An amusement park has 15 roller coasters. In how many ways can you choose 10 of the roller coasters to ride during your visit to the park? *

Answer:

the first one the measurement around the circle

Answer:

a) 60% probability that student took at least one online course

b) 40% probability that student did not take an online course

c) 12.96% probability that all 4 students selected took online courses.

Step-by-step explanation:

For each student, there are only two possible outcomes. Either they took at least one online course last fall, or they did not. The probability of a student taking an online course is independent of other students. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

3 out of 5 students enrolled in higher education took at least one online course last fall.

This means that [tex]p = \frac{3}{5} = 0.6[/tex]

a) If you were to pick at random 1 student enrolled in higher education, what is the probability that student took at least one online course?

This is P(X = 1) when n = 1. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 1) = C_{1,1}.(0.6)^{1}.(0.4)^{0} = 0.6[/tex]

60% probability that student took at least one online course.

b) If you were to pick at random 1 student enrolled in higher education, what is the probability that student did not take an online course?

This is P(X = 0) when n = 1.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{1,1}.(0.6)^{0}.(0.4)^{1} = 0.4[/tex]

40% probability that student did not take an online course

c) Now, consider the scenario that you are going to select random select 4 students enrolled in higher education. Find the probability that all 4 students selected took online courses

This is P(X = 4) when n = 4.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 4) = C_{4,4}.(0.6)^{4}.(0.4)^{0} = 0.1296[/tex]

12.96% probability that all 4 students selected took online courses.

Answer:

hope

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correct

Answer:

y = x/6 - 17/6

Step-by-step explanation:

     x - 6y = 17

<=>6y = x - 17  

<=> y  =x/6 - 17/6

Hope this helps!

Answer: x+9= -7

Step-by-step explanation:

What this statement means is that the sum or combining/adding of 9 and another number gives you -7 as the answer. We can write an equation to figure out what the other number is.

Let's use x as the unknown/other number.

x+9= -7

That is what your set up equation would look like. To solve for x, you simply subtract 9 on both sides.

x=-16

Answer:

  5.972 cm

Step-by-step explanation:

Using implicit differentiation, we have ...

  0 = (2πr +π(√(r^2+h^2) +r^2/√(r^2+h^2))·dr/dh +πrh/√(r^2+h^2)

For the given values of r and h, this is ...

  0 = (12π +π(10 +36/10))dr/dh +48π/10

  dr/dh = -4.8/(12+13.6) = -0.1875

Then the tangent line is ...

  r = -0.1875(h -8) +6

__

For a height of 8 +15/100 = 8.15, the estimated value of r is ...

  r = -0.1875(8.15 -8) +6 = -0.1875(0.15) +6 = 5.971875

The estimated value of r is 5.972 cm.

Answer:

a) margin of error ME = 5.77

b) Margin of error becomes smaller

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

x+/-ME

Where margin of error ME = zr/√n

a)

Given that;

Mean = x

Standard deviation r = 25

Number of samples n = 72

Confidence interval = 95%

z(at 95% confidence) = 1.96

Substituting the values we have;

ME = 1.96(25/√72)

ME = 1.96(2.946278254943)

ME = 5.774705379690

ME = 5.77

b)

For n = 89

ME = 1.96(25/√89)

ME = 1.96(2.649994700015)

ME = 5.193989612031

ME = 5.19

5.19 is smaller than 5.77 in a) above. So,

Margin of error becomes smaller

Answer:

-9

Step-by-step explanation:

164-43=121

121-139=-18

-18/2=-9

Answer:

-9

Step-by-step explanation:

164= x-43

164-43=x

x=121

164-43=121

121-139=18

-18/2= -9

Answer:

6x -16

Step-by-step explanation:

f(x) = 6x + 2

f(x-3) =

Replace x with x-3

f(x) = 6(x-3) + 2

   Distribute

    = 6x - 18 +2

    = 6x -16

The right answer is 6x-16

please see the attached picture for full solution

Hope it helps

Good luck on your assignment..

Answer:

1/8

Step-by-step explanation:

Answer:

When you simplify it, you get the answer of 1.

Step-by-step explanation:

Order of operation rules are required that you multiply and divide before you carrying out addition and/or subtraction.

So, simplify 2/3 / (-4) first, obtaining -1/6.

Now, you have -1/6 - 1/6 + 8/6, which combines to 1 or 6/6.

Answer:

2/3 feet.

Step-by-step explanation:

We have to calculate the length of the base of the triangle, in this case they give us the area of the triangle but still it is necessary to know the height of the triangle to calculate the length of the base, otherwise it would be impossible.

