The total charge for a yearly internet DVD rental membership is $231. A registration fee of $15 is paid up front , and the rest is paid monthly. Write an equation to determine how much new members pay each month, m.
How much do new members pay each month,m.

The forecast for May using a five-month moving average is 39 (Option E).

Moving average is used for smoothing out time series data to find any trends or cycles within the data. A five-month moving average is the average of the past five months. To calculate the moving average, add up the sales for the previous five months and divide it by five.

According to the question, the sales for the previous five months are: Nov. 39 Dec. 27 Jan. 40 Feb. 42 Mar. 41 April 47

We have to add the sales of these five months, which gives:

27 + 40 + 42 + 41 + 47 = 197

To find the moving average for May, we divide this sum by 5:

197 / 5 = 39.4

Since we have to round the answer to the nearest whole number, we round 39.4 to 39, which is option E.

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Answer:

16

Step-by-step explanation:

\( \tan(x) = \frac{13}{46} \)

\( \tan {}^{ - 1} ( \frac{13}{46} ) = 16\)

The cylindrical coordinates of (−7, 7, 7) are (√98, -π/4, 7). cylindrical coordinate (−7, 7 3 , 1) is  (14, -π/3, 1).

We must switch from rectangular to cylindrical coordinates in the provided problem. (let r ≥ 0 and 0 ≤ θ ≤ 2π.)

A)(−7, 7, 7)

Given rectangular coordinates(x, y, z) =(−7, 7, 7)

The cylindrical coordinates are (r, θ, z)

As a result, we determine each value of r and θ  separately.

r = √x²+y²

r = √(-7)²+(7)²

r = √49+49

r = √98

θ = tan⁻¹ (y/x)

θ =tan⁻¹  (7/-7)

θ =tan⁻¹  (-1)

θ = -π/4

So cylindrical coordinate = (r, θ, z) = (√98, -π/4, 7)

B) (-7,7√3,1)

Given rectangular coordinates(x, y, z) = (-1,1,1)

The cylindrical coordinates are (r, θ, z)

As a result, we determine each value of r and θ  separately.

r = √x²+y²

r = √(-7)²(7√3)²

r = √49+147

r = √196

r = 14

θ = (y/x)

θ = (7√3/-7)

θ = (-√3)

θ = -π/3

So cylindrical coordinate = (r, θ, z) = (14, -π/3, 1)

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Answer:

5 months

Step-by-step explanation:

Given

\(c = 30m + 50\)

\(c = 20m + 100\)

Required [Missing from the question]

At what month will the cost be equal

To do this, we equate both expressions

\(c = c\)

This gives:

\(30m + 50 = 20m + 100\)

Collect like terms

\(30m - 20m = 100 - 50\)

\(10m = 50\\\)

Solve for m

\(m = \frac{50}{10}\)

\(m = 5\)

Answer:

15 pies sold and 10 cakes sold.

Step-by-step explanation:

Let p be the number of pies sold.  So, the number of cakes sold is 25-p.

5.99p + 9.99(25-p) = 189.75

5.99p + 249.75 - 9.99p = 189.75

4p = 60

p = 15

25 - p = 10

Answer:

A=13, b= 28, c= 6 d=22 e=31

Step-by-step explanation:

E = 15 +16 = 31

6 males like cats ( the middle section) so C = 6

d = 6 +16 = 22

a = 19-6 = 13

b = 50-22 = 28

so in order: a = 13, b = 28, c = 6, d = 22, e = 31

Answer:

A=13

B=28

C=6

D=22

E=31

Step-by-step explanation:

We can use the fact that the sum of all angles in a triangle is 180° to find the missing angles in both triangles.Therefore, the missing angles in ΔABC are ∠E = 47° and ∠F = 76°, and in ΔDEF is ∠D = 93°.

A geometric figure formed by two rays that share a common endpoint is termed as an angle. It is measured in degrees or radians and has different types based on its measure.

In ΔABC, we know that ∠A = 57° and that the other two angles are ∠E and ∠F. Therefore, we have:

∠A + ∠E + ∠F = 180°

57° + ∠E + ∠F = 180°

∠E + ∠F = 180° - 57°

∠E + ∠F = 123°

In triangle ΔDEF, we know that one angle is 40° and the other angle is ∠D. Therefore, we have:

∠D + 40° + ∠E = 180°

∠D + ∠E = 180° - 40°

∠D + ∠E = 140°

We now have two equations with two unknowns (∠E + ∠F = 123° and ∠D + ∠E = 140°). Solving the system of equations simultaneously gives us:

∠E = 47°

∠F = 76°

∠D = 93°

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Answer:

The first number line because a negative number plus a positive number would give you zero if the digit before the signs are the same (eg. -5+5=0)

A Box and Whisker Plot is a graphical representation of a dataset that displays the median, quartiles, and outliers of the data. To create a Box and Whisker Plot for the given dataset, we first need to find the minimum value, maximum value, median, and quartiles.

