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3 years ago

25° У x 120° y = [ ? ] Enter

Mathematics

2 answers:

Mkey [24]3 years ago

6 0

9514 1404 393

Answer:

y = 95°

x = 60°

Step-by-step explanation:

The applicable theorem is the one that says the exterior angle (120°) is the sum of the remote interior angles:

120° = 25° +y

95° = y . . . . . . . . . . subtract 25° from both sides

_____

If you like, you can get there by calculating x (or not):

x = 180° -120°

y = 180° -25° -x = 180° -25° -(180° -120°)

y = 120° -25° . . . . . simplify — notice we didn't actually have to compute x

Alex3 years ago

5 0

95 degrees

you do 180-120 and get 60 and then add 60 and 25 together and that is 85. then u do 180-85 and get 95

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An SRS of 350 high school seniors gained an average of x¯=21 points in their second attempt at the SAT Mathematics exam. Assume

Lynna [10]

Answer:

a) $21-2.58\frac{52}{\sqrt{350}}=13.83$

$21+2.58\frac{52}{\sqrt{350}}=28.17$

So on this case the 99% confidence interval would be given by (13.83;28.17)

b) $ME=2.58\frac{52}{\sqrt{350}}=7.17$

c) $ME=2.58\frac{52}{\sqrt{100}}=13.42$

d) D. Decreasing the sample size increases the margin of error, provided the confidence level and population standard deviation remain the same.

Step-by-step explanation:

Previous concepts

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".

Part a

$\bar X=21$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=52$ represent the population standard deviation

n=350 represent the sample size

99% confidence interval

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

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

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that $z_{\alpha/2}=2.58$

Now we have everything in order to replace into formula (1):

$21-2.58\frac{52}{\sqrt{350}}=13.83$

$21+2.58\frac{52}{\sqrt{350}}=28.17$

So on this case the 99% confidence interval would be given by (13.83;28.17)

Part b

The margin of error is given by:

$ME=2.58\frac{52}{\sqrt{350}}=7.17$

Part c

The margin of error is given by:

$ME=2.58\frac{52}{\sqrt{100}}=13.42$

Part d

As we can see when we reduce the sample size we increase the margin of error so the best option for this case is:

D. Decreasing the sample size increases the margin of error, provided the confidence level and population standard deviation remain the same.

6 0

3 years ago

Simplify 8-(-5) - 4(-7).<br> О-63<br> оо ООО

Sergeeva-Olga [200]

8- (-5) - 4 (-7) = 41

3 0

3 years ago

the direction angle for vectors 135° the X component of the vector is -3 what is the Ywhat is what what is the Y component of th

blagie [28]

Well, the X component (assuming x is the horizontal) is equal to RCosZ

Where Z is the angle and R is the size of the resultant

Substitute into formula :

X component = RcosZ
-3 = Rcos135°
R = -3/cos135°
R = 4.24264...
R = 4.24 (2dp)

The vertical component (or Y component) is equal to RSinZ

Vertical component = RSinZ
= 4.24264... × Sin135°
= 3

The answer is 3

Please feel free to ask any questions you have

3 0

3 years ago

(Score for Question 2: ___ of 5 points)

GuDViN [60]

Answer:

Since you don't show your triangles, I'm guessing it is this one...?

△DWP D = (-2, 4), W = (-1, 2), P = (3, 3)

△MJS M = (-4, -4), J = (-2, -3), S = (-3, 1)

There are 2 steps:

1. 90° counterclockwise rotation about the origin

2. Translation downward 2 units

Step-by-step explanation:

1. 90° counterclockwise rotation about the origin = (x, y) to (-y, x),

D moves from (-2, 4) to (-4, -2)

W moves from (-1, 2) to (-2, -1)

P moves from (3, 3) to (-3, 3)

2. Translation downward 2 units = (x, y) to (x, y-2),

D moves from (-4, -2) to (-4, -4) = M

W moves from (-2, -1) to (-2, -3) = J

P moves from (-3, 3) to (-3, 1) = S

Therefore △DWP IS congruent to △MJS.

4 0

3 years ago

What is 412, 825 round to the nearest ten?

RideAnS [48]

Tens place is 2
look to teh right
5> or = to 5 so round up:
412,830

5 0

3 years ago