In a class of 30 students x +10 study algebra, 10+3 study statistics, 4 study both algebra and statistics. 2x study only Algebra and 3 study neither algebra nor statistics
1. Illustrate the information one a Venn diagram.
2. How many students study;
A. Algebra
B. Only statistics
Answers
1. The Venn diagrams are attached
2. When the statistics students number = 10·x + 3, we have;
The number of students that study
a. Algebra = 128/11b. Statistic = 213/11When the statistics students number = 2·x + 3, we have;
The number of students that study
a. Algebra = 16b. Statistic = 15How to solve thisThe parameters given are;
Total number of students = 30
Number of students that study algebra n(A) = x + 10Number of students that study statistics n(B) = 10·x + 3Number of student that study both algebra and statistics n(A∩B) = 4Number of student that study only algebra n(A\B) = 2·xNumber of students that study neither algebra or statistics n(A∪B)' = 3Therefore;
The number of students that study either algebra or statistics = n(A∪B)
From set theory we have;
n(A∪B) = n(A) + n(B) - n(A∩B)
n(A∪B) = 30 - 3 = 27
Therefore, we have;
n(A∪B) = x + 10 + 10·x + 3 - 4 = 2711·x+13 = 27 + 4 = 31=11·x = 18x = 18/11The number of students that study
a. Algebra
n(A) = 18/11 + 10 = 128/11
b. Statistic
n(B) = 213/11
Hence, we have;
n(A - B) = n(A) - n(A∩B) = 128/11 - 4 = 84/11
Similarly, we have;
n(B - A) = n(B) - n(A∩B) = 213/11 - 4 = 169/11
However, assuming n(B) = (2·x + 3), we have;
n(A∪B) = n(A) + n(B) - n(A∩B)
n(A∪B) = 30 - 3 = 27
Therefore, we have;
n(A∪B) = x + 10 + 2·x + 3 - 4 = 27
2·x+3 + x + 10= 27 + 4 = 31
3·x = 18
x = 6
Therefore, the number of students that study
a. Algebra
n(A) = 16
b. Statistics
n(B) = 15
Hence, we have;
n(A - B) = n(A) - n(A∩B) = 16 - 4 = 12
Similarly, we have;
n(B - A) = n(B) - n(A∩B) = 15 - 4 = 11
The Venn diagrams can be presented as follows;
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Related Questions
What are the zeros of this function?
A. -1, 3
B. 3, 1
C. 0, 1.5
D. 1, 2
Answers
Answer:
B
Step-by-step explanation:
the zeros are the values of x on the x- axis where the graph crosses
the graph crosses the x- axis at 1 and 3
then the zeros are x = 1 , x = 3
Sets A and B are subsets of the universal set U.
These sets are defined as follows.
U= {f, k, m, q, x,y}
A={f, k, m, y}
B = {f, m,q}
Find the following sets.
Write your answer in roster form or as Ø.
(a) AUB' =
(b) A' B' =
Answers
(a) The union set is AUB'={f, k, m, x, y}.
(b) The union set is A'UB'={q,k, x, y}.
What is the union of two sets?The union of two sets is also a set. This set contains all the elements of both two sets.
The universal set is U= {f, k, m, q, x,y} and two subsets are A={f, k, m, y} and B = {f, m,q}.
(a)
B' is the complementary set of B. So, find the elements of B'=U-B.
B'= {f, k, m, q, x,y}-{f, m,q}
={k, x,y}
Now, find the union set AUB'.
AUB' ={f, k, m, y}U{k, x,y}
={f, k, m, x, y}
Therefore, the required answer is AUB'={f, k, m, x, y}.
(b)
Also, A' is the complementary set of A. So, find the elements of A'=A-B.
A'= {f, k, m, q, x,y}-{f, k,m, y}
={q,x}
Now, find the union set A'UB'.
A'UB' ={q,x}U{k, x,y}
={q,k, x, y}
Therefore, the required answer is A'UB'={q,k, x, y}.
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Endpoints of a diameter are (−5,−11) and (−1,1) Find the standard form of the equation for the circle with the following properties.
Answers
Answer:
Standard form of the equation for the circle
(x + 3)² + (y + 5)² = 40
Step-by-step explanation:
The equation of a circle in standard form is
[tex]\boxed{(x - a)^2 + (y-b)^2= r^2}[/tex]
where (a, b) is the center of the circle and r is the radius
To find center of circle
The end points of the diameter are (-5, -11) and (-1, 1)
The center of the circle is midway between these two points
The x-coordinate of the midpoint = (-5 + -1)/2 = -6/2 = -3
The y-coordinate of the midpoint is (-11 + 1) /2 = -10/2 = -5
So the center of the circle is at (-3, -5)
To find the radius,
Calculate the distance from (-3, -5) to any of of the endpoints.
