Tossing coins imagine tossing a fair coin 3 times. (a) what is the sample space for this chance process? (b) what is the assignment of probabilities to outcomes in this sample space?

w - width

2.5w - length

84m - perimeter

w + w + 2.5w + 2.5w = 7w - perimeter

The equation:

7w = 84    divide both sides by 7

w = 12 m

length = 2.5w → 2.5w = 2.5(12) = 30 m

Answer:

(-3,3)

Step-by-step explanation:

3x=36-15y and 11x =-78+15y

We move all x  and y terms to the left hand side of the equation , so that we can apply elimination method

3x=36-15y , Add 15 y on both sides , 3x + 15y = 36

11x =-78+15y, subtract 15y on both sides, 11x -15y = -78

Now we add both equations

3x  + 15y = 36

11x -15y = -78

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

14x  = -42

divide both sides by 14

x= -3

Now Plug in -3 for x in any one of the given equation

3x=36-15y

3(-3) = 36 - 15y

-9 = 36 - 15y

Subtract 36 on both sides

-45 = -15y

Divide both sides by -15

So y= 3

Answer is (-3,3)

Answer:

Can not be determined.

Step-by-step explanation:

We can easily notice that the limit is x tends to infinity, whereas x is not present in the given function, we are given (1 + 1/n). So we can not evaluate the given limit for x as parameter, we must have some function of x to solve this problem.

Hence, option C is correct i.e. the limit can not be determined.

Answer:

Sequence 1 is an 'Arithmetic but not Geometric Sequence'

Sequence 2 is 'Geometric but not Arithmetic Sequence'

Step-by-step explanation:

We know that,

1. Arithmetic Sequence is a sequence in which the difference of one term and the next term is a same constant for all terms.

2. Geometric Sequence is a sequence in which the division of two terms gives the same value for all terms.

Now, we check the above properties in the given options,

In Sequence 1 i.e. [tex]\frac{1}{2} , \frac{7}{6} ,\frac{11}{6} ,\frac{5}{2}[/tex] , . . . .

We see that the difference between the terms comes out to be [tex]\frac{2}{3}[/tex],

for eg. [tex]\frac{7}{6} - \frac{1}{2}[/tex] = [tex]\frac{4}{6} = \frac{2}{3}[/tex]

But, the division of two terms gives different values,

for eg. [tex]\frac{\frac{7}{6} }{\frac{1}{2} } = \frac{7}{3}[/tex] and [tex]\frac{\frac{11}{6} }{\frac{7}{6} } = \frac{11}{7}[/tex]

Hence, this sequence is not a Geometric Sequence but an Arithmetic Sequence.

In Sequence 2 i.e. [tex]\frac{1}{2} , \frac{1}{3} ,\frac{2}{9} ,\frac{4}{27}[/tex] , . . . .

We see that the difference of terms is not same constant but are different values,

for eg. [tex]\frac{1}{3} - \frac{1}{2}[/tex] =  [tex]\frac{-1}{6}[/tex] and [tex]\frac{1}{3} - \frac{2}{9}[/tex] = [tex]\frac{1}{9}[/tex]

But, the division of different terms gives same constant i.e. [tex]\frac{2}{3}[/tex],

for eg. [tex]\frac{\frac{1}{3} }{\frac{1}{2} } = \frac{2}{3}[/tex].

Hence, this sequence is not a Arithmetic Sequence but a Geometric Sequence.

Answer:

1

Step-by-step explanation:

well 3x2^2-7x2+9 = 7

well 2x2^2+4x2−8 = 8

8-7 =1

The difference is x² - 11x + 17 and the value is -1.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Difference = ( 3x²−7x+9 ) - ( 2x²+4x−8 )

Difference = x² - 11x + 17

The value of expression at x= 2 will be calculated as,

E = x² - 11x + 17

E =  (2)² - ( 11 x 2 ) + 17

E = 4 - 22 + 17

E = -1

Therefore, the difference is x² - 11x + 17 and the value is -1.

