The student council consists of 10 juniors and 12 seniors. If two members are voted to be officers, what is the probability they are both seniors? Round the answer to two decimal places.
Answers
To find the probability of two events without replacement, we can use the general multiplication rule, which states that:
P(A and B) = P(A) * P(B|A)
where P(A and B) is the probability of both events occurring, P(A) is the probability of the first event occurring, and P(B|A) is the probability of the second event occurring given that the first event has occurred.
In this case, we want to find the probability that both members are seniors. Let A be the event that the first member is a senior, and B be the event that the second member is a senior. Then:
P(A) = 12/22
since there are 12 seniors out of 22 members.
P(B|A) = 11/21
since there are 11 seniors left out of 21 members after choosing one senior.
P(A and B) = P(A) * P(B|A)
= (12/22) * (11/21)
= 132/462
= 0.2857
Rounding to two decimal places, the probability is **0.29**.
Related Questions
What is the volume, to the nearest whole cubic inch, of a cylinder with a height of 10 inches and a radius of 8 inches? Use
* = 3.14 and round your answer to the whole number.
cubic inches
Answers
Answer:
2,009.6 inches³
Step-by-step explanation:
The formula for the volume of a cylinder:
V = πr²h
Let's substitute into the given equation:
V = πr²h
V = (3.14)(8²)(10)
Solve:
V = (3.14)(8²)(10)
V = (3.14)(64)(10)
V = (200.96)(10)
V = 2,009.6
Therefore, the volume of the cylinder is 2,009.6 cubic inches.
What was the percent increase of China's
population from 1970 to 1995?
56.25%
45%
156.25%
9.405%
China's Population
Population
(billions)
0.7
Year
1965
1970
1975
1980
1985
1990
1995
2000
0.8
0.92
0.98
1.08
1.14
1.25
1.26
Answers
The percentage increase China's population from 1970 to 1995 is: 56.25%.
How to Calculate Percentage Increase?Percentage increase = (Final Value - Original Value)/Original value × 100.
Given the following:
Original value = 0.8 billion
Final Value = 1.25 billion
Final Value - Original Value = 1.25 - 0.8
Final Value - Original Value = 0.45
Percentage increase = 0.45/0.8 × 100 = 56.25%.
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ILL GIVE 20 POINTS !!!! PLSS HELP ASAP
Answers
Answer: 10/40 or 1/4
Step-by-step explanation:
Add up all the amount of rolls, so 10+6+4+8+6+6=40
then add the probability of rolling a 3 or 6 = 10
divide that quantity out of the whole
answer is 10/40 and simplified is 1/4
hope it helps
Find the inverse of A = 9, -2 -10, 7 , if it exists.
Answers
The inverse of matrix A, if it exists, is:
A^(-1) = [7/43, 2/43; 10/43, 9/43]
To find the inverse of a matrix A, we need to determine if the matrix is invertible by calculating its determinant. If the determinant is non-zero, then the matrix has an inverse.
Given the matrix A = [9, -2; -10, 7], we can calculate its determinant as follows:
det(A) = (9 * 7) - (-2 * -10)
= 63 - 20
= 43
Since the determinant is non-zero (43 ≠ 0), we can proceed to find the inverse of matrix A.
The formula to calculate the inverse of a 2x2 matrix is:
A^(-1) = (1/det(A)) * [d, -b; -c, a]
Plugging in the values from matrix A and the determinant, we have:
A^(-1) = (1/43) * [7, 2; 10, 9]
Simplifying further, we get:
A^(-1) = [7/43, 2/43; 10/43, 9/43].
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What ratio is equivalent to 8/6
Answers
Answer:
3rd option: 32/24
Step-by-step explanation:
8/6 = 4/3
1st option: Now let's change the denominator to 24:
4/3 ==> ?/24
4/3 =
4*8 / 3*8 = 32/24, not 3/24.
2nd option: Now let's change the numerator to 24:
4/3 ==> 24/?
4/3 =
4*6 / 3*6 = 24/18, not 24/32
24/32 = 3/4, not 4/3 ==> don't get confused by this
3rd option: 32/24 is correct [Look at the explanation for 1st option]
4/3 ==> ?/24
4/3 =
4*8 / 3*8 = 32/24, not 3/24.
Hence, the 3rd option is correct.
