a)The expression for the total cost for all four classes can be given as 32s + 200. b) the rational expression for the cost per student is 2(4s+25)/s c) if each class has 20 students then the cost per student is equal to $10.50.
a) Total cost expression can be determined as follows:
total fees of admission + fees of bus = total cost
total cost = (4s × 8) + 200
total cost = 32s + 200
b) A rational expression to determine the cost per student can be calculated as follows:
cost per student = total cost ÷ the total number of students
cost per student = 32s + 200 ÷ 4s
We now factor the numerator by using its GCF;
cost per student = 4 × 2 (4s + 25) / 4×s
cost per student =2 (4s + 25) / s
c) Now using this expression we can find the cost per student if each class has 20 students;
cost per student = 2 (4s + 25) / s
cost per student = 2 ( 4×20 + 25)/ 20
cost per student = 2 ( 80 + 25) / 20
cost per student = 2 (105) / 20
cost per student = 210 / 20 = $10.50
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Help me with this problem will mark brainelist answer needs to be in scientific notation!
Answer:2.04x10 to the 4th
Step-by-step explanation:
multiply 20.4 x 1000
Then write the answer like this: 20,400
now make a decimal under ten countaining all #s that arent 0: 2.04
count the decimal places between the end of the 2 and the last 0 in the number 20,400
There are 4 places so thats 10 the power of 4
Now just put it all together
How many square metres of sheet metal are needed to make this grain storage silo? (The floor is not included)
Answer: We will be needing 78.54 square meters of sheet metal to make the grain storage silo shown.
Step-by-step explanation: to calculate he total square meters of sheet metal needed to make this grain storage silo we need to calculate the total surface area of the entire structure
for the given structure,
Total surface area = Curved surface area of the cone + curved surface area of the cylinder
curved surface area of cone = [tex]\pi rl[/tex] where r= radius of the base of cone
Given, [tex]2r= 4m[/tex]
⇒[tex]r = \frac{4}{2}=2 metres[/tex]
slant height of cone [tex]l=\sqrt{(r^{2}+h^{2} ) }[/tex] where h=1.5 m is the vertical height of the cone
∴ [tex]l = \sqrt{(2^{2}+1.5^{2} ) }=\frac{5}{2}=2.5 m[/tex]
∴curved surface area of cone [tex]= \pi rl= \pi *2*2.5=5\pi =15.71m^{2}[/tex] (1)
curved surface area of cylinder(without the floor) =[tex]2\pi rh[/tex]
where r= radius of cylinder and h= height of the cylinder
Given r= 2 m and h=5 m
∴curved surface area of cone =[tex]2\pi rh[/tex]=[tex]2*\pi *2*5=20\pi =62.83m^{2}[/tex] (2)
From results (1) and (2)
the total surface area of silo = (15.71 + 62.83)[tex]m^{2}[/tex] = 78.54[tex]m^{2}[/tex]
Thus we need 78.54 [tex]m^{2}[/tex] of sheet metal to make the grain storage silo
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7c+36
5c+40
Find x
X
Answer:
130 degrees
Step-by-step explanation:
When two lines intersect, the opposite angles are equal, therefore, in this example, 7c+36 = 5c+40. We can find c using this equation.
7c+36 = 5c+40
7c-5c = 40-36
2c = 4
c = 4/2 therefore c=2
now that we know c is equal to 2, we can find out both of those angles.
therefore 5c+40 = (5*2)+40 = 10+40= 50
and 7c+36 = (7*2)+36 = 14 +36 = 50
now we know that those two angles add up to 100.
to find the sum of x and the angle opposite to x, subtract 100 from 360
360-100 = 260
since the angle opposite of x is equal to x, x+x = 260
2x=260
x=260/2 = 130
x is 130 degrees
Answer:
x = 130
Step-by-step explanation:
7c + 36 and 5c + 40 are vertically opposite angles and are congruent , so
7c + 36 = 5c + 40 ( subtract 5c from both sides )
2c + 36 = 40 ( subtract 36 from both sides )
2c = 4 ( divide both sides by 2 )
c = 2
Then
7c + 36 = 7(2) + 36 = 14 + 36 = 50
5c + 36 and x are a linear pair and sum to 180° , that is
50 + x = 180 ( subtract 50 from both sides )
x = 130
HELP MEH PLS PLS WIL GIVE BRAINLY OR WTV
Answer:
It would go 3 to the write of x.
Step-by-step explanation:
If B is the 3 spaces to the left of x and T is three spaces to the right of x, x would be in the middle.
In the picture, you have B=2, X= 5
so T goes if X is the midpoint of BT is
X= (B+T)/2
5 x 2= 2+ T
10 = 2+T
therefore, T = 8
Dorothy is 7 years older than her brother William. If the product of their ages is 78, how old is Dorothy?
Select all of the digital construction tools that do the same job as a pencil alone (without straightedge or compass).
-Circle with center through point
-Line
-Polygon
-Point of intersection
-Point plotted on an object
The correct answers are point of intersection and point plotted on an object.
The stock price for JSR was $52.33 in October. In November the stock had increased by 9%, but in December the price fell by 9%. What was the price of JSR stock in December? Round your answer to the nearest cent, if necessary.
Despite that JSR stock price was $52.33 in October, when the stock increase and decrease are accounted for, then, the price of the stock in December equals to $51.91.
What is a stock price?Also known as share price, it refers to the price of a single share of a number of sale-able equity shares of a company.
Given data
Stock price for JSR was $52.33 in October.
November, the stock had increased by 9%
December, the price fell by 9%.
In November, the firm's stock price will be:
= Stock price in October * (1 + 0.09)
= $52.33 * (1.09)
= $57.0397
In December, the firm's stock price will be:
= $57.0397 * (1 - 0.09)
= $57.0397 * 0.91
= $51.906
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PLSSS HELP! THIS IS EXTREMELY URGENT!!!!!!!
Sean and Emily love making origami. Sean can make a paper crane in 6 minutes, and Emily can make a paper crane in 8 minutes. One day, they decided to make some paper cranes together. They started making cranes at the same time, and after a while, they have 112 total paper cranes. How many of those paper cranes did Sean make?
====================================================
Explanation:
Sean can make 1 paper crane in 6 minutes. His unit rate is 1/6 of a paper crane per minute.
Emily's unit rate is 1/8 of a paper crane per minute.
Their combined unit rate is 1/6 + 1/8 = 4/24 + 3/24 = 7/24 of a paper crane per minute.
Each minute, they can make 7/24 of a paper crane. Put another way, every 24 minutes, they can make 24*(7/24) = 7 cranes.
Let x be the number of minutes needed to make 112 paper cranes.
Multiply the combined unit rate with x and set it equal to 112
(combined unit rate)*(amount of time) = amount made
(7/24)x = 112
x = 112*(24/7)
x = 384
They need 384 minutes if they work together to make 112 paper cranes.
Sean can make 384/6 = 64 paper cranes while Emily can make 384/8 = 48 paper cranes. As a check, 64+48 = 112 to help confirm the answer.
I need to find the slope of (-19, -6), (-19, 20)
The entered points belong to a vertical line. There is no slope.
Equation: x = -19.
Please helppp. 15 pointtts
Answer:
Y = 60x
Step-by-step explanation:
Find the slope by finding Y2 - Y1/X2 - X1, 1 and 2 being two separate points on the graph. 120-0/2 = 6
The diagram shows a 5 cm x 5 cm x 5 cm cube.
A
B
5 cm
AB=
5 cm
ļ
5 cm
Calculate the length of the diagonal AB.
Give your answer correct to 1 decimal place.
+ cm
Submit Answer
The length of the diagonal AB of the cube is 8.7 cm.
What is the Diagonal of a Cube?A cube's diagonal is a line segment that joins any two of its non-adjacent vertices.Because it has 12 equally spaced edges and is one of the most prevalent forms in our surroundings, the cube is one of the most significant geometric shapes. A cube is a three-dimensional figure, hence it has two different types of diagonals: the face diagonal and the body diagonal.Length of a face diagonal of cube = √2a, where a = Length of each side of a cube.
