1. There are 40 students in Mr. Jackson's math club. All the students are between the ages of 15 and 18, inclusive. The table shows how many students in the club are each age.

Answer:

Step-by-step explanation:

y=8x-7

9=8x-7

9+7=8x-7+7

16=8x

16/8=8x/8

2=x

1) Based on the slope equation, between 2003 and 2008, the school population grew by 265 students.

2) It took 5 years for the school population to grow from 1,389 to 1,654.

3) The average population growth per year was 53 students per year.

4) In the year 2000, the school population was 1,230.

5) The equation for the population, P, of the school in t years after 2000 is given as P = 1,230 + 53t.

6) Based on the equation above, the population of the school can be predicted to be 2,025 in 2015.

The slope describes the quotient or ratio of the rise and run.

The slope is found from the linear equation, y = mx + b, where m is the slope and b is the y-intercept.

The school population in 2003 = 1,389

The school population in 2008 = 1,654

Rise (increase) in population = 265 (1,654 - 1,389)

Run (Increase) in years = 5 years (2008 - 2003)

The slope = Rise/Run = 265/5 = 53

Annual increase in the school population = 53 students

Population in 2000:

Difference in years between 2003 and 2000 = 3

Population in 2000 = 1,389 + 53(-3)

= 1,230

Population after 2000:

= 1,230 + 53t

In 2015, the Population should be:

1,230 + 53t

1,230 + 53(15)

= 1,230 + 795

= 2,025

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Answer:

42°

Step-by-step explanation:

A right-angled triangle can formed in this scenario (image attached), where:

θ = angle of elevation of the sun

Opposite side = The height of the tower

Adjacent side = Length of the shadow

Trigonometric function will be used to determine the angle of elevation:

tanθ = [tex]\frac{opposite}{adjacent}[/tex]

        [tex]= \frac{118 feet}{130 feet}[/tex]

feet in the numerator and denominator will cancel each other out completely:

θ =[tex]tan^{-1} (\frac{118}{130})[/tex]

 θ = 42.23°

∴ θ = 42° (Rounded to the nearest degree)

The rate of change of the profit when the item price is $30 is $3600 per dollar increase in price.

Two or more expressions with an Equal sign is called as Equation.

Let's call the number of items sold at a price of $p as x(p).

Based on the information given, we can write an equation for x(p) as:

x(p) = 2000 - 400(p - 30)

The profit from selling the items at a price of $p is given by the product of the number of items sold and the price:

Profit(p) = x(p)×p

Taking the derivative of the profit function with respect to the price, we can find the rate of change of the profit:

dProfit/dp = dx/dp×p + x(p)

= -400 p + 400 ( 30) + 2000 - 400(p - 30)

= -400 p + 12000

When p = 30, the rate of change of the profit is:

dProfit/dp = -400(30 )+ 12000

= 3600

So the rate of change of the profit when the item price is $30 is $3600 per dollar increase in price.

Hence,  the rate of change of the profit when the item price is $30 is $3600 per dollar increase in price.

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Answer:

Step-by-step explanation:

You want the costs of an oscilloscope and a multimeter when the sum of their costs is $574, and the difference of their costs is $356.

Let o and m represent the costs of the oscilloscope and multimeter, respectively. Then the costs can be described by ...

  o +m = 574

  o -m = 356

Adding these two equations gives ...

  2o = (574+356) = 930

  o = 465 . . . . . . . . . . . . divide by 2

Subtracting the second equation from the first gives ...

  2m = 574 -356 = 218

  m = 109 . . . . . . . . . . . . divide by 2

The oscilloscope costs $465; the multimeter costs $109.

__

Additional comment

This is the generic solution to a "sum and difference" problem: the higher value is half the sum of the given numbers, and the lower value is half their difference.

The row with the most sucktastic runtime is the one with[tex]2^n[/tex], as it takes exponentially longer to run than the other runtimes.

No, we do not have any non-integer answers.

