S=2(3.14)zx+4(3.14)z^2

Use the identity (x+y)(x2−xy+y2)=x3+y3 to find the sum of two numbers if the product of the numbers is 10, the sum of the square

professor190 [17]

Answer:

The sum of two numbers is 7.

Step-by-step explanation:

Given : the product of the numbers is 10, the sum of the squares of the numbers is 29, and the sum of the cubes of the numbers is 133.

Using identity $(x+y)(x^2-xy+y^2)=x^3+y^3$ and given details, we have to find the sum of two numbers.

Since, given that the product of the numbers is 10 that is $xy=10$

Also, given the sum of the squares of the numbers is 29 that is $x^2+y^2=29$

and the sum of the cubes of the numbers is 133 that is $x^3+y^3=133$

Using, the given identity $(x+y)(x^2-xy+y^2)=x^3+y^3$ ,

Substitute, the given values, we have,

$(x+y)(29-10)=133$

Simplify , we get,

$(x+y)(19)=133$

Divide both side by 19, we have,

$(x+y)=7$

Thus, the sum of two numbers is 7.

7 0

3 years ago

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Find the probability that the senator was in the Democratic party, given that the senator was returning to office.

shutvik [7]

Answer:

The probability that the senator was in the Democratic party, given that the senator was returning to office is 0.4715.

Step-by-step explanation:

The complete question is:

Sophia made the following two-way table categorizing the US senators in 2015 by their political party and whether or not it was their first term in the senate.

Democratic Republican Independent Total

First Term 11 28 11 50

Returning 33 26 11 70

Total 44 54 22 120

Find the probability that the senator was in the Democratic party, given that the senator was returning to office.

Solution:

The conditional probability of an event A given that another event X has already occurred is given by:

$P(A|X)=\frac{P(A\cap X)}{P(X)}$

The probability of an event E is given by the ratio of the number of favorable outcomes to the total number of outcomes.

$P(E)=\frac{n(E)}{N}$

Compute the probability of selecting an US senator who is a Democratic and was returning to office as follows:

$P(D\cap R)=\frac{33}{120}=0.275$

Compute the probability of selecting an US senator who was returning to office as follows:

$P(R)=\frac{70}{120}=0.5833$

Compute the conditional probability, P (D | R) as follows:

$P(D|R)=\frac{P(D\cap R)}{P(R)}$

$=\frac{0.275}{0.5833}\\\\=0.4714555\\\\\approx 0.4715$

Thus, the probability that the senator was in the Democratic party, given that the senator was returning to office is 0.4715.

4 0

3 years ago

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a water tank is draining at a constant rate if after five minutes the tank is drained by 4.5 gallons what is the rate in gallons

vova2212 [387]

Answer:

The rate is 0.9 gallon per minute

Step-by-step explanation:

Here, we have 4.5 gallons drained in 5 minutes but we are interested in calculating the rate per minute

Let the amount drained per minute be x

4.5 gallons = 5 minutes

x gallon = 1 minute

Let’s cross multiply;

x * 5 = 4.5 * 1

5x = 4.5

x = 4.5/5

x = 0.9 gallons

8 0

3 years ago

The Chinese Institute of Health Statistics reported that of every 7,883 deaths in recent years, 624 resulted from a traffic acci

elena-s [515]

Answer:

7.92% probability that a particular death is due to a traffic accident

Step-by-step explanation:

The relative frequency approach to find the probability that a particular death is due to a traffic accident is the number of deaths due to traffic accidents divided by the total number of deaths.

We have that:

624 deaths from traffic accidents

7883 total deaths.

So

$p = \frac{624}{7883} = 0.0792$

7.92% probability that a particular death is due to a traffic accident

8 0

2 years ago

Write the EQ of circle i find center and radius given x² + y²-4x+12y =-4

rusak2 [61]

Answer:

CENTER :(2,-6)

RADIUS: 6

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3 0

3 years ago

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