Anyone know advanced linear algebra and modern algebra?

Answer:

[tex]\frac{61}{99}[/tex]

Step-by-step explanation:

let x = 0.616161 (etc.)

make a second equation because you multiply by 100:

100x = 61.616161 (etc.)

subtract from each other

100x = 61.616161

     x =  0.616161

you get

99x = 61

solve for x

[tex]\frac{61}{99}[/tex]

Answer:

[tex]\boxed{2^{\frac{802}{27}} \cdot 3^9}[/tex]

Step-by-step explanation:

I will try to give as many details as possible.

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[tex]$(3^{-2} \cdot 4^{-5} \cdot 5^0)^{-3} \cdot (4^{-\frac{4}{3^3} })\cdot 3^3$[/tex]

Note that

[tex]\boxed{a^{-b} = \dfrac{1}{a^b}, a\neq 0 }[/tex]

The denominator can't be 0 because it would be undefined.

So, we can solve the expression inside both parentheses.

[tex]\left(\dfrac{1}{3^2} \cdot \dfrac{1}{4^5} \cdot 5^0 \right)^{-3} \cdot \left(\dfrac{1}{4^{\frac{4}{3^3} } }\right)\cdot 3^3[/tex]

Also,

[tex]\boxed{a^{0} = 1, a\neq 0 }[/tex]

[tex]\left(\dfrac{1}{9} \cdot \dfrac{1}{1024} \cdot 1 \right)^{-3} \cdot \left(\dfrac{1}{4^{\frac{4}{27} } }\right)\cdot 27[/tex]

Note

[tex]\boxed{\dfrac{1}{a} \cdot \dfrac{1}{b}= \frac{1}{ab} , a, b \neq 0}[/tex]

[tex]\left(\dfrac{1}{9216} \right)^{-3} \cdot \left(\dfrac{1}{4^{\frac{4}{27} } }\right)\cdot 27[/tex]

[tex]\left(\dfrac{1}{9216} \right)^{-3} \cdot \left(\dfrac{27}{4^{\frac{4}{27} } }\right)[/tex]

[tex]\left( \dfrac{1}{\left(\dfrac{1}{9216}\right)^3} \right)\cdot \left(\dfrac{27}{4^{\frac{4}{9} } }\right)[/tex]

[tex]\left( \dfrac{1}{\left(\dfrac{1}{9216}\right)^3} \right)\cdot \left(\dfrac{27}{4^{\frac{4}{27} } }\right)[/tex]

Note

[tex]\boxed{\dfrac{1}{\dfrac{1}{a} } = a}[/tex]

[tex]9216^3\cdot \left(\dfrac{27}{4^{\frac{4}{9} } }\right)[/tex]

[tex]\left(\dfrac{ 9216^3\cdot 27}{4^{\frac{4}{27} } }\right)[/tex]

Once

[tex]9216=2^{10}\cdot 3^2 \implies 9216^3=2^{30}\cdot 3^6[/tex]

[tex]\boxed{(a \cdot b)^n=a^n \cdot b^n}[/tex]

And

[tex]$4^{\frac{4}{27}} = 2^{\frac{8}{27} $[/tex]

We have

[tex]\left(\dfrac{ 2^{30} \cdot 3^6\cdot 27}{2^{\frac{8}{27} } }\right)[/tex]

Also, once

[tex]\boxed{\dfrac{c^a}{c^b}=c^{a-b}}[/tex]

[tex]2^{30-\frac{8}{27}} \cdot 3^6\cdot 27[/tex]

As

[tex]30-\dfrac{8}{27} = \dfrac{30 \cdot 27}{27}-\dfrac{8}{27} =\dfrac{802}{27}[/tex]

[tex]2^{30-\frac{8}{27}} \cdot 3^6\cdot 27 = 2^{\frac{802}{27}} \cdot 3^6 \cdot 3^3[/tex]

[tex]2^{\frac{802}{27}} \cdot 3^9[/tex]

Answer:

B. Add/subtract the same quantity from both sides.

in this case, it would be adding x to both sides to simplify the equation.

Answer: ADD/SUB THE SAME QUANTITY TO/FROM BOTH SIDES

YES: THEY ARE EQUIVALENT

Step-by-step explanation:

Answer: 30 cents

Step-by-step explanation:

1/20 of a dollar is 5 cents

Then we multiply by the numerator (6) to get our answer....

5x6= 30

Hoped this helps! :)

Answer:

a. 80 students

b. 92 students

Step-by-step explanation:

Represent arts students with A and Dance students with D.

