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3 years ago

What’s the missing side length?

Mathematics

2 answers:

Karo-lina-s [1.5K]3 years ago

8 0

Answer:

14 cm

Step-by-step explanation:

this is because of the far left side of the shape being 6cm and as well as with the 8 cm from one side of the shape being another component to the origin of the side length, this would give us the equation 6 + 8 with out sum coming out to 14 cm being identified as the right unknown length.

Nimfa-mama [501]3 years ago

6 0

Answer: 14cm

Steps:
6cm + 8 cm = 14cm

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A survey of magazine subscribers showed that 45.2% rented a car during the past 12 months for business reasons, 56% rented a car

IgorLugansk [536]

Answer:

a. 0.692 or 69.2%; b. 0.308 or 30.8%.

Step-by-step explanation:

This is the case of the probability of the sum of two events, which is defined by the formula:

$\\ P(A \cup B) = P(A) + P(B) - P(A \cap B)$ (1)

Where $\\ P(A \cup B)$ represents the probability of the union of both events, that is, the probability of event A plus the probability of event B.

On the other hand, $\\ P(A \cap B)$ represents the probability that both events happen at once or the probability of event A times the probability of event B (if both events are independent).

Notice the negative symbol for the last probability. The reason behind it is that we have to subtract those common results from event A and event B to avoid count them twice when calculating $\\ P(A \cup B)$ .

We have to remember that a sample space (sometimes denoted as S) is the set of the all possible results for a random experiment.

<h3>Calculation of the probabilities</h3>

From the question, we have two events:

Event A: event subscribers rented a car during the past 12 months for business reasons.

Event B: event subscribers rented a car during the past 12 months for personal reasons.

$\\ P(A) = 45.2\%\;or\;0.452$

$\\ P(B) = 56\%\;or\;0.56$

$\\ P(A \cap B) = 32\%\;or\;0.32$

With all this information, we can proceed as follows in the next lines.

The probability that a subscriber rented a car during the past 12 months for business or personal reasons.

We have to use here the formula (1) because of the sum of two probabilities, one for event A and the other for event B.

Then

$\\ P(A \cup B) = P(A) + P(B) - P(A \cap B)$

$\\ P(A \cup B) = 0.452 + 0.56 - 0.32$

$\\ P(A \cup B) = 0.692\;or\;69.2\%$

Thus, the probability that a subscriber rented a car during the past 12 months for business or personal reasons is 0.692 or 69.2%.

The probability that a subscriber did not rent a car during the past 12 months for either business or personal reasons.

As we can notice, this is the probability for the complement event that a subscriber did not rent a car during the past 12 months, that is, the probability of the events that remain in the sample space. In this way, the sum of the probability for the event that a subscriber rented a car plus the event that a subscriber did not rent a car equals 1, or mathematically:

$\\ P(\overline{A \cup B}) + P(A \cup B)= 1$

$\\ P(\overline{A \cup B}) = 1 - P(A \cup B)$

$\\ P(\overline{A \cup B}) = 1 - 0.692$

$\\ P(\overline{A \cup B}) = 0.308\;or\;30.8\%$

As a result, the requested probability for a subscriber that did not rent a car during the past 12 months for either business or personal reasons is 0.308 or 30.8%.

We can also find the same result if we determine the complement for each probability in formula (1), or:

$\\ P(\overline{A}) = 1 - P(A) = 1 - 0.452 = 0.548$

$\\ P(\overline{B}) = 1 - P(B) = 1 - 0.56 = 0.44$

$\\ P(\overline{A \cup B}) = 1 - P(A \cup B) = 1 - 0.32 = 0.68$

Then

$\\ P(\overline{A \cup B}) = P(\overline{A}) + P(\overline{B}) - P(\overline{A\cap B})$

$\\ P(\overline{A \cup B}) = 0.548 + 0.44 - 0.68$

$\\ P(\overline{A \cup B}) = 0.308$

3 0

4 years ago

In a class of 30 students (x+10) study algebra, (10x+3) study statistics, 4 study both algebra and statistics. 2x study only alg