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The x-intercept of the graph of the function y = cot(3x) is [tex]x = \frac{\pi}6[/tex]

The graph of the function is given as:

y = cot(3x)

To determine the x-intercept of the graph, we set the graph to 0.

So, we have:

cot(3x) = 0

Take the arccot of both sides

3x = arccot(0)

Evaluate the arccot of 0

[tex]3x = \frac{\pi}2[/tex]

Divide both sides by 3

[tex]x = \frac{\pi}6[/tex]

Hence, the x-intercept of the graph of the function y = cot(3x) is [tex]x = \frac{\pi}6[/tex]

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The x-intercepts of the graph of the function  [tex]\( y = \cot(3x) \)[/tex] occur at points where  y = 0 , which happens when [tex]\( \cot(3x) = 0 \).[/tex]

1. Set [tex]\( y = \cot(3x) \)[/tex] and solve for  x : [tex]\( \cot(3x) = 0 \).[/tex]

2. Since [tex]\( \cot(x) = \frac{1}{\tan(x)} \)[/tex], this equation becomes [tex]\( \frac{1}{\tan(3x)} = 0 \)[/tex].

3. Tangent is zero at multiples of [tex]\( \frac{\pi}{2} \)[/tex], so [tex]\( \tan(3x) \)[/tex] is zero at [tex]\( 3x = \frac{\pi}{2} \)[/tex], [tex]\( 3x = \frac{3\pi}{2} \)[/tex], [tex]\( 3x = \frac{5\pi}{2} \)[/tex], and so on.

4. Solve for [tex]\( x \)[/tex]: [tex]\( x = \frac{\pi}{6} \)[/tex], [tex]\( x = \frac{\pi}{2} \)[/tex], [tex]\( x = \frac{5\pi}{6} \)[/tex], and so on.

5. Each of these values represents an x-intercept on the graph of [tex]\( y = \cot(3x) \)[/tex].

A recursive rule for a geometric sequence:

[tex]a_1\\\\a_n=r\cdot a_{n-1}[/tex]

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

[tex]a_1=27;\ a_2=9;\ a_3=3;\ a_4=1;\ ...\\\\r=\dfrac{a_{n+1}}{a_n}\to r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}=...\\\\r=\dfrac{9}{27}=\dfrac{1}{3}\\\\\boxed{a_1=27;\qquad a_n=\dfrac{1}{3}\cdot a_{n-1}}[/tex]

Answer:

55 degrees

Step-by-step explanation:

Answer: the no. is doubled every time we get an answer. therefore the next two no.s n the sequence are 48, 96

Answer:

3, 6, 12, 24 , 48, 96

Answer:

[tex]\frac{7}{20}[/tex]

EXPLANATION:

The coin is flipped 20 times. 13 times it lands on tails. 20-13 = 7

Each floor is 3.35 feet taller than each floor of the Aon Center

Each floor of Burj I Arab Hotel is 3.815 feet taller than the height of Aon Center.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

As per the given,

Height of Burj l Arab Hotel = 1053 feet

Number of floors = 60

Per floor height = 1053/60 = 17.55 feet

Height of Aon center = 1140 feet

Number of floors = 83

Per floor  height = 1140/83 = 13.73 feet

17.55 - 13.73 = 3.815 feet bigger than the Aon center.

Hence "Each floor of Burj I Arab Hotel is 3.815 feet taller than the height of Aon Center".

