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3 years ago

Can someone help me find x

Mathematics

1 answer:

Viefleur [7K]3 years ago

4 0

Answer:

Rounded to the nearest tenth: $x=5.7$ in

Rounded to the nearest hundredth: $x=5.74$ in

Step-by-step explanation:

We have a right triangle with a given angle of 35°. We also have the opposite side of that angle, $x$ , and its hypotenuse 10 in. To find $x$ , we are using the trig function that relates the opposite side with the hypotenuse; in other words, the sine trig function.

$sin\alpha =\frac{opposite}{hypotenuse}$

$sin(35)=\frac{x}{10}$

$x=10sin(35)$

$x=5.735764364$

Rounded to the nearest tenth: $x=5.7$ in

Rounded to the nearest hundredth: $x=5.74$ in

You might be interested in

You weigh a random sample of adult golden retrievers and get the following results: 55, 64, 58, 61, 69, 64, 59, 69, 72, and 65.

Andre45 [30]

Answer:

The 98% confidence interval for the mean of the population is (59, 68.2).

Step-by-step explanation:

Before building the confidence interval, we need to find the sample mean and the sample standard deviation.

Sample mean:

$\overline{x} = \frac{55+64+58+61+69+64+59+69+72+65}{10} = 63.6$

Sample standard deviation:

$s = \sqrt{\frac{(55-63.6)^2+(64-63.6)^2+(58-63.6)^2+(61-63.6)^2+(69-63.6)^2+(64-63.6)^2+(59-63.6)^2+(69-63.6)^2+(72-63.6)^2+(65-63.6)^2}{10}} = 5.142$

Confidence interval:

We have the standard deviation for the sample, and thus, we use 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 = 10 - 1 = 9

98% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 9 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.98}{2} = 0.99$ . So we have T = 2.821

The margin of error is:

$M = T\frac{s}{\sqrt{n}} = 2.821\frac{5.142}{\sqrt{10}} = 4.6$

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

The lower end of the interval is the sample mean subtracted by M. So it is 63.6 - 4.6 = 59

The upper end of the interval is the sample mean added to M. So it is 63.6 + 4.6 = 68.2.

The 98% confidence interval for the mean of the population is (59, 68.2).

6 0

2 years ago

PLS HELP ASAP. IM TIMED

ycow [4]

44 square feet

Diameter (4) divided by 2 is radius (2).

SA = 2πr^2 + 2πrh

SA = 2 * 3.14 * 2^2 + 2 * 3.14 * 2 * 3

SA = 2 * 3.14 * 4 + 2 * 3.14 * 2 * 3

SA = 6.28 * 4 + 6.28 * 3

SA = 25.12 + 18.84

SA = 43.96

Round to the nearest tenth.

SA = 44 square feet

Please consider marking this answer as Brainliest to help me advance.

5 0

3 years ago

Find the derivative of f(x) = 6x + 2 at x = 1.

earnstyle [38]

$f'(x_0)=\lim\limits_{x\to x_0}\dfrac{f(x)-f(x_0)}{x-x_0}\\\\f(x)=6x+2;\ x_0=1\\\\f'(1)=\lim\limits_{x\to x_0}\dfrac{(6x+2)-(6\cdot1+2)}{x-1}=\lim\limits_{x\to x_0}\dfrac{6x+2-8}{x-1}\\\\=\lim\limits_{x\to x_0}\dfrac{6x-6}{x-1}=\lim\limits_{x\to x_0}\dfrac{6(x-1)}{x-1}=\lim\limits_{x\to x_0}6=6\\\\\\Answer:\boxed{f'(1)=6}$