Suppose that your boss must choose three employees in your office to attend a conference in Jamaica. Because all 17 of you want to go, he decides that the only fair way is to draw names out of a hat. What is the probability that you, Anna, and Kevin are chosen? Enter a fraction or round your answer to 4 decimal places, if necessary.

We have found that: AB = (BD/2) * (XZ/AY) and we can solve for BD:

BD = 2 * AB * AY / XZ

What is triangle?

A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.

Since BD is a median of triangle ABC, it divides side AC into two equal parts. Let's label the midpoint of AC as M. Similarly, YW is a median of triangle XYZ and it divides side XZ into two equal parts, with the midpoint labeled as N.

Since AABC~AXYZ, we know that the corresponding sides are proportional. Thus,

AB/AX = AC/AY = BC/BZ

Since AB = BC (given that B is a vertex of both triangles), we have:

AB/AX = AC/AY

We can rewrite this equation as:

AB/AC = AX/AY ----(1)

Since BD is a median of triangle ABC, we have:

BD = 1/2 AC ----(2)

Similarly, since YW is a median of triangle XYZ, we have:

YW = 1/2 XZ ----(3)

From equation (1), we have:

AB/AC = AX/AY

Multiplying both sides by AC, we get:

AB = AX * (AC/AY)

Now, using equation (2), we can substitute AC/2 for BD:

AB = AX * BD/AY

Finally, using equation (3), we can substitute XZ/2 for YW:

AB = (BD/2) * (XZ/AY)

Therefore, we have found that:

AB = (BD/2) * (XZ/AY)

Hence, we can solve for BD:

BD = 2 * AB * AY / XZ

Note that we need to know the actual values of AB, AY, and XZ to find BD.

To learn more about triangle from the given link:

https://brainly.com/question/2773823

#SPJ1

Answer:A

Step-by-step explanation:

In the Neolithic Revolution, people formed civilizations.

Step-by-step explanation:

median :

first, arrange the numbers

= 9,11,13,37,48

then, determine the middle

= 13

mean :

mean = total numbers ÷ numbers

mean = (9 + 11 + 13 + 37 + 48) ÷ 5

= 118 ÷ 5

= 23.6

Answer:

t ≤ -3

Step-by-step explanation:

4t + 5 ≤ -7

4t ≤ -12

t ≤ -3

To estimate the amount of sales, x, will result in each of them earning the same amount for the week and we can set up the following equation:

T = R

825 + 0.06x = 1350 + 0.02x

Simplifying the equation, we get

x = 13125

We require a total of 13125 for the number of sales to maintain the same amount for Ramon and Teresa at the end of the week.

For this case, we can assume that the total salary for Teresa T is given by T = 825 + 0.06x

Where x represents the number of sales. And similarly the total salary of Ramon we have:

R = 1350 + 0.02x

We want to estimate the amount of sales, x, will result in each of them earning the same amount for the week and we can set up the following equation:

T= R

825 + 0.06x = 1350 + 0.02x

Multiply both sides by 100

\($825 \cdot 100+0.06 x \cdot 100=1350 \cdot 100+0.02 x \cdot 100$\)

82500 + 6x = 135000 + 2 x

Subtract 82500 from both sides

82500 + 6x - 82500 = 135000 + 2x - 82500

6x = 2x + 52500

Subtract 2x from both sides

6x - 2x = 2x + 52500 - 2x

4x = 52500

Divide both sides by 4

\($\frac{4 x}{4}=\frac{52500}{4}$\)

x = 13125

So then we require a total of 13125 for the number of sales to maintain the same amount for Ramon and Teresa at the end of the week.

To learn more about the value of x refer to:

https://brainly.com/question/16568278

#SPJ9

Answer:

it will be c because you see the points on the grid if its wrong my bad

Step-by-step explanation:

Step-by-step explanation:

Okay so, let's turn these into decimals first (rounded to nearest 2 thousandths).

2/3 = 0.66666 (repeating), to the nearest 2 thousandths would be 0.66.

-2 1/4 = -9/4 = -2.25

-1 1/2 = -3/2 = -1.5

then we set up the problem

0.66 × -2.25 × -1.5 = 2.2275 rounded 2.22 as an improper fraction 111/50 and that cannot be simplified any smaller.

The correct representations of the inequality –3(2x – 5) < 5(2 – x)  are:

B. - 6x + 15 < 10 - 5x and

D. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.

To solve this inequality, –3(2x – 5) < 5(2 – x), we will have to express the figures fully in which case the results will be: -6x + 15 < 10 -5x. When we collect like terms, we will have; -x < -5. On solving for x, we will arrive at the expression, x < 5.

If this result is expressed in a number line, there will be a bold line that starts from the number five and points to the right to show an increment. So, the two selected options are right.

Learn more about inequalities here:

https://brainly.com/question/24372553

#SPJ1

Step-by-step explanation:

If r is 1/6 then we'll have 1/4*1/6+7/24.

Firstly we will multiply 1/4 and 1/6 which will give us 1/24.

Then we will add 1/24 and 7/24 which will give us 8/24.

Then we reduce it to it's lowest term that is 1/3.TRY THIS.

A) The probability that a piece of toast lands butter side down when dropped from a 2.5-foot high table is 0.81 means that out of all possible outcomes of dropping a piece of toast from that height, 81% of the time it will land with the butter side facing down.

B) No, it does not mean that exactly 81 out of 100 pieces of toast will land butter side down. The probability of a single piece of toast landing butter-side down is 0.81, so when 100 pieces of toast are dropped, we can expect around 81 of them to land butter-side down on average, but the actual number may vary due to randomness.

C) Maria may or may not be surprised, depending on her expectations and the level of significance she sets for her test. To carry out a simulation, we can use a random number generator to simulate dropping 10 pieces of toast with a probability of 0.81 of landing butter side down. We can repeat this simulation multiple times, say 1000 times, and count the number of times the simulation yields 4 or fewer pieces of toast landing butter side down. If this rarely happens (e.g., less than 5% of the time), we can say that Maria should be surprised.

D) The dot plot displaying the results of 50 simulated trials of dropping 10 pieces of toast can provide some information about the variability of the outcomes. If most of the dots are clustered around 8 or 9 (which would correspond to 80% or 90% of the pieces of toast landing butter side down), then Maria's result of only 4 out of 10 pieces landing butter side down would be considered unusual, and she should be surprised. However, if the dots are spread over a wide range, it would suggest that getting 4 out of 10 is not that uncommon, and Maria should not be surprised.

To learn more about probability, visit here

https://brainly.com/question/30034780

#SPJ4

Answer:

Equal???

Step-by-step explanation:

Answer:

NO ANS

Step-by-step explanation:

The numbers could be:

6.45, 6.46, 6.47, 6.48, 6.49, 6.50, 6.51, 6.52, 6.53, and 6.54.

The place value of a number is given as:

Example:

1234.567

1 = thousand place value

2 = hundred place value

3 = tens place value

4 = ones place value

5 = tenths place value

6 = hundredths place value

7 = thousandths place value

We have,

Shawn rounded a number to the nearest tenth and got 6.5.

When he rounded it to the nearest whole number, he got 6.

Now,

The number = 6.45

Rounded to the nearest tenth = 6.5

Rounded to the nearest whole number = 6

The numbers can be 6.45, 6.46, 6.47, 6.48, 6.49, 6.50, 6.51, 6.52, 6.53, and 6.54.

Thus,

The possible numbers are:

6.45, 6.46, 6.47, 6.48, 6.49, 6.50, 6.51, 6.52, 6.53, and 6.54.

Learn more about place value here:

https://brainly.com/question/27734142

#SPJ1

Answer:

-4

Step-by-step explanation:

10 - 4x

Here  10  is the constant

In term -4x,  -4 is the coefficient

Answer:

-4 is the coefficient.

Step-by-step explanation:

We are given the expression:

\(\huge{10-4x}\)

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

A coefficient is a term that is multiplied by a variable.

In the expression given, '-4' is getting multiplied by 'x'.

This means that '-4' would be the coefficient in the equation.

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

Hope this helps.

