b) Graph the probability distribution using a histogram and describe its shape
c) Find the probability that a randomly selected student is less than 20 years old.
d) Find the probability that a randomly selected student's age is more than 18 years
old but no more than 21 years old.

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The surface area of the surface generated by rotating the curve y = x² about the y-axis, and we found that the surface area is approximately 54.33 square units.

In this case, the curve we want to rotate is y = x², and we want to rotate it about the y-axis. To use the formula above, we need to express the equation of the curve in terms of x. Therefore, we need to rewrite y = x² as x = √y.

Next, we need to find the derivative of x = √y with respect to y, which is:

dx/dy = 1/2√y

Substituting this into the formula for the surface area, we get:

Surface Area = 2π ∫[0,4] √y √(1+(1/2√y)²) dy

Simplifying the expression inside the square root, we get:

Surface Area = 2π ∫[0,4] √(y+(1/4)) dy

We can evaluate this integral using the power rule of integration, which gives:

Surface Area = 2π [2/3(y+(1/4))^(3/2)]₀⁴

Simplifying further, we get:

Surface Area = 2π [2/3(17/4)^(3/2)]

Surface Area ≈ 54.33 square units

Therefore, the surface area of the surface generated by rotating the curve y = x² about the y-axis is approximately 54.33 square units.

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Complete Question:

How do you find the area of the surface generated by rotating the curve about the y-axis y = x^2 , 0 ≤ x ≤ 2 ?

Answer:

Se depositan $ 8.000 en un banco que reconoce una tasa de interés del 36% anual, capitalizable mensualmente. ¿Cuál será el monto acumulado en cuatro años?

Step-by-step explanation:

Para resolver este problema, podemos utilizar la fórmula del interés compuesto:

A = P*(1 + r/n)^(n*t)

Donde:

A: el monto acumulado después de t años

P: el capital inicial

r: la tasa de interés anual

n: el número de veces que se capitaliza el interés por año

t: el tiempo en años

En este caso, tenemos:

P = $8.000

r = 36% = 0.36

n = 12 (ya que la tasa de interés se capitaliza mensualmente)

t = 4 años

Sustituyendo estos valores en la fórmula, obtenemos:

A = $8.000*(1 + 0.36/12)^(124)

A = $8.000(1 + 0.03)^48

A = $8.000*(1.03)^48

A = $16.751,83

Por lo tanto, el monto acumulado en cuatro años será de $16.751,83.

The cost of producing an additional 200 items due to increased demand is 180,000 Botswana Pula.

Marginal cost is the additional cost incurred by producing one additional unit of a good or service. In other words, it is the cost of producing one more unit of output.

The marginal cost (MC) equation given is MC = 2x - 100, where x is the number of units produced.

To find the cost of producing an additional 200 items due to increased demand, we need to calculate the marginal cost of producing these 200 items and then multiply that by 200.

The marginal cost of producing 200 additional items is given by:

MC(200) = 2(300 + 200) - 100

MC(200) = 2(500) - 100

MC(200) = 900

So the marginal cost of producing 200 additional items is 900. To find the total cost of producing these 200 items, we can simply multiply the marginal cost by the number of units produced, which in this case is 200:

Total cost = MC(200) × 200

Total cost = 900 × 200

Total cost = 180,000

Therefore, the cost of producing an additional 200 items due to increased demand is 180,000 Botswana Pula.

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The perimeter of the pond is 2.92 meters.

A right-angled triangle is a triangle in which one of the angles measures exactly 90 degrees, also known as a right angle.

The side opposite the right angle is called the hypotenuse, and the other two sides are called the legs.

The perimeter of a right-angled triangle is the sum of the lengths of its three sides.

Here we have

The Hypotenuse of the triangle is 1.46 m    

The angle between hypotenuse and perpendicular height = 73°

From triagonometric ratios,

=> cos A = Perpendicular height/ Hypotenuse.

=> cos (73) = Perpendicular height/1.46

=> Perpendicular height = 1.46 × 0.29 = 0.42 m

As we know from Pythagoras' theorem,

Hypotenuse² = side² + side²    

Side = √Hypotenuse² - side²  

= √[(1.46)²- (0.42)²]  = 1.04

Therefore, the sides of the pond are 1.46 m, 0.42 m, and 1.04

Hence, perimeter of the pond =  1.46 + 0.42 + 1.04 = 2.92 meters  

Therefore,

The perimeter of the pond is 2.92 meters.

