James wants to sort the numbers on his teddy bears from greatest to least. After he sorts the numbers. What number would come next?

First, let's simplify the expression (4c + 8) + 3c - 2:

(4c + 8) + 3c - 2

= 4c + 3c + 8 - 2 (rearrange terms)

= 7c + 6 (combine like terms)

So the first expression simplifies to 7c + 6.

Next, let's simplify the expression 4c + 2(0.5c + 1):

4c + 2(0.5c + 1)

= 4c + 2(0.5c) + 2(1) (distribute the 2)

= 4c + c + 2 (simplify the parenthesis)

= 5c + 2 (combine like terms)

So the second expression simplifies to 5c + 2.

Now we can compare the two expressions:

7c + 6 vs. 5c + 2

These expressions are not equivalent because they do not have the same coefficients or constants.

Answer:

4096/15625 or

0.262144 or

(4/5)^6

The equation to represent the situation is 96 = 12 + 8x and the number of hours she rent the boat is 10.5 hours.

During a vacation, Alice went fly-fishing. She rented a drift boat. Rick's Rental fishing rod drift boat cost $12 plus $8/hour.

She spent a total of 96 dollars. The equation to solve the situation can be calculated as follows:

Hence,

y = 12 + 8x

where

Therefore,

96 = 12 + 8x

8x = 96 - 12

8x = 84

divide both sides by 8

x = 84 / 8

x = 10.5 hours

Therefore,

hours she rented the boat = 10.5 hours

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Answer:

We can use the half-angle formula for sine to find the exact value of sin(a/2) in terms of sin(a):

sin(a/2) = ±√[(1 - cos(a))/2]

where the ± sign depends on the quadrant of a/2.

To use this formula, we first need to find cos(a). We can do this using the identity:

sin^2(a) + cos^2(a) = 1

Substituting sin(a) = 7/9, we get:

(7/9)^2 + cos^2(a) = 1

Simplifying and solving for cos(a), we get:

cos(a) = ±4/9

Since a is in quadrant I, we take the positive value of cos(a):

cos(a) = 4/9

Now we can use the half-angle formula for sine to find sin(a/2):

sin(a/2) = ±√[(1 - cos(a))/2]

Substituting cos(a) = 4/9, we get:

sin(a/2) = ±√[(1 - 4/9)/2]

Simplifying, we get:

sin(a/2) = ±√(5/18)

Since a is in quadrant I, a/2 is also in quadrant I, so we take the positive value of sin(a/2):

sin(a/2) = √(5/18)

Therefore, the exact value of sin(a/2) is √(5/18)

The no of people take more than 19 mins are above 50%

1. Break it down: Divide the topic into smaller subtopics or concepts. This can make it easier to understand and digest each piece of information.
2. Research: Look up definitions, explanations, or examples related to the terms or concepts you're trying to understand. This can help clarify any confusion or uncertainty.
3. Take notes: Write down important information, key points, or definitions as you research. This can help you remember and better understand the material.
4. Ask questions: If you're still unsure about certain aspects, don't hesitate to ask for help or clarification from a teacher, tutor, or friend.
5. Practice: Apply what you've learned to related problems or questions. Practicing can help reinforce your understanding

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Answer: Exponential & $11,709.83

Step-by-step explanation:

The growth of the investment can be represented by an exponential function because the interest is being compounded quarterly, which means that the interest is being added to the account balance and the account balance is growing exponentially over time.

The formula for the future value of an investment with continuous compounding is:

A = P e^(rt)

Where A is the future value, P is the principal investment, e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate expressed as a decimal, and t is the time in years.

In this case, the principal investment is $10,000, the annual interest rate is 3.2%, and the interest is compounded quarterly, so the quarterly interest rate is 3.2%/4 = 0.8%. The time period is 5 years, so t = 5.

The formula for the future value of an investment with quarterly compounding is: A = P (1 + r/n)^(nt)

Where n is the number of compounding periods per year, which is 4 in this case.

Substituting the values, we get:A = $10,000 (1 + 0.032/4)^(4*5) = $11,709.83

Therefore, the value of the account after 5 years is $11,709.83 rounded to the nearest cent.

