seventy of myra’s classmates are traveling by the bus to a football game in another town. they hired 2 buses, but there were only 64 seats. the remaining 6 students had to travel in a separate van the equation 2b+6=70 represents the given scenario. what does b represent

Answer:

1,968

Step-by-step explanation:

Let x₁ and x₂, y₁ and y₂, and z₁ and z₂ represent the 3 pairs of siblings, and let;

Set X represent the set where the siblings x₁ and x₂ sit together

Set Y represent the set where the siblings y₁ and y₂ sit together

Set Z represent the set where the siblings z₁ and z₂ sit together

We have;

Where the three siblings don't sit together given as [tex]X^c[/tex]∩[tex]Y^c[/tex]∩[tex]Z^c[/tex]

By set theory, we have;

[tex]\left | X^c \cap Y^c \cap Z^c \right |[/tex] = [tex]\left | X^c \cup Y^c \cup Z^c \right |[/tex] =  [tex]\left | U \right | - \left | X \cup Y \cup Z \right |[/tex]

[tex]\left | U \right | - \left | X \cup Y \cup Z \right |[/tex] = [tex]\left | U \right | - \left (\left | X \right | + \left | Y\right | + \left | Z\right | - \left | X \cap Y\right | - \left | X \cap Z\right | - \left | Y\cap Z\right | + \left | X \cap Y \cap Z\right | \right)[/tex]

Therefore;

[tex]\left | X^c \cap Y^c \cap Z^c \right | = \left | U \right | - \left (\left | X \right | + \left | Y\right | + \left | Z\right | - \left | X \cap Y\right | - \left | X \cap Z\right | - \left | Y\cap Z\right | + \left | X \cap Y \cap Z\right | \right)[/tex]

Where;

[tex]\left | U\right |[/tex] = The number of ways the 3 pairs of siblings can sit on the 7 chairs = 7!

[tex]\left | X\right |[/tex] = The number of ways x₁ and x₂ can sit together on the 7 chairs = 2 × 6!

[tex]\left | Y\right |[/tex] = The number of ways y₁ and y₂ can sit together on the 7 chairs = 2 × 6!

[tex]\left | Z\right |[/tex] = The number of ways z₁ and z₂ can sit together on the 7 chairs = 2 × 6!

[tex]\left | X \cap Y\right |[/tex] = The number of ways x₁ and x₂ and y₁ and y₂ can sit together on the 7 chairs = 2 × 2 × 5!

[tex]\left | X \cap Z\right |[/tex] = The number of ways x₁ and x₂ and z₁ and z₂ can sit together on the 7 chairs = 2 × 2 × 5!

[tex]\left | Y \cap Z\right |[/tex] = The number of ways y₁ and y₂ and z₁ and z₂ can sit together on the 7 chairs = 2 × 2 × 5!

[tex]\left | X \cap Y \cap Z\right |[/tex] = The number of ways x₁ and x₂,  y₁ and y₂ and z₁ and z₂ can sit together on the 7 chairs = 2 × 2 × 2 × 4!

Therefore, we get;

[tex]\left | X^c \cap Y^c \cap Z^c \right |[/tex] = 7! - (2×6! + 2×6! + 2×6! - 2 × 2 × 5! - 2 × 2 × 5! - 2 × 2 × 5! + 2 × 2 × 2 × 4!)

[tex]\left | X^c \cap Y^c \cap Z^c \right |[/tex] = 5,040 - 3072 = 1,968

The number of ways where the three siblings don't sit together given as [tex]\left | X^c \cap Y^c \cap Z^c \right |[/tex]  = 1,968

Answer:

Yes

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

Point (1, 4)

y = 8x - 4

Step 2: Find

yes.

you just have to check like this: 1 is x and 4 is y.

4 = 8(1) - 4

4 = 8 - 4

4 = 4

hope it helps.

Also, I think that Brainly is an awesome app, but there's an app which is doing great work for me in maths, named Gauthmath. I will suggest it. Video concepts and answers from real tutors.

