There are 1540 different ways to fill the three 2nd grade teaching positions from the 22 applicants.
To determine the number of ways to fill the three 2nd grade teaching positions from 22 applicants, we can use the concept of combinations. Combinations allow us to calculate the number of different selections without considering the order of the chosen items.
The formula for combinations is C(n, k) = n! / (k! * (n-k)!), where "n" represents the total number of items to choose from (in this case, 22 applicants), "k" is the number of items to be chosen (3 teaching positions), and "!" denotes factorial.
Applying this formula, we have:
C(22, 3) = 22! / (3! * (22-3)!)
C(22, 3) = 22! / (3! * 19!)
C(22, 3) = (22 * 21 * 20 * 19!) / (3! * 19!)
C(22, 3) = (22 * 21 * 20) / (3 * 2 * 1)
C(22, 3) = 1540
So, there are 1540 different ways to fill the three 2nd grade teaching positions from the 22 applicants.
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Which graph does not represent a function
Answer:
When two or more y values go into one x value.
Step-by-step explanation:
X. Y
3—4 and also 10
Find the equation of the line through point (−5,5) and perpendicular to y=59x−4
Answer:
Step-by-step explanation:
NEED HELP!
The number of minutes it takes to shovel the sidewalk' varies directly to the length
of sidewalk. If it takes 20 minutes to shovel a sidewalk that's 64 feet in length,
how long would you predict it would take to shovel one that's 96 feet long?
Answer:
30 minutes
Step-by-step explanation:
20 * 96 / 64 = 30
NEED HELP ASAP MARK YOU BRAINLIEST what is 30+35+30=
Answer:
95
Step-by-step explanation:
30+30 is 60
60+35 is 95
Another way to do this is to use multiplication then add. (30x2=60)
Hope I helped!
95!
30+35=65
65+30=95
It helps to break up the problem.
Identify the slope of the line y−1=−6(x−3).
Answer:
The slope of the line is -5
Need the answer to the problem below.
((6 * 5) ^ 10) ^ 8 =
Answer:
Here is your answer
((6 * 5) ^ 10) ^ 8 =
(30 ^ 10) ^ 8 =
590490000000000 ^ 8 = 14780882941434592331608321020638329760100000000000000000000000000000000000000000000000000000000000000000000000000000000
Step-by-step explanation:
What is the circumference of a circle circumcised around a rectangle with sides 7 cm and 24 cm
The circumference of the circle circumscribed around the rectangle with sides 7 cm and 24 cm is approximately 78.54 cm.
To find the circumference of a circle that is circumscribed around a rectangle, we need to determine the diagonal of the rectangle, which will be equal to the diameter of the circle.
Given:
Length of the rectangle = 24 cm
Width of the rectangle = 7 cm
To find the diagonal of the rectangle, we can use the Pythagorean theorem:
Diagonal^2 = Length^2 + Width^2
Diagonal^2 = 24^2 + 7^2
Diagonal^2 = 576 + 49
Diagonal^2 = 625
Taking the square root of both sides, we get:
Diagonal = √625
Diagonal = 25 cm
Since the diameter of the circle is equal to the diagonal of the rectangle, the diameter of the circle is 25 cm.
The circumference of a circle can be calculated using the formula:
Circumference = π * Diameter
Circumference = π * 25 cm
Using an approximate value of π ≈ 3.14159, we can calculate:
Circumference ≈ 3.14159 * 25 cm
Circumference ≈ 78.54 cm
Therefore, the circumference of the circle circumscribed around the rectangle with sides 7 cm and 24 cm is approximately 78.54 cm.
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Simplify. Your answer should only contain exponents. Please explain how to do this.
Answer:
\(1. \: \frac{8v {}^{5} }{u} \)
\(2. \: 32 {}^{6} y {}^{8} \)
Step-by-step explanation:
\(2vu {}^{ - 4} .4u {}^{3} v {}^{4} = 8.(v {}^{1} \times v {}^{4} ).(u {}^{ - 4} \times u {}^{3} ) = 8.v {}^{5} .u {}^{ - 1} = 8.v {}^{5} . \frac{1}{u} = \frac{8v {}^{5} }{u} \)
\(4x {}^{3} y {}^{2} .2y {}^{4} .4x {}^{3} = (4 \times 2 \times 4).(x {}^{3} \times x {}^{3} ).(y {}^{2} \times y {}^{4} ) = 32.x {}^{3 + 3}.y {}^{2 + 6} = 32x {}^{6} y {}^{8} \)
Max is already 224 miles into his road trip. if he is averaging 52 miles per hour and the trip is 640 miles total, how many more hours does he have left to drive.
