there are 329 students in a college who have taken a course in calculus, 217 who have take a course in discrete mathematics, and 148 who have taken a course in both calculus and discrete mathematics. how many students at this college have taken a course in either calculus or discrete mathematics?
Answers
408 students selected either calculus or discrete math.
Define the term intersection of sets?The symbol "∩' can be used to represent the intersection of sets. According to the definition given above, an intersection between two sets A and B is the collection of all the elements that are shared by both sets.The stated data in the question-
329 people opt to study calculus.There are 217 persons who select discrete mathematics.148 people selected Calculus and discrete mathematics.Therefore,
The number of people who pick calculus or discrete math is equal to the sum of the number of people who select calculus and the number of people who choose discrete math.
Thus,
Discrete maths or calculus is preferred by = 339 + 217 - 148 students.
Discrete maths or calculus is preferred by = 408 students.
Thus, 408 people selected either calculus or discrete math.
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Related Questions
Help will give brainliest. Doc uploaded
Answers
Answer:
y = 3x + 5
Step-by-step explanation:
slope intercept form is y = mx + b where m is the slope and b is the y intercept.
b = 5
m = rise over run or (y2 - y1)/(x2 - x1)
m = (8-5)/1 -0
m = 3
thus, the equation of the line is:
y = 3x + 5
six and two thirds divided by twelve
Answers
The value of 6⅔ ÷ 12 is 5/9
What are mathematical operations?The mathematical “operation” refers to calculating a value using operands and a math operator.
Mathematical operations include; Addition subtraction, multiplication, division. This operations are used to define the relationship between two terms.
PEDMAS is used for orderly arrangements for the operation.
6²/3 ÷ 12
We first convert the mixed fraction into improper fraction.
= 20/3 × 1/12
= 20/36
divide through by 4, then we have
= 5/9
Therefore the value of 6⅔ ÷ 12 is 5/9
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CAN SOMEONE CHECK MY GEOMETRY WORK? 25 POINTS.
Picture attached. If so please tell me what I did wrong thx
Answers
Step 3 is unnecessary (the statement is already given, plus you haven't proven the triangle is isosceles anyway).
After, omit step 5 and jump straight to 6.
After this, step 6 is the statement that used to be step 5, which is true by CPCTC.
Then, you can prove the required statement by definition from this.
please help is this correct
Answers
Answer:
yes its correct
Step-by-step explanation:
you dont really need work because its really just substitution.
Are these shapes similar or congruent? H E L P !
Answers
Answer: similar
Step-by-step explanation: they are not congruent
Answer:
similar
Step-by-step explanation:
im pretty sure dats right
find a formula for the general term a n an of the sequence assuming the pattern of the first few terms continues. { 3 , − 1 , − 5 , − 9 , − 13 , ... } {3,-1,-5,-9,-13,...}
Answers
The formula will be an = 7 - 4n.
The given sequence is an arithmetic sequence, where each term is obtained by subtracting a fixed number from the preceding term. To find this fixed number, we can subtract any two consecutive terms in the sequence.
Subtracting the second term (-1) from the first term (3), we get:
a2 - a1 = -1 - 3 = -4
So, the fixed number is -4. We can use this to find the nth term of the sequence using the formula:
an = a1 + (n-1)d
where a1 is the first term, d is the common difference, and n is the term we want to find.
Substituting a1 = 3 and d = -4, we get:
an = 3 + (n-1)(-4)
Simplifying, we get:
an = 7 - 4n
Therefore, the formula for the general term an of the sequence {3,-1,-5,-9,-13,...} is:
an = 7 - 4n
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HELP ASAP PLEASE!!
