Mathematics College

What's Ta
Try solving the following problem
In a group of 120 students, 68 had ridden a bus, 78 had ridden the LRT. 33
had ridden a jeep, while 40 had ridden both the bus and the LRT, 20 had ridden
the bus and the jeep, 19 had ridden the LRT and the jeep and 15 had ridden the
bus, the LRT and the jeep.
a. How many had ridden the bus only?
b. How many had ridden the LRT only?
c. How many had ridden the jeep only?
d. How many did not ride on any of the three modes of transportation?

Answers

Answer 1

Answer:

A.) bus only = 23

B.) LRT only = 34

C.) Jeep only = 9

D.) 5

Step-by-step explanation:

Let :

B = bus ; J = Jeep ; L = LRT

KINDLY CHECK ATTACHED PICTURE FOR DETAILED EXPLANATION

What's TaTry Solving The Following ProblemIn A Group Of 120 Students, 68 Had Ridden A Bus, 78 Had Ridden

Answer 2

A set is a group of related item.

34 had ridden on LRT only23 had ridden on bus only9 had ridden on jeep only5 did not ride on any

Let:

[tex]Total =120[/tex]

[tex]B = 68 \to Bus[/tex]

[tex]L = 78 \to LRT[/tex]

[tex]J =33 \to Jeep[/tex]

[tex]n(B\ n\ L) = 40[/tex]

[tex]n(B\ n\ J) = 20[/tex]

[tex]n(L\ n\ J) = 19[/tex]

[tex]All = 15[/tex]

(a) Bus only

This is calculated using:

[tex]B\ only = B - n(B\ n\ L) - n(B\ n\ J) + All[/tex]

So, we have:

[tex]B\ only = 68 - 40 - 20 + 15[/tex]

[tex]B\ only = 23[/tex]

(b) LRT only

This is calculated using:

[tex]L\ only = L - n(B\ n\ L) - n(L\ n\ J) + All[/tex]

So,

[tex]L\ only = 78 - 40 - 19 + 15[/tex]

[tex]L\ only = 34[/tex]

This is calculated using:

[tex]J\ only = J - n(B\ n\ J) - n(L\ n\ J) + All[/tex]

So, we have:

[tex]J\ only = 33 - 20 - 19 + 15[/tex]

[tex]J\ only = 9[/tex]

(d) None

Let x represents those that took none of the means of transport.

So, we have:

[tex]Total = B\ only + J\ only + L\ only + [n(B\ n\ L) -All] +[n(B\ n\ J) -All] +[n(L\ n\ J) -All] + All + x[/tex]

This gives

[tex]120= 34 + 23 + 9 + [40 -15] +[20 -15] +[19 -15] + 15 + x[/tex]

[tex]120= 115 + x[/tex]

Collect like terms

[tex]x = 120 - 115[/tex]

[tex]x = 5[/tex]

See attachment for the Venn diagram of the set.

Related Questions

PLSSSS HELLPPPP MEEEEEEE ASAPPPP I WIILL GIVE BRAINLIEST!!!!!!!!! PLS SHOW WORK STEP BY STEP

Answers

Answer:

y = -3x + 3

Step-by-step explanation:

Slope = -3

y-intercept = 3

Substitute values into slope intercept form :

y=mx + b

Where :

m= Slope

b = y-intercept

[tex]y = - 3x + 3[/tex]

A florist must make 5 identical
bridesmaid bouquets for a wedding. The budget is
$160, and each bouquet must have 12 flowers. Roses
cost $2.50 each, lilies cost $4 each, and irises cost
$2 each. The florist wants twice as many roses as the
other two types of flowers combined.

Answers

Answer:

A. 40x + 10y + 10z = $160

B. 8 Roses, 2 lilies and 2 irises

1. 20x + 5y + 5z = $80

2. 4x + y + z = $16

3. 8x + 2y + 2z = $32

Step-by-step explanation:

Cost for each flower = $160/5 = $32

So we have $32 for each bouquet consisting of 12 flowers each.

Roses = x = $2.50 each

lilies = y = $4 each

irises = z = $2 each

8x + 2y + 2z = $32

8($2.50) + 2($4) + 2($2) = $32

$20 + $8 + $4 = $32

$32 = $32

a. Maximum budget is $160

40x + 10y + 10z = $160

40($2.50) + 10($4) + 10($2) = $160

$100 + $40 + $20 = $160

$160 = $160

b. From above

8x + 2y + 2z = $32

8 Roses, 2 lilies and 2 irises

c. No. There are other solutions If total cost is not limited

1. 20x + 5y + 5z

20($2.50) + 5($4) + 5($2)

$50 + $20 + $10

= $80

2. 4x + y + z

4($2.50) + $4 + $2

$10 + $4 + $2

= $16

3. 8x + 2y + 2z

8($2.50) + 2($4) + 2($2)

$20 + $8 + $4

= $32

Divide.
636-3
The quotient is
and the remainder is

Answers

Answer:

212

Step-by-step explanation:

3 goes into 6 = 2 times

3 goes into 3 = 1 time

3 goes into 6 = 2 times

2 → 1 → 2 = 212

Hope this helps .

P. S pls mark as brainliest

Change 3.5 decimal into a percent

Answers

Like out of 100? Then it would be 3.5%

The answer you're looking for is: 350%

(Tell me if i'm wrong please)

Triangle ABC is shown below.
What is the length of line segment AC?
A
A
O 7
O 9
2x
3x-7
O 14
O 18
B
4x - 10
с

Answers

Answer:

the answer is 14 C

Step-by-step explanation:

just took the test?

Two angles form a linear pair. The measure of one angle is 6 less then the measure of the other angle. Find the measure of each angle

Answers

Answer: one angle would be 50 degrees while the other would be 130 degrees.

Step-by-step explanation:

Whats the function to this math prob

Answers

Answer:

some reason i cant see the image is this just me

Step-by-step explanation:

Y is the vertical distance. The top of the curve is at y = 4 and the bottom of the curve is at y = -5, so the function would be between y -5 and y 5 which is written as :

D. -5 <= y <= 5

How do you solve this? Without going into anything to complicated as this should be Year 10 maths

Answers

Given : ABCD is a square with each side 5cm .

To Find : The area of the shaded region .

Solution : On observing the figure we can see two quadrants , quadrant ADC & quadrant ABC .

If we join A to C , then it will be common for triangles ADC & ABC . And they will be congruent by SSS congruence condition.

Therefore the area of both quadrants will also be equal . Now we can find area of quadrant as ;

[tex]\large\boxed{\red{\bf Area_{quadrant}=\dfrac{\pi r^2}{4}}}[/tex]

Here radius will be equal to 5cm .

⇒ Area = πr² / 4 .

⇒ Area = π (5cm)² / 4 .

⇒ Area = 22/7 × 25 × 4 cm².

⇒ Area = 19.64 cm² .

So , total area of both quadrants = 39.28 cm² .

Also , area of square will be :

[tex]\large\boxed{\bf{\red{Area_{square}=(side)^2}}}[/tex]

⇒ Area = 5cm × 5cm .

⇒ Area = 25 cm².

Now , subtract area of one quadrant from the area of square = 25cm² - 19.64 cm² = 5.36 cm².

Similarly area of other white region = 5.36cm² .

And the areas sum will be = 5.36cm² × 2 = 10.72cm² .

Now , from the figure it's clear that ,

⇒ Area of unshaded region + Area of shaded region = 25cm².

⇒ 10.72cm² + ar( Shaded region ) = 25cm².

⇒ ar ( Shaded region ) = 25cm² - 10.72cm².

⇒ ar ( Shaded region ) = 14.28 cm².

Hence the area of shaded region is 14.28 cm².

[tex]\large\boxed{\red{\bf Answer = 14.28cm^2}}[/tex]

Picture is it............

Answers

In this triangle the three interior angles are = ∠82° , ∠54° and ∠x .

Then ;

∠82° + ∠54° + ∠x = 180° ( under angle sum property which says that the sum of the three interior angles of a triangle is equal to 180° )

= 136 ° + x = 180

= x = 180 - 136

= x = 44°

∠x and ∠y will sum up to 180° as they are a linear pair .

= 44° + y = 180

= y = 180 - 44

= y = 136°

Since ∠y and ∠z are vertically opposite angles their angle measure will be equal . Which means ;

= ∠y = ∠z

= 136° = ∠z

= ∠z = 136°

Therefore :-

The value of x = 44°

Suppose A is a 5x7 matrix. How many pivot columns must A have if its columns span R^5? Why?

a. The matrix must have nothing pivot columns. If A had fewer pivot columns, then the equation A would have only the trivial solution.
b. The matrix must have nothing pivot columns. The statements "A has a pivot position in every row" and "the columns of A span " are logically equivalent.
c. The matrix must have nothing pivot columns. Otherwise, the equation A would have a free variable, in which case the columns of A would not span .
d. The columns of a 57 matrix cannot span because having more columns than rows makes the columns of the matrix dependent

Answers

Answer:

The answer is "Option B".

Step-by-step explanation:

In the given choices there is some mistake so, the correct choice can be defined in the attached file. please find it.

In the given question, If the column of [tex]5 \times 7[/tex] matrix, and the A span is equal to [tex]R^5[/tex], and then the value of A has a pivot in each row, that's why in each pivot its position in the different columns of A has the five pivot columns, that's why the choice B is correct.

If the volleyball team washes 10 more cars, then they will have met their overall goal of
washing 60 cars to raise money for their season. Let c represent the number of cars that
the volleyball team has washed so far. Which of the following equations can be used to
solve for c?

Answers

Answer:

Step-by-step explanation:

60-10=50

they washed 50 cars.

NEED HELP WITH MATH! Will Give Brainliest! Image is below.

Answers

Answer:

Step-by-step explanation:

Please help me!!! ASAP!

Answers

Option C

Olivia paid $ 15683.28 after 8 years

2/3 divided by ? = 6/8 ASAP

Answers

Answer: 1/72 in decimal form 0.01389

Step-by-step explanation:

Answer:

im pretty sure it is 8/9

Step-by-step explanation:

6/8 x 8/9 =2/3

15 men can dig a ditch in 10 days, how many day
Will 10men take working at the same rate

Answers

Answer:

If 10 men dig a ditch in 12 days .

Total man-days required to dig the ditch

= 10 men × 12 days

= 120 man-days

how long would 15 men take to dig it?

No of days required to finish the job by 15 men

= 120 men-days / 15 men

= 8 days

Answer: 8 days will be required to finish the job by 15 men

Step-by-step explanation:

Hope this helps u

Crown me as brainliest:)

Translate subtract 10 from r, then subtract 4 from the result

Answers

Answer:

reste 10 de r, luego reste 4

Step-by-step explanation:Lets say the result is x x is a letter driving from spain so x=Spanish so translating that sentence to spanish is easy

Answer:

-r+6

Step-by-step explanation:

What is 86.929 rounded to the nearest tenth ?

Answers

Answer:

86.9

Step-by-step explanation:

This is because after the decimal point, it goes to the tenths place and then the thousands place, therefore, if you round it, it would be 86.9.

x=4/9,y=1/2, and z=3/5 6wy-3z

Answers

Answer: The answer would be - 7/5 or (-0.46)

Plug in the numbers that each letter equals. So you get 6(4/9)(1/2) - 3(3/5). Then you just simplify.

PLEASE HEELP
Match the inverse, converse, contrapositive, and biconditional with their sentences.

Conditional Statement: If two angles are congruent, then they have the same measure.

Question 1 options:

converse

biconditional

inverse

contrapositive

1.
If two angles have the same measure, then they are congruent.

2.
If two angles are not congruent, then they do not have the same measure.

3.
If two angles do not have the same measure, then they are not congruent.

4.
Two angles are congruent if and only if they have the same measure.

Answers

Answer:

First, let's define each case:

A conditional statement is:

If P then Q.

P = hypothesis

Q = conclussion.

Converse: If Q then P.

Biconditional: P if and only if Q.

Inverse: If not P, then not Q.

Contrapositive: If not Q, then not P.

Our statement is:

"If two angles are congruent, then they have the same measure."

P = two angles are congruent.

Q = they have the same measure.

Now let's look at the options:

1) If two angles have the same measure, then they are congruent.

or: if Q then P, this is converse.

2) If two angles are not congruent, then they do not have the same measure.

or: If not P, then not Q, this is inverse.

3) If two angles do not have the same measure, then they are not congruent.

or: If not Q, then not P, this is the contrapositive.

4) Two angles are congruent if and only if they have the same measure.

or: P if and only if Q, this is biconditional.

A process is normally distributed and in control, with known mean and variance, and the usual three-sigma limits are used on the control chart, so that the probability of a single point plotting outside the control limits when the process is in control is 0.0027. Suppose that this chart is being used in phase I and the averages from a set of m samples or subgroups from this process are plotted on this chart. What is the probability that at least one of the averages will plot outside the control limits when m = 5? Repeat these calculations for the cases where m = 10, m = 20, m = 30, and m = 50.

Required:
Discuss the results that you have obtained.

Answers

Answer:

The solution to the issue is outlined in the following portion of the summary.

Step-by-step explanation:

The given value is:

p = 0.0027

When m = 5,