how many students have used all three modes of transportation? solution please​

Answers

Answer 1

Complete question is;

In a class of 40 students, 17 have ridden an airplane, 28 have ridden boat, 10 have ridden a train, 12 have ridden an airplane and a boat, 3 have ridden a train only, and 4 have ridden airplane only. Some students in the class have not ridden any of the three modes of transportation and an equal number have taken all three. How many students have used all three modes of transportation?

Answer:

4 students

Step-by-step explanation:

Let the number of students who used airplane be A

Let the number of students who used boat be B

Let the number of students who used train be C

Now, we are told that 17 rode plane.

Thus; A = 17

28 rode boat; B = 28

10 rode train; C = 10

12 rode airplane and boat; A ∩ B = 12

4 rode plane only; A' = 4

3 rode boat only; C' = 3

Total number of students; T = 40

Now, total number of students is represented by;

T = A - B - C - (A ∩ B) - (B ∩ C) - (C ∩ A) + (A ∩ B ∩ C)

We don't have (B ∩ C) and (C ∩ A).

Now, the can be derived from the expression of C' which is;

C' = C - (B ∩ C) - (C ∩ A)

C' = C - [(B ∩ C) + (C ∩ A)]

We are given C' = 3 and C = 10

Thus;

3 = 10 - [(B ∩ C) + (C ∩ A)]

10 - 3 = [(B ∩ C) + (C ∩ A)]

7 = [(B ∩ C) + (C ∩ A)]

Rearranging the total number of students equation, we now have;

T = A - B - C - (A ∩ B) - [(B ∩ C) + (C ∩ A)] + (A ∩ B ∩ C)

Where;

(A ∩ B ∩ C) is the number of students that used all three modes of transportation.

Thus, plugging in the relevant values;

40 = 17 + 28 + 10 - 12 - 7 + (A ∩ B ∩ C)

40 = 36 + (A ∩ B ∩ C)

(A ∩ B ∩ C) = 40 - 36

(A ∩ B ∩ C) = 4


Related Questions

Solve the equation 3 + x/-2 =10

Answers

3+x/-2 =10

x/-2 = 10-3

x/-2 = 7

x = 7*-2

x = -14

Answer:

x= -14

Step-by-step explanation:

Find 8% of $40 answers with the nearest penny

Answers

Answer:

3.20

Step-by-step explanation:

Sorry i had the same question and i asked the teacher if he could help and he did but he sorta juts gave me the answer so cant really give an explanation so sorry.

find the value of x ​

Answers

Answer:

141°

 

Step-by-step explanation:

  The angle given is 39°;

 

Since this problem deals with angles in a transversal, it is easy to solve.

Now;

       Angle given is a corresponding angle to the angle a;

  Corresponding angles are equal; so angle a  = 39°

Also,

   angle a is corresponding to angle b;

         angle b  = 39°

So, angle b and x are on a straight line;

           b  + x  = 180

                  x = 180 - 39  = 141°

 

What is the value of 4(x - 2)(x + 3) + 7(x - 2)(x - 5) - 6(x - 3)(x - 5) when x = 5?

Answers

Answer:

96

Step-by-step explanation:

Put x = 5 to the expression 4(x - 2)(x + 3) + 7(x - 2)(x - 5) - 6(x - 3)(x - 5)

4(5 - 2)(5 + 3) + 7(5 - 2)(5 - 5) - 6(5 - 3)(5 - 5)

= 4(3)(8) + 7(3)(0) - 6(2)(0) = 96 + 0 - 0 = 96

You measure the mass of a book and it’s 420.0890g how many significant digits are in the measurement

Answers

9514 1404 393

Answer:

  7

Step-by-step explanation:

All of the digits in the given number are significant. There are 7 significant digits.

__

Comment on other cases

When there are non-zero digits to the left of the decimal point in a number with a decimal point, all of the digits are significant.

When there are no non-zero digits to the left of the decimal point, leading zeros are not significant. All digits following the leading zeros are significant.