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The complete Question is given below

Answer:

2

Step-by-step explanation:

since d=7 and the equation is d-5 in the place of d we'll put 7 therefore 7-5=2

Answer:

21 years old

Step-by-step explanation:

Set Alan's age as x, Bernice's age as y

2x=y

x-4+y-4=55

x+y=63

3y=63

x=21

y=42

The probability that, out of 18 independent samples received from one river, just two were contaminated is 0.8438.

In the following 18 samples to be evaluated,

Let X = the number of samples that now the pollutant is present in.

Thus, with p = 0.10 and n = 18, X is a binomial random variable.

Using the binomial theorem:

[tex](^{n} _{r} ) p^{x} q^{n-x}[/tex]

p = 0.10

q = 1 - 0.10 = 0.9

n = 18

The likelihood that only two samples out of 18 obtained in different ways from the same river were polluted

P(x = 2) = [tex](^{18} _{2} ) (0.1)^{2} (0.9)^{18-2}[/tex]

=  [tex](^{18} _{2} ) (0.1)^{2} (0.9)^{16}[/tex]

= 153 x 0.01 x 0.1853

= 0.8438

Thus, the probability that, out of 18 separate samples received from one river, just two were contaminated is 0.8438.

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Answer:

According to the scale, 1 inch on the drawing represents 1.5 feet in real life. So, to find the actual length of the door, we need to multiply the length on the drawing by the scale factor:

4 inches x 1.5 feet/inch = 6 feet

Similarly, to find the actual width of the door, we need to multiply the width on the drawing by the scale factor:

7 inches x 1.5 feet/inch = 10.5 feet

Therefore, the actual measurements of the door are 6 feet by 10.5 feet.

[tex]\begin{cases} x=\frac{2+i\sqrt{2}}{3}\implies 3x=2+i\sqrt{2}\implies 3x-2-i\sqrt{2}=0\\\\ x=\frac{2-i\sqrt{2}}{3}\implies 3x=2-i\sqrt{2}\implies 3x-2+i\sqrt{2}=0 \end{cases} \\\\\\ \stackrel{ \textit{original polynomial} }{a(3x-2-i\sqrt{2})(3x-2+i\sqrt{2})=\stackrel{ 0 }{y}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{ \textit{difference of squares} }{[(3x-2)-(i\sqrt{2})][(3x-2)+(i\sqrt{2})]}\implies (3x-2)^2-(i\sqrt{2})^2 \\\\\\ (9x^2-12x+4)-(2i^2)\implies 9x^2-12x+4-(2(-1)) \\\\\\ 9x^2-12x+4+2\implies 9x^2-12x+6 \\\\[-0.35em] ~\dotfill\\\\ a(9x^2-12x+6)=y\hspace{5em}\stackrel{\textit{now let's make}}{a=-\frac{1}{9}} \\\\\\ -\cfrac{1}{9}(9x^2-12x+6)=y\implies \boxed{-x^2+\cfrac{4}{3}x-\cfrac{2}{3}=y}[/tex]

In order to see the school of fish, the scuba diver descended to a depth of 14 feet below sea level.

Hοw far sοmething stretches is described by the cοncept οf depth. The pοοl has a six-fοοt depth. Unknοwn is the well's depth. We can use the fοllοwing equatiοn tο determine the scuba diver's initial depth:

Initial depth = Final depth + Depth Change The scuba diver's change in depth is positive because he rose f feet (positive because he went up) and ended up 16 feet below the surface. Therefοre:

initial depth = 16 + f - 30 initial depth.

Simplifying the phrase:

Original depth = -14 + f

The scuba diver reached his initial depth there after descended another 14 feet below sea level to observe the school of fish.

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Questions-

A scuba diver was 30 feet below sea level when he ascended f feet to a depth of 16 feet below sea level to see a school of fish. what is her new elevation now?

In respοnse tο the questiοn, we may say that As a result, FHJ stοck has equatiοn highest cοefficient οf variatiοn, with a value οf arοund 4.33%.

In mathematics, an equatiοn is a statement that expresses the equality οf twο expressiοns. Equatiοn is made up οf twο sides that are jοined by the algebraic symbοl (=). Fοr example, in this argument, it is asserted that "2x + 3 = 9" denοtes that "2x plus 3" equals the number "9".

