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3 years ago

36. GEOMETRY Write an algebraic expression to

Mathematics

1 answer:

Stels [109]3 years ago

6 0

Answer:

108 in²

Step-by-step explanation:

Area of a triangle is given as ½*base*height

The base of the given triangle = h + 6

height = h

Algebraic expression for its area = $\frac{1}{2}*(h + 6)*h = \frac{1}{2}(h^2 + 6h) = \frac{h^2 + 6h}{2}$

Evaluate the area if h is given as 12 inches.

Plug in the value of h into the algebraic expression:

$\frac{h^2 + 6h}{2} = \frac{12^2 + 6(12)}{2}$

$= \frac{144 + 72}{2}$

$= \frac{216}{2} = 108 in^2$

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For example, let's say we had the equation x = x+2. Subtracting x from both sides leads to 0 = 2 which is a false statement. No matter what we replace x with, the equation x = x+2 is always false. That's why we don't have any solutions here.

For an equation like x + 2 = x + 2, subtracting x from both sides leads to 2 = 2 which is always true. A true equation is one where the same number is on both sides. No matter what we replace x with, the equation will be true. Therefore, there are infinitely many solutions.

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2 years ago

What is 2/3 - 5 9th in fractions

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Answer:

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Step-by-step explanation:

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2 years ago

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What are the next three numbers in this pattern? 11, 22, 12, 23, ...

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2 years ago

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Suppose approximately 75% of all marketing personnel are extroverts, whereas about 70% of all computer programmers are introvert

Setler [38]

Answer:

$P(x \ge 5) = 1.000$ ---- At least 5 from marketing departments are extroverts

$P(x=15) = 0.013$ ---- All from marketing departments are extroverts

$P(x = 0) = 0.002$ ---------- None from computer programmers are introverts

Step-by-step explanation:

See comment for complete question

The question is an illustration of binomial probability where

$P(x) = ^nC_x * p^x * (1 - p)^{n-x}$

$(a):\ P(x \ge 5)$

$n = 15$ --- marketing personnel

$p = 75\%$ --- proportion that are extroverts

Using the complement rule, we have:

$P(x \ge 5) = 1 - P(x < 5)$

So, we have:

$P(x < 5) =P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3) + P(x = 4)$

$P(x = 0) = ^{15}C_{0} * (75\%)^0 * (1 - 75\%)^{15 - 0} = 1 * 1 * (0.25)^{15} = 9.31 * 10^{-10}$

$P(x = 1) = ^{15}C_{1} * (75\%)^1 * (1 - 75\%)^{15 - 1} = 15* (0.75)^1 * (0.25)^{14} = 4.19 * 10^{-8}$

$P(x = 2) = ^{15}C_{2} * (75\%)^2 * (1 - 75\%)^{15 - 2} = 105* (0.75)^2 * (0.25)^{13} = 8.80 * 10^{-7}$

$P(x = 3) = ^{15}C_{3} * (75\%)^3 * (1 - 75\%)^{15 - 3} = 455* (0.75)^2 * (0.25)^{12} = 0.0000153$

$P(x = 4) = ^{15}C_{4} * (75\%)^4 * (1 - 75\%)^{15 - 4} = 1365 * (0.75)^4 * (0.25)^{11} = 0.000103$

So, we have:

$P(x < 5) = (9.31 * 10^{-10}) + (4.19 * 10^{-8}) + (8.80 * 10^{-7}) + 0.0000153 + 0.000103$

$P(x < 5) = 0.00011922283$

Recall that:

$P(x \ge 5) = 1 - P(x < 5)$

$P(x \ge 5) = 1 - 0.00011922283$

$P(x \ge 5) = 0.9998$

$P(x \ge 5) = 1.000$ --- approximated

$(b)\ P(x = 15)$

$n = 15$ --- marketing personnel

$p = 75\%$ --- proportion that are extroverts

So, we have:

$P(x) = ^nC_x * p^x * (1 - p)^{n-x}$

$P(x=15) = ^{15}C_{15} * 0.75^{15} * (1 - 0.75)^{15-15}$

$P(x=15) = 1 * 0.75^{15} * (0.25)^{0$

$P(x=15) = 0.013$

$(c)\ P(x = 0)$

$n=5$ ---------- computer programmers

$p = 70\%$ --- proportion that are introverts

So, we have:

$P(x) = ^nC_x * p^x * (1 - p)^{n-x}$

$P(x = 0) = ^{5}C_0 * (70\%)^0 * (1 - 70\%)^{5-0}$

$P(x = 0) = 1 * 1 * (0.30)^5$

$P(x = 0) = 0.002$

3 0

1 year ago

Which graph represents a proportional relationship?

Vadim26 [7]

Answer:

The one shown in the photo

Step-by-step explanation:

A proportional relationship is one in which the relationship increases steadily, which looks like a straight line when graphed. Also, the line should pass through the <em>origin</em>, which is the point (0, 0) on a graph.

The graph shown increases steadily (it's a straight line), and passes through the origin (point 0,0) as well. So, it's proportional. Hopefully that's helpful! :)

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2 years ago