In a number with no decimal point, the leading and trailing zeros are not significant.

If the number is written in scientific notation, all digits of the mantissa are significant. (This can be a way to ensure the correct number of significant digits is known in a number with trailing zeros.)

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.

Algebra Find the missing number.
12. 34 – 8 = 35 -
n 5
Topic 6 Lesson 5

Answers

The answer is 9 because 34-8 = 26 so then if you 35-26= 9 then add 9+26=35

Can someone please tell me answerrrrrrr

Answers

Answer: B

Steps: $208.08

PLz mark brainliest:)

What is the value of f(0) on the following graph?
y = f(x)

Answers

Answer:

f(0)=2

Step-by-step explanation:

As the graph states y=f(x), so to solve you must find the value of y when x=0 (because that is what is in the paratheses). So go to the place on the graph where x equals 0 then follow up until you intersect with the function. If x=0 then y=2.

What is wrong with the picture? Show work.

Answers

Answer:

The mistake is in the angles

Either both should be 69° or 70°

Hope this helps you Stay happy and safe Do mark as brainliest ✌️

Restless Leg Syndrome and Fibromyalgia
People with restless leg syndrome have a strong urge to move their legs to stop uncomfortable sensations. People with fibromyalgia suffer pain and tenderness in joints throughout the body. A recent study indicates that people with fibromyalgia are much more likely to have restless leg syndrome than people without the disease. The study indicates that, for people with fibromyalgia, the probability is 0.33 of having restless leg syndrome, while for people without fibromyalgia, the probability is 0.03. About 2% of the population has fibromyalgia. Create a tree diagram from this information and use it to find the probability that a person with restless leg syndrome has fibromyalgia.

Answers

Answer:

The probability that a person with restless leg syndrome has fibromyalgia is 0.1833.

Step-by-step explanation:

Denote the events as follows:

F = a person with fibromyalgia

R = a person having restless leg syndrome

The information provided is as follows:

P (R | F) = 0.33

P (R | F') = 0.03

P (F) = 0.02

Consider the tree diagram attached below.

Compute the probability that a person with restless leg syndrome has fibromyalgia as follows:

[tex]P(F|R)=\frac{P(R|F)P(F)}{P(R|F)P(F)+P(R|F')P(F')}\\\\=\frac{(0.33\times 0.02)}{(0.33\times 0.02)+(0.03\times 0.98)}\\\\=0.183333\\\\\approx 0.1833[/tex]

Thus, the probability that a person with restless leg syndrome has fibromyalgia is 0.1833.

please i need some help due in some mins

Answers

the answer is a 0.1 hope this helped

Una empresa dedicada a la venta de buzos en La Victoria, dispone para la confección de 500 m de tela algodón y 520 m de tela poliéster. Cada pantalón del buzo necesita 1 m de algodón y 2 m de poliéster; para cada casaca se necesitan 2 m de algodón y 1 m de poliéster. La ganancia por cada pantalón es de S/ 9 y la ganancia por cada casaca es de S/ 12. El fabricante sabe que sus máquinas en promedio demoran 4 minutos en confeccionar un pantalón y 10 minutos en confeccionar una casaca; él promete entregar un pedido en una semana trabajando sus máquinas de lunes a viernes 8 horas diarias.
a) Modele la función objetivo y elabore el SIL para las restricciones.
b) ¿Cuánto será el pedido máximo de buzos (casaca y pantalón) que podrá entregar en una semana de trabajo? ¿Cuánto será su ganancia máxima?

Answers

Answer:

x₁ = 60 pantalón de buzo

x₂ = 0  casaca

z(max) = 540 unidades de monedas

Step-by-step explanation:

El problema se resolverá usando un software de solución de problemas de optimización (integer linear programming solver)

z = 9*x₁ + 12*x₂       a maximizar

Sujeto a:

1) Primera restricción disponibilidad de algodón 500 m de tela

1*x₁ + 2*x₂   ≤ 500

2)Segunda restricción disponibilidad de poliester  520 m de tela

2*x₁ + 1*x₂ ≤ 520

3) Tercera restricción  tiempo disponible 8 h/d * 5 d/s = 40 h/s

40 * 60  = 240 minutos disponibles, entonces

4*x₁ + 10*x₂  ≤ 240

4)Restricciones generales  x₁ ≥ 0 ;   x₂ ≥ 0 ambas solo deben tomar valores enteros

Con el uso del calculador en línea se obtiene:

x₁ = 60

x₂ = 0

z(max) = 540

Find the coordinates of the midpoint of LB if L(8, 5) and B(-6, 2)

Answers

Answer:

The coordinates of the midpoint of LB are (1, 3.5)

Step-by-step explanation:

The rule of the midpoint of a segment its endpoints are (x1, y1) and (x2, y2) is [tex]M=(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]

Let us use this rule to solve the question

∵ M is the midpoint of segment LB

∵ The coordinates of point L are (8, 5)

x1 = 8 and y1 = 5

∵ The coordinates of point B are (-6, 2)

x2 = -6 and y2 = 2

→ Substitute these values in the rule of the mid point above

∵ [tex]M=(\frac{8+-6}{2},\frac{5+2}{2})[/tex]

→ Remember (+)(-) = (-)

∴ [tex]M=(\frac{8-6}{2},\frac{7}{2})[/tex]

∴ [tex]M=(\frac{2}{2},\frac{7}{2})[/tex]

M = (1, 3.5)

The coordinates of the midpoint of LB are (1, 3.5)

HELP WITH MATH!!! 20 points
the questions are solving systems by substitution

Answers

Answer: 1. 2x-3y=-1 y=x-1 2. y=6x-11 -2-3y=-7 3. y=3x+5 5x-4y=-3

#1. 2x-3y=-1 and y=x-1

#2. y=6x-11 and -2x-3y=-7

#3. y=-3x+5 and 5x-4y=-3

The length of a table is 110 cm to the nearest cm
Write down the error interval using inequalities.

10 points for right answer

Answers

Answer: they didn’t give the exact answer.

Step-by-step explanation: they rounded to the nearest.

Can someone plz explain to me how to do this !? Geometry

Answers

The scale factor is 3

if you look at the graph its y3 x3 the larger one is y9 x9 if you divide the two you get 3

can you please give brainliest

Paula walked 4.5 miles. How many kilometers did Paula walk? I mile = 1.61 kilometers

Answers

Answer:

2.79 kilometers

Step-by-step explanation:

4.5/1.61

I have no idea how to do this

Answers

Answer:

it's ok!! thats why you have us!! we're here to help!

13/z

have a nice day!! also hope this helps!

Step-by-step explanation:

Answer:

13 on top

Z on the bottom

Step-by-step explanation:

6 plus 7 is 13

Maura runs 5 miles in 1.25 hours. Ava runs 3 miles in 50 minutes or 0.83¯ hour.
Who runs faster? Use the drop-down menu to show your answer.

Answers

Answer:

Ava

Step-by-step explanation:

because we multiply by 3 miles, 50 minutes, 0.83

and you get 124.5

its not maura because if you multiply 5 miles, by 1.25 hours you get 6.25

sorry if wrong! hope this helps!


O SYSTEMS OF EQUATIONS AND MATRICES
Solving a word problem using a 3x3 system of linear equations....
Over the last 3 evenings, Latoya received a total of 96 phone calls at the call center. The second evening, she received 2 times as many calls as the third
evening. The third evening, she received 8 fewer calls than the first evening. How many phone calls did she receive each evening?

Answers

Answer:

Find the midpoint of the line segment joining the points ​R(​,​) and ​S(​,​).

Step-by-step explanation:

If lim f(x)=5 g(x)=0 and h(x)=-2 then find (3h/2f+g)(x)

Answers

Answer:

B

Step-by-step explanation:

edg 2021 unit test review

According to a survey, 74% of households said that they have never purchased organic fruits or vegetables. Suppose that this result is true for the current population of households. a. Let x be a binomial random variable that denotes the number of households in a random sample of 10 who have never purchased organic fruits or vegetables. What are the possible values that x can assume

Answers

Complete Question

According to a survey, 74% of households said that they have never purchased organic fruits or vegetables. Suppose that this result is true for the current population of households. a. Let x be a binomial random variable that denotes the number of households in a random sample of 10 who have never purchased organic fruits or vegetables. What are the possible values that x can assume? Integers to . b. Find to 3 decimal places the probability that exactly 6 households in a random sample of 10 will say that they have never purchased organic fruits or vegetables. Use the binomial probability distribution formula. Probability

Answer:

a

The possible value of x is 0, 1 ,2,3,4,5,6,7,8,9,10

b

[tex]P(X = 6) =   0.158 [/tex]

Step-by-step explanation:

From the question we are told that

 The proportion that stated that they have not purchased organic fruits or vegetables is [tex]p =0.74[/tex]

   The sample size is  n = 10

The possible value x can take is  0, 1 ,2,3,4,5,6,7,8,9,10

Generally the probability that exactly 6  households in a random sample of 10 will say that they have never purchased organic fruits or vegetables is mathematically represented as

      [tex]P(X = 6) =  ^nC_6 * p^{6}* (1-p)^{n-6}[/tex]

Here C denotes combination

So

        [tex]P(X = 6) =  ^{10}6 * (0.74)^{6}* (1-0.74)^{10-6}[/tex]

=>    [tex]P(X = 6) =   0.158 [/tex]

Your cell phone plan is $40 per month plus $0.10 per minute for each minute over 300 minutes of call time. Your cell phone bill came to $110.00. How many mintes did you go over your alloted timed?

Answers

i have no idea :) sooooo yea

a b c d or d helpp pleas!

Answers

Answer:

The answer is B

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The rates of b, c, d make sense in relation to each other. A is the only one dealing with decimal points; whilst the other numbers are dealing with the same x and y values just different sized graphs.

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Answers

Answer:

it is already an equation

Step-by-step explanation:

Answer:

Already and equation!

Step-by-step explanation:

PLEASE HELP ASAP

can you help me please​

Answers

so x is equal to 40 so the length of M and N is 140 and no is 70 with the total length being 210 hope I helped could I get a brainliest!!

What are the angles x?

Answers

Answer:

TOP LEFT TRIANGLE:  x=28°

BOTTOM LEFT TRIANGLE:  x=90°

TRIANGLE ON THE RIGHT:  x=34°

Step-by-step explanation:

TOP: the triangle on the right has 90 and 39.  That makes the third one 51. It’s supplement is 129.  129+23=152. 180-152=28. X=28°

BOTTOM: 180-119=61.  61+29=90.  180-90=90.  X=90°

RIGHT: right triangle has 90 and 70.  90+70=160. 180-160=20

180-70-41-15-20=34°

You decide to purchase a bond for $500. It pays 5% simple interest per year and matures in 5 years. How much interest will you earn once the bond matures? Round your answer to the nearest dollar.
Do NOT round until you have calculated your final answer.

Answers

Answer:

$625

Step-by-step explanation:

You start with $500

The interest per year is 5% or 500 x 0.05 = $25

If it matures 5 years and each year has an increase of $25 then

Year 1 - $525

Year 2 - $550

Year 3 - $575

Year 4 - $600

Year 5 - $625

Answer:

Step-by-step explanation:

We express the interest rate r in decimal form, so we have r=5%=5100=0.05. The principal is P=500 and the time in years is t=5. So, the interest is I=Prt=(500)(0.05)(5)=$125. The interest earned is $125.

Alice was rock climbing. She climbed to a height of 22 feet. Next, she descended 8 feet. Then, she ascended another 34 feet. What was
Alice's elevation?

Answers

Answer:

48 brainlest plz

Step-by-step explanation:

22-8=14

14+34=48

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