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Answer:

Thermometer reading of the lowest recorded temperature at Oymyakon was -96.2° F

Thermometer reading of the lowest recorded temperature at Prospect Creek was -80° F

Step-by-step explanation:

If the temperature is x° F below 0° F then the thermometer reading is -x° F

It is given that the Lowest temperature recorded at Oymyakon in Russai was 96.2°F below 0°F

So the thermometer reading of the lowest recorded temperature at Oymyakon was -96.2° F

Also it is given that the Lowest temperature recorded at Prospect Creek in Alaska  was 80°F below 0° F

So the thermometer reading of the lowest recorded temperature at Prospect Creek was -80° F

Answer:

-96.2 first, -80

Step-by-step explanation:

I took le test it was le correct

Answer:

There is around a 40% chance if I have done my calculations correctly

Answer: 17.19%

Step-by-step explanation:

[tex]P=\dfrac{_{10}C_7 + _{10}C_8 + _{10}C_9 + _{10}C_{10}}{2^{10}}[/tex]

   [tex]= \dfrac{120+45+10+1}{1024}[/tex]

   [tex]= \dfrac{176}{1024}[/tex]

  = 0.171875

  = 17.1875%

Answer:

13.9%

Step-by-step explanation:

The value of car is modeled as:

[tex]V(t)=21,000(0.861)t[/tex]

Here we can see that, each year Nathan has considered 0.861 of the previous year value or we can say that Nathan has considered 86.1% of the previous year value. So,

[tex]100-86.1=13.9[/tex]

We subtract the percentage value considered from 100 to find out the percentage decrease in the value of the car.

The value of new car is decreasing by 13.9% each year.  

Final answer:

Nathan's car decreases in value by 13.9% each year according to the depreciation model [tex]V(t) = 21,000(0.861)^t.[/tex]

Explanation:

The value of Nathan's car decreases by a certain percentage each year, which can be determined from the depreciation model [tex]V(t) = 21,000(0.861)^t.[/tex]The model shows that each year, the value is multiplied by 0.861. To find the percent decrease, we subtract this number from 1 and then convert the result into a percentage:

1 - 0.861 = 0.139

0.139  imes 100% = 13.9%

Therefore, the value of Nathan's car decreases by 13.9% each year based on this model.

Problem 1

Answers:

Percentage of patients that were dogs = 46%

Standard Error = 0.07048404074682

Margin of error for 90% confidence interval = 0.11594624702851

Margin of error for 95% confidence interval = 0.13814871986377

Round the decimal values however you need them

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

To get the first answer, you add up the numbers given (7,4,5,5,2) and divide that over 50. So 7+4+5+5+2 = 23 which leads to 23/50 = 0.46 = 46%; therefore phat = 0.46 is the sample proportion of dogs.

Use the SE (standard error) formula given to you with phat = 0.46 and n = 50 to get SE = 0.07048404074682

The critical z value at 90% confidence is 1.645; this value is found in your Z table (back of your stats textbook). Multiply the SE value by 1.645 to get 0.07048404074682*1.645 = 0.11594624702851

Also found in your textbook is 1.960 which is the z critical value at 95% confidence. Multiply this with the SE value to get 0.07048404074682*1.960 = 0.13814871986377

===============================================

Problem 2

Answer: Choice B) picking balls from a bin; the 60 randomly selected get chosen for the first bus, while the remaining 60 go to the second bus

-----------

Choice A is fairly vague on what the lower and upper boundaries are. What is the smallest number allowed? What about the largest? This isn't clear so it's possible that we could end up with more positive numbers than negative (eg: if we had an interval -10 < x < 110). So choice A is false. A similar issue shows up with choice D.

Choice B is true. Assuming the selection process is random and not biased, then each ball is equally likely for each selection. The fact that the balls are colored seems to be extra info which I'm not sure why your teacher threw that in there.

Choice C is false because choice B is true

Choice D is false for similar reasons as choice A. It's not clear where we start and where we end. If we had the interval 2 < x < 6 then x could take on the values {3, 4, 5} and we see that picking an odd number is twice as likely than picking an even. In this example, there is bias.

