Simplify \sqrt[3]{576000 \cdot 4 \cdot 48}

Answer:

To find out how much interest Jenny earns in one year, we can use the formula:

interest = principal x rate x time

where:

the principal is the amount of money in the savings account

rate is the interest rate per year, expressed as a decimal

time is the length of time the money is in the account, in years

In this case, Jenny's principal is $1200, the rate is 3% or 0.03 as a decimal, and the time is 1 year. Plugging these values into the formula, we get:

interest = 1200 x 0.03 x 1

interest = $36

Therefore, Jenny earns $36 in interest in one year.

The coordinate of the resulting point C' after 270-degree rotation clockwise is (-2, -3).

Given that:

Point, C(-3, 2)

Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.

The coordinate of the resulting point C' after 270-degree rotation clockwise is given as,

C' = (-y, x)

C' = (-2, -3)

The coordinate of the resulting point C' after 270-degree rotation clockwise is (-2, -3).

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222 gallons of milk containing 7% butterfat and 111 gallons of milk containing 4% butterfat must be used to obtain 333 gallons of milk containing 6% butterfat.

Let's assume that x gallons of milk containing 7% butterfat are needed, and y gallons of milk containing 4% butterfat are needed to obtain 333 gallons of milk containing 6% butterfat.

We can set up two equations to represent the given information:

Equation 1: x + y = 333

Equation 2: 0.07x + 0.04y = 0.06(333)

Simplifying Equation 2, we get:

0.07x + 0.04y = 19.98

Multiplying both sides of Equation 1 by 0.04, we get:

0.04x + 0.04y = 13.32

Subtracting this equation from Equation 2, we get:

0.03x = 6.66

Dividing both sides by 0.03, we get:

x = 222

Substituting x = 222 into Equation 1, we get:

222 + y = 333

y = 111

Therefore, 222 gallons of milk containing 7% butterfat and 111 gallons of milk containing 4% butterfat must be used to obtain 333 gallons of milk containing 6% butterfat.

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Answer: h(-8) = 21

Step-by-step explanation:

Answer: 21

Step-by-step explanation:

You equation is h(y)  but you need to find h(-8) which means substitute y for -8 into equation

h(-8)= 4|(-8)+2| -3             do what's inside absolute value first

=4|-6| -3                           for absolute value, take positive of number

=4(6)-3                             multiply

=24-3                               subtract

=21

The distribution is roughly symmetric, we can use the mean as a measure of center and the standard deviation as a measure of spread.

The distribution of miles ran each week by Elisa is relatively symmetric and centered around 30 miles per week, with a relatively tight spread of about 2.3 miles per week.

We have,

a.

Since the distribution is roughly symmetric, we can use the mean as a measure of center and the standard deviation as a measure of spread.

However, the distribution also has some slight right-skewness, so we may want to consider using the median instead of the mean, depending on the context and purpose of the analysis.

b.

The mean of the distribution is:

= (28 + 29 + 30 + 31 + 32 + 33 + 34)/7

= 30.1

So the center of the distribution is around 30 miles per week.

The standard deviation of the distribution is approximately 2.3 miles per week, which tells us that the spread of the distribution is relatively tight.

Alternatively, we could use the median as a measure of the center.

Since there are 7 data points, the median is the average of the 4th and 5th values (30 and 31):

= (30 + 31)/2

= 30.5

So the center of the distribution is also around 30 miles per week using the median.

Thus,

The distribution is roughly symmetric, we can use the mean as a measure of center and the standard deviation as a measure of spread.

The distribution of miles ran each week by Elisa is relatively symmetric and centered around 30 miles per week, with a relatively tight spread of about 2.3 miles per week.

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The smallest positive integer n that makes the fourth root of 56n360 an integer is n = 81.

We can start by simplifying the expression inside the fourth root:

56 * n * 360 = [tex]2^{3}[/tex] * 7 * n * [tex]2^{3}[/tex] * [tex]3^{2}[/tex] * 5

= [tex]2^{6}[/tex] * [tex]3^{2}[/tex] * 5 * 7 * n

Taking the fourth root of this expression gives:

[tex](56*n*360)^{(1/4)}[/tex] = [tex](2^{6}*3^{2}*5*7*n) ^{(1/4)}[/tex]

= [tex]2^{(6/4)}[/tex] * [tex]3^{(2/4)}[/tex] * [tex]5^{(1/4)}[/tex] * [tex]7^{(1/4)}[/tex] * [tex]n^{(1/4)}[/tex]

= 4 * [tex]3^{(1/2)}[/tex] * [tex]5^{(1/4)}[/tex] *  [tex]7^{(1/4)}[/tex] * [tex]n^{(1/4)}[/tex]

For the fourth root to be an integer, [tex]n^{(1/4)}[/tex] must be an integer, and since we want n to be as small as possible, we want  [tex]n^{(1/4)}[/tex] to be as small as possible.

