22.22 was spent on a pass and lunch for each student.
Now, According to the question:
Total money spend on passes = 674.73
Total no. of people = 47 + 2
= 49
Money spend on pass for each person = 674.73/49
= 13.77
Total money spend on lunch = 414.07
Total no. of students = 49
Money spend on lunch for each student = 414.07/49
= 8.45
Total = 13.77 + 8.45
= 22.22
Hence, 22.22 was spent on a pass and lunch for each student.
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How is factor theorem derived?
Factor theorem is most commonly used for factoring a polynomial or integer and searching the roots of the polynomial. It is a particular case of a polynomial remainder theorem.
As defined in the introduction, a polynomial f(x) has a factor (x-a), if and only if, f(a) = 0. It is one of the processes to do the factorization of a polynomial.
Here we can prove the factor theorem, according to which we can.
factories the polynomial.
Consider a polynomial f(x) which is divided by (x-b), then f(c)=0.
Using remainder theorem,
f(x)= (x-b) q(x)+f(b)
Where f(x) is the target polynomial and q(x) are the quotient polynomial.
because f(b) = 0, So,
f(x)= (x-b) q(x)+f(b)
f(x) = (x-b) q(x)+0
f(x) = (x-b) q(x)
So, (x-b) is a factor of the polynomial f(x).
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help ,,,,,,,,,,,................................
The graph of the reflected function: g(x) = 3^(-x) can be seen in the image at the end.
Which graph represents the reflection of the parent function?First, for any function y = f(x), a reflection across the y-axis is written as:
g(x) = f(-x)
So we only change the sign of the argument of the function.
The graphed function is the parent function:
f(x) = 3^x
A reflection across the y-axis, will give the new function:
g(x) = f(x) = 3^(-x)
The graph of this will be like the graph of f(x) but reflected across the y-axis, like the graph below.
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What is the exponential form of 4x4x4?
Answer:
4^3
Step-by-step explanation:
4x4 would be squared aka 4^2 but since theres three itd be cubed aka 4^3
PLEASE HELP ME!!!!!! I need to turn this in before the grading period is over.
The equation h=40t-16t² describes the height (h) of a ball that is thrown straight up as a function of the (t) that the ball has been in the air. At what time does the ball reach its maximum height? What is the maximum height?
At 2.5 seconds the ball reach its maximum height.
And, Its maximum height will be 25 feet.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The equation that describes the height (h) of a ball that is thrown straight up as a function of the (t) that the ball has been in the air is,
⇒ h = 40t - 16t²
So, For the time does the ball reach its maximum height, we can put h = 0, so we get;
⇒ h = 40t - 16t²
⇒ 40t - 16t² = 0
⇒ 16t² - 40t = 0
⇒ t (16t - 40) = 0
⇒ 16t - 40 = 0
⇒ 16t = 40
⇒ t = 40/16
⇒ t = 2.5 seconds
Now, The height function is a quadratic function which has the zeroes at t = 0 and t = 2.5.
So, It has the maximum at x = midpoint between the roots 0 and 2.5, i.e. 1.25 seconds.
Hence, Substitute this value t = 1.25 seconds into the given height function, we get;
⇒ h = 40t - 16t²
⇒ h = 40 × 1.25 - 16 (1.25)²
⇒ h = 50 - 25
⇒ h = 25 feet
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Does 7 cm 8 cm 9 cm form a triangle?
No, these measurements do not form a triangle. The sum of any two sides of a triangle must be greater than the third side. In this case, 7 cm + 8 cm = 15 cm, which is not greater than the third side, 9 cm.
A triangle is a three-sided polygon, and all three sides must meet certain criteria in order to form a triangle. Specifically, the sum of any two sides must be greater than the third side. In this case, the given measurements are 7 cm, 8 cm, and 9 cm. When adding the 7 cm and 8 cm together, the sum is 15 cm, which is not greater than the third side, 9 cm. Therefore, these measurements do not form a triangle. To determine if a triangle can be formed with any given measurements, one must sum any two sides and ensure that the sum is greater than the third side. If the sum is not greater than the third side, then the measurements do not form a triangle.
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which relation is a function ?
Answer:
the third one
Step-by-step explanation:
it only passes once
Which expressions are equivalent to 2(b+3c)2(b+3c)2, left parenthesis, b, plus, 3, c, right parenthesis ?
