A roller coaster has 3 trains with 7 rows per train. Riders stand in rows of 6, for a total of 42 riders per train. The operators of the coaster recorded the number of riders on each train during a run. On the first train, the operators reported that 6 rows were filled. On the second train, all 7 rows were filled. On the third train, 4 rows were filled. How many rows were empty on the first train? How many additional riders would it take to fill those empty rows?

Answer:

The lengths 7, 40 and 41 cannot be sides of a right triangle. The lengths 12, 16, and 20 can be sides of a right triangle.

Step-by-step explanation:

You can test this by using the Pythagorean theorem, which states a^2+b^2=c^2

with 7,40 and 41

7^2+40^2 does not equal to 41^2

but with 12,16, and 20

12^2+16^2=20^2

therefore, the last statement is correct.

The triangles are the same

CA= 8.5

AT=5

DG=12

T=70

O=57

C=53

Step-by-step explanation:

This can be a little brain bending but try to imagine rotating ∆DOG to the left once. The bottom side is now OGD. Now, the triangles will look similar. Here is the rule:

The SAS rule states that: If two sides and the included angle of one triangle are equal to two sides and included angle of another triangle, then the triangles are congruent. An included angle is an angle formed by two given sides.

so, side CA is equal to side DO. Side CT is equal to side DG, and side AT is equal to side OG. The answers to the first column are:

CA=8.5m

AT=5m

DG=12m

Now, because the sides are equal, the angles are equal:

>T is the same as >G. =70°

>A is the same as>O = 57°

The angles of a triangle have to add up to 180°, so

70° + 57° = 127°

180°- 127° = 53°

So, angles D and C equal 53°.

How this helps.

Answer:

(-3,-1)

Step-by-step explanation:

Answer: 7

Step-by-step explanation: 4+3 = 7.

Answer:

110%

Step-by-step explanation:

if each square is a whole, then when one is filled, it's 100% . 10% of the other square is filled so you just add the two.

Answer:

6x - 9 = y

x - (-1.5)

x - (-1.5) = y

Step-by-step explanation:

Answer:

-9

Step-by-step explanation:

8(x - 1) = 5x - 35

8x - 8 = 5x - 35

8x - 5x = 8 - 35

3x = -27

x = -27/3

x = - 9

Answer:

we could migrate here

Step-by-step explanation:

Answer:

I feel like I answered this before

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

nick's number = 91

eddie's number = 39

Step-by-step explanation:

n = nick's number

[tex]\frac{3}{7}[/tex]n = eddie's number

[tex]\frac{7}{7}[/tex]n - [tex]\frac{3}{7}[/tex]n = 52

[tex]\frac{4}{7}[/tex]n = 52

cross-multiply:  4n = 52(7)

                         4n = 364

                          n = 364/4 = 91

eddie's number:  [tex]\frac{3}{7}[/tex] · 91 =  273/7 = 39

Nick's number is 91

Eddie's number is 39

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division. The terms involved in an expression in math are:

Constant: A constant is a fixed numerical value.

Variable: A variable is a symbol that doesn't have a fixed value.

Term: A term can be a single constant, a single variable, or a combination of a variable and a constant combined with multiplication or division.

Coefficient: A coefficient is a number that is multiplied by a variable in an expression.

Given,

Eddie's number is 3/7 of Nick's number

Let Nick's number be x

Then Eddie's number = 3x/7

Difference of the numbers is 52

x - 3x/7 = 52

(7x - 3x)/7 = 52

4x/7 = 52

4x = 52×7

x = 364/4

x = 91

Another number = 3x/7

                            = 3(91)/7

                            = 3 × 13

                            = 39

Hence, 91 is Nick's number and 39 is Eddie's number.

Learn more about expression here:

https://brainly.com/question/14083225

#SPJ5

Answer:

p=10n

Step-by-step explanation:

You need to find how many pencils (=) and we dont know how many packs there are (n) but we do know how many there are in each pack (10)

Answer:

r≈5

the answer is b

Answer:I’m pretty sure it’s 6 correct me if I’m wrong

Step-by-step explanation:

Answer:

third option

Step-by-step explanation:

let g(x)=y

(x-1)³/2-3=y

(x-1)³/2-3/1=y

(x-1)³-6/2=y

(x-1)³-6=2y

(x-1)³=2y+6(find cubic root of both sides)

(x-1)=³√(2y+6)

x=³√(2y+6)+1

Replace y with g for the inverse

g^-1(x)=³√(2x+6)+1

Answer:

y=-2x + 1

Step-by-step explanation:

y=mx+b      (0,1)

11-2=9

9-2=7

7-2=5

5-2=3

3-2=1

Answer:

12x^2+4

Step-by-step explanation:

4(3x^2+1)

Answer:

He needs 4 packs.

Step-by-step explanation:

6*4=24 So we would need 4 packs, which gives him 24 but at least we have 23 cups.

Answer:

a_n = 39(1.06)^(n - 1)

Step-by-step explanation:

We are told that a_n is the number of raccoons in a given n number of years.

After 6 years, there are 52 raccoons.

Also after 8 years there are 58 raccoons.

Using formula for geometric sequence, we have;

a_n = ar^(n - 1)

After 6 years, there are 52 raccoons

Thus;

a_6 = 52 = ar^(6 - 1)

ar^(5) = 52 - - - (eq 1)

Also after 8 years there are 58 raccoons. Thus;

a_8 = 58 = ar^(8 - 1)

ar^(7) = 58 - - - (eq 2)

Divide eq 1 by eq 2 to get;

(r^(7))/(r^(5)) = 58/52

r² = 58/52

r = √(58/52)

r ≈ 1.06

Put 1.06 for r in eq 1 to get;

a(1.06)^(5) = 52

1.3382a = 52

a = 52/1.3382

a ≈ 39

Thus,the explicit rule is;

a_n = 39(1.06)^(n - 1)

Answer:

A) 0.10565

B) 0.33846

C)

Step-by-step explanation:

The length of time that it takes for a ferry to reach a summer resort from the mainland is approximately normally distributed with a mean of 2 hours and a standard deviation of 12 minutes.

Note that, all units must be in minutes

We solve this question using z score formula

= z = (x-μ)/σ

where

x is the raw score

μ is the population mean = 2 hours

Converting to minutes

1 hour = 60 minutes

2 hour = x

Cross Multiply

x = 2 × 60 minutes

x = 120 minutes

Mean = 120 minutes

σ is the population standard deviation = 12 minutes

Over many past trips, what proportion (area) of times has the ferry reaches the island in

A) less than 1 hour, 45 minutes?

Converting 1 hour 45 minutes to minutes

60 minutes = 1 hour

Hence:

60 + 45 minutes = 105 minutes

For x < 105 minutes

= 105 - 120/12

= -1.25

Probability value from Z-Table:

P(x<105) = 0.10565

B) more than 2 hours, 5 minutes?

Converting 2 hours 5 minutes to minutes

Hence:

1 hour = 60 minutes

2 hour = x

Cross Multiply

x = 2 × 60 minutes

x = 120 minutes

Hence:

120 + 5 minutes = 125 minutes

For x < 125 minutes

z = 125 - 120/12

z = 0.41667

Probability value from Z-Table:

P(x<125) = 0.66154

P(x>125) = 1 - P(x<125) = 0.33846

C) between 1 hour, 50 minutes and 2 hours, 20 minutes?

Converting 1 hour, 50 minutes to minutes

= 60 minutes = 1 hour

Hence:

60 + 50 minutes = 110 minutes

For x = 110 minutes

= 110 - 120/12

= -0.83333

Probability value from Z-Table:

P(x = 110) = 0.20233

Converting 2 hours, 20 minutes to minutes

= 1 hour = 60 minutes

2 hour = x

Cross Multiply

x = 2 × 60 minutes

x = 120 minutes

Hence:

120 + 20 minutes = 140 minutes

For x = 140minutes

z = 140 - 120/12

= 1.66667

Probability value from Z-Table:

P(x = 140) = 0.95221

Answer:

49?

Step-by-step explanation:

9514 1404 393

Answer:

  a) 720°

  b) 98

Step-by-step explanation:

a) The sum of interior angles of an n-gon is (n-2)×180°. For n=6, the sum is ...

  (6 -2)×180° = 4×180° = 720°

__

b) The sum of the marked angles is 622°, so the value of x is ...

  x = 720 -622

  x = 98

Answer:

It is the y intercept

Step-by-step explanation:

what do you need help with?

Where is the question?

Please make sure to input complete.

Answer:

1. AD

2. 5.2 cm

3. x = 4

4. BC

5. 3

6. x = 12

Step-by-step explanation:

Answer:

First number = 60 and another number = 48

Step-by-step explanation:

Let two numbers are 5x and 4x.

The two number are differ by 12. We need to find the numbers.

ATQ,

5x-4x = 12

x = 12

Now first number = 5x

= 5(12)

= 60

Other number = 4x

= 4(12)

= 48

Hence, the numbers are 60 and 48.

Answer:

5

Step-by-step explanation:

add 3u to both sides

7u=35

divide both sides by 7

u=5