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Maurinko [17]
2 years ago
8

To cover a rectangle region of her yard, Penny needs at least 170.5 square feet of sod. The length of the region is 15.5 feet. W

hat are the possible widths of the region?
Mathematics
1 answer:
gulaghasi [49]2 years ago
4 0
We know that the perimeter of a rectangle is 2(width)+2(length). We can multiply the length by 2 to find out how much remaining fencing we have, then divide that number by 2 to find the width.

15.5*2=31
170.5-31=139.5
139.5/2=69.75

A possible width is 69.75 feet.
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Mr. Montes is writing a short, three-question, true or false quiz for his Algebra 2 classes. He had planned on using a random an
belka [17]

Answer:

There are 4 questions to answer here and the answers are given below:

1. COMBINATION

2. SET 2  

3. {S2, S3, S4, S5}

4. { }  OR  ∅

Step-by-step explanation:

The key topics here are PERMUTATION & COMBINATION and SETS & VENN DIAGRAMS.

The assignment has 5 questions in all. The options for each question are listed below and separated by commas:

1. True, False

2. True, False

3. A, B, C, D

4. A, B, C, D

5. A, B, C, D

Mr. Montes derives his answers from a random answer generator; same way Amisha generated her answers by random selection.

<u>QUESTION 1</u>

If you want to find the odds that Amisha got at least 3/5 of the answers correctly, would you use a permutation or a combination?

<u>ANSWER TO QUESTION 1</u>

You would use a combination. Note that as much as 'permutation' is distinctly defined from 'combination', in many complex cases both are used to derive the solution. In this case though, a combination is used. For each of the 5 questions, there are a number of possible answers. Questions 1 and 2 have only <em>two possible answers</em> (also known as options) while questions 3, 4 and 5 have <em>four possible answers</em>/<em>options</em> to choose from. Amisha can only have one set of five answers; each to each question. So this is a combination! If you want to find the odds that Amisha got at least 3 of her 5 answers correct, you would use a combination of the various possible answers to check.

<u>QUESTION 2</u>

Find "Set 1 ∩ Set 2" and explain the notation in the sentence.

<u>ANSWER TO QUESTION 2</u>

First list out relevant information:

- The correct answers to questions 3, 4 and 5 are respectively C, B, A

- The universal set consists of five students: S1, S2, S3, S4, S5 hence

Ц = {S1, S2, S3, S4, S5}

Next, enlist the elements of each defined set

Set 1: {S1, S2, S3, S4, S5}     Set 2: {S2, S3, S4}     Set 3: {S4, S5}

Note: Set 1 is equal to the universal set.

Now this notation "∩" means "intersect". It requires an action - checking out which elements in one set also appear in a second set and then bringing those elements to form a new set.

In the case of this question, we're to find Set 1 intersect Set 2. The elements present in Set 1 and also present in Set 2 are {S2, S3, S4}.

If you look closely, you'll observe that these are the same elements in Set 2! This brings to remembrance, one of the laws of sets:

The intersect of any subset and the universal set (recall that Set 1 happens to be equal to or have the same elements as the universal set) is equal to that subset.

So the answer to question 2 is

Set 1 ∩ Set 2 = Set 2

<u>QUESTION 3</u>

Find "Set 2 ∪ Set 3" and explain the notation in the sentence.

<u>ANSWER TO QUESTION 3</u>

The notation ∪ represents "union". This is the act of putting together the elements in two sets, to form a new set. In this activity, if an element appears in both sets, it is only written once in the new set, not twice.

So, Set 2 union Set 3 = {S2, S3, S4, S5}

As earlier stated, Student 4 isn't appearing twice in the new set.

<u>QUESTION 4</u>

Find the ' of Set 1 and explain the notation in this sentence.

<u>ANSWER TO QUESTION 4</u>

The symbol ' means "complement of a set". Finding the complement of a set is like subtracting the elements of that set from the universal set.

Since Set 1 contains the same elements as the universal set, subtracting Set 1 from the universal set will give you nothing. In this case, the complement of Set 1 is a null set!

Set 1 ' Ц = { }  or  ∅

where the empty bracket symbol and the slashed zero symbol represent null set.

Kudos!

3 0
3 years ago
Solve the system by substitution<br><br> -5x+3y=2<br> y=2x
serious [3.7K]

Answer:

(x,y)=(0,0)

Step-by-step explanation:

Simplify -5x+3y=2x

2y=2x

multiply both sides -7x+3y=0

-x+y=0

eliminiate one vaiable

4 0
2 years ago
How many real solutions will y=x^2 and y=-2x have? what are the solutions?
kogti [31]

Answer:

there is none

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
The diagram shows the ratio of trees Maeve plants to the trees she harvests.
AnnZ [28]

Answer:

WEDNESDAY: 45 planted.

THURSDAY: 22 Harvested.

Step-by-step explanation:

Based on the information given in the problem, Maeve plants 5 trees for every 2 tree she harvests. Then the ratio can be expressed as following:

5:2 or \frac{5}{2}

Then, you can complete the values in the table as you can see below:

<u>WEDNESDAY</u>

\frac{5}{2}=\frac{planted}{18}\\\\planted=\frac{18*5}{2}\\\\planted=45

<u>THURDAY</u>

\frac{5}{2}=\frac{55}{harvested}\\\\(harvested)(\frac{5}{2})=55\\\\harvested=\frac{55*2}{5}\\\\harvested=22

6 0
3 years ago
8. Video games are on sale this week for 20% off. The video game originally costs $42.
Phoenix [80]

Answer:

  • $8.4
  • $33.6
  • I= $384

Step-by-step explanation

  • Amount of discount: 20%= 0.20; 0.20×42= $8.4
  • Sale price: $42-$8.4= $33.6

For interest question, plug in the values:

P= $3200

r= 3%÷100 = 0.03

t= 4 years

Calculate:

I=Prt

= 3200×0.03×4

=$384

3 0
2 years ago
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