Yellowstone National Park is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 5 vans and 2 buses y with 115 students. High School B rented and filled 1 van () and 6 buses () with 163 students. Each van carried the same number of students and each bus carried the same number of students. Write equations to represent the scenario. Then, graph to find the number of students in each van and in each bus.

Answer:

Step-by-step explanation:

The correct answer would be C (-6,3).  The y axis is the bold line going up and down on the middle of the page.   If you were able to pick up triangle and flip it over the y axis.  Point C would land at (-6,3).

Also, you can see that point C is six spaces to the right of the y axis.  That means when we flipped it over the axis, it will now be six paces to the right of the y axis.  Since the point did not go up or down when you flipped it.  It is still 3 spaces above the x axis.

Answer:

D (-6, 3)

Step-by-step explanation:

the point C is originally (6, 3).

that means the x coordinate is 6, the y coordinate is 3.

now, if we reflect (= mirror) that point across the y axis, that means we mirror it to the other side of the y axis.

the y axis is the vertical coordinate axis in the middle of the graph.

so, what is going to happen to the point ?

will the y coordinate change ? no. the point will move over to the other side of the y line in the same "height" as before. nothing will move it higher or lower.

so, it will keep the same y coordinate : 3.

will the x coordinate change ? oh, yes. because the point will move from the right of the y axis to the left of the y axis. and it will be the same distance to the left as it was originally to the right.

so, +6 turns into -6 (as the y axis represents x=0).

The correct probability that Juan's bus is going to be late every week next week is 20 percent.

We have the total number in the stimulation on to be from 0 to 9

On the fact that it would be late, the number ranges from 2 to 9

Hence the fact that it would be late would be

2/10

= 0.2

0.2 is also the same as 20 percent.

Juan rides the bus to school each day. He always arrives at his bus stop on time, but his bus is late 80% of the time. Juan runs a simulation to model this using a random number generator. He assigns these digits to the possible outcomes for each day of the week:

• Let 0 and 1 = bus is on time

• Let 2, 3, 4, 5, 6, 7, 8, and 9 = bus is late

The table shows the results of the simulation.

Read more on simulation here:

https://brainly.com/question/24912812

#SPJ1

The volume of the rectangular prism is 8 1 / 8 units³

volume of a rectangular prism = lwh

where

Therefore,

volume of a rectangular prism = base area × height

volume of a rectangular prism = 16 1 / 4 × 1 / 2

volume of a rectangular prism = 65 / 4 × 1 / 2

volume of a rectangular prism =  65 / 8

volume of a rectangular prism =  8 1 / 8 units³

learn more on volume here: https://brainly.com/question/12420093

#SPJ1

Answer:

-36 and 36

Step-by-step explanation:

moving the 9x to the left it changes to -9x and that plus -27x is -36x

-27-9 = -36

moving -27x to the right it changes to 27x so that plus 9x is 36x

27+9 = 36

Answer:

A. -36

F. 36

Step-by-step explanation:

Using addition or multiplication, Teresa has twice a number of wood as Samuel.  

According to the question,

Teresa needs twice as many feet of wood as Samuel  in order to find the number of pieces of wood Teresa need only if we add the number Teresa has by itself or multiply it by 2.

Hence, we need to do only multiply it by 2

Learn more about addition and multiplication here

https://brainly.com/question/15370422

#SPJ4

Answer:

51

Step-by-step explanation:

Translate the problem into an equation and solve the equation.

(x - 9)/6 = 7

x - 9 = 42

x = 51

Answer: 51

Answer:

51

Step-by-step explanation:

Create an equation.

[tex]\frac{(x-9)}{6} = 7[/tex]

Multiply 6 to both sides.

x-9 = 42

Add 9 to both sides.

x=51

To check if this is correct follow the steps given in the question.

51-9=42

42÷6=7

It is correct.

Hope this helps!

The p-value from the hypothesis test is 0.142 i.e., greater than the given significance level of 0.05. So, the null hypothesis is not rejected. The z-score for the given sample is 1.471.