===============================================

Problem 3

Answer: Choice B) Roll a die; each number corresponds to a different class

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

Choice A is false because choice B being the answer contradicts it

Choice B is true: there are 6 sides on the die, and each side is equally likely to be landed on, so each class is equally likely

Choice C is false because 2*2*2 = 8 represents the number of combos you can have when you flip three coins (one combo being HTH for heads tail heads) but there are 6 classes, not 8

Choice D is false because while we want 6 regions on the spinner. Each region must have the same area; otherwise, one class is weighted heavier than the others making it more likely you select that particular class.

The guy above me is correct but for the margin of error, I got 34%, 58% for the 90% interval and 32%, 60% for 95% interval. He just didnt take his margin of errors numbers and times them by 100 to get a percentage, and then round it so you get 12% for 90% and 14% for 95%. Then add and minus 12 percent to the 46% and thats how you get it. Then do the same with 95%

Answer:

The value of x nearest to tenth is, 1.5 units

Step-by-step explanation:

In right angle triangle as shown in figure

by definition of tangent ratio i,e   [tex]\tan \theta = \frac{opposite side}{Adjacent side}[/tex]

[tex]\tan 37^{\circ} = \frac{x}{2.1}[/tex]

[tex]0.7535540501= \frac{x}{2.1}[/tex]

or

[tex]x = 0.7535540501 \times 2.1 = 1.58246351[/tex] units

Therefore, the value of x nearest to tenth is, 1.5 units

Answer:

Choice D which is 6x - 9(-4x + 8) = 12

Step-by-step explanation:

The first equation solves to y = -4x+8 when you subtract 4x from both sides. This to undo the addition of 4x done to y.

Then you replace every copy of "y" in the second equation with (-4x+8). The parenthesis is important so that you multiply properly

We go from 6x - 9y = 12 to 6x - 9( -4x+8 ) = 12

The resulting equation after an equivalent expression for y is substituted into the second equation is 6x - 9(-4x + 8) = 12, option D.

The student asks about substituting an expression for y from the first equation into the second equation in a system of linear equations. The first equation gives us y in terms of x, which can be expressed as y = 8 - 4x. Substituting this expression into the second equation, 6x - 9y = 12, will result in the compound equation 6x - 9(8 - 4x) = 12. which is same as 6x - 9(-4x + 8) = 12 , option D.

Answer:

It goes to zero three times

Step-by-step explanation:

s(t) = e^ cos(x)

To find the velocity, we have to take the derivative of the position

ds/dt =  -sin x e^ cos x dx/dt

Now we need to find when this is equal to 0

0 =  -sin x e^ cos x

Using the zero product property

-sin x=0   e^cos x= 0

sin x = 0

Taking the arcsin of each side

arcsin  sinx= arcsin 0

x = 0 ,pi, 2 pi

e^cos x= 0

Never goes to zero

Answer:

The velocity is equal to 0 for 3 times.

Step-by-step explanation:

Given position function s = ecos(x)

Its velocity function, s' = ds/dt = e(-sinx)dx/dt

Between [0,2π], s'=0, -e(sinx)dx/dt=0

sinx=0

x=0, π, 2π

The velocity is equal to 0 for 3 times.

The student is seeking the solution for a linear equation in the form 'y = mx + b'. From the problem, the equation is 'y = 2x +1' and we have to find the x value (α) for y = 9. The answer is α = 4 when (α, 9) is a solution to our equation.

The subject of this problem is Mathematics, and it specifically deals with linear equations, in the form of y = mx + b, where 'm' is the slope and 'b' is the y-intercept. The equation given in the problem is y = 2x + 1. The student wants to find the value of α such that (α, 9) is a solution to the equation.

To solve this, we substitute 9 for y in the equation and solve for x:

9 = 2x + 1

Subtract 1 from both sides:

8 = 2x

Finally, divide both sides by 2 to solve for x:

x = 4

Thus, the value of α that makes (α, 9) a solution to the equation y = 2x + 1 is α = 4.

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Answer:

12 muffins can be made.

