A bag of cat food has 16 1/2 cups of food. Cupcake (the cat) eats 1 1/2 cups a day. How many days will the bag of cat food last?

Answer:

60

Step-by-step explanation:

To find the least common multiple of 15 and 12, we can list the multiples of 15 and 12 and find the smallest number that appears in both lists:

Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, ...

Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ...

The least common multiple of 15 and 12 is 60, so Cameron and Brooks will go to the grocery store on the same day every 60 days.

Answer:

x= 2 and x= -(2/3)

Step-by-step explanation:

Step 1 :Multiply all terms by the same value to eliminate fraction denominators

x^2/ x+6 = 1/2

2(x+6)*(x^2/x+6) = 2(x+6) * 1/2

Step 2: Cancel multiplied terms that are in the denominator

2x^2= x+6

Step 3: Move terms to the left side

2x^2 - (x+ 6) = 0

Step 4: Distribute

2x^2 - x - 6 = 0

Step 5: Use the quadratic formula

x= ( - (-1) +- Squar((-1)^2-4*2(-6)) ) / 2*2

Step 6: Simplify

x= (1+- 7)/ 4

Step7: Separate the equations

x= (1+7)/ 4 and x= (1- 7)/ 4

Step 8: Solve that 2 small equation

x= 2 and x= -(3/2)

Answer:

x = - [tex]\frac{3}{2}[/tex] , x = 2

Step-by-step explanation:

x² : x + 6 = 1 : 2

express the ratio in fractional form

[tex]\frac{x^2}{x+6}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

2x² = x + 6 ( subtract x + 6 from both sides )

2x² - x - 6 = 0 ← in standard form

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 2 × - 6 = - 12 and sum = - 1

the factors are - 4 and + 3

use these factors to split the x- term

2x² - 4x + 3x - 6 = 0 ( factor the first/second and third/fourth terms )

2x(x - 2) + 3(x - 2) = 0 ← factor out (x - 2) from each term

(x - 2)(2x + 3) = 0 ← in factored form

equate each factor to zero and solve for x

x - 2 = 0 ⇒ x = 2

2x + 3 = 0 ⇒ 2x = - 3 ⇒ x = - [tex]\frac{3}{2}[/tex]

The probability that this person has an IQ greater than 95 =62.93%

The area of mathematics known as probability is concerned with the outcomes of random events. Probability refers to a chance or potential for something to happen. It explains the likelihood that a specific event will take place.

We frequently say things like, "It will probably rain today," "He will probably pass the test, "There is very little chance of getting a storm tonight," and "Most likely the price of onions will increase once more." We substitute the word probability for all of the words chance, doubt, maybe, likely, etc. in these sentences.

In essence, probability is the ability to forecast an outcome based on the variety and quantity of potential outcomes or the analysis of historical data.

Let X be the IQ

IQ is normally distributed with a mean of 100 and a standard deviation of 15.

a) the probability that this person has an IQ greater than 95

=62.93%

b) the probability that this person has an IQ less than 125

=4.75%

c) Sample size =500

No of people = 0.2486(500) =124.3

d)

No of persons = 0.0047(500) = 2.35

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Answer:

Step-by-step explanation:

3x - 19 = 2x + 1

x - 19 = 1

x = 20

2(20) + 1 + 5y + 19 = 180

40 + 1 + 5y + 19 = 180

41 + 5y + 19 = 180

5y + 19 + 41 = 180

5y + 60 = 180

5y = 120

y = 24

The document do you need to have on hand when preparing to file your tax return is W-2

A tax return is a form or forms filed with a tax authority that reports income, expenses, and other pertinent tax information.

To file your return, you'll need the following on hand: Your W-2: This form will come from your company and list not only your salary for the year, but the amount of taxes withheld along the way. You're required to file your W-2 along with your taxes, so if you're a salaried employee, this form is non-negotiable.

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Answer:

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

Given:

Find the discount:

Find the discount %:

The number of hours in a week a student played basketball is [tex]11\frac{3}{8}[/tex].

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, One week a student exercised 3 hours at school and another 1/4 of an hour at home.

Also given that 1/4 of the exercise of a student came from playing basketball.

Therefore, Time playing basketball is one-fourth of the total time exercised which is,

= (3 + 1/4)×(1/4).

= (13/4)×(1/4).

= (13/8).

Therefore, In a week the student played (13/8)×7.

= 91/8.

= [tex]11\frac{3}{8}[/tex].

