Suppose that 511,969 is invested at an interest rate of 5 2% per year, compounded continuously a) Find the exponential function that describes the amount in the account after timet in years b) What is the balance after 1 year? 2 years? 5 years? 10 years? c) What is the doubling time?

The image of point a after reflection over the y axis followed by dilation with a scale factor of 3 centered at the origin is,

⇒ (6, 9)

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

Given that;

The coordinates of point a are,

⇒ a =  (-2,3)

Now, We can multiply by 3 in the point;

⇒ (- 2, 3) = (- 2 × 3, 3×3)

              = (- 6, 9)

Now, After reflection over the y axis,

Image of the point are,

⇒ (6, 9)

Thus, The image of point a after reflection over the y axis followed by dilation with a scale factor of 3 centered at the origin is,

⇒ (6, 9)

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It wiII cοst Jοnah $63.36 tο decοrate the 3-tiered circuIar wedding cake with fresh red rοses arοund the base οf each IeveI.

Tο caIcuIate the cοst οf decοrating the cake with rοses, we need tο first determine the circumference οf each tier, which wiII teII us hοw many rοses are needed fοr each tier.

The circumference οf a circIe can be caIcuIated using the fοrmuIa C = πd, where C is the circumference, π is the mathematicaI cοnstant pi (apprοximateIy 3.14), and d is the diameter.

Fοr the bοttοm tier with a diameter οf 14 inches, the circumference is C = πd = 3.14 x 14 = 43.96 inches.

Fοr the middIe tier with a diameter οf 10 inches, the circumference is C = πd = 3.14 x 10 = 31.4 inches.

Fοr the tοp tier with a diameter οf 6 inches, the circumference is C = πd = 3.14 x 6 = 18.84 inches.

Nοw, we need tο determine hοw many rοses are needed fοr each tier. Tο dο this, we need tο caIcuIate hοw many rοses wiII fit arοund the circumference οf each tier. We can dο this by dividing the circumference οf each tier by the width οf the rοses, which is 1.5 inches.

Fοr the bοttοm tier: 43.96 inches / 1.5 inches per rοse = 29.3, rοunded up tο 30 rοses.

Fοr the middIe tier: 31.4 inches / 1.5 inches per rοse = 20.9, rοunded up tο 21 rοses.

Fοr the tοp tier: 18.84 inches / 1.5 inches per rοse = 12.6, rοunded up tο 13 rοses.

Nοw that we knοw hοw many rοses are needed fοr each tier, we can caIcuIate the tοtaI cοst οf the rοses. Each rοse cοsts $0.99, sο the cοst οf the rοses fοr each tier is:

Bοttοm tier: 30 rοses x $0.99 per rοse = $29.70

MiddIe tier: 21 rοses x $0.99 per rοse = $20.79

Tοp tier: 13 rοses x $0.99 per rοse = $12.87

The tοtaI cοst οf decοrating the cake with rοses is the sum οf the cοsts fοr each tier:

$29.70 + $20.79 + $12.87 = $63.36

Therefοre, it wiII cοst Jοnah $63.36 tο decοrate the 3-tiered circuIar wedding cake with fresh red rοses arοund the base οf each IeveI.

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Option d) The missing quantity A is $2520. The formula for future value is A=P(1+rt), where A is the future value, P is the principal amount, r is the interest rate, and t is the time period.

We are given the values of P, r, and t, and we need to find the value of A.

P = $1800
r = 8% = 0.08
t = 5 years

Plugging these values into the formula, we get:

A = P(1 + rt)
A = $1800(1 + 0.08*5)
A = $1800(1 + 0.4)
A = $1800(1.4)
A = $2520

Therefore, the future value of the investment is $2520. The correct answer is A = $2520.

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Answer:

x=2

Step-by-step explanation:

2(5x+3)=26

expand the bracket first

10x+6=26

take away 6 from both sides

10x=20

divided by 10 on each side

x=2

Answer:

You would use the PEDMAS rule for this equation.

First, distribute 2 inside the parentheses so the equation is 10x + 6 = 26

Then, subtract 6 from both sides 10x = 20

The answer is x = 2.

