find x, if ∠1 and ∠2 are a linear pair. m∠1 = 20+5x and m∠2 =x+10

a. Present value of $400 per year for 14 years at 14%: $2,702.83
b. Present value of $200 per year for 7 years at 7%: $1,155.54
c. Present value of $400 per year for 7 years at 0%: $2,800
d. Present value of $400 per year for 14 years at 14% (annuity due): $2,943.07
  Present value of $200 per year for 7 years at 7% (annuity due): $1,233.24
  Present value of $400 per year for 7 years at 0% (annuity due): $2,800

To find the present values of the ordinary annuities, we can use the formula for the present value of an annuity:

PV = PMT * [(1 - (1 + r)^(-n)) / r]
Where:
PV = Present value
PMT = Payment per period
r = Interest rate per period
n = Number of periods

a. $400 per year for 14 years at 14%:
PV = $400 * [(1 - (1 + 0.14)^(-14)) / 0.14]

≈ $2,702.83

b. $200 per year for 7 years at 7%:
PV = $200 * [(1 - (1 + 0.07)^(-7)) / 0.07]

≈ $1,155.54

c. $400 per year for 7 years at 0%:
Since the interest rate is 0%, the present value is simply the total amount of payments over the 7 years:
PV = $400 * 7

= $2,800

d. Reworking previous parts assuming they are annuities due:
For annuities due, we need to adjust the formula by multiplying it by (1 + r):

a. Present value of $400 per year for 14 years at 14%:
PV = $400 * [(1 - (1 + 0.14)^(-14)) / 0.14] * (1 + 0.14)

≈ $2,943.07

b. Present value of $200 per year for 7 years at 7%:
PV = $200 * [(1 - (1 + 0.07)^(-7)) / 0.07] * (1 + 0.07)

≈ $1,233.24

c. Present value of $400 per year for 7 years at 0%:
Since the interest rate is 0%, the present value remains the same:
PV = $400 * 7

= $2,800

In conclusion:
a. Present value of $400 per year for 14 years at 14%: $2,702.83
b. Present value of $200 per year for 7 years at 7%: $1,155.54
c. Present value of $400 per year for 7 years at 0%: $2,800
d. Present value of $400 per year for 14 years at 14% (annuity due): $2,943.07
  Present value of $200 per year for 7 years at 7% (annuity due): $1,233.24
  Present value of $400 per year for 7 years at 0% (annuity due): $2,800

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Answer:

7 y /5

Step-by-step explanation:

To find the proportionality of a table, you need to determine if the relationship between two variables in the table is proportional or not.

Calculating the ratio between each pair of data in a table allows you to determine whether a proportional relationship is there. The table depicts a proportionate relationship if all of those ratios are the same.

This can be done by dividing one variable by the other and checking if the ratio is equal for all data points in the table. If the ratio is constant, then the variables are proportional and the table is considered proportional.

Given that the question is incomplete and does not show the proportionality table, it is worth it to show how to find the proportionality of a table which would help solve the solution and gain knowledge.

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The question translated in English is:

Complete the following proportionality tables

Answer:

11 1/5

Step-by-step explanation:

3 1/5 ÷ 2/7 =

16/5 ÷ 2/7 =

KCF (Keep, Change, Flip)

Keep 16/5

Change ÷ to ×

Flip 2/7 to 7/2

16/5 × 7/2

16 x 7 = 112

5 x 2 = 10

112/10

11 2/10

11 1/5

Hope that helps :)

The domain and the range for the quadratic function in this problem are given as follows:

The function is defined for all real values, assuming values of -4 and greater, hence the domain and range are given as follows:

The problem asks for the domain and the range of the quadratic function in this problem.

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The complete statement is :-

DOMAIN is made up of inputs or x values while the RANGE is made up of outputs or y values.

In a relation R from set A to set B, we write,

R (a) = b

Here we put a relation on the input a and an output b comes.

Where,

a is an element from A and,

b is an element from B

Also, usually we always take x as the independent variable and y as the dependent variable.

Hence, we can say that,

Domain is made up of inputs or x values while range is made up of outputs or y values.

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The cost for Farris Pharmacy to store one bottle of Zithromax antibiotics is 8,005.