Length of body diagonal of a cube = √3a, where a = Length of each side of a cube.
Given:
Side length of the cube(a) = 5 cm
We have to find the length of the diagonal AB which is a body diagonal.
Length of Body diagonal(AB) = √3a
Substituting the given value in the formula,
Length of the body diagonal of cube = √3a
⇒ √3a ⇒√3 × 5 = 8.7 cm
Therefore, the length of AB i.e. the body diagonal of the cube is 8.7 cm.
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5a3 x 2b2 x 4a2b5/ 3a2 x 5b3
5a^3 x 2b^2 x 4a^2 x b^5 / 3a^2 x 5b^3 (rewrite)
= 20a^5 x 2b^7 / 3a^2 x 5b^3
= 40a^5 x b^7 / 15a^2 x b^3
= (8/3) x a^3 x b^5
please help! will give brainliest!
Answer:
The correct answer is C. On the vertex of Figure A.
Step-by-step explanation:
Before you can find the answer to the question, you must first know what the center of dilation means in math. The center of dilation is a reference point used to appropriately scale the dilation of a figure. The vertex is the the point opposite to and farthest from the base of a geometrical figure, or the common endpoint of the sides of an angle.
Hope that helps! Have an amazing rest of your day!! :)
please help i don’t get it and grades are due soon and i need to get this done would be very helpful if you explain it. thank you
The length of the line segment bridging two points on a plane is known as the distance between the points. d=((x2 - x1)2 + (y2 - y1)2) is a common formula to calculate the distance between two points.
What is the separation between A and B?Except for when the points coincide, distances in geometry are always positive. The distance between points A and B is equal to their respective distances. We take two points A(a,b) and B into consideration in order to calculate the formula for the distance between two points in the plane (c,d).
What is a sample of the distance formula?In coordinate geometry, the distance between two given points is calculated using the distance formula. D=(x2x1)2+(y2y1)2 D = (x 2 x 1) 2 + (y 2 y 1) 2 is the formula for calculating the distance between two points (x1,y1) (x 1, y 1) and (x2,y2) (x 2, y 2).
Say, for instance, that you are asked to determine the distance between two points at ( -6,-2 ) and ( -1,10).
First step:
Give x 1, y 1, x 2, and y 2 their respective assignments.
Consider the cases where (x 1, y 1 ) = ( -6,-2)) and (x 2, y 2 ) = ( -1,-10).
x1 = -6
y1 =- 2
x2 = -1
y2 = 10
Second Step:
Replace in the Distance Formula
Now that we know the numbers for x1, y1, x2, and y2, we can enter them into the Distance Formula.
d = √(-6,-2)² + (-1-10)²
= √(8)² + (11)²
= √16+22
= √38.
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Find the value of x that will make A parallel to B
6 8 and 10
!! how to solve for the x
6) to solve for x just simplify both equations and set it to 180; they are co-interior angles which is why they both add to 180.
12x-29 + 4x + 1
16x -28 = 180
16x = 208;
x = 13
8) 4x - 18 = 90;
4x = 108
x = 27
The babysitter charges $8 per hour plus $4 for gas to come to the house. If the babysitter earned $36, how many hours did the babysitter work?
Answer: The answer should be 3 hours
Step-by-step explanation: 8+4=12, divide the sum by 36: 36÷12=3
She had worked 3 hours.
35. 1 and 2 are vertical angles. If m/1 =
(5x + 12) and m/2 = (6x - 11)°, find m21.
We can conclude that Angle ∠2 is 127°.
What are angles?An angle is a figure in Euclidean geometry made up of two rays that share a common endpoint and are referred to as the angle's sides and vertex, respectively. The names of fundamental angles include acute, obtuse, right, straight, reflex, and full rotation. A geometrical shape called an angle is created by joining two rays at their termini.So, in order to solve for x, you must first write an expression using the following measurements from both ∠1 and ∠2.
