Over the past month, a hairstylist has had 49 female clients and 21 male clients. What is the ratio of male clients to female clients for this hairstylist?

Answers

Answer 1

The ratio is 21:49, 21/49, or 21 to 49

Answer 2

The ratio of male clients to female clients for the hairstylist is 21:49, which simplifies to 3:7 after dividing both numbers by the GCD of 7.

The question asks to find the ratio of male clients to female clients for a hairstylist. In this scenario, the hairstylist has had 49 female clients and 21 male clients. To find the ratio of male to female clients, we compare the number of male clients to the number of female clients.

The ratio is expressed as male clients : female clients. Thus, the ratio of male clients to female clients is:

21 male clients : 49 female clients

To simplify the ratio, we find the greatest common divisor (GCD) of 21 and 49, which is 7. Dividing both numbers by 7, we get:

3 male clients : 7 female clients

Related Questions

What is the following product? 3 sqrt d x 3 sqrt d x 3 sqrt d

Answers

[tex]\bf 3\sqrt{d}\times 3\sqrt{d}\times 3\sqrt{d}\implies (3)(3)(3)\sqrt{d\times d\times d}\\\\\\ 27\sqrt{d^2d}\implies 27d\sqrt{d}[/tex]

Answer: the first option, d.

Step-by-step explanation:

Which simplified equation is equivalent to the equation shown below?
4x+x-3-9+4x=6

a.5x-8=6

b.-3x=6

c. 9x-12=6

d. 8x-12=6

Answers

4x+x-3-9+4x=6
9x-12=6
Answer C

We need to group the like terms and combine like terms to get the simplified equation.

[tex] 4x+x-3-9+4x=6\\ \\ Step \; 1: \; Group \; like\; terms\\ \\ 4x+x+4x-3-9=6\\ \\ Step \; 2: \; Combine \; like\; terms\\ \\ 9x-12=6 [/tex]

Conclusion:

Option C is the right answer !!

The percentage of high school students who drink and drive stood at 17.5% at the beginning of 2001 and declined linearly to 10.3% at the beginning of 2011.† (a) find a linear function f(t) giving the percentage of high school students who drink and drive in year t, where t = 0 corresponds to the beginning of 20

Answers

1) The linear function : f(t) = -0.72t + 17.5

2) When t = 14 the value is 7.42

Part A

For this case we have the following information given:

t= 2001 (0) f(0)= 17.5%

t= 2011 (10) f(10)= 10.3

Slope= [tex]\frac{10.3-17.5}{10-0}[/tex]

10.3 = -0.72*10 +b

b= 10.3 +10*0.72

= 17.5

Then the equation is:

f(t) = -0.72t + 17.5

Part B

For 2015 the value of t = 2015-2001

= 14

Substitute in function,

f(14)= -0.72×14 + 17.5

= 7.42

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Complete question:

The percentage of high school students who drink and drive was 17.5% at the beginning of 2001 and declined linearly to 10.3% at the beginning of 2011.†(a) Find a linear function f(t) giving the percentage of high school students who drink and drive in year t, where t = 0 corresponds to the beginning of 2001.f(t) = (b) If the trend continued, what was the percentage of high school students who drank and drove at the beginning of 2015? %

Final answer:

To find the linear function that represents the percentage of high school students who drink and drive in a given year, we can use the slope-intercept form of a linear equation. We can determine the slope and y-intercept by using the given data points. The linear function is f(t) = -0.82%t + 17.5%.

Explanation:

To find a linear function f(t) giving the percentage of high school students who drink and drive in year t, we can use the slope-intercept form of a linear equation, which is y = mx + b. In this case, y represents the percentage of students who drink and drive, and t represents the year. We know that at the beginning of 2001 (t=0), the percentage was 17.5%, and at the beginning of 2011 (t=10), the percentage was 10.3%. Using this information, we can find the slope (m) and the y-intercept (b) of the linear function.

Step 1: Calculate the slope (m):

m = (y2 - y1) / (t2 - t1) = (10.3% - 17.5%) / (10 - 0) = -0.82% per year.

