Yall help me out please :(

Answer:

n = 17

Step-by-step explanation:

The difference between the 5th and 6th terms is 13 - 11 = 2

Therefore, the next term can be found by adding 2 each time.

If we continue with this sequence, we get:

5 = 11

6 = 13

7 = 13 + 2 = 15

8 = 15 + 2 = 17

9 = 17 + 2 = 19

10 = 19 + 2 = 21

So n = 17

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

Arithmetic sequence

General form of an arithmetic sequence: \(a_n=a+(n-1)d\)

where:

Given terms of the sequence:

\(a_5=11\\a_6=13\\a_8=n\\a_{10}=21\)

The common difference can be found by subtracting one term from the next term:

\(d=13-11=2\)

To find a, substitute the found value of d into the equation for one of the given terms:

\(\begin{aligned}a_5 =a+(5-1)2 & =11\\ a+8 & =11\\ a & = 3\end{aligned}\)

Therefore, the formula to find the nth term is:

\(\implies a_n=3+(n-1)2\)

\(\implies a_n=2n+1\)

So, the 8th term is:

\(\implies a_8=2(8)+1=17\)

Lets form a equation

Slope:-

Equation:-

So

Put x=8

The probability that the events do not occur is 0.6778`.

The probability that the events do not occur is given by `P(Ac)=1-P(A)` and `P(Bc)=1-P(B)`.

The given probabilities are `P(A)=0.2272` and `P(B)=0.4506`.

Using the formula `P(A∪B)=P(A)+P(B)-P(A∩B)`, we have `P(A∩B) = P(A) + P(B) - P(A∪B)`

Using the fact that the two events are mutually exclusive, we get `P(A∩B) = 0`.

Thus, `P(A∪B) = P(A) + P(B) = 0.2272 + 0.4506 = 0.6778`.

The probability that either A or B but not both occurs is given by `P(AΔB) = P(A∪B) - P(A∩B) = 0.6778 - 0 = 0.6778`.

Hence, the required probability is `P(AΔB) = 0.6778`.

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Using the volume formula it is obtained that the amount of concrete needed by Tobias is -

Option B: 3(2/3)π feet³.

What is volume?

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

To find the volume of each pylon, we need to calculate the volume of the cylinder and the cone and then add them together.

The volume of a cylinder is given by -

V(cylinder) = πr²h

where r is the radius and h is the height of the cylinder.

The volume of a cone is given by -

V(cone) = (1/3)πr²h

where r is the radius and h is the height of the cone.

In this case, the cylinder has a height of 3 feet and the cone has a height of 2 feet, so the total height of the pylon is 3 + 2 = 5 feet.

The radius of the cylinder is also the radius of the base of the cone, which is 1 foot.

Therefore, the volume of each pylon is -

V(pylon) = V(cylinder) + V(cone)

= π(1)²(3) + (1/3)π(1)²(2)

= 3π + (2/3)π

= (9/3)π + (2/3)π

= (11/3)π

Therefore, Tobias will need (11/3)π cubic feet or 3(2/3)π cubic feet of concrete for each pylon.

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Answer:

6

Step-by-step explanation:

1. The Formula for volume of a Square is V=πr2h

2. So u would plug everything in.. so v- π4²12

3. so then u get 6

Answer:

0.74

Step-by-step explanation:

Answer:

v = (- 5, 9 )

Step-by-step explanation:

v = terminal point - initial point

  = (3, 6 ) - (8, - 3 ) ← subtract corresponding components

  = (3 - 8, 6 - (- 3) )

  = (- 5, 6 + 3)

  = (- 5, 9 )

Answer:

4

Step-by-step explanation:

2 + 2 = 4

you have two and you add 2

you get 4

Hope this helps!

Answer; present value of $12,200 to be received 4 years from today, with a discount rate of 5 percent, is $10,027.51.