Let's take the endpoint (-1, 1) and find its distance from (-3, -5)
The distance between any two points (x₁, y₁) and (x₂, y₂) is calculated from the formula
[tex]d^2 = {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2[/tex]
Substituting
(x₁, y₁) = (-1, 1)
(x₂, y₂) = (-3, -5)
and r for distance
we get
[tex]r^2 = {(-3 - (-1))^2 + (-5 - 1)^2[/tex]
[tex]r^2 = {(-2)^2 + (-6)^2}[/tex]
[tex]r^2 = {{4} + {36}}[/tex]
[tex]r^2 = {40}[/tex]
So the center (a, b) is (-3, -5) and r² =40
Plugging this into the circle equation:
(x - (-3))² + (y - (-5))² = 40
(x + 3)² + (y + 5)² = 40
How many numbers of the form x15y are divisible by 15
Answers
hope it helps:)
x^{2}-2x+ and completing the square ( Algebra 2 )
Answers
x^2 - 2x + 1 is the required quadratic equation using the completing the square
Perfect square trinomials using the completing the square
Given the quadratic expression below
x^2 - 2x
We need to determine the constant that will make the expression a perfect square.
The constant will be the half of the square of coefficient of 'x'
Coefficient of 'x' = -2
Half of the coefficient of 'x' = -2/2 = -1
Square of the coefficient = (-2/2)^2
Square of the coefficient = 1
Hence the complete quadratic expression using the completing the square is x^2 - 2x + 1
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An electric clock is stopped by a power failure. What is the probability that the second hand is stopped between the 4 and the 9?
Answers
Answer: the answer is 5/12
CJ has three more pet pigs than Jacqui has. Let’s write an expression to represent how many pigs CJ has. To do that, we follow these steps:
Identify the constants and the variables.
There is one known number or constant here: it is 3. CJ has 3 more pigs than Jacqui. That number, 3, won’t change. The variable is the number of pets Jacqui has. Let’s call that j.
Identify the operations.
The phrase “more than” tells us we need to add. There are no other operations in this expression.
Rewrite the phrase as an expression.
“Three more pet pigs than Jacqui has” is 3 + j.
Last year, Shailyn read four fewer books than Oswaldo. Which expression shows how many books Shailyn read last year?
Answers
Answer: Let's follow the same steps as in the previous example:
Identify the constants and the variables.
The known constant here is 4. Shailyn read 4 fewer books than Oswaldo. Let's call the number of books Oswaldo read "o".
Identify the operations.
The phrase "four fewer" tells us we need to subtract.
Rewrite the phrase as an expression.
"Four fewer books than Oswaldo" is o - 4.
So, the expression that shows how many books Shailyn read last year is o - 4.
Step-by-step explanation:
A candle is burning. It starts out 12 inches long. After 1 hour, it is 10 inches long. After 3 hours, it is 5.5 inches
1. Explain one reason why it might be reasonable to model the relationship between time and height of the candle with a linear function.
2. Explain one reason it might NOT be reasonable to model this relationship with a linear relationship
Answers
The reasons for (1) and (2) are added below
Why it is reasonable to use a linear functionOne reason why it might be reasonable to model the relationship between time and height of the candle with a linear function is that the rate of change of the candle's height appears to be constant over time.
Why it is unreasonableOne reason why it might NOT be reasonable to model this relationship with a linear function is that the candle's height cannot continue to decrease indefinitely.
This means that the candle's height is bounded and cannot continue to decrease linearly forever.
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estimate the population in the year 2040
Answers
well, in 2007 it was 12000, so initially that's what it was, and in 2019 it went to 23000, so that's 12 years later, and in 2040, that'll be 33 years later.
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 23000\\ P=\textit{initial amount}\dotfill &12000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &12\\ \end{cases} \\\\\\ 23000 = 12000(1 + \frac{r}{100})^{12}\implies \cfrac{23000}{12000} =\left(1+ \cfrac{r}{100} \right)^{12} \\\\\\ \cfrac{23}{12}=\left(\cfrac{100+r}{100} \right)^{12}\implies \sqrt[12]{\cfrac{23}{12}}=\cfrac{100+r}{100}[/tex]
[tex]100\sqrt[12]{\cfrac{23}{12}}=100+r\implies 100\sqrt[12]{\cfrac{23}{12}}-100=r\implies \boxed{5.57\approx r} \\\\[-0.35em] ~\dotfill\\\\ \qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &12000\\ r=rate\to 5.57\%\to \frac{5.57}{100}\dotfill &0.0557\\ t=years\dotfill &\stackrel{year~2040 }{33}\\ \end{cases} \\\\\\ A \approx 12000(1 + 0.0557)^{33} \implies \boxed{A \approx 71782}[/tex]
One cubic foot holds 7.48 gallons of water, and 1 gallon of water weighs 8.33 pounds. How much does 4.4 cubic feet of water weigh in pounds? In tons?
