How many different committees can be formed from 10 teachers and 41 students if the committee consists of 2 teachers and 2 students?
A total of 279 tickets were sold for the school play. they were either adult or student tickets. the number of student tickets sold was two times the number of adult tickets sold. how many adult tickets were sold?
Final answer:
The number of adult tickets sold for the school play is 93, calculated by setting up an equation based on the information that the total tickets sold were 279 and student tickets were two times the number of adult tickets.
Explanation:
The question asks us to determine the number of adult tickets sold when a total of 279 tickets were sold for the school play, and the number of student tickets is two times the number of adult tickets sold. We can set up an equation to solve this problem.
Let A be the number of adult tickets, and S be the number of student tickets. The problem gives us two equations:
S = 2A (The number of student tickets is two times the number of adult tickets)
A + S = 279 (The total number of tickets sold is 279)
Substituting the first equation into the second gives us:
A + 2A = 279
3A = 279
A = 279 / 3
A = 93
Therefore, 93 adult tickets were sold for the school play.
Which pair of non-congruent figures must be similar? two squares two parallelograms (not rectangles) two right triangles two isosceles triangles (not equilateral)
What is the median of the data set given below? 19, 22, 46, 24, 37, 16, 19, 33
"let v = r 2 with the usual addition and scalar multiplication defined by k(u1, u2) = (ku1, 0). determine which of the five axioms of vector spaces involving scalar multiplication v satisfies and which fail. for the ones it satisfies, prove that it satisfies the axiom. for those that fail, show that it fails with a counterexample."
M(5, 7) is the midpoint of rs The coordinates of S are (6, 9). What are the coordinates of R?
(5.5, 8)
(7, 11)
(10, 14)
(4, 5)
Factor of x^3-x^2-24x-36
If 52/x is a positive integer, how many integer values are possible for x?
There are a total of 6 integer values that are possible for x: 1, 2, 4, 13, 26, and 52.
What is the quotient?If 52/x is a positive integer, it means that 52 is divisible by x, and x is a factor of 52. In other words, x must be a positive divisor of 52.
The positive divisors of 52 are: 1, 2, 4, 13, 26, and 52.
Thus;
52/1 = 52 (a positive integer)
52/2 = 26 (a positive integer)
52/4 = 13 (a positive integer)
52/13 = 4 (a positive integer)
52/26 = 2 (a positive integer)
52/52 = 1 (a positive integer)
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If, on average, Bob can make a sale to every 3rd person that comes into his store, how many people must come into Bob�s store if he wanted to make approximately fifteen (15) sales?
Guess the value of the limit (correct to six decimal places). (if an answer does not exist, enter dne.) lim hâ0 (4 + h)5 â 1024 h
The amount of carbon-14 present in animal bones t years after the animal's death is given by P(t)= -0.00012097t. How old is an ivory tusk that has lost 34% of its carbon-14?
I believe the equation you gave is wrong because the standard form of equation for C-14 decay is in the form of:
A = Ao e^-kt
So I think the right form of equation is (correct me if I’m wrong):
P(t) = Po e^(-0.00012097t)
Where,
Po = initial value of C-14 at t = 0
t = time elapsed
Since it is given that:
P = (1 – 0.34) Po
P = 0.66 Po
Therefore, t is:
0.66 Po = Po e^(-0.00012097 t)
0.66 = e^(-0.00012097 t)
taking ln of both side:
ln 0. 66 = -0.00012097 t
t = - ln 0. 66 / 0.00012097
t = 3,434.86 years
Therefore the ivory tusk is about 3,435 years old.
A psychologist claims that less than 5.8 percent of the population suffers from professional problems due to extreme shyness. Express the null hypothesis and the alternative hypothesis in symbolic form. Use p, the true percentage of the population that suffers from extreme shyness. Select one: a. H0: p = 5.8% H1: p < 5.8% b. H0: p > 5.8% H1: p ≤ 5.8% c. H0: p < 5.8% H1: p ≥ 5.8% d. H0: p = 5.8% H1: p > 5.8%
Answer:
Step-by-step explanation:
Let (-7, -4) be a point on the terminal side of theta. Find the exact values of Sin, CSC and COT
a total of 321 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was two times the number of adult tickets sold. How many adult tickets were sold
Find the length of the third Angelou a triangle given that the first two angels are 35 and 70 show your work
angles in a triangle = 180 degrees
70 +35 = 105 degrees
180-105 = 75 degrees
3rd angle = 75 degrees
If 4 1/2 = 2, 8 1/3 = 2, and 16 1/4 = 2, then for what value of x would x 1/5 = 2?
2
4
24
32
Which number is greater? 0 -1 -25 -50?
what is the answer to 11 over 7 in improper fractions
Using 8(-20) in a real world situation
Which question is not a good survey question?
a) Don’t you agree that the financial crisis is essentially over?
b) On average, how many hours do you sleep per day?
c) What is your opinion of educational funding this year?
d) Are you happy with the availability of electronic products in your state?
Answer:
See image
Step-by-step explanation:
Plato
a,(-a)^2=a^2 This is true or false?
Solve the equation by graphing. x^2+14x+45=0 First, graph the associated parabola by plotting the vertex and four additional points, two on each side of the vertex. Then, use the graph to give the solution(s) to the equation. If there is more than one solution, separate them with commas.
Points:
Solution(s):
The perimeter of a rectangle is 56 feet. Describe the the possible lengths of a side if the area of the rectangle is not to exceed 132 square ft
The possible lengths of sides of the rectangle will be [tex](6,22)[/tex] or [tex](22,6)[/tex] .
What is area ?Area is the space which is occupied by any [tex]2D[/tex] surface.
Area of rectangle [tex]=Length\ *\ Breadth[/tex]
Perimeter of rectangle [tex]=2(Length\ +\ Breadth)[/tex]
We have,
Perimeter of rectangle [tex]=56[/tex] feet
Area of rectangle [tex]=132[/tex] squared feet
Let,
Length of rectangle [tex]=x[/tex]
Breadth of rectangle [tex]=y[/tex]
So,
Perimeter of rectangle [tex]=2(Length\ +\ Breadth)[/tex]
[tex]56=2(x+y)[/tex]
[tex]28=(x+y)[/tex]
⇒ [tex]x=28-y[/tex] [tex]........(i)[/tex]
Now,
Area of rectangle [tex]=Length\ *\ Breadth[/tex]
[tex]132=x\ *\ y[/tex] [tex]........(ii)[/tex]
Now substitute value of [tex]x[/tex] in [tex](ii)[/tex],
[tex]132=(28-y)y[/tex]
[tex]132=28y-y^2[/tex]
⇒[tex]y^2-28y+132=0[/tex]
Now using Middle term split method;
[tex]y^2-28y+132=0[/tex]
[tex]y^2-22y-6y+132=0[/tex]
[tex]y(y-22)-6(y-22)=0[/tex]
[tex](y-6)(y-22)=0[/tex]
⇒
[tex](y-6)=0[/tex]
⇒ [tex]y=6[/tex]
[tex](y-22)=0[/tex]
⇒ [tex]y=22[/tex]
So,
Now if we take [tex]y=6[/tex], then
[tex]x=28-6[/tex]
[tex]x=22[/tex]
And,
if we take [tex]y=22[/tex], then
[tex]x=28-22[/tex]
[tex]x=6[/tex]
So, the possible lengths of sides of the rectangle are [tex](6,22)[/tex] or [tex](22,6)[/tex] .
Hence, we can say that he possible lengths of sides of the rectangle are [tex](6,22)[/tex] or [tex](22,6)[/tex] .
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An ellipse has vertices along the major axis at (0, 8) and (0, –2). The foci of the ellipse are located at (0, 7) and (0, –1). What are the values of a, b, h, and k, given the equation below? (y-k)^2/a^2+(x+h)^2/b^2=1
Answer: The values for a, b, h, and k are a = 5, b = 3, h = 0, k = -3.
Step-by-step explanation: In this problem, we know ellipse has vertices along the major axis at (0, 8) and (0, -2). The foci of the ellipse are located at (0, 7) and (0, -1). We are asked to determine the values of a, b, h, and k.
We were also then provided with the equation for vertical eclipse:
[tex]\frac{(x-h)^2}{b^2} + \frac{(y -k)^2}{a^2}[/tex]
Before we begin, we need to first define our values for a, b, h, and k.
a - distance to vertices from the centerb - distance to co-vertices from the center(h, k) - represents the center of the eclipseThe first step, we need to determine the center of the eclipse. We can use the midpoint formula to determine the midpoint between the vertices along the major axis: (0, 8) and (0, -2).
[tex]M = (\frac{x_{1} +x_{2} }{2} , \frac{y_{1} + y_{2} }{2} )[/tex]
[tex]M = (\frac{0 + 0}{2} , \frac{-2 + 8}{2} )\\M = (0, 3)[/tex]
We now know that our center (h, k) is (0, 3). Which means our values for h and k are 0 and 3. Next, we have to determine our values for a and b. Considering the center of our eclipse is not at the center, we can use one of our vertices to determine our value for a.
[tex]V_{1}[/tex] = (h, k±a)
(0, 8) = (0, 3±a)
3 ± a = 8
±a = 5
Now, we know that a = 5. For us to get b, we need to use this formula: [tex]c^2 = a^2 - b^2[/tex]. Let's rewrite this formula, so we can focus on getting our b-value.
[tex]c^2 - a^2 = -b^2[/tex]
For us to use this formula, we need to determine our c value. To find our c-value, we have use of our foci points: (h, k±c). C is the units away/further from the center towards our foci points.
(0, 3±c) = (0, 7)
3 + c = 7
7 - 3 = c
4 = c
Now, we know that our value for c is 4. Now, let's plug into the formula.
[tex](4)^2 - (5)^2 = -b^2\\16 - 25 = -b^2\\\frac{-9}{-1} = \frac{-b^2}{-1} \\\sqrt{b^2} = \sqrt{9} \\b = 3[/tex]
Our value for b is 3. If we put into our eclipse formula:
[tex]\frac{(x-0)^2}{3^2} + \frac{(y -(-3))^2}{5^2}[/tex]
Line segment AB is congruent to line segment CD.
A.AB overbar similar to CD overbar
B.AB overbar congruent to CD overbar
C. AB overbar equal to CD overbar
D. AB overbar element to CD overbar
When two line segments are congruent, what it really means is that the length of the line segments are equal. Congruent is usually interchanged with the word equal since it means the same: equal lengths. However, congruent is very specific in the sense that it means “equal lengths”. When we say equal alone, it may refer to different properties, congruent however is very specific.
Now the answer to this question should be:
B. AB overbar congruent to CD overbar
Not similar, not equal, and definitely not element. What we mean in this case is “equal lengths”, therefore the perfect word is congruent.
The probability that you will win a game is 0.18. if you play the game 504 times, what is the most likely number of wins?
Find an ordered pair (x , y) that is a solution to the equation
The adult child radio at a local daycare center is 3 to 16.at the same rare how many adults are needed for 48 children?
To find the number of adults needed for 48 children at a daycare with an adult to child ratio of 3:16, we set up a proportion and solve for the unknown number of adults. We cross-multiply and divide to find that 9 adults are required.
The question asks us to calculate how many adults are needed for 48 children in a daycare center given an adult to child ratio of 3:16. To solve this, we need to set up a proportion based on the ratio and solve for the number of adults needed.
We have the ratio of adults to children as 3:16, which means for every 3 adults, there are 16 children. To find out how many adults are needed for 48 children, we set up the proportion:
3 adults / 16 children = x adults / 48 children
Now we cross-multiply and solve for x:
(3 adults) / (48 children) = (16 children)
144 = 16x
x = 144 / 16
x = 9
Therefore, 9 adults are needed to take care of 48 children at the daycare center.
Find the percent equivalent to the ratio 8 to 20
divide the ratio:
8/20 = 0.4
0.4 = 40%
What's 10⁄12 written as a fraction in simplest form?
A. 5⁄6
B. 10⁄6
C. 3⁄5
D. 5⁄12