solve the literal equation: 2ax+9=23 for x and show your work
Answers
Answer:
x = 7/a
Step-by-step explanation:
2ax + 9 = 23
Inverse operations
2ax + 9 = 23
-9 -9
2ax = 14
/2 /2
ax = 7
/a /a
x = 7/a
Consider the ordered bases B=([ 3
0
−2
3
],[ −1
0
1
−1
],[ 2
0
0
3
]) and C=([ 4
0
−3
−1
],[ 1
0
4
3
],[ 1
0
−1
−2
]) for the vector space V of upper triangular 2×2 matrices. a. Find the transition matrix from C to B. T C
B
=[] b. Find the coordinates of M in the ordered basis B if the coordinate vector of M in C is [M] C
= ⎣
⎡
−2
2
−1
⎦
⎤
[M] B
=[ −1
] c. Find M
M=[
]
Answers
The transition matrix from the basis C to the basis B, denoted as \($T_{CB}$\), is given by: \(\[T_{CB} = \begin{bmatrix} 3 & -1 & 2 \\ 0 & 0 & 0 \\ -2 & 1 & 0 \\ 3 & -1 & 3\end{bmatrix}\]\)
The coordinate vector of matrix M in the basis C, denoted as \($[M]_C$\), is given as:
\(\[[M]_C = \begin{bmatrix} -2 \\ 2 \\ -1\end{bmatrix}\]\)
To find the coordinates of M in the basis B, denoted as \($[M]_B$\), we multiply the transition matrix \($T_{CB}$\) by the coordinate vector \($[M]_C$\):
\(\[[M]_B = T_{CB} \cdot [M]_C = \begin{bmatrix} 3 & -1 & 2 \\ 0 & 0 & 0 \\ -2 & 1 & 0 \\ 3 & -1 & 3\end{bmatrix} \cdot \begin{bmatrix} -2 \\ 2 \\ -1\end{bmatrix} = \begin{bmatrix} -7 \\ 0 \\ 4 \\ -4\end{bmatrix}\]\)
Therefore, the coordinates of matrix M in the basis B are \($[M]_B = [-7, 0, 4, -4]$\).
In summary, the transition matrix from basis C to B is given by \($T_{CB}$\), and the coordinates of matrix M in the basis B are \($[M]_B = [-7, 0, 4, -4]$\).
The transition matrix from basis C to B is obtained by arranging the basis vectors of B as columns in the order specified by the basis C. The coordinate vector of matrix M in basis C represents the coefficients of the linear combination of the basis vectors of C that gives M. To find the coordinates of M in the basis B, we multiply the transition matrix from C to B by the coordinate vector of M in basis C. This multiplication yields the coordinate vector of M in the basis B, which represents the coefficients of the linear combination of the basis vectors of B that gives M. Therefore, the resulting coordinate vector \([M]_B\) represents the coordinates of matrix M in the basis B.
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Which type of rigid transformation is the equivalent of two reflections across intersecting lines?
Answers
according to the question,
given data in the question,
the type of rigid transformation is the equivalent of two across intersecting lines
Rotation is the process of changing the orientation of a shape by mirroring two intersecting line segments.
The intersection of the two reflection lines is the center of rotation.
An isometric drawing is a composite of two isometric drawings. The combination of two reflections on two parallel lines corresponds to translation.
The configuration of the two reflections is either translational or rotational. A translation occurs when a reflection is followed by a parallel reflection. Reflections following reflections from intersecting lines cause rotation
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The type of transformation that is equivalent to 2 reflections across intersecting lines is rotation
Which transformation is equivalent to a double reflection over parallel lines?A slide or a shift is a translation. By executing two composite reflections along parallel lines, translations may be produced. Translations maintain orientation and are isometric.
Which type of isometry is the equivalent of two reflections in parallel lines?An isometry is made up of two other isometries. The translation is equal to the combination of two reflections over two parallel lines.
according to the question,
the type of rigid transformation is the equivalent of two across intersecting lines
Rotation is the process of changing the orientation of a shape by mirroring two intersecting line segments.
The intersection of the two reflection lines is the center of rotation.
An isometric drawing is a composite of two isometric drawings. The combination of two reflections on two parallel lines corresponds to translation.
The configuration of the two reflections is either translational or rotational. A translation occurs when a reflection is followed by a parallel reflection. Reflections following reflections from intersecting lines cause rotation
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Can anyone please answer this question
Answers
The area of shaded part in the figures are
1. 7.07cm²
2. 19.54cm²
What's area of a shape?The area is the amount of space within the perimeter of a 2D shape. It is measured in square units, such as cm², m², etc.
The area of a sector is expressed as:
A= tetha/360 × πr²
Area of the shaded part = area of big sector - area of small sector.
1. area of big sector = 90/360 × 3.14 × 5²
= 7065/360
= 19.63cm²
area of small sector = 90/360 × 3.14 × 4²
= 12.56cm²
area of shaded part = 19.63 - 12.56
= 7.07cm²
2. Area of big sector = 40/360 × 3.14 × 9²
= 28.26cm²
area of small sector = 40/360 × 3.14 × 5²
= 8.72
area of shaded part = 28.26-8.72
= 19.54cm²
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The value of y is directly proportional to the value of x. When x = 3.5, the value of y is 14.
What is the value of y when x = 28?
Record your answer and fill in the bubbles on your answer document.
Answers
The value of y when x = 28 is y = 112. Since y is directly proportional to the value of x, we can write y = kx.
What is meant by directly proportional?When a quantity 'p' is increasing with an increase in the other quantity 'q' or decreases with a decrease in 'q', both quantities are said to be directly proportional.