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
A
3(b+2c)3(b+2c)3, left parenthesis, b, plus, 2, c, right parenthesis
(Choice B)
B
(b+3c)+(b+3c)(b+3c)+(b+3c)left parenthesis, b, plus, 3, c, right parenthesis, plus, left parenthesis, b, plus, 3, c, right parenthesis
(Choice C, Checked)
C
2(b)+2(3c)2(b)+2(3c)
The expression that is equivalent to 2(b+3c) is C.
2(b) + 2(3c).
How to calculate the expression?It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.
The expression 2(b + 3c) will be:
= 2b + 6c
3(b + 2c) will be:
= 3b + 6c
2(b) + 2(3c) will be:
= 3b + 6c
The correct option is C since they gave same value.
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6.
In George's classroom, there are 6 girls for every 2 boys. What is the ratio of boys to the total number of students
A. 1:3
B. 3:1
C. 1:4
D. 4:1
Answer:
B
I am sorry if this is wrong
HEEEEEELP IT’S TIMED
(Zoom in for less lines)
Answer: is A
Step-by-step explanation:
30% of the members of a club are female and 20% of these females on cars. 30 female members in the club own cars.
(a) How many female members are there?
(b) What is the total number of members?
(c) How many new female members have to be recruited to increase the percentage of female members to 37.5%?
(a) We know that 30% of the members of the club are female and 20% of these females own cars, and 30 female members own cars.
We can use this information to calculate the total number of female members in the club.
If 30% of the members are female and 20% of these females own cars,
then 20/100*30 female members = 6% of the total members own cars.
This means that 6% of the total members are female members who own cars.
Therefore, 30 female members / 6% = 500 female members.
So there are 500 female members in the club.
(b) If 30% of the members are female, then the total number of members is (100/30)*500 female members = 1666.67 members
(c) To increase the percentage of female members to 37.5%, we need to calculate the number of additional female members required to reach this goal. The current percentage of female members is 30% and we want to increase it to 37.5%. Therefore, we need an additional 37.5-30 = 7.5%. If the current number of female members is 500, to increase the percentage by 7.5%, we need an additional of 7.5/100*1666.67 = 125 additional female members.
What is the rule about 3 side lengths forming a triangle?
Answer:
there some rules
Step-by-step explanation:
Look carefully at the completed Punnett Squares A, B, and C. Use these letters to answer the questions below. Answers may be used more than once. Which Punnett Square shows: 2. 25% wrinkled offspring? Fill in the blank text field 1 Enter Text Here 3. 50% wrinkled offspring? Fill in the blank text field 2 Enter Text Here 4. 75% round offspring? Fill in the blank text field 3 Enter Text Here 5. 100% round offspring? Fill in the blank text field 4 Enter Text Here Check Answer Three Punnett squares.
Answer: A C A B
Step-by-step explanation:
PLS HELP!!
Solve the equation on the interval [0,2π)
cot(x-pi/2)=1
The solution to the trigonometric equation is x = ( 3π/4 ) , x = ( 7π/4 )
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin (-θ) = -sin (θ)
csc (-θ) = -csc (θ)
cos (-θ) = cos (θ)
sec (-θ) = sec (θ)
tan (-θ) = -tan (θ)
cot (-θ) = -cot (θ)
In the first quadrant, sin, cos and tan are all positive.
In the second quadrant going anti-clockwise, only sin is positive.
In the third quadrant going anti-clockwise, only tan is positive.
In the fourth quadrant going anti-clockwise, only cos is positive
Given data ,
Let the trigonometric equation be represented as A
Now , the value of A is
cot ( x - π/2 ) = 1 be equation (1)
On simplifying the equation , we get
cot ( - ( π/2 - x ) ) = 1
Now , cot (-θ) = -cot (θ)
So , - cot ( π/2 - x ) = 1
And , the value of cot ( π/2 - θ ) = tan θ
Substituting the values in the equation , we get
-tan x = 1 over the interval [ 0 , 2π ]
The value of x for -tan x = 1 is given by x = ( 3π/4 ) + nπ
when n = 1
x = ( 7π/4 )
So , the values of x are ( 3π/4 ) and ( 7π/4 )
Hence , the solutions are ( 3π/4 ) and ( 7π/4 )
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This question has two parts. Use the graph to answer Part A and Part B.
The graph shows y as a function of x.
Part A
What is the output when the input is -3? Enter the answer in the box.
Part B
What is the input when the output is 2? Enter the answer in the box.
The equation showing y as a function of x is given as y = -x - 2
What is an equation?An equation is an expression relating two or more numbers and variables.
