Justin completes 8 extra credit problems on the first day and then 4 problems each day until the worksheet is complete. There are 28 problems on the worksheet. Write and solve an equation to find how many days it will take Justin to complete the worksheet after the first day.

Answer:

How many siblings do you have?

(a) The probability that a single randomly selected value is greater than 19.4. P(X> 19.4) = 0.6965.

(b) The probability that a sample of size n = 20 is randomly selected with a mean greater than 19.4. P(M> 19.4) =  0.9883.

To solve these probability questions, we can utilize the properties of the standard normal distribution since we know the mean and standard deviation of the population.

(a) Find the probability that a single randomly selected value is greater than 19.4.

To calculate this probability, we need to standardize the value 19.4 using the formula: z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.

z = (19.4 - 42.3) / 44.6 = -22.9 / 44.6 ≈ -0.51498

Using the standard normal distribution table or a calculator, we can find the corresponding probability for z > -0.51498, which is approximately 0.6965.

Therefore, P(X > 19.4) ≈ 0.6965.

(b) Find the probability that a sample of size n = 20 is randomly selected with a mean greater than 19.4.

For this question, we need to consider the sampling distribution of the sample mean. The mean of the sampling distribution is equal to the population mean (μ = 42.3), and the standard deviation of the sampling distribution, also known as the standard error, is equal to σ / √n, where σ is the population standard deviation and n is the sample size.

Standard error = 44.6 / √20 ≈ 9.9766

To find the probability that the sample mean is greater than 19.4, we need to standardize the sample mean using the formula: z = (x - μ) / (σ / √n), where x is the value (19.4 in this case), μ is the mean, σ is the standard deviation, and n is the sample size.

z = (19.4 - 42.3) / (44.6 / √20) ≈ -22.9 / 9.9766 ≈ -2.2972

Using the standard normal distribution table or a calculator, we can find the corresponding probability for z > -2.2972, which is approximately 0.9883.

Therefore, P(M > 19.4) ≈ 0.9883.

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Answer:

y€ R : y greater than or equal to 1

The first three terms of x[n] using the power series expansion are x[0] = 73, x[1] = 2, and x[2] = 13.

We can select the first three terms of x[n] using the power series development by expressing the given articulation X(z) as a polynomial in z. We should modify the articulation as follows to obtain the power series development: By comparing the given expression to the power series form, the coefficients can be identified: X(z) equals 2z3, 13z2, 7z, 73, 722/z, 2/z, and 1: a0 rises to 73, a1 approaches 2, a2 approaches 13, and a3 approaches 7. X(z) = a0, a1z, a2z2, a3*z3, and... Consequently, the following are the first three terms of x[n]:

The initial three terms of x[n] are provided by the power series development: x[0] = a0; x[1] = a1; x[2] = a2; x[0] = a0; The values of x[0] and x[1] are 73, 2, and 13.

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Answer:  1/5 of a jar

Step-by-step explanation:

1/2 times 2/5= .2 = 1/5.

Answer:

1/5 of a jar

Step-by-step explanation:

a) The solution to the given problem isL(F) = f(t) = 0 + (-(10 + 7C)/6)[tex]e^{-2t}[/tex]) + C[tex]e^{-3t}[/tex]+ D[tex]e^{-3t}[/tex]

b) The solution to the given problem isL(F) = [tex]e^{-2t}[/tex] [sin t + cos t](c)

c) The solution to the given problem is L(F) = 1/9 [[tex]e^{2t}[/tex] sin 9t - 3[tex]e^{2t}[/tex]) cos 9t]

(a)The inverse Laplace transform of F(s) = 10/s(s + 2)(s + 3)² can be found as follows:

L(F) = L{10/[s(s + 2)(s + 3)²]}

= 10 ∫∞₀[tex]e^{-st}[/tex]) /[s(s + 2)(s + 3)²] dt

L{F} = L⁻¹{10/[s(s + 2)(s + 3)²]}

By using partial fractions, we can simplify the equation and get it in a form that can be integrated easily.

L(F) = 10 ∫∞₀ {1/s - 2/(s + 2) + 3/(s + 3) - 2/(s + 3)² + 1/(s + 2)(s + 3)} [tex]e^{-st}[/tex]dt

L{F} = L⁻¹{1/s} - 2L⁻¹{1/(s + 2)} + 3L⁻¹{1/(s + 3)} - 2L⁻¹{d/ds[1/(s + 3)]} + L⁻¹{1/(s + 2)}

As the inverse Laplace transform of L{F} is given by L(F)

= L⁻¹{1/s} - 2L⁻¹{1/(s + 2)} + 3L⁻¹{1/(s + 3)} - 2L⁻¹{d/ds[1/(s + 3)]} + L⁻¹{1/(s + 2)}

Thus, the solution to the given problem isL(F) = f(t) = 0 + (-(10 + 7C)/6)[tex]e^{-2t}[/tex]) + C[tex]e^{-3t}[/tex]+ D[tex]e^{-3t}[/tex]

(b)

The inverse Laplace transform of F(s) = s/[s² + 4s + 5] can be found as follows:

L(F) = L{s/[s² + 4s + 5]}

= ∫∞₀ s e^(–st) / (s² + 4s + 5) dt

L{F} = L⁻¹{s/[s² + 4s + 5]}

By using partial fractions, we can simplify the equation and get it in a form that can be integrated easily. L(F) = ∫∞₀ [s/(s² + 4s + 5)] [tex]e^{-st}[/tex]) dt

L{F} = L⁻¹{s/(s² + 4s + 5)}

The solution to the given problem isL(F) = [tex]e^{-2t}[/tex] [sin t + cos t](c)

c) The inverse Laplace transform of F(s) = ([tex]e^{-3s}[/tex]) s/[(s - 2)² + 81] can be found as follows:

L(F) = L{([tex]e^{-3s}[/tex]) s/[(s - 2)² + 81]}= ∫∞₀ ([tex]e^{-st}[/tex]) s/[(s - 2)² + 81] dt

L{F} = L⁻¹{([tex]e^{-3s}[/tex])) s/[(s - 2)² + 81]}

So, The solution to the given problem is L(F) = 1/9 [([tex]e^{2t}[/tex]) sin 9t - 3([tex]e^{2t}[/tex]) cos 9t]

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Answer:

132 dollars I think

Step-by-step explanation:

The perimeter is the distance all the way around. So it's the sum of the lengths of all 4 sides.

From the picture, you can clearly see the lengths of all 4 sides.

Writum down and adum up !

Answer:

A.

Step-by-step explanation:

Answer:

A. 4,000,000 + 600,000 + 10,000 + 2,000 + 200 + 50 + 8 + 9

Step-by-step explanation:

Answer:

80

Step-by-step explanation:

the linear approximation at z = 0 to sin(42) is A + Bz, where A = sin(42) and B is the coefficient of z, which is cos(42).

The linear approximation of a function f(x) at a point x = a is given by the equation f(x) ≈ f(a) + f'(a)(x - a). In this case, we want to approximate sin(42) at z = 0.

The derivative of the sine function is cos(x), so the derivative of sin(42) with respect to z is cos(42). Evaluating the derivative at z = 0, we have cos(42).

To find A in the linear approximation A + Bz, we substitute z = 0 into the original function sin(42) and obtain A = sin(42).

Therefore, the linear approximation at z = 0 to sin(42) is A + Bz, where A = sin(42) and B is the coefficient of z, which is cos(42).

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a)  Bryan is 1,168 meters away from the base of the watchtower

b) The nearest meter, Bryan and Lily are 315

a) To the nearest meter, Bryan is 1,168 meters away from the base of the watchtower.

Let AB be the watchtower. From B, the angle of elevation to the top of the tower is 20°.

We have to find BC.

BC/AB = tan 20°

BC = AB tan 20°

BC = 90 tan 20°

BC = 32.3

Therefore, BC = 32 meters

Now we have to find AC. AC is the distance between the foot of the watchtower and Bryan's position.

To do that, let BD = h be the height of the tower and AD = x be the distance between A and D.

From the information given, we know that tan 85° = h/x.

Rearranging the formula, x = h/tan 85°

x = 90/tan 85°

x = 418.55 meters

Therefore, AC = x + BC

AC = 418.55 + 32.3

AC = 450.85 meters

So, to the nearest meter, Bryan is 1,168 meters away from the base of the watchtower.

b) To the nearest meter, Bryan and Lily are 315 meters apart.

Let E be the position of Lily and AD be the distance from the foot of the watchtower to the position of Bryan. We have already found that AD = 418.55 meters.

Bryan and Lily are along the same horizontal line.

So, BE is the distance between them. We have to find BE.

From triangle AEB, tan 20° = h/AE.

Rearranging the formula, AE = h/tan 20°

AE = 90/tan 20°

AE = 267.9 meters

From triangle DEC, tan 85° = h/DE.

Rearranging the formula, DE = h/tan 85°

DE = 90/tan 85°

DE = 3,442.97 meters

Therefore, EC = DE - DC = 3,442.97 - 350 = 3,092.97 meters

Now, BE = AC - EC

BE = 450.85 - 3,092.97

BE = -2,642.12 meters (negative value means Bryan is to the left of Lily)So, to the nearest meter,

Bryan and Lily are 315 meters apart. Answer: (a) 1168m and (b) 315m

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Answer:

23

Step-by-step explanation:

please mark me as brainliest

Answer:

∠R = 38°

Step-by-step explanation:

∠R = 1/2(arc PE - arc SQ)

∠R = 1/2(140 - 64) = 1/2(76) = 38°

Answer:

hi

Step-by-step explanation:

Answer:

18 in

Step-by-step explanation:

len = y

width= y - 6

the area of rectangle is len x width

(Y) x (Y-6) = 216

Y^2 - 6Y = 216, Y^2 - 6y -216 = 0

y = (36 /2) or (-24 /2)

len couldn't be negative so 18

there will be 27 zeros at the end of 115!.

To determine the number of zeros at the end of 115!, we need to consider the prime factorization of the number and examine how many factors of 5 are present.

A zero at the end of a factorial occurs when there is a factor of 10 present, which is equivalent to having both factors of 2 and 5. Since the number of factors of 2 is usually abundant, the crucial factor is the number of factors of 5.

In the prime factorization of 115!, the factors of 5 arise from the multiples of 5 (5, 10, 15, 20, ...) as well as higher powers of 5 (25, 50, 75, ...). We need to determine how many multiples of 5, multiples of 25, multiples of 125, and so on are present.

1. Multiples of 5: The number of multiples of 5 in 115! is given by ⌊115/5⌋ = 23.

2. Multiples of 25: The number of multiples of 25 in 115! is given by ⌊115/25⌋ = 4.

3. Multiples of 125: The number of multiples of 125 in 115! is given by ⌊115/125⌋ = 0 since there are no numbers in the range 1 to 115 that are multiples of 125.

Adding up these counts, we have 23 + 4 = 27 factors of 5.

Therefore, there will be 27 zeros at the end of 115!.

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To find the arc of circle WTV, you need the arc length or central angle. Use formulas: Arc Length = (Arc Angle / 360) × (2πr) or Arc Length = (Central Angle / 360) × (2πr).

To find the arc of a circle, WTV, you would need to know either the length of the arc or the measure of the central angle subtended by the arc. If you have the length of the arc, you can use the formula:

Arc Length = (Arc Angle / 360 degrees) × (2πr),

where r is the radius of the circle. Rearranging the formula, you can solve for the Arc Angle:

Arc Angle = (Arc Length / (2πr)) × 360 degrees.

