Find all solutions of the equation. Check your solutions in the original equation. 8 x^3 − 343=0

Answers

Answer 1

Answer: $8x^3-343=0\ \ \ \ \ |add\ 343\ to\ both\ sides\n\n8x^3=343\ \ \ \ \ \ |divide\ both\ sides\ by\ 8\n\nx^3=(343)/(8)\n\nx=\sqrt[3]{(343)/(8)}\n\nx=\frac{\sqrt[3]{343}}{\sqrt[3]8}\n\nx=(7)/(2)$

$solution:x=(7)/(2)\n\ncheck:\n\n8\cdot\left((7)/(2)\right)^3-343=0\n\n8\cdot(343)/(8)-343=0\n\n343-343=0\n\n0=0$

Answer 2

Answer: $8 x^3-343=0\n\n(2x)^3-7^3=0\ \ \ \ \ \ and\ \ \ \ \ \ a^3-b^3=(a-b)(a^2+ab+b^2)\n\n(2x-7)(4x^2+14x+49)=0\n\n2x-7=0\ \ \ or\ \ \ 4x^2+14x+49=0\n2x=7\ \ \ \ \ \ \ \ \ \ \ \ \ \ \Delta=14^2-4\cdot4\cdot49=196-784=-588\n x= (7)/(2) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \Rightarrow\ no\ solution\n.\ \ \ \ \ \ \ \ Ans.\ x= (7)/(2) \n\ncheck:\nL=8x^3-343=\n=8\cdot( (7)/(2) )^3-343=8\cdot (7^3)/(2^3) -343=8\cdot (343)/(8) -343=343-343=0$

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Fifteen times a number subtracted from 80 is 25

Answers

The required number would be 11 / 3 which represents " Fifteen times a number subtracted from 80 is 25".

What are Arithmetic operations?

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 12 -2 = 10

* Multiplication operation: Multiplies values on either side of the operator

For example 12*2 = 24

To determine the number which is Fifteen times a number subtracted from 80 is 25

Let the number be x.

As per the given condition,

Here the required number would be Fifteen times = 15x and

Then this is subtracted from 80; 80 - 15x

⇒ 80 - 15x = 25

⇒ -15x = 25 - 80

⇒ -15x = -55

⇒ x = -55 / -15

Apply the Division operation, and we get

⇒ x = 11/3

Therefore, the required number would be 11 / 3.

Learn more about Arithmetic operations here:

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Let the number be x.

15 times the number = 15x

This is subtracted from 80, 80 - 15x

80 - 15x = 25

-15x = 25 - 80

-15x = -55

x = -55 / -15

x = 11/3

So the number is 11 / 3.

Power set of {e,f,m,n,o}

Answers

$\{\emptyset,\{e\},\{f\},\{m\},\{n\},\{o\},\{e,f\},\{e,m\},\{e,n\},\{e,o\},\{f,m\},\{f,n\},\n \{f,o\},\{m,n\},\{m,o\},\{n,o\},\{e,f,m\},\{e,f,n\},\{e,f,o\},\{e,m,n\},\n \{e,m,o\},\{e,n,o\},\{f,m,n\},\{f,m,o\},\{f,n,o\},\{m,n,o\},\{e,f,m,n\},\n \{e,f,m,o\},\{e,f,n,o\},\{e,m,n,o\},\{f,m,n,o\},\{e,f,m,n,o\}\}$

$n=5\ \ \ \Rightarrow\ \ \ 2^n=2^5=32\n\n$

$\emptyset;\n\{e\},\{f\},\{m\},\{n\},\{o\};\n\{e,f\},\{e,m\},\{e,n\},\{e,o\},\{f,m\},\{f,n\},\{f,o\},\{m,n\},\{m,o\},\{n,o\};\n\{e,f,m\},\{e,f,n\},\{e,f,o\},\{e,m,n\},\{e,m,o\},\{e,n,o\},\{f,m,n\},\n\{f,n,o\},\{f,m,o\},\{m,n,o\};\n\{e,f,m,n\},\{e,f,m,o\},\{e,f,n,o\},\{e,m,n,o\},\{f,m,n,o\};\n\{e,f,m,n,o\}$

Write a multiplication equation that represents the question: how many 3/8 s are in 5/4 ? y'all help mee

Answers

Answer:1/4

Step-by-step explanation:

Plz halp i need to get this right.

Answers

Answer:

Step-by-step explanation:

A savings account earns simple interest at a rate of 6% per year. Last year the account earned $10.86 in interest. What was the balance in the account at the beginning of last year?

Answers

Answer:

The balance in the account at the beginning of last year was $181.

Step-by-step explanation:

Consider the provided information.

A savings account earns simple interest at a rate of 6% per year.

6% can be written as: 6/100=0.06

Last year the account earned $10.86 in interest.

Let the amount invested is represented by x.

$0.06* x=10.86$

$x=(10.86)/(0.06)$

$x=(1086)/(6)$

$x=181$

Hence, the balance in the account at the beginning of last year was $181.

In this case, you have to find out the number whose 6% is 10.86.

So, Let the number be x.

x * 6/100 = 10.86

x * 6 = 1086

x = 181.

So, the account balance at the beginning of last year was $181.

Did you understand?

On discovering that her family had a 70% risk of heart attack, Erin took a treadmill test to check her own potential of having a heart attack. The doctors told her that the reliability of the stress test is 67%. What is the probability that Erin will not have a heart attack and the test predicts that she will?

Answers

Answer:

A. 0.099

Step-by-step explanation:

Answer-

The probability that Erin will not have a heart attack and the test predicts that she will is, 46.5% .

Hint- This a conditional probability problem where Bayes theorem should be applied.

Solution-

Applying Bayes theorem,

$P(No\ heart\ attack\ |\ Correctly\ tested)$

$=(P(Correctly\ tested\ |\ No\ heart\ attack)P(No\ heart\ attack))/(P(Correctly\ tested))$

$P(Correctly\ tested\ |\ No\ heart\ attack)=67\%=0.67$

$P(No\ heart\ attack)=1-P(heart\ attack)=1-0.7=0.3$

$P(Correctly\ tested)=[P(No\ heart\ attack)* P(Correctly\ tested)]+[P(Heart\ attack)* (Incorrectly\ tested)]$

$=[0.3* 0.67]+[0.7* 0.33]=0.432$

Putting the values,

$P(No\ heart\ attack\ |\ Correctly\ tested)=(0.67* 0.3)/(0.432) =0.465$

∴ There is a 46.5% chance that Erin will not have a heart attack even though the test predicts that she will.

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