Algebra 2 <br><br> Simplify 3+i/2-i

The first term of a geometric sequence is 6, and the common ratio is 3. What is the 7th term of the sequence?

-BARSIC- [3]

An = a1 r^(n-1)

here a1 = 6 and r = 3 so

a7 = 6 * 3^(7-1)

= 4374 answe

8 0

4 years ago

Of is directly proportional toy and x = 45 when

kompoz [17]

Answer:

if x=ky, where k is constant.

value of x

45/3=k3/3

15=k, constant is 15

value of x when y =6

x=ky

x=15(6)

x=80

4 0

3 years ago

A carpenter is putting a skylight in a roof. If the roof measures 10 + 8 by 8 + 6 and the skylight measures + 5 by 3 + 4, what i

Usimov [2.4K]

Answer:

The area is: $77x^2 + 105x + 28$ , option b.

Step-by-step explanation:

Rectangular area:

The area of a rectangular space is given bt the multiplication of its measures.

Area of the roof:

Dimensions of 10x + 8 and 8x + 6. So

$A_{r} = (10x+8)(8x+6) = 80x^2 + 60x + 64x + 48 = 80x^2 + 124x + 48$

Area of the skylight:

Dimensions of x + 5 and 3x + 4. So

$A_{s} = (x+5)(3x+4) = 3x^2+4x+15x+20 = 3x^2 + 19x + 20$

What is the area of the remaining roof after the skylight is built?

Total subtracted by the skylight, which is a subtraction of a polynomial, in which we subtract the like terms. So

$A_{r} - A_{s} = 80x^2 + 124x + 48 - (3x^2 + 19x + 20) = 80x^2 - 3x^2 + 124x - 19x + 48 - 20 = 77x^2 + 105x + 28$

The area is: $77x^2 + 105x + 28$ , option b.

3 0

3 years ago

The prices of all college textbooks follow a bell-shaped distribution with a mean of $113 and a standard deviation of $12. Using

Soloha48 [4]

Step-by-step explanation:

In statistics, the empirical rule states that for a normally distributed random variable,

68.27% of the data lies within one standard deviation of the mean.

95.45% of the data lies within two standard deviations of the mean.

99.73% of the data lies within three standard deviations of the mean.

In mathematical notation, as shown in the figure below (for a standard normal distribution), the empirical rule is described as

$\Phi(\mu \ - \ \sigma \ \leq X \ \leq \mu \ + \ \sigma) \ = \ 0.6827 \qquad (4 \ \text{s.f.}) \\ \\ \\ \Phi(\mu \ - \ 2\sigma \ \leq X \ \leq \mu \ + \ 2\sigma) \ = \ 0.9545 \qquad (4 \ \text{s.f.}) \\ \\ \\ \Phi}(\mu \ - \ 3\sigma \ \leq X \ \leq \mu \ + \ 3\sigma) \ = \ 0.9973 \qquad (4 \ \text{s.f.})$

where the symbol $\Phi$ (the uppercase greek alphabet phi) is the cumulative density function of the normal distribution, $\mu$ is the mean and $\sigma$ is the standard deviation of the normal distribution defined as $N(\mu, \ \sigma)$ .

According to the empirical rule stated above, the interval that contains the prices of 99.7% of college textbooks for a normal distribution $N(113, \ 12)$ ,

$\Phi(113 \ - \ 3 \ \times \ 12 \ \leq \ X \ \leq \ 113 \ + \ 3 \ \times \ 12) \ = \ 0.9973 \\ \\ \\ \-\hspace{1.75cm} \Phi(113 \ - \ 36 \ \leq \ X \ \leq \ 113 \ + \ 36) \ = \ 0.9973 \\ \\ \\ \-\hspace{3.95cm} \Phi(77 \ \leq \ X \ \leq \ 149) \ = \ 0.9973$

Therefore, the price of 99.7% of college textbooks falls inclusively between $77 and $149.

5 0

2 years ago

According to a survey, 78% of residents in Summerville own a home. If 30 residents

rosijanka [135]

Answer:

0.1732 = 17.32% probability exactly 24 residents own a home.

Step-by-step explanation:

For each resident, there are only two possible outcomes. Either they own a home, or they do not. The probability of a resident owning a home is independent of any other resident. This means that the binomial probability distribution is used 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.

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