Answer:

To find the total surface area of the square pyramid, we need to find the area of each of its faces and add them up.

The pyramid has a square base with sides of 8 inches and each triangular face has an isosceles right triangle shape with two sides of 8 inches and a hypotenuse of 2 x 8 = 16 inches (using the Pythagorean theorem).

The total surface area is then:

Area of the square base: 8 x 8 = 64 square inches

Area of each triangular face: 1/2 x 8 x 8 = 32 square inches (since each triangle is isosceles with base and height of 8 inches)

Total surface area: 4 x 32 + 64 = 192 + 64 = 256 square inches

Therefore, the total surface area of the square pyramid is 256 in². So, the closest answer option is 256 in, 2.

We may conclude after answering the presented question that This ratio indicates that the guys picked up 5 pieces of rubbish for every 8 pieces of rubbish picked up by the girls.

In mathematics, ratios demonstrate how frequently one number is contained in another. For example, if there are 8 oranges and 6 lemons in a fruit plate, the ratio of oranges to lemons is 8 to 6. In a similar vein, the orange-to-whole-fruit ratio is 8, whereas the lemon-to-orange ratio is 6:8. A ratio is an ordered pair of integers a and b represented as a / b, where b is not zero. A ratio is an equation that equates two ratios. For example, if there is one male and three girls (for every boy she has three daughters), 3/4 are girls and 1/4 are boys.

The ratio in the narrative is represented by the following diagram:

Girls : Boys=8:5

This indicates that the guys picked up 5 pieces of rubbish for every 8 pieces of rubbish picked up by the girls.

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For the given expression the value of [tex](f^{-1})'(3)[/tex] ≈ 0.052.

What is expression?

In mathematics, an expression is a combination of numbers, variables, operators, and symbols that represents a mathematical quantity or relationship.

To find the derivative of the inverse function, we use the formula:

[tex](f^{-1})'(x) = 1 / f'(f^{-1}(x))[/tex]

First, we need to find the inverse function [tex]f^{-1(x)[/tex]. To do that, we can solve for x in terms of f(x):

[tex]f(x) = (1/4)x^3 + x - 1\\y = (1/4)x^3 + x - 1\\x^3 + 4x - 4 = 4y\\x^3 + 4x - 4 = 4f^{-1}(x)\\f^{-1}(x) = (x^3 + 4x - 4) / 4[/tex]

Now, we can find the derivative of the inverse function:

[tex](f^{-1})'(x) = 1 / f'(f^{-1}(x))\\(f^{-1})'(3) = 1 / f'(f^{-1}(3))[/tex]

To find [tex]f^{-1}(3)[/tex], we plug in x = 3 into the expression for [tex]f^{-1}(x)[/tex]:

[tex]f^{-1}(3) = (3^3 + 4(3) - 4) / 4 = 8.75[/tex]

To find [tex]f'(f^{-1}(3))[/tex], we plug in [tex]f^{-1}(3) = 8.75[/tex] into the expression for f'(x):

[tex]f'(8.75) = (3/4)(8.75)^2 + 1 = 19.2031[/tex]

Now we can find the derivative of the inverse function at x = 3:

[tex](f^{-1})'(3) = 1 / f'(f^{-1}(3))\\(f^{-1})'(3) = 1 / f'(8.75)\\(f^{-1})'(3) = 1 / 19.2031[/tex]

[tex](f^{-1})'(3)[/tex] ≈ 0.052

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Answer:

x = 52

Step-by-step explanation:

The angle x is vertical angle to the 52° angle. Meaning they have the same measurement.

Looking at the options, the answer is x = 52.

All four ratios are equal to 1/3, the scale factor of the dilation is 1/3

In mathematics, a scale factor is a ratio that describes how much larger or smaller an object or shape is in comparison to its original size. In particular, a scale factor is often used to describe the effect of dilation on an object.

Dilation is a transformation in which an object is enlarged or reduced uniformly in all directions from a fixed point known as the center of dilation. The scale factor for dilation is the ratio of the length of the image to the length of the pre-image.

