Select the correct answer from each drop-down menu. Consider the function f(x) = 3x + 1 and the graph of the function g(x) shown below. A coordinate plane linear graph function shows a line intersecting Y-axis at minus 5 and X-axis at 1.5. The graph g(x) is the graph of f(x) translated units , and g(x) = .

Answer:

0.5

Step-by-step explanation:

0.5=0.42 then the answer is 0.5

The binomial expansion of (1 + i)^2n can be written as ∑(n choose k)(i^k)(1^(n-k)), where (n choose k) represents the binomial coefficient of n and k. And that's the binomial expansion of (1+i)^2n * 2^n * cos(nπ/2).

Using the identity cos(npi/2) = 0 when n is odd and cos(npi/2) = (-1)^n/2 when n is even, we can simplify the expression to:
(1 + i)^2n * 2^n * cos(npi/2) = ∑(n choose k)(i^k)(1^(n-k)) * 2^n * cos(npi/2)
When n is odd, cos(npi/2) = 0, so the expression simplifies to:
∑(n choose 2k)(i^(2k))(1^(n-2k)) * 2^n
When n is even, cos(npi/2) = (-1)^n/2, so the expression simplifies to:
∑(n choose 2k)(i^(2k))(1^(n-2k)) * 2^n * (-1)^(n/2)
Therefore, the binomial expansion of (1 + i)^2n * 2^n * cos(npi/2) can be written as either of these simplified forms, depending on whether n is odd or even.

The binomial expansion of (1+i)^2n * 2^n * cos(nπ/2).
Step 1: Apply the binomial theorem to the term (1+i)^2n.
The binomial theorem states that (a+b)^n = Σ [n! / (k!(n-k)!) * a^k * b^(n-k)], where the sum runs from k=0 to k=n.
In this case, a=1 and b=i. Applying the theorem:
(1+i)^2n = Σ [2n! / (k!(2n-k)!) * 1^k * i^(2n-k)]
Step 2: Simplify the expression for the binomial expansion.
For the complex number i, we have i^2 = -1, i^3 = -i, and i^4 = 1. Using this pattern, we can rewrite the i^(2n-k) term in the expansion:
(1+i)^2n = Σ [2n! / (k!(2n-k)!) * 1^k * (-1)^((2n-k)/2) * i^(k % 4)], for even k values.
Step 3: Multiply the binomial expansion by 2^n * cos(nπ/2).
Now, we just need to multiply our expansion by the given factors:
(1+i)^2n * 2^n * cos(nπ/2) = Σ [2n! / (k!(2n-k)!) * 1^k * (-1)^((2n-k)/2) * i^(k % 4) * 2^n * cos(nπ/2)], for even k values.
And that's the binomial expansion of (1+i)^2n * 2^n * cos(nπ/2).

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Answer:

The third option is the answer.

Step-by-step explanation:

In the formula y = mx + b, using the equation given,

Answer:

the 3rd option

Step-by-step explanation:

In the formula y = tx + b, using the equation given,

t = 2, which means that the line goes up 2 units and right 1 unit.

b = 1, which means that the y-intercept, or where the line touches the y-axis, is 1.

Answer:

4 miles

Step-by-step explanation:

3 miles plus 1 additional mile is 4 miles.

i^93 = i^92 x i

i^92 =(i^2)^46

Now you have i(i^2)^46

i^2 = -1

Now you have i(-1)^46

-1^46 = 1

Now you have 1i which = i

The answer is i

The interest payment in the monthly payment of $297.02 for a financing of $12,000 at 7% over 5 years is $70. Option b is correct.

The interest payment of the given financing can be calculated by the given parameters as follows:

We are given that the amount financed is $12,000 for a period of 5 years and an annual interest rate of 7%.The monthly payment is given to be $297.02.

Compute the total interest on the loan over the 5-year period using the below formula:

Total Interest = (Amount Financed) x (Annual Interest Rate) x (Number of Years)

Total Interest = $12,000 x 7% x 5 years

Total Interest = $4,200

Compute the total number of monthly payments:

Total number of payments = Number of years x 12

Total number of payments = 5 x 12

Total number of payments = 60

Finally, calculate the interest payment component of the monthly payment using the below formula:

Interest payment = Total interest / Total number of payments

Interest payment = $4,200 / 60

Interest payment = $70

Therefore, the interest payment is $70. Option b is correct.

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The formula for finding the sum of a geometric series is:

S n = a₁ (1-rⁿ )/(1-r)

The four quantities in the formula are S n, a₁, r, n

An infinite geometric series is the outcome of an unlimited geometric sequence. An infinite geometric series is the outcome of an unlimited geometric sequence. This series wouldn't have a finish. It is possible to calculate the sum of all finite geometric series.

The terms in the sequence will grow steadily larger, but adding the larger numbers together will not provide a solution if the common ratio of an infinite geometric series is greater than one.

The formula for finding the sum of a geometric series is:

S n = a₁ (1-rⁿ )/(1-r)

The four quantities in the formula are S n, a₁, r, n

The description is as follows:

n be the number of terms

a₁ be the first term

r be the common ratio

\(S_n\) be the sum of a geometric series

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Answer:

Step-by-step explanation:

6x-y=-5

-6x+y=5

Adding the 2 equations we have:

0 + 0 = 0

0 = 0

This means there are infinite solutions

- the equations are identical.

System B

x+3y=13

-x+3y=5

Adding:

6y = 18

y = 3.

x = 13 - 3(3) = 4.

The system has a unique solution

(x. y) = (4, 3).

Answer:

It's J

Step-by-step explanation:

when has only ONE zero it'll intercept the x axis one time

Answer:

  a) 489.77 ft from friend

  b) 470.80 ft from cliff

Step-by-step explanation:

Given a man on a 135 ft cliff sees his friend at an angle of depression of 16°, you want to know the distance of the man from his friend, and the distance of the friend from the cliff.

The relevant trig relations are ...

  Sin = Opposite/Hypotenuse

  Tan = Opposite/Adjacent

The 135 ft height of the cliff is modeled as the side of a right triangle that is opposite the angle of elevation from the friend to the top of the cliff. (See attachment 2.) That angle is the same as the angle of depression from the top of the cliff to the friend.

The hypotenuse of the triangle is the distance between the man and his friend. The side of the triangle adjacent to the friend is the distance to the cliff.

Using the above relations, we have ...

  sin(16°) = (cliff height)/(distance to friend)

  tan(16°) = (cliff height)/(distance to cliff)

Solving for the variables of interest gives ...

  distance to friend = (cliff height)/sin(16°) = (135 ft)/sin(16°) ≈ 489.77 ft

  distance to cliff = (cliff height)/tan(16°) = (135 ft)/tan(16°) ≈ 470.80 ft

The ma is 489.77 ft from his friend; the friend is 470.80 ft from the cliff.

__

Additional comment

The distances are given to more decimal places than necessary so you can round the answer as may be required.

<95141404393>

*see attachment for the diagram of the information given

Answer:

115.8°

Step-by-step explanation:

Due west = 83 miles

Northwest = 111 miles

Distance to its original position = 165 miles

Let x represent the degree north of west that it turned when it changed direction which is the opposite angle of 165 miles.

Thus, to find x, we'd apply the Law of Cosine which is given as:

c² = a² + b² - 2ab*cos C

Where,

C = x

a = 83 miles

b = 111 miles

c = 165 miles

Plug in the values

165² = 83² + 111² - 2*83*111*Cos x

27,225 = 19,210 - 18,426*Cos x

27,225 - 19,210 = - 18,426*Cos x

8,015 = -18,426*Cos x

8,015 = -18,426*Cos x

8,015/-18,426 = Cos x

-0.434983176 = Cos Cmx

Cos x = -0.434983176

x = cos^{-1}(-0.434983176)

x = 115.784223°

x = 115.8°

The scale factor, if MJ is 25 ft. long and M'J' is 5 feet long is 1/5

If MJ is considered as the original figure, it is 25 ft. long.

The image of MJ, M'J' is 5 feet long

Scale factor is generally understood as the number of times the dimensions of the image is enlarged or diminished

Scale factor = Dimension of the new image ÷ Dimension of the original shape

Scale factor = M'J' length/ MJ length

k = 5/25

k = 1/5

The value of scale factor = 1/5, which means the new image is diminished.

Therefore the scale factor, if MJ is 25 ft. long and M'J' is 5 feet long is 1/5.

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Answer:

B. 6

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Identify.

\(\displaystyle \frac{3 \sqrt{20}}{\sqrt{5}}\)

Step 2: Simplify

Answer:21

Step-by-step explanation:12 times three is 36 and 7 times 3 is 21

Using Pythagorean Theorem, the length of the line segment from (-3, 10) to (4, -1) is 13 units.

Pythagorean theorem describes the relationship between the sides of a right triangle. It states that the square of the hypotenuse is equal to the sum of the squares of the two other side.

c² = a² + b²

Let a = vertical distance between the two points

b = horizontal distance between the two points

c = distance between the two points / length of line segment

Hence, c² = (|y₂ - y₁|)² + (|x₂ - x₁|)².

Substitute the values of x and y and solve for c.

c² = (|y₂ - y₁|)² + (|x₂ - x₁|)²

c² = (|-1 - 10|)² + (|4 - -3|)²

c² = (|-11|)² + (|7|)²

c² = 11² + 7²

c² = 121 + 49

c² = 170

c = 13.04

length of line segment ≅ 13 units

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For a random sample of 155 observations results in 62 successes.

a) A 90% confidence interval for the population proportion of successes is equals to the (0.335 , 0.465).

b) A 90% confidence interval for the population proportion of failure is equals to the (0.535 , 0.665).

We have a random sample of 155 observations results in 62 successes. So,

Observed value, x = 62

Sample size,n = 155

Population Proportion, p = x/n

= 62/155

= 0.4

a) We have to determine 90% confidence interval for the population proportion of successes. Using the distribution table, for 90% confidence interval, z-score value is equals to 1.6. Consider Confidence interval formula with proportion, CI \(= p ± z×\sqrt\frac{p(1-p)}{n}\)

substitute all known values in above formula, \(= 0.4 ± 1.64\sqrt\frac{0.4(1- 0.4)}{155}\)

= 0.4 ± 0.0645

= (0.4 - 0.0645 , 0.4 + 0.0645)

= (0.335 , 0.465)

b) Now, we have to determine a 90% confidence interval for the population proportion of failures.

Now consider, here failure observed values, x = 155 - 62

= 93

proportion, p = x/n

= 93/155 = 0.6

Consider the confidence interval formula, CI \(= p ± z×\sqrt\frac{p(1-p)}{n}\)

substitute values, \(= 0.6 ±1.64×\sqrt\frac{0.6(1-0.6)}{155}\)

= 0.6 ± 0.0645

= (0.6 - 0.0645 , 0.6 + 0.0645)

= (0.535 , 0.665)

Hence, required value is (0.535 , 0.665).

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Answer:

y = 200 + 50x

Step-by-step explanation:

y = cost

x = number of months

The cost is equal to the cost to open the plan plus the monthly fee times the number of months

y = 200 + 50x

Answer:

y = 200 + 50x

Step-by-step explanation:

the cost = the base cost plus the monthly charge ($50 per the number of months you pay it)

hope this helps (/o.o)/<3

Answer:

a = 2, b = 4

Step-by-step explanation:

The equation of a parabola in standard form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is the coefficient of the x² term.

Here (h, k ) = (- 1, 3 ) and coefficient of x² term = 1 , then

y = (x - (- 1))² + 3 , that is

y = (x + 1)² + 3 ← expand factor using FOIL

y = x² + 2x + 1 + 3

y = x² + 2x + 4 ← in standard form

compare to y = x² + ax + b

with a = 2 and b = 4

The values of a and b are a = 1 and b = 3.

To find the values of a and b, we can use the fact that the turning point of a quadratic function in the form y = ax² + bx + c is given by the vertex (-b/2a, f(-b/2a)).

In this case, the turning point is (-1, 3), which gives us the following equations:

\(-\frac{b}{2a} = -1 (equation 1) \\f(-\frac{b}{2a}) = 3 (equation 2)\)

Plugging equation 1 into equation 2:

f(-1) = 3

Substituting -1 into x² + ax + b:

1 - a + b = 3

Simplifying:

b - a = 2 (equation 3)

Since a and b are integers, we can try different combinations of integers that satisfy equation 3. One such pair is a = 1 and b = 3:

b - a = 3 - 1 = 2

So, the values of a and b are a = 1 and b = 3.

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As the spacing between joists increases, the maximum span for any board size will B. decrease only. This is because the wider the spacing between joists, the more weight and pressure will be placed on the boards that are spanning the gap between them.

This means that the boards will need to be stronger in order to support the weight without bending or breaking.
If the boards are not strong enough, they may sag or bow under the weight, which can create safety hazards or damage to the structure. Therefore, it is important to use the appropriate board size and spacing between joists for any given application in order to ensure structural integrity and safety.
In summary, increasing the spacing between joists will result in a decrease in the maximum span for any board size, as the boards will need to be stronger in order to support the weight and pressure. It is important to choose the right board size and joist spacing to maintain the structural integrity and safety of the building or structure.

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Arrange the functions according to the average rate of change in the interval 1<1. ×< 3 is:   g(x) < f(x) = h(x) 

In other words, g(x) has the smallest average rate of change, while f(x) and h(x) have the same largest average rate of change.

A function is a mathematical rule that takes an input (or inputs) and produces a corresponding output.

It describes a relationship between two quantities, where each input is associated with exactly one output.

