The profit ,P dollars, earned by students at a high school selling boxes of chocolates is approximated to be P= -60x^2+600x , where x dollars is the selling price of one box of chocolates. What selling price gives the maximum profit?

Answer:

The last one(D)

Step-by-step explanation:

-1×-1=1

1*3=3

____

9*1=9

12-9=3

The population of birds to increase by 50% in 31.25 years.

The differential equation for the population of birds is:

dp/dt = 0.016P

where P is the population of birds and t is time in years.

To obtain the time it takes for the population to increase by 50%, we need to solve for t when P increases by 50%.

Let P0 be the initial population of birds, and P1 be the population after the increase of 50%.

Then we have:

P1 = 1.5P0 (since P increases by 50%)

We can solve for t by integrating the differential equation:

dp/P = 0.016 dt

Integrating both sides, we get:

ln(P) = 0.016t + C

where C is the constant of integration.

To obtain the value of C, we can use the initial condition that the population at t=0 is P0:

ln(P0) = C

Substituting this into the previous equation, we get:

ln(P) = 0.016t + ln(P0)

Taking the exponential of both sides, we get

:P = P0 * e^(0.016t)

Now we can substitute P1 = 1.5P0 and solve for t:

1.5P0 = P0 * e^(0.016t

Dividing both sides by P0, we get:

1.5 = e^(0.016t)

Taking the natural logarithm of both sides, we get:

ln(1.5) = 0.016t

Solving for t, we get:

t = ln(1.5)/0.016

Using a calculator, we get:

t ≈ 31.25 years

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To solve this system of linear equations, we need to find the values of x and y that make both equations true at the same time. One method to solve this is to use elimination or substitution.

First, let's rearrange the first equation:

y = 2x

Next, we can substitute y = 2x into the second equation:

-7x + 3y = 2

-7x + 3(2x) = 2

-7x + 6x = 2

-x = -2

So, x = 2.

Finally, we can use the first equation to find y:

y = 2x

y = 2 * 2

y = 4

So, the solution to the system of equations is (x, y) = (2, 4).

Answer:

Volume, Mass

Step-by-step explanation:

Mass is how much stuff something is made of. Volume is how much space an object takes up. 1.

Answer:

154

Step-by-step explanation:

You add 56+98 to get 154

The value of the score that was removed is 15.

We have,

To find the value of the score that was removed, we can use the formula for the mean (average):

Mean = Sum of scores / Number of scores

Initially, the population of 10 scores has a mean of µ = 6.

Therefore, the sum of the 10 scores is 10 x 6 = 60.

After one score is removed, the mean becomes µ = 5.

The number of scores is now 10 - 1 = 9.

The new sum of the 9 scores is 9 * 5 = 45.

To find the value of the score that was removed, we can subtract the new sum from the initial sum:

Value of removed score = Initial sum - New sum

= 60 - 45

= 15

Therefore,

The value of the score that was removed is 15.

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The mean absolute deviation of the scores 299, 281, 285, 269, 280, 269, 286, 287 is (D) 6.75.

The mean absolute deviation (MAD) is a measure of the dispersion of a set of data. It is calculated as the average absolute difference between each data point and the mean of the set.

To find the MAD for the given scores, first find the mean of the scores:

(299 + 281 + 285 + 269 + 280 + 269 + 286 + 287) / 8 = 280.5

Then, find the absolute difference between each score and the mean, and take the average of these differences:

(|299 - 280.5| + |281 - 280.5| + |285 - 280.5| + |269 - 280.5| + |280 - 280.5| + |269 - 280.5| + |286 - 280.5| + |287 - 280.5|) / 8 = (18.5 + 0.5 + 4.5 + 11.5 + 0.5 + 11.5 + 5.5 + 6.5) / 8 = 7.5

So the mean absolute deviation of the scores is 7.5.

Therefore, the correct answer to the question is (D) 6.75.

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Answer:

38m and 90cm

1m = 100cm

3890cm = 38m and 90cm

Step-by-step explanation:

1m = 100cm

3890cm = 38m and 90cm

It is 3890 cm long

1 m = 100cm -->  3890cm = 38.9 meters

Hope that helps!

Answer:

perimeter=40in

area=120.71

Step-by-step explanation:perimeter= 5inches*number of sides

5*8=40in

The statistical method that is used for identifying the cost behavior is  (e) Least Squares regression method .