The minimum value in the dataset is 5, the maximum value is 34, and the median is the average of the two middle numbers, which are 11 and 12.5. Thus, the median is (11+12.5)/2 = 11.75. The lower quartile (Q1) is the median of the lower half of the dataset, which includes the numbers 5, 6, 7, 8, 10, and 11. Thus, Q1 is (7+8)/2 = 7.5. The upper quartile (Q3) is the median of the upper half of the dataset, which includes the numbers 17, 20, 21, 25, and 34. Thus, Q3 is (20+21)/2 = 20.5.

To create the Box and Whisker Plot, we draw a number line and label it with the minimum value, maximum value, and quartiles. We then draw a box from Q1 to Q3, with a vertical line at the median. Finally, we draw whiskers from the box to the minimum and maximum values, and we plot any outliers outside the whiskers.

In this case, the Box and Whisker Plot would have a box extending from 7.5 to 20.5, with a line at 11.75, representing the median. The whiskers would extend from 5 to 34, and there are no outliers.

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Answer:

b

Step-by-step explanation:

its b                                                                                                sooooooooooooooooooooooooooooo

Answer:

liked = 45 ; disliked = 18

Step-by-step explanation:

Let the number of songs he liked be x & disliked be y.

The ratio of x & y :-

\( \frac{x}{y} = \frac{5}{2} \\ = > 2x = 5y \: \: \: \: \)

And total number of songs he listened = 63

Then, x + y = 63...................eqn.1

=> x = 63 - y

Substituting the value of x in eqn. 2x = 5y gives :-

2(63 - y) = 5y

=> 126 - 2y = 5y

=> 7y = 126

=> y = 18

Substituting the value of y in eqn.1 gives

x = 63 - 18

= 45

Hence no. of songs he liked = 45 & disliked = 18

The validity of Universal Modus Tollens relies on the validity of Universal Instantiation and Modus Tollens, which are well-established logical rules.

The validity of the Universal Modus Tollens can be derived from the validity of Universal Instantiation and Modus Tollens. Let's examine the logic behind each of these rules and how they lead to the validity of Universal Modus Tollens.

Universal Instantiation (UI): This rule allows us to infer a specific instance of a universally quantified statement. For example, if we have the universal statement "For all x, if P(x) then Q(x)," we can instantiate it to a particular instance by replacing the variable x with a specific element, resulting in "If P(a) then Q(a)." This rule is valid and widely accepted in formal logic.

Modus Tollens (MT): Modus Tollens is a deductive rule of inference used to infer the negation of the consequent of a conditional statement. It states that if we have a conditional statement "If P, then Q," and we know the negation of Q (¬Q), we can conclude the negation of P (¬P). This rule is also valid and widely accepted.

Now, let's demonstrate how the validity of Universal Instantiation and Modus Tollens leads to the validity of Universal Modus Tollens:

Universal Modus Tollens (UMT): If we have the universally quantified statement "For all x, if P(x) then Q(x)," and we know the negation of Q for a specific instance, ¬Q(a), then we can conclude the negation of P for that same instance, ¬P(a).

To derive UMT, we can apply the following steps:

Apply Universal Instantiation (UI) to the universally quantified statement, replacing x with a specific element, let's say a. This gives us "If P(a) then Q(a)."

Assume the negation of Q for that specific instance, ¬Q(a).

Apply Modus Tollens (MT) to the conditional statement "If P(a) then Q(a)" and the negation of Q, which allows us to conclude the negation of P, ¬P(a).

Thus, by using Universal Instantiation to instantiate a universally quantified statement, and then applying Modus Tollens to the instantiated conditional statement and the negation of the consequent, we can derive Universal Modus Tollens.

It's important to note that the validity of Universal Modus Tollens relies on the validity of Universal Instantiation and Modus Tollens, which are well-established logical rules.

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Answer:

Set 16/2000 = x/5000 and solve for x. = 40 trees saved.

Step-by-step explanation:

Answer: the answer would be 42.5 but i’m assuming that you would round.

Step-by-step explanation:

2000/ 17 = 5000/ x

cross multiply

85,000 = 2,000x

simplify(divide by 2000)

x= 42.5

the center of the ball rests on the table which implies that the y-coordinate of the center of the ball is zero since we have selected the table as the reference plane

the bottom of the ball as its reference point, the y-axis along a vertical line, and the positive direction as pointing upward can be calculated as follows:The y-coordinate of the ball = (y-coordinate of the center of the ball) - (the radius of the ball)As per the given problem, the center of the ball rests on the table which implies that the y-coordinate of the center of the ball is zero since we have selected the table as the reference plane.Hence, the y-coordinate of the ball = 0 - 2= -2Therefore, the y-coordinate of the ball is -2.

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Answer: 15

Step-by-step explanation:

Answer:

\(\sqrt{160}\)

Step-by-step explanation:

\(a^{2} +b^{2} =c^{2} \\4^{2} +12^{2} =c^{2} \\16+144=c^{2} \\160=c^{2}\\\sqrt{160}=\sqrt{c^{2} }\)

Hope this helps

Answer:

a) 1.07, b) 0.1423

Step-by-step explanation:

please mark me as brainlest

The appropriate hypotheses

Н0 = μ = 23.9

HA = μ > 23.9

The first step in hypothesis testing is to state the null hypothesis (H0) and the alternative hypothesis (HA). In this case, the null hypothesis is that the mean age at which men first marry has not changed since 1960. The alternative hypothesis is that the mean age at which men first marry has increased since 1960.

H0 = μ = 23.9

HA = μ > 23.9

If the sample mean age is significantly greater than 23.9 years, we would reject the null hypothesis and conclude that there has been an increase in the mean age at which men first marry in the region since 1960.

If the sample mean age is not significantly greater than 23.9 years, we would fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the mean age at which men first marry has increased since 1960.

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Reason:

Vertical angles form after intersecting two lines in an X shape. The vertical angles are opposite one another. They do not have to be vertically aligned.

The other pair of vertical angles are ADB and XDF.

Vertical angles are always congruent.

Using the speed formula we know that the speed of the runner is 7.55 m/s.

Speed is calculated as follows: speed = distance/time.

Knowing the units for distance and time is necessary to calculate the units for speed.

The units will be in meters per second (m/s) in this example since the distance is measured in meters (m) and the time is measured in seconds (s).

For instance, if a car drives 120 miles in 2 hours, we may calculate the speed as 120 x 2 = 60 miles per hour.

So, we know that the speed formula is:

Speed = distance/time

Distance = 275-50 = 225 meters

Time = 29.8 sec

Now, place the values in the formula as follows:

Speed = distance/time

Speed = 225/29.8

Speed = 7.55 m/s

Therefore, using the speed formula we know that the speed of the runner is 7.55 m/s.

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Fatima's monthly payment would be $466.57 if she decided to buy a $25,000 car and wanted to own it after 5 years at a 4.7% interest rate.

To calculate Fatima's monthly payment for a $25,000 car loan at a 4.7% interest rate over 5 years, we can use the formula for the monthly payment on a fixed-rate loan:

\(P = (r * A) / (1 - (1 + r)^{(-n)})\)

Where:

P = monthly payment

r = monthly interest rate (which is the annual interest rate divided by 12)

A = total loan amount

\(n = total number of months of the loan term (which is the number of years multiplied by 12)\)

Plugging in the given values, we get:

A = $25,000

r = 4.7% / 12

r = 0.00392 (monthly interest rate)

\(n = 5 years * 12\)

\(n = 60 months\)

P = \((0.00392 * $25,000) / (1 - (1 + 0.00392)^{(-60)})\)

P = \((98)/ (1-(1.00392)^{(-60)})\)

P ≈ $466.57

Therefore, Fatima's monthly payment for the car loan would be approximately $466.57.

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Answer:

Commutative property

Step-by-step explanation:

addition is commutative for example 2+3=3+2

multiplication is also commutative 3*2=2×3

Experiment with different combinations and flavors to create unique and delicious passed appetizers using the leftover ingredients.

When utilizing leftover raw salmon, dairy products, a baguette, and random herbs for passed appetizers, Dorothy has several options to consider. The choice between cold or hot appetizers will depend on her preferences and the available cooking equipment. Here are a few ideas for both cold and hot appetizers:

Cold Appetizers:

Salmon Bruschetta: Slice the baguette and top each slice with thinly sliced raw salmon. Add a dollop of herbed cream cheese or yogurt on top and garnish with fresh herbs.

Smoked Salmon Canapés: Cut the baguette into small rounds and top each with a spread of cream cheese or crème fraîche. Place a piece of smoked salmon on top and garnish with dill or chives.

Salmon Tartare: Finely chop the raw salmon and mix it with diced onions, capers, and a creamy dressing made with dairy products. Serve it on toasted baguette slices and garnish with herbs.

Hot Appetizers:

Salmon Croquettes: Combine leftover raw salmon with mashed potatoes, herbs, and breadcrumbs. Shape the mixture into small patties and pan-fry them until golden brown. Serve with a dip made from dairy products and herbs.

Salmon Stuffed Mushrooms: Remove the stems from large mushrooms and fill the caps with a mixture of cooked salmon, cream cheese, herbs, and breadcrumbs. Bake them until the mushrooms are tender and the filling is golden.

Salmon and Cream Cheese Puff Pastry Pinwheels: Roll out puff pastry dough and spread a layer of cream cheese mixed with herbs. Place strips of smoked salmon on top and roll the pastry into a log. Slice into pinwheels and bake until golden and puffed.

Remember to adjust the recipes based on the available ingredients and personal preferences. Experiment with different combinations and flavors to create unique and delicious passed appetizers using the leftover ingredients.

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A bicycle repair shop that offers two service packages: a tune-up and a complete overhaul.

The shop operates for 60 hours per week and receives an average of 180 bicycles each week. To analyze the capacity and utilization of the process, we need to consider the time taken at each stage and the demand for each service option. We'll break down the problem into multiple parts and provide a detailed explanation using mathematical terms.

a) Creating the Demand Matrix:

To create a demand matrix, we need to determine the number of bicycles going through each stage of the process. Let's denote the demand for tune-up as T and the demand for additional services as A.

Given that the average number of bicycles received per week is 180 and 25% of customers opt for additional services, we can calculate the demands as follows:

Demand for tune-up (T) = Total demand - Demand for additional services

T = 180 - (0.25 * 180)

T = 180 - 45

T = 135

Demand for additional services (A) = 0.25 * Total demand

A = 0.25 * 180

A = 45

Now, we can create a demand matrix based on the demand for each service option:

Demand Matrix:

Tune-up Additional Services Wheel Balancing

Tune-up  [135  0  0]

Additional [0  45  0]

Services

Total [ 135  45  0 ]

The demand matrix shows the number of bicycles flowing through each stage of the process.

b) Daily Capacity at Each Stage:

To calculate the daily capacity at each stage, we need to consider the time taken for each service option. Given that the shop operates for 60 hours per week, we can calculate the daily capacity at each stage:

Tune-up technician time per bicycle (\(T_{tuneup}\)) = 75 minutes

Additional services technician time per bicycle (\(T_{additional}\)) = 72 minutes

Wheel balancing specialist time per bicycle (\(T_{balancing}\)) = 20 minutes

Daily Capacity (C) = (60 hours * 60 minutes) / (\(T_{tuneup}\) + \(T_{additional}\) + \(T_{balancing}\))

Substituting the given values:

C = (60 * 60) / (75 + 72 + 20)

C = 21600 / 167

C ≈ 129.34 bicycles per day

Therefore, the daily capacity at each stage of the process is as follows:

Tune-up: 129 bicycles per day

Additional Services: 129 bicycles per day

Wheel Balancing: 129 bicycles per day

c) Implied Utilizations:

To find the implied utilizations, we need to compare the demand and the capacity at each stage of the process. Utilization can be calculated as the demand divided by the capacity.

Implied Utilization (U) = Demand / Daily Capacity

For the Tune-up stage:

\(U_{tuneup}\) = 135 / 129 ≈ 1.05

For the Additional Services stage:

\(U_{additional}\) = 45 / 129 ≈ 0.35

For the Wheel Balancing stage:

\(U_{balancing}\) = 0 / 129 = 0

The implied utilizations show how efficiently each stage of the process is being utilized. Utilization values greater than 1 indicate that the stage is operating beyond its capacity.

d) Weekly Capacity of the Process:

To calculate the weekly capacity of the process, we multiply the daily capacity by the number of days the shop is open per week:

Weekly Capacity = Daily Capacity * Number of days shop is open per week

Given that the shop is open for 60 hours per week, the number of days the shop is open per week can be calculated as follows:

Number of days shop is open per week = 60 hours / 24 hours per day = 2.5 days

Therefore, the weekly capacity of the process is:

Weekly Capacity = Daily Capacity * Number of days shop is open per week

Weekly Capacity = 129 bicycles per day * 2.5 days

Weekly Capacity = 322.5 bicycles per week

e) Flow Rate and Constraint Analysis:

To determine if the flow rate of the process is capacity-constrained or demand-constrained, we compare the weekly capacity to the demand for each service option.

Demand for Tune-up (\(T_{demand}\)) = 135 bicycles per week

Demand for Additional Services (\(A_{demand}\)) = 45 bicycles per week

Comparing the demands with the weekly capacity:

\(T_{demand}\) < Weekly Capacity (135 < 322.5)

\(A_{demand}\) < Weekly Capacity (45 < 322.5)

Since both the demands for tune-up and additional services are less than the weekly capacity, the flow rate of the process is demand-constrained. This means the shop has the capacity to handle the current demand without operating beyond its limits.

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The number of individuals in Chicago that will respond positively to Program 2 is 22 out of 25.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.

Given that the chances of a positive response from Chicago residents to two government programs are 65.9% for Program 1 and 87.5%  for Program 2, the likelihood of a positive response for Program 2 given that the person is from Los Angeles must be calculated as follows:

87.5 100 = X

43.75 / 50 = X

21.875 / 25 = X

Therefore, 22 out of 25 individuals in Chicago  will respond positively to Program 2.

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