The probabilities are shown in the following table. Find the standard deviation for the probability distribution. (Round answer to the nearest hundredth.) Girls ...

Answer: A. -1

Explanation: 4-5/5-4= -1/1 = -1

Based on the fractional winning of ³/₈, the team's win-loss ratio is 3:5.

The ratio shows the relative size that one quantity or value has when compared to another quantity or value.

We depict ratios in decimals, fractions, or percentages.  We can also use the standard ratio form (:) to show ratios.

The fraction of games won by the team = ³/₈

The fraction of games lost by the ream = ⁵/₈ (1 - ³/₈)

The implication is that for every 8 games, the team won 3 but lost 5 games.

The ratio of win-loss = 3:5

The sum of ratios = 8 (3 + 5)

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The first 3 terms of the sequence are 21, 24 and 29

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

n² + 20

This means that

f(n) = n² + 20

The first 3 terms of the sequence is when n = 1, 2 and 3

So, we have

f(1) = 1² + 20 = 21

f(2) = 2² + 20 = 24

f(3) = 3² + 20 = 29

Hence, the first 3 terms of the sequence are 21, 24 and 29

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Answer:

your answer will be option C

Step-by-step explanation:

hope it helps

have a great day

Answer:

Negative

Step-by-step explanation:

Find slope by determining rise over run

Rise = -3

Run = 1

The slope is -3 (or -3/1)

This is a negative number, therefore the slope is negative.

The z-score for x = 30.2 is approximately -0.49.

What is z-score measures?

The z-score, also known as the standard score, is a measure used in statistics to quantify the number of standard deviations that a given data point is from the mean of a dataset.

To calculate the z-score for x = 30.2, we use the formula:

z = (x - μ) / σ

where x is the observed value, μ is the population mean, and σ is the population standard deviation. In this case, we are given the sample mean and sample standard deviation, so we will use them as estimates for the population parameters.

Substituting the given values, we have:

z = (30.2 - 33.7) / 7.2

Simplifying, we get:

z = -0.49

Rounding to two decimal places, we have:

z ≈ -0.49

Therefore, the z-score for x = 30.2 is approximately -0.49.

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===================================================

Explanation:

A truncated cone is where we start with a regular 3D cone and chop off the top. The portion up top is a smaller cone, which we'll ignore. The bottom part is the truncated cone portion.

In the real world, a lampshade is one example of a truncated cone.

----------------

Let x be the radius of the sphere.

We'll be focusing on a vertical cross section of the truncated cone. Refer to figure 1 in the diagram below.

We have the following points

We'll connect a few of those points forming the dashed lines in figure 1.

To start off, draw a segment from D to G. This forms rectangle BGDE with sides of EB = 2x and BG = 2. The side BC is 18 units, so that must mean GC = BC - BG = 18 - 2 = 16.

Since EB = 2x, this means DG is also 2x.

------------------

Now focus on triangles ABC and AFC. They are congruent right triangles. We can prove this using the HL (hypotenuse leg) theorem. Recall that the radius of a circle is perpendicular to the tangent line, which is why angle AFC is 90 degrees. Angle ABC is a similar story.

Because they are congruent right triangles, this indicates side BC is the same length as side FC. Therefore, FC = 18

Through similar logic, triangles ADE and ADF are congruent as well which leads to ED = FD = 2.

Combine sides FD and FC to get the length of DC

DC = FD+FC = 2+18 = 20

This is the hypotenuse of the right triangle GCD

------------------

After all that, we have the right triangle GCD with the legs of 2x and 16. The hypotenuse is 20. Refer to figure 2 shown below.

As you can probably guess, we'll use the pythagorean theorem to find the value of x.

a^2 + b^2 = c^2

(DG)^2 + (GC)^2 = (CD)^2

(2x)^2 + (16)^2 = (20)^2

4x^2 + 256 = 400

4x^2 = 400-256

4x^2 = 144

x^2 = 144/4

x^2 = 36

x = sqrt(36)

x = 6 is the radius of the sphere.

The yy-component of vector a a is -y-direction, which is equal to 0 m/s2.the product of the second term of the vector with unit vector j^j^, which is in the direction of the y-axis.

