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3 years ago

How do we solve this?

Mathematics

2 answers:

Elan Coil [88]3 years ago

8 0

Answer:

$= - \frac{1}{36(6x + 1) ^{6} } + c$

<h3>I hope I helped you^_^</h3>

White raven [17]3 years ago

6 0

Answer:

$-\frac{1}{36\left(6x+1\right)^6} +C$

Step-by-step explanation:

we're going to us u substitution

$\int (6x+1)^-7 dx$

$u=6x+1$

$\int\frac{1}{6u^7} du$

take out the constant, $\frac{1}{6}$

$\frac{1}{6}$ · $\int u^-7du$

next use the power rule, $\int x^adx=\frac{x^{a+1}}{a+1},\:\quad \:a\ne -1$

$\frac{1}{6}\cdot \frac{u^{-7+1}}{-7+1}$

simplify by substituting $6x+1$ for $u$

$\frac{1}{6}\cdot \frac{(6x+1)^{-7+1}}{-7+1} = -\frac{1}{36\left(6x+1\right)^6}$

add a constant, $C$

$-\frac{1}{36\left(6x+1\right)^6} +C$

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The scheduled arrival time for a daily flight from Boston to New York is 9:30 am. Historical data show that the arrival time fol

mamaluj [8]

Answer:

a) $E(A)=\frac{0+50}{2}=25 min$

$Sd(A) =\sqrt{208.3333 min^2}=14.43 min$

b) $P(A>25) = 1-P(A\leq 25)=1-\frac{25-0}{50-0}= 1-0.5 = 0.5$

Step-by-step explanation:

Part a

Let A the random variable that represent "The arrival time (minutes) for a daily flight from Boston to New York ". And we know that the distribution of A is given by:

$A\sim Uniform(a=0 ,b=50)$

We select our starting point a=0 representing 9:05 AM and the amount of minutes between 9:05 am to 9:55 am are 50 ans for this reason b =50

For ths uniform distribution the expected value is given by $E(X) =\frac{a+b}{2}$ where X is the random variable, and a,b represent the limits for the distribution. If we apply this for our case we got:

$E(A)=\frac{0+50}{2}=25 min$

And the variance is given by:

$Var(A)= \frac{(b-a)^2}{12}=\frac{(50-0)^2}{12}=208.3333 min^2$

And the standard deviation by definition is just the square root of the variance:

$Sd(A) =\sqrt{208.3333 min^2}=14.43 min$

Part b

If we convert 9:30 AM to our scale we know that we have 25 minutes between 9:05 AM and 9:30 AM.

For this case we want to find this probability: $P(A>25)$

And we can find this probability using the complement rule like this:

$P(A>25) = 1-P(A\leq 25)$

And we can use the cumulative distribution function given by:

$F(A) = \frac{A-a}{b-a}$

And we got:

$P(A>25) = 1-P(A\leq 25)=1-\frac{25-0}{50-0}= 1-0.5 = 0.5$

5 0

3 years ago

9/6 × 4/5 <br> 1 <br>) 36/11<br>) 6/5<br>) 32/30<br>) 13/15

erik [133]

Answer:

6/5

Step-by-step explanation:

9×4=36

6×5=30

36/30÷2

18/15÷3

6/5

6 0

3 years ago

Watch help video

Oksanka [162]

Answer:

Step-by-step explanation:

Using the distance formula, the distance is ...

d = √((x2 -x1)^2 +(y2 -y1)^2)

d = √((-2-4)^2 +(-4-4)^2) = √((-6)^2 +(-8)^2) = √(36 +64)

d = √100 = 10

The distance between the two points is 10 units.

3 0

3 years ago

Place the indicated product in the proper location on the grid. (a+b-c)(a+b+c)

aliina [53]

Answer:

The required location on the gird is shown below.

Step-by-step explanation:

Consider the provided expression.

We need to place the indicated product in the proper location on the grid.

First open the parenthesis as shown:

$(a+b-c)(a+b+c)=a(a+b+c)+b(a+b+c)-c(a+b+c)$

$(a+b-c)(a+b+c)=a^2+ab+ac+ab+b^2+bc-ac-bc-c^2$

Now add the like terms as shown:

$(a+b-c)(a+b+c)=a^2+b^2-c^2+2ab$

Hence, the required location on the gird is $(a+b-c)(a+b+c)=a^2+b^2-c^2+2ab$

3 0

3 years ago

Natasha, Mark and Henry share some sweets in the ratio 7:3:2. Natasha gets 75 more sweets than Henry. How many sweets are there

Solnce55 [7]

Answer:

180

Step-by-step explanation:

Given the ratio = 7 : 3 : 2 = 7x : 3x : 2x ( x is a multiplier ), then

7x = 2x + 75 ( Natasha gets 75 more sweets than Henry )

Subtract 2x from both sides

5x = 75 ( divide both sides by 5 )

x = 15

Thus

total number of sweets = 7x + 3x + 2x = 12x = 12 × 15 = 180

7 0

3 years ago