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Arlecino [84]
3 years ago
7

Explain why in the Venn Diagram example the number who liked Hip Hop plus the number who liked Country was NOT the same as the n

umber in the union of the two sets.
Mathematics
1 answer:
svlad2 [7]3 years ago
6 0

Answer:

Suppose that you have 50 people that like hip hop and 50 people that like country.

Now, the union of those sets would be 50 + 50 = 100 people, right?

Well, this may be incorrect, because in the 50 people that like hip hop, we may have, for example, 10, that also like country (this means that in the 50 people that like country, we also have 10 that like hip hop).

Then when we are adding 50 + 50 we are counting those 10 people in both groups, and that is why the direct addition may be different than the union of both sets.

In more technical words, the union of two sets is equal to the addition of the elements of both sets minus the elements in the intersection of both sets (in our prior example, the 10 people that like hip hop and country music are the intersection of both sets)

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On the graph of the equation 8x – 3y = 24, what is the value of the y-intercept?
ella [17]
8x - 3y = 24

y-intercept ⇒ x = 0

subtitute

8 · 0 - 3y = 24

-3y = 24    |divide both sides by (-3)

y = -8
3 0
3 years ago
What interest rate, to the nearest tenth of a percent, that is required for an investment subject to continuous compounding to i
Sunny_sXe [5.5K]

Answer:

It will take an interest rate of 8.1% to get 150% of the initial investment in just 5 years.

Step-by-step explanation:

Use the formula for continuous compounding

X(t) = Pe^{rt}

where r stands for the (annual) interest rate, t for time in years, P for the initial principal (investment) and X is the amount after t years.

(this formula can be beautifully derived from just basic considerations, btw)

We are given t=5, and percent increase on the initial P, so we can solve for r

X(5) = 1.5P=Pe^{r\cdot5}\\1.5=e^{r\cdot5}\\\ln 1.5=\ln e ^{5r}\\\ln 1.5=5r\\r = \frac{\ln 1.5}{5}=0.081\rightarrow 8.1\%

It will take an interest rate of 8.1% to get 150% of the initial investment in just 5 years.

5 0
3 years ago
3. How is the Fundamental Theorem of Algebra true for quadratic polynomials?
myrzilka [38]

Answer:

Step-by-step explanation:

Theorm-The Fundamental Theorem of Algebra: If P(x) is a polynomial of degree n ≥ 1, then P(x) = 0 has exactly n roots, including multiple and complex roots.

Let's verify that the Fundamental Theorem of Algebra holds for quadratic polynomials.

A quadratic polynomial is a second degree polynomial. According to the Fundamental Theorem of Algebra, the quadratic set = 0 has exactly two roots.

As we have seen, factoring a quadratic equation will result in one of three possible situations.

graph 1

The quadratic may have 2 distinct  real roots. This graph crosses the

x-axis in two locations. These  graphs may open upward  or downward.

graph 2

It may appear that the quadratic  has only one real root. But, it  actually has one repeated root.  This graph is tangent to the x-axis  in one location (touching once).

graph 3

The quadratic may have two  non-real complex roots called  a conjugate pair. This graph will  not cross or touch the x-axis, but  it will have two roots.

6 0
2 years ago
What is the solution of the following system of equations?<br> 2x + y = -7<br> -3x - 2y = 10
pentagon [3]

Answer:

the solution is    (-4, -3)

Step-by-step explanation:

Multiply the first equation by 2.  This produces 4x + 2y = -14.

Now combine this result with the second equation:

4x + 2y = -14

-3x - 2y = 10

------------------

 x          = -4

Subbing -4 for x in the first equation yields 2x - 4 = -7, or 2x = -3.  

Then x = -3/2, and the solution is    (-4, -3)

8 0
2 years ago
how can you use the metric prefixes milli, centi, and kilo to help you decide if a metric conversion is reasonable
serious [3.7K]
I remember it as a meter in the middle a 100 cents in a dollar and a millimeter is just one one-thousandth of a meter. A kilo is 100 times a meter.
3 0
3 years ago
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