All categories

2 years ago

X − y = 12 x + 2y = 21

Mathematics

1 answer:

olga55 [171]2 years ago

5 0

Answer: x=15, y=3

Step-by-step explanation:

Subtracting the two equations, we get -3y=-9, meaning y=3.

Substituting this into the first equation, we get that x-3=12, and thus, x=15.

You might be interested in

A medical device company knows that 11% of patients experience injection-site reactions with the current needle. If 4 people rec

Orlov [11]

Answer: 0.6274

Step-by-step explanation:

Given: The proportion of patients experience injection-site reactions with the current needle : p=0.11

Sample size : n= 4

Let x be a binomial random variable that represents the people get an injection-site reaction.

Binomial probability formula: $P(X=x)= ^nC_x p^x(1-p)^{n-x}$

The required probability : P(x=0)

$=\ ^4C_0(0.11)^0(1-0.11)^4\\\\=(1)(1)(0.89)^4\\\\=0.62742241\\\approx0.6274$

Hence, the probability that none of the 4 people get an injection-site reaction = 0.6274

6 0

4 years ago

In a study to compare two different corrosion inhibitors, specimens of stainless steel were immersed for four hours in a solutio

djverab [1.8K]

Answer:

$(242-220) -1.988 \sqrt{\frac{20^2}{47} +\frac{31^2}{42}}= 10.862$

$(242-220) +1.988 \sqrt{\frac{20^2}{47} +\frac{31^2}{42}}= 33.138$

And the 95% confidence interval for the difference in the means is given by: $10.862 \leq \mu_A -\mu_B \leq 33.138$

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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".

$\bar X_A = 242$ sample mean for inhibitor A

$s_A = 20$ sample standard deviation for inhibitor A

$n_A = 47$ sample size for A

$\bar X_B = 220$ sample mean for inhibitor B

$s_B = 31$ sample standard deviation for inhibitor B

$n_B = 42$ sample size for A

Solution to the problem

For this case the confidence interval for the difference of means is given by:

$(\bar X_A -\bar X_B) \pm t_{\alpha/2} \sqrt{\frac{s^2_A}{n_A} +\frac{s^2_B}{n_B}}$

The degrees of freedom are given by:

$df = n_A +n_B -2 = 47+42-2= 87$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,87)".And we see that $t_{\alpha/2}=1.988$

And replacing we got:

$(242-220) -1.988 \sqrt{\frac{20^2}{47} +\frac{31^2}{42}}= 10.862$

$(242-220) +1.988 \sqrt{\frac{20^2}{47} +\frac{31^2}{42}}= 33.138$

And the 95% confidence interval for the difference in the means is given by: $10.862 \leq \mu_A -\mu_B \leq 33.138$

4 0

3 years ago

The baby giraffe weighed 132 pounds at

Amiraneli [1.4K]

Answer: 58lbs

Step-by-step explanation:

Calculate the difference between 132 and 538. You can do this by subtracting.

538

- 132

----------

406

Now divide this by the amount of months.

406/7=58

Therefore, he gained 58lbs each month.

3 0

3 years ago

Given that QT is and altitude of triangle QRS and that m

iris [78.8K]

Hello from MrBillDoesMath!

Answer:

Discussion:

Given: measure angle STQ = 7x + 55. But, as shown, STQ is a right angle so

7x + 55 = 90 => subtract 55 from each side

7x = 90 -55 = 35 => divide each side by 7

x = 35/7 = 5

Since RS = (x+1) + (2x-1) where x = 5.

RS = (5 + 1) + (2*5 -1)

= 6 + 9

= 15

I don't know what choice the answer is as your diagram only shows Choice A

Thank you,

MrB

3 0

3 years ago

Read 2 more answers

How dose using scientific Notion help compare when comparing with very small very large numbers

rewona [7]

Scientific notation is just a way to simplify a very large and oftentimes complicated number to a smaller one with the exact same value. For example, if I am given the number 1,656,000 to simplify using scientific notation, I would write it out as 1.656 x 10^6

The value at the end is exactly the same as the number I started out with. It is just written differently.

4 0

4 years ago