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3 years ago

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Mathematics

1 answer:

lord [1]3 years ago

6 0

Answer:

32 yards

Step-by-step explanation:

Carmen walked 30 yards due North and 12 yards West.

Now, if we join the initial and final position of Carmen and in this path Carmen comes back to her original position then the path, traveled by Carmen will form a right triangle and the direct path from her initial point to final point will be the hypotenuse of the right triangle.

Now, the two perpendicular legs of the triangle are respectively 30 yards and 12 yards.

Therefore, Carmen travel (Applying Pythagoras Theorem) to get back to her initial position by $\sqrt{30^{2} + 12^{2}} = 32.31$ yards ≈ 32 yards (to the nearest yard). (Answer)

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A hockey team is convinced that the coin used to determine the order of play is weighted. The team captain steals this special c

fredd [130]

Answer:

Since x= 12 (0.006461) does not fall in the critical region so we accept our null hypothesis and conclude that the coin is fair.

Step-by-step explanation:

Let p be the probability of heads in a single toss of the coin. Then our null hypothesis that the coin is fair will be formulated as

H0 :p 0.5 against Ha: p ≠ 0.5

The significance level is approximately 0.05

The test statistic to be used is number of heads x.

Critical Region: First we compute the probabilities associated with X the number of heads using the binomial distribution

Heads (x) Probability (X=x) Cumulative Decumulative

0 1/16384 (1) 0.000061 0.000061

1 1/16384 (14) 0.00085 0.000911

2 1/16384 (91) 0.00555 0.006461

3 1/16384(364) 0.02222

4 1/16384(1001) 0.0611

5 1/16384(2002) 0.122188

6 1/16384(3003) 0.1833

7 1/16384(3432) 0.2095

8 1/16384(3003) 0.1833

9 1/16384(2002) 0.122188

10 1/16384(1001) 0.0611

11 1/16384(364) 0.02222

12 1/16384(91) 0.00555 0.006461

13 1/16384(14) 0.00085 0.000911

14 1/16384(1) 0.000061 0.000061

We use the cumulative and decumulative column as the critical region is composed of two portions of area ( probability) one in each tail of the distribution. If alpha = 0.05 then alpha by 2 - 0.025 ( area in each tail).

We observe that P (X≤2) = 0.006461 > 0.025

and

P ( X≥12 ) = 0.006461 > 0.025

Therefore true significance level is

∝= P (X≤0)+P ( X≥14 ) = 0.000061+0.000061= 0.000122

Hence critical region is (X≤0) and ( X≥14)

Computation x= 12

Since x= 12 (0.006461) does not fall in the critical region so we accept our null hypothesis and conclude that the coin is fair.

3 0

3 years ago

I need help with number 10 ASAP

anzhelika [568]

i'm 75% sure the answer is C hope this helps

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3 years ago

D/d{cosec^-1(1+x²/2x)} is equal to

SIZIF [17.4K]

Step-by-step explanation:

$\large\underline{\sf{Solution-}}$

$\rm :\longmapsto\:\dfrac{d}{dx} {cosec}^{ - 1} \bigg( \dfrac{1 + {x}^{2} }{2x} \bigg)$

Let assume that

$\rm :\longmapsto\:y = {cosec}^{ - 1} \bigg( \dfrac{1 + {x}^{2} }{2x} \bigg)$

We know,

$\boxed{\tt{ {cosec}^{ - 1}x = {sin}^{ - 1}\bigg( \dfrac{1}{x} \bigg)}}$

So, using this, we get

$\rm :\longmapsto\:y = sin^{ - 1} \bigg( \dfrac{2x}{1 + {x}^{2} } \bigg)$

Now, we use Method of Substitution, So we substitute

$\red{\rm :\longmapsto\:x = tanz \: \rm\implies \:z = {tan}^{ - 1}x}$

So, above expression can be rewritten as

$\rm :\longmapsto\:y = sin^{ - 1} \bigg( \dfrac{2tanz}{1 + {tan}^{2} z} \bigg)$

$\rm :\longmapsto\:y = sin^{ - 1} \bigg( sin2z \bigg)$

$\rm\implies \:y = 2z$

$\bf\implies \:y = 2 {tan}^{ - 1}x$

So,

$\bf\implies \: {cosec}^{ - 1}\bigg( \dfrac{1 + {x}^{2} }{2x} \bigg) = 2 {tan}^{ - 1}x$

Thus,

$\rm :\longmapsto\:\dfrac{d}{dx} {cosec}^{ - 1} \bigg( \dfrac{1 + {x}^{2} }{2x} \bigg)$

$\rm \: = \: \dfrac{d}{dx}(2 {tan}^{ - 1}x)$

$\rm \: = \: 2 \: \dfrac{d}{dx}( {tan}^{ - 1}x)$

$\rm \: = \: 2 \times \dfrac{1}{1 + {x}^{2} }$

$\rm \: = \: \dfrac{2}{1 + {x}^{2} }$

Hence, 

$\purple{\rm :\longmapsto\:\boxed{\tt{ \dfrac{d}{dx} {cosec}^{ - 1} \bigg( \dfrac{1 + {x}^{2} }{2x} \bigg) = \frac{2}{1 + {x}^{2} }}}}$

Hence, Option (d) is correct.

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2 years ago

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Answer:

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Step-by-step explanation:

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3 years ago

Read 2 more answers

What is a line that passes through (-7,3 and (-6,-1)

Serggg [28]

Answer:

y=-4x-25

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-1-3)/(-6-(-7))

m=-4/(-6+7)

m=-4/1

m=-4

y-y1=m(x-x1)

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3 years ago