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3 years ago

Cot y, if csc y =-10/3 and cos y< 0

1 answer:

7 0

$\csc y=-\dfrac{10}3\implies\sin y=-\dfrac3{10}$

$\cos^2y=1-\sin^2y\implies \cos y=\pm\sqrt{1-\dfrac9{100}}=\pm\dfrac{\sqrt{91}}{10}$

You're told that $\cos y$ , so omit the positive root.

$\cot y=\dfrac{\cos y}{\sin y}=\dfrac{-\frac{\sqrt{91}}{10}}{-\frac3{10}}=\dfrac{\sqrt{91}}3$

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Choose all the number sentences that have a sum less than 345,195: A) 189,753 + 155,655 B) 324,675 + 19,285 C) 185,476 + 155,923

fgiga [73]

Answer:

C, D

Step-by-step explanation:

Calculate the sum of all.

C and D have less then 345,195.

That is the answer.

5 0

2 years ago

Read 2 more answers

A consumer survey indicates that the average household spendsμ= $185on groceries each week. The distribution of spending amounts

Vitek1552 [10]

Answer:

$P(X>200)=P(\frac{X-\mu}{\sigma}>\frac{200-\mu}{\sigma})=P(Z>\frac{200-185}{25})=P(Z>0.6)$

And we can find this probability using the complement rule and with the normal standard table or excel:

$P(Z>0.6)=1-P(z$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the average household spent of a population, and for this case we know the distribution for X is given by:

$X \sim N(185,25)$

Where $\mu=185$ and $\sigma=25$

We are interested on this probability

$P(X>200)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X>200)=P(\frac{X-\mu}{\sigma}>\frac{200-\mu}{\sigma})=P(Z>\frac{200-185}{25})=P(Z>0.6)$

And we can find this probability using the complement rule and with the normal standard table or excel:

$P(Z>0.6)=1-P(z$

7 0

3 years ago

What do I put in the boxes if the answer is 1.74%?

gavmur [86]

If a credit card advertises an annual interest rate of 23%, then the equivalent monthly interest rate is 1.74%

The annual interest rate = 23%

The credit card interest rate the amount you have to pay to borrow the money from them. The credit card interest rate is usually expressed in yearly rate. This is called annual percentage rate.

The monthly interest rate = $(1+\frac{23}{100})^{(1/12)}$

= $(1+0.23)^{(1/12)}$

= 1.0174

Then,

= (1.0174-1) × 100%

Subtract the terms first

= 0.0174 × 100%

Multiply it

= 1.74%

Hence, if a credit card advertises an annual interest rate of 23%, then the equivalent monthly interest rate is 1.74%

Learn more about annual percentage rate here

brainly.com/question/10795072

#SPJ1

6 0

10 months ago

(4+8+12+16+...+204):(2+4+6+...+102=

Vikki [24]

Both numerator and denominator are a sum of 51 terms, counted skipping 4s (numerator) and 2s (numerator).

So, you have

$\dfrac{\displaystyle\sum_{i=1}^{51} 4i}{\displaystyle\sum_{i=1}^{51} 2i}$

Use the linearity of sum to rewrite this as

$\dfrac{\displaystyle4\sum_{i=1}^{51} i}{\displaystyle2\sum_{i=1}^{51} i}$

So, as you can see, the numerator is exactly twice the numerator: you can cancel out the sum and you have

$\dfrac{4}{2} = 2$

8 0

3 years ago

At a bus station, buses begin their routes at 6.am. The schedule for two of the buses is based on time intervals listen below-

Anastaziya [24]

Answer:

Part A: The two buses leave the bus station at 7 : 15 am

Part B: The steamboat travels 25 miles per hour

Step-by-step explanation:

* Lets explain how to solve the problem

Part A

- Buses begin their routes at 6 am at a bus station

- Bus A leaves every 75 minutes

- Bus B leaves every 15 minutes

- We want to know the next time Bus A and Bus B will leave the bus

station at the Same time

# Bus A

∵ Bus A leaves every 75 minutes

- Lets change 75 minutes to hours and minutes

∵ 1 hour = 60 minutes

∴ 75 minutes = 75/60 = 5/4

- Change 5/4 to mixed number

∵ 5/4 = 1 1/4

∴ 75 minutes = 1 1/4 hours

- Lets change 1/4 hour to minutes

∴ 1/4 × 60 = 15 minutes

∴ 75 minutes = 1 hour and 15 minutes

∵ Bus A leaves the station at 6 am

- Add 1 hour and 15 minutes to that time

∵ 6 + 1 : 15 = 7 : 15

∴ Bus A leaves the station nest time at 7 : 15 am

# Bus B

∵ Bus B leaves every 15 minutes

∵ Bus B leaves the station at 6 am

- Add 15 minutes to 6 am

∴ Bus B leaves the station next time at 6 : 15 am

- Add another 15 minutes for next time

∴ Bus B leaves the station next time at 6 : 30 am

- Add another 15 minutes for next time

∴ Bus B leaves the station next time at 6 : 45 am

- Add another 15 minutes for next time

∵ 15 + 45 = 60 ⇒ add 6 by 1 because 60 minutes = 1 hour

∴ Bus B leaves the station next time at 7 am

- Add another 15 minutes for next time

∴ Bus B leaves the station next time at 7 : 15 am

- The 2 buses leave the station at the same time again at 7:15 am

* The two buses leave the bus station at 7 : 15 am

Part B

- It takes a steamboat 12 hours to travel 300 miles

- We need to find how many miles it travels per hour

∵ The steamboat travels 300 miles in 12 hours

- Divide the distance by the time to find its rate

∵ 300 ÷ 12 = 25

- That means it travels 25 miles per hour

∴ The steamboat travels 25 miles per hour

3 0

3 years ago