A rock falls from a tower that is 352 feet high. As it is falling, its height is given by the formula h=352-16t^(2). How many seconds (in tenths ) will it take for the rock to hit the ground (h)=(0)?

a complete description of simple harmonic motion must take into account several physical quantities and various mathematical relations then the position of a 60 gg oscillating mass is given by x(t) -20 sin 10t

this information is needed to solve oscillation problems of this type

the position of a 60 gg oscillating mass is given by x(t)

x = 2 cos wt = 2 cos 10t ; w = 10

velocity = dx/dt = -2 x 10 sin 10 t.=- 20 sin 10t

t = .4

velocity = -20 sin 10 x .4 = -20 sin 4 = -20 x -0.7568 = 15.136 cm /s

w = √ k / m = 10 = √ k / .05

k = 15.136  N/m

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the mean and standard deviation of the random variable X, which represents the income from insuring four 21-year-old men, is 2000 and 27.22, respective

Mean: $2,000

Standard Deviation: $741.42

The mean of the random variable X is calculated by taking the sum of the products of the probability of each outcome and the corresponding value of X. The probabilities of each outcome, in this case, are 0, 0.38, 0.59, and 0.03, respectively. The corresponding values of X are $1000, 2000, 3000, and 4000$. Thus, the mean of X is calculated as:

Mean =[tex]$\sum_{i=1}^{N} P(X = x_i)*x_i[/tex]

= 0*1000 + 0.38*2000 + 0.59*3000 + 0.03*4000

= 2000

The standard deviation of the random variable X is calculated by taking the square root of the sum of the products of the probability of each outcome and the square of the difference between the corresponding value of X and the mean. The probabilities of each outcome, in this case, are 0, 0.38, 0.59, and 0.03, respectively. The corresponding values of X are $1000, 2000, 3000, and 4000$. The mean of X is 2000. Thus, the standard deviation of X is calculated as:

Standard Deviation = [tex]$\sqrt{\sum_{i=1}^{N} P(X = x_i)(x_i - \mu)^2}[/tex]

= [tex]\sqrt{(0(1000-2000)^2[/tex] + [tex]0.38*(2000-2000)^2[/tex] + [tex]0.59*(3000-2000)^2 + 0.03*(4000-2000)^2)}[/tex]

= [tex]\sqrt{741.42} = 27.22$[/tex]

Therefore, the mean and standard deviation of the random variable X, which represents the income from insuring four 21-year-old men, is 2000 and 27.22, respective

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Answer:

this very easy to factorize this because (-+)is- (+-)-

(++)+ (--)+ but the sign which is bigger we have to keep that

Answer:

5x + 2x + 5x + (3/5x) = 180

12x + 0.6x = 180

12.06x = 180

x = 14

Step-by-step explanation:

Answer:

x = 0

Step-by-step explanation:

x + 5/4 = 20/16

x + 5/4 = 5/4

x = 0

The area of the regular hexagon value calculated using given perimeter of the regular hexagon is equal to option C. 600√3 square meters.

As given in the question,

Perimeter of the regular hexagon is equal to 'P' = 120m

Relation between the area of the regular hexagon 'A' and the perimeter of the regular hexagon 'P is given by :

A = √3 × ( P²/24 )

  = √3 × [(120)²/ 24]

  = √3 × ( 14400 / 24 )

  = √ 3 × 600

 = 600√3 square meters

Therefore, the area of the regular hexagon using the perimeter of the regular hexagon is equal to Option C.  600√3 square meters.

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The students ratio expressed in fraction as 6/4 = 4/x is incorrect for the similar triangles, and the correct ratio is x : 3 = 10 : 6 expressed in fraction as x/3 = 10/6. The value for x = 5.

Since the triangles are similar, it implies that the length 3 of the smaller triangle is similar to the length x of the larger triangle,

Also the length 6 of the smaller triangle is similar to the length of the larger triangle (4 + 6 = 10).

