All categories

2 years ago

SIMPLIFY USING THE DISTRIBUTIVE PROPERTY OF RATIONAL NUMBERS 1/5+ (2/5+3/5)

Mathematics

1 answer:

Lemur [1.5K]2 years ago

4 0

Answer:

6/5

Step-by-step explanation:

1/5 + (2/5 + 3/5)

solve for the bracket first

1/5 +(2+3/5)

1/5 + (5/5)

1/5 + 1

1+1*5/5

6/5

another method

1/5 + (2/5 +3/5)

open brackets)

1/5 + 2/5 + 3/5

since their denominator are same u can add their numerator

1+2+3/5

6/5

You might be interested in

Is the bisector of ∠ABC and is the bisector of ∠ACB.

ycow [4]

Answer:

ASA

Step-by-step explanation:

You can show the angles at either end of segment BC in triangles MBC and LCB are congruent, so you have two angles and the segment between. The appropriate theorem in such a case is ASA.

7 0

3 years ago

Which of the following probabilities is equal to approximately 0. 2957? Use the portion of the standard normal table below to he

Travka [436]

Probability of an event is the measure of its chance of occurrence. The event out of the listed events whose probability is 0.2957 is given by : Option C: $P(0.25 \leq Z \leq 1.25)$

<h3>How to get the z scores?</h3>

If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z-score.

If we have

$X \sim N(\mu, \sigma)$

(X is following normal distribution with mean $\mu$ and standard deviation $\sigma$ )

then it can be converted to standard normal distribution as

$Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)$

(Know the fact that in continuous distribution, probability of a single point is 0, so we can write

$P(Z \leq z) = P(Z < z) )$

Also, know that if we look for Z = z in z tables, the p-value we get is

$P(Z \leq z) = \rm p \: value$

Using the z-table, we get the needed probabilities as:

Case 1:

$P(-1.25 \leq Z \leq 0.25) = P(Z \leq 0.25) - P(Z \leq -1.25) \approx 0.5987 - 0.1056 = 0.4931$

Case 2:

$P(-1.25 \leq Z \leq 0.75) = P(Z \leq 0.75) - P(Z \leq -1.25) \approx 0.7734- 0.1056=0.6678$

Case 3:

$P(0.25 \leq Z \leq 1.25) = P(Z \leq 1.25) - P(Z \leq 0.25) \approx 0.8944 - 0.5987=0.2957$

Case 4:

$P(0.75 \leq Z \leq 1.25) = P(Z \leq 1.25) - P(Z \leq 0.75) \approx 0.8944 - 0.7734 =0.1210$

Thus, the event out of the listed events whose probability is 0.2957 is given by : Option C: $P(0.25 \leq Z \leq 1.25)$

Learn more about z-scores here:

brainly.com/question/13299273

5 0

2 years ago

List some ways that modern cities in developed countries have improved sanitation conditions over the last 200 years.

lorasvet [3.4K]

Answer:

They can build pipes for clean water, and building toilets can also help get rid of unhygienic.... You know Also, hygiene education would help too.

Hope that helped ya, vote, thanks, and brainliest. Have an great day! :D

4 0

3 years ago

Read 2 more answers

The image of F(-5,-9) after translating along <4, 6 > and then translating along < 3, 5> is? F’(?,?)

dusya [7]

<h3>Answer: (2, 2)</h3>

==============================================

Explanation:

The phrasing "translated along <4,6>" is another way of saying "shift 4 to the right, shift 6 up"

In general, "translated along <m,n>" is the same as writing $(x,y) \to (x+m, y+n)$ . If m is positive, then we shift m units to the right. If m is negative, then we shift to the left. The same story happens with the n, but we focus on the y coordinate.

-------------

With all that in mind, starting at F(-5,-9) and translating along <4,6> has us arrive at (-1, -3). Add 4 to the x coordinate and add 6 to the y coordinate.

We can say

$(x,y) \to (x+4,y+6)\\\\(-5,-9) \to (-5+4,-9+6)\\\\(-5,-9) \to (-1,-3)\\\\$

Showing that (-5,-9) moves to (-1,-3)

This is after the first translation, but there's a second translation.

We'll apply the same idea, but different numbers this time

$(x,y) \to (x+3,y+5)\\\\(-1,-3) \to (-1+3,-3+5)\\\\(-1,-3) \to (2,2)\\\\$

So (-1,-3) moves to (2,2)

Overall we have

(-5,-9) move to (-1,-3) after the first translation
(-1,-3) move to (2,2) after the second translation

Therefore, the original point ends up at (2,2) which is the final answer

--------------

Extra info:

A nice shortcut is that the vectors <4,6> and <3,5> can be added to get <4+3,6+5> = <7,11>. So overall, we're shifting 7 units to the right and 11 units up when we combine the two translation vectors.

5 0

3 years ago

Which of the following is an improper integral?

guapka [62]

Answer:

A) $\displaystyle \int\limits^3_0 {\frac{x + 1}{3x - 2}} \, dx$

General Formulas and Concepts:

<u>Calculus</u>

Discontinuities

Removable (Hole)
Jump
Infinite (Asymptote)

Integration

Integrals
Definite Integrals
Integration Constant C
Improper Integrals

Step-by-step explanation:

Let's define our answer choices:

A) $\displaystyle \int\limits^3_0 {\frac{x + 1}{3x - 2}} \, dx$

B) $\displaystyle \int\limits^3_1 {\frac{x + 1}{3x - 2}} \, dx$

C) $\displaystyle \int\limits^0_{-1} {\frac{x + 1}{3x - 2}} \, dx$

D) None of these

We can see that we would have a infinite discontinuity if x = 2/3, as it would make the denominator 0 and we cannot divide by 0. Therefore, any interval that includes the value 2/3 would have to be rewritten and evaluated as an improper integral.

Of all the answer choices, we can see that A's bounds of integration (interval) includes x = 2/3.

∴ our answer is A.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Book: College Calculus 10e

6 0

3 years ago