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3 years ago

In circle J with mZHLK = 18, find the mZHJK.

Mathematics

1 answer:

zysi [14]3 years ago

3 0

Answer:

The measure of angle HJK is 36°

Step-by-step explanation:

In a circle, the measure of the inscribed angle equal half the measure of the central angle subtended by the same arc

In circle J

∵ J is the center of the circle

∵ H and K lie on the circle

∴ ∠HJK is a central angle subtended by arc HK

∵ L lies on the circle

∴ ∠HLK is an inscribed angle subtended by arc HK

→ By using the rule above

∵ ∠HJK and ∠HLK are the central angle and inscribed angle

subtended by the same arc HK

∴ m∠HLK = $\frac{1}{2}$ m∠HJK

∵ m∠HLK = 18°

∴ 18 = $\frac{1}{2}$ m∠HJK

→ Multiply both sides by 2

∴ 36 = m∠HJK

∴ The measure of angle HJK is 36°

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The gym has a total of 25 treadmills and stationary bikes. there are seven more stationary bikes than treadmills.

Rudik [331]

The system of equations is $t+b=25\\b=t+7$

Step-by-step explanation:

We can answer this question as follows.

First of all, we call:

t = number of treadmills

b = number of stationary bikes

The two conditions that we have can be translated into equations as follows:

- The gym has a total of 25 treadmills and stationary bikes:

$t+b=25$

- There are seven more stationary bikes than treadmills:

$b=t+7$

So the system of equations to solve is

$t+b=25\\b=t+7$

We now solve it in the following way: first, we rewrite the second equation by bringing t on the left side,

$t+b=25\\b-t=7$

Now we add the 1st equation to the 2nd equation:

$(t+b)+(b-t)=25+7\\t+b+b-t=32\\2b=32\\b=\frac{32}{2}=16$

And therefore,

$t+b=25\\t+16=25\\t=25-16=9$

So, there are 16 stationary bikes and 9 treadmills.

Learn more about systems of equations:

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3 years ago

Solve the equation 4*e+2=1 (mod5)

otez555 [7]

Here's a way to do it.

Let 4e +2 = 5n +1 . . . . . . for some integer n

Then e = (5n -1)/4 = n + (n -1)/4

We want (n-1)/4 to be an integer, so let it be integer m.

... m = (n -1)/4

... 4m = n -1

... 4m +1 = n

Substituting this into our expression for e gives

... e = (5(4m+1) -1)/4 = (20m +4)/4 = 5m +1

e = 5m+1 for any integer m

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4 years ago

10. If both equations have the same slope and the same y-intercepts, which

Papessa [141]

The answer is C because it’s the same line

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2 years ago

5x+y=27 y=4x using substitution method

Dvinal [7]

5x + y = 27
substitute: 5x + 4x = 27
combine: 9x = 27
divide (by 9): x = 3

4 0

3 years ago

Read 2 more answers

In a survey of 2065 adults in a certain country conducted during a period of economic uncertainty, 63 % thought that wages paid

LenKa [72]

Answer:

a) D.The interpretation is flawed. No interval has been provided about the population proportion.

b) D.The interpretation is flawed. The interpretation indicates that the level of confidence is varying.

c) A.The interpretation is reasonable.

d) C.The interpretation is flawed. The interpretation suggests that this interval sets the standard for all the other intervals, which is not true.

Step-by-step explanation:

(a) We are 95 % confident 63 % of adults in the country during the period of economic uncertainty felt wages paid to workers in industry were too low. Is the interpretation reasonable?

D.The interpretation is flawed. No interval has been provided about the population proportion.

The sample proportion alone will not give us any confidence in estimating the true proportion of adults in the country during the period of economic uncertainty felt wages paid to workers in industry were too low.

We need a 95% confidence interval to claim that the true proportion is within this interval. In this case, as the margin of error is 4%, the 95% CI is 59% and 67%.

(b) We are 91 % to 99 % confident 63 % of adults in the country during the period of economic uncertainty felt wages paid to workers in industry were too low. Is the interpretation reasonable?

D.The interpretation is flawed. The interpretation indicates that the level of confidence is varying.

The confidence is set at a fixed value and from that value the confidence interval is estimated. It still uses the sample proportion instead of the confidence interval to estimate the true proportion.

(c) We are 95 % confident the proportion of adults in the country during the period of economic uncertainty who believed wages paid to workers in industry were too low was between 0.59 and 0.67. Is the interpretation reasonable?

A.The interpretation is reasonable.

It uses the right sample data and interpret correctly the meaning of the confidence interval.

(d) In 95 % of samples of adults in the country during the period of economic uncertainty, the proportion who believed wages paid to workers in industry were too low is between 0.59 and 0.67. Is the interpretation reasonable?

C.The interpretation is flawed. The interpretation suggests that this interval sets the standard for all the other intervals, which is not true.

This confidence interval is an estimation about the parameter of the population. It doesn't give information to estimate the sampling distribution, as it only has information of one specific sample.

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3 years ago