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2 years ago

Find the value of y and z

Mathematics

1 answer:

elena55 [62]2 years ago

3 0

$\qquad\qquad\huge\underline{{\sf Answer}} \huge♨$

In the given figure, NQ acts as a diameter and since diameter subtends 90° at the arc of the circle, so we can conclude that ~

$\qquad \sf \dashrightarrow \:3y = 90 \degree$

$\qquad \sf \dashrightarrow \:y = 90 \degree \div 3$

$\qquad \sf \dashrightarrow \:y = 30 \degree$

Now, Let's use Angle sum property of Triangle to solve for z :

$\qquad \sf \dashrightarrow \:4z + 3y + 50 \degree = 180 \degree$

$\qquad \sf \dashrightarrow \:4z +90 \degree + 50 \degree = 180 \degree$

$\qquad \sf \dashrightarrow \:4z = 180 \degree - (50 \degree + 90\degree)$

$\qquad \sf \dashrightarrow \:4z = 180 \degree - (140\degree)$

$\qquad \sf \dashrightarrow \:4z = 40 \degree$

$\qquad \sf \dashrightarrow \:z = 40 \degree \div 4$

$\qquad \sf \dashrightarrow \:z = 10 \degree$

I hope you understood the procedure, you can ask me in comments if you have any doubts.

You might be interested in

A pair of perpendicular lines intersect at the point (5,9). Write

maw [93]

Answer:

The equation of the line that is perpendicular to the line that passes through the point (-4, 2) is y = -9·x/5 + 18

Step-by-step explanation:

The coordinates of the point of intersection of the two lines = (5, 9)

The coordinates of a point on one of the two lines, line 1 = (-4, 4)

The slope of a line perpendicular to another line with slope, m = -1/m

Therefore, we have;

The slope, m₁, of the line 1 with the known point = (9 - 4)/(5 - (-4)) = 5/9

Therefore, the slope, m₂, of the line 2 perpendicular to the line that passes through the point (-4, 4) = -9/5

The equation of the line 2 is given as follows;

y - 9 = -9/5×(x - 5)

y - 9 = -9·x/5 + 9

y = -9·x/5 + 9 + 9

y = -9·x/5 + 18

Therefore, the equation of the line that is perpendicular to the line that passes through the point (-4, 2) is y = -9·x/5 + 18.

6 0

3 years ago

Suppose that the researchers wanted to estimate the mean reaction time to within 6 msec with 95% confidence. Using the sample st

Lisa [10]

Answer:

a) The 95% confidence interval would be given by (509.592;550.308)

b) n=523 rounded up to the nearest integer

Step-by-step explanation:

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".

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".

$\bar X=530$ represent the sample mean for the sample

$\mu$ population mean

s=70 represent the sample standard deviation

n=48 represent the sample size (variable of interest)

Confidence =95% or 0.995

Part a

The confidence interval for the mean is given by the following formula:

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

The degrees of freedom are df=n-1=48-1=47

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,47)".And we see that $z_{\alpha/2}=2.01$