MATHEMATICS HIGH SCHOOL

Using the figure on the left, what is the measure of

Answers

Answer 1

Answer:

Answer:

c = 30°

d = 60°

Step-by-step explanation:

Angle ZWC is a 90° angle

Angle YWX is a 60° angle

add them together and you get 150°

180 - 150 = c = 30°

c + d + 90° = 180°

substitute

30° + d + 90° = 180°

combine like terms

120° + d = 180°

subtract 120° from both sides

d = 60°

hope this helps!!

Answer 2

Answer:

Answer:

c is 30 and d is 60

Step-by-step explanation:

I did it for hw

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What is 12 percent of 120?

Answers

12% of 120 is 14.4

Change the percentage into a decimal by dividing over 100:

12 / 100 = 0.12

Multiply:

0.12 × 120 = 14.4

Answer:

$12\% \: of \: 120 \n (12)/(100) * 120 \n (1440)/(100) \n \boxed{14.4}$

Which of the the following could be the ratio between the lengths of the two legs of a 30-60-90?Check all that apply. (A)Sqrt2:Sqrt3 (B)1:Sqrt2 (c)Sqrt2:Sqrt2 (D)2Sqrt3:Sqrt6 (E)1:Sqrt3 (F)Sqrt3:Sqrt3

Answers

This is worth remembering:

In a 30-60-right triangle,
-- the side opposite the 30 is 1/2 the hypotenuse
-- the side opposite the 60 is (1/2 the hypotenuse) times (square root of 3).

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I believe Choice-'E' is the only one you could make with the above rule.

$(a)/(a √(3) ) = (1)/( √(3) ) \ \ \ \Rightarrow\ \ \ Ans.\ E\n\n(2a)/(a √(3) ) = (2)/( √(3) )=(2\cdot √(2) )/( √(3)\cdot √(2) )=(2 √(2) )/( √(6) ) \neq (2 √(3) )/( √(6) ) \n\n (a)/(2a ) = (1)/( 2 )$

PLEASE HELP !The graph shows the ages of different concertgoers who have backstage passes.

Which statement is true about the graph?

A) A late arrival who is 21 years old with a back-stage pass will make the mean greater than the median.
B) The two holders of back-stage passes whose ages are above 40 make the mean age higher than the median age.
C) The ages of concert-goers with backstage passes are skewed left, so the mean age is less than the median age.
D) A concert-goer who is 18 years old and wins a back-stage pass will pull the mean more than 2 years less than the median.

Answers

In the given graph, we calculate the mean by dividing the product of the midpoint of each age interval and the frequency by the total frequency. Mean = [13.5(3) + 16.5(6) + 19.5(8) + 22.5(6) + 25.5(5) + 28.5(4) + 31.5(3) + 43.5 + 46.5] / (3 + 6 + 8 + 6 + 5 + 4 + 3 + 1 + 1) = 856.5 / 37 = 23.15 The median is given by the middle age interval (i.e. the age interval which falls in the (37 + 1) / 2 = 38 / 2 = 19th position) which is the 21 - 24 age inteval. To get the value of the median we use the formular Median = L1 + C[n/2 - summation (Fl)] / Fm where: L1 is the lower class boundary of the median class, C is the class size, n is the total frequency, summation (Fl) is the summation of all frequencies below the mediam class and Fm is the median class frequency. Median = 21 + 4[37/2 - (3 + 6 + 8)] / 6 = 21 + 4[18.5 - 17] / 6 = 21 + 4(1.5) / 6 = 21 + 6 / 6 = 21 + 1 = 22. Thus the mean of 23.15 is greater than the median of 22. Calculating the mean without the two numbers above 40 gives Mean = (856.5 - 43.5 - 46.5) / 35 = 766.5 / 35 = 21.9 Therefore, the statement that is true about the graph is "The two holders of back-stage passes whose ages are above 40 make the mean age higher than the median age." (option B)

The two holders of back-stage passes whose ages are above 40 making the mean age higher than the median age is correct about the graph.

What is a Graph?

This can be defined as pictorial representation of data or values in an organized manner.

From the graph we can calculate mean.

Mean = [13.5(3) + 16.5(6) + 19.5(8) + 22.5(6) + 25.5(5) + 28.5(4) + 31.5(3) + 43.5 + 46.5] / (3 + 6 + 8 + 6 + 5 + 4 + 3 + 1 + 1)

= 856.5 / 37

= 23.15

Median = (37 + 1) / 2 = 38 / 2 = 19th position between 21 - 24 age interval. Median = L1 + C[n/2 - summation (Fl)] / Fm

where L1 = lower class boundary of the median class, C = class size, n = total frequency, summation (Fl) = summation of all frequencies below median class, Fm= median class frequency.

Median = 21 + 4[37/2 - (3 + 6 + 8)] / 6

= 21 + 4[18.5 - 17] / 6

= 21 + 4(1.5) / 6

= 21 + 6 / 6 = 21 + 1 = 22.

Mean of 23.15 is greater than the median of 22.

Mean without two numbers above 40

= (856.5 - 43.5 - 46.5) / 35 = 766.5 / 35 = 21.9.

Therefore the two holders of back-stage passes whose ages are above 40 make the mean age higher than the median age which makes option B the most appropriate choice

Read more about Graph here brainly.com/question/25184007

What is the equation of the line that passes through (1, 2) and is parallel to the line whose equation is 4x + y - 1 = 0?

Answers

Answer: The required equation of the line is $4x+y=6.$

Step-by-step explanation: We are given to find the equation of the line that passes through (1, 2) and is parallel to the line whose equation is as follows:

$4x+y-1=0~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

The slope-intercept form of the given line (i) is

$4x+y-1=0\n\n\Rightarrow 4x+y=1\n\n\Rightarrow y=-4x+1,$

where, slope of the line is, m = - 4.

Since parallel lines have equal slopes, so the slope of the new line that passes through the point (1, 2) is

m = - 4.

Therefore, the equation of the line will be

$y-2=m(x-1)\n\n\Rightarrow y-2=-4(x-1)\n\n\Rightarrow y-2=-4x+4\n\n\Rightarrow 4x+y=6.$

Thus, the required equation of the line is $4x+y=6.$

y=-4x+6
or if you need it in the original format
4x+y-6=0

In a small company of 10 people the salaries are as follows: 5 people earn $25,000, 3 earn $27,000, 1 earns $34,000, and the owner earns $60,000 What is the mean and standard deviation (to the nearest dollar) of their salaries?Mean salary: $________a0

Standard Deviation: $_________a1

Answers

Answer:

The mean is 30000 and standard deviation is 9746.79.

Step-by-step explanation:

Formula of mean

$Mean=\bar{x}=(\sum x_i)/(n)$

Formula of standard deviation:

$S.D.=\sigma=\sqrt{\frac{\sum{(x-\bar{x})^2}}{n}}$

Using the below table.

$Mean=\bar{x}=30000$

$S.D.=\sigma=9746.794345\approx 9746.79$

Therefore the mean is 30000 and standard deviation is 9746.79.

The mean is 30,000

The standard deviation is 10,893.42

What do you mean by a0 and a1?

Which inequality is represented by this graph?

Answers

Answer: Choice B. $y \le -(1)/(3)x+1$

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Explanation:

We need to know the equation of the boundary line. This boundary goes through (0,1) and (3,0). Find the slope of the line through these points

m = (y2-y1)/(x2-x1)

m = (0-1)/(3-0)

m = -1/3, negative slope means the line goes downhill as we move from left to right.

The y intercept is b = 1 as this is where the boundary crosses through the y axis

y = mx+b turns into y = (-1/3)x+1 after replacing m and b with m = -1/3 and b = 1 respectively.

The equation of the boundary line is y = (-1/3)x+1

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The shading is below the boundary, so we'll have a "less than" sign involved here. More specifically, we'll have a "less than or equal to" sign because the boundary is a solid line rather than a dashed one. A solid line tells us "points on the boundary are part of the solution set". The inclusion is because of the "or equal to" portion.

Change the equal sign to a less than or equal to sign to get the final answer of $y \le -(1)/(3)x+1$ which is choice B.