How many times smaller is 1.2 × 106 than 1.47 × 107?

The amount of time it would take to drain the swimming pool is equal to 75 minutes..

Generally speaking, a mathematical model for any quantity (water) that decreases by r percent per unit of time is an exponential function of this form:

[tex]P(t) = I(1 - r)^t[/tex]

Where:

Next, we would determine the amount of time it would take to have 0 gallons in the swimming pool:

20 gallons = 3 minutes

5,000 gallons = x minutes

20x = 1500

x = 1500/20

x = 75 minutes.

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the inverse of the function f(x) = 3 + 5x is f^(-1)(x) = (x - 3) / 5.To find the inverse of the function f(x) = 3 + 5x, we need to solve for x in terms of y, then replace y with the inverse notation f⁻¹(x).

what is  inverse of the function  ?

The inverse of a function is a new function that "undoes" the effect of the original function, meaning that if we apply the inverse function to the output of the original function, we get back the input.

In the given question,

To find the inverse of the function f(x) = 3 + 5x, we need to solve for x in terms of y, then replace y with the inverse notation f⁻¹(x). The steps to find the inverse are as follows:

Step 1: Replace f(x) with y.

y = 3 + 5x

Step 2: Solve for x in terms of y.

y - 3 = 5x

x = (y - 3) / 5

Step 3: Replace x with f⁻¹(x) to get the inverse function.

f⁻¹(x) = (x - 3) / 5

Therefore, the inverse of the function f(x) = 3 + 5x is f⁻¹(x) = (x - 3) / 5.

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The given system of equations can be written as a vector equation [tex]7x^1+x^2-3x^3[/tex] = 7 and as a matrix equation = , where A = [7 1 -3 3 2 2] and B = [7 0].

An equation is a mathematical statement that expresses the equality of two expressions. It usually consists of two expressions separated by an equals sign (=). The expressions may contain numbers, variables, and operations, such as addition, subtraction, multiplication, and division. The solution of an equation is the value of the variable that makes the equation true.

Vector equation:

[tex](7x^1+x^2-3x^3)=7[/tex]

Part 2

Write the system as a matrix equation. Select the correct choice below and fill in any answer boxes to complete your choice.

Matrix equation:

=

A =

[7 1 -3

3 2 2]

B =

[7

0]

Conclusion:

The given system of equations can be written as a vector equation [tex](7x^1+x^2-3x^3)[/tex] = 7 and as a matrix equation = , where A = [7 1 -3 3 2 2] and B = [7 0].

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Answer:

A- 304.8 cm²

Step-by-step explanation:

Find the area for the 4 sides (excluding both the top and base).

(2(12×7.5))+(2(12×5.2)) = 302.8

Answer:

A.  304.8 cm²

Step-by-step explanation:

The rectangular prism has a total of 6 rectangular sides

~   two at the bottom and top both of equal dimensions 5.2 x 7.5

~   two at the front and back both of equal dimensions 12 x 7.5

~    two one on the left side and the other on the right side both of equal dimensions 12 x 5.2

The question is asking only for the lateral surface area. This means we ignore the top and bottom surfaces

For each of the other two pairs of rectangles, the surface area is nothing but the product of the dimensions for each rectangle

Therefore area of all the 4 rectangles is
2(5.2 x 7.5 + 12 x 5.2)

We multiply by 2 since there are 2 of each rectangular surface

2(5.2 x 7.5 + 12 x 5.2) = 304.8 cm²   ANSWER

Answer:

n + 8

M - x

z - 12

c + d

2f + 20 or 20 + 2f

(x + y)^2 or (x + y) × (x + y)

2mn or 2 × m × n

2b - 6 or 6 - 2b

u^2 + v^2 or v^2 + u^2

(xy)/2 or xy/2

In a case whereby Juan buys candy that costs $8 per pound and will spend at least $48 on candy  the possible numbers of pounds he will buy written in inequality is is p>5 (at least 5 pounds).

Inequality in math refers to a statement that one quantity is either greater than, less than, or not equal to another quantity. Inequalities are often represented using symbols such as "<" (less than), ">" (greater than), or "≤" (less than or equal to) and "≥" (greater than or equal to). For example, the inequality "x > 3" states that the variable "x" is greater than the value of 3. The inequality "y ≤ 5" means that the variable "y" is less than or equal to 5.

From the question, p = number of pounds Juan will buy.

candy=costs $8 per pound

$20/$4 = 5 pounds

p>5

at least 5 pounds

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Step-by-step explanation:

706 -25 = 681 ====>    which is three pieces of 681/3 = 227 m

              but one is 25 m longer so 227,  227 , and 227 + 25 =252 m

The true-relationship between 1 inch and 1 foot is  (b) 1 foot is 12 times as long as 1 inch.

An "inch" is a unit to measure length and is equal to 1/12th of a foot. It is denoted by symbol "in"

A "foot" is a unit which measures the length and is equal to 12 inches. It is denoted as "ft" .

In the imperial system, the unit of length is the foot, and it is divided into 12 smaller units called inches,

So, 1 foot is equal to 12 inches, and we can write this as : 1 foot = 12 inches,

We rearrange this equation to get the relationship between 1 inch and 1 foot,

⇒ 1 inch = 1/12 foot,

This means that 1 inch is equal to one-twelfth of a foot. In other words, it takes 12 inches to make 1 foot.

Therefore, the correct option is (b).

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Answer

15,625

Step-by-step explanation:

Solution of expression 625 x 25 is, 15,625

We have to given that,

An expression to solve,

625 x 25

Since,To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We can multiply is,

625 x 25

= 15,625

Therefore, Solution of expression 625 x 25 is, 15,625

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Answer:

AM and AR

Step-by-step explanation:

A is the center, AR is a radius and so is AM

An equation that shows the relationship between the print time in minutes, x, and the number of pages printed, y is y = 32x

The equation that shows the relationship between the print time in minutes, x, and the number of pages printed, y, can be obtained using the following formula:

y = r * x

where r represents the rate of printing in pages per minute, which in this case is 32 pages per minute.

Therefore, the equation becomes:

y = 32x

This equation states that the number of pages printed, y, is directly proportional to the print time in minutes, x, at a rate of 32 pages per minute.

For example, if Mr. Hernandez wants to print 128 pages, we can use the equation to find out how long it will take him:

128 = 32x

x = 128/32

x = 4

Therefore, it will take Mr. Hernandez 4 minutes to print 128 pages on his high-speed printer.

In summary, the equation y = 32x represents the relationship between the print time in minutes, x, and the number of pages printed, y, when using a high-speed printer that can produce 32 pages per minute.

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The value of measure of ∠ RST is,

⇒ ∠ RST = 34°

We have to given that;

In circle S with m ∠RUT = 17°

Hence, We get;

⇒ ∠ RST = 2 × ∠ RUT

⇒ ∠ RST = 2 × 17°

⇒ ∠ RST = 34°

Thus, The value of measure of ∠ RST is,

⇒ ∠ RST = 34°

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Answer:

Option A, is 8x^6.

Step-by-step explanation:

4x³ × 2x³ = (4 × 2) x^(3+3) = 8x^6

Therefore, 4x³ × 2x³ simplifies to 8x^6.

You're welcome. :)

A) 8x⁶

Exponents have different rules for operations such as multiplication.

Multiplying Coefficients

When multiplying different terms with exponents, the first thing we should do is multiply the coefficients. Even though there are variables with different exponents, we still multiply the coefficients like normal. This means that the coefficient of the answer should be 8 because 4 * 2 =8. However, you should note that you can only multiply the coefficients and simply the expression if the terms have the same variable.

Multiplying Exponents

To multiply 2 terms with exponents, you should add the exponents together. For example, x⁴ * x⁶ = x¹⁰. No matter what the coefficients are, if the variables are the same, then this method will work. This means that x³ * x³ = x⁶. Then, combine this with the coefficient from before and 4x³ * 2x³ = 8x⁶.

Answer:

min: 56

lower quartile: 70

median: 74

upper quartile: 80

max: 86

The perimeter of the given shape in terms of pi is 22 cm + 25 pi cm.

The circumference of the rectangle is equal to the sum of the lengths of its four sides. It is simple to do this because there are two of each side length; all that is needed is to sum the length and width and multiply the result by two.

By multiplying half of the semicircle's circumference by the diameter's length, one can determine the semicircle's perimeter. Thus, the semicircle's perimeter is as follows:

Perimeter of semicircle = 6 cm + (1/2) x pi x 6 cm

Perimeter of semicircle = 6 cm + 3 pi cm

Each quarter circle has a perimeter that is just one-fourth of its circumference. Consequently, the 14 cm quarter circle's perimeter is as follows:

Perimeter of quarter circle with radius 14 cm = (1/4) x 2 pi x 14 cm

Perimeter of quarter circle with radius 14 cm = 7 pi cm

And, the perimeter of the quarter circle with radius 30 cm is:

Perimeter of quarter circle with radius 30 cm = (1/4) x 2pi x 30 cm

Perimeter of quarter circle with radius 30 cm = 15 pi cm

Therefore, the total perimeter of the given shape is:

Perimeter = Perimeter of semicircle + Perimeter of quarter circle with radius 14 cm + Perimeter of quarter circle with radius 30 cm

Perimeter = (6 cm + 3 pi cm) + (7 pi cm) + (15 pi cm)

Perimeter = 22 cm + 25 pi cm.

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If the vector is drawn from (0,0) to (5, -1), the outcome or the required vector is drawn.

A mathematical concept known as a vector has both a magnitude and a direction. Physical quantities like force, velocity, and acceleration are represented by it. In the physical sciences, engineering, and computer graphics, vectors are frequently employed. They can also be used to represent abstract concepts like magnitude, directions, and other things.

Here in the question,

(0, 0) is the beginning position. There should be an arrow above each vector name listed below.

Ink a line beginning at (3, -1). A vector has an origin of (0,0) and a destination of (3, -1).

Put a line through points (2,2). The vector B has a start point of (0, 0) and an end point of (2, 2).

These two vectors add up to: a + b = (3-1) + (2,2) = (5,1) when combined.

Whatever order they are in, b + a = (2,2) + (3, -1) = (5,1) regardless.

Either way, the same conclusion is reached.

The terminal point of A + B is at (5, 1).

If the vector is drawn from (0,0) to (5, -1), the outcome vector is drawn.

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The value of P for A and B to be independent is 3/8.

Probability is a mathematical concept used to determine the likelihood or chance of an event occurring. It's a measure of how likely it is that a specific outcome will happen in a given situation. Probability values are expressed as numbers between 0 and 1, where 0 means the event is impossible, and 1 means it is certain to occur.

The probability of an event is calculated by dividing the number of outcomes that favor the event by the total number of possible outcomes. The total number of outcomes is the number of ways the event could happen, while the number of favorable outcomes is the number of outcomes that satisfy the event's conditions.

Probability theory has many applications in various fields, including finance, economics, science, engineering, and statistics. It is an essential tool for analyzing data, predicting outcomes, and making decisions.

Two events A and B are independent if and only if P(A and B) = P(A) * P(B).

Using the formula for the probability of the union of two events, we have:

P(A or B) = P(A) + P(B) - P(A and B)

Substituting the given values, we get:

1/2 = 1/5 + P - P(A and B)

Simplifying, we get:

3/10 = P - P(A and B)

We also know that P(A) = 1/5. Using the formula for the probability of the intersection of two events, we have:

P(A and B) = P(A) * P(B | A)

Substituting the given values, we get:

P(A and B) = (1/5) * P

Since we want to find the values of P for which A and B are independent, we can substitute this expression for P(A and B) in the earlier equation:

3/10 = P - (1/5) * P

Simplifying and solving for P, we get:

P = 3/8

Therefore, A and B are independent if and only if P = 3/8.

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(1) The inverse function is:  [tex]f^-1 (y)[/tex] = (y - 8)/0.75 (2) In the inverse function, y represents the number of units produced and x is the hourly wage.(3) an hourly wage of $22.25 is approximately 14.93.

If a vertical line drawn anywhere on the graph of a relation only intersect at one point on the graph, then this graph represents a function. If a vertical line can intersect the graph at two or more points,  the graph does not represent a function.

(a) To find the inverse function, we must solve for x in terms of y.

y = 8 + 0.75x

y - 8 = 0.75x

x = (y - 8)/0.75

So the inverse function is:

[tex]f^-1 (y)[/tex] = (y - 8)/0.75

(b) In the inverse function, y represents the number of units produced and x is the hourly wage.

(c) To determine the number of units produced when the hourly wage is $22.25, we need to plug  y = 22.25 into the inverse function we found in part (a):

[tex]f^{-1}[/tex](22.25) = (22.25 - 8)/0.75

[tex]f^{-1}[/tex](22.25) = 14.93

Therefore, the number of units produced at an hourly wage of $22.25 is approximately 14.93.

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Answer:

1) -8m

2) -x

3) -4y

4)

[tex] - 17x {y}^{3} [/tex]

5) p

6) 0

7) 15m + 10

8) r - 7

9) 5x - 22

10)

[tex]3 {m}^{2} [/tex]

11)

[tex]7 {x}^{2} - x[/tex]

12) 22pq - 8p

13)

[tex] - 13 {r}^{2} - 6r[/tex]

14) -19

15) 0

16) 3.07y

17)

[tex] - 4 {m}^{2} - 35m[/tex]

18)

[tex]x {y}^{2} - 3 {x}^{2} y[/tex]

19) .3mn + 4.7m

20) 3r + 2j + m + 3

21)

[tex] - 4 {x}^{2} - 16x + 11[/tex]

22)

[tex]3 {y}^{4} - {y}^{2} + 11[/tex]

The single payment Jacob would make in 24 months from now, to pay off the two obligations under the new agreement is $7,620.

We shall be solving this using the formula for Simple Interest,

The interest accrued on each payment can be calculated using the formula for Simple Interest:

Interest = Principal × Rate × Time

where:

Principal = amount borrowed,

Rate = simple interest rate,

Time = time period in years.

Under the original agreement, Jacob shall make two payments of $3000 each, one 6 months from now and the other 12 months from now.

For payment1, the interest accrued would be:

Interest1 = $3000 × 0.10 × (6/12) = $150

For payment2, the interest accrued would be:

Interest2 = $3000 × 0.10 × (12/12) = $300

So the total amount Jacob was to pay under the original agreement is:

Total1 = $3000 + $150 + $3000 + $300 = $6,450

Now let's calculate the amount Jacob would have to pay under the new agreement.

Original principal for each payment is $3000.

The interest accrued on the sum of both payments can be calculated using the same formula for simple interest:

Interest3 = ($3000 + $150 + $3000 + $300) × 0.10 × (24/12) = $720

So the total amount Jacob would pay under the new agreement is:

Total2 = $3000 + $150 + $3000 + $300 + $720 = $7,620

So, Jacob would make a single payment of $7,620, 24 months from now,

to pay off both loans under the new agreement.

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The coordinates of the figure after translation & dilation are A''(1,3) ,R''(-1/2,1) , G''(-1,-3/2), Y''(5/2,5/2).

A quadrilateral is a polygon with four sides and four vertices. Some examples of quadrilaterals include squares, rectangles, parallelograms, trapezoids, and rhombuses.

Scale factor refers to the ratio of the length or size of an object in one dimension to the length or size of a corresponding object in another dimension. It is commonly used in mathematics and geometry to describe the relationship between two similar figures. For example, if one square has a side length of 4 cm and another square is similar to it with a side length of 8 cm, the scale factor between the two squares is 2:1.

A(2,8) R(3,4) G(2,-1) Y(9,7)

Translate it to 4 units left gives the result:

A'(-2,6) ,R'(-1,2) ,G'(-2,-3), Y'(5,5)

Now dilate it:

A''=(-1,3), R''(-1/2,1), G''(-1,-3/2), Y''(5/2,5/2)

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The potential roots of the function p(x) = x² - 9x² - 4x + 12 are x = 1, -1.5, and 12.

Degree of a polynomial is the highest power of the variable in that polynomial. For example, in a cubic polynomial, the variable [[tex]\bold{x}[/tex]] has the highest power of 3.

Given is the following function with degree of 2 as -

We will plot the graph and find the roots of this function. The number of x - intercepts [coordinates where the graph cuts the x axis] will give us the roots or zeroes of the polynomials. Refer to the graph attached, it shows that the graph intercepts the x - axis at three different coordinates which are → x = 1, x = -1.5, and x = 12. Hence, these three values of [x] are the potential roots of the function p(x) = x² - 9x² - 4x + 12.

Therefore, the potential roots of the function p(x) = x² - 9x² - 4x + 12 are x = 1, -1.5, and 12.

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The potential roots of the given polynomial equation are +4 and -3. These roots are found by factoring the equation, setting each factor equal to zero and solving for x.

To find the potential roots of the polynomial equation p(x) = x² - 9x - 12, we can set the equation to zero and solve for x: 0 = x² - 9x - 12.

Next, we look for the factors of 12 which when multiplied would give you -12 and when subtracted would give you 9. There we have -4 and +3. Therefore the factors of the equation are (x - 4)(x + 3) = 0.

So, Final answer:

The potential roots of the given polynomial equation are +4 and -3. These roots are found by factoring the equation, setting each factor equal to zero and solving for x.

To find the potential roots of the polynomial equation p(x) = x² - 9x - 12, we can set the equation to zero and solve for x:

0 = x² - 9x - 12.

Next, we look for the factors of 12 which when multiplied would give you -12 and when subtracted would give you 9. There we have -4 and +3. Therefore the factors of the equation are (x - 4)(x + 3) = 0.

So, potential roots of the equation are x = 4 and x = -3 if we set each factor equal to zero and solve for x. This means that from the given options, the potential roots to the equation would be +4 and -3 (though -3 is not mentioned). of the equation are x = 4 and x = -3 if we set each factor equal to zero and solve for x. This means that from the given options, the potential roots to the equation would be +4 and -3 (though -3 is not mentioned).

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The result of (6 - 25) = (6² - √25) = (36 - 5) = 31

A sequence is a list of numbers arranged in a specific order, while a series is the sum of the terms of a sequence. In other words, a sequence is a collection of numbers that follow a particular pattern or rule, and a series is the result obtained by adding these numbers together.

The sequence of equations, it appears that each result is obtained by subtracting the square of first number to the square root of second number:

2 - 1 = 2² - √1 = 4 - 1 = 3

3 - 4 = 3² - √4 = 9 - 2 = 7

4 - 9 = 4² - √9 = 16 - 3 = 13

5 - 16 = 5² - √16 = 25 - 4 = 21

3 - 81 = 3² - √81 = 9 - 9 = 0

Similarly,

6 - 25 = 6² - √25 = 36 - 5 = 31

Therefore, the result of 6 - 25 = 6² - √25 = 36 - 5 = 31

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The value of y in the triangle is 20.

What is the triangle?

A triangle is a polygon with three sides and three angles. It is the simplest and most basic polygon in Euclidean geometry.

According to the given information:

From the figure, we can say that ΔABC and ΔABI are similar.

we can write proportions as

[tex]\frac{y}{30} =\frac{30}{y+25}[/tex]

y(y+25) = 30*30

[tex]y^{2}[/tex]+25y=900

[tex]y^{2}[/tex]+25y-900 = 0

On solving we can use quadratic formula y = (-b ± √(b^2 - 4ac)) / (2a)

For the given equation y^2 + 25y - 900 = 0, we can identify a = 1, b = 25, and c = -900.

Plugging these values into the quadratic formula, we get:

y = (-25 ± √(25^2 - 4 * 1 * -900)) / (2 * 1)

Simplifying further:

y = (-25 ± √(625 + 3600)) / 2

y = (-25 ± √(4225)) / 2

y = (-25 ± 65) / 2

Now we can solve for two possible values of y:

y = (-25 + 65) / 2 = 40 / 2 = 20

y = (-25 - 65) / 2 = -90 / 2 = -45

So the two possible values of y that satisfy the given equation are y = 20 and y = -45.

distance cannnot be negative, so the value of y is 20.

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Answer: Jenny's score is no less than 5 points greater than 4/5 of Terrance's score.

Step-by-step explanation:

The inequality that represents the situation described is:

Jenny's score (denoted as "J") is no less than 5 points greater than 4/5 of Terrance's score (denoted as "T"):

J ≥ (4/5)T + 5

In this inequality, we are saying that Jenny's score "J" must be greater than or equal to 4/5 of Terrance's score "T", plus an additional 5 points. This reflects the condition that Jenny's score should be at least 5 points higher than 4/5 of Terrance's score.

For example, if Terrance's score "T" is 80, then 4/5 of Terrance's score is (4/5) * 80 = 64. Adding 5 points to this gives us 69. Therefore, Jenny's score "J" must be greater than or equal to 69 in this case, since it should be no less than 5 points greater than 4/5 of Terrance's score.

Answer:2^1 × 3^2 × 13^1

Step-by-step explanation:

There are currently about 10,361,248 people requesting financial aid, which is an increase of 6.74% from ten years ago.

By reducing the financial barrier, it supports the advancement of your academic and professional ambitions.

Its current number of applications can be determined by multiplying 9,720,000 with 1.0674 (which equals a 6.74% increase)

If there were 9,720,000 people asking for financial help 10 years ago and there have been 6.74 times as many applicants since then. As a result, there are currently 10,361,248 applicants for financial aid, or 9,720,000 x 1.0674.

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The range of the function is all real numbers.

In mathematics, a function is an expression, rule, or law that specifies a relationship between two variables (the independent variable and the dependent variable). Functions are common in mathematics and are required for the formulation of physical relationships in the sciences.

We know,

The x-values (Input values) on the graph define the domain of the function.

and, The y-values (output values) on the graph determine the range of a function.

From the graph attached,

Here the x value start from +1 to ∞.

Thus, the range of the function is all real numbers.

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