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4 years ago

27a⁰c³ for a =⅔, c = -⅓

Mathematics

1 answer:

Aleonysh [2.5K]4 years ago

6 0

Answer:

- 1

Step-by-step explanation:

Using the rules of exponents

$a^{0}$ = 1

$(a^n)^{m}$ = $a^{nm}$

Given

27 $a^{0}$ $(-\frac{1}{3}) ^{3}$

Note $a^{0}$ = 1 for any value of a, thus

= 27 × 1 × - $\frac{1}{3^{3} }$

= 27 × 1 × - $\frac{1}{27}$ ← cancel the 27 on numerator/ denominator

= 1 × - 1

= - 1

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There are 10 cups of blue paint and 6 red cups of paint.whats the ratio of blue paint to red paint?

noname [10]

10:6

blue paint= 10

red paint= 6

ratio is blue:red

therefore, the answer is 10:6

7 0

3 years ago

Y decreased by 25 =10

KonstantinChe [14]

Written in standard form, y decreased by 25 = 10 is y - 25 = 10

Now let's solve:

y - 25 = 10
y = 10 + 25
y = 35

to check:

35 - 25 = 10

so, y equals 35

8 0

3 years ago

Read 2 more answers

A computer system uses passwords that are exactly six characters and each character is one of the 26 letters (a–z) or 10 integer

ELEN [110]

Answer:

The number of hits would follow a binomial distribution with $n =10,\!000$ and $p \approx 4.59 \times 10^{-6}$ .

The probability of finding $0$ hits is approximately $0.955$ (or equivalently, approximately $95.5\%$ .)

The mean of the number of hits is approximately $0.0459$ . The variance of the number of hits is approximately $0.0459\!$ (not the same number as the mean.)

Step-by-step explanation:

There are $(26 + 10)^{6} \approx 2.18 \times 10^{9}$ possible passwords in this set. (Approximately two billion possible passwords.)

Each one of the $10^{9}$ randomly-selected passwords would have an approximately $\displaystyle \frac{10,\!000}{2.18 \times 10^{9}}$ chance of matching one of the users' password.

Denote that probability as $p$ :

$p := \displaystyle \frac{10,\!000}{2.18 \times 10^{9}} \approx 4.59 \times 10^{-6}$ .

For any one of the $10^{9}$ randomly-selected passwords, let $1$ denote a hit and $0$ denote no hits. Using that notation, whether a selected password hits would follow a bernoulli distribution with $p \approx 4.59 \times 10^{-6}$ as the likelihood of success.

Sum these $0$ 's and $1$ 's over the set of the $10^{9}$ randomly-selected passwords, and the result would represent the total number of hits.

Assume that these $10^{9}$ randomly-selected passwords are sampled independently with repetition. Whether each selected password hits would be independent from one another.

Hence, the total number of hits would follow a binomial distribution with $n = 10^{9}$ trials (a billion trials) and $p \approx 4.59 \times 10^{-6}$ as the chance of success on any given trial.

The probability of getting no hit would be:

$(1 - p)^{n} \approx 7 \times 10^{-1996} \approx 0$ .

(Since $(1 - p)$ is between $0$ and $1$ , the value of $(1 - p)^{n}$ would approach $0\!$ as the value of $n$ approaches infinity.)

The mean of this binomial distribution would be: $n\cdot p \approx (10^{9}) \times (4.59 \times 10^{-6}) \approx 0.0459$ .

The variance of this binomial distribution would be:

$\begin{aligned}& n \cdot p \cdot (1 - p)\\ & \approx(10^{9}) \times (4.59 \times 10^{-6}) \times (1- 4.59 \times 10^{-6})\\ &\approx 4.59 \times 10^{-6}\end{aligned}$ .

4 0

3 years ago

PLS HELP WILL MARK BRAINLIEST!!!!!!!! answer both questions (they are two separate questions)

Angelina_Jolie [31]

Answer A is correct for both questions.

Step-by-step explanation:

The area of the rectangle is lengthxwidth. To find the length, we can divide the area by the width.

$\frac{(4x^2-43x+63)}{(4x-7)}$ is the equation.

We need to simplify it (or just divide). Since the coefficient of the area (on the x^2) is the same as that on the width, we know that that same coefficient on the length is 1.

This gets us to the basic frame (1x+/-y).

To find the value of y, we need to pay attention to the "-43x+63" and "-7" aspects of the area and width, respectively. To get "63," the "-7" was multiplied by the y — by dividing 63 by -7, we know that the value of y is -9 (the numbers both have to be negative to multiply to a positive number).

We are left with the length (x-9). Put together, this means (x-9)(4x-7) is the area. Multiplying, that makes (4x^2-7x-36x+63), or (4x^2-43x+63). Since this is the area given to us, we know our answer is correct. For this question, the answer is A.

*****

Divide $9x^4-2-6x-x^2$ by $3x-1$ . First, put the first equation in order by exponents. We get $\frac{9x^4-x^2-6x-2}{3x-1}$ . Since the exponent on the upper equation goes up to x^4, and we are dividing by a simple x, we know that the first exponent in our answer will be x^3. Since our coefficient needs to have a product of 9 when multiplied by 3, it is 3. The first part of our answer is $(3x^3)$ . Since there is no exponent of 3 for x in the upper equation, and since the "x^2" that has to be the next term in the equation due to it being present in each answer choice, we know that it as to be a "+x^2" — the "3x^3 that result from the "-1" (in the lower equation) being multiplied by 3x^3 have to be cancelled out by a "-3x^3", and if the sign for the term "x^2" is negative, we end up with tw0 "3x^3" that add up to "6x^3" instead of cancelling each other out.

Now, we have $(3x^3-x^2)$ . We can immediately rule out C. Moving on.

We now have $(3x-1)(3x^3+x^2)=9x^4-x^2$ . We can rule out answer choice B because it is incomplete - we are missing the second part of the upper equation, "-6x-2." Both of the remaining answers include "-2" as the next term, whether with an x or without.

Honestly, I haven't done algebra in a few years — while I know there's a way to deduce the rest of the equation, let's solve the equation using the two remaining answer choices and see which one is correct.

A: $(3x-1)(3x^3+x^2-2-\frac{4}{3x-1} )$

$=9x^4+3x^3-6x -3x^3-x^2+2-4$ (FOIL) (3x-1 times $-\frac{4}{3x-1}$ = -4)

$=9x^4+3x^3-3x^3-x^2-6x+2-4$ (in order of exponents)

$=9x^4-x^2-6x+2-4$ (simplify)

$=9x^4-x^2-6x-2$ (simplify)

D: $(3x-1)(3x^3+x^2-2x-\frac{4}{3x-1} )$

$=9x^4+3x^3-6x^2-\frac{4}{1} -3x^3-x^2+3x+\frac{4}{1}$ (FOIL)

$=9x^4+3x^3-3x^3-7x^2-4+4$ (in order of exponents)

$=9x^4-7x^2$ (simplify)

A is exactly the long fraction we started with ( $9x^4-2-6x-x^2$ ), just in a different order! This means that answer A, when multiplied by (3x-1), equals the same thing which, if divided by (3x-1), yields answer A. Because of the rules of multiplication/division (xy=z, z/x=y, z/y=z), this means that we have the proper set of numbers. Answer A is correct.

I hope this helps!!!!! Let me know if there's anything else I can help with :)

5 0

2 years ago

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Pani-rosa [81]

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3 years ago