PLEASE HELPP!!! I don’t know how to do this
Answer:
773.8 inch²
Step-by-step explanation:
Find the surface area at first
the top and bottom = 6²π = 36π
around is circumference x by height = 12π x 15 = 180 π
multiply these by 3/4
top = 27π
bottom = 27π
around = 135π
add the two rectangles = 180 inch²
Total = 773.8
The two lines graphed on the coordinate grid each represent an equation.
Which ordered pair represents a solution to both equations?
A:(3, 6)
B:(-3, 0)
C:(6, 3)
D:(0, -3
a rectangular bin 4 feet long, 3 feet wide, and 2 feet high is solidly packed with bricks whose dimensions are 8 inches by 4 inches by 2 inches. the number of bricks in the bin is
In the trash can, there are 648 bricks. when the measurements are 8 by 4 by 2 The right response is so (C).
This same total mass of a three-dimensional shape is referred to as its porous structure. A cuboid with six rectangular faces has a surface area equal to the sum of the areas of each face. The cuboid's length, width, and height can also be labeled, and indeed the surface area (SA) can indeed be calculated using the equation SA=2lw+2lh+2hw.
Based on this equation, surface area is equivalent to two times overall combination of width and length, two times its products of length and height, and two times the ratio of both height and width.
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someone please help!!
Answer:
mistake is
\( \sqrt{18} \)
Step-by-step explanation:
it should be like=
\( \sqrt{2} \sqrt{9} = \sqrt{18} \)
mark as brainliest please
Help me please with math
Answer:
B. 1 and 10
Step-by-step explanation:
x + 4y = 13
x - y = 3
systems of equations I need help on a couple of these like ASAP
1. How long does it take running at a rate of 12m/s over a distance of 360m?
Step-by-step explanation:
T=D/S
D=360m
S=12m/s
360m÷12m/s
Time=30s
apply the method of undetermined coefficients to find a particular solution to the following system. x' = x-17y+4cos4t y'=x-y
The particular solution to the given system is: x_p(t) = (-1/17)cos(4t) + Bsin(4t) and y_p(t) = Ccos(4t) + Bsin(4t). This particular solution satisfies the given system of equations.
To find a particular solution using the method of undetermined coefficients, we assume that the particular solution can be written in the form of:
x_p(t) = A cos(4t) + B sin(4t)
y_p(t) = C cos(4t) + D sin(4t)
Taking the derivatives, we have:
x'_p(t) = -4A sin(4t) + 4B cos(4t)
y'_p(t) = -4C sin(4t) + 4D cos(4t)
Substituting these into the given system of equations:
-4A sin(4t) + 4B cos(4t) = A cos(4t) + B sin(4t) - 17(C cos(4t) + D sin(4t)) + 4cos(4t)
-4C sin(4t) + 4D cos(4t) = A cos(4t) + B sin(4t) - (C cos(4t) + D sin(4t))
Simplifying these equations, we get:
(-17A + 1)cos(4t) + (17B - 17C)sin(4t) = 4cos(4t)
(A - C)cos(4t) + (B - D)sin(4t) = 0
Comparing the coefficients of cos(4t) and sin(4t) on both sides, we can equate them to find the values of A, B, C, and D:
-17A + 1 = 4
17B - 17C = 0
A - C = 0
B - D = 0
Solving these equations, we find:
A = -1/17
B = C
D = B
Therefore, the particular solution to the given system is:
x_p(t) = (-1/17)cos(4t) + Bsin(4t)
y_p(t) = Ccos(4t) + Bsin(4t)
This particular solution satisfies the given system of equations.
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Which describes how triangle FGH could be transformed to triangle F prime G prime H prime in two steps?
On a coordinate plane, triangle F G H has points (negative 2, 1), (negative 3, 3), (0, 1). Triangle F prime G prime H prime has points (negative 8, negative 4), (negative 12, negative 12), (0, negative 4).
