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3 years ago

15. I had 180 mL of water in a measuring cylinder. I added a stone. The reading is now 195 mL. What is the volume of the stone?

Mathematics

1 answer:

alexira [117]3 years ago

7 0

Answer: 15 mL

Step-by-step explanation:

Before the stone the reading was 180 mL

When the stone was added the reading rose to 195 mL

So, we subtract them both, this will give us the volume of the stone

195 mL - 180 mL = 15 mL

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I NEED HELP PLEASE, THANKS! :) Heather invests $4,900 in an account with a 3.5% interest rate, making no other deposits or withd

Alex

Answer: $5,828.28

<u>Step-by-step explanation:</u>

Use the Compound Interest formula: $A=P(1+\frac{r}{n})^{nt}$ where

A is the accrued amount (balance)
P is the principal (initial amount invested)
r is the interest rate (in decimal form)
n is the number of times compounded each year
t is the time of the investment (in years)

Given: P = 4,900

r = 3.5% (0.035)

n = 2

t = 5

$A=4,900\bigg(1+\dfrac{0.035}{2}\bigg)^{2(5)}\\\\\\.\qquad = 4900(1.0175)^{10}\\\\\\.\qquad = \large\boxed{5,828.28}\\$

5 0

3 years ago

You are at a stall at a fair where you have to throw a ball at a target. There are two versions of the game. In the first

Tomtit [17]

Answer:

$P(X=0)=(3C0)(0.1)^0 (1-0.1)^{3-0}=0.729$

And the probability of loss with the first wersion is 0.729

$P(Y=0)=(5C0)(0.05)^0 (1-0.05)^{5-0}=0.774$

And the probability of loss with the first wersion is 0.774

As we can see the best alternative is the first version since the probability of loss is lower than the probability of loss on version 2.

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Alternative 1

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=3, p=0.1)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

We can find the probability of loss like this P(X=0) and if we find this probability we got this:

$P(X=0)=(3C0)(0.1)^0 (1-0.1)^{3-0}=0.729$

And the probability of loss with the first wersion is 0.729

Alternative 2

Let Y the random variable of interest, on this case we now that:

$Y \sim Binom(n=5, p=0.05)$

The probability mass function for the Binomial distribution is given as:

$P(Y)=(nCy)(p)^y (1-p)^{n-y}$

Where (nCx) means combinatory and it's given by this formula:

$nCy=\frac{n!}{(n-y)! y!}$

We can find the probability of loss like this P(Y=0) and if we find this probability we got this:

$P(Y=0)=(5C0)(0.05)^0 (1-0.05)^{5-0}=0.774$

And the probability of loss with the first wersion is 0.774

As we can see the best alternative is the first version since the probability of loss is lower than the probability of loss on version 2.

4 0

4 years ago

Find the perimeter of the polygon round your answer to the nearest tenth.

Volgvan

The correct answer is 39 units.Parameter is the
sum of the lengths of all sides of a polygon.
The sides of the polygon are PT, TS, SR, RQ,
and QP.

3 0

2 years ago

You flip an unfairly weighted coin 4 times. If the probability of getting a tail is 0. 38.

anygoal [31]

Answer:

0.84306608

Step-by-step explanation:

The probability of an event, e, occurring exactly r times over n trials follows the formula

(n combination r) * p^r * q ^ (n-r)

with p being the probability the event will occur and q being the probability the event will not occur.

I assume you have a calculator/can find one online that can do combinations.

Here, we want to figure out if you get:

- 0 tails

- 1 tail

- 2 tails

If you get 3 or 4 tails, we are getting more than the 2 tails desired

For 0 tails:

- p is the probability a tail will occur = 0.38

- we want it to occur 0 times, so r = 0

- q is (1-p) = 1- 0.38 = 0.62

- we have 4 trials, as we flip it 4 times

(n combination r) * p^r * q ^ (n-r) = (4 combination 0) * (0.38) ^0 * (0.62) ^(4-0) = 1 * (0.38) ^0 * (0.62) ^(4-0) = 0.14776336

For 1 tail:

- p = 0.38, q = 0.62 as with 0 tails

- r = 1, n = 4

(n combination r) * p^r * q ^ (n-r) = (4 combination 1) * (0.38) ^1 * (0.62) ^(4-1) = 4* (0.38) ^1 * (0.62) ^(4-1) = 0.36225856

For 2 tails:

- p = 0.38, q = 0.62 as with 0 tails

- r = 2, n = 4

(n combination r) * p^r * q ^ (n-r) = (4 combination 2) * (0.38) ^1 * (0.62) ^(4-2) = 6* (0.38) ^2 * (0.62) ^(4-2) = 0.33304416

add our 3 probabilities together

0.33304416 + 0.36225856 + 0.14776336 = 0.84306608 as our answer

8 0

2 years ago

Can someone please write the equation for this?

8_murik_8 [283]

Answer:

y = 2 $\sqrt{x}$ - 3

Step-by-step explanation:

6 0

3 years ago

15. I had 180 mL of water in a measuring cylinder. I added a stone. The reading is now 195 mL. What is the volume of the stone?​

15. I had 180 mL of water in a measuring cylinder. I added a stone. The reading is now 195 mL. What is the volume of the stone?