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The instantaneous rate of change of f(x) = x³ − 5 at (2,3) is (b) 12

From the question, we have the following parameters that can be used in our computation:

Function: f(x) = x³ − 5

Point = (2, 3)

Differentiate the function to get the instantaneous rate

This is represented as

f'(x) = 3x²

Substitute 2 for x in the equation

The 2 is coming from the x-coordinate in (2, 3)

So, we have

f'(2) = 3(2)²

Evaluate

f'(2) = 12

Hence, the instantaneous rate of change is 12

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Tritan purchased a new car in 2000 for $22,800. The value of the car ha been depreciating exponentially at a constant rate then the Cost of the car in year 2016 will be $2811.

Cost price of the car = $22800

Value of the car has been depreciating exponentially, so the formula for value   of the car after t years,

Here P(t) = Final value after t years

A = Cost price or initial value

r = rate of depreciation

t = duration in years

r = 100(1 - 0.87737)

r = 12.26%

Now cost of the car in year 2016 (After 16 years)

P(16)  = 2810.99

       = $2811

Therefore, cost of the car in year 2016 will be $2811.

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Answer:

try 5/15 or 1/15

Step-by-step explanation:

this is because it shows one shaded box we know it's a third out of just that one column

so you multiple a third by 5 and you get 15 what ever you do to the denominators you do to the numerator

Answer:

Correct Statement : The y- intercept of Function A is greater than the y- intercept of Function B

Answer:

11

Step-by-step explanation:

x + 6 + 2y

x + 2y + 6

x + 2y = 5

5 + 6 = 11

A group of nine people can now be seated in a row in 40320 different ways.

The two people who insist on sitting next to one other can be situated in one of two ways. The remaining seven people can be seated in seven different ways.

As a result, the total number of ways in which the nine persons can be seated in a row is 1 x 7! = 40320.

In this situation, the two people who dislike each other can be seated in

(7-1)! different ways.

The remaining seven people can be seated in seven different ways.

As a result, the total number of possible combinations for seating 9 individuals in a row is (7-1)! x 7! = 40320.

A combination is a mathematical technique for determining the number of potential arrangements in a set of objects where the order of the selection is irrelevant. You can choose the components in any order in combinations. Permutations and combinations are often mistaken.

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The probability that the deal of a five-card hand provides a pair of aces is 0.0399

In this question, we have been given a deck of playing cards contains 52 cards, four of which are aces.

We need to find the probability that the deal of a five-card hand provides a pair of aces.

The sample space for given experiment is: choosing 52 cars choosing 5.

n(S) = 52C_5

We need to find the chance of getting a pair of aces, there are 4 aces in the pack on 2 of them.

So, n(A) = 4C_2

So that means there are 48 cards left which are not aces in the pack and want 2 of those.

So, the required probability is:

P(A) = (4C_2 * 48C_3) / 52C_5

P(A) = (6 * 17296) /2598960

P(A) = 103776 / 2598960

P(A) = 0.0399

Therefore, the required probability is 0.0399

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Answer:

y=5x

Step-by-step explanation:

If y is 25 and x is 5

25 = 5 (5)

25=25

She sold more cheese boxes on Tuesday.

Comparing numbers in maths is defined as a process or method in which one can determine whether a number is smaller, greater, or equal to another number according to their values.

Given that, Marietta is selling cheeses for the holiday fundraiser. On Monday, she sold seven-ninths of the boxes of cheeses. On Tuesday, she restocked her supply and sold 0.85 of the boxes of cheeses.

On Monday = 7/9 = 0.777

On Tuesday = 0.89

Since, 0.89 > 0.777

Hence, she sold more on Tuesday.

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Surface area implies the external surface that bounds a given shape. The surface area of the shape is 384 sq in.

The surface area of a shape is the external side of the shape that can be seen. Sometimes, a given shape may have different shapes that forms its surface area.

From the given question,

i. The area of triangular surface = 1/2 * base* height

                          = 1/2*12*8

                          = 48

Area of the triangular surface = 48 sq in.

ii. The area of its rectangular sides = length * width

                                  = 9* 10

                                  = 90

Area of its rectangular sides = 90 sq in.

iii. The area of its base = length * width

                             = 9 * 12

                             = 108

Area of its base = 108 sq in.

Therefore,

the surface area of the shape = (2*48) + (2*90) + 108

                            = 96 + 180 + 108

                            = 384 sq in.

The surface area of the given shape is 384 square inches.

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Answer: About 2.2

Step-by-step explanation: Since 13 divided by 6 is 2.16 repeating, you can use the 6 to round up the 1, making it about 2.2

Answer:

x = -3

Step-by-step explanation:

See the picture below

Answer:

22.5

Step-by-step explanation:

total bill =$150

tip percentage =15%

now,

tip money = 15% of $150

=150×15/100

=2250/100

=$22.5

As per the Newton's method, the equal ration of the Pizza is 3: 2: 3

In math, Newton's method states that a technique for solving equations of the form f(x)=0 by successive approximation

Here we have given that three calculus students entered a pizza parlor. they were quite hungry and ordered an entire pie, instead of having the pizza maker cut the pie in the usual manner they asked her to slice the pie into three equal areas using only two parallel slices.

And we need to find these slices be made in order to accomplish this

Here let us assuming that the pizza has unit radius, and the area of the pizza is π and each piece has to have area π/3.

Therefore, the given details is enough to find the height of a circle segment such that its area is one third of the original circle,

As per the Newton's method, we get the value of h as,

=> h ≈ 0.735068 ≈ 4492/6111,

Therefore the three slices have widths approximately proportional to 3:2:3.

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Answer:

To determine the percentage decrease in W when x is decreased by 9.75%, we need to first determine the relationship between w and x. Since w is proportional to the square root of x, we can write an equation to represent this relationship as follows:

w = k * √x

where k is the proportionality constant.

If the value of x is decreased by 9.75%, we can write the new value of x as follows:

x' = x * (1 - 0.0975) = x * 0.9025

Substituting this expression for x' into the equation above, we get:

w' = k * √(x * 0.9025)

To determine the percentage decrease in w, we can divide the new value of w by the original value of w and multiply by 100% to get the percentage change, or:

percentage decrease in w = (w' / w) * 100%

Substituting the expressions for w' and w into this equation, we get:

percentage decrease in w = [(k * √(x * 0.9025)) / (k * √x)] * 100%

Simplifying this expression, we get:

percentage decrease in w = (√(0.9025)) * 100%

Since the square root of 0.9025 is approximately 0.95, we can say that the percentage decrease in w is approximately 5%. This means that the value of w decreases by approximately 5% when the value of x decreases by 9.75%.

Answer:

d = 0

Step-by-step explanation:

7.5d = 2.5d

Divided both sides by factors and we get

d = 0

The required solutions are as follows,
1. Angle e = Angle a
2. Angle f = Angle c
3. Ange a, b, and c add up to 180°.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°

here.
Angle e = Angle and as they are alternate angles,
Angle f = Angle c as they are alternate angles,

Ange a, b, and c add up to 180°. as they lie on a straight line.
Therefore angles e, f, and b also be added to  180°

Thus, the solution of the angles is shown above.

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The function available capacity for the four classes is 40 seats each. The protection level for class 1 is 40 seats, meaning that 40 seats are protected for class 1. 40 + 40 + 40 + 40 = 160

The booking limits for the four fare classes in a flight are given as 40, 40, 40, and 40, respectively. This means that the available capacity for these four classes is 40 seats each. The protection level for class 1 is 40 seats, meaning that 40 seats are specifically reserved for passengers in class 1. This ensures that passengers in class 1 are guaranteed at least 40 seats on the flight. The protection level for the other classes is also 40 seats each, ensuring that at least 40 seats are available for each class. This allows airlines to ensure that all of their classes have sufficient seating capacity for their passengers. 40 + 40 + 40 + 40 = 160

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Answer: 168

Step-by-step explanation: f(51)= 3(51)+15, 3(51)=153.  153+15=168

Answer:

x = 12

Step-by-step explanation:

given

f(x) = 51

f(x) = 3x + 15

51 = 3x + 15

3x = 51 - 15

3x = 36

x = 12

The length of ladder leaning against the side of a house is 10.44 m .

As  shown in the figure below h is the length of the house so we have to find h .

the ladder form a right angled traingle where base of the ladder is 3 m.

and the height of wall to which ladder is leaning against is 10m. and the ladder is the longest side of the right angled traingle i.e Hypotenuse

so we wil use Pythagoras theorem to find the longest side of ladder + wall system

so for a right angled traingle Pythagoras theorem states that

[tex]h^2 = p^2 + b^2[/tex]

where h=Hypotenuse ,p=perpendicular , b=base.

so we have to find h given p= 10m ,b=3m

so putting the values of p and b in the above equation we get

[tex]h^2 = 10^2 +3^2 =109[/tex]

so

[tex]h=\sqrt{109} = 10.44 m[/tex]

so the length of ladder is 10.44 m

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