Which of the following is the equation of a line that is perpendicular to the graph of y=2/5x-1

alekssr [168]

A: Universe (It surrounds everything) B: Galaxy (Smaller than the universe but larger than the rest) C: Solar System D: Mars
Cant help you for number 2 though. Hope this helps :)

8 0

3 years ago

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The measure of angle θ is 7pi/4 . The measure of its reference angle is *Blank* °, and tan θ is *blank*

sukhopar [10]

Since the measure of angle $\Theta$ is $\frac{7\Pi }{4}$

The measure of its reference angle = $\frac{7\times 180^{\circ}}{4}$

= $=315^{\circ}$

Now we have to compute the value of $\tan \Theta$

$\tan \Theta = \tan \frac{7\Pi }{4}$

$= \tan (2\Pi -\frac{\Pi }{4})$

The value of ( $(2\Pi -\frac{\Pi }{4})$ ) lies in the fourth quadrant. In fourth quadrant, the value of tan is always negative.

So, $\tan (2\Pi -\frac{\Pi }{4})$

$= -\tan (\frac{\Pi }{4})$

= -1.

5 0

3 years ago

A couple intends to have two children, and suppose that approximately 52% of births are male and 48% are female.

Pachacha [2.7K]

a) Probability of both being males is 27%

b) Probability of both being females is 23%

c) Probability of having exactly one male and one female is 50%

Step-by-step explanation:

a)

The probability that the birth is a male can be written as

$p(m) = 0.52$ (which corresponds to 52%)

While the probability that the birth is a female can be written as

$p(f) = 0.48$ (which corresponds to 48%)

Here we want to calculate the probability that over 2 births, both are male. Since the two births are two independent events (the probability of the 2nd to be a male does not depend on the fact that the 1st one is a male), then the probability of both being males is given by the product of the individual probabilities:

$p(mm)=p(m)\cdot p(m)$

And substituting, we find

$p(mm)=0.52\cdot 0.52 = 0.27$

So, 27%.

b)

In this case, we want to find the probability that both children are female, so the probability

$p(ff)$

As in the previous case, the probability of the 2nd child to be a female is independent from whether the 1st one is a male or a female: therefore, we can apply the rule for independent events, and this means that the probability that both children are females is the product of the individual probability of a child being a female:

$p(ff)=p(f)\cdot p(f)$

And substituting

$p(f)=0.48$

We find:

$p(ff)=0.48\cdot 0.48=0.23$

Which means 23%.

c)

In this case, we want to find the probability they have exactly one male and exactly one female child. This is given by the sum of two probabilities:

- The probability that 1st child is a male and 2nd child is a female, namely $p(mf)$

- The probability that 1st child is a female and 2nd child is a male, namely $p(fm)$

So, this probability is

$p(mf Ufm)=p(mf)+p(fm)$

We have:

$p(mf)=p(m)\cdot p(f)=0.52\cdot 0.48=0.25$

$p(fm)=p(f)\cdot p(m)=0.48\cdot 0.52=0.25$

Therefore, this probability is

$p(mfUfm)=0.25+0.25=0.50$

So, 50%.

Learn more about probabilities:

brainly.com/question/5751004

brainly.com/question/6649771

brainly.com/question/8799684

brainly.com/question/7888686

#LearnwithBrainly

5 0

3 years ago

Evaluate the integral by changing to polar coordinatesye^x dA, where R is in the first quadrant enclosed by the circle x^2+y^2=2

34kurt

$\displaystyle\iint_Rye^x\,\mathrm dA=\int_{\theta=0}^{\theta=\pi/2}\int_{r=0}^{r=5}r^2\sin\theta e^{r\cos\theta}\,\mathrm dr\,\mathrm d\theta$

which follows from the usual change of coordinates via

$\begin{cases}\mathbf x(r,\theta)=r\cos\theta\\\mathbf y(r,\theta)=r\sin\theta\end{cases}$

and Jacobian determinant

$|\det J|=\left|\begin{vmatrix}\mathbf x_r&\mathbf x_\theta\\\mathbf y_r&\mathbf y_\theta\end{vmatrix}\right|=|r|$

Swap the order, so that the integral is

$\displaystyle\int_{r=0}^{r=5}\int_{\theta=0}^{\theta=\pi/2}r^2\sin\theta e^{r\cos\theta}\,\mathrm d\theta\,\mathrm dr$

and now let $\sigma=r\cos\theta$ , so that $\mathrm d\sigma=-r\sin\theta$ . Now, you have

$\displaystyle\int_{r=0}^{r=5}\int_{\sigma=0}^{\sigma=r}re^\sigma\,\mathrm d\sigma\,\mathrm dr=\int_{r=0}^{r=5}r(e^r-1)\,\mathrm dr=4e^5-\dfrac{23}2$

7 0

3 years ago

Please help I’m gonna fail

Brums [2.3K]

Answer:

A is the answer

if you are happy with my answer, please give brainliest :)

Step-by-step explanation:

7 0

2 years ago