If a tank holds 6000 gallons of water, which drains from the bottom of the tank in 50 minutes, then Toricelli's Law gives the volume V of water remaining in the tank after t minutes as

V=5000 (1-1/50*t)^2 0⤠t ⤠50.

1. Find the rate at which water is draining from the tank after the following amount of time. (Remember that the rate must be negative because the amount of water in the tank is decreasing.)

a. 5 min
b. 10 min
c. 20 min
d. 50 min

2. At what time is the water flowing out the fastest?
3. At what time is the water flowing out the slowest?

Answer:

total = m/n * c

m/n gives u the number of pounds u have bought, multplied by the cost of the candies per pound gives u the total amount of money she paid

Answer:

9+4y ≥ -15

y ≥ -6

Step-by-step explanation:

Nine Increased by the product of a number

9+4y

is greater than or equal to -15

9+4y ≥ -15

Subtract 9 from each side

9-9+4y ≥ -15-9

4y ≥ -24

Divide by 4

4y/4 ≥ -24/4

y ≥ -6

Hy mate!!

The answer of your question is in the attachment..!!

.

.

Hope this answer helps you..!!

.

.

Select it as the BRAINLIEST..!!

Answer:

Step-by-step explanation:

If 7 people can pave the drive in 9 hours, we can use that information in equation form to find out how long it would take 1 person to pave the drive alone.

[tex]\frac{7}{x}=\frac{1}{9}[/tex] and cross multiply

x = 63. That means that it would take 1 person, working alone, 63 hours to get the job done. If that be the case, and assuming that the 2 added people work at the same rate as do the first 9, we simply divide that time alone into 11 parts.

It would take 11 people [tex]5.\bar{27}[/tex] hours to pave that driveway.

5+5x>8(x-1)

5+5x>8x-8

5x-8x>-8+5

-3x>-3

5 + 5x > 8(x-1) is equivalent to -3x > -13.

Let, the expression be 5 + 5x > 8(x-1)

By applying Multiplicative Distribution Law, we get

5 + 5x > 8x - 8

Rearrange unknown terms to the left side of the equation, then

5x - 8x > -8 - 5

Combine like terms, we get

-3x > -8 - 5

Calculate the sum or difference

-3x > -13

Divide both sides of the inequality by the coefficient of the variable, then we get

[tex]$x < \frac{-13}{-3}$[/tex]

Determine the sign for multiplication or division:

[tex]$x < \frac{13}{3}$[/tex]

Therefore, the correct answer is -3x > -13.

Complete question:

Which of the following is equivalent to 5 + 5x > 8(x - 1)?

-3x > -12

3x < 13

3x < 6

-4x > -12

To learn more about algebraic expression

https://brainly.com/question/4344214

#SPJ2

Answer:

9 1/14

Step-by-step explanation:

127 ÷14

127 divided by 14 equals

9 with a remainder of 1

Answer:

Should be (B).

8.5

ED2021

Answer: B

Step-by-step explanation:

Answer:

Step-by-step explanation:

The position function for this is:

[tex]s(t)=-16t^2+88t+9[/tex]. We can use this equation to find the position (or height) of the rocket at ANY TIME during its flight. I could find out the height of the rocket at 3 seconds by plugging in a 3 for t and solving for s(t); I could find the height of the rocket at 12 seconds by plugging in a 12 for t and solving for s(t), etc.

The first derivative of position is velocity:

v(t) = -32t + 88.

If we are looking for the time the rocket reaches it max height, we need to remember from physics class that this happens when the velocity of the object is at 0. We set the velocity equation equal to 0 then and solve for t:

0 = -32t + 88 and

-88 = -32t so

t = 2.75 seconds. This means that 2.75 seconds after the rocket is launched, it reaches its max height. In order to find what that max height is we plug 2.75 into the position equation for t and solve:

[tex]s(2.75)=-16(2.75)^2+88(2.75)+9[/tex] to get that

s(2.75) = 130

The max height is 130 feet and it reaches this point at 2.75 seconds into its motion.

Answer:

Hello,

Answer B

Step-by-step explanation:

Since A=15*20+B and B<15

The max for B is 14

==> 300+14=314

9514 1404 393

Answer:

  -1/512

Step-by-step explanation:

The first term is -4, and the common ratio is -2/-4 = 1/2. Then the n-th term is ...

  an = -4·(1/2)^(n-1)

and the 12th term is ...

  a12 = -4(1/2)^(12 -1) = -4/2048

  a12 = -1/512

The maximum length of the seesaw is option c  4.00 meters.

A right-angled triangle is one in which one of the angles is equal to 90 degrees. A 90 degree angle is called a right angle, which is why a triangle made up of right angle is termed a right angled triangle.

A right-angled triangle has three sides- hypotenuse, base and height. Hypotenuse is the longest and also the opposite side of the right angle of the triangle, base and height of a right triangle are always the sides adjacent to the right angle.

The formula for measuring the hypotenuse is,

Height / Hypotenuse = Sinθ , where θ is the angle opposite to the height of the triangle.

In the given question, the seesaw should make an angle of 30° with the ground and the maximum height it should rise is 2 meters so the height here is 2 meters. So the seesaw will make a right angled triangle.

Height = 2 meters, θ = 30°,

Now using the formula,

2 / Hypotenuse = Sin30°

Rearranging we get,

Hypotenuse = 2 / Sin30°

The value of Sin30° is 1/2 and putting the value we get,

Hypotenuse = 2 / (1/2)

                     = 2 × 2

                     = 4 meters.

Therefore, the maximum length of the seesaw (that is the hypotenuse ) is 4 meters.

To learn more about right-angled triangles and finding sides of it click here-brainly.com/question/10331046

#SPJ2

Answer:

Confidence Interval

Lower Limit = $4,233.3

Upper Limit = $4,766.7

With 95% confidence, the mean profit per customer that SoftBus can expect to obtain is between $4,233.30 and $4,766.7 based on the given sample data.

Step-by-step explanation:

The z-score of 95% = 1.96

             Profit         Mean      Square Root

                          Difference    of MD

P1        $5,000       $500        $250,000

P2         4,500          0              0

P3         4,000       -500         $250,000

Total $13,500                        $500,000

Mean $4,500 ($13,500/3)    $166,667 ($500,000/3)

Standard Deviation = Square root of $166,667 = 408.2

Margin of error = (z-score * standard deviation)/n

= (1.96 * 408.2)/3

= 266.7

= $266.7

Confidence Interval = Sample mean +/- Margin of error

= $4,500 +/- 266.7

Lower Limit = $4,233.3 ($4,500 - $266.7)

Upper Limit = $4,766.7 ($4,500 + $266.7)

Answer:

Step-by-step explanation:

3

Answer:

Approximately 68% of people have IQs between 84 and 116.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean of 100, standard deviation of 16.

Percentage of people with IQs between 84 and 116.

84 = 100 - 16

116 = 100 + 16

So within 1 standard deviation of the mean, which, by the Empirical Rule, is approximately 68%.

Answer:

D

Step-by-step explanation:

inverse just means opposite so if its shown dividing it first then adding, then the inverse is multiplying then subtracting

Answer:

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The numerical coefficient is sqrt(8/3), so all you have eliminated is D.

Now you have to consider the literal all by itself.

sqrt(x^2)/sqrt(x) can be written as (sqrt(x^2/x)) = sqrt(x)

x^2 when divided by x leaves x

another way of looking at it is sqrt(x)*sqrt(x) / sqrt(x) = sqrt(x)

So the answer is sqrt(8/3 * x)

Answer:

I didn't find the answer in the options

the height of the bigger triangle is 11√6/√3 = 11√2

x = 11√2 × √2 = 11×2 = 22

Answered by GAUTHMATH

Answer:

0.1151 = 11.51% probability of completing the project over 20 days.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Expected completion time of the project = 22 days.

Variance of project completion time = 2.77

This means that [tex]\mu = 22, \sigma = \sqrt{2.77}[/tex]

What is the probability of completing the project over 20 days?

This is the p-value of Z when X = 20, so:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{20 - 22}{\sqrt{2.77}}[/tex]

[tex]Z = -1.2[/tex]

[tex]Z = -1.2[/tex] has a p-value of 0.1151.

0.1151 = 11.51% probability of completing the project over 20 days.

Answer:

5/6

Step-by-step explanation:

12/3 × 1/2 = 5/6

hope it helps

please mark Brainliest

Answer:

20/x

Step-by-step explanation:

speed = distance /time

x km/h is speed

20 km is distance

x= 20/t

t= 20/x

Answer:

hiuu ui9i io9

Step-by-step explanation:

iu9uj k

Base case (n = 1):

• left side = 1×2² = 4

• right side = 1×(1 + 1)×(3×1² + 11×1 + 10)/12 = 4

Induction hypothesis: Assume equality holds for n = k, so that

1×2² + 2×3² + 3×4² + … + k × (k + 1)² = k × (k + 1) × (3k ² + 11k + 10)/12

Induction step (n = k + 1):

1×2² + 2×3² + 3×4² + … + k × (k + 1)² + (k + 1) × (k + 2)²

= k × (k + 1) × (3k ² + 11k + 10)/12 + (k + 1) × (k + 2)²

= (k + 1)/12 × (k × (3k ² + 11k + 10) + 12 × (k + 2)²)

= (k + 1)/12 × ((3k ³ + 11k ² + 10k) + 12 × (k ² + 4k + 4))

= (k + 1)/12 × (3k ³ + 23k ² + 58k + 48)

= (k + 1)/12 × (3k ³ + 23k ² + 58k + 48)

On the right side, we want to end up with

(k + 1) × (k + 2) × (3 (k + 1) ² + 11 (k + 1) + 10)/12

which suggests that k + 2 should be factor of the cubic. Indeed, we have

3k ³ + 23k ² + 58k + 48 = (k + 2) (3k ² + 17k + 24)

and we can rewrite the remaining quadratic as

3k ² + 17k + 24 = 3 (k + 1)² + 11 (k + 1) + 10

so we would arrive at the desired conclusion.

To see how the above rewriting is possible, we want to find coefficients a, b, and c such that

3k ² + 17k + 24 = a (k + 1)² + b (k + 1) + c

Expand the right side and collect like powers of k :

3k ² + 17k + 24 = ak ² + (2a + b) k + a + b + c

==>   a = 3   and   2a + b = 17   and   a + b + c = 24

==>   a = 3, b = 11, c = 10

Answer:

7/18

Step-by-step explanation:

1/6 x 3 = 3/18

3/18 + 4/18 = 7/18

Answer:

7/18

Step-by-step explanation:

Make the denominators the same!

You can turn 1/6 into 3/18 by multiplying the numerator and denominator by 3. Then you add the numerators of 3/18 and 4/18 together to get 7/18.

It can't be simplified any further :)

Answer:

picture not clear what is the length

Answer:

b = 53

c = 53

Step-by-step explanation:

Alright so we already know that b and c are going to have the same angle measures. We can find b by subtracting 180 degrees to 127. Why you may ask? Its because when b and 127 are added together its obvious that it creates a straight line (supplementary angle). This means that two angles will sum up to 180 degrees. We can create an easy equation and solve for b.

127 + b = 180

b = 53 and c = 53

Best of Luck!

9514 1404 393

Answer:

  (b)  (−3, −5), because the point satisfies both equations

Step-by-step explanation:

Any solution to a system of two equations must satisfy both equations. The only reasonable explanation of "why" is the one associated with the answer shown above.

-291x+10

:)))))) Have fun

We have a function,

[tex]f(x)=x^2-1[/tex]

and we are asked to find its inverse function.

An inverse function essentially gets you the original value that was dropped into a function.

For example,

If I put 5 into [tex]f(x)[/tex] I will get 24. Now If I take 24 and put it into the inverse function I have to get number 5 back.

The way to determine the inverse function swap the x and the [tex]f(x)[/tex], then solve for [tex]f(x)[/tex],

[tex]x=f(x)^2-1[/tex]

[tex]f(x)^2=x+1[/tex]

[tex]f(x)=\pm\sqrt{x+1}[/tex]

Of course the notation demands that the obtained function be called,

[tex]f^{-1}(x)=\pm\sqrt{x+1}[/tex]

Hope this helps :)

Answer:

352

Step-by-step explanation:

I = PRT  where P is the principle, I is the interest rate, T is the time

I = 275 ( .08) ( 16)

I = 352