Three generous friends, each with some cash, redistribute their money as follows: Ami gives enough money to Jan and Toy to double the amount that each has. Jan then gives enough to Ami and Toy to double their amounts. Finally, Toy gives Ami and Jan enough to double their amounts. If Toy has $36 when they begin and $36 when they end, what is the total amount that all three friends have?

Answer:

[tex]x=-\frac{11}{6}[/tex]

Step-by-step explanation:

8x2=6x=5

16+6x=5

6x=5-16

6x=-11

[tex]x=-\frac{11}{6}[/tex]

Answer:

See below.

Step-by-step explanation:

[tex]8x^2+6x=5[/tex]

Reformat this so the equation equals zero:

[tex]8x^2+6x-5=0[/tex]

[tex]a=8, b=6, c=-5[/tex]

[tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

[tex]x=\frac{-(6)\pm\sqrt{(6)^2-4(8)(-5)} }{2(8)}[/tex]

[tex]x=\frac{-6\pm\sqrt{36+160} }{16}[/tex]

[tex]x=\frac{-6\pm\sqrt{196} }{16}[/tex]

[tex]x=\frac{-6\pm14 }{16}[/tex]

[tex]x=\frac{-6+14}{16}=8/16=1/2[/tex] or

[tex]x=\frac{-6-14}{16}=-20/16=-5/4[/tex]

Answer:

It is not normally distributed as it has it main concentration in only one side.

Step-by-step explanation:

So, we are given that the class width is equal to 0.2. Thus we will have that the first class is 0.00 - 0.20, second class is 0.20 - 0.40 and so on(that is 0.2 difference).

So, let us begin the groupings into their different classes, shall we?

Data given:

0.31 0.31 0 0 0 0.19 0.19 0 0.150.15 0 0.01 0.01 0.19 0.19 0.53 0.53 0 0.

(1). 0.00 - 0.20: there are 15 values that falls into this category. That is 0 0 0 0.19 0.19 0 0.15 0.15 0 0.01 0.01 0.19 0.19 0 0.

(2). 0.20 - 0.40: there are 2 values that falls into this category. That is 0.31 0.31

(3). 0.4 - 0.6 : there are 2 values that falls into this category.

(4). 0.6 - 0.8: there 0 values that falls into this category. That is 0.53 0.53.

Class interval            frequency.

0.00 - 0.20.                   15.

0.20 - 0.40.                    2.

0.4 - 0.6.                        2.

Answer: 1/5

Step-by-step explanation:

given data;

chances of winning = 1/3

chances of losing = 1/3

chances of tying in a given round = 1/3

solution:

probability that you would win atleast 2 in any 3 matches without a tied match is

1/3 /  ( 2 - 1/3 )

= 1/3 / 5/3

= 1/5

the probability of winning 2 of 3 games without a tie is 1/5

Answer:

Step-by-step explanation:

Total inches grown last year by matthew = 2.7inches

Total inches grown this year by Matthew = 4.4 inches

Total inches grown by Matthew over the last two years combined will be the sum of heights of matthew for both the previous year and the current year.

Total inches grown = 2.7 inches + 4.4 inches

Total inches grown over the last two years = 7.1 inches

Answer:

There are 2 * 32 = 64 possible ways for choosing three course meal.

Step-by-step explanation:

1-If we choose an appetizer, main course and a soup then there are 32 ways to choose this three course meal. 4 * 2 * 4 = 32 ways. There will be an appetizer, main course and a soup in the meal.

2-If we choose a soup, main course and a dessert then there are 32 ways to choose this three course meal. 4 * 2 * 4 = 32 ways. There will be a soup, main course and a dessert in the meal.

There are 2 possible ways to choose either an appetizer or dessert in a 3 course meal. There will be 64 ways in total for the three course meal.

Answer:

0.0499

Step-by-step explanation:

The p-value can be calculated using technology. The p-value is computed by using F distribution right tailed excel function. The excel function "F.DIST.RT(4.76,3,6)" gives desired p-value which is 0.0499.

The p-value shows that the for 5% level of significance the null hypothesis can be rejected.

Answer:

solution

given a=1_9k and b=j+k

Now,ab=(1_9k)(j+k)

=1((j+k)-9k(j+k)

=j+k_9jk-9k^2

=k_9k^2+j_9jk

=k((1_9k)+j(1_9k)

=(1_9k)(k+k)

Answer: (84.876, 87.124)

Step-by-step explanation:

Confidence interval for population mean if population standard deviation is unknown:

[tex]\overline{x}\pm t_{\alpha/2}(\dfrac{s}{\sqrt{n}})[/tex]

, where n= sample size

s= sample standard deviation

[tex]\overline{x}[/tex] = sample mean

[tex]\alpha=[/tex] significance level

[tex]t_{\alpha/2}[/tex] = critical-t value

Given:  n= 64

Degree of freedom = n-1 = 63

s= 4.5

[tex]\overline{x}[/tex] = 86

[tex]\alpha=[/tex] 0.05

[tex]t_{\alpha/2}[/tex] = 1.9983

Now, the required 95% confidence interval would be:

[tex]86\pm (1.9983)(\dfrac{4.5}{\sqrt{64}})\\\\=86\pm (1.9983)(\dfrac{4.5}{8})\\\\=86\pm (1.9983)(0.5625)\\\\\approx86\pm 1.1240\\\\ =(86-1.1240,\ 86+1.1240)\\\\=(84.876,\ 87.124)[/tex]

The 95% confidence interval for the population mean μ is between: (84.876, 87.124)

Answer:

Step-by-step explanation:

when h(t)=0

-4.9 t²+19.6t=0

4.9t(-t+4)=0

either t=0 or t=4

so domain is 0≤t≤4

for range

h(t)=-4.9t²+19.6t

=-4.9(t²-4t+4-4)

=-4.9(t-2)²+19.6

so range is 0≤h≤19.6

Domain = 0<t<4, make sure to use less than or equal to signs not just less than signs.

Range = 0<h<19.6, again, use less than or equal to signs.

Answer:

79.95, 82.62

Step-by-step explanation:

using excel to find a 95% confidence interval for the mean bounce height of the golf ball

Heights given are :

81.4

80.8

84.4

85.6

82.9

76.0

80.0

83.2

80.8

79.6

82.9

83.4

82.2

86.0

76.2

84.8

82.0

76.3

77.0

75.4

82.0

79.8

80.4

86.9

82.1

The statistical out put of the problem after solving with excel is attached below

therefore the 95% confidence interval from the attached solution will be ( 79.95, 82.62 )

Answer: (79.95, 82.61)

Step-by-step explanation:

Use Excel to calculate the 95% confidence interval, where α=0.05 and n=25.

1. Open Excel and enter the given data in column A. Find the sample mean, x¯, using the AVERAGE function and the sample standard deviation, s, using the STDEV.S function. Thus, the sample mean, rounded to two decimal places, is 81.28 and the sample standard deviation, rounded to two decimal places, is 3.23.

2. Click on any empty cell, enter =CONFIDENCE.T(0.05,3.23,25), and press ENTER.

3. The margin of error, rounded to two decimal places, is 1.33. The confidence interval for the population mean has a lower limit of 81.28−1.33=79.95 and an upper limit of 81.28+1.33=82.61.

Thus, the 95% confidence interval for the mean bounce height of the golf balls is (79.95, 82.61).

Answer:

x = 28, y = 23

Step-by-step explanation:

5y - 4 and 3y are alternate exterior angles and are supplementary, thus

5y - 4 + 3y = 180

8y - 4 = 180 ( add 4 to both sides )

8y = 184 ( divide both sides by 8 )

y = 23

Thus

3y = 3 × 23 = 69

2x + 13 and 3y are corresponding angles and congruent, thus

2x + 13 = 69 ( subtract 13 from both sides )

2x = 56 ( divide both sides by 2 )

x = 28

Answer:

x1= -4, x2 = 7

Step-by-step explanation:

Move expression to the left-hand side:

1/4x-3/4-7/x=0

Write all the numerators above a common denominator:

x^2 - 3x - 28 /4x =0

When the quotient of expressions equal 0, the numerator has to be 0

x^2 + 4x - 7x - 28 = 0

x(x+4) - 7(x+4) =0

(x+4) × (x-7) =0

Separate into possible cases:

x+4=0

x-7=0

Answer: -9

Step-by-step explanation:

Problem 3

----------

Work Shown:

Use either the FOIL method, distributive property, or the box method to get the following

(x-2)*(x-5) = x^2 - 5x - 2x + 10 = x^2 - 7x + 10

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

Problem 4

----------

Work Shown:

Same idea as problem 3 above

(x-3)(x+2) = x^2+2x-3x-6 = x^2 - x - 6

Answer:

3. y = x² - 7x + 10

4. y = x² - x - 6

Step-by-step explanation:

Answer:

The pie chart representing for this question is presented in the attached image to this solution.

Step-by-step explanation:

Complete Question

Draw a pie chart for the percent of the money spent on various types of books by a library in a year.​

Type of book | %

Fiction | 20%

Classics | 15%

Sports | 10%

Biography | 12.5%

Magazines | 22.5%

Others | 20%

Solution

A pie chart is a graphical representation of a set of numerical data which comes in a circular shape divided into slices, with the size of each slice corresponding to the proportion of the numerical data it represents.

Because it is a circle, the total angles in a pie chart is 360°.

The angles are divided into slices with the size of each slice corresponding to how large the data it represents is.

So, we first convert the data given into degrees.

Since the data is given in percentage, for each of the groups, the conversion from percentage will be

Angle = (Proportion) × 360°

Type of book | % | Angle

Fiction | 20% | 72°

Classics | 15% | 54°

Sports | 10% | 36°

Biography | 12.5% | 45°

Magazines | 22.5% | 81°

Others | 20% | 72°

The pie chart representing this data is presented in the attached image to this solution.

Hope this Helps!!!

Answer:

170.67

Step-by-step explanation:

Answer:

171

Step-by-step explanation:

Modeling the situation

If we fill the pyramid mold 2\text{ cm}2 cm2, start text, space, c, m, end text from the top, we have a smaller pyramid that's similar to the original pyramid.

Since the pyramids are similar, we can set up a proportional equation to find the side lengths and height of the smaller pyramid, and then find its volume.

Hint #22 / 4

Base and height of smaller pyramid

The height of the smaller pyramid is 10-2=8\text{ cm}10−2=8 cm10, minus, 2, equals, 8, start text, space, c, m, end text.

We can solve for the length \blueE{\ell}ℓstart color #0c7f99, ell, end color #0c7f99 in the smaller pyramid using a proportional equation.

\begin{aligned} \dfrac{\blueE{\ell}}{10} &= \dfrac{8}{10} \\\\ \blueE{\ell} &= \blueE{8} \end{aligned}  

10

ℓ

​  

ℓ

​  

=  

10

8

​  

=8

​  

Hint #33 / 4

Volume of smaller pyramid

\begin{aligned} \text{volume}_{\text{pyramid}} &= \dfrac13(\text{base area})(\text{height}) \\\\ &= \dfrac13 \cdot (\blueE{\ell})^2\cdot (\text{height}) \\\\ &= \dfrac13 \cdot \blueE{8}^2\cdot(8)\\\\ &= \dfrac{512}{3}=170.\overline{6}\\\\ &\approx \purpleD{170.67} \end{aligned}  

volume  

pyramid

​  

​  

=  

3

1

​  

(base area)(height)

=  

3

1

​  

⋅(ℓ)  

2

⋅(height)

=  

3

1

​  

⋅8  

2

⋅(8)

=  

3

512

​  

=170.  

6

≈170.67

​  

Hint #44 / 4

To the nearest cubic centimeter, the volume of the smaller pyramid is about 171\text{ cm}^3171 cm  

3

171, start text, space, c, m, end text, cubed.

Answer:

B

Step-by-step explanation:

Since the vertex of the function is (-6, -3), we know the equation must be y = |x + 6| - 3.

Answer:

B. |x+6|-3

Step-by-step explanation:

Well we can tell by looking at the graph that the line has a y-intercept of +3,

meaning we can cross out choices A and C.

Now we can graph B and D,

Look at the image below ↓

By looking at the graphed lines we can tell that y = |x+6|-3 is the correct answer.

Wel can also conclude that choice B is correct because of its vertex being at (-6,-3).

Thus,

answer choice B is the correct answer.

Hope this helps :)

Answer:

B. 4

Step-by-step explanation:

Let the side of the square= a

Then the area of the square= a²

Given:

Then:

Considering the value of the area, 12 units

Correct choice is B. 4

Answer:

The answer should be B: 5n+300=1,500.

Step-by-step explanation:

The number of people to attend is going to vary and 300 is a set variable, so it won't change of be affected. Since the team doesn't know how many people will be able to attend in order to reach their goal, n is going to take the place for the amount of people.

If you were to solve this, the answer would be:

5n+300=1,500

5n=1,500-300

5n=1,200

n=240

So 240 people can attend the dance.

Answer:5n-300=1,500

Step-by-step explanation:

Answer:

5,2

Step-by-step explanation: (-7+12=5,-6=8=2) And I Got It Correct On Khan Academy :)

Hope this helps you!!

The coordinate of Q under the translation (x,y)→(x+12,y+8) will be located at Q'(5, 2)

Translation of image is a mathematical term used to move an object through a distance.

Given the coordinate point Q(-7, 6), if this coordinate is under the translation (x,y)→(x+12,y+8), this means we are to shift the x coordinate of Q to the right by 12units and the y-coordinates of Q up by 8 units to get the new location at Q'. Hence:

Q' = (-7 + 12, -6 + 8)

Q' = (5, 2)

This shows that the coordinate of Q under the translation (x,y)→(x+12,y+8) will be located at Q'(5, 2)

Learn more about translation here: https://brainly.com/question/10704056

Answer:

[tex]\mathrm{B.}[/tex] All real numbers except x = 2, x = 5

Step-by-step explanation:

If the denominator is equal to 0 then the function would be undefined.

Set the denominator equal to 0.

x² - 7x + 10 = 0

Factor the left side of the equation.

(x - 5)(x - 2) = 0

Set the factors equal to 0.

x - 5 = 0

x = 5

x - 2 = 0

x = 2

The domain is all real numbers except x = 2 and x = 5.

Answer:

A.

Step-by-step explanation:

Hello,

g(x-4)=f(x) so the graph of g is the graph of f shifted 4 units to the left.

For any x, the point (x-4, g(x-4)) is 4 units to the left of the point (x,f(x)).

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

A

Step-by-step explanation:

:) i just took the test and it was right

Answer:  B) 10 three-point questions and 14 five-point questions

Step-by-step explanation:

x represents three-point questions

y represents five-point questions

3x + 5y = 100  →  1(3x + 5y = 100)  =  3x + 5y = 100

 x  +  y  = 24   → -3(x  +  y  = 24)   = -3x  -3y  = -72

                                                                  2y = 28

                                                                    y = 14  (five-point questions)

x +  y = 24

x + 14 = 24

     x = 10  (three-point questions)

Use the binomial theorem:

[tex](1+1)^{16}=\displaystyle\sum_{k=0}^{16}\binom{16}k1^{16-k}1^k[/tex]

So

[tex]\dbinom{16}0+\dbinom{16}1+\cdots+\dbinom{16}{16}=\boxed{2^{16}}[/tex]

More generally,

[tex]\displaystyle\sum_{k=0}^n\binom nk=2^n[/tex]

Answer:

19

Step-by-step explanation:

7 supersricpt 8

Answer:

a[tex]\geq[/tex]-3

Step-by-step explanation:

Answer:

-3  ≤  a

Step-by-step explanation:

6≥ -6(a+2)

Divide each side by -6, remembering to flip the inequality

6/-6 ≤ -6/-6(a+2)

-1 ≤ (a+2)

Subtract 2 from each side

-1 -2  ≤  a+2-2

-3  ≤  a

Answer:

A. 70 dimes, 30 quarters

Step-by-step explanation:

Only options A and B create a total of 100 coins. It cannot be option B because 80 quarters by itself, is already over $14.50.

Answer:

  64.8 and 75.2

Step-by-step explanation:

A suitable probability calculator can show you the middle 40% is between about 64.8 and 75.2.

Answer:

answer is

B) 36,72,80

Step-by-step explanation:

because is the right angle it is exactly 90°