Which set of ordered pairs represents a function?
A. {(1,3), (3,5), (5,7), (7,5), (5,3)}
B. {(6, 1), (6,2), (6,3), (6,4),(6,5)}
C. {0, 1), (2, 1), (4, 1), (6, 1), (8, 1)}
D. {(1,3), (2,3), (3, 3), (3, 2), (2, 1)}

Answer: π

Step-by-step explanation:

To convert from degrees to radians, you want to multiply the degrees by (π/180). In this case, we would multiply 180° by (π/180).

\(180*\frac{\pi }{180} =\pi\)

Answer:

d: distributive

Step-by-step explanation:

8 ( 8 + 7 ) = 6 x 8 + 6 x 7, it may seem like commutative, except it pulls the parentheses  out making it distributive.

The marginal revenue function, locate the demand function is P = 0.02x² -0.025x + 152 when R'(x) = 0.06x² - 0.05x + 152.

Given that,

We have to find for the marginal revenue function, locate the demand function.

Remember that the income is zero if no things are sold:

R'(x) = 0.06x² - 0.05x + 152

p(x) is what.

We know that,

MR = dTR/dx = 0.06x² - 0.05x + 152

Integrating the marginal revenue function , we get total revenue function,

MR = TR

= (0.06x²⁺¹)/(2+1) - (0.05x¹⁺¹)/(1+1) + 152x

= (0.06x³)/3 - (0.05x²)/2 + 152 x

TR  = 0.02 x³ - 0.025 x² + 152 x

TR = (P)(Q) = (P)(x) =  0.02 x³ - 0.025 x² + 152 x

P = ( 0.02 x³ - 0.025 x² + 152 x)/x

P = 0.02x² -0.025x + 152

Therefore, The marginal revenue function, locate the demand function is P = 0.02x² -0.025x + 152 when R'(x) = 0.06x² - 0.05x + 152.

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The compound inequality that correctly shows the amount of money, m, the teacher can spend if the monthly budget for entertainment is between 5% and 10% is given as follows:

$154.17 ≤ m ≤ $308.33.

The total bi-weekly pay of the teacher is given as follows:

$1,541.65.

A bi-weekly pay means that the teacher is paid twice a month, hence, applying the proportion, his monthly payment is given as follows:

2 x 1541.65 = $3,083.3.

The lowest amount that can be spent on entertainment is 5% of that, hence:

0.05 x 3083.3 = $154.17.

The highest amount that can be spent on entertainment is 10% of that, hence:

0.1 x 3083.3 = $308.33.

These two values are the bounds of the compound inequality.

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The correct answer is B. \(16 m^{2}\)

Explanation:

In a flat squared surface such as the one of a shed, the area is calculated by multiplying two sides. In this case, the side is 4 meters long, and therefore the formula to calculate the area is  A (area) = side x side

A = 4 meters x 4 meters

A=  (4 x 4) (m x m)

A= 16 \(m^{2}\)

This means the correct answer is B because this shows the correct number of meters in the area (16) and using square meters or \(m^{2}\) is the correct unit to express the area or measurement of a surface.

Answer:

0.71, 78%, 0.8, \(\frac{7}{8}\)

Step-by-step explanation:

78% = 0.78

7/8 = 0.875

Answer:

x-intercept is 5

y-intercept is -3

Step-by-step explanation:

For the x-intercept:

\(3x - 5(0) = 15\)

\(3x = 15\)

\(x = 5\)

For the y-intercept:

\(3(0) - 5y = 15\)

\( - 5y = 15\)

\(y = - 3\)

Answer:

Y intercept= -3

x-intercept = 5

Step-by-step explanation:

So you would want to get your y alone for it to be in slome intercept form (y=mx+b) so you would:

1. Subtract 3x from both sides to get -5y= -3x+15

2. then you would divide each side by -5 to get y= \(\frac{3}{5}\) x -3

And since in slope intercept form, b= the y-intercept, The y-intercept =-3 and to find the x-intercept you would have to solve for y=0 in your new-found equation.

sorry if this was long

Answer:

3

Step-by-step explanation:

Answer:

Total amount = $150160.24

Step-by-step explanation:

The amount deposit by the Bob annually (annuity) = $900

Number of years for which annuity made = 12 years

Inerest rate = 7.6% or 0.076

After 35 years the amount grows at the rate of 7.6% till the age of 65, the total number of years = 30 years.

Now we have to find the total amount after 65 years.

Total amount = annuity [((1+r)^n – 1) / r] × (1+r)^n

Total amount = 900[((1+ 0.076)^12 – 1) / 0.076] × (1+ 0.076)^30

Total amount = $150160.24

Answer:

144

Step-by-step explanation:

first you gotta do 3x4 which is 12 then 12x12. and then you get 144.

Robert will run a total of 144 miles during the 12 weeks.

Given:

Robert runs 3 times a week for 12 weeks.

So, total number of runs will be:

= 3 runs/week * 12 weeks

= 36 runs

Since each run is 4 miles, multiply the total number of runs by the distance per run:

= 36 runs * 4 miles/run

= 144 miles

Therefore, Robert will run a total of 144 miles.