Answer:

3m-8n

Step-by-step explanation:

Set up an equation:

(5m-3n)-(2m+5n) = ?

Solve:

   5m-3n

-  2m+5n

   3m-8n

Hope this helps!

Answer:

[tex]q=8.5[/tex]

Step-by-step explanation:

The ratio of the side lengths (AB) and (BC) is given. One is also given an expression for the side lengths of each of these sides. Set up a proportion to describe this scenario, then solve using cross products;

[tex]\frac{AB}{BC}=\frac{3}{4}[/tex]

Substitute,

[tex]\frac{60}{10q+15}=\frac{3}{4}[/tex]

Cross products,

[tex]\frac{60}{10q+15}=\frac{3}{4}[/tex]

[tex](60)(4)=(10q+15)(3)\\\\240=30q+45[/tex]

Inverse operations,

[tex]240=30q+45\\\\195=30q\\\\8.5=q[/tex]

Mean:

E[Y] = E[3X₁ + X₂]

E[Y] = 3 E[X₁] + E[X₂]

E[Y] = 3µ + µ

E[Y] = 4µ

Variance:

Var[Y] = Var[3X₁ + X₂]

Var[Y] = 3² Var[X₁] + 2 Covar[X₁, X₂] + 1² Var[X₂]

(the covariance is 0 since X₁ and X₂ are independent)

Var[Y] = 9 Var[X₁] + Var[X₂]

Var[Y] = 9σ² + σ²

Var[Y] = 10σ²

Answer:

I believe the answer is 24.

Step-by-step explanation:

hope it helps.

Answer:

A. 24.2°

Step-by-step explanation:

I'm correct if I'm rwong

Answer:

1=85

2=10

3=108

Step-by-step explanation:

Number 1: Calculate each angle...and you know a straight line is 180°. N the interior sum of a quadrilateral is always 360°.

Number2: Use corresponding, alternate and interior angles method. It will help

Number 3: It's just about solving the interior sum of the pentagon

Answer:

2. 10 degrees

3. 108 degrees

Step-by-step explanation:

sorry I reposted it because the previous answer was deleted and plz mark me as a brainliest.

Answer:

40°

Step-by-step explanation:

As sum of angles of the triangle is 180°

therefore the third angle will be 180 -( 75 + 65)=40°

x=40°= vertically opposite angle

Answer:

x = 40°

Step-by-step explanation:

a + 65 + 75 = 180  {Angle sum property}

a + 140 = 180

     a = 180 - 140

    a = 40

x = a  {Vertically opposite angles}

x = 40°

Answer:

D.supplementary angles

Step-by-step explanation:

81+99=180

Answer:  15 = -i & 12=1

use the pattern : i, -1, -i, 1

Step-by-step explanation:

i = [tex]\sqrt{-1}[/tex]

[tex]i^{2}[/tex] = [tex]\sqrt{-1}[/tex]

[tex]i^{3}[/tex] = [tex]\sqrt{-1}[/tex]

[tex]i^{4}[/tex] = [tex]\sqrt{-1}[/tex]

the pattern just repeats from here

5 = i

6 = -1

7 = -i

8  = 1

9 = i

10 = -1

11 = -i

12  = 1

13 = i

14 = -1

15 = -i

16  = 1

Answer:

Following are the solution to the given question:

Step-by-step explanation:

Its area includes all Sahara's locations in North Africa, South Arabia, Iran's and Iraq's larger parts, North-Western India, California throughout the United States, South Africa but most of Australia.

Half-arid temperatures include places like the Utah, Montana, and Gulf Coastal regions of sagebrush. Also, it comprises regions in Iceland, Russia, Scandinavia, Greenland, and Northeast India. Semi-arid thankless than tube called per year of rain and up to 20 inches per year at much more than arid deserts.

Regions from of the latitude of 25° to 35° usually develop desert, because air sinks and is heated under pressures in this area. The world's dry and semi-arid desert regions are between 20°C and 35°C north latitude and between 20°C and 35°C South latitude.

