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3 years ago

Solve the equation v^3=80

Mathematics

2 answers:

In-s [12.5K]3 years ago

5 0

Answer: $v=2\sqrt[3]{10}$ or 4.3

Step-by-step explanation:

Step 1 Take the cube root of both sides.

$v=\sqrt[3]{80}$

Step 2 Simplify $3\sqrt{80}$ to $2\sqrt[3]{10}$

$v=2\sqrt[3]{10}$

Decimal Form: 4.3

Luba_88 [7]3 years ago

3 0

Answer:

4.31

Step-by-step explanation:

Find the cube root of both sides of the equation.

$^3\sqrt{v^3}$ = $^3\sqrt{80}$

The cube root will cancel out the cubed in the variable.

v = $^3\sqrt{80}$

Find the cube root of 80. I rounded to the nearest hundredth.

v = 4.31

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3 years ago

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One household is to be selected at random from a town. The probability that the household has a cat is 0.20.2 . The proba

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Answer:

There is a 50% probability that the household has a dog, given that the household has a cat.

Step-by-step explanation:

We solve this problem building the Venn's diagram of these probabilities.

I am going to say that:

A is the probability that a household has a cat.

B is the probability that a household has a dog.

We have that:

$A = a + (A \cap B)$

In which a is the probability that a household has a cat but not a dog and $A \cap B$ is the probability that a household has both a cat and a dog.

By the same logic, we have that:

$B = b + (A \cap B)$

The probability that the household has a cat or a dog is 0.5

$a + b + (A \cap B) = 0.5$

The probability that the household has a dog is 0.4

$B = 0.4$

$B = b + (A \cap B)$

$b = 0.4 - (A \cap B)$

The probability that the household has a cat is 0.2.

$A = 0.2$

$A = a + (A \cap B)$

$a = 0.2 - (A \cap B)$

$a + b + (A \cap B) = 0.5$

$0.2 - (A \cap B) + 0.4 - (A \cap B) + (A \cap B) = 0.5$

$A \cap B = 0.1$

What is the probability that the household has a dog, given that the household has a cat?

20% of the households have a cat, and 10% have both a cat and a dog. So

$P = \frac{A \cap B}{A} = {0.1}{0.2} = 0.5$

There is a 50% probability that the household has a dog, given that the household has a cat.

4 0

3 years ago

PLZ HELP ASAP

Ksenya-84 [330]

the height of the prism is 12 centimeters

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3 years ago

256x²+² - x²y² + 49y²+²

ipn [44]

$\\ \sf\longmapsto 256x^2y^2-x^2y^2+49y^2x^2$

$\\ \sf\longmapsto 256x^2y^2-x^2y^2+49x^2y^2$

$\\ \sf\longmapsto (256-1+49)x^2y^2$

$\\ \sf\longmapsto 304x^2y^2$

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2 years ago

Show that if x and y may both be written as the sum of the squares of two rational integers, then their product xy may also be w

Georgia [21]

Answer:

See proof below

Step-by-step explanation:

One way to solve this problem is to "add a zero" to complete the required squares in the expression of xy.

Let $x=m^2+n^2$ and $y=l^2+k^2$ with $m,n,l,k\in \mathbb{Z}$ . Multiplying the two equations with the distributive law and reordering the result with the commutative law, we get $xy=(m^2+n^2)(l^2+k^2)=m^2l^2+m^2k^2+n^2l^2+n^2k^2=n^2l^2+m^2k^2+m^2l^2+n^2k^2$

Now, note that $0=2lkmn-2lkmn=2nkml-2nlmk$ by the commutativity of rational integers. Add this convenient zero the the previous equation to obtain $xy=n^2l^2-2nlmk+m^2k^2+m^2l^2+2nkml+n^2k^2=(nl-mk)^2+(ml+nk)^2$ , thus xy is the sum of the squares of $nl-mk,ml+nk\in \mathbb{Z}$ .

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3 years ago