To calculate the number of different ways 30 qualifiers can be selected from 50 competitors in a ski jumping event, use the combination formula C(n, k) = n! / (k!(n - k)!), where in this case n=50 and k=30.
Explanation:The question here is focused on finding the number of different combinations in which the qualifying round can be selected from a group of competitors in a sport event, specifically men’s ski jumping. This falls under the category known as combinatorics, which is a part of mathematics that deals with counting, both in a concrete and abstract way, as well as finding certain properties of finite structures.
The total number of different ways 30 competitors can be chosen from a group of 50 can be found using the combination formula, which is expressed as C(n, k) = n! / (k!(n - k)!), where "n" is the total number of competitors, "k" is the number of competitors to choose, "n!" signifies the factorial of "n", and "(n - k)!" is the factorial of the difference between "n" and "k".
In this situation, to find the number of different ways to select the 30 qualifiers from 50 competitors, we plug the values into the formula to calculate C(50, 30).
Final answer:
To find the number of different ways the qualifying round can be selected, you need to use combinations. The formula for combinations is C(n, r) = n! / (r!(n-r)!), where n is the total number of competitors and r is the number of competitors moving on to the qualifying round.
Explanation:
To find the number of different ways the qualifying round can be selected, we need to use combinations. The formula for combinations is C(n, r) = n! / (r!(n-r)!), where n is the total number of competitors and r is the number of competitors moving on to the qualifying round.
In this case, n = 50 and r = 30. Plugging these values into the formula, we get C(50, 30) = 50! / (30!(50-30)!). Simplifying this expression, we find that C(50, 30) = 211915132760.
Therefore, there are 211,915,132,760 different ways the qualifying round can be selected.
Simplify the expression. 33 • 32 + 12 ÷ 4
The expression 33 • 32 + 12 ÷ 4 simplifies to 1059.
Explanation:To simplify the expression 33 • 32 + 12 ÷ 4, we follow the order of operations - performing multiplication and division before addition.
Multiply 33 and 32 to get 1056.Divide 12 by 4 to get 3.Now we can add the results: 1056 + 3 = 1059.
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A marina is in the shape of a coordinate grid. Boat A is docked at (4.2, −2) and Boat B is docked at (−5.2, −2). The boats are ____ units apart. A) 6.2 B) 7.2 C) 9.4 D) 13.4
Answer:
Your answer will be D.
Step-by-step explanation:
I did it on the test and got it correct.
What is the limit for lim x -> 2 int x
Bill's Roast Beef sells 5 times as many sandwiches as Pete's Deli. The difference between their sales is 360 sandwiches. How Many did each sell ?
Answer:
5y-y =360
4y =360
y= 90 sandwiches by Pete's deli
x= 5(90) = 450 sandwiches by Bills Roast Beef
Step-by-step explanation:
A bird feeder is in the shape of a cylinder. It has a volume of about 100 cubic inches. It has a radius of 2 inches. What is the approximate height of the bird feeder? Use 3.14 for pi
volume = pi x r^2x h
100 = 3.14 x 2^2 x h
100 =3.14 x 4 x h
100 = 12.56 x h
h = 100/12.56 = 7.9617
the height is approximately 8 inches tall
Suppose Q and R are independent events. Find P(Q and R) if P(Q) =4/5 and P(R) =4/11
A cold front moved in last weekend. In eight hours overnight, the temperature outside dropped from 14 degrees to -10. What was the average temperature change for each hour ?
A total of 487 tickets were sold for the school play. They were either adult tickets or student tickets. There were 63 fewer student tickets sold than adult tickets. How many adult tickets were sold?
Final answer:
To determine the number of adult tickets sold for the school play, a system of equations is set up and solved, revealing that 275 adult tickets were sold.
Explanation:
To find the number of adult tickets sold for the school play, we need to set up a system of equations based on the information given. Let x represent the number of adult tickets and y represent the number of student tickets. According to the problem, the following two statements are true:
The total number of tickets sold is 487: x + y = 487
There were 63 fewer student tickets sold than adult tickets: y = x - 63
We can substitute the second equation into the first to find the value of x:
x + (x - 63) = 487
2x - 63 = 487
2x = 487 + 63
2x = 550
x = 275
Therefore, 275 adult tickets were sold.
How many millimeters are there in 5 meters?
1 meter = 1000 mm
so 5 meters = 5 x 1000 = 5,000 millimeters
222+203 is rounded up to what?
A farmer is going to plant carrots on 5 3/14 acres, corn on 4 23/42 acres and peppers on 2 5/21 acres. If each acre requires 6 bags of fertilizer, how many bags of fertilizer does the farmer need to plant all the acres?
A company made 4 million in the second quarter this is 1/3 more then it made in the first quarter and 4/5 of what it made in the third quarter how much did the company make in all 3/4 combined
Round to the nearest while decimal 6.7
A figure has a vertex at (5, 2). If the figure has line symmetry about the y-axis, what are the coordinates of another vertex of the figure?
Answer:
[tex](-5,2)[/tex]
Step-by-step explanation:
We have been given that a figure has a vertex at (5,2). The figure has line symmetry about the y-axis.
We know that if a figure is symmetric about y-axis, then its x-coordinate changes to opposite sign and y-coordinate remains same.
We can see that x-coordinate of our given point is 5, so x-coordinate of another vertex of the figure would be -5.
Therefore, the point [tex](-5,2)[/tex] is symmetric about y-axis for our given point.
A total of 504 tickets were sold for the school play. They were either adult tickets or student tickets. There were 54 more student tickets sold than adult tickets. How many adult tickets were sold?
Using algebra, we find that 225 adult tickets were sold out of a total of 504 tickets.
Explanation:Let's denote the number of adult tickets as x. Since there were 54 more student tickets sold than adult tickets, we can represent the number of student tickets as x + 54. The total number of tickets sold is 504, so we set up the equation x + (x + 54) = 504.
Combining like terms, we get 2x + 54 = 504. Subtracting 54 from both sides gives us 2x = 450. Finally, dividing both sides by 2 gives us x = 225.
Therefore, 225 adult tickets were sold.
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True or False: The sample size you need to estimate the population distribution should always be at least 10% of the population size.
False. The sample size needed to estimate the population distribution should not always be at least 10% of the population size.
Explanation:False. The statement that the sample size needed to estimate the population distribution should always be at least 10% of the population size is not true. The size of the sample needed depends on various factors such as the original population, the level of confidence desired, and the margin of error allowed. For example, if the population is large and diverse, a smaller sample may still provide a reliable estimate of the population distribution. It is important to consider statistical concepts such as normal distribution and sampling techniques when determining the appropriate sample size.
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the base of this solid crate has an area of 6 square centimeters the height of the crate is 4 meters what is the volume of the crate
Answer:
2 × 10³ cm³
Step-by-step explanation:
Given data
Area of the base: 6 cm²Height of the crate: 4 m = 4 × 10² cmConsidering the crate is a cuboid, its volume (V) is:
V = length × width × height
Since
area of the base = length × width
We get
V = area of the base × height
V = 6 cm² × 4 × 10² cm
V = 2.4 × 10³ cm³ ≈ 2 × 10³ cm³ (we round off to 1 significant figure)
which number produces a rational number when added to 0.5
Answer:
Any rational number.
Step-by-step explanation:
∴ [tex]x+0.5[/tex] is rational if and only if x is rational.
To proveL: we proceed as follows:
Suppose that [tex]x+0.5[/tex] is rational.
Then there are some integers p , q with [tex]q\neq 0[/tex] such that
[tex]x+\frac{1}{2}=\frac{p}{q}[/tex]
Subtract both sides by [tex]\frac{1}{2}[/tex], we get
[tex]x=\frac{p}{q}-\frac{1}{2}=\frac{2p-q}{2q}[/tex] which is rational.
Conversely, if x is rational, then there are integers a,b with b>0 such that [tex]x=\frac{a}{b}[/tex] then we have,
[tex]x+\frac{1}{2}=\frac{a}{b}+\frac{1}{2}=\frac{2a+b}{2b}[/tex] which is also a rational.
Sales tax on an item is directly proportional to the cost of the item purchased. If the tax on a $500 item is $30, what is the sales tax on a $900 item?
Answer: $54
Step-by-step explanation:
The equation to show the direct variation in two quantities x and y is given by :-
[tex]\dfrac{x_1}{y_1}=\dfrac{x_2}{y_2}[/tex]
The tax on a $500 item is $30.
Let 'x' be the sales tax on a $900 item.
Then , we have the following equation:-
[tex]\dfrac{x}{900}=\dfrac{30}{500}\\\\\Rightarrow\ x=\dfrac{900\times30}{500}\\\\\Rightarrow\ x=54[/tex]
Hence, the sales tax on a $900 item = $54
the length of the hypotenuse is:
6.
12.
36.
[tex]6 \sqrt{3[/tex]
Find the value of y, rounded to the nearest tenth. Please help me, I'd appreciate it!!
Three counters are used for a board game.If the counters are tossed,how many ways can at least one counter with Side A occur?
Linda deposits $500 into an account that pays simple interest at a rate of 4% per year. How much interest will she be paid in the first 4 years?
In how many different ways can you make exactly 0.75 using only nickles dimes and quarters if you have at least one of each coin?
Express the volume of a cone, V, as a function of its radius, r, if the radius is 1/5 of the height.
What is the slope of a line that passes through the following points (-3,8) and (2,1)
Hello!
Step-by-step explanation:
Slope: [tex]\frac{Y^2-Y^1}{X^2-X^1}=\frac{rise}{run}[/tex]
[tex]\frac{1-8=-7}{2-(-3)=2+3=5}=\frac{-7}{5}=-\frac{7}{5}[/tex]
Slope is -7/5
Answer is -7/5
Hope this helps!
Thanks!
-Charlie
:)
:D
One school survey showed that 3 out of 5 students own a pet. Another survey showed that 6 out of 11 students owned a pet. Are these results equivalent? Explain your reasoning.
richerd works at an ice cream shop. regular cones get two scopes of ice cream and large cones get three scoops. One hot saturday richard scooped 234 regular cones and 156 large cones one scoop of ice cream is 3 ounces a tub of ice cream is 10 pounds how many tubs of ice cream did richerd use to make the cones?
234 x 2 = 468 scoops
156 x 3 = 468 scoops
468 + 468 = 936 total scoops
936 x 3 = 2808 ounces
16 ounces = 1 pound
2808/16 = 175.5 pounds
175.5/10 = 17.55 tubs
round answer as needed
Sara must plant 340 trees. In the past 6 days Sara planted 204 trees. If she continues at this rate, how many more days will it take her to plant all the trees?
Suppose y varies directly with x, and y = 8 when x = –6. What direct variation equation relates x and y? What is the value of y when x = –2?
Answer:
Direct variation states that the relationship between two variables in which one is a constant multiple of the other one.
In other words, when one variable changes the other one changes in proportion to the first.
i.e, if y is directly proportional to x then, the equal will be of the form is, y= kx where k is the constant of variation.
Given: y varies directly with x, and y = 8 when x = –6
By definition of direct variation,
y = kx
Substitute the values of x = -6 and y=8 to solve for k;
8 = -6k
Divide both sides by -6 we get;
[tex]k = -\frac{8}{6} = -\frac{4}{3}[/tex]
Now, to find the value of y when x = 2 we have;
[tex]y = -\frac{4}{3}x[/tex]
Substitute the given value of x =-2 we have;
[tex]y = -\frac{4}{3} \cdot -2 = \frac{8}{3}[/tex]
Therefore, the direct variation related x and y is, [tex]y = -\frac{4}{3}x[/tex]
and the value of [tex]y =\frac{8}{3}[/tex] when x = -2