Answer:
[tex]sin(6\theta)sin(2\theta)[/tex]
Step-by-step explanation:
We are given that an expression
[tex]\frac{1}{2}cos(4\theta)-\frac{1}{2}cos(8\theta)[/tex]
The expression can be written as
[tex]\frac{1}{2}(cos(4\theta)-cos(8\theta))[/tex]
[tex]\frac{1}{2}(-2 sin (\frac{4\theta+8\theta}{2})sin(\frac{4\theta-8\theta}{2}))[/tex]
Using identity: [tex] cos A-cos B=-2 sin(\frac{A+B}{2})sin(\frac{A-B}{2})[/tex]
[tex]-sin(6\theta)sin(-2\theta)[/tex]
We know that
[tex] Sin(-x)=-Sin x[/tex]
By using this property
We get
[tex]sin(6\theta)sin(2\theta)[/tex]
Jackson and kate jones do not pay their credit care in full, the average daily balance is $$875 and the monthly periodic rate is 2.25%, what should be the fiance charge on the statement?
Answer:
The finance charge is $19.68
Step-by-step explanation:
The finance charge on a credit card is given by the formula:
Finance Charge = The Average Daily Balance x Monthly Periodic Rate
We know that:
Average Daily Balance = $875
Monthly Periodic Rate = 2.25% = 0.0225
Using in Formula:
Finance Charge = $875 x 0.0225
Finance Charge = $19.68
To calculate the finance charge on the statement, multiply the average daily balance by the monthly periodic rate.
Explanation:To calculate the finance charge on the statement, we can use the formula:
Finance Charge = Average Daily Balance × Monthly Periodic Rate
First, convert the percentage rate to decimal form:
2.25% = 0.0225
Then, substitute the given values into the formula:
Finance Charge = $875 × 0.0225
Using a calculator, multiply $875 by 0.0225:
Finance Charge = $19.69
Therefore, the finance charge on the statement should be $19.69.
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In June 2005, a CBS News/NY Times poll asked a random sample of 1,111 U.S. adults the following question: "What do you think is the most important problem facing this country today?" Roughly 19% of those sampled answered "the war in Iraq" (while the rest answered economy/jobs, terrorism, healthcare, etc.). Exactly a year prior to this poll, in June of 2004, it was estimated that roughly 1 out of every 4 U.S. adults believed (at that time) that the war in Iraq was the most important problem facing the country. We would like to test whether the 2005 poll provides significant evidence that the proportion of U.S. adults who believe that the war in Iraq is the most important problem facing the U.S. has decreased since the prior poll. Which of the following are the appropriate hypotheses in this case?a. H0: p = .19 vs. Ha: p < .19
b. H0: p = .19 vs. Ha: p > .19
c. H0: p < .25 vs. Ha: p = .25
d. H0: p = .25 vs. Ha: p < .25
e. H0: p = .25 vs. Ha: p not equal to .25
Answer:
d. H0: p = .25 vs. Ha: p < .25
Step-by-step explanation:
A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".
The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".
The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".
On this case the claim that they want to test is: "If the proportion of 2005 has decreased from the info of 2004". So we want to check if the population proportion for 2005 is less than 0.25 (the value for 2004), so this needs to be on the alternative hypothesis and on the null hypothesis we need to have the complement of the alternative hypothesis.
Null hypothesis:[tex]p \geq 0.25[/tex]
The null hypothesis can be on this way: [tex]p=0.078[/tex], but is better put the complement of the alternative hypothesis.
Alternative hypothesis:[tex]p > 0.25/tex]
And the correct option would be:
d. H0: p = .25 vs. Ha: p < .25
Beneficial terms of trade are the terms or prices that are between the two parties' oppotunity costs
Answer:
Beneficial terms of trade or trading price between two parties are opportunity costs lower than the cost to manufacture them locally which benefits both parties. They must be less enough to cover the freight charges or additional service charges that may arise.
What is the cross section shown below?
Circle
Ellipse
Parabola
Hyperbola
Explanation:
Imagine that white rectangle as a blade that cuts the cylinder as the diagram shows. If you pull the top cylinder off and examine the bottom of that upper piece, then you'll see a circle forms. It's congruent to the circular face of the original cylinder. This is because the cutting plane is parallel to both base faces of the cylinder. Any sort of tilt will make an ellipse form. Keep in mind that any circle is an ellipse, but not vice versa.