For example, if a square has a side length of 4 units and is dilated by a factor of 2, the resulting image will have a side length of 8 units. In this case, the scale factor for dilation is 2.

More generally, if an object is dilated by a factor of k, then the length of any given segment in the image will be k times the length of the corresponding segment in the pre-image. Thus, the scale factor for dilation is simply k.

To find the scale factor of the dilation, we need to find the ratio of the corresponding side lengths of the trapezoid A'B'C'D' to the side lengths of trapezoid ABCD.

We can start by finding the length of each side of trapezoid ABCD:

AB = √[(9-(-3))² + (3-0)²] = √(144+9) = √153

BC = √[(9-9)² + (9-3)²] = 6

CD = √[(-3-9)² + (3-9)²] = √(144+36) = √180

DA = √[(-3-(-3))² + (3-0)²] = 3

Next, we can find the length of each corresponding side of trapezoid A'B'C'D':

A'B' = √[(3-(-1))² + (1-0)²] = √(16+1) = √17

B'C' = √[(3-3)² + (3-1)²] = 2

C'D' = √[(-1-3)² + (1-3)²] = √(16+4) = √20

D'A' = √[(-1-(-3))² + (1-0)²] = √4 = 2

Finally, we can find the ratio of the corresponding side lengths of the trapezoid A'B'C'D' to the side lengths of trapezoid ABCD by dividing the lengths of the corresponding sides:

[tex]\frac{A'B'}{AB} =\frac{\sqrt{17} }{153} \\\frac{B'C'}{BC} =\frac{2}{6}=\frac{1}{3} \\\frac{C'D'}{CD} =\frac{\sqrt{20} }{80} =\frac{\sqrt{45} }{445} =\frac{\sqrt{5} }{3\sqrt{5} } =\frac{1}{3} \sqrt{5} \\\frac{D'A'}{DA} =\frac{2}{3}[/tex]

Since all four ratios are equal to 1/3, the scale factor of the dilation is 1/3.

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10. The table is mentioned below 11. the product of the number of cubes long and the number of cubes wide is equal to 12. 12. The number of unit cubes needed to make this model is 24.

A cube is a three-dimensional geometric shape that has six square faces, 12 edges, and eight vertices (corners). All six faces of a cube are congruent squares, and all edges have the same length. The cube is a regular polyhedron, meaning that it has congruent faces and angles, and its symmetry group is the group of rotations and reflections that preserve the cube's structure. Cubes are widely used in geometry, mathematics, and physics because of their symmetry and regularity, and they also have practical applications in fields such as architecture and engineering.

10. Different ways a rectangular prism can have a volume of 12 cubic units:

Number of Cubes Long     Number of Cubes Wide Number of Cubes Tall

               1                                      1                                        12

               2                                      2                                        1.5

               2                                      3                                         1

               3                                      2                                         2

               4                                      3                                          1

               6                                      2                                          1

11. The pattern we see is that for each row, the product of the number of cubes long and the number of cubes wide is equal to 12.

12. A rectangular prism that is 4 units long, 2 units wide, and 1 unit tall would have a volume of 8 cubic units. To make a rectangular prism with a volume of 12 cubic units, we can add another layer of 4 cubes to the top of this prism. Therefore, a rectangular prism that is 4 units long, 2 units wide, and 2 units tall would have a volume of 12 cubic units. The number of unit cubes needed to make this model is 24.

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Answer: It snowed 3.5 inches on Monday and Tuesday combined.

Step-by-step explanation: 3 + 0.5 = 3.5 inches of snow

Hope this helped!

5.394366197183099*10^4

Step-by-step explanation:1. Write the number as a decimal 53943.66197183099

2. Make it a new number between 1 and 10

Move the decimal point to make 53943.66197183099 a new number between 1 and 10. Because our number is greater than 10, we move the decimal point to the left. Drop any trailing zeros and place the decimal point after the first non-zero digit. Keep track of how many times we move the decimal point.

53943.66197183099 -> 5.394366197183099

Our new number is 5.394366197183099. We moved the decimal point 4 times.