The decision rule based on p-value states,

Since it is given that the valve would produce a mean pressure of 5.4 pounds/square inch. I.e., μ = 5.4 p/si

So, Defining the hypothesis:

Null hypothesis H0: μ = 5.4

Alternative hypothesis Ha: μ ≠ 5.4

It is given that,

The valve was tested on 24 engines. I.e., Sample size n = 24

The sample mean X = 5.7

Standard deviation σ = 1.0 and

The significance level = 0.05

Since the population distribution is approximately normal,

the test statistic is calculated as follows:

z = (X - μ)/(σ/[tex]\sqrt{n}[/tex])

On substituting the value,

z = (5.7 - 5.4)/(1.0/[tex]\sqrt{24}[/tex])

  = (0.3)/0.204

  = 1.471

Fron this z-score, the p-value is calculated as 0.142.

Since, the value of p > 0.05 (significance level), the null hypothesis is not rejected.

Learn more about hypothesis testing here:

https://brainly.com/question/22078281

#SPJ4

Answer:

By 3.

Step-by-step explanation:

-12-3=-15

Hope this helps!

Answer:

-12 exceeds -15 by 3

Step-by-step explanation:

To find out by how much a exceeds b, subtract a - b.

For example, by how much does 8 exceed 6?

Here, a = 8 and b = 6.

a - b = 8 - 6 = 2

2 is correct since we know that 8 is 2 greater than 6.

Now we do this problem.

By how much does -12 exceed -15?

a = -12; b = -15

a - b = -12 - (-15) = -12 + 15 = 3

Answer: -12 exceeds -15 by 3

Answer:

[tex]\frac{32\pi }{9}[/tex] or [tex]11.17[/tex]

Step-by-step explanation:

[tex]2\pi 8(\frac{80}{360} )[/tex]

[tex]=16\pi (\frac{80}{360} )[/tex]

[tex]=16\pi (\frac{2}{9})[/tex]

[tex]=\frac{32\pi }{9}[/tex]

The probability of picking a card with an even number is [tex]\frac{3}{10}[/tex].

To find the probability of picking a card with an even number:

Therefore, the probability of picking a card with an even number is [tex]\frac{3}{10}[/tex].

Know more about probability here:

https://brainly.com/question/24756209

#SPJ4

COMPLETE QUESTION:

The numbers 7, 11, 12, 13, 14, 18, 21, 23, 27, and 29 are written on separate cards, and the cards are placed on a table with the numbers facing down. The probability of picking a card with an even number is _____.

Answer:

54 degrees

Step-by-step explanation:

The actual angles of the triangle are not changing since this is just a reflection. The angles inside a triangle all add up to 180, so we can do 180-59-67 to get 54.

Answer:

x=15

Step-by-step explanation:

Use the Pythagorean Theorem: a^2+b^2=c^2

1. a = 20, b = x, c = 25

2. 20^2+b^2= 25^2

3. Expand: 400+b^2= 625

4. Subtract + Simplify: b^2= 625-400

5. Fully Solve: b^2 = 225 -> Square root of b^2 = Square root of 225

6. Last Step: Simplify: b = 15.

Here is a similar problem for you to solve, put your answer in the comments.

a= 12, b=5, c=?

Solve for c using the Pythagorean theorem.

The area of the shaded region = area of larger circle - area of smaller circle = 423.9 yd².

Area = πr²

Area of the shaded region = area of larger circle - area of smaller circle

Area of larger circle = πr² = (3.14)(16²) = 803.84 yd²

Area of smaller circle = πr² = (3.14)(11²) = 379.94 yd²

Area of the shaded region = 803.84 - 379.94 = 423.9 yd².

Learn more about the area of a circle on:

https://brainly.com/question/12269818

#SPJ1

The correct answer is  8.5 in.

we know that

The formula of area of triangle is equal to

             [tex]A = \frac{1}{2} (b) (h)[/tex]

We have

b = BC = 6 in

h = AD = x in

substitute

[tex]A = \frac{1}{2} (6) (x)[/tex]

[tex]A = 3x^{2} in^{2} ..................(1)[/tex]

Heron's Formula is a method for calculating the area of a triangle when you know the lengths of all three sides.  

Let  a,b,c be the lengths of the sides of a triangle.  

