Find the 20th term of the arithmetic sequence 4,10,16,22,28

Answer:

91 cents per ounce

Step-by-step explanation:

Divide 13.59 by 15

Answer: $0.91

Step-by-step explanation:

Take $13.59 divided by 15 = $0.91 per ounce

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(a) The total amount Bill ended up paying for the equipment, including the down payment and monthly payments, can be calculated by adding the down payment to the total amount paid through monthly payments over the years.

(b) To determine the amount of interest Bill paid on the loan, we need to subtract the initial loan amount (rest of the equipment cost after the down payment) from the total amount paid.

(a) The total amount Bill ended up paying for the equipment can be obtained by adding the down payment to the total amount paid through monthly payments. The down payment represents the initial contribution made towards the purchase, while the monthly payments gradually cover the remaining cost of the equipment over the years. By summing up these two amounts, we obtain the total amount paid by Bill for the lab equipment.

(b) To calculate the amount of interest Bill paid on the loan, we need to subtract the initial loan amount from the total amount paid. The initial loan amount corresponds to the cost of the equipment minus the down payment. This represents the principal amount that Bill borrowed to finance the purchase. By subtracting the principal amount from the total amount paid, we can determine the interest paid on the loan.

It's important to note that the specific values for the down payment, loan amount, and monthly payments are not provided in the question. To obtain the exact total amount paid and the interest paid, these values would need to be known or provided.

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Answer:

x=8

Step-by-step explanation:

The given limit can be expressed as the definite integral ∫[3π, 5π] cos(x) dx over the interval [3π, 5π].

To express the limit as a definite integral, we can rewrite the sum as a Riemann sum and take the limit as n approaches infinity.

The given sum can be written as:

lim(n → ∞) [Σ(i = 1 to n) cos(xi) Δxi],

where Δxi = (b - a) / n is the width of each subinterval, xi is a sample point in the i-th subinterval, and [a, b] is the interval [3π, 5π].

To express the limit as a definite integral, we can rewrite the sum using the definite integral notation:

lim(n → ∞) [Σ(i = 1 to n) cos(xi) Δxi] = ∫[3π, 5π] cos(x) dx,

where dx represents an infinitesimally small change in x. By taking the limit as n approaches infinity, the sum converges to the definite integral.

Therefore, the given limit can be expressed as the definite integral ∫[3π, 5π] cos(x) dx over the interval [3π, 5π].

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The best estimate of the product is b) 1 times 10.

The expression (7/8)8(1/10) can be simplified by canceling out the factor of 8 in the numerator and denominator. This yields the expression 7/10. Therefore, the best estimate of this expression would be 1 times 10, since 7/10 is closest to 1 when rounded to the nearest whole number, and 10 is the closest whole number to the denominator of 7/10.

Thus, the answer is option b, 1 times 10. It is important to note that when estimating products or other mathematical expressions, it is important to consider the context and choose an estimate that is reasonable and makes sense in the given situation.

Correct Question :

Which expression is the best estimate of the product of (7/8)8(1/10)?

a) 0 times 8

b) 1 times 10

c) 7 times 8

d) 1 times 8

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Answer:

No this is not a function because the x-values repeat. In a function you can have the the output duplicate but not the input. The input at 3 has duplicates s o this is not a function.

Step-by-step explanation:

Definition

A relation is called to be a function if every domain has an unique range

Here

As

f(3) has 2 corresponding values it's not a function

Answer:

A; 10

Step-by-step explanation:

What we can see here is that the triangles are similar.

Hence, the ratio of their sides are equivalent.

Thus, mathematically;

ED/BA = DF/AC = BC/EF

what we want to calculate is ED = x

Thus;

x/15 = 12/18

Cross multiply;

18 * x = 12 * 15

18x = 180

x = 180/18

x = 10

A quadratic regression equation for this set of data is y(x) = -69.27x² + 4921.02x - 37722.14.

For a selling price of 19.5 dollars, the profit is 31897.83.

In Mathematics, the standard form of a quadratic function is represented by the following equation;

ax² + bx + c = 0

Next, we would create a system of equation by using the data points provided above;

a(15.75)² + b(15.75) + c = 22602

248.06a + 15.75b + c = 22602    .....equation 1.

a(18.25)² + b(18.25) + c = 29017

333.06a + 18.25b + c = 29017    .....equation 2.

a(23.00)² + b(23.00) + c = 38820

529.00a + 23.00b + c = 38820    .....equation 3.

