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3 years ago

What is 33(4/6)+43/4

1 answer:

3 0

(132 + 198) + 10.75
how i got my answer:
33 x 4 = 132
33 x 6 = 198
and 43 divided by 4 = 10.75
i hope this helps! (if not lmk and i’ll help more)

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Find S^20 if the series 1 + 1.1 ..... is a (a) arithmetic (b) geometric

quester [9]

I'm guessing S^20 is actually referring to the 20th partial sum $S_{20}$ , with

$S_{20}=1+(1+1\times0.1)+(1+2\times0.1)+\cdots+(1+18\times0.1)+(1+19\times0.1)$

in the arithmetic case, and

$S_{20}=1+1.1+1.1^2+\cdots+1.1^{18}+1.1^{19}$

in the geometric case.

(a) Combining like terms, we have

$S_{20}=20+0.1(1+2+\cdots+18+19)$

and invoking the formula

$1+2+\cdots+(n-1)+n=\dfrac{n(n+1)}2$

we end up with

$S_{20}=20+0.1\dfrac{19\times20}2=39$

(b) Multiply $S_{20}$ by 1.1, then subtract this from $S_{20}$ :

$1.1S_{20}=1.1+1.1^2+1.1^3+\cdots+1.1^{19}+1.1^{20}$

$S_{20}-1.1S_{20}=-0.1S_{20}=1-1.1^{20}$
$\implies S_{20}=\dfrac{1.1^{20}-1}{0.1}\approx57.275$

7 0

3 years ago

Factor completely h^3+2h^2-9h-18

guapka [62]

Step 1: Group this into two groups:

$h^3 + 2h^2-9h-18=(h^3 + 2h^2)+(-9h-18)$

When you do that, be sure to group the "–" into the group with the 9 and make sure there's "+" between the groups.

Step 2: Factor out the GCF from both individual groups:

$(h^3 + 2h^2)+(-9h-18) = h^2 (h+2) -9(h+2)$

Step 3: Notice both groups have that (h+2)? That's a new GCF between the two groups, so factor that out:

$h^2 (h+2) -9(h+2) = (h+2)(h^2-9)$

Step 4: That $(h^2-9)$ piece can be factored further, since it's a difference of squares:

$(h+2)(h^2-9) = (h+2)(h+3)(h-3)$

Now it's factored.

8 0

2 years ago

In a basketball game Fintan made 16 baskets. Each of the baskets is worth either 2 or 3

jekas [21]

Let x represent a 2-point basket, and y represent a 3-point basket.

Basket equation: x + y = 16
Point equation 2x + 3y = 39

Solve using system of equations:
if x + y = 16, then x = 16 - y

Plug into the second equation:
2(16-y) + 3y = 39
32 - 2y + 3y = 39
32 + y = 39
y = 7

So the number of 3-point baskets scored was 7. Hope this helps, let me know if there’s a step you don’t understand! :)

8 0

3 years ago

Above is a table with missing terms. Come up with a possible common difference that makes sense and list the missing terms.

Rina8888 [55]

Answer:

common ratio:2 2. 18 3.36 4.72 equation: 4.5( $2^x$ )

Step-by-step explanation:

144=2*2*2*2*3*3 9=3*3

the common ratio would be 2

2. 9*2=18

3. 18*2=36

4. 36*2=72

(check) 72*2=144

0. 9/2=4.5

equation: 4.5( $2^x$ )

7 0

3 years ago

According to national data, 5.1% of burglaries are cleared with arrests. A new detective is assigned to six different burglaries

blagie [28]

Answer:

26.95% probability that at least one of them is cleared with an arrest

Step-by-step explanation:

For each burglary, there are only two possible outcomes. Either it is cleared, or it is not. The probability of a burglary being cleared is independent of other burglaries. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$