Answers
Answer:
4.4 cubic feet of water weighs approximately 273.5016 pounds or 0.13676 tons.
Step-by-step explanation:
To find the weight of 4.4 cubic feet of water in pounds, we need to find the number of gallons it contains and then multiply it by the weight of one gallon of water.
1 cubic foot = 7.48 gallons
So, 4.4 cubic feet = 4.4 * 7.48 = 32.912 gallons
And the weight of 32.912 gallons of water in pounds is:
32.912 gallons * 8.33 pounds/gallon = 273.5016 pounds
To convert this weight to tons, we divide the weight in pounds by 2000:
273.5016 pounds / 2000 = 0.13676 tons
So, 4.4 cubic feet of water weighs approximately 273.5016 pounds or 0.13676 tons.
Graph the following points on the coordinate plane. Find the measure of ∠ACB
to the nearest tenth.
A (-3, 2), B (0, 0), C (2, 3)
Answers
The measure of angle ∠ACB is 45 degrees
How to find the measure of ∠ACBFrom the question, we have the following parameters that can be used in our computation:
A (-3, 2), B (0, 0), C (2, 3)
The graph is attached
The lines AB and BC are perpendicular lines
This means that
∠B = 90 degrees
Calculate the length AB and BC using
distance = √[(x2 - x1)² + (y2 - y1)²]
So, we have
AB = √[(-3 - 0)² + (2 - 0)²] = √13
BC = √[(0 - 2)² + (0 - 3)²] = √13
The angle C is then calculated as
tan(C) = AB/BC
tan(C) = √13/√13
tan(C) = 1
Take the arctan of both sides
C = 45
Hence, the measure of ∠ACB is 45 degrees
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mr ramirez bought a watermelon that weighs 12 pounds for a picnic he cuts it into pieces that each weigh 1.5 pounds. how many pieces of water melon can mr ramiez cut?
Answers
Equivalence means to be same, whether it be value, temperature, size, etc.
Let's make an equation to solve this problem. We first would need to take the total (12 pounds) and divide that total by the amount each slice must weigh (1.5 pounds) to get an equal number of slices.
12 ÷ 1.5 = 8To check our work, we can take number of slices (8), and multiply that by the weight of each slice (1.5 pounds) to get the original weight of the watermelon.
8 × 1.5 = 12Now, we know for sure that Mr. Ramirez can make 8 watermelon slices each weighing 1.5 pounds if he has a 12-pound watermelon.
Xin is going to invest in an account paying an interest rate of 5.8% compounded annually. How much would Xin need to invest, to the nearest hundred dollars, for the value of the account to reach $2,290 in 16 years?
Answers
The amount that should be invested in order to have $2,290 in 16 years is $929.11.
What is compound interest?
The interest on a deposit calculated using both the initial principle and the accrued interest from prior periods is known as compound interest. In other words, compound interest is interest that is earned on interest.
Here, we have
Given: Xin will invest in an account paying an interest rate of 5.8% compounded annually.
Amount to invest = Future value / (1 + r)ᵗ
Where:
r = interest rate
t = time
X = $2,290 / (1 + 0.058)¹⁶
X = 2,290 / 2.46474
X = $929.11
Hence, the amount that should be invested in order to have $2,290 in 16 years is $929.11.
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A car travels 55 mph and passes a truck travelling 50 mph. How long will it take the car to be
more than 23 mi ahead?
Answers
Answer:you never asked for like in what minutes or hours?
Step-by-step explanation:
The car, traveling at a speed 5 mph faster than the truck, will take more than 4.6 hours to be more than 23 miles ahead.
Explanation:This question pertains to relative speed. When the car is traveling at 55 mph and the truck at 50 mph, the car is effectively moving away from the truck at (55 mph - 50 mph) = 5 mph. To calculate the time it will take for the car to be more than 23 miles ahead, we can use the formula: Time = Distance/Speed. So the time it would take is Time = 23 miles / 5 mph = 4.6 hours. Therefore, it will take the car more than 4.6 hours to be more than 23 miles ahead.
