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3 years ago

6

If an arithmetic sequence has a1=5 d=-2 and n=18 what is sn?

1 answer:

bonufazy [111]3 years ago

7 0

Answer:

sn = -216

Step-by-step explanation:

If an arithmetic sequence has a1=5 d=-2 and n=18 what is sn?

The formula for sn is given as:

sn = n/2[2a +(n - 1)d]

Hence, we fill in our values

sn = 18/2 [2 × 5 + (18 - 1)-2]

sn = 9 [ 10 + (17)-2]

sn = 9 [10 - 34]

sn = 9 × -24

sn = -216

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What are the zeros of the polynomial function? f(x)=x^4−4x^3−22x^2+4x+21

USPshnik [31]

Answer:

{-3, -1, 1, 7}

Step-by-step explanation:

f(x)=x^4−4x^3−22x^2+4x+21 is of the fourth order, and thus we can expect four zeros. There are various ways in which we could identify the zeros. One would be to check each of the given possible answers and determine whether the equation takes on the value 0 in each case; any such value 0 indicates that the possible zero chosen is indeed a zero.

Important: The Rational Root Theorem applies here. We can assume that there are at least some rational roots, which take the form of fractions, whose numerators are plus and minus factors of the constant term, 21, and whose denominators are plus and minus factors of the coefficient of the leading term of the function (which here is just 1). Thus, factors of the given function will be factors, plus or minus, of the constant term, 21, with the coefficient 1 of the highest power term not making any difference. That list of factors is already given: plus or minus 3, plus or minus 1, 0 and 7.

I will arbitrarily choose -1 and determine using synthetic division whether or not this -1 is a zero of the polynomial. Recall that if synthetic div. produces a zero remainder, then the divisor chosen is indeed a zero of the polynomial.

--------------------------------

-1 / 1 -4 -22 4 21

-1 +5 18 -22

-----------------------------------

1 -5 -17 22 -1

Because the remainder is -1, not 0, -1 is not a zero of the given function.

We must move on and try others from the given list. Eliminate -1 and 0. Try 3:

--------------------------------

3 / 1 -4 -22 4 21

+3 -3 -75 -213

-----------------------------------

1 -1 -25 -71 -192

So we conclude that 3 is not a zero.

Try +1:

--------------------------------

1 / 1 -4 -22 4 21

+1 -3 -25 -21

-----------------------------------

1 -3 -25 -21 0

Since the remainder is zero, we know that +1 is a zero of the given function.

Using the same method, we can show that -3, -1, 1 and 7 are zeros.

7 0

4 years ago

The weights of cockroaches living in a typical college dormitory are approximately distributed with a mean of 80 grams and a sta

Romashka [77]

Answer:

The percentage of cockroaches weighing between 77 grams and 83 grams is about 55%.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 80, \sigma = 4$

The percentage of cockroaches weighing between 77 grams and 83 grams

This is the pvalue of Z when X = 83 subtracted by the pvalue of Z when X = 83. So

X = 83

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{83 - 80}{4}$

$Z = 0.75$

$Z = 0.75$ has a pvalue of 0.7734

X = 77

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{77 - 80}{4}$

$Z = -0.75$

$Z = -0.75$ has a pvalue of 0.2266

0.7734 - 0.2266 = 0.5468

Rounded to the nearest whole number, 55%

The percentage of cockroaches weighing between 77 grams and 83 grams is about 55%.

7 0

4 years ago

Can someone answer this for me (in the picture)

lozanna [386]

My answer would be D, but I am not sure.

5 0

3 years ago

19/92 written as a percentage

Solnce55 [7]

Answer:

20.65%

Step-by-step explanation:

$\frac{19}{92} \\ \\ = \frac{19 \times 100}{92} \% \\ \\ = \frac{1900}{92} \% \\ \\ = 20.6521739 \%\\ \\ = 20.65\%$

4 0

3 years ago

The zero of the polynomial 8x+3 is

Vera_Pavlovna [14]

Answer:

$- 3 \div 8 \\$

4 0

4 years ago

Read 2 more answers