Ask question

Ask question

All categories

3 years ago

12

Which number below is a prime number? A. 17 B. 12 C. 18 D. 28 SUBM

1 answer:

julia-pushkina [17]3 years ago

3 0

Answer:

17

Step-by-step explanation:

You might be interested in

4-Fui al supermercado y había un descuento del 15% en el total de la compra, si pagaba en efectivo. Gasté $ 2.400. ¿Qué cantidad

Grace [21]

Answer:

$2.040

Step-by-step explanation:

Para calcular la cantidad que fue abonada en realidad, debes encontrar el valor del descuento calculando el 15% del valor total de la compra y este resultado se debe restar del total:

$2.400*15%= $360

$2.400-$360= $2.040

De acuerdo a esto, la cantidad abonada en realidad es: $2.040.

6 0

2 years ago

Let a1, a2, a3, ... be a sequence of positive integers in arithmetic progression with common difference

Bezzdna [24]

Since $a_1,a_2,a_3,\cdots$ are in arithmetic progression,

$a_2 = a_1 + 2$

$a_3 = a_2 + 2 = a_1 + 2\cdot2$

$a_4 = a_3+2 = a_1+3\cdot2$

$\cdots \implies a_n = a_1 + 2(n-1)$

and since $b_1,b_2,b_3,\cdots$ are in geometric progression,

$b_2 = 2b_1$

$b_3=2b_2 = 2^2 b_1$

$b_4=2b_3=2^3b_1$

$\cdots\implies b_n=2^{n-1}b_1$

Recall that

$\displaystyle \sum_{k=1}^n 1 = \underbrace{1+1+1+\cdots+1}_{n\,\rm times} = n$

$\displaystyle \sum_{k=1}^n k = 1 + 2 + 3 + \cdots + n = \frac{n(n+1)}2$

It follows that

$a_1 + a_2 + \cdots + a_n = \displaystyle \sum_{k=1}^n (a_1 + 2(k-1)) \\\\ ~~~~~~~~ = a_1 \sum_{k=1}^n 1 + 2 \sum_{k=1}^n (k-1) \\\\ ~~~~~~~~ = a_1 n + n(n-1)$

so the left side is

$2(a_1+a_2+\cdots+a_n) = 2c n + 2n(n-1) = 2n^2 + 2(c-1)n$

Also recall that

$\displaystyle \sum_{k=1}^n ar^{k-1} = \frac{a(1-r^n)}{1-r}$

so that the right side is

$b_1 + b_2 + \cdots + b_n = \displaystyle \sum_{k=1}^n 2^{k-1}b_1 = c(2^n-1)$

Solve for $c$ .

$2n^2 + 2(c-1)n = c(2^n-1) \implies c = \dfrac{2n^2 - 2n}{2^n - 2n - 1} = \dfrac{2n(n-1)}{2^n - 2n - 1}$

Now, the numerator increases more slowly than the denominator, since

$\dfrac{d}{dn}(2n(n-1)) = 4n - 2$

$\dfrac{d}{dn} (2^n-2n-1) = \ln(2)\cdot2^n - 2$

and for $n\ge5$ ,

$2^n > \dfrac4{\ln(2)} n \implies \ln(2)\cdot2^n - 2 > 4n - 2$

This means we only need to check if the claim is true for any $n\in\{1,2,3,4\}$ .

$n=1$ doesn't work, since that makes $c=0$ .

If $n=2$ , then

$c = \dfrac{4}{2^2 - 4 - 1} = \dfrac4{-1} = -4 < 0$

If $n=3$ , then

$c = \dfrac{12}{2^3 - 6 - 1} = 12$

If $n=4$ , then

$c = \dfrac{24}{2^4 - 8 - 1} = \dfrac{24}7 \not\in\Bbb N$

There is only one value for which the claim is true, $c=12$ .

3 0

1 year ago

The distance between my house and Memphis is 150 km. If I drive in my car, it takes me 72 min to make the first 100 km of the dr

Cloud [144]

Set up a ratio:

You drove 72 minutes and 100 km = 72/100

You want the number of minutes (x) to drive 150 km = x/150

Set the ratios to equal each other and solve for x:

72/100 = x/150

Cross multiply:

(72 * 150) = 100 * x)

Simplify:

10,800/100x

Divide both sides by 100:

x = 10800/100 = 108

This means it would take 108 minutes to drive 150 km.

Now subtract the time you have already driven to fin how much more you need:

180 - 72 = 36 more minutes.

4 0

3 years ago

Read 2 more answers

2/3 × 42 pls explain in steps

sergij07 [2.7K]

Answer:

28

Step-by-step explanation:

Convert element to fraction:

2/3 x 42/1

Cross-cancel common factor:

2/1 x 14/1

Multiply Factors:

2 x 14

1 x 1

Multiply the numbers 14 x 2 = 28

And boom, the answer is 28!

8 0

3 years ago

Read 2 more answers

Find the value of Angle X

jarptica [38.1K]

<u>The angle based on the diameter is always right</u>

Then <ABC=90 and ∠BAC=∠ACB=45° ; and ∠BCD=180-45=135 then x=(180-135):2=22,5°

3 0

2 years ago