Ben uses clay to make the rectangular prism to the left. Naomi uses cardboard to make the triangular prism to the right. Compare the volumes of the prisms.

In the given equation, We can start by isolating the square root term on one side of the equation. The answer is {-2, 10}.

x + 6 - 9 = [tex]\sqrt{2x+29}[/tex]

Simplifying the left-hand side:

x - 3 = root(2x + 29)

Squaring both sides of the equation to eliminate the square root:

(x - 3)^2 = 2x + 29

Expanding the left-hand side:

[tex]x^2[/tex] - 6x + 9 = 2x + 29

Moving all the terms to one side of the equation:

[tex]x^2[/tex] - 8x - 20 = 0

We can now use the quadratic formula to solve for x:

x = (-b ± sqrt([tex]b^2[/tex] - 4ac)) / 2a

where a = 1, b = -8, and c = -20.

Substituting these values into the formula, we get:

x = (-(-8) ± sqrt([tex](-8)^2[/tex] - 4(1)(-20))) / 2(1)

Simplifying the equation:

x = (8 ± sqrt(144)) / 2

x = (8 ± 12) / 2

So, we have two possible solutions:

x1 = 10

x2 = -2

Thus, the answer is {-2, 10}.

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The coefficient of variation for the off-cuts lengths is 30.0%, which indicates a relatively high degree of variability in the data.

The coefficient of variation (CV) is a measure of relative variability, which is calculated by dividing the standard deviation by the mean, and expressing the result as a percentage. It is used to compare the variability of different datasets, particularly when they have different units or scales.

To calculate the CV for the off-cuts lengths in this problem, we first need to calculate the mean and the standard deviation. The mean is calculated by adding all the values together and dividing by the number of values:

Mean = (5.2 + 6.6 + 3.5 + 8.9 + 7.5 + 7.3) / 6 = 6.5 cm

Next, we need to calculate the standard deviation, which measures the dispersion of the data points from the mean. We can use the formula:

Standard Deviation = √(Σ(xi - x)² / (n - 1))

where xi is the value of each data point, x is the mean, and n is the number of data points.

Standard Deviation = √[(5.2 - 6.5)² + (6.6 - 6.5)² + (3.5 - 6.5)² + (8.9 - 6.5)² + (7.5 - 6.5)² + (7.3 - 6.5)²] / 5

Standard Deviation = 1.951 cm

Finally, we can calculate the coefficient of variation by dividing the standard deviation by the mean, and multiplying by 100 to express the result as a percentage:

CV = (1.951 / 6.5) x 100 = 30.0%

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Only [tex]0.03125 ml[/tex] of the technetium-99m will be left after 24 hours.

After 6 hours, half of the original amount will decay.

After another, leaves 1/4 of the original amount.

After another, leaves 1/8 of the original amount.

After another, leaves 1/16 of the original amount.

We will below formula calculate the amount of technetium-99m left after 24 hours: N = N0 * (1/2)^(t/T)

N = 0.5 * (1/2)^(24/6)

N = 0.5 * (1/2)^4

N = 0.5 * 1/16

N = 0.03125 ml

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The Simple Interest (SI) for a principal amount of $1000, a rate of interest of 3%, and a time period of 2 years is $60.

Using the formula for Simple Interest (SI):

SI = (P x r x t) / 100

where P is the principal amount, r is the rate of interest, and t is the time period in years.

Substituting the given values:

SI = (1000 x 3 x 2) / 100

SI = 60

Therefore, the Simple Interest (SI) for a principal amount of $1000, a rate of interest of 3%, and a time period of 2 years is $60.

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The probability of having regular illness is (0.16) when compared to those with good sleep (0.12).

Let's calculate the probability of having regular illness given poor sleep:

P(regular illness | poor sleep) = 16% = 0.16

Now, let's calculate the probability of having regular illness given good sleep:

P(regular illness | good sleep) = 24 / (24 + 176) = 0.12

Hence, the probability of having regular illness is (0.16) when compared to those with good sleep (0.12).

This supports the doctor's claim that poor sleep increases the probability of having regular illness.

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The measures of angles and classification for the triangles are:

(20). m∠A = 33, m∠B = 66, m∠C = 81. Acute triangle

(21) m∠R = 20, m∠S = 140, m∠T = 20. Isosceles triangle

(22). m∠W = 75, m∠Y = 15, m∠Z = 90. Right triangle.

The sum of the interior angles of a triangle is equal to 180°, thus;

(20). x + 2x + 2x + 15 = 180°

x = 165/5

x = 33°

m∠A = 33

m∠B = 2(33) = 66

m∠C = [2(33) + 15] = 81

This is an acute triangle, as all its angles are less than 90°.

(21). x + 7x + x = 180°

9x = 180

x = 20

m∠R = 20

m∠S = 7(20) = 140

m∠T = 20.

