Find the volume of the figure. If necessary, round the answer to the nearest whole number.

9514 1404 393

Answer:

   5/9 m/min

Step-by-step explanation:

The depth of the water is 2/5 of the depth of the trough, so the width of the surface will be 2/5 of the width of the trough:

  2/5 × 2 m = 4/5 m

Then the surface area of the water is ...

  A = LW = (18 m)(4/5 m) = 14.4 m²

The rate of change of height multiplied by the area gives the rate of change of volume:

  8 m³/min = (14.4 m²)(h')

  h' = (8 m³/min)/(14.4 m²) = 5/9 m/min

Answer:

39

Step-by-step explanation:

5 + 15 + 12 + 7 = 39

Answer:

39

Step-by-step explanation:

5 + 15 = 20, 12 + 7 = 19, 20 + 19 = 39.

Answer:

A since A is left blank its A

Answer:

she will be using more orange juice

Answer:

she will be using more orange juice

A function f : X → Y assigns only one value of y ∈ Y to any given x ∈ X.

For each of the three elements in {a, b, c}, there are 5 choices of values to assign from {1, 2, 3, 4, 5}, so there are 5³ = 125 possible functions.

Answer:

[tex]S.E = 0.108[/tex]

Step-by-step explanation:

From the question we are told that:

Mean age [tex]\=x=5.5[/tex]

standard deviation [tex]\sigma= 0.7 years.[/tex]

Sample size [tex]n=43[/tex]

Generally the equation for Standard error is mathematically given by

[tex]S.E= \sigma \bar x[/tex]

[tex]S.E= \frac{\sigma}{\sqrt n}[/tex]

[tex]S.E= \frac{0.7}{\sqrt 43}[/tex]

[tex]S.E = 0.108[/tex]

Answer:

A mutually exclusive event is when there are two events that can occur, such as flipping a coin, either it will be a head or a tail. Hence, both the events here are mutually exclusive.

An independent event is termed as an event that occurs without being affected by other events. The happening of one event has nothing to do with the happening of the other and there is no cause-effect between the two.

Answer:

36151,82923

Step-by-step explanation:

30000* ( 1+12,5%/12)^18

Answer:

12

Step-by-step explanation:

arrange the numbers in ascending order and cross out from either side till you have a middle line

FINAL ANSWER:

12

Step-by-step explanation:

Median is the middle number in the data set.

so first of ... we need to arrange the group of numbers from lower to greater.

16, 12, 10, 15, 7, 9, 16 ⇒ 7, 9, 10, 12, 15, 16, 16

Now that we have arranged the numbers from least to greatest all we need to do is to find the middle number of the data set (data set? they are the group of numbers)

Ok, so what you want to do here is to just count the numbers until you get to the middle number of the data set...

7, 9, 10, 12, 15, 16, 16

the median in the given data set is 12.

I hope this helps you!!! Let me know if my answer is incorrect or not...

HAVE A GREAT DAY AND GOD BLESS YOU ;)!!!

Answer:

1 2/3.

Step-by-step explanation:

4 - 2 3/9

= 4 - 2 1/3

= 4 - 7/3

= 12/3 - 7/3

= 5/3

= 1 2/3

(a) The n-th partial sum of the infinite series,

[tex]\displaystyle\sum_{n=0}^\infty\frac5{4^n}[/tex]

is

[tex]S_n = \displaystyle\sum_{k=0}^n\frac5{4^k} = 5\left(1+\frac14+\frac1{4^2}+\cdots+\frac1{4^n}\right)[/tex]

Multiplying both sides by 1/4 gives

[tex]\dfrac14S_n = \displaystyle\sum_{k=0}^n\frac5{4^k} = 5\left(\frac14+\frac1{4^2}+\frac1{4^3}+\cdots+\frac1{4^{n+1}}\right)[/tex]

Subtract this from [tex]S_n[/tex] and solve for [tex]S_n[/tex] :

[tex]S_n-\dfrac14S_n = 5\left(1-\dfrac1{4^{n+1}}\right)[/tex]

[tex]\dfrac34 S_n = 5\left(1-\dfrac1{4^{n+1}}\right)[/tex]

[tex]S_n = \dfrac{20}3\left(1-\dfrac1{4^{n+1}}\right)[/tex]

(your solution is also correct)

(b) The infinite sum is equal to the limit of the n-th partial sum:

[tex]\displaystyle\sum_{n=0}^\infty \frac5{4^n} = \lim_{n\to\infty} \boxed{\sum_{k=0}^n \frac5{4^k}}[/tex]

and the sum indeed converges to 20/3.

Answer:

The second statement is the CONVERSE of the first.

Step-by-step explanation:

x ⇒ y ----> Statement

y ⇒ x ----> Converse

Say there is a statement as follows:

If it rains then it is a holiday.

The converse of the statement would be:

If it is a holiday then it is raining.

In Mathematics, the converse of statements need not always be true.

For example, the school wouldn't be closed only when it is raining. It could close for many other reasons as well.

Consider the following mathematical example.

Statement: If f is a function, then it is a relation.

Converse:   If f is a relation then it is a function, which need not always be true.

When the converse of a statement is also true we can say it is an if and only if (iff) statement.

Statement: If a - b > 0, then a > b.

Converse: If a > b then a - b > 0.

Here, the converse is also true.

W can write the statement as:

a - b > 0 ⇔ a > b

Hope this helps :)!

Answer:

x = 12 m and y = 22 m

Step-by-step explanation:

Total area = 264 [tex]m^2[/tex]

∴ xy = 264

 [tex]$y=\frac{264}{x}$[/tex]     ............(1)

Cost function = [tex]C(x,y) = 2 x (15.60) + 2y(15.60) + 2x(13)[/tex]

                          [tex]C(x,y) = 57.2 x + 31.2y[/tex]

Therefore, using (1),

[tex]$C(x) = 57.2x+31.2 \left(\frac{264}{x} \right)$[/tex]

[tex]$C(x) = 57.2x+\frac{8236.8}{x} \right)$[/tex]

So, cost C(x) minimum where C'(x) = 0

[tex]$C'(x) = 57.2 - \frac{8236.8}{x^2}=0$[/tex]

[tex]$x^2=\frac{8236.8}{57.2}$[/tex]

[tex]$x^2=144$[/tex]

[tex]$x=12$[/tex] m

Therefore, [tex]$y=\frac{264}{x}$[/tex]

                      [tex]$=\frac{264}{12}$[/tex]

                      = 22 m

So the dimensions are  x = 12 m and y = 22 m.

Answer:

Step-by-step explanation:

This is the combination of 2 out of 20:

We have to find,

The number of ways in which he can choose two students.

Now the 2 out of 20 combination is,

→ 20C2

→ 20!/18!2!

→ 20 × 19/2

→ 10 × 19

→ 190 ways

Hence, there are 190 ways.

Step-by-step explanation:

[tex] \boxed{cos^2x=\frac{1-cos2x}{2}}\\cos^2(45+A)+cos^2(45-A)=\frac{1-cos2(45+A)}{2}+\frac{1-cos2(45-A}{2}\\=\frac{1 - cos(90 +2A) }{2} + \frac{1 - cos(90 - 2A) }{2} \\ = \frac{2- ( - sin 2A) - sin2A}{2} \\ = \frac{2 + sin2A -sin2A }{2} \\ = \frac{2}{2} \\ = 1[/tex]

Step-by-step explanation:

Prove that

[tex]\cos^2(45+A)+\cos^2(45-A) =1[/tex]

We know that

[tex]\cos (\alpha \pm \beta) = \cos \alpha\cos \beta \mp \sin \alpha \sin\ beta)[/tex]

We can then write

[tex]\cos (45+A)=\cos 45\cos A - \sin 45\sin A[/tex]

[tex]\:\:\:\:\:\:\:\:= \frac{\sqrt{2}}{2}(\cos A - \sin A)[/tex]

Taking the square of the above expression, we get

[tex]\cos^2(45+A) = \frac{1}{2}(\cos^2A - 2\sin A \cos A + \sin^2A)[/tex]

[tex]= \frac{1}{2}(1 - 2\sin A\cos A)\:\:\;\:\:\:\:(1)[/tex]

Similarly, we can write

[tex]\cos^2(45-A) =\frac{1}{2}(1 + 2\sin A\cos A)\:\:\;\:\:\:\:(2)[/tex]

Combining (1) and (2), we get

[tex]\cos^2(45+A)+\cos^2(45-A)[/tex]

[tex]= \frac{1}{2}(1 - 2\sin A\cos A) + \frac{1}{2}(1 + 2\sin A\cos A)[/tex]

[tex]= 1[/tex]

Given:

The given expression is:

[tex]3.5\times 10^{-2}+2.3\times 10^{-2}[/tex]

To find:

The simplified form of the given expression.

Solution:

We have,

[tex]3.5\times 10^{-2}+2.3\times 10^{-2}[/tex]

It can be written as:

[tex]=(3.5+2.3)\times 10^{-2}[/tex]

[tex]=5.8\times 10^{-2}[/tex]

Therefore, the simplified form of the given expression is [tex]5.8\times 10^{-2}[/tex].

Answer:

1640

Step-by-step explanation:

Take the total amount and divide by the amount for one

Make sure to write 6 cent in dollar form (.06)

98.41 / .06

1640.1666

Round down since we need to buy whole bottles

1640

Answer:  (4, -2)  which is choice A

Explanation:

The rule I used is [tex](x,y) \to (-x,-y)[/tex]

Simply swap the sign of each x and y coordinate to go from (-4, 2) to (4, -2)

This rule only works for 180 degree rotations. It doesn't matter if you go clockwise or counterclockwise.

Answer:

2/5

Step-by-step explanation:

Answer:

Step-by-step explanation:

There are 10 even numbers from 1 to 20

2 4 6 8 10 12 14 16 18 20

There 20 possible choices.

P(Even) = 10 /20 = 1/2

Answer:

c. -[tex]x^{2}[/tex] + 8x + 6

Step-by-step explanation:

2[tex]x^{2}[/tex] + 7x + 6 - (3[tex]x^{2}[/tex] - x)

2[tex]x^{2}[/tex] + 7x + 6 - 3[tex]x^{2}[/tex] + x   (Distributed the negative to terms inside parentheses)

-[tex]x^{2}[/tex] + 8x +6                   (Combine like terms)

Answer:

(negative infinity, positive infinity)

Any value of x makes the equation true.

Step-by-step explanation:

-5(3-4x) = -6+20x - 9

-15 + 20x = -15 + 20x

(negative infinity, positive infinity)

Answer:

True for all x

Step-by-step explanation:

-5(3-4x) = -6+20x - 9

Distribute

-15 +20x = -6+20x - 9

Combine like terms

-15 +20x = -15+20x

Subtract 20x from each side

-15 +20x-20x = -15+20x -20x

-15 =-15

This is true for all x

Th

Answer:

2437miles

Step-by-step explanation:

amount left before it starts over = 999999-98654 = 1354

amount it will show = 3782-1354 = 2437

The odometer will show 2437 miles after 3782 miles if the odometer on your car shows the total number of miles traveled up to 99,999 miles, after it turns over it starts over at 0.

Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.

We have:

The odometer on your car shows the total number of miles traveled up to 99,999 miles.

Current reading = 98,654 miles

After 99,999 miles the odometer turns over it and starts over at 0

The differnece = 99999 - 98654 = 1354

After 1354 miles odometer turns over and starts over at 0

Now, take the difference between 3782 and 1354

= 3782 - 1354

= 2437 miles

After 3782 miles the meter will show 2437 miles

Thus, the odometer will show 2437 miles after 3782 miles if the odometer on your car shows the total number of miles traveled up to 99,999 miles, after it turns over it starts over at 0.

Learn more about the distance here:

brainly.com/question/26711747

#SPJ5

Answer:

The standard error for the new sample size is of 23.4.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Interpretation:

From this, we can gather that the standard error is inversely proportional to the square root of the sample size, that is, for example, if the sample size is multiplied by 4, the standard error is divided by the square root of 4, which is 2.

Standard error of 52.4, sample size multiplied by 5. What is the standard error for the new sample size?

The standard error of 52.4 divided by the square root of 5. So

[tex]s = \frac{52.4}{\sqrt{5}} = 23.4[/tex]

The standard error for the new sample size is of 23.4.

Answer:

The sum of the probabilities of all possible outcomes is not 1, which means that a probability distribution is not given.

Step-by-step explanation:

We are given these following probabilities:

[tex]P(X = 0) = 0.6591[/tex]

[tex]P(X = 1) = 0.2872[/tex]

[tex]P(X = 2) = 0.0503[/tex]

[tex]P(X = 3) = 0.0044[/tex]

[tex]P(X = 4) = 0.0015[/tex]

Determine whether a probability distribution is given.

We have to see if the sum of the probabilities of all possible outcomes is 1. So

[tex]0.6591 + 0.2872 + 0.0503 + 0.0044 + 0.0015 = 1.0025[/tex]

The sum of the probabilities of all possible outcomes is not 1, which means that a probability distribution is not given.

Answer:

The image shows the graph of y = 2 tan x.

[tex] \sf Q) \: {3}^{3} + {4}^{2} = {?}[/tex]

[tex] \sf \to \: {3}^{3} + {4}^{2} [/tex]

[tex] \sf \to \: 27 + 16= 43 [/tex]

Thus, the value is 43.