I have found an image where the graph is, which I will attach where you can see that the height is 6/5 ft. The area of the triangle is:

A = b * h / 2

solved for b which is the length of the base of the triangle would be:

b = 2 * A / h

replacing:

b = 2 * (2/5) / (6/5)

b = 20/30

b = 2/3

Which means that the length of the base of that triangle is 2/3 feet.

AnswerSo C:

Step-by-step explanation:

Answer:

the equation of the circle is

[tex](x-2)^2+(y+4)^2 = 34[/tex]

Step-by-step explanation:

Recall that the equation of a circle is given by [tex](x-h)^2+(y-k)^2 = r^2[/tex] where r is the radius, and (h,k) is the center. Recall that given two points that are the endpoints of a diameter, the center of the circle is their correspondent midpoint. Also, recall that given points (a,b), (c,d) their midpoint is obtained by [tex](\frac{a+c}{2},\frac{b+d}{2})[/tex]

In this case we are given the endpoints (-1,-9), (5,1). So the center of the circle is the midpoint obtained by [tex](\frac{-1+5}{2},\frac{-9+1}{2}) = (2, -4)[/tex]. Recall that the radius of a circle is the distance from the radius to any of the points of the circle. So, the radius is the distance between the center and the point (-1,-9). We will calculate r^2, by using the distance formula. REcall that the distance between points (a,b), (c,d) is given by

[tex]\sqrt[]{(a-c)^2+(b-d)^2}[/tex]. So, its square is

[tex](a-c)^2+(b-d)^2[/tex].

In our case,

[tex]r^2 = (2-(-1))^2+(-4-(-9))^2 = 3^2+5^2 = 34[/tex]

So, the equation of the circle is

[tex](x-2)^2+(y+4)^2 = 34[/tex]

Answer:

2.08 x 10^11

Step-by-step explanation:

To put a number into scientific notation you move the decimal to the spot right after the first digit. To figure out what the power is you count how many digits you moved it past in order to get to the spot you want it (right after the first digit; in this case the 2)

So in this case you would move the decimal from the end of the number backwards past 9 zeros, the 8, and another zero, which is a total of 11 digits.

From there you take the number with the new decimal place and multiply by 10 to the power of the number you counted earlier, which for this example is 11

So the final answer is 2.08 x 10^11

Answer:

True

Step-by-step explanation:

First start at B point than go to C point than go to A point

Answer:

It's B I think.

Step-by-step explanation: If they the lines intersected then it'd mean they crashed.

The graph below shows a recent 10-meter race between two remote-control automobiles. The racial assertions in A, B, and C are true.

A graph that shows the relationship between two or more variables, each of which is measured along one of two axes that are at right angles to one another.

At 6 meters into the race, the blue car overtook the red car because, at that moment, the blue car had a bigger distance than the red car.

Due to the greater slope of the blue vehicle's path compared to the red car's line, the blue car is faster.

Because the blue car's x-intercept is at (3, 0), where x stands for time and y for distance from the starting line, it began 3 seconds later than the other cars.

Hence Statements B, C, and D about race are true.

Q.The graph below represents a recent 10-meter race between two remote control cars.

A graph titled Remote Control Car Race has seconds after the race starts on the x-axis and distance from the start line (meters) on the y-axis. A line labeled red car goes through (3, 2) and (6, 4). A line labeled blue car goes through (3, 0) and (5, 2).

Which statements about race are true? Check all that apply.

The red car won the race because it started above the blue car.

The cars crashed 9 seconds into the race because that is the point of intersection, and neither car continued on after that point in time.

The blue car passed the red car at 6 m into the race because that is the point of intersection, and the blue car has a greater distance than the red car after that time.

The blue car is faster because the slope of its line is steeper than the slope of the line representing the red car.

The blue car started 3 seconds late because it has an x-intercept of (3, 0) and x represents the time and y represents the distance from the starting line.

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function is: f(x)=(x+10)^2

The quadratic function f whose only zero is −10 should be [tex]f(x)=(x+10)^2[/tex].

A quadratic function should be the one of the form f(x) [tex]= ax^2 + bx + c[/tex], where a, b, and c are numbered with a not equal to zero. The graph of a quadratic function is a curve known a parabola.

So here we assume that the The quadratic function f whose only zero is −10 should be [tex]f(x)=(x+10)^2[/tex].

Learn more about function here: https://brainly.com/question/13223520

Answer: True

Step-by-step explanation:

Sensitivity in such a scenario is used to measure the accuracy of the screening method. In other words, how effective is the screening method at detecting Colon Cancer.

The sensitivity of the method can be calculated by dividing the amount of people that it showed as positive by the number of people that were actually tested.

The number of people who showed positive were 14 and the amount of people tested were 16.

Sensitivity therefore is,

= 14/16

= 0.875

They should indeed determine the sensitivity of the newly proposed screening method to be .875.