Step-by-step explanation:

The simplified form of the radical expressions are:
a) −12x2y6
b) 284x7t4y3

To simplify the following radical expressions, we need to factor the radicand and then use the properties of radicals to simplify.

For a) −72x4y122x8y2, we can factor the radicand as follows:

−72x4y12 = −(2*2*2*3*3)x4y12 = −(2*2*2*3*3)(x4)(y12)

Now we can use the properties of radicals to simplify:

√−(2*2*2*3*3)(x4)(y12) = √−(2*2)(2*2)(3*3)(x4)(y12) = −(2*2*3)(x2)(y6) = −12x2y6

For b) 7z21128x14t8y6, we can factor the radicand as follows:

1128x14t8y6 = (2*2*2*2*71)(x14)(t8)(y6)

Now we can use the properties of radicals to simplify:

√(2*2*2*2*71)(x14)(t8)(y6) = √(2*2)(2*2)(71)(x14)(t8)(y6) = (2*2*71)(x7)(t4)(y3) = 284x7t4y3

So the simplified form of the radical expressions are:

a) −12x2y6
b) 284x7t4y3

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Answer:

The answer is [tex](u + 3)(5u^{2} - 1)[/tex]

At least 75% of healthy adults have body temperatures within the range of 96.99°F to 99.67°F.

What is standard deviations?

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

Chebyshev's theorem states that for any distribution (not just the normal distribution), regardless of shape, at least 1 - 1/k^2 of the data values will be within k standard deviations of the mean, where k is any number greater than 1.

In this case, we want to know the percentage of healthy adults with body temperatures that are within 2 standard deviations of the mean. So we need to use Chebyshev's theorem with k = 2.

At least 1 - 1/2^2 = 1 - 1/4 = 0.75, or 75%, of the healthy adults have body temperatures within 2 standard deviations of the mean.

To find the minimum and maximum possible body temperatures that are within 2 standard deviations of the mean, we can use the formula:

Minimum = Mean - k * Standard deviation

Maximum = Mean + k * Standard deviation

Plugging in the values for this problem, we get:

Minimum = 98.33 - 2 * 0.67 = 96.99°F

Maximum = 98.33 + 2 * 0.67 = 99.67°F

Therefore, we can say that at least 75% of healthy adults have body temperatures within the range of 96.99°F to 99.67°F.

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Answer:

Rational numbers are those that can be expressed as a ratio of two integers whereas irrational numbers are those which cannot be expressed as a ratio of two integers.

Rational numbers can be written in the form of a fraction whereas irrational numbers cannot be written in the form of fractions.

Rational numbers comprise of those perfect squares whereas irrational numbers comprise of surds.

Answer:

see below

Step-by-step explanation:

(6x-1)(3x-2)= 6x*(3x-2) - 1*(3x-2)

=6x*3x - 6x*2 -1*3x - (-1)*2

= 18x² - 12x - 3x + 2

=18x² - 15x + 2

Answer:

18x²-15x+2

Step-by-step explanation:

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The inequality (x + 2)/(x - 7)>0 can be solved algebraically by first subtracting 2 from both sides. This results in the inequality (x - 7) > 2. By dividing both sides by (x-7), the inequality can be simplified to 1>2/x-7. This simplifies further to -7>2/x, or x>-7/2. Therefore, the solution to the inequality is x>-7/2.

In plain terms, this means that a value of x must be greater than -7/2 in order for the inequality to be true. This implies that the value of x must be a number greater than -3.5, since -7/2 is the same as -3.5. Thus, if x is any number greater than -3.5, then the inequality (x + 2)/(x - 7) > 0 will be satisfied.

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Answer: Y=-3X+5

Step-by-step explanation:

Slope intercept form is Y=mx+b where m is slope and b is slope intercept to graph you can use desmos which is a free graphing calculator just punch in the equation exactly as I gave it. since m is slope it is -3 and b is y intercept so 5 so Y=-3x+5

Answer:

y = -3x + 5

Step-by-step explanation:

y = mx + b  The m is the slope and the b is the y intercept.  Substitute in the slope and the y-intercept

y = -3x + 5

First, graph the y-intercept.  That will be at the point (0, 5).  From that point, go down 3 units and then go one unit right.  You will be back on the line.  That is the slope.

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There are infinitely many expressions equivalent to 11x + 10, including 22x + 20, 11(x+1)-1, -11(-x)-10, and 11(x+2)-12.

What is expression ?

In mathematics, an expression is a combination of numbers, symbols, and/or variables that are put together in a meaningful way, usually to represent a quantity or a mathematical relationship.

There are infinitely many expressions that are equivalent to 11x + 10, because you can add or subtract any expression to both sides of the equation to get a new equivalent expression. Here are some examples:

22x + 20: This is equivalent to 11x + 10 because if you distribute 11 to x and 10, you get 11x + 10.

11(x + 1) - 1: This is also equivalent to 11x + 10 because if you distribute 11 to x and 1, you get 11x + 11 - 1, which simplifies to 11x + 10.

-11(-x) - 10: This is equivalent to 11x + 10 because if you distribute -11 to -x, you get 11x + 10.

11(x + 2) - 12: This is also equivalent to 11x + 10 because if you distribute 11 to x and 2, you get 11x + 22 - 12, which simplifies to 11x + 10.

In general, any expression of the form 11x + k, where k is a constant, is equivalent to 11x + 10.

Therefore, there are infinitely many expressions equivalent to 11x + 10, including 22x + 20, 11(x+1)-1, -11(-x)-10, and 11(x+2)-12.

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The correct answer is b. 95%.

According to the Empirical rule, for a symmetric data set, 68% of the data falls within 1 standard deviation of the mean, 95% falls within 2 standard deviations of the mean, and 99.7% falls within 3 standard deviations of the mean.

In this particular case, the mean response time is 26 minutes and the standard deviation is 3 minutes. Therefore, 1 standard deviation from the mean is 23 to 29 minutes, 2 standard deviations from the mean is 20 to 32 minutes, and 3 standard deviations from the mean is 17 to 35 minutes.

Since the question asks for the percentage of response times that fall between 20 to 32 minutes, we are looking for the percentage of data that falls within 2 standard deviations of the mean. Therefore, the correct answer is 95%.

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The intersection points between the two equations are (1, 3) and (-4, 2)

Here we have the system of equations:

(x+4)^2+(y−3)^2=25

y=x+2

We can replace the second equation into the first one to get:

(x+4)^2+(x + 2−3)^2 = 25

(x + 4)^2 + (x - 1)^2 = 25

Now let's solve that:

x^2 + 8x + 16 + x^2 - 2x + 1 = 25

2x^2 + 6x + 17 - 25 = 0

2x^2 + 6x - 8 = 0

x^2 + 3x - 4 = 0

Using the quadratic formula:

[tex]x = \frac{-3 \pm \sqrt{3^2 - 4*1*-4} }{2} \\\\x = \frac{-3 \pm5 }{2}[/tex]

So the two solutions are:

x = (-3 + 5)/2 = 1

x = (-3 - 5)/2 = -4

Evaluating the line in these values:

y = 1 + 2 = 3 ----> we have the point (1, 3)

y = -4 + 2 = -2 ----> we have the point (-4, -2)

These are the intersection points.

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The area that can be watered if the length of the pipe is 400, 700, or 1,100 inches long are:

Where L = 400, A [tex]\approx[/tex] 12.82

Where L = 700 A [tex]\approx[/tex] 44.43

Where L = 1,100 A [tex]\approx[/tex]  86.13

The length of the pipe is given by the function:

L =  111.25√A.

Where a = (L/111.25)²

Thus, for L = 400inches

A =  (400/111.24)²

(400/111.24)² = (400²)/(111.24)²

(400²)/(111.24)² = (160000)/(12369.5776)
Divide 160000 by 12369.5776 to get:

(160000)/(12369.5776) = 12.820128200735

Therefore, A = 12.820128200735,

A [tex]\approx[/tex] 12.82

Thus:

Where L = 700;
A = 44.434243
A [tex]\approx[/tex] 44.43

Where L = 1,100
A = 86.129479

A [tex]\approx[/tex] 86.13

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The two values of x that are roots of the given equation are approximately 3.618 and 1.382.

What is quadratic equation ?

Quadratic equations are used to model a wide range of phenomena in many areas of science and engineering, including physics, biology, economics, and finance. They are also used extensively in mathematics for their elegant properties and applications in algebra, geometry, and calculus.

We start with the quadratic equation:

[tex]$x^2 - 5x + 5 = 0$[/tex]

To find the roots of this equation, we use the quadratic formula:

[tex]$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$[/tex]

where [tex]$a$, $b$,[/tex] and [tex]$c$[/tex] are the coefficients of the quadratic equation.

In this case, we have [tex]a = 1$, $b = -5$, and $c = 5$.[/tex] Substituting these values into the quadratic formula, we get:

[tex]$x = \frac{5 \pm \sqrt{(-5)^2 - 4(1)(5)}}{2(1)}$[/tex]

Simplifying the expression under the square root, we get:

[tex]$x = \frac{5 \pm \sqrt{5}}{2}$[/tex]

Therefore, the two roots of the equation are:

[tex]$x = \frac{5 + \sqrt{5}}{2} \approx 3.618$[/tex]

[tex]$x = \frac{5 - \sqrt{5}}{2} \approx 1.382$[/tex]

Hence, the solutions to the equation [tex]$x^2 - 5x + 5 = 0$[/tex] are approximately 3.618 and 1.382.

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Answer:

The answer to your problem is, $0.60

Step-by-step explanation:

1 banana and 1 orange = 1.20.

We divide next:

1.20 / 2 = 0.60.

We know that because in the question it says one banana and one orange is 1.20. Next we divide because two items are sharing the same number.

1.20 / 2 = ? ( ? = 0.60 or 0.6 )

Thus the answer to our problem is, $0.60

The value of x for the given pentagon will be 125 degrees.

In Mathematics, a polygon can be defined as a two-dimensional geometric figure that consists of straight line segments and a finite number of sides. Additionally, some examples of a polygon include the following:

• Triangle

• Quadrilateral

• Pentagon

• Hexagon

• Heptagon

• Octagon

• Nonagon

Given the values exterior angles of the pentagon such that, 70°, 60°, 65°, 40°, x°.

To calculate the value of x.

Since the Sum of all exterior angles of a pentagon is 360°,

Thus,

70 + 60 + 65 + 40 +x = 360

x + 235 = 360

x = 360 - 235

x = 125°

Therefore, the value of x for the given pentagon will be 125 degrees.

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The perimeter of kite FGHJ is 39. Rounded to 2 decimal places, the answer is 39.00.

What is the perimeter?

The perimeter is the total distance around the boundary of a two-dimensional shape. It is calculated by adding up the lengths of all the sides of the shape.

First, we need to find the length of the other two sides of the kite:

Since FH = 17 and FT = 10, we can find the length of TH by subtracting: TH = FH - FT = 17 - 10 = 7.

Similarly, since GJ = 10 and TJ = 5, we can find the length of GT by subtracting: GT = GJ - TJ = 10 - 5 = 5.

Now we can find the perimeter of the kite by adding up the lengths of all four sides:

Perimeter = FH + TH + GJ + GT

Perimeter = 17 + 7 + 10 + 5

Perimeter = 39

Therefore, the perimeter of kite FGHJ is 39. Rounded to 2 decimal places, the answer is 39.00.

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Complete question:

What is the 'perimeter of kite FGHJ? Round to 2 decimal places?

The answer of Caroline is 19.33 years old and Cameron is 53.67 years old

Let's start by assigning variables to represent Caroline's age and Cameron's age. We'll use C for Caroline's age and M for Cameron's age.

According to the problem, the sum of their ages today is 73, so we can write the equation:

C + M = 73

Five years ago, Cameron was 2 times older than Caroline. so we can write the equation:

M - 5 = 2(C - 5)

Now we can use the first equation to solve for one of the variables. Let's solve for C:

C = 73 - M

Next, we can substitute this value of C into the second equation:

M - 5 = 2(73 - M - 5)

Simplifying the equation gives us:

M - 5 = 146 - 2M - 10

3M = 161

M = 53.67

Now we can use this value of M to find C:

C = 73 - 53.67

C = 19.33

So Caroline is 19.33 years old and Cameron is 53.67 years old.

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The correct methods for mental arithmetic are those that break down the calculation into smaller, easier-to-manage parts and simplify the calculation to make it easier to solve.

The correct methods for "thinking out computation" (mental arithmetic) are a, b, and c.

a) 7+8 Think: 7 plus 7 is 14, plus 1 more is 15. This method is correct because it breaks down the calculation into smaller, easier-to-manage parts.

b) 38 - 17 Think: 38 minus 10 is 28, minus 7 more is 21. This method is also correct because it simplifies the calculation by subtracting 10 first, and then subtracting the remaining 7.

c) 999 x 3 Think: 1000 threes is 3000 minus 1 three is 2997. This method is correct because it simplifies the calculation by multiplying 1000 by 3 first, and then subtracting 1 three to get the correct answer.

d) 150 ÷ 3 Think: what equals 150 x 3, that's 450. This method is incorrect because it is actually doing the opposite operation (multiplication instead of division) and therefore does not result in the correct answer. The correct method would be to think about how many times 3 can go into 150, which is 50.

In conclusion, the correct methods for mental arithmetic are those that break down the calculation into smaller, easier-to-manage parts and simplify the calculation to make it easier to solve.

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The correct methods for "thinking out computation" (mental arithmetic) are:
A) 7+8 Think: 7 plus 7 is 14, plus 1 more is 15
B) 38 - 17 Think: 38 minus 10 is 28, minus 7 more is 21
C) 999 x 3 Think: 1000 threes is 3000 minus 1 three is 2997
D) 150 ÷ 3 Think: what equals 150 x 3, that's 450

All four methods of "thinking out computation" provided in the question are correct and valid.

Method (a) is using the "doubles" method, which is a common mental arithmetic technique. By recognizing that 7+7 is 14, it is easy to add 1 more to get 15.

Method (b) is using the "subtracting by tens" method. By recognizing that 38 minus 10 is 28, it is easy to subtract 7 more to get 21.

Method (c) is using the distributive property of multiplication. By recognizing that 999 is very close to 1000, we can multiply 3 by 1000 and then subtract 3 to get 2997.

Method (d) is using the inverse operation of multiplication. By recognizing that 150 is a multiple of 3, we can think of 150 as 3 times some unknown number, and then determine that number by dividing 150 by 3. The answer is 50, which is the same as thinking of what equals 150 times 3 (450).

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The value of the algebraic expression [tex]b^(2)-4ac for a=-4,b=-2,c=6[/tex] is 100.

An algebraic expression is an expression that consists of constants, variables, and some algebraic operations. To solve it, simply use multiplication, division, addition, and subtraction when necessary to isolate the variable and solve.

To evaluate the given algebraic expression, we will substitute the given values of a, b, and c into the expression and simplify.

Step 1: Substitute the given values into the expression.
[tex]b^(2)-4ac = (-2)^(2)-4(-4)(6)[/tex]

Step 2: Simplify the expression.
[tex]= 4+96= 100[/tex]

Therefore, the value of the algebraic expression [tex]b^(2)-4ac[/tex] for [tex]a=-4,b=-2,c=6 is 100.[/tex]

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Answer:

a,b,c,d

Step-by-step explanation:

all are rational except efg

The probability of generating a value between -0.9900 and 2.9000 from a standard normal distribution is 0.4781. The probability of generating a value between -2.4200 and 2.4200 from a standard normal distribution is 0.9804. The probability of generating a value between -0.9900 and 20.1 from a standard normal distribution is 1.0000.

The standard normal distribution, also called the z-distribution, is a special normal distribution where the mean is 0 and the standard deviation is 1. Any normal distribution can be standardized by converting its values into z scores.The standard normal distribution is one of the forms of the normal distribution. It occurs when a normal random variable has a mean equal to zero and a standard deviation equal to one. In other words, a normal distribution with a mean 0 and standard deviation of 1 is called the standard normal distribution.

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Answer:

14.1 feet

Step-by-step explanation:

Amount of liquid gallons in 1 cubic foot= 7.48

Radius of the cylindrical water tank= 2.2 feet

Amount of liquid gallons it can hold= 1,600

Volume of the cylindrical water tank to carry 1,600 liquid gallons= [tex]\frac{1600}{7.48}[/tex]

                                                                                                           = 213.90 ft³

Volume of the cylinder= [tex]\pi r^{2} h[/tex]

                            213.9= 3.14 x 2.2 x 2.2 x h

                            213.9= 3.14 x 4.84 x h

                            213.9= 15.2 x h

                                  h= [tex]\frac{213.9}{15.2}[/tex]

                                  h= 14.07

                                  h= 14.1 feet

∴ height of the water tank is 14.1 feet.

\( 7 \sqrt[3]{8 x^{2} y}+6 \sqrt[3]{x^{5} y^{4}} \) = \( 13 \sqrt[3]{x^{5} y^{4}} \)

Adding/subtracting radical expressions and simplifying can be done as follows:

(a) \( -2 y \sqrt{28 x^{3}}+3 x \sqrt{63 x y^{2}}-3 \sqrt{112 x^{3} y^{2}} \)

\(-2 y \sqrt{28 x^{3}}+3 x \sqrt{63 x y^{2}}-3 \sqrt{112 x^{3} y^{2}}\) = \( -2 y \sqrt{28 x^{3}}+3 x \sqrt{63 x y^{2}}-3 \sqrt{28 x^{3} \cdot 4 y^{2}}\)

\(-2 y \sqrt{28 x^{3}}+3 x \sqrt{63 x y^{2}}-3 \sqrt{28 x^{3} \cdot 4 y^{2}}\) = \( -2 y \sqrt{28 x^{3}}+3 x \sqrt{63 x y^{2}}-12 y \sqrt{7 x^{3}}\)

\(-2 y \sqrt{28 x^{3}}+3 x \sqrt{63 x y^{2}}-12 y \sqrt{7 x^{3}}\) = \( -14 y \sqrt{7 x^{3}}+3 x \sqrt{63 x y^{2}}\)

(b) \( 7 \sqrt[3]{8 x^{2} y}+2 \sqrt[3]{27 x^{5} y^{4}} \)

\( 7 \sqrt[3]{8 x^{2} y}+2 \sqrt[3]{27 x^{5} y^{4}} \) = \( 7 \sqrt[3]{8 x^{2} y}+2 \sqrt[3]{3^3 \cdot x^{5} y^{4}} \)

\( 7 \sqrt[3]{8 x^{2} y}+2 \sqrt[3]{3^3 \cdot x^{5} y^{4}} \) = \( 7 \sqrt[3]{8 x^{2} y}+6 \sqrt[3]{x^{5} y^{4}} \)

\( 7 \sqrt[3]{8 x^{2} y}+6 \sqrt[3]{x^{5} y^{4}} \) = \( 13 \sqrt[3]{x^{5} y^{4}} \)

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Since TB = TS and OT is perpendicular to RS, it follows that BO is also perpendicular to RS, and hence RS is the diameter of the circle.

The circle is defined as the locus of the point traces around a fixed point called the centre and is equidistant from the out trace.

Since T is the midpoint of both chords PQ and RS, it follows that the perpendicular bisectors of these chords pass through the centre of the circle. Let O be the centre of the circle.

Consider the perpendicular bisector of PQ passing through T. Let it intersect the circle at point A. Since TA = TP and OT is perpendicular to PQ, it follows that AO is also perpendicular to PQ, and hence PQ is the diameter of the circle.

Similarly, consider the perpendicular bisector of RS passing through T. Let it intersect the circle at point B. Since TB = TS and OT is perpendicular to RS, it follows that BO is also perpendicular to RS, and hence RS is the diameter of the circle.

Therefore, PQ and RS are both diameters of the circle.

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Answer: The probability of choosing a sophomore on the first draw is 125/512. Since the selection is random and without replacement, the probability of choosing another sophomore on the second draw is 124/511. Therefore, the probability of choosing two sophomores in a row is:

(125/512) x (124/511) = 0.0603 or approximately 0.06 (rounded to two decimal places).

Step-by-step explanation:

The exponential function that models the percentage as a function of P is given as follows:

P(t) = 100(0.705)^t.

The standard definition of an exponential function is given as follows:

y = a(b)^x.

In which:

The parameters for this problem are given as follows:

Hence the function that models the data in the table is defined as follows:

P(t) = 100(0.705)^t.

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