Step 2: Substitute one of the points and the slope into the slope-intercept form to find the y-intercept (b). Using the point (0, 17.5%):

17.5% = -0.82%(0) + b

b = 17.5%.

Therefore, the linear function f(t) is: f(t) = -0.82%t + 17.5%.

which of the following is equivalent to the polynomial below

Answers

Try this solution:
1. to find the roots of the equation (D=-36):
[tex] \left[\begin{array}{ccc}x=5+6i\\ x=5-6i\end{array}\right[/tex]
2. to simplify the polinom:
x²-10x+61=(x-(5-6i))(x+(5+6i))
Answer: 1

1.The sales tax rate in a certain state is 8%. How much would you pay in total for a taxable item that costs $25.25?

2.Alicia answered 20 out of 25 problems correctly on a test. What percent did she get correct?

3.Jim bought a fishing rod for $42. This price was 70% of the original price. What was the original price?

4.An auctioneer sold items totaling $42,000. If her rate of commission was 7%, what was her income from commissions?

5.At a local hardware store, Ms. Jones learned that 1 would cost her $.50, 12 would cost $1.00, and the price of 144 would be $1.50. What was Ms. Jones buying?

6.People sometimes use credit cards to purchase items they can’t afford to pay for at the moment of purchase. If you’re one of these people, you should know that the monthly finance charge on credit purchases is based on percent. Let’s say you have an outstanding balance of $800 on your credit card. The credit card company charges 1.6% per month. What finance charge will you have to pay for one month?

Answers

For numbers 1, 2, 3, 4, and 6 you just need to remember this formula:

P = r x b
where: P = Percentage (Portion)
r = rate
b = base amount

1. Your given for number 1 is as follows:

rate = 8%
Base amount = $25.25

You are looking for how much you would pay in total. First you need to find out how much your going to pay in taxes, based on the base amount. To get that, you need to convert the rate in its decimal form by dividing it by 100.

rate = 8/100 = 0.08

Next you need to find how much you will pay in taxes, you can do that by using the formula:

P = r x b
= 0.08 x $25.25
= $2.02 This is how much you will pay in taxes.

To get the total amount you will pay, just add it to the original price:

$25.25 + $2.02 = $27.27

2. Your given will be:
p = 20
b = 25
r = ?

All you have to do is input what you know in the formula:

P = r x b
20 = r x 25

Transpose the 25 to the other side of the equation to get the rate and divide:

20/25 = r
0.8 = r

For this case it is asking for the rate in percent, all you need to do is multiply your computed rate by 100% and you will get 80%.

3. If your given would be:

P = $42.00
r = 70%
b = ?

Base is the unknown here, because you are looking for the original price. So we put this into our equation again:

$42.00 = 0.70 x b

Transpose the 0.70 to the other side of the equation again and divide:

$42.00/0.70 = $60.00

The original price was $60.00

4. The given would be:

P = ?
r = 7% or 0.07
b = $42,000

We are looking for how much he got, or the portion he got, so we are looking for the percentage. Input what you know into our formula:

P = 0.04 x $42,000
= $2,940.00

6. Your given would be as follows:
P = ?
r = 1.6% or 0.016
b = $800

You are looking for how much you would pay in finance charge, or the portion that will be added, based on your base amount so you will be looking for the percentage. Input your given into the formula:

P = 0.016 x $800
= $12.80

As for number 5, that is a trick question. The prices are different and no matter what formula you will use, you will not come up with a mathematical sound answer. Consider the situation, what can you buy in local hardware store that has 1, 12, and 144? The answer is HOUSE NUMBERS.

1. $27.27
2. 80%
3. $60
4. $2,940
5. Ms. Jones was buying house numbers. Her house number was 112144. Each separate number would cost $.50. Therefore, the number 1 would cost $.50, the numbers 1 and 2 (12) would cost $1.00, and the numbers 1, 4, and 4 (144) would cost $1.50.
6. $12.80

The length of a rectangle if the length is twice the size of the width increased by one

Answers

the correct question is
The length of a rectangle if the length is twice the size of the width increased by 1 is it one of the following answers:
A) l= 2w-1
B) l= 2w+1
C) l= 3w
D) none of the choices given

Let
l--------------> length of a rectangle
w-------------> width of a rectangle

we know that
if the length is twice the size of the width increased by 1
l=2w+1

the answer is the option B) l= 2w+1

Which triangle is it ?