So it will be wrong to write 6/4 = 4/x, rather the correct fraction will be;

x : 3 = 10 : 6

which when expressed as fraction, we get;

x/3 = 10/6

x = (10 × 3)/6

x = 30/6

x = 5

Therefore, the students expression 6/4 = 4/x is incorrect representation for the lengths of the similar triangles. And the correct expression is x/3 = 10/6, which gives us the value of x equal to 5.

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Using the Pythagorean triplet, the value of AB is 2.

In the given question we have to find the length of AB.

From the given diagram we can see that;

ED = 2, DC = 8 and BC = 6.

To solve this question we use the Pythagorean Triplet.

Pythagorean triples consist of the three positive numbers a, b, and c, where a^2+b^2 = c^2. The symbols for these triples are (a,b,c). Here, a represents the right-angled triangle's hypotenuse, b its base, and c its perpendicular.

Since we have to find the value of AB.

So we can write it as

EC^2 = AE^2+AC^2

(ED+DC)^2 = AE^2+(AB+BC)^2

Now putting the value

(2+8)^2 = AE^2+(6+AB)^2

10^2 = AE^2+(6+AB)^2

As we know that triplet (6,8,10).

The value of EC is 10, AE = 6, the value of AC can't be 6 because one part of value of AC is already given 6. So the value of AC is 8. AS BC=6, so AB=2.

Hence, the value of AB is 2.

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The height of the rocket in given time using regression equation is 586 feet.

The regression equation is, y =  7.70961x² + 176.30826x - 12.44515

Given,

A rocket is shot off from a launcher. The accompanying table represents the height of the rocket at given times, where x is time, in seconds, and y is height, in feet

That is,

x ; 0.6, 1.3, 1.8, 2.5, 3.1

y ; 108, 218, 285, 368, 436

We have to write a quadratic regression equation for the given set;

The quadratic regression equation is;

y =  7.70961x² + 176.30826x - 12.44515

Now,

We have to find the height at a time of 3 seconds using the equation;

So,

y =  7.70961 x 3² + 176.30826 x 3 - 12.44515

y =  69.38649 + 528.92478 - 12.44515

y = 585.86612

y = 586

Height of the rocket= 586 feet

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a. The number of students who were in math only is 7 students.

b. The number of students who were not majoring in computer science is 15.

c. The number of students who were not math or computer science is 8

From the information given, in a class of 25 students, there were 13 math majors, 10 were computer science majors, and 6 were dual majors in both.

It should be noted that the number of math majors only will be:

= 13 - 6

= 7

The number of students not majoring in computer science will be:

= 25 - 10

= 15

Those not math or computer science majors will be:

= 25 - 6 - 7 - (10 - 6)

= 8

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The equation of the linear regression is y = 1.49x- 2.76

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

X 1 2 3 4 5 6 7 8

Y 0,5 0,8 1,2 1,9 3 4,8 7,5 11,9

Rewrite as

X 1 2 3 4 5 6 7 8

Y 0.5  0.8  1.2  1.9  3  4.8 7.5 11.9

When the points are entered in a graphing calculator, we have

The regression equation is represented as

Regression Equation

ŷ = bX + a

Substitute the known values in the above equation, so, we have the following representation

b = SP/SSX = 62.6/42 = 1.49048

a = MY - bMX = 3.95 - (1.49*4.5) = -2.75714

So, we have

y = 1.49048X - 2.75714

Approximate

y = 1.49x- 2.76

Hence, the regression equation is y = 1.49x- 2.76

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Complete question

Given that

X 1 2 3 4 5 6 7 8

Y 0,5 0,8 1,2 1,9 3 4,8 7,5 11,9

Calculate the regression linear equation

The DF value we get after is 143 and the integration value we get is 1.76

What is a value ?

Value in ethics and social sciences refers to the degree of significance of something or an activity, with the goal of deciding the best courses of action to take or the best ways to live, or to define the significance of certain activities.

The value describes the value of each digit in relation to its position in the number. The place value and face value of the digit are multiplied to arrive at the answer. Value equals Place Value minus Face Value. Consider this: If we take 45 into consideration. The tens column is where the fourth digit is located in this instance.

The things that someone values are known as their values. In other terms, values are what a person or a group of people see as "important."

