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3 years ago

Convert this identity to one using sine term(s) only. 1-2cos(r)^2

Mathematics

1 answer:

Natali5045456 [20]3 years ago

8 0

Pythagorean identity:
sin²+cos²=1
Then cos²=1-sin²
Substitute:
1-2cos²
1-2(1-sin²)
1-2+2sin²
2sin²-1

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Juliet is selling photographs as part of a project for her entrepreneurship class. She sells the first 20 photographs for $10 ea

Murljashka [212]

Answer:

option (B) 20

Step-by-step explanation:

Data provided in the question:

Number of photographs initially sold = 20

selling price of first 20 photographs = $10 each

Therefore,

Revenue from 20 photographs = 20 × $10 = $200

Selling price of further photographs = $15

Let the number of additional photographs sold be 'x'

thus,

total revenue = $200 + $15x

now,

according to the question

80% of ($200 + $15x) = $400

0.80 × ($200 + $15x) = $400

($200 + $15x) = $500

$15x = $300

x = 20

Hence,

the answer is option (B) 20

5 0

4 years ago

Suppose the time a child spends waiting at for the bus as a school bus stop is exponentially distributed with mean 7 minutes. De

Gala2k [10]

Answer:

The probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning is 0.148.

Step-by-step explanation:

Let the random variable <em>X</em> represent the time a child spends waiting at for the bus as a school bus stop.

The random variable <em>X</em> is exponentially distributed with mean 7 minutes.

Then the parameter of the distribution is, $\lambda=\frac{1}{\mu}=\frac{1}{7}$ .

The probability density function of <em>X</em> is:

$f_{X}(x)=\lambda\cdot e^{-\lambda x};\ x>0,\ \lambda>0$

Compute the probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning as follows:

$P(6\leq X\leq 9)=\int\limits^{9}_{6} {\lambda\cdot e^{-\lambda x}} \, dx$

$=\int\limits^{9}_{6} {\frac{1}{7}\cdot e^{-\frac{1}{7} \cdot x}} \, dx \\\\=\frac{1}{7}\cdot \int\limits^{9}_{6} {e^{-\frac{1}{7} \cdot x}} \, dx \\\\=[-e^{-\frac{1}{7} \cdot x}]^{9}_{6}\\\\=e^{-\frac{1}{7} \cdot 6}-e^{-\frac{1}{7} \cdot 9}\\\\=0.424373-0.276453\\\\=0.14792\\\\\approx 0.148$

Thus, the probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning is 0.148.

6 0

3 years ago

A convex octagon has interior angles with measures (x + 55). (3x + 20), 4x°. (4x - 10). (6x - 55) (3x + 52). 3.xº, and (2x + 30)

Brilliant_brown [7]

Answer:

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6 0

3 years ago

Given the follow statistics about scores on the last math test, what is the best description of the shape of the distribution?

julia-pushkina [17]

The shape of the distribution, is symmetric, is the best description of statistics about scores.

<h3 /><h3>What is standard deviation ?</h3>

The standard deviation is the positive square root of the variance of this data set. Variance of a data set is the sum of squared differences of the data values from its mean to the total count of data values.

The given data in the problem is;

Mean = 78%

Standard deviation = 4%

Min = 64

Median = 78

Q1 = 72

Q3 = 84

Max = 99

The condition for the symmetric distribution is found as;

$(\rm Q_2-Q_1)=Q_3-Q_2)$

From the data we have;

$(\rm Q_2-Q_1)=Q_3-Q_2)\\\\ (\rm Q_2-Q_1)= (\rm 84-78)= 6 \\\\ Q_3-Q_2)=(78-72) = 6 \\\\$

So that , $(\rm Q_2-Q_1)=Q_3-Q_2)$ .

Hence, the condition of symmetry is followed.

To learn more about the symmetry, refer to the link;l

brainly.com/question/15970176

#SPJ2

7 0

3 years ago

The students at Central Elementary School are planning a dinner for their parents.

blsea [12.9K]

They will need 20 pans

5 0

3 years ago