Answers

the answer in attached figure

we know that
sin(30°)=0.5 cos(30°)=√3/2
sin(60°)=√3/2 cos(60°)=0.5

sin(60)=BC/AC=5√3/10=√3/2-------------- is ok
cos (60)=AB/AC=5/10=0.5---- is ok

sin(30)=BA/AC=5/10=0.5-------------- is ok
cos (30)=BC/AC=5√3/10=√3/2-------------- is ok

if angle B is 90°
then
AB²+BC²=AC²------------> 5²+(5√3)²=10²=(25+75)=100------------- > is ok

the solution in the attached figure

The scale on a map is 1 cm:35 mi. The distance on the map between Los Angeles, CA, and San Francisco, CA, is 10.8 cm. What is the actual distance between Los Angeles and San Francisco?

Answers

It is 378 miles. :)
this is answer

Step 1: Let us assign variable for the unknown that we need to find.

' x ' be the actual distance between Los Angeles and San Francisco

Step 2: Set up an equation based on the given statement "The scale on a map is 1 cm:35 mi. The distance on the map between Los Angeles, CA, and San Francisco, CA, is 10.8 cm."

[tex] \frac{distance \; in \; cm}{distance\; in\; miles}=\frac{1}{35}=\frac{10.8}{x} \\ \\ Cross \; Multiply\\ \\ 1 \cdot x = 35 \cdot 10.8\\ \\ x = 378 [/tex]

Conclusion:

The actual distance between Los Angeles and San Francisco is 378 miles.

1. A rectangular prism is defined as the drawing shows. Note B at (0, 5, 0) and F (0, 0, 4). The prism is reflected over the xz-plane. The reflected image is then translated 2 units back, 3 units left, and 1 unit up.
a.) Show the results of your calculations for points A, B, C and D from the reflection.
b.) Show the results of your calculations for points A, B, C and D from the translation.

Answers

Initial coordinates:
A (0,0,0)
B (0,5,0)
C (3,5,0)
D (3,0,0)
E (3,0,4)
F (0,0,4)
G (0,5,4)
H (3,5,4)

a.) The prism is reflected over the xz-plane.
Reflection Point P(x,y,z) over the xz-plane is P'(x,-y,z):
Reflection P(x,y,z) over the xz-plane → P'(x,-y,z)

Reflection A(0,0,0) over the xz-plane → A'(0,-0,0) = A'(0,0,0)
Reflection B(0,5,0) over the xz-plane → B'(0,-5,0)
Reflection C(3,5,0) over the xz-plane → C'(3,-5,0)
Reflection D(3,0,0) over the xz-plane → D'(3,-0,0) = D'(3,0,0)

b.) The reflected image is then translated 2 units back, 3 units left, and 1 unit up.
Translation P'(x,-y,z) 2 units back, 3 units left, and 1 unit up is P''(x-2,-y-3,z+1):
Translation P'(x,-y,z) → P''(x-2,-y-3,z+1)

Translation A'(0,0,0) →A''(0-2,0-3,0+1) = A''(-2,-3,1)
Translation B'(0,-5,0) →B''(0-2,-5-3,0+1) = B''(-2,-8,1)
Translation C'(3,-5,0) →C''(3-2,-5-3,0+1) = C''(1,-8,1)
Translation D'(3,0,0) →D''(3-2,0-3,0+1) = D''(1,-3,1)

8. The U.S. population was 309 million in 2010. If the U.S. had had the same firearm death rate as Australia in 2010, how many firearm deaths would the U.S. have expected to have that year? Australia’s population was 22.3 million people in 2010. Australia had 236 firearm deaths in 2010. (round to the nearest person)

Answers

To answer this question I would use ratios . I would set this up as 236 deaths/22.3 million people = x number of deaths/ 309 million people. You could use cross products to solve for x. 309 x 236= 22.3x. 72924= 22.3x. Divide both sides by 22.3 to solve for X, or the number of deaths in the US. X = 3270 deaths. Another way to figure this out would be to figure out how many groups of 22.3 million Australian people there are in 309 million Americans. This factor would then be multiplied by 236 to get the number of deaths in the United States. The answer would be the same.