(a)

DF for Factor A = 6 - 1 = 5

DF for Factor B = 4 - 1 = 3

DF for Interaction of Factor A and B = 5*3 = 15

Number of replications per cell = 6

Total no of observations = 6*(N_Factor A)*(N_Factor B) = 6 * 6 * 4 = 144

DF Residuals = 144 - 5 - 3 - 15 - 1 = 120

Total DF = N - 1 = 143

(b) Critical F values

Factor A = F(5,120) = 2.30

Factor B = F(3,120) = 2.69

Interaction = F(15,120) = 1.76

(c) As F statistics for Factor A, Factor B as well as Interaction is >> Fc, Hence we can Reject the Null Hypothesis and warrant the rejection of the claim for equality of means

Hence there is a significant difference in Factor A and there is a significant difference in Factor B.

(d) As the F statistics for Interaction = 4.2 >> Fc (1.76), Hence we can conclude that there is a significant Interaction impact of Factor A and Factor B.

Hence there is a significant difference for Interaction term.

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Answer:

21.4

Step-by-step explanation:

If the ladder originally reaches up 21 feet on the side of the house, and Elijah pulls it 4 feet farther away from the house, the distance from the base of the ladder to the side of the house will increase by 4 feet. This means that the new distance from the base of the ladder to the side of the house will be 21 feet + 4 feet = 25 feet.

Since the height of the ladder is the same, and the base of the ladder is now 25 feet from the side of the house, the ladder will still reach up 21 feet on the side of the house. Therefore, the new distance from the top of the ladder to the ground will be 25 feet - 21 feet = <<25-21=4>>4 feet.

To find the new distance from the top of the ladder to the side of the house, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, we have a right triangle with legs of lengths 21 feet (the height of the ladder) and 4 feet (the distance from the top of the ladder to the ground), and we want to find the length of the hypotenuse (the distance from the top of the ladder to the side of the house). We can use the formula c^2 = a^2 + b^2 to find the length of the hypotenuse:

c^2 = 21^2 + 4^2

= 441 + 16

= 457

c = sqrt(457)

= 21.37

Therefore, the distance from the top of the ladder to the side of the house is 21.37 feet, and the ladder will reach up 21.37 feet on the side of the house after Elijah pulls it 4 feet farther away. Round to the nearest tenth of a foot, the ladder will reach up 21.4 feet on the side of the house.

The answer would not be 17 feet because the height of the ladder and the distance from the base of the ladder to the side of the house are two separate and independent quantities. The height of the ladder is a fixed distance and does not change, regardless of the position of the base of the ladder. Therefore, even if Elijah pulls the ladder 4 feet farther away from the house, the height of the ladder will still be 21 feet and the ladder will still reach up 21 feet on the side of the house. The only change will be the distance from the base of the ladder to the side of the house, which will increase by 4 feet.

Step-by-step explanation:

it is really a simple concept : instead of the isolated variable x you grab the whole function of g(x) and put that into the place of any x appearance in f(x) : g(x) becomes the input argument for f(x).

so,

f(g(x)) = sqrt(36/(x + 3)) = 6×sqrt(1/(x + 3))

The long-term probability that a given marked rat is in room 4 is 1/3

What is meant by probability?

In statistics, probability is defined as the measure of the likelihood of an event to happen and it measures the certainty of the event.

Here we have given that Forty rats are placed at random in a house having 4 rooms. There is one door between rooms 1 and 2, one door between rooms 1 and 4, one door between rooms 2 and 4, one door between rooms 2 and 3, and two doors between rooms 3 and 4 see the book for a picture). There are no doors between rooms 1 and 3. After each minute, a rat may change rooms, or stay still.

And we need to find the  the long-term probability that a given marked rat is in room 4.

By using the eigenvalues method, we know that

Room 4 has the 3 exits that is from Room 1, Room 2 and Room 3.

So, here we have 3 possibilities for the exit so, the rat can choose any one these three ways,

So, the probability can be written as,

=> 1/3

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The the probability of being dealt no hearts is 0.75 and probability of being dealt at least one heart is 0.25 .

