Suppose a ball is thrown upward to a height of h 0 meters. After each​ bounce, the ball rebounds to a fraction r of its previous height. Let h Subscript n be the height after the nth bounce. Consider the following values of h 0 and r. Complete parts​ (a) and​ (b) below. h0=30​, r=0.25
a- find the first 4 terms of the sequence of heights(hn)
b- find a general expression for the nth term of the sequence (hn)

Answer:

  39.5 ft

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relation between angles and sides of a right triangle.

  Tan = Opposite/Adjacent

This lets us write two equations in two unknowns:

  tan(67°) = AD/CD . . . . . . . . . . angle at guy point

  tan(39°) = AD/(CD+32) . . . . . .angle 32' farther

__

Solving the first equation for CD and using that in the second equation, we can get an equation for AD, the height of the tower.

  CD = AD/tan(67°)

  tan(39°)(CD +32) = AD . . . . eliminate fractions in the second equation

  tan(39°)(AD/tan(67°) +32) = AD

  32·tan(39°) = AD(1 -tan(39°)/tan(67°)) . . . simplify, subtract left-side AD term

  32·tan(39°)tan(67°)/(tan(67°) -tan(39°)) = AD . . . . divide by AD coefficient

  AD ≈ 39.486 . . . . feet

The tower is about 39.5 feet high.

Answer:

[tex]F = \frac{3}{5} x - 8\cdot \ln |x| + C[/tex]

Step-by-step explanation:

Let be [tex]f(x) = \frac{3}{5}-\frac{8}{x}[/tex] and [tex]F[/tex] is the antiderivative of [tex]f(x)[/tex] such that:

1) [tex]F = \int {\left(\frac{3}{5}-\frac{8}{x} \right)} \, dx[/tex] Given.

2) [tex]F = \frac{3}{5} \int \, dx -8\int {\frac{dx}{x} }[/tex] ([tex]\int {[f(x)+g(x)]} \, dx = \int {f(x)} \, dx + \int {g(x)} \, dx[/tex])

3) [tex]F = \frac{3}{5} x - 8\cdot \ln |x| + C[/tex], where [tex]C[/tex] is the integration constant. ([tex]\int {k} \, dx = k\cdot x[/tex]; [tex]\int {\frac{dx}{x} } = \ln|x|[/tex], [tex]\int {k\cdot f(x)} \, dx = k\int {f(x)} \, dx[/tex]) Result.

Answer:

slope of the line through (3, 7) and (-1, 4) is

[tex]m = \frac{4 - 7}{ - 1 - 3} \\ \\ = \frac{ - 3}{ - 4} \\ \\ = \frac{3}{4} [/tex]

Hope this helps you

Answer:

3/4

Step-by-step explanation:

Using the slope formula

m = (y2-y1)/(x2-x1)

   = (4-7)/(-1-3)

   = -3/-4

   = 3/4

Answer:

(a) (1,5)

(b) Every subset of a cartesian product is a relation, therefore this is a relation.

(c) The relation IS NOT a function.

Step-by-step explanation:

(a)

(1,5)

Notice that  3(1) +1 = 4  < 5 therefore (1,5) is an order pair that satisfies the equation.

(b)

Every subset of a cartesian product is a relation, therefore this is a relation.

(b)

A relation is a function of  the following condition holds

if    (a,b) and (c,b) belong to the relation then (a=c)

In this case, (1,5), (0,5) belong to the relation but  0 is different than 5, therefore the relation IS NOT a function.

Hey there! I'm happy to help!

We see that it takes 45 minutes for a person to drive 50 miles. We can write this as a fraction that is 45/50, which simplifies to 9/10, meaning it would take this person 9 minutes to travel 10 miles.

So, how long would it take to travel 120? Well, we know that if we take 10 miles and multiply it by 12 we will have 120 miles. If we take the time it takes to drive those ten miles (9 minutes) and multiply it by 12, we will figure out how long it takes to drive 120 miles!

9×12=108

However, we want this to be written in hours. We know that there are 60 minutes in an hour, and if we subtract 60 from 108 we have 48. This gives us 1 hour and 48 minutes.

Therefore, it will take 1 hour and 48 minutes for this person to travel 120 miles at the same rate.

Have a wonderful day! :D

Answer: [tex]H_0:p=0.29[/tex]

[tex]H_a: p \neq0.29[/tex]

Step-by-step explanation:

A null hypothesis[tex](H_0)[/tex] is a type of statement used in statistics that proposes that there is no difference between particular characteristics of a population whereas the alternative hypothesis[tex](H_a)[/tex] proposes that there is a difference.

Let p be the population proportion of workers got their job through networking.