As per linear equation, in 2010 the expected firearm death U.S. had is 3270.

What is a linear equation?

A linear equation represents an equation that has one or multiple variables with the highest power of the variable is 1.

Australia’s population was 22.3 million people in 2010.

Australia had 236 firearm deaths in 2010.

Therefore, portion of Australian population had firearm deaths is

[tex]= \frac{236}{22.3(10)^{6} } \\= 0.000011[/tex]

The U.S. population was 309 million in 2010.

Therefore, the expected firearm deaths in U.S. in 2010 was

[tex]= (309) (10^{6}) (0.000011)\\= 3270.13\\= 3270[/tex]

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1.Write equatios to represent the distances the family drove on the given days.

2. construct a math argument to explain why your answer to 5 is correct.

3. How can you check that your answer is reasonable?

Answers

equations are (174+106) (112+165) (121+168) (172+113)
i think this is correct because you need morning and evening combined to know a exact answer.
you can check this by calculating you equations and u will end up with Wednesday as the longest amount of miles

How to start the problem off. (substitution)

Answers

Do you have to use substitution?

A triangle has one 60 degree angle and one 20 degree angle. The third angle in the triangle must be
a.acute
b.obtuse
c.commplementary
d.straight

Answers

The 3rd angle has to be b. obtuse because a triangle's angles must add to 180°. 20° and 60° add to 80, and you must have a 100° for them to add to 180°. Any angle above 90° is known as an obtuse angle, so that's your answer.

A triangle on a coordinate plane is translated according to the rule T–3, 5(x, y). Which is another way to write this rule?

(x, y) → (x – 3, y + 5)
(x, y) → (x – 3, y – 5)
(x, y) → (x + 3, y – 5)
(x, y) → (x + 3, y + 5)

Answers

we have that

the original (x,y) coordinates are being moved to the left by 3 units and up by 5 units.

therefore
the answer is the option
(x, y) → (x – 3, y + 5)

Another way to write the given rule is (x, y) → (x – 3, y + 5).

Given that,

There are the original x and y coordinates that are being moved to the left-hand side by 3 units and go up by 5 units.

Based on the information, we can conclude that another way to write the given rule is (x, y) → (x – 3, y + 5).

Hence, the other options are incorrect.

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Evaluate g(n-5) if g(x)=x^2-6/2x

Answers

g(x) = (x^2-6) / 2x

g( n-5) = ( [n-5]^2 -6) / 2(n-5)

= ( n^2 -10n +25 -6 ) / 2(n-5) or ( n^2 -10n +25 -6 ) / (2n-10)
Your Answer

I did foil first and got n^2-10n+25
then did 25-6 to get 19.
so n^2-10n+25 is on top.////// should have been n^2 -10n +19
and the bottom is 2(n-5) so I distributed the 2 and got 2n-10

so n^2-10n+25
2n-10
= (n^2 -10n +19) / 2(n-5)

Answer: We want to evaluate g(x) in x = n -5, where g(x) = (x^2-6)/2x

then, doing it step by step: [tex]g( n- 5)= \frac{(n-5)^{2} - 6 }{2*(n-5)}= \frac{(n^{2} - 2*5*n + 25) - 6 }{2n - 10} = \frac{n^{2} - 10n + 19 }{2n - 10}[/tex]

where i used that (a - b)^2 = a^2 -2ab + b^2

So the correct option is C.

the average airspeed velocity of an unladen European swallow is approximately 24 miles per hour at this rate how many hours will it take to swallow to fly from Appin to Glen Coe about 18 Miles??

Answers

We can set this up as:
[tex]x = \frac{18}{24} = 0.75 [/tex]

So, it would take him:
[tex]0.75(60) = 45[/tex]

So, it will be 45 mins.

It will take the swallow approximately 3/4 of an hour to fly from Appin to Glen Cove.

The answer should be a fraction

Answers

ok so 40y2/50y3.... you are going to cancel out the common factor (10)

4y2/5y3..
now apply the exponent rule, which is : xa /xb = 1/ xb-a

so...y2/y3 = 1/ y3 - 2 = 1/y

ANSWER : 4/5y

Hello! : )

The correct answer to your question is... [tex] 2^{3} y^{5} [/tex]

Evidence:
Step 1: Simplify [tex] y^{2} [/tex]/5

( 40 multiplied by [tex] y^{2} [/tex]/5 multiplied by [tex] y^{3} [/tex] )

Step 2: [tex] y^{2} [/tex] multiplied by [tex] ^{3} [/tex] = y(2 + 3) = [tex]y^{5} [/tex]

So the correct answer is... [tex] 2^{3} y^{5} [/tex]

I hope this helped! : )
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Please mark as Brainliest!

Have a wonderful day! : )

3/4,19/20,1/6,3/5,8/15 what is lcd

Answers

You just have to find the lcm or least common factors of the denominators which is 60.

The least common multiple of denominators
.. 4 = 2^2
.. 5
.. 6 = 2*3
.. 15 = 3*5
.. 20 = 2^2*5
is 2^2*3*5 = 60

The lowest common denominator is 60.

If you take out a loan that costs $130.50 over nine years at an interest rate of 10%, how much was the loan for?

Answers

Final answer:

The original loan amount for which the final amount payable is $130.50 over nine years at an interest rate of 10% was approximately $55.39.

Explanation:

To find out the original amount of the loan for which the final amount payable is $130.50 over nine years at an interest rate of 10%, we will use the formula for the present value of a loan.

The formula given is P = A / (1 + r/n)^nt, where P is the principal (initial loan amount), A is the final amount, r is the annual interest rate (expressed as a decimal), n is the number of times that interest is compounded per year, and t is the time the money is borrowed for in years.

As the question doesn't specify how many times the interest is compounded per year, we will assume it is compounded once a year (n=1).

We have:

A = $130.50,r = 10% or 0.10,n = 1,t = 9 years.

Plugging these values into the formula:

P = $130.50 / (1 + 0.10/1)^(1*9)

P = $130.50 / (1 + 0.10)^9

P = $130.50 / (1.10)^9

P = $130.50 / 2.35794769

P = $55.39 approximately

Therefore, the original loan amount was approximately $55.39.

What is the value of x?

Enter your answer in the box.

x=

Answers

The angles have equal measure because they are vertically opposite angles.

3x + 50 = 6x - 10
3x - 6x = -10 - 50
-3x = -60
x = 20

The answer is x=20.

what is the word form and the expanded form of 427.968?

Answers

The word form for this number is "Four hundred twenty-seven and nine hundred sixty-eight thousandths", and the expanded form of this number is:
400 + 20 + 7 + .900 + .060 + .008

I hope this helps!

The word form is four hundred twenty-seven and nine hundred sixty-eight thousandths, and the expanded form is 400 + 20 + 7 + 0.900 + 0.060 + 0.008

The number is given as: 427.968

To expand, we make use of the addition arithmetic operator.

So, we have:

[tex]\mathbf{427.968 = 400 + 20 + 7 + 0.900 + 0.060 + 0.008}[/tex]

Hence, the expanded form of 427.968 is 400 + 20 + 7 + 0.900 + 0.060 + 0.008

In the expanded form above, we have the following numbers:

400 - Four hundreds.20 - Twenty.7 - Seven.0.900 - Nine tenths.0.0600 - Six hundredths.0.008 - Eight thousandths.

Combine the above words to give four hundred twenty-seven and nine hundred sixty-eight thousandths.

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HELP PLEASE
Translate the answer, T2 = A3, into words:

The BLANK of the orbital period, T, of a
planet is equal to the BLANK of the average distance, A, of the planet from the Sun.

Square
Square Root
Cube

Answers

SQUARE and CUBE are the answers i just did it.

Answer: The square of the orbital period, T, of a planet is equal to the cube of the average distance, A, of the planet from the Sun.

Step-by-step explanation:

In mathematics, A number or variable 'a' to its second power is said to be square of 'a' i.e. [tex]\ a^2[/tex] is the square of a.

A number or variable 'b' to its third power is said to be cube of 'b' i.e. [tex]\ b^3[/tex] is the cube of b.

In the given equation: [tex]T^2 = A^3[/tex]

Here, [tex]T^2 [/tex] is square of T.

And [tex]A^3[/tex] is cube of A.

Therefore, The square of the orbital period, T, of a planet is equal to the cube of the average distance, A, of the planet from the Sun.

Can you answer this one for my plz I need before Monday ty

Answers

Since you need the vertex, and knowing the vertex will tell you the axis of symmetry, it is convenient to put the equation in vertex form.
.. -x^2 -4x +1
.. = -(x^2 +4x) +1
.. = -(x^2 +4x +(4/2)^2) +1 -(-(4/2)^2) . . . . complete the square
.. = -(x +2)^2 +5

The vertex is (-2, 5).
The axis of symmetry is x = -2.

A circular city park has a sidewolk directly through the rmiddle that is 111- feet long. I each bag of fertilizer covers 50 square feet, then determine how many bags of tertilizer the Parks and Recreation department needs to use to cover the circular park. Ignore oll the sidewalks around and through the park.

Answers

The area of a circle with a diameter of 111 ft is
.. A = (π/4)d^2
.. = (π/4)*(111 ft)^2 ≈ 9676.9 ft^2

The number of bags of fertilizer required will be
.. (9676.9 ft^2)*(1 bag)/(50 ft^2) = 193.5 bags

Parks & Rec needs to use 193.5 bags of fertilizer to cover the park.

_____
No doubt, P&R has half a bag left over from a previous use of fertilizer in the park, so they will not have to purchase a whole bag to cover the fraction.

If the test scores of a class of 34 students have a mean of 73.1 and the test scores of another class of 26 students have a mean of 66.4, then the mean of the combined group is

Answers

Combined mean
= (73.1 * 34 + 66.4 * 26) / (34 + 26)
= (2485.4 + 1726.4) / 60
= 70.2 (rounded)

The Mean of the combined class is 70.19.

Mean

Mean is the average of a set of two or more numbers. The arithmetic and geometric mean are the types of mean that can be calculated.

Mean formula

[tex]\rm Mean = \dfrac{sum\ of\ the\ term}{total\ number\ of\ term}[/tex]

Given

The test scores of a class of 34 students have a mean of 73.1 and

The test scores of another class of 26 students have a mean of 66.4.

To find

The mean of the combined group.

How to get the mean of the combined group?

The sum of the total of the test score = Total number of students x Mean

Class 1 sum will be

The sum of the total test score = 34 x 73.1

The sum of the total test score = 2485.4

Class 2 sum will be

The sum of the total test score = 26 x 66.4

The sum of the total test score = 1726.4

Than Mean for the combine will be

[tex]\rm Mean = \dfrac{sum\ of\ the\ term}{total\ number\ of\ term}\\\\Mean = \dfrac{2485.4+1726.4}{34+26} \\\\Mean = \dfrac{4211.8}{60} \\\\Mean = 70.19[/tex]

Thus the Mean of the combined class is 70.19.

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let f(x)=4x+3 and g(x)=-2+5. find (fog) (5)

Answers

the correct question is
let f(x)=4x+3 and g(x)=-2x+5. find (fog) (5)

we have that
f(x)=4x+3
g(x)=-2x+5
(fog) (x)---------> f(g(x))------> 4*[-2x+5]+3---------> f(g(x))=-8x+20+3
f(g(x))=-8x+23
then
(fog) (5)=-8*5+23---------> (fog) (5)=-40+23
(fog) (5)=-17

the answer is (fog) (5)=-17

HELP ME ANSWER THIS QUESTION!

Boyd (B) is trapped in a soccer training circle. Albert (A) and Carlos (C) kick the ball to Boyd in rotation. Determine how far Boyd needs to kick the ball to Carlos if he is located in the center of his training circle and Carlos is located at the outer rim.

