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3 years ago

ℜ 0, -180 is the same rotation as _______.

Mathematics

2 answers:

Kaylis [27]3 years ago

8 0

Answer:

option A) 0,180

Step-by-step explanation:

Given that there is a rotation of 0,-180. That is x is not rotated but y is rotated exactly 180 degrees clockwise.

A rotation is a type of transformation that takes each point in a figure and rotates it a certain number of degrees around a particular point sometimes origin.

Counterclockwise rotations are positive while clockwise rotations are negative.

WE know that 180 degrees clockwise and 180 degrees anticlockwise would give the same result as total angle around a point is 360 degrees.

Hence correct answer is option A) 0,180

OleMash [197]3 years ago

3 0

The correct answer is A. O, 180. I hope this helps.

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when jane uses her calling card overseas, the cost of a phone call is .75 for the first three minutes and. 12 for each additiona

artcher [175]

26 minutes, would = 3.51. if you add .12 to that it is 3.63.
so the most that she could talk would be 26 minutes.

7 0

3 years ago

According to the bar graph above, which salary range is the least frequent?

Elis [28]

9514 1404 393

Answer:

D. $101,000 – $120,000

Step-by-step explanation:

The bar graph is not completely labeled, but in the context of the question it seems safe to assume that the vertical scale can be considered to represent relative frequency.

So, the shortest bar is the one with the lowest frequency. The horizontal scale identifies that as 101-120. If we assume that is salary in thousands of dollars, then Choice D is appropriate.

5 0

3 years ago

To make iced tea, 5 tea bags can be added to 1 gallon of water. Find how many bags can be used for 4 gallons of water

Nata [24]

Answer:

20 tea bags

Step-by-step explanation:

if 5 is 1 gallon then you do 5x4=20

4 0

3 years ago

Some types of algae have the potential to cause damage to river ecosystems. Suppose the accompanying data on algae colony densit

Phantasy [73]

Answer:

$y=-2.95836 x +234.56159$

Step-by-step explanation:

We assume that th data is this one:

x: 50, 55, 50, 79, 44, 37, 70, 45, 49

y: 152, 48, 22, 35, 43, 171, 13, 185, 25

a) Compute the equation of the least-squares regression line. (Round your numerical values to five decimal places.)For this case we need to calculate the slope with the following formula:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

So we can find the sums like this:

$\sum_{i=1}^n x_i =50+ 55+ 50+ 79+ 44+ 37+ 70+ 45+ 49=479$

$\sum_{i=1}^n y_i =152+ 48+ 22+ 35+ 43+ 171+ 13+ 185+ 25=694$

$\sum_{i=1}^n x^2_i =50^2 + 55^2 + 50^2 + 79^2 + 44^2 + 37^2 + 70^2 + 45^2 + 49^2=26897$

$\sum_{i=1}^n y^2_i =152^2 + 48^2 + 22^2 + 35^2 + 43^2 + 171^2 + 13^2 + 185^2 + 25^2=93226$

$\sum_{i=1}^n x_i y_i =50*152+ 55*48+ 50*22+ 79*35+ 44*43+ 37*171+ 70*13+ 45*185+ 49*25=32784$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=26897-\frac{479^2}{9}=1403.556$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}=32784-\frac{479*694}{9}=-4152.22$

And the slope would be:

$m=-\frac{-4152.222}{1403.556}=-2.95836$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{479}{9}=53.222$

$\bar y= \frac{\sum y_i}{n}=\frac{694}{9}=77.111$

And we can find the intercept using this:

$b=\bar y -m \bar x=77.1111111-(-2.95836*53.22222222)=234.56159$

So the line would be given by:

$y=-2.95836 x +234.56159$

7 0

2 years ago

Suppose a couple planned to have three children. Let X be the number of girls the couple has.

sesenic [268]

Answer:

a) {GGG, GGB, GBG, BGG, BBG, BGB, GBB, BBB}

b) {0,1,2,3}

$P(X=2) = \dfrac{3}{8}$

$P(\text{3 boys}) = \dfrac{1}{8}$

Step-by-step explanation:

We are given the following in the question:

Suppose a couple planned to have three children. Let X be the number of girls the couple has.

a) possible arrangements of girls and boys

Sample space:

{GGG, GGB, GBG, BGG, BBG, BGB, GBB, BBB}

b) sample space for X

X is the number of girls couple has. Thus, X can take the values 0, 1, 2 and 3 that is 0 girls, 1 girl, 2 girls and three girls from three children.

Sample space: {0,1,2,3}

c) probability that X=2

P(X=2)

That is we have to compute the probability that couple has exactly two girls.

$\text{Probability} = \displaystyle\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$

Favorable outcome: {GGB, GBG, BGG}

$P(X=2) =\dfrac{3}{8}$

d) probability that the couple have three boys.

Favorable outcome: {BBB}

$P(BBB) = \dfrac{1}{8}$

8 0

3 years ago