Since the interval of interest is not provided, I will assume that the interval is 1 < x < 3, based on the graphs of the functions given.

To determine the ordering of the functions according to their average rates of change on the interval 1 < x < 3, we can use the following formula:

Average rate of change = (f(b) - f(a)) / (b - a)

where a and b are the endpoints of the interval.

Using this formula, we can calculate the average rates of change of the three functions on the interval 1 < x < 3. Here are the results:

f(x): average rate of change = (f(3) - f(1)) / (3 - 1) = (2 - (-2)) / 2 = 2

g(x): average rate of change = (g(3) - g(1)) / (3 - 1) = (-3 - (-1)) / 2 = -1

h(x): average rate of change = (h(3) - h(1)) / (3 - 1) = (0 - (-4)) / 2 = 2

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The complete question is given below:

Arrange the functions in the period 1 according to the average rate of change. 3 is: g(x) f(x) = h(x)

In other words, g(x) has the lowest average rate of change, whereas f(x) and h(x) both have the highest average rate of change.

A function is a mathematical rule that accepts an input (or inputs) and generates an output.

It defines a relationship among two quantities in which each input corresponds to only one output.

Because the interval of interest is not specified, I will assume that it is 1 x 3 based on the graphs of the functions supplied.

We can use the formula that follows to find the ordering of the functions based on their average frequencies of change on the interval 1 x 3:

Change at an Average Rate = (f(b) - f(a)) / (b - a)

where a and b are the interval's ends.

We can compute the average rates of change of all three functions on the interval 1 x 3 using this formula. Here are the outcomes:

f(x): average rate of change = (f(3) - f(1)) / (3 - 1)

                                              = (2 - (-2)) / 2

                                              = 2

g(x): average rate of change = (g(3) - g(1)) / (3 - 1)

                                               = (-3 - (-1)) / 2

                                               = -1

h(x): average rate of change = (h(3) - h(1)) / (3 - 1)

                                               = (0 - (-4)) / 2

                                               = 2

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8 a) The fifth term in the expansion is 8,960.

b) The sixth term in the expansion is -11,264.

c) The seventh term in the expansion is approximately 28.6152.

9) The expansion of 2/(1-3x^2) up to the term in x^8 is 2 + 24x^2 + 162x^4 + 972x^6 + 1458x^8.

8) a) To find the fifth term in the expansion of (1 + 4x)^7, we use the binomial theorem formula:

(1 + 4x)^7 = C(7,0) + C(7,1)(4x) + C(7,2)(4x)^2 + C(7,3)(4x)^3 + C(7,4)(4x)^4 + C(7,5)(4x)^5 + ...

The fifth term corresponds to the coefficient of (4x)^4, which is given by:

C(7,4)(4)^4 = 35 x 256 = 8,960

b) To find the sixth term in the expansion of (2 - x)^11, we use the same formula as above:

(2 - x)^11 = C(11,0) + C(11,1)(-x) + C(11,2)(-x)^2 + C(11,3)(-x)^3 + C(11,4)(-x)^4 + C(11,5)(-x)^5 + ...

The sixth term corresponds to the coefficient of (-x)^5, which is given by:

C(11,5)(-1)^5(2)^6 = -11 x 32 x 32 = -11,264

c) To find the seventh term in the expansion of (3 - (2/3x))^12, we again use the same formula:

(3 - (2/3x))^12 = C(12,0) + C(12,1)(-2/3x) + C(12,2)(-2/3x)^2 + C(12,3)(-2/3x)^3 + ...

The seventh term corresponds to the coefficient of (-2/3x)^6, which is given by:

C(12,6)(-2/3)^6 = 924 x (2/3)^6 = 28.6152

9) To obtain the expansion of 2/(1-3x^2) up to the term in x^8, we can use the formula for the geometric series:

2/(1-3x^2) = 2(1 + (3x^2) + (3x^2)^2 + (3x^2)^3 + ...)

To find the term in x^8, we need to find the coefficient of (3x^2)^4:

C(n,r) = n!/[r!(n-r)!]

C(4,0) = 1, C(4,1) = 4, C(4,2) = 6, C(4,3) = 4, C(4,4) = 1

The term in x^8 is then given by:

2C(4,0) + 2C(4,1)(3x^2) + 2C(4,2)(3x^2)^2 + 2C(4,3)(3x^2)^3 + 2C(4,4)(3x^2)^4

= 2 + 24x^2 + 162x^4 + 972x^6 + 1458x^8

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To simulate the minutes between customer arrivals in Excel, one would use the Exponential distribution function in Excel.

This function is part of the Statistical functions category and can be found under the "Statistical" tab in Excel.

An exponential distribution is a probability distribution that describes the time between events in a Poisson process, where events occur continuously and independently at a constant average rate.

The Exponential distribution function in Excel takes two arguments: Lambda and x.

Lambda is the rate parameter, which describes the average number of events per unit of time.

In this case, the rate is 6 customers per hour, so Lambda would be equal to 6.

X is the time interval, and in this case, it would be the time between customer arrivals in minutes.

Therefore, to simulate the minutes between customer arrivals, one would use the following formula in Excel: =EXPON.DIST(x/60,1/6,TRUE)

The "x/60" part of the formula is used to convert the time interval from minutes to hours, as the rate is given in customers per hour.

The "1/6" part of the formula is used to set the Lambda value to 6.

The "TRUE" part of the formula is used to specify that we want the cumulative distribution function (CDF), which gives the probability that the time between events is less than or equal to x.

To simulate the minutes between customer arrivals in Excel, we would use the Exponential distribution function with Lambda = 6 and x being the time interval between customer arrivals in minutes.

The formula would be = EXPON.DIST(x/60,1/6,TRUE).

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Using Hypothesis testing,

a) Two samples are independent.

b)H₀: an expectant mother's cigarette smoking has any not effect on the bone mineral content of her otherwise healthy child.

Hₐ : an expectant mother's cigarette smoking has any effect on the bone mineral content of her otherwise healthy child.

c) Null hypothesis is accepted.

so, an expectant mother's cigarette smoking has no effect on the bone mineral.

We have given that,

A study which is conducted for check an expectant mother's cigarette smoking has any effect on the bone mineral content of her otherwise healthy child.

For new-born whose mother's cigarette smoking

sample size , n₁= 77

X-bar, x₁-bar = 0.098 g/cm

standard deviations, s₁ = 0.026 g/cm

For new-born whose mother did not cigarette smoking

sample size , n₂ = 161

standard deviations, s₂ = 0.025 g/cm.

mean (X-bar) , x₂-bar = 0.095 g/cm

a) the two samples are independent since they are different types of mothers, smoking mothers and non smoking mothers

b)H₀: an expectant mother's cigarette smoking has any not effect on the bone mineral content of her otherwise healthy child.

Hₐ: an expectant mother's cigarette smoking has any effect on the bone mineral content of her otherwise healthy child.

c) Test statistic:

t = (x₁-bar - x₂-bar )/S (√1/n₁+1/n₂)

where , S = √(s₁²(n₁ - 1) + s₂²(n₂ -1))/n₁+n₂ - 2

S = √((0.026)²(76) +(0.025 )²(160))/236

= 0.0253

then, t = (0.098 - 0.095 )/0.0253(√1/77 +1/161 )

=> t = 0.859

Using the critacal table critical t is

Critical t = ±1.970065

Degrees of freedom =236.0000

P-Value=0.3935 which is greater than α(0.05),

So , we accept H₀

Thus, an expectant mother's cigarette smoking has not effect on the bone mineral content of her otherwise healthy child.

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Answer: Commutative property

A) the three inequalities that must be satisfied are:

B) Graph shaded and satisfying all conditions is attached.

An inequality in mathematics is a relationship that makes a non-equal comparison between two integers or other mathematical expressions.

It is most commonly used to compare the sizes of two numbers on a number line.

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Answer: b=112 degrees and c=68

Step-by-step explanation:

Answer:

b = 112, c = 68

Step-by-step explanation:

The angle of a line is 180 degrees.

If an angle is 112, 180-112=68 so that blank space will be 68 degrees.

180-68=112, so b=112.

Since b is 112, we now that c is 68.

Answer:

The answer is D.

Step-by-step explanation:

Look at the amount of zeros went over to the left so negative 3

Based on the amount of Nacho cheese corn chips and the calories per gram, the calories per party bag is 1,094.6 calories

First, convert ounces to grams:

= 1 ounce is 28.3495 grams

Party bag in grams:

= 15 x 28.3495

= 425.243 grams

The amount of calories is:

= 425.243 x 28.6% x 9

= 1,094.6 calories

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The predicted number of runs for the player with only 86 hits can be calculated using the equation Runs = Hits + Walks - Home Runs. Plugging in the values given, we get: Runs = 86 + Walks - Home Runs. Therefore, the predicted number of runs for the player is dependent on the number of walks and home runs they have.

To solve for the predicted number of runs, we can use the following steps:

Therefore, the predicted number of runs for the player with only 86 hits can be calculated by plugging in the values of the number of walks and home runs into the equation Runs = Hits + Walks - Home Runs.

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