You need at least $48,000 in two years. If you earn 4.8% compounded annually, how much principle do you need to invest?

The rational roots of the given polynomial are +/- 1, +/- 2, +/- 3, +/- 4, +/- 6, +/- 12, +/- 1/2, +/- 1/4, +/- 1/5, +/- 1/10, and +/- 1/20.

To find the rational roots of the polynomial, we can use the Rational Root Theorem. This theorem states that if a polynomial of the form a_n*x^n + a_{n-1}x^{n-1} + ... + a_1x + a_0 has a rational root, then that root must be of the form p/q, where p is a divisor of a_0 and q is a divisor of a_n.

In this case, the polynomial is

f(x) = 20x^4 - 8x^3 - x^2 + 12x,

so a_0 = 12 and a_4 = 20. The divisors of 12 are 1, 2, 3, 4, 6, and 12. The divisors of 20 are 1, 2, 4, 5, 10, and 20. Therefore, the possible rational roots of the polynomial are

p/q = +/- 1, +/- 2, +/- 3, +/- 4, +/- 6, +/- 12, +/- 1/2, +/- 1/4, +/- 1/5, +/- 1/10, and +/- 1/20.

We can then test each of these values to see if they are actually roots of the polynomial. If a value is a root, then substituting it into the polynomial will result in a value of 0.

Therefore, the rational roots of the given polynomial are +/- 1, +/- 2, +/- 3, +/- 4, +/- 6, +/- 12, +/- 1/2, +/- 1/4, +/- 1/5, +/- 1/10, and +/- 1/20.

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This theorem states that if a polynomial of the form a_n*x^n + a_{n-1}x^{n-1} + ... + a_1x + a_0 has a rational root, then that root must be of the form p/q, where p is a divisor of a_0 and q is a divisor of a_n.

f(x) = 20x^4 - 8x^3 - x^2 + 12x,

p/q = +/- 1, +/- 2, +/- 3, +/- 4, +/- 6, +/- 12, +/- 1/2, +/- 1/4, +/- 1/5, +/- 1/10, and +/- 1/20.

Therefore, the rational roots of the given polynomial are +/- 1, +/- 2, +/- 3, +/- 4, +/- 6, +/- 12, +/- 1/2, +/- 1/4, +/- 1/5, +/- 1/10, and +/- 1/20.

An employee earns $14 per hour and a trainer charges $20 for every 30 minutes of training plus a $5 tip are a constant rate per unit interval. Therefore, options A and E are the correct answers.

Given that:

an employee earns $14 per hour.

constant rate of change :

When something has a constant rate of change, one quantity changes in relation to the other. For example, for every half hour the pigeon flies, he can cover a distance of 25 miles. We can write this constant rate as a ratio. For ratios, it's always a good idea to state both units in whole terms.

A). Let the number of hours be x and the total money earned be y

So, y = 14x

B). Let the money earn by an employee each year be a and total earning in a year be b.

So, b=a+3% of a

⇒ b = a + 0.03a

⇒ b = 1.03a

C) Let the number of months be m and the total charge be t

So, t=50+30m

D) Let cost of gym equipment be p, rate of change =8% and time period = 6 months

So,

E) Let the number of hour be x.

Here, 30 minutes = 1/2 hours

Total charge = 20 + 5x/2

An employee earns $14 per hour and a trainer charges $20 for every 30 minutes of training plus a $5 tip are a constant rate per unit interval. Therefore, options A and E are the correct answers.

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Full question :

For which situation does one quantity change at a constant rate per unit interval relative to another quantity? responses.

Select all that apply

A. An employee earns $14 per hour.

B. An employee earns a 3% raise each year.

C. A gym charges a $50 down payment plus $30 per month.

D. A piece of gym equipment decreases 8% in value every 6 months.

E. A trainer charges $20 for every 30 minutes of training plus a $5 tip.

360° is all the way around a circle. The length of the intercepted arc is equal to the circumference of the circle.