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Answer:

the answer is 133

Step-by-step explanation:

we do substitution

2*3^2=18

3^3=27

5(27-4)=115

27+115=133

The maximum of the sinusoidal function is 5.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

From the graph,

The maximum point of the sinusoidal function is the point where the function is at its highest and lowest on the y-axis.

We see that the sinusoidal function y-coordinate is at 1 as its lowest point and 5 as its maximum point.

So,

The maximum value is 5.

Thus,

The maximum of the sinusoidal function is 5.

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Answer:

The answer is explained below

Step-by-step explanation:

The question is not complete, the complete question is Suppose you revolve the plane region completely about the given line to sweep out a solid of revolution. Describe the solid. Then find its surface area in terms of pi.

i) about the y axis

ii) about the x axis

Also the image is attached below.

Answer:

i) about the y axis

If it is revolved about the y axis, the solid produced is a cone with a radius of of 4 units (r = 4) and a height of 3 units (h = 3). The surface area of the cone is:

Surface area = πr (r + √(r² + h²)) = π × 4 (4 + √(4² + 3²)) = 4π (4 + √25) = 4π (4 + 5) = 4π × 9 = 36π unit²

ii) about the x axis

From the image attached, If it is revolved about the x axis, the solid produced is a cone with a radius of of 3 units (r = 3) and a height of 4 units (h = 4). The surface area of the cone is:

Surface area = πr (r + √(r² + h²)) = π × 3 (3 + √(4² + 3²)) = 3π (3 + √25) = 3π (3 + 5) = 3π × 8 = 24π unit²

Answer:

It would take \(2.7\) seconds, correct to 1 decimal place/nearest tenth.

Step-by-step explanation:

Step 1: Understanding the formula

The formula is given as \(h=16t^{2}\), where \(h\) represents the height, and \(t\) represents the time.

Step 2: Substituting and solving

The question asks for the time that would take when the height is \(117~\text{feet}\).

So, substitute \(117\) for \(h\) in the formula, since \(h\) denotes the height:

\(h=16t^{2}\\117=16t^{2}\)

Now, let's solve the equation to find the time, \(t\):

\(117=16t^{2}\\\\\text{Divide by 16 on both sides of the equation:}\\\frac{117}{16}=\frac{16t^{2}}{16}\\\\\text{Simplify:}\\7.3125=t^{2}\\\\\text{Square root both sides of the equation:}\\\sqrt{7.3125}=\sqrt{t^{2}}\\\\\text{Calculate:}\\2.7 \approx t\\\\\text{Rearrange the equation:}\\t\approx2.7\)

So, it takes about \(2.7\) seconds to travel \(117\) feet, according to the formula.

Answer:

Your answer would be 7,600.

Step-by-step explanation:

7,605 rounded to the nearest hundred would be 7,600 because:

The 7 is the thousands.

The 6 is the hundreds.

The 0 is the tens

The 5 is the ones.

So, we need to find which number makes sense to round. Is 605 closer to 600 or 700? 600. So, we have: 7,600

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The solution of the inequality (x-3)(x-5) ≥ 0 is union of two intervals

 (-∞,3] or  [5,∞) that is x ≥5 or x≤3

An inequality is a statement that compares two expressions using ≤, ≥, <, > .

We can solve an inequality by adding same number to both sides or by subtracting same number from both side. While adding or subtracting the sign of the inequality will not change.

Given inequality (x-3)(x-5) ≥ 0

It generates two cases either case1 is true or case 2.

Case1.   (x-3)(x-5) ≥ 0 when (x-3) ≥0 and (x-5)≥0

       ⇒(x-3) ≥0 and (x-5)≥0

     ⇒ x ≥ 3 and x ≥ 5

     ⇒ x ∈ [3,∞) and x∈ [5,∞)

    ⇒  x ∈ [3,∞) ∩[5,∞)

    ⇒ x ∈ [5,∞)

∴ x is greater than or equal to 5

Case 2: (x-3)(x-5) ≥ 0 when (x-3) ≤0 and (x-5)≤0

      ⇒(x-3) ≤0 and (x-5)≤0

     ⇒ x ≤3 and x ≤ 5

     ⇒ x ∈ (-∞,3] and x∈ (-∞,5]

    ⇒  x ∈ (-∞,3] ∩ (-∞,5]

    ⇒ x ∈  (-∞,3]

∴ x is less than or equal to 3

Solution of the given inequality is case 1 or case 2

⇒  x ∈ [5,∞) or  x ∈  (-∞,3]

⇒ x  x ∈  (-∞,3] ∪ [5,∞)

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With a frame length of 1, the expectation is 5 seconds and the         standard deviation is approximately 3.464 seconds for the number of seconds between two consecutive connections.

(a) To determine the frame length Δ that gives a probability of 0.15 of an arrival during any given frame, we need to consider the Binomial counting process and its probability distribution.

