles from a common vertex, we may end up forming some of the same triangles using different vertices. For example, the triangle formed by connecting vertices 1, 6, and 9 is the same as the triangle formed by connecting vertices 9, 6, and 1.

To avoid double-counting, we can divide the total number of triangles by 3, since each triangle is counted 3 times in the process of forming triangles from a common vertex. Therefore, the number of distinct triangles that can be formed using diagonals from a 13-gon is 143/3 = 47.

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