It takes 4 minutes to complete an administrative task. There are 60 seconds in 1 minute. How many seconds does it take to complete the same task?

slope = -5, y intercept = 2

The graph is below.

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Work Shown:

20x+4y = 8

4y = 8-20x

4y = -20x + 8

y = (-20x+8)/4

y = -20x/4 + 8/4

y = -5x + 2 is the final answer

slope = -5, y intercept = 2

Two points on this line are (0,2) and (1, -3)

The graph is below. I used GeoGebra to make it, but Desmos is another good choice.

The equation of the line in point-slope form that passes through (1, -7) and has a slope of -2/3 is y + 7 = -2/3(x-1). Correct option is B.

The point-slope form of a linear equation is given by:

y - y₁ = m(x - x₁)

where m is the slope of the line and (x₁, y₁) is a point on the line.

We are given a point (1, -7) that the line passes through and a slope of -2/3. Therefore, we can substitute these values into the point-slope form equation to obtain:

y - (-7) = (-2/3)(x - 1)

Simplifying this equation, we get:

y + 7 = (-2/3)x + (2/3)

Taking 2/3 common from right sides, we get:

y + 7 = -2/3(x-1)

Therefore, Correct option is B.

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The amount of sand Eloise will put in each sandbox is 7.5 pounds (30 divided by 4).

The temperature at the end of 5 minutes is given as 87.09 F

71 = 60 + (135 - 60) * e^(-2k)

11 = 75 * e^(-2k)

e^(-2k) = 11/75

-2k = ln(11/75)

k = -0.5 * ln(11/75) ≈ 0.2036

Now we have the value of k, we can find the temperature of the object at the end of 5 minutes, T(5):

T(5) = 60 + (135 - 60) * e^(-0.2036 * 5)

T(5) = 60 + 75 * e^(-1.018)

T(5) ≈ 60 + 75 * 0.3612

T(5) ≈ 60 + 27.09

T(5) ≈ 87.09

The temperature at the end of 5 minutes is given as 87.09 F

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The surface area of the given composite figure is: 484.38 cm²

The formula for the area of a rectangle is:

Area = Length * Width

The formula for the area of a square is:

Area = side * side

The surface area is simply the area of each of the surfaces of the figure.

Thus, surface area of the given composite figure is:

4(13 * 10) + (10 * 10) + (10 * 10) - 3π(5²))

= 484.38 cm²

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The three equivalent numerical expressions are  1/32, 0.03125, 3.125 x 10^-2

Using the exponential rules, we can simplify the expressions as:

(2^-3)(2^5)/2^7)

= 2^(5-3)/2^7

= 2^2/2^7

= 1/2^(7-2)

= 1/2^5

= 1/32

Therefore, three equivalent numerical expressions for the given expression are: 1/32, 0.03125, 3.125 x 10^-2

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The most likely number of minutes of usage recorded by Jason is A . approximately 50.

We can see that initially, the temperature of the electronic system began to increase as the time increased. It then began to decrease from the 20 minute and ketp decreasing till the 40th minute.

Assuming that the temperature keeps decreasing, it would mean that at 50 minutes, the temperature would be more than the temperature at 40 minutes and so would most likely be 48 degrees.

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The area of the curve in the first quadrant is A = 2/7 units²

Given data ,

Let the region described is bounded by the curves y = x^(2/5) and y = 1 be in the first quadrant

Now , the point of intersection of these two curves is given by

x^(2/5) = 1

x = 1^5

So the two curves intersect at x = 1

Now , the area of the curve is given by y = x^(2/5) is the lower curve and y = 1 is the upper curve in the given interval [0, 1]

And , the , integral is used to find the area

∫[from 0 to 1] (1 - x^(2/5)) dx

∫(1 - x^(2/5)) dx = x - (5/7)x^(7/5) + C

Evaluated from 0 to 1, we get:

[(1 - (5/7)(1^(7/5))) - (0 - (5/7)(0^(7/5)))]

Simplifying further, we get:

[(1 - 5/7) - 0] = 2/7 units²

Hence , the area of the region bounded by the curves y = x^(2/5) and y = 1 in the first quadrant is 2/7 square units

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The factor that one should consider when choosing a career is D. All of the above.

In choosing a career, a student should consider the required education and training involved, the work environment, and their potential earnings.

Other factors to consider include:

Thus, all the listed factors should be considered when choosing a career.

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If you invest $2,000 at the end of each year for the next 30 years and earn an annual rate of return of 13%, you would have a total of approximately $75,994.18 saved for retirement.