The smallest possible value of n that makes  [tex]n^{(1/4)}[/tex]an integer is when n is a fourth power of a prime number. Therefore, we can let n = [tex]p^{4}[/tex], where p is the smallest prime number that makes the expression under the fourth root an integer.

From the expression above, we can see that p must be a factor of 7 and [tex]35^{2}[/tex] in order to make the expression under the fourth root an integer. The smallest prime factor of 7 and [tex]35^{2}[/tex] is 3, so we can let p = 3. Then:

n =  [tex]p^{4}[/tex] = [tex]3^{4}[/tex] = 81

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Answer:

(2, -5)

(4, -3)

(3, -1)

Step-by-step explanation:

When reflected across the X-axis, the sign of the y will change to the opposite.

(x, y) → (x, -y)

Let's solve

(2,5) → (2, -5)

(4,3) → (4, -3)

(3,1) → (3, -1)

So, the missing coordinates are: (2, -5)

                                                       (4, -3)

                                                       (3, -1)

Answer:

jordans van

Step-by-step explanation:

yes satiscal

If the radius is 3 cm, the height of the cylinder is approximately 7.06 cm, which is closest to option B, 7 cm. The correct option is B.

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

We are given that the volume of the cylinder is 637 cm³ and the radius is 3 cm. Substituting these values into the formula, we get:

637 = π(3²)h

Simplifying:

637 = 9πh

h = 637 / (9π)

h ≈ 7.06

Thus, the height of the cylinder is approximately 7.06 cm, which is closest to option B, 7 cm.

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Answer:

the answer is (b)

because;

a^2-10a+24

product:24

sum:-10

factor:-6,-4

a(a-6)-4(a-6)

(a-6)(a-4)

therefore:two solutions but only one is given

Answer: Letter C

Step-by-step explanation:

In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.

Since c is saying that congruent arcs associated with chords are perpendicular its wrong.

The quadratic value equation of triangle area is solved and x = 12 m

Given data ,

Let the triangle be represented as ΔABC

Now , the height of the triangle is h = x m

The base of the triangle is = ( x + 6 ) m

Area of triangle = ( 1/2 ) base x height

A = 108 m² = ( 1/2 ) ( x ) ( x + 6 )

216 = x² + 6x

Subtracting 216 on both sides , we get

x² + 6x - 216 = 0

On factorizing the equation , we get

( x + 18 ) ( x - 12 ) = 0

So , the solution is x = 12 m

Hence , the height of the triangle x = 12 m

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Expression used for area of a rectangle is 12x² + 74x + 44 .

Its degree and classification is 2 and quadratic

and demonstration of a closure property is given by product of a polynomial is a polynomial.

Length of the rectangle = (6x + 4) units

and Width of the rectangle = (2x + 11) units.

The area of the rectangle is given by the product of its length and width,

Area = (6x + 4) × (2x + 11)

Find the product,

⇒ Area = 6x × 2x + 6x × 11 + 4 × 2x + 4 × 11

Simplifying this expression, we get,

⇒ Area = 12x² + 74x + 44

The expression that represents the area of the rectangle is 12x² + 74x + 44.

The degree of the expression 12x² + 74x + 44 is 2,

since the highest power of x is 2.

The classification of this expression is quadratic.

Part A demonstrates the closure property for polynomials because the product of two polynomials is also a polynomial.

Here, the area of the rectangle is the product of two polynomials (6x + 4) and (2x + 11).

And the result is also a polynomial (12x² + 74x + 44).

This shows that the set of polynomials is closed under multiplication.

Which is one of the defining properties of a mathematical system.

Therefore, the expression for area of a rectangle is (12x² + 74x + 44) ,

Degree and classification is 2 and quadratic and closure property is demonstrate by product of a polynomial.

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The values of the trigonometric functions are

1. sin A = 12/13

2. cos A = 5/13

3. Tan A = 12/5

4. cot A = 5/12

5. cosec A = 13/12

6. sec A = 13/5

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. Examples of these functions are; sin, cos , tan cot, cosec , sec e.t.c

Sin(tetha) = opp/hyp

cos(tetha) = adj/hyp

tan(tetha) = opp/adj

here the opposite side to angle A is 12 and the adjascent is 5 while the hypotenuse is 13.

Therefore,

1. sin A = 12/13

2. cos A = 5/13

3. Tan A = 12/5

4. cot A =1/tan A = 5/12

5. cosec A = 1/sin = 13/12

6. sec A = 1/cos = 13/5

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The volume of the cardboard box with given dimensions changes at the fastest average rate over the interval of  option c.  [1,5].

Length of the cardboard box = x + 1

Width of the cardboard box = 5  - x

Height of the cardboard box = x - 1

Volume of the box V (x) =  length × width × height

Substitute the values we have,

V(x) = (x+1)(5-x)(x-1)

Expanding this expression gives,

V(x) = -x³ + 5x² + x - 5

To know where Volume is changing at the fastest average rate,

Find the maximum value of the absolute value of the derivative of V(x) over each of the given intervals.

Taking the derivative of V(x), we get,

V'(x) = -3x²+ 10x + 1

Taking the absolute value of this expression, we get,

|V'(x)| = 3x² - 10x - 1

Now, we can calculate the maximum value of |V'(x)| over each interval,

At [1,2]

|V'(1)| = 8

|V'(2)| = 9

[1,3.5]

|V'(1)| = 8

|V'(3.5)| = 0.75

[1,5]

|V'(1)| = 1

|V'(5)| = 24

[0,3.5]

|V'(0)| = 1

|V'(3.5)| = 0.75

The maximum value of |V'(x)| occurs on interval [1,5].

Therefore, the volume of the box is changing at the fastest average rate over the interval option c . [1,5].

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The above question is incomplete, the complete question is:

A cardboard box manufacturing company is building boxes with length represented by x + 1, width by 5 − x, and height by x − 1. the volume of the box is modeled by the function below. over which interval is the volume of the box changing at the fastest average rate?

a. [1,2]

b. [1,3.5]

c. [1,5]

d. [0,3.5]

Answer:

(5,5π/4)

(5,−3π/4)

(−5,π/4)

(−5,−7π/4)

Step-by-step explanation:The correct answer is:

r = 5 units (distance from the pole)

θ = 5π/4 radians (angle measured counterclockwise from the ray θ = 0)

Note: The polar coordinates for point A on the given graph are r = 5 and θ = 5π/4. The r-value represents the distance from the pole to the point, and the θ-value represents the angle measured counterclockwise from the reference ray θ = 0.

Answer:

a = 3

Step-by-step explanation:

Collect like-terms:

[tex] - 16 = a - 19[/tex]

[tex]a = - 16 + 19[/tex]

[tex]a = 3[/tex]

Answer: 3

Step-by-step explanation: you take 19 from 3 giving you -16

4/5 is a real number.

A real number is a value in mathematics that expresses a quantity along a continuous line. Real numbers can be expressed as fractions or decimals and can be positive, negative, or zero.

4/5 is a rational number in this situation, which is a form of real number that may be written as a ratio of two integers. A real number can also be irrational, which means that it cannot be stated as a ratio of two integers and that its decimal representation goes on indefinitely without repeating.

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Marcus jogged [tex]2\frac{1}{2}[/tex] miles over the weekend.

Marcus jogged [tex]1\frac{2}{5}[/tex] miles on Saturday and 9/10 miles on Sunday.

we first need to find a common denominator:

[tex]1\frac{2}{5}[/tex]  = 7/5

9/10 = 0.9 miles

Now, we can round each of these to the nearest 1/2:

7/5 is closer to [tex]1\frac{1}{2}[/tex] than 1, so we round to [tex]1\frac{1}{2}[/tex]

0.9 is closer to 1 than 1/2, so we round to 1

Adding these rounded values, we get:

[tex]1\frac{1}{2}[/tex] + 1 =[tex]2\frac{1}{2}[/tex]

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Answer:

There is no square root function mentioned to compare with, but assuming you meant the parent square root function y = sqrt(x), the correct answer is:

A.) "stretched by a factor of 2, reflected over the x-axis, and translated 9 units right"

To see this, note that the equation y = 4x + 38 can be rewritten as y - 38 = 4(x - (-9.5)). This means that the graph of y = 4x + 38 is a transformation of the parent function y = sqrt(x) as follows:

So the correct answer is (a) stretched by a factor of 2, reflected over the x-axis, and translated 9 units right.

Answer:

answer is (a) stretched by a factor of 2, reflected over the x-axis, and translated 9 units right.

Step-by-step explanation:

The rate of the speeding car is 0.493.

We have,

The police car is at 80 mph and it is 44 yards from the intersection, is increasing at 45 mph, while the other car is 117 yards away from the intersection.

So, Rate of speeding car

= (45- 80)/ (117- 44)

= -35/(-73)

= 35/73

= 0.493

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Answer: (10 * 6) + (9 * 6) = 114

Step-by-step explanation:

Using the distributive property, we can write:

19 × 6 = (10 + 9) × 6

= (10 × 6) + (9 × 6) // Distributive property of multiplication over addition

= 60 + 54

= 114

Therefore, 19 × 6 = 114 when using the distributive law.

By translation, the image of the triangle X is equivalent to the triangle E.

Herein we find the representation of a triangle, whose vertices are described below:

A(x, y) = (5, 5), B(x, y) = (5, 6), C(x, y) = (7, 5)

Whose image must be determined by a rigid transformation known as translation:

P'(x, y) = P(x, y) + T(x, y)

Where:

Now we proceed to determine the images of the vertices of the triangle:

A'(x, y) = (5, 5) + (4, - 3)

A'(x, y) = (9, 2)

B'(x, y) = (5, 6) + (4, - 3)

B'(x, y) = (9, 3)

C'(x, y) = (7, 5) + (4, - 3)

C'(x, y) = (11, 2)

Therefore, the triangle E is the image of the triangle X.

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The normal curve represents a distribution where the mean, median, and mode are equal to each other.

The normal curve denotes a distribution in which the mean, median, and mode are all equal. As a result, the right answer is:

The curve of a normal distribution is symmetrical and bell-shaped, with the mean, median, and mode placed in the center. The standard deviation is a measure of the data's spread or dispersion around the mean.

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The larger cube is made up of 384 small cubes, each with a volume of 1/4.

We have,

If we assume that 96 is the total volume of a larger cube made up of smaller cubes, and each small cube has a volume of 1/4.

We can make the following calculation:

Let x be the number of small cubes that make up the larger cube.

The volume of the larger cube = Volume of each small cube x Number of small cubes

96 = (1/4) x

Solving for x.

Multiply 4 on both sides.

96 x 4 = x

x = 384

Therefore,

The larger cube is made up of 384 small cubes, each with a volume of 1/4.

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t < 8 is the inequality to solve the variable "t" as per the given data.

The cost C (in dollars) of renting the room for t hours can be expressed as:

C(t) = 4t + 18

To spend less than $50, we can set up an inequality:

C(t) < 50

Substituting the expression for C(t), we have:

4t + 18 < 50

Subtracting 18 from both sides, we get:

4t < 32

Dividing both sides by 4, we obtain:

t < 8

Therefore, the chemistry club could rent the meeting room for any number of hours less than 8 in order to spend less than $50.

The inequality solved for t is:

t < 8

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If you can buy 1 bunch of seedless green grapes for $2, then $18 we can buy 9 bunches.

The concept used here is a simple division to find out how many bunches of seedless green grapes can be purchased with a given amount of money.

In this case, we know the cost of one bunch of seedless green-grapes ($2) and we are given a total amount of money ($18) that we can spend on grapes. We can use division to find out how many bunches we can buy with that amount.

⇒ Number of bunches = ($18)/($2) per bunch,

⇒ Number of bunches = 9 bunches;

Therefore, with $18, you can buy 9 bunches of seedless green grapes.

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Answer:

An inequality that represents this situation is:

x + 5 ≤ 11

where x is the number of outfits you can pack in addition to the 5 you already have.

Step-by-step explanation:

i got a what if If you have 6 outfits packed already, then the inequality becomes:

x + 6 ≤ 11

where x is the number of outfits you can pack in addition to the 6 you already have. happy to help