Another example of a cross section: cut an orange along its center and notice that a circle (more or less) forms showing the inner part of the orange.
Yet another example of a cross section: Imagine an egyptian pyramid cut from the top most point on downward such that you vertically slice it in half. If you pull away one half, you should see a triangular cross section forms.
Good morning,
Answer:
it’s a circleStep-by-step explanation:
Because the plane is parallel to the cylinder base.
:)
the graph of f(x) can be compressed vertically and shifted to the left to produce the graph of g(x). if f(x) =x^3, which of the following could be the equation of g(x)?
Answer: [tex]B.\ g(x)=\frac{1}{4}(x+3)^3[/tex]
Step-by-step explanation:
The misssing options are: [tex]A.\ g(x)=4(x-3)^3\\\\B.\ g(x)=\frac{1}{4}(x+3)^3\\\\C.\ g(x)=4(x+3)^3\\\\D.\ g(x)=\frac{1}{4}(x-3)^3[/tex]Some transformations for a function f(x) are shown below:
1. If [tex]f(x-k)[/tex], the function is shifted right "k" units.
2. If [tex]f(+k)[/tex], the function is shifted left "k" units.
3. If [tex]bf(x)[/tex] and [tex]b>1[/tex], the function is stretched vertically by a factor of "b".
4. If [tex]bf(x)[/tex] and [tex]0<b<1[/tex], the function is compressed vertically by a factor of "b".
In this case, you know that the parent function f(x) is:
[tex]f(x)=x^3[/tex]
If the graph of the function g(x) is obtained by compressing vertically and shifting the function f(x) to the left, then:
[tex]g(x)=bf(x+k)[/tex] and [tex]0<b<1[/tex]
Based on this, you can identify that the following function could be the equation of the g(x):
[tex]g(x)=\frac{1}{4}(x+3)^3[/tex]
The sum of three consecutive integers is 9. What is the equation that represents the scenario?
n + (n + 1) + (n + 2) = 9
n – (n + 1) – (n + 2) = 9
n + (n – 1) + (n – 2) = 9
n = 9
The equation that represents the scenario is:
Option 1: n + (n + 1) + (n + 2) = 9
Step-by-step explanation:
We have to convert the given statement in an equation. As the variable used in the choices is n, so we will also use n.
Let n be an integer
then
The next integer will be n+1
and next integer to n+1 will be n+1+1 = n+2
So,
putting it in equation form
[tex]n + (n+1) + (n+2) = 9[/tex]
Hence,
The equation that represents the scenario is:
Option 1: n + (n + 1) + (n + 2) = 9
Keywords: Variables, equations
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Answer:
N+(N+1)+(N+2)=9
Step-by-step explanation:
just did it on edge
Yee Yee MERICA
While some nonsmokers do not mind being seated in a smoking section of a restaurant, about 60% of the customers demand a smoke-free area. A new restaurant with 120 seats is being planned.
How many seats should be in the nonsmoking area in order to be very sure of having enough seating there? Comment on the assumptions and conditions that support your model, and explain what "very sure" means to you.
Answer: There are 72 seats in order to be very sure of having enough seating.
Step-by-step explanation:
Since we have given that
Total number of seats is being planned = 120
Percentage of customers demand a smoke free area = 60%
So, Number of seats that should be in the non smoking area in order to be very of having enough seating would be
[tex]\dfrac{60}{100}\times 120\\\\=0.6\times 120\\\\=72[/tex]
Hence, there are 72 seats in order to be very sure of having enough seating.
Craig earns 5 points each time he catches a bad guy in his game.He catches 2 types of bad guys,pirates and ghosts.Craig caught 24 ghost and 36 pirates.How many points did he earn?
Answ300er:
300
24+36=60
60x5=300
Step-by-step explanation:
Answer:he would earn 300 points
Step-by-step explanation:
Let x represent the number of pirates that Craig catches.
Let y represent the number of ghosts that Craig catches.
Craig earns 5 points each time he catches a bad guy in his game. The total number of points that Craig will earn if he catches x pirates and y ghosts would be
5x + 5y
Craig caught 24 ghost and 36 pirates. Therefore, total number of points earned would be
5×36 + 5×24 = 180 + 120 = 300 points.
What is the average rate of change of the function on the interval from x = 0 to x = 5?
f(x)=
1/2^(3)x
Final answer:
The average rate of change of the function on the interval from x = 0 to x = 5 is 1/8.
