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3 years ago

1,a) Find a recursive formula for the sequence 1, 2, 6, 24, 120, . . . .

Mathematics

1 answer:

miss Akunina [59]3 years ago

3 0

a) The n-th term in the sequence is the product of the first n natural numbers:

1 • 2 = 2

1 • 2 • 3 = 6

1 • 2 • 3 • 4 = 25

1 • 2 • 3 • 4 • 5 = 120

and so on. Recursively, the n-th term is a function of the (n - 1)-th term as

a(n) = n a(n - 1)

b) Using the rule above, the 6th and 7th terms are

a (6) = 6 a (5) = 6 • 120 = 720

and

a (7) = 7 a (6) = 7 • 720 = 5040

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0.25 to 0.5 Find the percent of change. Round to the nearest tenth of a percent if necessary.

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25% just like money 25 50 75 1.00 same thing just going from .25 to .5 so 25%

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3 years ago

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You and your friend sell lemonade. You get 1/3 of the total money. Your friend gets $20 less than the total amount collected. Wr

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If your friend made $20 dollars they made 2/3 of the money, and you got 1/3 of the total money then that means you made $10 dollars.

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4 years ago

Chrystelle's mother is 1 2/3ft taller than Chrystelle. If

nadezda [96]

Answer:

4 5/6 feet.

Step-by-step explanation:

The least common multiple for 2 and 3 is 6, so if we change the denominators to 6, we get Chrystelle's height as 3 3/6, and her mother is 1 4/6 ft taller than her.

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(Written as an Improper fraction)

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I hope this helps!

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3 years ago

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I need help with this ASAP!!!

hjlf

Answer:

sqrt d = 10

d = (10)^2

d = 100

Part b

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Step-by-step explanation:

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3 years ago

Fairfield Homes is developing two parcels near Pigeon Fork, Tennessee. In order to test different advertising approaches, it use

evablogger [386]

Answer:

(1) Null Hypothesis, $H_0$ : $\mu_1 = \mu_2$

Alternate Hypothesis, $H_1$ : $\mu_1\neq \mu_2$

(2) Test statistics = -1.48

(3) At the 0.05 significance level, Fair field conclude that the population means are same.

Step-by-step explanation:

Let $\mu_1$ = mean annual family income for 12 people making inquiries at the first development

$\mu_2$ = mean annual family income for 24 people making inquiries at the second development

$s_1$ = standard deviation of annual family income for 12 people making inquiries at the first development

$s_2$ = standard deviation of annual family income for 24 people making inquiries at the second development

$n_1$ = sample of people of first development i.e. 12

$n_2$ = sample of people of second development i.e. 24

(1) Null Hypothesis, $H_0$ : $\mu_1 = \mu_2$ {population means are same}

Alternate Hypothesis, $H_1$ : $\mu_1\neq \mu_2$ {population means are different}

DECISION RULE ;

If the test statistics is less than the critical value of t from table at 5% significance level, then we will accept null hypothesis, $H_0$ .
If the test statistics is more than the critical value of t from table at 5% significance level, then we will reject null hypothesis, $H_0$ .

(2) The test statistics is given by;

$\frac{(X_1bar -X_2bar) - (\mu_1-\mu_2)}{s_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }$ ~ $t_n__1+n_2-2$

where, $X_1bar$ = Sample mean income of people at first development

= $153,000

$X_2bar$ = Sample mean income of people at second development = $171,000

$s_1$ = $42,000 and $s_2$ = $30,000

$s_p= \sqrt{\frac{(n_1-1)s_1^{2}+(n_2-1)s_2^{2} }{n_1+n_2-2}}$ = $\sqrt{\frac{(12-1)42000^{2}+(24-1)30000^{2} }{12+24-2}}$ = 34344.30

Test statistics = $\frac{(153000 -171000) - 0}{34344.30\sqrt{\frac{1}{12}+\frac{1}{24} } }$ ~ $t_3_4$

= -1.48

(3) At 5% level of significance, t table gives critical value of 2.032 at 34 degree of freedom.Since our test statistics is less than the critical value of t so considering our decision rule, we will accept null hypothesis.

And conclude that population means are same.

4 0

4 years ago