The average (arithmetic mean) of a, a + 1, and a + 2 is c, and the average of b, b + 1, and b + 2 is d. What is the average of c and d?

Answer:

y = 1/2x -1

Step-by-step explanation:

The amount of money in the account after 9 years is $2549.68.

The formula A=P(1+(r)/(n))^(nt) is used to calculate the amount of money in an account after a certain amount of time, given the principal amount (P), the interest rate (r), the number of times interest is compounded per year (n), and the number of years (t).

To find A when P=2000, r=3%, n=12, and t=9, we can plug these values into the formula and simplify:

A = 2000(1+(0.03)/(12))^(12*9)

A = 2000(1+0.0025)^(108)

A = 2000(1.0025)^(108)

A = 2000(1.2748)

A = 2549.68

Therefore, $2549.68 is the amount of money in the account after 9 years.

"

Correct question

Ulas and Applications:

If A=P(1+(r)/(n))^(nt)

Find A when P=2000,r=3%,n=12, and t=9.

"

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The measures of the angles in the figure are DBE = 64 degrees, CBE = 26 degrees. Others are shown below

Figure 7

The angle DBC is right angled

So, we have

17x + 13 + 32 - 2x = 90

This gives

15x + 45 = 90

So, we have

x = 3

Solving for the other angles, we have

DBE = 17 * 3 + 13 = 64

CBE = 32 - 2 * 3 = 26

Figure 8

Here, we have

5x + 29 = 9x - 15 -- alternate angles

So, we have

4x = 44

Divide

x = 11

Solving for the other angles, we have

WVZ = 9 * 4 - 15 = 21

CBE = 90 - 21 = 69

Figure 9

Here, we have

8x - 17 = 5x + 13 -- alternate angles

So, we have

3x = 30

Divide

x = 10

Solving for the other angles, we have

RTS = 5 * 10 + 13 = 63

PTQ = 90 - 63 = 27

Figure 10

Here, we have

6x + 25 + 2x + 23 = 180 -- angles on a straight line

So, we have

8x = 132

Divide

x = 16.5

Solving for the other angles, we have

EFG = 6 * 16.5 + 25 = 124

IFH = 180 - 124 = 56

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Answer:

To find the values of a and b that make the power function y = ax^b pass through the points (2,5) and (6,9), we can use the following system of equations:

5 = a2^b

9 = a6^b

We need to solve for a and b in this system.

One way to do this is to divide the second equation by the first equation, which eliminates a and gives:

9/5 = (6/2)^b

Simplifying this gives:

9/5 = 3^b

Taking the logarithm of both sides (with any base) gives:

log(9/5) = log(3^b)

Using the logarithmic property that log(a^b) = b*log(a), we get:

log(9/5) = b*log(3)

Solving for b, we get:

b = log(9/5) / log(3)

Plugging this value of b into one of the original equations (e.g., the first one) gives:

5 = a*2^(log(9/5)/log(3))

Solving for a, we get:

a = 5 / 2^(log(9/5)/log(3))

Answer:

16

Step-by-step explanation:

8-4x times y^2, x=3 and y=-2

First, plug in both variables. Since x=3, you would substitute 4x in the equation to 4(3). You would do the same to y, but instead it would be in replace of y^2. So it would be -2^2. You now have a new equation:

8-4(3) times -2^2

Next, you start solving the equation. You should follow PEMDAS (Parenthesis, Exponent, Multiplication, Division, Addition, Subtraction). This method is sometimes controversial, but it still works for this problem.

Start by multiplying 4 times 3 which equals 12. Then I solve the exponent. The exponent -2^2 is the same as -2 times -2. The -2 is the number that gets multiplied, and the exponent is how many times -2 gets multiplied times itself. -2 times -2 is 4. You can plug your new numbers back in the equation now.

8-12 times 4

The equation is much easier to solve now. 8-12 is -4. -4 times 4 is 16.

The answer is 16.

Answer:

Step-by-step explanation:

The Domain is (x) values that a certain line covers on a graph.

This line is a segment, so it has a very specific domain.

The domain is written in the form of =>     [tex]a\leq x\leq b[/tex]

    - In which (a) and (b) are the smallest and largest numbers on the domain, respectively.

Here, the line starts at (-11,6) and goes all the way to (2,1)

From here - we take out the y-values to get that the x-values go from (-11) to (2)

That means that the domain. of this here line, is:

[tex]Domain = -11\leq x\leq 2[/tex]

No, these two matrices are not equal.

The first matrix is a 3x3 matrix with the elements [[3,-1,7],[2,6,-9],[-5,4,-2]] and the second matrix is also a 3x3 matrix with the elements [[-2,-9,7],[4,6,-1],[-5,2,3]]. In order for two matrices to be equal, they must have the same dimensions and the corresponding elements must be equal. In this case, the dimensions are the same, but the corresponding elements are not equal. For example, the first element in the first matrix is 3, but the first element in the second matrix is -2. Therefore, these two matrices are not equal.

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Answer:

Step-by-step explanation:

based on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole number based on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole number based on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole number

To find f(i), we will substitute i for x in the given function and simplify:

f(i) = (i^{26} + i^{24} + 2i^{22})/(i-1)
= ((i^{22})(i^4 + i^2 + 2))/(i-1)
= ((i^{22})(1 + (-1) + 2))/(i-1)
= ((i^{22})(2))/(i-1)
= (2i^{22})/(i-1)
= (2i^{22})/((-1)(1-i))
= (2i^{22})/((-1)(1-i)) * ((1+i)/(1+i))
= (2i^{22})(1+i)/((-1)(1-i)(1+i))
= (2i^{22})(1+i)/((-1)(1^2 - i^2))
= (2i^{22})(1+i)/((-1)(1 - (-1)))
= (2i^{22})(1+i)/(2)
= i^{22} + i^{23}
= i^{22}(1 + i)
= (i^{22})(1 + i)
= (1)(1 + i)
= 1 + i

Therefore, the answer is (d) (1+i).

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The individual would need $405,840.13 at the start of retirement to make semiannual withdrawals of $15,265 for 35 years from an account paying 4.5% compounded semiannually.

What is the Present Value of an Annuity?

With a specific rate of return, or discount rate, the present value of an annuity is the current value of the future payments from an annuity. The present value of the annuity decreases as the discount rate increases.

To determine the amount needed for retirement, we can use the formula for the present value of an annuity:

  [tex]PV= PMT* \frac{1-\frac{1}{(1+r)^{n} } }{r}[/tex]

where PV is the present value, PMT is the payment amount, r is the interest rate per period, and n is the number of periods.

In this case, PMT = $15,265, r = 4.5%/2 = 0.0225 (since the interest is compounded semi-annually), and n = 35 x 2 = 70 (since there are 70 semiannual periods in 35 years).

Plugging in these values, we get:

[tex]PV = (15,265\times(1 - (1 + 0.0225)^{(-70))) / 0.0225[/tex]

PV = $405,840.13

Therefore, the individual would need $405,840.13 at the start of retirement to make semiannual withdrawals of $15,265 for 35 years from an account paying 4.5% compounded semiannually.

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The volume of the resulting sugar mixture is less than the sum (20 mL sugar + 50 mL water) of the volumes of the unmixed sugar and water.

When sugar is dissolved in water, the sugar molecules fit into the spaces between the water molecules, resulting in a decrease in volume. To explain this further, let's use the following steps:

1. Start with 20 mL of sugar and 50 mL of water in separate containers. 2. Pour the sugar into the water.

3. Stir the mixture until the sugar is completely dissolved.

4. Measure the volume of the resulting sugar mixture. You will notice that the volume of the sugar mixture is less than the sum of the volumes of the unmixed sugar and water (70 mL).

This is because the sugar molecules are now occupying the spaces between the water molecules, resulting in a decrease in volume.

In conclusion, the volume of the resulting sugar mixture is less than the sum (20 mL sugar + 50 mL water) of the volumes of the unmixed sugar and water.

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Sum of the first 15 terms of the series given is = 10485.36

What is sequence and series?

A sequence is a collection or sequential arrangement of numbers that adheres to a predetermined order or set of criteria. A series is created by adding the terms of a sequence. In a sequence, a single sentence could appear more than once.

Sequences can be divided into two categories: endless sequences and finite sequences. By merging the terms of the sequence, series are defined. A series may, in exceptional cases, also have a sum of infinite terms.

In the given question,

Antonio is working with a new geometric series generated by the following equation:

A(n) = 12(1.5) ⁿ-1

Now to find the sum of the first 15 terms of the series,

S(n) = a{rⁿ)-1}/r-1

So, we have,

a = 12

r = 1.5

n = 15

Using the values in the equation:

S (15) = 12 (1.5¹⁵ - 1)/1.5-1

= 12 × (437.89-1)/0.5

= 12 × 873.78

= 10485.36

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Answer:

1/6

Step-by-step explanation:

Step-by-step explanation: There are 4 primes. So the probability for the first draw is 4/9. Since the card is not replaced, the second probability is 3/8. 3/8 * 4/9 is 12/72, which simplifies into 1/6.

Answer: Without knowing the specifics of the spinner, it's not possible to list all the possible outcomes.

However, we can determine the total number of possible outcomes by multiplying the number of outcomes for each event. For example, if the coin has two possible outcomes (heads or tails) and the spinner has six possible outcomes, then the total number of possible outcomes would be:

2 (outcomes for the coin) x 6 (outcomes for the spinner) = 12 possible outcomes

If you provide me with the specific details of the spinner (such as the number of sections and what each section represents), I could list all the possible outcomes.

Step-by-step explanation:

Equation connecting C and d is C = 5/3 d.

Direct Proportion of two quantities can be defined as that when one of the quantity increases, the other one also increases and vice versa.

(a) Given that,

C is directly proportional to d.

Equation can be written as C = kd, for some constant k.

Also, given,

C=100 when d=60

100 = 60k

k = 100/60 = 10/6 = 5/3

Equation is C = 5/3 d

(b) When d = 45 km

C = 5/3 × 45 = 75

Cost of transporting goods for 45 km is $75.

(c) When C = $120,

120 = 5/3 d

d = 120 × 3/5 = 72 km

Hence the distance is 72 km when the cost of transporting goods is $120.

Hence the equation is C = 5/3 d.

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The equation of the line is x = 3.

To find the equation of a line passing through two points, we need to use the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.

First, let's find the slope of the line using the formula: m = (y2 - y1) / (x2 - x1)

Plugging in the given points, we get:

m = (-8 - 9) / (3 - 3) = -17 / 0

Since the denominator is zero, this means that the slope of the line is undefined. This means that the line is vertical and has an equation of the form x = c, where c is a constant.

Since both of the given points have an x-coordinate of 3, the equation of the line is:

x = 3

So, the equation of the line passing through the given points is x = 3. This is the final answer in slope-intercept form.

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Answer: True

Step-by-step explanation:

Answer: No

Step-by-step explanation:

Definitely not.

By angle angle similarity ΔWYZ ≈ Δ WZX ≈ ΔZYX are similar.

Triangles with exactly similar corresponding angle configurations are said to be similar triangles. This implies that equiangular triangles are comparable. All equilateral triangles are thus interpretations of similar triangles.

In the given statements, thus the similar triangle are:

ΔWYZ ≈ Δ WZX ≈ ΔZYX

A,

∠Y is common

∠x = ∠z = 90°

Therefore, by angle angle similarity ΔWYZ ≈ Δ WZX ≈ ΔZYX are similar.

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Answer:

Yes, the perimeter and side length of a square are proportional. This is because a square has four equal sides, so if you increase the length of one side by a certain factor, the perimeter (which is the sum of all four sides) will also increase by the same factor. In other words, if you double the length of a side of a square, you will also double its perimeter. Similarly, if you reduce the length of a side by a certain factor, the perimeter will also be reduced by the same factor. This relationship holds true for all squares, regardless of their size or orientation.

The equation of the parabola is (y-5)^2=16(x-3)

To find the equation for the parabola with vertex (3,5) and focus (7,5), we can use the formula for a parabola with a horizontal axis of symmetry:

(y-k)^2=4p(x-h)

Where (h,k) is the vertex and p is the distance from the vertex to the focus.

In this case, the vertex is (3,5) and the focus is (7,5), so we have:
(y-5)^2=4p(x-3)
The distance from the vertex to the focus is 4, so p=4. Plugging this value into the equation gives us:
(y-5)^2=16(x-3)
This is the equation for the parabola with vertex (3,5) and focus (7,5).

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The value of  sin(θ/2) is √6/4.

We can start by using the identity:

sin(θ/2) = ±√[(1 - cosθ)/2]

However, before we apply this identity, we need to determine the quadrant in which θ lies, so that we can determine the sign of sin(θ/2).

From the given information, we know that cos θ = 1/4. Using the unit circle or a trigonometric table, we find that θ is a first quadrant angle whose reference angle is arc cos(1/4) ≈ 75.52°.

Since csc > 0, we know that sinθ > 0, which means that θ is either in the first or second quadrant.

However, since cosθ is positive (i.e., in the first or fourth quadrant), we know that θ must be in the first quadrant, and so sinθ > 0.

