Peter has invented a game with paper cups. He lines up 121 cups face down in a straight line from left to right and consecutively labels them from 1 to 121. He then walks from left to right down the line of cups, flipping all of the cups over. He returns to the left end of the line, then makes a second pass from left to right, this time flipping cups 2,4,6,8... On the third pass, he flips cups 3,6,9,12.... He continues like this: On the ith pass, he flips over cups i, 2i, 3i, 4i,.... (By "flip," we mean changing the cup from face down to face up or vice versa.) After 121 passes, how many cups are face up?

Answer:

The probability that if Sunday is sunny, then Tuesday is also sunny is 0.86.

Step-by-step explanation:

Let us denote the events as follows:

Event 1: a sunny day

Event 2: a rainy day

From the provided data we know that the transition probability matrix is:

                 [tex]\left\begin{array}{ccc}1&\ \ \ \ 2\end{array}\right[/tex]

[tex]\text{P}=\left\begin{array}{c}1&2\end{array}\right[/tex]  [tex]\left[\begin{array}{cc}0.90&0.10\\0.50&0.50\end{array}\right][/tex]

In this case we need to compute that if Sunday is sunny, what is the probability that Tuesday is also sunny.

This implies that we need to compute the value of P₁₁².

Compute the value of P² as follows:

[tex]P^{2}=P\cdot P[/tex]

     [tex]=\left[\begin{array}{cc}0.90&0.10\\0.50&0.50\end{array}\right]\cdot \left[\begin{array}{cc}0.90&0.10\\0.50&0.50\end{array}\right]\\\\=\left[\begin{array}{cc}0.86&0.14\\0.70&0.30\end{array}\right][/tex]

The value of P₁₁² is 0.86.

Thus, the probability that if Sunday is sunny, then Tuesday is also sunny is 0.86.

Answer:

0

Step-by-step explanation:

6-24n=3n+6

Add 24n to both sides of the equation:

6=27n+6

Subtract 6 from both sides:

27n=0

Therefore, n=0.

Hope this helps!

Answer:

Step-by-step explanation:

A. The front elevation of the pyramid in the direction of the arrow is herewith attached to this answer.

B. Base of the pyramid is a square of side 12 cm.

   The height of the pyramid is 8 cm.

   Slant height, XT, is 10 cm.

The total surface area of the pyramid can be determined by adding the surface areas that make up the shape.

Area of the triangular face = [tex]\frac{1}{2}[/tex] × base × slant height

                                            =  [tex]\frac{1}{2}[/tex] × 12 × 10

                                            = 60 [tex]cm^{2}[/tex]

Area of the square base = length × length

                                         = 12 × 12

                                         = 144  [tex]cm^{2}[/tex]

Total surface area of the pyramid = area of the base + 4 (area of the triangular face)

                              = 144 + 4(60)

                              = 144 + 240

                              = 384 [tex]cm^{2}[/tex]

Therefore, total surface area of the pyramid is 384 [tex]cm^{2}[/tex].

Answer:

3/5

Step-by-step explanation:

because there are more red than blue and the fraction is 3/5 and the probability to pick a red worm is a lot higher than the blue. well there are 4 red worms and 1 blue so it would be 3 red worms out of 5 in total. this is more than 1 blue over 5. 3/5 is more than 1/5

hope this helped

Answer: 3/5

Step-by-step explanation:

Since 4 red gummies you have four out of 5 chance of getting red gummies. Without replacement there are now 4 gummies left and 3 red gummies. There for 3 out of 4 chance of getting another red gummy. Since at same time multiply. 4/5*3/4 = 12/20

Which can be simplified to 3/5

Answer:

Option (2). 14 m

Step-by-step explanation:

Formula to get the area of a circle 'A' = [tex]\pi r^{2}[/tex]

where r = radius of the circle

Given in the question,

Area of the circle = 153.86 square meters

By putting the values in the formula,

153.86 = πr²

r = [tex]\sqrt{\frac{153.86}{\pi } }[/tex]

r = [tex]\sqrt{49}[/tex]

r = 7 meters

Diameter of circle = 2 × (radius of the circle)

                              = 2 × 7

                              = 14 meters

Therefore, diameter of the circle is 14 meters.

Option (2) is the answer.

Answer:

14m

Step-by-step explanation:

Answer:

61.8

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 172.6, \sigma = 42.4[/tex]

What percentage of women have weights between the ejection seat’s weight limits (that is, 133.8 to 208.0 lb)?

