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Scilla [17]
3 years ago
12

Evaluate the series

Mathematics
1 answer:
dalvyx [7]3 years ago
6 0

Answer:

the value of the series;

\sum_{k=1}^{6}(25-k^2) = 59

C) 59

Step-by-step explanation:

Recall that;

\sum_{1}^{n}a_n = a_1+a_2+...+a_n\\

Therefore, we can evaluate the series;

\sum_{k=1}^{6}(25-k^2)

by summing the values of the series within that interval.

the values of the series are evaluated by substituting the corresponding values of k into the equation.

\sum_{k=1}^{6}(25-k^2) =(25-1^2)+(25-2^2)+(25-3^2)+(25-4^2)+(25-5^2)+(25-6^2)\\\sum_{k=1}^{6}(25-k^2) =(25-1)+(25-4)+(25-9)+(25-16)+(25-25)+(25-36)\\\sum_{k=1}^{6}(25-k^2) =24+21+16+9+0+(-11)\\\sum_{k=1}^{6}(25-k^2) = 59\\

So, the value of the series;

\sum_{k=1}^{6}(25-k^2) = 59

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Lelu [443]

Answer: aA 90% confidence interval for the population proportion of adults in the U.S. who have donated blood in the past two years = (0.163,0.189)

Step-by-step explanation:

Let p = population proportion of adults in the U.S. who have donated blood in the past two years.

Given: A Gallup survey of 2322 adults (at least 18 years old) in the U.S. found that 408 of them have donated blood in the past two years.

Sample size: n= 2322

Sample proportion q=\dfrac{408}{2322}=0.176

Critical z-value for 90% confidence level : z*=1.645

The confidence interval for population proportion:

q\pm z^*(\sqrt{\dfrac{q(1-q)}{n}})

A 90% confidence interval for the population proportion of adults in the U.S. who have donated blood in the past two years:

0.176\pm (1.645)(\sqrt{\dfrac{0.176(1-0.176)}{2322}})\\\\=0.176\pm (1.645)(0.0079)\\\\=(0.176\pm0.013)\\\\=(0.176-0.013,0.176+0.013))\\\\=(0.163,0.189)

Hence,

6 0
3 years ago
. The two bottles are similar in shape. The larger bottle holds 100 m/ of perfume. Calculate how many millilitres of perfume the
FromTheMoon [43]

Answer:

The smaller bottle holds 12.5 ml of perfume.

====================

<h2>Given</h2>

  • Two bottles of similar shape;
  • Larger bottle has volume of 100 ml;
  • The length of larger bottle is 10 cm;
  • The length of smaller bottle is 5 cm.

<h2>To find </h2>

  • The volume of smaller bottle.

<h2>Solution</h2>

Find the scale factor, the ratio of corresponding dimensions:

  • k = 5/10 = 1/2

We know the volume is the function of three dimensions, therefore the ratio of volumes is the cube of the scale factor:

  • V_{small}/V_{large} = k^3\\

Substitute the known values and find the volume of small bottle:

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The smaller bottle holds 12.5 ml of perfume.

4 0
1 year ago
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Answer:

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Step-by-step explanation:

[ Refer to the attachment ]

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3 years ago
True or false: in order to fill the following box, you would need to fill in 2 unit cubes in length, 2 unit cubes in width, and
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Answer:

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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