A ball is released at a height of 16 inches to roll inside a half-cylinder. It rolls
to a height of 8 inches on the other side of the cylinder on roll 1. Each time it
rolls up a side of the cylinder, the ball reaches a point that is as high as it
had reached on the other side.
-lo
This explicit formula models the height of the ball, in inches, the nth time it
rolls up a side of the cylinder.

How high does the ball roll on its 5th time up the cylinder's side?​

Answer:

3,069

Step-by-step explanation:

The sequence is doubling, so terms 1 through 10 are:

3, 6, 12, 24, 48, 96, 192, 384, 768, 1,536

3 + 6 + 12 + 24 + 48 + 96 + 192 + 384 + 768 + 1,536 = 3,069

Answer:

A=108 cm²

Step-by-step explanation:

length (l)=3w

perimeter=2l+2w

P=2(3w)+2w

48=6w+2w

width=48/8

w=6

l=3w=3(6)=18

Area=l*w

A=18*6

A=108 cm²

Answer:

Option (2)

Step-by-step explanation:

In an arithmetic progression,

[tex]a_1,a_2,a_3.........a_{n-1},a_n[/tex]

First term of the progression,

a = [tex]a_1[/tex]

Common difference 'd' = [tex](a_2-a_1)[/tex]

Recursive formula for the sequence,

a = [tex]a_1[/tex]

[tex]a_n=a_{n-1}+d[/tex]

By applying these rules in the recursive formula,

[tex]a_1=\frac{4}{5}[/tex]

[tex]a_n=a_{n-1}+\frac{3}{2}[/tex]

Common difference 'd' = [tex]\frac{3}{2}[/tex]

Therefore, Option (2) will be the answer.

Answer:

[tex]\large \boxed{\sf \bf \ \ k=320 \ \ }[/tex]

Step-by-step explanation:

Hello,

The number of weekly social media posts varies directly with the square root of the poster’s age and inversely with the cube root of the poster’s income.

If a 16-year-old person who earns $8,000 makes 64 posts in a week, what is the value of k?

[tex]64=\dfrac{\sqrt{16}}{\sqrt[3]{8000}}\cdot k=\dfrac{4}{20}\cdot k=\dfrac{1}{5}\cdot k=0.2\cdot k\\\\k=64*5=320[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

C. 47.5%

Step-by-step explanation:

The  summary of the given statistics include:

mean =150000

standard deviation: 1200

The  objective is to use tributed with a mean of $150,000. Use the 68-95-99.7 rule to find the percentage of buyers who paid: between $150,000 and $152,400

The z score formula can be use to calculate the percentage of the buyer who paid.

[tex]z = \dfrac{X - \mu}{\sigma}[/tex]

For the sample mean x = 150000

[tex]z = \dfrac{150000 - 150000}{1200}[/tex]

[tex]z = \dfrac{0}{1200}[/tex]

z = 0

For the sample mean x = 152400

[tex]z = \dfrac{152400 - 150000}{1200}[/tex]

[tex]z = \dfrac{2400 }{1200}[/tex]

z  = 2

From the standard normal distribution tables

P(150000 < X < 152400) = P(0 < z < 2 )

P(150000 < X < 152400) =P(z<2) -P(z<0)

P(150000 < X < 152400) =0.9772 -0.5

P(150000 < X < 152400) = 0.4772

P(150000 < X < 152400) = 47.7%  which is close to 47.5% therefore option C is correct

This question is based on concept of  statistics. Therefore, correct option is C i.e. 47.5% of buyers who paid: between $150,000 and $152,400 if the standard deviation is $1200.

Given:

Mean is $150,000, and

Standard deviation is $1200.

We need to determined the percentage of buyers who paid: between $150,000 and $152,400 as per given mean and standard deviation.