Given a vector, a⃗ a→ = (5.0 m/s2, −y−direction)Find the yy -component of the given vector a⃗ a→.Solution: The yy-component of the given vector a⃗ a→ = -y-directionTo find the yy-component of the given vector a⃗ a→, we have to take the product of the second term of the vector with unit vector j^j^, which is in the direction of the y-axis.Therefore, the yy-component of vector a⃗ a→ is :a_yy = -y-direction = (-1)(0) = 0 m/s²  Answer: 0 m/s².

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The yy-component of vector a⃗ a→ is -y-direction.

The yy-component of a vector represents the magnitude of the vector in the y-direction.

In this case, the vector a⃗ a→ is given as (5.0 m/s2, −y-direction).

Since the yy-component is the magnitude in the y-direction, the yy-component of the vector a⃗ a→ is -y-direction.

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Answer:

(2, –3) is a solution to the system of linear equations.

Step-by-step explanation:

Given: Equations:

3x - y = 9 --------(1),

4x + y = 5 --------(2),

Add Equation (1) + Equation (2),

3x + 4x = 9 + 5

7x = 14  ( Combine like terms )

x = 2   ( Divide both sides by 7 ),

From equation 1:

3(2) - y = 9

6 - y = 9

-y = 9 - 6    ( Subtraction 6 on both sides )

-y = 3

y = - 3     ( Multiplying -1 on both sides )

The process of checking the correctness of an integration answer is essentially the reverse process of integration, called differentiation. By taking the derivative and comparing it to the original function, you can confidently determine if your integration solution is accurate.

The answer to an integration question, also known as the integral, represents the accumulated sum of a given function over a specified interval. In other words, integration helps us find the area under a curve or the total accumulated value of a continuously changing quantity.
To check the answer of an integration problem and ensure its correctness, you can use the following steps:
Perform the integration: Compute the integral of the given function over the specified interval, which will result in a new function or a constant value.
Take the derivative: To verify the correctness of the computed integral, take the derivative of the resulting function (if the integral resulted in a function) or the constant value. This process is called differentiation.
Compare the derivative with the original function: After obtaining the derivative of the integral, compare this derivative to the original function given in the integration problem. If the derivative matches the original function, then the computed integral is correct.
Verify any boundary conditions: If the integration problem involves definite integrals (integrating over a specific range or interval), ensure that the computed integral satisfies any given boundary conditions or constraints.
Remember, the process of checking the correctness of an integration answer is essentially the reverse process of integration, called differentiation. By taking the derivative of the integral and comparing it to the original function, you can confidently determine if your integration solution is accurate.

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Answer:

tape

Step-by-step explanation:

tape is tape

450 miles

Explanation

Step 1

Let

Step 2

how many times the distnce (E-M) is the distance(E-S)

so, the distance is

I hope this helps you

The estimated population for an area can be Red is 2611.2 and Green is 1894.4 respectively.

Given the population for a 1 cm2 area, the population of a 20 cm by 40 cm area is;

Green = 1894.4 Red = 2611.2

How can you determine the population using the population density?

The following are some probable details for a population density of 1 cm2:

The number of people per 6.25 cm2 is;

Red = 20.4

Green ≈ 14.8

Therefore, the density per 1 cm2 is;

Red = 20.4/6.25 = 3.264

Green ≈ 14.8 = 2.368

Consequently, the inhabitants of a 20 by 40 cm region are;

Red = 3.264 × 20 × 40 = 2611.2

Green ≈ 14.8 = 2.368 = 1894.4

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The numbers arranged in order from least to greatest is: √146, 12.39, 12.62, 12⅝, and 12¾. The third option is correct.

The ordering of numbers refers to arranging numbers in a specific sequence based on their magnitude or value. The ordering of numbers is determined by their relative values. Comparisons are made between numbers to determine their position in the order.

12⅝ = 101/8 = 12.645

12.62 = 12.62

√146 = 12.0830

12.39 = 12.39

12¾ = 51/4 = 12.75

Therefore, the numbers arranged in order from least to greatest is: √146, 12.39, 12.62, 12⅝, and 12¾.

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The highest score is 32.

The mean refers to the average of a set of values.

Total players = 8

Mean= 14.5

Now, total score of 8 players,

= 14.5*8

=116

and, Total score for the remaining 7 players

= 12 * 7

= 84

Hence, the highest score is 116-84 =32

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Answer:

625πmm³

Step-by-step explanation:

The exact volume of the figure will be the sum total of volume of the two comes and one cylinder.