The area is given by:-

[tex]A = \sqrt{p(p-a) (p-b) (p-c)}[/tex]                     where p is half the perimeter

[tex]p = \frac{a +b+ c}{2}[/tex]

a = 9 in , b= 9 in, c = 6 in

[tex]p = \frac{9 + 9 + 6}{2} = 12 in[/tex]

Find the area

[tex]A = \sqrt{12( 12 - 9) (12-9) (12 - 6)}[/tex]

[tex]A = \sqrt{12 (3)(3)(6)}[/tex]

[tex]A = \sqrt{648}[/tex]

[tex]A = 25.46 in^{2}[/tex]

Substitute the value of the area in the equation 1 and solve for x

[tex]A = 3x in^{2}[/tex]

25.46 = 3x

x = 25.46/3

x = 8.5 in

Learn more about Heron's Formula

brainly.com/question/22391198

#SPJ4

The complete question is -

HELP PLEASE! Find the height of the triangle by applying formulas for the area of a triangle and your knowledge about triangles.

A. 8 in.

B. 11.3 in.

C. 8.5 in.

D. 6.2 in.

Answer:

3.64 × 10(raised to the power 7)

2.6 × 10⁴

Answer:

95 - 20[tex]\sqrt{15}[/tex]

Step-by-step explanation:

(5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] )²

= (5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] )(5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] )

each term in the second factor is multiplied by each term in the first factor, that is

5[tex]\sqrt{3}[/tex] (5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] ) - 2[tex]\sqrt{5}[/tex] (5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] ) ← distribute parenthesis

= 75 - 10[tex]\sqrt{15}[/tex] - 10[tex]\sqrt{15}[/tex] + 20 ← collect like terms

= 95 - 20[tex]\sqrt{15}[/tex]

Answer:

95 - 20√15

Step-by-step explanation:

I assume the expression is (5√3 − 2√5)^2 (?).

(5√3 − 2√5)*(5√3 − 2√5)

25√3^2 - 20√15 + 4√5^2

25*3 - 20√15 +4*5

75 - 20√15 +20

95 - 20√15

The solution of the recurrence relation is [tex]a_n=3.2^n[/tex]

For given question,

We have been given a recurrence relation [tex]a_n = 2a_{n-1}[/tex] for n ≥ 1

and an initial condition [tex]a_0=3[/tex]

Let [tex]a_n[/tex] = m², [tex]a_{n-1}[/tex] = m and [tex]a_{n-2}[/tex] = 1

So from given recurrence relation we get an characteristic equation,

⇒ m² = 2m

⇒ m² - 2m = 0                     .........( Subtract 2m from each side)

⇒ m(m - 2) = 0                     .........(Factorize)

⇒ m = 0    or  m - 2 = 0

⇒ m = 0   or   m = 2

We know that the solution of the recurrence relation is then of the form

[tex]a_n=\alpha_1 {m_1}^n + \alpha_2 {m_2}^n[/tex]  where [tex]m_1,m_2[/tex] are the roots of the characteristic equation.

Let, [tex]m_1[/tex] = 0   and [tex]m_2[/tex] = 2

From above roots,

[tex]\Rightarrow a_n=\alpha_1 {0}^n + \alpha_2 {2}^n\\\\\Rightarrow a_n=0+\alpha_2 {2}^n\\\\\Rightarrow a_n=\alpha_2 {2}^n[/tex]

For n = 0,

[tex]\Rightarrow a_0=\alpha_2 {2}^0\\\\\Rightarrow a_0=\alpha_2 \times 1\\\\\Rightarrow a_0=\alpha_2[/tex]

But  [tex]a_0=3[/tex]

This means [tex]\alpha_2=3[/tex]

so, the solution of the recurrence relation would be [tex]a_n=3.2^n[/tex]

Therefore, the solution of the recurrence relation is [tex]a_n=3.2^n[/tex]

Learn more about the recurrence relation here:

https://brainly.com/question/27618667

#SPJ4

Answer:

3/8

Step-by-step explanation:

There are 8 equal slices so each slice is 1/8th of the whole pizza

1/8+1/8=2/8 he ate right away

2/8+1/8 for what he ate before going to sleep

2/8+1/8=3/8

Rule 1: Multiply by 2 then add 1 starting

( n x 2 +1) => 2n + 1

n is the position of our terms, so I substitute 1 because you're told to start from 1 which becomes our first term

2n + 1

2 x 1 + 1 =3

2 x 2 + 1 = 5

2 x 3 + 1 = 7

2 x 4 + 1 = 9

3,5,7,9....

(you can clearly see the sequence increasing by 2 each time, not following Multiply by 2 then add 1)

However, if we were to do add one each time, you'll add one to your pervious answer. So, this time I'll substitute the pervious answer

2 x 1 + 1 =3

2 x 3 + 1 = 7

2 x 7 + 1 = 15

2 x 15 + 1 = 31

3,7,15,31....

(from 3 to 7, you clearly see its multiplied by 2, then +1 & that's our sequence, this method apply to the second rule too of using previous)

Rule 2: Divide by 2 then add 4

(n ÷ 2 + 4) => n/2 + 4

n/2 + 4

(starting from 40.)

40/2 + 4 = 24

24/2 + 4 = 16

16/2 + 4 = 12

12/2 + 4 = 10

24,16,12,10.....

Answer: (started off with the number it asked of)

R 1 -

1,3,7,15,31....

(1 x 2 +1 does give 3)

R 2 -

40, 24,16,12,10.....

(40÷2 = 20, then + 4, gives 24)

Hope this helps!

Therefore, the 500th term of the sequence exists 3517.

The given sequence is 24, 31, 38, 45, 52, ...

It exists an Arithmetic progression.

Here, the First term = 24

Common difference = 31 - 24 = 7

The given explicit formula for the nth term exists

an = a₁ + (n - 1)d

Where a₁ exists the first term, d exists a common difference.

Substitute a₁ = 24, d = 7 and n = 500

a(500) = 24 + (500 - 1)7

 = 24 + (499)7

 = 24 + 3493

a(500) = 3517

Therefore, the 500th term of the sequence exists 3517.

To learn more about Arithmetic progression refer to:

https://brainly.com/question/16982185

#SPJ9

Answer + Step-by-step explanation:

2x – y + 1 = 0

We know that the graph of a linear equation is a line.

So ,in order to draw it we need to find two points A and B of the line

Afterward, we join A and B to get the graph.

2x – y + 1 = 0

If x = 0 → y = 1 ⇒ A(0 , 1) lie on the line AB (the graph)

If x = 1 → y = 3 ⇒ B(1 , 3) lie on the line AB

Now ,all we have to do is plotting A and B

on the coordinates plane ,then connecting then with a line.

According to the graph (check the attached image) :

If (h,4) ∈ line AB ⇒ h = 3/2

If (1/2 , k) ∈ line AB ⇒ k = 2

Answer:

x=9.73

Step-by-step explanation:

This is trigonometry work! :)

So cos46°=x/14

          x=14×cos46°

          x≈9.73

Hope this helps <3

Answer:

16x-2

Step-by-step explanation:

Perimeter is 2w+2l

so we plug it in

2(3x+1) + 2(5x-2)

now we distribute

6x+2 + 10x -4

now we add like terms

6x+10x+2-4

16x-2

Answer:

1. a = 32, c = 24

Step-by-step explanation:

a = c+8

a-20 = 3(c-20)

(c+8)-20 = 3c-60

c = 24

a = 24+8

a = 32

2. t = 15, j = 9

t-3 = 2(j-3)

t-3 = 2j-6

t = 2j-3

t + 2 + j + 2 = 28

(2j-3)+ 2 + j + 2 = 28

3j + 1 = 28

3j = 27

j = 9

t-3 = 2(9-3)

t-3 = 2(6)

t-3=12

t = 15

3. b=36, s=31

b = s + 5

b+s = 67

(s+5)+s = 67

2s+5 = 67

2s = 62

s = 31

b = 31+5

b = 36

4. 231

h + t + u = 6

(with h=hundreds digit, t=tens digit, u=units digit)

h = 2u

t = h+u

t = (2u) + u

(2u) + (2u +u) + u = 6

6u = 6

u = 1

h = 2

t = 3

the number is 231

5. 48

u = 2t

the 2-digit number is 10t+u

2(10t+u) = 10u+t+12

2(10t + 2t) = 10(2t) + t + 12

20t + 4t = 20t + t + 12

24t = 21t + 12

3t = 12

t = 4

u = 2*4

u = 8

the number is 48

Answer:

4 : 9

Step-by-step explanation:

ratio of corresponding sides and ratio of perimeter are equal

then ratio of perimeter = 4 : 9

False, Whales evolved in the early Cambrian and include transitional species such as Kutchicetus and Rodhocetus.

What animals evolved during Cambrian period?

When did animals evolve in the Cambrian?

What long lived group of arthropods went extinct at the end of the Permian?

Learn more about Cambrian animals evolved.

brainly.com/question/1451687

#SPJ4

The complete question is -

True or false . Whales evolved in the early Cambrian and include transitional species such as Kutchicetus and Rodhocetus.

Answer:

[tex]y^6[/tex]

Step-by-step explanation:

So there is an exponent identity that states: [tex](x^b)^a = x^{a*b}[/tex] which means this question becomes: [tex](y^2)^3 = y^{2*3} = y^6[/tex].

Just so you completely understand why this works, it might help to express y^2, as what it truly represents: [tex]y^2=y*y[/tex]. So using this definition we can substitute it into the equation so it becomes: [tex](y*y)^3[/tex]. Now let's use the definition of exponents like we just did with the y, to redefine this in terms of multiplication: [tex](y*y)^3 = (y * y) * (y * y) * (y * y)[/tex]. We can just multiply all these out, and we get: [tex]y * y * y * y * y * y =y^6[/tex].

To make it a bit more general when we have the exponent: [tex]x^b[/tex] it can be expressed as: [tex](x*x*x...\text{ b amount of times})[/tex] now when we raise it to the power of a. we get: [tex](x * x * x...\text{ b amount of times})^a[/tex] which can further be rewritten using the definition of an exponent to become the equation: [tex](x*x*x\text... \text{ b amount of times}) * (x * x * x...\text{ b amount of times})...\text{ a amount of times}[/tex] which just simplifies to: [tex]x*x*x*x...\text{ a times b amount of times}[/tex]. Hopefully this makes the identity a bit more understandable

Answer:

A. (-1, 3) (3, 2) (-2, 1)

B. [tex]\sqrt{17}[/tex]   [tex]\sqrt{5}[/tex]  [tex]\sqrt{26}[/tex]  

Step-by-step explanation:

The formula for finding the midpoints is [tex](\frac{x_{1}+x_{2} }2}, \frac{y_{1}+y_{2} }2} )[/tex].

MIDPOINTS

[tex](\frac{x_{1}+x_{2} }2}, \frac{y_{1}+y_{2} }2} )[/tex] = [tex](\frac{4-6}2,\frac{4+2 }2} )[/tex] = (-1, 3)

[tex](\frac{x_{1}+x_{2} }2}, \frac{y_{1}+y_{2} }2} )[/tex] = [tex](\frac{4+2}2,\frac{4+0 }2} )[/tex] = (3, 2)

[tex](\frac{x_{1}+x_{2} }2}, \frac{y_{1}+y_{2} }2} )[/tex] = [tex](\frac{-6+2}2,\frac{2+0 }2} )[/tex] = (-2, 1)

Next, we will use the distance formula, [tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2} }[/tex].

DISTANCE

[tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2} }[/tex] = [tex]\sqrt{(-1-3)^{2} + (3-2)^{2} }[/tex] = [tex]\sqrt{17}[/tex]

[tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2} }[/tex] = [tex]\sqrt{(-1+2)^{2} + (3-1)^{2} }[/tex] = [tex]\sqrt{5}[/tex]

[tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2} }[/tex] = [tex]\sqrt{(3+2)^{2} + (2-1)^{2} }[/tex] = [tex]\sqrt{26}[/tex]  

a. To find the coordinates of endpoints we must add two x values and divide by 2 and then add 2 y- values and divide by 2.

(4-6)/2=-1  (4+2)/2=3

Repeat for other sides.

(2-6)/2=-2 (2+0)/2=1

(2+4)/2=3  (4+0)/2=2

Coordinates of midpoints are (-1,3), (-2,1), (3,2)

b. Now we use the distance formula for each midpoint to find the length of the inner- triangle.

sqrt((-1+2)^2 + (3-1)^2)

Sqrt(5)

Repeat.

Sqrt(17)

Sqrt(26)

The lengths of the inner triangle are as follows:

(-1,3), (-2,1) = Sqrt(5)

(-1,3), (3,2) = Sqrt(17)

(-2,1), (3,2) = Sqrt(26)