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2 years ago

Simplify the following expression to its simplest form

Mathematics

1 answer:

SashulF [63]2 years ago

5 0

Step-by-step explanation:

$\sin(\pi - x) + \tan(x) \cos(x) (x - \frac{\pi}{2}$

$\sin( - x + \pi ) + \tan(x) ( \cos(x - \frac{\pi}{2} ) )$

Sin is odd function, so if you add pi to it, it would become switch it sign.

$- \sin( - x) + \tan(x) \cos(x - \frac{\pi}{2} )$

Also since sin is again, a odd function, we can just multiply the inside and outside by -1, and it would stay the same.

$\sin(x) + \tan(x) \cos(x - \frac{\pi}{2} )$

Cosine is basically a sine function translated pi/2 units to the right or left so

$\sin(x) + \tan(x) \sin(x)$

$\sin(x) ( 1 + \tan(x) )$

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Name two intersecting line segments that are not perpendicular.

liubo4ka [24]

I don't see anything, but any line that doensnt have the right angle sign is not perpendicular.

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4 years ago

-1/4u+3/2=-6 solve for U

Brums [2.3K]

$-\dfrac{1}{4}u+\dfrac{3}{2}=-6\qquad|\cdot4\\\\\not4^1\cdot\left(-\dfrac{1}{\not4_1u}\right)+\not4^2\cdot\dfrac{3}{\not2_1}=4\cdot(-6)\\\\-u+2\cdot3=-24\\\\-u+6=-24\qquad|-6\\\\-u=-30\qquad|\cdot(-1)\\\\\boxed{u=30}$

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4 years ago

A six-sided die is rolled.

insens350 [35]

Answer:

a.) 1/3

Step-by-step explanation:

1/6 is a 2 is rolled

1/6 if a 4 is rolled

so 2/6 if either are rolled

which simplifies to 1/3

8 0

3 years ago

Read 2 more answers

if £5000 Is placed into a bank account that pays 2% compound interest per year, how much will be in the account after two years

timurjin [86]

Answer:

£5200

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 2%/100 = 0.02 per year,

then, solving our equation

I = 5000 × 0.02 × 2 = 200

I = £ 200.00

The simple interest accumulated

on a principal of £ 5,000.00

at a rate of 2% per year

for 2 years is £ 200.00.

5 0

3 years ago

Tim claims that a coin is coming up tails less than half of the time. In 110 tosses, the coin comes up tails 47 times. Using P-v

lilavasa [31]

Answer:

$z=\frac{0.427 -0.5}{\sqrt{\frac{0.5(1-0.5)}{110}}}=-1.531$

$p_v =P(z$

If we compare the p value obtained and using the significance level given $\alpha=0.1$ we have that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 10% of significance the proportion of tails is significantly less than 0.5.

Step-by-step explanation:

1) Data given and notation

n=110 represent the random sample taken

X=47 represent the number of tails obtained

$\hat p=\frac{47}{110}=0.427$ estimated proportion of tails

$p_o=0.5$ is the value that we want to test

$\alpha=0.1$ represent the significance level

Confidence=90% or 0.90

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the proportion of tails is lower than 0.5:

Null hypothesis: $p\geq 0.5$

Alternative hypothesis: $p < 0.5$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

3) Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.427 -0.5}{\sqrt{\frac{0.5(1-0.5)}{110}}}=-1.531$

4) Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.1$ . The next step would be calculate the p value for this test.

Since is a left tailed test the p value would be:

$p_v =P(z$

6 0

3 years ago