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3 years ago

Given that cos (x) = 1/3, find sin (90 - x)

2 answers:

3 0

$\sin{(A - B)} \equiv \sin{A}\cos{B} - \cos{A}\sin{B} \\\\
\therefore \sin{(90 - x)}\\
 = \sin{(90)}\cos{(x)} - \cos{(90)}\sin{(x)} \\
= (1)\cos{(x)} - (0)\sin{(x)} \\
= \cos{x} - 0 \\
= \cos{x} \\
= \frac{1}{3}
$

denis23 [38]3 years ago

3 0

$90а= \frac{ \pi }{2} \\ sin(90а-x)=sin (\frac{ \pi }{2}-x)=cos (x) \\ cos(x)= \frac{1}{3} \\ sin(x)= \frac{1}{3} \approx0.33333 \\ x=19а$

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The national mean sales price for a new one-family home is $181,900. A sample of 40 one-family homes in the south showed a sampl

SIZIF [17.4K]

Answer:

The null hypothesis is $\mu = \$181,900$

The alternative hypothesis is $\mu < \$ 181.900$

$t = -2.92$

$p-value = 0.0016948$

There no sufficient evidence to support the conclusion that the population mean sales prices for new one-family homes in the South is less expensive than the national mean of $181,900

Step-by-step explanation:

From the question we are told that

The population mean is $\mu = \$ 181, 900$

The sample size is $n = 40$

The sample mean is $\= x = \$ 166,400$

The sample standard deviation is $s= \$ 33, 500$

The null hypothesis is $\mu = \$181,900$

The alternative hypothesis is $\mu < \$ 181.900$

Generally the test statistics is mathematically represented as

$t = \frac{ \= x - \mu }{ \frac{s}{\sqrt{n} } }$

=> $t = \frac{ 166400 - 181900 }{ \frac{33500}{\sqrt{40} } }$

=> $t = -2.92$

Generally the p-value is obtain from the z-table the value is

$p-value = P(Z < t ) = P(Z < -2.93) = 0.0016948$

=> $p-value = 0.0016948$

From the calculation we see that

$p-value > \alpha$ hence we fail to reject the null hypothesis

Thus there no sufficient evidence to support the conclusion that the population mean sales prices for new one-family homes in the South is less expensive than the national mean of $181,900

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3 years ago

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

From the question we are given the formula below

s = rwt ..........eqn(1)

Where s= π/3m, r=3 m, t= 4 sec

We were not given value of " w" which implies we are required to find out values of" w"

We can make " w " the subject of the formula from eqn(1)

s = rwt

w= s/(rt)........eqn(2)

Then substitute for the values in eqn(2)

w= (π/3m ) / ( 3m × 4 sec)

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2 years ago

If a weak monoprotic acid, HA, is titrated with strong base, what is NOT true at the half equivalence point?pH = pKapH = 7.0[HA]

leonid [27]

Answer:

pH can be different from 7 ( second statement is false)

Step-by-step explanation:

since

pH=pKa + log [A-]/[HA]

at half of the equivalence point

[HA]= [A-] (third statement is true)

and therefore

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since pH = pKa , pH can be different from 7 ( second statement is false)

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