Answers
Answer:
There are 24 students and teachers that rode in vans, and there are 385 students and teachers that rode in buses.
Step-by-step explanation:
First we are going to set up a system of equations where:
b= number of buses
v= number of vans
We know from the equation that each bus transported 55 people and that each van transported 12 people and that there was a total of 409 people transported. We also know that the number of buses was 5 more than the number of vans.
Knowing that we can set up our system:
[tex]\left \{ {{55b+12v=409} \atop {b=v+5\\}} \right.[/tex]
Since we know what b is equal to, we can now use the substitution method to plug the value of b from the bottom equation into the one on the top and solve for variable v.
55(v +5)+12v =409
From there we can distribute 55 into (v+5)
55v +275+12v =409
We can now combine like terms.
67v +275 = 409
From there we subtract 275 from both sides of the equation to isolate the variable.
67v +275 = 409
-275 -275
After doing this, we now divide both sides of the equation by 67 to solve for v.
[tex]\frac{67v}{67} =\frac{134}{67}[/tex]
We now know that v, the number of vans is 2 and can plug that into our bottom equation from our system of equations ([tex]b=v+5[/tex]).
[tex]b=2+5\\b=7[/tex]
Knowing that there are 7 buses and 2 vans, we can now plug these numbers into the terms in the top equation of our system. 55b and 12v.
[tex]55(7)=385[/tex]
[tex]12(2)= 24\\[/tex]
385 people rode buses. 24 people rode vans
Check your equation
409 people went in total. 385 + 24 = 409.
person above is correct
Related Questions
simplify 2(-n-3)-7(5+2n)
Answers
Answer:
-16n - 41
Step-by-step explanation:
To simplify the equation, you need to get rid of the parentheses by multiplying the numbers outside the parentheses to the numbers inside. Then, you can combine the similar terms.
2(-n - 3) - 7(5 + 2n) <---- Original equation
-2n - 6 - 7(5 + 2n) <---- Expand first parentheses by mult.
-2n - 6 - 35 - 14n <---- Expand second parentheses by mult.
-16n - 6 - 35 <---- Combine terms with "n"
-16n - 41 <---- Combine whole numbers
Answer:-2n-29
Step-by-step explanation:2*-n=-2n
2*-3=-6
-7*5=35
-7*2n=-4n
2n-6-35-44n
2n-4n=-2n
6-35=-29
2n-29
The vertices of figure A are located at (2, 2), (4, 2), (4, 4). The transformation f(x, y) = (½x, ½y+2) transforms figure A into figure B. Which of the following sets of transformations would transform figure B back into figure A?
A dilation by a factor of 2 centered at the origin, followed by a translation down 4 units.
A translation down 4 units, followed by a dilation by a factor of 2 centered at the origin.
A dilation by a factor of ½ centered at the origin, followed by a translation up 2 units.
A dilation by a factor of 2 centered at the origin, followed by a translation down 2 units.
Answers
Answer:
b
Step-by-step explanation:
because its a reasonal answer if you do the math
find the measure of MNI. please help! i’ll give you brainlist!
Answers
Answer:
[tex]m\angle MNI = 135^{\circ}[/tex]
Step by step explanation:
[tex]\text{The exterior angle of a triangle = sum of two opposite interior angles.}[/tex]
[tex]~~~~~~\angle MNI = \angle LMN + \angle MLN\\\\\implies 19x+2=(15x-12)+6x\\\\\implies 19x +2 = 21x-12\\\\\implies 21x -19x = 12+2\\\\\implies 2x = 14\\\\\implies x=\dfrac {14}2\\\\\implies x = 7\\\\\text{So,}~ m\angle MNI = 19(7)+2=135^{\circ}[/tex]
An Iowa farmer grows wheat and corn on his farm. This year, he planted 215 acres of corn. He planted 60 fewer acres of wheat than of corn this year. How much wheat did the farmer plant this year?
Answers
Answer:
155 acres
Step-by-step explanation:
corn = 215
wheat = 215 - 60 = 155
215-60=155
Are you able to use a calculator? Because thats the best solution to basic math!!
Answer the following sections about adjacent angles
Answers
Answer:
adjacent angles are angles that share a side and a common vertex, basically, they are just angles next to each other that are formed by the same point.
Step-by-step explanation:
all adjacent angles are
2,1
2,3
1,4
3,4
6,7
6,5
8,5
8,7
10,11
10,9
12,9
12,11
2,3
1.4
3.4
6.7
6.5
8,5
8.7
10,11
10,9
12,9
12,11
What is the least positive integer by which 24 should be divided so that the resulting integer is a perfect square?
24 = 2 × 2 × 2 × 3
In a perfect square, all the prime factors occur in pairs.
In 2 × 2 × 2 × 3, 2 occurs in a pair, and only one each of 2 and 3 remains unpaired.