∠1 = 5x + 12∠2 = 6x - 11Then, 5x + 12 = 6x - 11
Now, solve for x as follows:
5x + 12 = 6x - 115x + 12 - 6x = 6x - 6x - 11-x + 12 = -11-x + 12 - 12 = -11 - 12-x = -23-x/-1 = -23/-1x = 23We know that x = 23.
∠2 = 6x - 11Solve for ∠2 as follows:
6x - 116(23) - 11138 - 11127°Therefore, angle ∠2 is 127°.
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48. nbc news reported on may 2, 2013, that 1 in 20 children in the united states have a food allergy of some sort. consider selecting a random sample of 25 children and let x be the number in the sample who have a food allergy. then x∼bin(25,.05). a. determine both p(x≤3) and p(x<3). b. determine p(x≥4). c. determine p(1≤x≤3). d. what are e(x) and σx? in a sample of 50 children, what is the probability that none has a food allergy?
The following are the solutions to the given problems by using binomial probability principle:
P(X ≤ 3) = 0.966 and P(X < 3) = 0.873P(X ≥ 4) = 0.034 and P(1 ≤ X ≤ 3) = 0.689σ(X) = 1.090 and P(X = 0) = 0.0769What is defined as the binomial probability?The probability of precisely x successes on n multiple trials in an experiment with two possible outcomes is referred to as binomial probability (called a binomial experiment).If the success probability on an individual trial is p, therefore the binomial probability is: P(x = x) = nCx * p^x * q^(n-x)p = 0.05q = 1 - 0.05 = 0.95n = sample size = 25 children1.) P(X ≤ 3)
P(X ≤ 3) = p(x = 0) + p(x = 1) + p(x = 2) + p(x = 3)
Use a binomial probability calculator :
P(X ≤ 3) = 0.277 + 0.365 + 0.231 + 0.093
P(X ≤ 3) = 0.966
2.) P(X < 3)
P(X < 3) = p(x = 0) + p(x = 1) + p(x = 2)
Use a binomial probability calculator :
P(X < 3) = 0.277 + 0.365 + 0.231
P(X < 3) = 0.873
3.)P(X ≥ 4)
P(X ≥ 4) = p(x = 4) + p(x = 5) +...+ p(x = 50)
Use a binomial probability calculator :
P(X ≥ 4) = 0.034
4.) P(1 ≤ X ≤ 3)
P(1 ≤ X ≤ 3) = p(x =1) + p(x =2) + p(x =3)
Use a binomial probability calculator :
P(1 ≤ X ≤ 3) = 0.365 + 0.231 + 0.093
P(1 ≤ X ≤ 3)= 0.689
D.) σ(X)
E(X) = np = 25 × 0.05
E(X) = 1.25
σ(X) = √(npq)
σ(X) = √(25 × 0.05 × 0.95)
σ(X) = √1.1875
σ(X) = 1.090
E. Probability for none do have food allergy :
P(X = 0) = ⁵⁰C₀ × 0.05^0 × 0.95^50
P(X = 0) = 0.0769
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Subtract.
−6/7−(−5/7)
Enter your answer in the box as mixed number in simplest form.
Step-by-step explanation:
-1/7 is exact form and Slash or / is division . -0.142857, Decimal form and horizontal line is division too . It is the simplest form .
Which equation is represented by the graph?
y = −x2 + 4x + 1
y = 2x2 + 4x + 1
y = x2 + 4x + 1
y = −x2 + 1
The equation that is represented by the graph is
y = x2 + 4x + 1
This is further explained below.
What is a Graph?Generally, The collection of ordered pairings where f(x)=y exists constitutes the graph of a function.
These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the typical situation when x and f(x) are real integers.
In conclusion, Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex: (-2,-3)
Focus:[tex]\left(-2,-\frac{11}{4}\right)[/tex]
Axis of Symmetry: x=-2
Directrix: [tex]y=-\frac{13}{4}[/tex]
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11. Select all the angles for which HA and HE
are the sides.
