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Galina-37
2 months ago
6

On a final exam, each multiple-choice question is worth 4 points and each word problem is worth 8 points. Lorenzo needs at least

50 points on the final to earn a "B" in the class. Which inequality represents x, the number of correct multiple-choice questions, and y, the number of correct word problems, he needs to earn a "B"?
Mathematics
2 answers:
zzz [12.3K]2 months ago
5 0

Answer:

2x+4y\leq 25

Step-by-step explanation:

Points awarded for multiple-choice questions = 4 points.

Points for each word problem = 8 points.

Let x represent the number of correct multiple-choice questions and y the number of correct word problems.

So,

The points garnered from correct multiple-choice questions = 4x.

The points garnered from correct word problems = 8y.

Lorenzo's target for a B is a minimum of 50 points.

The total points from correct multiple-choice questions plus points from correct word problems \leq 50.

4x+8y\leq 50

Taking 2 as a common factor yields 2x+4y\leq 25.

Zina [12.3K]2 months ago
3 0
Lorenzo earns 4 points for every x and 8 points for each y, requiring a minimum of 50 points for a B. The inequality can be expressed as:

4x + 8y ≥ 50, which simplifies to 2x + 4y ≥ 25 after factoring out 2 from both sides.
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The general form of the equation of a circle is x2 + y2 + 8x + 22y + 37 = 0. The equation of this circle in standard form is (x
Leona [12618]
Greetings: 
<span>x² + y² + 8x + 22y + 37 = 0
(x² +8x) +(y² +22y) +37 = 0

</span>(x² +8x+4²)-4² +(y² +22y+11²) -11²+37 = 0
(x+4)² +(y+11)²-16-121+37 =0

(x+4)² +(y+11)² =10²...(<span>standard form )
</span><span>The circle's center is located at (-4, -11) and has a radius of 10</span>
3 0
2 months ago
(1 point) Rework problem 15 in section 2 of Chapter 5 of your textbook about the growing suburb and the declining city using the
Leona [12618]

Answer:

16 years

Step-by-step explanation:

Let x represent the count of years. The suburb population increases at a rate of 5000 annually, which can be formulated as:

320000 + 5000x

The city population decreases at a rate of 14000 per year, represented as:

624000 - 14000x

The point in time when both the suburb and city populations will match can be derived from:

320000 + 5000x = 624000 - 14000x

14000x + 5000x = 624000 - 320000

19000x = 304000

x = 304000 / 19000

x = 16

In 16 years, the populations of both the suburb and the city will be equivalent

6 0
2 months ago
Suppose that the universal set is U={1,2,3,4,5,6,7,8,9,10}. Express each of the following subsets with bit strings (of length 10
lawyer [12517]

Response:

0011100000

1010010001

0111001110

Detailed explanation:

Since the question is incomplete, here is the full question.

Assume the universal set is U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Represent each of these sets using bit strings, where the ith bit indicates 1 if the element i is part of the set, and 0 otherwise.

a) {3, 4, 5}

b) {1, 3, 6, 10}

c) {2, 3, 4, 7, 8, 9}.

Thus, we need to convert a), b), and c) into bit strings.

To begin with, the number of items in the universal set determines the number of bits in the bit string.

Next, a 1 denotes the presence of an element both in the universal set and in the subset.

A 0 indicates that an element is absent from the subset but present in the universal set.

Therefore, we obtain:

a) Subset {3,4,5} = 0011100000  (As it contains 3 ones, it shows that only 3,4,5 are included in both the universal and the subset.

In the same way,

b) Subset {1, 3, 6, 10} = 1010010001

c) Subset {2, 3, 4, 7, 8, 9} = 0111001110

5 0
2 months ago
Anna has 7 baskets and some flowers. She has 5 fewer baskets than flowers. How many flowers does anna have?
Leona [12618]
Response: I’m uncertain but I believe it’s 12

Step-by-step breakdown:
Since Anna has 5 fewer baskets than she does flowers, that implies 5 + 7 = the total number of flowers, which amounts to 12. I trust this is helpful!:-)
6 0
2 months ago
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