How many solutions for x does the following equation have?

2. How many more possible arrangements can be made using the letters of the word PERMUTATIONS than using the letters of the word

Pavel [41]

PERMUTATIONS - $\dfrac{12!}{2!}$

COMBINATIONS - $\dfrac{12!}{2!2!}$

$\dfrac{\dfrac{12!}{2!}}{\dfrac{12!}{2!2!}}=\dfrac{12!}{2!}\cdot\dfrac{2!2!}{12!}=2!=2$

4 0

3 years ago

Help meeee!! I’ll give brainliest!!!

dimulka [17.4K]

Answer:

x = 9

y = 13

Step-by-step explanation:

Side-Side-Side or SSS means that if all three sides of one triangle are equal to all three corresponding sides of another triangle, then the two triangles are considered to be congruent (equal).

Therefore, GH = PM ⇒ 7x + 8 = 6y - 7

and, GP = HM ⇒ 8x - 10 = 5y - 3

Rewrite the first expression to make x the subject, then substitute this into the second equation, and solve for y:

GH = PM

⇒ 7x + 8 = 6y - 7

⇒ 7x = 6y - 15

⇒ x = (6/7)y - 15/7

Substituting x = (6/7)y - 15/7 into GP = HM:

GP = HM

⇒ 8x - 10 = 5y - 3

⇒ 8[(6/7)y - 15/7] - 10 = 5y - 3

⇒ (48/7)y - 120/7 - 10 = 5y - 3

⇒ (13/7)y = 169/7

⇒ y = 13

Now we have found a value for y, substitute this into one of the expressions and solve for x:

8x - 10 = 5y - 3

⇒ 8x - 10 = (5 x 13) - 3

⇒ 8x - 10 = 62

⇒ 8x = 72

⇒ x = 9

3 0

2 years ago

A survey shows that college students spend on average about $20 per month on Yum Good Ramen. a. Assume that the survey was condu

lawyer [7]

Answer:

a) The 95% confidence interval would be given by (19.168;20.832)

b) The 95% confidence interval would be given by (19.182;20.416)

c) The 95% confidence interval would be given by (19.412;20.588)

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".

$\bar X$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma$ represent the population standard deviation

n represent the sample size

Part a

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

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: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$