9. After a mild heart attack, Mary spent 3 days in a coronary care unit. Her

-2x + y = 0<br> x - y = -3

miv72 [106K]

Answer:

The value of x is 3 and y is 6.

Step-by-step explanation:

You can solve this simultaneous equation by elimination method :

$- 2x + y = 0 - - - (1)$

$x - y = - 3 - - - (2)$

$(1) + (2)$

$- 2x + y + x + (- y) = 0 + ( - 3)$

$- x = - 3$

$x = 3$

$substitute \: x = 3 \: into \: (2)$

$(2)⇒$

$3 - y = - 3$

$- y = - 6$

$y = 6$

7 0

3 years ago

How many times bigger is earth than mercury

irina1246 [14]

Answer:

Mercury has a diameter of 3,032 miles (4,879 km) making it a little more than one third the size of Earth.

If Earth were the size of a baseball, Mercury would be about the size of a golf ball. The diameter of Mercury is 4,879 km, which is approximately 38% the diameter of Earth. In other words, if you put three Mercury's side by side, they would be a little larger than the Earth from end to end. While this makes Mercury smaller than the largest natural satellites in our system – such as Ganymede and Titan – it is more massive and far more dense than they are.

In fact, Mercury’s mass is approximately 3.3 x 1023 kg (5.5% the mass of Earth) which means that its density – at 5.427 g/cm3 – is the second highest of any planet in the Solar System, only slightly less than Earth’s (5.515 g/cm3). This also means that Mercury’s surface gravity is 3.7 m/s2, which is the equivalent of 38% of Earth’s gravity (0.38 g). This means that if you weighed 100 kg (220 lbs) on Earth, you would weigh 38 kg (84 lbs) on Mercury.

5 0

3 years ago

A teacher gives a test to a large group of students. The results are closely approximated by a normal curve. Teh mean is 73, wit

zavuch27 [327]

Answer:

The bottom for an A is 75. Round to the nearest whole number as needed.

Step-by-step explanation:

1) 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".

Let X the random variable that represent the scores on this case, and for this case we know the distribution for X is given by:

$X \sim N(\mu=73,\sigma=7)$

And let $\bar X$ represent the sample mean, the distribution for the sample mean is given by:

$\bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}})$

2) The bottom for an A is _____. Round to the nearest whole number as needed.

And we want the top 5.5% of the scores, so we need a value a such that:

$P(X>a)=0.055$ or $P(X$

We need on the right tail of the distribution a value a that gives to us 94.5% of the area below and 5.5% of the area above. Both conditions are equivalent.

Let's use the condition $P(X$ , the best way to solve this problem is using the z score with the following formula:

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

So we need a value from the normal standard distribution that accumulates 0.945 of the area on the left and 0.055 on the right. This value on this case is 1.598 and we can founded with the following code in excel:

"=NORM.INV(0.945,0,1)"

If we apply the z score formula to our case we have this:

$P(X$

So then based on the equalities we have this:

$\frac{a-73}{7}=1.598$

And if we solve for a we got:

$a=(7*1.598) +73=84.186$

So then we need a score of 84.186 rounded to the nearest whole number 75 or higher in order to get an A

8 0

3 years ago

Willy has compounded monthly to invest his summer earnings of $4259 in the

pogonyaev

We have been given that Willy has compounded monthly to invest his summer earnings of $4259 in the Rock Solid Bank. The bank is offering 6%. We are asked to find the amount of money will be after 5 years.

We will use compound interest formula to solve our given problem.

$A=P(1+\frac{r}{n})^{nt}$ , where,

A = Final amount after t years,

P = Principal amount,

r = Annual interest rate in decimal form,

n = Number of times interest is compounded per year.

t = Time in years.

$6\%=\frac{6}{100}=0.06$

Since interest is compounded monthly, so $n=12$ and $P=4259$ .

$A=\$4259(1+\frac{0.06}{12})^{12\cdot 5}$

$A=\$4259(1+0.005)^{60}$

$A=\$4259(1.005)^{60}$

$A=\$4259(1.3488501525493161)$

$A=\$5744.752799707\approx \$5744.75$

Therefore, Will will have approximately $\$5744.75$ in 5 years.

7 0

3 years ago

A medical researcher wants to investigate the amount of time it takes for patients' headache pain to be relieved after taking a

Mariana [72]

<span>A medical researcher wants to investigate the amount of time it takes for patients' headache pain to be relieved after taking a new prescription painkiller. She plans to use statistical methods to estimate the mean of the population of relief times. She believes that the population is normally distributed with a standard deviation of 18 minutes. How large a sample should she take to estimate the mean time to within 4 minutes with 97% confidence?
-----
n = [z*s/E]^2
---

n = [2.17*18/4]^2 = 96 when rounded up

</span>

3 0

3 years ago