Equatiοn sοlving is the prοcess οf determining the value(s) οf the variable(s) required fοr the equatiοn tο be true. There are many different kinds οf equatiοns, such as regular and nοnlinear οnes with οne οr mοre elements. This fοrmula raises the variable x tο the secοnd pοwer: "x² + 2x - 3 = 0." Lines are used in the study οf mathematics in the fields οf algebra, calculus, and geοmetry.

The cοefficient οf variatiοn (CV) represents the standard deviatiοn as a percentage οf the mean and is a relative measure οf variability. It is cοmputed as fοllοws:

CV = (standard deviatiοn / mean) multiplied by 100%

Tο determine which οf the three stοcks has the highest cοefficient οf variatiοn, we must cοmpute the CV fοr each and cοmpare the results.

Fοr ACE inventοry:

CV = (1.5 / 37.03) x 100% ≈ 4.05%

In the case οf FHJ stοck:

CV = (2.62 / 60.55) x 100% ≈ 4.33%

In the case οf LMP stοck:

CV = (3.06 / 124.9) x 100% ≈ 2.45%

As a result, FHJ stοck has the highest cοefficient οf variatiοn, with a value οf arοund 4.33%.

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Answer:

Step-by-step explanation:

This is an example of a hypergeometric distribution problem, where we have a population of 10,000 clock radios with 500 defective ones, and we want to calculate the probability of getting at least one defective radio in a random sample of 10 without replacement.

The probability of getting no defective radios in the sample is:

(9500/10000) * (9499/9999) * (9498/9998) * ... * (9491/9992)

This is because, for the first radio, there are 9500 good radios out of 10,000, and for the second radio, there are 9499 good radios out of 9,999, and so on.

The probability of getting at least one defective radio in the sample is then:

1 - (9500/10000) * (9499/9999) * (9498/9998) * ... * (9491/9992)

which is approximately equal to 0.401.

Therefore, the probability that the entire batch will be rejected is 0.401.

Answer:

30 pounds

Step-by-step explanation:

Since the jumper costs 50 pounds, the decimal for the number will be:

50.

To find ten percent of the number, you move the decimal one time to the LEFT.

Therefore, 10% of 50 pounds will be 5 pounds. To find 40%, we simply will multiply the 10% amount by 4.

40% of 50 will be:

20

Therefore, the jumper will have 20 pounds off.

Since the original cost is 50 pounds, we simply will just subtract 50 - 20:

50 - 20 = 30

The jumper will cost 30 pounds with the sale deal.

a) The domain and the range of the function are given as follows:

The graph of the function is given by the image presented at the end of the answer.

b) The trip was 5.1875 hours long.

The function for this problem is defined as follows:

g(t) = 23 - 3.2t.

The domain is the set of input values that can be assumed by the function. The time cannot have negative measures, hence the lower bound of the domain is of zero, while the gas cannot be negative, hence the upper bound of the volume is given as follows:

23 - 3.2t = 0

3.2t = 23

t = 23/3.2

t = 7.1875 hours.

The range is given by the set of all output values assumed the function, which are the values of the gas, hence it is [0,23].

The graph is a linear function between points (0, 23) and (7.1875, 0).

At the end of the trip there were 6.4 gallons left, hence the length of the trip is given as follows:

23 - 3.2t = 6.4

t = (23 - 6.4)/3.2

t = 5.1875 hours.

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It ahs been proved by mathematical induction that the sum of the squares of 4 consecutive integers is an even integer.

To prove that the sum of the squares of 4 consecutive integers is an even integer.

Let x, (x + 1), (x + 2), (x + 3) be the four consecutive integers.

The sum of the squares of these integers are:

S = x² + (x + 1)² + (x + 2)² + (x + 3)²

Expanding this gives us:

S = 4x² + 12x + 14

Simplifying this gives:

S = 2(2x² + 6x + 7)

The number 2x² + 6x + 7 is either even number or odd number.

However, since it is multiplied by 2x² + 6x + 7, the sum will always be an even number.