In a Binomial distribution, the probability of success (an arrival) is given by p, and the probability of failure (no arrival) is given by q = 1 - p. In this case, p = 12 connections per minute.

We can use the cumulative distribution function (CDF) of the Binomial distribution to find the frame length Δ. The CDF gives the probability of having k or fewer arrivals in a given number of frames.

Using a binomial probability table or a calculator, we find that when p = 0.15, the corresponding value of k is 1. Therefore, the frame length Δ that gives a probability of 0.15 of an arrival during any given frame is 1 frame.

(b) With a frame length Δ of 1, we can compute the expectation (mean) and standard deviation for the number of seconds between two consecutive connections.

The average rate of connections is 12 per minute. To find the average time between two consecutive connections, we take the reciprocal of the rate: 1/12 minutes per connection.

To convert minutes to seconds, we multiply by 60: (1/12) * 60 = 5 seconds.

Therefore, the expectation (mean) for the number of seconds between two consecutive connections is 5 seconds.

The standard deviation can be calculated using the formula for the standard deviation of a Poisson process, which is the limit of the Binomial distribution as the number of trials becomes large. For a Poisson process, the standard deviation is equal to the square root of the average rate: √(12) ≈ 3.464 seconds.

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Answer:

13x-2y=25

4x+3y=-14

39x-6y=75

8x+6y=-28

47x=47

x=1

If x=1, then:

4(1)+3(y)=-14

4+3y=-14

3y=-18

y=-6

So the answer is (1,-6)

Let me know if this helps!

Answer:

c

Step-by-step explanation:

Answer:

$7.50

Step-by-step explanation:

15% of $50 is 7.50, so she or he made $7.50 from that piece of clothing

Answer:

A: False B: False C: False D: False

Step-by-step explanation:

569x 102 = 58038

569x 10 = 5690

103x 569 = 58607

102x 569 =  58038

Answer: 5.184 ft

Step-by-step explanation:

Therefore, the slope of the line passing through the points (0, 3) and (2, 6) is 3/2.

In mathematics, the slope refers to the measure of steepness or inclination of a line. It is defined as the ratio of the vertical change (rise) between two points on the line to the horizontal change (run) between those points. In other words, the slope of a line is the change in y divided by the change in x between any two points on that line. The slope can be positive, negative, or zero, and it determines the direction and the steepness of the line. The slope is an important concept in algebra, geometry, and calculus, and it is used to describe many real-world phenomena, such as the velocity of an object, the rate of change of a function, and the growth or decline of a population.

Here,

To find the slope of the line passing through the points (0, 3) and (2, 6), we can use the formula:

slope = (change in y) / (change in x)

So, we have:

slope = (6 - 3) / (2 - 0)

slope = 3 / 2

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The correct option is a. mean: $64 median: $65 mode: $71, the mean is the average of all the values in a data set.

To calculate the mean, add up all the values and then divide by the number of values. In this case, the mean is $64.

The median is the middle value in a data set when the values are arranged in ascending or descending order. In this case, the median is $65.

The mode is the most frequently occurring value in a data set. In this case, the mode is $71.

Here is a table of the data with the mean, median, and mode calculated:

Value | Mean | Median | Mode

------- | -------- | -------- | --------

$71 | $64 | $65 | $71

$66 |     |     |

$81 |     |     |

$53 |     |     |

$64 |     |     |

$71 |     |     |

$68 |     |     |

$45 |     |     |

$50 |     |     |

$61 |     |     |

$63 |     |     |

$75 |     |     |

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Answer:

X in.

Step-by-step explanation:

Answer:

1/6 for white and 1/2 for black

Step-by-step explanation:

My knowledge!

Hope it helps!

Answer:

4/15

Step-by-step explanation:

There are 6 white+4black = 10 marbles in the bag

P (white) = white marbles / total marbles = 6/10 = 3/5

We keep the marble

There are 5 white+4black = 9 marbles in the bag

P (black) = black/total = 4/9

P(white, black no replacement) = 3/5 * 4/9 = 3/9 *4/5 = 1/3*4/5 = 4/15

Answer:

68

Step-by-step explanation:

79 - 11 is 68, so I think 68 is the answer.

An index of refraction is the ratio of the speed of light in a vacuum to the speed of light in a material. In other words, it's a measure of how much a material can slow down the speed of light. When light passes from one medium to another with a different index of refraction, it bends or refracts.

The ratio of the speed of light in material A to the speed of light in material B can be found by using the formula

V = c/n,

where V is the speed of light in the medium, c is the speed of light in a vacuum, and n is the index of refraction.

We can write this formula as V = c * (1/n).

So, the ratio of the speed of light in material A to the speed of light in material B can be found as follows:

Va/Vb = (c/4/3) / (c/5/4) = (5/4) / (4/3) = 15/16

Therefore, Va/Vb = 15/16.

An index of refraction is the ratio of the speed of light in a vacuum to the speed of light in a material. In other words, it's a measure of how much a material can slow down the speed of light. When light passes from one medium to another with a different index of refraction, it bends or refracts.

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