Using Venn sets, it is found that:
12 students are taking English only.6 students are taking Math only.5 students are taking Chemistry only.3 students are not taking any of the classes.What are the Venn Sets?For this problem, we consider the following sets:
Set A: students taking Math.Set B: students taking English.Set C: students taking Chemistry.2 are taking all subjects, hence:
(A ∩ B ∩ C) = 2.
8 are taking chemistry and math, hence:
(A ∩ C) + (A ∩ B ∩ C) = 8.
(A ∩ C) = 6.
6 are taking math and english, hence:
(A ∩ B) + (A ∩ B ∩ C) = 6.
(A ∩ B) = 4.
4 are taking chemistry and english, hence:
(B ∩ C) + (A ∩ B ∩ C) = 4.
(B ∩ C) = 2.
15 are taking chemistry, hence:
C + (A ∩ C) + (B ∩ C) + (A ∩ B ∩ C) = 15.
C + 6 + 2 + 2 = 15.
C = 5.
20 are taking english, hence:
B + (A ∩ B) + (B ∩ C) + (A ∩ B ∩ C) = 20
B + 4 + 2 + 2 = 20
B = 12.
18 are taking math, hence:
A + (A ∩ B) + (A ∩ C) + (A ∩ B ∩ C) = 18
A + 4 + 6 + 2 = 18
A = 6.
There is a total of 40 students, hence:
None + A + B + C + (A ∩ B) + (A ∩ C) + (B ∩ C) + (A ∩ B ∩ C) = 40.
None + 6 + 12 + 5 + 4 + 6 + 2 + 2 = 40.
None + 37 = 40.
None = 3.
Hence:
12 students are taking English only.6 students are taking Math only.5 students are taking Chemistry only.3 students are not taking any of the classes.More can be learned about Venn sets at brainly.com/question/24388608
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Determine the slope of the line that contains the given points.
E(6,3), F(-6,3)
The slope of the line that contains the given points E(6,3) and, F(-6,3) is 0.
It is given in the question that the line contains the points E(6,3) and F(-6,3).
We know that:-
The formula to find the slope of a line that contains points (a,b) and (c,d) is given by:-
m = (d-b)/(c-a)
Here, we have
m = slope of the line
(a,b) = (6,3)
(c,d) = (-6,3)
Hence, putting the values of (a,b) and (c,d) , we get
Slope of the line that contains the given points E(6,3) and, F(-6,3) is given by:-
(3-3)/(-6-6) = 0/-12= 0
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which algebraic expression is a difference with two terms
A.5y - 7
B-2y + 5 + 3
C.3y + 1
D.5(y - 6)
The expression that is a difference between two terms is:
5y - 7
which algebraic expression is a difference withtwo terms?
An algebraic expression should have at least one variable, and here we know that we should find a difference (remember that a difference is a subtraction).
And it must have two terms, then the expression is something like:
A - B
Such that A or B depend on the variable.
With this in mind, we can see that the correct option (the only subtraction with two terms) is the first one:
5y - 7
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Which describes the pilot’s distance in section i? zero constant decreasing increasing
The pilot's distance is increasing.
In the graph, we can see distance on y axis and time on x axis. It is clearly visible that at 2 minutes, the distance covered is 0.4 miles. Further, at 4 minutes, the distance covered increases to 0.8 miles. At 6 minutes, the distance covered again increases by 0.4 miles and is 1.2 miles. At 8 minutes, the distance covered in 1.6 miles, which again increases by 0.4.
Now, it is evident that distance is increasing.
We can further calculate the speed using given information -
Speed = distance/time
Total distance = 1.6 - 0.0
Total distance = 1.6 miles
Total time = 8 - 0
Total time = 8 minutes
Speed = 1.6/8
Speed = 0.2 miles per minute.
Hence, the distance of pilot is increasing at constant rate or speed of 0.2 miles per minute.
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The complete question and figure is attached -
The graph below represents the distance a pilot is from the home airport during a period of time. A 2-column table with 5 rows titled Time and Distance Ran by Myra. The first column is labeled Time (minutes) with entries 0, 2, 4, 6, 8. The second column is labeled Distance (miles) with entries 0.0, 0.4, 0.8, 1.2, 1.6. Which describes the pilot’s distance in section I? zero constant decreasing increasing
Write an equation of each line in point-slope form.
(0,0) and (-4,-5)
The equation of the line in point-slope form, which passes through the pair of points located at (0 , 0) and (-4 , -5), is y + 5 = 5/4(x + 4).
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).
Getting the slope of the two points: (0 , 0) and (-4 , -5)
m = (y2 - y1)/(x2 - x1)
m = (-5 - 0)/(-4 - 0)
m = -5/-4
m = 5/4
Using the point slope form, plug in the values of the slope and Point A to set up the equation.
(y - y1) = m(x - x1)
where m = 5/4 and (x1 , y1) = (-4 , -5)
(y - -5) = 5/4(x - -4)
y + 5 = 5/4(x + 4)
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A camper lost in the woods points his compass in a random direction. Find the probability that the camper is heading in the N to NE direction.
The probability that the camper is heading in the N to NE direction when a camper lost in the woods points his compass in a random direction is 1/8.
As given,
Compass is divided into 8 sectors N→NE→E→SE→S→SW→W→NW→N
Whole compass represents the circle with area 360 degrees
Area of each sector is equal to 45 degrees
Probability that the camper is heading in the N to NE direction
=45/360
=1/8
Therefore, the probability that the camper is heading in the N to NE direction when a camper lost in the woods points his compass in a random direction is 1/8.
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Look at the picture and help me figure how many planes are in the figure.
Answer: C
Step-by-step explanation:
6 planes
Answer: C, 6)
Step-by-step explanation: Area of square = a2 Square units, where a is the side length of square.
Area of rectangle = l × b Square units, where l is the length, b is the breadth.
Area of circle = π × r2 Square units, where r is the radius of a circle.
Find the seventh term of each geometric sequence. 100,20,4, . . . . . . .
The seventh term of the given geometric sequence is: [tex]\frac{4}{625}[/tex].
What is a geometric progression?A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.Given: 100, 20, 4, ....
Here, a₁ = 100, r = [tex]\frac{100}{20}=\frac{20}{4}=\frac{1}{5}[/tex], for the given geometric progression.
In the formula: [tex]a_n=a_1(r^{n-1})[/tex]
For n = 7, a₇ = 100 ([tex](\frac{1}{5})^{7-1}[/tex]
=> a₇ = 100 [tex](\frac{1}{5})^6[/tex]
=> a₇ = 4([tex]\frac{1}{625}[/tex])
Hence, The seventh term of the given geometric sequence is: [tex]\frac{4}{625}[/tex].
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Look at the pattern shown.
144,72,36,. . .
a. What is a rule for the pattern?
Answer:
I hope it's helpful.........
10-ounce package of cashews costs $8.11, and a 16-ounce package of cashews costs $12.
a. What is the cost per ounce for the 10-ounce packages of cashews?
b. What is the cost per ounce for the 16-ounce packages of cashews?
c. Which package is the better buy?
Answer:0-ounce package of cashews costs $8.11 is better then a 16-ounce package of cashews costs $12 , because cost per ounce for the 10-ounce package of cashews = $ is greater then cost per ounce for the 16-ounce package of cashews = $
Step-by-step explanation:
For f(x)=-4 x+1 , what is the output for the given input?
b. 0
f (0) = 1 is the output for the given input .
What is linear function ?
A straight line on the coordinate plane is represented by a linear function. As an illustration, the equation y = 3x – 2 depicts a linear function because it is a straight line in the coordinate plane. This function can be expressed as f(x) = 3x - 2 since y can be replaced with f(x).f(x)= -4 x+1
Put x = 0 ⇒ - 4 × 0 + 1
⇒ 0 + 1
⇒ 1
Therefore f (0) = 1
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“Twice a number minus 5 is 7”
Answer: the number would be 6
Step-by-step explanation:
6 x 2 = 12, 12 - 5 = 7, so the number is 6
Make an equation equal to an odd number
rules:
1. numbers must be the same Example: 5x5
2. only 1 mathematical symbol can be used example: 5+5, 5-5, 5x5, & 5/5
Step-by-step explanation:
35×35 may be ?? ..........
Two vertices of $\triangle ABC$ are $A\left(3,\ 0\right)$ and $B\left(7,\ 3\right)$ . Find the coordinates of $C$ on the positive $x$ -axis such that the value of the perimeter of the triangle is twice the value of the area of the triangle.
The coordinate of C=(4,0).
What is Area of triangle?The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h.
Given:
ΔABC with
A(3, 0), B(7, 3)
let the coordinate of c(x, y)
Also, Perimeter of triangle = 2 * Area of triangle
Area of triangle=1/2 * b * h
Area=1/2 * 4 * 3
Area=1/2 * 12
Area=6 units
Perimeter= AB + BC + CA
Now,
Now, using distance formula
AB = √(7-3)² + (3-0)²
AB = √16+9
AB= 5 units
Perimeter of triangle=5+4+3
Perimeter =12
So, the coordinate of C=(0+4,0)
C=(4, 3-3)
C=(4,0)
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Simplify by combining like terms. 6 r+3 s+2 s+4 r
By combining the like terms, the simplified form of the expression 6r+3s+2s+4r is 10r+5s
Given,
The expression = 6r+3s+2s+4r
Rearrange the terms
6r+4r+3s+2s
Combine the like terms
6r+4r+3s+2s=(6+4)r+(3+2)s
=10r+5s
Hence, By combining the like terms, the simplified form of the expression 6r+3s+2s+4r is 10r+5s.
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Mr. Olsen uses an unusual grading system in his class. After each test, he transforms the scores to have a mean of 0 and a standard deviation of 1. Mr. Olsen then assigns a grade to each student based on the transformed score. On his most recent test, the class’s scores had a mean of 68 and a standard deviation of 15. What transformations sho
In order to get standard deviation of 15. Subtract 68 from everybody's score, then divide these values by 15.
What is Standard deviation?The square root of the variance is used to determine the standard deviation. An alternative method of calculating it is to identify the mean of a data set, compare each data point to the mean, square the differences, add them all together, divide by the number of points in the data set minus 1, and then compute the square root.
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Complete question -Mr. Olsen uses an unusual grading system in his class. After each test, he transforms the scores to have a mean of 0 and a standard deviation of 1. Mr. Olsen then assigns a grade to each student based on the transformed score. On his most recent test, the class's scores had a mean of 68 and a standard deviation of 15. What transformations should he apply to each test score? Explain.
Suppose the flight leaves 30 minutes early. What function represents this transformation?
The function that represents the Transformation of the graph is F(X+1/2).
Different non-vertical lines have different slopes and/or y-intercepts. They are graphs of various linear functions. If there are two such lines, one can be considered a transformation of the other. There is a group of functions called the family, each function being a transformation of a special function called a parent. Linear functions form a series of functions. All linear functions are transformations of the function y = x. The function y = x is an upper linear function. Each family role is a transformation of a parent's role. The conversion type is translation. A translation moves the graph of the parent function horizontally, vertically, or both without changing shape or orientation. So, the function that represents this transformation is F(X+1/2).
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1. Solve the equation:
6(x + 1) = 3x - 14
Answer: x=-20/3
Step-by-step explanation:
6(x + 1) = 3x - 14
6x+6 = 3x - 14
6x-3x+6 = 3x-3x - 14
3x+6 = -14
3x+6-6=-6-14
3x=-20
x=-20/3
Simplify the expression (62)4.
Make a conjecture about the measure of an exterior angle and the sum of the measures of its nonadjacent interior angles.
Here we can conjecture that :
The measure of an exterior angle is equal to the sum of measures of its nonadjacent interior angles.
What is interior and exterior angle ?The exterior angle of any polygon is defined as the angle which is at the outside boundaries of that polygon. whereas, the interior angle is defined as the angle which is inside the polygon. In the other words if the polygon has the point within the angle it is in the interior of the angle , but if the point is outside then is it said to be in the exterior of the angle.
What is Non adjacent interior angle ?Non adjacent angles are those angles which are not adjacent to each other. The non adjacent angles follow one of the properties which are listed below:
They do not share a common vertex or common side.They can share a side, but not share the common vertex.They share a common vertex, but not share the common side.In the given question,
taking a example say a triangle ABC with ∠A=64, ∠B = 45 and an external angle x to the side AC.
as sum of angles equal to 180
thus, ∠A + ∠B + ∠C = 180
64 + 45 + ∠C = 180
∠C = 180-109 = 71
now as x is external to ∠C,
therefore x = 180 - ∠C = 180 - 71
x = 109 = ∠A + ∠B
Hence we can make the conjecture that, the measure of an exterior angle is equal to the sum of measures of its nonadjacent interior angles.
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find the vertical asymptotes if any. f(x)= 1/x^2
Answer:
x = 0
Step-by-step explanation:
Vertical asymptotes are vertical lines which correspond to the zeroes of the denominator of a rational function
For f(x) set the denominator = 0 and solve for x
For [tex]\frac{1}{x^2}[/tex]
set x² = 0
x = √0 = 0 which is the vertical asymptote
Answer:
x = 0
Step-by-step explanation:
The Vertical asymptotes are vertical lines which correspond to zeroes of denominators.
For f(x) set the denominator = 0 and solve for x
For \fract {1}{x^2}
you set x² = 0
x = √0 = 0 which is the vertical asymptote
Which equation in slope intercept form, matches equation shown
A• y=4/7x-4
B• y= -4/7x+1
C• y= -5/6x-4
B• y= 5/6x+1
Answer:
c
Step-by-step explanation:
If you look at the two points on the graph you can see that the point that crosses the y axis is at -4
If you use the two points and count the slope you see that it is down 5 over 6 which gives it a slope of -5/6
A car is traveling at a speed of 100 kilometers/hour. How many hours will it take to cover a distance of 750 kilometers?
Answer:
7.5 hours
Step-by-step explanation:
Answer:
7.5 hours
Step-by-step explanation:
A car is traveling at 100 km/hr. How many hours will it take to cover a distance of 750 km? 750km ÷ 100km/hr = 7.5 hrs.
(Give brainlist?)
Solve each equation. Check each solution. 2/x = x/2
2 and -2 both are the solution of the equation x/2 = 2/x.
According to the given question.
We have an equation 2/x = x/2.
As we know that, as we know that, an equation is a condition on a variable such that two expressions in the variable should have equal value.
Therefore, the solution of the equation 2/x = x/2 is given by
2/x = x/2
⇒ 2 = (x/2)x (multiplying both the sides by x)
⇒ 2 = x^2/2
⇒ 2(2) = x^2 (multiplying by 2 both the sides by 2)
⇒ 4 = x^2
⇒ x^2 = 4
⇒ x = √4
⇒ x = ±2
⇒ x = 2 or -2
Now we will check 2 is the solution of the given equation or not.
Therefore,
LHS = 2/2 = 1
RHS = 2/2 = 1
Here, LHS = RHS. Therefore, 2 is the solution of the given equation.
Similarly, for -2
LHS = 2/-2 = -1
RHS = -2/2 = -1
Here. RHS = LHS. Therefore, -2 is also the solution of the given equation.
Hence, 2 and -2 both are the solution of the equation x/2 = 2/x.
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Write 2.702x10^-7 as an ordinary number
Answer:
0.0000002702
Step-by-step explanation:
2.702 * 10^-7
Write a recursive definition for each sequence. -2,7,16,25, . . . . .
The recursive formula for the arithmetic sequence [tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + d
A recursive formula is a sequence in which terms are defined using one or more previous terms which are given. If we know the nth term of an arithmetic sequence and you know a common difference, d, we can find the (n+1)th term using the recursive formula.
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + d
The sequence -2, 7, 16, 25,.... is in arithmetic sequence and its common difference is 7 - (-2) = (16-7)= 9 .
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Two angles form a linear pair. The measure of one angle is 3.5 times the measure of the other angle. Find the measure of each angle.
Given that the two angles form a linear pair, the measure of each angle is 40° and 140°.
What is the measure of each angle?The sum of angles of a linear pair is always equal to 180°.
Given the data the data in the question;
Let x represent the measure of the first angle.
Measure of angle 1 = xMeasure of angle 2 = 3.5xSince the sum of angles of a linear pair is always equal to 180°.
m∠1 + m∠2 = 180
x + 3.5x = 180
Solve for x
4.5 = 180
x = 180/4.5
x = 40
Hence,
Measure of angle 1 = x = 40°
Measure of angle 2 = 3.5x = 3.5(40) = 140°
Given that the two angles form a linear pair, the measure of each angle is 40° and 140°.
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An airplane on a long-distance flight flew the first 1295 miles of it's journey on 3 hours and 33 minutes. After that, the wind changed, and it took the plane 1 hour and 47 minutes to cover the remaining 738 miles. What was the plane's average speed during the flight?
Round to the nearest tenth
The plane's average speed during the flight is 381.43 miles per hour.
What is the average speed?The average speed is the quotient of the total distance covered during the flight divided by the total time used.
The Average Speed is the scalar quantity that shows the rate of change in displacement from one point to another.
Data and Calculations:The distance for the first miles = 1,295 miles
The time it took the plane to cover the distance = 3 hours 33 minutes
The distance for the last lap = 738 miles
The time it took the plane to cover the last distance = 1 hour 47 minutes
The total distance covered for the journey = 2,033 miles (1,295 + 738)
The total time for the journey = 5 hours 20 minutes or 5.33 hours
Average Speed = 2,033/5.33
= 381.43 miles per hour
Thus, the plane's average speed during the flight is 381.43 miles per hour.
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What is the probability of spinning B on the first spinner and a number less than 6 on the second spinner?
Answer:
Not possible without knowing what the spinners are
Find the next two terms in each sequence. Write a formula for the n th term. Identify each formula as explicit or recursive. 49,64,81,100,121, ......
Answer:
The next two terms is 144 and 169
Find the distance between the points (–
1,–
1) and (7,8).
Write your answer as a whole number or a fully simplified radical expression. Do not round.
Step-by-step explanation:
In order to get answer of this question, we should use the distance formula. So, what is that formula? let us see the formula and simplify to get the answer :)
[tex]{ \red{ \tt{given}}}[/tex]
[tex]{ \orange{ \tt{(1, - 1)}}} = { \green{ \tt{(x1,y1)}}}[/tex]
[tex]{ \orange{ \tt{(7,8)}}} = { \green{ \tt{(x2,y2)}}}[/tex]
[tex]{ \blue{ \tt{d}}} = { \green{ \tt{ \sqrt{ {(x1 - x2)}^{2} + ( {y1 - y2)}^{2}}}}}[/tex]
[tex]{ \blue{ \tt{d}}} = { \green{ \tt \sqrt{ {(1 - 7)}^{2} + { (- 1 - 8)}^{2}}}}[/tex]
[tex]{ \blue{ \tt{d}}} = { \green{ \tt{ \sqrt{ {(6)}^{2} + {( - 9)}^{2}}}}} [/tex]
[tex]{ \blue{ \tt{d}}} = { \green{ \tt{ \sqrt{36 + 81}}}}[/tex]
[tex]{ \blue{ \tt{d}}} = { \green{ \tt{ \sqrt{117}}}} [/tex]units.