Use a calculator and get the values from both equations, 3.83×10^7 and 7.1×10^2 then put the first value 38300000 into a calculator, then divide 38300000/710 and you will get the value 53,943.66197183099. Then run that through a scientific notion calculator to get 5.394366197183099*10^4.

There you go.

Approximately 54,000 horses weigh as much as one cruise ship.

To find out how many horses weigh as much as one cruise ship, we need to divide the weight of the cruise ship by the weight of a horse. In scientific notation, the weight of the cruise ship is 3.83x107 kg and the weight of a horse is 7.1x102 kg.

Dividing the weight of the cruise ship by the weight of a horse, we get:

(3.83x107 kg) ÷ (7.1x102 kg) = 5.4x104

So approximately 54,000 horses weigh as much as one cruise ship.

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Answer:

D. 50 square centimeters

Answer:

Picture number 1: y=1/2x+2

Picture number 2: y=3x-5

Picture number 3 : y=-x

Picture number 4: y=(x+3)^2-2

Answer:

Assuming that the expression is asking for the tangent of 1 radian, we can use the tangent half-angle formula to find an exact value:

tan(1) = 2tan(1/2) / (1 - tan^2(1/2))

To find tan(1/2), we can use the half-angle formula for tangent:

tan(1/2) = sin(1) / (1 + cos(1))

We cannot simplify this expression any further without a calculator. Therefore, the exact value of tan(1) is:

tan(1) = 2sin(1) / (cos(1) - cos^2(1) + 1)

Again, we cannot simplify this expression any further without a calculator.

For the second expression, we are asked to find the value of:

tan(arctan(6/4))

By definition, tan(arctan(x)) = x for all x, so we have:

tan(arctan(6/4)) = 6/4 = 3/2

Therefore, the exact value of the expression tan(6/4) is 3/2.

Answer:

7/20

its the answer to your question

Answer: $28,383.68.

Step-by-step explanation:

The first step is to determine the number of monthly payments over the 5-year period, which is 5 years x 12 months/year = 60 months.

Next, we can use the formula for the future value of an annuity, which is:

FV = P * ((1 + r/n)^(n*t) - 1) / (r/n)

where:

FV is the future value of the loan (the amount owed at the end of the 5-year period)

P is the initial principal amount ($20,000 in this case)

r is the annual interest rate (6%)

n is the number of compounding periods per year (12 for monthly compounding)

t is the total number of years (5)

Plugging in these values, we get:

FV = $20,000 * ((1 + 0.06/12)^(12*5) - 1) / (0.06/12)

FV = $28,383.68

Therefore, the balance owed at the end of the 5-year period would be $28,383.68.

Answer:

Step-by-step explanation:

Answer: 49,000

48805 is greater than 48500, so it rounds to 49,000

Answer:

It is not true (equal sign with a slash in it) one side’s 23 and the other side is 20

Answer: 9x^2y

the gcf of -63 , 9 and 90 is 9

And the gcf of the variables is x^2 and y

So, 9x^2y

The linear equation in y=mx+b form that represents this scenario is:

y = -10x + 450.

What is a linear equation?

A linear equation is a mathematical equation in which the highest power of the variable(s) is one.

ax + b = 0

or

y = mx + b

where a, b, and m are constants and x and y are variables. In the first form, x is a variable and a and b are constants. In the second form, x and y are variables, m is the slope of the line, and b is the y-intercept.

Let x be the number of weeks that have passed since Todd started withdrawing money from his savings account. Initially, Todd had $450 in his savings, so the amount of money he has left after x weeks is:

450 - 10x

The rate of change of the amount of money Todd has with respect to time is -10, since he is withdrawing $10 per week. Therefore, the slope of the line that represents this situation is -10.

The y-intercept represents the initial amount of money Todd had in his savings, which is $450. Therefore, the linear equation in y=mx+b form that represents this scenario is:

y = -10x + 450

where y is the amount of money Todd has in his savings after x weeks.

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Based on the information in the image, we can infer that the recipe that takes the longest is the one for spaghetti sauce.