Arc Length of a Circle:

Length. A practical way to determine the length of an arc in a circle is to plot two lines from the arc's endpoints to the center of the circle, measure the angle where the two lines meet the center, then solve for L by cross-multiplying the statement: measure of angle in degrees/360° = L/circumference.

Does arc length have to be in radians?

Arc length is a measurement of distance, so it cannot be in radians. The central angle, however, does not have to be in radians. It can be in any unit for angles you like, from degrees to arcsecs. Using radians, however, is much easier for calculations regarding arc length, as finding it is as easy as multiplying the angle by the radius.

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Step-by-step explanation:

∠1 + 49° + 49° = 180°

∠1 = 180-98

The length of the side of the smaller box is 6 and the length of the side of the larger box is 20. The equation for the difference in volume of the boxes is, y3 - x3 = 7784 .

Let us consider the length of side of small box be x inch & length of large box be y inch.

Length of smallest box is 30% of the length of the side of the largest box 

x=30%*y

   = 30 * y / 100

x = 3y / 10

Volume of the smallest box is x3.

volume of the largest box is y3.

Volume of largest box is 7784 cubic inches more than the volume of smallest box. Therefore,

y3 =  x3 + 7784

     = (3y/ 10 )3 + 7784

     = 27y3 / 1000 + 7784

y3 - 27y3 / 1000 = 7784

973 y3  / 1000 = 7784

973 y3 = 7784 * 1000

y3 = 7784 * 1000 / 973

y3 = 8000

   y = 20

Now find the smaller side.

x = 3y / 10

putting the value of y  this we get,

x = 3 * 20 / 10

   x= 6    

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Answer:

2

Step-by-step explanation:

The original amount is 10 and the new quantity is 14 percent increase  is 40%

An quantity or part that is contained in each hundred is known as a percentage. The symbol "%" signifies that it is a fraction with 100 as the denominator.

Here,

The increase in percentage is equal to (New quantity - Original quantity)/Original quantity 100

(14-10)/10* 100.

4/10 × 100

40%

A 40% increase from the original amount to the new quantity may be calculated as a result.

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The two distinct real number zeros of f(x) left parenthesis, x, right parenthesis are -2 + sqrt(7) and -2 - sqrt(7).

The discriminant of a polynomial is a quantity that determines the number of distinct real roots of a polynomial equation. For a polynomial of degree n, the discriminant is calculated as the square of the coefficient of the nth degree term multiplied by the product of the coefficients of the remaining terms, minus the square of the product of the coefficients of the lower degree terms. In the case of [tex]f(x)=3x^2+12x+5[/tex], the discriminant is given by[tex]D=12^2 - 4*3*5 = 144 - 60 = 84.[/tex]

Since the discriminant is greater than 0, it follows that the polynomial equation has two distinct real number zeros. To find the zeros of the equation, we must solve the equation by setting it equal to zero and factorising it. Doing so, we find that the zeros are given by [tex]x = (-12 +/- sqrt(84))/6 = -2 +/- sqrt(7)[/tex]. Hence, the two distinct real number zeros of f(x) are -2 + sqrt(7) and -2 - sqrt(7).

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Answer:

range

Step-by-step explanation:

the x values or inputs are called the domain

the y values or outputs are called the range

The median for the next batch of observations is 5.

The median is the value in the middle of a data set, which indicates that 50% of the data points have a value less than or equal to the median, and 50% have a value greater than or equal to the median. The median is the number in the middle of a set of numbers. The median represents the 50th percentile of the set of numbers. In other words, the median is the value in the center of a set of numbers where half are less than the median and half are more than the median.

Here,

given set of observation,

=2,3,4,5,6,7,8

n=7

median=(7+1)/2

=4th term

=5

The median for following set of observation is 5.

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Answer:

The value of 9^(x) is 3.

Step-by-step explanation:

To find the value of 9^(x), we can use the equation:

(a^x) = (b^y)

Where a and b are different bases, and x and y are different exponents.

We can rewrite this equation as:

x = y * log(a) / log(b)

Plugging in the values given in the question, we get:

x = log(8) / log(4)

Solving for x, we get:

x = 3

Therefore, the value of 9^(x) is 3.