This is an Isosceles triangle, because it have two equal base angles.

(22). x - 15 + 2x - 165 + 90 = 180°

3x - 90 = 180°

x = 270/3

x = 90.

m∠W = (90 - 15) = 75

m∠Y = [2(90) - 165] = 15

m∠Z = 90.

This is a Right triangle because it as one of its angle equal to 90°.

Therefore, the measures of angles and classification for the triangles are:

(20). m∠A = 33, m∠B = 66, m∠C = 81. Acute triangle

(21) m∠R = 20, m∠S = 140, m∠T = 20. Isosceles triangle

(22). m∠W = 75, m∠Y = 15, m∠Z = 90. Right triangle.

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Answer:

c and d

Step-by-step explanation:

it is a 2d object

so it can only be measured in 2 directions (up and side) it has no depth as it is 2 dimensional. and it is round and cannot have a point.

Answer:

D. It is a two-dimensional object.

The statement D is true about the figure above. The figure is a circle, which is a two-dimensional object.

Statement A is not true. A point is a location in space, but a circle is a shape that takes up space and has a defined area.

Statement B is not true either. A circle has only one measurement, which is its radius or diameter. The radius is the distance from the center of the circle to any point on its circumference, while the diameter is the distance across the circle through its center.

Statement C is also not true. A circle cannot "grow" into a three-dimensional object because it is a two-dimensional object that exists in a flat plane. However, multiple circles can be stacked on top of each other to form a cylinder, which is a three-dimensional object.

The new shares which the contribution buy is:

= $200 / $40/share

= 5 new shares.

There are 5 shares bought on Feb 15. Therefore, the total shares owned = 5.

An amount of $200 is spent on Feb 15. So, the total spent will be $200.

Average cost per share = Total spent / Total shares owned

Average cost per share = $200 / 5 shares

Average cost per share = $40/share

Current value of portfolio = Total shares owned × Current share price

Current value of portfolio = 5 shares × $40/share

Current value of portfolio = $200

I benefited from the share price dropping because the subsequent monthly contributions could buy more shares for the same amount of money.

However, the downside of the share price dropping is that the current value of the portfolio decreases which potentially leads to lower returns when selling the shares in the future.

Missing words "To minimize risk, you’ve decided to invest your IRA money in a low cost index fund called Einstein’s Index Fund 500 (EIF). You’ve decided you can afford to invest $200 per month, and your account is set to automatically buy $200 worth of shares on or near the 15th of every month."

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Answer:

This equals (2x-9), you cannot simplify it more because it's a variable and number.  They have to both be numbers without variables or both variables to simplify.

Step-by-step explanation:

? This makes no sensibility.....

Answer:  -14

Step-by-step explanation:

I hope this helps

The 8th term of the geometric sequence is -4374.

Given that we need to find the 8th term of the geometric sequence with the first term 2 and common ratio -3.

So,

aₙ = a₁ rⁿ⁻¹

So,

the 8th term of the geometric sequence =

a₈ = 2 (-3)⁸⁻¹

a₈ = 2 × (-3)⁷

a₈ = 2 × (-2187)

a₈ = -4374

Hence, the 8th term of the geometric sequence is -4374.

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Detailed expressions of distributive property are simplified below.

Using the distributive property, simplify each expression as follows:

-2t(-9+9t) = 18t - 18t²

-9n(-8n-7) = 72n + 63n = 63n - 72n = -9n

-3b (6b+6) = -18b - 18

-7r(8+ 3r) = -56r - 21r²

3m(-2+3m) = -6m + 9m²

7w(-8 +3w) = -56w + 21w²

2w(-w-4) = -2w² - 8w

69(-4+8q) = -276 + 552q

-8v (-2-5v) = 16v + 40v²

-8a(7a + 2) = -56a - 16a²

5g(g-1) = 5g² - 5g

y(-9 + 6y) = -9y + 6y²

6b (8+7b) = 48b + 42b²

3r(-4r-8) = -12r² - 24r

3d(-5+8d) = -15d + 24d²

-7r(4-6r) = -28r + 42r²

-8j(7-6j) = -56j + 48j²

-3j (9+9j) = -27j - 27j²

2m(4-4m) = 8m - 8m²

8c(-5c+9) = -40c + 72c²

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The equation of the parabola to the left in factored form is y = (x - 2)(x - 7).

In Mathematics and Geometry, the general form of a quadratic function can be modeled and represented by using the following quadratic equation;

y = ax² + bx + c

Where:

Next, we would solve the quadratic function by using the factors (zeros or roots) provided as follows;

y = (x - 2)(x - 7)

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To find the circumscribed side of a triangle, the steps to follow are:

1. Construct the perpendicular bisector of one of the sides of the triangle.

2. Construct the perpendicular bisector of the second side of the triangle.

3. Identify the point of intersection for the two perpendicular bisectors. This is the circumcenter of the triangle and the center of the circumscribed triangle.

