Combinations- how to show that 10C2=10C8
The most effective way to show that 10C2 = 10C8 is to solve for the values of each combination. To solve for the values, we have to make use of the combination formula:
nCr = n! / r! (n – r)!
where n is the total sample size and r is the selected sample size
Calculating the value of 10C2:
10C2 = 10! / [2! (10 – 2)!]
10C2 = 10! / (2! * 8!)
10C2 = 45
Calculating the value of 10C8:
10C8 = 10! / [8! (10 – 8)!]
10C8 = 10! / (8! * 2!)
10C8 = 45
Therefore,
10C2 = 10C8
Any help like i just had
Two Runners are to race one lap on a circular track the radius on the inside Lane is 50 m the radius to the outside Lane is 51 M how much of a head start should the runner on the outside get
Rose plans to go for vacation to europe in 6 years from now. she estimates that she will need $24,388 for the trip. how much does she need to place in a saving account today that earns 5.13% per year (compounded annually) to accumulate this amount? all the work has to be shown! round the answer to two decimal places.
Shea and her best friend Kelly both babysit during the summer. Shea charges $4 per hour plus a $3 service fee, while Kelly charges $3.50 per hour plus a $6 service fee. After how many hours will they earn the same amount of pay? Write an equation to represent Kelly's total pay. Let h = hours worked and p = total pay.
Median MH is 6 units longer than median KP triangle GHI is similar to triangle JKL. If GH:JK=7:5, find the length of KP
Answer: KP=15
Step-by-step explanation:
HM/KP = 7/5.
HM = KP+6, so:
(KP+6)/KP =7/5.
cross multiply
5(KP+6) = 7KP
5KP + 30 = 7KP
30 = 2KP and KP = 15
Hope this helps, have a BLESSED and wonderful day! :-)
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The following data show the prices of different types of outfits at a store: $2, $2, $28, $26, $25, $27, $25, $27, $26, $28, $30 Which statement is correct about the box plot for the above data?
Answer:
C
2, 2, 25, 25, 26, 26, 27, 28, 28, 30
Minimum: 2
Maximum: 30
Median: 26
Lower quartile: 25
Upper quartile: 28
Step-by-step explanation:
Charlie cannot remember how much he financed to buy his car. He does remember that his monthly payment is $200. His add-on interest rate was 9% and he made a total of 30 payments. Find the amount of his loan to the nearest penny.
The initial amount that Charlie financed to buy his car is approximately $5,364.93. This was calculated using the add-on interest loan formula with the provided monthly payments, interest rates, and number of payments.
Explanation:The question is asking us to find out the initial amount that Charlie financed to buy his car, given that he made monthly payments of $200 at an interest rate of 9% over a total of 30 payments. This is a simple interest loan problem in mathematics, specifically dealing with add-on interest. To determine the original loan amount, we will use the formula for calculating the loan amount in an add-on interest loan. It is calculated by dividing the amount paid in total by the sum of one plus the product of the rate and time: Loan Amount = Total Payment / (1 + (Interest Rate * Time)) .
In this case, the total repayment made by Charlie is $200 * 30 = $6,000. The interest rate is 9% per year, but since he is making monthly payments we need to divide this by 12 to get the monthly interest rate, which is 0.0075. The time is 30 months. Substituting these values into our formula gives: Loan Amount = 6,000 / (1 + (0.0075 * 30)).
Hence, after calculations, the initial amount that Charlie financed to buy his car is approximately $5,364.93.
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kurt had 653.22 in his checking account , and a check that he wrote to his landlord for 675.00 was just deposited. this will result in which of the following fees?
Apex Answer: Overdraft fee
If 3x^2=4y=12 what is the value ofx^2y
Susan and Jessica play a,card game Susan win 60percent of time they play nine games,what is the probability that Jessica will have worn more games than susan?
To find the probability of Jessica winning more games than Susan in a card game, we need to calculate the probabilities for each outcome.
Explanation:To determine the probability that Jessica will have won more games than Susan, we need to calculate the probability of each possible outcome.
Given that Susan wins 60% of the time, the probability of Susan winning a game is 0.6 and the probability of Jessica winning a game is 0.4.
To calculate the probability of Jessica winning more games, we can use combinations. In this case, we need to find the sum of the probabilities of Jessica winning 0, 1, 2, 3, 4, 5, 6, 7, and 8 games out of 9.
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In what instance would you use the upside down U when doing interval notation
The number 4 is the smallest positive integer that has exactly three factors: 1, 2, and 4. If k is the next-highest integer that also has exactly three factors, what is the sum of the three factors of k
To solve this problem, we must do a method of trial and error to find for the next highest integer with exactly three factors. We know that the value of k must be greater than 4, therefore by using trial and error to find for the correct answer:
Factors of 5:1, 5
Factors of 6:1, 2, 3, 6
Factors of 7:1, 7
Factors of 8:1, 2, 4, 8
Factors of 9:1, 3, 9
Therefore we stop at 9 since this is already our answer. It has exactly three factors.
The sum of the factors is:
sum of factors = 1 + 3 + 9
sum of factors = 13
A bag has 2 red marbles and 16 blue marbles. Half of the blue marbles are made of glass. A marble is selected at random from the bag. What is the probability that it is a blue, glass marble? Write your answer as a fraction in simplest form.
Zach bought two new jet skis for 15,490. He will make 36 equal payments . How much will each payment be?
A solid has all of the following charateristics, except for which? A. has a closed space B. is three-dimensional C. has an open space D. is measured in volume
Simplifying the following Expressions by combining adding together what is alike like term 8n+5-n+13
At the theater, the worth family spent $18.00 on adult tickets, $16.50 on childrens tickets and $11.75 on refreshments. How much did you spend in all?
Twice x,plus 3,is the same as -6
write the equation out as given:
2x+3=-6
subtract 3 from each side
2x = -9
x=-9/2
x = -4.5
A tree has a shadow of 30ft how tall is the tree? And a triangle has a right angle with a line of 2ft tall and the base of 5ft what do they have in common.
What is the product of the smallest prime number and the largest negative number?
On a baseball field, the pitcher’s mound is 60.5 feet from home plate. During practice, a batter hits a ball 195 feet at an angle of 32° to the right of the pitcher’s mound. An outfielder catches the ball and throws it to the pitcher. Approximately how far does the outfielder throw the ball?
The outfielder throws the ball approximately 168 ft to the pitcher.
Explanation:The outfielder throws the ball to the pitcher at an angle of 32° to the right of the pitcher's mound. To find the distance the outfielder throws the ball, we need to break down the component of the throw in the direction perpendicular to the path of the ball. This can be done by finding the horizontal component of the throw.
To find the horizontal component, we can use the equation:
horizontal component of throw = distance * cos(angle)
Substituting the given values, we have:
horizontal component of throw = 195 ft * cos(32°)
Calculating this, we find that the horizontal component of the throw is approximately 168 ft.
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Need help on this problem plz
Standard form to 15409
How many perfect cube whole numbers are between 6000 and 8500?
An amount of $3000 is deposited for one year at an interest rate of 5.5% per annum. How much interest will be earned?
Answer:
$165
Step-by-step explanation:
In 1 years, you will have $165.00 of simple interest.
Calculations: The Final Investment Value, using the simple interest formula: A = P(1 + rt) where P is the Principal amount of money to be invested at an Interest Rate R% per period for t Number of Time Periods. Where r is in decimal form; r=R/100; r and t are in the same units of time.
The accrued amount of an investment is the original principal P plus the accumulated simple interest, I = Prt, therefore we have:
A = P + I = P + (Prt), and finally A = P(1 + rt)
Calculate Total Amount Accrued (Principal + Interest), solve for A
A = P(1 + rt)
Calculate Principal Amount, solve for P
P = A / (1 + rt)
Calculate rate of interest in decimal, solve for r
r = (1/t)(A/P - 1)
Calculate rate of interest in percent
R = r * 100
Calculate time, solve for t
t = (1/r)(A/P - 1)
Final answer:
The simple interest earned on a $3000 deposit at a 5.5% annual interest rate for one year is $165. This is found using the simple interest formula: Interest = Principal x Rate x Time.
Explanation:
To calculate the amount of simple interest earned on a $3000 deposit at an interest rate of 5.5% per annum for one year, we use the simple interest formula: Interest = Principal x Rate x Time.
In this case:
Principal (P) is $3000,
Rate (R) is 5.5% per annum, or 0.055 when expressed as a decimal,
Time (T) is 1 year.
So, the interest earned can be calculated as follows:
Interest = $3000 x 0.055 x 1
Interest = $165
Therefore, the amount of simple interest earned on the $3000 deposit after one year is $165.
which number is the standard equation for a circle centered at the origin should one increase to make the circle larger
The diagram below shows the partial construction of which shape?
a circle inscribed in a circle
an equilateral triangle inscribed in a circle
a regular hexagon inscribed in a circle
a square inscribed in a circle
Answer:
The correct option is 2.
Step-by-step explanation:
Steps for construction of a circle inscribed in a circle:
1. Draw a circle using compass.
2. Draw a diameter of that circle, using the scale.
3. Place the compass on a end point of diameter and draw a full circle, without changing the span on compass.
4. Mark the points of intersection of the two circle.
5. Using scale connect both points of intersection.
6. Using the scale connect each in intersection point with the second end point of diameter.
The diagram below shows the partial construction of a circle inscribed in a circle. Therefore the correct option is 2.
A roulette wheel contains the integers 1 through 36, 0, and 00. suppose that you spin the wheel 6 times and that each time you bet on a single number. what is the probability (rounded to the nearest hundredth) that you win on at least one bet?
Answer:
18/38
Step-by-step explanation:
edmentum/plato
At the pie eating contest, Max ate 2⁄5 of a pie and Jen ate 6⁄8 of a pie. How many pies did they eat all together?
Max and Jen ate a total of 1 3/20 pies together.
Explanation:To find out how many pies Max and Jen ate all together, we need to add the fractions of the pies that each of them ate.
Max ate 2/5 of a pie and Jen ate 6/8 of a pie. To add these fractions, we need to find a common denominator. The common denominator of 5 and 8 is 40.
Multiplying the numerator and denominator of 2/5 by 8, we get 16/40. Multiplying the numerator and denominator of 6/8 by 5, we get 30/40.
Now we can add the fractions: 16/40 + 30/40 = 46/40.
Since 46/40 is an improper fraction, we can simplify it to a mixed number by dividing the numerator by the denominator. 46 divided by 40 is 1 with a remainder of 6, so the mixed number is 1 6/40.
However, we can simplify the fractional part of the mixed number further. Both 6 and 40 are divisible by 2, so we can divide both the numerator and denominator by 2: 6 divided by 2 is 3, and 40 divided by 2 is 20. Therefore, the simplified mixed number is 1 3/20.
Therefore, Max and Jen ate a total of 1 3/20 pies together.
Final answer:
Max ate 2/5 of a pie and Jen ate 6/8 of a pie. The total is 1 and 6/40 pies.
Explanation:
To find out how many pies Max and Jen ate all together, we need to add the fractions of pies they each ate. Max ate 2/5 of a pie and Jen ate 6/8 of a pie. To add these fractions, we need to have a common denominator.
To find the common denominator, we can multiply the denominators together. In this case, the common denominator would be 5 * 8 = 40.
Now, we can convert both fractions to have a denominator of 40.
Max's fraction becomes 16/40 and Jen's fraction becomes 30/40.
Finally, we add the two fractions together:
16/40 + 30/40 = 46/40.
So, Max and Jen ate a total of 46/40 or 1 and 6/40 pies all together.