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2 years ago

Given the sequence 8, 12, 16, 20, 24, what is the sum of the 31st and 19th terms?

Mathematics

1 answer:

erica [24]2 years ago

7 0

Answer:

First term (a) =8

Common difference (d)= t2-t1

=12-8

Now, sum of first 31th term (tn31) =n/2{2a+(n-1)d}

= 31/2{2×8+(31-1)4}

=31/2{16+(30×4)

=31/2(16+120)

=31/2×126

=31×63

Step-by-step explanation:

Similarly use 19 as (n) for the 19th term

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There are 16 ounces in a pound. If Jack has 64 ounces of pasta to make for a dinner party, how many pounds does he have? If he h

Natalka [10]

Hey there! :) How are you? Basically what you said is right.

Question 1: There are 16 oz (ounces) in a pound, so we do 64/16= 4 lbs (pounds).

Question 2: If Jack has 3 pounds of pasta, that would mean he has 48 ounces, since 1 pound is 16 oz, so 16*3= 48 ounces.

Hoped I helped! Have a nice day, and keep smiling! :)

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3 years ago

Sam takes out a $167,000 mortgage for 20 years. He makes monthly payments and at the end calculates

cupoosta [38]

Answer:

The Annual rate of interest for the mortgage is 1.8%

Step-by-step explanation:

Given as :

The mortgage principal = p = $167,000

The time period of mortgage = t = 20 years

The Amount paid towards mortgage in 20 years = A = $240,141

Let the Annual percentage rate on interest = r % compounded annually

Now, <u>From Compound Interest method</u>

Amount = Principal × $(1+\dfrac{\textrm rate}{100})^{\textrm time}$

Or, A = p × $(1+\dfrac{\textrm r}{100})^{\textrm t}$

Or, $240,141 = $167,000 × $(1+\dfrac{\textrm r}{100})^{\textrm 20}$

or, $\dfrac{240,141}{167,000}$ = $(1+\dfrac{\textrm r}{100})^{\textrm 20}$

Or , 1.437 = $(1+\dfrac{\textrm r}{100})^{\textrm 20}$

Or, $(1.437)^{\frac{1}{20}}$ = $(1+\dfrac{r}{100})$

or, 1.018 = $(1+\dfrac{r}{100})$

Or, $\dfrac{r}{100}$ = 1.018 - 1

Or, $\dfrac{r}{100}$ = 0.018

∴ r = 0.018 × 100

i.e r = 1.8

So, The rate of interest applied = r = 1.8 %

Hence, The Annual rate of interest for the mortgage is 1.8% Answer

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3 years ago

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Gala2k [10]

Answer:

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Step-by-step explanation:

A distribution is called uniform if each outcome has the same probability of happening.

The uniform distributon has two bounds, a and b, and the probability of finding a value between c and d is given by:

$P(c \leq X \leq d) = \frac{d - c}{b - a}$

A particular employee arrives at work sometime between 8:00 a.m. and 8:30 a.m.

We can consider 8 am = 0, and 8:30 am = 30, so $a = 0, b = 30$

Find the probability that the employee will arrive between 8:15 a.m. and 8:25 a.m.

Between 15 and 25, so:

$P(15 \leq X \leq 25) = \frac{25 - 15}{30 - 0} = 0.3333$

0.3333 = 33.33% probability that the employee will arrive between 8:15 a.m. and 8:25 a.m.

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2 years ago

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2 years ago

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anyanavicka [17]

Answer:

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Step-by-step explanation:

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3 years ago

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