Explanation:
The average rate of change of a function on an interval is calculated by finding the slope of the secant line between two points on the interval. In this case, the interval is from x = 0 to x = 5.
The function is [tex]f(x) = (1/2^(3))x.[/tex]
To find the average rate of change, we need to calculate the slope between the points (0, f(0)) and (5, f(5)).
Using the formula for slope, [tex]m = (y2 - y1) / (x2 - x1)[/tex], we substitute the values from the given function and interval:
[tex]m = ((1/2^(3))(5) - (1/2^(3))(0)) / (5 - 0)[/tex]
m = (5/8 - 0) / 5 = 5/40 = 1/8
Therefore, the average rate of change of the function on the interval from x = 0 to x = 5 is 1/8.
Following the guidelines of the Food and Drug Administration, Dale tries to eat at least 5 servings of fruit each day. For the first six days of one week, she had 4, 5, 3, 5, 4, and 4 servings. How many servings of fruit should Dale eat on Saturday to average at least 5 servings per day for the week?
Answer:
[tex] x = 35-4-5-3-5-4-4=10[/tex]
So then the value for Saturday should be equal or higher to 10 servings per day in order to have an average of 5 or higher.
Step-by-step explanation:
First we can begin finding the original average for the first 6 days of the week. We assume that the week start at Sunday, and we have data for Sunday, Monday, Tuesday, Wednesday, Thrusday, Friday. And we can find the average like this:
[tex]\bar X_i =\frac{4+5+3+5+4+4}{6}=4.167[/tex]
And for this case we have the original average under the goal of 5, so we need to find a value x, such that the final average taking in count the 7 days of the week would be 5.
[tex]\bar X_f = \frac{4+5+3+5+4+4+x}{7}=5[/tex]
So we can nultiply both sides by 7 and we got:
[tex]4+5+3+5+4+4+x = 35[/tex]
And then solving for x we got:
[tex] x = 35-4-5-3-5-4-4=10[/tex]
So then the value for Saturday should be equal or higher to 10 servings per day in order to have an average of 5 or higher.
Ishaan is 727272 years old and William is 444 years old. How many years will it take until Ishaan is only 555 times as old as William?
Answer:
It will take 13 years to Ishaan age will be 5 times William age.
Step-by-step explanation:
Given : Ishaan is 72 years old and William is 4 years old.
To find : How many years will it take until Ishaan is only 5 times as old as William?
Solution :
Let x be years since today.
According to question,
Ishaan's age is I=72+x
William's age is W=4+x
Now, We want the time for Ishaan age will be 5 times William's age:
i.e. [tex]I=5W[/tex]
[tex]72+x=5(4+x)[/tex]
[tex]72+x=20+5x[/tex]
[tex]72-20=5x-x[/tex]
[tex]52=4x[/tex]
[tex]x=13[/tex]
It will take 13 years to Ishaan age will be 5 times William age.
By this time William will be 17 years old and Ishaan will be 85 years old.
It will take 13 years to Ishaan age will be 5 times William age.
Given that,
Ishaan is 72 years old and William is 4 years old.Based on the above information, the calculation is as follows:
Let x be years since today.
So,
Ishaan's age is I=72+x
William's age is W=4+x
Now
I = 5W
72 +x = 5(4 + x)
72 + x = 20 + 5x
52 = 4x
x = 13
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In June 1990, a small academic press published an initial run of 2,500 copies of linguist Chloe Vermeulen’s first book, Speech and Speaking. Because the first run was selling well, a second, larger run was produced in June 1995. Total sales for the period from June 1995–June 2000 represented an increase of 52 percent over total sales for the preceding five years; by June 2000, Vermeulen’s book had sold a total of 3,843 copies. In 2000, Speech and Speaking was cited in an influential paper; subsequently, for the period June 2000–June 2005, sales of Vermeulen’s book were double the sales for the previous five-year period.
In the table, identify the number of books that most closely approximates the total sales of Speech and Speaking for each of the five-year periods June 1990–June 1995 and June 2000–June 2005, based on the information given. Make only two selections, one in each column.
A) June 1990–June 1995
B) June 2000–June 2005
C) Total sales for the period
Answer:
A) 1525
B) 4636
C) 8479
Step-by-step explanation:
Lest say that The book had been sold x copies in the period of June 1990-June 1995. And we know that the book had been sold 152*x/100 copies in the period of June 1995–June 2000. By June 2000 in total 3843 book had been sold. Therefore number of the copies that sold in the period of June 1990-June 1995 is:
[tex]252*x/100=3843\\x=1525[/tex]
number of the copies that sold in the period of June 1995-June 2000 is:
[tex]152*x/100=2318[/tex]
For the period June 2000–June 2005 2318*2=4636 book had been sold.
Four circles of unit radius are drawn with centers (1,0), (-1,0), (0,1), and (0,-1). A circle with radius 2 is drawn with the origin as its center. What is the area of all points that are contained in an odd number of these 5 circles? (Express your answer in the form "a pi + b" or "a pi - b", where a and b are integers.)
Answer:
4π -8
Step-by-step explanation:
Consider the attached diagram. The purple areas are those contained within 1 or 3 circles. The red areas are fully equivalent to the purple areas. The area of interest is the sum of the purple and red areas, or twice the red area.
Twice the red area is the area of the circle of radius 2 less the area of a square of diagonal 4.
For a circle of radius 2, its area is ...
A = πr² = π·2² = 4π
For a square of diagonal 4, its area is ...
A = (1/2)d² = (1/2)4² = 8
The area of interest is the difference of these, ...
area of interest = circle area - square area
= 4π -8
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Let f(x) = 36x^5 − 44x^4 − 28x^3 and g(x) = 4x^2. Find f(x)/g(x) .
A. 9x^2 − 11x − 7
B. 9x^2 + 11x + 7
C. 9x^3 − 11x^2 − 7x
D. 9x^3 + 11x^2 + 7x
Answer:
C. 9x³ − 11x² − 7xStep-by-step explanation:
[tex]f(x)=36x^5-44x^4-28x^3\\\\g(x)=4x^2\\\\\dfrac{f(x)}{g(x)}=\dfrac{36x^5-44x^4-28x^3}{4x^2}\\\\\dfrac{f(x)}{g(x)}=\dfrac{(4x^2)(9x^3)-(4x^2)(11x^2)-(4x^2)(7x)}{4x^2}\\\\\dfrac{f(x)}{g(x)}=\dfrac{(4x^2)(9x^3-11x^2-7x)}{4x^2}\qquad\text{cancel}\ 4x^2\\\\\dfrac{f(x)}{g(x)}=9x^3-11x^2-7x[/tex]
Answer:option C is the correct answer
Step-by-step explanation:
f(x) = 36x^5 − 44x^4 − 28x^3
g(x) = 4x^2
We want to determine f(x)/g(x). It becomes
(36x^5 − 44x^4 − 28x^3) /(4x^2)
Looking at the numerator, each term in the numerator can divide the term in the denominator without remainder. it means that the term in the denominator is a common factor of the numerator and thus, 4x^2 can be factorized out of the numerator. It becomes
4x^2(9x^3 − 11x^2 − 7x) /(4x^2)
4x^2 in the numerator cancels out 4x^2 in the denominator. It becomes
9x^3 − 11x^2 − 7x
On a cross-country.The anderson family planned to average 500 miles and 10 hours of drivind each day. On average,how many miles per hour did the anderson planhto drive?
Answer:
50 miles per hour
Step-by-step explanation:
Given:
Distance planned to travel each day is, [tex]D=500\ mi[/tex]
Hours of driving for covering the above distance is, [tex]t=10\ h[/tex]
The question asks to find the number of miles per hour Anderson plan to drive.
In other words, we need to calculate the average speed with which Anderson has to drive in order to cover 500 miles in 10 hours daily.
Therefore, the formula to calculate speed when distance covered and time taken are known is given as:
Average speed = [tex]\frac{Distance}{Time}[/tex]
Average speed = [tex]\frac{D}{t}[/tex]
Plug in 500 miles for 'D', 10 h for 't' and solve for speed. This gives,
[tex]\textrm{Average speed}=\frac{500}{10}\ mi/h\\\textrm{Average speed}=50\ mi/h[/tex]
Therefore, Anderson need to drive at an average of 50 miles per hour to cover the distance of 500 miles in 10 hours.
Adult and student tickets were sold for a school concert. The adult tickets cost $12 each, and the student tickets cost $8 each. If a total of 360 tickets were sold for $3,480, how many of each kind of ticket were sold?
Answer: the number of adult tickets sold is 150
the number of student tickets sold is 210
Step-by-step explanation:
Let x represent the number of adult tickets sold.
Let y represent the number of student tickets sold.
The adult tickets cost $12 each, and the student tickets cost $8 each. The total cost of tickets sold $3,480. This means that
12x + 8y = 3480 - - - - - - - - - -1
The total number of tickets sold is 360. This means that
x + y = 360 - - - - - - - - - -2
Multiplying equation 1 by 1 and equation 2 by 12, it becomes
12x + 8y = 3480
12x + 12y = 4320
Subtracting
-4y = -840
y = -840/-4 = 210
Substituting y = 210 into equation 2, it becomes
x = 360 - y = 360 - 210
x = 150
To find the number of adult and student tickets sold, we can set up a system of equations and solve for the variables. Using the given information, we find that 150 adult tickets and 210 student tickets were sold.
Explanation:To solve this problem, we can set up a system of equations. Let's let x represent the number of adult tickets and y represent the number of student tickets. From the given information, we can set up the following equations:
x + y = 360
12x + 8y = 3480
We can solve this system using the substitution method or the elimination method. Let's solve it using the substitution method:
From the first equation, we can express x in terms of y: x = 360 - y
Substituting this expression for x in the second equation, we get: 12(360 - y) + 8y = 3480
Simplifying the equation, we get: 4320 - 12y + 8y = 3480
Combining like terms, we have: -4y = -840
Dividing both sides by -4, we find: y = 210
Substituting this value of y back into the equation x + y = 360, we get: x + 210 = 360. Solving for x, we find: x = 150
Therefore, 150 adult tickets and 210 student tickets were sold.
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There are two spinners. The first spinner has three equal sectors labeled 1, 2, and 3. The second spinner has four equal sectors labeled 3, 4, 5, and 6. Spinners are spun once.
How many outcomes do not show an odd number on the first spinner and show a 5 on the second spinner?
1
2
3
5
=========================
Explanation:
Let's label each pair of outcomes as an ordered pair (x,y)
x = first spinner outcome
y = second spinner outcome
We have these 12 different possible combos
(1,3), (1,4), (1,5), (1,6)
(2,3), (2,4), (2,5), (2,6)
(3,3), (3,4), (3,5), (3,6)
Focus on the third column where y = 5 for each (x,y) pair. Of this column only (2,5) has x be an even number. The other results in that column have x be odd.
Basically (1,5) is the only possible outcome if we want the first spinner to lan on an even number, and the second spinner to land on 5.
In these conditions, there is only one outcome where the first spinner does not show an odd number and the second spinner shows a 5.
Explanation:The problem involves two spinners. The first spinner has three sections labeled as 1, 2, and 3, while the second spinner has four sections labeled as 3, 4, 5, and 6. We are looking for cases where the result from the first spinner is not an odd number and the result from the second spinner is 5.
On the first spinner, the only non-odd digit is '2'. On the second spinner, the number '5' is what we seek. Therefore only one outcome will satisfy both conditions - when the first spinner lands on 2 and the second spinner on 5.
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Jariah volunteers at the hospital during the week. She volunteers 3 hours on monday and thursday, 4 hours on saturday and sunday, and 2 hours on tuesday. How many hours does jariah volunteer at the hospital during the week?
Answer:
16
Step-by-step explanation:
Monday: 3
Thursday:3
Saturday:4
Sunday: 4
Tuesday:2
3+3+4+4 + 2 = 16
You're dealt three cards in a row at random from a standard deck of 52 cards.Now suppose that you are dealt a pair or three of a kind in the three cards. What are the odds that you had a pair on your first two cards; that is, that your first two cards were of the same denomination? A) 22,776/132,600B) 1/13C) 7,800/22,776D) 3/51
Answer:D
Step-by-step explanation:
Given
There are 52 cards out which we have to choose 3 cards
and starting 2 will have same denomination
For first card we can withdraw any card of any denomination and for second card we have to choose card of same denomination
There are total of 4 cards of same denomination and after 1 st card is drawn we need to choose 1 card out of 3 card
Probability[tex]=\frac{^3C_1}{^{51}C_1}[/tex]
[tex]=\frac{3}{51}[/tex]
AB = 4x DC = x + 9 AD = 6 BC = 2y Quadrilateral ABCD is a parallelogram if both pairs of opposite sides are congruent. Show that quadrilateral ABCD is a parallelogram by finding the lengths of the opposite side pairs.
Answer:
Therefore the lengths of the opposite side pairs, AB and BC are 12 units and 6 units .
Step-by-step explanation:
Given:
[] ABCD is a Parallelogram.