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sum of 2nd term of an infinite geometric series is -1/2 and the third term is 1/4 find the sum of series
Answers
Answer:
2
Step-by-step explanation:
1 plus 1 due to the characterisation of the number 1 increasing by 1 gives you 2
If the scale factor of figure A to figure B is 3:8 find x
Answers
8x = 72
9
product p of three numbers x ,y,and z
Answers
Answer:
p = x(y)(z)
Step-by-step explanation:
product is multiplication.
multiplication has no specific order.
p = x * y * z
Where x, y, and z are the three numbers whose product we want to find.
cathy invest $3,700 into an account with a 3.75% annual interest rate, making no other deposits or withdrawals.
a) what with cathy’s balance be after 6 years if the interest rate is compounded quarterly?
b) how much more (or less) money would be in cathy’s account if the interest is compounded continuously?
Answers
Answer: no
Step-by-step explanation:
Can someone please help me do this
Answers
The vertices of the image of triangle ABC are A''(x, y) = (- 6, 8), B''(x, y) = (- 8, 4) and C''(x, y) = (- 4, 4).
How to determine the image of a triangle set on Cartesian plane
Any triangle can be generated by three points that are not collinear, in this problem we need to determine the image of a triangle, which is the result of two rigid transformations: (i) Reflection over the y-axis, (ii) Dilation centered at the origin with a scale factor of 2, whose definitions are shown below:
Reflection over the y-axis:
(x, y) → (- x, y)
Dilation centered at the origin with a scale factor of 2:
(x, y) → (2 · x, 2 · y)
If we know that A(x, y) = (3, 4), B(x, y) = (4, 2), C(x, y) = (2, 2), then the image of the vertices are determined below:
Reflection over the y-axis
A'(x, y) = (- 3, 4), B'(x, y) = (- 4, 2), C'(x, y) = (- 2, 2)
Dilation centered at the origin with a scale factor of 2
A''(x, y) = (- 6, 8), B''(x, y) = (- 8, 4), C''(x, y) = (- 4, 4)
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Find
(M.
f(x)=√√√x²-1
g(x)=√√√x-1
a. √√x+1
b. √√x-1
C.
d.
-X+1
1
X+1
Answers
The function operation (f/g)(x) in the functions f(x) = √( x² - 1 ) and g(x) = √( x - 1 ) is √( x + 1).
What is the function operation (f/g)(x) in the function?A function is simply a relationship that maps one input to one output.
Given the functions in the question;
f(x) = √( x² - 1 )g(x) = √( x - 1 )(f/g)(x) = ?To evaluate (f/g), replace the function designators in f/g with the actual functions.
(f/g)(x) = f(x) / g(x)
(f/g)(x) = ( √( x² - 1 ) ) / ( √( x - 1 ) )
Now, rewrite 1 as 1²
(f/g)(x) = ( √( x² - 1² ) ) / ( √( x - 1 ) )
Factor using difference of square
(f/g)(x) = ( √( (x - 1)(x + 1 ) ) / ( √( x - 1 ) )
Combine into a single radical
(f/g)(x) = √( ( (x - 1)(x + 1) ) / ( x - 1 ) )
Now, cancel out the common factors (x-1)
(f/g)(x) = √( (x + 1) / 1 )
(f/g)(x) = √( x + 1)
Therefore, the function operation (f/g)(x) is √( x + 1).
Option A) √( x + 1) is the correct answer.
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Counting back from 18, what number follows 17?
Answers
Answer:
16
Step-by-step explanation:
As the question states, we are counting downwards which means with every interval we are going back -1. Therefore, 17 - 1 = 16
Find the value of X
Please help! Asap
Answers
Answer:
Step-by-step explanation:
Calculate the area of the triangle
Answers
find the length of the x
a^2 + b^2 = c^2
12x^2 + b^2 = 13^2
144 + b^2 = 169
b^2 = 25
b = 25; x = 5
use the formula
a = (1/2)(24)(5)
a = (1/2)(120)
area = 60
2. What is the equation of the parabola that passes
through the points (-1,0), (7, 0) and (3,-16)?
3. What is the equation of the parabola that passes
through the points (-4,9), (-3, 2) and (0,-7) and (4,9)?
Answers
The equations of the parabolas are y = x² - 6x - 7 and y = x² - 7
How to determine the equation of the parabolasParabola 1
Given that
The points (-1,0), (7, 0) and (3,-16)
The equation is represented as
y = ax² + bx + c
So, we have
a - b + c = 0
49a + 7b + c = 0
9a + 3b + c = -16
Make c the subject in a - b + c = 0
c = b - a
So, we have
49a + 7b + b - a = 0
9a + 3b + b - a = -16
48a + 8b = 0
8a + 4b = -16
Multiply 8a + 4b = -16 by 2
48a + 8b = 0
16a + 8b = -32
Subtract
32a = 32
So, we have
a = 1
Recall that 48a + 8b = 0
So, we have
48 + 8b = 0
This gives
8b = -48
Divide
b = -6
Also, we have
c = b - a
This gives
c = -6 - 1
c = -7
So, the equation is
y = x² - 6x - 7
Parabola 2
Given that
The points (-4,9), (-3, 2) and (0,-7) and (4,9)
The equation is represented as
y = ax² + bx + c
So, we have
16a - 4b + c = 9
9a - 3b + c = 2
c = -7
16a + 4b + c = 9
The equations become
16a - 4b = 16
9a - 3b = 9
16a + 4b = 16
Add (1) and (3)
32a = 32
So, we have
a = 1
Subtract (1) and (3)
-8b = 0
So, we have
b = 0
So, the equation is
y = x² - 7
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simplify 3-2(b-2)=2-7b solve for b
Answers
The required value of the given expression which satisfy it is b = 3/5.
What is Simplification?To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.
According to question:We have,
3 - 2(b - 2) = 2 - 7b
= 3 - 2b - 4 = 2 - 7b
= 5b = 3
= b = 3/5
Thus, required value of the b for the given function is b = 3/5.
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If joes shoes cost 44 dollars and 20 cents and joe has 10
dollars and 68 cents. How much money does joe need?
Answers
Answer: 44.20-10.68=33.52
He need 33.52$
Step-by-step explanation:
A positive integer is twice another. The difference of the reciprocals of the two positive integers is frac(1,10). Find the two integers.
Answers
The two integers are 5 and 10.
What do you mean by Integers?
An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero.
Integer is a Latin word which means 'whole' or 'intact'. This means integers do not include fractions or decimals.
A number is positive if it is greater than zero, so it said to be positive integers
A number is negative if it is less than zero, so it said to be negative integers.
A number line is a visual representation of numbers on a straight line. This line is used for the comparison of numbers that are placed at equal intervals on an infinite line that extends on both sides, horizontally.
Given:
Let x be the positive number
2x be the other positive number
Find the first integer
[tex]\frac{1}{x} - \frac{1}{2x} = \frac{1}{10}[/tex]
[tex]\frac{2x - x}{2x^2} = \frac{1}{10}[/tex]
[tex]\frac{x}{2x^2} = \frac{1}{10}[/tex]
[tex]\frac{1}{2x} = \frac{1}{10}[/tex]
2x = 10
x = 5
Therefore, the first positive integer is 5.
Find the other integer
2x = 2(5) = 10
Therefore, the other integer is 10.
To check:
[tex]\frac{1}{x} - \frac{1}{2x} = \frac{1}{10}[/tex]
[tex]\frac{1}{5} - \frac{1}{10} = \frac{1}{10}[/tex]
[tex]\frac{2}{10} - \frac{1}{10} = \frac{1}{10}[/tex]
[tex]\frac{1}{10} = \frac{1}{10}[/tex]
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Determine whether the statement is true or false. 1. A census is a count of part of a population.. O True O False
Answers
The statement regarding the census in this problem is classified as a True statement.
What are the concepts of population and sample?Population: Collection or set of individuals or objects or events whose properties will be studied.
Sample: The sample is a subset of the population, and a well chosen sample, that is, a representative sample will contain most of the information about the population parameter. A representative sample means that all groups of the population are inserted into the sample.
A Census is when a group of the population is chosen, that is, a sample is chosen, hence the statement for this problem is true.
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tell how the communative and associative properties of adddition can help you evsaluate the expression using mental math? 8+(-8-5)
Answers
Using commutative and associative properties of addition, the solution for given expression is -5.
What is commutative and associative property?
The associative and commutative characteristics are universal principles that apply to addition and multiplication. The associative property states that rearranging the numbers will get the same result, while the commutative property states that rearranging the numbers will yield the same result.
These properties tell that one can add in any order, the result will always be the same.
We are given an expression as 8+(-8-5).
So, in this instead of adding from left to right, we can see that the 8 + (-8) will be zero and only -5 will be left as an answer.
Hence, the solution for given expression is -5.
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Rob loaded 9 trucks in 1 hour find his loading speed per hour
Answers
Answer:
9 trucks/hour
Step-by-step explanation:
If he loaded 9 trucks in one hour, his loading speed is 9 trucks per hour.
