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Oksi-84 [34.3K]
3 years ago
12

uppose that a single die with 8 sides (numbered 1, 2, 3, ... , 8) is rolled twice. What is the probability that the sum of the t

wo rolls equals 5
Mathematics
1 answer:
Lilit [14]3 years ago
4 0

Answer:

1/16 = 0.0625 = 6.25% probability that the sum of the two rolls equals 5.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Die with 8 sides

This means that the total number of outcomes is T = 8^2 = 64

Outcomes in which the sum of the two rolls is 5:

(1,4), (4,1), (2,3), (3,2)

4 desired outcomes, so D = 4

What is the probability that the sum of the two rolls equals 5?

p = \frac{D}{T} = \frac{4}{64} = 0.0625

1/16 = 0.0625 = 6.25% probability that the sum of the two rolls equals 5.

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Answer:

If the lines area parallel: x = 69 degrees

Step-by-step explanation:

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2 years ago
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Find the indefinite integral. (Use C for the constant of integration.) <br> e2x 25 e4x dx.
Sladkaya [172]

Answer:

The solution is  \frac{1}{10} * tan^{-1}[\frac{e^{2x}}{5} ] +  C

Step-by-step explanation:

From the question

    The function given is  f(x) =  \frac{e^{2x}}{ 25 + e^{4x}} dx

The  indefinite integral is  mathematically represented as

          \int\limits  {\frac{e^{2x}}{ 25 + e^{4x}}} \, dx

Now  let  e^{2x} =  u

=>   \frac{du}{dx} 2e^{2x}

=>   2 e^{2x}dx =  du

So

\int\limits  {\frac{e^{2x}}{ 25 + e^{4x}}} \, dx =  \int\limits  {\frac{1}{ 2(25 + u^2)} } \, du

= \frac{1}{2} \int\limits  {\frac{1}{ 25 + u^2)} } \, du

=  \frac{1}{2} \int\limits  {\frac{1}{ 5^2 + u^2)} } \, du

= \frac{1}{2} \frac{tan^{-1} [\frac{u}{5} ]}{5}  +  C

Now substituting for  u

\frac{1}{10} * tan^{-1}[\frac{e^{2x}}{5} ] +  C

3 0
3 years ago
If you multiply two binomials together, what type of polynomial will the product be?
Arturiano [62]
Depends
it can be a trinomial example
(x-3)(x-4)=x²-7x+12

it can be a binomial example
(x-3)(x+3)=x²-9

depends
7 0
3 years ago
In a recent survey, 72 out of 100 consumers reported that they preferred plastic bags instead of paper bags for their groceries.
kupik [55]

Answer:

a) P=0.03

b) α=0.05

c) 0.72

d) 100

e) 0.72

Step-by-step explanation:

a) The P-value is the probability of the sample result. In this case the P-value is 0.03.

b) The level of significance is the threshold of probabilty for the null hypothesis to be reejcted or not. It is contrasted with the P-value to know if the effect is significant. In this case, the level of significance is 0.05.

NOTE: if it is a two-side test, the level of significance is 0.1 (two times 0.05).

c) The sample proportion is the one that results from the sample data. In this case, the sample proportion is 0.72.

p=72/100=0.72

d) The sample size is the amount of consumers reported. In this case is 100 customers.

e) The null value is 0.72 (equal to the sample proportion), because it is tested if there is no difference between the population proportion and the sample proportion.

3 0
3 years ago
Which polynomial is in standard form?
Tamiku [17]

Answer:

D). 5x^7y^2+7x^6y^5-14x^3y^7+51x^2y^9

Step-by-step explanation:

For better clarity let us re write the options

A).2xy^3+3x^3y^4-4x^4y^5+9x^5y^6

B).8x^5-5y^4-2xy^5+x^2y

C).x^3y^2-3x^2y-9x^4y^3+11x

D).5x^7y^2+7x^6y^5-14x^3y^7+51x^2y^9

To express polynomial with mixed variables in standard form, we begin by the highest coefficient of x to the smallest (we place high precedence on the coefficient  x terms)

5 0
3 years ago
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