All categories

2 years ago

Given circle X with radius 5 units and chord AB with length 8 units, what is the

Mathematics

1 answer:

kvv77 [185]2 years ago

3 0

Answer: The correct option is (B) 3.

Step-by-step explanation: We are given a circle X with radius 5 units and chord AB with length 8 units.

We are to find the length of segment XC that bisects chord.

We know that the line segment drawn from the center of a circle to the midpoint of a chord is perpendicular to the chord.

So, in the given circle X, the segment XC is perpendicular to chord AB. Then, triangle XCB will be a right angled triangle with hypotenuse XB.

Since XC bisects AB, so the length of BC will be

$BC=\dfrac{AB}{2}=\dfrac{8}{2}=4~\textup{units}.$

And, radius, XB = 5 units.

Using Pythagoras theorem in triangle XCB, we have

$XB^2=XC^2+BC^2\\\\\Rightarrow XC^2=XB^2-BC^2\\\\\Rightarrow XC^@=5^2-4^2\\\\\Rightarrow XC^2=9\\\\\Rightarrow XC^2=3^2\\\\\Rightarrow XC=3.$

Thus, the length of the segment XC is 3 units.

Option (B) is CORRECT.

You might be interested in

Given that a 90% confidence interval for the mean height of all adult males in Idaho measured in inches was [62.532, 76.478]. Us

grigory [225]

Answer:

The confidence interval on this case is given by:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

For this case the confidence interval is given by (62.532, 76.478)[/tex]

And we can calculate the mean with this:

$\bar X = \frac{62.532+76.478}{2}= 69.505$

So then the mean for this case is 69.505

Step-by-step explanation:

Previous concepts

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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".

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

$\bar X$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma$ represent the population standard deviation

n represent the sample size

Assuming the X follows a normal distribution

$X \sim N(\mu, \sigma)$

The confidence interval on this case is given by:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

For this case the confidence interval is given by (62.532, 76.478)[/tex]

And we can calculate the mean with this:

$\bar X = \frac{62.532+76.478}{2}= 69.505$

So then the mean for this case is 69.505

5 0

2 years ago

Yuri is thinking of a 4-digit whole number. He rounds his number to the nearest thousand. His answer is 4000, what is the smalle

konstantin123 [22]

Answer:

Smallest number = 3500

Step-by-step explanation:

Rounding of numbers involve replacing numbers with simpler numbers. In order to round a number to the nearest thousand, the last 3 digits of the number should be considered. If the last 3 digits are less than 500, the number is rounded down(the thousand figure is unaffected), but if the last 3 digits are greater or equal to 500, the number is rounded up.

In this case, Yuri is thinking of a 4-digit whole number and he rounds his number to the nearest thousand. Since his answer is 4000, the smallest number yuri could be thinking of would be 3500 and the highest number he could be thinking of is 4499.

Thus, the smallest number Yuri could be thinking of is 3500

6 0

2 years ago

suppose you could make a single "lump sum" deposit of $3679, in an investment that provides an annual percentage rate(apr) of 4%

yaroslaw [1]

Answer:

$\$5,698.30$

Step-by-step explanation:

The compound interest formula is equal to

$A=P(1+\frac{r}{n})^{nt}$

where

A is the Final Investment Value (future value)

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

$t=11\ years\\ P=\$3,679\\ r=4\%=4/100=0.04\\n=365$

substitute in the formula above

$A=3,670(1+\frac{0.04}{365})^{365*11}$

$A=\$5,698.30$

3 0

2 years ago

Trains A and B, 200 km apart on the same straight track, travel at speeds of 50 km/hr and 65 km/hr respectively. At the end of 1

Gwar [14]

Answer:

Ok, at the beginning the distance between the trains is 200km:

IPa(0s) - P(0s)I = 200km.

where Pa is the position of train A, and Pb is the position of train B.

Now, the speed of train A is:

Sa = 50km/h

Sb = 65km/h

Now, remember the relation:

Distance = Speed*time.

So, in one hour, the displacement of train A is:

Distance = 50km/h*1h = 50km

The displacement of train B is:

distance = 65km/h*1h = 65km.

Now, if at the beginning train A is 200km ahead of train B, then we have:

Pa - Pb = (Pa(0s) + 50km) - (Pb(0s) + 65km)

= (Pa(0s) - Pb(0s)) + (50km - 65km) = 200km - 15km = 185km.

Now, if train B was 200km ahead of train A, we have:

Pb - Pa = (Pb(0s) + 65km) - (Pa(0s) - 50km) =

(Pb(0s) - Pa(0s)) + (65km - 50km) = 200km + 15km = 215km

4 0

2 years ago

Diego has 75% of $10. Noah has 25% of $30. Diego thinks he has more money than Noah, but Noah thinks they have an equal amount o

Fynjy0 [20]

Answer:

Noah

Step-by-step explanation:

75%*10=7.5

25%*30=7.5

The answers are both 7.5, which are equal

5 0

2 years ago

Read 2 more answers