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miss Akunina [59]
2 years ago
14

7 2 − 140 degrees for angles

Mathematics
1 answer:
pickupchik [31]2 years ago
6 0

Answer:

What?

Step-by-step explanation:

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Expreess 3.81 as a mixed number
Luba_88 [7]

Answer:

3.81 = 3 81/100

Step-by-step explanation:

This can’t be simplified so it stays as 3 \frac{81}{100}

8 0
3 years ago
Given a leading coefficient of 8, polynomial roots of 1 & 2, and the known point on the graph (4,5). Write an equation that
m_a_m_a [10]

Given:

The leading coefficient of a polynomial is 8.

Polynomial roots are 1 and 2.

The graph passes through the point (4,5).

To find:

The 3rd root and the equation of the polynomial.

Solution:

The factor form of a polynomial is:

y=a(x-c_1)(x-c_2)...(x-c_n)

Where, a is a constant and c_1,c_2,...,c_n are the roots of the polynomial.

Polynomial roots are 1 and 2. So, (x-1) and (x-2) are the factors of the polynomial.

Let the third root of the polynomial by c, then (x-c) is a factor of the polynomial.

The leading coefficient of a polynomial is 8. So, a=8 and the equation of the polynomial is:

y=8(x-1)(x-2)(x-c)

The graph passes through the point (4,5). Putting x=4,y=5, we get

5=8(4-1)(4-2)(4-c)

5=8(3)(2)(4-c)

5=48(4-c)

Divide both sides by 48.

\dfrac{5}{48}=4-c

c=4-\dfrac{5}{48}

c=\dfrac{192-5}{48}

c=\dfrac{187}{48}

Therefore, the 3rd root on the polynomial is \dfrac{187}{48}.

8 0
2 years ago
Suppose a bag of marbles has 4 green, 2 red, 5 yellow, 1 brown, and 7 blue marbles. What is the probability of picking a red mar
swat32

Assuming that each marble can be picked with equal probability, we notice that there is a total of

4+2+5+1+7 = 19

marbles, of which 2 are red.

So, the probability of picking a red marble is

\dfrac{2}{19}

In fact, as in any other case of (finite) equidistribution, we used the formula

P(\text{event}) = \dfrac{\text{number of favourable cases}}{\text{number of all possible cases}}

4 0
2 years ago
Approximately 12.6% of all (untreated) Jonathan apples had bitter pit in a study conducted by the botanists Ratkowsky and Martin
bagirrra123 [75]

Answer:

Step-by-step explanation:

Let n be a random variable that represents the first Jonathan apple chosen at random that has bitter pit.

a) P(X = n) = q(n-1)p, where q = 1 - p.

From the information given, probability if success, p = 12.6/100 = 0.126

b) for n = 3, the probability value from the geometric probability distribution calculator is

P(n = 3) = 0.096

For n = 5, the probability value from the geometric probability distribution calculator is

P(n = 5) = 0.074

For n = 12, the probability value from the geometric probability distribution calculator is

P(n = 12) = 0.8

c) For n ≥ 5, the probability value from the geometric probability distribution calculator is

P(n ≥ 5) = 0.58

d) the expected number of apples that must be examined to find the first one with bitter pit is the mean.

Mean = 1/p

Mean = 1/0.126 = 7.9

Approximately 8 apples

7 0
3 years ago
If the sum of the even integers between 1 and k, inclusive, is equal to 2k, what is the value of k?
Alisiya [41]
If k is odd, then

\displaystyle\sum_{n=1}^{\lfloor k/2\rfloor}2n=2\dfrac{\left\lfloor\frac k2\right\rfloor\left(\left\lfloor\frac k2\right\rfloor+1\right)}2=\left\lfloor\dfrac k2\right\rfloor^2+\left\lfloor\dfrac k2\right\rfloor

while if k is even, then the sum would be

\displaystyle\sum_{n=1}^{k/2}2n=2\dfrac{\frac k2\left(\frac k2+1\right)}2=\dfrac{k^2+2k}4

The latter case is easier to solve:

\dfrac{k^2+2k}4=2k\implies k^2-6k=k(k-6)=0

which means k=6.

In the odd case, instead of considering the above equation we can consider the partial sums. If k is odd, then the sum of the even integers between 1 and k would be

S=2+4+6+\cdots+(k-5)+(k-3)+(k-1)

Now consider the partial sum up to the second-to-last term,

S^*=2+4+6+\cdots+(k-5)+(k-3)

Subtracting this from the previous partial sum, we have

S-S^*=k-1

We're given that the sums must add to 2k, which means

S=2k
S^*=2(k-2)

But taking the differences now yields

S-S^*=2k-2(k-2)=4

and there is only one k for which k-1=4; namely, k=5. However, the sum of the even integers between 1 and 5 is 2+4=6, whereas 2k=10\neq6. So there are no solutions to this over the odd integers.
5 0
3 years ago
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