Omar says 0.35 is smaller than
5
Explain why he is correct
Answers
Answer:
Because a decimal leading with a zero is always smaller than a whole number
Step-by-step explanation:
fraction that is equivalent to 3/9 and has a denominator of 3."
Answers
, The fraction equivalent to 3/9 with denominator 3 is the proper fraction p=1/3
What is a fraction in math?A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.
Given here: The fraction 3/9
Now we can simplify the fraction further by dividing both the numerator and denominator by 3
let p=3/9
then p=3/3 / 9/3
p= 1/3
Hence, The fraction equivalent to 3/9 with denominator 3 is the proper fraction p=1/3
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The perimeter is 18ft write an equation and use it to find the value of R.
Answers
The need to find the value of r.
The given figure is a rectangle and we can find the perimeter when we sum all its sides.
P = r ft +r ft +3ft + 3ft
and the sum has to be equal to 18ft, then:
r ft +r ft +3ft + 3ft = 18 ft
Solve the equation for r to find it value:
r ft +r ft +3ft + 3ft = 18ft
2r ft + 6 ft = 18 ft
Subtract 6ft on both sides
2r ft + 6ft - 6ft = 18ft -6ft
2r ft =12ft
Divide by 2 on both sides
2r/2 ft = 12/2 ft
r = 6 ft
So 6ft its the value of r
Replace this value on the equation to confirm the result:
r ft +r ft +3ft + 3ft = 18ft
6 ft + 6ft + 3ft + 3ft = 18ft
12ft + 6ft = 18ft
18 ft = 18ft
The result is correct.
can you pls also explain
Answers
Answer:
1.33 secondsStep-by-step explanation:
Use the given equation and substitute h with 9:
- 9 = -16t²t² = 16/9t = √(16/9)t = 4/3 ≈ 1.33Answer:
0.75
Step-by-step explanation:
16t² = 9
t² = 9/16
t = √{9/16}
t = 3/4
t = 0.75 s
sin(19/12 pi)=-(sqrtA(sqrtB +1))/4
Answers
Answer:
−0.965926=
−1 /4 /√a√b+ −1 4 /√a
Step-by-step explanation:
Two factory plants are making TV panels. Yesterday, Plant A produced 2000 panels. Two percent of the panels from Plant A and 7% of the panels from Plant B
were defective. How many panels did Plant B produce, if the overall percentage of defective panels from the two plants was 5%?
Answers
3000 panels were created by B.
What is an operation in mathematics?The operators that are utilized to solve expressions might be referred to as mathematical operations. Addition, subtraction, multiplication, and division are some of these operators. The BODMAS rule, a mathematical procedure, already has a standard attribute defined.
Let's assume that B generated 'x' panels, as indicated by the query. With the aid of the mathematical operation, it is resolved.
As a result, the quantity of damaged panels from B may be expressed as follows:
Panels from Plant B with defects: 7% (given)
(7/100) × (x) = 0.07x
Similar to that, there are: faulty panels from A.
Panels from Plant A with defects: 2% (given)
(2/100) × (2000) = 40
To determine the total number of faulty panels:
40 + 0.07x
Similarly, the total number of panels produced is:
2000 + x
Consequently, 5% of the panels are faulty overall.
Now that we've connected every equation and piece of information, we have the necessary expression:
(40 + 0.07x) / (2000 + x) = 0.05
40 + 0.07x = (2000 + x) 0.05
40 + 0.07x = 100 + 0.05x
putting similar phrases together:
0.07x - 0.05x = 100 - 40
0.02x = 60
x = 60/0.02
x = 3000
As a result, B created 3000 panels.
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Solve for 4|u-2| +6 < 42
Answers
Find the solution to the system of equations.
You can use the interactive graph below to find the solution
- 72 - 2y = 14
ALE
са
6x + 6y = 18
AS
y =
JO
y
7
AS
6
5
4
3
2
Со
+2
1 2 3 4 5 6 7
-7-6-5-4-3-2
SA
Pro
Do noble
Answers
9514 1404 393
Answer:
x = -4y = 7Step-by-step explanation:
It looks like your interactive graphing tool needs you to plot some points on each of the lines. For these lines, it is convenient to use the x- and y-intercepts. Each intercept can be found by dividing the constant by the coefficient of the variable.
-7x -2y = 14
The x-intercept is 14/-7 = -2. Plot (-2, 0) on the x-axis.