So, the least positive integer by which 24 should be divided to get a perfect square = 2 × 3 = 6.
What is the least positive integer by which 224 should be divided so that the resulting integer is a perfect square?
The least positive integer =
The resultant integer =
pls explain to me I need to understand too
answer quickly
Answers
Answer: divide by 6?
Step-by-step explanation:
What is the least positive integer by which 24 should be divided so that the resulting integer is a perfect square?
If we actually guess and check by dividing by 1, then 2, then 3, then etc. we will get the answer. I tried and divided by 6, which is 4, which is a perfect square. Do not trust me completely on this, for I am not quite sure.
PLEASE HELP ME MY BRIAN IS LIKE PUTTY 50 points for correct answerr
Triangle PQR is transformed to triangle P'Q'R'. Triangle PQR has vertices P(3, −6), Q(0, 9), and R(−3, 0). Triangle P'Q'R' has vertices P'(1, −2), Q'(0, 3), and R'(−1, 0).
Plot triangles PQR and P'Q'R' on your own coordinate grid.
Part A: What is the scale factor of the dilation that transforms triangle PQR to triangle P'Q'R'? Explain your answer.
Part B: Write the coordinates of triangle P"Q"R" obtained after P'Q'R' is reflected about the y-axis.
Part C: Are the two triangles PQR and P''Q''R'' congruent? Explain your answer.
Answers
Answer:
Part A :
The scale factor of the dilation that transforms triangle PQR to triangle P'Q'R' is divided by 3.
Part B :
P"(-1,2), Q"(0,3), R"(1,0)
Part C :
Triangle PQR and P"Q"R" are not congruent because congruent means equal and similar but triangle PQR and P"Q"R" are proportional because they are rational to each other but do not have the same measures of sides but the angles are congruent.
This is the graphing of the triangle.
part b: p” -> (-1,2) q” -> (0,3) r” -> (1,0)
What is the least common denominator of 1/4 and 2/5?
Answers
Answer:
20
Step-by-step explanation:
because 4 can go into 20 5 times without a remainder
Answer:
1/4 = 1/4 × 5/5 = 5/20
2/5 = 2/5 × 4/4 = 8/20
Therefore, the LCD is 20
Step-by-step explanation:
I’m studying for a test, could you help me with A, B, and C? (image below)
Answers
Answer:
a = 51
b = 51 (??not so sure)
c = 20 cents
Step-by-step explanation:
a) 25 x 408 = 10200
10200 ÷ 200 = 51 square ft is one one roll.
b) the surface area of an average gift is 51 sq ft (?)
c) 40 ÷ 200 = 0.2
each roll costs $40 dollars. each roll can wrap 200 gifts so 40 ÷ 200 = $0.20/ 20 cents
Please, my brain went blank and I didn't know how to answer this
Answers
The area of one square side is: 3 x 3 = 9
There are 6 sides on a cube so: 9 x 6 = 54
HELP ASAP!!!! which measurements could create more than one triangle?
Answers
Answer:
75 degrees, 45 degrees, and 60 degrees
Step-by-step explanation:
When we are given three angles any number of triangles can be formed.
Answer:
More than one triangle can be formed by three angles measuring 75°, 45° and 60
Step-by-step explanation: So, the answer would be (A)
The number of hours of TV watched each week by 8 seventh grade students is shown below.
11, 7, 9, 3, 3, 8, 10, 5
a. What is the mean number of hours of TV watching?
b. Mean absolute deviation =
c. Explain the meaning of the mean absolute deviation as it relates to the number of hours of TV watched.
Answers
Answer:
a) 7 hours ; b) 2.5 hours ; c) look at explanation
Step-by-step explanation:
a)
The mean of a data set is what we usually refer to as the average. To find the mean, you add up all of the values and divide by the number of values.
So, to find the mean, you need to add all of the values (the "value" is the the number hours each student watched)
11 + 7 + 9 + 3 + 3 + 8 + 10 + 5
= 56
You have 8 seventh-grade students, so your number of values is 8.
Dividing the sum of the values by the number of values would then be:
56 / 8
= 7
So, your mean is 7.
---------------------------------------
b)
(A deviation is how much a value differs from a certain value. If a person was supposed to be 5 feet tall, and they were 6 feet tall, they would deviate 1 foot from the value of 5. If the person was 4 feet tall, they would also have a deviation of 1 foot.)
The mean absolute deviation is complicated. You probably want to set up two columns (or at least this is how I was taught to do it), the first column being the value (represented by x in the mean absolute deviation formula), the second column being the difference between the mean of the data set and the value (the mean is represented as x with a line over it).
∑ is the sum of the values of the second column.
To find the mean (remember, mean = average) of the deviations, you are going to add all of the deviations together, and divide by your number of values.
I'll write out the second column (the difference from mean) below:
| x - [tex]\frac{}{x}[/tex] |
4
0
2
4
4
1
3
2
if you add all of these values up, you will get 20; ∑ = 20
[ | | means absolute value--essentially the distance of the value from 0, so a negative number is written as a positive numbers; |-3| = 3 ; |3| = 3 ]
Now you will find the mean of your deviations. The sum of all deviations (∑) = 20. The number of deviations/the number of values is 8.
So, the equation of 20 / 8 will give us the absolute mean deviation.
20/8 = Mean Absolute Deviation
Mean Absolute Deviation = 2.5
Your Mean Absolute Deviation is 2.5 [hours] .
------------------------------------------------
c)
Now you are being asked to interpret what this 2.5 indicates. It means that each student has, on average, a difference of 2.5 hours of TV watched from the mean. The Mean Absolute Deviation gives us a sense of how spread out the values of a data set are. We know that a mean absolute deviation of 0 would indicate that all values of the set are exactly identical. A mean deviation of 100 would indicate that all of the values are drastically different. So, a mean deviation of 2.5 indicates that all of the values (each student's watch hours) are fairly similar.
Step-by-step explanation:
a)
The mean of a data set is what we usually refer
to as the average. To find the mean, you add
up all of the values and divide by the number of
values.
So, to find the mean, you need to add all of the
values (the "value" is the the number hours
each student watched)
11+7+9+3+3+8+10 + 5
= 56
You have 8 seventh-grade students, so your
number of values is 8.
Dividing the sum of the values by the number
of values would then be:
56 / 8
=7
So, your mean is 7.
The amount of sports drink in a cooler during practice is modeled by the equation y = 648 -24x
y = the number of ounces in the cooler after practice
x = the number of players at practice who take drinks from the cooler
What does the SLOPE mean?
Answers
I need an answer. What is 485-352?
Answers
Answer:
133
Step-by-step explanation:
Which data set contains an outlier:
Answers
ill give brainly and 20 points
Answers
3% of a university's freshman class are majoring in Computer Science. If 231 students in the freshman class are Computer Science majors, how many students are in the freshman class?
Answers
Explanation: if 231 students are freshman’s in CS and that’s 3% we need to multiply and divide. 231x100=23100/3=7,700
First to finish 1-4 gets Brainliest
Answers
Answer:
No explanation, THIS IS ALL ABOUT SPEED
*speedrunning intensifies*
1.
B, 8x + 12
2.
G, she subtracted before adding
3.
C, 3x + 6
4.
F, Student 1 and 4
Answer:
1. B
2. G
3. C
4. F
Step-by-step explanation:
1. Soln:
4(2x+3)
=4*2x+4*3
=8x+12 ans.
2. Soln:
14-8/2+3*4
=14-4+3*4
=14-4+12
=26-4
=22 ans.
3. Soln:
=x+x+x+1+1+1+1+1+1+1+1-1-1
=3x+8-2
=3x+6 ans.
The diagram shows a sailboat. What is the approximate length of the sail shown?
RIGHT Triangle Dimensions:
Leg 1: 14 feet
Leg 2: Missing "X"
Hypotenuse: 18 feet
Answers
Answer: 8√2
Step-by-step explanation:
Plug in with the Pythagorean theorem: a^2 + b^2 = c^2
So we have 18^2=14^2 + x^2
Solve for X
X is 8√2
please help me thank you
Answers
Answer:
Unit fraction cubes is 8
Blue cube = 1/2
Step-by-step explanation:
1/2 in × 1/2 in × 1/2 in = 1/8 in³
unit fraction cubes × 1/8 in³ = 1 in³
then the unit fraction cubes is equal to 8
8 × 1/8 in³ = 1 in³
Answer:1/8 cubic inches is the volume of the cube
Step-by-step explanation:
(Will give 25 points!) Solve the system of linear equations by substitution. 3x - 2y = 12 and 4x + 2y = 16
Answers
Let
Eq1 : x - 2y = 12
Eq2 : 4x + 2y = 16
For substitution, we need to rearrange on of the equations so that we can substitute it in the other. Let's pick eq2 and rewrite it as 2y = 16 - 4x. We see that eq1 also has 2y in it, so we can plug this new version of eq2 in there.
3x - (16-4x) = 12
Now solve for x.
7x=28, so x=4
Plug that into either equation to solve for y. You get y=0.
So your answer is x=4, y=0
Answer:
i think its X squared=y squared +4
Step-by-step explanation:
thats what i got
Graphing Coordinates
Help!
I already did the drawing part I just need the numbers!
(The door that needs to be coordinated is the one on the bottom)
Answers
Answer:
(-10,0)(-5,0)(-10,-10)(-10,-5)
Step-by-step explanation:
If we count each box as one unit then we just count and if you left or down it is negative
To the nearest thousandth, what is the decimal form of 9/14
Answers
Answer:
.643
Step-by-step explanation:
just put it in the calc and round
Answer:
0.6429
Step-by-step explanation:
[tex]9\sqrt{14} = 0.64285\\round up to nearest thousandth = 0.6429[/tex]
3a: complete the table with values for x and y that makes this equation true 3x+y=15
3b: create a graph, plot these points, and find the slope of the line that goes through them.
Answers
Answer:
a. see the attachment for the table (also reproduced below)
b. slope = -3; see the attachment for a graph
Step-by-step explanation:
A table of values for the function can be filled a couple of ways. One way is to draw the graph of the equation, and read the point values from it. Another way is to solve for each of the variables, and use those equations to find the missing table values.
__
a.Solving the equation for y, we get ...
3x +y = 15
y = -3x +15 . . . . . . subtract 3x; this is "point-slope form"
For the purpose of evaluating for different values of x, we can rearrange this a bit to ...
y = 3(5 -x) . . . . factor out 3
The given table has x-values of 0, 2, 3, 6. The corresponding y-values are ...
y = 3(5 -{0, 2, 3, 6}) = 3{5, 3, 2, -1} = {15, 9, 6, -3} . . . . for x={0, 2, 3, 6}
Solving the equation for x, we get ...
y/3 = 5 -x . . . . . divide the above equation by 3
x = 5 -(y/3) . . . . . add x-(y/3)
For y-values {0, 3, 8}, the corresponding x-values are ...
x = 5 -{0, 3, 8}/3 = 5 -{0, 1, 8/3} = {5, 4, 7/3} . . . . for y={0, 3, 8}
Then our table of values is ...
[tex]\begin{array}{|c|c|c|c|c|c|c|c|}\cline{1-8}x&2&4&6&0&3&5&7/3\\y&9&3&-3&15&6&0&8\\\cline{1-8}\end{array}[/tex]
__
b.The points in the above table can be plotted, and the line drawn through them. Sometimes using the points that are farthest apart makes this easier: (0, 15) and (6, -3).
slope
When we solved for y, we had the equation in slope-intercept form. The slope is the x-coefficient in that equation:
y = -3x +15 ⇒ slope = -3
What is the answer? please
Answers
Answer:
The answer is 8
Please mark me as brainliest
Answer:
8
Step-by-step explanation:
Pythagoras theorem
A^2 +b^2 = C^2
please mark as brainliest
I'm trying to find .580 (only the 80 is repeating in the decimal) rewritten as a simplified fraction. thanks in advance, this one is really tricking me up.
Answers
Answer:
Step-by-step explanation:
assuming its repeating as .580808080 etc your answer would be 115/198 :)
Answer:
115/198
Step-by-step explanation:
.580 = .5808080
.5808080 = x
5.808080 = 10x
58.08080 = 100x
580.8080 = 1000x
1000x - 10x = 575
575 = 990x
x = 575/990
Simplify:
575/990 = 115/198
Hope this helps :)
Keiko surveyed people with cell phones.
Ages in years = a
Texts they send per day = t
He drew a best-fit line and determined its equation.
Evaluate how many texts a 15 year old would send each day according to Keiko's trend line equation.
Answers
Answer:
67.69
Step-by-step explanation:
You have your equation, t = -1.63 a + 92.14
a = age
a = 15
if you update your equation to fill in for a you get:
= -1.63 (15) + 92.14
-1.63 x 15 = -24.45
-24.45 + 92.14 = 67.69
67.69
Answer:
67.69
Step-by-step explanation:
You have your equation, t = -1.63 a + 92.14
a = age
a = 15
if you update your equation to fill in for a you get:
= -1.63 (15) + 92.14
-1.63 x 15 = -24.45
-24.45 + 92.14 = 67.69
67.69
two semicircles are used to make the shaded shape below one semiciricle has a diameter of 16 cm and the other has a diameter of 20 cm work out the area of the shaded shape
Answers
I do not have a diagram so this may be incorrect, but find the the area of the 16 diameter semicircle, find the area of the 20 diameter semicircle, and then add them both together.
Formula: A=1/2pir^2; Total area=A1+A2
Step one: A1=(1/2)pi(8^2)
A1=1/2pi(64)=32pi
Step two: A2=(1/2)pi(10^2)
A2=1/2pi(100)=50pi
Step three: 50pi+32pi= 82pi≈257.6106
Select the table that represents a linear function. (Graph them is if necessary)
Answers
Type a digit that makes this statement true.
64,638,7
3 is divisible by 3.
Answers
Answer:
The digit that makes the statement true is 2...hope this helps:)
Answer:
The digit is two.
Step-by-step explanation:
It is very simple, to find if a number is divisible by 3 specifically, you need to add all the digits together. All the digits together added up to 37, which is not divisible by 3. But if you make the missing digit 2 then the digits add up to 39 which is divisible by 3.