Volume of a cone = 1/3πr²h

r is the radius of the cone

h is the height of the cone

Since the cone are 15mm high, their individual height = 15mm

Diameter = 10mm, radius = 5mm

Volume of a cone = 1/3× π × 5²×15

Volume of a cone = 1/3 × π × 25 × 15

Volume of a cone = 125πmm³

Volume of both cones = 2(125π) = 250πmm³

Volume of a cylinder = πr²h

Height of the cylinder = 15mm

Radius of the cylinder = 5mm

Volume of the cylinder = π(5)²×15

Volume of the cylinder = 375πmm³

Volume of the composite solid = volume of the two cones + volume of cylinder.

= 250πmm³+375πmm³

= 625πmm³

Answer: 625pimm^3

Step-by-step explanation:

Both teams can complete the search in a time period of 4 hours.

Distance is a measurement of how far apart two points or objects are from one another. Time is a unit used to describe how long it takes for an object to travel between two points. Speed is a unit used to describe how quickly or slowly an item or a point moves.  

Here we have

Two search-and-rescue teams leave base camp at the same time,
looking for a lost child.

The first team, on horseback, heads north at 3 mph,  

The second team, on foot, heads south at 2.5 mph.

Let both teams complete searching in 'x' mins

The distance traveled by 1st team in 'x' mins = 3 × x  

= 3x  m

The distance traveled by 2nd team in 'x' mins = 2.5 × x  

= 2.5x m    

As we know total distance = 22 miles

=> 3x + 2.5x = 22 miles

=> 5.5x = 22 miles

=> x = 4 hrs  

Therefore,

Both teams can complete the search in a time period of 4 hours.

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Answer:D,E

Step-by-step explanation:

9/3=3

36=9×4

The simplified form of the complex fraction is (x^2 + 4x - 65)(x^2+6x-7) / (-57(x^2+6x-25)).

To simplify the complex fraction (6/(x+5) + (x-7)/(x-5))/(1/(x-4) - 58/(x^2+6x-7)), we can start by finding a common denominator for each fraction within the numerator and denominator separately. The common denominator for the numerator fractions is (x+5)(x-5), and the common denominator for the denominator fractions is (x-4)(x^2+6x-7).After obtaining the common denominators, we can combine the fractions: [(6(x-5) + (x+5)(x-7)) / ((x+5)(x-5))] / [((x-4) - 58(x-4)) / ((x-4)(x^2+6x-7))] Next, we simplify the expression by multiplying the numerator and denominator by the reciprocal of the denominator fraction: [(6(x-5) + (x+5)(x-7)) / ((x+5)(x-5))] * [((x-4)(x^2+6x-7)) / ((x-4) - 58(x-4))]

Simplifying further, we can cancel out common factors and combine like terms:[(6x-30 + x^2-2x-35) / (x^2+6x-25)] * [((x-4)(x^2+6x-7)) / (-57(x-4))] Finally, we can simplify the expression by canceling out common factors and expanding the numerator: [(x^2 + 4x - 65) / (x^2+6x-25)] * [((x-4)(x^2+6x-7)) / (-57(x-4))] The (x-4) terms in the numerator and denominator cancel out, leaving: (x^2 + 4x - 65)(x^2+6x-7) / (-57(x^2+6x-25))

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Answer:

1/9

Step-by-step explanation:

With replacement, we use the principle of multiplication with counting.

\(\frac{3redballs}{9total balls} * \frac{3redballs}{9total balls} = \frac{1}{3}* \frac{1}{3} = \frac{1}{9}\)

The probability of selecting two red marbles with replacement is 1/9.

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain to occur.

If we select a marble at random from the bag, there are 3 red marbles out of 9 total marbles. After replacing the marble back in the bag, the probability of selecting another red marble is still 3/9 (assuming the first marble selected was red).

To find the probability of selecting two red marbles with replacement, we need to multiply the probabilities of each event happening.

Therefore, the probability of selecting two red marbles with replacement can be calculated as follows:

P(selecting two red marbles with replacement) = P(selecting a red marble) x P(selecting a red marble given that the first marble was red)

P(selecting two red marbles with replacement) = (3/9) x (3/9)

P(selecting two red marbles with replacement) = 1/9

Therefore, the probability of selecting two red marbles with replacement is 1/9.