The y-intercept is 14/-2 = -7. Plot (0, -7) on the y-axis.
6x +6y = 18
The x-intercept is 18/6 = 3. Plot (3, 0) on the x-axis.
The y-intercept is 18/6 = 3. Plot (0, 3) on the y-axis.
__
The point of intersection of the two lines is the solution: (x, y) = (-4, 7).
If a video game tested 50 games how many will not work
Answers
Answer:
Can you add to the question? This isn't possible to answer without more information.
Step-by-step explanation:
Sorry :/
The word isometric can be broken into two parts. The prefix "iso-” means "of the same,” and "-metric” means "measure.” How does the meaning of the word isometric relate to determining if an isometric transformation occurred? Include the defining characteristics of angle measure and line segments in your response.
Answers
The term "isometric" has the Greek roots "isos," which means "same," and "metron," which means "measure." The definition of an isometric transformation is one in which the original figure and its transformed equivalent have the same shape, size, and orientation.
When we speak about geometric figures, the concept of shape, size, and orientation come into play.The defining characteristics of angle measure and line segments play a critical role in determining whether an isometric transformation has occurred. In geometry, angle measures are the measurements of angles in a geometric figure. An angle is formed by two line segments that share a common endpoint. It is a unit used to calculate the measure of a plane figure's interior or exterior, such as a polygon. In other words, the size of the angle doesn't change during an isometric transformation.Line segments are the building blocks of geometric figures. They are used to construct geometric figures such as polygons, triangles, and rectangles, among others. In an isometric transformation, the length of the line segments remains constant because the shape and size of the original figure and its transformed equivalent remain the same.In conclusion, the word "isometric" implies that the transformation has the same measurements of the original figure. It is a transformation that retains the original geometric figures' shape, size, and orientation. The defining characteristics of angle measure and line segments remain unchanged during the isometric transformation. This means that if an isometric transformation occurs, the original and transformed figures have the same measurements of angles and line segments.For such more question on isometric
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a triangle is shown drag graphs to the table to ahow the image of the triangle after it is reflected over the x-axis, the y-axis, or the line y = x.
Answers
The graphs have been correctly dragged to the table to show the image of the triangle after it is reflected over the x-axis, the y-axis, and the line y = x.
How to reflect the triangle based on the transformation rule?By applying a reflection over the x-axis to the coordinates of this triangle, we have the following coordinates of the image triangle;
(x, y) → (x, -y)
(1, -3) → (1, -(-3)) = (1, 3)
(3, -2) → (3, -(-2)) = (3, 2)
(4, -5) → (4, -(-5)) = (4, 5)
By applying a reflection over the y-axis to the coordinates of this triangle, we have the following coordinates of the image triangle;
(x, y) → (-x, y)
(1, -3) → (-1, -3)
(3, -2) → (-3, -2)
(4, -5) → (-4, -5)
By applying a reflection over the line y = x to the coordinates of this triangle, we have the following coordinates of the image triangle;
(x, y) → (y, x)
(1, -3) → (-3, 1)
(3, -2) → (-2, 3)
(4, -5) → (-5, 4)
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a fan pays $1175 for 4 premium seat tickets. Another fan pays $1675 for 6 premium seat tickets
Answers
Step-by-step explanation:
I do not understand
What are you to fine
I need help PLZZZ!!!
Subtract
-5-(-6)=
Answers
Answer:
1 is the answer
Step-by-step explanation:
-5-(-6) = x
-5 + 6 = x
1 = x
Answer:
s1: -5-(-6)
s2: -5 + 6. multiply minus with minus first
s3: +1. simply arthmatic.
In the equation (x-3)²+(y-2)2=16, the radius of the circle is...
16
3
32
4
Answers
Step-by-step explanation:
This is of the form
(x-h)^2 + ( y-k)^2 = r^2 so r^2 = 16 means r = 4 units
Pablo used a total of 5 3/4 gallons of gas while driving his car. Each hour he was driving, he used 5/6 gallons of gas. What was the total number of hours he was driving? Write your ans
Answers
We know that he used 5/6 gallons of gas per hour of driving.
So, the total amount of gas he used is 5/6 * x.
We also know that he used a total of 5 3/4 gallons of gas.
