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erma4kov [3.2K]
3 years ago
7

Joanna plans on hanging 3 pictures of different sizes on the wall of her staircase. She thinks it will look best if all 3 rectan

gular pictures are similar. The two sizes she has already are 25 in. by 35 in.and 35 in. by 49 in. Which of the following is a possible size of the third picture?
A.
5 in. by 6 in.
B.
30 in. by 42 in.
C.
45 in. by 70 in.
D.
50 in. by 63 in.
Mathematics
1 answer:
Natasha2012 [34]3 years ago
5 0
In similar figures, the ratio between corresponding sides are the same.

\frac{25}{35}=\frac{35}{49}

Simplify the two to see that they are equal.
The top and bottom of the left fraction are divisible by 5.
The top and bottom of the right fraction are divisible by 7.

\frac{5}7=\frac{5}7

Of course, the dimensions of that third picture would have to be this fraction.
Let's test these answers.

\frac{5}6\neq\frac{5}7 ⇒ A is not a solution

\frac{30}{42}=\frac{5}7 ⇒ B is the solution
(divide the top and bottom by 6)
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Answer:

B same form

Step-by-step explanation:

By using them for fractions or decimals. You can compare fractions by having them from least to greatest and it helps in getting the same denominator for fractions.

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3 years ago
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A veterinarian will prescribe an antibiotic to a dog based on its weight. The effective dosage of the antibiotic is given by d ≥
gregori [183]

Answer:

B) (35, 260)

Step-by-step explanation:

A veterinarian will prescribe an antibiotic to a dog based on its weight. The effective dosage of the antibiotic is given by d ≥ 1∕5w2, where d is dosage in milligrams and w is the dog's weight in pounds. Which of the following ordered pairs gives an effective dosage of antibiotics for a 35-pound dog?

A) (35, 240)

B) (35, 260)

C) (260, 35)

D) (240, 35)

Ordered pairs is composed of pairs, usually an x coordinate and a y coordinate. It refers to a location of a point on the coordinate. It matches numbers to functions or relations.

Given the relation between d is dosage in milligrams and w is the dog's weight in pounds as d ≥ 1∕5w²

For a 35 pound dog (i.e w = 35 pound). The dosage is given as:

d ≥ 1∕5(35)² ≥ 245 milligrams.

For an ordered pair (x, y), x is the independent variable (input) and y is the dependent variable (output).

The dog weight is the independent variable and the dosage is the dependent variable.

From the ordered pairs, the best option is (35, 260) because 260 ≥ 240

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3 years ago
A basketball team is down by 2 points with only a few seconds remaining in the game. There is a 60% chance that the team will be
Mashcka [7]

Answer:

This means that the coach should have the team going for the 2 point shot. There is a 36% probability of making the 2 point shot and winning overtime.

Step-by-step explanation:

We have these following probabilities:

A 60% probability of tying the game on a 2 point shot. In this case, the game goes to overtime, in which the team has a 60% probability of winning.

A 30% probability of making the 3 point shot and winning.

What should the coach do, go for the 2 point shot or the 3 point shot?

In which case the team has a higher probability of winning?

The team has:

A 60% probability of tying the game on a 2 point shot. In this case, the game goes to overtime, in which the team has a 60% probability of winning. So, going for the 2 point shot, the team has a 0.6*0.6 = 0.36 = 36% probability of winning.

Going for the 3 point shot, the team has a 30% probability of winning.

This means that the coach should have the team going for the 2 point shot. There is a 36% probability of making the 2 point shot and winning overtime.

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