The given function is c(x)=5x+8000/x

We can calculate the cost for Farris Pharmacy to store one bottle of Zithromax antibiotics by using the provided equation C(x).

To find the cost of storing one bottle, we will simply set x equal to 1. Therefore, C(1) = 5(1) + 8,000/1 = 8,005.

This means that the cost for Farris Pharmacy to store one bottle of Zithromax antibiotics is 8,005.

Therefore, the cost for Farris Pharmacy to store one bottle of Zithromax antibiotics is 8,005.

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Answer: 14.60

Step-by-step explanation:

we have

14 3/5

This is a mixed number

we know that

A mixed number is a combination of a whole number and a fraction.

So

14 3/5 is equal to

14+3/5

where

14 is the whole number

3/5 is the fraction

3/5 = 0.60

14 + 3/5 = 14 + 0.60

therefore

= 14.60

the answer is

14.60

Answer:

-2 < a

Step-by-step explanation:

By unitary method 24 students/(64/9) yards squared times 1600 yards squared equals 5400 students.

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

Students traverse a total area of 40 yards by 40 yards, or 1600 yards.

24 kids covered an area of 8 ft x 8 ft, or (8 ft x 1 yd/3 ft)2 = [(8/3) yard]2 = (64/9) yd.

The number of students present is calculated by multiplying the number of students per yard, or 24 students/(64/9) yd2, by the area that students cover.

Therefore: 24 students/(64/9) yards squared times 1600 yards squared equals 5400 students.

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(a) Expected number of repairs per year is 0.33 (b) Standard deviation of number of repairs per year is 0.749, (c) The mean and standard deviation of annual expense are $136.55 and $26.217 respectively.

Standard deviation is a measure in statistics which measures the amount of deviation a set of data has with respect to their mean.

(a) Expected number of repairs for the freezer per year is the sum of the product of number of repairs to their probability.

E(Repairs) = (0 × 0.80) + (1 × 0.11) + (2 × 0.05) + (3 × 0.04)

                 = 0.33

(b) Standard deviation of number of repairs per year can be calculated as,

SD(Repairs) = \(\sqrt{[(0 - 0.33)^{2}(0.8)]+[(1-0.33)^{2}(0.11)] + [(2-0.33)^{2}(0.05)]+[(3-0.33)^{2}(0.04)] }\)

= √ (0.5611)

= 0.749

(c) Mean of the restaurant's annual expense with service contract is,

Mean = Expected cost = $125 + ($35 × 0.33) = $136.55

Standard deviation of the restaurant's annual expense with service contract is,

SD = \(\sqrt{35^{2}(0.5611) }\) = 35 × 0.759 = 26.217

Hence the expected number of repairs is 0.33, standard deviation of number of repairs is 0.749, mean and standard deviation of annual expense is $136.55 and $26.217 respectively.

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Answer: FALSE

Step-by-step explanation:

                                   1500 decagram = 15 kg

                                      1 decagram = 0.01 kg

                                       1500 decagram = 1500/0.01 kg

                                                                   = 1500/100 kg

                                        1500 decagram = 15kg  

Answer:

Mean Hypothesis is Mean values of the treatment and the control group is not equal

Step-by-step explanation:

The null hypothesis is mostly the problem statement.

Here the problem statement is

To check whether there is a difference in treatment result of two groups of patient; one which has received the treatment and the other is the control group.

Thus, the null hypothesis is

H0 - Mean values of the treatment and the control group is not equal

The Domain is (0, ∞) or {x | x > 0} and Range is  (-∞, ∞) or {y | y ∈ ℝ} with inequality notation.

To graph the function, we can plot the given points on a coordinate plane. The x-values in the table represent the input values (x), and the y-values represent the corresponding output values (f(x)).

Let's plot the points (x, y) from the table:

(1/125, -3)

(1/25, -2)

(1/5, -1)

(1, 0)

(5, 1)

(25, 2)

(125, 3)

Now, let's connect the points to create the graph of the function.

     |

     |

     |

     |

   3 |                   *

     |

     |

   2 |             *

     |

     |

   1 |       *

     |

     |

     | *

   0 |________________________

     -3  -2  -1   0   1   2   3

Based on the graph, we can observe that the function represents a logarithmic curve. As the x-values increase, the corresponding y-values increase logarithmically.

Domain:

The domain of a logarithmic function is the set of all positive real numbers (x > 0), since the logarithm of a negative number or zero is undefined. In this case, since all the x-values in the table are positive, the domain of f(x) is x > 0.

Domain notation:

Interval notation: (0, ∞)

Set-builder notation: {x | x > 0}

Range:

The range of a logarithmic function depends on its base. Since the base is not specified in the given information, we assume the common logarithm (base 10) as the default. The range of a common logarithmic function is all real numbers.

Range notation:

Interval notation: (-∞, ∞)

Set-builder notation: {y | y ∈ ℝ}

In summary: Domain: (0, ∞) or {x | x > 0} and Range: (-∞, ∞) or {y | y ∈ ℝ}

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Answer:

-1/3

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

Answer:

27,032 Rupees

Step-by-step explanation:

$1.09 x 400 = $436

$436 x 62 = 27,032

(Hope this helps and that it's not wrong ^-^)

Y in represents the following in this linear regression Y = α₀+α₁X+α₂X₂+ε: C. dependent variable.

In Mathematics and Geometry, a regression line is a statistical line that best describes the behavior of a data set. This ultimately implies that, a regression line simply refers to a line which best fits a set of data.

In Mathematics and Geometry, the general functional form of a linear regression can be modeled by this mathematical equation;

Y = α₀+α₁X+α₂X₂+ε

Where:

In conclusion, Y represent the dependent variable or response variable in a linear regression.

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a. Universal set `[MC(N-R)] × N` is equal to `

{(-8, 1), (3, 1), (6, 1), (-8, 2), (3, 2), (6, 2), (-8, 3), (3, 3), (6, 3), (-8, 4), (3, 4), (6, 4), (-8, 5), (3, 5), (6, 5), (-8, 6), (3, 6), (6, 6), (-8, 7), (3, 7), (6, 7), (-8, 8), (3, 8), (6, 8)}`.

a. Universal set

The universal set of a collection is the set of all objects in the collection. Given that

`N = {x|x is a natural number less than 9}`,

the universal set for this collection is the set of all natural numbers which are less than 9.i.e.

`U = {1,2,3,4,5,6,7,8}`

b. `[MC(N-R)] × N`

Let `M = {m - 10, 2, 3, 6}`,

`R = {4,6,7,9}` and

`N = {x|x is a natural number less than 9}`.

Then,

`N-R = {1, 2, 3, 5, 8}`

and

`MC(N-R) = M - (N-R) = {m - 10, 3, 6}`

Therefore,

`[MC(N-R)] × N = {(m - 10, n), (3, n), (6, n) : m - 10 ∈ M, n ∈ N}`

Now, substituting N, we get:

`[MC(N-R)] × N = {(-8, 1), (3, 1), (6, 1), (-8, 2), (3, 2), (6, 2), (-8, 3), (3, 3), (6, 3), (-8, 4), (3, 4), (6, 4), (-8, 5), (3, 5), (6, 5), (-8, 6), (3, 6), (6, 6), (-8, 7), (3, 7), (6, 7), (-8, 8), (3, 8), (6, 8)}`

Therefore,

`[MC(N-R)] × N = {(-8, 1), (3, 1), (6, 1), (-8, 2), (3, 2), (6, 2), (-8, 3), (3, 3), (6, 3), (-8, 4), (3, 4), (6, 4), (-8, 5), (3, 5), (6, 5), (-8, 6), (3, 6), (6, 6), (-8, 7), (3, 7), (6, 7), (-8, 8), (3, 8), (6, 8)}`

Thus,

`[MC(N-R)] × N` is equal to

` {(-8, 1), (3, 1), (6, 1), (-8, 2), (3, 2), (6, 2), (-8, 3), (3, 3), (6, 3), (-8, 4), (3, 4), (6, 4), (-8, 5), (3, 5), (6, 5), (-8, 6), (3, 6), (6, 6), (-8, 7), (3, 7), (6, 7), (-8, 8), (3, 8), (6, 8)}`.

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Answer:

11:27 am.

Step-by-step explanation:

The time which has passed when Tom overtakes Hazel is after Hazel has walked 1 hr 15 minutes and in that time Hazel has walked

1.25 * 4.8

= 6 km.

So, Tom runs 6 km in 10:15 - 9.39 = 36 minutes

= 0.6 hrs.

So, Tom's speed is 6/0.6 = 10 km/hr.

,

and Tom will take 18/10 = 1.8 hours to finish the route,

= 1 hr 48 minutes

So he finishes the route at

9:39 + 1:48

= 11:27 am.

Answer:

112.5°

Step-by-step explanation:

its the same as G, but I need to know if you have any measurements?

f=67.5 e=75  h=105

180-67.5= 112.5

since G and I are interior opposite angles then they are the same. So I equals 112.5  

Answer:

3 represents the hours and 6 represents the lawns

The coordinates mean that in 3 hours she'll get 6 lawns mowed.

Step-by-step explanation:

Lawn = 2 × hour

The expected value of the random variable X, given the probability mass function (pmf) f(X=n) = n(n+1)(n+2)/4, is E[X] = 2.

To find the expected value (mean) of a random variable, we need to multiply each possible value of the random variable by its corresponding probability and sum them up. In this case, we are given the pmf f(X=n) = n(n+1)(n+2)/4 for X.

To calculate E[X], we need to find the sum of n * f(X=n) over all possible values of n. Plugging in the given pmf, we have:

E[X] = Σ (n * f(X=n))

      = Σ (n * n(n+1)(n+2)/4)

      = Σ (n²(n+1)(n+2)/4)

By expanding and simplifying the expression, we can calculate the sum. However, a more efficient approach is to recognize that the sum represents the formula for the expected value of n(n+1)(n+2)/4, which is simply 2.

Therefore, we can conclude that E[X] = 2 based on the given pmf.

The expected value represents the average value we would expect to obtain if we repeated the random variable experiment many times. In this case, on average, the value of X would be 2.

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Therefore, the maximum displacement of the particle is 4 units, and it occurs at time t = 1.

To find the maximum displacement, we need to first determine the particle's velocity and acceleration.

The velocity of the particle is given by the derivative of its position function:

\(v(t) = y'(t) = 3t^2 - 12t + 9\)

The acceleration of the particle is given by the derivative of its velocity function: a(t) = v'(t) = 6t - 12

Now, to find the maximum displacement, we need to find the time at which the particle comes to rest.

This occurs when its velocity is zero:

\(3t^2 - 12t + 9 = 0\)

Simplifying this equation, we get:

\(t^2 - 4t + 3 = 0\)

This quadratic equation factors as:

(t - 1)(t - 3) = 0

So the particle comes to rest at t = 1 or t = 3.

Next, we need to determine whether the particle is at a maximum or minimum at each of these times.

To do this, we look at the sign of the acceleration:

When t = 1, a(1) = 6(1) - 12 = -6, which is negative.

Therefore, the particle is at a maximum at t = 1.

When t = 3, a(3) = 6(3) - 12 = 6, which is positive.

Therefore, the particle is at a minimum at t = 3.

Finally, we need to find the displacement of the particle at each of these times:

\(y(1) = 1^3 - 6(1)^2 + 9(1) = 4\)

\(y(3) = 3^3 - 6(3)^2 + 9(3) = 0.\)

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The rate of return for Nichole's investment is approximately 22%.

To calculate the rate of return, we need to determine the percentage increase in value from the initial investment to the final sale.

Nichole bought 500 shares at $8.24 per share, which amounts to a total investment of 500 * $8.24 = $4,120.

After one year, she sold all her shares for $10.10 per share, resulting in a total sale value of 500 * $10.10 = $5,050.

Her profit from the investment is $5,050 - $4,120 = $930.

To find the rate of return, we divide the profit by the initial investment and multiply by 100: ($930 / $4,120) * 100 ≈ 22.6%.

Therefore, her rate of return is approximately 22.6%, which corresponds to option A.

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The best point estimate for the average number of classes per semester for all students at the local college is 4, based on the study that found students completed an average of 4 classes per semester and the sample of 132 students that was taken.

Based on the information provided, the best point estimate for the average number of classes per semester for all students at the local college can be calculated as follows:
1. Identify the sample average: In this case, it is given that students completed an average of 4 classes per semester.
2. Determine the sample size: Here, the sample size is 132 students.
Since the point estimate is essentially the sample average, the best point estimate for the average number of classes per semester for all students at the local college is 4.

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Answer:

65 inches

Step-by-step explanation:

The solution to the equation is a = 3 1/3

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

a + 5 and two-thirds = 9

Express properly

So, we have

a + 5 2/3 = 9

Subtract 5 2/3 from both sides of the equation

This gives

a = 9 - 5 2/3

Evaluate the difference

a = 3 1/3

Hence, the solution is a = 3 1/3

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The height and radius that minimize the amount of material needed to manufacture the can are given by h = 500 / ((500/π)^(2/3)) , r = (500/π)^(1/3)

To minimize the amount of material needed to manufacture the can, we can consider the volume of the cylindrical can as the objective function to minimize.

Let's denote the height of the can as "h" and the radius of the base as "r". The volume of a cylinder is given by the formula V = πr^2h, where V is the volume, r is the radius, and h is the height.

We need to find the values of r and h that satisfy the condition of holding 500 cm^3 of liquid while minimizing the surface area of the can. The surface area of the can consists of the curved surface area and the area of the circular base.

To minimize the surface area, we can use the constraint that the volume is 500 cm^3 to eliminate one variable.

From the volume equation, we have:

πr^2h = 500

Solving for h, we get:

h = 500 / (πr^2)

Now, we can substitute this value of h in terms of r into the surface area formula, which is given by:

A = 2πrh + πr^2

Substituting the value of h, we have:

A = 2πr(500 / (πr^2)) + πr^2

A = (1000/r) + πr^2

To minimize the surface area, we need to find the value of r that minimizes A. We can do this by finding the critical points of A, which occur when the derivative of A with respect to r is equal to zero.

Differentiating A with respect to r, we have:

dA/dr = -1000/r^2 + 2πr

Setting this derivative equal to zero and solving for r, we get:

-1000/r^2 + 2πr = 0

-1000 + 2πr^3 = 0

2πr^3 = 1000

r^3 = 500/π

r = (500/π)^(1/3)

Substituting this value of r back into the equation for h, we get:

h = 500 / (π((500/π)^(1/3))^2)

h = 500 / ((500/π)^(2/3))

Therefore, the height and radius that minimize the amount of material needed to manufacture the can are given by:

h = 500 / ((500/π)^(2/3))

r = (500/π)^(1/3)

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There are many questions and problems for which efficient algorithms exist, but there are also many others for which no efficient algorithm is currently known, and some for which it has been proven that no algorithm can exist.

The field of computer science and mathematics known as computational complexity theory studies which problems can be solved by algorithms and how efficient those algorithms are. The theory classifies problems into different complexity classes based on the resources required to solve them, such as time, space, or the number of processors.

There are certain classes of problems for which efficient algorithms are known to exist. For example, sorting a list of numbers or searching for an item in a database can be done in polynomial time, which means that the time required to solve the problem grows at most as a polynomial function of the size of the input.

On the other hand, there are problems for which no efficient algorithm is currently known. One famous example is the traveling salesman problem, which asks for the shortest possible route that visits a set of cities and returns to the starting point. While algorithms exist to solve this problem, they have an exponential running time, meaning that the time required to solve the problem grows exponentially with the size of the input, making them infeasible for large inputs.

There are also problems for which it has been proven that no algorithm can exist that solves them efficiently. For example, the halting problem asks whether a given program will eventually stop or run forever. It has been proven that there is no algorithm that can solve this problem for all possible programs.

In summary, there are many questions and problems for which efficient algorithms exist, but there are also many others for which no efficient algorithm is currently known, and some for which it has been proven that no algorithm can exist.

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32 x 134

Partial product: Multiply each digit of 32 by each digit of 134, maintain each digit place.

(30x100) + (30x 30) + (30 x4)+ (2 x 100) + (2x30) + (2 x 4)

3,000 + 900+120+200+60+8 = 4,288