ANSWER NEEDED ???????

The Number of ways that four people can be seated on the bench so that john is not next to paul is 12

In mathematics, An arrangement of things or items in a specific sequence is known as a permutation. One should think about both the selection and the arrangement while dealing with permutation. In permutations, ordering is crucially important.

The arrangement of n items in r ways is given by

Here we have

4 people (John, Paul, George, and Ringo) are seated in a row on a bench

Here total No of ways that 4 can be seated = 4 × 3 × 2 × 1 = 24

The number of ways of seating the four people so that john is next to paul is 12

Then the number of ways the four people on the bench so that john is not next to paul can find as given below

= Total No of ways, 4 can be seated - No of ways that john next to paul  

= 24 - 12 = 12        

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The size of the angle marked y in the triangle is 50 degrees

The complete question is added as an attachment

Given that the triangle is an isosceles triangle

An isosceles triangle is a triangle with two sides of equal length. This means that two of the angles opposite to those sides are congruent.

Using the above definition, we have the following equation

y + 2 * 65 = 180

So, we have

y + 130 = 180

Evaluate the like terms

y = 50

Hence. the value of y is 50 degrees

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Using multiple line and angle theorems, the values of each of the 14 angles are given.

Using the geometry theorems :

1.)

∠2 is a right angle = 90°

2.)

∠1 + ∠2 + ∠3 = 180° (sum of angle on a straight line)

90 + ∠1 + 54° = 180°

∠1 = (180 - 144) = 36°

(∠2 and ∠5) ; (∠3 and ∠6) ; (∠1 and ∠4) are vertically opposite ;

Hence,

∠4 = 36°

∠5 = 90°

∠6 = 54°

∠3 = ∠8 = 54° (corresponding angles)

∠9 + ∠8 = 180° (sum of angle on a straight line)

∠9 = (180 - 54) =126°

∠7 = ∠9 = 126° (vertically opposite angles)

∠8 = ∠10 = 54° (vertically opposite angles)

∠4 = ∠13 = 36° (corresponding angles )

∠12 + ∠13 = 180° (sum of angle on a straight line)

∠12 = (180 - 36) =126°

∠11 = ∠13 = 36° (vertically opposite angles)

∠12 = ∠14 = 126° (vertically opposite angles)

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Answer:

the ratio of the surface area of A to the surface area of B is 36 ÷ 49

Step-by-step explanation:

The computation of the ratio of the surface area of A to the surface area of B is shown below;

= Surface area of the sphere a ÷ surface area of the sphere b

= 4πr^2 ÷ 4πr^2

= 6^2 ÷ 14 ÷ 2^2

= 36 ÷ 49

hence, the ratio of the surface area of A to the surface area of B is 36 ÷ 49

The same would be considered and relevant too

Answer:

You are left with $1.44

Step-by-step explanation:

Subtract the amount of money you payed to how much the cost actually was to get your answer.

The interest paid in the 11th year of a $95,000 mortgage with a 5.5% interest rate and a 25-year term is approximately $3,638.

This is calculated by first determining the remaining balance after 10 years, which is $64,516. Then, the interest paid for each monthly payment in the 11th year is calculated, and the sum of these monthly interest payments is $3,638.

Here are the steps involved in calculating the interest paid in the 11th year:

Input the loan amount ($95,000), the interest rate (5.5%), and the loan term (25 years) into a mortgage calculator.

Determine the remaining balance after 10 years.

Calculate the monthly payment for the mortgage.

Calculate the interest paid for each monthly payment in the 11th year.

Sum the monthly interest payments to get the total interest paid in the 11th year.

The total interest paid in the 11th year can also be calculated using the following formula:

Interest paid = (Remaining balance × Interest rate) / 12

In this case, the interest paid in the 11th year is:

Interest paid = ($64,516 × 0.055) / 12 = $3,638

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Answer:

m∠2 = 104°

m∠3 = 76°

m∠4 =  104°

Step-by-step explanation:

∠1 and ∠3 are vertical angles

That means they are of the same value.

∠2 and∠4 are also vertical angles and we can find the value like this:

Sum of all angles = 360°

Total value of found angles = 152°

Number of angles need to be found = 2x (note: this is 2x because both angles are the same)

Equation = 360 - 152 = 2x

208 = 2x

x = 208/2

x = 104

So angle m∠4 = 104°

and m∠2 = 104°

The largest value among F(0), F(3), F(6), F(9), and F(12) depends on the function f(t) and cannot be determined without additional information.

