1 1/4 gallons fill 5/6 of a bucket. how many gallons will it take to fill the entire bucket?

9514 1404 393

Answer:

  7953.873

Step-by-step explanation:

The first derivative is ...

  f'(x) = 4·3x²·e^x +4x³·e^x = e^x(4x³ +12x²)

Then the second derivative is ...

  f''(x) = (12x² +24x)e^x +(4x³ +12x²)e^x

  f''(x) = e^x(4x³ +24x² +24x)

So, f''(3) = (e^3)(4·27 +24·9 +24·3) = 396e^3 = 7953.87262158

Rounded to thousandths, this is ...

  f''(3) = 7953.873

Answer:

f''(x) ≈ 7953.87

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Calculus

Derivatives

Basic Power Rule:

Product Rule: [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]

Derivative Rule: [tex]\displaystyle \frac{d}{dx} [e^x]=e^x[/tex]

Step-by-step explanation:

Step 1: Define

f(x) = 4x³eˣ

f''(x) is x = 3 for 2nd Derivative

Step 2: Differentiate

Step 3: Evaluate

Answer:

the first one and that's the only one

[tex]3i\sqrt{3} \ \text{ and } \ i\sqrt{27}[/tex]

===================================================

Work Shown:

We will use the rule that sqrt(A*B) = sqrt(A)*sqrt(B) to get the following

[tex]x = \sqrt{-27}\\\\x = \sqrt{-1*27}\\\\x = \sqrt{-1}*\sqrt{27}\\\\x = i\sqrt{27} \ \text{ ... one answer; choice D}\\\\x = i\sqrt{9*3}\\\\x = i\sqrt{9}*\sqrt{3}\\\\x = i*3*\sqrt{3}\\\\x = 3i\sqrt{3} \ \text{ ... another answer; choice A}\\\\[/tex]

While choices C and D seem to look equivalent, note how the 'i' is under the square root in choice C. The 'i' term must be outside the root to be equivalent to the original expression. We denote [tex]i=\sqrt{-1}[/tex]

Answer:

140°

Step-by-step explanation:

angle D+ angle A=180°(by co interior angle)

40°+a=180°

a=180°-40°

a=140°

Answer:

(48.70-1.20)/4.75 = x x=10

Step-by-step explanation:

you should get the x by its self by moving the 1.20 over to the other side then divide by the 4.75 this would get x by its self leaving you to answer and get an answer of 10

Chase rode the taxi for 10 miles.

Let the number of miles in the taxi ride be represented by x.

Pick up fee = $1.20

Amount per mile = $4.75 per mile.

Therefore, the number of miles in the taxi ride will be:

1.20 + (4.75 × x) = 48.70

1.20 + 4.75x = 48.70

Collect like terms

4.75x = 48.70 - 1.20

4.75x = 47.50

Divide both side by 4.75

4.75x/4.75 = 47.50/4.75.

x = 10

Therefore, the number of miles is 10 miles

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Answer:

'less than or equal to' sign

Answer:

here

Step-by-step explanation:

2.000.000.099

Answer:

7.50 dollar

Step-by-step explanation:

Answer:

$7.50

Step-by-step explanation:

300 divided by 40 is 7.50

Answer:

25%

Step-by-step explanation:

25/100 = 25%

The percentage value of $0.25 in one dollar is 25%.

Given data:
The initial amount is represented as $0.25.

The value of one dollar is $1.

To determine what percent $.25 is of one US dollar, divide $.25 by $1 and then multiply by 100 to express it as a percentage.

($.25 / $1) * 100 = 0.25 * 100

0.25 * 100 = 25 %

So, the value is 25 %.

Hence, $.25 is 25% of one US dollar.

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#SPJ6

Answer: 13/24

Step-by-step explanation: M A T H W A Y Calculator

Answer:

0.54166666666 or 13/24

Step-by-step explanation:

Answer:

csd zxsd

Step-by-step explanation:

Answer:

2 and then 1

Step-by-step explanation: 1 is the slideing line that goes up to down and 2 is the angle that goes left & right (thats all i can exsplain sorry ;(      )

Step-by-step explanation:

(-23) x 93 = - 2139

(- 16 ) x (- 30) = 480

14 x (- 12) = - 168

9514 1404 393

Answer:

  80

Step-by-step explanation:

ab is the product of 'a' and 'b'. For the given values, that is the product ...

  ab = (-16)(-5) = 80

_____

When the number of minus signs is even, the resulting product is positive.

Answer:

There is an outlier because she was injured and could not run.

Step-by-step explanation:

There are several reasons why Cassie wouldn't have been able to run on Sunday, but a potential reason is because she had a minor injury that took her one day to heal. Because of her taking this day off, it creates an outlier in our table.

Answer:

m>1

Step-by-step explanation:

inverse operations... add 3 to both sides so you get -2+3=1!!

Answer:

There are 20 students in the class

Step-by-step explanation:

Answer:

I believe it is 20

Step-by-step explanation:

Tell me if  I am wrong so I can improve.

Answer:

340

Step-by-step explanation:

Answer:

8(-5 - -2) = 24. Inside the parantheses is 3. Then you'd multiply 8, which is 24

Step-by-step explanation:

Answer:

-24

Step-by-step explanation:

I got my answer by plugging in the value of the variables into the equation:

8(x - y)

8((-5) - (-2))

8(-3)

-24

I hope this helps! :)

9514 1404 393

Answer:

  C) Rotation 90° CW about the origin

Step-by-step explanation:

The transformation for rotation CW 90° is ...

  (x, y) ⇒ (y, -x)

This is apparently the transformation that gets ...

  A(1, 3) ⇒ A'(3, -1)

__

Additional comment

Attached is a list of the commonly used transformations for your reference.

Answer:

C

Step-by-step explanation:

Answer:

1486.14

Step-by-step explanation:

Answer:

Area of triangle is 1 inches²

Step-by-step explanation:

We are given:

Base of triangle = 16 inches

Height of triangle = [tex]\frac{1}{8} \:[/tex] inches

We need to find:

Area of triangle

The formula used to find Area of triangle is:

[tex]Area \:of\: triangle=\frac{1}{2}\times b \times h[/tex]

where b is base and h is height.

Putting values and finding area:

[tex]Area \:of\: triangle=\frac{1}{2}\times 16 \times \frac{1}{8}\\ Area \:of\: triangle=\frac{16}{16}\\ Area \:of\: triangle=1\:inches^2[/tex]

So,  Area of triangle is 1 inches²

Answer:

Answer will be A 200( 12+3)

Answer:56 :)

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

Answer:

16t=69

Step-by-step explanation:

Answer:

The inequality would be (310-120)/10 less than or equal to x

19 hours minimum

Step-by-step explanation:

(310-120)/10

190/10

19

Answer:

h(x) = [tex](x+5)^{2}[/tex] -18

Step-by-step explanation:

-b/2a is the formula to find the vertex's x coordinate.

-10/2(1) = -5 and "(x+5)" represents a translation to the left 5 units, so that must be the answer

Answer:

a) 0.5488 = 54.88% probability that the family did not make a trip to an amusement park last year.

b) 0.3293 = 32.93% probability that the family took exactly one trip to an amusement park last year.

c) 0.1219 = 12.19% probability that the family took two or more trips to amusement parks last year.

d) 0.8913 = 89.13% probability that the family took three or fewer trips to amusement parks over a three-year period.

e) 0.1912 = 19.12% probability that the family took exactly four trips to amusement parks during a six-year period.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

Poisson distributed, with a mean of 0.6 trips per year

This means that [tex]\mu = 0.6n[/tex], in which n is the number of years.

a.The family did not make a trip to an amusement park last year.

This is P(X = 0) when n = 1, so [tex]\mu = 0.6[/tex].

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-0.6}*(0.6)^{0}}{(0)!} = 0.5488[/tex]

0.5488 = 54.88% probability that the family did not make a trip to an amusement park last year.

b.The family took exactly one trip to an amusement park last year.

This is P(X = 1) when n = 1, so [tex]\mu = 0.6[/tex].

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 1) = \frac{e^{-0.6}*(0.6)^{1}}{(1)!} = 0.3293[/tex]

0.3293 = 32.93% probability that the family took exactly one trip to an amusement park last year.

c.The family took two or more trips to amusement parks last year.

Either the family took less than two trips, or it took two or more trips. So

[tex]P(X < 2) + P(X \geq 2) = 1[/tex]

We want

[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]

In which

[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.5488 + 0.3293 = 0.8781[/tex]

[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.8781 = 0.1219[/tex]

0.1219 = 12.19% probability that the family took two or more trips to amusement parks last year.

d.The family took three or fewer trips to amusement parks over a three-year period.

Three years, so [tex]\mu = 0.6(3) = 1.8[/tex].

This is

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-1.8}*(1.8)^{0}}{(0)!} = 0.1653[/tex]

[tex]P(X = 1) = \frac{e^{-1.8}*(1.8)^{1}}{(1)!} = 0.2975[/tex]

[tex]P(X = 2) = \frac{e^{-1.8}*(1.8)^{2}}{(2)!} = 0.2678[/tex]

[tex]P(X = 3) = \frac{e^{-1.8}*(1.8)^{3}}{(3)!} = 0.1607[/tex]

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.1653 + 0.2975 + 0.2678 + 0.1607 = 0.8913[/tex]

0.8913 = 89.13% probability that the family took three or fewer trips to amusement parks over a three-year period.

e.The family took exactly four trips to amusement parks during a six-year period.

Six years, so [tex]\mu = 0.6(6) = 3.6[/tex].

This is P(X = 4). So

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 4) = \frac{e^{-3.6}*(3.6)^{4}}{(4)!} = 0.1912[/tex]

0.1912 = 19.12% probability that the family took exactly four trips to amusement parks during a six-year period.

Probabilities are used to determine the chances of events.

The given parameters are:

[tex]p = 0.6[/tex]

The distribution is given as a Poisson distribution.

So, we have:

[tex]P(x) = \frac{e^{-\mu} \times \mu^x}{x!}[/tex]

Where:

[tex]\mu = np[/tex]

Last year means that:

[tex]n = 1[/tex] --- the number of years.

No trip, means that:

[tex]x = 0[/tex]

So, we have:

[tex]\mu = np[/tex]

[tex]\mu = 1 \times 0.6[/tex]

[tex]\mu = 0.6[/tex]

The probability becomes

[tex]P(x) = \frac{e^{-\mu} \times \mu^x}{x!}[/tex]

[tex]P(0) = \frac{e^{-0.6} \times 0.6^0}{0!}[/tex]

[tex]P(0) = \frac{0.5488 \times 1}{1}[/tex]

[tex]P(0) = 0.5488[/tex]

Hence, the probability that the family did not make a trip to an amusement park last year is 0.5488

This means that:

x = 1.

So, we have:

[tex]P(x) = \frac{e^{-\mu} \times \mu^x}{x!}[/tex]

[tex]P(1) = \frac{e^{-0.6} \times 0.6^1}{1!}[/tex]

[tex]P(1) = \frac{0.5488 \times 0.6}{1}[/tex]

[tex]P(1) = 0.3293[/tex]

Hence, the probability that the family took exactly one trip to an amusement park last year is 0.3293

This means that:

x = 2,3...

So, we make use of the following complement rule:

[tex]P(x\ge 2) = 1 - P(x < 2)[/tex]

This gives

[tex]P(x\ge 2) = 1 - P(0) - P(1)[/tex]

So, we have:

[tex]P(x\ge 2) = 1 - 0.5488 - 0.3293[/tex]

[tex]P(x\ge 2) = 0.1219[/tex]

Hence, the probability that the family took two or more trips to an amusement park last year is 0.1219

For a three-year period, we have:

[tex]n = 3[/tex]

So, the mean of the distribution is:

[tex]\mu = np[/tex]

[tex]\mu = 3 \times 0.6[/tex]

[tex]\mu = 1.8[/tex]

The probability is then represented as:

[tex]P(x \le 3) = P(0) + P(1) + P(2) + P(3)[/tex]

Calculate P(0) to P(3) using:

[tex]P(x) = \frac{e^{-\mu} \times \mu^x}{x!}[/tex]

So, we have:

[tex]P(0) = \frac{e^{-1.8} \times 1.8^0}{0!}[/tex]

[tex]P(0) = \frac{0.1653 \times 1}{1}[/tex]

[tex]P(0) = 0.1653[/tex]

[tex]P(1) = \frac{e^{-1.8} \times 1.8^1}{1!}[/tex]

[tex]P(1) = \frac{0.1653 \times 1.8}{1}[/tex]

[tex]P(1) = 0.2975[/tex]

[tex]P(2) = \frac{e^{-1.8} \times 1.8^2}{2!}[/tex]

[tex]P(2) = \frac{0.1653 \times 3.24}{2}[/tex]

[tex]P(2) = 0.2678[/tex]

[tex]P(3) = \frac{e^{-1.8} \times 1.8^3}{3!}[/tex]

[tex]P(3) = \frac{0.1653 \times 5.832}{6}[/tex]

[tex]P(3) = 0.1607[/tex]

So, we have:

[tex]P(x \le 3) = P(0) + P(1) + P(2) + P(3)[/tex]

[tex]P(x \le 3) = 0.1653 + 0.2975 + 0.2678 + 0.1607[/tex]

[tex]P(x \le 3) = 0.8913[/tex]

Hence, the probability that the family took three or fewer trips to amusement parks over a three-year period is 0.8913

A six-year period means that:

[tex]n = 6[/tex]

So, the mean of the distribution is:

[tex]\mu = np[/tex]

[tex]\mu = 6 \times 0.6[/tex]

[tex]\mu = 3.6[/tex]

The probability is then calculated as:

[tex]P(x) = \frac{e^{-\mu} \times \mu^x}{x!}[/tex]

So, we have:

[tex]P(4) = \frac{e^{-3.6} \times 3.6^4}{4!}[/tex]

[tex]P(4) = \frac{0.0273 \times 167.9616}{24}[/tex]

[tex]P(4) = 0.1911[/tex]

Hence, the probability that the family took exactly four trips to amusement parks over a six-year period is 0.1911

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