Answer:

ok

Step-by-step explanation:

mark me the brainlieast since your question is incomplete

Answer:

1228 is your answer

Step-by-step explanation:

Answer:

2/12

Step-by-step explanation:

The answer is 2/12 because there are two dice, each with 6 sides and the probability on each dice is one sixth

Explanation:

Normally, cosine has a period of 2pi. This means that the curve repeats itself every 2pi units. However, this graph has a period of pi.

We can see this by noting that the distance from one peak such as x = 0 to another adjacent peak x = pi is exactly pi units across.

Since T = pi is the period, we then know that

B = (2pi)/T

B = (2pi)/(pi)

B = 2

Then recall that the general template is y = Acos(B(x-C))+D

In this case, A = 1, C = 0 and D = 0. So all of this leads to y = cos(2x)

Answer:

please I don't know can u please help me out

Answer:

The answer to your question where SAS is given  

∠T ≈∠ W

Answer:

The work done is - 200 μJ.

Step-by-step explanation:

The potential difference between two points M and N is UMN = 100 V. A charge q = -2μC moves from M to N, the work of the electric force is:

Potential difference, V = 100 V

Charge, q = - 2 μC

The potential difference is defined as the amount of work done in bringing a unit positive test charge from one point to another in the electric field.

So, W = q V

W = - 2 μC x 100 V = - 200 μJ

Answer:

105.

Step-by-step explanation:

.

Answer:

7[tex]\sqrt{x}[/tex] = 14, D

Step-by-step explanation:

A radical equation is defined by having a variable under a radical sign. This is the only option with a variable (x) under the radical sign. Hence, 7[tex]\sqrt{x}[/tex] = 14 is the correct option.

Answer:

[tex]volume=1/3 ~BH[/tex]

[tex]=1/3(16)^{2} \sqrt{17^{2} -8^{2} }[/tex]

[tex]=1/3\times256\times15[/tex]

[tex]=1280 ~ft^{3}[/tex]

------------------------

hope it helps...

have a great day!!

Answer:

y - 2 = 36(x - 4)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = 36 and (a, b ) = (4, 2 ) , then

y - 2 = 36(x - 4) ← equation of line

Answer:

The number of bacteria in 0.25 mL is 6.25 x 10^3.

Step-by-step explanation:

5 liter flask contains 1.25 x 10^8 bacteria.

So, 1liter flask contains = [tex]\frac{1.25 \times 10^8}{5} =2.5\times 10^7[/tex]

Now

0.25 mL contains = [tex]2.5\times 10^7 \times0.25\times 10^{-3} = 6.25\times 10^3[/tex]

Answer:

-6

Step-by-step explanation:

Answer:

4

−

4

+

8

2

+

8

Step-by-step explanation:

Answer:

31°

Step-by-step explanation:

The theorem states that all angle sums of any triangle add up to 180°.

128 + 21 = 149, and to find ?°, subtract 149 from 180 to get 31°.

Answer:

trinomial = 5x

GCF = 2x(x + 5) + 5(x + 5)

Step-by-step explanation:

2x^2 + 15x + 25

using middle term break method

2x^2 + (10 + 5)x + 25

2x^2 + 10x + 5x + 25

therefore trinomial = 2x^2 + 10x + 5x + 25

GCF(Greatest Common Factor) = 2x^2 + 10x + 5x + 25

=2x(x + 5) + 5(x + 5)

take (x + 5 ) as common

(x + 5)(2x + 5)

(x + 5)(5 + 2x)since the sign of 5 and 2x is same i.e plus sign u can change their place.

Answer:

57 students

Step-by-step explanation:

Since 6 students count not fit and they had to go in cars, there is a remainder of 6. Subtract that from the total, 405, and you get 399.

Then, divide that by 7, and you get the answer. 57.

Hope it helps!

Answer:

57 students

Step-by-step explanation:

405-6=399

399÷7=57