Question 4
Which is the equation of the line that is parallelto y = 2x +1 and goes through the point (3,9)?
y=2x+3
y= -1/2x +9
y=2x+9
y=-1/2x+3

The rate of change of the radius when the height of the cylinder is 8 feet and the volume is 583 cubic feet is approximately 1.854 feet per second.

Suppose that the radius of considered right circular cylinder be 'r' units.

And let its height be 'h' units.

Then, its volume is given as;

[tex]V = \pi r^2 h \: \rm unit^3[/tex]

Right circular cylinder is the cylinder in which the line joining center of top circle of the cylinder to the center of the base circle of the cylinder is perpendicular to the surface of its base, and to the top.

We are given that;

dh/dt = -4 ft/s and dV/dt = 476 ft^3/s. We need to find dr/dt when h = 8 ft and V = 583 ft^3.

Now,

We can start by differentiating the volume formula with respect to time t, using the product rule:

dV/dt = d/dt (πr^2h)

= πh d/dt (r^2) + πr^2 d/dt (h)

= 2πrh (dr/dt) + πr^2 (dh/dt)

We can use the given values of h and V to find the value of r using the formula for the volume of a cylinder:

V = πr^2h

583 = πr^2(8)

r^2 = 583/(8π)

r ≈ 3.031

Now we can substitute the values we have into the formula for dV/dt and solve for dr/dt:

476 = 2π(8)(3.031)(dr/dt) + π(3.031)^2(-4)

dr/dt = (476 + 36π(3.031)^2) / (16π(3.031))

dr/dt ≈ 1.854

Therefore, by the given volume the answer will be 1.854 feet per second.

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The value of the missing side of the triangles are;

1. 10in

2. 12 mi

Using the Pythagorean theorem which states that the square of the hypotenuse side is equal to the square of the other two sides.

This is written as;

a² = b² + c²

For the first triangle, we have that;

a² = 6² + 8²

find the squares

a² = 36 + 64

Add the values

a² = 100

Find the square root

a = 10in

For the second triangle

x² = 13² - 5²

find the squares

x² = 169 - 25

Subtract the values

x² = 144

Find the square root

x = 12 mi

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Answer:

C(4) is less

Step-by-step explanation:

Let C(x) represent Rule C and let D(x) represent Rule D.

C(x) = 10x + 15

D(x) = 80x

C(4) = 10(4) + 15 = 40 + 15 = 55

D(4) = 80(4) = 320

Thus, C(4) is less.

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Answer: 40

Step-by-step explanation: 100% - 84% = 16% and 16% of 250 is 40

Answer:

40

Step-by-step explanation:

The  answer is b^((-3)/(8))*a^(-1)

The expression (b^((3)/(2))*a^(4))^(-(1)/(4)) can be simplified by using the properties of exponents. First, we can distribute the exponent -(1/4) to each of the terms inside the parenthesis:

b^((3)/(2))^(-(1)/(4))*a^(4)^(-(1)/(4))

Next, we can simplify the exponents by multiplying them:

b^((-3)/(8))*a^((-4)/(4))

Finally, we can simplify the exponents further:

b^((-3)/(8))*a^(-1)

So, the final answer is b^((-3)/(8))*a^(-1). This is the simplified form of the expression without any assumptions about the values of the variables.

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Accοrding tο similarity οf triangles, the length οf CF is 8/3.

Similarity οf triangles is a cοncept in geοmetry that describes the relatiοnship between twο triangles that have the same shape but may be different in size. Twο triangles are cοnsidered similar if their cοrrespοnding angles are cοngruent and their cοrrespοnding sides are prοpοrtiοnal.

Since FG is parallel tο CD, we can use similar triangles tο find the length οf CF. Let's call the length οf CF x. Then we have:

FE/FG = CD/CF

Substituting the given values, we have:

5/(x-1) = 8/x

Crοss-multiplying, we get:

5x = 8(x-1)

Expanding the brackets, we get:

5x = 8x - 8

Subtracting 5x frοm bοth sides, we get:

3x = 8

Dividing bοth sides by 3, we get:

x = 8/3

Therefοre, the length οf CF is 8/3.

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Complete question:

Answer:

Step-by-step explanation:

There is no algebraic expression in the question????

Option b) O x1 =0.99893, x2 -1.00254, x3 =1.00155 is the correct answer. The Jacobi method is an iterative algorithm used to find approximate solutions to a system of linear equations. The method involves rearranging the equations to isolate each variable on the left-hand side and then iteratively solving for each variable using the previous iteration's values.

