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3 years ago

What is the range of y = -5sin(x)?

Mathematics

1 answer:

klemol [59]3 years ago

8 0

Answer:

[-5,5]

Step-by-step explanation:

The minimum value of just sin(x) would be -1, while the max would be 1.

Now we just have to multiply these by the -5 that is there. That gives us a min of -5 and a max of 5

You might be interested in

Kayla squared a number x and added this result to -6.5. This gave her an answer of 42.5.

ladessa [460]

Answer:

7, -7

Step-by-step explanation:

x^2-6.5= 42.5 add 6.5 to both sides

x^2= 49

The square root of 49 is 7 and -7.

7 0

3 years ago

Find the equations of the following lines

White raven [17]

You need these two basic solutions and facts to find the equation of a line:

If you know the gradient $m$ and one point $(x_0,y_0)$ :

$y-y_0=m(x-x_0)$

If you know the gradient two points $(x_1,y_1),\ (x_2,y_2)$ :

$\dfrac{x-x_2}{x_1-x_2}=\dfrac{y-y_2}{y_1-y_2}$

The slope of a line is the coefficient m when you write it in the $y=mx+q$ form
Parallel lines have the same slope
The slopes of perpendicular lines give -1 when multiplied

We can use this list to solve all the exercises:

Use the first equation to get

$y-1=-4(x-2) \iff y=-4x+9$

Use the second equation to get

$\dfrac{x-4}{2-4}=\dfrac{y-2}{-1-2} \iff \dfrac{x-4}{-2}=\dfrac{y-2}{-3}\iff 3(x-4)=2(y-2) \iff 3x-12=2y-4 \iff 2y = 3x-8 \iff y = \frac{3}{2}x-4$

d) same as c)

e) We derive the slope of the line by writing it as

$5y = -x-15 \iff y = -\dfrac{1}{5}x-3$

So, the slope is -1/5. From here, it's the same as b)

f) same as e)

g) Again we find the slope as

$3x+y+2=0\iff y=-3x-2$

so the slope is -3, and a perpendicular line has slope 1/3. From there, it's the same as b).

6 0

4 years ago

Hi everyone, I’m currently trying to dive into some lessons before school starts and I’m taking algebra 2 this year and the less

3241004551 [841]

An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit i, which is defined by its property i² = −1. The square of an imaginary number bi is −b². For example, 5i is an imaginary number, and its square is −25

5 0

3 years ago

For the hypothesis test H0: μ = 10 against H1: μ >10 and variance known, calculate the Pvalue for each of the following test

Basile [38]

Answer:

a) $p_v =P(Z>2.05)=1-P(z$

b) $p_v =P(Z>-1.84)=1-P(z$

c) $p_v =P(Z>0.4)=1-P(z$

Step-by-step explanation:

Some previous concepts

The p-value is the probability of obtaining the observed results of a test, assuming that the null hypothesis is correct.

A z-test for one mean "is a hypothesis test that attempts to make a claim about the population mean(μ)".

The null hypothesis attempts "to show that no variation exists between variables or that a single variable is no different than its mean"

The alternative hypothesis "is the hypothesis used in hypothesis testing that is contrary to the null hypothesis"

Hypothesis

Null hypothesis: $\mu=10$

Alternative hypothesis: $\mu >10$

If the random variable is distributed like this: $X \sim N(\mu,\sigma)$

We assume that the variance is known so the correct test to apply here is the z test to compare means, the statistic is given by the following formula:

$z_o=\frac{\bar X -\mu}{\sigma}$

Since we have the values for the statistic already calculated we can calculate the p value using the following formulas:

Part a

$p_v =P(Z>2.05)=1-P(z$

And in order to find the answer using excel we can use the following code:

"=1-NORM.DIST(2.05,0,1,TRUE)"

Part b

$p_v =P(Z>-1.84)=1-P(z$

And in order to find the answer using excel we can use the following code:

"=1-NORM.DIST(-1.84,0,1,TRUE)"

Part c

$p_v =P(Z>0.4)=1-P(z$

And in order to find the answer using excel we can use the following code:

"=1-NORM.DIST(0.4,0,1,TRUE)"

Conclusions

If we use a reference value for the significance, let's say $\alpha=0.05$ . For part a the $p_v$ so then we can reject the null hypothesis at this significance level.