For George’s party, his dad bought an ice cream cake. After the party,
1/3 of the cake was left. The next day, George ate half of what was left. Choose the model that shows what fraction of cake George ate.

2 is the fifth root of 32.

Using the problem as a starting point, we may write the equation as x5=32 x 5 = 32. This equation has to have a solution. The log function can be used to both sides of the equation. Therefore, the right response is 2.

A. In mathematics, the term "root" refers to a number that, when multiplied by itself, equals the original number.. Because 49 is created by multiplying 7 by itself twice in this instance, we refer to 7 as the square root of 49. Since 333=27, the cube root of 27 is 3.

[tex]\sqrt[5]{32}[/tex]

[tex]\sqrt[5]{2*2*2*2*2}[/tex]

= 2

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The simplified exponential expression is given as follows:

48x^13y^7.

The first term of the numerator is (4x²y)², hence, applying the power of power rule, it is given as follows:

(4x²y)² = 16x^4y². (apply the power of 2 to each factor).

The square root is equivalent to an exponent of 1/2, hence the power of power rule is also applied as follows:

square root (9x^6y²) = 3x³y.

At the denominator, we have that the term has a negative exponent, hence it is moved to the numerator, thus:

(x³y²)² = x^6y^4.

Now the expression is given as follows:

16x^4y² times 3x³y times x^6y^4

The multiplication of the coefficients is given as follows:

16 x 3 x 1 = 48.

For the variables x and y, we keep the bases and add the exponents, hence:

Hence the simplified expression is given as follows:

48x^13y^7.

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Answer:(x + 9)(x - 3)

Step-by-step explanation:

⇒x² + 6x - 27

breaking middle term

⇒x² + 9x - 3x - 27

⇒x (x + 9) - 3 (x + 9)

⇒(x + 9)(x - 3) ...answer

hope that helps ...

The number of silver and gold medals won is given as follows:

75.

The number of silver and gold medals is obtained applying the proportions in the context of this problem.

The percentage equivalent to silver and gold medals is given as follows:

20 + 30 = 50%.

Hence half the number of medals was either silver or gold, thus the number is given as follows:

0.5 x 150 = 75 meddals.

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There are 200 teachers in a school.

To determine the percentage, we have to divide the value by the total value and then multiply the resultant by 100, also defines a fraction or a ratio in which the value of the whole is always 100

Given information is

25 % of the teachers teach basic math, there are 50 basic math teachers

To calculate how many teachers are there in the school.

Let the total number of teachers =c

Number of basic maths teacher=50

Percentage of teachers of basic math = 25

According to question

25% of x=50

0.25*x=50

x=200

Hence the total number of teachers is 200

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If f′ is growing, the f graph is concave up on the interval. In the event that f′ is decreasing, the f graph is concave down on the interval. This has been obtained by using the concept of derivatives.

What are derivatives?

In mathematics, a quantity's instantaneous rate of change with respect to another is referred to as its derivative. Investigating the fluctuating nature of an amount is beneficial.

Assume that f is differentiable on interval I.

If f′ is increasing, the f graph is concave up on I. In the event that f′ is decreasing, the f graph is concave downward on I. The graph of f is considered to have no concavity if f′ is constant.

Hence, concave up is when f' is increasing and when it is decreasing, it is concave down.

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For given exponential function f(t), f(7)=24.7.

An exponential function is a Mathematical function in the form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.

Exponential Growth

In Exponential Growth, the quantity increases very slowly at first, and then rapidly. The rate of change increases over time. The rate of growth becomes faster as time passes. The rapid growth is meant to be an “exponential increase”. The formula to define the exponential growth is:

y = a ( 1+ r )ˣ

Where r is the growth percentage.

Exponential Decay

In Exponential Decay, the quantity decreases very rapidly at first, and then slowly. The rate of change decreases over time. The rate of change becomes slower as time passes. The rapid growth meant to be an “exponential decrease”. The formula to define the exponential growth is:

y = a ( 1- r )ˣ

Where r is the decay percentage.

Now,

Given function f(t)=300(0.7)ᵗ

f(7)=300*0.7⁷

f(7)=300*0.0823

f(7)=24.7

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Frequency and wavelength are related by the equation f=cλ, where c is the speed of light in a vacuum. The speed of light in a vacuum is 2.9979×108 m/s. Wavelength must be converted from kilometers to meters, then the values can be plugged into the equation. f=2.9979×108 m/s5,700 m=52,594 Hz. The resulting frequency is 52,594 Hz or 5.3×104 Hz when rounded to the correct number of significant figures.

