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STatiana [176]
3 years ago
8

Cos60° = x divided by 16

Mathematics
2 answers:
777dan777 [17]3 years ago
6 0
  • Answer:

<em>x = 8</em>

  • Step-by-step explanation:

<em>cos60° = x/16</em>

<em>1/2 = x/16</em>

<em>2x = 16</em>

<em>x = 16 : 2</em>

<em>x = 8</em>

Goryan [66]3 years ago
3 0

Answer:

\Huge \boxed{x=8}

Step-by-step explanation:

\sf \displaystyle cos(60\° ) = \frac{x}{16}

Multiplying both sides by 16.

\sf \displaystyle 16 \cdot cos(60\° )= \frac{x}{16} \cdot 16

Simplifying the equation.

\sf \displaystyle 16 \cdot \frac{1}{2} = x

\sf 8=x

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You plan to take a 7-day trip to California. You estimate that it will cost $275 per day to visit Los Angeles, and $400 per day
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Answer:

You can spend 4 days in Los Angeles and 3 days in San Francisco.

Step-by-step explanation:

From the information given, you can write the following equations:

x+y=7 (1)

275x+400y=2,300 (2), where:

x is the number of days to visit Los Angeles

y is the number of days to visit San Francisco

First, you can solve for x in (1):

x=7-y (3)

Now, you can replace (3) in (2):

275(7-y)+400y=2,300

1,925-275y+400y=2,300

125y=2,300-1,925

125y=375

y=375/125

y=3

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x=7-3

y=4

According to this, the answer is that you can spend 4 days in Los Angeles and 3 days in San Francisco.

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A news report states that the 99% confidence interval for the mean number of daily calories consumed by participants in a medica
expeople1 [14]

Answer:

The sample mean is of 1925 calories.

The margin of error is of 75 calories.

The sample standard deviation is of 109.7992 calories.

Step-by-step explanation:

Sample mean:

The sample mean is the mean value of the two bounds of the confidence interval. So

M = \frac{1850 + 2000}{2} = 1925

The sample mean is of 1925 calories.

The margin of error

Difference between the bounds and the sample mean. So

2000 - 1925 = 1925 - 1850 = 75 calories.

The margin of error is of 75 calories.

Sample standard deviation:

Here, I am going to expand on the t-distribution.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 18 - 1 = 17

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 17 degrees of freedom(y-axis) and a confidence level of 1 - \frac{1 - 0.99}{2} = 0.995. So we have T = 2.898

The margin of error is:

M = T\frac{s}{\sqrt{n}}

In which s is the standard deviation of the sample and n is the size of the sample.

Since M = 75, T = 2.898, n = 18

M = T\frac{s}{\sqrt{n}}

75 = 2.898\frac{s}{\sqrt{18}}

s = \frac{75\sqrt{18}}{2.898}

s = 109.7992

The sample standard deviation is of 109.7992 calories.

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