The graph of a line passes through the points (0, -2) and (6, 0). What is the equation of the line? CLEAR CHECK y = -2x + 6 y = 13x – 6 y = 3x – 2 y = 13x – 2

2025.8 = x  the cost of tuition as a function of x, the number of

years since 1990.

Linear function C(x) would be,

C(x) = 96 + 5(x - 1990)

(x is the year)

Now for x = 2002

C(2002) = 96..+ 5( 2002 - 1990)

C(2002) = 96 + 5(12)

C(2002) = 96 + 60

C(2002) =156

In year 2002 tution fee will be $238 per credit hour.

Now cost C(x) = 156

So,

456 = 98 + 10(x - 1990)

456- 98 = 10 (x - 1990)

358 = 10(x - 1990)

358/10 = x - 1990

35.8 + 1990 = x

2025.8 = x

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(a) To find the probability that 3 machines break in a two-week interval, we can use the Poisson distribution formula. In this case, the rate parameter λ is given as 1.5 per week, and we are interested in the number of breakdowns, which follows a Poisson distribution.

P(X = 3) = (e^(-λ) * λ^x) / x!

Plugging in the values, we have:

P(X = 3) = (e^(-1.5) * 1.5^3) / 3!

Calculate the expression to find the probability.

(b) The expected number of breakdowns in a four-week interval can be calculated by multiplying the rate parameter λ by the length of the interval. In this case, the rate is 1.5 per week, and the interval is four weeks.

Expected number of breakdowns = λ * interval

Calculate the expression to find the expected number.

(c) To find the probability of 3 breakdowns in the first two weeks and 6 breakdowns in the first 5 weeks, we can use the Poisson distribution for each interval separately. The probability of 3 breakdowns in the first two weeks is P(X = 3) as calculated in part (a). The probability of 6 breakdowns in the first 5 weeks is calculated similarly using the rate parameter for a 5-week interval.

Calculate the respective probabilities and multiply them to find the overall probability.

(d) The probability that the first breakdown occurs within the first week is equal to the rate parameter λ, which is given as 1.5 per week.

(e) The probability that the third breakdown occurs within the first 8 weeks can be calculated using the cumulative distribution function (CDF) of the Poisson distribution. We can subtract the probability of no breakdowns in the first 8 weeks and the probability of one or two breakdowns from 1 to find the probability of at least three breakdowns.

Calculate the expression to find the probability.

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Answer:

i have no clue

Step-by-step explanation:

To determine the forces developed in members FE, EB, and BC of the truss and whether they are in tension or compression, we need additional information such as the external loads applied to the truss and the geometry of the truss (lengths, angles, and supports).

Without specific details about the truss configuration and the applied loads, it is not possible to determine the forces and their nature (tension or compression) in the members accurately. Truss analysis requires information on the external forces and the geometry of the truss structure, including the lengths and angles of the members.

Each member in a truss can be subject to either tension or compression, depending on how the external loads and support conditions are distributed. The determination of forces in truss members involves solving a system of equilibrium equations considering the applied loads, supports, and member properties.

Therefore, to determine the forces and whether members FE, EB, and BC are in tension or compression, it is necessary to have more information about the truss, including the applied loads and the geometric properties of the truss members.

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Lengths of time it takes for new light bulbs to burn out are an example of continuous numerical data type.

Quantitative information that can be measured precisely and that can take on any value within a range is known as continuous numerical data. Measurements of length, time, weight, temperature, and many other quantifiable physical qualities are examples of continuous numerical data.

Continuous numerical data can have any value as long as it falls within a specified range, and using mathematical operations like addition, subtraction, multiplication, and division, it is possible to compare and analyze the numbers.

Since it alludes to a continuous range of precise numerical values. The duration of time in this scenario is expressed in hours, minutes, or seconds and can have any value within a specific range, for example, 0.5 hours, 1.25 hours, 2.75 hours, and so on.

Numerical data types like float and decimal can be used to represent continuous numerical data.

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Answer:

19 inches

Step-by-step explanation:

The rate is 3 inches per week. 4+3=7 and 7+3=10. To find the height for the fifth week, all you need to do is add 3 inches every week...

