rewrite each equation using the properties of exponents
1. ([tex](\frac{4}{64\frac{5}{6} })^{\frac{1}{2} }[/tex]
2. [tex]3m\frac{1}{4} (mn\frac{1}{3} ) ^{\frac{3}{2} }[/tex]
3.[tex]2a\frac{1}{2} (5a\frac{1}{2} b\frac{1}{4} )^{2}[/tex]

Answer: 14.5 climbers technically 14 because 1/2 a person is wrong

Step-by-step explanation:

The volume of air that the beach ball will hold is 36000π cubic cm

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

The radius of the beach ball is 30 cm.

This means that

r = 30

The volume of air that the beach ball will hold is calculated as

V = 4/3πr³

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

V = 4/3π * 30³

Evaluate

V = 36000π

Hence, the volume of air that the beach ball will hold is 36000π cubic cm

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The 5% discount is 8.10, Namas divide 42 between the percentage follow me and give me crown.

A discount is a reduction in the price of a product or service offered to customers. It is a common marketing strategy used by businesses to attract customers and increase sales. Discounts can be offered in various forms, such as percentage off, dollar off, or buy-one-get-one-free deals.

Discounts are often used to clear out old inventory, promote new products or services, and to reward customer loyalty. They can be temporary or ongoing, and the amount of the discount can vary depending on the product, service, or promotion. Customers benefit from discounts as they can purchase products or services at a lower price, saving them money. Businesses benefit from discounts as they can increase sales volume, clear out inventory, and attract new customers.

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Complete Question:-

Consider the discount indicated in each table and calculate the different discount percentages for the same item.

The approximate total amount Valerie will pay for her new car is $38,287.

How much will Valerie pay in total for her new car?

To calculate how much Valerie will pay in total for her new car, we need to consider several factors.

First, let's determine the trade-in value of her 2006 Hyundai Sonata. Since the car is in good condition, Valerie will receive 87.5% of the listed trade-in price for that year, which is $6,784. Therefore, the trade-in value is approximately $5,938.80 ($6,784 * 0.875).

Now, let's calculate the total cost of the new car. The list price is $32,495, and Valerie plans to make a down payment of $1,877. Thus, the remaining amount to be financed is $32,495 - $1,877 - $5,938.80 = $24,679.20.

Next, let's consider the interest on the financing. The interest rate is 8.64% per year, compounded monthly. Over five years, this amounts to 60 monthly payments. Using an amortization formula, we can determine that the monthly payment is approximately $516.27.

Additionally, Valerie will have to pay sales tax, vehicle registration fee, and documentation fee. The sales tax is 8.23% of the total cost, which is ($24,679.20 + $2,243) * 0.0823 = $2,329.48. The vehicle registration fee is $2,243, and the documentation fee is $314. The total additional fees amount to $2,329.48 + $2,243 + $314 = $4,886.48.

Finally, to calculate the total amount Valerie will pay, we add the down payment, monthly payments, trade-in value reduction, and additional fees: $1,877 + (60 * $516.27) + $5,938.80 + $4,886.48 = $38,285.88.

Rounding to the nearest cent, Valerie will pay approximately $38,286 for her new car. Thus, the correct answer is option c: $38,287.

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The difference between the volume and surface area of both balls is: 108101.69 cubic centimeters.

The formula for the volume of a sphere is V = (4/3)π[tex]r^3[/tex], where r is the radius of the sphere, and the formula for the surface area of a sphere is A = 4π[tex]r^2[/tex].

Let's start by finding the radius of each ball. The diameter of the first ball is 85 cm, so its radius is 85/2 = 42.5 cm. The diameter of the second ball is 65 cm, so its radius is 65/2 = 32.5 cm.

The volume of the first ball is:

V1 = (4/3)π[tex](42.5)^3[/tex] = 256905.53 cubic centimeters

The volume of the second ball is:

V2 = (4/3)π[tex](32.5)^3[/tex] = 139379.44 cubic centimeters

The difference in volume is:

V1 - V2 = 256905.53 - 139379.44 = 117526.09 cubic centimeters

To find the difference in surface area, we plug in the radius values:

A1 = 4π[tex](42.5)^2[/tex] = 22698.16 square centimeters

A2 = 4π[tex](32.5)^2[/tex] = 13273.76 square centimeters

The difference in surface area is:

A1 - A2 = 22698.16 - 13273.76 = 9424.40 square centimeters

Therefore, the difference between the volume and surface area of both balls is: 117526.09 cubic centimeters - 9424.40 square centimeters, rounded to the nearest hundredth, is 108101.69 cubic centimeters.

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Average speed going to work is 50 mph.

Let's assume that the average speed going to work is "x" miles per hour.

Since you can travel to work in the same time it takes for you to make it 28 miles on the trip back home, we can set up an equation using the formula:

time = distance / speed

The time it takes to travel 35 miles to work is:

time to work = 35 / x

The time it takes to travel 28 miles on the return trip is:

time to return = 28 / (x - 10)

We know that both times are equal, so we can set them equal to each other and solve for "x":

[tex]35 / x = 28 / (x - 10)[/tex]

Multiplying both sides by x(x - 10), we get:

[tex]35(x - 10) = 28x[/tex]

Expanding the left side and simplifying, we get:

[tex]35x - 350 = 28x[/tex]

[tex]7x = 35[/tex]

[tex]x = 50[/tex]

Therefore, your average speed going to work is 50 miles per hour.

To solve this problem, we used the formula for speed, distance, and time. We t up an equation using the fact that the time it takes to travel to work is equal to the time it takes to travel 28 miles on the return trip. We then solved for the average speed going to work by setting the two times equal to each other and solving for "x". Finally, we found that the average speed going to work is 50 miles per hour.

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The value of tanG is √3

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

sin(tetha) = opp/hyp

cos(tetha) = adj/hyp

tan(tetha) = opp/adj

The value of KY

Tan 30 = 27/KY

1/√3 = 27/KY

KY = 27√3

Tan G = 27√3/27

tanG = √3

therefore the value of tanG is √3

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To calculate ∑ (-1)^k pi^2k/2k, we can use the power series expansion for the cosine function:

cos(x) = ∑ (-1)^n x^(2n) / (2n)!

We can substitute pi^2 for x in this formula to get:

cos(pi^2) = ∑ (-1)^n (pi^2)^(2n) / (2n)!
= ∑ (-1)^n pi^(4n) / (2n)!

Now we can compare this to the original series we want to evaluate:

∑ (-1)^k pi^2k/2k = ∑ (-1)^n pi^(2n) / (2n)

We notice that the powers of pi in the two series match up, but the coefficients are different. However, we can use the identity cos(pi^2) = (-1)^n to rewrite the series we want to evaluate as:

∑ (-1)^n pi^(2n) / (2n) = ∑ (-1)^n pi^(4n) / (2n)! * (2n) / pi^2n

= pi^2 / 2 * ∑ (-1)^n pi^(4n) / (2n)!

Now we can substitute our expression for cos(pi^2) into this equation to get:

∑ (-1)^k pi^2k/2k = pi^2 / 2 * cos(pi^2)

= pi^2 / 2 * (-1)^n

Therefore, the value of the series is (-1)^n * pi^2 / 2.
To calculate the sum ∑ (-1)^k (pi^2k)/(2k), it is important to recognize that this is an alternating series with a general term given by a_k = (-1)^k (pi^2k)/(2k).

However, the question seems incomplete, as there is no specified range for the sum (i.e., the values of k). If you provide the range of k for which this sum is to be calculated, I would be glad to help you further.

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The error in finding area of the sector is in formula applied the correct  value is equal to 81.46 square feet.

Area of the sector with center Z is equal to 255 square feet.

Angle subtended in the center of the circle = 115 degrees

Let us consider 'r' be the radius of the circle.

And 'θ' be the angle subtended at the center of the circle.

Using the formula of a area of a sector we have,

Area of sector = θ/360 × πr²

Error in the calculation was made by applying wrong formula ,

Area of circle = 255 square feet

Center angle 'θ'  = 115°

Substitute the value in the formula we have ,

⇒ Area of sector = (115°/360) × 255

⇒ Area of sector = 81.4583 square feet

⇒ Area of sector ≈ 81.46 square feet

From the attached figure the area of sector is 162.32ft².

Therefore, the error in finding area of the sector is in formula the correct answer is 81.46 square feet.

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The above question is incomplete, the complete question is:

Correct the error in finding the area of sector XZY when the area of ⊙Z is 255 square feet. Round to the nearest tenth. The area should equal ft2

Attached figure.

The number does MOVED represent 1110.

Since GOD=605, we know that D=5. We can now substitute this value of D into the addition problem to get:

GOD+ DOG = MOVED

605+ 506 = 1111

Since M cannot be 0 (otherwise it wouldn't be a 4-digit number), we know that M=1.

We can now subtract 1 from both sides of the equation to get:

604+ 506 = 1110

Now we can see that E+4=10, so E=6. We can also see that O+0=0, so O=0. Finally, we can see that G+D=1, so G=6 and D=5.

Therefore, MOVED = 1110.

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75% of the bacteria to live for approximately 130.11 minutes

To answer your question, we'll be using the concept of standard deviation and the normal distribution.

Given that the average lifespan of bacteria in a culture is 2 hours (120 minutes) with a standard deviation of 15 minutes, we can expect at least 75% of the bacteria to live for a certain amount of time. Using the normal distribution, we can determine the corresponding z-score for the 75th percentile, which is approximately 0.674.

Now, we can apply the z-score formula:
z = (X - mean) / standard deviation

Rearrange the formula to solve for X (the time at which 75% of the bacteria will live):
X = mean + (z * standard deviation)

Plugging in the given values:
X = 120 + (0.674 * 15) ≈ 130.11 minutes

So, we can expect at least 75% of the bacteria to live for approximately 130.11 minutes.

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By  null hypothesis there is sufficient evidence at the 5% significance level to purchase the proposed panels.

To determine if there is sufficient evidence to purchase the proposed panels, we can perform a hypothesis test. Let's define the following:

- p: the proportion of all panels that produce an efficiency rating greater than 20%

- p0: the proportion specified in the proposal, which is p0 = 0.18

- n: the sample size, which is n = 140

- x: the number of panels in the sample that produce an efficiency rating greater than 20%, which is x = 32

We want to test the null hypothesis H0: p <= p0 against the alternative hypothesis Ha: p > p0. The significance level is alpha = 0.05.

We can use the normal approximation to the binomial distribution since both np0 and n(1-p0) are greater than 10, where np0 is the expected number of panels that produce an efficiency rating greater than 20% under the null hypothesis.

Under the null hypothesis, the test statistic z is approximately:

z = (x - np0) / sqrt(np0(1-p0))

Plugging in the values, we get:

z = (32 - 140*0.18) / sqrt(140*0.18*0.82) ≈ 1.96

The critical value of z at alpha = 0.05 with a one-tailed test is 1.645. Since our calculated z value is greater than the critical value, we reject the null hypothesis.

Therefore, there is sufficient evidence at the 5% significance level to purchase the proposed panels.

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The expression that is equivalent to the one Regina wrote is y + 27/4

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

y + 9 x 3/4

This means that

Expression = y + 9 x 3/4

Expanding the above expression, we have

Expanded expression = y + 27/4

Using the above as a guide, we have the following:

The expression that is equivalent to the one Regina wrote is y + 27/4

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If the system includes the inequality y < 0, then the shaded region would be below the x-axis (in the third and fourth quadrants).

The solutions to a system of linear inequalities can be graphed on a coordinate plane to form a shaded region.

The shaded region would be in the quadrant(s) that satisfies all the inequalities in the system. For example, if the system of inequalities includes the inequality x > 0, then the shaded region would be on the right-hand side of the y-axis (in the first and fourth quadrants).

If the system includes the inequality y < 0, then the shaded region would be below the x-axis (in the third and fourth quadrants).

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Answer:

x = 1/2, -4/3

Step-by-step explanation:

(2x - 1)(3x + 4) = 0

We know any number multiplied by 0 will be equal 0.

2x - 1 = 0

2x = 1

x = 1/2

3x + 4 = 0

3x = -4

x = -4/3

So, x = 1/2, -4/3

[tex]2x(3x + 4) - 1(3x + 4) = 0[/tex]

[tex]6 {x}^{2} + 8x - 3x - 4 = 0[/tex]

[tex]6 {x}^{2} + 5x - 4 = 0[/tex]

[tex]6 {x}^{2} + 5x = 4[/tex]

Answer:

Querido/a [Pen pal's name],

¡Hola! Espero que estés bien. Quería escribirte sobre mis gustos musicales. Me encanta la música de todo tipo, pero mis géneros favoritos son el pop y el rock. Me gusta escuchar artistas como Taylor Swift, Ed Sheeran, Coldplay y Queen. También disfruto escuchar música latina como el reggaetón y la salsa.

Además de escuchar música, también me gusta tocar algunos instrumentos. Toco la guitarra y el piano desde hace algunos años y me encanta aprender nuevas canciones y melodías en ambos instrumentos.

Creo que la música es una forma maravillosa de expresión y me encanta poder hacer música yo mismo.

¿Y tú? ¿Qué tipo de música te gusta? ¿Tocas algún instrumento? Me encantaría saber más sobre tus gustos musicales y si tienes algún hobby musical.

Espero tu respuesta pronto. ¡Cuídate mucho!

Saludos cordiales,

[Your name]

x = 4.56

y = 8.24

z = 12.99

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Answer:(x-4)^2-10

Step-by-step explanation:

The class boundaries are 0.5 - 3.5, 3.5 - 6.5, 6.5 - 9.5, 9.5 - 12.5, 12.5 - 15.5.

To find the class boundaries, we need to add and subtract 0.5 from the upper and lower limits of each class interval, respectively.

Using this formula, we get the following class boundaries:

Class Boundaries:

0.5 - 3.5, 3.5 - 6.5, 6.5 - 9.5, 9.5 - 12.5, 12.5 - 15.5

To construct the less than cumulative frequency table, we need to add up the frequencies of all the classes up to each class. For example:

Less than Cumulative Frequency Table:

Ages No. of Children Cumulative Frequency

1-3 10 10

4-6 12 22

7-9 15 37

10-12 13 50

13-15 9 59

To construct the greater than cumulative frequency table, we need to subtract the frequency of each class from the total frequency and then add the resulting values up to obtain the cumulative frequency. For example:

Greater than Cumulative Frequency Table:

Ages No. of Children Cumulative Frequency

13-15 9 59

10-12 13 50

7-9 15 37

4-6 12 22

1-3 10 10

Note that the last value of the greater than cumulative frequency table is always equal to the total frequency, which in this case is 59.

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Answer:

2

Step-by-step explanation:

The K and N are the trapeziums and the two lines opposite to them go in a parallel line

i) T3(x) = 1 + x + x^2 + x^3/3

ii) R3(x) = x^4/4 + x^5/5

iii) The maximum value of f(4)(x) on the interval |x| ≤ 0.1 is 144.

iv) Yes, Taylor's inequality holds true for R3(0.1) since the maximum value of f(4)(x) on the interval |x| ≤ 0.1 is less than or equal to 144, which is smaller than the upper bound of 625/24.

i) To find T3(x), we start by calculating the derivatives of f(x) up to order 3:

f(x) = 1 + x + x^2 + x^3 + x^4 + x^5

f'(x) = 1 + 2x + 3x^2 + 4x^3 + 5x^4

f''(x) = 2 + 6x + 12x^2 + 20x^3

f'''(x) = 6 + 24x + 60x^2

Then, we evaluate these derivatives at x = 0:

f(0) = 1

f'(0) = 1

f''(0) = 2

f'''(0) = 6

Using these values, we can write the Taylor polynomial of f at x = 0 with degree 3 as:

T3(x) = f(0) + f'(0)x + f''(0)x^2/2 + f'''(0)x^3/6

= 1 + x + x^2 + x^3/3

ii) To find R3(x), we use the remainder formula for Taylor polynomials:

R3(x) = f(x) - T3(x)

Substituting f(x) and T3(x) into this formula and simplifying, we get:

R3(x) = x^4/4 + x^5/5

iii) To find the maximum value of f(4)(x) on the interval |x| ≤ 0.1, we first calculate the fourth derivative of f(x):

f(x) = 1 + x + x^2 + x^3 + x^4 + x^5

f''''(x) = 24 + 120x

Then, we evaluate this derivative at x = ±0.1 and take the absolute value to find the maximum value:

|f(4)(±0.1)| = |24 + 12| = 36

Since 36 is the maximum value of f(4)(x) on the interval |x| ≤ 0.1, we know that the upper bound for the remainder formula is 625/24.

iv) Taylor's inequality states that the absolute value of the remainder Rn(x) for a Taylor polynomial of degree n at a point x is bounded by a constant multiple of the (n+1)th derivative of f evaluated at some point c between 0 and x. Specifically, we have:

|Rn(x)| ≤ M|x-c|^(n+1)/(n+1)!

where M is an upper bound for the (n+1)th derivative of f on the interval containing x.

In this case, we have n = 3, x = 0.1, and c = 0. The (n+1)th derivative of f is f(4)(x) = 24 + 120x.

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To start, let's call the width of the rectangle "w" and the height "h". We know that the area must be 500 square feet, so we can write an equation:

w*h = 500

We can solve this equation for h:

h = 500/w

Now we can express the total cost of the wire in terms of w. The cost of the wire for the width is $2.50 per foot, so the cost for that side is:

2.5w

The cost of the wire for the height is $4.25 per foot, so the cost for that side is:

4.25h = 4.25(500/w) = 2125/w

So the total cost of the wire is:

C(w) = 2.5w + 2125/w

This is our final answer expressed in function notation.
Let's denote the width of the rectangle as w and the height as h. We are given that the area of the rectangle must be 500 square feet, so we have:

w * h = 500

Now, we need to find the cost function based on the width. The cost of the wire for the width is $2.50 per foot and for the height is $4.25 per foot. Therefore, the total cost (C) can be expressed as:

C(w) = 2.50 * w + 4.25 * h

We need to express the height (h) in terms of the width (w) using the area equation:

h = 500 / w

Now, we can substitute this expression for h in the cost function:

C(w) = 2.50 * w + 4.25 * (500 / w)

This is the cost function for building the rectangle out of wire as a function of its width, given that the enclosed area must be 500 square feet.

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Answer:

The price of the meal after the discount was (A)$48.11 and the final price of the meal was (B)$57.73.

Step-by-step explanation:

Let us consider the amount of money $56.60 as the cost of the meal.

So the amount of money is 56 dollars and 60 cents.

A: The family has a 15% off coupon.

Discount = 15% of 56.60=0.15x56.60=8.49

Now we subtract the discount amount from the original amount.

Cost of the meal = 56.60-8.49=48.11

So the final price of the meal for the family is $48.11 or 48 dollars and 11 cents.

B: The family gave a tip of 20%.

Amount of money tipped= 20% of 48.11=0.20 x 48.11=9.622

To get the final amount we add the tip to the discounted price.

The final cost of the meal= 48.11+9.622=57.732=57.73

Therefore the family paid a total of 57 dollars and 73 cents for the final cost of the meal after the discount and tip.

Hope this helps :)

Since polygon A prime B prime C prime D prime above is above the image of polygon ABCD, the type of transformation shown is: D. vertical translation.

In Mathematics and Geometry, a transformation can be defined as the movement of a point from its initial position to a new location. This ultimately implies that, when a function or object is transformed, all of its points would also be transformed.

In Mathematics and Geometry, a horizontal translation to the right is modeled by this mathematical equation g(x) = f(x - N) while a vertical translation to the positive y-direction (upward) is modeled by this mathematical equation g(x) = f(x) + N.

Where:

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Answer:

Vertical translation

Step-by-step explanation:

I am in the middle of taking the quiz and belive this is the correct answer!

Thus, the value of the angle x for the given angles of value 100 and 112 is found as 36.

An adjacent pair of additional angles is known as a linear pair. Adjacent refers to being next to one another, and supplemental denotes that the sum of the two angles is 180 degrees. As previously said, neighbouring angles are those that are close to one another.

An angle pair that forms a line is known as a "line-ar pair."

For the given triangle:

Using the triangle's angle sum property:

x + (180 - 100) + (180 - 112) = 180

(the other two angles except x are linear pair with the angles of value 100 and 112)

So,

x + 80 + 180 - 112 = 180

x = 112 - 80

x = 32

Thus, the value of the angle x for the given  angles of value 100 and 112 is found as 36.

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Answer:

Step-by-step explanation:

To use a number line to find the number that is 7 more than -9, we start by finding -9 on the number line. Then, we move 7 units to the right (because we want to find a number that is 7 more), staying on the number line.

Starting from -9 on a number line, we can count 7 units to the right, which brings us to:

-9 + 7 = -2

Therefore, the number that is 7 more than -9 is -2.

The lateral surface area of a cylinder is given by the formula:

Lateral surface area = 2πrh

where r is the radius of the cylinder and h is the height of the cylinder.

In this case, the height of the cylinder is 8 ft and the radius of the cylinder is 4 ft (half of the diameter). So, we can plug in these values to get:

Lateral surface area = 2π(4 ft)(8 ft)

Lateral surface area = 64π square feet

Rounding to the nearest tenth, we get:

Lateral surface area ≈ 201.1 square feet (rounded to one decimal place)

Therefore, the lateral surface area of the cylinder is approximately 201.1 square feet.

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Answer:

22.25

Step-by-step explanation:

8x+ (11*2)=200

first, multiply 11 and 2 =22

that leaves 8x+22=200

so now let's subtract the 22 from both sides

8x=178 now divide the 8

x= 22.25 so that is the most the jackets could have cost

The equation of curve passing through the point (9,8) with slope [tex]6\sqrt{x}[/tex] is [tex]y = 4\times x^{(3/2)} -100[/tex] .

Slope of curve is given by [tex]6\sqrt{x}[/tex] and curve is passing through point (9,8) .

A curve can be represented in a graph using the standard form of equations. Equation will represent the slope of curve and point through which the curve is passing.

Equation of curve :

Differentiate the slope equation,  

dy/dx =  [tex]6\sqrt{x}[/tex]

dy = [tex]6\sqrt{x}[/tex] dx

Integrating both sides,

Integration rule : [tex]\int\ {x^n} \, dx = x^{n+1}/n+1 + c[/tex]

[tex]y = 6 \times (x^{3/2})/(3/2) +c[/tex]

[tex]y = 4 x^{(3/2)} + c[/tex]

Now substitute (9,8) in the equation of y,

[tex]8 = 4\times (9)^{3/2} + c[/tex]

[tex]c = -100[/tex]

Substitute the value to get the equation of curve,

The equation of curve is [tex]y = 4\times x^{(3/2)} -100[/tex] .

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