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The bottleneck time is 10. This is the longest time it takes to complete any task in the assembly line, and all the other tasks must be completed within this time frame.

The bottleneck time is the longest time it takes to complete any task in the assembly line. In this case, the longest time needed is 10, which is the last station. This means that all the other tasks must be completed within 10 seconds in order for the entire assembly line to proceed.

The bottleneck time is 10. This is the longest time it takes to complete any task in the assembly line, and all the other tasks must be completed within this time frame.

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The unsigned binary equivalent of the following unsigned decimal integer value 12 is 1100

An integer is a whole number that can be positive, negative, or zero. An unsigned integer is a non-negative integer that only represents positive values or zero.

To convert an unsigned decimal integer to its equivalent binary representation, you'll need to understand the basic concepts of binary and the process of converting decimal to binary.

Here we have to consider the unsigned decimal integer value 12.

To convert it to binary, start by determining the largest power of 2 that is less than or equal to 12, which is

=>  2³ = 8.

Write a 1 in the binary place corresponding to 2³ and subtract 8 from 12 to get 4.

=> 12 - 8 = 4

Then, determine the largest power of 2 that is less than or equal to 4, which is

=> 2² = 4.

Write a 1 in the binary place corresponding to 2² and subtract 4 from 4 to get 0.

=> 4 - 4 = 0

The binary equivalent of 12 is 1100.

Complete Question:

what is the unsigned binary equivalent of the following unsigned decimal integer value 12?

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The slope-intercept form of the function described by this line is y = x + 1

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

x   y

0   1

From the above table of values, we can see that

The difference between the x and the y value is 1

Mathematicallly, this can be represeted as

y - x = 1

Add x to both sides

y - x + x = x + 1

Evaluate the like terms

So, we have the following representation

y = x + 1

The above equation is in the slope intercept form, y = mx + c

Hence, the equation is y = x + 1

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Complete question

Can you find the slope-intercept equation of each line and type the correct code? Please remember to type in ALL CAPS with no spaces. *

x   y

0   1

well, 100% - 20% = 80%, so the discounted price is really 80% of the original 20 bucks, what's 80% of 20?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{80\% of 20}}{\left( \cfrac{80}{100} \right)20}\implies \text{\LARGE 16}[/tex]

To do this you would do

$20 times (20/100) to get $20*(.20) = $4 which is the discounted price.

%(Percent) means "a specified amount in or for every hundred." In this case 20 for every 100.

Answer:

Step-by-step explanation:

solve what's in the parenthesis.

1,204-299=905

so....

905/1

answer is: 905.

if you would like, use a website called Desmos graphing calculator.

its a calculator of all subjects, and it graphs.

Answer:

20

Step-by-step explanation:

Ariana has 3 milk bones and she wants to give them to three of her 6 dogs, with each getting one bone. In 20 ways this can be done.

Ariana has 3 milk bones and she wants to give them to three of her 6 dogs, with each getting one bone.

We have to determine how many ways this can be done.

We have to distribute 3 milk bones to the 6 dogs.

Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.

So the possibilities = [tex]^6C_{3}[/tex]

Using the formula; [tex]^nC_{r}=\frac{n!}{r!(n-r)!}[/tex]

[tex]^6C_{3}=\frac{6!}{3!(6-3)!}[/tex]

[tex]^6C_{3}=\frac{6!}{3!3!}[/tex]

[tex]^6C_{3}=\frac{6\times5\times4\times3!}{3\times2\times1\times3!}[/tex]

[tex]^6C_{3}[/tex] = 5 × 4

[tex]^6C_{3}[/tex] = 20

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Average rate of change for the given function is 2.

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

Given that the graph is a line. So the function is linear.

Average rate of change of a linear function is equal to the slope of the given function, and it will be a constant at any two points on the line.

We have two points from the line (-2, -3) and (1, 3).

Slope of a line with two points (x, y) and (x', y') is,

slope = (y' - y) / (x' - x)

Slope of the given function with two points (-2, -3) and (1, 3) is,

Slope = (3 - -3) / (1 - -2) = 6/3 = 2

Average rate is same value from x = 1 to x = 2.

Hence the average rate of change is 2 for the given function.

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She used 7.90 paint with white paint on her bedroom walls.

To solve such problems we must know about fractions and subtraction.

