You have a machine that can add exactly 46,899 pieces of candy per scoop to a giant vat and another machine that can remove exactly 13,576 pieces of candy with a different scoop from the giant vat. You have a total supply of 600,000 pieces of candy. Your giant vat starts out empty. The first machine adds scoops of candy, and then the second machine removes scoops of candy. When these two machines are done, there is only one piece of candy left in the vat. How many scoops of candy did the first machine add to the vat?

The probability that a student takes art, given that the student takes music is 10.8%

In probability, we say two events are independent if knowing one event occurred doesn't change the probability of the other event.

For example, the probability that a fair coin shows "heads" after being flipped is 1/21/21, slash, 2. What if we knew the day was Tuesday? Does this change the probability of getting "heads?" Of course not. The probability of getting "heads," given that it's a Tuesday, is still 1/21/21, slash, 2. So the result of a coin flip and the day being Tuesday are independent events; knowing it was a Tuesday didn't change the probability of getting "heads."

Two events, A and B, are independent if

P(A ∣ B)=P(A)

P(A).P(B) = P(A ∩ B)

In the given question there are independent events.

Given:-

P(A) = Student takes both art and music = 0.9

P(B) = Student takes music = 0.12

P(A ∩ B) = student takes art, given that the student takes music

Thus by using the formula we get,

P(A ∩ B) = 0.9 x 0.12 = 0.108 = 10.8%

The probability that a student takes art, given that the student takes music is 10.8%

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(a) Fermat's little theorem states that for any prime [tex]p[/tex], we have

[tex]a^{p-1} \equiv 1 \pmod p[/tex]

for any integer [tex]a[/tex]. Then

[tex]999,999 \equiv 1,000,000 - 1 \equiv 10^6 - 1 \equiv 1 - 1 \equiv 0 \pmod 7[/tex]

so 7 does indeed divide 999,999.

(b) Generalizing, we have

[tex]10^{12n} - 1 \equiv \underbrace{999\ldots999}_{12n \text{ nines}} \equiv (10^n)^{12} - 1 \equiv 0 \pmod {13}[/tex]

for positive integer [tex]n[/tex]. Now, since 1 = 1001 - 1000 and [tex]-1\equiv1000\pmod{1001}[/tex], it follows that [tex]10^3[/tex] is its own inverse modulo 1001, i.e.

[tex]10^3 x \equiv 1\pmod{1001} \implies x = 10^3[/tex]

This means

[tex]10^{12n} \equiv (10^3\times10^3)^{2n} \equiv 1^{2n} \equiv 1\pmod{1001} \\\\ \implies 10^{12n} - 1 \equiv 0 \pmod{1001}[/tex]

which is what we wanted to show.

a = 3, b = 4, and c = 2

a + b = c

3 + 4 = 2

3a + 4b = 2c
       -4     -4
     3a = -6c
      3       3
       a = -2

3a + 4b = 2c
-3             -3
      4b = -1c
        4     4

A)√500 is the correct answer.

It is an expression that has the same value but does not look the same. If you simplify an expression, you're  trying to write it in the simplest way possible.

According to the question,

The given expression is 10√5.

By computing the number out of the square root,

So,

[tex]=10 \sqrt{5} \\=\sqrt{10^2(5)} \\=\sqrt{100 (5)} \\=\sqrt{500}[/tex]

Therefore,

The equivalent expression for 10√5 is √500.

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Answer:

$30

Step-by-step explanation:

Let,

  x - fiction book

  x + $6 - novel

EQUATION:

  4(x) + 2(x + $6) = $84

  6x + $12 = $84

  6x = $84 - $12

  6x = $72

  x = $12

SUBSTITUTE:

    novel = $12

    fiction = $18

TOTAL COST OF NOVEL AND FICTION

$18 + $12 = $30

Answer:

Step-by-step explanation:

5x-9 = 2(x+23) or 5x-9 = 2x+46

Let' x be the "number."

"Five times a number decreased by nine" means: 5x - 9

"equal to twice the number increased by 23" means:  = 2(x+23)

Put them together:  5x-9 = 2(x+23)

5x-9 = 2(x+23)

5x-9 = 2x+46

[The formatting of the possible answers does not include parentheses nor algebraic symbols, making selection of a correct answer difficult. ]

Answer:

f(5)=17

Step-by-step explanation:

if,f(x)=3x+2

Then,f(5)=3*5+2

f(5)=17

Answer:

Step-by-step explanation:

at first decreased by 60% now increased by 80%

100 - 60% = 40

40 + 80% =

40 + 40 :100 * 80 =

40 + 32 =

72

Considering the given table, we have that:

A function has a relative maximum when it changes from increasing to decreasing.

Looking at the given table, it happens when x is near 3.

Also, looking at the table, for x > 3 the function is decreasing, hence as x approaches positive infinity, the value of the function approaches negative infinity.

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Answer: 1344

Step-by-step explanation:

Using the Pythagorean theorem, if we consider the unknown leg of the base, we get that it has a length of 12.