We have to find the pvalue of Z when X = 208 subtracted by the pvalue of Z when X = 133.8 for the proportion. Then we multiply by 100 to find the percentage.

X = 208

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{208 - 172.6}{42.4}[/tex]

[tex]Z = 0.835[/tex]

[tex]Z = 0.835[/tex] has a pvalue of 0.798

X = 133.8

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{133.8 - 172.6}{42.4}[/tex]

[tex]Z = -0.915[/tex]

[tex]Z = -0.915[/tex] has a pvalue of 0.180

0.798 - 0.18 = 0.618

0.618*100 = 61.8%

Without the %, the answer is 61.8.

Answer:

[tex]the \: answer \: is \: d.(x + 4) {}^{2} = 8(y + 4)[/tex]

Answer:

[tex]\frac{7}{3}[/tex]

Step-by-step explanation:

csc(Ф) is equivalent to the inverse of sin(Ф)

Since sin(Ф) = 3/7, the inverse of this would be 7/3

So, [tex]csc = \frac{1}{\frac{3}{7} }=\frac{7}{3}[/tex]

Answer:

979

Step-by-step explanation:

Answer:

115/198

Step-by-step explanation:

khan

Answer:

m=-30

Step-by-step explanation:

5m+100=2m+10

We want to get the variable on one side of the equation. First we subtract 100 from both sides.

5m=2m-90

Subtract 2m from both sides.

3m=-90

Divide both sides by 3.

m=-30

Answer:

a) [tex]x(t) = 13*e^(^-^\frac{t}{100}^)[/tex]

b) 10.643 kg

Step-by-step explanation:

Solution:-

- We will first denote the amount of salt in the solution as x ( t ) at any time t.

- We are given that the Pure water enters the tank ( contains zero salt ).

- The volumetric rate of flow in and out of tank is V(flow) = 50 L / min  

- The rate of change of salt in the tank at time ( t ) can be expressed as a ODE considering the ( inflow ) and ( outflow ) of salt from the tank.

- The ODE is mathematically expressed as:

                            [tex]\frac{dx}{dt} =[/tex] ( salt flow in ) - ( salt flow out )

- Since the fresh water ( with zero salt ) flows in then ( salt flow in ) = 0

- The concentration of salt within the tank changes with time ( t ). The amount of salt in the tank at time ( t ) is denoted by x ( t ).

- The volume of water in the tank remains constant ( steady state conditions ). I.e 10 L volume leaves and 10 L is added at every second; hence, the total volume of solution in tank remains 5,000 L.

- So any time ( t ) the concentration of salt in the 5,000 L is:

                             [tex]conc = \frac{x(t)}{1000}\frac{kg}{L}[/tex]

- The amount of salt leaving the tank per unit time can be determined from:

                         salt flow-out = conc * V( flow-out )  

                         salt flow-out = [tex]\frac{x(t)}{5000}\frac{kg}{L}*\frac{50 L}{min}\\[/tex]

                         salt flow-out = [tex]\frac{x(t)}{100}\frac{kg}{min}[/tex]

- The ODE becomes:

                               [tex]\frac{dx}{dt} = 0 - \frac{x}{100}[/tex]

- Separate the variables and integrate both sides:

                       [tex]\int {\frac{1}{x} } \, dx = -\int\limits^t_0 {\frac{1}{100} } \, dt + c\\\\Ln( x ) = -\frac{t}{100} + c\\\\x = C*e^(^-^\frac{t}{100}^)[/tex]

- We were given the initial conditions for the amount of salt in tank at time t = 0 as x ( 0 ) = 13 kg. Use the initial conditions to evaluate the constant of integration:

                              [tex]13 = C*e^0 = C[/tex]

- The solution to the ODE becomes:

                           [tex]x(t) = 13*e^(^-^\frac{t}{100}^)[/tex]

- We will use the derived solution of the ODE to determine the amount amount of salt in the tank after t = 20 mins:

                           [tex]x(20) = 13*e^(^-^\frac{20}{100}^)\\\\x(20) = 13*e^(^-^\frac{1}{5}^)\\\\x(20) = 10.643 kg[/tex]

- The amount of salt left in the tank after t = 20 mins is x = 10.643 kg

Answer:

(a) 5* 10¹⁰ (b) 5* 10⁴ particles / m²

Step-by-step explanation:

Solution

(a) We find the number of particles that is created

Now,

The energy will change into particles of masses that is averaging  200 MeV/c²

The number of particles that were created is stated as follows:

n = Ec/Er

Ec =This is the cosmic energy

Er =The rest mass energy

Thus, we  replace 10¹⁰ with Ec and (0.200 GeV/c²)c² for Er

This gives us the following:

n = 10¹⁰ GeV/ (0.200 GeV/c²)c²

= 5* 10¹⁰

Hence the number of particle created is 5* 10¹⁰

(b) We now find how many particles are there per square meter

Thus,

n/m² = 5* 10¹⁰ particles/(1000 m)²

= 5* 10⁴ particles / m²

Hence, the particles that are there per square meter is 5* 10⁴ particles / m²

Note: Kindly find an attached copy of the complete question to this solution below.

Answer:

[tex]E_{A} =0.25*160=40[/tex]  

[tex]E_{B} =0.25*160=40[/tex]

[tex]E_{C} =0.4*160=64[/tex]

[tex]E_{D} =0.05*160=8[/tex]  

[tex]E_{F} =0.05*160=8[/tex]  

And now we can calculate the statistic:  

[tex]\chi^2 = \frac{(36-40)^2}{40}+\frac{(42-40)^2}{40}+\frac{(60-64)^2}{64}+\frac{(14-8)^2}{8}+\frac{(8-8)^2}{8} =5.25[/tex]  

The answer would be:

c. 5.25

Step-by-step explanation:

The observed values are given by:

A: 36

B: 42

C: 60

D: 14

E: 8

Total =160

We need to conduct a chi square test in order to check the following hypothesis:  

H0: There is no difference in the proportions for the final grades

H1: There is a difference in the proportions for the final grades

The level of significance assumed for this case is [tex]\alpha=0.01[/tex]  

The statistic to check the hypothesis is given by:  

[tex]\chi^2 =\sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}[/tex]  

Now we just need to calculate the expected values with the following formula [tex]E_i = \% * total[/tex]  

And the calculations are given by:  

[tex]E_{A} =0.25*160=40[/tex]  

[tex]E_{B} =0.25*160=40[/tex]

[tex]E_{C} =0.4*160=64[/tex]

[tex]E_{D} =0.05*160=8[/tex]  

[tex]E_{F} =0.05*160=8[/tex]  

And now we can calculate the statistic:  

[tex]\chi^2 = \frac{(36-40)^2}{40}+\frac{(42-40)^2}{40}+\frac{(60-64)^2}{64}+\frac{(14-8)^2}{8}+\frac{(8-8)^2}{8} =5.25[/tex]  

The answer would be:

c. 5.25

Now we can calculate the degrees of freedom for the statistic given by:  

[tex]df=(categories-1)=(5-1)=4[/tex]

And we can calculate the p value given by:  

[tex]p_v = P(\chi^2_{4} >5.25)=0.263[/tex]  

The p value is higher than the significance so we have enough evidence to FAIL to reject the null hypothesis

Answer:

Step-by-step explanation:

[tex]y = f(x) =\frac{1}{\sqrt{3 \pi} } e^{-x^{2/3}}[/tex]

y = 0, x = 0 and x = 3

Consider an element of thickness dx at a distance x from the origin. By Cylindirical Shell Method, the volume of the element is given by

[tex]dV=(2\pi rdr)h=(2\pi xdx)f(x) => dV=(2\pi xdx) \frac{1}{\sqrt{3\pi}}e^{-x^{\frac{2}{3}}}[/tex]

[tex]dV=2\sqrt{\frac{\pi}{3}}xe^{-x^{\frac{2}{3}}}dx[/tex]

Integrate the above integral over the limits x=0 to x=3 which implies

[tex]\int_{0}^{V}dV=2\sqrt{\frac{\pi}{3}}\int_{0}^{3}xe^{-x^{\frac{2}{3}}}dx[/tex]

Solve by subsititution

[tex]Let,\\ -x^{\frac{2}{3}}=y => \frac{-2}{3}x^{\frac{-1}{3}}dx=dy => x^{\frac{-1}{3}}dx=\frac{-3}{2}dy[/tex]

Also, apply the new limits

[tex]At,\\\\ x=0, y=0 \ and \ At, x=3, y=-\sqrt[3]{9}[/tex]

This implies,

[tex]\int_{0}^{V}dV=2\sqrt{\frac{\pi}{3}}\int_{0}^{3}x^{\frac{4}{3}}e^{-x^{\frac{2}{3}}}x^{\frac{-1}{3}}dx=2\sqrt{\frac{\pi}{3}}\int_{0}^{-\sqrt[3]{9}}y^{2}e^{y}(\frac{-3}{2})dy[/tex]