Fraction

A fraction is a way to describe a part of a whole, the amount of white paint Jane used is 7.4 pints.

Given to us,

Total paint used my Jane = 8.3 pints = 83/10 pints,

the amount of blue paint = 2/5 pints,

Amount of white paint

amount of white paint = Total paint used - the amount of blue paint

=83/10-2/5

=83/10-2*2/5*2

=83/10-4/10

=79/10

=7.9pints

Hence, the amount of white paint Jane used is 7.9pints.

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Answer:

Step-by-step explanation:

400x2% of that amont would equal 800

He must anticipate drawing a red tile. 30 times minimum.

Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Given this, Alex placed 8 blue tiles and 12 red tiles in a container. He plans to draw a tile, record its color, and replace it in the container before drawing another.

Let X be the number of times a red tile is drawn from the container

Number of red tiles = 12

Total tiles = 12 + 8 = 20

p = P(randomly drawing a red tile) = 12/20 = 0.6

n = 50 number of draws or trials

Since Alex replaces the tile before he draws the next tile, we can model

the distribution of X according to Binomial Distribution

Thus, X ~ Binomial with n = 50 and p = 0.6

The Expected value of a binomial variable is E(X) = np

E(X) = n * p

= 50 * 0.6

= 30

therefore,  he should expect to draw a red tile At least 30 times.

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Answer: The 4th option

Step-by-step explanation:

4 cm x 3cm is 12 cm. 2 cm x 5 cm is 10 cm.

Answer:

  see attached

Step-by-step explanation:

You want the expressions in the correct sequence to prove ...

  z + z + z + z = 4z

The multiplicative identity property tells you z × 1 = z. Anything multiplied by 1 is unchanged. This lets us replace z in the original expression by z·1 in every case.

The distributive property tells you that multiplication distributes over addition. This means ...

  z ·1 + z · 1 + z · 1 + z · 1 = z · (1 + 1 + 1 + 1)

The properties of addition and the set of integers tell us that ...

  1 + 1 + 1 + 1 = 4

so we can replace the indicated sum by its value:

  z · (1 + 1 + 1 + 1) = z · 4

The commutative property of multiplication says a product is the same if the operands are in a different order:

  z · 4 = 4·z = 4z

This is the last step in showing z + z + z + z = 4z.

The correct order of tiles is shown in the attachment.

<95141404393>

The value of the logarithmic expression is (b) 0

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

log₉(1ˣ)

The logarithmic rule log(1^b) = 0 can be used to evaluate log(1^x) base 9:

log₉(1ˣ)

This is true because

Since 1^x = 1, no matter what the value of x is,

Then log(1^x) base 9 = x = 0.

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The function f(x) = -9 + 4x - x³ is increasing on the intervals (-∞, -√(4/3)) and (√(4/3), +∞), and decreasing on the interval (-√(4/3), √(4/3)).

The relative minima occur at x = ±√(4/3).

A function is a mathematical mapping from one set of values to another set of values.

To find the first derivative of the function, we need to take the derivative of each term in the function. The derivative of -9 is 0, the derivative of 4x is 4, and the derivative of -x³ is -3x². So the first derivative of the function f(x) is:

f'(x) = 4 - 3x²

We want to find the values of x where f'(x) = 0 (because this will tell us where the function changes from increasing to decreasing, or vice versa). Solving for x, we get:

=> 0 = 4 - 3x²

=> 3x² = 4

=> x² = 4/3

=> x = ±√(4/3)

The first derivative of the function f(x) is positive for x values less than -√(4/3) and for x values greater than √(4/3), so the function f(x) is increasing on those intervals.

The first derivative of the function is negative for x values between -√(4/3) and √(4/3), so the function f(x) is decreasing on that interval.

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Answer:

The answer is 1548.99ft.

Step-by-step explanation:

To determine the length of the strip needed for waterproofing, you need to calculate the circumference of the circular floor. The formula for the circumference of a circle is 2π times the radius. If the floor of the treehouse has a radius of 490.625/2= 245.3125ft, then the circumference of the floor is:

2π x 245.3125ft = 1548.99ft

So, the length of the strip needed for waterproofing around the floor is approximately 1548.99ft.

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Have a nice day.

Kylar is a lifeguard at a swimming pool, The total number of hours in a single shift done by Kylar is 3 hours.