To calculate the future value of the investment, we can use the formula for the future value of an annuity:

[tex]FV = PMT \times \dfrac{((1 + r)^{n - 1})} { r}[/tex]

where PMT is the annual payment, r is the annual interest rate, and n is the number of periods.

In this case, we have PMT = $2,000, r = 0.13 (since the stock market has earned 13% per year), and n = 30 (since we are investing for 30 years).

Plugging in the values, we get:

FV = $2,000 x ((1 + 0.13)³⁰ - 1) / 0.13

= $2,000 x (4,919.04) / 0.13

= $75,994.18

Therefore, a total of about $75,994.18 would be saved for retirement if you invested $2,000 at the end of each year for the next 30 years and saw a 13% annual return.

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Evaluating the expression (x - 2)/(x - 1) = (x - 1 + 2)/(x + 1)(x - 1), we get x = 1

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

(x - 2)/(x - 1) = (x - 1 + 2)/(x + 1)(x - 1)

Evaluating the like terms, we have

(x - 2)/(x - 1) = (x + 1)/(x + 1)(x - 1)

Cancel out the common factors

So, we have

(x - 2) = 1

Add 2 to both sides

x = 3

Hence, the solution is 3

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Her rate loss in pounds per week is given as follows:

3.75 pounds per week.

Her rate loss in pounds per week is obtained applying the proportions in the context of the problem.

A proportion is applied as the rate loss is given by the division of the loss by the number of weeks.

The parameters are given as follows:

Hence the rate loss is given as follows:

r = 60/16

r = 3.75 pounds per week.

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Using the net, the correct surface area of the prism is 216 square units

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

The triangular prism

Using the net, the surface area is

Surface area = Sum of areas of individual shapes

So, we have

Surface area = 2 * 1/2 * 3 * 4 + 17 * 5 + 17 * 4 + 17 * 3

Evaluate

Surface area = 216

Hence, the surface area of the prism is 216 square units

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The value of the expression is 2x³ + 3x² - 27x + 40

It is important we know that algebraic expressions are described as expressions that are composed of factors, constants, variables, coefficients and terms.

Algebraic expressions are also made up of arithmetic operations, such as;

From the information given, we have;

1. (x + 5)(2x² -7x + 8)

expand the bracket

2x³ - 7x² + 8x + 10x² -35x + 40

collect like terms

2x³ - 7x² + 10x² + 8x - 35x + 40

Add the like terms

2x³ + 3x² - 27x + 40

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Answer: The correct answer is option A. a reference point.

Step-by-step explanation:

An reference point is required to determine whether or not an object moves.

The amount of wax needed to make 288 candles is  41472 inches³.

A company makes wax candles in the shape of a rectangular prism. Each candle is 6 inches long, 3 inches wide, and 8 inches tall.

Therefore, the amount of wax to make 288 candles can be calculated as follows:

Hence,

volume of each rectangular prism = 6 × 3 × 8

volume of each rectangular prism = 18 × 8

volume of each rectangular prism = 144 inches cube

Therefore,

1 candle =  144 inches cube

288 candles = ?

cross multiply

volume of wax for 288 candles = 288 × 144

volume of wax for 288 candles = 41472 inches³

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Answer:

-5.44

Step-by-step explanation:

Y/3.4+4.1 =2.5

Y+(3. 4)(4.1)/(3.4)=2.5

Y+13.94/3.4 =2.5 cross multiply (3.4)(2.5)to get

Y+13.94=8.5

Y=8.5-13.94

= (-5.44)

If the number of bacteria triples every 4 hours, then after 1 day (24 hours), the number of bacteria will triple 6 times.

Tripling a number 6 times is the same as multiplying it by 3 raised to the power of 6, or 3^6.

So, if there are 25 bacteria to start, the number of bacteria after 1 day will be:

25 x 3^6 = 25 x 729 = 18,225 bacteria.

Answer:

Step-by-step explanation:

It is not possible to accurately determine the number of bacteria in the glass after 4 hours without additional information such as the rate of bacterial growth, the environmental conditions, and whether any bacteria were removed or added during that time.

The slope of the line that cuts through the points (1, -5) and (3, 5) is equal to 2.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the slope formula, we have the following;

Slope (m) = (5 - (-5))/(3 - 1)

Slope (m) = (5 + 5)/(2)

Slope (m) = 10/2

Slope (m) = 2.

Based on the graph, the slope is the change in y-axis with respect to the x-axis and it is equal to 2.

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The ordered pairs to a solution for the given linear equation are (-1, 3.5) and (4, -4).

To find the ordered pair that is a solution to the equation 6x + 4y = 8, we can substitute the given value of x or y and solve for the other variable.

For the first option, substituting x = -1, we get:

6(-1) + 4y = 8

-6 + 4y = 8

4y = 14

y = 3.5

So, the ordered pair (-1, 3.5) is a solution to the equation.

For the second option, substituting y = -4, we get:

6x + 4(-4) = 8

6x - 16 = 8

6x = 24

x = 4

So, the ordered pair (4, -4) is a solution to the equation.

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Answer:

B. f(x) = 4x² + x - 3

Step-by-step explanation:

A quadratic is a second-degree polynomial. This means that the highest power that x is raised to is 2.

We can see that option B is the only one that meets this requirement. Option A is a third-power monomial, so it is not a quadratic. Option C is a linear function, so it is not a quadratic.

Answer:

relation 1-function

relation 2-not a function

relation 3-function

relation 4-funtion

a) The mean number of paintings owned by these five people is 40. b) No, the mean is not a good average to use to describe the number of paintings that these people own

a) To find the mean number of paintings owned, we add up all the values and divide by the total number of people:

Mean = (1+0+2+196+1)/5 = 40

Therefore, the mean number of paintings owned by these five people is 40.

b) No, The mean is not necessarily a good average to use to describe the number of paintings that these people own.

This is because the data is skewed by the one outlier value of 196, which is much larger than the other values.

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Answer:

10miles I think

Step-by-step explanation:

The required distance between, Nate's house and the restaurant is 7.5 miles.

From the graph,

Consider point C on the graph, which is 6  and 8 units apart from A and B respectively.

The distance between, Nate's house and the restaurant is given as,
AB = √[AC² + BC²]
AB = √[6² + 8²]
AB = 10 units

Now 1 unit = 3/4 miles
AB = 10 * 3/4
AB = 7.5 miles

Thus, the required distance between, Nate's house and the restaurant is 7.5 miles.

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The probability of landing on a white square is 4/5.

We have toss board of measurement 5 x 5.

Total squares in board = 25

White square = 20

Black square= 5

So, the probability of landing on a white square

= 20 / 25

= 4/5

Thus, the required probability is 4/5.

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The probability of flipping tails at least two times in three flips is 1/2.

When flipping a coin, there are two possible outcomes: heads or tails. Each flip is independent of the previous flips, so the probability of getting tails on any given flip is always 1/2 (assuming the coin is fair).

To find the theoretical probability of flipping tails at least two times in three flips, we can use the binomial probability formula:

P(x ≥ k) = 1 - P(x < k)

where P(x < k) is the probability of getting tails fewer than k times in three flips.

To find P(x < k), we can add up the probabilities of getting tails 0 times and getting tails 1 time:

P(x < 2) = P(0 tails) + P(1 tail)

P(0 tails) = (1/2)⁰ x (1/2)³ = 1/8

P(1 tail) = 3 x (1/2)  (1/2)² = 3/8 (since there are three ways to get exactly one tail: TTH, THT, HTT)

P(x < 2) = 1/8 + 3/8 = 1/2

Therefore, the probability of flipping tails at least two times in three flips is:

P(x ≥ 2) = 1 - P(x < 2) = 1 - 1/2 = 1/2

So the theoretical probability of flipping tails at least two times in three flips is 1/2 or 0.5 as a decimal.

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The picture for reduction and enlargement is attached

Scale factors are used to increase or decrease image. The situation of increment is usually called magnifying. while that of decrease is reduction.

The drawing of the the reduction is a square of side 8 units. The scale factor given is 1/2 hence we have the dimensions are as follows

preimage: 8 units x 8 units

image: 4 units x 4 units

The drawing of the the enlargement is a circle of radius 2 units. The scale factor given is 2, hence we have the dimensions are as follows

preimage: radius = 2 units

image: radius = 4 units

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The ratio of Murkas age to Ivans age is M : I = 6 : 1

Given data ,

Let Murkas age be M and Ivans age be I

Given that 1/3 of Murka's age is twice as much as Ivan's age

So ,

1/3 ( M ) = 2 ( I )

On simplifying the proportion , we get

Multiply by 3 on both sides , we get

M = 6 ( I )

Divide by I on both sides , we get

M / I = 6

Hence , the proportion is 6 : 1

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