[tex]V=-\sqrt{3\pi}\int_{0}^{-\sqrt[3]{9}}y^{2}e^{y}dy[/tex]

Let,

[tex]I=\int_{0}^{-\sqrt[3]{9}}y^{2}e^{y}dy[/tex]

Integrate by parts the above integral

[tex]u=y^2 \ and \ dv=e^ydy => du=2y \ and \ v=e^y[/tex]

Integrate by parts formula

[tex]\int udv=uv-\int vdu => y^2e^y-\int 2ye^ydy[/tex]

Again integrate by parts

[tex]u=y \ and \ dv=e^ydy => du=1 \ and \ v=e^y[/tex]

Integrate by parts formula

[tex]\int udv=uv-\int vdu => y^2e^y-2[ye^y-e^y]=e^y[y^2-2y+2][/tex]

Therefore,

[tex]I=[e^y(y^2-2y+2)]_{0}^{-\sqrt[3]{9}}\\\\=e^{-2.0802}[(2.0802)^2+2(2.0802)+2]-e^{0}[0-0+2]\\\\\frac{(4.3272+4.1604+2)}{8.0061}-2\\\\=\frac{10.4876}{8.0061}-2\\\\=1.3099-2\\\\=-0.6901[/tex]

This implies, the volume is

[tex]V=-\sqrt{3\pi}I\\\\=-\sqrt{3\times 3.142} \times (-0.6901)\\\\=3.0701 \times 0.6901\\\\=2.1186[/tex]

That is, up to three decimal places

[tex]V\approx 2.118[/tex]

Answer:

Y=(-1,0)

G=(0,1)

F=(-1,3)

Step-by-step explanation:

Answer:

The probability that the next mattress sold is either king or queen-size is P=0.8.

Step-by-step explanation:

We have 3 types of matress: queen size (Q), king size (K) and twin size (T).

We will treat the probability as the proportion (or relative frequency) of sales of each type of matress.

We know that the number of queen-size mattresses sold is one-fourth the number of king and twin-size mattresses combined. This can be expressed as:

[tex]P_Q=\dfrac{P_K+P_T}{4}\\\\\\4P_Q-P_K-P_T=0[/tex]

We also know that three times as many king-size mattresses are sold as twin-size mattresses. We can express that as:

[tex]P_K=3P_T\\\\P_K-3P_T=0[/tex]

Finally, we know that the sum of probablities has to be 1, or 100%.

[tex]P_Q+P_K+P_T=1[/tex]

We can solve this by sustitution:

[tex]P_K=3P_T\\\\4P_Q=P_K+P_T=3P_T+P_T=4P_T\\\\P_Q=P_T\\\\\\P_Q+P_K+P_T=1\\\\P_T+3P_T+P_T=1\\\\5P_T=1\\\\P_T=0.2\\\\\\P_Q=P_T=0.2\\\\P_K=3P_T=3\cdot0.2=0.6[/tex]

Now we know the probabilities of each of the matress types.

The probability that the next matress sold is either king or queen-size is:

[tex]P_K+P_Q=0.6+0.2=0.8[/tex]

The slope is zero. Slope formula is Y=mx+b and since B is 1.5 and it is a straight line, Y=mx+1.5. What plus 1.5 is 1.5? 0. Hope this helps.

Answer:

The capital B refers to the base of the area

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The capital B means the area of the base

Answer:

n = -1

Step-by-step explanation:

So first subtract 9 to both sides

8n = -n - 9

Now you want the n on one side and the constant on the other

so add the single n to the n side

9n = -9

Divide 9 to both sides to solve for n

n = -1

Answer:

a) Q1= 144.10

Median = 150

Q3=155.90

b) The 99 percentile would be:[tex]a=150 +2.33*8.75=170.39[/tex]

And represent a value who accumulate 99% of the values below

Step-by-step explanation:

Let X the random variable that represent the scores of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(150,8.75)[/tex]  

Where [tex]\mu=150[/tex] and [tex]\sigma=8.75[/tex]

Part a

Lets begin with the first quartile:

[tex]P(X>a)=0.75[/tex]   (a)

[tex]P(X<a)=0.25[/tex]   (b)

We can find the quantile in the normal standard distribution and we got z=-0.674.

And we can apply the z score formula and we got:

[tex]z=-0.674<\frac{a-150}{8.75}[/tex]

And if we solve for a we got

[tex]a=150 -0.674*8.75=144.10[/tex]

The median for this case is the mean [tex]Median =150[/tex]

For the third quartile we find the quantile who accumulate 0.75 of the area below and we got z=0.674 and we got:

[tex]a=150 +0.674*8.75=155.90[/tex]

Part b

We can find the quantile in the normal standard distribution who accumulate 0.99 of the area below and we got z=2.33.

And we can apply the z score formula and we got:

[tex]z=2.33<\frac{a-150}{8.75}[/tex]

And if we solve for a we got

[tex]a=150 +2.33*8.75=170.39[/tex]

And represent a value who accumulate 99% of the values below

Answer:

Graph 2

Step-by-step explanation:

You can see that all the shaded numbers are above negative 25 in that graph. Hope this helped!

Answer:

1.5 meters

Step-by-step explanation:

The formula for the area of a trapezoid is h * (a+b)/2, where a is the first base and b is the second base. Now, we can work backwards to determine the height of the trapezoid:

3.75=h*(1.7+3.3)/2

3.75=h*2.5

h=3.75/2.5=1.5

Hope this helps!

Answer:

Step-by-step explanation:

use the formula and rearrange for h.

1/2 x h x  (a + b) = A

1/2 x (1.7 + 3.3) x h = 3.75

2.5 x h = 3.75

h = 1.5

hope this helps! :)

Use the Pythagorean theorem to solve.

Height = sqrt(12^2 -3^2)

Height = sqrt(144-9)

Height = sqrt(135)

Height = 11.6189 = 11.6 feet

Answer:

  On a graph, plot the line y = -x + 1, which has y-intercept = 1 and slope = -1, and y = 2x + 4, which has y-intercept = 4 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution.

Step-by-step explanation:

Each equation is in slope-intercept form:

  y = mx + b . . . . . where m is the slope, and b is the y-intercept

The first equation is ...

  y = -x +1

so the slope is -1, and the y-intercept is +1.

__

The second equation is ...

  y = 2x +4

so the slope is 2, and the y-intercept is 4.

__

The slopes and intercepts are properly described in the last selection.

The right answers are:

Hope it helps.

please see the attached picture for full solution

Good luck on your assignment

Answer:

-7,9

Step-by-step explanation:

x-1=-8

x=-7

x-1=8

x=9

Answer:

[tex] Median = \frac{60+60}{2}=60[/tex]

And we see that the closest values to 60 are 62 and 63 and then the answer would be:

The values closest to the middle are 62 inches and 63 inches.

Step-by-step explanation:

We have the following dataser given:

62 33 50 90  80 50 40 70  50 63 74 53  55 64 60 60  78 70 43 82

We can sort the values from the lowest to the highest and we got::

33 40 43 50 50 50 53 55 60 60 62 63 64 70 70 74 78 80 82 90

Now we see that we have n=20 values and the values closest to the middle and we can use the middle as the median and for this case the median can be calculated from position 10 and 11th and we got:

[tex] Median = \frac{60+60}{2}=60[/tex]

And we see that the closest values to 60 are 62 and 63 and then the answer would be:

The values closest to the middle are 62 inches and 63 inches.

The values closest to these middle elements are 60 and 63 inches

The dataset is given as:

62 33 50 90 80 50 40 70 50 63 74 53 55 64 60 60 78 70 43 82

Next, we sort the data elements in ascending order

33 40 43 50 50 50 53 55 60 60 62 63 64 70 70 74 78  80 82 90

The length of the dataset is 20.

So, the elements at the middle are the 10th and the 11 elements.

From the sorted dataset, these elements are: 60 and 62

Hence, the values closest to these middle elements are 60 and 63

Read more about median at:

https://brainly.com/question/14532771

Answer:

The second choice.

Step-by-step explanation:

Answer:

2nd graph down

Step-by-step explanation:

3a+11 > 5

Subtract 11 from each side

3a+11-11 > 5-11

3a > -6

Divide each side by 3

3a/3 > -6/3

a >-2

Open circle at 02

line going to the right

Answer:

I think it’s -4

Step-by-step explanation:

-2 plus -2 is -4

since 2 plus 2 is 4

Hope this helps ;)

Answer:

Step-by-step explanation:

It is because 2 plus 2 is 4

so -2 plus -2 is -4

hth!

Answer:

6^5

Step-by-step explanation:

6 multiplied with itself 5 times is equal to 6^5