Total number of cards = 52

A : the probability of being dealt no hearts

B: the probability of being dealt with hearts

P( A ) = 1 - P( B)

= 1 - 13/52

= 1 -0.25

=0.75

C : probability of being dealt at least one heart

P(C) = 13C1 / 52C1

= 13 / 52

=0.25

Probability is a way to tell or calculate the possibility of an event to occur. Using it, we can make predictions about the likelihood of an event happening, or how likely it is , it helps to make predictions more clear .

The probability can be between 0 and 1 here , P being 0 means a failure and P being 1 means a success.

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What the value of k means in the proportional relationship y =kx is; the change in depth per second of the ascent.

We are told that;

James Cameron descended to the bottom of Challenger Deep in the Marianas Trench; the deepest point in the ocean.

The vessel he rode in called DeepSea Challenger was 35,814 feet deep at its lowest point.

Now, if the time spent is denoted as x in seconds and the depth is denoted as y, the the relationship will be;

y = -kx

where -k is the constant of proportionality which is the change in depth per second of descent.

Now, if the ascent can be modeled by a different proportional relationship y = kx, then it means that k here will be the change in depth per second of the ascent.

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The set of events that the sum of the numbers showing face up is at least 9 is E = {36, 45, 46, 54, 55, 56, 63, 64, 65, 66} and the probability is 5/18.

In the roster form, the elements (or members) of a set are listed in a row between curly brackets. For the event that the sum of the numbers showing face up is at least 9 and is written as a set, look at the sum of values of blue and gray dies that has values greater than equal to 9.

Here, the total outcome S = 36

By doing that, we get,

E = {36, 45, 46, 54, 55, 56, 63, 64, 65, 66} = 10

Then, the probability of getting a sum of at least 9 is calculated as,

[tex]\begin{aligned}P(X\geq 9)&=\frac{\text{Number of favorable outcomes}}{\text{total number of outcomes}}\\&=\frac{n}{S}\\&=\frac{10}{36}\\&=\frac{5}{18}\;\text{or}\;0.28\end{aligned}[/tex]

The answer is 5/18.

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Answer:

  62 square units

Step-by-step explanation:

You want the surface area of a rectangular prism 3 units high, 2 units wide, and 5 units long.

The surface area of a rectangular prism is given by the formula ...

  SA = 2(LW +H(L +W))

Using the given dimensions, L=5, W=2, H=3, the area is ...

  SA = 2(5·2 +3(5 +2)) = 2(10 +3(7)) = 2(31)

  SA = 62 . . . square units

The surface area of the prism is 62 square units.

The computation of the future value is $92,691.08

As we know that

Future value = Present value × (1 + interest rate)^number of years

where, the Present value is $24275

The Interest rate is 4.05%

And, the number of the year is 10 years

Now placing these values to the above formula;

So, the future value is;

Future value = Present value × (1 + interest rate)^number of years

= $24275× (1 + 0.0405)^10

= $24275× 1.448298166

= $92,691.08

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From the first two rows we can see that:

Fill in the missing values.

Answer:

0.5a + 0.75p ≤ 23

Step-by-step explanation:

Cost of a apples: 0.5a

Cost of p pears: 0.75p

The total cost must be $23 or less.

0.5a + 0.75p ≤ 23

Answer:

  see the attachment

Step-by-step explanation:

You want to match several expressions with fractional exponents to their equivalent radical forms.

The relationship between the two forms is ...

  [tex]a^{\frac{m}{n}}=\sqrt[n]{a^m}[/tex]

If n=2, or m=1, these are omitted from the radical form.

The attachment shows the matching values.

On solving the question we got to know that - Answer: For every ticket sold, 52$ is made, 1 : 52

A diagram or graphical representation that organizes the depiction of data or values is known as a graph. The relationships between two or more items are frequently represented by the points on a graph.

A graph is a type of non-linear data structure that consists of nodes and links. While the vertices are often sometimes referred to as nodes, in a graph the edges are the lines or arcs that connect any two nodes. The vertices (V) and edges (E) that make up a graph are what constitute it most rigorously ( E ). The prefix "G" appears in the graph (E, V).

y = mx - rise/run  = 208/4,  m = 52

The proportion is that for every ticket sold, 52 $ is made, 1 : 52

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The money he will have in this account if he keeps it for 5 years is $358.