The Least Squares Regression method is defined as a statistical technique that is used to determine the relationship between two variables, which are , "the cost" and its "corresponding activity level" .

This method also involves plotting data points on a scatter diagram and fitting a straight line to data points.

The line that best fits data is line that minimizes sum of squared vertical distances between the data points and the line, this is why it is called the Least Squares regression method.

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The given question is incomplete , the complete question is

A statistical method for identifying cost behavior is the:

(a) Scatter diagram method

(b) High low method

(c) Composite method

(d) CVP charting method

(e) Least Squares regression method

Answer:

m=-1/13 is the slope of the line

The sequence is defined by adding 2 to the previous term. We can find the first six partial sums by adding the terms of the sequence together up to a certain point.

Given that the first term is 4, we can start calculating the partial sums:

S1 = 4

S2 = 4 + 6 = 10

S3 = 4 + 6 + 8 = 18

S4 = 4 + 6 + 8 + 10 = 28

S5 = 4 + 6 + 8 + 10 + 12 = 40

S6 = 4 + 6 + 8 + 10 + 12 + 14 = 54

So the first six partial sums are:

S1 = 4

S2 = 10

S3 = 18

S4 = 28

S5 = 40

S6 = 54

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The correct option for the given question is 1/3 distance from the fulcrum which is option B according to the balance rule.

On a balanced seesaw, the torques around the fulcrum calculated on one side and on another side must be equal. This means that the:\(W_1 d_1 = W_2 d_2\)

where we label the things here,

\(W_1\) is the weight of the boy

\(d_1\) is its distance from the fulcrum

\(W_2\) is the weight of his partner

\(d_2\) is the distance of the partner from the fulcrum

We know that the boy is three times heavier than his companion in this situation, so

\(W_1 = 3 W_2\)

If we plug this into the equation, we get:

\((3 W_2) d_1 = W_2 d_2\)

and by simplifying:

\(3 d_1 = d_2\\\\d_1 = \frac{1}{3}d_2\)

From the above equation, we get that the boy sits at 1/3 the distance from the fulcrum.

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Answer:

169 \(cm^2\)

Step-by-step explanation:

The surface area is the two-dimensional distance around a figure. In essence, if one was going to wrap the figure in paper, the surface area would be the amount of paper one would need. To find the surface area, one would have to find the area of each individual face, and add up the values.

(7) * (5) = (35)

(9) * (5) = (45)

(7) * (5) = (35)

(\(\frac{1}{2}\)) * (6) * (9) = (27)

(\(\frac{1}{2}\)) * (6) * (9) = (27)

Add up all of the values:

(35) + (45) + (35) + (27) + (27) = 169

The answers to each part is mentioned above.

Given is that Aiko works in the fish department of a pet store. She must drain, clean, and refill two reef tanks. The first tank hold 175 gallons of water and drains at a rate of 25 gallons per hour. The second tank holds 200 gallons of water and drains at a rate of 30 gallons per hour.

Equation for tank {1} -

y = 175 - 25x

Equation for tank {2} -

y = 200 - 30x

For the solution we can write -

175 - 25x = 200 - 30x

- 25x + 30x = 200 - 175

5x = 25

x = 5

and

y = 200 - 150

y = 50

For the same amount of water we can write -

175 - 25x = 200 - 30x

- 25x + 30x = 200 - 175

5x = 25

x = 5 hours

In tank (1), there is : 175 - 25 x 5 = 50 gallons

In tank (2), there is : 200 - 30 x 5 = 50 gallons

Therefore, the answers to each part is mentioned above.

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The inequality is equivalent to the given inequality? -4(x+7)< 3(x-2) is x>-22/7

Inequality is a mathematical statement which shsow that two quantities are not the same or that they are not equal.

The given inequality is -4(x+7) < 3(x-2)

Opening the brackets to have

-4x-28<3x-6

Collecting like terms to have

-4x-3x<-6+28

This shows that -7x<22

Making x the subject of the relation we have

x>-22/7

The inequality that satisfies the given inequality is x>-22/7

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Answer:

Step-by-step explanation:

\((3, - 3) \\ y = 3x - 4 \\ m \: = 3 \\ for \: parallelism \: m1 = m2 \\ (3, - 3)\)

\(x1 = 3 \\ y1 = - 3 \\ y - y1 = m(x - x1) \\ y - ( - 3) = 3(x - 3) \\ y + 3 = 3x - 9\)

\(y = 3x - 9 - 3 \\ y = 3x - 12\)

To find the largest number of passengers in the tram, we need to calculate the maximum number of passengers who can go without a ticket.

Given that 12% of passengers go without a ticket, we can set up the following equation:

12% of x = 60

To solve for x, we can divide both sides of the equation by 0.12:

x = 60 / 0.12

x = 500

Therefore, the largest number of passengers in the tram, if it is not greater than 60, would be 500.

To find the largest number of passengers in the tram, we use the percentage given and set it equal to the number of passengers. By solving for x, we determine that the largest number of passengers in the tram is 500.

The largest number of passengers in the tram, if it is not greater than 60, is 500.

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a. The chart did not maintain consistent scaling

b. The graph is not the appropriate graph type to display such data

c.  The display had inaccurate or distorted visual representations

When the actual data may not support it, changing the scales on the axes might give the appearance of big changes or differences.

The visual effect of data can be exaggerated or minimized, for instance, by adopting a non-linear scale or deleting specific sections of the axis.

So it important to Choose appropriate graph type that best represents the data and the relationship you want to convey.

It also advisable to make use of  clear and accurate labeling with descriptive titles and units of measurement.

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Answer:

To find the length of DE, we need to use the fact that the two triangles are similar. This means that the corresponding sides of the triangles are proportional.

Let's use the following variables to represent the lengths of the sides:

BC = x

BF = y

DE = z

From the given information, we know that:

- BF = 20

- BC = 15

- Angle FBC = 56 degrees

- Angle EDC = 85 degrees

- Angle BFC = 90 degrees

Since angle BFC is a right angle, we can use trigonometry to find the length of BF:

sin(56) = BF / BC

BF = BC * sin(56)

BF = 15 * 0.829

BF = 12.435

Now we can set up a proportion using the corresponding sides of the two triangles:

BC / BF = DE / EF

Substituting the values we know:

15 / 12.435 = z / 24

Simplifying:

z = 15 * 24 / 12.435

z = 28.93

So the length of DE is approximately 28.93.

hope it helps you...

If e is a nonempty compact subset of x and a is a closed subset of x, and e ∩ a = ∅, then there is a positive "gap" between e and a. This can be proven by showing that the infimum of the distances between points in e and a is greater than zero.


1. Let e be a nonempty compact subset of x and a be a closed subset of x. Since e is compact and a is closed, both sets are bounded and closed, which implies that they are disjoint (e ∩ a = ∅).

2. Consider the set S = {d(x, a) : x ∈ e, a ∈ a}. This set consists of the distances between each point in e and each point in a.

3. Since e and a are disjoint, S contains only positive distances. Moreover, since both e and a are compact and closed, the distance function d(x, a) is continuous. Therefore, S is a nonempty set of positive real numbers.

4. By the properties of real numbers, S has a minimum element, which we denote as inf{d(x, a) : x ∈ e, a ∈ a}. Since S contains only positive distances, this minimum element must be greater than zero. Hence, there is a positive "gap" between e and a.

Therefore, if e is a nonempty compact subset of x and a is a closed subset of x, and e ∩ a = ∅, then there is a positive "gap" between e and a. This can be proven by showing that the infimum of the distances between points in e and a is greater than zero.

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The probability that exactly three of the marbles Shelby grabs are red is approximately 27.97%.

To find the probability that exactly three of the marbles Shelby grabs are red, we can use the formula for combinations and probability. The probability can be calculated as follows:

Probability = (Number of favorable outcomes) / (Total possible outcomes)

First, we'll find the total possible outcomes by using the combination formula, which is C(n, k) = n! / (k! (n-k)!) where n is the total number of marbles, and k is the number of marbles being grabbed.

Total marbles = 5 red + 3 green + 6 blue = 14 marbles
Total possible outcomes = C(14, 6) = 14! / (6! * (14-6)!) = 3003

Next, we'll find the number of favorable outcomes. To get exactly three red marbles, Shelby must grab 3 red marbles, 2 non-red marbles (green or blue), and 1 more non-red marble (green or blue). We'll find the combinations for each case and multiply them together.

Favorable outcomes = (C(5, 3) * C(9, 3)) = (5! / (3! * (5-3)!)) * (9! / (3! * (9-3)!)) = 10 * 84 = 840

Finally, we'll calculate the probability:

Probability = Favorable outcomes / Total possible outcomes = 840 / 3003 ≈ 0.2797 or 27.97%

So, the probability that exactly three of the marbles Shelby grabs are red is approximately 27.97%.

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Answer:

1/2(7.9-0.08) = 3.91

Step-by-step explanation:

Answer:

x = 16.64

option A

Step-by-step explanation:

Using the pythagoreom therom

Answer:

16.64

Step-by-step explanation:

Since it's a right angled triangle, we use Pythagoras theorem:

(Hypotenuse)² = (base)² + (perpendicular)²

x² = 14² + 9²

x² = 196 + 81

x² = 277

√x² = √277

x = 16.64

Answer:

Approximately 1.2078566715...

Step-by-step explanation:

Very tricky question! Because the picture doesn't seem to be drawn to scale...

With point O being the center of the circle, construct segments KO, LO, and MO, all of them are the radius of the circle, thus, equivalent.

Since KL=LM, then triangle KLM is an isosceles triangle and angle K is equal to angle M.

\(m<K=m<M\\17=m<M\)

(Yes that means "measure of angle")

And because both angles K and M are 17 degrees, then angle L must be 146 degrees.

Now, focus on triangle LOK, since KO=LO, triangle LOK is also an isosceles triangle, thus:

\(m<LKO=m<KLO\\m<LKO=73\)

(Since half of angle L is 73)

Then m<KOL must be 34 degrees, and m<KOM will be 68 degrees.

After that, we can use the law of cosine to solve for KM:

\((KM)^2=1.08^2+1.08^2-2(1.08)(1.08)Cos(68)\\(KM)^2=1.1664+1.1664-2.3328(0.37460659341...)\\(KM)^2=2.3328-0.87388226112...\\(KM)^2=1.45891773888...\\KM=1.2078566715...\)

The only thing that bothers me is angle KOM being 68 degrees because in the figure angle KOM is clearly an obtuse angle.

I hope I am not tripping.

Answer:

Step-by-step explanation:

Draw a really careful diagram of Circle with center O and ΔKLM Then make <K = 17° and <M = 17°

Draw line Segment LO

Draw line Segment KO

Mark the intersection point of LO and KM as C

Since KL = LM the vertex is  

<KLM + 17 + 17 = 180

<KLM + 34 = 180

<KLM = 180 - 34

<KLM = 146

The diagonal LO bisects < KLM

Therefore <KL0 = 1/2 <KLM

<KLO = 73

KM and LO intersect at right angles because ΔKCL and MCL are congruent making <KCL = <MCL

2x = 180

x = 90

Now consider ΔKLO

It isosceles because it is made up of 2 radii.

That means that <OKL = 73

But OKC + OKL = 73

<OKC + 17 = 73

<OKC = 56

Now we are home free. We have the hypotenuse and an angle. We can find KC

Cos(56) = KC/KO

Cos(56) = KC/1.08

0.5592 * 1.08 = KC

kc = 0.6039

KM = twice that amount which is 1.2079

Answer:

y = 2x2

y + 3x = 2x2 – 8

Step-by-step explanation:

The equations that are quadratic in nature are -

A quadratic equation is a equation that is of the form -

y = f{x} = ax² + bx + c.

Given are the set of equations.

A quadratic equation is a equation of degree 2. The equation with degree 2 are -

Therefore, the equations that are quadratic in nature are -

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The sides RS and ST are equal because they are the side of the congruent triangle that is RS ≅ ST. Then the correct option is D.

It is a locus of a point drawn equidistant from the center. The distance from the center to the circumference is called the radius of the circle.

In circle Q, ∠RQS ≅ ∠SQT.

In ΔRQS and ΔTQS

∠RQS ≅ ∠SQT (Given)

QS = QS (Common side)

RQ = QT (Radius of the circle)

The ΔRQS and ΔTQS triangles are congruent to each other. That is given as ΔRQS ≅ ΔTQS.

The sides RS and ST are equal because they are the side of the congruent triangle that is RS ≅ ST. Then the correct option is D.

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Answer:

D. rs≅st

Step-by-step explanation:

i did it

Answer:

9 x 20 x 19 = 3420

6 x 18 x 21 x 19 x 20 x 1 x 20 x 9 x 14 x 7 = 15202857600

3420 x 15202857600 = 5199377299200

Therfore, the answer is 5199377299200.