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2 years ago

Find all polar coordinates of point P where P = ordered pair 5 comma negative pi divided by 6 .

Mathematics

1 answer:

max2010maxim [7]2 years ago

6 0

Answer:

The correct option is B.

Step-by-step explanation:

If polar coordinates of point P are

$P=(r,\theta)$

Where, r is real number and θ is in radian, then all polar coordinates of point P are defined as

$P=(r,\theta+2n\pi)$

$P=(-r,\theta+(2n+1)\pi)$

The given coordinates are $P(5,-\frac{\pi}{6})$ . So, all polar coordinates of point P are

$P=(5,-\frac{\pi}{6}+2n\pi)$

$P=(-5,-\frac{\pi}{6}+(2n+1)\pi)$

Therefore correct option is B.

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Cards numbered 500 through 799 are placed into a box. How many of the cards satisfy both of the conditions shown below?

ololo11 [35]

Answer:

Step-by-step explanation:

4 0

2 years ago

A manufacturing company produces valves in various sizes and shapes. One particular valve plate is supposed to have a tensile st

maxonik [38]

Answer:

$z=\frac{5.0611-5}{\frac{0.2803}{\sqrt{42}}}=1.413$

$p_v =2*P(z>1.413)=0.158$

If we compare the p value and the significance level given $\alpha=0.1$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the average tensile strength is different from 5lbs/mm at 10% of signficance

Step-by-step explanation:

Data given and notation

$\bar X=5.0611$ represent the sample mean

$\sigma=0.2803$ represent the population standard deviation for the sample

$n=42$ sample size

$\mu_o =5$ represent the value that we want to test

$\alpha=0.1$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the true mean is different from 5, the system of hypothesis would be:

Null hypothesis: $\mu = 5$

Alternative hypothesis: $\mu \neq 5$

If we analyze the size for the sample is > 30 but and we know the population deviation so is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{5.0611-5}{\frac{0.2803}{\sqrt{42}}}=1.413$

P-value

Since is a two sided test the p value would be:

$p_v =2*P(z>1.413)=0.158$

Conclusion

8 0

2 years ago

"Which of the following are continuous functions? (Select all that apply.)

Natasha2012 [34]

Answer:

□ The temperature at a specific location as a function of time.

□ The temperature at a specific time as a function of the distance due west from New York City.

□ The altitude above sea level as a function of the distance due west from New York City.

Step-by-step explanation:

Temperature tends to vary continuously over distance and time.

Altitude rarely changes so abruptly we'd have to say it is a discontinuous function. Even a cliff has a (very high) defined slope.

Taxi charges tend to increment according to a rate schedule. That is, for each passing minute or fraction of a mile, the amount due jumps to a new value. We'd have to say those are discontinuous.

The nature of electrical circuits is such that current is never discontinuous. Even when the circuit is disconnected by a switch, the arcing at the switch contacts ensures the current is continuous as it rapidly goes to zero.

8 0

2 years ago

Grandpa ernie is shrinking! Over the past 4 years, his hight decressed by a total of 2.4cm. It decresed by the same amount each

dolphi86 [110]

Answer: 0.6 cm

Step-by-step explanation:

Given : Over the past 4 years, Grandpa Ernie's height decreased by a total of 2.4 cm.

If the height is decreased by the same amount each year.

Then, the change in Grandpa Ernie's height each year will be =

Total decrease in height ÷ 4

= 2.4 cm ÷ 4 = 0.6 cm

Hence, the change in Grandpa Ernie's height each year = 0.6 cm