Camilla and Aisha are sisters and go to the same school. This morning, Camilla decided to bike to school, and Aisha decided to walk. They left home at the same time. Camilla’s speed was 6.5 miles per hour, and Aisha’s speed was 2 mph. When Camilla reached the school, Aisha was 1.5 miles behind. How far away from their house is the school?

Answer:

the average number of cars waiting in line L[tex]q[/tex] is 0.45

Step-by-step explanation:

Given the data in the question;

Cars arrive at an automatic car wash system every 10 minutes on average.

Car arrival rate λ = 1 per 10 min = [ 1/10 × 60 ]per hrs = 6 cars per hour

Washing time for each is 6 minutes per car

Car service rate μ = 6min per car = [ 1/6 × 60 ] per hrs = 10 cars per hour

so

P = λ/μ = 6 / 10 = 0.6

Using the length of queue in M/D/1 system since there is only one service bay;

L[tex]q[/tex] = [tex]\frac{1}{2}[/tex][ P² / ( 1 - P ) ]

so we substitute

L[tex]q[/tex] = [tex]\frac{1}{2}[/tex][ (0.6)² / ( 1 - 0.6 ) ]

L[tex]q[/tex] = [tex]\frac{1}{2}[/tex][ 0.36 / 0.4 ]

L[tex]q[/tex] = [tex]\frac{1}{2}[/tex][ 0.9 ]

L[tex]q[/tex] = 0.45

Therefore, the average number of cars waiting in line L[tex]q[/tex] is 0.45

Answer:

Hello,

5 s

Step-by-step explanation:

[tex]h(t)=-16t^2+48t+160\\=-16(t^2-3t-10)\\=-16(t^2-5t+2t-10)\\=-16(t(t-5)+2(t-5))\\=-16(t-5)(t+2)\\\\h(t)=0 \Longleftrightarrow\ t=-2\ or\ t=5\\\\Only\ t=5\ is \ a\ answer.(time\ must\ be\ positive)[/tex]

The 3rd one

Step-by-step explanation:

Reason being that it has no factors, meaning it cannot be simplified any further, but quadratic method can be used to attain factors.

hope it makes sense :)

Answer: y = x - 7

Slope intercept form: y = mx + b

[tex]2x-2y=14\\\\-2y=-2x+14\\\\y=\frac{-2x+14}{-2} =\frac{-2(x-7)}{-2} =x-7[/tex]

Answer:

The answer is 890 . ...... :D

Answer: 0.38

Step-by-step explanation:

Since the variable x is represented by a standard normal distribution, the probability of x > 0.3 will be calculated thus:

P(x > 0.3)

Then, we will use a standard normal table

P(z > 0.3)

= 1 - p(z < 0.3)

= 1 - 0.62

= 0.38

Therefore, p(x > 0.3) = 0.38

The probability of x > 0.3 is 0.38.

Answer:

125000000

Step-by-step explanation:

1.25 x 10^8

Move the decimal 8 places to the right

1.25

We can move it two places

125

We need to add 6 more zeros

125000000

Answer: 125,000,000

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

Part A

The slope is found by

m = ( y2-y1)/(x2-x1)

    = ( 1200-1500)/(4-0)

    = -300/4

    =-75

Part B

point slope  y-y1 = m(x-x1)  where m is the slope and (x1,y1) is a point on the line

y-1200 = -75(x-4)

slope intercept  y = mx+b  where m is the slope and b is the y intercept

y = -75x + 1500

standard form  Ax+By =C

75x + y = 1500

Part C

Change y to g(x) in the slope intercept form

g(x) = -75x + 1500

Part D

Let x = 5

g(5) = -75(5) + 1500

      =-375+1500

      =1125

[tex]\sf\huge\underline\color{pink}{༄Answer:}[/tex]

[tex]\tt3 \frac{1}{3} = \frac{x}{6} \\ = \tt \frac{10}{3} = \frac{x}{6} \\ = \tt \frac{x}{6} = \frac{10}{3} \\ = \tt6 \frac{x}{6} = 6( \frac{10}{3} ) \\ = \tt\large\boxed{\tt{\color{pink}{x = 20}}}[/tex]

[tex]\color{pink}{==========================}[/tex]

#CarryOnLearning

Answer:

The sequence has first term 7 and common difference is 8.

So the sequence is f(n)=7 + 8(n-1)

Step-by-step explanation:

Let a be the first term.

Let a+d be the second term where d is the common difference.

Then a+2d is the third....

And a+(n-1)d is the nth term.

Adding these terms we get:

an+(n-1)(n)/2×d

For the first term of this sum I seen we had n amount of a's and for the second term I used the well known identity sum of the first n positive integers is n(n+1)/2.

Let's simplify:

an+(n-1)(n)/2×d

Distribute:

an+(n^2d/2)-(nd/2)

Find common denominator:

(2an/2)+(n^2d/2)-(nd/2)

Combine terms into one:

(2an+n^2d-nd)/2

Reorder terms:

(n^2d+2an-nd)/2

Regroup terms:

(n^2d+(2a-d)n)/2

We want the following sum though:

4n^2+3n

This means d/2=4 (so d=8) and (2a-d)/2=3.

So plug d=8 into second equation to solve for a.

(2a-8)/2=3

2a-8=6

2a=14

a=7

The sequence has first term 7 and common difference is 8.

So the sequence is f(n)=7 + 8(n-1).

Answer:

0.0009765625

Step-by-step explanation:

This is what i got its probally incorrect

Answer:

There are three basic trigonometric ratios: sine , cosine , and tangent .

Step-by-step explanation:

Answer:

base-2 base-10

110011 = 51

110100 = 52

110101 = 53

110110 = 54

21 more rows

Answer: the radius is perpendicular to the chord.

If a radius of a circle bisects a chord which is not diameter, then the radius is perpendicular to the chord.

Answered by Gauthmath must click thanks and mark brainliest

The radius is perpendicular to the chord.

If the radius of the circle is perpendicular to the chord of the circle, the radius bisects the chord. The two strings are congruent only if they are equidistant from the center of the circle.

No, not all strings in a circle are diameters because the diameter passes through the center of the circle. Therefore, all the diameters of a circle are also strings, not all the strings of a circle.

Learn more about chord at

https://brainly.com/question/1869643

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Answer:

x=1.7099

Step-by-step explanation:

2x³=10

x³=10/2

x³=5

x=∛5

x=1.7099

9514 1404 393

Answer:

Step-by-step explanation:

Reflection over the x-axis changes the sign of the y-coordinate. Reflection over the y-axis changes the sign of the x-coordinate. We can summarize the transformations as ...

  preimage point ⇒ reflection over x ⇒ reflection over y

A(−8,−2) ⇒ A'(-8, 2) ⇒ A"(8, 2)

B(−4,−3) ⇒ B'(-4, 3) ⇒ B"(4, 3)

C(−2,−8) ⇒ C'(-2, 8) ⇒ C"(2, 8)

D(−10,−6) ⇒ D'(-10, 6) ⇒ D"(10, 6)

Answer:

12/55

Step-by-step explanation:

Probability is the ratio of the number of possible outcomes to the number of total outcomes.

Given that the bag contains 8 red balls and 3 white balls, the probability of picking a red ball

p(r) = 8/(8+3) = 8/11

Probability of picking a white ball

= 3/11

when a red ball is picked first, the total number of balls reduces to 10 hence the probability that the second ball is white, given that the first ball is red

=8/11 * 3/10

= 24/110

= 12/55

Answer:

(cosB-1)(cosB+6)

Step-by-step explanation:

use u substitution . u = cosB

u^2+5u-6

factor

(u-1)(u+6)

put cosB back in for u

(cosB-1)(cosB+6)

Answer:

statistics are when data analyzed in order to make decisions about the population behind the data.

The correct answer to the question is Statistics (Option D).

What is statistics?

Statistics is a field of study in mathematics which deals with raw data. It is a tool which refines the data to produce meaningful results and a pathway to better understanding of it.

Some examples of raw data can be population sample which loves to see a particular TV show or a sample of students getting so and so marks in Math test.

Data is analyzed mainly by three different measure of central tendency that is mean, median and mode.

Therefore, Statistics the correct answer.

To know more about statistics refer:https://brainly.com/question/10734660

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Answer:

Whole number —> X

Twice the square of the number —> 2X²

X + 2X² = 10

2X²+X –10 =0

(2x + 5) ( x–2) =0

2x +5=0 —> 2x= – 5 —> x= – 5/2 = —> x= - 2.5 (rejected)

x–2=0 —> x= 2

So Ans ; X= 2 ( the number )

I hope I helped you^_^

Answer:

See pic below.

Answer: C. 380°

Step-by-step explanation:

Answer:

The answer is A

Step-by-step explanation:

The answer needs to be in slope-intercept form or y=mx+b because the amount of carpet being cleaned every minute is a constant decrease of 9 square feet.

So our b value (or how much carpet cleaned at 0 minutes) is 220

And our m value (or slope or how much carpet is being cleaned every minute) is 9

So if we plug the variables with the tangible numbers we get A(t) = -9x+220 or A(t) = 220-9x.

provided by gauth math

Answer:

All of area is πr²

Step-by-step explanation:

and we should write the area kind of radian. So if all area is π*(12)²= 144π - this for 360°- and 240° is 96π

but we must add area of the triangle which has two same side and has 6 high so it's area is 6*12√3/2 = 36✓3

our answer is 96π+ 36✓3

Answer:

3/4

Step-by-step explanation:

To find the common ratio, take the second term and divide by the first term

3/4

Check with the third and second terms

9/4 ÷3

9/4 *1/3= 3/4

The common ratio is 3/4

Answer:

1 + 7n

Step-by-step explanation:

7-(3n+6)+10n​

7 - 3n - 6 + 10 n

1 - 7n

Answered by Gauthmath

Answer:

20+(x+1) = 5x

x=21/4

x= 5.25

The entrance ticket per person can be calculated using algebraic equation. We have create the algebraic expression as per the question.

The entrance ticket per person is Rs. 5.25.

Given:

Total boys are 5

4 boys has 5 rupee each so total rupee are [tex]=5\times 4=20[/tex].

Let the entrance ticket per boy is [tex]x[/tex].

One boy had 1 rupee more than entrance ticket [tex](x+1)[/tex].

Write the algebraic expression to calculate the entrance ticket per person.

[tex]5x=20+(x+1)\\5x=20+x+1\\5x-x=20+1\\4x=21\\x=5.25[/tex]

Thus, the entrance ticket per person is Rs. 5.25.

Learn more about algebraic expression here:

https://brainly.com/question/953809

Answer:

c=80

Step-by-step explanation:

Based on my reading the critical damping occurs when the discriminant of the quadratic characteristic equation is 0.

So let's see that characteristic equation:

20⁢r^2+c⁢r+80⁢=0

The discriminant can be found by calculating b^2-4aC of ar^2+br+C=0.

a=20

b=c

C=80

c^2-4(20)(80)

We want this to be 0.

c^2-4(20)(80)=0

Simplify:

c^2-6400=0

Add 6400 on both sides:

c^2=6400

Take square root of both sides:

c=80 or c=-80

Based on further reading damping equations in form

a⁢y′⁢′+b⁢y′+C⁢y=0

should have positive coefficients with b also having the possibility of being zero.