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a) D. No. A person can be both male and bet on professional sports at the same time

b) If the events A and B are independent, P(A&B) = P(A) x P(B)

P(male and also bets on professional sports) = 0.484x0.13 = 0.0629

c) P(male or bets in professional sports) = P(male) + P(bets in professional sports) - P(male and also bets on professional sports)

= 0.484 + 0.13 - 0.0629

= 0.5511

d) A. The assumption was incorrect and the events are not independent

(if the were independent, the percentage would have been 6.29)

e) A. P(male or bets on professional sports = 0.484 + 0.13 - 0.081

= 0.5330

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The average rate of change on the intervals [0, 3], [3, 5], [5, 7], and [7, 9] are 2, -1.5, 1, and -1.5, respectively.

It expresses how much the function changed per unit on average during that time period. It is computed by taking the slope of the straight line connecting the interval's endpoints on the function's graph.

To calculate the average rate of change for the intervals shown in the graph, we must first determine the slope of the line connecting the endpoints of each interval.

0-3 interval:

Because the interval's endpoints are (0, 1) and (3, 7), the slope of the line connecting them is:

slope = (y change) / (x change) = (7 - 1) / (3 - 0) = 2

pauses [3, 5]:

Because the interval's endpoints are (3, 7) and (5, 4), the slope of the line connecting them is:

slope = (y change) / (x change) = (4 - 7) / (5 - 3) = -1.5

[5–7] Interval:

Because the interval's endpoints are (5, 4) and (7, 6), the slope of the line connecting them is:

slope = (y change) / (x change) = (6 - 4) / (7 - 5) = 1

Interval 7 and 9:

Because the interval's endpoints are (7, 6) and (9, 3), the slope of the line connecting them is:

slope = (y change) / (x change) = (3 - 6) / (9 - 7) = -1.5

As a result, the average rate of change on the intervals [0, 3], [3, 5], [5, 7], and [7, 9] is 2, -1.5, 1, and -1.5.

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In the word problem,

a)Gallons per minute change is -2/3 gallons per minute

b) 7.5 minutes to drain the other 5 gallons

c)The tank was full 4 1/2 minutes before Jada arrived.

What is word problem?

Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided statements are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.

a) Gallons per minute change is -2/3 gallons per minute  since it decreases by 2 gallons in 3 minutes.

b)  we have 5 gallons and lose 2/3 gallons per minute

=> (2/3 gal/minute)(x minutes) = 5 gallons

=> x = 5(3/2) = 15/2 = 7.5 minutes to drain the other 5 gallons

c)  There was 10 gallons when the tank is full . That is 3 gallons more than the 7 gals there when Jada arrived.

=>  (2/3)(x) = 3

=> x = 3(3/2) = 9/2 = 4 1/2 minutes

The tank was full 4 1/2 minutes before Jada arrived.

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Sacramento, California's electricity demand on a scorching summer day is depicted in a function graph. The domain is 24 hours of a day.

The site is available around-the-clock.

One thousand two hundred megawatts are consumed at eight in the morning.

The hours between 4:00 and 6:00 pm saw the highest electricity use, while 4:00 am saw the lowest use.

It would be 1,900 megawatts for f (12).

From 4 am to 5 pm, usage rises, and from 5 pm to 4 am, it falls.

Because each point on the graph reflects a different megawatt usage, the graph is a function. As this graph of electricity usage illustrates, the domain would be available throughout the entire day.

At 8 a.m., these megawatts are used:

= 1, 300 - ( 200 / 2 )

equal to 1,200 megawatts

As people get ready for work and leave for work, we can observe an increase in power demand from 4 am to 5 pm, but a reduction from 5 pm to 4 am.

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Answer:

Step-by-step explanation:

In the boys triangle:

  [tex]tanx=\frac{56}{48}[/tex]

        [tex]x=tan^{-1}(\frac{56}{48} )=49.4\textdegree[/tex]

Because triangles are similar:

   [tex]tan 49.8=\frac{h}{32}[/tex]

[tex]h=32tan49.8 = 37.3[/tex]

Answer:

7,560 inches.

Step-by-step explanation:

Given: 7 in x 3 in x 6 in x 4 in x 15 in = ?

First, multiply 7 and 3:

21 in x 6 in x 4 in x 15 in

Then multiply 21 and 6:

126 in x 4 in x 15 in

Then multiply 4 and 15:

126 in x 60 in

Finally, multiply 126 and 60:

= 7,560 inches.

Step 1: Arrange the arrays so that A and B are in the same order: A = [ 1 2 4 0 5 6 ], B = [ 7 3 2 5 1 9]

Step 2: To find C = A+B, add each element of A and B together.

