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katen-ka-za [31]

3 years ago

12

On the coordinate grid of a map, Josie's house is located at (2,7). Her school is located at (-5,5). If each map unit equals one

mile, what is the approximate distance from her house to school?
A) 2.83 miles
B) 4.79 miles
C) 7.28 miles
D) 12.37 miles

2 answers:

Firdavs [7]3 years ago

6 0

The answer is C 7.28

tankabanditka [31]3 years ago

4 0

C. is the answer hope this helps

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Suppose that prior to conducting a coin-flipping experiment, we suspect that the coin is fair. How many times would we have to f

STALIN [3.7K]

Answer: b) 84

Step-by-step explanation:

Let p be the prior estimate of the required proportion.

As per given , we have

p =0.5 (The probability of getting heads on a fair coin is 0.5)

Significance level : $\alpha: 1-0.90=0.10\\$

Critical z-value (using z-value table ) : $z_{\alpha/2}=1.645$

Confidence interval width : w= 0.18

Thus , the margin of error : $E=\dfrac{w}{2}=0.09$

Formula to find the sample size ( if prior estimate of proportion is known.):-

$n=p(1-p)(\dfrac{z_{\alpha/2}}{E})^2$

Substitute the values , we get

$n=0.5(1-0.5)(\dfrac{1.645}{0.09})^2$

Simplify ,

$n=83.5192901235\approx84$ [Round of to the next whole number.]

Hence, the number of times we would have to flip the coin =<u>84</u>

hence, the correct answer is b) 84

8 0

3 years ago

The largest angle in a triangle is three times as big as the smallest angle, and the middle angle is twice as big as the smalles

PtichkaEL [24]

Let X = smallest angle
largest 3x
middle=2x. add the 3 angles of any triangle and you get ,180

x+2x+3x=180
6x=180
x= 30
smallest =30
middle=60
largest=90

8 0

3 years ago

-a + 4a - 9 = 8a + 6

wel

Answer:

-3=a

Step-by-step explanation:

-a+4a-9=8a+6

3a-9=8a+6

3a-9-6=8a+6-6

3a-15=8a

3a-3a-15=8a-3a

-15=5a

-15/5=5a/5

-3=a

3 0

3 years ago

<img src="https://tex.z-dn.net/?f=%20%5Crm%20%5Cint_%7B0%7D%5E%7B%20%20%5Cpi%20%7D%20%5Ccos%28%20%5Ccot%28x%29%20%20%20%20-%20%2

Nikolay [14]

Replace x with π/2 - x to get the equivalent integral

$\displaystyle \int_{-\frac\pi2}^{\frac\pi2} \cos(\cot(x) - \tan(x)) \, dx$

but the integrand is even, so this is really just

$\displaystyle 2 \int_0^{\frac\pi2} \cos(\cot(x) - \tan(x)) \, dx$

Substitute x = 1/2 arccot(u/2), which transforms the integral to

$\displaystyle 2 \int_{-\infty}^\infty \frac{\cos(u)}{u^2+4} \, du$

There are lots of ways to compute this. What I did was to consider the complex contour integral

$\displaystyle \int_\gamma \frac{e^{iz}}{z^2+4} \, dz$

where γ is a semicircle in the complex plane with its diameter joining (-R, 0) and (R, 0) on the real axis. A bound for the integral over the arc of the circle is estimated to be

$\displaystyle \left|\int_{z=Re^{i0}}^{z=Re^{i\pi}} f(z) \, dz\right| \le \frac{\pi R}{|R^2-4|}$

which vanishes as R goes to ∞. Then by the residue theorem, we have in the limit

$\displaystyle \int_{-\infty}^\infty \frac{\cos(x)}{x^2+4} \, dx = 2\pi i {} \mathrm{Res}\left(\frac{e^{iz}}{z^2+4},z=2i\right) = \frac\pi{2e^2}$

and it follows that

$\displaystyle \int_0^\pi \cos(\cot(x)-\tan(x)) \, dx = \boxed{\frac\pi{e^2}}$

7 0

2 years ago

The area of a circle is 43.25cm2.<br> Find the length of the radius rounded to 2 DP.

Monica [59]

Answer:

3.71 cm

Step-by-step explanation:

Hi there!

Area of a circle equation: $A=\pi r^2$ where r is the radius

Plug in the area 43.25 cm²

$43.25=\pi r^2$

Divide both sides by π to isolate r²

$\frac{43.25}{\pi} =\frac{\pi r^2}{\pi} \\\frac{43.25}{\pi}=r^2$

Take the square root of both sides to isolate r

$\sqrt{\frac{43.25}{\pi}} =r\\3.71=r$

Therefore, the length of the radius rounded to 2 decimal points is 3.71 cm.

I hope this helps!

8 0

3 years ago