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Paul [167]
3 years ago
12

Which answer represents the series in sigma notation? −5+(−1)+3+7+11

Mathematics
1 answer:
madam [21]3 years ago
5 0

Answer:

In sigma notation, the series may be represented as,

\sum_{x = 0}^{4}(-5 + 4x)

It is an arithmetic progression with

1st term = -5

common difference = 4

no, of terms = 5

Step-by-step explanation:

The finite series is given by,

-5 + (-1) + 3 + 7 + 11

In sigma notation, the series may be represented as,

\sum_{x = 0}^{4}(-5 + 4x)

It is an arithmetic progression with

1st term = -5

common difference = 4

no, of terms = 5

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I need to know if the volume is 108 or 900
slega [8]
The answer is neither 108 or 900, but it is V = 1357.17

To solve, use the formula for the volume of a cone:
\frac{ \pi r^2h}{3}

fill r with 6 and h with 36

\frac{ \pi (6)^2(36)}{3}

When you solve that, you get 1357.17
5 0
3 years ago
Suppose a lawn and garden company wants to determine the current percentage of customers who use fertilizer on their lawns. How
marishachu [46]

Answer:

n=601

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The population proportion have the following distribution

p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by \alpha=1-0.95=0.05 and \alpha/2 =0.025. And the critical value would be given by:

z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96

The confidence interval for the mean is given by the following formula:  

\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}

The margin of error for the proportion interval is given by this formula:  

ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}    (a)  

And on this case we have that ME =\pm 0.04 and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}   (b)  

Since we don't have a prior estimation for the proportion we can use 0.5 as estimation. And replacing into equation (b) the values from part a we got:

n=\frac{0.5(1-0.5)}{(\frac{0.04}{1.96})^2}=600.25  

And rounded up we have that n=601

3 0
3 years ago
The area of the bottom of a shoebox can be written as a(x) = 2x2 - 4 and the height of the shoebox can be written as h(x) = 3x +
Helga [31]

Answer:V(x) = 6x³ + 4x² - 12x - 8

Step-by-step explanation:

The shoe box can either be cube shaped or cubiod shaped. The volume of the box is length × breadth × height

Since Area = Length × Breadth

Volume = Area × Height

V(x) = A(x) × H(x)

A(x) = 2x² - 4

H(x) = 3x + 2

V(x) = (2x² - 4)(3x + 2)

V(x) = 6x³ + 4x² - 12x - 8

8 0
3 years ago
Write and solve an equation to find the unknown side length x (in feet). Perimeter =34.6 ft
Advocard [28]

Answer: x=11.9

Step-by-step explanation:

Equation: x=34.6-22.7

5 0
3 years ago
PLEASE HALP IM TIMED!!! WILL GIVE 25 PTS
MatroZZZ [7]

So basically, we have [-83, -77] as the whole thing.
There's a circle that limits [-83, -79) as a shaded zone.

Vera claims that -78.9999 \geq X, which is false.
Vera wrote a relation symbol that doesn't represent the ray's direction. She went the other way around.

4 0
2 years ago
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