By using z score formula can be use to calculate the percentage of the buyer who paid,

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

As given in question sample mean i.e. X= 150,000

[tex]z=\dfrac{150000-150000}{1200} \\\\z= \dfrac{0}{1200}\\\\z=0[/tex]

Now for the sample mean X = 152,400 ,

[tex]z=\dfrac{152400-150000}{1200} \\\\\\z= \dfrac{24000}{1200}\\\\\\z=2[/tex]

By using standard normal distribution table,

P(150000 < X < 152400) = P(0 < z < 2 )

P(150000 < X < 152400) =P(z<2) -P(z<0)

P(150000 < X < 152400) =0.9772 -0.5

P(150000 < X < 152400) = 0.4772

P(150000 < X < 152400) = 47.7%  which is close to 47.5%

Therefore, correct option is C that is 47.5%.

For further details, please prefer this link:

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Answer:

3.416, bar above 6

Step-by-step explanation:

41/12 = 3.4166666666666

41/12 = 3 & 5/12

Answer:

66

Step-by-step explanation:

41/12 = 3.4166

Answer:

A. 55, 89

Step-by-step explanation:

In a Fibonacci sequence, you start with 2 given numbers. Then each subsequent number is the sum of the last two numbers.

12, 21, 34

12 + 21 = 34

34 + 21 = 55

55 + 34 = 89

Answer: 55, 89

Answer:

√(x)

Step-by-step explanation:

(1)/(x^-(1/2)) that's 3 goes into -3 leaving 1 and goes into 6 leaving 2

1/2 is same as 2^-1

so therefore we can simplify the above as

x^-(-1/2)

x^(1/2)

and 4^(1/2)

is same as √(4)

so we conclude as

√(x)

Answer:

-1 and 1

Step-by-step explanation:

Reciprocal means "one divided by...".

1/-1 = -1 and 1/1 = 1

Answer:

Hey there!

The slope is -1/3, because the rise over run is -1/3.

Let me know if this helps :)

Answer: А.

The function f intersects the x-axis at two points, and the function g never intersects the x-axis.

Step-by-step explanation:

In the graph we can see f(x), first let's do some analysis of the graph.

First, f(x) is a quadratic equation: f(x) = a*x^2 + b*x + c.

The arms of the graph go up, so the leading coefficient of f(x) is positive.

The vertex of f(x) is near (-0.5, -2)

The roots are at x = -2 and x = 1. (intersects the x-axis at two points)

Now, we know that:

g(x) has a positive leading coefficient, and a vertex at (0, 3)

As the leading coefficient is positive, the arms go up, and the minimum value will be the value at the vertex, so the minimum value of g(x) is 3, when x = 0.

As the minimum value of y is 3, we can see that the graph never goes to the negative y-axis, so it never intersects the x-axis.

so:

f(x) intersects the x-axis at two points

g(x) does not intersect the x-axis.

The correct option is A.

Answer:

The answer is A.) The function f  intersects the x-axis at two points, and the function g never intersects the x-axis.

Step-by-step explanation:

I took the test and got it right.

Question

In a study of 100 new cars, 29 are white. Find p and q , where p is the proportion of new cars that are white.

Answer:

p = 0.29  and q = 0.71

Step-by-step explanation:

Given

Total new cars =  100

White new cars = 29

Required

Determine p and q

From the question;

p represents white new cars

Hence;

[tex]p = 29[/tex]

Note that;

[tex]p + q = 100[/tex]

Substitute 29 for p

[tex]29 + q = 100[/tex]

[tex]29 - 29 + q = 100 - 29[/tex]

[tex]q = 100 - 29[/tex]

[tex]q = 71[/tex]

The proportion of p is calculate by dividing p by the total number of new cars (Same process is done for q)

For proportion of p

[tex]Proportion,\ p = \frac{p}{new\ cars}[/tex]

[tex]Proportion,\ p = \frac{29}{100}[/tex]

[tex]Proportion,\ p = 0.29[/tex]

For proportion of q

[tex]Proportion,\ q = \frac{q}{new\ cars}[/tex]

[tex]Proportion,\ q = \frac{71}{100}[/tex]

[tex]Proportion,\ q = 0.71[/tex]

Answer:

6x-3=21

6x=24

x=4

........

6x+27=39

6x=39-27

6x=12

x=2

........

8x-10=14

8x=24

x=3

.........

6+6x=22

6x=22-6

x=3

......

12x-2=28

12x=26

x=3

.....

8-4x=16

-4x=8

x=-2

.....