Vladimir [108]

Answer:

1. The Venn diagrams are attached

2. When the statistics students number = 10·x + 3, we have;

The number of students that study

a. Algebra = 128/11

b. Statistic = 213/11

When the statistics students number = 2·x + 3, we have;

The number of students that study

a. Algebra = 16

b. Statistic = 15

Step-by-step explanation:

The parameters given are;

Total number of students = 30

Number of students that study algebra n(A) = x + 10

Number of students that study statistics n(B) = 10·x + 3

Number of student that study both algebra and statistics n(A∩B) = 4

Number of student that study only algebra n(A\B) = 2·x

Number of students that study neither algebra or statistics n(A∪B)' = 3

Therefore;

The number of students that study either algebra or statistics = n(A∪B)

From set theory we have;

n(A∪B) = n(A) + n(B) - n(A∩B)

n(A∪B) = 30 - 3 = 27

Therefore, we have;

n(A∪B) = x + 10 + 10·x + 3 - 4 = 27

11·x+13 = 27 + 4 = 31

11·x = 18

x = 18/11

The number of students that study

a. Algebra

n(A) = 18/11 + 10 = 128/11

b. Statistic

n(B) = 213/11

Hence, we have;

n(A - B) = n(A) - n(A∩B) = 128/11 - 4 = 84/11

Similarly, we have;

n(B - A) = n(B) - n(A∩B) = 213/11 - 4 = 169/11

However, assuming n(B) = (2·x + 3), we have;

n(A∪B) = n(A) + n(B) - n(A∩B)

n(A∪B) = 30 - 3 = 27

Therefore, we have;

n(A∪B) = x + 10 + 2·x + 3 - 4 = 27

2·x+3 + x + 10= 27 + 4 = 31

3·x = 18

x = 6

Therefore, the number of students that study

a. Algebra

n(A) = 16

b. Statistics

n(B) = 15

Hence, we have;

n(A - B) = n(A) - n(A∩B) = 16 - 4 = 12

Similarly, we have;

n(B - A) = n(B) - n(A∩B) = 15 - 4 = 11

The Venn diagrams can be presented as follows;

6 0

3 years ago

(y+1)^5 divided by (y+1)^2 will mark brainliest

Sergeeva-Olga [200]

Answer:

(y+1)^3

Step-by-step explanation:

When dividing powers, subtract them. Therefore, 5-2 = 3. So, (Y+1)^5/(Y+1)^2 = (Y+1)^3

4 0

4 years ago

Calculate: 3 gallons = ? liters

sergij07 [2.7K]

Answer:

There is exactly 11.3562 liters of liquid but to round it would be about 11.36 liters of liquid

Step-by-step explanation:

1 gallon =3.78541 liters

4 0

3 years ago

13 points if you can answer the problem AND teach me how to answer the problem

Harman [31]

<h3>Answer:</h3>

Y = 3X + 12

<h3>Explanation:</h3>

You are given several points on the line, so you can use a couple of them to find the slope, then write the equation in point-slope form and rearrange it to the desired form.

... slope = (change in Y)/(change in X)

Using the first two points, this is ...

... slope = (69 -51)/(19 -13) = 18/6 = 3

Point-Slope Form

The point-slope form of the equation of a line is usually written ...

... y -y1 = m(x -x1) . . . . . . where m = slope, (x1, y1) = point

This can be put into a y= form by adding y1:

... y = m(x -x1) +y1

Your Equation

Filling in m=3, (x1, y1) = (13, 51), the equation becomes

... y = 3(x -13) +51

... y = 3x -39 +51 . . . . . eliminate parentheses

... y = 3x +12 . . . . . . . . . simplify to slope-intercept form

_____

Alternate Solution

Having found the slope to be 3, you can write the slope-intercept form and fill in what you know.

... y = mx + b . . . . . slope-intercept form

... 51 = 3·13 +b . . . . slope-intercept form with slope and first point filled in

... 51 -39 = b = 12 . . . . equation solved for b by subtracting 39

Now you know that the equation is

... y = 3x +12

3 0

3 years ago