To find the largest value among F(0), F(3), F(6), F(9), and F(12), we need to evaluate the function f(x) = ∫\(x^6\) f(t) dt for each given value of x.

The given function represents the indefinite integral of f(t) with respect to t, where f(t) is the function whose graph is given.

The integral represents the area under the curve of f(t) from 0 to \(x^6\). By evaluating the integral at different values of x, we can find the corresponding values of F(x).

Since the function f(t) is not specified, we cannot determine the exact values of F(0), F(3), F(6), F(9), and F(12) without additional information.

The values of F(x) depend on the specific form and properties of f(t).

To find the largest value among F(0), F(3), F(6), F(9), and F(12), we would need to know the function f(t) and evaluate the integral at each specific value of x.

Without further information, it is not possible to determine which of the given values is the largest.

In summary, the largest value among F(0), F(3), F(6), F(9), and F(12) depends on the function f(t) and cannot be determined without additional information.

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The simplified expression for (f ∘ g)(x) is 2 + x (option d).

To find and simplify (f ∘ g)(x), we need to substitute the expression for g(x) into f(x) and simplify.

Given:

f(x) = log₃(9x)

g(x) = \(3^x\)

Substituting g(x) into f(x):

(f ∘ g)(x) = f(g(x)) = log₃\((9 * 3^x)\)

Now, we simplify the expression:

log₃\((9 * 3^x)\) = log₃(9) + log₃\((3^x)\)

Since logₓ(a * b) = logₓ(a) + logₓ(b), we have:

log₃(9) + log₃\((3^x)\) = log₃\((3^2)\) + x

Using the property logₓ\((x^a)\) = a * logₓ(x), we get:

log₃\((3^2)\) + x = 2 * log₃(3) + x

Since logₓ\((x^a)\) = a, where x is the base, we have:

2 * log₃(3) + x = 2 + x

Therefore, (f ∘ g)(x) simplifies to:

(f ∘ g)(x) = 2 + x

So, the correct answer is (d) 2 + x.

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Complete Question:

Given f(x)=log₃(9x) and g(x)=\(3^x\). Find and simplify (f ∘ g)(x)

(a) 2x

(b) x

(c) \(27^x\)

(d) 2+x

(e) None of these.

The value of the union of sets A and B is, P(A ∪ B) is 0.64.

The union of two sets means the total elements in both the sets combined.

Given: sets P(A) = 0.38, P(B) = 0.83, and  intersection P(A ∩ B) = 0.57

We need to find the union of P(A ∪ B).

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Let us substitute the given values in the formula.

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

=0.38+0.83-0.57

=1.21-0.57

=0.64

Therefore, the value of union of sets P(A ∪ B) is 0.64.

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Answer:

B. 7−10; 11−14; 15−18; 19−22

Step-by-step explanation:

Answer:

\(33.69^{\circ}\)

Step-by-step explanation:

In right triangles only:

The sine of an angle is equal to its opposite side divided by the hypotenuse. (o/h)

The cosine of an angle is equal to its adjacent side divided by the hypotenuse. (a/h)

The tangent of an angle is equal to its opposite side divided by its adjacent side. (o/a)

Therefore, we have the following equation:

\(\tan B = \frac{6}{9},\\B=\tan^{-1}(\frac{6}{9})\approx \boxed{33.69^{\circ}}\)

Answer:

33.69

Step-by-step explanation:

khan

401(k) investment has over other types of investments is the employer match and contribution.

The graphic shows that for the sample 401(k) investment, there is an annual contribution of $5,000 from the individual. Additionally, there is an employer match of 5% and an employer contribution of $2,500, bringing the total contribution to $7,500.

The advantage of this 401(k) investment is that the employer is providing additional funds towards the individual's retirement savings. The employer match means that for every dollar the individual contributes, the employer contributes an additional 5 cents. This is essentially free money added to the investment, which can significantly boost the overall savings over time.

Furthermore, the employer contribution of $2,500 further enhances the advantage of this 401(k) investment. This contribution is made by the employer without any additional cost to the individual, increasing the overall investment amount.

Compared to other types of investments, such as individual retirement accounts (IRAs) or taxable investment accounts, the employer match and contribution in a 401(k) provide an immediate boost to the individual's retirement savings.

