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gayaneshka [121]

3 years ago

9

Evaluate the algebraic expressions, and put their values in order from least (1) to greatest (4), for a = 2 and b = 5. 1.50 − b2

+ a 2.a2(5 − b) 3.b2 − 10 4.a(b − 3)

1 answer:

Aneli [31]3 years ago

8 0

Is it possible to add a picture to this

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Calculate the sample mean and sample variance for the following frequency distribution of heart rates for a sample of American a

spin [16.1K]

Answer:

$Mean = 68.9$

$s^2 =18.1$ --- Variance

Step-by-step explanation:

Given

$\begin{array}{cccccc}{Class} & {51-58} & {59-66} & {67-74} & {75-82} & {83-90} \ \\ {Frequency} & {6} & {3} & {11} & {13} & {4} \ \end{array}$

Solving (a): Calculate the mean.

The given data is a grouped data. So, first we calculate the class midpoint (x)

For 51 - 58.

$x = \frac{1}{2}(51+58) = \frac{1}{2}(109) = 54.5$

For 59 - 66

$x = \frac{1}{2}(59+66) = \frac{1}{2}(125) = 62.5$

For 67 - 74

$x = \frac{1}{2}(67+74) = \frac{1}{2}(141) = 70.5$

For 75 - 82

$x = \frac{1}{2}(75+82) = \frac{1}{2}(157) = 78.5$

For 83 - 90

$x = \frac{1}{2}(83+90) = \frac{1}{2}(173) = 86.5$

So, the table becomes:

$\begin{array}{cccccc}{x} & {54.5} & {62.5} & {70.5} & {78.5} & {86.5} \ \\ {Frequency} & {6} & {3} & {11} & {13} & {4} \ \end{array}$

The mean is then calculated as:

$Mean = \frac{\sum fx}{\sum f}$

$Mean = \frac{54.5*4+62.5*3+70.5*11+78.5*13+86.5*4}{6+3+11+13+4}$

$Mean = \frac{2547.5}{37}$

$Mean = 68.9$ -- approximated

Solving (b): The sample variance:

This is calculated as:

$s^2 =\frac{\sum (x - \overline x)^2}{\sum f - 1}$

So, we have:

$s^2 =\frac{(54.5-68.9)^2+(62.5-68.9)^2+(70.5-68.9)^2+(78.5-68.9)^2+(86.5-68.9)^2}{37 - 1}$

$s^2 =\frac{652.8}{36}$

$s^2 =18.1$ -- approximated

5 0

3 years ago

Evaluate the line integral, where c is the given curve. C xeyz ds, c is the line segment from (0, 0, 0) to (2, 3, 4)

Arada [10]

The value of line integral is, 73038 if the c is the given curve. C xeyz ds, c is the line segment from (0, 0, 0) to (2, 3, 4)

<h3>What is integration?</h3>

It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.

The parametric equations for the line segment from (0, 0, 0) to (2, 3, 4)

x(t) = (1-t)0 + t×2 = 2t

y(t) = (1-t)0 + t×3 = 3t

z(t) = (1-t)0 + t×4 = 4t

Finding its derivative;

x'(t) = 2

y'(t) = 3

z'(t) = 4

The line integral is given by:

$\rm \int\limits_C {xe^{yz}} \, ds = \int\limits^1_0 {2te^{12t^2}} \, \sqrt{2^2+3^2+4^2} dt$

$\rm ds = \sqrt{2^2+3^2+4^2} dt$

After solving the integration over the limit 0 to 1, we will get;

$\rm \int\limits_C {xe^{yz}} \, ds = \dfrac{\sqrt{29}}{12} (e^{12}-1)$ or

= 73037.99 ≈ 73038

Thus, the value of line integral is, 73038 if the c is the given curve. C xeyz ds, c is the line segment from (0, 0, 0) to (2, 3, 4)

Learn more about integration here:

brainly.com/question/18125359

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7 0

2 years ago

Rename the number 780000 = 78

AfilCa [17]

<span>We need to rename the given number which is 780 000 into 78 ________.
=> But before we rename it, we need to find the value of 78
=> Since this is a 6 digit whole number, we have ones, tens, hundreds, thousands, ten thousands, hundred thousands.
=> 7 = hundred thousands
=> 8 = ten thousands
=> 7 hundred thousands + 8 ten thousands
=> Thus, the renamed of 780 000 is 7 hundred 8 ten thousands.

</span>

3 0

3 years ago

What is -3/11 divided by -5/6

Masja [62]

Answer:

0.00909090909

Step-by-step explanation:

8 0

3 years ago

Ms. Adler bought x bags of

OLga [1]

Answer:

Step-by-step explanation:

Number of bags = Total money spent / Cost of each bag

x = number of bags of chips

Simply divide 17.50 by 1.25 to work out how many bags of chips he can purchase.

Number of bags = Total money spent / Cost of each bag

$x = \frac{17.50}{1.25}$ = ?

8 0

3 years ago

Read 2 more answers