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Alika [10]
1 year ago
6

Hi, can you help to find (all the roots/zeros), please!!!

Mathematics
1 answer:
OLga [1]1 year ago
4 0

Solution

Given the quadratic equation

x^2-2x-38=0

we need to find the zeros of the equation

To do that, we use the completing the square method

Step 1. Add 38 to both sides

\begin{gathered} \Rightarrow x^2-2x-38+38=38 \\  \\ \Rightarrow x^2-2x=38 \end{gathered}

Step 2: add the square of half of the coefficient of x to both sides

That is;

\begin{gathered} \Rightarrow x^2-2x+(\frac{1}{2}\cdot(-2))^2=38+(\frac{1}{2}\cdot(-2))^2 \\  \\ \Rightarrow x^2-2x+1=38+1 \\  \\ \Rightarrow x^2-2x+1=39 \\  \\ \Rightarrow(x-1)^2=39 \end{gathered}

Step 3: Simplify the above expression;

\begin{gathered} \Rightarrow x-1=\pm\sqrt[]{39} \\  \\ \Rightarrow x=1\pm\sqrt[]{39} \end{gathered}

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Naddik [55]
Let the number of cards in each group be 2x and 3x.
So,
2x + 3x = 120
5x = 120
x = 120 / 5
x = 24
Number of cards in each group is
2x = 2 × 24 = 48
3x = 3 × 24 = 72
7 0
3 years ago
Is 15/28 equivalent to 25/45
Lana71 [14]
No, it's not.

15/28 equals to (about) 0.54 while 25/45 is (about) 0.56.
They are close, but not equivalent.<span />
7 0
3 years ago
The Washington, DC, region has one of the fastest-growing foreclosure rates in the nation, as 15,613 homes went into foreclosure
Ilia_Sergeevich [38]

Answer:

a) 0.6226 = 62.26% probability that in a given year, fewer than 2 out of 100 houses in the Washington, DC area will go up for foreclosure.

b) 0.7837 = 78.37% probability that in a given year, fewer than 2 out of 100 houses in the nation will go up for foreclosure.

c) The proportion of foreclosures in the Nation is lower than in Washington, which means that with a sample size of 100, it is likely to have a small number(fewer than 2) of foreclosures than Washington DC.

Step-by-step explanation:

For each home, there are only two possible outcomes. Either it goes into foreclosure, or it does not. The probability of a home going into foreclosure is independent of other homes. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

a. What is the probability that in a given year, fewer than 2 out of 100 houses in the Washington, DC area will go up for foreclosure?

The foreclosure rate is 1.31% for the Washington, DC area, which means that p = 0.0131

We wanto to find, with n = 100:

P(X < 2) = P(X = 0) + P(X = 1)

In which

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{100,0}.(0.0131)^{0}.(0.9869)^{100} = 0.2675

P(X = 1) = C_{100,1}.(0.0131)^{1}.(0.9869)^{99} = 0.3551

P(X < 2) = P(X = 0) + P(X = 1) = 0.2675 + 0.3551 = 0.6226

0.6226 = 62.26% probability that in a given year, fewer than 2 out of 100 houses in the Washington, DC area will go up for foreclosure.

b. What is the probability that in a given year, fewer than 2 out of 100 houses in the nation will go up for foreclosure?

Foreclosure rate of 0.87% for the nation, which means that p = 0.0087. So

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{100,0}.(0.0087)^{0}.(0.9913)^{100} = 0.4174

P(X = 1) = C_{100,1}.(0.0087)^{1}.(0.9913)^{99} = 0.3663

P(X < 2) = P(X = 0) + P(X = 1) = 0.4174 + 0.3663 = 0.7837

0.7837 = 78.37% probability that in a given year, fewer than 2 out of 100 houses in the nation will go up for foreclosure.

c. Comment on the above findings.

The proportion of foreclosures in the Nation is lower than in Washington, which means that with a sample size of 100, it is likely to have a small number(fewer than 2) of foreclosures than Washington DC.

7 0
3 years ago
A right circular cylinder has a height of 22 1/4 ft and a diameter 2 2/5 times its height. What is the volume of the cylinder? E
Triss [41]

Answer:

The volume of cylinder is:

49806.06 ft^3

Step-by-step explanation:

We are given a right circular cylinder with:

Height(h)=22\frac{1}{4}ft=\dfrac{89}{4}ft

and a diameter is 2\frac{2}{5} times it's height.

i.e. \dfrac{12}{5} times it height.

i.e. the diameter is given as:

\dfrac{12}{5}\times \dfrac{89}{4}=\dfrac{267}{5}ft.

We know that the radius of cylinder is half the diameter.

Hence, radius(r) of cylinder is:

\dfrac{1}{2}\times \dfrac{267}{5}\\\\=\dfrac{267}{10}

The volume(V) of cylinder is given by:

V=\pi r^2h

V=3.14\times (\dfrac{267}{10})^2\times \dfrac{89}{4}\\\\V=\dfrac{19922423.94}{400}\\\\V=49806.06ft^3

Hence, the volume of cylinder is:

49806.06 ft^3

7 0
4 years ago
Which polynomial is in standard form? A) 2x + 3x3 + 5x5 + 9x4 + 2x B) 5 + 3x + x2 + 2x4 + 2x5 C) 8x7 + 3x6 + x5 + 5x4 − 2x3 D) 8
sasho [114]
Answer:  [C]:  "<span> 8x</span>⁷<span> + 3x</span>⁶<span> + x</span>⁵<span> + 5x</span>⁴<span> − 2x</span>³<span> </span>" .
__________________________________________________
6 0
3 years ago
Read 2 more answers
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