I.e., p ∝ q ⇔ p = kq
Where k is the proportionality constant.
Calculation:It is given that, the value of y is directly proportional to the value of x.
I.e., y ∝ x
Then, y = kx
If x = 3.5 and y = 14, then k is
k = y/x = 14/3.5 = 4
So, if k = 4 and x = 28, then y is
y = kx = 4 × 28 = 112
Therefore, the value of y is 11.
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A password consists of 3 digits (0 - 9) followed by two letters (a-z or A-Z; note: 26 letters in the alphabet). i) How many different passwords are possible if repetition of digits and letters is allowed and passwords are not case sensitive (so 123AB is the same as 123aB)? ii) How many different passwords are possible if repetition of digits and letters is not allowed and the passwords are case-sensitive? (s0 123AB is different from 123aB)? b) A 4-student committee is to be randomly selected from a pool of 5 Biology Majors, 10 Math Majors and 5 Music Majors. 1) What is the probability that all 4 randomly selected students were Math Majors? (State your answer as a reduced fraction OR a decimal rounded to 3 places) ii) Suppose now that the 4 student committee needs to have exactly two math majors. How many different pairs of math majors could be chosen.
Answers
a. i. There are 27,040,000 different passwords are possible if repetition of digits and letters is allowed and passwords are not case sensitive (so 123AB is the same as 123aB)
ii. There will be 99,532,800 different passwords are possible if repetition of digits and letters is not allowed and the passwords are case-sensitive
b. i. The probability that all 4 randomly selected students were math majors is 0.520
ii. There are 4,725 different pairs of math majors that could be chosen for the committee.
a. i) There are 10 choices for each of the first 3 digits, and 26 choices for each of the last 2 letters. Since the password is not case sensitive, we can choose either uppercase or lowercase letters, so there are 26 + 26 = 52 choices in total for each letter. Therefore, the total number of different passwords is:
10 x 10 x 10 x 52 x 52 = 27,040,000
ii) There are 10 choices for the first digit, 9 choices for the second digit (since we can't repeat the first digit), 8 choices for the third digit (since we can't repeat the first two digits), and 52 choices for the first letter. For the second letter, there are 51 choices left (since we can't repeat the first letter), but we need to distinguish between uppercase and lowercase letters, so there are 52 x 51 = 2,652 choices for the two letters in total. Therefore, the total number of different passwords is:
10 x 9 x 8 x 52 x 2,652 = 99,532,800
b) i) The total number of ways to select a 4-student committee from 20 students is:
20 choose 4 = 4,845
The number of ways to select a committee consisting of 4 math majors is:
10 choose 4 = 2,520
Therefore, the probability that all 4 randomly selected students were math majors is:
2,520 / 4,845 = 0.520
ii) The number of ways to select a 4-student committee with exactly two math majors is:
(10 choose 2) x (10 choose 2) x (15 choose 0) = 4,725
(We choose 2 math majors from 10, and 2 non-math majors from 15, since there are 5 biology majors and 5 music majors to choose from.)
Therefore, there are 4,725 different pairs of math majors that could be chosen for the committee.
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2x+5y=10
Solve for y
Answers
2x+5y=10
Move constant to the left by adding its opposite to both sides
2x+5y-10=10-10
the sum of two opposites equals 0
Answer: 2x+5y-10=0
PLEASE MARK ME AS BRAINLIEST
Please help me!
A
B
C
D
Answers
Which translation for: y = (x+3)^2+4
If you can't see the picture zoom in.
Answers
Answer:
The answer is B.
Step-by-step explanation:
The original graph of y = x^2 has a vertex at (0,0)
The formula for graph translations is y = (x-#)^2+#
The number inside the parentheses is a horizontal translation.
So, we are given y = (x-(-3))^2+#
The vertex of the graph moves 3 points left, since the number is negative (-3).
The number at the end of the equation is a vertical translation.
So, we are given y = (x+3)^2+4
The vertex of the graph moves 4 points up, since the number is positive (4).
The new vertex is at (-3,4)
A book costs euro 10.00 in germany. a canadian bookshop owner buys it in canadian dollars (1 cad = 0.65 euros) and sells it to a us customer for usd 35. if usd 1.00 = 0.85 euro, what is the percentage of profit for the shop owner?
Answers
The percentage profit for the shop owner is 197.6%.
What is percentage profit?Percentage profit is the ratio of the profit on a good or item and the the cost price expressed as a percentage.