Answer:120

Step-by-step explanation:

1,440 divided by 12 equals 120 so 120 shelves are needed

Answer:

15 storage towers

Step-by-step explanation:

first you need to find out how many video games can fit into one storage tower.

8 times 12 is 96,meaning 96 per tower.

Then you would one to get the total number of video games and divide it by 96 to find out how many towers are needed.

If done correctly you will end up with 15.

The age of the son and father obtained after solving the equation will be equal to 6 years and 34 years.

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given information in the question,

Let the age of the father is f and the age of the son be s.

As per the given statement in the question,

The sum of the ages of a father and his son is 40 years.

f + s = 40   (i)    and,

f + s + 2(f -s) = 96    

3f - s = 96       (ii)

Add equations (i) and (ii)

4f = 136

f = 136/4

f = 34 years

Put f = 34 in equation (i)

f + s = 40

34 + s = 40

s = 40 - 34

s = 6 years.

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Answer:

y= -1/3x+7

i graphed it so it should be right

There are nine numbers in this set, so the median is the fifth number. The fifth number in this set is 14, so the median is 14.

The median of a set of numbers is the value that is exactly in the middle of the set when it is ordered from least to greatest. In this case, the set of numbers is 13, 16, 12, 14, 19, 12, 14, 13, 14. When we order this set from least to greatest, we get 12, 12, 13, 13, 14, 14, 14, 16, 19. There are nine numbers in this set, so the median is the fifth number. The fifth number in this set is 14, so the median is 14.

To find the median, we first need to arrange the numbers in order from least to greatest. If there is an odd number of numbers in the set, the median is the middle number. If there is an even number of numbers in the set, the median is the average of the two middle numbers. In this case, there are nine numbers in the set, so the median is the middle number.

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The general formula for the variance varies according to the distribution, For the discrete and continuous probability distribution, The expected values formula varies. The variance is given by [tex]E(X^{2})-(E(X))^{2}[/tex] .

A probability distribution is a mathematical function used in probability theory and statistics that estimates the likelihood that various possible outcomes of an experiment will occur. In terms of its sample space and event probability, it is a mathematical description of a random phenomena.

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.

If distribution is discrete  , E(X) = x*P(x).

If distribution is continuous , E(x) = x *f(x).

Variance =  [tex]E(X^{2})-(E(X))^{2}[/tex]

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To solve this equation, use the distributive property to rewrite it as 4x - 2y = 12. Then, solve the equation using either addition or subtraction.

To solve the equation 4x 2y = -12, the first step is to use the distributive property to rewrite the equation as 4x - 2y = 12. This allows us to solve the equation using either addition or subtraction. If we choose to use addition, we can add 2y to both sides of the equation to get 4x + 2y = 12. We can then subtract 2y from both sides to get 4x = 12 - 2y. Dividing both sides of the equation by 4 gives us the solution x = (12 - 2y)/4. If we choose to use subtraction, we can subtract 2y from both sides of the equation to get 4x - 2y = 12. We can then add 2y to both sides to get 4x = 12 + 2y. Dividing both sides of the equation by 4 gives us the solution x = (12 + 2y)/4. In either case, the solution is x = (12 ± 2y)/4.

Addition:

4x + 2y = 12

4x = 12 - 2y

x = (12 - 2y)/4

Subtraction:

4x - 2y = 12

4x = 12 + 2y

x = (12 + 2y)/4

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The percent that the average score on the test increased during the two months is 12.5%.

It should be noted that mean simply means the average of a set of numbers that are given. In this case, the average test score of RSM students in September increased by 10%. In October it increased by another 15%..

The average of the increase will be:

= (10% + 15%) / 2

= 25% / 2

= 12.5%

The average is 12.5%.

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Python's Transform function returns a self-produced data frame with transformed values after applying the function specified in its parameter. This data frame has the same length as the passed data frame.

Now, According to the question:

Python's Transform function returns a self-produced data frame with transformed values after applying the function specified in its parameter. This data frame has the same length as the passed data frame.

