Answer:
We are given that a fair coin is tossed 3 times.
We know that if a fair coin is tossed 3 times, then there are 8 possible outcomes.
(a) what is the sample space for this chance process?
The sample space associated with tossing a fair coin three times are:
Ω = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
Where:
H denotes the head and T denotes the tail.
(b) what is the assignment of probabilities to outcomes in this sample space?
We are given that a fair coin is tossed 3 times, which means that all the possible outcomes in the above mentioned sample space has equal chance being selected. Therefore, the assignment of probabilities to outcomes in this sample space is same for all outcomes and is given below:
[tex]p= \frac{1}{8}[/tex]
Anyone please help!!!
15 points and will give brainliest to excellent answer
Thanks ^ ^
please see attachments
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%
Emily is making a meal for her family. She uses coconut milk for the dessert she is making. The coconut milk is in a can but she doesn't know how much the can holds. The can is 12cm high and 8cm in diameter. Using the formula V=pie r squared h. Work out how much coconut milk is in the can
Two angles are complementary . The first angle measures 35 Percent . What's the measurement of the second angle ?
Answer:
55 degrees
Step-by-step explanation:
lim
x->infinity (1+1/n)
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.
Which function's graph passes through the points (1,4), (2,9), and (3,16)?
y=5x+4
y=(x+1)^2
y=(x+3)^2
y=7x-5
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: Only y = (x + 1)²Answer:
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]
Arnolds workout consisted of 10 minutes of warm up exercises 25 minutes of lifting weights and 15 minutes on the treadmill. What was the ratio of the number of minutres he lifted weights to the total number of minitues of his entire workout
For what value of α is (α, 9) a solution of the equation y=2x+1?
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.
Explanation: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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Geometric or arithmetic or neither ?
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.
Please help me with this!!!!
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
Solve this system of linear equations. Separate the x- and y- values with a coma. 3x=36-15y. 11x =-78+15y
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)
The lowest temperature ever recorded at Oymyakon in Russia was 96.2°F below 0°F. The lowest temperature ever recorded at Prospect Creek in Alaska was 80°F below 0°F. The thermometer reading of the lowest recorded temperature at Oymyakon was °F. The thermometer reading of the lowest recorded temperature at Prospect Creek was °F.
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
I need help with this right away. Please.
Given the system of equations.
4x+y=8
6x-9y=12
Which of the options represents the resulting equation after an equivalent expression for y is substituted into the second equation?
6x - 9(4x - 8) = 12
4x + 4x - 8 = 8
6(4x - 8) - 9y = 12
6x - 9(-4x + 8) = 12
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.
Angel Grant takes out a $150,000 mortgage this is a 30 year at $725 per month what is the total amount of interest that angel will pay on this mortgage
A coin is flipped 20 times. 13 times the coin lands on heads. What is the theoretical probability that the coin lands on tails?
Answer:
[tex]\frac{7}{20}[/tex]
EXPLANATION:
The coin is flipped 20 times. 13 times it lands on tails. 20-13 = 7
Find the value of x to the nearest tenth.I will mark the brainlest
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
A particle moves along the x-axis with position function s(t) = ecos(x). How many times in the interval [0, 2π] is the velocity equal to 0?
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.
A recipe for 9 banana dash nut muffins calls for 1 cup of flour. The number of muffins that can be made varies directly with the amount of flour used. There are 1 1/3 cups of flour available. How many muffins can be? made?
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.
Nathan has just bought a new car. He models the value, V, in dollars, of the car after t years as V(t) = 21,000(0.861)t. Based on this model, by what percent does the value of Nathan's car decrease each year?
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.
Which is an x-intercept of the graph of the function y=cot(3x)
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].
How much less than 3x^2−7x+9 is 2x^2+4x−8? What is the value of the result when x=2?
^=power
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.
What is an expression?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 perimeter of a rectangle is 84m. The length is two and a half times the width. Find the dimensions of the rectangle. Question 5 options: Length = 30m; Width = 12m Length = 28m; Width = 70m Length = 12m; Width = 30m Length = 70m; Width = 28m
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: length = 30m; width = 12mA student who didn't study for the upcoming quiz decides to 'wing it' and just guess on the 10 question quiz. Every question is a True/False question. What is the pobability that he will pass the quiz with a grade of at least 70%? Please express your answer as a percent rounded to the hundredths decimal place. Include the '%' symbol.
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%
Burj l Arab Hotel,one of the world's tallest buildings,was finished in 1999.Located in Dubai,it is 1,053 feet high with 60 stories.If each floor is the same height,how much taller or shorter is each floor than the height of the floors in the Aon Center?
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.
What is the arithmetic operator?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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The length of a rectangular room is 5 feet more than its width. The perimeter of the room is 66 feet. Let L represent the length of the room and let W represent the width in feet. What are the room's dimensions?
The width of a painting is 4 inches less than the length , and the surface area is 320 square inches. Find the length.
IF=2x+2, IZ=2x+12 solve for x
PLEASE HELP!!!!!
WILL MARK BRAINLIEST!!!!
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.
help!! at least take a look
What is the recursive rule for this geometric sequence?
27, 9, 3, 1, ...
Enter your answers in the boxes.
an= ⋅an−1
a1=
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]
Determine the domain and range for the inverse of f(x) = 1/4x + 2
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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