Week 3: 10+3=13

Week 4: 13+3=16

Week 5: 16+3=19

At the same rate, the plant will be 19 inches tall after the fifth week.

Hope this helps you out!! Have a great day!! C:

Answer:

19 inch

Step-by-step explanation:

because we use simple rule of three

2 inches ---------------- 5 miles

20inch -------------- xmiles

x = 100/2

x = 50

The economic order quantity (EOQ) for the switch connectors is approximately 97 units.

To determine the economic order quantity (EOQ) for the switch connectors, we can use the following formula:

EOQ = √((2 * Annual Demand * Order Cost) / Holding Cost)

Given the following information:

Annual Demand = 15,400 units

Holding Cost = $24 per unit

Order Cost = $74 per order

Plugging in the values into the formula, we get:

EOQ = √((2 * 15,400 * 74) / 24)

EOQ = √(227,200 / 24)

EOQ = √(9,466.67)

EOQ ≈ 97.28

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Answer:

The base of a power is the factor that is repeatedly multiplied by itself.

Answer:

1. $16

2.$61.75

3. $222

4.$130

Step-by-step explanation:

1.     20% of $20 is $4.

$20-$4=$16

2.    35% of $95 is $33.25.

$95-$33.25=$61.75

3.    $55.50 divided by 1-.75=222

4.     $78 divided  by 1-.40=130

Hope this helped :)

The probability of picking a red counter is therefore; 8/25.

Since the ratio of red to green is 2 :3 and there are 24 green counters, it follows that the number of red counters is;

x = (2/3)× 24 = 16 red.

The total of red and green is; 16 +24 = 40 which constitutes 80% of the total counters.

The total number of counters is therefore; 40/0.8 = 50 counters.

The probability of picking a red counter is therefore; 16/50 = 8/25.

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Answer:

22 feets

Step-by-step explanation:

From the diagram attached :

We have two similar triangles which can be related proportionally :

Hence ;

Mitchell's height / distance from mirror = cliff height / cliff distance

Michelle's height = 5.5

Michell's distance from mirror = 4

Cliff height = h

Cliff distance from mirror = 16

We have ;

5.5 / 4 = h / 16

Cross multiply :

4 * h = 5.5 * 16

h = 88 / 4

h = 22 feets

Answer:

75 in^2

Step-by-step explanation:

Given data

From the figure

We can see a rectangle and a triangle

The area of the rectangle is

Area= L*W

Area= 13*5

Area= 65 in^2

Area of the triangle

Area= 1/2b*h

Area= 1/2*4*5

Area= 2*5

Area= 10 in^2

Hence the area of the composite figure is

Area= 65+10

Area= 75 in^2

Answer:

A

Step-by-step explanation:

if we simplify 8/12 we would get 2/3.

which means 8/12 is an equivalent fraction so comparing them would give us the same value which is true

Answer:

12x - 8y

Step-by-step explanation:

Combine like terms.

10x - 5y + 2x -3y =

= 10x + 2x - 5y - 3y

= 12x - 8y

The function h(x) = 4x + 1 does not have a point where the slope equals 3.

The function h(x) is defined as h(x) = 4x + 1. To find where the slope of the function is equal to 3, we need to find the x-value(s) that satisfy this condition.

The slope of a function represents how steep the function is at a given point. In this case, the slope of h(x) is equal to the coefficient of x, which is 4. To find where the slope equals 3, we need to find the x-value(s) that make the coefficient of x equal to 3.

Setting the coefficient of x equal to 3, we have:

4 = 3

To solve for x, we subtract 1 from both sides:

4 - 1 = 3 - 1
3 = 2

This equation is not true, which means there is no x-value that makes the slope of h(x) equal to 3. Therefore, the answer is none of the given options (OX = 1, X = 2, x =3, X = 4).

In summary, the function h(x) = 4x + 1 does not have a point where the slope equals 3.

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Answer:

take the output and take away from the the input

Step-by-step explanation:

The area of the polygon is 80 units².

What is a Polygon?

A polygon is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its edges or sides.