What does transform () do?

The transform CSS property lets you rotate, scale, skew, or translate an element. It modifies the coordinate space of the CSS visual formatting model.

The transform() function is used to call function on self producing a Series with transformed values and that has the same axis length as self. Function to use for transforming the data.

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Value of  [tex]1^{3} + 10^{3} + 11^{3} +12^{3} +......+30^{3}[/tex] is "216225".therefore the correct option is C.

Natural Numbers are the counting numbers that start from 1 and go on till infinity. To find the sum of cube of first n natural numbers means to add the cube of a specific number of natural numbers starting from 1 and get the answer.

There are a lot of patterns in mathematics. One analogous pattern of numbers is the sum of cube of n natural numbers.

Given:  Equation  = [tex]1^{3} + 10^{3} + 11^{3} +12^{3} +......+30^{3}[/tex]

            Here  N=30  , We have given

solution:

                                              [tex]S=\frac{{n^{2} (n+1)^{2}}}{4} \\=\frac{30^{2} (30+1)^{2}}{4}\\=\frac{900 (31)^{2}}{4}\\=\frac{900 (961)}{4}\\=\frac{864900}{4}\\=216225[/tex]

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Answer:

B - 50

Step-by-step explanation:

the exterior angle is 105, and as it's on a straight line, the interior angle is 180-105=75

75+55=130

angles in a triangle are 180

180-130=50

Answer:50 degrees

Step-by-step explanation: The 105degrees angle forms a supplementary angle with the missing degrees in the triangle

so the missing value which is not requested is 180degrees-105 degrees=75 degrees

No we have two angles inside the triangle. We can now work out the missing angle for x

We know that a triangle adds up to 180 degrees

So x=180-55-75=50 degrees as the answer

Answer:

y=(2/3) x+7

Step-by-step explanation:

2/3 is the slope which would be parallel

Answer:

A whole number is a number without fractions or intergers

Step-by-step explanation:

An example of this wou;d be 0, 16, etc too find one you have to look at the qualities and see if it fits

The solution of the linear equations 2x + y = 8 and y = 3x - 2 will be (2, 4).

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The equations are given below.

2x + y = 8             ...1

y = 3x - 2             ...2

From equations 1 and 2, then the value of the variable 'x' is calculated as,

2x + 3x - 2 = 8

5x = 10

x = 2

Then the value of the variable 'y' will be calculated as,

y = 3(2) - 2

y = 6 - 2

y = 4

The solution of the linear equations 2x + y = 8 and y = 3x - 2 will be (2, 4).

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The example of a rational function  is f ( x) = x 2 − 1 2 x + 21.  , we can represent this function in terms of ratio of p and q.

Other than than a real world example can be that , a cookie being divided among two children , the representation will be , 1 / 2.

A graph of a rational function has asymptotes which are of three types and that is what makes them different from the rest of the functions. Rational functions are the functions which can be represented in the ratio of two polynomials p and q. The solution of this equation is know as the roots of the equation.

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We require both to ascertain whether the findings are independent, this criterion is applied.

Statistics frequently employs the binomial distribution as a discrete distribution. When compared to a binomial distribution, the normal distribution is continuous. The chance for 'x' success of an investigation in 'n' trials is represented by the binomial distribution.

As per the given information in the question,

The normal distribution can be used to approximate the binomial distribution. The situation when performing a normal approximation is as follows:

np ≥ 10 and,

np(1 - p) ≥ 10

This criterion is used to determine whether the results are independent.

We are aware that when n and p are combined, the results are independent.

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If in the past month Kaylynn rented one video game in for DVDs. the total amount that Kaitlyn spent on video game and DVD rentals in the past month. is : $7.60.

We would have to make use of this formula to find the total amount that Kaitlyn spent on video game and DVD rentals in the past month.

Total amount = (Number of video game × Video game rental price ) + Rental price for DVD

Let plug in the formula

Total amount = (1 × $3.30) + $4.30

Total amount = $3.30 + $4.30

Total amount = $7.60

Therefore we can conclude that the total amount is $7.60.

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