If you know the measure of the central angle, you can calculate the arc length using a similar formula:

Arc Length = (Central Angle / 360 degrees) × (2πr).

To find the radius, you would need additional information such as the diameter or circumference of the circle. Once you have the radius, you can substitute the values into the appropriate formula to find either the arc length or the central angle of the circle.

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The zeros of the polynomial function f(x) = x^2 - 9x - 70 can be found by factoring or using the quadratic formula. The zeros are -5 and 14.

To find the zeros of the polynomial function f(x) = x^2 - 9x - 70, we can factor the expression or use the quadratic formula. Let's factor the expression:

f(x) = x^2 - 9x - 70

= (x - 14)(x + 5)

Setting each factor equal to zero, we get:

x - 14 = 0 --> x = 14

x + 5 = 0 --> x = -5

Therefore, the zeros of the polynomial function are x = -5 and x = 14. These values represent the x-coordinates where the function intersects the x-axis, indicating the points where the function equals zero.

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The sum of the mean and the median of the given dataset, which consists of the scores 7, 4, 9, 6, 10, 9, 5, and 4, is 13.25.

To find the sum of the mean and the median, we first need to calculate the mean and median of the given dataset.

The dataset is: 7, 4, 9, 6, 10, 9, 5, 4

To find the mean, we sum up all the numbers in the dataset and divide by the total number of data points:

Mean = (7 + 4 + 9 + 6 + 10 + 9 + 5 + 4) / 8 = 54 / 8 = 6.75

To find the median, we arrange the numbers in ascending order:

4, 4, 5, 6, 7, 9, 9, 10

Since we have 8 data points, the median will be the average of the two middle numbers:

Median = (6 + 7) / 2 = 6.5

Now we can find the sum of the mean and the median:

Sum of mean and median = 6.75 + 6.5 = 13.25

Therefore, the sum of the mean and the median of the given dataset is 13.25.

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Answer:

the cost of the replacement window will be $1501.44.

Step-by-step explanation:

area of an equilateral triangle:

[tex]A = \frac{\sqrt{3}}{4} a^{2}[/tex]

A = (√3)/4 * (17)^2

A = 125.12 in^2

125.12 * 12 = $1501.44

C ≈ 62.83cm is the answer!

Hope this helps!

Answer:

i think you forgot to add how little he wants to spend

Step-by-step explanation:

Reuben wants the total number of dollars he spends on admission and rides to be fewer than ??? whats the number that he wants to spend

The equation c₁ · a · c · x / b₁ · d · iₙ can have a solution for x if and only if the matrices a, b, and c are compatible and satisfy certain conditions.

Further information about the matrices and their properties is required to determine the specific solution.

To determine if the equation c₁ · a · c · x / b₁ · d · iₙ has a solution, we need to consider the compatibility and properties of the matrices involved.

Let's break down the equation:

c₁: The first column of matrix c.

a: Matrix a.

c: Matrix c.

x: The solution vector.

b₁: The first row of matrix b.

d: Matrix d.

iₙ: The identity matrix of size n.

For the equation to have a solution, the matrices a, b, and c need to be compatible, meaning their dimensions align appropriately for matrix multiplication. Specifically, the number of columns in matrix a should match the number of rows in matrix c.

Additionally, certain conditions or properties of the matrices may be required to ensure a solution exists. Without additional information about the specific matrices a, b, c, and d, it is not possible to determine the solution for x.

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Answer:

Option 4

Step-by-step explanation:

The smaller sides must add up to be greater than the largest side so:

1) 6 + 8 < 15

1) No

2) 6 + 9 = 15

2) No

3) 9 + 6 < 16

3) No

4) 9 + 8 > 16

4) Yes

The number that has no composite factors is (c) 77

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

Number = 21

The factors of 21 are 3 and 7

These factors are composite numbers because they are prime numbers

using the above as a guide, we have the following:

The number 77 has no composite factors

This is so because

77 = 7 * 11

These factors are composite numbers because they are prime numbers

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