Dividing the polygon into parts marked in the attached figure so as to calculate the area easily.

For triangle, DEF

Area = \(\frac{1}{2} bh\)

        = \(\frac{1}{2}\) × 3 × 4

       = 6 units²

For triangle BCD

Area = \(\frac{1}{2}bh\)

        = \(\frac{1}{2}\) × 2 × 4

        = 4 units²

For trapezoid ABFG,

Area = \(\frac{1}{2} (a + b) h\)

        = \(\frac{1}{2}\) × (5.5 + 12) × 8

        = 70 units²

Hence, total area = 6 + 4 + 70

                             = 80 units².

Therefore, the total area of the polygon is 80 units².

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The correct choice is the sequence is not monotonic. The sequence is bounded. The sequence converges, and the limit is -2 (option c).

The given sequence (-2) does not vary with the index n, as it is a constant sequence. Therefore, the sequence is both monotonic and bounded.

Since the sequence is bounded and monotonic (in this case, it is non-decreasing), we can conclude that the sequence converges.

The limit of a constant sequence is equal to the constant value itself. In this case, the limit of the sequence (-2) is -2.

Therefore, the correct choice is:

OC. The sequence is not monotonic. The sequence is bounded. The sequence converges, and the limit is -2.

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The limit of the sequence is -2.

Given sequence is ((-2)}

To find the limit of the given sequence, we have to use the following formula:

Lim n→∞ anwhere a_n is the nth term of the sequence.

So, here a_n = -2 for all n.

Now,Lim n→∞ a_n= Lim n→∞ (-2)= -2

Therefore, the limit of the given sequence is -2.

Also, the sequence is not monotonic. But the sequence is bounded.

So, the correct choice is:

The sequence is not monotonic.

The sequence is bounded.

The sequence converges, and the limit is -2.

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The maximum profit is 6 and it is obtained when we mix 0.6 kg of type A, 0 kg of type B, and 0.4 kg of type C.

The optimal mix for the maximum profit can be found as follows:

The company mixes three types of toffees, A, B, and C. Let the weights of type A, B, and C be a, b, and c kg, respectively. Let us assume that we are making 1kg of toffee pack. Therefore, the weight of type C should be 1 - (a + b) kg. Also, the mixture must contain at least 300 gms of type A i.e a >= 0.3 kg

Also, the weight of the first two types (A and B) must be at least equal to the weight of type C, i.e a + b >= c. This condition can also be written as a + b - c >= 0

Let us now calculate the total cost of making 1kg of toffee pack.

Cost = 20a + 10b + 5c

If the pack is sold at Rs. 17, then the profit per 1kg of toffee pack is by

Profit = Selling Price - Cost = 17 - (20a + 10b + 5c)

Now we have the following linear programming problem:

Maximize P = 17 - (20a + 10b + 5c)

Subject to constraints: a + b + c = 1 (since we are making 1kg of toffee pack)

a >= 0.3a + b - c >= 0a, b, c >= 0

We can use the simplex method to solve this linear programming problem. However, to save time, we can solve it graphically. The feasible region is as follows:

We can see that the corner points of the feasible region are: (0.3, 0, 0.7), (0.6, 0, 0.4), (0, 0.5, 0.5), and (0, 1, 0).

Let us calculate the profit at each of these corner points. For example, at the point (0.3, 0, 0.7), we have a = 0.3, b = 0, and c = 0.7. Therefore, the profit is

P = 17 - (20(0.3) + 10(0) + 5(0.7)) = 3.5

Similarly, we can calculate the profit at the other corner points as well. The corner point (0.3, 0, 0.7) gives a profit of 3.5

Corner point (0.6, 0, 0.4) result in a profit of 6

Corner point (0, 0.5, 0.5) results in a profit of 5

Corner point (0, 1, 0) gives a profit of 3

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Answer:

m∠1 = 148°  and m∠2 = 32°

Step-by-step explanation:

m∠1 + m∠2 = 180°  (supplementary angles)

4x° + (x - 5)° = 180  (substitution)

4x + x - 5 = 180

5x - 5 = 180

5x = 185

x = 37

m∠1 = 4(37)° =148°  and m∠2 = (37 - 5)° = 32°

Answer:

The magnitude is sqrt((-4)^2 + (-9)^2) = 9.85. The angle is atan(-9/-4) = 180 deg + 66 deg = 246 deg = -114 deg.

Step-by-step explanation:

hope it help

Answer:

9.85

Step-by-step explanation:

|v|= √9²+(-4)²

=√81+16

=√97

|v|= 9.85

Answer:

The formula for the nth term of a geometric sequence is given by an = a1 * r^(n-1), where a1 is the first term and r is the common ratio.

In this case, a1 = -8 and r = -2. Therefore, we have:

a2 = a1 * r = (-8) * (-2) = 16

a3 = a2 * r = 16 * (-2) = -32

a4 = a3 * r = (-32) * (-2) = 64

So, the next three terms of the sequence are 16, -32, and 64.

Answer:

a₂ = 16

a₃ = -32

a₄ = 64

Step-by-step explanation:

The general formula for a geometric sequence is:

\(a_n=a_1 \cdot r^{n-1}\)

where:

Substitute the given values of a₁ and r into the formula to create an equation for the nth term:

\(\implies a_n=(-8) \cdot (-2)^{n-1}\)

To find the values of a₂, a₃ and a₄, substitute n = 2, n = 3 and n = 4 into the equation.

\(\begin{aligned}\implies a_2&=(-8) \cdot (-2)^{2-1}\\&=(-8) \cdot (-2)^{1}\\&=(-8) \cdot (-2)\\&=16\end{aligned}\)

\(\begin{aligned}\implies a_3&=(-8) \cdot (-2)^{3-1}\\&=(-8) \cdot (-2)^{2}\\&=(-8) \cdot (4)\\&=-32\end{aligned}\)

\(\begin{aligned}\implies a_2&=(-8) \cdot (-2)^{4-1}\\&=(-8) \cdot (-2)^{3}\\&=(-8) \cdot (-8)\\&=64\end{aligned}\)

There are 9,680 people living in the central region of the city.

To determine how many people live in the central region of the city, we need to use the probability distribution table and calculate the actual number of residents based on the proportions given.

According to the table, the proportions for the five different regions are:

- Region 1: 24,200

- Region 2: 24,200

- Region 3: 4,840

- Region 4: 4,840

- Region 5: 10,648

To find the number of people living in the central region, we need to add the proportions for Region 3 and Region 4, as they represent the central region.

Number of people in the central region = Region 3 + Region 4

        = 4,840 + 4,840 = 9,680

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The first step used in the elimination method is to align the coefficients of one chosen variable in both equations.

To solve a system of equations using elimination, the first step is to align the coefficients of one variable in both equations.

This involves multiplying one or both equations by a constant to create equal coefficients for the chosen variable.

This allows for easy elimination when adding or subtracting the equations.

Once the coefficients are aligned, you can proceed to the next step of eliminating one variable by adding or subtracting the equations.

After eliminating one variable, the resulting equation will have only one variable, which can then be solved for its value.

This value can be substituted back into either of the original equations to find the value of the other variable. Finally, the solution to the system of equations is the values of both variables.

In conclusion, the first step used in the elimination method is to align the coefficients of one chosen variable in both equations.

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Colin has lived by the biblical ideal of avoiding debt, purchasing the lowest item, repaying a loan, and being financially honest.

With an auto loan, you may borrow money from a bank and use it to purchase a vehicle. The loan must be repaid with interest over a defined period of time in fixed instalments from you.

Lenders will aim for a credit score of at least 750 when you apply for a vehicle loan.

The additional costs won't dramatically raise the price of the automobile because of the low interest rate. The periodic payments won't put undue strain on your current or next finances.

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Answer:

Infinitely many solutions.

Step-by-step explanation:

Multiply the second equation by -2, then add the equations together

(20x+2y=18)

−2(10x+y=9)  

20x+2y=18

−20x−2y=−18

Add these equations to eliminate x

0=0

Infinitely many solutions.

Given

Trigonometric function

Procedure