The present value of $12,200 to be received 4 years from today can be calculated using the formula for present value. The formula is:

Present Value = Future Value / (1 + Discount Rate)^n

Where:
- Future Value is the amount to be received in the future ($12,200 in this case)
- Discount Rate is the interest rate used to discount future cash flows (5 percent in this case)
- n is the number of periods (4 years in this case)

Plugging in the given values into the formula:

Present Value = $12,200 / (1 + 0.05)^4

Calculating the exponent first:

(1 + 0.05)^4 = 1.05^4 = 1.21550625

Dividing the future value by the calculated exponent:

Present Value = $12,200 / 1.21550625

Calculating the present value:

Present Value = $10,027.51

Therefore, the present value of $12,200 to be received 4 years from today, with a discount rate of 5 percent, is $10,027.51.

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The probability that the number of people who show up will exceed the capacity of the plane is approximately 0.0885, or 8.85%.

To solve this problem, we first need to find the expected number of people who will show up on the flight. Since the airline estimates that 96% of people booked will actually show up, we can estimate that 0.96 x 70 = 67.2 people will show up.

Next, we need to find the probability that the number of people who show up will exceed the capacity of the plane, which is 65. To do this, we can use the normal distribution with a mean of 67.2 and a standard deviation of √(70 x 0.96 x 0.04) = 1.63.

We want to find the probability that the number of people who show up is greater than 65. To do this, we can standardize the value of 65 using the formula z = (x - mu) / sigma, where x is the value we want to standardize (65), mu is the mean (67.2), and sigma is the standard deviation (1.63).

z = (65 - 67.2) / 1.63 = -1.35

Using a standard normal distribution table or calculator, we can find that the probability of a standard normal variable being less than -1.35 is 0.0885. Therefore, the probability that the number of people who show up will exceed the capacity of the plane is approximately 0.0885, or 8.85%.

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The error occurred in step 1

The justification for solving the equation -2(t + 3) + 4 = 12 + 6t is below;

2 |a + 1| = 5

Step 1:

2 |a + 1| = 5 or 2 |a + 1| = -5

2a + 2 = 5 or 2a + 2 = -5

combine like terms

2a = 5 - 2 or 2a = -5 - 2

2a = 3 or 2a = -7

divide both sides by 2

a = 3/2 or a = -7/2

2.

-2(t + 3) + 4 = 12 + 6t original equation

-2t - 6 + 4 = 12 + 6t Distributive property

-2t - 2 = 12 + 6t Addition property of equality

-2t - 2 - 6t = 12 + 6t - 6t Subtraction property of equality

-8t - 2 + 2 = 12 + 2 combine like terms

-8t / -8 = 14 / -8 Division property of equality

t = 14/-8 solution

t = 7/-4 simplified solution

Therefore, the equation -2(t + 3) + 4 = 12 + 6t has a simplified solution of t = 7/-4

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a. Completeness Axiom for real numbers: The real numbers are a complete, ordered field. This means that every nonempty set of real numbers that has an upper bound has a least upper bound. The least upper bound is called the supremum of the set, and it is denoted by sup(S).

b. Proof that the supremum of a subset of R is unique or does not exist:

Suppose S is a nonempty subset of R, and suppose S has an upper bound.

Then, by the completeness axiom, S has a least upper bound sup(S). If there are two distinct least upper bounds of S, say a and b, then by definition of the least upper bound, both a and b are upper bounds for S. Then a <= b, and b <= a. So a = b. Therefore, the supremum of a subset of R is unique.

If S does not have an upper bound, then sup(S) does not exist.

c. Let f : R -> R be a function such that for any a ∈ R.

We need to prove that lim x -> infinity f(x) = positive infinity.

Suppose that lim x -> infinity f(x) = L, where L is a finite number. Then there exists an M > 0 such that for all x > M, we have |f(x) - L| < 1. Therefore, for any a ∈ R, there exists N ∈ N such that n > N implies f(a + n) > L - 1. Since the limit of f(a + n) as n approaches infinity is positive infinity, for any a ∈ R, there exists an N ∈ N such that n > N implies f(a + n) > M. Combining these two inequalities, we get n > max{M, N} implies f(a + n) > max{L - 1, M}.

This contradicts the hypothesis that the limit of f(a + n) as n approaches infinity is positive infinity.

