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4 years ago

What are the simplified forms of the expression

Mathematics

1 answer:

anastassius [24]4 years ago

4 0

Answer:

It's is A and D.

Step-by-step explanation:

Tan^2 theta cos 2theta

= (sin^2 theta / cos^2 theta )( 2 cos^2 theta - 1)

= 2 sin^2 theta - sin^2 theta / cos^2 theta

= 2 sin^2 theta - tan^2 theta.

Tan^2 theta cos 2theta

= ( 1 / cot^2 theta) * cos 2theta

= cos 2theta / cot^2 theta.

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Use the information given to enter an equation in standard form.

Natasha_Volkova [10]

Answer:

2x - y = -2

Step-by-step explanation:

$m=\frac{y^2-y^1}{x^2-x^1}$

$m = \frac{10-12}{4-5} =\frac{-2}{-1} =2$

$10=2(4)+b\\10=8+b\\2=b\\y=2x+2\\2x-y=-2$

3 0

3 years ago

Read 2 more answers

Which transformation of f(x) will produce the same graph as g(x)?

Vera_Pavlovna [14]

g(x) =f(x) +3

given f(x) =3x

i.e. g(x) =3x+3

For F(x) to be same as g(x)

3 must be added to f(x)

i.e. h(x) =3x+3

->h(x)= 3x +3(1)

-> h(x) = f(x) +f(1)

-> h(x) =f(x+1)

Hence Option (a) is your answer...

Hope it helps...

Regards

Leukonov/Olegion

7 0

4 years ago

Read 2 more answers

Select all of the following expressions that are equivalent to 0.25.. . 1. (0.5)2. 2. (-0.2) + (-0.05). 3. |-3 + 2.75|. 4. -(-0.

shepuryov [24]

The solutions for the following expressions are:
1. 0.5*2 = 1
2. -0.2+-0.05= -0.25
3. absolute value of (-3+2.75) = 0.25
4. -(-0.25) = 0.25
5. 2x-1.75x = 0.25x

The expression equivalent to 0.25 is numbers 3 and 4.

7 0

3 years ago

Two numbers have the ratio of 4:7 if their sum is 143 what are the numbers?

garri49 [273]

Answer:

52:91

Step-by-step explanation:

To find a ratio value you need to think of it more as two numerators that together equal one whole. 4+7 is 11 so that would be the denominator. If the sum is 143, then we divide by 11 since one number is 4/11s of 143, and the other is 7/11s of 143. 143/11=13

now we multiply both:

4(13)=52

7(13)=91

Check:

91+52=143

52/91 simplifies to 4/7 or 4:7

i hope this helps!

3 0

3 years ago

A recent study focused on the number of times men and women send a WeChat message in a day. The information is summarized next.

Ratling [72]

Answer:

1)Null hypothesis: $\mu_{men}=\mu_{women}$

Alternative hypothesis: $\mu_{men} \neq \mu_{women}$

2) Two critical values are $z_{\alpha/2}=-2.58$ and $z_{1-\alpha/2}=2.58$

3) $z=-2.40$

4) $p_v =2*P(z$

5) Comparing the p value with the significance level given $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we FAIL to reject the null hypothesis, and a would NOT be a significant difference in the mean number of times men and women send a Twitter message in a day.

Step-by-step explanation:

Data given and notation

$\bar X_{men}=23$ represent the mean for the sample men

$\bar X_{women}=28$ represent the mean for the sample women

$\sigma_{men}=5$ represent the population standard deviation for the sample men

$\sigma_{women}=10$ represent the population standard deviation for the sample women

$n_{men}=25$ sample size for the group men

$n_{women}=30$ sample size for the group women

t would represent the statistic (variable of interest)

$\alpha=0.01$ significance level provided

1）Develop the null and alternative hypotheses for this study?

We need to conduct a hypothesis in order to check if the means for the two groups are different, the system of hypothesis would be:

Null hypothesis: $\mu_{men}=\mu_{women}$

Alternative hypothesis: $\mu_{men} \neq \mu_{women}$

Since we know the population deviations for each group, for this case is better apply a z test to compare means, and the statistic is given by:

$z=\frac{\bar X_{men}-\bar X_{women}}{\sqrt{\frac{\sigma^2_{men}}{n_{men}}+\frac{\sigma^2_{women}}{n_{women}}}}$ (1)

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

2）Determine the critical value(s).

Based on the significance level $\alpha=0.01$ and $\alpha/2=0.005$ we can find the critical values with the normal standard distribution, we are looking for values that accumulates 0.005 of the area on each tail on the normal distribution.

For this case the two values are $z_{\alpha/2}=-2.58$ and $z_{1-\alpha/2}=2.58$

3) Calculate the value of the test statistic for this hypothesis testing.

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

$z=\frac{23-28}{\sqrt{\frac{5^2}{25}+\frac{10^2}{30}}}}=-2.40$

4）What is the p-value for this hypothesis test?

Since is a bilateral test the p value would be:

$p_v =2*P(z$

5）Based on the p-value, what is your conclusion?

Comparing the p value with the significance level given $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we FAIL to reject the null hypothesis, and a would NOT be a significant difference in the mean number of times men and women send a Twitter message in a day.

4 0

3 years ago