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2 years ago

A series contains 18 numbers and has a sum of 4,185. The last number of the series is 275. What is the first number?

1 answer:

3 0

The sum of arithmetic series is given by:
Sn=n/2(a1+an)
where:
n=number of terms
a1=first term
an=nth term
but
n=18, an=275, Sn=4185
plugging the values in the formula we get:
4185=18/2(a1+275)
simplifying this we get:
4185=9(a1+275)
dividing through by 9 we get:
465=a1+275
thus
a1=465-275
a1=190

Answer: first number is 190

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What is the value of k such that x-5 is a factor of x3 – x2 + kx - 30?

Paraphin [41]

Answer:

k = - 14

Step-by-step explanation:

given that (x - 5) is a factor of the polynomial then x = 5 is a root and

x³ - x² + kx - 30 = 0 for x = 5, that is

5³ - 5² + 5k - 30 = 0

125 - 25 + 5k - 30 = 0

70 + 5k = 0 ( subtract 70 from both sides )

5k = - 70 ( divide both sides by 5 )

k = - 14

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2 years ago

1. Miguel is playing a game in which a box contains four chips with numbers written on them. Two of the chips have the number 1,

zzz [600]

Answer:

Step-by-step explanation:

Given that Miguel is playing a game

The box contains 4 chips, 2 with number 1, and other two differntly numbered as 3 and 5.

OUt of these 4, 2 chips are drawn

P(drawing same number) = 2C2/4C2 = $\frac{1}{6}$

Prob (drawing differnt numbers) = 1-1/6 = $\frac{5}{6}$

Hence prob of winning 2 dollars = $\frac{1}{6}$

Prob of losing 1 dollar = $\frac{5}{6}$

b) Expected value = sum of prob x amount won

= $\frac{1}{6}2+\frac{5}{6}(-1)=-\frac{1}{2}$

c) Miguel can expect to lose 1/2 dollars for every game he plays

d) If it is to be a fair game expected value =0

i.e. let the amount assigned be s

Then $\frac{1}{6}s-\frac{5}{6}=0\\s=5$

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1 year ago

Read 2 more answers

An Epson inkjet printer ad advertises that the black ink cartridge will provide enough ink for an average of 245 pages. Assume t

Neko [114]

Answer:

35.2% probability that the sample mean will be 246 pages or more

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

$\mu = 245 \sigma = 15, n = 33, s = \frac{15}{\sqrt{33}} = 2.61$

What the probability that the sample mean will be 246 pages or more?

This is 1 subtracted by the pvalue of Z when X = 246. So

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

By the Central Limit Theorem

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

$Z = \frac{246 - 245}{2.61}$

$Z = 0.38$

$Z = 0.38$ has a pvalue of 0.6480.

1 - 0.6480 = 0.3520

35.2% probability that the sample mean will be 246 pages or more

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2 years ago

nikki backyard is in the shape of a rectangle. the length is 27 feet. The width is one-third the length plus 4 feet. write and e

PIT_PIT [208]

Answer:

A= Length x Width

A= 27 x (1/3 x 27 + 4)

A=27 x (9 + 4)

A= 27 x 13

A= 351

Step-by-step explanation:

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1 year ago

Lamark goes to a bowling alley to test his belief that rolling a bowling ball slowly will result in knocking down more pins. He

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Answer: Ball's kinetic energy became potential energy

Step-by-step explanation:

There are no options attached but this should be along the lines of what happened.

Kinetic energy refers to energy that an object has as a result of it moving whilst potential energy is the opposite and is energy that an object stores within itself due to several factors whilst it is not in motion.

The ball was initially in motion which means that it had kinetic energy but as the ball was slowing down, this energy was gradually converted to potential energy until the balls came to a standstill.

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2 years ago