A piece of copper wire which is 56cm long is bent to form a rectangle of area 171cm².find the length and the width of this rectangle.​

Dilating a shape will proportionately affect its side lengths.

To find the scale factor between the given triangles, take one side on the larger triangle and divide it by the corresponding side on the smaller triangle. I will divide the triangles' top sides (24 and 8).

\(\text{scale factor}=\dfrac{24}{8} =3\)

So, the scale factor used was 3.

Answer: 3

Step-by-step explanation:

I took the quiz so you do not have to!

The value of the expression given the information about the quotient is 8.

From the information given, the equation will be:

= (10/n - 3) + 6

where n = 2

(10/2 - 3) + 6

= (5 - 3) + 6

= 2 + 6

= 8

In conclusion, the correct option is 8.

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a. The missing value in the table 0.03

b. The mean is 4.18

c. The variance is 3.23 and standard deviation is 1.80

d.  The larger the standard deviation, the greater the spread of the probability distribution.

A random variable is a variable that can take on different values depending on the outcome of a random event. In this case, the random variable X represents the number of calls per hour to a call center in the last month.

a. The missing value in the table is the number of calls per hour for the probability 0.03. From the table, we see that the number of calls per hour is 7.

b. The mean, also known as the expected value, is a measure of the center of the probability distribution. It is calculated by taking the sum of the product of each possible value of X and its corresponding probability. In mathematical terms, the mean of X is given by:

E(X) = 1 * P(1) + 2 * P(2) + 4 * P(4) + 5 * P(5) + 6 * P(6) + 7 * P(7)

E(X) = 0.01 + 0.2 + 1.04 + 1.65 + 1.08 + 0.21 = 4.18

So, the mean number of calls per hour to the call center in the last month is 4.18.

c. The variance of X is a measure of the spread of the probability distribution. It is calculated by taking the sum of the squared differences between each possible value of X and the mean, multiplied by the corresponding probability. In mathematical terms, the variance of X is given by:

Var(X) = (1 - 4.18)² * P(1) + (2 - 4.18)² * P(2) + (4 - 4.18)² * P(4) + (5 - 4.18)² * P(5) + (6 - 4.18)² * P(6) + (7 - 4.18)² * P(7)

Var(X) = 3.23

The standard deviation is the square root of the variance, and it is also a measure of the spread of the probability distribution. In mathematical terms, the standard deviation of X is given by:

=> SD(X) = √(Var(X)) = √(3.23) = 1.80

d. Interpretation:

The mean of 4.18 calls per hour represents the average number of calls to the call center in the last month.

The standard deviation of 1.80 indicates that the number of calls per hour deviates from the mean by approximately 1.80 calls on average.

This means that about 68% of the time, the number of calls per hour will be between 2.38 (4.18 - 1.80) and 6.08 (4.18 + 1.80).

Complete Question:

The random variable X represents the number of calls per hour to a call center in the last month. The probability distribution for X is below.

x 1 2 4 5 6 7

P(x) 0.01 0.10 0.26 0.33 0.18 0.06 0.03

a. What is the missing value in the table?

b. Find the mean.

c. Find the variance and standard deviation.

d. Interpret your results.

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As per the error function, \(\int e^{-5t^2} dt\) is a erf(bx) | = 0

To illustrate this concept, let us consider the integral ∫ e^(-5t²) dt with limits of integration from 0 to x. We can rewrite this integral in terms of the error function by making the substitution u = √5t, which gives us du/dt = √5 and dt = du/√5. Thus, the integral becomes ∫ (e^-u²) (du/√5), with limits of integration from 0 to √(5x²).

Next, we can express the integrand as e^(-u²) = (2/√π) ∫ e^(-v²) dv, which follows from the standard result that ∫ e^(-x²) dx = √π/2. Substituting this expression into our integral, we obtain:

∫ (e^-u²) (du/√5) = (2/√(5π)) ∫ ∫ e^(-v²) du dv,

with limits of integration from 0 to √5x and 0 to u, respectively. Interchanging the order of integration, we get:

∫ (e^-u²) (du/√5) = (2/√(5π)) ∫ ∫ e^(-v²) dv du

= (2/√(5π)) ∫ e^(-v²) (u=0 to u=√5x) dv

= (2/√π) ∫ e^(-5x²) dx.