Compound interest is the term used to describe interest on savings that is calculated using both the initial principal and interest that has accrued over time. You can earn interest on interest, which is known as compound interest.

WE have given $100 and it earns 5% interest annually, you will have $105 at the end of the first year. You will have $110.25 by the conclusion of the second year.

Given,

P = $800

Time t=5 years

Interest rate= 2.9%

Hence, the amount will have in his account is:

=[tex]P(1 + 10 / 2000)^{2t}[/tex]

Here, the interest is compounded semiannually.

[tex]800 (1 + 2.9 / 200)^{10}[/tex]

=$358

Therefore, if the interest rate is compounded semiannually then the money he will have in this account if he keeps it for 5 years is $358.

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Answer:

-12

Step-by-step explanation:

If g(x) = 5x, then plugging in -60 for g(x) gives -60 = 5x. Dividing both sides of this equation by 5 gives -12 = x. Therefore, the correct answer is -12.

Answer:

True

Step-by-step explanation:

This is true by definition.

The best prediction of the number of clicks on the advertisement if 1,500 people visit the website is; C: 83

We want to find the best prediction of the number of clicks on the advertisement if 1,500 people visit the website.

Now, we see the coordinates from the table;

(1045, 60)

(1106, 63)

(1500, y)

where y  is the best prediction of the number of clicks on the advertisement if 1,500 people visit the website.

By interpolation, we can say that;

(y - 63)/(1500 - 1106) = (63 - 60)/(1106 - 1045)

(y - 63)/394 = 3/39

(y - 63)/394 = 1/13

Cross multiply to get;

y - 63 = 394/13

y = 93

Looking at the options, the closest option is option C.

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The growth constant is 1.0986 and the trout population will increase to 14600 after 2.1 years. The result is obtained by using the logistic equation.

The increase of population can be found by using the logistic equation. It is

[tex]P(t) = \frac{K}{1 + Ae^{-kt} }[/tex]

Where

Sunset Lake is stocked with the rainbow trout. We have

Find the growth constant k and time t when P(t) = 14600!

A = (K - P₀)/P₀

A = (28000 - 2800)/2800

A = 25200/2800

A = 9

After 1 year, we have 7000 rainbow trout. The growth constant is

[tex]7000 = \frac{28000}{1 + 9e^{-k(1)} }[/tex]

[tex]1 + 9e^{-k} = 4[/tex]

[tex]9e^{-k} = 3[/tex]

[tex]e^{-k} = \frac{1}{3}[/tex]

k = - ln (1/3)

k = 1.0986

Use k value to find the time when the population will increase to 14600!

[tex]14600 = \frac{28000}{1 + 9e^{-1.0986t} }[/tex]

[tex]1.9178 = 1 + 9e^{-1.0986t}[/tex]

[tex]0.9178 = 9e^{-1.0986t}[/tex]

[tex]\frac{0.9178 }{9} = e^{-1.0986t}[/tex]

[tex]t = \frac{ln \: 0.10198}{-1.0986}[/tex]

t = 2.078

t ≈ 2.1 years

It is in another 1.1 years after t = 1.

Hence, the growth constant k is 1.0986 the population will increase to 14600 when t is 2.1 years.

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the base of a solid is a circular disk with radius 3. Therefore, the volume of the solid is 27π.

The volume of a solid is determined using the formula V = πr²h, where r is the radius of the base and h is the height of the solid. In this problem, the base is a circular disk with radius 3, and the cross-sections are isosceles right triangles with hypotenuse lying along the base. Since the cross-sections are isosceles right triangles, the height of each triangle is equal to the radius of the base, which is 3. Therefore, the height of the solid is also 3. Substituting these values into the formula gives V = π(3)²(3), which simplifies to V = 27π.

Therefore, the volume of the solid is:

V = πr²h

V = π(3)²(3)

V = 27π

Therefore, the volume of the solid is 27π.

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