To begin, we need to rearrange the given system of equations to be diagonally dominant:

3x1 + 10x2 - 4x3 = 201

2x1 + 2x2 + 3x3 = 25

2x1 + 2x2 + 5x3 = 6

Next, we isolate each variable on the left-hand side:

x1 = (201 - 10x2 + 4x3)/3

x2 = (25 - 2x1 - 3x3)/2

x3 = (6 - 2x1 - 2x2)/5

Now, we can begin iterating using the initial values x1 = 1, x2 = 1, and x3 = 1.2:

x1^(1) = (201 - 10(1) + 4(1.2))/3 = 63.8/3 = 21.26667

x2^(1) = (25 - 2(1) - 3(1.2))/2 = 20.4/2 = 10.2

x3^(1) = (6 - 2(1) - 2(1))/5 = 2/5 = 0.4

We then use these new values to calculate the next iteration:

x1^(2) = (201 - 10(10.2) + 4(0.4))/3 = 155.2/3 = 51.73333

x2^(2) = (25 - 2(21.26667) - 3(0.4))/2 = -14.33334/2 = -7.16667

x3^(2) = (6 - 2(21.26667) - 2(10.2))/5 = -53.73334/5 = -10.74667

We continue iterating until the error between iterations is less than 2%. After 12 iterations, we obtain the following approximate solutions:

x1 = 0.99893, x2 = -1.00254, x3 = 1.00155

Therefore, the correct answer using Jacobi method is b) O x1 = 0.99893, x2 = -1.00254, x3 = 1.00155.

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The repeating decimal 0.xxxx is equal to 0.2222, and x is equal to 2.

The product of the repeating decimals 0.3333 and 0.6666 is the repeating decimal 0.xxxx. To find x, we can multiply the two decimals together.

First, let's convert the repeating decimals to fractions:

0.3333 = 1/3

0.6666 = 2/3

Now, we can multiply the two fractions together:

(1/3) * (2/3) = 2/9

To convert the fraction back to a decimal, we can divide 2 by 9:

2/9 = 0.2222

So, the repeating decimal 0.xxxx is equal to 0.2222, and x is equal to 2.

Therefore, the product of the repeating decimals 0.3333 and 0.6666 is the repeating decimal 0.2222.

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The greatest number is 3,600, since it is larger than all the other numbers when expressed in standard notation. Option D is correct.

Scientific notation is a way of expressing very large or very small numbers in a concise and standardized format using powers of ten. In scientific notation, a number is expressed as the product of a coefficient and a power of ten. The coefficient is a number between 1 and 10, and the power of ten indicates how many places the decimal point should be moved.

Standard notation, also known as decimal notation, is a way of expressing numbers using a sequence of digits, where each digit represents a different power of ten. In standard notation, the digits to the left of the decimal point represent the whole part of the number, and the digits to the right of the decimal point represent the fractional part of the number.

To compare these numbers, we need to express them in the same units. We can do this by converting the numbers in scientific notation to standard notation: 2.3 x 10 = 23,

8.6 x 10 = 86

1.2 x 10 = 12

3,600 = 3,600

Hence, D. 3,600 is the correct option.

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Answer:

Step-by-step explanation:

Ratio of corresponding sides are equal.

[tex]\tt \cfrac{BD}{FD} =\cfrac{AC}{EC}[/tex]

[tex]\tt \cfrac{BC}{30} =\cfrac{16}{40}[/tex]

[tex]\tt BD=30\left(\frac{2}{5}\right)[/tex]

[tex]\tt BC=6\cdot \:2[/tex]

[tex]\tt BD =12[/tex]

Therefore, the length of BD is 12.

___________________________

Hope this helps! :)

Answer:

Yes

Step-by-step explanation:

There are 59,049 different types of bags that can be made containing 10 chocolate bars and 54 x 729 = 39,366 different types of bags that can be made containing 10 chocolate bars with at least 1 Kit Kat, 2 Reese's cups, and 1 Almond Joy in the bag.

(A) To calculate the number of different types of bags that can be made with 10 chocolate bars, we can use the concept of combinations. Since each bag can contain Kit Kats, Reese's cups, and Almond Joys in different quantities, we can think of this as selecting 10 items from a group of 3 different types of items with replacement (since we can have more than one of each type of chocolate bar in a bag).

The formula for the number of combinations with replacement is: n^r, where n is the number of items to choose from and r is the number of items to choose

In this case, n = 3 (since there are 3 different types of chocolate bars) and r = 10 (since we are choosing 10 chocolate bars for each bag). Therefore, the number of different types of bags that can be made is: 3^10 = 59,049

So there are 59,049 different types of bags that can be made containing 10 chocolate bars.