∴ pairs of opposite sides are congruent
∴ AB = DC and
BC = AD
To Find:
Length of AB = ?
Length of BC = ?
Solution:
[] ABCD is a Parallelogram. .............Given
∴ pairs of opposite sides are congruent
∴ AB = DC and BC = AD
On substituting the values we get
For 'x' i.e AB = DC
[tex]4x=x+9\\\\4x-x=9\\\\3x=9\\\\x=\frac{9}{3}\\ \\x=3[/tex]
For 'y' i.e BC = AD
[tex]2y=6\\\\y=\frac{6}{2} \\\\y=3\\[/tex]
Now substituting 'x' and 'y' in AB and BC we get,
[tex]Length\ AB=4\times 3 =12\ units\\\\Length\ BC=2\times 3 =6\ units[/tex]
Therefore the lengths of the opposite side pairs, AB and BC are 12 units and 6 units .
C) 12, 6
Set opposite sides equal to each other and solve for x or y.
AB = DC → 4x = x + 9 → 3x = 9 → x = 3
So, AB = DC = 12
And,
AD = BC → 6 = 2y → y = 3
So, AD = BC = 6
Dans sporting goods received a shipment of 120 sweatshirts. Half of the sweatshirts were size large. One-fourth of the large sweatshirts were red. What was the total number of sweatshirts in the shipment that were both large and red?
Answer:
15
sweatshirts were large and red.
Step-by-step explanation:
Hope this helps
Answer:the total number of sweatshirts in the shipment that were both large and red is 15
Step-by-step explanation:
The total number of sweatshirts received by Dans sporting goods is 120. Half of the sweatshirts were size large. This means that the number of sweatshirts that were size large is 120/2 = 60.
One-fourth of the large sweatshirts were red. This means that the number of large sweatshirts that were also red would be
1/4×60 = 15
onsider the following problem: A box with an open top is to be constructed from a square piece of cardboard, 3 ft wide, by cutting out a square from each of the four corners and bending up the sides. Find the largest volume that such a box can have. (a) Draw several diagrams to illustrate the situation, some short boxes with large bases and some tall boxes with small bases. Find the volumes of several such boxes
Answer:
V (max) = 2 ft³
and x side of the base is x = 0,5 feet
Step-by-step explanation: See annex ( two different cubes)
We have a square piece of cardboard of 3 inches wide
Let x be lenght of side to cut in each corner
Then the base of the (future cube) is 3 - 2x, and the area is
( 3 - 2x )²
And the height is x Then volume of the cube as a function of x is:
V(x) = ( 3 - 2x )² *x or V(x) = ( 9 + 4x² - 12x )*x
V(x) = 4x³ - 12x² + 9x
Taking derivatives on both sides of the equation
V´(x) = 12x² - 24x + 9
V´(x) = 0 12x² - 24x + 9 = 0 simplifying 4x² - 8x + 3 = 0
Second degree equation solving for x
x₁,₂ = [ 24 ± √( 576) - 432 /24
x₁,₂ = [24 ±√144 ]/24
x₁,₂ = ( 24 ± 12) /24 x₁ = 1.5 feet x₂ = 0,5 feet
Of these two values we have to dismiss x₁ because if x = 1.5 we don´t have a cube ( 0 height )
Then we take x = 0,5 feet
And
V (max) = (2)²*0,5 = 4*0,5
V (max) = 2 ft³
Suppose the two cards dealt to you are of different denominations. What is the probability that you'll be able to make four of a kind out of all seven cards available to you?
Answer:
The probability of getting a four of a kind is 29/23030 = 0.00126.
Step-by-step explanation:
The poker deck has 52 cards, divided in 4 suits, and each suit has 13 different denominations.
In this exercise you are given that the 2 cards you are dealt have different denominations, lets call them A and B, so in order to make a 4 of a kind, you need to get from the 5 remaining community cards, 3 cards that have the denomination of one of A or B.
You cant get a four of a kind with two different denominations at the same time, because you need to reserve the majority of the community cards for just one of them. So each four of a kind is a disjoint event from the others.
Recall that, apart from the obvius four of a kind that you can get with A and B, you can still get four of a kind with any other denomination, because 4 of the community cards can still have the same denomitation.
Lets first calculate the probability to get a four of a kind with A. With B it is the same computation and the result will, therefore, be the same.