Therefore, we have shown that the integral ∫ e^(-5t²) dt with limits of integration from 0 to x can be expressed as:

| (2/√π) ∫ e^(-5x²) dx = a erf(bx) |,

where a = √(2/π) and b = 1/√5. Here, erf(bx) denotes the error function evaluated at the argument bx.

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Answer:

Step-by-step explanation:

Any number divided by itself is 1. In the expression-1 times -10 over -1 times -60 ,the -1s in the numerator and the denominator cancel each other out to give the result , or 6.

Answer:

Any number divided by itself is 1. In the expression-1 times -10 over -1 times -60 ,the -1s in the numerator and the denominator cancel each other out to give the result , or 6.

Step-by-step explanation:

S received $1050, J received $0, and the ratio of the money shared between S and J is 0:1. A received 23.33% of the total amount.

Step 1: Determine the amount A received.

We know that A received 1/2 of the total amount, which is $1050. Therefore, the total amount can be calculated by multiplying A's portion by 2: 1050 * 2 = $2100.

Step 2: Calculate the amount J received.

To find the amount J received, we need to subtract A's and S's amounts from the total.

From Step 1, we know that the total is $2100. S received the same amount as A, which is $1050.

Therefore, we subtract A's and S's amounts from the total: 2100 - 1050 - 1050 = $0.

Since J received the remainder, we see that J did not receive any amount from the initial sum of $4500.

Step 3: Calculate the amount S received.

To find the amount S received, we need to subtract S's amount from the total.

Again, from Step 1, we know that the total is $2100. S received the same amount as A, which is $1050.

Therefore, we subtract S's amount from the total: 2100 - 1050 = $1050.

Step 4: Calculate the ratio in which the money was shared between S and J.

Since J did not receive any amount, the ratio of the money shared between S and J is 0:1.

Step 5: Calculate the percentage of the total amount that A received.

To find the percentage, we divide A's amount by the total and multiply by 100: (1050/4500) * 100 = 23.33%.

Therefore, S received $1050, J received $0, and the ratio of the money shared between S and J is 0:1.

A received 23.33% of the total amount.

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Answer:

Step-by-step explanation:

a ) -3x

b ) x - 4

c ) 3

Answer:

The volume of a cylinder with diameter 8 and height 10 is 502.65.

The volume of a cylinder with radius 7 and height 4 is 615.75.

The volume of a cone with radius 18 and height 6 is 2035.75.

The volume of a cone with diameter 12 and height 8 is 1206.37.

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

Work Shown for problem 1

P(pink, then violet) = P(pink)*P(violet given 1st was pink)

= (4/14)*(2/13)

= 8/182

= 4/91

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

Work Shown for problem 2

P(gray, then gray)

= P(gray)*P(gray given 1st was gray)

= (3/14)*(2/13)

= 6/182

= 3/91

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

Work Shown for problem 3

P(not yellow, not yellow)

= P(not yellow)*P(not yellow given 1st was not yellow)

= (9/14)*(8/13)

= 72/182

= 36/91

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

Work Shown for problem 4

P(yellow, not yellow)

= P(yellow)*P(not yellow given 1st was yellow)

= (5/14)*(9/13)

= 45/182

With its price of $2.20 for 11 ounces, Brand C has a higher cost per ounce of $0.20, whereas Brand B has a higher price per ounce of $0.0833. The answer is (Choice A) Brand A.

The brand with the least expensive corn per ounce is Brand A. It offers a price of $1.50 for 18 ounces. To determine the cost per ounce, we divide the total price by the total number of ounces:

Cost per ounce = Price / Ounces = $1.50 / 18 = $0.0833 per ounce.

Comparing this with the other options, Brand B has a higher price per ounce of $0.0833, while Brand C, with its price of $2.20 for 11 ounces, has a higher cost per ounce of $0.20.

Therefore, the answer is:

(Choice A) Brand A

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It is TRUE to state that w/ a discount factor less than 1, value iteration is guaranteed to converge.

