What type of parent function is this? What is the domain and range of this function? write it in interval notation

The expected value of the random variable is 3.4.

The expected value of a random variable is a measure of its central tendency and represents the mean of all possible outcomes.

To find the expected value in this case, we need to multiply each outcome by its probability and then sum up the products.

The formula for expected value is:

E(x) = Σ[x * P(x)]

where E(x) is the expected value, x is the possible outcome, and P(x) is the probability of that outcome.

Using the given values in the table, we can calculate the expected value as follows:

E(x) = (2 * 0.2) + (3 * 0.4) + (4 * 0.2) + (5 * 0.2)

E(x) = 0.4 + 1.2 + 0.8 + 1

E(x) = 3.4

Therefore, the expected value of the random variable is 3.4.

This means that if we were to repeat this experiment multiple times, on average we would expect the value of x to be around 3.4.

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Answer:

c = 5

Step-by-step explanation:

the equational set up is easy 50 is how much she has, 10 is how much they cost so

50/10 is the equation

and 5 is the answer.

D: II and III only.

The solutions to the differential equation y" - 10y' + 9y = 0 are D: II and III only.

This can be determined by using the method of undetermined coefficients. Specifically, II is y = 5e^x and III is y = C, where C is a constant.

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Answer:

B

Step-by-step explanation:

Answer:

x ≈ 9.4

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Trigonometry

Step-by-step explanation:

Step 1: Define

We are given a right triangle. We can use PT to find the missing length.

Step 2: Identify Variables

Leg a = 9

Leg b = x

Hypotenuse c = 13

Step 3: Solve for x

The measures are WZ = a = 4, ZN = b = 2, ZY = c = 4. The medians divide each other in a 2:1 ratio

In a triangle, the centroid is the point of intersection of the medians. The medians divide each other in a 2:1 ratio. Let's denote the length of WZ as "a", ZN as "b", and ZY as "c".

Given:

WZ = 4

ZN = 14

ZY = 10

Since the medians divide each other in a 2:1 ratio, we can set up the following equations:

a/b = 2/1

a/c = 2/1

To find the values of "a", "b", and "c", we can solve these equations.

From the first equation, we can write:

a = (2/1) * b

a = 2b

Substituting this value into the second equation, we get:

2b/c = 2/1

Cross-multiplying, we have:

2b = c

Now, we can substitute the given values:

4 = 2b

b = 2

Substituting this value back into the equation a = 2b, we have:

a = 2(2)

a = 4

Finally, using the equation 2b = c, we find:

2(2) = c

c = 4

Therefore, the measures are:

WZ = a = 4

ZN = b = 2

ZY = c = 4

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Answer:

90 degrees counterclockwise rotation about the origin followed by a translation 1 unit to the right

Step-by-step explanation:

Answer:

(-6, 2)

Step-by-step explanation:

Multiply the second equation by 2

2x - 6y = -24

then add both equations together.

4x + 6y = -12

6x          = -36, divide both sides by 6

x = -6

then plug -6 back into either equation and solve for y

-6 - 3y = -12

-3y = -6

y = 2

Answer:

Where's the grid?

Step-by-step explanation:

Answer:

7 units. I hope I was able to help kiddo :)

Answer:

Step-by-step explanation:

It would take 300 minuets

Answer:

t = 9

Step-by-step explanation:

This is the answer because:

1) \(9^{2}\) is the same as 9 x 9

2) 9 x 9 = 81

Hope this helps!

The required final answer is option a) Incentre

The point of concurrency of the angle bisectors of a triangle is known as the "Incentre".

It is the center of the circle inscribed within the triangle, which is equidistant from all three sides of the triangle.

The incentre is the point where the angle bisectors of a triangle intersect, forming the incircle, which is the largest circle that can be inscribed inside the triangle.

The incentre is always within the triangle and is equidistant from all three sides of the triangle, making

it a useful tool in construction and design applications. In summary, the incentre is the center of the incircle of a triangle, and it is the point where the angle bisectors of the triangle intersect.

Thus, required answer is "Incentre".

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Therefore, the correct option is (b) 46 that is the number of students who like Twix and Reese's peanut butter cups only (region D) by principle of inclusion-exclusion, we need to subtract the number of students who like Snickers, as well as the number of students who like all three kinds of candy, from the number of students who like Twix and Reese's peanut butter cups along with one or both of the other kinds of candy.

We can start by using the principle of inclusion-exclusion, which tells us that:

|A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C|

where |X| denotes the number of elements in set X.

Using the numbers given in the problem, we have:

|A| = 129

|B| = 118

|C| = 145

|A ∩ B| = 22

|B ∩ C| = 54

|A ∩ C| = 55

|A ∩ B ∩ C| = 8

Substituting these values into the formula, we get:

|A ∪ B ∪ C| = 129 + 118 + 145 - 22 - 55 - 54 + 8 = 269

This tells us that 269 students like at least one of the three kinds of chocolate candy.

To find the number of students who like Twix and Reese's peanut butter cups only (region D), we need to subtract the number of students who like Snickers, as well as the number of students who like all three kinds of candy, from the number of students who like Twix and Reese's peanut butter cups along with one or both of the other kinds of candy:

|D| = |B ∩ C| - |A ∩ B ∩ C|

= 54 - 8

= 46

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hope this helps you

Answer:

B. 140π units²

Step-by-step explanation:

Surface area of a cylinder:

2πrh + 2πr²

2π(5)(9) + 2π(5²)

90π + 50π

140π

Answer:

The correct answer is 140 pi units ^2.

Step-by-step explanation:

The interest paid each year is $1353

The formula for simple interest is given as: = PRT/100

Interest = $36,736 - $20,500 = $16236

Therefore, the number of years will be:

16236 = (20500 × 6.6 × T) / 100

Cross multiply

16236 × 100 = 135300 × T

1623600 = 135300T

T = 1623600/135300

T = 12

The number of years is 12 years.

Therefore, the interest paid each year will be:

= Total interest / Number of years

= $16236 / 12

= $1353

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Answer:

$1,353 paid interest each year

Julia has 2020 stickers remaining.

Julia initially had 202 sheets of stickers, and each sheet had 14 stickers. So the total number of stickers she had was 202 sheets * 14 stickers/sheet = 2828 stickers.

She then gave away 808 stickers to her friends.

To find out how many stickers Julia has remaining, we subtract the number of stickers given away from the total number of stickers she had:

Remaining stickers = Total stickers - Stickers given away

= 2828 stickers - 808 stickers

= 2020 stickers

Therefore, Julia has 2020 stickers remaining.

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Answer: 20%

Step-by-step explanation:

Answer:

Radius

314 cm²

Step-by-step explanation:

They gave you the diameter which you can find the radius from, and you need the radius to find the area. The radius is 10, and that squared is 11. Multiply 3.14 times 100 to get 314.

Answer:

I personally don’t know

Step-by-step explanation:

LOOK IN YOUR NOTES

Answer:

D: \(\begin{pmatrix}10&-5\\ -4&7\end{pmatrix}\)

Step-by-step explanation:

\(\begin{pmatrix}5&0\\ 3&-5\end{pmatrix}\begin{pmatrix}2&-1\\ 2&-2\end{pmatrix}\)

\(\begin{pmatrix}5\cdot \:2+0\cdot \:2&5\left(-1\right)+0\cdot \left(-2\right)\\ 3\cdot \:2+\left(-5\right)\cdot \:2&3\left(-1\right)+\left(-5\right)\left(-2\right)\end{pmatrix}\)

\(\begin{pmatrix}10&-5\\ -4&7\end{pmatrix}\)

The area of the shaded sector is 4π square units.

To find the area of the shaded sector, we need to calculate the central angle formed by the sector. In this case, we are given that the angle JIK is 90 degrees, which means it forms a quarter of a full circle.

Since a full circle has 360 degrees, the central angle of the shaded sector is 90 degrees.

Next, we need to determine the radius of the circle. The line segment IJ represents the radius of the circle, and it is given as 4 units.

The formula to calculate the area of a sector is A = (θ/360) * π * r², where θ is the central angle and r is the radius of the circle.

Plugging in the values, we have A = (90/360) * π * 4².

Simplifying, A = (1/4) * π * 16.

Further simplifying, A = (1/4) * π * 16.

Canceling out the common factors, A = π * 4.

Hence, the area of the shaded sector is 4π square units.

Therefore, the area of the shaded sector, expressed as a fraction times π, is 4π/1.

In summary, the area of the shaded sector is 4π square units, or 4π/1 when expressed as a fraction times π.

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Answer:

7.5 MW

Step-by-step explanation:

The power generated from a falling water is a function of its height and volume. The power generated an be calculated using the formula:

Power (P) = Density(ρ) * volume flow rate(Q) * acceleration due to gravity(g) * height(h)

P = ρQgh

But Qh = Velocity(v) * volume(V).

Hence power = ρvgV

Given that ρ of water = 1000 kg/m³, v = 75 m/s, V = 10 m³, g = 10 m/s². Substituting:

P = ρvgV = 1000 * 75 * 10 * 10 = 7500000 W

P = 7.5 MW

The correct solution to this problem is option e. 1/e. We can find it in the following manner.

The time constant of an RC circuit is the time in which the current decreases to 1/e (approximately 0.368) of its initial value.

This can be derived from the equation for the current in an RC circuit:

\(I=10 * e^({-t/RC} )\)

where I is current at time t, I0 is the initial current, R is the resistance, C is the capacitance, and e is the mathematical constant approximately equal to 2.71828.

To find the time constant, we set the exponent to -1:

\(e^({-t/RC} ) = 1 /e\)

Solving for t/RC, we get:

t/RC = 1

Therefore, the time constant is equal to RC, and the current decreases to 1/e of its initial value in one time constant.

So the answer is e. 1/e.

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The Alternating Series Test (AST) is used to determine if a series is convergent or divergent. It assumes that the terms alternate in sign and are monotonically decreasing in magnitude, and if lim_(n)a_n = 0, then the series is convergent. The series is given in the general formula for the AST, and the absolute value of each term is equal to the corresponding term.

The series for convergence or divergence using the alternating series test is given below:

[infinity] (−1)n 2nn n! n = 1

The general formula for the alternating series test is as follows. Assume that a series [a_n]_(n=1)^(∞) is defined such that the terms alternate in sign and are monotonically decreasing in magnitude.

If lim_(n→∞)△a_n = 0, where △a_n denotes the nth term of the series,

then the alternating series [a_n]_(n=1)^(∞) is convergent. We must evaluate if the alternating series is monotonically decreasing and if the absolute value of each term of the series is decreasing as well. If both conditions are met, we may apply the Alternating Series Test (AST). Let's take a look at the given series below:(-1)^n(2^n)/(n!) for n = 1 to infinity The series is given in the general formula for the AST. Because the series is already in the right form, we do not need to test it first.

The terms of the sequence decrease since (n+1)!/(n!) = (n+1), which is a positive number. Furthermore, since (n+1) > n for any natural number n, the sequence decreases monotonically. When we take the absolute value of each term in the series, it is equal to the corresponding term since all terms are positive.

Therefore, the series is convergent according to the Alternating Series Test.

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The maximum value of z is 0, and the values of the decision variables are x1 = 0, x2 = 10, x3 = 0, x4 = 0.

maximize: z = c1x1 + c2x2 + ... + cnxn

subject to

a11x1 + a12x2 + ... + a1nxn ≤ b1

a21x1 + a22x2 + ... + a2nxn ≤ b2

am1x1 + am2x2 + ... + amnxn ≤ bmxi ≥ 0 for all i

In our case,

the given LP is:maximize: z = 36x1 + 30x2 - 3x3 - 4x

subject to:

x1 + x2 - x3 ≤ 5

6x1 + 5x2 - x4 ≤ 10

xi ≥ 0 for all i

We can rewrite the constraints as follows:

x1 + x2 - x3 + x5 = 5  (adding slack variable x5)

6x1 + 5x2 - x4 + x6 = 10  (adding slack variable x6)

Now, we introduce the non-negative variables x7, x8, x9, and x10 for the four decision variables:

x1 = x7

x2 = x8

x3 = x9

x4 = x10

The objective function becomes:

z = 36x7 + 30x8 - 3x9 - 4x10

Now we have the problem in standard form as:

maximize: z = 36x7 + 30x8 - 3x9 - 4x10

subject to:

x7 + x8 - x9 + x5 = 5

6x7 + 5x8 - x10 + x6 = 10

xi ≥ 0 for all i

To apply the simplex algorithm, we initialize the simplex tableau as follows:

  |  Cj   |   x5   |   x6   |   x7   |   x8   |   x9   |   x10  |    RHS  |

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

z |  0    |   0    |   0    |  36    |   30   |   -3   |   -4   |    0    |

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

x5|   0   |   1    |   0    |   1    |   1    |   -1   |   0    |    5    |

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

x6|   0   |   0    |   1    |   6    |   5    |   0    |   -1   |   10    |

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

Now, we can proceed with the simplex algorithm to find the optimal solution. I'll perform the iterations step by step:

Iteration 1:

1. Choose the most negative coefficient in the 'z' row, which is -4.

2. Choose the pivot column as 'x10' (corresponding to the most negative coefficient).

3. Calculate the ratios (RHS / pivot column coefficient) to find the pivot row. We select the row with the smallest non-negative ratio.

Ratios: 5/0 = undefined, 10/(-4) = -2.5

4. Pivot at the intersection of the pivot row and column. Divide the pivot row by the pivot element to make the pivot element 1.

5. Perform row operations to

make all other elements in the pivot column zero.

After performing these steps, we get the updated simplex tableau:

  |  Cj   |   x5   |   x6   |   x7   |   x8   |   x9   |   x10  |    RHS  |

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

z |  0    |   0    |  0.4   |  36    |   30   |   -3   |   0    |   12    |

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

x5|   0   |   1    |  -0.2  |   1    |   1    |   -1   |   0    |   5     |

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

x10|   0  |   0    |   0.2  |   1.2  |   1   |   0    |   1    |   2.5   |

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

Iteration 2:

1. Choose the most negative coefficient in the 'z' row, which is -3.

2. Choose the pivot column as 'x9' (corresponding to the most negative coefficient).

3. Calculate the ratios (RHS / pivot column coefficient) to find the pivot row. We select the row with the smallest non-negative ratio.

Ratios: 12/(-3) = -4, 5/(-0.2) = -25, 2.5/0.2 = 12.5

4. Pivot at the intersection of the pivot row and column. Divide the pivot row by the pivot element to make the pivot element 1.

5. Perform row operations to make all other elements in the pivot column zero.

After performing these steps, we get the updated simplex tableau:

  |  Cj   |   x5   |   x6   |   x7   |   x8   |   x9   |   x10  |    RHS  |

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

z |  0    |   0    |  0.8   |  34    |   30   |   0    |   4    |   0     |

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

x5|   0   |   1    |  -0.4  |   0.6  |   1    |   5   |   -2   |   10    |

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

x9|   0   |   0    |   1    |   6    |   5    |   0   |   -5   |   12.5  |

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

Iteration 3:

No negative coefficients in the 'z' row, so the optimal solution has been reached.The optimal solution is:

z = 0

x1 = x7 = 0

x2 = x8 = 10

x3 = x9 = 0

x4 = x10 = 0

x5 = 10

x6 = 0

Therefore, the maximum value of z is 0, and the values of the decision variables are x1 = 0, x2 = 10, x3 = 0, x4 = 0.

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For test statistic: 1. Yes 2. Optimistic or pessimistic 3. Frequency of recycling per month 4. Two tail hypothesis 5. NA 6. Critical value is 2.00 7. Without knowing sample sizes can't get t-value 8. Decision undetermined 9. NA 10. NA

1. Yes, this is a quasi-experimental design because participants are not randomly assigned to groups.

2. The independent variable in this study is the attitude towards eco-friendly behaviors (optimistic or pessimistic).

3. The dependent variable in this study is the frequency of recycling per month.

4. This is a two-tail hypothesis because we are testing whether there is a difference in recycling behaviors between the two groups, not specifically whether one group recycles more or less than the other.

5. NA, since this is a two-tail hypothesis.

6. The critical value for this t-test at a .05 level of significance with a two-tail hypothesis and using a t-table can be found. Since we don't know the degrees of freedom, let's assume a large sample size (e.g., df = 60). In this case, the critical value would be ±2.00.

7. To calculate the test statistic (t-value) for this test, follow these steps:
 a. Calculate the difference between the means (M1 - M2): 2.9 - 6.8 = -3.9
 b. Calculate the pooled variance: \([(SD1^2 / n1) + (SD2^2 / n2)]\)
 c. Take the square root of the pooled variance: sqrt(pooled variance)
 d. Divide the difference between means by the result from step c: (-3.9) / sqrt(pooled variance)
 Without knowing the sample sizes (n1 and n2), we cannot calculate the exact t-value.

8. Given that we cannot compute the exact t-value without sample sizes, the decision for this test cannot be determined.

9. NA, since we cannot determine the significance of the test without the test statistic.

10. NA, since we cannot compute the effect size without the test statistic.

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Given:

Bird center bar chart is given.

Option D is the final answer.