Answer:
Translation: Shift the entire triangle 6 units to the left and 5 units down.
Dilation: Enlarge the triangle by a factor of 4.
Step-by-step explanation:
To describe how triangle FGH can be transformed to triangle F'G'H' in two steps, we need to identify the specific transformations applied.
Translation:
The first step involves a translation, where the entire triangle is shifted by a certain amount horizontally and vertically. To determine the translation vector, we subtract the coordinates of corresponding vertices from F'G'H' from those of FGH.
Translation vector = (x-coordinate difference, y-coordinate difference) = ((-8) - (-2), (-4) - 1) = (-6, -5)
So, the translation vector is (-6, -5), indicating that the triangle is shifted 6 units to the left and 5 units down.
Dilation:
The second step involves a dilation, which changes the size of the triangle. To determine the dilation factor, we can compare the lengths of corresponding sides.
The length of side FG is given by the distance formula:
FG = sqrt((x2 - x1)^2 + (y2 - y1)^2) = sqrt((-3 - (-2))^2 + (3 - 1)^2) = sqrt(1^2 + 2^2) = sqrt(5)
The length of side F'G' is given by the distance formula as well:
F'G' = sqrt((x2 - x1)^2 + (y2 - y1)^2) = sqrt((-12 - (-8))^2 + (-12 - (-4))^2) = sqrt(4^2 + 8^2) = sqrt(80) = 4sqrt(5)
The dilation factor is the ratio of the corresponding side lengths:
Dilation factor = F'G' / FG = (4sqrt(5)) / sqrt(5) = 4
The dilation factor is 4, indicating that the triangle is enlarged by a factor of 4.
Bags of dog food are labeled 1 through 50. What is the probability that the dog will choose a numbered dog bag that is not a multiple of 11
Probability helps us to know the chances of an event occurring. The probability that the dog will choose a numbered dog bag that is not a multiple of 11 is 8%.
Given that Bags of dog food are labelled 1 through 50.
Now, the bags that are multiples of 11 are 11, 22, 33, and 44, therefore, a total of 4 bags are there.
Now, the probability that the dog will choose a numbered dog bag that is not a multiple of 11 is,
Probability = Number of bags that are not a multiple of 11/Total number of bags
= (50 - 4)/50
= 23/25
= 0.92
Hence, the probability that the dog will choose a numbered dog bag that is not a multiple of 11 is 8%.
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Helppppp rn due soon
1. The part that sufficient to prove ΔDEF is congruent to ΔJIH is DF = JH.
2. The part that sufficient to prove DBA is congruent to CBA is
<BAD = <CAB
We have,
1. DE = JI and <D = <J
So, the part that sufficient to prove ΔDEF is congruent to ΔJIH is
DF = JH
Then, By SAS congruence rule the triangle can be congruent.
2. Triangle DAC is an isosceles triangle.
So, to prove DBA is congruent to CBA we need
AD = AC
AB = AB
<BAD = <CAB
Then, By SAS congruence rule the triangle can be congruent.
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I’ll give brainliest!!! Can somebody pls explain how to do these
1. there are 18 mathematics majors and 325 computer science majors at a college. a) in how many ways can two representatives be picked so that one is a mathematics major and the other is a computer science major? b) in how many ways can one representative be picked who is either a
a) two representatives be picked in 5850 ways so that one is a mathematics major and the other is a computer science major. b) one representative be picked in 343 ways who is either a mathematics major or a computer science major.
Product Rule: If one event occurs in m ways and a second event occurs in n ways, the number of ways the two events occur in the sequence is m×n ways.
Sum Rule: If an event occurs either in m ways or in n ways (non-overlapping), the number of ways the event can occur is m+n ways.
according to the question,
Mathematics majors =18 and Computer science majors = 325
A. We need to use the product rule because the first event is picking up a Mathematics major and the second event is picking up a computer science major.
= 18 x 325
= 5850
B. Here sum rule is applicable because the event is picking up a mathematics major or a computer science major.
= 18 + 325
= 343
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(complete question)
there are 18 mathematics majors and 325 computer science majors at a college. a) in how many ways can two representatives be picked so that one is a mathematics major and the other is a computer science major? b) in how many ways can one representative be picked who is either a mathematics major or a computer science major.
For the pair of functions, write the composite function and its derivative in terms of one input variable. k(t) = 4.5+3 – 7t2 + 3t – 4; t(x) = In x
The composite function k(t(x)) is -2.5 - 7(ln x)^2 + 3(ln x), and its derivative is -14ln x + 3/x.
To find the composite function k(t(x)), we substitute the expression for t(x) into the function k(t) as follows:
k(t(x)) = 4.5 + 3 - 7t(x)^2 + 3t(x) - 4
k(t(x)) = 4.5 + 3 - 7(ln x)^2 + 3(ln x) - 4
Simplifying this expression, we obtain:
k(t(x)) = -2.5 - 7(ln x)^2 + 3(ln x)
To find the derivative of the composite function, we use the chain rule as follows:
k'(t(x)) = k'(t) * t'(x)
where k'(t) is the derivative of the function k(t) with respect to t, and t'(x) is the derivative of the function t(x) with respect to x.
The derivative of k(t) with respect to t is:
k'(t) = -14t + 3
The derivative of t(x) with respect to x is:
t'(x) = 1/x
Substituting these expressions into the chain rule, we obtain:
k'(t(x)) = (-14t(x) + 3) * (1/x)
k'(t(x)) = (-14ln x + 3/x)
Therefore, the composite function k(t(x)) is -2.5 - 7(ln x)^2 + 3(ln x), and its derivative is -14ln x + 3/x.
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1/3 plus -2 1/4 equals what
Answer:
-1 11/12
Step-by-step explanation:
1/3=4/12 -2 1/4= -9/4 = -27/12
4/12 + -27/12 = -23/12
-23/12 = -1 11/12
b2+16 ? #Evaluate the expression when b=5.
Answer:
41
Step-by-step explanation:
I persume you mean b²+16 which gives us (5)²+16=25+16=41 after plugging in b=5
How do you find the eigenvectors and eigen values of a 3x3 matrix?
A 3x3 matrix's must first be calculated in order to determine the eigenvectors and eigenvalues of the matrix, using the quadratic formula, get the eigenvalues, determine the associated eigenvectors.
A 3x3 matrix's determinant must first be calculated in order to determine the eigenvectors and eigenvalues of the matrix. This may be accomplished by applying the expansion on eigenvalues may then be determined by using the quadratic formula to the eigenvalue equation. , the newly obtained eigenvalues may be used to solve the system of equations derived from the eigenvalue equation in order to get the associated eigenvectors. After the eigenvectors have been identified, they may be to the matrix's eigenvalues. You may eigenvalues and eigenvectors. To the matrix's structure and identify its distinctive equation, eigenvectors and eigenvalues. The solutions to a system of equations as well as the stability of the system may be found using eigenvectors and eigenvalues.
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Kendra earns $11.60 per hour working at the movie theater. Each week, she donates of
10
her earnings to Best Friends Animal Society, her favorite charity. If Kendra worked 8 hours
2
last week, how much money did she donate to the charity?
Answer:
$9.86
Step-by-step explanation:
First, write both numbers in the same form. Convert 8
1
2
to a decimal.
8
1
2
= 8+
1
2
= 8+
1×5
2×5
= 8+
5
10
= 8+0.5
= 8.5
Multiply.
11.6
× 8.5
580
+ 9280
98.60
Kendra earned $98.60 last week.
Now multiply to find how much money Kendra donated to the charity last week. She earned $98.60, and she donates
1
10
of her earnings each week.
First, write both numbers in the same form. Convert
1
10
to a decimal.
1
10
=0.1
Multiply.
98.6
× 0.1
9.86
Kendra donated $9.86 to the charity last week.
Please help.. ty if you do
Answer:B
Step-by-step explanation: x is less than 1 so it is a open circle on the graph and x is greater than or equal to -1 so it is a closed circle on -1, B has both of these so B is the answer
Qu es un circuito electrónico
Answer: Electrical network
Step-by-step explanation: this is the answer hope it helps
Which ratio is equivalent to the ratio 18:24
Answer:
8 : 24 36 : 48 54 : 72 72 : 96 90 : 120
108 : 144 126 : 168 144 : 192 162 : 216 180 : 240
Step-by-step explanation:
MAth