Therefore, we conclude that lim x -> infinity f(x) = positive infinity.

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The time taken by a student to finish a statistics exam can be modeled using the following cumulative distribution function: F(x) = 1 - e^-0.9, x > 0

Suppose that the time taken for a student to finish the exam is constant from student to student.

Then the mean number (to the nearest whole number) of students who will finish the exam in less than 1 hour for 12 students randomly selected is 7

.Step-by-step explanation:

The cumulative distribution function is given by, F(x) = 1 - e^-0.9, x > 0

Now, let X be the time taken by a student to finish the statistics exam

Then, X ~ Exp (0.9 )

We know that the cumulative distribution function (CDF) of the exponential distribution with parameter λ is given by,F(x) = P(X ≤ x) = 1 - e^(-λx) , x > 0Here, λ = 0.9.

Therefore, the CDF of X is given by,F(x) = P(X ≤ x) = 1 - e^(-0.9x) , x > 0

The probability that a student finishes the exam in less than 1 hour is, P(X ≤ 1) = F(1) = 1 - e^(-0.9) ≈ 0.5271

This means that out of 12 students randomly selected,

The expected number of students who finish the exam in less than 1 hour is,μ = np= 12 × 0.5271≈ 6.3252

Hence, the mean number (to the nearest whole number) of students who will finish the exam in less than 1 hour for 12 students randomly selected is 7.

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The translation of the points S(-3, 3), C(-1, 4), and W(-2, -1) is S(3, 0), C(5, 1), and W(4, -4) after moving 6 units to the right and 3 units down.

The translation of a point involves shifting it horizontally (right or left) and vertically (up or down) by a certain number of units. In this case, we are asked to perform a translation of 6 units right and 3 units down.

Original Points:

1. S(-3, 3)

2. C(-1, 4)

3. W(-2, -1)

Translation process:

1. For the point S(-3, 3):

  - Move 6 units to the right: x-coordinate becomes -3 + 6 = 3

  - Move 3 units down: y-coordinate becomes 3 - 3 = 0

  So, the translated point S(3, 0).

2. For the point C(-1, 4):

  - Move 6 units to the right: x-coordinate becomes -1 + 6 = 5

  - Move 3 units down: y-coordinate becomes 4 - 3 = 1

  So, the translated point C(5, 1).

3. For the point W(-2, -1):

  - Move 6 units to the right: x-coordinate becomes -2 + 6 = 4

  - Move 3 units down: y-coordinate becomes -1 - 3 = -4

  So, the translated point W(4, -4).

After the translation, the new coordinates for each point are as follows:

1. S(3, 0)

2. C(5, 1)

3. W(4, -4)

These are the points obtained after moving each original point 6 units to the right and 3 units down.

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The derivative of f(x) = arccos(x^2) is: f'(x) = -2x / √(1-x^4)

The derivative of f(x) = arccos(x^2), we'll use the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function. In this case, the outer function is arccos(u) and the inner function is u = x^2.

First, let's find the derivative of the outer function, arccos(u). The derivative of arccos(u) is -1/√(1-u^2). Next, we'll find the derivative of the inner function, x^2. The derivative of x^2 is 2x.

Now we'll apply the chain rule. We have:

f'(x) = (derivative of outer function) * (derivative of inner function)

f'(x) = (-1/√(1-u^2)) * (2x)

Since u = x^2, we'll substitute that back into our equation:

f'(x) = (-1/√(1-x^4)) * (2x)

So, the derivative of f(x) = arccos(x^2) is:

f'(x) = -2x / √(1-x^4)

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The expected value of the number of patients that will be cured is 2.78 which has been obtained by using probability.

It is feasible to determine the expected value of the number of patients who will be cured by multiplying each potential result by the appropriate probability and adding the results. The following probability and outcomes are:

0 patients cured: P(X=0) = 0.01

1 patient cured: P(X=1) = 0.08

2 patients cured: P(X=2) = 0.27

3 patients cured: P(X=3) = 0.40

4 patients cured: P(X=4) = 0.24

To calculate the expected value, we multiply each outcome by its probability and sum them up:

E(X) = (0 * 0.01) + (1 * 0.08) + (2 * 0.27) + (3 * 0.40) + (4 * 0.24)

Simplifying the calculation, we find:

E(X) = 0 + 0.08 + 0.54 + 1.20 + 0.96

E(X) = 2.78

Therefore, the expected value of the number of patients that will be cured is 2.78, rounded to two decimal places.