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The statistical decision based on the reported results of the hypothesis test is that the null hypothesis was rejected at the α = .05 significance level.

The t-value reported is 2.38, and the degrees of freedom are 21. This suggests that the test was likely a t-test with an independent samples design, where the sample size was n = 22 (since df = n - 1).

The p-value reported is less than .05, which indicates that the probability of obtaining the observed results, or results more extreme, under the assumption that the null hypothesis is true, is less than .05. Therefore, the null hypothesis is rejected at the .05 significance level in favor of the alternative hypothesis.

In conclusion, the statistical decision is that there is sufficient evidence to suggest that the population means are not equal, and the sample size was 22. However, we do not have information about the direction of the effect (i.e., whether the difference was positive or negative).

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The augmented matrix is [C:b1 b2] = 1 -1 0 1 | 1 2 -1 3 -4 1 | 1 1 2 -1 | 6 4 -2 5.By using Gaussian elimination, we get [I:b1' b2'] = 1 0 0 1 | -2 0 1 | 3 0 1 | -1 0 1 | 1. Hence, the solution to Cx = b1 is x1 = [-2, 3, -1, 1](T), and the solution to Cx = b2 is x2 = [0, 1, 1, 0](T).

By applying the same elementary row operations to the right of C, the inverse C-1 is obtained. C -1=1/10 [3 -7 3 -1 -5 2 -3 7 -2 1 3 -1 -1 3 -1 1](2.2) The system Cx = b is solved using C-1. Cx = b; x = C-1 b = [1,1,0,-1](T).The system Cx = 62 is also solved using C-1.Cx = 62; x = C-1 62 = [9,-7,7,1](T).(2.3) The solution to the two systems is found by multiplying the matrix [b1 b2] by the inverse obtained in (2.1) above. Comparing the solution with that obtained in (2.2).For b1, Cx = b1, so x = C-1 b1 = [1,1,0,-1](T).For b2, Cx = b2, so x = C-1 b2 = [9,-7,7,1](T). The two results agree with those obtained in (2.2).(2.4) To solve the linear systems in (2.2) above by applying Gaussian elimination to the augmented matrix (C:b1 b2].

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The aditive inverse of a number is given by itself multiplied by -1. Then if we have any number x its additive inverse is -x and their sum is:

Then theanswer is the second option, 0.

Answer:

less than 1 and 1/2

Step-by-step explanation:

1/3 + 1/5 + 1/2 = 31/30 which is also equal to 1 1/30

Answer:so wut the answer?

Step-by-step explanation:im dum i dont know

Based on the fact that the expressions to be subtracted have the same base, the result is 8.305 x 10⁸.

The first number in standard form is:

= 8.4 x 10⁸

= 840,000,000

The second number in standard form is:

= 9.5 x 10⁶

= 9,500,000

The result is:

= 840,000,000 - 9,500,000

= 830,500,000

In scientific notation this is:

= 8.305 x 10⁸

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Based on the calculations, the values that could be the length of the third side are B. 10 and E. 8. Therefore, the correct options are B. 10 and E. 8.

To determine the possible values for the length of the third side of the triangle, we can use the triangle inequality theorem. According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Given sides of lengths 5 and 13, we can check which values satisfy the triangle inequality:

The sum of the lengths of the two sides must be greater than the length of the third side:

5 + 13 > Third side

18 > Third side

Now let's check each given value:

A. 2: Not possible, since 18 > 2 does not hold true.

B. 10: Possible, since 18 > 10 holds true.

C. 24: Not possible, since 18 > 24 does not hold true.

D. 5: Not possible, since the given length is already one of the sides.

E. 8: Possible, since 18 > 8 holds true.

F. 19: Possible, since 18 > 19 does not hold true.

Based on the calculations, the values that could be the length of the third side are B. 10 and E. 8.

Therefore, the correct options are B. 10 and E. 8.

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Answer:

the maximum height of the ball is 42.25 m

Step-by-step explanation:

Given the height function as;

h(t) = -16t² + 12t + 40

At maximum height, the final velocity of the ball will be zero.

The final velocity is calculated as follows;

\(v = \frac{dh(t)}{dt} = -32 t+ 12\\\\at \ maximum \ height\ v = 0\\\\Thus, -32 t+ 12 = 0\\\\32t = 12\\\\t = \frac{12}{32} \\\\t = 0.375 \ s\)

At maximum height, the time of motion of the ball is 0.375 s.

The maximum height is calculated as follows;

h(t) = -16t² + 12t + 40

h(0.375) = -16(0.375)²   +   12(0.375)    +   40

h(0.375) = -2.25  +  4.5  +  40

h(0.375) = 42.25 m

Therefore, the maximum height of the ball is 42.25 m

A chord is a combination of three or more tones (notes) played together.

To determine the notes in a chord, we need to calculate the intervals between the notes. An interval is the distance between two notes. Intervals are measured in half steps (or semitones). A half step corresponds to the interval between two adjacent keys of a piano.

In a major chord, the formula for determining the intervals is 1-3-5. This means the root note (1st note) is a major third (4 half steps) away from the 3rd note and a perfect fifth (7 half steps) away from the 5th note.

For example, if the root note is C, the 3rd note is E and the 5th note is G. The intervals in this chord are C to E (4 half steps) and C to G (7 half steps). Therefore, the chord is a C major chord.

In a minor chord, the formula for determining the intervals is 1-b3-5. This means the root note is a minor third (3 half steps) away from the 3rd note and a perfect fifth (7 half steps) away from the 5th note.

For example, if the root note is F, the 3rd note is Ab and the 5th note is C. The intervals in this chord are F to Ab (3 half steps) and F to C (7 half steps). Therefore, the chord is a F minor chord.

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\(\huge \bf༆ Answer ༄\)

The Angles marked there forms linear pair, and therefore they add up to be equal to 180°

That is ~

Therefore, value of x is 50°

Five e minus one e equal to ten

Four e equal to ten

e equal to ten over four

e equal to 2.5

Answer:

a reflection in the y-axis followed by a translation down by 7 units

Step-by-step explanation:

just answered it

The transformations of the graph is a reflection in the x-axis followed by a translation down by 7 units.

Option (C) is correct.

It is required to choose  the transformations of the graph.

A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure. The original shape of the object is called the Pre-Image and the final shape and position of the object is the Image under the transformation.

Given:

We have a given a graph of y = f(-x) – 7.

The transformations in order are the following:

Reflection over the x-axis.

Horizontal translation of 7 units to the left.

Therefore, the transformations of the graph is a reflection in the x-axis followed by a translation down by 7 units.

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C. The statement is true. A larger margin of error creates a wider confidence interval, which is more likely to contain the population parameter.

In statistical inference, a confidence interval is a range of values that is used to estimate an unknown population parameter with a certain level of confidence. The margin of error represents the degree of precision of the confidence interval, while the level of confidence represents the probability that the true population parameter falls within the interval. The sample size also plays a role in determining the width of the confidence interval.
When the level of confidence is higher, it means that we are more certain that the true population parameter falls within the confidence interval. However, this also means that we need to be more precise in our estimate, which requires a smaller margin of error. Therefore, for a given sample size, higher confidence means a larger margin of error, as more precision is required to achieve the same level of confidence.
A larger margin of error creates a wider confidence interval, which means that the range of possible values for the population parameter is larger. This makes it more likely that the true parameter falls within the interval, as there are more possible values that it could take. Therefore, option C is the correct answer.

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The surface area obtained by rotating the curve y = x² from x = 0 to x = 8 about the y-axis is 2048π square units.

We are given that the curve y = x² is rotated from x = 0 to x = 8. So our range of integration is from x = 0 to x = 8.

To use the disk method, we need to express the curve in terms of y instead of x. For the equation y = x², we can rewrite it as x = √y.

The radius of each disk is the distance between the y-axis and the curve. Since we are rotating the curve around the y-axis, the radius will be the value of x for a given y. Therefore, the radius is x = √y.

The area of each disk can be found using the formula for the area of a circle, which is A = πr². In this case, the area is A = π(x²) = π(√y)² = πy.

To find the total surface area, we need to sum up the areas of all the disks. We integrate the area function πy with respect to y from y = 0 to y = 64 (since x = 8 corresponds to y = 64).

Surface Area = ∫(πy)dy from 0 to 64

= π∫y dy from 0 to 64

= π[y²/2] from 0 to 64

= π[(64²/2) - (0²/2)]

= π[2048]

= 2048π square units.

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Answer:

i need help too

Step-by-step explanation: