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3 years ago

6

You drink 2/7 of a pitcher of lemonade. Your friend drinks 3/14 of the pitcher. What fraction of the pitcher do you and your fri

end drink?

1 answer:

Strike441 [17]3 years ago

4 0

Answer:

7.8

Step-by-step explanation:

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Zak has 3/5 pack of pencils. Of these, 2/7 are blue. How many blue pencils does Zak have?

Basile [38]

Answer:

11/35

Step-by-step explanation:

First, you would have to make a common denominator. To do this, multiply these 2 denominator, 5 and 7. You should get 35. Then, you would have to make the numerator equal to the denominator. In this case, multiply 3 to 7 and 2 to 5. Now you have 21/35 and 10/35. Now subtract 21 from 10, and simplify if needed. I hope this helps!

7 0

3 years ago

Read 2 more answers

Solve the equation by completing the square. If necessary, round to the nearest hundredth.

diamong [38]

Ax^2+bx=c
REMEMBER THIS

ok
first, make sure that a is 1
done

now take 1/2 of b and square it

-18/2=-9, (-9)^2=81
add that to both sides

x²-18x+81=19+81
x²-18x+81=99
factor perfect square
(x-9)²=100
square root both sides
don't forget positive and negative root
x-9=10
x-9=-10
ad 9 to both sides

x=19
x=-1

answer is -1; 19

2nd choice is answer

8 0

4 years ago

Read 2 more answers

Need help with Calculus 1 inverse trig functions

lidiya [134]

Answer:

$\displaystyle y'=3\frac{1+\frac{x}{\sqrt{1+x^2}}}{2+2x^2+2x\sqrt{1+x^2}}$

Step-by-step explanation:

<u>The Derivative of a Function</u>

The derivative of f, also known as the instantaneous rate of change, or the slope of the tangent line to the graph of f, can be computed by the definition formula

$\displaystyle f'(x)=\lim\limits_{\Delta x \rightarrow 0}\frac{f(x+\Delta x)-f(x)}{\Delta x}$

There are tables where the derivative of all known functions are provided for an easy calculation of specific functions.

The derivative of the inverse tangent is given as

$\displaystyle (tan^{-1}u)'=\frac{u'}{1+u^2}$

Where u is a function of x as provided:

$y=3tan^{-1}(x+\sqrt{1+x^2})$

If we set

$u=(x+\sqrt{1+x^2})$

Then

$\displaystyle u'=1+\frac{2x}{2\sqrt{1+x^2}}$

$\displaystyle u'=1+\frac{x}{\sqrt{1+x^2}}$

Taking the derivative of y

$y'=3[tan^{-1}(x+\sqrt{1+x^2})]'$

Using the change of variables

$\displaystyle y'=3[tan^{-1}u]'=3\frac{u'}{1+u^2}$

$\displaystyle y'=3\frac{u'}{1+u^2}=3\frac{1+\frac{x}{\sqrt{1+x^2}}}{1+(x+\sqrt{1+x^2})^2}$

Operating

$\displaystyle y'=3\frac{1+\frac{x}{\sqrt{1+x^2}}}{1+x^2+2x\sqrt{1+x^2}+1+x^2}$

$\boxed{\displaystyle y'=3\frac{1+\frac{x}{\sqrt{1+x^2}}}{2+2x^2+2x\sqrt{1+x^2}}}$

8 0

3 years ago

Using complete sentences, explain the differences between an expression and an equation I need it asap

borishaifa [10]

Answer:

Expression is a mathematical phrase which combines, numbers, variables and operators to show the value of something. An equation is a mathematical statement wherein two expressions are set equal to each other. What is it? A sentence fragment, that stands for a single numerical value.

Step-by-step explanation:

That was the step-by-step explanation. <3

7 0

3 years ago

Read 2 more answers

A car insurance company has determined that 8% of all drivers were involved in a car accident last year. Among the 15 drivers li

svetlana [45]

Answer:

There is an 11.3% probability of getting 3 or more who were involved in a car accident last year.

Step-by-step explanation:

For each driver surveyed, there are only two possible outcomes. Either they were involved in a car accident last year, or they were not. This means that we solve this problem using binomial probability concepts.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

In which $C_{n,x}$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And $\pi$ is the probability of X happening.

In this problem

15 drivers are randomly selected, so $n = 15$ .

A success consists in finding a driver that was involved in an accident. A car insurance company has determined that 8% of all drivers were involved in a car accident last year. This means that $\pi = 0.08$ .

What is the probability of getting 3 or more who were involved in a car accident last year?

This is $P(X \geq 3)$ .

Either less than 3 were involved in a car accident, or 3 or more were. Each one has it's probabilities. The sum of these probabilities is decimal 1. So:

$P(X < 3) + P(X \geq 3) = 1$

$P(X \geq 3) = 1 - P(X < 3)$

In which

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)$

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

$P(X = 0) = C_{15,0}.(0.08)^{0}.(0.92)^{15} = 0.2863$

$P(X = 1) = C_{15,1}.(0.08)^{1}.(0.92)^{14} = 0.3734$

$P(X = 2) = C_{15,2}.(0.08)^{2}.(0.92)^{13} = 0.2273$

So

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2863 + 0.3734 + 0.2273 = 0.887$

Finally

$P(X \geq 3) = 1 - P(X < 3) = 1 - 0.887 = 0.113$

There is an 11.3% probability of getting 3 or more who were involved in a car accident last year.

5 0

3 years ago