So, the area of the base is 96.

Multiplying this by the height, we get the volume is 1344 cubic inches.

The table that has a constant average rate of change represents a linear function.

The average rate of change of a function is given by the change in the output of the function divided by the change in the input.

When this rate is constant, the function is said to be linear, hence the table that has a constant average rate of change represents a linear function.

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Answer:

C

Step-by-step explanation:

The method that Chris can use to make sure the segments in the pattern are all parallel is to treat AI as a single line that acts as a transversal for the lines that need to be parallel.

Within the set of lines which need to be parallel, the acute angles must be congruent.

Both angles CDE and EDF need to be 180° minus twice the measure of one of the congruent acute angles.

The pair of the acute angles previously within each of the two sets of parallel lines are corresponding.

The fact that the transversals go through endpoints, there are no alternate angles, interior or exterior because alternate angles are on opposite sides of the transversal.

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Answer:

373 feet

Step-by-step explanation:

Since the rate of the machine producing ribbon is proportional to time, we can determine the number of inches of ribbon in 8 hours by some quick operations.

There are 16 1/2 hours in 8 hours, so we can multiply 280 by 16.

[tex]280 *16=4480[/tex]

Now, we have the number of inches it can produce in an 8-hour work day. However, we must convert to feet since that is the form of measurement the question is asking for. We can do so by dividing by 12.

[tex]4480/12=373.33[/tex]

Therefore, the number of feet the machine can produce in an 8-hour work day is 373.

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Step-by-step explanation:

the other answer is correct.

a few add-ons :

1 ft = 12 in

30 minutes = 1/2 hour (as every hour has 60 minutes)

every hour has therefore 2 half hours.

1 hour = 2 × 1/2 hour

8 hours = 8 × 2 × 1/2 hours = 16 × 1/2 hour

so, in 16 times the amount of time (8 hours) the machine can produce 16 times the amount of ribbon (16 × 280 in).

16 × 280 = 4480 in

and because every 12 in is 1 ft, this is then

4480/12 = 373.3333333... ft

therefore, 373 is the right answer (rounded).

Answer:

(2, - 2 )

Step-by-step explanation:

4x - y = 10 → (1)

x - 4 = y → (2)

substitute x - 4 = y into (1)

4x - (x - 4) = 10 ← distribute parenthesis on left side by - 1

4x - x + 4 = 10

3x + 4 = 10 ( subtract 4 from both sides )

3x = 6 ( divide both sides by 3 )

x = 2

substitute x = 2 into either of the 2 equations and solve for y

substituting into (2)

2 - 4 = y

- 2 = y

solution is (2, - 2 )

Answer:

x = 2 , y = -2

Step-by-step explanation:

I will use the elimination method :

4x-y = 10 - Equation Number 1

x-4 = y  - Equation Number 2

For the second equation we add 4 to both sides and subtract y from both sides :

x = y + 4

x - y = 4 - Let's call this equation number 3 :

Now we can subtract the equation 1 with 3 to eliminate y :

3x = 6

x = 2

Now we substitute this value into equation 2 to solve for y :

(2)-4 = y

y = -2

Substitute these values into equation 1 to verify :

4(2) - (-2) = 10

8 + 2 = 10

10 = 10

So these values must be correct

Hope this helped and have a good day

The equation that represents the line that passes through the points is [tex]y-1 = \frac{5}{4}(x-1)[/tex]. The correct option is D. [tex]y-1 = \frac{5}{4}(x-1)[/tex]

From the question, we are to determine the equation of the line that passes through the given points

Using the formula

[tex]\frac{y-y_{1} }{x-x_{1}} =\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]

From the give information,

[tex]x_{1} = 1 \\y_{1} = 1\\{x_{2} =5[/tex]

[tex]y_{2} = 6\\[/tex]

Putting the parameters into the formula,

[tex]\frac{y-1 }{x-1} =\frac{6-1}{5-1}[/tex]

[tex]\frac{y-1 }{x-1} =\frac{5}{4}[/tex]

∴ [tex]y-1 = \frac{5}{4}(x-1)[/tex]

Hence, the equation that represents the line that passes through the points is [tex]y-1 = \frac{5}{4}(x-1)[/tex]. The correct option is D. [tex]y-1 = \frac{5}{4}(x-1)[/tex]

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The range of the step function is all negative integers, thus, the correct option is A.

Domain is the set of values for which the given function is defined.

Range is the set of all values which the given function can output.

For the given function h(x)=-2|x|, any value of x will return a negative value, therefore, the range of the function is all negative numbers. This can be observed in the graph given below.

Hence, the range of the step function is all negative integers, thus, the correct option is A.

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The thing that best describes the values of x and y is option B; they will be real numbers greater than or equal to 0.

The real number refers to the union of both rational and irrational numbers that can have negative or positive values.

From the given information:

Peaches are being bought and sold for $2 per pound.

There is no negative value used here if x represents the number of pounds of peaches bought and y represents the total cost of the peaches.

Thus, a conclusion that can be reached as to the values of x and y is that they contain real numbers greater than or equal to 0.

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Answer:

im pretty sure its d

Step-by-step explanation:

----- ______------

We gujra weeeeeeee

We gujra weeeeeeee

We gujra weeeeeeee

We gujra weeeeeeee

Two triangles are said to be congruent if they have similar properties. Thus the required options to complete the paragraph proof are:

a. angle 1 is congruent to angle 2.

b. alternate angles are congruent if two parallel lines are cut by a transversal.

c. [tex]\frac{AD}{CD}[/tex] = [tex]\frac{AB}{CB}[/tex]

The similarity property of two or more shapes implies that the shapes are congruent. Thus they have the same properties.

From the given diagram in the question, it can be deduced that

ΔABC ≅ ΔABE (substitution property of equality)

Given that EA is parallel to BD, then:

i. <2 ≅ <3 (corresponding angle property)

ii. <1 ≅ < 4 (alternate angle property)

Thus, the required options to complete the paragraph proof are:

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The reason why people sometimes assume that the calculation 9 + 10 = 21 is as explained below.

We want to find out the reason why people say that; 9 + 10 = 21

Now, the way you have explained it is one way to look at it by utilizing number bases to play around with the figures to arrive at 21.

However, another way is to use algebra trick pattern which is;

9 can be expressed as 3 * 3

Also, 10 can be expressed as 5 * 2. Thus, we now have;

(3 * 3) + (5 * 2)

The applying properties of algebra to cross multiply gives;

(3 * 2) + (5 * 3)

= 6 + 15

= 21

Now, though your explanation arrived at 21 and mine also 21, but those are not correct mathematical methods as 9 + 10 must be equal to 19 and not 21.

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Answer:

28 should do it

Step-by-step explanation:

35+35+82= 152

180-152=28

Answer:

36 pieces of ribbon

Step-by-step explanation:

When Audrey cuts the ribbon into pieces that are each 1/3 yards long, she has 18 pieces (1/3 * 18 is 6, or the other way to think about it would be, 6 / (1/3) = 18). If she were to cut each of the pieces in half one more time, she would have 18 * 2 or 36 pieces of ribbon

Answer:

The relation {(2,1),(3,2),(-1,1),(0,-2)} is a function because the domain {2,3,-1,0} and range {1,2,1,-2} of the relation is paired exactly only once.

Step-by-step explanation:

The given relation is {(2,1),(3,2),(-1,1),(0,-2)}.

It is required to determine the relation is a function.

Step 1 of 1

The given relation is {(2,1),(3,2),(-1,1),(0,-2)}.

This relation shows that the domain of the relation {2,3,-1,0} is paired with one element of the range {1,2,1,-2}.

Hence, the relation is a function.

Answer:

x = 4

Step-by-step explanation:

3(-3x -3) + 2x + 4 = -33

(3*-3x + 3*-3) + 2x + 4 = -33

(-9x - 9) - 2x + 4 = -33

-9x + 2x - 9 + 4 = -33

-7x -5 = -33

-7x = -33 + 5

-7x = -28

x = -28/-7

x = 4

Check:

3((-3*4)-3) + 2*4 + 4 = -33

3(-12-3) + 8 + 4 = -33

3(-15) + 12 = -33

-45 + 12 = -33

Answer:

  30.70 ft

Step-by-step explanation:

For shadow problems, we make the assumption that an object's height and its shadow length are proportional.

The proportion for the two objects is ...

  height/shadow = pole/(22 ft) = (6 ft)/(4.3 ft)

Multiplying by 22 ft, we find the pole height to be ...

  pole = (22 ft)(6 ft)/4.3) ≈ 30.70 ft

The flagpole is about 30.70 feet tall.

Answer:

Given :- ABCD is a square.

To proof :- AC = BD and AC ⊥ BD

Proof :- In △ ADB and △ BCA

AD = BC [ Sides of a square are equal ]

∠BAD = ∠ABC [ 90° each ]

AB = BA [ Common side ]

△ADB ≅ △BCA [ SAS congruency rule ]

⇒ AC = BD [ Corresponding parts of congruent triangles are equal ]

In △AOB and △AOD

OB = OD [ Square is also a parallelogram therefore, diagonal of parallelogram bisect each other ]

AB = AD [ Sides of a square are equal ]

AO = AO [ Common side ]

△AOB ≅ △ AOD [ SSS congruency rule ]

⇒ ∠AOB = ∠AOD [ Corresponding parts of congruent triangles are equal]

∠AOB + ∠AOD = 180° [ Linear pair ]

∠ AOB = ∠AOD = 90°

⇒ AO ⊥ BD

⇒ AC ⊥ BD

Hence proved, AC = BD and AC ⊥BD

Answer:

The 3rd graph from the top.

Step-by-step explanation:

Just Like the story, the third graph goes up slowly and plateaus for the duration of a school day, then goes back down quicker than it went up.