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2 years ago

Need help please :( What is the second term of (s+v)^5?

1 answer:

Citrus2011 [14]2 years ago

3 0

First compute the coefficient like this:
$C_5^1=\frac{5!}{1!(5-1)!}=\frac{5!}{4!}=\frac{5\times4!}{4!}$
Simplifying the fraction over 4! we get:
$C_5^1=5$
and the variables are $s^4v$ . So answer $5s^4v$ .

The correct answer is C then.

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Which of the following are roots of the polynomial function?

Bingel [31]

Answer:

1 and -5

Step-by-step explanation:

$~~~~~x^3+3x^2-9x+5=0\\\\\implies x^3-x^2+4x^2-4x-5x+5=0\\\\\implies x^2(x-1)+4x(x-1)-5(x-1)=0\\\\\implies (x-1)(x^2 +4x -5) = 0\\\\\implies (x-1)(x^2+5x -x -5) = 0\\\\\implies (x-1)[x(x+5) -(x+5)] =0\\\\\implies (x-1)(x-1)(x+5)= 0\\\\\implies (x-1)^2(x+5) = 0\\\\\implies x = 1,~~ x = -5$

6 0

1 year ago

The areas of two similar triangles are 18 cm^2 and 8 cm^2. One of the sides of the first triangle is 4.5 cm. What is the length

Nataly_w [17]

Answer:

3 cm

Step-by-step explanation:

The ratio of areas of similar figures is the square of the ratio of linear dimensions. That means the ratio of linear dimensions is the square root of the area ratio. The ratio of the smaller triangle dimensions to the larger is then ...

k = √((8 cm^2)/(18 cm^2)) = √(4/9) = 2/3

Then the corresponding side of the smaller triangle is ...

... k · (4.5 cm) = (2/3)·(4.5 cm) = 3 cm

5 0

3 years ago

The mean amount purchased by a typical customer at Churchill's Grocery Store is $26.00 with a standard deviation of $6.00. Assum

Vadim26 [7]

Answer:

a) 0.0951

b) 0.8098

c) Between $24.75 and $27.25.

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 problem, we have that:

$\mu = 26, \sigma = 6, n = 62, s = \frac{6}{\sqrt{62}} = 0.762$

(a)

What is the likelihood the sample mean is at least $27.00?

This is 1 subtracted by the pvalue of Z when X = 27. So

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

By the Central Limit Theorem

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

$Z = \frac{27 - 26}{0.762}$

$Z = 1.31$

$Z = 1.31$ has a pvalue of 0.9049

1 - 0.9049 = 0.0951

(b)

What is the likelihood the sample mean is greater than $25.00 but less than $27.00?

This is the pvalue of Z when X = 27 subtracted by the pvalue of Z when X = 25. So

X = 27

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

$Z = \frac{27 - 26}{0.762}$

$Z = 1.31$

$Z = 1.31$ has a pvalue of 0.9049

X = 25

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

$Z = \frac{25 - 26}{0.762}$

$Z = -1.31$

$Z = -1.31$ has a pvalue of 0.0951

0.9049 - 0.0951 = 0.8098

c)Within what limits will 90 percent of the sample means occur?

50 - 90/2 = 5

50 + 90/2 = 95

Between the 5th and the 95th percentile.

5th percentile

X when Z has a pvalue of 0.05. So X when Z = -1.645

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

$-1.645 = \frac{X - 26}{0.762}$

$X - 26 = -1.645*0.762$

$X = 24.75$

95th percentile

X when Z has a pvalue of 0.95. So X when Z = 1.645

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

$1.645 = \frac{X - 26}{0.762}$

$X - 26 = 1.645*0.762$

$X = 27.25$

Between $24.75 and $27.25.

3 0

2 years ago

Identify all factors of the expression 12x^2-14x-6

Evgen [1.6K]

Let's solve this by using the quadratic formula:

$\frac{-b+-\sqrt{b^2-4ac} }{2a}$

Note that we only use the coefficients so a=12, b=-14, and c=-6.

Plug values in the quadratic equation:

$\frac{ - ( - 14)± \sqrt{ {( - 14)}^{2} - 4(12)( - 6) } }{2(12)}$

And so by evaluating those values we obtain:

$\frac{14+-\sqrt{484} }{24}=\frac{14+-22}{24} \\\\$

Now we have two answers which are our factors one where we add another where we subtract and so:

First factor:

$\frac{14+22}{24}=\frac{36}{24}=\frac{3}{2}$

Second Factor:

$\frac{14-22}{24}=\frac{-8}{24}=-\frac{1}{3}$

And so your factors are

$\frac{3}{2},-\frac{1}{3}$

meaning that those are your roots/x-intercepts.

6 0

3 years ago

Write and expression for 7 divided by c

Over [174]

Answer:

7/c

Step-by-step explanation:

7 0

2 years ago