The standard form of a linear equation is:
Ax + By = C
where A, B and C are constants
The slope - intercept form of a linear equation is:
y = mx + b
Where m is the rate of change(slope) and b is the y intercept.
The graph passes through points (-2, 0) and (0, -2). Hence, the equation is::
y - 0 = [(-2-0)/(0 - (-2)](x - (-2))
y = -1(x + 2)
y = -x - 2
a) When the input is -3, that is x = -3:
y = -(-3) - 2 = 1
The output is 1 when the input is -3
b) When the output is 2, that is y = 2:
2 = -x - 2
-x = 4
x = -4
The input is -4 when the output is 2
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31202 imagine math help
the 1srt one
Step-by-step explanation:
A Scottish dance team used 140 yards of tartan to make
dancing skirts. The heights of the team members vary. The skirt
3
pattern for the shorter members uses 3- yards of fabric, and
4 3
the skirt pattern for the taller members uses 4 yards of fabric.
4
Let s represent the number of shorter skirts and t represent the
number of longer skirts. Which equation represents the
relationship between the number of short skirts and the number
of long skirts that were made?
A
C
3 3
3 +4
4 4
3
3
st=140
140
3 3
4 4
B s+t=3 +4
D
-t=140
The equation showing the relation between shorter and longer skirt is 3s+4t = 140.
Given that the Scottish dance team used 140 yards of tartan to make dancing skirts.
The skirt pattern for the shorter members is 3- yards of fabric, and the skirt pattern for the taller members is 4 yards of fabric.
So, we need to find the equation represents the relationship between the number of short skirts and the number of long skirts that were made,
So, if there are s short skirts and t long skirts,
So,
The relation will be =
3s + 4t = 140
Hence the equation showing the relation between shorter and longer skirt is 3s+4t = 140.
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The perimeter of a rectangle is 70 cm. If its length is decreased by 5 cm and its width is increased by 5 cm, its area will increase by 50 cm². Find the length and the width of the original rectangle.
The requried dimension of the original rectangle is given as length = 25 cm, width = 10 cm.
What is a rectangle?The rectangle is 4 sided geometric shape whose opposites are equal in length and all angles are about 90°.
Let the length and width of the original rectangle be x and y,
According to the quesiton,
The perimeter of a rectangle is 70 cm.
2 [x + y] = 70
x + y = 35 - - - -(1)
Now,
its length is decreased by 5 cm and its width is increased by 5 cm, its area will increase by 50 cm².
Area of the new rectangle = area of the original rectangle + 50
(x - 5)(y + 5) = xy + 50
from equation 1,
(x - 5)(35 - x + 5) = x(35 - x) + 50
-x² - 200 + 40x + 5x = 35x - x² + 50
45x - 35x = 50 + 200
10x = 250
x = 25
Now,
y = 35 - 25
y = 10
Thus, the requried dimension of the original rectangle is given as length = 25 cm, width = 10 cm.
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Is x² a coefficient?
In the equation 3x², the variable x²'s coefficient is 3.
The formula is 3x2.
To determine: The expression's variable x2's coefficient
The number next to the variable in the equation is the coefficient.
Three is the coefficient of x in 3x².
The coefficient of a number is the product of the number and the variable. For example, 6 is the value of the x² coefficient in the formula 6x2+99.
The word that is multiplied by x² is 3, as can be seen.
Consequently, the value of x² in the equation 3x² is 3.
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Complete question - What is the coefficient of x² in 3x²?
i need help with this asap please
Answer:it is 900 because that’s a number that is irrational
Step-by-step explanation:
I am a 2-digit odd number. The product of my digits is 36. What is my last digit?
please reply
A sequence starts with: 390625, 78125, 15625, 3125
Work out the next four sequences.
Answer:
625, 125, 25, 5
Step-by-step explanation:
390625, 78125, 15625, 3125
We need to find out the relationship between a number and the previous number.
We can tell that there is no common difference since 78125 - 390625 cannot possibly equal 3125 - 15625.
We can try to check if this is a geometric sequence.
78125/390625 = 0.2
15626/78125 = 0.2
3125/15625 = 0.2
Each number is 1/5 of the previous number.
3125/5 = 625
625/5 = 125
125/5 = 25
25/5 = 5
Answer: 625, 125, 25, 5
Need this asap if you help Tysm!!!
Answer:
B. -$0.75
Step-by-step explanation:
that is really very simple.
the value on day 1 (the begin) is $2.50.
the value on day 5 (the end of the week I assume) is $1.75.
so, the value changed by -$0.75 from $2.50 to $1.75.
yes, this is the sum of all little individual changes day by day. but there is no need to do these detailed calculations. at the end it is just
value end - value begin
These triangles are congruent by the triangle congruence postulate...
