What is the difference of the two expressions? ( 3 7 + 9) − ( 2 7 − 3)

Why is -csc^2 (pi/4) = -2 ?

sweet-ann [11.9K]

Sin(pi/4) = 1/sqrt(2)
csc(pi/4) = sqrt(2)
csc^2(pi/4) = 2
-csc^2(pi/4) = -2

8 0

2 years ago

Solve the equation: [3 2 5 5] [x1 x2]+ [1 2]= [2 -3]

dsp73

9514 1404 393

Answer:

(x1, x2) = (3, -4)

Step-by-step explanation:

As with any 2-step linear equation, subtract the constant, then multiply by the inverse of the coefficient of the variable.

$\left[\begin{array}{cc}3&2\\5&5\end{array}\right]\left[\begin{array}{c}x\\y\end{array}\right]+\left[\begin{array}{c}1\\2\end{array}\right]=\left[\begin{array}{c}2\\-3\end{array}\right]\\\\\left[\begin{array}{cc}3&2\\5&5\end{array}\right]\left[\begin{array}{c}x\\y\end{array}\right]=\left[\begin{array}{c}1\\-5\end{array}\right]\\\\\left[\begin{array}{c}x\\y\end{array}\right]=\dfrac{1}{5}\left[\begin{array}{cc}5&-2\\-5&3\end{array}\right]\left[\begin{array}{c}1\\-5\end{array}\right]$

Performing the multiplication of the matrix by the vector gives the solution.

x = ((5)(1) +(-2)(-5))/5 = 15/5 = 3

y = ((-5)(1) +(3)(-5))/5 = -20/5 = -4

Using your variables, x1, x2, the solution is ...

(x1, x2) = (3, -4)

7 0

2 years ago

5y + 3 > -7 + 13 how do i do this

ASHA 777 [7]

5y + 3 > -7 + 13

First add -7 + 13 = 6

5y + 3 > 6

Subtract 3 from both sides

5y + 3 -3 > 6 - 3

5y > 3

Divide both sides by 5

5y/5 > 3/5

y > 3/5

5 0

3 years ago

Jon invests $2300 at 7.5% annual interest, compounded continuously. How long will it take this money to double in value?

meriva

For it to double in value it would take 13 years and 4 months

7 0

3 years ago

Company A makes a large shipment to Company B. Company B can reject the shipment if they can conclude that the proportion of def

boyakko [2]

Answer:

$z=\frac{0.1475-0.1}{\sqrt{\frac{0.1(1-0.1)}{400}}}=3.17$

The p value for this case would be given by:

$p_v =P(z>3.17)=0.00076$

For this case the p value is lower than the significance level so then we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 0.1 and then Company B can reject the shipment

Step-by-step explanation:

Information provided

n=400 represent the random sample taken

X=59 represent number of defectives from the company B

$\hat p=\frac{59}{400}=0.1475$ estimated proportion of defectives from the company B

$p_o=0.1$ is the value to verify

$\alpha=0.05$ represent the significance level

z would represent the statistic

$p_v$ represent the p value

Hypothesis to test

We want to verify if the true proportion of defectives is higher than 0.1 then the system of hypothesis are.:

Null hypothesis: $p \leq 0.1$

Alternative hypothesis: $p > 0.1$

The statistic would be given by:

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

Replacing the info given we got:

$z=\frac{0.1475-0.1}{\sqrt{\frac{0.1(1-0.1)}{400}}}=3.17$

The p value for this case would be given by:

$p_v =P(z>3.17)=0.00076$

For this case the p value is lower than the significance level so then we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 0.1 and then Company B can reject the shipment

8 0

3 years ago