Percentage profit = profit/cost price * 100%The cost price of the book in US dollars will be: 10 * 1/0.85 = 11.76 USD
Selling price in USD = 35 USD
Profit = 35 - 11.76
Profit = 23.24 USD
Percentage profit = 23.24/11.76 * 100%
Percentage profit = 197.6%
In conclusion, the percentage profit is the profit expressed as a percentage of the cost price.
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a child advocate collects data by randomly selecting 4 of the 25 state orphanages and surveys every child in the four orphanages.
Answers
The child advocate collects data by randomly selecting 4 out of the 25 state orphanages. In each of the four selected orphanages, the child advocate surveys every child.
This approach allows the child advocate to obtain information from a representative sample of children in state orphanages. By surveying every child in the selected orphanages, the child advocate ensures that no child is excluded from the data collection process. This method provides a comprehensive understanding of the experiences, needs, and concerns of the children in the four chosen orphanages.
By collecting data in this manner, the child advocate can gather valuable insights that can inform policies and interventions to improve the well-being and support for children in state orphanages.
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-5x -2y= -9
8x + 8y= 24
Answers
Answer:
x=5
y=-17
Step-by-step explanation:
basically what I did was:
1) I multiplied the first equation by 4 , solved for x
2) I used the value of x that i found and substituted in one of the equations to find y
Answer: x=0 y=2
..................
researchers wanted to study if wearing cotton clothes is related to depression. they surveyed a large group of people. the data are shown in the contigency table below. what is the relative risk of being depressed for those who wear cotton clothes?
Answers
The probability of being depressed and wearing cotton clothes is 0.39.
How to determine the probabilityNote that the probability of something happening is the chance of occurrence versus the total possibilities obtainable. So, for the data we are given, we will find the probability of being depressed and wearing cotton clothes this way:
Probability of being depressed and cotton/probability of being cotton
= 122/994 ÷ 311/994
= 122/311
= 0.39
So, the relative risk of being depressed and wearing cotton clothes is 0.39.
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Please help!
Show your work if you can!
Thank you!
Answers
Answer:
4
Step-by-step explanation:
your slope-intercept will be 4
Answer:
y = 4x + 5
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 4x - 3 ← is in slope- intercept form
with slope m = 4
Parallel lines have equal slopes
Thus parallel line has m = 4 and c = 5
y = 4x + 5 ← equation of parallel line
For the expression 6 − y + 3, determine the coefficient for the variable term.
−1
0
3
6
Answers
Answer:
0
Step-by-step explanation:
Answer:
-1
Step-by-step explanation:
The y is the variable.
There’s a imaginary -1 in front of the y
Use the graph of the quadratic function, g(x), to answer each question.
Answers
Answer:
it is -3 8 and 2
Step-by-step explanation:
Answer:
i think its -3 8 and 2 (maybe)
Step-by-step explanation:
i asked my friend
Terri walked 3.825 miles yesterday. Today she walked 5.5 miles. How many more miles did Terri walk today than yesterday
Answers
Answer:
1.675 more
Step-by-step explanation:
5.5-3.825=1.675
Answer: Terry walked 1.675 miles today than yesterday
Step-by-step explanation:
What is the percent
increase from 70 to 77?
Answers
Percentage change = 10%
We can use the formula:
Percent change = \(\frac{New-Old}{Old}\) x 100
Percent change = \(\frac{77-70}{70}\)x100
Percent change = \(\frac{7}{70}\) x 100
Percent change = 0.1 x 100
Percent change = 10%
Answer: 53.9
Step-by-step explanation:
The area of a rectangular piece of paper is 150 square inches. The perimeter is 50 inches. What are the dimensions of the paper? Can you awnser this "challage"?
Answers
Answer:
12.5?
Step-by-step explanation:
you might have to do 50÷4
The answer please it’s from khan academy
Answers
Answer:
Step-by-step explanation:
Before removing brackets, multiply everything inside them by two.
2*1/5 m - 2 * 2/5 + 3/5
2/5 m - 4/5 + 3/5
2/5 m - 1/5
That's as much as you can do. No further reduction is possible.
Answer:
\(\frac{2m-1}{5}\)
Step-by-step explanation:
\(2(\frac{1}{5} m-\frac{2}{5} )+\frac{3}{5}\)
First, simplify \(\frac{1}{5} m\) to \(\frac{m}{5}\):
\(2(\frac{m}{5} -\frac{2}{5} )+\frac{3}{5}\)
Merge the denominators:
\(2(\frac{m-2}{5} )+\frac{3}{5}\)
Simplify:
\(\frac{2m-4}{5} +\frac{3}{5}\)
Merge the denominators again:
\(\frac{2m-4+3}{5}\)
Simplify one final time:
\(\frac{2m-1}{5}\)
Please mark brainliest if this helps you, and I can provide more information if needed.
The average age in a sample of 90 students at City College is 20. As a result of this sample, it can be concluded that the average age of all the students at City College:
Answers
If the sample is not truly representative, the conclusion may not accurately reflect the actual average age of all the students at the college.
Based on the given information, it can be concluded that the average age of all the students at City College is likely around 20. However, it's important to note that this conclusion is only valid if the sample of 90 students is representative of the entire student population at City College. If the sample is not truly representative, the conclusion may not accurately reflect the actual average age of all the students at the college.
The average age in a sample of 90 students at City College is 20. However, based on this sample alone, it cannot be conclusively determined that the average age of all the students at City College is also 20. This is because the sample may not be fully representative of the entire student population. More information or a larger sample would be needed to make a more accurate conclusion about the average age of all students at City College.
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If the sample of 90 students is representative of the entire student population at City College, then we can conclude that the average age of all students is approximately 20 years old.
Based on the given information, the average age in a sample of 90 students at City College is 20.
To determine if this sample can be used to conclude the average age of all students at City College, we need to consider these terms:
Sample:
A subset of a population, which in this case is the group of 90 students at City College.
Population:
The entire group of students at City College that we want to make a conclusion about.
Average (Mean) Age:
The sum of ages divided by the total number of students, in this case, 20 years.
Representativeness:
How well the sample reflects the characteristics of the entire population.
If the sample of 90 students is representative of the entire student population at City College, then we can conclude that the average age of all students is approximately 20 years old.
However, if the sample is not representative, the conclusion may not be accurate.
To make a more accurate conclusion, it is important to ensure that the sample is representative by using a larger sample size or random sampling methods.
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The graph of function f is shown.
Which statement correctly compares the two functions?
A. They have the same x- and y-intercepts.
B. They have the same x-intercept and the same end behavior as x approaches ∞.
C. They have different x- and y-intercepts but the same end behavior as x approaches ∞.
D. They have the same y-intercept and the same end behavior as x approaches ∞.
Answers
In the picture, there is a graph and table. It displays the graph of the function f. Option C is correct, As x approaches, they have different x- intercept and y-intercepts but the same end behavior∞.
Given that,
In the picture, there is a graph and table.
It displays the graph of the function f.
Which of the two statements compares the two functions correctly.
A. Their x- and y-intercepts are identical.
B. As x gets closer to, they exhibit the same x-intercept and end behavior∞.
C. As x approaches, they have different x- and y-intercepts but the same end behavior∞.
D. As x gets closer to, they exhibit the same y-intercept and end behavior∞.
So, from the given table and graph we get
Option C is correct.
Therefore, Option C is correct.
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One grain of this sand approximately weighs 6 x 10^-6g.
b) How many grains of sand are there in 7200 kg of sand?
Give your answer in standard from.
Answers
Answer:
1.2×10¹² grainsStep-by-step explanation:
1 grain = 6×10⁻⁶ g
7200 kg = 7200000 g = 7.2×10⁶ g = 7.2×10⁶ ÷ 6×10⁻⁶ = (7.2÷6)×10⁶⁻ ⁽⁻⁶⁾ =1.2×10¹² grainsfind two unit vectors that make an angle of 60° with v = 6, 8 .
Answers
Answer:
((3-4√3)/10, (4+3√3)/10)((3+4√3)/10, (4-3√3)/10)Step-by-step explanation:
You want two unit vectors that make an angle of 60° with v(6, 8).
Unit vectorAfter we normalize v to a unit vector, we can find the two desired vectors by adding or subtracting 60° from its angle. The normalized vector v is ...
v = (6, 8)/√(6² +8²) = (3/5, 4/5)
RotatedThis can be rotated 60° CCW by the transformation ...
(x, y) ⇒ (x·cos(60°)-y·sin(60°), x·sin(60°)+y·cos(60°)) = (x-y√3, x√3+y)/2
(3/5, 4/5) ⇒ ((3-4√3)/10, (3√3+4)/10) . . . . 60° CCW from v
It can be rotated 60° CW by the transformation ...
(x, y) ⇒ (x·cos(60°)+y·sin(60°), -x·sin(60°)+y·cos(60°)) = ((x+y√3, -x√3+y)/2
(3/5, 4/5) ⇒ ((3+4√3)/10, (4-3√3)/10)
__
Additional comment
When the vector is written as a complex number, it can be rotated by multiplying by 1∠±60° = (cos(60°)±i·sin(60°). That is what the calculator did.
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