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3 years ago

CAN SOMEONE PLEASE PLEASE HELP ME ON THIS IM DESPERATE

Mathematics

1 answer:

storchak [24]3 years ago

5 0

Answer:

The angle has a measure of $\frac{5\pi}{6}$ radians.

Step-by-step explanation:

According to the statement, an angle centered at the center of the circle covers an arc of $\frac{25\pi}{6}$ units, the arc is a portion of the circunference. We include a figure representing the circle below.

Where:

$R$ - Radius, measured in units.

$s$ - Arc, measured in units.

$\alpha$ - Angle of the arc, measured in radians.

From Geometry, we can calculate the length of the arc by means of this equation:

$s = \alpha\cdot R$ (1)

If we know that $R = 5$ and $s = \frac{25\pi}{6}$ , then the angle of the arc is:

$\alpha = \frac{s}{R}$

$\alpha = \frac{\frac{25\pi}{6} }{5}$

$\alpha = \frac{25\pi}{30}$

$\alpha = \frac{5\pi}{6}\,rad$

The angle has a measure of $\frac{5\pi}{6}$ radians.

You might be interested in

The amount of time that people spend at Grover Hot Springs Spa is normally distributed with a mean of 63 minutes and a standard

PtichkaEL [24]

Answer:

a) $X \sim N(63,18)$

Where $\mu=63$ and $\sigma=18$

b) $P(X>90)=P(\frac{X-\mu}{\sigma}>\frac{90-\mu}{\sigma})=P(Z>\frac{90-63}{18})=P(Z>1.5)$

And we can find this probability using the complement rule and with the normal standard table or excel:

$P(Z>1.5)=1-P(Z$

c) $P(X$

$P(Z$

d) $P(60$

$P(-0.167$

e) IQR = 75.13-50.87=24.26

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Part a

Let X the random variable that represent the amount of time that people spend at Grover Hot Springs of a population, and for this case we know the distribution for X is given by:

$X \sim N(63,18)$

Where $\mu=63$ and $\sigma=18$

Part b

We are interested on this probability

$P(X>90)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X>90)=P(\frac{X-\mu}{\sigma}>\frac{90-\mu}{\sigma})=P(Z>\frac{90-63}{18})=P(Z>1.5)$

And we can find this probability using the complement rule and with the normal standard table or excel:

$P(Z>1.5)=1-P(Z$

Part c

We are interested on this probability

$P(X$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X$

And we can find this probability using the normal standard table or excel:

$P(Z$

Part d

If we apply this formula to our probability we got this:

$P(60$

And we can find this probability with this difference:

$P(-0.167$

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.

$P(-0.167$

Part e

For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.75$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.25 of the area on the left and 0.75 of the area on the right it's z=-0.674. On this case P(Z<-0.674)=0.25 and P(z>-0.674)=0.75

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=-0.674$

And if we solve for a we got

$a=63 -0.674*18=50.87$

So the value of height that separates the bottom 25% of data from the top 75% is 50.87.

Since the distribution is symmetrical we repaeat the procedure for Q1 but now with z= 0.674

$z=0.674$

And if we solve for a we got

$a=63 +0.674*18=75.13$

And then the IQR = 75.13-50.87=24.26

3 0

3 years ago

Please help me with this please

anastassius [24]

First one is A
Second one is C
Third one is B
Trust me

4 0

4 years ago

Can you please help me with this math question number 10

andrezito [222]

We have the following equation,

$16-2x=88$

and we need to find x. Then, by subtracting 16 to both sides, we have

$\begin{gathered} 16-16-2x=88-16 \\ 0-2x=72 \\ -2x=72 \end{gathered}$

and by dividing both sides by -2, we get

$\begin{gathered} x=\frac{72}{-2} \\ x=-\frac{72}{2} \end{gathered}$

which gives

$x=-36$

Therefore, the answer is x= -36

3 0

1 year ago

What is the equation of the line passing through the points (2/5, 19/20) and (1/3, 11/12) in slope-intercept form?

antiseptic1488 [7]

Answer: b is the answer

Step-by-step explanation:

4 0

3 years ago

In 11 and 12, use the map in Example 2 and write

Ket [755]

Answer:

11. Ellipse

12. Washington Monument

Step-by-step explanation:

You are being asked to locate points on a graph, given an ordered pair.

The first number of the pair is the x-coordinate, the distance to the right of the y-axis. The second number of the pair is the y-coordinate, the distance up from the x-axis. When it is negative, the point will be found below the x-axis.

On this coordinate plane, there are 4 grid lines between integer labels, so each grid line stands for 1/4 unit, or 0.25 units.

(0.5, 0) will be 2 grid lines to the right of the y-axis, and on the x-axis. That location is labeled <em>Ellipse</em>.

(3/4, -1/2) will be 3 grid lines to the right of the y-axis, and 2 grid lines below the x-axis. That location is labeled <em>Washington Monument</em>.

8 0

2 years ago