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Answer:

the mean of which the team won is 8.75

The mean of which the team lost is 11.5

Step-by-step explanation:

add all the numbers of which the team won by then divide the sum by the number of numbers there are

example:

7+8+11+9=35/4=8.75

Answer:

62.5 mph

Step-by-step explanation:

Given that :

Peter :

Speed = 50mph

Start Time = 9 a. M

Emily :

Start time = 9:30

Speed = x

In other to catch up at 11:30 :

Peter (11:30 - 9:00) = 2hours 30 minutes = 2.5 hrs

Total distance moved by Peter :

Speed * time = 50 * 2.5 = 125miles

For Emily to cover 125 miles in (11:30 - 9:30) = 2 hours

Speed = distance / time

Speed = 125 miles / 2 hours

Speed = 62.5 miles per hour

Answer:

x=5

Step-by-step explanation:

An isosceles trapezoid has two pairs of congruent base angles. This means angle F has to equal angle E. So we have 2x^2+21=3x^2-4. Move the variables to one side and we get 25=x^2. Square root both sides and we get two values x=5 and x=-5. Since angles cannot necessarily be negative, we only want the positive value. In this case x=5.  

A Communication system consists of n components.

a) Binomial distribution,

P(X=x) = ⁿC ₓ p ˣ (1-p) ⁽ⁿ⁻ˣ⁾

b) For 5-component system,

P(X= 5) = ⁵Cₓ pˣ (1-p)⁵⁻ˣ , x= 3,4,5

c) 5-component system is effectively than a 3-component system if 0.5<p<1 where p is probability of functioning components.

Communication system consists of n components and functions with probability p . Then the probability of components which are not function from n components is q = 1-p .

(a) Let x denotes number of functioning components i.e., their probability value is p . And system is effectively operate when atleast one half of components are function. So, the distribution of x is binomial distribution P (X=x) = ⁿCₓ pˣ (1-p)⁽ⁿ⁻ˣ⁾ where n is total number of components, x numbers of functioning components, p is probability of functioning components.

(b) Now , 5-component system is function . That is n=5

Probability that 5-components system will function is P(X= 5)

= ⁵C ₓ p ˣ(1-p)⁽⁵⁻ˣ⁾ , x= 3,4 ,5 ( because one half of components are function)

(c) Because the number of functioning components is a binomial random variable with parameters (n, p), it follows that the probability that a 5-component system will be effective is

⁵ C₃ p³(1-p)² + ⁵C₄ p⁴ (1-p)¹+ ⁵C ₅ p⁵ (1-p)⁰ = 10 p³ (1-p)² + 5 p⁴(1-p) + p⁵

Whereas the corresponding probability for a 3-components system

³ C ₓ p ˣ ( 1-p)⁽ⁿ⁻ˣ⁾ , x= 2,3

³ C₂ p²(1-p)¹ + ³C₃p³(1-p)⁰ = 3 p² 1-p) + p³

5-Component system is better than 3-Components system if

10 p³ (1-p)² + 5p⁴ (1-p) + p⁵= 3p²(1-p) + p³

=> 10 p⁵ + 10 p³– 20 p⁴+ 5 p⁴ – 5p⁵ + p⁵ = 3p² + p³ – 3p²

Which reduce to

3( 2p -1) (1-p) 2 > 0 , either (2p-1) > 0 or 3(1-p) 2>0

either p> ½ or p <1

=> p belongs to ( 0.5, 1)

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You can substitute any vector v to find its image under the transformation t.

By multiplying the transformation by the vector, we can determine the image of a given vector under the linear transformation t. Let's call the given vectors v1, v2, and v3, as well as the images that correspond to them, t(v1), t(v2), and t(v3), respectively.

Given:

t(1, 1, 1) = (2, 0, -1) t(0, -1, 2) = (-2, 5, -1) t(1, 0, 1) = (1, 1, 0) Using the information provided, we can construct a system of equations:

This system of equations can be represented as: x1(1, 1) + x2(0, -1, 2) + x3(1, 0, 1) = (2, 0, -1) y1(1, 1) + y2(0, -1, 2) + y3(1, 0, 1) = (-2, 5, -1) z1(1, 1) + z2(0, -1, 2) + z3(1, 0, 1) = (1, 1, 0)

| 1 0 1 | | x1 0 1 | | 2 0 -1 | | 1 -1 0 | = |-2 5 -1 | | 1 2 1 | | x3 2 1 | | 1 1 0 | We can use matrix inversion to solve this system. The matrix on the left will be referred to as A, and the matrix on the right will be referred to as B. A * X = B In order to determine X, we can multiply both sides of the equation by the inverse of A:

We have: A1 * A = A1 * B because A1 * A is the identity matrix.