Given: 29% of workers got their job through networking.

i.e. [tex]H_0:p=0.29[/tex]

A researcher feels this percentage has changed.

i.e. [tex]H_a: p \neq0.29[/tex]

Hence, the required null and alternative hypotheses in symbolic form for this claim:

[tex]H_0:p=0.29[/tex]

[tex]H_a: p \neq0.29[/tex]

Answer:

[tex] f(x) =\sqrt{x} sin (x)[/tex]

And on this case we can use the product rule for a derivate given by:

[tex] \frac{d}{dx} (f(x)* g(x)) = f'(x) g(x) +f(x) g'(x)[/tex]

Where [tex] f(x) =\sqrt{x}[/tex] and [tex] g(x) =sin (x)[/tex]

And replacing we have this:

[tex] f'(x)= \frac{1}{2\sqrt{x}} sin (x) + \sqrt{x}cos(x)[/tex]

Step-by-step explanation:

We assume that the function of interest is:

[tex] f(x) =\sqrt{x} sin (x)[/tex]

And on this case we can use the product rule for a derivate given by:

[tex] \frac{d}{dx} (f(x)* g(x)) = f'(x) g(x) +f(x) g'(x)[/tex]

Where [tex] f(x) =\sqrt{x}[/tex] and [tex] g(x) =sin (x)[/tex]

And replacing we have this:

[tex] f'(x)= \frac{1}{2\sqrt{x}} sin (x) + \sqrt{x}cos(x)[/tex]

Answer:

Step-by-step explanation:

Length the length and breadth of the rectangle be x and y.

Area of the rectangle A = Length * breadth

Perimeter P = 2(Length + Breadth)

A = xy and P = 2(x+y)

If the area of the rectangle is 512m², then 512 = xy

x = 512/y

Substituting x = 512/y into the formula for calculating the perimeter;

P = 2(512/y + y)

P = 1024/y + 2y

To get the value of y, we will set dP/dy to zero and solve.

dP/dy = -1024y⁻² + 2

-1024y⁻² + 2 = 0

-1024y⁻² = -2

512y⁻² = 1

y⁻² = 1/512

1/y² = 1/512

y²  = 512

y = √512 m

On testing for minimum, we must know that the perimeter is at the minimum when y = √512

From xy = 512

x(√512) = 512

x = 512/√512

On rationalizing, x = 512/√512 * √512 /√512

x = 512√512 /512

x = √512 m

Hence, the dimensions of a rectangle is √512 m  by √512 m

Answer:

62

Step-by-step explanation:

Turn 4 and 1/2 into a decimal.

4.5

Divide 279 by 4.5

279/4.5=62

You can cut 62 4 and 1/2 inch pieces.

Answer:

candles = $400

matches = $20

Step-by-step explanation:

Let cost of candles = $c

Let cost of matches = $m

c = 20 m (20 times m)

c + m = 420

20m + m = 420

21 m = 420

m = 20

c = 20 (20) = 400

Answer:

97 m

Step-by-step explanation:

Perimeter = 2 * (length + width); perimeter = 344, width = 75 (solving for length)

344 = 2(length + 75)

172 = length + 75

length = 97

Answer: 6 with milk, 9 without

Step-by-step explanation:

2/5 of the cookies he eats are dunked.  Thus, simply do 2/5, or .4*15 to get that 6 cookies are dunked, and 15-6 to get that 9 cookies are not dunked.

Hope it helps <3

Answer:

Step-by-step explanation:

6y = -5x + 18

y = -5/6x + 3

perp slope: 6/5

y - 7 = 6/5(x - 10)

y - 7 = 6/5x - 12

y = 6/5x - 5

Here, we are required to write an equation perpendicular to 5x + 6y = 18.

6x - 5y = 25.

Therefore, slope of equation 5x + 6y = 18 is -5/6.

Therefore, m1m2 = -1

Therefore, the slope of the required line, m2 is;

m2 = 6/5

Therefore, the equation of a line perpendicular to the equation 5x+6y=18 and passes through the point (10,7) is given as;

6/5 = (y - 7)/(x - 10).

By cross product; we have;

6x - 60 = 5y - 35

6x - 5y = 25.

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Answer: 4.3 mi

Step-by-step explanation:

From Oxford, getting to Kingswood takes 7.5mi, and getting to Norwood takes 11.8mi.  Thus, simply do 11.8-7.5 to get 4.3mi.

Hope it helps <3

[tex]\frac{257}{4}[/tex]

[tex]64\frac{1}{4}=\frac{64*4+1}{4}=\frac{256+1}{4}=\frac{257}{4}[/tex]

The conversion of this mixed number 64 1/4 into an improper fraction is 257/4.

In Mathematics and Geometry, a fraction simply refers to a numerical quantity (numeral) which is not expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.

In this exercise and scenario, we would convert the given mixed fraction into an improper fraction into a  by multiplying and adding as follows;

64 1/4 = ((4 × 64) + 1)/4

64 1/4 = 257/4

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Answer:

It should be about $19,500

Step-by-step explanation:

Answer:

$19,511.10

Step-by-step explanation:

1203*4.7= The total change over 4.7 years.

1203*4.7=5654.10

5654.10+13857=The total price after 4.7 years.

5654.10+13857=19,511.10

Answer:

C.

Step-by-step explanation:

So, here's what you need to remember:

If we have a function f(x) and a factor k:

k(f(x)) will be a vertical stretch if k is greater than 1, and a vertical compression if k is greater than zero but less than 1.

f(kx) will be a horizontal compression if k is greater than 1, and a horizontal stretch if k is greater than zero but less than 1.

We are multiplying 0.5 to the function. In other words: 0.5f(x).

This is outside the function, so it's vertical.

0.5 is less than 1, so this would be a vertical compression

Answer:

a. uses a related sample - repeated measures

c. uses a related sample (matched subjects)

Step-by-step explanation:

A) You are interested in a potential treatment for compulsive hoarding. You treat a group of 50 compulsive hoarders and compare their scores on the Hoarding Severity scale before and after the treatment. You want to see if the treatment will lead to lower hoarding scores.  

The design described uses a related sample - repeated measures because the scores were compared on the Hoarding Severity scale before and after the treatment.

B) John Caccioppo was interested in possible mechanisms by which loneliness may have deterious effects of health. He compared the sleep quality of a random sample of lonely people to the sleep quality of a random sample of nonlonely people.

The design described uses a related sample (matched subjects)

Answer:

2π/7

Step-by-step explanation:

A cosine wave is:

y = A cos(2π/T x + B) + C

where A is the amplitude,

T is the period,

B is the horizontal shift,

and C is the vertical shift.

In this case:

7 = 2π/T

T = 2π/7

Answer:

The period the la function  is with the formula that will be explained below

Step-by-step explanation:

The period is calculated with this formula:

                   2 π

                     b

The absolute value is the distance between a number and zero, therefore the distance between zero and 7 is therefore 7; therefore we finally have:

Periodo:  

2 π

  7  

Answer:

3.

Step-by-step explanation:

Solve in the order of pemdas.

Answer:

[tex]\boxed{\sf 3}[/tex]

Step-by-step explanation:

Solve brackets first.

[tex]2[16-5 \cdot 2]\div4[/tex]

Multiply the terms in the brackets.

[tex]2[16-10]\div4[/tex]

Subtract the terms in the brackets.

[tex]2[6]\div4[/tex]

Divide the numbers.

[tex]2(\frac{6}{4} )[/tex]

Multiply.

[tex]\frac{12}{4} =3[/tex]

Answer:

shape is how it looks like Square is a shape and size is how big something in like my size of my foot is 6 inches

Step-by-step explanation:

well idk your real question i think it is that your shape and size can change

Answer:  see below

Step-by-step explanation:

1) An inequality is an equation that uses >, ≥, <, or ≤ instead of an equal sign.

Example:  3x + 2 ≥ 10

2) A compound inequality is when 2 inequalities are combined using either "and" or "or".  

Example:     x > -2  and  x < 4       rewrite as: -2 < x < 4

Graph:        -2 o-----------------o 4        one line segment between the #'s

Example:          x < -2 or x > 4

Graph:        ←-----------o -2    4 o----------→      two lines in opposite directions

3) The GPA is dependent on the number of hours she studies.

Independent: hours Beth studies

Dependent: GPA

Answer:A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.

A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.

A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.

A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.

A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.

Step-by-step explanation:

The cylinder is given by A = pi/4 the volume of the prism or π/4  x (4r²h) or π x r² x h

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder. The volume of a cylinder is

Volume of Cylinder = πr²h

Surface area of cylinder = 2πr ( r + h )

where r is the radius of the cylinder

h is the height of the cylinder

Given data ,

Area circle is A = πr²

Area square with side s = s²

The side of the square is equal to the diameter of the circle

Area square = D²

A diameter of square is always twice the radius

Area square = (2r)² = 2²r² = 4r²

So , on simplifying , we get

Area circle/Area square = (πr²)/(4r²)

Area circle/Area square = π/4

Now , The volume Prism = Area Square x h

Volume Prism =  4r²h

Volume of Cylinder= Area Circle x h

Volume of Cylinder = π x r² x h

So , Volume Cylinder/Volume Prism = π x r² x h/4r² x h

Volume of Cylinder/Volume of Prism = π/4

Volume of Cylinder = π/4 x Volume Prism

And , The volume of Cylinder = π/4  x (4r²h)

Hence , the volume of cylinder is V = π/4  x (4r²h)

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Answer:

4

Step-by-step explanation:

g(x) = x² − 2x + 5

g'(x) = 2x − 2

g'(3) = 4

Answer:

The  probability is  [tex]P(X < 900 ) = 0.0918[/tex]

Step-by-step explanation:

From the question we are told that

   The sample mean is  [tex]\= x = 1100[/tex]

    The  standard deviation is  [tex]\sigma = 150[/tex]

     The random number value is  x =900

The probability that a trainee earn less than 900 a month is mathematically represented as

       [tex]P(X < x) = P(\frac{X -\= x}{\sigma} < \frac{x -\= x}{\sigma} )[/tex]

Generally the z-value for the normal distribution is mathematically represented as

       [tex]z = \frac{x -\mu }{\sigma }[/tex]

So From above we have

      [tex]P(X < 900 ) = P(Z < \frac{900 -1100}{150} )[/tex]

      [tex]P(X < 900 ) = P( Z <-1.33)[/tex]

Now from the z-table

    [tex]P(X < 900 ) = 0.0918[/tex]

Answer:

C. 1/8

Step-by-step explanation:

Probability of shooting a goal on a throw is 2/4 = 1/2.

Probability of 3 in a row is (1/2)³ = 1/8.

Answer:

Step-by-step explanation:

This problem is on the mensuration of solids, a box

we know that the volume of a box is give by the expression

[tex]Volume= L^3[/tex]

now to find the dimension of the box, we need to find L

Given data

volume = [tex]62,500 cm^3[/tex].

[tex]62,500 cm^3= L^3\\L=\sqrt[3]{62500} \\\L=39.69 cm[/tex]

Answer:

The dimensions of box that will minimize the amount of material used is [tex]39.69cm[/tex]

Step-by-step explanation:

Given information

Volume [tex]V=62500cm^3[/tex]

As given in question the box is of square shape:

So the volume will be

[tex]V=L^3[/tex]

where, L is the side of the square

[tex]V=L^3=62500\\L=\sqrt[3]{62500} \\L=39.69 cm\\[/tex]

Hence, The dimensions of box that will minimize the amount of material used is [tex]39.69cm[/tex].

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Answer:

49.923 mph

Step-by-step explanation:

we know that the car traveled 133 miles in h hours at an average speed of x mph.

That is, xh = 133.

We can also write this in terms of hours driven: h = 133/x.

If x was 30 mph faster, then h would be one hour less.

That is, (x + 30)(h - 1) = 133, or h - 1 = 133/(x + 30).

We can rewrite the latter equation as h = 133/(x + 30) + 1

We can then make a system of equations using the formulas in terms of h to find x:

h = 133/x = 133/(x + 30) + 1

133/x = 133/(x + 30) + (x + 30)/(x + 30)

133/x = (133 + x + 30)/(x + 30)

133 = x*(133 + x + 30)/(x + 30)

133*(x + 30) =  x*(133 + x + 30)

133x + 3990 = 133x + x^2 + 30x

3990 = x^2 + 30x

x^2 + 30x - 3990 = 0

Using the quadratic formula:

x = [-b ± √(b^2 - 4ac)]/2a  

= [-30 ± √(30^2 - 4*1*(-3990))]/2(1)  

= [-30 ± √(900 + 15,960)]/2

= [-30 ± √(16,860)]/2

= [-30 ± 129.846]/2

= 99.846/2  -----------  x is miles per hour, and a negative value of x is neglected, so we'll use the positive value only)

= 49.923

Check if the answer is correct:

h = 133/49.923 = 2.664, so the car took 2.664 hours to drive 133 miles at an average speed of 49.923 mph.

If the car went 30 mph faster on average, then h = 133/(49.923 + 30) = 133/79.923 = 1.664, and 2.664 - 1 = 1.664.

Thus, we have confirmed that a car driving 133 miles at about 49.923 mph would have arrive precisely one hour earlier by going 30 mph faster

Answer:

Step-by-step explanation:

g(x) = |x – 8| + 6 was transformed from the parent function g(x) = |x|:

8 unit right

6 units up

a parent absolute value function has a vertex at (0,0)

if the function is moved so is the vertex:

(0+8,0+6)

(8,6)

So, the vertex of this function is at (8,6)

Answer:  vertex = (8, 6)

Step-by-step explanation:

The Vertex form of an absolute value function is: y = a|x - h| + k   where

g(x) = |x - 8| + 6 is already in vertex form where

h = 8 and k = 6

so the vertex (h, k) = (8, 6)