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3 years ago

Is (x-4, y-11) reflection flip rotation or turn, translation, slide or dilation

Mathematics

1 answer:

Keith_Richards [23]3 years ago

4 0

Translation- you subtract 4 from the given x-coordinate and subtract 11 from the given y-coordinate.

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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

Convert 65,000,000 to scientific notation please help!!

Mice21 [21]

You have to move the decimal point from the end to between the 6 and 5 then count how many spaces you moved it because this will become the power on the 10.
6.5 x 10^7

3 0

4 years ago

Sin x = - 1/2 where (-360 < x < 360)

dimulka [17.4K]

Answer:

-30, 210 and 330 degrees

Step-by-step explanation:

Given the expression Sin x = - 1/2

x = arcsin(-1/2)

x = -30 degrees

Since sin is negative in the third and fourth quadrant

x = 180 + 30

x = 210 degrees

In the fourth quadrant

x = 360 - 30

x = 330

Hence the value of x within the interval -360 < x < 360 are -30, 210 and 330 degrees

3 0

3 years ago

Find the diameter of a cone that has a volume of 104.67 cubic inches and a height of 4 inches. Use 3.14 for pi. 4 inches 6 inche

aleksandr82 [10.1K]

V: volume of a cone = (πr²h)/3 = 104.67 in³
π: pi = 3.14
r: radius = 1/2 diameter = [unknown]
h: height = 4 in

V = (πr²h)/3
V = r²(πh)/3

r² = (3V)/(πh)
r² = (3 ×104.67)/(3.14 × 4)
r² = 25

r = √25
r = 5 (but remember the radius is only 1/2 the diameter)

thus . . .

d = 10 in 

8 0

3 years ago

Read 2 more answers

A spherical balloon is inflated so that its volume is increasing at the rate of 3 ft3/min. How fast is the diameter of the ballo

beks73 [17]

When an spherical balloon volume is increasing at the rate of $3ft^3/min$ then the diameter of the balloon is increasing $\frac{3}{2\pi }ft /min$