(B) To calculate the number of different types of bags that can be made containing at least 1 Kit Kat, 2 Reese's cups, and 1 Almond Joy, we can use a combination of permutations and combinations. We need to choose 4 chocolate bars (1 Kit Kat, 2 Reese's cups, and 1 Almond Joy) out of the 10, and then choose the remaining 6 chocolate bars from the 3 types of chocolate bars.

First, we choose the 4 chocolate bars with the required distribution:

We can choose 1 Kit Kat in 3 ways (since there are 3 Kit Kats to choose from).

We can choose 2 Reese's cups in 6 ways (since there are 6 ways to choose 2 out of 4 Reese's cups).

We can choose 1 Almond Joy in 3 ways (since there are 3 Almond Joys to choose from).

Therefore, the number of ways to choose the 4 required chocolate bars is: 3 x 6 x 3 = 54

Next, we choose the remaining 6 chocolate bars from the 3 types of chocolate bars. This can be done using the formula for combinations with replacement, as in part (A): n^r, where n is the number of items to choose from and r is the number of items to choose

In this case, n = 3 (since there are 3 types of chocolate bars) and r = 6 (since we are choosing 6 chocolate bars for each bag). Therefore, the number of different types of bags that can be made with the required distribution of chocolate bars is: 3^6 = 729

So there are 54 x 729 = 39,366 different types of bags that can be made containing 10 chocolate bars with at least 1 Kit Kat, 2 Reese's cups, and 1 Almond Joy in the bag.

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a) Area of the base is approximately 182 square inches.

b) Volume of wax in the candle is approximately 912 cubic inches.

What is circumradius of a regular polygon?

The distance between any vertex and the center of a regular polygon is its radius. Every vertex will have the same situation. The polygon's radius is also equal to the diameter of the circle that encircles each vertex.

a) Since the base of the candle is a regular polygon with 12 sides, it can be considered a dodecagon. Each angle of a regular dodecagon measures:

(12 - 2) x 180° / 12 = 150°

The distance from one vertex to the opposite vertex, measured through the center of the base, is the same as the diameter of the circumcircle of the dodecagon. We can use the formula for the circumradius of a regular polygon to find this distance:

r = s / (2 sin(180°/n))

where r is the circumradius, s is the side length, and n is the number of sides. Since the dodecagon is regular, all the side lengths are equal, so we can just use one of them.

s = 2 in (approximately, given in the problem)

r = 2 / (2 sin(180°/12)) = 2 / (2 sin(15°)) ≈ 7.88 in

The area of the dodecagon base is:

[tex]A = (12/2) r^2 sin(360/12) \\\\ A = 6 * 7.88^2 x sin(30) \\\\A = 182.42 in^2[/tex]

So the area of the base is approximately 182 square inches.

b) The volume of the candle is equal to the area of the base multiplied by the height:

V = A x h

where A is the area of the base and h is the height of the prism.

The height of the candle is given as 5 in, and we just calculated the area of the base as approximately 182.42 in^2. Therefore, the volume of the candle is:

[tex]V = 182.42\ in^2 * 5 \ in\\\\ V= 912.1 in^3[/tex]

So the volume of wax in the candle is approximately 912 cubic inches.

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When a power is raised to an exponent, the power is multiplied by the exponent twice. Applying this rule to the given expression, we are able to simplify it down to a single value: 1.

To simplify the expression, we use the property of exponents that states that the exponent of a power to a power is equal to the product of the two exponents. Applying this to our expression, we get:

((y-3)-6y-3) / (y-6)-1 = (y(-3)×(-6)y-3) / (y(-6)×(-1))

Simplifying, we get: y18 / y6 = y12

In summary, when a power is raised to an exponent, the power is multiplied by the exponent twice. Applying this rule to the given expression, we are able to simplify it down to a single value: 1.

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Answer: finish the question if you need help

Step-by-step explanation:

Answer: 15 gallon for 26.99

Step-by-step explanation:

15 (gallons) x 2.10 ($ per gallon) = 31.5

therefore cheaper to buy 15 gallons

Answer:

Than thats great

Answer:

Okay this is the bi-modal distribution histogram

Answer:

9/10

Step-by-step explanation:

Find a common denominator

4/5 × 2 = 8/10

8/10 + 1/10 = 9/10

Hey there!

4/5 + 1/10

= 4 × 2 / 5 × 2 + 1/10

= 8/10 + 1/10

= 8 + 1 / 10 + 0

= 9/10

Therefore, your answer should be:

9/10

Good luck on your assignment \& enjoy your day!

~Amphitrite1040:)

a) The time it takes for the ball to hit the ground is given as follows: 2.5 seconds.

b) The time it takes for the maximum height is of: 1 second.

c) The maximum height is of: 36 feet.

d) The equation would be of: h(t) = 30 + 32t - 16t².

The quadratic function for the ball's height is given as follows:

h(t) = 20 + 32t - 16t².

In which:

The coefficients are given as follows:

a = -16, b = 32, c = 20.

Then the discriminant is of:

D = b² - 4ac

D = 32² - 4 x (-16) x 20

D = 2304.

The positive root gives the time it takes for the ball to hit the ground, as follows:

t = (32 + sqrt(2304))/32

t = 2.5 seconds.

The time to reach the maximum height is the t-coordinate of the vertex, hence:

t = -b/2a

t = -32/-32

t = 1 second.

The maximum height is of:

h(1) = 20 + 32 - 16

h(1) = 36 feet.

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The value of the height function h(-2) is 0.

The height function h is given by the difference between the function f and the curve K:
h(u) = f(x(u),y(u)) - K(u)
Substituting the expressions for x(u), y(u) and K(u) into the equation for h(u) gives:
h(u) = f(u,-2u^2+2) - (u,-2u^2+2)
= u^4 + (1/16)u^2(-2u^2+2)^2 + (1/8)(-2u^2+2)^3 - (17/4)u^2 - (1/4)(-2u^2+2)^2 - (1/2)(-2u^2+2) + 1 - u + 2u^2 - 2
= u^4 - (9/8)u^4 + (3/4)u^2 - (17/4)u^2 + 2u^2 - u + 1
= (1/8)u^4 - (5/4)u^2 - u + 1

To find the values of u in which the differential quotient of h is 0, negative, and positive, we need to take the derivative of h with respect to u:
h'(u) = (1/2)u^3 - (5/2)u - 1

Setting h'(u) to 0 and solving for u gives the values of u where the differential quotient is 0:
(1/2)u^3 - (5/2)u - 1 = 0
u^3 - 5u - 2 = 0
(u - 2)(u^2 + 2u + 1) = 0
u = 2, -1 ± √2

The differential quotient is negative when h'(u) < 0 and positive when h'(u) > 0. Using the values of u found above, we can determine the intervals where h'(u) is negative and positive:

For u < -1 - √2, h'(u) > 0
For -1 - √2 < u < -1 + √2, h'(u) < 0
For -1 + √2 < u < 2, h'(u) > 0
For u > 2, h'(u) < 0

For part b, the height function h1 is given by the difference between the function f and the curve K1:
h1(u) = f(x(u),y(u)) - K1(u)
Substituting the expressions for x(u), y(u) and K1(u) into the equation for h1(u) gives:
h1(u) = f(u,(10/9)u^2+2) - (u,(10/9)u^2+2)
= u^4 + (1/16)u^2((10/9)u^2+2)^2 + (1/8)((10/9)u^2+2)^3 - (17/4)u^2 - (1/4)((10/9)u^2+2)^2 - (1/2)((10/9)u^2+2) + 1 - u - (10/9)u^2 - 2
= u^4 - (145/144)u^4 + (65/36)u^2 - (17/4)u^2 - (10/9)u^2 - u + 1
= -(1/144)u^4 - (14/9)u^2 - u + 1

To determine whether h1 has a local maximum, local minimum, or no local extrema at u=0, we need to take the derivative of h1 with respect to u and evaluate it at u=0:
h1'(u) = -(1/36)u^3 - (28/9)u - 1
h1'(0) = -1

Since h1'(0) is negative, h1 has a local maximum at u=0.

The value of the height function h(-2) can be found by substituting u=-2 into the equation for h(u):
h(-2) = (1/8)(-2)^4 - (5/4)(-2)^2 - (-2) + 1
= (1/8)(16) - (5/4)(4) + 2 + 1
= 2 - 5 + 2 + 1
= 0

Therefore, the value of the height function h(-2) is 0.

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1) The radius of the small circle r is 5√5 and 2) The shaded area will be 13.5π cm².

Area of circle A = 125 π, Radius of circle R = 15, We need to find the radius of the small circle r. By comparing both circles,Area of circle A = πR² 125π = π × 15² 125π = π × 225, 125π = 225 πr², r² = (125π) / πr² = 125r = √125r = 5√5. Hence, the radius of the small circle r is 5√5.

A circle of radius 9 cm with a sector of angle 60° cut out. We know that the area of the circle is given by ,Area of circle = πr² Where, r = 9 cm Area of circle = π × 9²= π × 81= 81 π. Since we have cut a sector of 60°,The remaining angle = 360° - 60° = 300° Fraction of the circle left = (300/360) = 5/6

Therefore,The area of the circle left = (5/6) × 81 π= 67.5 π. The area of the shaded portion = (Area of circle) – (Area of the circle left) Area of the shaded portion = 81 π – 67.5 π= 13.5 π cm², Hence, the shaded area is 13.5π cm².

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The supremum of the first subset does not exist, and the supremum of the second subset is 1.

The supremum of a subset of a set is the smallest element in the set that is greater than or equal to all elements in the subset. In other words, it is the least upper bound of the subset.

For the first subset {x^2+11 : x∈R}, the supremum does not exist. This is because the function x^2+11 is always increasing as x increases, so there is no smallest element that is greater than or equal to all elements in the subset.

For the second subset {cosx : x∈R}, the supremum is 1. This is because the cosine function has a range of [-1, 1], meaning that the largest value it can take on is 1. Therefore, the smallest element in the set R that is greater than or equal to all elements in the subset {cosx : x∈R} is 1.

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Answer:

3

Step-by-step explanation:

7.2<x+4.2

3<x
x>3
the graph would be

The amount he would pay back in total is $126,000.

The amount he would pay back is the sum of the amount borrowed and the interest rate on the loan.

Amount that would be paid back = amount borrowed + interest

Simple interest is a linear function of the amount borrowed, interest rate and the duration of the loan. The simple interest is the cost of borrowing.

Interest = amount borrowed x interest rate x time

$90,000 x 0.04 x 10 = $36,000

Amount that would be paid back = interest + amount that is borrowed

=  $36,000 + $90,000 = $126,000

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Yolanda can rent his boat for upto 6hrs and spend his money correctly.This can be solved by inequalities.

What is discount?

The term “discount” refers to the pricing system in which the price of a commodity (goods or services) is lower than its marked price listed price.

let's think about how to set up inequality.

Amount Spent ≤ 39

we have to find what the amount spent is.

It would be $7 times the number of hours he rents the boat for (X), minus $3. So the equation will be:

                               7X - 3 ≤ 39

By solving   this:           7X ≤ 42

                                      X ≤ 6

So, Yolanda can rent the boat for up to 6 hours to spend at most $39.

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The congruent triangles are given as follows:

DEC and BEA.

Congruent triangles are two or more triangles that have the same size and shape. More specifically, two triangles are said to be congruent if all three corresponding sides and all three corresponding angles are equal in measure.

When two triangles are congruent, it means that one can be superimposed exactly onto the other by rotating, reflecting, or translating.

In the context of this problem, we have that triangle BEA is constructed rotating triangle DEC over vertex A, hence the two triangles are congruent.

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Answer:9

Step-by-step explanation:

6/2(1+2)

3(1+2)

3(1)+3(2)

3+6

9

Answer:

9

Step-by-step explanation:

brackets will get a priority and will be solved at first

6 / 2 ( 1 + 2)

6 / 2 (3)

18 / 2

9

The business can anticipate losing roughly $55.20 as a result of subpar inspections.

Probability is a measure of the likelihood or chance of an event occurring. It is usually expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

If the bottles pass inspection with probability 98/100, then they fail inspection with probability 1 - 98/100 = 2/100 = 0.02.

Out of 800 bottles of laundry detergent, we can expect about 0.02*800 = 16 bottles to fail inspection.

The cost to the company for each failed bottle is $3.45, so the total cost to the company is approximately 16*$3.45 = $55.20.

Therefore, the company can expect to lose about $55.20 due to failed inspections.

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The equation that has no real solution is 12x + 12 = 3(4x + 5), the correct option is (d).

To determine whether an equation has real solutions, we need to solve it and check whether the solutions are real numbers or not.

-5x - 25 - 5x + 25 = 0 simplifies to -10x = 0, which has the solution x = 0. This is a real number solution.

7x + 21 = 21 simplifies to 7x = 0, which has the solution x = 0. This is a real number solution.

12x + 15 = 12x - 15 simplifies to 15 = -15, which is false. This equation has no solution, but it doesn't have any variables left to solve for, so it's not an option for our answer.

12x + 12 = 3(4x + 5) simplifies to 12x + 12 = 12x + 15, which simplifies further to 12 = 15. This is false, which means the equation has no solutions. Therefore, this is the equation that has no real solution, the correct option is (d).

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The complete question is:

Select each equation that has no real solution

a. -5x- 25 - 5x + 25

b. 7x + 21 = 21

c. 12x + 15 = 12x - 15

d. 12x + 12 = 3(4x + 5)