Answer:

[tex]1.\ 8p = 64, p =8[/tex]

[tex]2. -\dfrac{w}{4} = 8, w = -32[/tex]

[tex]3. -5c = -20, c =4[/tex]

[tex]4.\ 9m=45, m = 5[/tex]

[tex]5. \dfrac{b}{25} = -3, b =-75[/tex]

[tex]6. \dfrac{d}{-2} = 20, d=-40[/tex]

Step-by-step explanation:

Now let us see the detailed solution of each part:

Part 1:

[tex]8p -15 = 49\\\Rightarrow 8p =49+15\\\Rightarrow 8p = 64\\\Rightarrow p =8[/tex]

Part 2:

[tex]\dfrac{-w}{4}+18=26\\\Rightarrow \dfrac{-w}{4} = 26-18\\\Rightarrow \dfrac{-w}{4} = 8\\\Rightarrow -w = 8 \times 4\\\Rightarrow w =-32[/tex]

Part 3:

[tex]-5c-15=-35\\\Rightarrow -5c = -35 +15\\\Rightarrow -5c = -20\\\Rightarrow c = 4[/tex]

Part 4:

[tex]9m +10=55\\\Rightarrow 9m =55-10\\\Rightarrow 9m =45\\\Rightarrow m =5[/tex]

Part 5:

[tex]\dfrac{b}{25}-83=-86\\\Rightarrow \dfrac{b}{25} = -86 +83\\\Rightarrow \dfrac{b}{25} = -3\\\Rightarrow b = -75[/tex]

Part 6:

[tex]\dfrac{d}{-2}+85=105\\\Rightarrow \dfrac{d}{-2} = 105-85\\\Rightarrow \dfrac{d}{-2} = 20\\\Rightarrow d=20 \times -2\\\Rightarrow d =-40[/tex]

Please refer to attached image for the answers.

Answer:

[tex]t=\frac{4.1-4.5}{\frac{1.2}{\sqrt{14}}}=-1.25[/tex]  

The degrees of freedom are given by:

[tex] df=n-1= 14-1=13[/tex]

And the p value would be:

[tex]p_v =P(t_{13}<-1.25)=0.117[/tex]  

Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly less than 4.5 minutes.

Step-by-step explanation:

Information given

[tex]\bar X=4.1[/tex] represent the sample mean

[tex]s=1.2[/tex] represent the sample deviation

[tex]n=14[/tex] sample size  

[tex]\mu_o =4.5[/tex] represent the value to test

[tex]\alpha=0.01[/tex] represent the significance level

t would represent the statistic

[tex]p_v[/tex] represent the p value

Hypothesis to test

We want to test if the true mean is less than 4.5, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \geq 4.5[/tex]  

Alternative hypothesis:[tex]\mu < 4.5[/tex]  

The statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)  

Replacing the info given we got:

[tex]t=\frac{4.1-4.5}{\frac{1.2}{\sqrt{14}}}=-1.25[/tex]  

The degrees of freedom are given by:

[tex] df=n-1= 14-1=13[/tex]

And the p value would be:

[tex]p_v =P(t_{13}<-1.25)=0.117[/tex]  

Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly less than 4.5 minutes.

this one is kinda Hard ill do sum research and help

Answer:

Step-by-step explanation:

(a)

The number of receivers is 5.

The number of CD players is 4.

The number of speakers is 3.

The number of cassettes is 4.

Select one receiver out of 5 receivers in [tex]5C_1[/tex] ways.

Select one CD player out of 4 CD players in [tex]4C_1[/tex] ways.

Select one speaker out of 3 speakers in [tex]3C_1[/tex] ways.

Select one cassette out of 4 cassettes in [tex]4C_1[/tex] ways.

Find the number of ways can one component of each type be selected.

By the multiplication rule, the number of possible ways can one component of each type be selected is,

The number of ways can one component of each type be selected is

[tex]=5C_1*4C_1*3C_1*4C_1\\\\=5*4*3*4\\\\=240[/tex]

Part a

Therefore, the number of possible ways can one component of each type be selected is 240.

(b)

The number of Sony receivers is 1.

The number of Sony CD players is 1.

The number of speakers is 3.

The number of cassettes is 4.

Select one Sony receiver out of 1 Sony receivers in ways.

Select one Sony CD player out of 1 Sony CD players in ways.

Select one speaker out of 3 speakers in ways.

Select one cassette out of 4 cassettes in [tex]4C_1[/tex] ways.

Find the number of ways can components be selected if both the receiver and the CD player are to be Sony.

By the multiplication rule, the number of possible ways can components be selected if both the receiver and the CD player are to be Sony is,

Number of ways can one components of each type be selected

[tex]=1C_1*1C_1*3C_1*4C_1\\\\=1*1*3*4\\\\=12[/tex]

Therefore, the number of possible ways can components be selected if both the receiver and the CD player are to be Sony is 12.