Now that we know the inverse of A, we can find X by multiplying it by B: X = A * B.

We can use matrix row operations to reduce A to the identity matrix and keep track of the row operations performed to apply the same operations to the identity matrix. A = | 1 0 1 | | 1 -1 0 | | 1 2 1 |

| 1 0 1 | | 1 0 1 | | 1 -1 0 | | 1 2 1 | | 0 0 1 | | 0 0 1 | | 0 0 1 | | 0 0 1 | | 0 0 1 | | 0 0 1 | | 0 0 1 | | 0 0 1 | | 0 0 1 | The matrix A has been reduced to the identity matrix. As a result, A1 is:

A1 = | 1 0 0 | | 0 0 1 | Now, we can find X by multiplying A1 by B:

A * B = | 1 0 0 | | 2 0 -1 | | 0 0 1 | | 1 0 0 | = | 2 0 -1 | | 2 5 -1 | | 1 1 0 | The system of equations' solution reads as follows:

X = | 2 0 - 1 |

|-2 5 - 1 |

| 1 1 0 |

The picture of any vector under the direct change t can be gotten by increasing the vector by the grid X:

Any vector v can now be used to find its image under the transformation t if t(v) = X * v.

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The regular price of the camera is $227.

Given that, the total amount paid=$201.75 and the cost of the memory card=$12.35.

Cost of camera=201.75-12.35=$189.4

A discount is a deduction from the usual price of something. To discount means to deduct an amount from the price.

Discount is given to the camera=20%.

The regular price of the camera=189.4+20% of 189.4

=189.4+0.2×189.4=189.4+37.88=$227.28

The estimation to the nearest the whole number is $227.

Therefore, the regular price of the camera is $227.

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answer

yes do it your self

a. The assumption that more is better is satisfied for both goods in the given utility function U(x, y) = 3x + y.

b. The marginal utility of x diminishes as the consumer buys more x.

c. The marginal rate of substitution (MRS) of x for y is 3.

d. The MRS of x and y is constant as the consumer substitutes x for y along an indifference curve.

e. On a graph, a typical indifference curve will exhibit a diminishing MRS. Additionally, a second indifference curve U2 > U1 can be drawn.

a. The assumption that more is better is satisfied for both goods because the utility function U(x, y) = 3x + y implies that increasing the quantities of both goods x and y will lead to higher utility.

b. The marginal utility of x diminishes as the consumer buys more x. This is because the marginal utility of x (MUx) is given as 3, which is a constant value. As the consumer consumes more units of x, the additional satisfaction derived from each additional unit of x decreases, leading to a diminishing marginal utility.

c. The marginal rate of substitution (MRS) of x for y is 3. MRSxy represents the rate at which the consumer is willing to trade off one good (x) for another (y) while keeping the utility constant. In this case, the MRSxy is constant and equal to the ratio of the marginal utilities, which is 3 (MUx / MUy = 3/1 = 3).

d. The MRS of x and y is constant as the consumer substitutes x for y along an indifference curve. The given utility function does not exhibit changing MRS as the consumer substitutes one good for another along an indifference curve. The MRS remains constant at 3, indicating a consistent trade-off rate between x and y.

e. On a graph, a typical indifference curve for the utility function U(x, y) = 3x + y will exhibit a diminishing MRS. This means that as the consumer moves along the indifference curve, the slope (MRS) will decrease, reflecting a decrease in the rate at which the consumer is willing to trade off x for y. Additionally, a second indifference curve U2 > U1 can be drawn, representing higher levels of utility. The specific shapes and positions of the indifference curves will depend on the values of x and y chosen for each curve.

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If the jobs are sequenced according to the SLACK rule, Job A would be completed on day 12.

The SLACK rule involves calculating the slack time for each job, which is the difference between the due date and the completion time. The job with the least slack time is prioritized and scheduled first. In this case, the due dates for the jobs are as follows: Job A (12), Job B (15), Job C (17), Job D (10), and Job E (8).

Job A has a processing time of 8 days and a due date of 12, so the slack time is 12 - 8 = 4 days. Since Job A has the least slack time among all the jobs, it would be completed on day 12. Therefore, the answer is D. 12.

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