To find the recipe that takes the longest we must take into account the information of each of the recipes. In this case, we have preparation time and cooking time. To know the total time we must add these two values.

Additionally, we must establish a magnitude to be able to relate all the values, in this case the most appropriate would be the number of minutes.

So, the preparation of the spaghetti sauce takes 10 minutes and its cooking takes an hour and a half, that is, 90 minutes. On the other hand, strawberry bread takes 20 minutes to prepare and 55 to cook:

According to the above, the spaghetti sauce takes longer because it takes 25 minutes longer than the strawberry bread.

Note: This question is incomplete. Here is the complete information:

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Thus, we should order two large pizzas, that will cost $22, to serve a group of 12.

Costs in accounting are the dollar amounts paid for materials, labor, services, goods, equipment, and other purchases made for use by a company or even other accounting entity. This sum is listed as the price on invoices and is recorded as an expense of asset cost basis in bookkeeping records.

Solution:

Let x be the quantity of pizzas ordered.

12 x 2 = 24 slices are required because a large pizza contains 8 slices per slice.

As a result, the necessary quantity of pizzas is:

[tex]x\geq 3(x-1) \leq x[/tex]

In order to find the best price, we must reduce the total cost, that is determined by:

C(x) = 15x plus 5(x - 1) (x - 1) - 15

Using the cost function's derivative in relation to x, we may calculate:

C'(x) = 20 - 10[tex]/(x-1)^2[/tex]

Finding the critical points by setting the derivative to zero yields the following results:

20 - 10[tex]/(x-1)^2[/tex] = 0

Simplishing, we obtain:

[tex](x-1)^2[/tex]= 2

By solving for x using square root of the both sides, we arrive at:

x = 1 ± √2

The ideal quantity to order is two pizzas because x has to be an integer.

By adding x = 2 to the cost function, we can determine the total cost:

C(2) = 15(2) + 5(2 - 1) - 15 = 22

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In the circle , the value οf x is 50°.

A secant in geοmetry is a line that tοuches a curve at at least twο different pοints. The Latin wοrd secare, which means tο cut, is where the wοrd secant derives. A secant crοsses a circle at precisely twο pοints when it is a circle. A chοrd is the line segment that the twο pοints determine, i.e., the interval οn the secant whοse ends are the twο pοints.

Remember that a tangent line is οne that crοsses a circle at precisely οne pοint. The term "secant line" describes a line that passes thrοugh twο pοints οn a circle. Secant is a Latin wοrd that means "tο cut," and it is derived frοm secare. A chοrd is the line segment defined by the twο pοints where a secant tοuches a circle in a given space.

Here in the given circle using secant line fοrmula ,

=> 75° = [tex]\frac{1}{2}[/tex] (100°+x)

=> 2×75 = 100+x

=> 150 = 100+x

=> x= 150-100= 50°.

Hence the value of x is 50°.

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Answer:

There is 5% of the juice left.

Step-by-step explanation:

We know that originally, the container had 80 oz of orange juice, this is 100% in our case.

Then we can write a relation:

80 oz = 100%

Now there are 4 ounces left, in the same way as before, we can write this as:

4 oz = X%

We want to find X%

First, let's write our equations:

4 oz = X%

80 oz = 100%

We can take the quotient between these two equations to get:

(4oz/80oz) = (X%/100%)

We need to solve this for X%, then we get:

(4oz/80oz)*100% = X% = 5%

This means that 4 oz is 5% of the initial volume of the juice container.

Then we can conclude that there is 5% of the juice left.

Answer:

P = 8g⁵ - 15g + 14

Step-by-step explanation:

This question has expressions to represent the side lengths of a triangle.

The side lengths are:

-8g⁵ - 7g

10g⁵ - 8g

6g⁵ + 14

They ask for a simplified expression for the perimeter. The purpose of this question is to combine like terms.

P = s₁ + s₂ + s₃ where s is a side length of the triangle.

P = (-8g⁵ - 7g) + (10g⁵ - 8g) + (6g⁵ + 14)

P = 8g⁵ - 15g + 14