(c)

The number of receivers without Sony is 4.

The number of CD players without Sony is 3.

The number of speakers without Sony is 3.

The number of cassettes without Sony is 3.

Select one receiver out of 4 receivers in 4C_1 ways.

Select one CD player out of 3 CD players in 3C_1 ways.

Select one speaker out of 3 speakers in 3C_1 ways.

Select one cassette out of 3 cassettes in 3C_1 ways.

Find the number of ways can components be selected if none is to be Sony.

By the multiplication rule, the number of ways can components be selected if none is to be Sony is,

[tex]=4C_1*3C_1*3C_1*3C_1\\\\=108[/tex]

[excluding sony from each of the component]

Therefore, the number of ways can components be selected if none is to be Sony is 108.

(d)

The number of ways can a selection be made if at least one Sony component is to be included is,

= Total possible selections -Total possible selections without Sony

= 240-108

= 132  

Therefore, the number of ways can a selection be made if at least one Sony component is to be included is 132.

(e)

If someone flips the switches on the selection in a completely random fashion, the probability that the system selected contains at least one Sony component is,

[tex]= \text {Total possible selections with at least one Sony} /\text {Total possible selections}[/tex]

= 132  / 240

= 0.55

The probability that the system selected contains exactly one Sony component is,

[tex]= \text {Total possible selections with exactly one Sony} /\text {Total possible selections}[/tex][tex]\frac{1C_1*3C_1*3C_1*3C_1+4C_11C_13C_13C_1+4C_13C_13C_13C_1}{240} \\\\=\frac{99}{240} \\\\=0.4125[/tex]

Therefore, if someone flips the switches on the selection in a completely random fashion, then is the probability that the system selected contains at least one Sony component is 0.55.

If someone flips the switches on the selection in a completely random fashion, then is the probability that the system selected contains exactly one Sony component is 0.4125.

Answer:

sec²x

Step-by-step explanation:

sin²x + tan²x + cos²x

sin²x + cos²x + tan²x

1 + tan²x ( sin²x + cos²x = 1 )

sec²x ( 1 + tan²x = sec²x )

Answer:

Step-by-step explanation:

SIN^2x + tan^2 x + cos^2x

= x( sin^2 + tan^2+cos^2)

=x(1+tan^2)   since sin^2+cos^2 =1

=xsec^2 ( since sec^2 = 1+tan^2)

=sec^2x

hope it helps

Answer:

1 hour

Step-by-step explanation:

From Distance = speed × time

time = Distance/ speed

=66/66 = 1 hour

Answer:

I can confirm d

Step-by-step explanation:

Hen evaluated (Negative 2) squared as

An expression is a number, a variable, or a combination of numbers and variables and operation symbols

Hen evaluated the expression below. 2 (12 minus 14) squared minus (negative 5)+12=2 (negative 2) squared minus (negative 5) + 12 =2(negative 4) minus (negative 5) +12= negative 8+ 5+12=9. What was hen's error? He did not multiply 2 and 12 first. Hen evaluated Minus (negative 5) as 5. He was added and subtracted before multiplying. Hen evaluated (Negative 2) squared as

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Answer: Infintely many

Step-by-step explanation:

5(x + 10) - 25 = 5x + 25

5x +50 - 25 = 5x + 25

5x +25 = 5x + 25

Same equation

Answer:

Domain: [-3, 5]

Range: [-5, 4]

Step-by-step explanation:

The first thing is to define what is the domain and the range. The domain of a function f (x) is the set of all the values for which the function is defined, and the range of the function is the set of all the values that f takes.

In other words, the domain is the value on the "x" axis and the range is the value on the "y" axis.

In this case, both are an interval, the domain would be from -3 to 5 and in the case of the range it would be from -5 to 4.

Domain: [-3, 5]

Range: [-5, 4]

Answer:

The best estimate would be around 10-16

Step-by-step explanation:

The think is that they can be in many orders and since there is four of them it would be more orders.

Hope this helps

Answer:

58

Step-by-step explanation:

Answer:

58

Step-by-step explanation:

lolololololololol

Answer:

[/tex]y2=e^(-x)[/tex]

Step-by-step explanation:

CHECK THE ATTACHMENT BELOW FOR DETAILED EXPLANATION

Answer:

6

Step-by-step explanation:

Add all the numbers together and divide by the amount of numbers

6+9+3+8+9+3+4= 42

42/7 = 6

Answer:

6

Step-by-step explanation:

To find the mean or the average of the data set, you add all the numbers together and then divide the sum by the number of numbers in the data set.

6+9+3+8+9+3+4 =42

Then divided by the # of terms.

42/7= 6