4. Construct a circle that has a radius that is the length from the circumcenter to one of the vertices of the triangle.

A circumscribed triangle is one in which a circle is drawn in the center of the triangle and the circle goes round while touching only three vertices of the triangle.

To draw the circumscribed side of a triangle, you can start by constructing the perpendicular bisector of one of the sides and then the second side. Next, identify the point of intersection, and finally construct the circle.

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Answer:

Large Number = 34 & Smaller Number = 20

Step-by-step explanation:

1. Define Variables

     Large Number = n

     Smaller Number = s

2. Equations

     n + s = 54

     n - s = 14

3. Combine the Equations

     n + s + n - s = 54 + 14

     2n = 68

     n = 34

4. Find s

     34 + s = 54

     s = 20

The volume of a cylinder is thrice the volume of a cone with the same base and height.

The formula for the volume of a cylinder is V = πr²h, where r is the radius of the base and h is the height of the cylinder.

The formula for the volume of a cone is V = (1/3)πr²h, where r is the radius of the base and h is the height of the cone.

If we take a cone with the same base and height as a cylinder, the radius of the cone's base would be equal to the radius of the cylinder's base. Therefore, we can compare the volumes of a cylinder and a cone with the same base and height as follows:

Vcylinder = πr²h

Vcone = (1/3)πr²h

Dividing the volume of the cylinder by the volume of the cone, we get:

Vcylinder / Vcone = (πr²h) / [(1/3)πr²h]

Vcylinder / Vcone = 3

So the volume of a cylinder is three times the volume of a cone with the same base and height.

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Answer:

  £44,384

Step-by-step explanation:

Given the recurrence relation for profit is ...

you want the profit in 2021.

Using the given relations we have ...

  P[2019] = a·P[2018] +800

  29600 = a·24000 +800

  28800 = a·24000

  a = 288/240 = 1.2

Then the profit for the next two years is ...

  P[2020] = 1.2·P[2019] +800 = 1.2·29600 +800 = 36320

  P[2021] = 1.2·36320 +800 = 44384

The profit is predicted to be £44,384 in 2021.

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The expression shows the distance between the points -2.8, 1.6 is |x-y| units

When two numbers are pointed on the number line and they are x and y, then the expression to represent the difference between those two numbers is |x-y|

Let x = -2.8 and y = 1.6

Therefore, the distance between those two points is given by;

|x-y|

= |-2.8-1.6|

= |-4.4|

= 4.4 units.

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The total cost of repainting the 4 walls and floor of the pool would be $2800

Given that;

A swimming pool is in the shape of a right rectangular prism. the pool is 40 feet long,20 feet wide and 4 feet deep the cost of repainting the pool is $2.50 per square foot.

Here, The first step is to calculate the total surface area of the pool, which includes the four walls and the floor.

The area of the floor is simply the length times the width:

Area of floor = 40 ft x 20 ft = 800 square feet

The area of each of the four walls is the height times the width:

Area of each wall = 4 ft x 20 ft = 80 square feet

Since there are four walls, the total area of the walls is:

Total area of walls = 4 x 80 sq ft = 320 square feet

To find the total surface area of the pool, we add the area of the floor to the area of the walls:

Total surface area = Area of floor + Total area of walls

Total surface area = 800 sq ft + 320 sq ft = 1120 square feet

Finally, we can calculate the total cost of repainting the pool by multiplying the total surface area by the cost per square foot:

Total cost = Total surface area x Cost per square foot

Total cost = 1120 sq ft x $2.50/sq ft

Total cost = $2800

Therefore, the total cost of repainting the 4 walls and floor of the pool would be $2800

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Answer: 1/8

Step-by-step explanation:

First make the bottom half the same:

3/4*2/2=6/8

We don’t need to change the first portion since they have a common factor

7/8-6/8=1/8

Equation that represents the total number of miles he runs after weeks is n * (n + 2).

The equation that represents the total number of miles Tripp runs after "n" weeks can be written as:

Total miles = 3 + 5 + 7 + ... + (2n + 1)

We can see that the first week Tripp runs 3 miles, and every week after that, he adds 2 more miles to the previous week's total. So, for the second week, he runs 3 + 2 = 5 miles, and for the third week, he runs 5 + 2 = 7 miles, and so on.

To simplify the equation, we can use the formula for the sum of an arithmetic series:

S = (n/2) * (a + l)

where S is the sum of the series, n is the number of terms in the series, a is the first term, and l is the last term.

In this case, the first term is 3, and the last term is (2n + 1), since Tripp is adding 2 miles each week. So, we have:

Total miles = (n/2) * (3 + 2n + 1)

Simplifying this equation, we get:

Total miles = (n/2) * (2n + 4)

Total miles = n * (n + 2)

Therefore, the equation that represents the total number of miles Tripp runs after "n" weeks is:

Total miles = n * (n + 2)

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The simplification of the cube root of the given expression  ∛ ( 576000 × 4 × 48 ) is equal to 480.

The expression is equal to ,

  ∛ ( 576000 × 4 × 48 )

Write all the factors of the given numbers,

576000 = 576 × 1000

⇒ 576000 = 24 × 24 × 10³

Now,

48 = 24 × 2

And 4 = 2 × 2

Simplify this expression,

Use the fact that the cube root of a product is equal to the product of the cube roots of the factors.

∛ (a × b × c) = ∛a × ∛b × ∛c

Using this property, simplify ∛(576000 × 4 × 48) as follows,

∛(576000 × 4 × 48) = ∛(576000) × ∛(4) × ∛(48)

Rewrite the given expression in the factor form,

∛ ( 576000 × 4 × 48 )

= ∛ 24 × 24 × 10³ × 2 × 2 × 2 × 24

= ∛ 24³ × 10³ × 2³

= ∛(24)³ × ∛(10)³ × ∛(2)³

= 24 × 10 × 2

= 480

Therefore, the simplification of the given expression is equal to 480.

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The above question is incomplete, the complete question is:

Simplify   ∛ ( 576000 × 4 × 48 )

Emily will get a $1,040 annual pension payout from her former employer's pension plan.

Emily is not fully vested in the pension plan because she left her work after four years. She is vested in 20% of the pension plan under the graded 5-year vesting schedule.

We can use the following formula to compute Emily's annual pension:

Annual pension = (final average income) x (service years) x (2% multiplier)

Emily's final average income in this scenario was $65,000, and she worked for 4 years. As a result, her annual pension would be:

Annual pension = ($65,000) multiplied by (4 years) multiplied by 2%

Pension = $5,200 per year

Emily, on the other hand, is only vested in 20% of her pension plan because she quit her work before the entire 5-year vesting term. As a result, her real pension payment will be:

Annual pension = ($65,000) multiplied by (4 years) multiplied by 2%

Pension = $5,200 per year

Emily, on the other hand, is only vested in 20% of her pension plan because she quit her work before the entire 5-year vesting term. As a result, her real pension payment will be:

(vested percentage) x (annual pension) equals pension payment

(20% of $5,200) equals pension payout

$1,040 in pension payments

As a result, Emily will get a $1,040 annual pension payout from her former employer's pension plan.

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The calculated possible value in the unit for M is 2 units

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

The composite figure

The volume of the figure is the sum of the volumes of the individual figures

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

Volume = 3 * 1 * 5 + m * 1 * 4

This gives

Volume = 15 + 4m

Karen calculated the total volume as 23 cubic units.

So, we have

15 + 4m = 23

Evaluate

4m = 8

Divide by 4

m = 2

Hence, a possible value of m is 2

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The solutions to the quadratic equation 3y(-2y+x)-5y(-7x+y) are y = -16x + 32x√2 and y = -16x - 32x√2

To solve the quadratic equation 3y(-2y+x)-5y(-7x+y), we first need to simplify it by distributing the terms inside the parentheses:

3y(-2y+x) = -6y² + 3xy

-5y(-7x+y) = 35xy - 5y²

Next, we can substitute these expressions back into the original equation and simplify it further:

3y(-2y+x)-5y(-7x+y) = (-6y² + 3xy) - (35xy - 5y²) = -6y² + 3xy - 35xy + 5y² = -y² - 32xy

Now, we have simplified the quadratic equation to the standard form of ax² + bx + c = 0, where a = -1, b = -32x, and c = 0. To solve for y, we can use the quadratic formula:

y = (-b ± √(b² - 4ac)) / 2a

Plugging in the values for a, b, and c, we get:

y = (-(-32x) ± √((-32x)² - 4(-1)(0))) / 2(-1) = (32x ± √(1024x²)) / (-2)

Simplifying further, we get:

y = -16x ± 32x√2

In conclusion, we can simplify the given quadratic equation by distributing the terms inside the parentheses, and then rearrange it to the standard form ax² + bx + c = 0. We can then use the quadratic formula to solve for y, and simplify the solutions.

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Answer: the answer is D

Step-by-step explanation:

Remember that the coordinates (3,7π6) tell us the radius r=3 and the angle θ=7π6. So the point should be on the circle labeled 3 and form an angle of 7π6 with the positive x-axis. Point D is the correct point.

Answer: -2

Step-by-step explanation:

You can see it clearly passes through an origin consisting of -2

Answer:

Step-by-step explanation:

A -5        

Answer:

Answer = 30° , 90° , 150°

Step-by-step explanation:

Hope it helps you