The expected value represents the average number of patients that would be cured if the treatment is repeated many times. In this case, based on the given probabilities, we can expect that, on average, approximately 2.78 patients out of four will be successfully cured with chemotherapy for this particular type of cancer.

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The complete question has been attached below.

Answer:

Part A: Slope (m) = -75

Part B:

Point-slope form --- y - 1350 = -75(x - 2)

Slope-intercept form --- y = -75x + 1500

Standard form --- 75x + 1y = 1500

Part C: g(x) = -75x + 1500 (Just replace 'y' in y = mx + b with 'g(x)').

Part D: The balance in the bank account after 5 days equals $1,125.

Step-by-step explanation:

(Pertaining to Part D --- Plugging in variables):

To find the answer to Part D, we must first take the function notation equation from Part C and plug in the appropriate variables needed to find the balance in the bank account after 5 days. So, we plug in '5' for g(x), which would give us g(5). For the other x found in the equation, we also correspondingly replace it with '5'. Our equation now appears as g(5) = -75(5) + 1500.

Finally, we must solve this equation using the order of operations, which simplifies our equation to g(5) = -375 + 1500. We can simplify this further by adding 1500 to -375, giving us the final answer for Part D of $1,125 being the balance in the bank account after 5 days.

Hope that helps!!

Answer:

Part A: Slope (m) = -75

Part B:

Point-slope form --- y - 1350 = -75(x - 2)

Slope-intercept form --- y = -75x + 1500

Standard form --- 75x + 1y = 1500

Part C: g(x) = -75x + 1500 (Just replace 'y' in y = mx + b with 'g(x)').

Part D: The balance in the bank account after 5 days equals $1,125.

Answer: To find the RMS (Root Mean Square) of a function, you need to perform the following steps:

Square the function: For a function f(x), compute f(x)^2 for each x.

Compute the mean of the squared function: Find the average value of f(x)^2 over the range of x values. You can do this by integrating f(x)^2 over the range and then dividing by the range, or by computing the sum of f(x)^2 values and dividing by the number of values.

Take the square root of the mean: The RMS is the square root of the mean value of f(x)^2, calculated in step 2.

In mathematical notation, the RMS of a function f(x) over the range [a,b] is given by:

RMS = sqrt((1/(b-a)) * integral from a to b of (f(x))^2 dx)

or

RMS = sqrt((1/N) * sum from i=1 to N of (f(x_i))^2)

where N is the number of data points, x_i are the x values at each data point, and f(x_i) are the corresponding function values.

The RMS is a measure of the "effective" or "average" value of the function over the given range, and is often used in signal processing and electrical engineering to represent the magnitude of a varying signal.

Step-by-step explanation:

Answer:

Part A

y =($50 - ($23 × 2 + $5)+ $22)

y = $21

Part B

Clay can get his balance to zero by withdrawing or writing another check for $21

Step-by-step explanation:

Last week, Clay had a beginning balance of $50 in his account. He wrote 2 checks for $23 each from his checking account , withdrew another $5, and finally made a deposit of $22.

Part A: Write an expression and your answer to show his final account balance at the end of the week 23 * 2 = 46

Let his final Account Balance = y

y =($50 - ($23 × 2 + $5)+ $22)

y =$72 - $51

y = $21

Part B: Explain in words, what Clay should do to get his account balance to zero?

Clay can get his balance to zero by withdrawing or writing another check for $21

= $21 - $21

= $0

Answer:

Corresponding angles converse theorem

Step-by-step explanation:

If two lines (AB and CD) are intersected by a transversal (BD) and corresponding angles are congruent (∠B ≅ ∠D), then the lines are parallel.

Answer:

Corresponding angles converse theorem

Step-by-step explanation:

If two lines (AB and CD) are intersected by a transversal (BD) and corresponding angles are congruent (∠B ≅ ∠D), then the lines are parallel.

\((\stackrel{x_1}{-2}~,~\stackrel{y_1}{8.5})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{3.5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3.5}-\stackrel{y1}{8.5}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{(-2)}}} \implies \cfrac{-5}{0 +2}\implies -\cfrac{5}{2}\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{8.5}=\stackrel{m}{- \cfrac{5}{2}}(x-\stackrel{x_1}{(-2)}) \implies y -8.5= -\cfrac{5}{2} (x +2) \\\\\\ y-8.5=-\cfrac{5}{2}x-5\implies y=-\cfrac{5}{2}x-5+8.5\implies {\Large \begin{array}{llll} y=-\cfrac{5}{2}x+3.5 \end{array}}\)

Answer:

DFG= 52

JKL=38

Step-by-step explanation:

complementary angle means that the sum of the two angles are equal to 90° so

(x+5)+(x-9)=90

= x+5+x-9=90

= 2x-4=90

= 2x=94

= x= 94÷2=47

DFG= x+5= 47+5=52

JKL= x-9= 47-9=38

hope it helps

The value of 9u⋅(9u−10v) is 54.

First, let's expand the expression 9u⋅(9u−10v), we have to use  the concept of the dot product of two vectors

9u ⋅ (9u − 10v) = 81u⋅u - 90u⋅v

We are given that u⋅v = 3, so we can substitute that into the expression:

81u⋅u - 90u⋅v = 81u⋅u - 90(3)

Next, we can use the fact that ∥u∥=2 to find u⋅u:

∥u∥² = u ⋅ u

2² = u ⋅ u

4 = u ⋅ u

Substituting this back into the expression, we get

81u⋅u - 90(3) = 81(4) - 270

Simplifying

= 81(4) - 270

Do the arithmetic operations

= 54

Therefore, 9u⋅(9u−10v) = 54.

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I have solved the question in general, as the given question is incomplete.

The complete question is:

Assume that u⋅v=3, ∥u∥=2, and ∥v∥=8. What is the value of 9u⋅(9u−10v)?

Answer:

9.93

Step-by-step explanation:

Just add your tax to your price.

Answer:

Carbon dioxide is added to the atmosphere naturally when organisms respire or decompose (decay), carbonate rocks are weathered, forest fires occur, and volcanoes erupt. Carbon dioxide is also added to the atmosphere through human activities, such as the burning of fossil fuels and forests and the production of cement.

Step-by-step explanation:

Answer:

Step-by-step explanation: The first one on the left

Answer:

y = 15x + 50

Step-by-step explanation:

We set out by finding the slope

the two points give are (15,275) and (25,425)

Slope m is;

y2-y1/x2-x1 = (425-275)/25-15 = 150/10 = 15

So the equation is like;

y = 15x + b

To get b, let us use the point (15,275)

We have

275 = 15(15) + b

b = 275-225

b = 50

So the equation is;

y = 15x + 50

The angles (6·x + 17)° and (4·x + 23)°, which are same side interior angles, indicates that the measure of the angle (6·x + 17)° is 101°

Same side interior angles are angles formed on the same side of a transversal to two lines and on the interior part of two two lines.

The possible diagram in the question obtained from a similar online question and created with MS Word is attached.

The possible question is to find the measure of the angle with a measure of (6·x + 17)°

From the attached drawing, we get;

Angle 6·x + 17 and angle 4·x + 23 are same side interior angles

Same side interior angles are supplementary, therefore;

6·x + 17 + 4·x + 23 = 180° (definition of supplementary angles)

(10·x + 40)° = 180°

10·x = 180° -  40° = 140°

x = 140° ÷ 10 = 14°

x = 140° ÷ 10 = 14°

x = 14

The measure of the angle (6·x + 17)° is therefore;

(6·x + 17)° = (6 × 14 + 17)° = 101°

The possible question is to find the measure of the angle (6·x + 17)°

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Answer:

um 1/4

Step-by-step explanation: