Joe and Danny have just won 350 arcade tickets. If each arcade game can be played with 12 tickets, how many will they have left over at the end of the day, if they play the maximum number of games?

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Work Shown:

f ''' (x) = cos(x) .... third derivative

f '' (x) = sin(x)+C ... integrate both sides to get second derivative. Don't forget the +C at the end

We are given f '' (0) = 9, so we'll make use of this to find C

f '' (x) = sin(x)+C

f '' (0) = sin(0)+C

9 = sin(0) + C

9 = 0 + C

9 = C

C = 9

Therefore, f '' (x) = sin(x)+C turns into f '' (x) = sin(x)+9

------------

Integrate both sides of the second derivative to get the first derivative function

f '' (x) = sin(x)+9

f ' (x) = -cos(x)+9x+D ... D is some constant

Make use of f ' (0) = 4 to find D

f ' (x) = -cos(x)+9x+D

f ' (0) = -cos(0)+9(0)+D

4 = -1 + 0 + D

D = 5

So we have f ' (x) = -cos(x)+9x+D turn into f ' (x) = -cos(x)+9x+5

------------

Lastly, apply another round of integrals and substitutions to find the f(x) function. We'll use f(0) = 8.

f ' (x) = -cos(x)+9x+5

f(x) = -sin(x) + (9/2)x^2 + 5x + E .... E is some constant

f(0) = -sin(0) + (9/2)(0)^2 + 5(0) + E

8 = 0 + 0 + 0 = E

E = 8

------------

We have

f(x) = -sin(x) + (9/2)x^2 + 5x + E

turn into

f(x) = -sin(x) + (9/2)x^2 + 5x + 8

Answer:

a) More.

b) Less.

c) More.

Step-by-step explanation:

a) If you invest $10 with an interest rate of 50% (that's very high I know XD), you would earn 10 / 2 = $5 in interest. If you invest $100 with an interest rate of 50%, you would earn 100 / 2 = $50 in interest. So, the more principal invested, the more interest earned.

b) Let's say you are investing $100. If there is an interest rate of 50%, as stated before, you would earn $50 in interest. If the interest rate were lowered to 25%, you would earn 100 / 4 = $25 in interest. So, the lower the interest rate, the less the interest.

c) The same exact thing as part a.

Hope this helps!

Answer:

Step-by-step explanation:

The sides of the base are each 5 inches. We see 4 right angles so that we are dealing with a square.

The triangles look to be isosceles. In any event there are 4 of them. So the answer is the 3rd one down.

Answer:

C

Step-by-step explanation:

Answer:

For sample size n = 39 ; P(X < 31.6) = 0.9756

For sample size n = 76 ; P(X < 31.6) = 0.9970

Step-by-step explanation:

Given that:

population mean μ = 31

standard deviation σ = 1.9

sample mean  [tex]\overline X[/tex] = 31.6

Sample size n                 Probability

39

76

The probabilities that the sample mean is less than 31.6 for both sample size can be computed as  follows:

For sample size n = 39

[tex]P(X < 31.6) = P(\dfrac{\overline X - \mu}{\dfrac{\sigma }{\sqrt{n}}}< \dfrac{\overline X - \mu}{\dfrac{\sigma }{\sqrt{n}}})[/tex]

[tex]P(X < 31.6) = P(\dfrac{31.6 - \mu}{\dfrac{\sigma }{\sqrt{n}}}< \dfrac{31.6 - 31}{\dfrac{1.9 }{\sqrt{39}}})[/tex]

[tex]P(X < 31.6) = P(Z< \dfrac{31.6 - 31}{\dfrac{1.9 }{\sqrt{39}}})[/tex]

[tex]P(X < 31.6) = P(Z< \dfrac{0.6}{\dfrac{1.9 }{6.245}})[/tex]

[tex]P(X < 31.6) = P(Z< 1.972)[/tex]

From standard normal  tables

P(X < 31.6) = 0.9756

For sample size n = 76

[tex]P(X < 31.6) = P(\dfrac{\overline X - \mu}{\dfrac{\sigma }{\sqrt{n}}}< \dfrac{\overline X - \mu}{\dfrac{\sigma }{\sqrt{n}}})[/tex]

[tex]P(X < 31.6) = P(\dfrac{31.6 - \mu}{\dfrac{\sigma }{\sqrt{n}}}< \dfrac{31.6 - 31}{\dfrac{1.9 }{\sqrt{76}}})[/tex]

[tex]P(X < 31.6) = P(Z< \dfrac{31.6 - 31}{\dfrac{1.9 }{\sqrt{76}}})[/tex]

[tex]P(X < 31.6) = P(Z< \dfrac{0.6}{\dfrac{1.9 }{8.718}})[/tex]

[tex]P(X < 31.6) = P(Z< 2.75)[/tex]

From standard normal  tables

P(X < 31.6) = 0.9970

Answer:

[tex]f(5)=17[/tex]

Step-by-step explanation:

[tex]f(x)=3x+2[/tex]

[tex]f(5)=3(5)+2[/tex]

[tex]f(5)=15+2[/tex]

[tex]f(5)=17[/tex]

Answer:

17

Step-by-step explanation:

f(x) = 3x + 2

f(5) = 3(5)+ 2

f(5) = 15 + 2

f(5) = 17

Answer:

(0,-7)

Step-by-step explanation:

If nay point is form (x,y)

x is abscissa can be also called x axis coordinate

y is ordinate can be also called y axis coordinate

ordiantes are points lying on y axis.

For any point lying on y axis, its x-axis coordinate will be 0

given that ordinate is -7. it means that value of y coordinate is -7

Thus,  coordinates of the point is (0,-7)

Answer:

41/99

Step-by-step explanation:

There are two types of non terminating decimals. These are: Simple and Mixed

The one that you wrote up here is Simple, Since 41 is the only number that goes on repeating itself.

And mixed non terminating decimal is like 0.352 whereas 52 keeps repeating itself.

So when you change a non terminating decimal the denominator is always 9. But it depends on the decimal whether it is simple or mixed.

Since the decimal you wrote is simple and 2 digits keep on repeating themselves the denominator will be 99.

And the numerator will be the decimal number that keeps repeating itself without the repeating bar.

Therefore, the answer is 41/99.

Hope it helps ;) ❤❤❤

Answer:

942.5 in²  

Step-by-step explanation:

The formula for the area (A) of a sector of a circle is

A = ½r²θ

where θ is the angle in radians.

1. Convert the angle to radians

θ = 125°  

[tex]\theta = 125^{\circ} \times \dfrac{\pi \text{ rad }}{180^{\circ}} =\frac{25}{36} \pi\text{ rad}[/tex]

2. Area swept out by wiper arm

A = ½r²θ = ½ × (30 in)² × θ = ½ × 900 in²× θ = 450 θ in²

3. Area missed by wiper

A = ½r²θ = ½ × (6 in)² × θ = ½ × 36 in²× θ = 18 θ in ²

4. Area covered by wiper

A = 450 θ in² - 18 θ in² = 432 θ in²

5. Insert the value of θ

A = 432 × 25/36 π in² = 300π in² ≈ 942.5 in²

The area swept out by the wiper blade is 942.5 in².

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

            Hi my lil bunny!

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It looks lilke one of those old'n day Juice makers

2, 3 , and 4 would be the part im talking about.

You can write : I seleted the story called Old In Day Juice Makers

( I don't know about the paragraph, sorry)

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀

Answer:

9 and 23

Step-by-step explanation:

Let x be smaller length in inches.

x+3x-4=32

4x=36

x=9

9*3-4=23

So they're 9 and 23 inches long.

The lengths of the two parts of the pipe are 9 and 23 inches long.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Let x be the smaller length in inches.

x + 3x - 4 = 32

4x = 36

x  =9

Now substitute;

9*3 - 4 = 23

Hence, the lengths of the two parts of the pipe are 9 and 23 inches long.

Learn more about the unitary method;

https://brainly.com/question/23423168

#SPJ2

Answer:

25.52791653032955454422437424679625318128649677442393276098...

Step-by-step explanation:

You can just paste this into wolframalpha.

Answer: 970.72312

Step-by-step explanation:

Straightforward operation.

Answer: 180

Step-by-step explanation:

Let the tons of ice the ship was carrying when it set sail be y.

We are told that one third of the original cargo was lost because it had melted on the voyage and that it arrived in Calcutta with 120 tons remaining of its cargo of ice.

This means that (1 - 1/3 = 2/3) remained which was the 120 tons remaining. This implies that:

2/3 × y = 120

2y/3 = 120

2y = 120 × 3

2y = 360

y = 360/2

y = 180

The ship was carrying 180 tons of ice when it set sail

Answer:

(x - 7)² + (y - 4)² = 49

Step-by-step explanation:

Given

Equation: x² + y² = 49

Required:

New Equation when translated 7 units right and 4 units up

Taking it one step at a time.

When the equation is translated 7 units right, this implies a negative unit along the x axis.

The equation becomes

(x - 7)² + y² = 49

When the equation is translated 4 units up, this implies a negative unit along the y axis.

(x - 7)² + (y - 4)² = 49

The expression can be further simplified but it's best left in the form of

(x - 7)² + (y - 4)² = 49

Step-by-step explanation:

An algebraic expression haa atleast one variable and operator sign such as (+,-,×,÷)

According to the question, an algebraic expression should be made from difference of 'a' and 'b'

so, the expression is (a - b) or a - b.

Hope it helps!!!!

a) The population is all of the flights belonging to the particular airline. It's not all flights in general because the airline does not have control over a rival company's flight schedule.

------------------

b) The sample is the 5 airlines the company selected. Ideally the sample should represent the population as much as possible. The larger the sample, the more representative the sample is.

------------------

c) No, the sample is likely not representative because one day of flight does not represent the entire lifetime of all flights done so far for that company. This particular day could have been a very good day with good weather, which may explain why the 5 flights were all on time.

------------------

d) It would be better for the company to select the days at random and sample all of the flights for those particular days chosen. This is a cluster sample. Each cluster is a day. Also, I think more flights should be sampled. Five flights does not seem like enough.

Answer:

The tower is 73.4 m tall

Step-by-step explanation:

The height of the pole = 2.5 m

The shadow cast by the pole = 1.72 m

Shadow cast by tower = 50.5 m

To find the height of the tower, we proceed by finding the angle of elevation, θ, of the light source casting the shadows as follows;

[tex]Tan\theta =\dfrac{Opposite \ side \ to\ angle \ of \ elevation}{Adjacent\ side \ to\ angle \ of \ elevation} = \dfrac{Height \ of \ pole }{Length \ of \ shadow} =\dfrac{2.5 }{1.72}[/tex]

[tex]\theta = tan ^{-1} \left (\dfrac{2.5 }{1.72} \right) = 55.47 ^{\circ}[/tex]

The same tanθ gives;

[tex]Tan\theta = \dfrac{Height \ of \ tower}{Length \ of \ tower \ shadow} =\dfrac{Height \ of \ tower }{50.5} = \dfrac{2.5}{1.72}[/tex]

Which gives;

[tex]{Height \ of \ tower } = {50.5} \times \dfrac{2.5}{1.72} = 73.4 \ m[/tex]

Step-by-step explanation:

I DON'T KNOW WHICH ANSWER IS CORRECT .

BUT MY ANSWER CAME THIS .

I HOPE IT WILL HELP YOU.

HAVE A NICE DAY.....

Answer:

[tex]24200 mm^{2}[/tex]

Step-by-step explanation:

200*50+200*50+70*60

=24200 mm^{2}

Answer:

You have to shade 6 pieces.

Step-by-step explanation:

Hope it helps!

Answer:

Step-by-step explanation:

P (m) = a (m + 1) + b (m + 1) - c (m + 1)

P (m) = (a + b - c) (m + 1)

There are 2 prime factors

Answer:

C. 16π

Step-by-step explanation:

Well we need to find the area of the top circle which has a radius of 4cm.

π(4)^2

16π in terms of pi

Thus,

the answer is C. 16π.

Hope this helps :)

Answer:

Step-by-step explanation:

x-y=6

(0,-6),(6,0)

4x+y=4

(0,4),(1,0)

point of intersection:

Answer:

for first eq

three points are (7,-1) (6,0) and (5,1)

for second eq

three points are (1,0) (0,4) and (-1,8)

point of intersecton is (2,-4)

Step-by-step explanation:

check by substituting if u want

hope i helped

pls give brainliest

im trying to level up

This question is incomplete. Please find attached to this solved question, the diagram required to solve this question.

Answer:

11 units

Step-by-step explanation:

The shaded portion of the rectangle forms the shape of a trapezium

The area of a trapezium = 1/2(a + b)h

From the diagram, we can see than x = b

a = 7 units

b = 7 units

Area of the trapezium = Area of the shaded portion = 63 square units

A = 1/2(a + b)h

63 = 1/2(7 + b)7

63 = 1/2(49 + 7b)

63 × 2 = 49 + 7b

126 - 49 = 7b

7b = 77

b = 77/7

b = 11 units

Since x = b, x = 11 units

The value of x is 11

Start by calculating the area (A) of the trapezoid using

[tex]A= 0.5 * (a + b)h[/tex]

Using the parameters from the complete question, we have:

[tex]63 = 0.5 * (7 + x) * 7[/tex]

Multiply both sides by 2

[tex]126 = (7 + x) * 7[/tex]

Divide both sides by 7

[tex]18 = 7 + x[/tex]

Subtract 7 from both sides

[tex]x = 11[/tex]

Hence, the value of x is 11

Read more about shaded areas at:

https://brainly.com/question/24579466

Answer:

0.5333333333 or 0.53 when simplified.

Step-by-step explanation:

8/15 is simply 8÷15

15 into 8 is not possible so you annex a zero and write a decimal point.The 8 now becomes 80. We now say 80÷15,the answer is 5 because 15x5=75.The remainder is five.We annex another zero and it becomes 50,50÷15=3

I hope this helps.

Answer: The store must sell 40 bikes.

Step-by-step explanation:

y=60x+2400

y=120x

120x=60x+2400

-60x on both sides

60x=2400

divide 60 on both sides

2400/60=40

x=40  

Answer:

C= 3g

Step-by-step explanation:

[tex]\sqrt{3}x^2+10x+7\sqrt{3}=0\\\\\sqrt3(x^2+\dfrac{10x}{\sqrt{3}}+7)=0\\\\x^2+\dfrac{10x}{\sqrt{3}}+7=0\\\\x^2+\dfrac{10x}{\sqrt{3}}+\dfrac{25}{3}-\dfrac{25}{3} +7=0\\\\(x+\dfrac{5}{\sqrt{3}})^2 = \dfrac{4}{3}\\\\|x+\dfrac{5}{\sqrt{3}}| = \dfrac{2}{\sqrt{3}}\\\\x_1 = \dfrac{2}{\sqrt{3}}-\dfrac{5}{\sqrt{3}} = -\dfrac{3}{\sqrt{3}} = -\sqrt{3}\\\\x_2 = -\dfrac{2}{\sqrt{3}}-\dfrac{5}{\sqrt{3}} = \dfrac{-7}{\sqrt{3}} = -\dfrac{-7\sqrt{3}}{3}[/tex]

Answer:

your answer is k

Step-by-step explanation:

not all the isosceles triangles are similar

Answer:

2, 3 , 5, 7

Step-by-step explanation:

2(x - 2)/3 < (x + 1)/2 < 3(5x + 6)/4

Considering:

    2(x - 2)/3 < (x + 1)/2

<=>(2x - 4)/3 < (x + 1)/2

<=> (2x - 4)*2 < (x + 1)*3

<=> 4x - 8 < 3x + 3

<=> 4x - 3x < 8 + 3

<=> x < 11

Considering:

     (x + 1)/2 < 3(5x + 6)/4

<=>(x + 1)/2 < (15x + 18)/4

<=>(x + 1)*4 < (15x + 18)*2

<=> 4x + 4 < 30x + 36

<=> 4x - 30x < 36 - 4

<=> -26x < 32

<=> 26x > -32

<=> x > -32/26

=> -32/26 < x < 11

The prime numbers satisfy the above inequalities: 2, 3 , 5, 7

A) 22°

∡DBG = (360° - BD - BG)/2

= (360° - 170° - 146°)/2

= 44°/2

= 22°