The angles with sides HA and HE are ∠AHE and ∠EHA.
There are some angles given from which we need to find those with sides HE and HA.
The angles given are :
A. ∠AHE B. ∠AGE C. ∠EHA D. ∠EGA E. ∠AHB
For this first we need to understand the naming of angles.
An angle is either named by a single alphabet, mostly when the angle is not divided, or it is named using three letters from which we can clearly understand the sides of the angles.
For example, ∠XYZ has sides XY and YZ with the angle at the point Y.
So we will try to find the sides of each angles given in options.
A. ∠AHE has sides HA and HE with angle at the point H.
B. ∠AGE has sides AG and GE with angle at the point G.
C. ∠EHA has sides HE and HA with angle at the point H.
D. ∠EGA has sides EG and GA with angle at the point G.
E. ∠AHB has sides HA and HB with angle at the point H.
Hence the angles for which HA and HE are sides are ∠AHE and ∠EHA.
The question is incomplete. Find the complete question below:
Select all the angles for which HA and HE are the sides.
A. ∠AHE B. ∠AGE C. ∠EHA D. ∠EGA E. ∠AHB
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A camera has a listed price of 819.95 before tax. If the sales tax rate is 7.25 , find the total cost of the camera with sales tax included. Round your answer to the nearest cent, as necessary.
Answer:
$21.40
Step-by-step explanation:
List price = $19.95
Sales Tax Rate = 7.25%
Total sales tax = 19.95 x 7.25/100 = $ 1.45
Total cost = 19.95 + 1.45 = $21.40
The temperature drops to -6 in 1 hour. In the next hour it drops to -8. By how much would the temperature have to rise to get to 0?
An eleven-foot long board must be cut into three pieces so that one piece is 1-foot shorter than half
the length of the longest piece and the other piece is 3 feet shorter than the longest piece. How
long is the shortest piece?
Answer:
2'
Step-by-step explanation:
An eleven-foot long board must be cut into three pieces so that one piece is 1-foot shorter than half the length of the longest piece and the other piece is 3 feet shorter than the longest piece. How long is the shortest piece?
board 1 = 0.5L - 1
board 2 = L - 3
board 3 = L
so:
(0.5L - 1) + (L - 3) + L = 11'
0.5L - 1 + L - 3 + L = 11'
combine L on left side:
2.5L - 4 = 11
add4 from both sides:
2.5L - 4 + 4 = 11 + 4
2.5L = 15
divide both sides by 2.5:
2.5L/2.5 = 15/2.5
L = 6
Formula for boards are, substitute in L = 6:
board 1 = 0.5L - 1
= 0.5(6) - 1
= 3 - 1
= 2'
board 2 = L - 3
= 6 - 3
3'
board 3 = L
= 6
shortest board is board 1 at 2'
An interior designer is planning a room but needs to first figure out the dimensions. The length of the room is 17 inches on the architect’s plan. What is the actual length of the room in feet if the scale of the plan is 1.25 inches to 3 feet?
If the length of the room is 17 inches one the architect's plan, the actual length of the room in feet if the scale of the plan is 1.25 inches to 3 feet is
40.8 feet
The length of the room on the architect's plan = 17 inches
The scale of the plan = 1.25 inches to 3 feet
That means
The length on the plan/ The actual length = 1.25 inches / 3 feet
Substitute the value of the length on the plan in the equation
17 / The actual length = 1.25/3
The actual length of the room = 17/0.42
= 40.8 feet
Hence, if the length of the room is 17 inches one the architect's plan, the actual length of the room in feet if the scale of the plan is 1.25 inches to 3 feet is 40.8 feet
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Write the coordinates of the vertices after a translation 7 units left.
B'=
,
C'=
,
D'=
,
E'=,
please help
The coordinates of the images of the vertices of the rectangle are B'(x, y) = (- 4, 2), C'(x, y) = (- 4, 7), D'(x, y) = (0, 7) and E'(x, y) = (0, 2).
What are the coordinates of the images of the vertices of a rectangle
Rectangles are defined by the location of its four vertices set on Cartesian plane, whose images must be found by using a transformation known as translation, whose formula is defined below:
P'(x, y) = P(x, y) + T(x, y)
Where:
P(x, y) - Location of the vertex.T(x, y) - Translation vector.P'(x, y) - Location of the image of the vertex.If we know that B(x, y) = (3, 2), C(x, y) = (3, 7), D(x, y) = (7, 7), E(x, y) = (7, 2) and T(x, y) = (- 7, 0), then the images of the vertices are:
B'(x, y) = (3, 2) + (- 7, 0)
B'(x, y) = (- 4, 2)
C'(x, y) = (3, 7) + (- 7, 0)
C'(x, y) = (- 4, 7)
D'(x, y) = (7, 7) + (- 7, 0)
D'(x, y) = (0, 7)
E'(x, y) = (7, 2) + (- 7, 0)
E'(x, y) = (0, 2)
Now we proceed to present the resulting figure.
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NEED ASAP Create a unique table of data for two different linear functions. The table should use the same values of x for both functions. Based on your table, will the graphs of these two functions intersect? Explain your answer.
A table of data for two different linear functions using the same values of x for both functions is shown below:
From the table, it can be seen that when x = -1, the function y = 2x + 7 has a value of 5 and the function y = -x + 4 has a value of 5.
Therefore, the graph of the two functions will intersect at (1, 5)
Which represents the inverse of the function f(x) = 4x?
The inverse function of f(x) = 4x is:
f⁻¹(x) = (1/4)*x
So the correct option is the fourth one.
How to get the inverse of the given function?
For any function f(x) we define the inverse f⁻¹(x) such that:
f(f⁻¹(x)) =x
f⁻¹(f(x)) = x
In this case we have f(x) = 4*x
Then the inverse is also a linear function:
f⁻¹(x) = a*x + b
Using the rules for inverses we get:
f⁻¹(f(x)) = a*f(x) + b = a*(4x) + b = x
a*(4x) + b = x
Then we have b = 0
a*4x = x
a*4 = x/x
a*4 = 1
a = 1/4
The inverse is:
f⁻¹(x) = (1/4)*x
The correct option is the last one.
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Enter the Correct 4 Digit Code (no spaces)
The correct 4 Digit Code (no spaces) is 0164 .
In the question ,
the numbers representing the equation are given
to find
the first statement
-C.P-(-K.I)
From the figure we can see that C=2 ,P=7 ,K=5 ,I=4,
hence -C.P-(-K.I) = -2.7-(-5.4) = -14+20 = 6.0 .....(i)
the second statement
E/H + -L/T
From the figure we can see that E=3 ,H=4 ,L=5 ,T=8
hence E/H + -L/T = 3/4 + -5/8 = 3/4 - 5/8 = 1/8 ...(ii)
the third statement
B/W × -N/T
From the figure we can see that B=2 ,W=9 ,N=6 ,T=8
hence B/W × -N/T = 2/9 × -6/8 = -1/6 ...(iii)
the fourth statement
-F/J ÷ -M/V
From the figure we can see that F=3 ,J=5 ,M=6 ,V=8
hence -F/J ÷ -M/V = -3/5 ÷ -6/8 = 4/5 ....(iv)
From equation (i) , (ii) , (iii) and (iv) , we get
-C.P-(-K.I) = 6.0
E/H + -L/T = 1/8
B/W × -N/T = -1/6
-F/J ÷ -M/V = 4/5
the number from the red color lines are 0,1,6,4
hence the code is 0164 .
Therefore , the correct 4 Digit Code (no spaces) is 0164 .
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please help asap! i dont know what do to here
Answer:
y = - x - 6
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 = - x ← is in slope- intercept form
with slope m = - 1
• Parallel lines have equal slopes , then
y = - x + c ← is the partial equation of the parallel line
to find c substitute (- 8, 2 ) into the partial equation
2 = 8 + c ⇒ c = 2 - 8 = - 6
y = - x - 6 ← equation of parallel line