Answer:
SSS
Step-by-step explanation:
They share one common side, and the two other sides are marked with single and double line identifiers, meaning they are the same. Therefore, SSS.
30 points
please help
The time it takes Timothy to drive to his friend's house does not proportional to the distance. Because all ordered pairs do not pass through a straight line.
What is the ordered pair?
An ordered pair is a composition of the x coordinate (abscissa) and the y coordinate (ordinate), with two values, expressed between parenthesis in a predetermined order. It aids visual comprehension by locating a point on the Cartesian plane. An ordered pair's numeric values can be integers or fractions.
Given ordered pairs are (5,10), (11,15), and (18,20).
The ordered pairs are plotted on the graph.
A line can not draw through the ordered pairs.
Thus, time is not proportional to distance.
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Question 1
Part A
How can you represent 100 as an exponential expression with 10 as the base?
Answer:
10^2
Step-by-step explanation:
I hope this helps you
The students in Sam’s school voted for their favorite subject. Sam displayed the results in the cirlce graph shown.
Which statements are true about the data in the graph? Check all that apply.
A circle graph titled Favorite Subject. Math is 24 percent, language arts is 20 percent, science is 18 percent, social studies is 16 percent, art is 14 percent, and other is 8 percent.
a. If 100 students were surveyed, 34 would choose math as their favorite subject.
b. If 200 students were surveyed, 28 would choose art as their favorite subject.
c. If 400 students were surveyed, 64 would chose social studies as their favorite subject.
d. If 100 students were surveyed, 38 would choose science as their favorite subject.
e. If 200 students were surveyed, more than half would choose science or social studies as their favorite subject.
The statements that are true about the data in the graph include the following:
B. If 200 students were surveyed, 28 would choose art as their favorite subject.
C. If 400 students were surveyed, 64 would chose social studies as their favorite subject.
What is a pie chart?In Mathematics, a pie chart can be defined as a type of graph that is used for the graphical representation of the proportion relationship between each part or unit to a whole, especially by dividing a circle into various sectors or sections.
Assuming 200 students were surveyed at 14%, the number of students who would choose art as their favorite subject can be calculated as follows;
Number of students for arts = 14/100 × 200
Number of students for arts = 0.14 × 200
Number of students for arts = 28 students.
Assuming 400 students were surveyed at 16%, the number of students who would choose social studies as their favorite subject can be calculated as follows;
Number of students for social studies = 16/100 × 400
Number of students for social studies = 0.16 × 400
Number of students for social studies = 64 students.
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Simplify (10−6)2 + 8 − 22.
A.20
B.68
C.12
D.52
Answer: 20
Step-by-step explanation: i did this before on a quiz
Answer:
20
Step-by-step explanation:
online calcs can help with this
Find point Q on the line segment PR that partitions it into the segments PQ and QR in the ratio 4:5.
Answer: To find point Q on the line segment PR that partitions it into the segments PQ and QR in the ratio 4:5, we need to use the concept of proportion.
We can set up the proportion as:
PQ / QR = 4 / 5
To find the actual point Q on the line segment PR, we need to know the coordinates of points P and R. Without them, it is not possible to find the point Q. Once we have the coordinates of P and R, we can use the proportion above to find the coordinates of Q.
Alternatively, we can use the concept of a "partitioned ratio" which is a way to split a line segment into a certain ratio. It is found by adding the two ratios together and then dividing the length of the line segment by that number. In this case (4+5 =9) and then PQ = (4/9) * PR and QR = (5/9) * PR.
Step-by-step explanation:
how do i solve 15 x - 20 < 40
Answer:
x<4
Step-by-step explanation:
To solve and make the problem less intimidating, it is easier to just imagine that the < is a = sign. The only difference when solving a inequality versus an equation is that you flip the inequality sign when multiplying or dividing by a negative, which we won't need to worry about in this problem. Now, hopefully, this will make more sense when we are solving.
The first step is to add 20 to both sides:
15x - 20 < 40 (Add 20 to both sides)
15x < 60
Now, divide both sides by 15, so we are juts left with x:
15x < 60 (Divide both sides by 15)
x < 4
So, the inequality is true for any x value that is less than 4, or x<4.
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What is the distance between points (-4,2) and (1,-3) on the coordinate plane?
Answer:
7.07 units
Step-by-step explanation: