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What is the radical form of each of the given expressions?

Drag the answer into the box to correctly match each expression.

If a city's population doubles every 6 years, the city's population, 12 years from now, will be 2,152,000.

Every six months, the population increases by two times the current number.

Using multiplication by 2 or 4, we can determine the population in 12 years.

The current population of the city in Year 0 = 538,000

Doubling time = every 6 years

The estimated time = 12 years

In the first six years, the population will be 1,076,000 (538,000 x 2)

In the second six years, the number of people in the city will be 2,152,000 (1,076,000 x 2) or (538,000 x 4)

Thus, in 12 years, the city's population will become 2,152,000 people.

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Answer:

2,152,000

Step-by-step explanation:

The probability of getting a green wrinkled pea from a yyrr x yyrr cross is 1/4.

A cross was made between a pure round yellow seeded pea plant (RRYY) with wrinkled green seeded pea plant (rryy). The yellow colour is dominant over green and round seed shape is dominant over wrinkled seed shape.

The possibility of the result of any random event is known as probability. This phrase refers to determining the likelihood that any given occurrence will occur.

All of the children were yellow because yellow has a dominant gene over green. The green phenotype was no longer present. To see how the second generation would appear, let the yellow pea plants self-fertilize.

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All the given statements for the function g(x) is true.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

For the function g(x) -

When the value of x = 1, then the value of y = 22.

When the value of x = 3, then the value of y = -5.

When the value of x = 5, then the value of y = 6.

When 1 is an input, 22 is an output.

The point (-5, 3) lies on the graph of the function.

The solution to g(x) = -5 is x = 3.

When 6 is an input, 5 is an output.

The point (-5, 3) lies on the graph of the function.

The point, (5, 6) lies on the graph of the function.

Therefore, all the statements are true.

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The equation shown below can be used to find, the total number of ounces of almonds in the last bag.

y = 8/2 + 1 And y = 5 ounces of almonds in the last bag.

Two algebraic expressions having same value and symbol '=' in between are called as an equation.

Given:

Isabel has 8 ounces of almonds to divide equally into 2 bags

In the last bag, she adds an ounce of almonds.

The equation shown below can be used to find, the total number of ounces of almonds in the last bag.

y = 8/2 + 1

y = 4 + 1

y = 5 ounces of almonds in the last bag

Therefore,  5 ounces of almonds in the last bag

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The complete question:

Isabel has 8 ounces of almonds to divide equally into 2 bags. In the last bag, she adds an additional ounces of almonds. The equation shown can be used to find, the total number of ounces of almonds in the last bag. How many ounces of almonds are in the last bag?

Answer:  X= - 2

Step-by-step explanation:

True. Testing other points in addition to the vertices is necessary

True. When trying to optimize (find the max or min) of a function, it is not enough to test only the vertices. The function may have a maximum or minimum value at a point that is not a vertex, such as an inflection point, or a point on the edge of the domain.

Thus, testing other points in addition to the vertices is necessary in order to ensure that the maximum or minimum value of the function has been found.

Linear programming is a powerful tool that can be used to model and solve a wide range of real-world problems in fields such as finance, manufacturing, transportation, and resource allocation.

For example, it can help to determine the optimal number of products to produce, the best way to use resources (e.g. labor, materials) and the best scheduling to minimize costs and maximize profits.

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As per the combination method,

(a) at least one of each letter is 36

(b) at least two of each letter is 15

(c) at least one A, two Bs, and three Cs is 15

(d)  any number of each letter is 120

(e)  at least one A and at least two Bs is 36

In math the term combination method is known as  the number of possible combinations that can be obtained by taking a sample of items from a larger set.

Here we have given that the value of n is 10 and the value of r is 3.

Then the resulting values are calculated as,

Here for the letters with at least one of each letter then the length is 10 with a 3 elements to choose from the given set.

Here we know that 3 of the 10 slots will be taken up by A,B, and C. With 7 remaining, any letter could take up those spots it will be calculated as,

=> (7+3-1 choose 3-1)

=> (9 choose 2).

=> 36

Where as the other one is with at least two of each letter

Then here we have the letter with two of each letter 6 letters will take up 10 slots no matter what is calculated as,

=> 10-6 = 4

Now then we have 3 to choose from so (4 + 3 - 1 choose 3-1).

=> (6 choose 2)

=> 15

And the another option is to have at least one A, two Bs, and three Cs

=> 1A + 2B + 3C will take up 6 spots.

=> (4+ 3-1 choose 3-1)

=>  (6 choose 2).

=> 15

Where as the count is any number of each letter

=> 10 choose 3.

=> 120

Finally if we take at least one A and at least two Bs

Then at least 1 A and two Bs taking up a total of 3 slots is calculated as,

=> 10 - 3 = 7.

=>  (7 + 3 - 1 choose 3 - 1)

=> (9 choose 2) = 36

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Answer:

C & D

Step-by-step explanation:

The key formula will be y = mx + b

y = the function

m = slope

b = y - intercept

Another term for slope is rate of change

They asked for negative rare of change, so negative slope, which takes it to

y = -mx + b

The only two that work are C & D because C shows -4x and D shows -2x, both negative.

A & B are 7x and 2/3x, both positive.

a) Does not give an equivalent ratio

b) Does not give an equivalent ratio

c) Does not give  an equivalent ratio

d) Gives an equivalent ratio

An equivalent ratio is a ratio that is equal in value to a given ratio, but may have a different form. Two ratios are equivalent if they have the same relationship between the terms, even if the numbers are different.

In this case, we have the ratio 8/20. The process of addition or subtraction can not be able to give us the equivalent ratio that we are looking for but the multiplication  would do that. Recall that the original fraction is 8/20 so;

a) 10/22 = 5/11

b) 6/18 = 3/9

c) 4/10 = 2/5

d) 16/40 = 8/20

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All the correct expressions are,

Slope of BC = - 2/5

Slope of CD = 5/2

Slope of DE = - 3/5

Slope of EB = 3

Length of BC = √ 29

Length of CD = √ 29

Length of DE = √34

Length of EB = √40

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

Coordinate of B = (- 9, 1)

Coordinate of C = (- 4, - 1)

Coordinate of D = (- 2, 4)

Coordinate of E = (- 7, 7)

Now, We know that;

The slope of line passing through the points (x₁ , y₁) and (x₂, y₂) is,

⇒ m = (y₂ - y₁) / (x₂ - x₁)

Thus, Slope of BC is,

⇒ m = (- 1 - 1) / (- 4 - (-9))

⇒ m = - 2/5

Slope of CD is,

⇒ m = (4 - (-1)) / (- 2 - (-4))

⇒ m = 5/2

Slope of DE is,

⇒ m = (7 - 4) / (- 7 - (-2))

⇒ m = 3/- 5

⇒ m = - 3/5

Slope of EB is,

⇒ m = (1 - 7) / (- 9 - (-7))

⇒ m = - 6/-2

⇒ m = 3

Length of CD is,

⇒ CD = √ (- 2 - (-4))² + (4 - (- 1))²

         = √4 + 25

        = √ 29

Length of BC is,

⇒ BC = √ (- 4 - (-9))² + (- 1 - 1)²

         = √25 + 4

        = √ 29

Length of DE is,

⇒ DE = √ (- 2 - (-7))² + (4 - 7)²

         = √25 + 9

        = √ 34

Length of EB is,

⇒ EB = √ (- 7 - (-9))² + (7 - 1)²

         = √4 + 36

        = √ 40

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In the given situation the given values can be correctly modeled by a (B) linear function.

What is a linear function?
A linear function has a straight line as its graph. A linear function has the form shown below. a + bx = y = f (x).

A linear function consists of one independent variable and one dependent variable.

The independent and dependent variables are X and Y, respectively.

In mathematics, the terms "linear function" refers to two distinct but connected concepts: In calculus and related subjects, a polynomial function of degree zero or one with a graph that is a straight line is referred to as a linear function.

Therefore, in the given situation the given values can be correctly modeled by a (B) linear function.

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Answer: Martha earned $13,728.12 in interest over 8 years.

Step-by-step explanation:

The future value of Martha's investment can be calculated using the formula:

FV = PV (1 + r/n)^(nt)

Where:

PV = present value (initial investment) = $14,200

r = annual interest rate = 6%

n = number of times the interest is compounded per year = 12 (monthly)

t = number of years the investment is held = 8

Plugging in the values, we get:

FV = 14,200(1 + 0.06/12)^(12*8) = $27,928.12

The interest earned on her investment is the difference between the future value and the present value:

$27,928.12 - $14,200 = $13,728.12

So Martha earned $13,728.12 in interest over 8 years.

Answer:

$22,920.83

Step-by-step explanation:

assuming 6% is annual rate

so 12 months in a year = 6%/12 = 0.5% per month

so every month she gets  (1+0.5%)  growth on her previous balance

so for 8 years = 96 months,

she'll get that growth 96 times

so it'll be 14,200 *(1+0.5%) ^ 96 =22,920.83

Answer:

see below

Step-by-step explanation:

length = 10

circumference = 2πr = 8 π, so r=4

8π=25.12

cut half so length = 5, so lateral surface = 8π*5 = 40π =125.6

top circle area = πr² = 3.14*4² = 3.14 *16 = 50.24

top & bottom = 2*50.24 = 100.5

so total surface of EACH after cut in half = 100.5+125.6 =226.1

TWO of them = 2*226.1 =452.2

The dosage for Devon's body weight is 5.25 ounces.

Note that 50 pounds of body weight require 1.5 ounces of medication,

Here by dividing the given amount of medication by 50 find the amount of medication for 1 pound of body  

Now multiply the result by the present body weight of the Devons.  

Here we have

The dosage of the medication is 1.5 ounces for every 50 pounds

Weight of Devon = 190 pounds    

If he loses 15 pounds, present Devon's weight = 190 - 15 = 175

Dosage for Devon's body = [tex]\frac{1.5}{50} \times 175[/tex]  

= [tex]0.03 \times 175[/tex]  

= 5.25

Therefore,

The dosage for Devon's body weight is 5.25 ounces.    

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Answer: 21.3

Step-by-step explanation: Let us split the figure into two triangles. If the total bottom length is 22, than the triangle's base is 22/2=11

We can use the Pythagorean theorem to get: 11^2+x^2=24^2  or      121+x^2=576

576-121=455

sqrt 455=21.33................

rounds to 21.3

The areas of the given triangle and rectangle are 60 cm² and 120 cm² respectively.

What are a triangle and rectangle?

A triangle is a three-sided polygon which has 3 angles formed when two sides join to form a vertex.

A rectangle is a four-sided polygon whose opposite sides have the same lengths and all sides are perpendicular to each other.

The given triangle is a right-angled triangle.

The area of a right-angled triangle is 1/2*b*h

where,

    b= base of the triangle

   h = height of the triangle

From the figure, b = 10 cm and h = 12 cm

     Area of triangle = 1/2*10*12 = 60 cm²

The given rectangles have a length of 12 cm and a breadth of 10cm.

The area of the rectangle is given by the product of breadth and length.

Area of rectangle = 12 * 10 = 120 cm²

Therefore the areas of the given triangle and rectangle are 60 cm² and 120 cm² respectively.

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The correct alternatives are -

Given is the proportional relationship.

A line begins at point (0, 0) and continues to the right.

Direct variation of {y} with {x} means that as {x} increases, {y} increases uniformly with it. Mathematically -

{K} = y/x = constant

Scale factor {K} is a dimensionless value that indicates the constant ratio value indicating direct variation.

Therefore, the correct alternatives are -

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The length of the segment after dilation with a scale factor of -4 is -12.

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor.

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is a picture with the same shape as the original. However, there is a variation in the shape's size.

Given that the segment LP is dilated with a scale factor of -4. In simple words, the length of the segment is increased to -4 times of its original length.

This is represented as follows:

L'P' = -4 (LP)

Substitute the value of LP = 3:

L'P' = -4 (3)

L'P' = -12

Hence, the length of the segment after dilation with a scale factor of -4 is -12.

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The approximate distance the truck tire will travel in 1 full rotation is 62.8 inches.

The total distance travelled by truck on completing one full rotation will be equal to the circumference of the circle. The circumference of the circle is given by the formula -

Circumference = 2πr, where r refers to radius of truck tire.

Radius = diameter/2

Radius = 20/2

Radius = 10 inches

Keep the values in formula to find the distance travelled on full rotation of truck tire.

Circumference = 2×3.14×10

Performing multiplication on Right Hand Side of the equation

Circumference = 62.8 inches

Hence, the distance covered will be 62.8 inches.

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Answer: We can start by figuring out how much of the pizza was covered before Mrs. Magsanoc returned by adding the portion that she covered before the phone rang to the portion that Mr. Magsanoc covered while she was away.

Mrs. Magsanoc covered 3/8 of the pizza before the phone rang.

Mr. Magsanoc covered 1/3 of the pizza while she was away.

To add the two portions, we need to find a common denominator, which is the least common multiple of 8 and 3. That is 24.

3/8 of the pizza is (3/8) * (24/8) = 3/24

1/3 of the pizza is (1/3) * (24/3) = 8/24

So, the total portion of the pizza that was covered before Mrs. Magsanoc returned is 3/24 + 8/24

Which is 11/24 or 0.458 of the pizza.

Step-by-step explanation:

The monthly payment on a loan of $4,500 at 12% interest for a period of 48 months is: $128.34.

The monthly payment for a $4,500 loan at 12% interest for 48 months can be calculated using the formula:

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

Where:

M = the monthly payment

P = the principal (the amount of the loan)

r = the monthly interest rate (12% divided by 12 months)

n = the number of payments (48 months)

So the calculation is:

M = 4,500 * (0.01(1 + 0.01)^48) / ((1 + 0.01)^48 - 1)

This comes out to be $128.34.

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Answer: Frank owes $212 on his credit card and then charges $105 more, so the new balance on Frank's credit card is:

$212 + $105 = $317

So the new balance on Frank's credit card is $317.

Step-by-step explanation:

The equation of the new function is  f'(x) = -1/2x³

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

F(x) = x³

The transformations are given as

The rule of the above transformations is

f'(x) = -1/2f(x)

substitute the known values in the above equation, so, we have the following representation

f'(x) = -1/2x³

hence, the equation is f'(x) = -1/2x³

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Graph the equation y = x + 1l on a separate sheet of graph paper, and then click on the graph to make the right one appear. appears to be a house's roof. From the (0,0) line, it has moved forward one space.

The graph of y equal to the value of x minus 3 is the one that needs to be chosen in this challenge. Since these 3 units will now be moved to the right, the vertex will no longer be at the origin, where it normally is. You should choose the graph that has a form similar to what I'm going to create when I move 3 to the right .

The graph cannot represent a function if a vertical line can cross it at two or more different locations. To put it another way, the graph is said to reflect a function if a vertical line drawn anywhere only intersects it once, indicating that each x value has a single corresponding y value.

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The building is 39.06 yards tall.

The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

Hypotenuse (ramp)= 60 yards

Angle of Elevation = 41°

Using Trigonometry

sin 41= P/H

0.651 = P/60

P= 39.06 yard.

Hence, the height is 39.06 yard.

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Answer: We can start by using the following formula to find the time it takes for David to catch up with James:

time = (James' lead) / (David's rate - James' rate)

In this case, James' lead is 6 hotdogs, and we know that James eats 1 hotdog every 2 minutes, so his rate is 1/2 hotdog per minute. David's rate is 1.25 hotdogs per minute.

So, substituting these values into the formula:

time = (6) / (1.25 - (1/2))

time = 6 / (0.75)

time = 8 minutes

So it takes David 8 minutes to catch up with James.

Step-by-step explanation:

Answer: The domain of a function is the set of all input values (x-values) for which the function produces a valid output. In the case of the function f(x) = -x + 15, the function will take any real number as input and produce a corresponding output.

Therefore, the domain of the function f(x) = -x + 15 is all real numbers. This can be represented as (-∞, ∞) or simply as "all x".

Option O is correct: x are all real numbers

Option O x ≤ 30, O x > -2, O x >0 are incorrect

Step-by-step explanation:

The area of the customer's yard is 580π.

The distance formula is given as -

d = √(x₂ - x₁)² + (y₂ - y₁)²

Given is that this grid represents the customer’s yard. The bottom left corner is the origin point  O(0, 0), and the x- and y- axes represent the two fences. The rose bush is at point P(16, 18).

We can write the area of the customer's yard -

A = πr²

Here -

r = d

r² = d²

We can write -

A = πd²

A = π {(x₂ - x₁)² + (y₂ - y₁)²}

A = π{16 x 16 + 18 x 18}

A = 580π

Therefore, the area of the customer's yard is 580π.

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There are 22 purple notebooks in the bin.

There are 37 pink socks in the bin.

In order to determine the number of purple notebooks that are in the bin, we would develop an expression to multiply the total number of notebooks (T) by the percentage of the number of purple notebooks placed in the note bin as follows;

Total number of purple notebooks (P) = 25/100 × 88

Total number of purple notebooks (P) = 0.25 × 88

Total number of purple notebooks (P) = 22 notebooks.

Total number of socks (S) = 50/100 × 74

Total number of socks (s) = 0.50 × 74

Total number of socks (s) = 37 socks.

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The average number of burgers per person is 96

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given here; The function f(d) =200d³+542d²+179d+1605

The number of visitors is given by g(d)=100d+321

Thus in 7 days, The total number of burgers sold are given by

f(7)=200×7³+542×7²+179×7+1605

    =68600+26558+1253+1605

    =98016

And the number of visitors is given by g(7)=100×7+321

                                                                      =1021

Thus, The average number of burgers per person is given by

Avg= 98016/1021

      =96

Hence, The average number of burgers per person is 96

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