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Ghella [55]
2 years ago
10

Model the following problem with a quadratic equation. Then solve. Find the length of a side of a square with an area of 75 ft2.

Model the problem with a quadratic equation. Let x be the length of a side of the square.
Mathematics
1 answer:
Vaselesa [24]2 years ago
5 0

Answer:

x = 8.6603 m

Step-by-step explanation:

If x is the length of a side of the square, the area of the square will be x^2.

So, if the area of the square is 75 ft2, we can formulate the quadratic equation:

x^2 = 75

Now, solving the equation, we just need to make the square root of 75:

x = sqrt(75) = ±8.6603

x1 = 8.6603

x2 = -8.6603

Now, as x represents the length of a side of the square, and measurements can't be negative, we take only the positive value, so:

x = 8.6603 m

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Assume that we have two events, and , that are mutually exclusive. Assume further that we know and . If an amount is zero, enter
sweet [91]

Answer:

Explained below.

Step-by-step explanation:

The complete question is:

Assume that we have two events, A and B, that are mutually exclusive. Assume further that we know P(A) = 0.30 and P(B) =0.40.

What is P(A and B)?

What is P(A | B)?

Is P(A | B) equal to P(A)?

Are events A and B dependent or independent?

A student in statistics argues that the concepts of mutually exclusive events and independent events are really the same, and that if events are mutually exclusive they must be independent. Is this statement accurate?

What general conclusion would you make about mutually exclusive and independent events given the results of this problem?

Solution:

The probability of the two events <em>A</em> and <em>B</em> are:

P(A) = 0.30 and P(B) =0.40

(a)

Compute the value of P (A ∩ B) as follows:

P(A\cap B)=0

This is because mutually exclusive events are those events that cannot occur together.

(b)

Compute the value of P (A | B) as follows:

P(A|B)=\frac{P(A\cap B)}{P(B)}=\frac{0}{0.40}=0

Thus, the value of P (A | B) is 0.

(c)

No, P (A | B) is not equal to the P (A).

(d)

As mentioned in part (a), mutually exclusive events are those events which cannot occur together.

That is, P(A\cap B)=0.

Events A and B are independent  if the chance of their concurrent happening is equivalent to the multiplication of their distinct probabilities.

That is, P(A\cap B)=P(A)\times P(B).

The concepts of mutually exclusive events and independent events are not the same.

(e)

As the it is provided that A and B are mutually exclusive events, we know that P(A\cap B)=0.

Now compute the value of P(A)\times P(B) as follows:

               P(A)\times P(B)=0.30\times 0.40=0.12\neq 0

Thus, the events A and B are not independent.

Thus, if two events are mutually exclusive events they cannot be independent.

4 0
3 years ago
Which number is composite? 23897993
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Which number is composite in 23897993?
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Ms. Pearson kept track of student absences versus final average grades in her math dass for one semester, The
sammy [17]

The correct statement about the data collected by Ms. Pearson is that there is no association between a student's absences and the final average grades.

<h3>When do variables have a linear relationship?</h3>

The equation that represents a linear relationship is: a + bx

Where x represents the rate of increase. Thus, for linear equations, the functiion increases by a constant term.

Looking at the table, the average final grade does not increase by a constant term.

To learn more about linear functions, please check: brainly.com/question/26434260

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Percent increase = ((new number - original number) / (original number)) x 100.

percent increase = ((3000 - 2500) / 2500)) x 100 =
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7 0
3 years ago
Find the cos A and tan B to four decimal places. URGENT
Nikolay [14]

cos A is 0.8511 and tan B is 1.6

Step-by-step explanation:

Find the 3rd length or the hypotenuse.

<u>Pythagoras theorem</u>

hypotenuse^{2} = adjacent^{2} + opposite^{2}

hypotenuse^{2} = 8^{2} + 5^{2}

hypotenuse^{2} = 64 + 25

hypotenuse = \sqrt{89}

hypotenuse = 9.4

a) Cos A

<u>Data:</u>

Adjacent = 8

Hypotenuse = 9.4

<u>Formula:</u>

Cos (Angle) = \frac{adjacent}{hypotenuse}

Cos A =  \frac{8}{9.4}

Cos A = 0.8511

A = cos^{-1} (0.8511)

A = 31.7°

b) Tan B

<u>Data: </u>

Opposite = 8

Adjacent = 5

<u>Formula:</u>

Tan (Angle) = \frac{opposite}{adjacent}

Tan B = \frac{8}{5}

Tan B = 1.6

B =  cos^{-1} (1.6)

B = 58°

Therefore, cos A is 0.8511 and tan B is 1.6.

Keyword: cos, tan

Learn more about cos at

  • brainly.com/question/5013374
  • brainly.com/question/9532142

#LearnwithBrainly

3 0
3 years ago
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