Answer: -4x(x-2)(x+3)

Step-by-step explanation:

Answer:

y=5(cos 28)

Step-by-step explanation:

since the angle theta is given as 28°

the hypotenuse is given as 5

y is the adjacent

cos theta=adjacent/hypotenuse

cos28=y/5

y=5×cos28

y=5(cos 28)

Answer:

D. Quadrant IV

On the coordinate plane, you would go to the right two points, and then down 6, leading to quadrant IV

Answer:

The second is the answer

y= 1/2x+1

Step-by-step explanation:

Answer:

if no other cards had been drawn prior its 25%

The dividends per share for preferred stock for each year are: Year 1 - $1.25, Year 2 - $2.25, Year 3 - $3.25. The dividends per share for common stock for each year are all $0.

To determine the dividends per share for preferred and common stock for each year, we need to divide the total dividends by the number of shares for each type of stock.

Preferred Stock:

Dividends per share of preferred stock = Total dividends for preferred stock / Number of preferred shares

Year 1:

Dividends per share of preferred stock for Year 1 = $50,000 / 40,000 shares = $1.25

Year 2:

Dividends per share of preferred stock for Year 2 = $90,000 / 40,000 shares = $2.25

Year 3:

Dividends per share of preferred stock for Year 3 = $130,000 / 40,000 shares = $3.25

Common Stock:

Dividends per share of common stock = Total dividends for common stock / Number of common shares

Year 1:

Dividends per share of common stock for Year 1 = ($50,000 - Total dividends for preferred stock) / 100,000 shares = ($50,000 - $50,000) / 100,000 shares = $0

Year 2:

Dividends per share of common stock for Year 2 = ($90,000 - Total dividends for preferred stock) / 100,000 shares = ($90,000 - $90,000) / 100,000 shares = $0

Year 3:

Dividends per share of common stock for Year 3 = ($130,000 - Total dividends for preferred stock) / 100,000 shares = ($130,000 - $130,000) / 100,000 shares = $0

The dividends per share for preferred stock for each year are: Year 1 - $1.25, Year 2 - $2.25, Year 3 - $3.25. The dividends per share for common stock for each year are all $0.

for more questions on stock

https://brainly.com/question/18124452

#SPJ8

The graph that represents an exponential decay function is the second graph.

For you to determine which of the graphs represents an exponential decay, we will need to check the curve that passes through or lies on the x-axis.

we can draw a graph by putting the value of x and we are getting the value of y in this way we get the coordinates of a point

From both figures, we can see that the curve of the second graph almost lies on the x-axis as it curves downwards. This makes it an exponential decay function.

Hence the graph that represents an exponential decay function is the second graph.

Learn more on exponential here:

brainly.com/question/12940982

#SPJ4

complete question is

Which description matches the function represented by this graph?

A. exponential growth

B. linear growth

C. linear decay

D. exponential decay

Answer:

B or 2

Step-by-step explanation:

The answer above is correct.

For a line with a slope a and a known point (h, k), the point-slope form is:

y = a*(x - h) + k

A general linear equation can be written in slope-intercept form as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If we know that a line passes through a point (h, k), then the point-slope form of that line is:

y = a*(x - h) + k

Notice that particularly, the y-intercept can be written as (0, b), then the slope-intercept form is also a point-slope:

y = a*(x - 0) + b

y = a*x + b

Learn more about linear equations by reading:

https://brainly.com/question/1884491

#SPJ1

Answer:

See below

Step-by-step explanation:

r = 4*2 = 8

q = 4√3

p = q = 4√3

s = √(4√3)^2 + (4√3)^2) = √96 = 4√6

Answer:

assume male population = x then female = 8000 - x

New male pop = 1.1*x, New female pop = 1.08*(8000-x), new total pop = 1.09*8000

1.09*8000 = 1.1*x + 1.08*(8000-x)

> 8720 - 8640 = 0.02x

>x = 4000

The percent increase in the population will be 70.12%.

Consider the function:

y = a (1 ± r) ˣ

Where x is the number of times this growth/decay occurs, a = initial amount, and r = fraction by which this growth/decay occurs.

If there is a plus sign, then there is exponential growth happening by r fraction or 100r %

If there is a minus sign, then there is exponential decay happening by r fraction or 100r %

In 2012, the population of the town was 8,000 people. In 2017, the population was 11,400.

Then the percent increase in the population will be given as,

11,400 = 8,000× (1 + r)⁵

14.25 = (1 + r)⁵

1 + r = 1.701229

r = 0.7012

r = 70.12%

The percent increase in the population will be 70.12%.

More about the exponent link is given below.

https://brainly.com/question/5497425

#SPJ5

Answer: oh that's ava

Step-by-step explanation: ;w; I still don't know them-

Answer:

816

Step-by-step explanation:

also hazzy you can talk to me *hugs him* UwU dis ish toga btw

The results for each answer are given below.

It is the average value of the set given.

It is calculated as:

Mean = Sum of all the values of the set given / Number of values in the set

We have,

(a)

Mean.

= (290 + 190 + 175 + 165 + 155 + 155 + 140 + 140 + 140 + 140) / 10

= 165

(b)

We need to arrange the values in order.

140, 140, 140, 140, 155, 155, 165, 175, 190, 290

Now,

Median = 155

(c)

We need to find the value that appears most frequently in the data set.

140 appears four times.

So,

Mode = 140

(d)

We need to find the average of the smallest and largest values in the data set.

Midrange = (140 + 290) / 2

= 215

(e)

The results tell us that the net worth of celebrities is varying with a range of $150 million between the highest and lowest values.

The mean and median are both around $165 million, which suggests that the data is roughly symmetric.

The presence of mode at $140 million indicates that there may be a cluster of celebrities with this amount of net worth.

Thus,

The results for each answer is given above.

Learn more about mean here:

https://brainly.com/question/23263573

#SPJ1

Answer:

see below

Step-by-step explanation:

As sin(t) = -3 / 5 and in quadrant 4

so cos is positive

a) sin^2(t) + cos^2(t) = 1

(-3/5)^2 + cos^2(t) = 1

cos^2(t) = 1 - (9/25)

cos^2(t) = (25 - 9) / 25 = 16/25

cos(t) = +4/5

b) sin(2t) = 2 sin(t)cos(t)

= 2 * (-3/5) * (4/5)

= -24/25

c) cos(2t) = cos^(t) - sin^2(t)

= (4/5)^2 - (-3/5)^2

= 16/25 - 9 / 25

= 7 / 25

d) tan(2t) = sin(2t) / cos(2t)

= (-24/25) / (7/25)

= -24/7

e) as sin(2t) is negative and cos(2t) is positive

2t is in Quadrant 4

I am not sure for below three

f) cos(t) = cos^2(1/2 t) - sin^2(1/2 t) = 4/5

  cos^2(1/2 t) + sin^2(1/2 t) = 1

by adding and solving

1 + 4/5 = 2 * cos^2(1/2 t)

9/10 = cos^2(1/2 t)

cos(1/2 t) = +- 3/\(\sqrt{10}\)

and sin(t) = 2 * sin(1/2 t) * cos(1/2 t) = -3/5

2 * sin(1/2 t) * 3/sqrt{10} = -3/5

sin(1/2 t) = +- 1/sqrt{10}

means here sin and cos for 1/2 t should be opposite signs

so it is either 2nd or 4th quadrant

g) sin( 1/2 t) = +-1/sqrt{10}

h) cos(1/2 t) = +- 3/sqrt{10}

let's convert those $1.60 to pennies, that's 160 pennies, now, let's divide those 160 by (5 + 3) and distribute between the girls accordingly

\(\stackrel{Girl1}{5}~~ : ~~\stackrel{Girl2}{3} ~~ \implies ~~ \stackrel{Girl1}{5\cdot \frac{160}{5+3}}~~ : ~~\stackrel{Girl2}{3\cdot \frac{160}{5+3}} ~~ \implies ~~ \stackrel{Girl1}{5\cdot 20}~~ : ~~\stackrel{Girl2}{3\cdot 20} \\\\\\ \stackrel{Girl1}{100}~~ : ~~\stackrel{Girl2}{60}\qquad \textit{one girl got \underline{40 more cents } than the other girl}\)

Every point on a vertical line has the same x-value. Use the x-value of the point to find the equation of the vertical line.

Answer: X = 2