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3 years ago

Y = 3x + 5 step 1 of 3: determine the slope and y-intercept of the equation above

Mathematics

1 answer:

hram777 [196]3 years ago

7 0

Slope=3
y-intercept = 5

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Can I have help with 42?

Sphinxa [80]

#42.
14n - 32 = 22
add 32 to both sides
14n - 32 + 32 = 22 + 32
simplify
14n = 54
divide both sides by 14
14n/14 = 54/14
simplify
n = 3 12/14
n = 3 6/7 or n = 3.857

8 0

2 years ago

Read 2 more answers

1) Given P(A) = 0.3 and P(B) = 0.5, do the following.

Delicious77 [7]

Answer:

1) a) 0.8

b) 0.6

2) a) 0.08

b) 0.14

Step-by-step explanation:

1) Given

$P(A) = 0.3$ and $P(B) = 0.5$

Let us learn about a formula:

$P(A\ or\ B) = P(A) +P(B) -P(A\ and\ B)\\OR\\P(A\cup B) = P(A) +P(B) -P(A\cap B)$

(a) If A and B are mutually exclusive i.e. no common thing in the two events.

In other words:

$P(A\ and\ B)$ = $P(A \cap B)$ = 0

Using above formula:

$P(A\ or\ B) = P(A) +P(B) -P(A\ and\ B)\\\Rightarrow P(A\ or\ B) = 0.3 + 0.5 -0 = \bold{0.8}$

(b) P(A and B) = 0.2

Using above formula:

$P(A\ or\ B) = P(A) +P(B) -P(A\ and\ B)\\\Rightarrow P(A\ or\ B) = 0.3 + 0.5 -0.2 = \bold{0.6}$

*************************************

1) Given

$P(A) = 0.4$ and $P(B) = 0.2$

Let us learn about a formula:

$P(A\ and\ B) = P(B) \times P(A/B)$ for dependent events

$P(A\ and\ B) = P(A) \times P(B)$ for independent events.

(a) If A and B are independent events :

Using the above formula for independent events:

$P(A\ and\ B) = 0.4 \times 0.2 = \bold{0.08}$

(b) $P(A / B) = 0.7$

Using above formula:

$P(A\ and\ B) = P(B) \times P(A/B) = 0.2 \times 0.7 = \bold{0.14}$

6 0

2 years ago

Solve the problem below, simplify, add steps 1/3 √21 minus 2/3 √3 * √7

iogann1982 [59]

Do you want square root? And If so then here is the answer:Rewrite √3737 as √3√737.√3√737Multiply √3√737 by √7√777.√3√7√7√737⁢77Simplify. And in the end of, this I put the decimals.√217217The result can be shown in both exact and decimal forms.Exact Form:√217Decimal Form:0.65465367… not sure this answer.

4 0

3 years ago

Set up the integral that represents the arc length of the curve f(x) = ln(x) + 5 on [1, 3], and then use Simpson's Rule with n =

marta [7]

Answer:

The integral for the arc of length is:

$\displaystyle\int_1^3\sqrt{1+\frac{1}{x^2}}dx$

By using Simpon’s rule we get: 1.5355453

And using technology we get: 2.3020

The approximation is about 33% smaller than the exact result.

Explanation:

The formula for the length of arc of the function f(x) in the interval [a,b] is:

$\displaystyle\int_a^b \sqrt{1+[f'(x)]^2}dx$

We need the derivative of the function:

$f'(x)=\frac{1}{x}$

And we need it squared:

$[f'(x)]^2=\frac{1}{x^2}$

Then the integral is:

$\displaystyle\int_1^3\sqrt{1+\frac{1}{x^2}}dx$

Now, the Simposn’s rule with n=4 is:

$\displaystyle\int_a^b g(x)}dx\approx\frac{\Delta x}{3}\left( g(a)+4g(a+\Delta x)+2g(a+2\Delta x) +4g(a+3\Delta x)+g(b) \right)$

In this problem:

$a=1,b=3,n=4, \displaystyle\Delta x=\frac{b-a}{n}=\frac{2}{4}=\frac{1}{2},g(x)= \sqrt{1+\frac{1}{x^2}}$

So, the Simposn’s rule formula becomes:

$\displaystyle\int_1^3\sqrt{1+\frac{1}{x^2}}dx\\\approx \frac{\frac{1}{3}}{3}\left( \sqrt{1+\frac{1}{1^2}} +4\sqrt{1+\frac{1}{\left(1+\frac{1}{2}\right)^2}} +2\sqrt{1+\frac{1}{\left(1+\frac{2}{2}\right)^2}} +4\sqrt{1+\frac{1}{\left(1+\frac{3}{2}\right)^2}} +\sqrt{1+\frac{1}{3^2}} \right)$

Then simplifying a bit:

$\displaystyle\int_1^3\sqrt{1+\frac{1}{x^2}}dx \approx \frac{1}{9}\left( \sqrt{1+\frac{1}{1^2}} +4\sqrt{1+\frac{1}{\left(\frac{3}{2}\right)^2}} +2\sqrt{1+\frac{1}{\left(2\right)^2}} +4\sqrt{1+\frac{1}{\left(\frac{5}{2}\right)^2}} +\sqrt{1+\frac{1}{3^2}} \right)$