So, we have,

n(A) = 35

n(D) = 57

Required

Determine n(A or D)

Solving (a):

Here, we have:

n(A and D) = 12

n(A or D) is calculated as thus:

n(A or D) = n(A) + n(D) - n(A and D)

n(A or D) = 35 + 57 - 12

n(A or D) = 80

b. From the given details

n(A and D) = 0 because both students are not mixed up as in (a) above

Using the same formula as (a).

n(A or D) = n(A) + n(D) - n(A and D)

n(A or D) = 35 + 57 - 0

n(A or D) = 92

Answer:

i think it would be 11 cups

Answer:

X^2+5x-50

Step-by-step explanation:

X^2-5x+10x-50

Answer:

X² - 5x + 10x - 50

Step-by-step explanation:

Use the FOIL method!

Answer: x=8

Step-by-step explanation:

Answer:

0 degrees faranhiet

Step-by-step explanation:

when you add 14 and -5 you get 9 then the question says 9 degrees cooler so that would translate to the problem 9 - 9 which you get zero.

Answer:

We need the grid to figure this out

Answer:

The derivative is [tex]\frac{dR}{dM} = CM - M^2[/tex]

Step-by-step explanation:

From the question we are told that

The equation representing the reaction is [tex]R = M^2 (\frac{C}{2} - \frac{M}{3} )[/tex]

Generally this equation can be represented as

[tex]R = \frac{C M^2}{2} - \frac{M^3}{3}[/tex]

Generally [tex]\frac{dR}{dM}[/tex] as a function of M is mathematically represented as

[tex]\frac{dR}{dM} = 2 * \frac{C M^{2 - 1 }}{2} + 3 * \frac{M^{3-1}}{3}[/tex]

=> [tex]\frac{dR}{dM} = CM - M^2[/tex]

Answer:

-189

Step-by-step explanation:

Remember to follow the rules of signs:

- If there are two positive signs next to each other, you add:

- If there is one negative sign and one positive sign next to each other, you subtract.

- If there is two negative signs next to each other, you add:

- 412 - (-223) = -412 + 223

Subtract:

223 - 412 = -189

-189 is your answer.

~

Answer:

true

Step-by-step explanation:

Answer:

400, 000 is rounded to the nearest ten thousand

Step-by-step explanation:

There is nothing to round

Answer:

there are 32 bottles needed

Step-by-step explanation:

Thanks

Answer:

a) 0.2588

b) 0.044015

c) 0.12609

Step-by-step explanation:

Using the TI-84 PLUS calculator

The formula for calculating a z-score is is z = (x-μ)/σ,

where x is the raw score

μ is the population mean

σ is the population standard deviation.

From the question, we know that:

μ = 119 inches

standard deviation σ = 17 inches

(a) What proportion of trees are more than 130 inches tall?

x = 130 inches

z = (130-119)/17

= 0.64706

Probabilty value from Z-Table:

P(x<130) = 0.7412

P(x>130) = 1 - P(x<130) = 0.2588

(b) What proportion of trees are less than 90 inches tall?

x = 90 inches

z = (90-119)/17

=-1.70588

Probability value from Z-Table:

P(x<90) = 0.044015

(c) What is the probability that a randomly chosen tree is between 95 and 105 inches tall?

For x = 95

z = (95-119)/17

= -1.41176

Probability value from Z-Table:

P(x = 95) = 0.07901

For x = 105

z = (105 -119)/17

=-0.82353

Probability value from Z-Table:

P(x<105) = 0.2051

The probability that a randomly chosen tree is between 95 and 105 inches tall

P(x = 105) - P(x = 95)

0.2051 - 0.07901

= 0.12609

Answer:

The width is 34.6

Step-by-step explanation:

You have to assume that the cut is a straight cut.

Givens

c = 41

a = 22

b = ?

Formula

a^2 + b^2 = c^2

Solution

22^2 + b^2 = 41^2

484 + b^2 = 1681                   Subtract 484 from both sides

484-484 + b^2 = 1681-484   Combine

b^2 = 1197                              Take the square root of both sides.

sqrt(b^2) = sqrt(1197)

b = 3*sqrt(133)

b = 34.598  

b = 34.6

Answer:

at least 8 gallons

Step-by-step explanation:

Answer:

7

The difference between 9 a positive number and - 2 a negative number is 7 because the question States 9 - 2.

17 dollars total for Jose and Mila's jelly beans.

Add 1.5 and 2.75 together to get 4.25

Multiply 4.25 by 4 to get 17

that is a rational number.

Answer:

Positive

Step-by-step explanation:

A negative divided by a negative can cancel out to make a positive. So, [tex]\frac{-4}{-5} = \frac{4}{5}[/tex].

I hope this helps!

Answer:

i believe its positive because 2 negatives make a positive

Answer:

a. 160-24=g

b. 160-24=g

   -24

   136=g

c. 136

Answer:

m>6

Step-by-step explanation: