how to calculate cube root without using prime factorization? and how to calculate ³√60? or something else that has a decimal result?​

Answer:

A

Step-by-step explanation:

V = pie x r*2 x h

Explanation:

We have to multiply -4 by itself 3 times: (-4)³ = (-4)x(-4)x(-4)

The first time we'll have a positive number, because the product of two negative numbers is a positive number:

Now we just have to solve 16x(-4). The result will be a negative number, because the product between a positive and a negative number is negative:

Answer:

(-4)³ = -64

The correct simplified expression is \(\rm 28x^3-33x^2-33x+18\).

Given

Polynomial; \(\rm (7x - 3)(4x^2 -3x - 6)\)

Multiplication is the process of calculating the product of two or more numbers. The multiplication of numbers say, ‘a’ and ‘b’, is stated as ‘a’ multiplied by ‘b’.

Then,

The correct simplification of the expression is;

\(\rm \rm (7x - 3)\times (4x^2 -3x - 6)\\\\7x(4x^2 -3x - 6)-3(4x^2 -3x - 6)\\\\ 28x^3-21x^2-42x-12x^2+9x+18\\\\28x^3-33x^2-33x+18\)

Hence, the correct simplified expression is \(\rm 28x^3-33x^2-33x+18\).

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Answer:

r = 11 units

Step-by-step explanation:

Given that,

The measure of Arc CD is 11x

The arc is making an angle of 180°.

We know that,

Length of the arc, \(l=r\theta\)

Where

r is the radius of the circle

So,

\(r=\dfrac{l}{\theta}\\\\r=\dfrac{ 11\pi}{\pi}\\\\r=11\)

So, the radius of the circle is equal to 11 units.

Answer:

l = (3x+5)

Step-by-step explanation:

Given that,

The area of a room, \(A=3x^2-x-10\)

The width of the room, \(b=(x-2)\)

We need to find the length of the room.

The area of the room is given by :

A = lb

\(l=\dfrac{A}{b}\\\\l=\dfrac{3x^2-x-10}{x-2}\\\\l=\dfrac{(x-2)(3x+5)}{x-2}\\\\l=(3x+5)\)

So, the length of the room is equal to (3x+5).

There are 216 possible outcomes when rolling a die 3 times in a row. Each outcome represents a unique combination of numbers obtained from the three rolls.

When rolling a die 3 times in a row, we need to consider the number of possible outcomes for each roll and then multiply them together to find the total number of outcomes.

Since a standard die has 6 faces numbered 1 to 6, there are 6 possible outcomes for each roll. For the first roll, we have 6 choices, and for each choice of the first roll, we have 6 choices for the second roll, and similarly, 6 choices for the third roll.

To calculate the total number of outcomes, we multiply the number of choices for each roll:

Number of outcomes = 6 × 6 × 6 = 6^3 = 216.

Therefore, there are 216 possible outcomes when rolling a die 3 times in a row. Each outcome represents a unique combination of numbers obtained from the three rolls.

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Answer:

\(5.616\)

Step-by-step explanation:

Question :

\(1.56 \times 3.6\)

Simply solve this without considering the decimals

\(156 \\ \times 36 \\............ \\ \: \: \: \: \: \: \: 936 \\ + 4680 \\ ............ \\ = 5616\)

And now consider about the decimals

There are 3 decimal places

1.56 * 3.6

Now you can write answer like this,

\(5.616\)

Hope this helps you

Let me know if you have any other questions :-):-)

Answer:

5.616.

Step-by-step explanation:

First multiply 156 by 36

  156

 x 36    

      936      ( result from multiplying 156 by 6)      

+  4680      ( result from multiplying 156 by 30)      

    5616       ( after adding the last 2 numbers).

Now there are 3 numbers after the decimal point in 1.56 and 3.6 so we count 3 places back in 5616:

- to get 5.616.

Answer: 0.045%

Step-by-step explanation:

Answer:

1. n=-6

2. x=-17

Step-by-step explanation:

Darin drives (B) 2m - 20 miles.

To find how much Darin drives:

Given:

Therefore, Darin drives (B) 2m - 20 miles.

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Answer:

Step-by-step explanation:

6x+4y=-12

subtract 6x from both sides in order to move 6x to the other side.

4y=-12-6x

divide 4 from the whole equation in order to make the 4y to y.

y= -3-6/4x

and to simply

y= -1.5x-3

or y= -3/2x-3

Answer:

(-7,17)

Step-by-step explanation:

(4,-8) turns into (-4,8)

go left by 3 (-7,8)

go up by 9 (-7,17)

(a) The time (in h) will the plane take to reach the city is 7.09 hours or 7.1 hours.

(b) The plane flies through a constant tailwind blowing at 53.5 km/h, the time (in h) will it take to reach the city is 3.58 hours or 3.6 hours.

(c) The plane flies through a constant crosswind blowing east at 53.5 km/h, the time (in h) will it take to reach the city is infinite.

(a) To find the time it will take for the plane to reach the city with a headwind, we need to first find the plane's ground speed. The ground speed is the speed of the plane relative to the ground. We can find the ground speed by subtracting the speed of the headwind from the plane's airspeed.

Ground speed = Airspeed - Headwind speed

Ground speed = 163 km/h - 53.5 km/h

Ground speed = 109.5 km/h

Now that we know the ground speed, we can use the formula:

Time = Distance ÷ Speed

Time = 776 km ÷ 109.5 km/h

Time = 7.09 hours or 7.1 hours

(b) To find the time it will take for the plane to reach the city with a tailwind, we need to first find the plane's ground speed. The ground speed is the speed of the plane relative to the ground. We can find the ground speed by adding the speed of the tailwind to the plane's airspeed.

Ground speed = Airspeed + Tailwind speed

Ground speed = 163 km/h + 53.5 km/h

Ground speed = 216.5 km/h

Now that we know the ground speed, we can use the formula:

Time = Distance ÷ Speed

Time = 776 km ÷ 216.5 km/h

Time = 3.58 hours or 3.6 hours

(c) To find the time it will take for the plane to reach the city with a crosswind, we need to first find the component of the crosswind that is perpendicular to the plane's direction of travel. This component will not affect how long it takes for the plane to reach its destination.

Component of crosswind = Crosswind speed × sin(angle between direction of travel and crosswind)

Component of crosswind = 53.5 km/h × sin(90°)

Component of crosswind = 53.5 km/h

Now we can find the ground speed of the plane relative to its direction of travel:

Ground speed = Airspeed × cos(angle between direction of travel and crosswind)

Ground speed = 163 km/h × cos(90°)

Ground speed = 0 km/h

Since the ground speed is 0 km/h, the plane will not make any progress towards its destination. Therefore, it will take an infinite amount of time to reach the city with a crosswind.

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Answer:

1/2 is greater than -1 1/2.

Step-by-step explanation:

Answer:

Step-by-step explanation:

If a kilogram of sweet potatoes costs 25 cents more than a kilogram of tomatoes and 3 kilograms of sweet potatoes cost 12.45 you need to divide 12.45 by 3 to get the cost of 1 kilogram of sweet potatoes.

12.45/3=4.15

We then subtract 25 cents from 4.15 to get the cost of one kilogram of tomatoes because a kilogram of sweet potatoes costs 25 cents more.

4.15-.25=3.9

A kilogram of tomatoes costs 3.90$.

Answer:

your mom + your mom = big mama there you go your welcome

Step-by-step explanation:

your mom + your mom = big  mama there you go your welcome

Answer:

x ≥ 397

Step-by-step explanation:

x represents the rainfall in inches. The question seems incomplete, but this is what i got from the info you provided

Yes, the forester was justified in using a Normal model to analyze the woods, because the histogram is unimodal and symmetric. So option A is correct.

A histogram is a type of graph that uses vertical bars to show the distribution of a set of data. This particular histogram is unimodal, meaning that it has one peak which is an indication that the data is distributed normally. Additionally, the histogram is symmetric, which is another indication that the data is normally distributed.
Using a Normal model to analyze the woods is a valid approach because it allows the forester to identify the average diameter of the trees, as well as the spread of the data. It also allows him to check for any outliers, or points that fall outside the normal range. With this information, the forester can determine if the woods is suitable for sale, or if the buyer should be aware of any unexpected features.
Overall, the histogram is an effective way for the forester to analyze the data and determine if a Normal model is appropriate. By noting the unimodal and symmetric nature of the histogram, the forester can be sure that a Normal model will accurately represent the data, allowing him to make an informed decision about the woods.

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Answer:

The perimeter of Elie's vegetable garden is 34 meters.

Step-by-step explanation:

The formula for area is: a=w*l.

A = area

W = width

L = length

If the length is 9 meters, then we know two of the values, the area, and the length. Substitute.

72=w*9

You can divide both sides by 9 to get the width, which is 8 meters.

To find perimeter, we add l+w+l+w, or 2l+2w. Substitute for our values:

2(9)+2(8)=34

The perimeter of Elie's vegetable garden is 34 meters.

Answer:

B.

Step-by-step explanation:

Answer:

it say 5 points scam

Step-by-step explanation:

In the proportion , Nina ran \(51\frac{1}{5}\) laps in 1 hour.

What is proportion?

A percentage is created when two ratios are equal to one another. We write proportions to construct equivalent ratios and to resolve unclear values. a comparison of two integers and their proportions. According to the law of proportion, two sets of given numbers are said to be directly proportional to one another if they grow or shrink in the same ratio.

Here in 1/4 hour Nina ran = 12 4/5 = 64/5 laps.

Then in 1 hour Nina ran = x laps.

Now using proportion then,

=> 1/4 hour = 64/5

    1  hour   = x

=> x = \(\frac{\frac{64}{5}\times1}{\frac{1}{4}}\)

=> x = \(\frac{64}{5}\times4\)

=> x = 256/5 = 51 1/5 laps.

Hence Nina ran \(51\frac{1}{5}\) laps in 1 hour.

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In the proportion , Nina ran  \(51\frac{1}{5}\) laps in 1 hour.

What is proportion?

A percentage is created when two ratios are equal to one another. We write proportions to construct equivalent ratios and to resolve unclear values. a comparison of two integers and their proportions. According to the law of proportion, two sets of given numbers are said to be directly proportional to one another if they grow or shrink in the same ratio.

Here in 1/4 hour Nina ran = 12 4/5 = 64/5 laps.

Then in 1 hour Nina ran = x laps.

Now using proportion then,

=> 1/4 hour = 64/5

   1  hour   = x

=> x = \(\frac{\frac{64}{5}*1}{\frac{1}{4}}\)

=> x = \(\frac{64}{5} * 4\)

=> x = 256/5 = 51 1/5 laps.

Hence Nina ran  \(51\frac{1}{5}\) laps in 1 hour.

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bottem left and maybe top right.

if it means a single 90 degree rotation then its only bottem left but it doesn't specify so it could also be a single 180 degree rotation for top right

The Jacobian matrix represents the partial derivatives of one set of variables with respect to another set of variables. In this case, we need to find the Jacobian matrix for the transformation from (x, y, z) to (s, t, u) using the given equations:

The jacobian matrix J is given by:

J = ∂(x, y, z) / ∂(s, t, u)

To find the elements of the Jacobian matrix, we calculate the partial derivatives of each component of (x, y, z) with respect to (s, t, u).

∂x/∂s = -\(4s^3tu\)

∂x/∂t = -\(5s^4u\)

∂x/∂u = -\(s^4t\)

∂y/∂s = \(6s^2tu\)

∂y/∂t =\(4st^2u\)

∂y/∂u = 2stu

∂z/∂s = -3u

∂z/∂t = 1

∂z/∂u = -3s

Therefore, the Jacobian matrix J is:

J = \([-4s^3tu, -5s^4u, -s^4t]\)

\([6s^2tu, 4st^2u, 2stu]\)

[-3u, 1, -3s]

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We are given the following parametric equations:

x = 7 cos(t) − cos(7t)

y = 7 sin(t) − sin(7t)

We need to find the length of the curve defined by these equations, for 0 ≤ t ≤ π. We can use the arc length formula:

L = ∫[a,b] sqrt[dx/dt]^2 + [dy/dt]^2 dt

Here, a = 0 and b = π, so we have:

L = ∫[0,π] sqrt[(-7sin(t) + 7sin(7t))^2 + (7cos(t) - 7cos(7t))^2] dt

= ∫[0,π] sqrt[49sin^2(t) - 98sin(t)sin(7t) + 49sin^2(7t) + 49cos^2(t) - 98cos(t)cos(7t) + 49cos^2(7t)] dt

= ∫[0,π] sqrt[98 - 98sin(t)sin(7t) - 98cos(t)cos(7t)] dt

= ∫[0,π] sqrt[98 - 98cos(7t - t)] dt    (using the identity sin(a-b) = sin(a)cos(b) - cos(a)sin(b))

= ∫[0,π] sqrt[98 - 98cos(6t)] dt

Now we can use a trigonometric identity to simplify the integral further:

cos(6t) = 1 - 2sin^2(3t)

Substituting this, we have:

L = ∫[0,π] sqrt[98 - 98(1 - 2sin^2(3t))] dt

= ∫[0,π] sqrt[196sin^2(3t)] dt

= ∫[0,π] 14|sin(3t)| dt

= 28∫[0,π/6] sin(3t) dt

= 28[-cos(3t)/3] [0,π/6]

= 28/3 (1 - cos(π/2))

= 28/3

Therefore, the exact length of the curve is 28/3.

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Answer:

y = 2/3x - 5

Step-by-step explanation:

y = 2/3x + b

-1 = 2/3(6) + b

-1 = 4 + b

-5 = b

The cost of five and three-fourths pounds of beef is $28.69.

Given that;

Mrs. Figueroa made a spaghetti dinner for the cheerleaders after practice.

Here we have;

She purchased five and three-fourths pounds of beef for $4.99 per pound.

That is,

The cost of 1 pound of beef = $4.99

Hence, the cost of five and three-fourths pounds of beef is,

\(5 \dfrac{3}{4} \times 4.99\)

\(\dfrac{23}{4} \times 4.99\)

\(= 28.69\)

Therefore, the cost of five and three-fourths pounds of beef is $28.69.

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Answer:

f(x) = -3(2^x)

g(x) = -3 + 2x

h(x) = 2(3^x)

j(x) = -3 – 2x

So,

f(2) = -3(2^2)

f(2) = -3(4)

f(2) = -12

g(-2) = -3 + 2(-2)

g(-2) = -3 -4

g(-2) = -7

h(2) = 2(3^2)

h(2) = 2(9)

h(2) = 18

j(-2) = -3 – 2(-2)

j(-2) = -3 –4

j(-2) = -7

Answer: -3/4; -2/3; 0; 0.7

Answer:

Step-by-step explanation:

Triangle ABC is an equilateral triangle, then:

=> angle ABC = angle BAC = angle  ACB = 60 deg

AB // CE, according to alternative interior pair of angles theorem:

=> angle ACE = angle BAC = angle ABC = 60 deg   (1)

B, C, and D are colinear, then:

angle ECD + angle ACE + angle ACB = 180 deg

=> angle ECD = 180 - angle ACE - angle ACB = 180 - 60 - 60 = 60 deg   (2)

From (1) and (2):

=>angle ACE = angle ECD = 60 deg