First, note that the order in which the cards are given doesnt matter, so we can calculate the probability of getting triple A in the flop (in other words, the first 3 given cards), and then multiply by all possible permutations.
Since you start with one A in your hand, there are 3 in the deck of 50 cards (remove the two cards given to you). The probability of drawing the first A is 3/50. The probability to draw the second A once you drew the first one is 2/49 (because you removed another A from the deck). The probability for the third A to be drawn is 1/48. This gives us a probability of
3/50 * 2/49 * 1/48 = 1/19600
of drawing the 3 A in the first 3 given cards. The other 2 cards can be anything.
To draw 3 aces in 5 cards we need to multiply be the total amount of ways to put 3 cards in a set of 5. That number is equivalent to the number of ways to pick places for the three A ignoring the order for them. That is, [tex] {5 \choose 3} = 10 . [/tex] So, in total, the probability to get a four of the kind A is
10 * 1/19600 = 1/1960
Similarly, the probability to get a four of a kind with B is 1/1960.
To get a four of a kind with any other kind, we need first to specify the kind; we have 13-2 = 11 possibilities to choose (we substract the 2 kinds A and B). Then we need to specify how the cards of that kind will be placed among the community cards. We have as many possibilities as the total amount of ways to pick where the other card will be, that is, 5 possibilities. Hence, we have 55 possibilities to make a four of a kind with a kind different than A or B.
We need to calculate now what is the probability of getting 4 cards of a specific kind in a specific way, for example, the first four cards. That probability is
4/50 * 3/49 * 2/48 * 1/47 = 1/230300
because we start with 50 cards on the deck with 4 cards of them being of the kind we need, and we remove them one by one.
As a result, the probability of getting a four of a kind with a different kind than A and B is 55/230300 = 11/46060.
By summing disjoint cases, We conclude that that the probability to get a four of a kind is
11/46060 + 1/1960 + 1/1960 = 29/23030 = 0.00126
Samantha has a rectangular shaped fish tank in her room. The tank has a height of 2.6 ft, a width of 2.1 ft, and a length of 3.9 ft. What is the BEST approximation of the amount of water her fish tank can hold?
Answer: the BEST approximation of the amount of water her fish tank can hold is 21ft^3
Step-by-step explanation:
The shape of Samantha's fish tank is rectangular. The volume of the rectangular fish tank would be expressed as LWH
Where
L represents length of the tank
W represents the width of the tank.
H represents the height of the tank.
The tank has a height of 2.6 ft, a width of 2.1 ft, and a length of 3.9 ft.
This means that the volume of the fish tank would be
Volume = 2.6 × 2.1 × 3.9
= 21.294 ft^3
Yrone likes to snack on his big bag of candy. He takes 8888 pieces of candy from the bag each time he snacks. After eating 181 snacks, there are only 6 pieces of candy remaining in the bag. The number c of pieces of candy remaining in the bag is a function of s, the number of snacks Tyrone eats. Write the function's formula. c=, equals
Answer:
The Function formula is given by [tex]c = 150 -8s[/tex].
Step-by-step explanation:
Given:
Number of candies eaten each time he has snacks = 8
Number of snacks ate = 18
Now Number of candies eaten will be equal to number of snacks he ate multiplied by number of candies eaten each time he ate snacks
Hence. Number of candies he ate in 18 snacks = 18* 8 = 144 candies
Also given that 6 candies are remaining after eating 18 snacks;
Total Number of candies at the beginning will be = Number of candies he ate in 18 snacks + Number of candies remaining after 18 snacks
Total Number of candies at the beginning will be = 144 + 6 = 150 candies
Now, let The number of pieces of candy remaining in the bag be 'c'
Also Let the number of snacks Tyrone eats be 's'
Since it has been given that in number of candies in each snack is 8 candies.
Therefore,In 's' snacks , candies will be eaten by him = [tex]8s[/tex]
Total number of candies = 150
Now Remaining candies 'c' is equal to Total number of candies minus number of candies eaten in 's' snacks.
framing in equation form we get;
Remaining candies [tex]c = 150 -8s[/tex]
Hence the Function formula is given by [tex]c = 150 -8s[/tex].
write the standard form of the equation of the circle that passes through the origin, (2.8,0), and (5,2)
To find the standard form of the circle's equation, one must determine the center and radius by solving a system of equations derived from the circle passing through the points (0,0), (2.8,0), and (5,2).
Explanation:The question asks to write the standard form of the equation of the circle that passes through three given points, namely the origin, (2.8,0), and (5,2). The standard form for the equation of a circle is (x-h)² + (y-k)² = r², where (h,k) is the center of the circle, and r is the radius.
To find the equation, we need to determine the center and the radius. Since the circle passes through the origin, we can establish a system of equations based on the other two points which the circle passes through. We would end up with two equations:
By solving this system of equations, we can calculate the values of h, k, and r, and then plug these into the standard form equation of a circle.
The length of a rectangular room is 7 less than
three times the width, w, of the room. Which
expression represents the area of the room?
1 3w-4
2 3w-7
3 3w2 – 4w
4 3w²–7w
In a fruit survey, children choose their favorite fruit out of apples, bananas and oranges. 29% chose oranges and 30% chose bananas. What percentage chose apples?? show me your answer plz
Define g(n):=f(n!). We want to find a closed formula for g(n)g(n). First of all, we want to find a recurrence for g(n)g(n). If nn is odd, then it is pretty easy to see that g(n) = g(n-1)g(n)=g(n−1). If nn is even, try to write g(n)g(n) in terms of g(n/2)g(n/2).
Answer:
[tex]g(n)=g(n/2)+n/2[/tex]
Step-by-step explanation:
[tex](2k+1)!=1*3*5*7*...*(2k-1)*(2k+1)*2*4*6*8*...*(2k-2)*(2k)[/tex]
Notice that the odd factors of above equality don't contribute to the largest power of 2 that divides (2k+1)!
Therefore, we can conclude that [tex]g(2n+1)=g(2n)[/tex].
[tex](2k)!=1*3*5*7*...*(2k-3)*(2k-1)*2*4*6*8*...*(2k-2)*(2k)=\\= (1*3*5*...*(2k-3)*(2k-1))*((2*1)*(2*2)*(2*3)*...*(2*(k-1))*(2*k))=\\= (1*3*5*...*(2k-3)*(2k-1))*2^k*k![/tex]
Notice that the odd factors of above equality don't contribute to the largest power of 2 that divides (2k)!
Hence, [tex]g(2k)-g(k)=k[/tex]
So for [tex]k = n/2[/tex],
[tex]g(n)-g(n/2)=n/2\\g(n)=g(n/2)+n/2[/tex]
An independent-measures research study compares three treatment conditions using a sample of n = 5 in each treatment. For this study, the three sample means are, M1 = 1, M2 = 2, and M3 = 3. For the ANOVA, what value would be obtained for SSbetween?
a. 30b. 20c. 10d. 2
Answer: c. 10
Step-by-step explanation:
Given : An independent-measures research study compares three treatment conditions using a sample of n = 5 in each treatment.
For this study, the three sample means are, M1 = 1, M2 = 2, and M3 = 3.
Grand mean = [tex]\overline{X}=\dfrac{M1+M2+M3}{3}[/tex] [All sample have equal elements]
[tex]=\dfrac{1+2+3}{3}=2[/tex]
For ANOVA,
[tex]SS_{between}=n\sum(M_i-\overline{X})^2[/tex] , where i= 1, 2 , 3
[tex]SS_{between}=5((1-2)^2+(2-2)^2+((3-2)^2)[/tex]
[tex]SS_{between}=5((-1)^2+(0)^2+((1)^2)= 5(1+1)=10[/tex]
Hence,the value would be obtained for [tex]SS_{between}=10[/tex] .
hence, the correct answer = c. 10
Final answer:
For an independent-measures research study comparing three treatment conditions with n = 5 in each treatment, the SSbetween value calculated using ANOVA is 10.
Explanation:
To calculate the SSbetween (Sum of Squares Between) for an independent-measures research study using a one-way ANOVA, we first need the mean of the group means, also known as the grand mean (GM), and then use the formula to find SSbetween: SSbetween = ∑ n(M - GM)², where n is the number of subjects in each group, M is the group mean, and GM is the grand mean.
In this case, with three sample means of M1 = 1, M2 = 2, and M3 = 3, each with n = 5, the grand mean is GM = (1+2+3) / 3 = 2. Using the formula, we have:
SSbetween = 5(1 - 2)² + 5(2 - 2)² + 5(3 - 2)²
SSbetween = 5(-1)² + 5(0)² + 5(1)²
SSbetween = 5(1) + 5(0) + 5(1)
SSbetween = 5 + 0 + 5
SSbetween = 10.
Therefore, the value obtained for SSbetween in this study would be 10.