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4 years ago

Find the possible values of r in the inequality 5 > r - 3.

Mathematics

2 answers:

nevsk [136]4 years ago

4 0

Answer:A

Step-by-step explanation:

ioda4 years ago

3 0

The answer to this question is A

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Lake Superior, along the us Canada border, has a maximum depth of 1333 feet. There are 5280 feet in one mile. How deep is lake S

Reika [66]

Answer:

= 0.2525 miles

Step-by-step explanation:

7 0

3 years ago

I’ll give brainlest to anyone who can help me with this. Basically you have to state whether or not the number is a solution to

natali 33 [55]

Answer:

depends on what n is. but -2/3 - 4/9 = -10/9 aka -1 1/9

Step-by-step explanation:

6 0

3 years ago

A school authority claims that the average height of students is 178 cm. A researcher has taken a well-designed survey and his s

Hunter-Best [27]

Answer:

d) The difference exists due to chance since the test statistic is small

Step-by-step explanation:

From the given information:

Population mean = 178 cm

the sample mean = 177.5 cm

the standard deviation = 2

the sample size = 25

The null hypothesis and the alternative hypothesis can be computed as:

Null hypothesis:

$H_o: \mu = 178$

Alternative hypothesis:

$H_1: \mu \neq 178$

The t-test statistics is determined by using the formula:

$t = \dfrac{X - \mu}{\dfrac{\sigma}{\sqrt{n}}}$

$t = \dfrac{177.5 - 178}{\dfrac{2}{\sqrt{25}}}$

$t = \dfrac{-0.5}{\dfrac{2}{5}}}$

$\mathbf{t= -1.25}$

Degree of freedom df = n- 1

Degree of freedom df = 25 - 1

Degree of freedom df = 24

At the level of significance ∝ = 0.05, the critical value = 2.064

Decision rule: To reject the null hypothesis if the test statistics is greater than the critical value at 0.05 level of significance

Conclusion: We fail to reject the null hypothesis since the test statistics is lesser than the critical value and we conclude that the difference exists due to chance since the test statistic is small

5 0

3 years ago

Futhe Mathematics <img src="https://tex.z-dn.net/?f=%28Cos%20%7B%7D%5E%7B4%7Dt%20-Sin%20%7B%7D%5E%7B4%7Dt%20%29%20%20%5Cdiv%2

Nastasia [14]

Answer:

cos2t/cos²t

Step-by-step explanation:

Here the given trigonometric expression to us is ,

$\longrightarrow \dfrac{cos^4t - sin^4t }{cos^2t }$

We can write the numerator as ,

$\longrightarrow \dfrac{ (cos^2t)^2-(sin^2t)^2}{cos^2t }$

Recall the identity ,

$\longrightarrow (a-b)(a+b)=a^2-b^2$

Using this we have ,

$\longrightarrow \dfrac{(cos^2t + sin^2t)(cos^2t-sin^2t)}{cos^2t}$

Again , as we know that ,

$\longrightarrow sin^2\phi + cos^2\phi = 1$

Therefore we can rewrite it as ,

$\longrightarrow \dfrac{1(cos^2t - sin^2t)}{cos^2t}$

Again using the first identity mentioned above ,

$\longrightarrow \underline{\underline{\dfrac{(cost + sint )(cost - sint)}{cos^2t}}}$

Or else we can also write it using ,

$\longrightarrow cos2\phi = cos^2\phi - sin^2\phi$

Therefore ,

$\longrightarrow \underline{\underline{\dfrac{cos2t}{cos^2t}}}$

And we are done !

$\rule{200}{4}$

Additional info :-

Derivation of cos²x - sin²x = cos2x :-

We can rewrite cos 2x as ,

$\longrightarrow cos(x + x )$

As we know that ,

$\longrightarrow cos(y + z )= cosy.cosz - siny.sinz$

So that ,

$\longrightarrow cos(x+x) = cos(x).cos(x) - sin(x)sin(x)$

On simplifying,

$\longrightarrow cos(x+x) = cos^2x - sin^2x$

Hence,

$\longrightarrow\underline{\underline{cos (2x) = cos^2x - sin^2x }}$

$\rule{200}{4}$

7 0

3 years ago

What are the Factors of 2,3,4,5

Dominik [7]

Answer:for 5

Step-by-step explanation:1,5

7 0

3 years ago