Ask question

Ask question

All categories

2 years ago

6

The first term of a geometric sequence is 3. The sum of the first two terms is 15 and the sum of the first 3 terms is 63. Deter

mine the common ratio. Select one:
a. 3
b. 63
c. 4
d. 5

1 answer:

pav-90 [236]2 years ago

8 0

63 is the common term. 3+12+48=63

You might be interested in

Consider the following argument. If there are as many rational numbers as there are irrational numbers, then the set of all irra

FrozenT [24]

Answer:

b. form: p → q invalid, converse error q ∴ p

Step-by-step explanation:

Let

p = "there are as many rational numbers as there are irrational numbers,"

let

q = "the set of all irrational numbers is infinite."

We can write the above argument as:

If there are as many rational numbers as there are irrational numbers, then the set of all irrational numbers is infinite

p → q

The set of all irrational numbers is infinite

q

There are as many rational numbers as there are irrational numbers

p

So collectively it can be written as:

p → q

q

∴p

So it looks like

if p then q

q

therefore p

This is a fallacious argument. This means the conclusion can be false even when the premises are true. This type of argument is invalid.

Suppose we know that “If there are as many rational numbers as there are irrational numbers, then the set of all irrational numbers is infinite” is a true conditional statement. We also know that "the set of all irrational numbers is infinite" is true. This is not enough to say that "there are as many rational numbers as there are irrational numbers," is true. The reason for this is that there is nothing logically about “If p then q” and “q” that means p must follow. So this is a converse error and since converse error is an invalid method of inference rule so this argument is invalid.

Let us prove this argument is invalid with a truth table:

p q p → q q p

T T T T T

T F F F T

F T T T F

F F T F F

Since we know that the premises are:

p → q and q

and the conclusion is p

and an argument is valid if and only if all of its premises are true, then the conclusion is true. We should check that whenever both p → q and q are true then p is true but the third row fails. Thus this is an invalid argument.

6 0

3 years ago

Hector gave 1/4 of his money and an additional $1 to calista he gave 1/5 of his remaining money and an additional $4 to Karen th

Dvinal [7]

I believe in youuuu you can do itttt

6 0

3 years ago

Read 2 more answers

We wish to give a 90% confidence interval for the mean value of a normally distributed random variable. We obtain a simple rando

coldgirl [10]

Answer: $(9.27025,\ 11.12975)$

Step-by-step explanation:

Given : Sample size : n= 9

Degree of freedom = df =n-1 =8

Sample mean : $\overline{x}=10.2$

sample standard deviation : $s= 1.5$

Significance level ; $\alpha= 1-0.90=0.10$

Since population standard deviation is not given , so we use t- test.

Using t-distribution table , we have

Critical value = $t_{\alpha/2, df}=t_{0.05 , 8}=1.8595$

Confidence interval for the population mean :

$\overline{x}\pm t_{\alpha/2, df}\dfrac{s}{\sqrt{n}}$

90% confidence interval for the mean value will be :

$10.2\pm (1.8595)\dfrac{1.5}{\sqrt{9}}$

$10.2\pm (1.8595)\dfrac{1.5}{3}$

$10.2\pm (1.8595)(0.5)$

$10.2\pm (0.92975)$

$(10.2-0.92975,\ 10.2+0.92975)$

$(9.27025,\ 11.12975)$

Hence, the 90% confidence interval for the mean value= $(9.27025,\ 11.12975)$

6 0

3 years ago

A rectangle has a length of 17 less than 6 times it's width. If the area of the rectangle is 7585 square feet find the length of

anzhelika [568]

9514 1404 393

Answer:

205 ft

Step-by-step explanation:

Let w represent the width of the rectangle. Then the length is (6w-17) and the area is ...

A = LW

7585 = (6w-17)(w)

6w² -17w -7585 = 0

Perhaps most straightforward is using the quadratic formula to solve this.

For ax² +bx +c = 0, the solution is x = (-b±√(b²-4ac))/(2a). For the above quadratic, the solution is ...

$x=\dfrac{-(-17)\pm\sqrt{(-17)^2-4\cdot6\cdot(-7585)}}{2\cdot6}=\dfrac{17\pm\sqrt{182329}}{12}\\\\x=\dfrac{17\pm427}{12}=\{-34\frac{1}{6},37\}$

The width is 37 feet, so the length is ...

6(37) -17 = 205 . . . feet

The length of the rectangle is 205 feet.

8 0

2 years ago

Do anyoneeeeeee know this??????????????????????????????????????

Dennis_Churaev [7]

Answer is 12

K=y/x (rise over run)

The same rise over run happens to the next point, up 12 over 1

5 0

2 years ago

Read 2 more answers