Jesse spends 1/2 of his pocket money on Monday.
On Tuesday, he spends 2/3 of what is left.
On Wednesday, he spends 1/4 of what remains.
What fraction of the pocket money does he have left? Choose the most
reasonable answer

Answer:

[tex]\frac{9+5\sqrt6}{23}[/tex]

Step-by-step explanation:

We can rewrite the fraction as

[tex]\frac{2\sqrt{3}+3\sqrt{2}}{4\sqrt{3}+\sqrt{2}}[/tex]

In order to rationalize the denominator of such a complex fraction, we must multiply the fraction by the conjugate of the denominator. In this case, the conjugate of the denominator would be [tex]4\sqrt{3}-\sqrt{2}[/tex]. Multiplying both sides of the fraction by the conjugate of the denominator would result in the fraction:

[tex]\frac{9+5\sqrt6}{23}[/tex]

Answer:

y=-5/6

Step-by-step explanation:

-24y=20

y=-5/6

alternate:

-0.83

It looks like you're trying to evaluate the sum,

[tex]\displaystyle \frac2{4\times7} + \frac2{7\times10} + \frac2{10\times13}+\cdots+\frac2{49\times52}[/tex]

which can be written as

[tex]\displaystyle \sum_{n=1}^{16} \frac2{(3n+1)(3n+4)}[/tex]

Split up the summand into partial fractions:

[tex]\displaystyle \frac2{(3n+1)(3n+4)} = \frac a{3n+1} + \frac b{3n+4} \\\\ \implies 2 = a(3n+4)+b(3n+1) \\\\ \implies 2 = (3a+3b)n+4a+b[/tex]

so that

3a + 3b = 0, or a = -b

4a + b = 2

Solve for a and b :

4a + (-a) = 3a = 2   ==>   a = 2/3   ==>   b = -2/3

So the sum is

[tex]\displaystyle \frac23 \sum_{n=1}^{16} \left(\frac1{3n+1} - \frac1{3n+4}\right)[/tex]

Write out the first terms and observe that several terms cancel with each other:

2/3 (1/4 - 1/7)

+ 2/3 (1/7 - 1/10)

+ 2/3 (1/10 - 1/13)

+ …

+ 2/3 (1/43 - 1/46)

+ 2/3 (1/46 - 1/49)

+ 2/3 (1/49 - 1/52)

So the sum collapses and simplifies to

[tex]\displaystyle \sum_{n=1}^{16} \frac2{(3n+1)(3n+4)} = \frac23 \left(\frac14 - \frac1{52}\right) = \boxed{\frac2{13}}[/tex]

Answer:

D and E is the answer..

Step-by-step explanation:

nothing to explain .. D has the symbol of parallel.. and all parallel lines are coplaner

The correct answers are option D and option E that is AB || CD and the lines AB and CD are coplanar.

The lines which do not intersect each other at any point they can only intersect at infinity are called parallel lines. All the parallel lines are coplanar to each other.

From the above explanation, the parallel lines are represented as AB || CD and also coplanar to each other.

Therefore the correct answers are option D and option E that is AB || CD and the lines AB and CD are coplanar.

To know more about parallel lines follow

https://brainly.com/question/16742265

#SPJ2

Answer:

Hello,

Step-by-step explanation:

[tex]f(x)=\dfrac{4}{x} \\\\g(x)=\dfrac{4}{x} \\\\\\(gof)(x)=f(g(x))=f(\dfrac{4}{x} )=\dfrac{4}{\dfrac{4}{x} } =\dfrac{4*x}{4} =x\\\\\\(fog)(x)=g(f(x))=g(\dfrac{4}{x} )=\dfrac{4}{\dfrac{4}{x} } =\dfrac{4*x}{4} =x\\[/tex]

(Answer:

P(Bl or Yl) = 45%

(Pk on 2nd draw) = 18%

Step-by-step explanation:

There are a total of 20 marbles (3 + 4 + 5 + 8) in the bag. Since each marble is replaced once drawn, there is no change in the total count from one draw to another (unconditional probability).

So

P(Bl or Yl) = (5 + 4)/20 = 9/20 = .45 = 45%

Then

P(Pk on 2nd draw) = P(1st draw) * P(2nd draw)

     = 9/20 * 8/20 = 72/400 = 9/50 = .18 = 18%

Answer:

hope that helps i don't know it either tho

Answer:

145 degrees

Step-by-step explanation:

sum of a triangle is 180 and when the angle next to 145 degree one is supplementary to 145 degree the other two angles must be 145

Answer:

could you explain your question better please

Answer:

x=5

Step-by-step explanation:

1 - x = 16 - 4x

Rearrange :

-x +4x = 16 - 1

3x = 15

x = 5.

Hence, there is one solution : {5}

Answer:

x=5

Step-by-step explanation:

1-x=16-4x

-1 -1

-x=15-4x

+4x. +4x

3x=15

/3. /3

x=5

Answer:

the answer is 4x2

Step-by-step explanation:

p(X)-q(X) = x4 + 2x2 + 1 - ( x4 - 2x2 + 1 )

p(X)-q(X) = x4 + 2x2 + 1 - x4 + 2x2 - 1 )

p(X)-q(X) = 2x2 + 2x2

p(X)-q(X) = 4x2

Answer:

p(x) - q(x) = 4x²

Step-by-step explanation:

p(x) - q(x)

= [tex]x^{4}[/tex] + 2x² + 1 - ([tex]x^{4}[/tex] - 2x² + 1)  ← distribute parenthesis by - 1

= [tex]x^{4}[/tex] + 2x² + 1 - [tex]x^{4}[/tex] + 2x² - 1 ← collect like terms

= 4x²

Answer:

If the ladder is 9 m from the wall

cos theta = 9 / 20 = .45 and theta = 63.3  angle made with floor

So the angle made with the wall is 90 - 63.3 = 26.7

Answer:

b=x+1

Step-by-step explanation:

The equation is:

[tex]2x^2}+x-1=\frac{1}{2} b(4x-2)[/tex]

Isolate b by subtracting and dividing.

You end up with b= x+1

Answer:

720°

Step-by-step explanation:

The sum of the exterior angles of a polygon = 360°

Divide by 60 to find number of sides (n)

n = 360° ÷ 60° = 6

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 6 , then

sum = 180° × 4 = 720°

The sum of the exterior angles of a regular polygon is 360º

Each exterior angle of a regular polygon is 60º/n

360º/n=60º

360/60=n

6=n

A polygon with 6 sides is a hexagon.

Use the formula (n-2)×180

(6-2)*180=4*180=720º

another solution...

you have 6 interior angles (hexagon)

if an exterior angle is 60º, the corresponding interior angle is 180-60=120º

you have 6 of these 120º angles

6*120=720º

The median GPA of the  percussionists is 2.8

This question appears incomplete.

Here is the complete question :

Members of a band class were arguing over which instruments are played by the best academic students. A survey was conducted, and here are the results:

All 13 flute players had a grade point average (GPA) between 3.84 and 3.88.

There were only 3 percussionists. One had a GPA of 2.4, one had a GPA of 2.8, and one had a GPA of 3.2.

Among the saxophone players, 4 had a GPA of 3.9, and the other 5 had a GPA of 4.0.

For percussionists, the median GPA is _____.

Median can be described as the number that occurs in the middle of a set of numbers that are arranged either in ascending or descending order

Median is a measure of central tendency

Other measures of central tendency include  mean and mode.

The GPA of the 3 percussionists are 2.4, 2.8 and 3.2

This data has already been arranged in ascending order.

The number that is in the middle is 2.8

Conversely, if the GPA is arranged in descending order, it is 3.2, 2.8 and 2.4

The number that is in the middle is 2.8

For more information on how to calculate median, check : https://brainly.com/question/12528427?referrer=searchResults

Using angle sum property

[tex]\\ \sf\longmapsto x+44+29=180[/tex]

[tex]\\ \sf\longmapsto x+63=180[/tex]

[tex]\\ \sf\longmapsto x=180-63[/tex]

[tex]\\ \sf\longmapsto x=117°[/tex]

The angle sum property of a triangle:

[tex]\large\bf{\red{ \longrightarrow}} \: \tt \: x \: + \: 44 \degree \: + \: 29 \degree \: = \: 180 \degree[/tex]

[tex]\large\bf{\red{ \longrightarrow}} \: \tt \: x \: + \: 73 \degree \: = \: 180 \degree[/tex]

[tex]\large\bf{\red{ \longrightarrow}} \: \tt \: x \: = \: 180 \degree \: - \: 73 \degree \:[/tex]

[tex]\large\bf{\red{ \longrightarrow}} \: \tt \: x \: = \: 107 \degree[/tex]

Answer:4 ans x is -32/10

7 ans b  is 6

10 ans x is 25/7

13 ans x is 9/2

Step-by-step explanation:

please mark this answer as brainlist

[tex]\\ \sf\longmapsto 16-2r=3r+6r+1[/tex]

[tex]\\ \sf\longmapsto 16-2r=9r+1[/tex]

[tex]\\ \sf\longmapsto 16-1=9r+2r[/tex]

[tex]\\ \sf\longmapsto 11r=15[/tex]

[tex]\\ \sf\longmapsto r=\dfrac{15}{11}[/tex]

Answer: r = 15/11

Step-by-step explanation:

Given

16 - 2r = 3r + 6r + 1

Combine like terms

16 - 2r = 9r + 1

Add 2r on both sides

16 - 2r + 2r = 9r + 1 + 2r

16 = 11r + 1

Subtract 1 on both sides

16 - 1 = 11r + 1 - 1

15 = 11r

Divide 11 on both sides

15 / 11 = 11r / 11

[tex]\boxed{r=\frac{15}{11} }[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

v is 198 m/s

Step-by-step explanation:

[tex]v = \sqrt{gh} \\ v = \sqrt{9.8 \times 4000} \\ v = 198 \: m {s}^{ - 1} [/tex]

Answer:

B

Step-by-step explanation:

f(x) = 2x+5

f^(-1) (x) = (x-5)/2

f^(-1) (8) = 3/2

Answer:

252

Step-by-step explanation:

The conversion factor is

180/pi

7pi/5 * 180/pi = 7 *180/5 = 252 degrees

Answer:

4

Step-by-step explanation:

Im assuming you mean the first and second equation equal each other:

3x+2=2x+6

x=4

Answer:

d. 7

Step-by-step explanation:

A parallelogram has equal opposite sides that are parallel to each other. Therefore, opposite interior angles would be congruent to each other.

Thus:

3x - 17 = 25 - 3x

Add 3x from each side

3x - 17 + 3x = 25 - 3x + 3x

6x - 17 = 25

Add 17 to both sides

6x - 17 + 17 = 25 + 17

6x = 42

Divide both sides by 6

6x/6 = 42/6

x = 7

Using the intersecting chord theorem:

a x b = c x d

x+21 * 4 = x+3 * 10

Simplify:

4x+84 = 10x+30

Subtract 30 from both sides:

4x + 54 = 10x

Subtract 4x from both sides:

54 = 6x

Divide both sides by 6:

x = 9

Answer:

x=9

Step-by-step explanation:

(segment piece) x (segment piece) =   (segment piece) x (segment piece)

ab = cd

(x+21) *4 = (x+3)*10

Distribute

4x+84=10x+30

Subtract 4x from each side

84 = 10x-4x+30

84 = 6x+30

Subtract 30 from each side

54 = 6x

Divide by 6

54/6 = 6x/6

9=x

Answer:

169

Step-by-step explanation:

PEMDAS

Parenthesis first

Add -1 and -3 which is -4

Divide 24 by 6 which is 4

(4-2+5*3*-4÷4)^2

(4-2-15)^2

(2-15)^2

(-13)^2

Which is 169

Answer:

1/3

Step-by-step explanation:

Slope is rise over run

your rise is 1 (because you only go up one block each time)

your run is 3 ( because you go right three times)

so 1/3

$695.00 would be your answer :)