Tanya is 42 years old. she would like to open aretirement account so she will have half a million dollars in the account when she retires at the age 65. how much did she deposit each month into an account with an apr of 2.75% to reach her goal?
Assume that all six outcomes of a six-sided number cube have the same probability. What is the theoretical probability of each roll?
• 1:
• 2:
• 3:
• 4:
• 5:
• 6:
Using the uniform probability model you developed, what is the probability of rolling an even number?
1/6 Roll a number cube 25 times. Record your results here.
1st toss
2nd toss
3rd toss
4th toss
5th toss
6th toss
7th toss
8th toss
9th toss
10th toss
11th toss
12th toss
13th toss
14th toss
15th toss
16th toss
17th toss
18th toss
19th toss
20th toss
21st toss
22nd toss
23rd toss
24th toss
25 toss
How many results of 1 did you have? ______________
How many results of 2 did you have? ______________
How many results of 3 did you have? ______________
How many results of 4 did you have? ______________
How many results of 5 did you have? ______________
How many results of 6 did you have? ______________
Based on your data, what is the experimental probability of each roll? •
1 _______ • 2 _______ • 3 _______ • 4 _______ • 5 _______ • 6 _______ Using the probability model based on observed frequencies, what is the probability of rolling an even number? Was your experimental probability different than your theoretical probability? Why or why not?
The theoretical probability of rolling each number ([tex]1[/tex] through [tex]6[/tex]) on a six-sided number cube is [tex]\(\frac{1}{6}\)[/tex]. The probability of rolling an even number ([tex]2, 4,[/tex] or [tex]6[/tex]) is [tex]\(\frac{3}{6}\)[/tex] or [tex]\(\frac{1}{2}\).[/tex]
Since there are six possible outcomes when rolling a six-sided number cube and each outcome is equally likely, the probability of rolling any specific number is calculated by dividing the number of favorable outcomes (which is 1 for each specific number) by the total number of possible outcomes (which is [tex]6[/tex]). Therefore, the theoretical probability [tex]\(P\)[/tex] for each roll is:
[tex]\[ P(1) = P(2) = P(3) = P(4) = P(5) = P(6) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{1}{6} \][/tex]
To find the probability of rolling an even number, we consider the number of even outcomes ([tex]2, 4[/tex], and [tex]6[/tex]) and divide by the total number of possible outcomes:
[tex]\[ P(\text{even}) = P(2) + P(4) + P(6) = \frac{1}{6} + \frac{1}{6} + \frac{1}{6} = \frac{3}{6} = \frac{1}{2} \][/tex]
The experimental probability is calculated based on the results of the [tex]25[/tex]rolls. For each number, the experimental probability is the number of times that number was rolled divided by the total number of rolls ([tex]25[/tex]). For example, if the number [tex]1[/tex] was rolled [tex]4[/tex] times, the experimental probability of rolling a [tex]1[/tex] would be [tex]\(\frac{4}{25}\).[/tex]
The probability of rolling an even number based on observed frequencies would be the sum of the experimental probabilities of rolling a [tex]2, 4[/tex], or [tex]6[/tex]. If the number of rolls for each even number was [tex]\(x\), \(y\),[/tex] and [tex]\(z\)[/tex]respectively, then the experimental probability of rolling an even number would be [tex]\(\frac{x + y + z}{25}\).[/tex]
The experimental probability may differ from the theoretical probability due to random variation and the finite number of trials. In a small number of trials, the observed frequencies may not match the theoretical probabilities exactly. However, as the number of trials increases, the experimental probabilities should converge to the theoretical probabilities. This is due to the law of large numbers, which states that the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed.
WILL MARK BRAINLEST HELP FASTTT
Seven of the 10 children at Art can't make an average of 8 paintings. The remaining children make an average of 12 paintings. What is the average number of paintings made by children that are Camp. Enter your answer in the Box
11.34<11.340 true or false
Which correlation coefficient below is most likely to represented on the graph
Answer:
The correct option is D.
Step-by-step explanation:
The correlation coefficient represent the relationship between two variables. It is denoted by r and the value of r lies from -1 to 1.
If r=-1 and close to -1, then it represents strong negative correlation.
If -1<r<0 and close to -0.5, then it represents weak negative correlation.
If r=0 and close to 0, then it represents no correlation.
If 0<r<1 and close to 0.5, then it represents weak positive correlation.
If r=1 and close to 1, then it represents strong positive correlation.
From the given graph it is clear than the data represents the strong positive correlation because the data set lie close to the positive strait line. So, the value of r is near to 1.
Option 1, 2 represent the negative correlation and option 3 represents weak positive correlation.
Since 0.95 close to 1, therefore it represents strong positive correlation.
Hence option D is correct.
FInd the volume of the cylinder in terms of Pi.
The formula for the area of a cylinder is [tex]\pi[/tex][tex]r^{2}[/tex]×h
First, we do not have to worry about pi because we are leaving our answer in terms of it so we can move on to the radius squared.
The radius is halfway across a circle so our radius would be 4 and we have to square that and we will get a product of 16.
Lastly, we have to multiply 16 by 8 because 8 is the height of the cylinder
16 × 8 = 128
Therefore, the volume of the cylinder would be 128[tex]\pi[/tex] in.³
What is the y-value if the vertex of 4x^2 + 8x - 8
The x-value is -b/(2a) = -8/(2·4) = -1.
The corresponding y-value is ...
... 4(-1)² +8(-1) -8 = 4 -8 -8 = -12
The y-value of the vertex is -12.
Answer:
The y-value of the vertex is [tex]-12[/tex]
Step-by-step explanation:
we know that
The equation of a vertical parabola into vertex form is equal to
[tex]f(x)=a(x-h)^{2}+k[/tex]
where
(h,k) is the vertex of the parabola
In this problem we have
[tex]f(x)=4x^{2}+8x-8[/tex] -----> this a vertical parabola open upward
Convert to vertex form
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]f(x)+8=4x^{2}+8x[/tex]
Factor the leading coefficient
[tex]f(x)+8=4(x^{2}+2x)[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side
[tex]f(x)+8+4=4(x^{2}+2x+1)[/tex]
[tex]f(x)+12=4(x^{2}+2x+1)[/tex]
Rewrite as perfect squares
[tex]f(x)+12=4(x+1)^{2}[/tex]
[tex]f(x)=4(x+1)^{2}-12[/tex]
The vertex is the point [tex](-1,-12)[/tex]
The y-value of the vertex is [tex]-12[/tex]
what is the value of log 0.5^16?
A. -4.00
B. -0.25
C.1.51
D. 2.41
The above answer will be calculated as -
The cost of producing transistors decreases by 20% every year. If it currently costs $440 to produce a billion transistors, how much will it cost to produce a billion transistors in 7 years? If necessary, round your answer to the nearest cent.
What is the probability that the wine cooler would be less than 45 degrees?
A certain kind of animal weighs about 75 pounds at birth and gains about 2 pounds per day for the first few weeks. Determine those days for which the animal's weight is more than 125 pounds.
The animal's weight is more than 125 pounds when the animal is more than
........... days old.
25
Step-by-step explanation:Let w represent the weight of the animal in pounds, and d the age in days. The problem statement tells us ...
... w = 75 +2d
We want to find d when w > 125.
... 75 +2d > 125 . . . . . substitute the above expression for w
... 2d > 50 . . . . . . . . . subtract 75
... d > 25 . . . . . . . . . . . divide by 2
The animal will weigh more than 125 pounds when it is more than 25 days old.
Jill collected a total of 19 gallons of honey. If she distributed all of the honey equally between 9 jars how much will be in each ja
Divide 406 by −14. A) −29 B) −34 C) 34 D) 44
which expression is the best estimate of the product of 7/8 and 8 1/10
Answer:
1 x 8
Step-by-step explanation:
7/8 rounded up equals 1 whole. 8 1/10 rounded makes 8.
IMPORTANT HELP HURRY
Andrew is two years older than Beatrice, and Chris is three years younger than Beatrice. The product of Andrew's age and Chris' age is 66. How old is Beatrice? (1 point) Extra Content
HINT: Look at the Answers
A. A b2 − b − 72 = 0; 8 years old
B. B b2 − b − 72 = 0; 9 years old
C. C b2 − b − 72 = 0; 10 years’ old
D. D b2 − b − 72 = 0; 11 years’ old
Heather made a total of $451.78 last month at her part-time job. If she worked 14 hours, how much did she make per hour?
Heather made $32.27 per hour at her part-time job.
Explanation:To find out how much Heather made per hour at her part-time job, we need to divide her total earnings by the number of hours she worked. Heather made a total of $451.78 and worked 14 hours, so we can calculate her hourly rate by dividing $451.78 by 14.
$451.78 / 14 = $32.27 per hour
Therefore, Heather made $32.27 per hour at her part-time job.
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The graph of the equation xy=4 is symmetric with respect to which of the following?
a.
the y-axis
c.
the line y = x
b.
the line y=-x+4
d.
the x-axis
Answer:
a
Step-by-step explanation:
its a
A thin layer of paint is 7x10^-7 m thick. In contrast, a coin is 3.43 x 10^-3 m thick. How many layers of paint are in a stack that is the height of the coin?
hey can you please help me posted picture of question
What is the slope of the line that passes through (2, 5) and (-1, 5) ?
A. -3
B. 0
C. undefined
D. 3
The answer is to this is B. 0
Which of the following events has an expected value that is in the sample space? A. tossing a number cube once B. flipping a coin C. randomly picking a number between one and nine, inclusive D. randomly picking a number between one and ten, inclusive
A) The event is "tossing a number cube once"
The sample space of this event is {1,2,3,4,5,6}.
The expected value of this event is
[tex]1\times \frac{1}{6}+2\times \frac{1}{6}+3\times \frac{1}{6}+4\times \frac{1}{6}+5\times \frac{1}{6}+6\times \frac{1}{6}\\ \\ =\frac{1}{6}+\frac{1}{3}+\frac{1}{2}+\frac{2}{3}+\frac{5}{6}+1\\ \\ =\frac{7}{2} = 3.5[/tex]
Since 3.5 is not in the sample space of the event. Therefore, option (A) is not correct.
(B) The event is "Flipping a coin"
Sample space of this event is {HH,TT,HT,TH}
Since sample space of this event is not numbers, therefore, this cannot be the correct option either.
(C) The event is, "Randomly picking a number between 1 and 9, inclusive."
The sample space of this event is {1,2,3,4,5,6,7,8,9}.
Expected value of this event is [tex]\frac{1}{9}(1+2+3+4+5+6+7+8+9) = \frac{1}{9}(45) = 5[/tex]
Since 5 is the expected value and it is present in the sample space for this event. Therefore, option (C) is a correct choice.
(D) The sample is "Randomly picking a number between one and ten, inclusive".
The sample space of this event is {1,2,3,4,5,6,7,8,9,10}.
Therefore, expected value of the event is [tex]\frac{1}{10}(1+2+3+4+5+6+7+8+9+10) = \frac{1}{10}(55)=5.5[/tex]
Since 5.5 is not present in the sample space of this event. Therefore, option (D) is not correct either.
Hence, the correct choice is option (C).
The diagram below shows the radius of the circular opening of a drinking cup. which of the following is the closest to the circumference of the opening in cm
Answer:
Its a 12
Step-by-step explanation:
Ben purchased a 2 liter bottle of soda.
Which of these is equal to 2 liters?
A) 1,000 dl
B) 1,000 ml
C) 2,000 dl
D) 2,000 ml
The answer to the above question can be explained as under -
Here, we need to convert large units into smaller units of same class i.e. to convert liters into milliliters.
We know that,
1 liter = 1000 milliliters
So, 2 liter of soda will have -
2 X 1 liter = 2 X 1000 milliliters
2 liters of Soda = 2,000 milliliters
Thus, the correct option will be = D) 2,000 ml
your total savings varies inversely with the amount spent on Bill's. if your savings is $300 when your cost of Bill's are $65. What would your savings be when your cost of Bills is $145.
the library is 4 miles from the post office how many yards is the library from the post office
1.
Find the annual percentage rate, using the annual percentage rate table.
Amount Financed: $2,650
Finance Charge: $484.69
Number of Payments: 36
A ball is thrown into the air with an upward velocity of 32 ft/s. Its height h in feet after t seconds is given by the function h = –16t2 + 32t + 6. a. In how many seconds does the ball reach its maximum height? Round to the nearest hundredth if necessary. b. What is the ball’s maximum height?
a) It will reach the maximum in 1 second;
b) the maximum height is 22 feet.
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
We find the maximum by finding the vertex.
We first find the axis of symmetry, whose equation is,
x = -b/2a
x = -32/2(-16)
x = -32/-32
x = 1
This gives us that it reaches the maximum in 1 second.
And, To find the y-coordinate, the maximum height, we substitute this into the equation:
h(1) = -16(1²)+32(1)+6
h(1) = -16+32+6 = 22
Hence, It reaches a height of 22 feet.
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The Community center for Watercrest has a large glass wall that looks out the lake Find The Area For the glass wall
The simple linear regression model is yiequalsbeta0plusbeta1xiplusepsiloni. for what does yi stand? choose the correct answer below.
a. it is the slope of the population regression line.
b. it is the residual of the ith observation in the population.
c. it is the observed value of the response variable for the ith observation in the population.
d. it is the value of the explanatory variable for the ith observation in the population.
e. it is the y-intercept of the population regression line.
In the simple linear regression model, y[tex]_i[/tex] represents the observed value of the response variable for the [tex]i_{th}[/tex] observation. Therefore, the correct answer is option c.
The simple linear regression model is expressed as y[tex]_i[/tex] = β₀ + β₁x[tex]_i[/tex] + ε[tex]_i[/tex]. In this equation, y[tex]_i[/tex] stands for the observed value of the response variable for the i[tex]_{th}[/tex] observation in the population.
The equation y[tex]_i[/tex] = β₀ + β₁x[tex]_i[/tex] + ε[tex]_i[/tex] is used to model the relationship between a single explanatory variable and the response variable.
In this equation, y[tex]_i[/tex] denotes the observed value of the response variable.
The key components include β0 (y-intercept), β1 (slope), xi (explanatory variable), and εi (error term).
So, option c. it is the observed value of the response variable for the i[tex]_{th}[/tex] observation in the population, is the correct answer.