So, we can set up the equation:
5/6 * x = 5 3/4
To solve for x, we can first convert 5 3/4 to an improper fraction:
5 3/4 = 23/4
Then, we can multiply both sides of the equation by the reciprocal of 5/6:
x = (5 3/4) / (5/6)
x = (23/4) / (5/6)
x = (23/4) * (6/5)
x = 27.6/4
x = 6.9
Therefore, Pablo was driving for a total of 6.9 hours.
brainliest???
help me with this please
Answers
Answer:
the numbers that right of the origin on the x axis are positive numbers
Answer:
positive
Step-by-step explanation:
positive runs on the right of x -axis
negative runs on the left of the x-axis
prime and odd will never be running on either side of x-axis
hope it helps!!!!!!
An archaeologist found a fossil whose length is489.44 in.
Consult the conversion table to calculate the length of the fossil infeet.
Round your answer to the nearest tenth.
Answers
If the archaeologist found a fossil whose length is 489.44 inches, using the conversion table, the length in feet, to the nearest tenth, is 40.8 feet.
What is the conversion table?The conversion table refers to the tabulated standard units of measurement, showing temperature, length, area, volume, weight, and metric conversions
For instance, the conversion table shows that 12 inches equal 1 foot.
The length of the fossil = 489.44 inches
12 inches = 1 foot
489.44 inches = 40.8 feet (489.44 ÷ 12)
Thus, using the conversion table, which relies on multiplication or division operations using the conversion factors, the length in feet of the fossil is 40.8 feet.
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Find the equation (in terms of x ) of the line through the points (-3,4) and (1,-8)
Answers
Answer:
A(-3,4) B(1,-8)
y-y1/x-x1 =y2-y1/x2-x1
y-4/x--3 = -8-4/1--3
y-4/x+3 = -12/1+3
y-4/x+3 =-12/4
y-4/x+3 = -3
y-4 = -3(x+3)
y-4=-3x-9
y+3x +9-4=
y+3x+5=0
Answer:
y = -3x - 5
Step-by-step explanation:
-3, 4 and 1, -8
1 - -3 = 4
-8 - 4 = -12
\(\frac{-12}{4}\) = \(\frac{-3}{1}\) = -3
gradient/slope = -3
now substituting in the point -3, 4 to find the y intercept:
4= -3 x -3 + c
4 = 9 + c
-5 = c
y intercept = -5
equation is y = -3x - 5
Match the information on the left with the appropriate equation on the right.
An equation perpendicular to y = - 3x + 1 through the point
(3,-2)
An equation through the point ( - 2, 3) and parallel to
y = - 3x - 1
Answers
Find f(x) and g(x) so that the function can be described as y = f(g(x)). (1 point) y = Four divided by x squared. + 9
Answers
Answer:
ind f(x) and g(x) so that the function can be described as y = f(g(x)). (1 point) y = Four divided by x squared. + 9
=
Solve the equation below for x by graphing
3x =8_2x
Answers
The solution to the equation 3x = 8 - 2x is x = 1.6.
To solve the equation 3x = 8 - 2x by graphing, we can plot the two sides of the equation as functions of x and find the point(s) where they intersect. Here's a step-by-step explanation:
Express the equation in the form of y = f(x). Rearrange the equation:
3x + 2x = 8
5x = 8
x = 8/5 or 1.6
Graph the functions y = 3x and y = 8 - 2x on the same coordinate plane. The line represented by y = 3x is upward sloping, and the line represented by y = 8 - 2x is downward sloping.
Plot the points (1.6, 3(1.6)) and (1.6, 8 - 2(1.6)) on the graph.
The point of intersection represents the solution to the equation. In this case, the lines intersect at (1.6, 4.8).
Therefore, the solution to the equation 3x = 8 - 2x is x = 1.6.
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If xy=3 yz=6 zx=2 find x+y+z
Answers
Explanation: 1x3=3
3x2=6
2x1=2
suppose you draw 5 cards from a standard deck of 52 playing cards. (a) what is the probability that the hand contains exactly 3 cards from the heart suit? (b) what is the probability that the hand contains 4 or fewer cards from the heart suit? (c) what is the probability that every card in the hand is from a different suit? (d) what is the probability that every card in the hand is red or every card in the hand is black? 1
Answers
a. the probability of getting exactly 3 cards from the heart suit is approximately 0.0585. b. the probability of getting 4 or fewer cards from the heart suit is approximately 0.7681. c. the probability that every card in the hand is from a different suit is approximately 0.395. d. the probability that every card in the hand is red or every card in the hand is black is approximately 0.00198.
(a) To calculate the probability of getting exactly 3 cards from the heart suit, we can use the combination formula:
number of ways to choose 3 hearts out of 13 hearts * number of ways to choose 2 non-hearts out of 39 non-hearts / number of ways to choose 5 cards out of 52 cards
= (13 choose 3) * (39 choose 2) / (52 choose 5)
= 0.0585 (rounded to 4 decimal places)
Therefore, the probability of getting exactly 3 cards from the heart suit is approximately 0.0585.
(b) To calculate the probability of getting 4 or fewer cards from the heart suit, we can use the complement rule:
1 - (number of ways to choose 5 non-hearts out of 39 non-hearts / number of ways to choose 5 cards out of 52 cards)
= 1 - (39 choose 5) / (52 choose 5)
= 0.7681 (rounded to 4 decimal places)
Therefore, the probability of getting 4 or fewer cards from the heart suit is approximately 0.7681.
(c) To calculate the probability that every card in the hand is from a different suit, we can use the multiplication principle:
number of ways to choose 1 card of each suit / number of ways to choose 5 cards out of 52 cards
= (13 choose 1) * (13 choose 1) * (13 choose 1) * (13 choose 1) / (52 choose 5)
= 0.395 (rounded to 3 decimal places)
Therefore, the probability that every card in the hand is from a different suit is approximately 0.395.
(d) To calculate the probability that every card in the hand is red or every card in the hand is black, we can use the addition rule:
probability of all red cards + probability of all black cards
= (26 choose 5) / (52 choose 5) + (26 choose 5) / (52 choose 5)
= 0.00198 (rounded to 5 decimal places)
Therefore, the probability that every card in the hand is red or every card in the hand is black is approximately 0.00198.
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A rectangular field is ten times as long as it is wide. If the perimeter of the field is 1320 feet, what are the dimensions of the field?
A) Write an equation you can use to answer the given question. Let w be the width of the field.
The equation is ___
(Make sure you use the correct variable.)
B) Use your equation to find the dimensions of the field.
The width of the field is ___ feet.
The length of the field is ___ feet.
Answers
The equation is P = 2 ( L + W )
The width of the field is 60 feet.
The length of the field is 600 feet.
Given,
A rectangular field is ten times as long as it is wide.
The perimeter of the field is 1320 feet.
What is the area of a rectangle?Area of rectangle = Length x wide.
Perimeter = 2 ( Length + width )
Let the length of the rectangle be L
Width = W
L = 10W
Perimeter + 2 ( L + W )
1320 = 2 ( 10W + W )
Divide it by 2 into both sides.
1320/2 = 2/2 x 11W
660 = 11W
Divide both sides by 11.
660/11 = 11/11 W
60 = W
W = 60 feet
L = 10W = 10 X 60 = 600 feet
L = 600 feet
Thus,
The equation is P = 2 ( L + W )
The width of the field is 60 feet.
The length of the field is 600 feet.
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How many 5-letter code words can be formed from the letters T, Q, G, E, B if no letter is repeated? If letters can be repeated? If adjacent letters must be different?
Answers
The number of codes that can be made using the 5 letters given is 120 as calculated using permutation and combination.
Now when no letters are repeated:
5 letter codes to be made.
Possible options for each space = 5
so first digit has 5 options, second digit has 4 options , third digit has 3 options , fourth digit has 2 options and the final digit will have only 1 option left.
So total number of codes = 5 × 4 × 3 × 2 × 1 = 120 codes
if letters can be repeated
5 letter codes to be made.
Possible options for each space = 5
so first digit has 5 options, second digit has 5 options , third digit has 5options , fourth digit has 5 options and the final digit will have only 5 options also.
So total number of codes = 5 × 5 × 5× 5× 5= 3125 codes
if adjacent letters cannot be repeated
5 letter codes to be made.
Possible options for each space = 5
so first digit has 5 options, second digit has 4 options , third digit has 4 options , fourth digit has 4 options and the final digit will have only 4 options also.
So total number of codes = 5 × 4 × 4× 4× 4 = 1280 codes
Hence the total number of codes as calculated by permutation and combination is 1280.
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