Second: 72

Minute: 1000

Hour: [tex]2^(17)[/tex]

Day: [tex]2^25[/tex]

Month: [tex]2^30[/tex]

Year: [tex]2^35[/tex]

Second: f(n) = 72 => n = 72

Minute: f(n) = 1000 => n = 1000

[tex]Hour: f(n) = 2^n = > n = 17Day: f(n) = 2^n = > n = 25 Month: f(n) = 2^n = > n = 30Year: f(n) = 2^n = > n = 35[/tex]

Seconds: The runtime for an input of size n is 72 microseconds, so the largest input that can be calculated in a second is 72.

Minutes: The runtime for an input of size n is 1000 microseconds, so the largest input that can be calculated in a minute is 1000.

Hours: The runtime for an input of size n is[tex]2^n[/tex] microseconds, so the largest input that can be calculated in an hour is [tex]2^17.[/tex]

Days: The runtime for an input of size n is [tex]2^n[/tex] microseconds, so the largest input that can be calculated in a day is [tex]2^25[/tex]

Months: The runtime for an input of size n is [tex]2^n[/tex] microseconds, so the largest input that can be calculated in a month is [tex]2^30.[/tex]

Years: The runtime for an input of size n is [tex]2^n[/tex] microseconds, so the largest input that can be calculated in a year is [tex]2^35.[/tex]

The row with the most sucktastic runtime is the one with [tex]2^n[/tex], as it takes exponentially longer to run than the other runtimes. Therefore, the longer the time period, the larger the input size that can be calculated. No, we do not have any non-integer answers as the runtimes of the inputs are in microseconds and the input size is given as an integer.

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Answer:1200

Step-by-step explanation:1200

Answer:504

Step-by-step explanation:

We have the DE, [tex]y'+y=0[/tex], verify that [tex]y=e^{\frac{-x}{8}}[/tex] is a solution.

We have, [tex]y=e^{\frac{-x}{8}}[/tex], find [tex]y'[/tex].

=> [tex]y'=\frac{-1}{8} e^{\frac{-x}{8}}[/tex]

Plug [tex]y[/tex] and [tex]y'[/tex] into the DE.

=> [tex]y'+y=0[/tex]

=>[tex](\frac{-1}{8} e^{\frac{-x}{8}})+(e^{\frac{-x}{8}})=0[/tex]

=> [tex]e^{\frac{-x}{8}}=\frac{1}{8} e^{\frac{-x}{8}}[/tex]

=> [tex]e^{\frac{-x}{8}}\neq \frac{1}{8} e^{\frac{-x}{8}}[/tex]

Thus, [tex]y=e^{\frac{-x}{8}}[/tex], is not a solution to the given DE.

Answer:

[tex]\dfrac{11}{16}\\\\[/tex]
Option C

Step-by-step explanation:

We have the following information:

AB = 2DH

DH = 2BE or BE = DH/2

The area of square ABCD = (2DH)² = 4DH²

The area of square BEFG = BE² = (DH/2)² = DH²/4

The area of square DHFJ = DH²

Area of the unshaded region

= area of square BEFG  + area or square DHFJ

= DH²/4 + DH² = DH²/4 + 4DH²/4 = 5DH²/4

Area of shaded region

= area of square ABCD - area of unshaded region

[tex]= AB^2 - \dfrac{5}{4}DH^2\\\\= 4DH^2 - \dfrac{5}{4} DH^2\\\\= \dfrac{4DH^2 \cdot 4}{4} - \dfrac{5}{4} \cdot DH^2[/tex]

[tex]= \dfrac{16DH^2 - 5DH^2}{4}= \dfrac{11DH^2}{4}[/tex]

[tex]\textrm{Probability of a point falling in the shaded region} =\dfrac{\textrm{Area of shaded region}}{\textrm{Total area of both regions}}\\\\= \dfrac{11DH^2/4}{4DH^2} = \dfrac{11}{16}\\\\[/tex]

The amount of interest nearest to cent will be $22,184.62.

A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

The borrowing amount $83,500 at a rate of 4.005% over 6 years. Then the interest is given as,

I = A - P

I = $83,500 (1.04005)⁶ - $83,500

I = $105,684.62 - $83,500

I = $22,184.62

The amount of interest nearest to cent will be $22,184.62.

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After evaluating these expression it seems to be the option (a) math.hypot(3,4) == math.sqrt(25) evaluate that is True

The math.hypot function calculates the Euclidean distance between two points in a 2D space, which is equivalent to the length of the hypotenuse of a right triangle with sides of length a and b (where a and b are the arguments to math.hypot).

In this case, math.hypot(3, 4) calculates the length of the hypotenuse of a right triangle with sides of length 3 and 4, which is equal to 5.

The expression math.sqrt(25) calculates the square root of 25, which is equal to 5. Since math.hypot(3, 4) and math.sqrt(25) both evaluate to 5, the expression math.hypot(3, 4) == math.sqrt(25) evaluates to True.

The other expressions are not evaluating to True:

b. math.hypot(2,5) != math.trunc(2.5)

c. math.hypot(2,5) != math.true(2.5)

d. math.cell(2,5) does not exist. It is likely a typo for math.ceil which is not equal to math.floor(2.5)

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The correlation between Rate and Year is positive. The slope of the regression line is 0.0275 and the intercept is -9.8086. The model predicts that the interest rate in 2020 will be 2.38%.

The correlation between Rate and Year is positive, which means that as the years go by, the interest rate on 3-month Treasury bills is increasing. The slope of the regression line (0.0275) tells us that the average increase in the interest rate per year is 0.0275%. The intercept of the regression line (-9.8086) represents the interest rate in 1950.

This model predicts that the interest rate in 2020 will be 2.38%, which is obtained by plugging in 1970 for the Year variable and solving for the Rate. It's important to keep in mind that this model is based on historical data, and future interest rates may not follow the same pattern as in the past.

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Where the OADB is a sector of a circle, and Angle AOB  = 80°, and the Radius of OB = 12cm,:

A circular sector (symbol: ) is the piece of a disk (a closed region circumscribed by a circle) contained by two radii and an arc, where the smaller area is known as the minor sector and the bigger as the major sector.

Given m∠AOB = 98°, OB = OA = 25cm (The radii are congruent) Thus,

m∠OAB = m∠OBA,

m∠OAB = (180 - 98) /2

m∠OAB = 41°

In the Right Triangle OBC, OB = 25cm, m∠OBC = 41°

Hence,

OC /OB = Sin ∠OBC ,
OC = OB (Sin ∠OBC )

= 25 * Sin41°

= 16.4cm; thus,

OC = 16.4cm

Where BC/OB = Cos ∠OBC,

BC = OB ( Cos ∠OBC)

= 25 * Cos 41° Thus,

BC = 16.4cm


The area of the ΔOAB = 1/2 * OA * OB * Sin98°
= 1/2 * 25 * 25 * Sin 98°

= 309.5cm²


The area of the Sector OADB = (98°/360°) * π * 25²

= 0.2722222222 * 3.14 * 25²

= 0.2722222222 * 3.14 * 252

= 534.5cm²

The percentage of the diagram that is shaded is given as:

309.5/534.5 * 100

= 0.5790458372 *100

= 57.9%

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The triangle will by a right triangle if the sum of the squared side lengths is equals to the squared length of the hypotenuse.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

Hence, a triangle will only be a right triangle if the Pythagorean Theorem is respected, hence the sum of the squared side lengths must be compared to the square of the hypotenuse length.

The problem is incomplete, hence the procedure to verify whether the triangle is a right triangle was presented.

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Answer:

Happy New Years sir it is 12:00 in the morning.

Step-by-step explanation:

yes

The cubic function g(x) = -2(x + 4)³ - 5 can be obtained from f(x) = x³ by a translation of 4 units to the right, a vertical scaling by a factor of -2, and a reflection about the x-axis.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

The cubic parent function f(x) = x³ has been transformed to the function g(x) = −2(x + 4)³ − 5 through a combination of translations, scaling, and reflection.

Translation: The parent function has been shifted 4 units to the right, resulting in x + 4 instead of x in the argument of the function.

Scaling: The parent function has been scaled vertically by a factor of -2, resulting in a coefficient of -2 in front of the argument.

Reflection: The parent function has been reflected on the x-axis, resulting in the negative sign in front of the argument.

Thus, g(x) = -2(x + 4)³ - 5 can be obtained from f(x) = x³ by a translation of 4 units to the right, a vertical scaling by a factor of -2, and a reflection about the x-axis.

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a) The probability of having at least 1 rotten strawberry among the 5 is 0.262.

b) 1 strawberry must be picked so that the probability of having exactly 2 rotten strawberries among them equals 2/35.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

The probability that Kyle selects exactly k rotten strawberries among the five she randomly picks is -

P( exactly k rotten strawberries) = [tex]\frac{(^2c_k)(^{34}c_{5-k}) }{^{36}c_5}[/tex]

since if she picks k of the 2 rotten strawberries, Kyle must also select 5 - k of the 36 -2 = 34 good strawberries.

Therefore, the probability that Kyle picks at least one rotten strawberry is -

P(at least 1 rotten strawberry) = P(exactly 1 rotten strawberry) + P(exactly 2 rotten strawberries)

P(at least 1 rotten strawberry) =[tex]\frac{(^2c_1)(^{34}c_{4}) }{^{36}c_5} + \frac{(^2c_2)(^{34}c_{3}) }{^{36}c_5}[/tex]

P(at least 1 rotten strawberry) = [(2 × 46376) / 376992] + [(1 × 5984) / 376992]

P(at least 1 rotten strawberry) = (92752 / 376992) + (5984 / 376992)

P(at least 1 rotten strawberry) = 0.246 + 0.016

P(at least 1 rotten strawberry) = 0.262

The probability of selecting exactly 2 rotten strawberries among n is

P(exactly 2 rotten strawberries) = [tex]\frac{(^2c_2)(^{34}c_{n-2}) }{^{36}c_n} = \frac{(^{34}c_{n-2}) }{^{36}c_n}[/tex]

The value for n is 2/35.

P(exactly 2 rotten strawberries) =[tex]\frac{(^{34}c_{\frac{-33}{35}}) }{^{36}c_{\frac{2}{35} }}[/tex]

P(exactly 2 rotten strawberries) = 1 / 1

P(exactly 2 rotten strawberries) = 1

Therefore, the probability is 0.262 and 1 strawberry must be picked.

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Answer: The number of bacteria in the people of a town with a population of 200 thousand would be 200,000 * 600 million = 120 x 10^9 bacteria.

Step-by-step explanation:

When constructing bins for a frequency distribution, it is important to have equal widths, choose the number of bins based on the sample size, and consider outliers in the data.

A frequency distribution is a representation of data that shows the number of observations in each category or bin.

One of the most important principles is to have an equal number of observations in each bin. This is known as having equal widths for the bins.

To calculate the width of a bin, divide the range of the data by the number of bins desired. The range is then divided into equal parts, each of which becomes a bin width.

Another principle is to have the number of bins chosen based on the sample size.

A rule of thumb is to have at least five observations in each bin, but more bins may be necessary for larger samples.

Additionally, the choice of bin width can also be influenced by outliers in the data. If there are extreme values in the data, it may be necessary to create a separate bin for those values, so they do not dominate the frequency distribution.

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The volume of a frustum of a pyramid with given dimensions is 6260 cubic units.

What is frustum of pyramid?

The top of a conventional pyramid is removed to create the frustum, which is a pyramid. It is known as a truncated pyramid for this reason. The height of a pyramid is represented by the letter h and is the distance from its base to its summit. Similar to it, it has two bases and a slant height indicated by the letter "s" (top and bottom).

We are given frustum of a pyramid with square base of side 22, square top of side 13 and height 20.

We know that volume of frustum of pyramid(V) = h(b^2 + a^2 + ab)/3

We are given b = 22, a = 13 and h = 20

From this, we get

⇒V = h(b^2 + a^2 + ab)/3

⇒V = 20(22^2 + 13^2 + 22*13)/3

⇒V = 20(484 + 169 + 286)/3

⇒V = 20(939)/3

⇒V = 20*313

⇒V = 6260 cubic units

Hence, the volume of a frustum of a pyramid with given dimensions is 6260 cubic units.

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The linear equation that represents the relationship between P and C will be C = 0.39P + 6.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

You take a bundle to the nearby delivery organization. They charge a proper base expense of $6 per bundle in addition to an extra $0.39 per pound.

Let 'P' be the number of pounds and 'C' be the total cost. Then the equation is given as,

C = 0.39P + 6

The linear equation that represents the relationship between P and C will be C = 0.39P + 6.

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Answer: The best-fitting model for the data is a parabolic equation with the form y = ax^2 + bx + c. The coefficients a, b, and c represent the parameters that best describe the relationship between the time (x) and the height (y) of the baseball.

Based on the information provided, the best-fitting model is:

y = 1.553x^2 + 15.178x + 3.37

where y is the height of the baseball (in feet), x is the time (in seconds), 1.553 is the coefficient for x^2, 15.178 is the coefficient for x, and 3.37 is the constant term. This equation represents the best fit of the data to a parabolic function.

Step-by-step explanation:

Answer:

Equal to

Step-by-step explanation:

Answer:

The light beam will hit the ground at a distance of _756_ ft ahead of the car

Step-by-step explanation:

Let x be the distance in feet ahead of the car at which the light beam hits the ground.

Since the light beam drops 2 inches for each 21 feet measured horizontally, we can write the relationship between the height of the light beam and the distance x as:

24 - (2/21)x = 0

Solving for x, we get:

x = (21/2) * 24

x = 756

So the light beam will hit the ground 756 feet ahead of the car.

Answer:

1.             The pattern that I observe in the table above is that the fixed perimeter of these rectangles are 24 meters, and that the graph to represent this function is in the shape of a parabola with a vertex point at (6, 36). As for comparing the patterns to the graph in question A, assuming you're referring to the question I just answered, the graphs both are parabola shaped, with a vertex point and two zeros, one of them being the same at the origin of the coordinate plane (0, 0).

2.            The fixed perimeter for the rectangles represented by this table is 24 meters because if you want to find the fixed perimeter of these rectangles, you can pick any point that is not a zero point of the graph. For example, if the length of a rectangle is 1 meter, and the area is 11 [tex]m^2[/tex], we know the width would be 11 meters. Using this information, we know that the fixed perimeter would be (1 + 11) × 2 = 12 × 2 = 24 meters.

3.            The greatest area possible for a rectangle with a perimeter of 24 meters would be 36 [tex]m^2[/tex] because we can graph these points to form a parabola that represents this situation, and the vertex point of this graph would be the greatest area possible out of all the possible combinations of length and width that would still fit the criteria of having a perimeter of 24 meters.

              Based on the table, the vertex point of the graph would be (6, 36), therefore the greatest area possible for a rectangle with this perimeter would be 36 [tex]m^2[/tex]. As for the dimensions of this rectangle, we know the length is 6 meters, and the area is 36 [tex]m^2[/tex], so the width would be 36 ÷ 6 = 6 meters. Therefore the dimensions of this rectangle would be 6 meters in length and 6 meters in width.

Have a great day! Feel free to let me know if you have any more questions :)

Answer:

Each person will get 12 ounces of soda

Step-by-step explanation:

84 ounces divided by 7 people is 12 ounces per person

Answer:

each person will get 12oz

Step-by-step explanation:

84oz divided by the 7 people will get 12oz per person