4x-24=3x-3

4x-3x=24-3

x=21

....

9x+6=6x+12

9x-6x=12-6

3x=6

x=2

Answer:

Step-by-step explanation:

1. 3(2x - 1) = 21

 = 6x - 3 = 21

 = 6x = 24

 = x = 24/6 = 4

------------------------------

2. 3(2x+9) = 39

   = 6x + 27 = 39

   = 6x = 39 - 27

   = 6x = 12

   = x = 12/6 = 2

--------------------------------

3. 2(4x - 5) = 14

  = 8x - 10 = 14

  = 8x = 14+10

 = x = 3

-------------------------------

Answer:

A. 120

Step-by-step explanation:

The rest of the answers are acute.

120 is the only one that matches the type of angle <V is.

Always pay attention to the type of angle it is.

Answer:

its [c] if Bradley serves 4 tables he will earn an average of $25

Step-by-step explanation:

Answer: C

Step-by-step explanation:

Since this is an isosceles triangle as indicated by the markers on QP and PR, we know that QS and SR are equivalent.

To find the value of n, we set QS and SR equal to each other.

6n+3=4n+11                     [combine like terms]

2n=8                                 [divide both sides by 2]

n=4

Now that we know n=4, we know that A is incorrect. What we can do is use the value of n to solve for QS, SR, and QR.

QS

6(4)+3=13

Since the length of QS is 13, we know B is incorrect.

SR

4(4)+11=27

Since SR is 27, C is a correct answer.

QR

13+27=40

Since QR is 40, the only correct answer is C.

Answer: Find answer in the attached files

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hello, just apply the instructions as below.

[tex]3(x-2)^2(x+5)^3[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

3 years

Step-by-step explanation:

Use the formula I = prt, where I is the interest money made, p is the starting amount of money, r is the interest rate as a decimal, and t is the time the money was borrowed.

Plug in the values and solve for t:

108 = (1200)(0.03)(t)

108 = 36t

3 = t

= 3 years

Answer:

v (m/s) a(m/s2). √. ½. 0. ¼. √. -¼. Movimiento circular y M.A.S. Un punto se mueve ... como la que se ilustra en la figura, llamada onda cuadrada. ... Movimiento Armónico Simple I. Una partícula cuya masa es de 1 g vibra con movimiento ... Multiplicando por el Periodo de oscilación del sistema T (con ... distancia de 10 m?

Step-by-sv (m/s) a(m/s2). √. ½. 0. ¼. √. -¼. Movimiento circular y M.A.S. Un punto se mueve ... como la que se ilustra en la figura, llamada onda cuadrada. ... Movimiento Armónico Simple I. Una partícula cuya masa es de 1 g vibra con movimiento ... Multiplicando por el Periodo de oscilación del sistema T (con ... distancia de 10 m?tep explanation:

Answer:

81.432 minutes

Step-by-step explanation:

Given the following :

Video Games (Mins) - - - Time with Family(Mins)

40 - - - - - - - - - - - - - - - - - - - 80

55 - - - - - - - - - - - - - - - - - - - 75

70 - - - - - - - - - - - - - - - - - - - 69

85 - - - - - - - - - - - - - - - - - - - 64

Best fit line:

ý = -0.363x +94.5

For someone who spent 36 minutes playing video games, the predicted number of minutes spent with family according to the best fit line will be:

Here number of minutes playing video games '36' is the independent variable

ý is the dependent or predicted variable ;

94.5 is the intercept

ý = -0.363(36) +94.5

ý = −13.068 + 94.5

ý = 81.432 minutes

Which is about 81 minutes to the nearest whole number.

Answer:

True

Step-by-step explanation:

The statement given above in the question is correct. It is mentioned that men are free to create a list of women's according to their preferences. There will be order sequence of women and men places them in queue of their preference. The men proposes the women with highest ranking in the list then it is possible that all men gets their preferred choice.

Answer:

35/14

Step-by-step explanation: 35/14

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

Answer:

10 girls.

Step-by-step explanation:

Boys: 5x

Girls: 2x

next... 5x + 2x = 35

7x= 35

x=5

Answer. 10 girls.