C = [1+7, 2+3, 4+2, 0+5, 5+1, 6+9]

C = [8, 5, 6, 5, 6, 15]

Step 3: To find D = A-B, subtract each element of B from A.

D = [1-7, 2-3, 4-2, 0-5, 5-1, 6-9]

D = [-6, -1, 2, -5, 4, -3]

Answer:

x = 17

Step-by-step explanation:

Subtract 6x from both sides:

2x - 18 = 16

Add 18 on both sides to isolate the variable:

2x = 18 + 16

2x = 34

Divide by 2: x = 17

Answer:

Step-by-step explanation:

its C

The correct answer is C. A normal distribution is a symmetric probability distribution that is bell-shaped when graphed. When plotted on a horizontal scale, the curve starts on the horizontal axis, rises to a central peak, and then falls back to the horizontal axis.

The curve is symmetric, meaning that the left and right halves of the curve are mirror images of each other. The curve approaches the horizontal axis but never touches it, which indicates that there is a non-zero probability of observing values at any distance from the mean, although the probability decreases as the distance from the mean increases.

Normal distribution is a type of probability distribution that is commonly found in natural and social phenomena, where the majority of the observations tend to cluster around the mean, with fewer observations further away from the mean.

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Uri paid a total of $85.47 for the landscaping service including tax and tip.

Taxes are compulsory payments made by a government organisation, whether local, regional, or federal, to people or businesses. Tax revenues are used to fund a variety of government initiatives, such as Social Security and Medicare as well as public infrastructure and services like roads and schools. Taxes are borne by whoever bears the cost of the tax in economics, whether this is the entity being taxed, such as a business, or the final users of the items produced by the firm. Taxes should be taken into consideration from an accounting standpoint, including payroll taxes, federal and state income taxes, and sales taxes.

Given that company charged $74 for the service plus 5% tax.

The tax is 5%, that is:

Tax = 5% of $74 = 0.05 x $74 = $3.70

Cost after tax = $74 + $3.70 = $77.70

Now, tip is 10%:

Tip = 10% of $77.70 = 0.10 x $77.70 = $7.77

Total cost = $77.70 + $7.77 = $85.47

Hence, Uri paid a total of $85.47 for the landscaping service including tax and tip.

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The height of the pole is approximately 17.75 meters.

The main trigonometric functions are sine, cosine, and tangent, which are abbreviated as sin, cos, and tan, respectively. They are used to relate the angles of a right triangle to the lengths of its sides. The sine function gives the ratio of the length of the side opposite an angle to the length of the hypotenuse of the triangle. The cosine function gives the ratio of the length of the adjacent side to the length of the hypotenuse. The tangent function gives the ratio of the length of the opposite side to the length of the adjacent side.

Let's denote the height of the pole as h, and let's denote the distance between the pole and the student's original position (due west of the pole) as x.

From the student's original position, we have a right triangle with the pole being the hypotenuse. The angle opposite to the height of the pole is 40°. So, we have:

tan(40°) = h/x

From the student's new position (10 m due south of the original position), we have another right triangle with the pole being the hypotenuse. The angle opposite to the height of the pole is 35°. The distance between the pole and the student's new position is (x+10) meters (the student moved 10 m south). So, we have:

tan(35°) = h/(x+10)

Now we have two equations with two unknowns (h and x). We can solve for x in terms of h from the first equation:

x = h/tan(40°)

Substitute this expression for x into the second equation:

tan(35°) = h/((h/tan(40°))+10)

Simplify and solve for h:

h = (10 tan(35°) tan(40°)) / (tan(40°) - tan(35°)) ≈ 17.75 m

Therefore, the height of the pole is approximately 17.75 meters.

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If the slope of the graph is increasing from positive x-axis to negative x-axis, then the function is not that decreasing. Therefore, Jonathan's statement is incorrect.

The function is decreasing on intervals where the slope is negative. In this case, since the slope is increasing from positive x-axis to negative x-axis, the function is decreasing on the interval where x is negative.

To determine this interval more precisely, we would need to find the x-value(s) where the slope changes sign from positive to negative. These x-values correspond to critical points, such as local maximums or minimums. The function is decreasing before a local maximum and after a local minimum.

Therefore, Jonathan's statement is not correct, and the function represented by the graph is decreasing on the interval where x is negative.

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Answer:

the two numbers are 15 and 35, and their ratio is 3:7, and their difference is 20.

Step-by-step explanation: