The expected value of X is 297/35 and the variance of X is 774/1225.
Let's define the indicator random variable Xi as follows:
Xi = 1, if the i-th roll results in a new number (that hasn't been rolled before).
Xi = 0, otherwise.
Then, X is the sum of these indicator variables, that is:
X = X1 + X2 + X3
We know that E[Xi] = 1/p, where p is the probability of rolling a new number on the i-th roll, given that i - 1 distinct numbers have already been rolled. Since there are i - 1 distinct numbers already rolled, the probability of rolling a new number on the i-th roll is (6 - i + 1)/6.
Thus, we have:
E[Xi] = 6/(6-i+1) = 6/(7-i)
Using the linearity of expectation, we can find the expected value of X:
E[X] = E[X1] + E[X2] + E[X3] = 6/7 + 6/6 + 6/5 = 297/35
To find the variance of X, we need to calculate the variance of each Xi:
Var(Xi) = E[Xi^2] - E[Xi]^2
We know that:
E[Xi^2] = 1(6-i+1)/6 + 0(i-1)/6 = (7-i)/6
So, we have:
Var(Xi) = (7-i)/6 - (6/(7-i))^2
Using the linearity of variance, we can find the variance of X:
Var(X) = Var(X1) + Var(X2) + Var(X3)
= (4/6) - (6/7)^2 + (3/6) - (6/6)^2 + (2/6) - (6/5)^2
= 774/1225
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Write the equation of the line that passes through the points (-6,-3) and (-3,1)
Answer:
[tex] y = \frac{4}{3} x + 5[/tex]
Step-by-step explanation:
The slope is
[tex] \frac{ - 3 - 1}{ - 6 - ( - 3)} = \frac{4}{3} [/tex]
Substituting into point-slope form,
[tex]y - 1 = \frac{4}{3} (x + 3) \\ \\ y - 1 = \frac{4}{3} x + 4 \\ \\ y = \frac{4}{3} x + 5[/tex]
A softball pitcher has a 0.507 probability of throwing a strike for each pitch. If the softball pitcher throws 15 pitches, what is the probability that more than 8 of them are strikes
8/25 is the probability that more than 8 of them are strikes.
Lets simplify the problem,
We are given that a softball pitcher has a 0.507 probability of throwing a strike for each pitch. Also, the softball pitcher throws 15 pitches.
The above situation can be represented through Binomial distribution;
P(X = r) = 0,1,2,3,,.....
where, n = number of trials (samples) taken = 15 pitches
r = number of success = more than 8
p = probability of success which in our question is probability of
Throwing a strike for each pitch = 0.507
LET X = Number of strikes
So, it means X ~ n = 15, p = 0.507
So, Probability that more than 8 of them are strikes = P(X > 8)
P(X > 8) = P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15)
After putting the values in it we get,
P = 0.323
P= 8/25 approx
8/25 is the probability that more than 8 of them are strikes.
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What is the formula for margin of error?
Z•√√5
√r
OME =
OME =
OME =
z. √s
Z•
77
Z•S
√n
Z S
OME= 77
The margin of error is calculated using the formula, C. ME = z × s / √n.
What is the Formula Used to Determine Margin of Error?The formula for finding the margin of error is given as: ME = z × s / √n, where we have the following:
ME = margin of error
z = z-score
s = population standard deviation
n = sample size
The margin of error is used to determine amount of error in a random sampling.
Thus, the formula is: C. ME = z × s / √n.
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A researcher asked 520 randomly selected people of three different age groups (teen, young adult, and adult) about their favorite music genre. the two-way table displays the distribution of the responses. a 4-column table with 3 rows. column 1 has entries country, rock, oldies. column 2 is labeled teen with entries 61, 94, 15. column 3 is labeled young adult with entries 65, 84, 36. column 4 is labeled adult with entries 49, 54, 62. the columns are labeled age and the rows are labeled music. a participant is randomly selected. let c be the event that the participant prefers country music and let t be the event that the participant is a teen. what is the value of p(cc and tc)? 0.12 0.33 0.45 0.55
The value of p(cc and tc) is 0.1173
The distribution of the replies is 0.12, as shown by the two-way table.
We've done that.
520 randomly chosen individuals from the teen, young adult, and adult age groups were asked about their preferred musical genres by the researcher.
The distribution of the answers is shown in the two-way table.
There are 61 teenagers in the country.
seeing as how this is only one of 520,
The probability formula?
P(E) = (Number of favorable outcomes) = Probability of an Event (Sample space).
61/520=0.1173
We calculate 0.1173 by dividing 61 by 520 and rounding to the next hundredth to obtain 0.12.
Thus the value of p(cc and tc) is 0.1173.
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The equation shows the relationship between a planet’s orbital period, t, and the planet’s mean distance from the sun, a, in astronomical units, au. If the orbital period of planet y is twice the orbital period of planet x, by what factor is the mean distance increased?.
The mean distance is increased by a factor of [tex]2^{3/2}[/tex] if the orbital period of planet y is twice that of the planet x.
Description of the Kepler's law.
The orbital period T and the mean distance from the sun, A, expressed in astronomical units (AU), are related in accordance with Kepler's third law.
The mathematical formula is,
T² = A³
Here, T denotes the orbital period and A represents the average separation or mean distance from the sun.
Now, if T(y) = 2T(x)
⇒ A'³(y) = 2A³(x)
A'(y) = [tex]2^{3/2}[/tex]A(y)
Thus, if orbital period of planet y is twice the orbital period of planet x, the mean distance is lengthened by a factor of [tex]2^{3/2}[/tex].
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Answer:
2 Superscript three-halves
Step-by-step explanation:
Edge
Select the correct answer. Exponential function f is represented by the table. x -2 -1 0 1 2 f(x) -62 -30 -14 -6 -2 Function g is represented by the equation. Which statement correctly compares the two functions on the interval [-2, 1]? A. Only function f is increasing, and only function f is negative. B. Only function f is increasing, and both functions are negative. C. Both functions are increasing, but function g increases at a faster average rate. D. Both functions are increasing, but function f increases at a faster average rate.
based on the given exponential functions, we can tell that C. Both functions are increasing, but function g increases at a faster average rate.
what function is increasing faster?function g is represented by the model:
g(x) = -18 x (1/3)^x + 2
g(x)=-18(1/3)^x In(1/3)
In1/3 < 0
this means that:
g (x) > 0
for any interval, g(x) > f(x)
this means that g is increasing at a faster rate than f which is increasing as shown by the table given in the question.
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3 is subtracted from the product of 8 and a number
Answer: (8 * x) -3
Step-by-step explanation:
The term product refers to multiplication, so let the unknown number be x and multiply it by 8. Then you can subtract 3 afterwards.
*= multiplication
21. A triangle has vertices (1, 5), (2, 7), and (6, 5). After a reflection and a translation, the
coordinates of the image are (5,-2), (6,-4), and (10,-2). Describe the transformation.
22. Find the image of the point at (4, -7) under the translation along the vector (a, b).
Answer:
See below
Step-by-step explanation:
I am not sure about number 22. I think that they are asking you to apply the same rules to the point (4, -7), if that is what they mean, the answer is (8,10)
a data set has 8 numbers and 2 is the highest number what is the lowest?
The lowest number in the data set is -5.
How to illustrate the information?Let the data sets be consecutive numbers that has a highest number of 2.
Consecutive numbers mean that the.numvers follow each other. This will be:
-5, -6, -7, -8, -9, 0, 1, 2
Based on the numbers illustrated above, the lowest number is -5.
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which of the following points could be added to the graph f(x)=-|x+3| to keep the graph a function?
a.(0.3) b.(-3,-6)
c. both a and b d. none of the above
None of the points could be added to the graph f(x)=-|x+3| to keep the graph a function
How to determine the point?The equation of the function is given as:
f(x) = - |x + 3|
The points are given as:
(0, 3) and (-3, -6)
When x = 0, we have:
f(0) = - |0 + 3|
f(0) = -3 --- different y value from (0, 3)
When x = -3, we have:
f(-3) = - |-3 + 3|
f(-3) = 0 --- different y value from (-3, -6)
This means that the x values point to different y values (this does not represent a function)
Hence, none of the points could be added to the graph f(x)=-|x+3| to keep the graph a function
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a brick is in the shape of a rectangular prism with a length of 8 inches, a width of 3.5 inches, and a height of 2 inches. the brick has a density of 2.7 grams per cubic centimeter. find the mass of the brick to the nearest gram a brick is in the shape of a rectangular prism with a length of 8 inches, a width of 3.5 inches, and a height of 2 inches. the brick has a density of 2.7 grams per cubic centimeter. find the mass of the brick to the nearest gram
The mass of brick is 2478 gram.
What is a rectangular prism?A rectangular prism has a total of 6 faces, 12 sides, and eight vertices. Like a cuboid, it has three dimensions- the base width, the height, and the length. The top and base of the rectangular prism are rectangular in shape. The pairs of opposite faces of a rectangular prism are identical or congruent.
A brick is in the shape of a rectangular prism with a length of 8 inches, a width of 3.5 inches, and a height of 2 inches.
The volume of rectangular prism = length×width×height
= 8×3.5×2
= 56
Thus volume of brick is 56 cubic inches.
Convert inches to centimeter
1 inch = 2.54 centimeter
Therefore,
56 cubic inches = 56 x 2.54 x 2.54 x 2.54 cubic centimeter
56 cubic inches = 917.676 cubic centimeter
Thus, we get,
volume of a rectangular prism = 917.676 cubic centimeter
The brick has a density of 2.7 grams per cubic centimeter
Density = 2.7 grams
The mass of brick is given by formula = density × volume
[tex]\Rightarrow[/tex] = 2.7 × 917.676
[tex]\Rightarrow[/tex] = 2477.72
[tex]\Rightarrow[/tex] ≅ 2478
Thus mass of brick is 2478 gram.
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A university wants to determine the average salary of its graduating computer science majors. the university asks the graduating classes of 50 students to share their starting salaries when hired. the 50 students had an average salary of $100,000 with a standard deviation of $2,000. find a 95% confidence interval for the average starting salary of computer science majors from the university.
Option B. ($99,242.00, $100,758.01)
a) For n - 1 = 49 degrees of freedom, we have form t distribution tables:
P( t < 2.010) = 0.975
Therefore, P(-2.010 < t < 2.010) = 0.95
Therefore the confidence interval here is obtained as:
X +₋ t 8/√ⁿ
100 \pm 2.010*\frac{2}{\sqrt{50}}
100 \pm 0.5685
(99431.61, 100568.39)
Therefore A is the correct interval here.
Q2) From t distribution tables, we have here:
P(-2.680 < t < 2.680) = 0.99
Therefore the confidence interval here is obtained as:
100 \pm 2.010*\frac{2}{\sqrt{50}}
100 \pm 0.7580
(99242, 100785)
1) A university wants to determine the average salary of its graduating computer science majors. The university asks the graduating classes of 50 students to share their starting salaries when hired. The 50 students had an average salary of $100,000 with a standard deviation of $2,000. Find a 95% confidence interval for the average starting salary of computer science majors from the university.
a - ($99,431.61, $100,568.39)
b - ($99,445.64, $100,554.36)
c- ($99,982.26, $100,017.74)
d - The salaries are not normally distributed so we cannot compute a confidence interval
2) Find a 99% confidence interval for the previous problem.
a - ($99,271.44, $100,728.56)
b - ($99,242.00, $100,758.01)
c - ($99,996.46, $100,003.55)
d - The salaries are not normally distributed so we cannot compute a confidence interval
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Select all the correct answers.
Which expressions are equivalent to this exponential expression?
Answer:
The answer that you have highlighted is correct.
Step-by-step explanation:
When you are dividing, you divide the exponents
-10 - (-4)
-10 + 4
-6
Joe's company sold insurance policies over the phone. Last month, 2 employees sold three hurricane policies, 6 employees sold two hurricane policies, and 9 employees sold a single hurricane policy. If a single employee is picked at random, what is the probability that the employee sold two hurricane policies or sold one hurricane policy
The probability that the employee sold two hurricane policies or sold one hurricane policy is 15/17.
According to the statement
Number of employees who sold three hurricane policies is 2
Number of employees who sold two hurricane policies is 6
Number of employees who sold 1 hurricane policies is 9
SO,
The total number of employees is 2+6+9=17.
The number that sold two hurricane policies or sold one hurricane policy is 6+9=15,
so the Probability = Total number of policies sold / total number of employees
Probability = 15/17
So, The probability that the employee sold two hurricane policies or sold one hurricane policy is 15/17.
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Nakeisha read 2 and 3/5 pages in 6 minutes at what rate, in pages per hour, did she read?
The rate at which she reads is 26 pages per hour
How to determine the rate?The given parameters are
Pages = 2 and 3/5
Time = 6 minutes
Convert the time from minutes to hour
Time = 6/60 hour
This gives
Time = 0.1 hour
The rate at which she reads is calculated as:
Rate = Page/Time
This gives
Rate = (2 and 3/5)/0.1 hour
Rewrite as:
Rate = 2.6 pages/0.1 hour
Divide
Rate = 26 pages per hour
Hence, the rate at which she reads is 26 pages per hour
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My fruit basket contain apples and oranges.The ratio apples to oranges is 3:8.When I remove one apple the ratio changes to 1:3 .How many apples are in the basket
The number of apples in the basket are; 24 apples
How to simplify simultaneous equations?Let there be X number of apples and Y number of oranges.
Thus by the given ratio we can say that;
x/y = 3/8 -----(1)
(x — 1)/y = 1/3
3x — 3 = y ----(2)
Substitute 3x - 3 for y in eq 1 to get;
x/(3x - 3) = 3/8
8x = 9x - 9
9x - 8x = 9
x = 9
Thus;
y = 3(9) - 3
y = 24 apples
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Of the 30 cars in a parking lot, 12 are blue, 8 are red, 6 are white, and 4 are silver. In simplest form, what are the odds in favor of a red or white car leaving first?
A. 7:8
B. 8:7
C. 1:5
D. 5:1
Answer:
Step-by-step explanation:
8+6=14
14/30 = 7/15
So the final answer is 7/15
pls thank me pls :(
Briana is looking for jobs and is hoping to find one that will allow
her to make at least $2,000 in her first paycheck. She has found
one possible postion at the local shoe store that is offering $200
signing bonues and a wage of $15 per hour. How many hours will
Briana need to work to make $2,000 in her first paycheck?
Answer: 120 hr
Step-by-step explanation: 15$ every hr so for 120 hrs it would be 1,800$ plus the signing bonus of 200$ would total 2,000$ but with out the bonus she would have to work 134 hrs for 2,010$
It has taken 3 hours to fill a 5 gallon bucket from leaky hose what is the rate in gallons per hour
Answer: 1.7
Step-by-step explanation:
The rate of gallons per hour is the same as the unit rate. You want to find out how many gallons are filled in one hour, so divide 3 down to one, 3 divided by 3 is one. Then, also divide 5 by 3. 5 divided by 3 is 1.6666... and as an hour is out of 60, round it to 1.7.
I hope this helps!
ABCD is a rectangle. What is the value of x
A bag contains 1 white (W), 3 blue (B1, B2, B3), and 2 red (R1, R2) marbles.
Find the probability of tossing a head and drawing a red marble. Explain your reasoning.
Using it's concept, there is a 0.1667 = 16.67% probability of tossing a head and drawing a red marble.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, we have that:
For the coin, one out of two outcomes are heads.For the marble, two out of six marbles are red.Hence the probability of tossing a head and drawing a red marble is:
[tex]\frac{1}{2} \times \frac{2}{6} = \frac{1}{6} = 0.1667[/tex]
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Which system is equivalent to startlayout enlarged left-brace 1st row y = 9 x squared 2nd row x y = 5 endlayout
The set of equations that corresponds to the specified function are
y = 5 - x and 5 - x = 9x².
What is linear equation in two variables?
If an equation is expressed as ax + by + c=0, where a, b, and c are all real integers and a and b, the coefficients of x and y, respectively, are not equal to zero, then it is said to be a linear equation in two variables.
The given equation is :
[tex]y=9x^{2}[/tex] equation 1.
[tex]x+y=5[/tex] equation 2.
From equation 2.
[tex]x+y=5\\y=5-x[/tex]
substituting into 1 equation.
[tex]5-x=9x^{2}[/tex]
The system of equations that is equivalent to the provided function is shown by the resulting equation, which is y = 5 - x and [tex]5-x=9x^{2}[/tex]
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HURRY PLEASE!!!!!!
Jarrett splits his bag of j jelly beans into two equal piles and gives one pile to his brother. He then gives his brother seven more beans. Write an algebraic expression to represent the number of beans his brother has?
Need help understanding how to solve
For the two figures to be similar, the missing length must be 30.
What is the missing length?For the two figures to be similar, the dimension of each figures must be proportional to each other.
Let the missing length be x.
Hence,
x/25 = 24/20
We cross multiply
x × 20 = 24 × 25
x × 20 = 600
x = 600/20
x = 30
Therefore, for the two figures to be similar, the missing length must be 30.
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Someone pls pls PLS, help, its urgent!!! ASAP!!
“Complete the proof (geometry)”
1) [tex]\overline{AB} \perp \overline{BD}[/tex], [tex]\overline{AB} \cong \overline{DB}[/tex], [tex]\overline{AC} \cong \overline{DE}[/tex] (given)
2) [tex]\angle ACB[/tex] is a right angle (perpendicular lines form right angles)
3) [tex]\triangle ABC[/tex] and [tex]\triangle BED[/tex] are right triangles (a triangle with a right angle is a right triangle)
4) [tex]\therefore \triangle ACB \cong \triangle DEB[/tex] (HL)
5) [tex]\therefore \angle ACB \cong \angle DEB[/tex] (CPCTC)
Which equation describes how the parent function, y = x3, is vertically stretched by a factor of 4?
Oy=x³ +4
O y=(x+4)³
O. y=4x³
O y=x4
Answer: [tex]y=4x^3[/tex]
Step-by-step explanation:
See attached image.
The equation of function after vertically stretched by a factor of 4 is,
⇒ y = 4x³
What is Translation?A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
Given that;
The parent function is,
⇒ y = x³
Now, After vertically stretched by a factor of 4 we get;
The value of function is,
⇒ y = 4x³
Hence, The equation of function after vertically stretched by a factor of 4 is,
⇒ y = 4x³
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Use the drawing tools to form the correct answer on the provided graph.
Graph the line that represents the equation y= -2/3x + 1
The graph of the line is shown in the attached image.
Given that the equation of the line y=-2/3x+1.
The line equation is an algebraic representation of the set of points, which together form a line in an exceedingly frame of reference.
First, we'll take the intercepts of equation y=-2/3x+1 . find
Find the y-intercept
The y-intercept is that the value of y when the worth of x is adequate zero
For x=0
y=-2/3(0)+1
y=1
The y-intercept is that the point (0.1)
Find the x-intercept
The x-intercept is that the value of x when the worth of y is adequate to zero
For y=0
y=-(2/3)x+1
0=(-2/3)x+1
-1=(-2/3)x
x=3/2 or 1.5
The y-intercept is that the point (1.5,0).
To plot the line on a graph, draw the intercepts and connect the dots as shown within the figure.
Therefore, the graph for the line y=-(2/3)x+1 is attached below.
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Helppp please and thank uuu
What transformation is used to create this frieze pattern?
vertical reflection
glide reflection
horizontal reflection
180° rotation
Answer:
Using translation concepts, it is found that the transformation used to create this frieze pattern is a 180º rotation.
Step-by-step explanation:
A parabola, with its vertex at (0,0), has a focus on the negative part of the y-axis. which statements about the parabola are true? select two options.
The true statement of the parabola is (a) directrix will cross through the positive part of the y-axis.
What are parabolas?Parabolas are examples of a conic section such that it is formed by the intersection of a cone with a plane parallel to its side.
How to determine the true statements?From the question, the given parameters are:
Vertex = (0,0)
Focus = Negative side of the y-axis
A parabola has quite a number of forms, one of these forms is the general form.
The general form is represented as:
(x - h)^2 = 4p(y - k)
The vertex of the parabola is
(h, k) = (0, 0).
So, we have:
(x - 0)^2 = 4p(y - 0)
Evaluate the difference
x^2 = 4py
Since the focus is on the negative side, the value of p will be negative.
Also, because the vertex is at the origin, the directrix of the parabola will cross through the positive part of the y-axis.
This means that the true statement of the parabola is (a) directrix will cross through the positive part of the y-axis.
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Complete question
A parabola, with its vertex at (0,0), has a focus on the negative part of the y-axis. Which statements about the parabola are true?
Check all that apply.
The directrix will cross through the positive part of the y-axis.
The equation of the parabola will be in the form y2 = 4px where the value of p is negative.
The equation of the parabola will be in the form x2 = 4py where the value of p is positive.
The equation of the parabola could be y2 = 4x.
The equation of the parabola could be x2 = y.
Refreshment we’re set up in one area of the gym . hot pretzels were a dollar lemonade was 50 cents, fruit was 35 cents , and cookies were a quarter . if you purchase two of each . How much money would you needed
Answer:
$4.20
Step-by-step explanation:
1+1+.50+.50+.35+.35+.25+.25=4.20