Answer:

the number is 80

Step-by-step explanation:

let x be an unknown number so from the above question we deduce that

(70/100)*x=56

70x/100=56

70x=56*100

70x=5600

70x/70=5600/70

x=80

Answer:

720

Step-by-step explanation:

It takes 240 cherries to make 3 pies.

9 pies are 3 times 3 pies, so it takes 3 times as many cherries.

3 * 240 cherries = 720 cherries.

[tex]\text{Find how many cherries is needed for 9 pies}\\\\\text{We know that there are 240 total cherries on 3 pies}\\\\\text{Now we need to find how many cherries will 9 pies need}\\\\\text{We simply have to multiply 240 by 3, since 3 multiplied by 3 is 9 pies}\\\text{So we would do the same with the cherries by multiplying it by 3}\\\\240\cdot3=720\\\\\boxed{\text{720 cherries}}[/tex]

[tex] 1.2\times3.5\times4.1=[(1+0.2)(3+0.5)](4+0.1)[/tex]

$=[1\times3+1\times0.5+0.2\times3+0.2\times0.5](4+0.1)$

$=(3+0.5+0.6+0.1)(4+0.1)$

$=(4.2)(4+0.1)=(4+0.2)(4+0.1)$

$=4\times4+4\times0.1+0.2\times4+0.2\times0.1$

$=16+0.4+0.8+0.02=17.22$

Answer:

Sum : 65

Step-by-step explanation:

In this notation, n is our starting value, and hence we start at 3 and go to 7. Given the set of values : { 3, 4, 5, 6, 7 }, we can substitute in our expression " 4n - 7 " for n and solve. The sum of these values is our solution.

4( 3 ) - 7 = 12 - 7 = 5,

4( 4 ) - 7 = 16 - 7 = 9,

4( 5 ) - 7 = 20 - 7 = 13,

Our remaining values for n = 6 and n = 7 must then be 17 and 21. This is predictable as we have an arithmetic series here, the common difference being 4. As you can see 9 - 5 = 4, 13 - 9 = 4, 17 - 13 = 4, 21 - 17 = 4.

Therefore we have the series { 5, 9, 13, 17, 21 }. This adds to an answer of 65.

Answer:

Below

Step-by-step explanation:

● 1 + 3^2 × 2 -5

Start by calculating 3^2 wich is 9

● 1 + 9 × 2 -5

Multiply 2 by 9 (9×2=18)

● 1 + 18 -5

Add 1 to 18 (1+18 = 19)

● 19 -5

Substract 5 from 19 (19-5 = 14 )

● 14

Answer: B. Always

Explanation:

Two points always create a line. The correct answer is option B.

A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions.

If there are two points A(x₁,y₁) and B(x₂,y₂) then the distance between the two points will be the length of the line. The formula to calculate the distance is given as below:-

Distance = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Therefore, the two points always create a line. The correct answer is option B.

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Answer:

Step-by-step explanation:

Hello, the slope of the tangent is the value of the derivative.

f'(x) = 2*0.2x + 5 = 0.4x + 5

So we are looking for

[tex]-1\leq f'(x) \leq 1 \\ \\<=> -1\leq 0.4x+5 \leq 1 \\ \\<=> -1-5=-6\leq 0.4x \leq 1-5=-4 \\ \\<=> \dfrac{-6}{0.4}\leq 0.4x \leq \dfrac{-4}{0.4} \\\\<=> \boxed{-15 \leq x\leq -10}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Using derivatives, it is found that the x-values in which the slope belong to the interval (-1,1) are in the following interval is (-15,-10).

It is given by the derivative at x = x_0, that is:

m = f'(x_0)

In this problem, the function is:

f(x) = 0.2x^2 + 5x − 12

Hence the derivative is:

f'(x) = 0.4x + 5

For a slope of -1, we have that,

0.4x + 5 = -1

0.4x = -6

x = -15.

For a slope of 1, we have that,

0.4x + 5 = 1.

0.4x = -4

x = -10

Hence it is found that the x-values in which the slope belong to the interval (-1,1) are in the following interval is (-15,-10).

More can be learned about derivatives and tangent lines at;

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