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3 years ago

6

To encourage public transportation, Ronny wants to give some friends envelopes with bus tickets and subway tickets in them. If h

e has 18 bus tickets and 12 subway tickets to split equally among the envelopes and wants no tickets left over, what is the greatest number of envelopes Ronny can make?

1 answer:

Blizzard [7]3 years ago

6 0

Answer:

6 enevlopes

Step-by-step explanation:

18 divided by 6 equals 3

12 divided by 6 equals 3

hope this helps you :)

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In a group of 40 people, 27 can speak English and 25 can speak Spanish. How many can speak

Svetradugi [14.3K]

$\qquad {\: \:\bigstar \: {\underline{\overline{\boxed{\bf{Information \: provided \: with \: us }}}}}\: \bigstar}$

➻ In a group of 40 people, 27 can speak English and 25 can speak Spanish.

$\qquad {\: \:\bigstar \: {\underline{\overline{\boxed{\bf{What \: we \: have \: to \: find ? }}}}}\: \bigstar}$

➻ The required number of people who can speak both English and Spanish .

$\qquad {\: \:\bigstar \: {\underline{\overline{\boxed{\bf{Assumption}}}}}\: \bigstar}$

<u>Consider</u> ,

➻ A → Set of people who speak English.

➻ B → Set of people who speak Spanish

➻ A∩B → Set of people who can speak both English and Spanish

$\qquad {\: \:\bigstar \: {\underline{\overline{\boxed{\bf{Given}}}}}\: \bigstar}$

➻ n (A) = 27

➻ n (B) = 25

➻ n (A∪B) = 40

➻ n(A∩B) = ?

$\qquad {\: \:\bigstar \: {\underline{\overline{\boxed{\bf{Now}}}}}\: \bigstar}$

➻ n(A∪B) = n(A) + n (B) - n(A∩B)

➻ 40 = 27 + 25 - n (A∩B)

➻ 40 = 52 - n (A∩B)

➻ n (A∩B) = 52 - 40

➻ ∴ n (A∩B) = 12

$\qquad {\: \:\bigstar \: {\underline{\overline{\boxed{\bf{Therefore}}}}}\: \bigstar}$

∴ Required Number of persons who can speak both English and Spanish are <u>12 .</u>

━━━━━━━━━━━━━━━━━━━━━━

$\qquad {\: \:\bigstar \: {\underline{\overline{\boxed{\bf{Verification}}}}}\: \bigstar}$

➻ n(A∪B) = n(A) + n (B) - n(A∩B)

➻ 40 = 27 + 25 - 12

➻ 40 = 52 - 12

➻ 40 = 40

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━━━━━━━━━━━━━━━━━━━━━━

6 0

2 years ago

Please help me i need to solve for RS

Sonbull [250]

Answer:

<h2> RS = 47</h2>

Step-by-step explanation:

RV=VU and SW=WT ⇒ $VW=\dfrac{RS+UT}{2}$

So:

$3x+5=\dfrac{2x+15+6x-37}{2}\\\\3x+5=\dfrac{8x-22}{2}\\\\3x+5=4x-11\\^{\qquad-5\qquad-5}\\3x=4x-16\\^{-4x\qquad-4x}\\-x=-16\\^{\div(-1)\quad\div(-1)}\\x=16\\\\RS=2x+15=2\cdot16+15=32+15=47$

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3 years ago

Twenty-five randomly selected students were asked the number of movies they watched the previous week. The results are as follow

guajiro [1.7K]

Answer:

a) x = 1.52

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Step-by-step explanation:

We have that:

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9 students watched 1 movie.

5 students watched 2 movies.

5 students watched 3 movies.

1 student watched 4 movies.

(a) Find the sample mean x.

Sum divided by the number of students. So

$x = \frac{5*0 + 9*1 + 5*2 + 5*3 + 1*4}{5 + 9 + 5 + 5 + 1} = \frac{38}{25} = 1.52$

(b) Find the approximate sample standard deviation, s.

Standard deviation of the sample.

Square root of the sum of the squares of the values subtracted from the mean, divided by the sample size subtracted by 1. So

$s = \sqrt{\frac{5*(0-1.52)^2 + 9*(1-1.52)^2 + 5*(2-1.52)^2 + 5*(3-1.52)^2 + 1*(4-1.52)^2}{24}} = \sqrt{\frac{32.24}{24}} = 1.16$

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3 years ago

What is the slope of the line graphed on the coordinate plane?

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Rise: 8 Run: -2

8/2

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3 years ago

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A rectangle is inscribed in a right isosceles triangle, such that two of its vertices lie on the hypotenuse, and two other on th

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Answer:

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Part 2) The base is $7.5\ in$ and the height is $18.75\ in$

Step-by-step explanation:

case 1) Right isosceles triangle of the left

Let

x------> the base of the rectangle

y----> the height of the rectangle

Remember that

In a right isosceles triangle the lengths of the legs of the triangle is the same

$y+x+y=45$

$2y+x=45$ ----> equation A

$\frac{x}{y} =\frac{5}{2}$

$x=2.5y$ -----> equation B

substitute equation B in the equation A

$2y+2.5y=45$

$4.5y=45$

$y=10\ in$

Find the value of x

$x=2.5(10)=25\ in$

case 2) Right isosceles triangle of the right

Let

x------> the base of the rectangle

y----> the height of the rectangle

Remember that

In a right isosceles triangle the lengths of the legs of the triangle is the same

$y+x+y=45$

$2y+x=45$ ----> equation A

$\frac{y}{x} =\frac{5}{2}$

$y=2.5x$ -----> equation B

substitute equation B in the equation A

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$y=2.5(7.5)=18.75\ in$

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3 years ago