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3 years ago

Write each ratio in its simplest form.

Mathematics

2 answers:

Andrej [43]3 years ago

6 0

Answers:

A) 3:4

B) 5:2

C) 4:1

Step-by-step explanation:

Convert 4 yards to feet.

1 yard = 3 feet

4 yards = 12 feet

9 feet : 12 feet

Simplify the ratio.

9/3 : 12/3

3 feet : 4 feet

3 : 4

Convert 8 quarts to gallons.

1 quart = 0.25 gallons

8 quarts = 2 gallons

5 gallons : 2 gallons

5 : 2

Convert 2 meters into centimeters.

1 meter = 100 centimeters

2 meters = 200 centimeters

800 centimeters : 200 centimeters

Simplify the ratio.

4 : 1

Morgarella [4.7K]3 years ago

5 0

Answer:

A. 4 yards = 12 ft

9 ft : 12 ft = 3:4

B. 5 gallons = 20 quarts

20 quarts : 8 quarts = 5:2

C. 2 meters = 200 cm

800 cm : 200 cm = 4:1

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Joe's annual income has been increasing each year by the same dollar amount. The first year his income was $17 comma 90017,900

Vedmedyk [2.9K]

Answer:

In 17th year, his income was $30,700.

Step-by-step explanation:

It is given that the income has been increasing each year by the same dollar amount. It means it is linear function.

Income in first year = $17,900

Income in 4th year = $20,300

Let y be the income at x year.

It means the line passes through the point (1,17900) and (4,20300).

If a line passes through two points $(x_1,y_1)$ and $(x_2,y_2)$ , then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

The equation of line is

$y-17900=\frac{20300-17900}{4-1}(x-1)$

$y-17900=\frac{2400}{3}(x-1)$

$y-17900=800(x-1)$

$y-17900=800x-800$

Add 17900 on both sides.

$y=800x-800+17900$

$y=800x+17100$

The income equation is y=800x+17100.

Substitute y=30,700 in the above equation.

$30700=800x+17100$

Subtract 17100 from both sides.

$30700-17100=800x$

$13600=800x$

Divide both sides by 800.

$\frac{13600}{800}=x$

$17=x$

Therefore, in 17th year his income was $30,700.

5 0

3 years ago

In a certain assembly plant, three machines B1, B2, and B3, make 30%, 20%, and 50%, respectively. It is known from past experien

diamong [38]

Answer:

The probability that a randomly selected non-defective product is produced by machine B1 is 11.38%.

Step-by-step explanation:

Using Bayes' Theorem

P(A|B) = $\frac{P(B|A)P(A)}{P(B)} = \frac{P(B|A)P(A)}{P(B|A)P(A) + P(B|a)P(a)}$

where

P(B|A) is probability of event B given event A

P(B|a) is probability of event B not given event A

and P(A), P(B), and P(a) are the probabilities of events A,B, and event A not happening respectively.

For this problem,

Let P(B1) = Probability of machine B1 = 0.3

P(B2) = Probability of machine B2 = 0.2

P(B3) = Probability of machine B3 = 0.5

Let P(D) = Probability of a defective product

P(N) = Probability of a Non-defective product

P(D|B1) be probability of a defective product produced by machine 1 = 0.3 x 0.01 = 0.003

P(D|B2) be probability of a defective product produced by machine 2 = 0.2 x 0.03 = 0.006

P(D|B3) be probability of a defective product produced by machine 3 = 0.5 x 0.02 = 0.010

Likewise,

P(N|B1) be probability of a non-defective product produced by machine 1 = 1 - P(D|B1) = 1 - 0.003 = 0.997

P(N|B2) be probability of a non-defective product produced by machine 2 = 1 - P(D|B2) = 1 - 0.006 = 0.994

P(N|B3) be probability of a non-defective product produced by machine 3 = 1 - P(D|B3) = 1 - 0.010 = 0.990

For the probability of a finished product produced by machine B1 given it's non-defective; represented by P(B1|N)

P(B1|N) = $\frac{P(N|B1)P(B1)}{P(N|B1)P(B1) + P(N|B2)P(B2) + (P(N|B3)P(B3)}$ = $\frac{(0.297)(0.3)}{(0.297)(0.3) + (0.994)(0.2) + (0.990)(0.5)}$ = 0.1138

Hence the probability that a non-defective product is produced by machine B1 is 11.38%.

4 0

3 years ago

______________ Angles have each of the pairs of opposite angles made by two intersecting lines *

myrzilka [38]

$\huge \bf༆ Answer ༄$

The Correct choice is B. Vertical

<u>V</u><u>ertical</u> Angles have each of the pairs of opposite angles made by two intersecting lines .

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2 years ago

Read 2 more answers

8 Select the correct answer from each drop-down menu. Some of the images in the diagram are images of polygon 1 from similarity

makkiz [27]

It should be noted that Polygon 3 and polygon 4 are similar to polygon 1.

<h3>What exactly is polygon?</h3>

In geometry, it should be noted that a polygon is a plane figure which is described by a finite number of straight line segments that are connected in order to form a closed polygonal chain.

In this case, the bounded plane region, the bounding circuit, may be called a polygon. Also, a similarity transformation is the conformal mapping whose transformation matrix are identical.

In this case, it should be noted that Polygon 3 and polygon 4 are similar to polygon 1.

Learn more about polygon on:

brainly.com/question/24966296

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8 0

2 years ago

Which polynomial does this sum of tiles represent?

Goryan [66]

U need to show an example of the tiles in order for people to answer this

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3 years ago