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2 years ago

Without actually writing the formula, explain how to expand (x + 3)7 using the binomial theorem.

Mathematics

2 answers:

dusya [7]2 years ago

8 0

To write the coefficients of the 8 terms, either start with a combination of 7 things taken 0 at a time and continue to 7 things taken 7 at a time or use the 7th row of Pascal’s triangle.

For the first term, write x to the 7th power and 3 to the 0 power. Then decrease the power on x and increase the power on y until you reach x to the 0 and y to the 7.

Simplify by evaluating the coefficients and powers of 3.

GenaCL600 [577]2 years ago

8 0

Answer:

1)To write the coefficients of the 8 terms, either start with a combination of 7 things taken 0 at a time and continue to 7 things taken 7 at a time or use the 7th row of Pascal’s triangle.

2)For the first term, write x to the 7th power and 3 to the 0 power. Then decrease the power on x and increase the power on y until you reach x to the 0 and y to the 7.

3)Simplify by evaluating the coefficients and powers of 3.

Step-by-step explanation:

Choose any answer above; either way there all correct

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A pendulum is set swinging. its first oscillation is through 30 and each succeeding oscillation is through 95% of the angle of t

Marat540 [252]

Answer-

After 76 swings the angle through which it swings less than 1°

Solution-

From the question,

Angle of the first of swing = 30° and then each succeeding oscillation is through 95% of the angle of the one before it.

So the angle of the second swing = $(30\times \frac{95}{100})^{\circ}$

Then the angle of third swing = $(30\times (\frac{95}{100})^2)^{\circ}$

So, this follows a Geometric Progression.

$(30,\ 30\cdot \frac{95}{100},\ 30\cdot (\frac{95}{100})^2............,0)$

a = The initial term = 30

r = Common ratio = $\frac{95}{100}$

As we have to find the number swings when the angle swept by the pendulum is less than 1°.

So we have the nth number is the series as 1, applying the formula

$T_n=ar^{n-1}$

Putting the values,

$\Rightarrow 1=30(\frac{95}{100})^{n-1}$

$\Rightarrow \frac{1}{30} =(\frac{95}{100})^{n-1}$

Taking logarithm of both sides,

$\Rightarrow \log \frac{1}{30} =\log (\frac{95}{100})^{n-1}$

$\Rightarrow \log \frac{1}{30} =(n-1)\log (\frac{95}{100})$

$\Rightarrow -1.5=(n-1)(-0.02)$

$\Rightarrow 1.5=(n-1)(0.02)$

$\Rightarrow n-1=\dfrac{1.5}{0.02}$

$\Rightarrow n-1=75$

$\Rightarrow n=76$

Therefore, after 76 swings the angle through which it swings less than 1°

8 0

2 years ago

A bowl of flower seeds contains 5 petunia seeds and 15 begonia seeds. Riley calculated the probability that a random selected se

Vlad1618 [11]

Answer:

Riley divided the number of petunia seeds by the number of begonia seeds, getting $\frac {5}{15} = \frac {1}{3}$ . What you actually need to do to calculate the probability of selecting a petunia seed is divide the number of petunia seeds by the total number of seeds. 5 petunia seeds and 15 begonia seeds makes 20 total seeds, so you divide 5 petunia seeds by 20 total seeds to get $\frac {5}{20} = \frac {1}{4}$ .

7 0

2 years ago

Lisa says that the indicated angles cannot have the same measure. Marita disagrees and says she can prove that they can have the

AlexFokin [52]

I agree with Marita, that the angles could have the same measure. This can be proven if you set the two amounts equal and solve for x.

9x - 25 + x = x + 50 + 2x - 12

To begin, we should combine like terms on both sides of the equation to start simplifying the equation.

10x - 25 = 3x + 38

Next, we should subtract 3x from both sides and add 25 to both sides to get the variable x alone on the left side of the equation.

7x = 63

Finally, we should divide both sides by 7, to get rid of the coefficient of x.

x = 9

If you plug in 9 for x in our first equation, you get that both of the angle measurements equal 65 degrees. This means that Marita is correct, because if x = 9, then the angles would have the same measure.

8 0

2 years ago

If you were applying for a job and the boss said: “We have 7 employees and the average salary is $100,000,” would you hope that

julsineya [31]

When applying for the job, we would hope that is the mode. The mode is the value that appears most often; if most people in the office make $100,000 that may speak better of your potential salary.

8 0

2 years ago

The distribution of the number of moths captured per night by a certain moth trap is approximately normal with mean 103. If 28 p

Afina-wow [57]

Answer:

0.28 = (76 - 103)/σ (B)

Step-by-step explanation:

Let X be a random variable for capturing moths every night

Mean(μ) = 103

σ is the standard deviation

Pr(X<76) = 28%

Pr(X<76) = 0.28

For normal distribution, Z = (X - μ)/σ

Pr(X<76) = (X - μ)/σ

0.28 = (76 - 103)/σ

The equation to find the standard deviation is

0.28 = (76 - 103)/σ

5 0

2 years ago

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