The discount factor ranges from 0 to 1. To represent the importance of a reward R that happens N steps in the future from the current state, multiply it by γⁿ. Consider γ= 0.9 and a reward R = 10 that is three steps ahead of our current condition.

Hence, it is correct to indicate that value iteration is assured to converge if the discount factor 0 < γ < 1.

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Full Question:

For an infinite horizon MDP w/ a finite # of states and actions and w/ a discount factor γ that satisfies 0 < γ < 1, value iteration is guaranteed to converge.

a. true

b. false

Answer:

\(\huge\boxed{\sf x = 9}\)

Step-by-step explanation:

3(x + 4) - 11 = 28

3(x + 4) = 28 + 11

3(x + 4) = 39

3x + 12 = 39

3x = 39 - 12

3x = 27

x = 27/3

\(\rule[225]{225}{2}\)

The ratio of the length of the model to the actual length of the van in simplest form will be equal to 3 : 56.

We are given that the scale model of the van = 4 1/5 feet

This can also be written as:

Scale model of van = 6 / 5 feet

We are also given that:

The actual van = 22 2/5 feet

which can also be written as:

Actual van = 112 / 5 feet

The ratio of the length of the model to the actual length of the van in

simplest form will be:

6 / 5 : 112 : 5

= 6 : 112

= 3 : 56

Therefore, the ratio of the length of the model to the actual length of the van in simplest form will be equal to 3 : 56.

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Answer:

So the number of ways of choosing two distinct letters at a time is (42)=6. We can then add the duplicate pairs which are O,O and N,N to give a total of 8 possible pairs.

Answer:

15

Step-by-step explanation:

There are 6 letters in the word number

This is 6 choose 2

This is a combination

The formula is 6! / ( 2! * (6-2)! )

                           6! / 2! 4!

                           (6*5*4*3*2*1) / ( 2*1 *  4*3*2*1)

Canceling like factors

                             (6*5) / ( 2*1)

                              30/2

                                 15

There are 15 possible ways to have 6 choose 2

Answer:

\((x + 7) \times (3x - 4)\)

Step-by-step explanation:

\( {3}^{2} + 17x - 28\)

\(3 {x}^{2} + 21x - 4x - 28\)

\(3 \times x(x + 7) - 4x - 28\)

\(3x \times ( x + 7) - 4(x + 7)\)

\((x + 7) \times (3x - 4)\)

Answer:

8

Step-by-step explanation:

5 = 40

1 = x

Then we multiply by the rule of crisscrossing

5 x X = 40 x 1

5x = 40 then divide both by 5

X = 8

Answer:

The general term of the sequence is

\( { - 1}^{n - 1} \)

Step-by-step explanation:

The sequence above is a geometric sequence

For an nth term in a geometric sequence

\(u(n) = a(r) ^{n - 1} \)

Where n is the number of terms

a is the first term

r is the common ratio

From the above sequence

a = 1

r = -1/1 = -1

The nth term of the sequence is

\(u(n) = 1 ({ - 1})^{n - 1} \\ = { - 1}^{n - 1} \)

Hope this helps you

The coordinates of Kyle's house would be (x - 4, y + 2) relative to Luke's house, where x and y represent the Coordinates of Luke's house on the coordinate grid.

The grid representing Kyle's house. However, based on the given information, we can determine the coordinates of Kyle's house relative to Luke's house.

If Luke's house is located at the point (x, y), then Kyle's house is located 4 units to the left of Luke's house, which means the x-coordinate of Kyle's house is (x - 4). Similarly, Kyle's house is located 2 units up from Luke's house, which means the y-coordinate of Kyle's house is (y + 2).

Therefore, the coordinates of Kyle's house would be (x - 4, y + 2) relative to Luke's house, where x and y represent the coordinates of Luke's house on the coordinate grid.

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Answer:

Step-by-step explanation:

To find the inverse of a function, we need to switch the x and y values and solve for y (or x, depending on how the original function is written). The inverse of the function f(x) = 3x + 7 is written as f^-1(x). To find f^-1(x), we can follow these steps:

Replace the function f(x) with y to make it easier to manipulate: y = 3x + 7.

Swap the x and y variables: x = 3y + 7.

Solve for y:

Subtract 7 from both sides to get x - 7 = 3y.

Divide both sides by 3 to get (x - 7) / 3 = y.

Write the inverse function using f^-1(x) instead of y:

f^-1(x) = (x - 7) / 3

So, the inverse of the function f(x) = 3x + 7 is f^-1(x) = (x - 7) / 3.

Step-by-step explanation:

------------->Then f(-2)

= f(x) : 3x2 + 2x - 8

= f(-2) : 3(-2)2 + 2(-2) - 8

= f(-2) : (-6)2 + (-4) - 8

= f(-2) : (-12) + (-4) - 8

= f(-2) : (-16) - 8

Step-by-step explanation:

f(x) = 3x2 + 2x – 8

———» Then f(-2)

f(-2) = 3(-2)^2 + 2(-2) - 8

f(-2) = 3((-2) × (-2)) + (2 × (-2)) - 8

f(-2) = 3(4) + (-4) - 8

f(-2) = (3 × 4) + (-4) - 8

f(-2) = 12 + (-4) - 8

f(-2) = 8 - 8

f(-2) = 0

Answer:

10-x

Step-by-step explanation:

Answer:

What the question? I'm confused.

Answer:

what?????

Step-by-step explanation:

Hello!

miles driven = x

the initial cost = 29

f(x) = 29 + 0.35x

Answer:

6x6x6x6

Step-by-step explanation:

Answer:

the 4th one

Step-by-step explanation:

6.6.6.6

Answer:

\(103.78\:\mathrm{ft}\)

Step-by-step explanation:

We can form a right triangle where the distance between the ranger's current position and fire is the hypotenuse of the triangle. In a right triangle, the tangent of an angle is equal to its opposite side divided by the hypotenuse.

Therefore, we have:

\(\tan 34^{\circ}=\frac{70}{x}\), where \(x\) is the distance between the base of the tower and the fire.

Solving, we get:

\(x=\frac{70}{\tan 34^{\circ}}=103.779267796\approx \boxed{103.78\:\mathrm{ft}}\)

Answer:

The answer is 108

Step-by-step explanation:

I did this for my exam got 100

Together they can paint 5/108 of a wall in 1 minute.  So they can paint the entire wall in 108 minutes.

We have given that,

John can paint 1/54 of a wall in 1 minute.

James can paint 1/36 of a wall in 1 minute.

Total wall paint  of both in one minute is calculated by adding the both the paint in one minute it gives us the total paint in one minute

Therefore ,total wall paint in one minute =1/54 + 1/36

So if they work together, they can both paint 1/54 + 1/36 of a wall in 1 minute.

1/54 + 1/36 = 2/108 + 3/108 = 5/108 = 0.04629.

Therefore,together they can paint 5/108 of a wall in 1 minute.  So they can paint the entire wall in 108 minutes.

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Algebraically, the amount of money the insurance company will pay, represented as P, is equal to the total value of the stolen items (2b + t) minus the deductible (d).

Let's denote the amount of money the insurance company will pay as P. In this scenario, if the value of the stolen items is greater than the deductible, the insurance company will cover the loss, and Ron will receive compensation for the stolen items.

The total value of the stolen items can be calculated by adding the value of the bicycles (2b) and the value of the tools (t). So, the total value of the stolen items is 2b + t.

If the total value of the stolen items is greater than the deductible (d), then the insurance company will pay the difference between the total value and the deductible. Mathematically, this can be represented as:

P = (2b + t) - d

Therefore, algebraically, the amount of money the insurance company will pay, represented as P, is equal to the total value of the stolen items (2b + t) minus the deductible (d).

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The inequalities which satisfy the number line shown is x>2 and x>=2.

We are given that;

The number line showing inequality

Now,

x>2 satisfies the equation by the given number line

x>=2 satisfies the equation by the given number line

x<=-3 does not satisfies the equation by the given number line

x<=-3 does not satisfies the equation by the given number line

Therefore, by the number line the answer will be x>2 and x>=2 .

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The table of values does not show that it is a linear function.

Answer:

y =  +- 58°  +- 360° k

Step-by-step explanation: