an industrial manufacturing company uses an inverted conical (cone-shaped) tank to dispense liquid into containers. the tank measure 24 inches with a base radius of 48 inches. if the liquid flows out of the tank at a rate of 40 cubic inches per minute, at what rate is the height of the liquid falling when the height of the liquid is 10 inches deep?

The required measures of the angle A, L, and J is 40.8°, 83°, and 95° respectively.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
1.

The sum of the vertical angle is 180°. So,
∠A + ∠B = 180
Substitute value in the above equation,
x + 4x - 24 = 180
5x - 24 = 180
5x = 204
x = 204 / 5
x = 40.8°
∠A = 40.8°
Similarly,
2. ∠L = 83°
3. ∠J = 95°

Thus, the required measures of the angle A, L, and J is 40.8°, 83°, and 95° respectively.

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Explanation

Step 1

let x represents the numbers of days you can stay at the beach

then,

You estimate that it will cost $160 a day for food, entertainment and hotel, plus $230 round trip airfare.

so

but, you have only $1200, so the total needs to be smaller or equal than 1200

Step 2

solve the inequality

it means you can stay maximum 6 days

I hope this helps you

This is an example of a geometric distribution with success probability p=0.102

The expected number of rolls is 10.

This is an example of a geometric distribution with success probability p=0.102 The expected value of the random variable of a geometric distribution is 1/p=1/0.102=9.80

Therefore, the expected number of rolls is 10.

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Remember that the formula to calculate the total amount in an account with compoud interest is:

Where:

• P, is the principal (amount incially invested)

• r ,is the rate of interest

• n, is the times that the interest is compounded

Using this and the data given we'll get:

Thereby, we can conclude that the accounts balance after 9 years is $3,049.87

Answer:

(I) y=10-6x. (ii) y=x/-2 - 3

When two bills are drawn randomly without replacement,  the probability that their sum is $20 or more is 1/2.

Given,

An envelope contains 8 bills;

Two of $1 bills, Two of $5 bills, Two of $10 bills, Two of $20 bills.

When two bills are drawn randomly without replacement, we have to find the probability that their sum is $20 or more.

Total  outcomes = 2 x 2 x 2 x 2 = 16

Total possible outcomes, more than 20;

(1, 20), (20, 1), (5, 20), (20, 5), (10, 10), (20, 10), (10, 20), (20, 20) = 8 cases

That is,

The total possible outcomes is 8.

Now,

The probability of bill to be $20 or more = Possible outcome / Total outcome

Probability = 8/16 = 1/2

That is,

When two bills are drawn randomly without replacement,  the probability that their sum is $20 or more is 1/2.

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$3

the amount paid after adding tip is $21

the amount for the meal is $18

$21-$18=$3

The given expression is,

Multiplying all the terms with 5, we get

Thus, the solution is, x = 75.

Answer:

(7,-3)

Step-by-step explanation:

x = 7

-2x - 9y = 13

* Substituition is the easieat way to solve such a function.

- Firstly, put "7" instead of "x" in the equation.

- multiply "7" by "-2"

- Solve for "y"

* -2x-9y = 13

* -2×7-9y = 13

* -14-9y = 13

* -9y = 27

* -9y/-9 = 27/-9

* y = -3

# Since x = 7, the output/"y" will be -3

(7,-3)

We are given a graph and we are asked to determine if it is a function or not. To do that we will use the vertical line test. We will draw a vertical line and if the line touches the graph in more than two places in any given value of "x" then it is not a function. Therefore, the vertical line we get is:

Since the vertical line touches the graph in two axes this means that the given graph is not a function.

Answer:

The equations that have infinitely many solutions are;

Explanation:

For an equation to have infinitely many solutions, the left-hand side of the equation and the right side of the equation must be equivalent/equal.

That means that the expression before the equal sign must be equivalent to the expression after the decimal.

such as;

From the given equation, the equations that have their left and right sides equivalent are;

Therefore, the equations that have infinitely many solutions are;

Let

x -----> number of rides

y ----> the total cost

so

The linear equation that represents both situations are

y=40 -----> equation A

y=x+15 ----> equation B

equate both equations

40=x+15

solve for x

x=40-15

x=25

therefore

Using concept of Linear equations, we find $40 is the daily fee for renting a moving truck.

Linear equations are generally equations of the first order. The linear equations are defined for the lines in the coordinate system. When the equation having  a homogeneous variable of degree 1 (i.e. only one variable), then it is called as a linear equation in one variable. A linear equation can have more than one variables. If the linear equation has two variables, then it is known as  linear equations in two variables and so on. Some of the examples of linear equations which are listed here 2x – 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, 3x – y + z = 3.

So, lets suppose daily fee for renting a movie a truck is $x

Then according to question,

Daily fee+ total distance travelled × charge per mile=total cost

=>x+48×0.50=64

On solving x, we get x=40

Hence, daily fee cost is $40 which is required for renting a moving truck.

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As per the concept of Simple interest, the value of x that refers the time is 0.000057.

Simple interest:

Simple interest is obtained by multiplying the daily interest rate by the principal by the number of days that elapse between payments.

Give,

Here we have the expression like the following:

p*r*t=I

4350 * 4 * x =1

Here we need to find the value of x.

While we looking into the expression, we have identified that the value of

Principal amount (p) = 4350

rate of interest (r) = 4

Time = x

Interest amount (I) = 1

So, while we execute this expression then we get the value of times as,

=> 4350 x 4 x x = 1

Here we need the value of x so, we have to move the other to the right hand side, then we get,

=> x = 1/(4350 x4)

=> x = 1/17400

=> x = 0.000057

Therefore, the value of x is 0.000057.

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Answer:

Choice A. 1.1

Explanation:

According to Euler's Theorem, if gcd(a,n) = 1, then a(n) 1. (mod n). The number of relatively prime integers in the range of 1, 2,..., n-1 is represented by the Euler totient function.

The probability that mn has a units digit of 1 = 2/5

By Euler's Theorem, we have that [tex]$a^{4} \equiv 1 \pmod {10}$[/tex] if [tex]$\gcd(a,10)=1$[/tex] Hence[tex]$m=11,13,17,19$,[/tex][tex]$n=2000,2004,2008,2012,2016$[/tex] work.

Also note that [tex]$11^{\text{any positive integer}}\equiv 1 \pmod {10}$[/tex] because [tex]$11^b=(10+1)^b=10^b+10^{b-1}1+...+10(1)+1$[/tex], and the latter[tex]$\pmod {10}$[/tex]is clearly [tex]$m=11$[/tex],  [tex]$n=1999,2001,2002,2003,2005,...,2018$[/tex] work (not counting multiples of 4 as we would be double counting if we did).

We can also note that [tex]$19^{2a}\equiv 1 \pmod {10}$[/tex] because[tex]$19^{2a}=361^{a}$[/tex], and by the same logic as why [tex]$11^{\text{any positive integer}}\equiv 1 \pmod {10}$[/tex]we are done. Hence [tex]$n=2002, 2006, 2010, 2014, 2018$[/tex] and [tex]$m=19$[/tex] work (not counting any of the aforementioned cases as that would be double counting).

We cannot make any more observations that add more[tex]$m^n$[/tex] with unit digit [tex]$1$[/tex], hence the number of [tex]$m^n$[/tex] that have units digit one is [tex]$4\cdot 5+1\cdot 15+1\cdot 5=40$.[/tex] And the total number of combinations of an element of the set of all [tex]$m$[/tex]and an element of the set of all n is  [tex]$5\cdot 20=100$[/tex]. Hence the desired probability is [tex]$\frac{40}{100}=\frac{2}{5}$[/tex].

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Answer:

1. [tex]a=\frac{b}{zm-1}[/tex] 2. [tex]x=\frac{p-n-m}{1-y}[/tex] 3. [tex]a=\frac{z}{m+n+p}[/tex]

Step-by-step explanation:

1. zma = a+b  :    [tex]z=\frac{a+b}{ma} ;[/tex] [tex]m\neq 0[/tex]

zma = a + b  Divide both sides by ma: [tex]m\neq 0[/tex]

[tex]\frac{zma}{ma} =\frac{a}{ma} +\frac{b}{ma} ;[/tex] [tex]m\neq 0[/tex]

2. Subtract m from both sides

x + m - m = p - n + yx - m

Simplify

x = p - n + yx - m

Subtract yx from both sides

x - yx = p - n + yx - m - yx

simplify

x - yx = p - n - m

Factor x - yx:      x(1 - y)

x(1 - y) = p - n - m

simplify x = [tex]\frac{p -n-m}{1-y} ;y\neq 1[/tex]

3.Apply the sum /Different Rule :   (f + g)' = f ' + g'

= [tex]\frac{d}{dp} (am)+\frac{d}{dp} (an)+\frac{d}{dp} (ap)[/tex]

[tex]\frac{d}{dp} (am)=0[/tex]

[tex]\frac{d}{dp} (an)=0[/tex]

[tex]\frac{d}{dp} (ap)=a[/tex]

= 0 + 0 + [tex]a[/tex]

simplify

= a

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Answer:

mA = 69 degrees

Step-by-step explanation:

A complementary angle has a measure of 90 degrees.

(2x + 27) + (2x - 21) = 90

Simplify

4x + 6 = 90

-6

4x = 84

/4

x = 21

mA: 2(21) + 27 = 69

Answer:

A = 69°

Step-by-step explanation:

Complementary angles sum 90°

A + B = 90°

(2x + 27) + (2x-21) = 90°

4x + 27 - 21 = 90°

4x + 6 = 90°

4x = 90 - 6

4x = 84°

x = 84°/4

x = 21

Then A:

A = 2x + 27

A = 2*21  +  27

A = 42 + 27

A = 69°

B = 2x - 21

B = 2(21)  + 27

B = 42 - 21

B = 21°

Check:

69 + 21 = 90

The ∛35 will be plotted between 3 and 4, but closer to 3 on the number line.

In basic mathematics, real numbers are shown as a fine graphic of a graduated straight line which is called a number line.

We know that 35 lies between 27 and 64 , and 27 = 3³ and 64 = 4³.

Hence the ∛35 will be plotted between 3 and 4 and since 35 is closer to 27 than 64 , therefore it will be closer to 3.

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The answer after simplifying the expression, [tex]x^{-10} *x^{6}[/tex], will be [tex]1/x^{4}[/tex].

According to the question,

We have the following expression:

[tex]x^{-10} *x^{6}[/tex]

Now, we know that if two numbers are being multiplied with the same base but different powers then their powers are added.

(More to know: if the numbers are in division with the same base but different powers then their powers are subtracted.)

So, we have:

[tex]x^{-10+6}[/tex]

[tex]x^{-4}[/tex]

Now, we know that if powers are in negative then the number can be inverted to make the power positive (because it is given that the answer should have only positive exponents).

[tex]1/x^{4}[/tex]

Hence, the value after solving the expression is [tex]1/x^{4}[/tex].

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The greatest common factor of a polynomial is the largest expression that divides all of the terms of the polynomial. In this case, we have:

First, find the GCF of the coefficients of the terms. The coefficients are 2, 14 and 6, their GCF is 2.

On the other hand, notice that the factor (c+y) is a common factor for all three terms. Find the greatest power of (c+y) that divides all the terms. Since the lowest power of (c+y) in the expression is 2, then, the greatest power of (c+y) that divides all the terms is (c+y)^2.

The GCF of the expression is the product of the GCF of the coefficients and the GCF of the factors with variables.

Then, the GCF of the expression is:

Factor out 2(c+y)^2 from the expression:

Therefore, the answer is option A and the expression inside the box should be:

The given function F(x) is,

Take the limit of the function when x ix close to 2.

Hence, the function diverges.

The answer is not 1 so it is not that simple that you can divide it into 2 equal size subsets and ask whether the final sequence is in there. From what I got through his hints, it should be related to Central Limit theorem.

Given that,

One hundred coins are flipped, but the outcome is kept a secret. I am able to pose one yes/no query. I'll begin speculating on the outcomes of the coin toss following the response. I receive $1 for each accurate guess, and I lose $1 for each unreliable guess.

To find:

What is the most effective gaming approach and what is the highest possible return on investment

By Central Limit Theorem,

It is not straightforward to divide the response into two subsets of equal size and then check to see if the final sequence is present because the answer is not 1. His indications led me to believe that it should be connected to the Central Limit theorem.

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In the first graph, we have that the whole figure is 1

it is divided in 4 parts:

Then, we want to divide 1 into 4 parts. That is

Then, we have that:

It is the same for the second figure:

Each 1/4 corresponds to each part. Then if we add them:

Hello,

Two parallel lines have the same slope, which means that our line's slope, will also be 1.2.

So now we have a point and a slope, so we can use the following formula to find the equation of the line:

y-y1 = m (x-x1)

Where:

y1 - y coordinate of a point on the line

x1 - x coordinate of the same point on the line

m - slope

Plugging in we get:

y+3 = 1.2 (x-0)

y = 1.2x - 3 (slope intercept form)

or

5y-6x = -15 (standard form)

Cheers

Answer: He is not correct because when simplifying an expression, you can only add like terms together.  

Step-by-step explanation:

you are given the expression: x^2 + 4x - 2x

when simplifying an expression, you can only add/subtract like terms (terms that have the same variable which are raised to the same power).

in the expression, you can only subtract 4x - 2x because they have like terms/the same variable.

you cannot add x^2 to 4x because x^2 and x are NOT like terms/the same variable. (If 4x was 4x^2, then you would be able to add them together.

meaning the simplified expression should be: x^2 + 2x and not 3x^2

The sentence that represents the expression (5 + 5)ve y(5-5) u is:

love you.

The expression is given as follows:

(5 + 5)ve y(5-5)u

There are two operations in the expression, as follows:

Then the expression, with the numbers, is given as follows:

10ve y0o.

The number 10 can be interpreted as the two letters lo, as l and 1 are very similar symbols, as are 0 and o, then the updated expression is:

love y0u.

The same is applied to the final zero, as 0 and o are very similar symbols, hence the sentence that represents the expression is:

love you.

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We are given

Therefore the value of x can be gotten by simplifying the above equation

Given that x is 5, we can proceed to find the value of the expression.

This implies that