Let the total number of hours in a single shift be = A

Now , The total length of equal shifts Skylar worked last week = 3 3/4 shifts

The total length of equal shifts Skylar worked last week = 15 / 4 shifts

The total number of hours Skylar worked in the week = 11 1/4 hours

The total number of hours Skylar worked in the week = 45 / 4

Now , the equation will be

Total length of equal shifts Skylar worked last week is equal to total number of hours Skylar worked in the week.

So ,

Total length of one shift of Skylar = total number of hours Skylar worked in the week / Total length of equal shifts Skylar worked last week

On substituting the values in the equation , we get

Total length of one shift of Skylar A = ( 45/4 ) / ( 15/4 )

On simplifying the equation , we get

A = ( 45/4 ) / ( 15/4 )

A = 45 / 15

A = 3 hours

Therefore, The total number of hours in a single shift done by Kylar is 3 hours.

Complete question: Skylar is a lifeguard at a swimming pool. Last week, they worked 3(3)/(4) equal -length shifts, because rain closed the pool early one day. Those shifts totaled 11(1)/(4) hours of work. How long is a single shift?

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The solution to the inequality 5/w > 4/45 is given as follows:

w < 56.25.

The inequality for this problem is defined as follows:

5/w > 4/45.

Applying cross multiplication, we have that:

4w < 45 x 5

w < 45 x 5/4

w < 56.25.

The solution is found similarly to an equality, isolating the desired variable. The difference is that the solution is composed by infinity values in a range of values, instead of a finite number of values.

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Step-by-step explanation:

I cannot see the diagram at the bottom, so I cannot tell you a correct answer

Shelton needs a minimum of 46 ft of molding to go around the perimeter of the ceiling.

The minimum amount of molding Shelton needs can be calculated by finding the length of the perimeter of the square ceiling. To do this, we first need to find the length of a side of the square.

We can use the Pythagorean theorem to find the length of a side of the square. The theorem states that the sum of the squares of the sides of a right triangle is equal to the square of the length of the hypotenuse (in this case, the diagonal of the square).

Thus, we have the equation: side^2 + side^2 = diagonal^2.

Solving for the side length, we have side = sqrt(diagonal^2/2).

So, the side length is sqrt(23^2/2) = 11.5 ft.

Therefore, the perimeter of the square is 4 * 11.5 = 46 ft.

Therefore, Shelton needs a minimum of 46 ft of molding to go around the perimeter of the ceiling.

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Complete question:

A square ceiling ha a diagonal of 23 ft. Shelton wants to put molding around the perimeter of the ceiling. The molding is old by the foot. What i the minimum amount of molding he needs?

Filling in the chart below with the interest and maturity future value is as follows:

Purpose               Principal  Interest Term (Days)  a) Interest  b) Maturity

Wedding Dress  $250.00      6%       75 days           $3.10          $253.10

College Books   $360.50     3.5%    180 days          $6.28         $366.78

The future value represents the compounded present value.

Compounding involves the interest of subsequent months computed on the accumulated interest.

The future value can be computed using an online finance calculator.

N (# of periods) = 75 days

I/Y (Interest per year) = 6%

PV (Present Value) = $250

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $253.10

Total Interest = $3.10

N (# of periods) = 180 days

I/Y (Interest per year) = 3.5%

PV (Present Value) = $360.50

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $366.78

Total Interest = $6.28

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To find the OGF for the number of ternary sequences in which any occurrence of 2 has a 1 both immediately before and immediately after it, we can use a recursive approach.

Let A(x) be the OGF for sequences that start with a 1 and end with a 1. And let B(x) be the OGF for sequences that start with a 1, contain a 2, and end with a 1.

We have A(x) = x + [tex]x^{2}[/tex] + [tex]x^{3}[/tex] + [tex]x^{4}[/tex] + ...

And B(x) = x * [tex]A(x)^{2}[/tex], since a 2 can only appear after a 1 and must be immediately followed by another 1.

Finally, the OGF for the desired sequence is B(x) = x * x + [tex]x^{2}[/tex] + [tex]x^{3}[/tex] + [tex]x^{4}[/tex] + ...)^2 = x * [tex]A(x)^{2}[/tex]

So, the OGF for the number of ternary sequences in which any occurrence of 2 has a 1 both immediately before and immediately after it is x * ( x + [tex]x^{2}[/tex] + [tex]x^{3}[/tex]......)^2.

The ordinary generating function (OGF) for a sequence is a formal power series that encodes information about the sequence.

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