Answers

Here we have right-angle triangle. Sides are:
AB = 19+x
BC= x
AC= 30

From the picture we can see that side AB is hypothenuze. We are given number 19 as part of length of that hypothenuze. Other part is equal to distance from center to edge of circle. This length is same as side BC.

We will use Pythagorean theorem to solve this:
[tex] (AB)^{2} = (BC)^{2} + (AC)^{2} \\ (19+x)^{2} = x^{2} + 30^{2} \\ 361+38x+ x^{2} = x^{2} +900 \\ x^{2} - x^{2} +38x=900-361 \\ 38x=539 \\ x=14.2yard[/tex]

Phillip flips a coin, rolls a standard number cube, and randomly chooses a shape from the list below. Find the probability that the coin will show tails, the cube will show an odd number, and a red shape will be chosen. 1/6 1/2 None of these 1/12 1/8 HELPPP PLZ TODAY!!!!

Answers

3/6 and 1/2 man because there are three odd numbers on a cube

Answer:

thx for pts

Step-by-step explanation:

A bank runs a contest to encourage new customers to open accounts. In the contest, each contestant draws a slip representing a different reward—$5, $3, or $x—from a jar. At the beginning of the contest the jar contains 60 slips for $5, 40 slips for $3, and 50 slips for $x.
If the expected value of the first draw from the jar is $5.8, the value of x is__
At one point in the contest, the jar contains 3 slips for $5, 7 slips for $3, and y slips for $x. If the expected value on the next draw is $6, the value of y is __

Answers

Part 2:

We'll use x = 9 from part 1.

Again let,
A = event that the $5 reward is drawn
B = event that the $3 reward is drawn
C = event that the $x reward is drawn (x is some positive number)

We can update event C to say
C = event that the $9 reward is drawn

The probabilities change to
P(A) = 3/(10+y)
P(B) = 7/(10+y)
P(C) = y/(10+y)
where y is some positive whole number. It represents the number of slips in jar C

The net values are
V(A) = 5
V(B) = 3
V(C) = x = 9

Like before, multiply the probabilities and net values to get
P(A)*V(A) = (3/(10+y))*5 = 15/(10+y)
P(B)*V(B) = (7/(10+y))*3 = 21/(10+y)
P(C)*V(C) = (y/(10+y))*9 = (9y)/(10+y)

The results add up to
[ 15/(10+y) ] + [ 21/(10+y) ] + [ (9y)/(10+y) ]
(15+21+9y)/(10+y)
(36+9y)/(10+y)

That last expression is the expected value. The expected value is also given to be 6, so set the two expressions equal to each other and solve for y.
(36+9y)/(10+y) = 6
36+9y = 6(10+y)
36+9y = 6(10)+6(y)
36+9y = 60+6y
9y-6y = 60-36
3y = 24
3y/3 = 24/3
y = 8

The statement "y slips of $x" turns into "8 slips of $9" since x = 9 and y = 8.

x=9 and y =8.......................................

Suppose given an isosceles triangle with a leg measuring 5 in. Two lines are drawn through some point on the base, each parallel to one of the legs. Find the perimeter of the constructed parallelogram.

Answers

Let ΔABC be isosceles triangle with legs AB=BC=5 in. Draw an arbitrary point D on the base AC and spend two lines DE and DF such that DE || BC and DF || AB.

You get the parallelogram BFDE.

1. Consider ΔAED. This triangle is isosceles, because ∠ADE≅∠ACB as corresponding angles at parallel lines. The legs of this triangle are AE=ED.

2. Consider ΔDFC. This triangle is isosceles, because ∠FDC≅∠BAC as corresponding angles at parallel lines. The legs of this triangle are DF=FC.

3. Find the perimeter of parallelogram BFDE.

[tex]P_{BFDE}=BF+FD+ED+BE.[/tex]

Since AE=ED and DF=FC, you have that

[tex]P_{BFDE}=BF+FC+AE+BE=AB+BC=5+5=10\ in.[/tex]

Answer: 10 in.

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