By solving the system of equations simultaneously, the values of a, b, and c are as follows;

a = -69.27

b = 4921.02

c = -37722.14

Therefore, the required quadratic function in standard form is given by;

ax² + bx + c = 0

y(x) = -69.27x² + 4921.02x - 37722.14

For a selling price of 19.5 dollars, the profit can be calculated as follows:

y(19.5) = -69.27(19.5)² + 4921.02(19.5) - 37722.14

y(19.5) = 31897.83.

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Answer:

6.25 hours

Step-by-step explanation:

4 sheep/30 minutes

50 sheep/? minutes

50/4= 12.5

12.5 x 30 min = 375 min

375 min x \(\frac{1hr}{60 min}\) = 6.25 hrs

The exchange rate of US dollars to Polish zloty is 1:3.1264. The correct option is b. 1:3.1264

From the question, we are to determine the exchange rate of US dollars to Polish zloty

From the given information,

Gary exchanged US dollars for Euros at a rate of 1:0.7716

That is,

1 US dollar = 0.7716 Euros

Also, he exchanged Euros for Polish zloty at a rate of 1:4.0518

That is,

1 Euro = 4.0518 Polish zloty

Now, we will find the value of 0.7716 Euros in Polish zloty

Since 1 Euro = 4.0518 Polish zloty

Then,

0.7716 Euro = 0.7716 × 4.0518 Polish zloty

∴ 0.7716 Euro = 3.1264 Polish zloty

But

1 US dollar = 0.7716 Euros

Therefore,

1 US dollar = 3.1264 Polish zloty

Hence, the exchange rate of US dollars to Polish zloty is 1:3.1264. The correct option is b. 1:3.1264

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The value of  Pw(w) and Fw(w) are (0, 0.4, 0.8, 1) for different random variable X. And E[W] = -E[X] = -0 = 0.

(a) To find Pw(w), we need to determine the probability that the transformed random variable W takes on a specific value w. In this case, W = -X.

Since W is the negative of X, the probability that W equals w is equal to the probability that X equals -w.

Pw(w) = P(X = -w)

Considering the CDF of X, we have the following intervals:

For -∞ < x < -3: Fx(x) = 0

For -3 < x < 5: Fx(x) = 0.4

For 5 < x < 7: Fx(x) = 0.8

For 7 < x < ∞: Fx(x) = 1

Since W = -X, we can rewrite the intervals as:

For ∞ < w < 3: Fw(w) = 0 (since X = -w is not within the range of X)

For -3 < w < -5: Fw(w) = 0.4

For -5 < w < -7: Fw(w) = 0.8

For -∞ < w < -7: Fw(w) = 1

(b) To find Fw(w), we need to determine the cumulative distribution function (CDF) of W. From the previous calculations:

For ∞ < w < 3: Fw(w) = 0

For -3 < w < -5: Fw(w) = 0.4

For -5 < w < -7: Fw(w) = 0.8

For -∞ < w < -7: Fw(w) = 1

(c) To find E[W], we need to calculate the expected value of W. Since W = -X, we can express E[W] as:

E[W] = E[-X] = -E[X]

We can use the CDF Fx(x) to find the expected value of X:

E[X] = ∫ x * f(x) dx

Using the intervals and probabilities from the CDF:

E[X] = (-3 * 0.4) + (0 * (0.8 - 0.4)) + (6 * (1 - 0.8))

E[X] = -1.2 + 0 + 1.2

E[X] = 0

Therefore, E[W] = -E[X] = -0 = 0.

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The limit is -243/75 or -3.24.

To compute the limit using the Maclaurin series for trigonometric and inverse trigonometric functions, express each term in the given expression using their respective series expansions. Break down each term:

1. The Maclaurin series expansion for tangent (tan) function is:

tan(x) = x + (x³)/3 + (2x⁵)/15 + (17x⁷)/315 + ...

Substitute 9x for x in this series expansion to get the Maclaurin series for tan(9x):

tan(9x) = 9x + (81x³)/3 + (2 x (729x⁵))/15 + (17 × (6561x⁷))/315 + ...

2. The Maclaurin series expansion for cosine (cos) function is:

cos(x) = 1 - (x²)/2 + (x⁴)/24 - (x⁶)/720 + ...

Again, substitute 9x for x in this series expansion to get the Maclaurin series for cos(9x):

cos(9x) = 1 - (81x²)/2 + (6561x⁴)/24 - (59049x⁶)/720 + ...

3. The cubic term, 243x³, does not require substitution or approximation.

Now, rewrite the given expression using the Maclaurin series for trigonometric and inverse trigonometric functions:

lim(x->0) [tan(9x) - 9x cos(9x) - 243x³]/75

= lim(x->0) [(9x + (81x³)/3 + (2 × (729x⁵))/15 + (17 × (6561x⁷))/315) - 9x(1 - (81x²)/2 + (6561x⁴)/24 - (59049x⁶)/720) - 243x³]/75

Now, simplify and collect the terms with the same power of x:

= lim(x->0) [(9x - 9x) + (81x³/3 - 81x³/2) + (2 × (729x⁵)/15) - (17 × (6561x⁷)/315) + (9x³/2) - (81x⁵/24) + (729x⁷/80) - (17 × (6561x⁷)/315) - 243x³]/75

The terms (9x - 9x) and (81x³/3 - 81x³/2) cancel out, leaving:

= lim(x->0) [(2 × (729x⁵)/15) - (17 × (6561x⁷)/315) + (9x³/2) - (81x⁵/24) + (729x⁷/80) - (17 × (6561x⁷)/315) - 243x³]/75

Now, simplify further and remove the common factor of x³ from the remaining terms:

= lim(x->0) [(2 × (729x²)/15) - (17 x (6561x⁴/315) + (9x/2) - (81x²/24) + (729x⁴80) - (17 x. (6561x⁴)/315) - 243]/75

Finally, take the limit as x

approaches 0 by directly substituting x = 0 into the expression:

= [(2 × (729(0)²)/15) - (17 x (6561(0)⁴)/315) + (9(0)/2) - (81(0)²/24) + (729(0)⁴/80) - (17 × (6561(0)⁴)/315) - 243]/75

= [-243]/75

Simplifying further:

= -243/75

Therefore, the limit is -243/75 or -3.24.

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Answer:

If you are asking to factorise..

Step-by-step explanation:

=> 5x² + 28x + 15

=> 5x² + (25+3)x + 15

=> 5x² + 25x + 3x + 15

=> 5x(x + 5) + 3(x + 5)

=> (x + 5)(5x + 3)

Answer:

5x² +28x+15

5x² +25x+3x+15

5x(x+5)+3(x+5)

(x+5)(5x+3)

By answering the presented question, we may conclude that I used the following procedures to produce this graph.

Mathematicians use graphs to visually display or chart facts or values in order to express them coherently. A graph point usually represents a connection between two or more items. A graph, a non-linear data structure, is made up of nodes (or vertices) and edges. Glue the nodes, also known as vertices, together. This graph contains vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical graphs (bar graphs, pie graphs, line graphs, and so on) are graphical representations of exponential development. a logarithmic graph shaped like a triangle.

I used the following procedures to produce this graph:

I classified the personnel as full-time, part-time, and temporary.

I estimated the proportion of employees who assessed the company's work-life balance as "very good" or "excellent" for each employee category, as well as the percentage who rated it as "good" or "fair/poor."

I used the following procedures to produce this graph:

I classified the personnel as full-time, part-time, and temporary.

I estimated the proportion of employees who assessed the company's work-life balance as "very good" or "excellent" for each employee category, as well as the percentage who rated it as "good" or "fair/poor."

I made the segmented bar graph using these percentages.

The graph was made using Excel technology. You may make a similar graph with Excel or any other software that supports segmented bar graphs.

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Organizations that build strategic information systems create systems that are paramount to business success. The correct option is(D).

Strategic information systems are those that support the long-term goals and objectives of an organization, aligning the use of technology with the strategic direction of the business. These systems provide a competitive advantage by enabling the organization to achieve its strategic goals and objectives more efficiently and effectively.

They typically involve the integration of different types of information systems, such as transaction processing systems, decision support systems, and executive information systems, to support the decision-making process at all levels of the organization.

By building strategic information systems, organizations can improve their overall performance, enhance their operational efficiency, and gain a competitive advantage in the marketplace.

Such systems can help organizations to better understand their customers, identify new market opportunities, improve supply chain management, and optimize business processes.

In today's rapidly changing business environment, strategic information systems are essential for organizations to remain competitive and achieve long-term success.

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Answer:

-6n-4+3<17

-6n-1<17

-6n<17+1

-6n<18

DIVIDE BOTH SIDE WITH THE COEFFICIENT OF n WHICH IS (-6)

-6n =18

-6 -6

n= -3

17.5 hours of sleep did he get on Saturday.

What is sleep ?

If Mr. Aubry's average amount of sleep for the week was 7.5 hours of sleep per night, then his total amount of sleep for the week was:

7.5 x 7 = 52.5 hours

To determine how many hours of sleep he got on Saturday, we can subtract the total amount of sleep he got on the other six days from the total amount of sleep for the week:

52.5 - 6 - 5 - 9 - 8 - 7.5 - ? = hours of sleep on Saturday

Simplifying the equation, we get:

? = 52.5 - 35

So, Mr. Aubry slept for:

? = 17.5 hours on Saturday.

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Answer:450

Step-by-step explanation:

450/100=4.5

Answer: 0.045

Step-by-step explanation:

4.5/100 = 0.045

(Check Work)

0.045 × 100 = 4.5

The probability of having three or more consecutive years with two or fewer compressor failures per year is about 6.16%.

Clark Property Management should expect to experience some consecutive years with higher compressor failure rates.

Let X represent the number of AC compressor failures. Thus, the probability distribution of X is as follows :

Number of Compressor Failures Probability (Relative Frequency)

0 0.061 0.132 0.253 0.284 0.205 0.076 0.01.

We will select two-digit random numbers from a table of random numbers. We will simulate 20 years of compressor failure.

As a result, there will be a total of 20 values of X, each representing a year's worth of data.

We may now determine whether it is typical to have three or more consecutive years with two or fewer compressor failures per year.

The Monte Carlo simulation is used to complete this task. We may use an online random number generator if a table of random numbers is not available.

Monte Carlo simulation is a statistical modeling method that employs random sampling techniques to simulate the output of a complicated system.

It is a stochastic modeling technique that allows for uncertainty and risk evaluation in complex systems where deterministic methods are insufficient.

Monte Carlo simulation generates random input values for a system with a mathematical model, allowing it to calculate possible outcomes.

These results are then used to generate probability distributions of potential results.

In essence, the Monte Carlo simulation is an experiment conducted on a computer that provides insight into the degree of risk related to decision-making.

1. Set up a model: Determine the system and create a mathematical model that will be utilized in the Monte Carlo simulation.

2. Define input values: Identify the variables that will affect the model's output and define input probability distributions for each.

3. Generate random numbers: Using the input probability distributions, generate random numbers for each variable

4. Run simulations: Run a large number of simulations using the random numbers generated in step 3.

5. Analyze the results: Using the outputs of the Monte Carlo simulation, estimate potential outcomes and the likelihood of different results.

6. Make decisions: Use the data and insights obtained from the Monte Carlo simulation to inform your decision-making.

After conducting the Monte Carlo simulation, it was determined that it is unusual to have three or more consecutive years with two or fewer compressor failures per year.

The probability of having three or more consecutive years with two or fewer compressor failures per year is about 6.16%.

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Answer:

60

Step-by-step explanation:

Step-by-step explanation:

Given:

An angle in radian measure is

Required:

Find the degree measure of the angle.

Explanation:

The radian measure is

To convert the radian measure multiply it by

Final Answer:

Option b is the correct answer.

Answer:

q=10sin(30)/sin(80)       (that is a fraction)

Step-by-step explanation:

simplify the equation using cross-multiplication:

sin(80)·q=10sin(30)

divide both sides of the equation by sin (80):

q=10sin(30)/sin(80)

Answer:

q ≈ 5.1

Step-by-step explanation:

Given

\(\frac{q}{sin30}\) = \(\frac{10}{sin80}\) ( cross- multiply )

q × sin80° = 10 × sin30° ( divide both sides by sin80° )

q = \(\frac{10sin30}{sin80}\) ≈ 5.1 ( to 1 dec. place )

The torque which is being created by the biceps is: O 27Nm flexion torque.

To calculate the torque created by the biceps, you need to consider the force and the perpendicular distance from the elbow joint.

The biceps are concentrically contracting with a force of 900N at a perpendicular distance of 3cm (0.03m) from the elbow joint.

To calculate the torque, you can use the formula: torque = force × perpendicular distance.

Torque = 900N × 0.03m = 27Nm

Therefore, the biceps are creating a 27Nm flexion torque. Answer is: O 27Nm flexion torque.

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