Step-by-step explanation:

12 muffins because if one cup makes 9 muffins, and 1/3 of 9 is 3. Than 9+3=12 so you can make 12.

Answer:

D

Step-by-step explanation:

Rational functions are functions whose main operation on the variable is a ratio or fraction. This means we find x or the input value in the denominator of the function. Since fractions involve division and division has special circumstances, this reflects on the graph. Because when we divide we cannot divide by 0, any x value which makes the denominator 0 is an asymptote. On the graph, asymptotes are represented by dashed lines where the function doesn't follow.

To find the asymptotes, we set the factors in the denominator to 0 and solve for x. Let's do the each for each options:

a. (x+5)=0 so x=-5 and (x-2)=0 so x=2. This matches our graph.

b. x=0 and x+5=0 so x=-5. This does not match the graph.

c. x=0. This does not match the graph.

d. (x+5)=0 so x=-5 and (x-2)=0 so x=2. This matches our graph.

This means only a and d are options. We will substitute a value to see the behavior of the graph. We pick x=-2. In D, this would give us a positive y. This matches the graph. In A, this would give us a negative y which does not match the graph.

The required domain of the inverse function is {2}, and the range is (-∞, 0) U (0, +∞).

To determine the domain and range of the inverse of the function f(x) = 1/(4x) + 2, we need to find the domain and range of the original function.

The domain of f(x) is the set of all possible values for x that make the function defined. In this case, the only restriction is that the denominator (4x) should not be zero since division by zero is undefined. So, we need to find the values of x that make 4x ≠ 0. Dividing both sides of the inequality by 4, we get x ≠ 0. Therefore, the domain of f(x) is all real numbers except 0, or (-∞, 0) U (0, +∞).

To find the range of f(x), we consider the behavior of the function as x approaches positive infinity and negative infinity. As x approaches negative infinity, the term 1/(4x) approaches zero, and adding 2 to zero gives us 2. As x approaches positive infinity, the term 1/(4x) approaches zero as well, and again adding 2 gives us 2. Therefore, the range of f(x) is the single value 2, or {2}.

Now, to find the domain and range of the inverse function, we interchange the domain and range of the original function. So, the domain of the inverse function is {2}, and the range is (-∞, 0) U (0, +∞).

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Put the coordinates of the points to the equations of the functions and check:

for (1, 4)

y = 5x + 4 → 4 = 5(1) + 4 → 4 = 5 + 4 → 4 = 9  FALSE

y = (x + 1)² → 4 = (1 + 1)² → 4 = 2² → 4 = 4 CORRECT

y = (x + 3)² → 4 = (1 + 3)² → 4 = 4² → 4 = 16  FALSE

y = 7x - 5 → 4 = 7(1) - 5 → 4 = 7 - 5 → 4 = 2  FALSE

Only y = (x + 1)².

Check other points:

for (2, 9)

9 = (2 + 1)² → 9 = 3² → 9 = 9   CORRECT

for (3, 16)

16 = (3 + 1)² → 16 = 4² → 16 = 16   CORRECT

Answer:

second option is correct

Step-by-step explanation:

Let equation be y = [tex]ax^{2} +bx+c \\[/tex]

here plugging x =1 ,x=2 and x= 15

we have

[tex]a(1)^{2} +b(1)+c \\[/tex] = 4  

            a +b +c = 4 .................... equation (1)

similarly

[tex]a(2)^{2} +b(2)+c \\[/tex]= 9  

       4a+2b+c = 9 ....................... equation (2)

plugging x =3 ,we get

[tex]a(3)^{2} +b(3)+c \\[/tex] =16

    9a+ 3b +c = 16  .........................  equation (3)

solving these equations simultaneously ,we have

a =1, b= 2   and c =1 ,

y= [tex](1)x^{2} +2x+1\\[/tex]

y = [tex](x+1)^{2} \\[/tex]