Now we can use the half-angle identity:

sin(θ/2) = ±√[(1 - cosθ)/2]

Plugging in cosθ = 1/4, we get:

sin(θ/2) = ±√[(1 - 1/4)/2] = ±√(3/8) = ±(√3/2)(√2/2) = ±(√3/2)(1/√2)

Since θ is in the first quadrant, we know that sin(θ/2) > 0, so we take the positive root:

sin(θ/2) = (√3/2)(1/√2) = √3/2√2 = √6/4

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Equation of straight line parallel to y = 3x - 2 and passing through (1, 9) is

y = 3x + 6

A straight line is an infinite length line that does not have any curves on it. A straight line can be formed between two points also but both the ends extend to infinity. A straight line is a figure formed when two points A (x1, y1) and B (x2, y2) are connected with the shortest distance between them, and the line ends are extended to infinity.

Given,

Line y = 3x - 2

Comparing with y = mx + c

slope = 3

Line parallel to y = 3x - 2 and passing through (1, 9)

Slope of the parallel line = slope of line y = 3x - 2

slope m = 3

Equation of the line,

y - y' = m(x - x')

y - 9 = 3(x - 1)

y - 9 = 3x - 3

y = 3x + 6

Hence y = 3x + 6 is equation of line parallel to y = 3x - 2 and passing through (1, 9)

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The solution to the compound inequality is x > -3 and x <= -4, or (-4, -3] in interval notation.

A compound inequality contains at least two inequalities that are separated by either "and" or "or.  The graph of a compound inequality with an "and" represents the intersection of the graph of the inequalities.

The compound inequality 8x - 6 > -30 OR -2x + 4 >= 12 can be solved by solving each inequality separately and then combining the results.

Solve 8x - 6 > -30:
8x - 6 > -30
8x > -24
x > -3

Solve -2x + 4 >= 12:
-2x + 4 >= 12
-2x >= 8
x <= -4

The solution to the compound inequality is x > -3 and x <= -4, or (-4, -3] in interval notation.

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Answer:-4.5

Step-by-step explanation:

-6+-30=-36

-36 divided by 8= -4.5

The simplified expression is -22 degrees (rounded to the nearest degree).

What is Trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles, and the functions that describe those relationships. It has applications in fields such as engineering, physics, astronomy, and navigation.

We can use the following trigonometric identity to simplify the expression:

arctan(x) + arctan(y) = arctan[(x+y) / (1-xy)]

In this case, we can substitute x = 5 and y = 6 to get:

arctan 5 + arctan 6 = arctan[(5+6) / (1 - 5*6)]

Simplifying the denominator, we get:

arctan 5 + arctan 6 = arctan(11/-29)

To find the degree measure of this angle, we can use a calculator to evaluate the inverse tangent of -11/29 and convert the result to degrees.

The result is approximately -22 degrees (rounded to the nearest degree).

Therefore, the simplified expression is:

arctan 5 + arctan 6 = -22 degrees (rounded to the nearest degree).

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The quotient of (12x^(3)-9x^(2)-21x+22) divided by (3x-3) is 4x^2 + 6x + 7, and the remainder is 0.

To find the quotient, use long division. First, divide the highest degree term of the numerator by the highest degree term of the denominator: 12x3 ÷ 3x = 4x2. Multiply the denominator by the quotient, then subtract this product from the numerator:

12x3 - 3x(4x2) = 9x2 - 4x2 = 5x2.

Divide the highest degree term of the new numerator by the highest degree term of the denominator: 5x2 ÷ 3x = 5x. Multiply the denominator by the quotient, then subtract this product from the numerator:

9x2 - 3x(5x) = -21x - 15x = -36x.

Divide the highest degree term of the new numerator by the highest degree term of the denominator: -36x ÷ 3x = -12. Multiply the denominator by the quotient, then subtract this product from the numerator:

-21x - 3x(-12) = 22 - (-36) = 58.

Divide the highest degree term of the new numerator by the highest degree term of the denominator: 58 ÷ 3 = 19. Since the degree of the numerator is lower than the degree of the denominator, 19 is the remainder.

Therefore, the quotient of (12x3 - 9x2 - 21x + 22) divided by (3x - 3) is 4x2 + 6x + 7, and the remainder is 0.

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The value of a when b = 8 and c = 5 is 41.351.

Jointly proportional refers to a relationship between two or more variables in which all of the variables increase or decrease together in the same ratio. For example, if one variable doubles, the other variables double as well.

The variable a is jointly proportional to b and the cube of c. This means that a = k*b*c^3, where k is a constant. We can use the given values to find k:

127 = k*6*8^3

127 = k*3072

k = 127/3072

k = 0.041351

Now we can use this value of k to find the value of a when b = 8 and c = 5:

a = 0.041351*8*5^3

a = 0.041351*8*125

a = 41.351

So the value of a when b = 8 and c = 5 is 41.351.

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