Express the following sum in sigma notation:
1+4+7+10+13

Final answer:

After purchasing an album for $12.99 from the $50 gift card, the remaining balance is $37.01, which allows the purchase of 37 more single tracks, assuming each track costs $1.

Explanation:

To determine how many songs can be bought with a $50 gift card after purchasing an album for $12.99, we need to subtract the cost of the album from the total amount on the gift card. So, we have:

Subtracting the cost of the album from the gift card amount gives us:

$50 - $12.99 = $37.01

Assuming that each single track costs $1 as per the scenario provided, we can divide the remaining balance by the cost per single track:

$37.01 ÷ $1 per track = 37 tracks

This means that you can purchase 37 more single tracks with the remaining balance on the gift card.

the value of k is 40.

to solve for k when 28 is 12 less than k, we set up an equation and then solve it.

Let's denote k as the unknown number. According to the problem, 28 is 12 less than k, which can be written as:

28 = k - 12

To solve for k, we need to isolate k on one side of the equation.

28 = k -12

28 + 12 = k

40 = k

k = 40

So, the value of k is 40.

The complete question is:

28 is 12 less than k. 28=12-k Solve for k.

The system of equations 4x-y=4(x+1) and y=6 has no solution.

To determine the solution(s) of the system of equations, let's analyze each equation:

Equation 1: 4x - y = 4(x + 1)

Equation 2: y = 6

To simplify Equation 1, we can distribute 4 on the right side:

4x - y = 4x + 4

By rearranging terms, we have:

- y = 4

Comparing Equation 2 with this result, we see that the two equations are contradictory. Equation 2 states that y = 6, while the modified Equation 1 states that y = -4. This means there is no value of y that can simultaneously satisfy both equations.

Thus, the system of equations has no solution.

Therefore, the correct answer is C. no solution.

To know more about system of equations, refer here:

https://brainly.com/question/30127282

#SPJ6

25 less than 6 times a number is 107 then that number will be 22 it can be determined by the formation of the equation.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Let's say that number is x

6 times x number

⇒ 6x

25 less than 6x

⇒ 6x - 25

It is equal to 107

So,

6x - 25 = 107

6x = 132

x = 132/6

x = 22

Hence "25 less than 6 times a number is 107 then that number will be 22".

For more about the equation

https://brainly.com/question/10413253

#SPJ6

To find the polynomial difference, Lorne transformed the subtraction into addition of the opposite, combined like terms, and simplified the expression to get the result of -9x³ + 5x² + 6x - 10.

To find the difference between the two polynomials, Lorne correctly followed the steps of subtraction by changing the subtraction to the addition of the opposite. The process is outlined below:

Add the opposite of the second polynomial to the first polynomial by changing the sign of each term in the second polynomial.

Combine like terms by adding the coefficients of terms with the same degree of x.

Rearrange the terms in descending order of their degrees.

Write down the final simplified form of the polynomial.

By following these steps, the result would be:

Step 1:

(-3x³ + 5x² + 4x - 7) + (-6x³ + 2x - 3)

Step 2:

(-3x³ + 5x² + 4x - 7) + (-6x³) + 2x + (-3)

Step 3:

[(-3x³) + (-6x³)] + [4x + 2x] + [(-7) + (-3)] + [5x²]

Step 4:

-9x³ + 6x + (-10) + 5x2

Step 5:

-9x³ + 5x² + 6x - 10

Lorne subtracted [tex]6x^{3} - 2x + 3[/tex] from [tex]-3x^{3} + 5x^{2} + 4x - 7[/tex]. So, the main answer is 5. [tex]-9x^{3} +5x^{2} +6x-10.[/tex]

The steps Lorne used to find the difference between [tex]-3x^{3} +5x^{2} +4x-7[/tex] and [tex]6x^{3} -2x+3[/tex] are:

[tex]1. (-3x^{3} +5x^{2} +4x-7)+(-6x^{3} +2x-3)\\2. (-3x^{3} )+5x^{2} +4x+(-7)+(-6x^{3} )+2x+(-3)\\3. [(-3x^{3} )+(-6x^{3} )]+[4x+2x]+[(-7)+(-3)]+[5x^{2} ]\\4. -9x^{3} +6x+(-10)+5x^{2} \\5. -9x^{3} +5x^{2} +6x-10[/tex]

So, the main answer is 5. [tex]-9x^{3} +5x^{2} +6x-10.[/tex]

Lorne first added the two polynomials by combining like terms, then simplified the result by collecting like terms. The final expression represents the difference between the two polynomials after combining and simplifying.

COMPLETE QUESTION:

Lorne subtracted [tex]6x^{3} - 2x + 3[/tex] from [tex]-3x^{3} + 5x^{2} + 4x - 7[/tex]. Use the drop-down menus to identify the steps Lorne used to find the difference.

[tex]1. (-3x^{3} +5x^{2} +4x-7)+(-6x^{3} +2x-3)\\2. (-3x^{3} )+5x^{2} +4x+(-7)+(-6x^{3} )+2x+(-3)\\3. [(-3x^{3} )+(-6x^{3} )]+[4x+2x]+[(-7)+(-3)]+[5x^{2} ]\\4. -9x^{3} +6x+(-10)+5x^{2} \\5. -9x^{3} +5x^{2} +6x-10[/tex]

Answer:

  58

Step-by-step explanation:

Put 30 where x is in the expression and do the arithmetic.

  55 + 30 - 27 = 85 - 27 = 58

__

It can be advantageous to use the associative property of addition to evaluate the expression as ...

  55 + (30 -27) = 55 +3 = 58

On the attached diagram red curve is the graph of the quadratic function [tex]y = 2(x - 2)^2 + 2.[/tex] As you can see this graph has no intersections with x-axis, this means that there are no solutions.

If you translate red curve 2 units down, you obtaine the graph (blue curve) of the function [tex]y = 2(x - 2)^2[/tex] and this graph has one common point with x-axis. This means that there will be exactly one solution.

Answer: k=-2 (you add -2 to the function [tex]y = 2(x - 2)^2 + 2[/tex] to obtain the function [tex]y = 2(x - 2)^2[/tex]).

Answer: 0 ZERO

Step-by-step explanation:

To solve for b in the equation 7b divided by 12 equals 4.2, multiply both sides by 12 and then divide by 7, resulting in b being equal to 7.2.

To solve the equation 7b ÷ 12 = 4.2 for b, we must isolate b on one side of the equation. We can begin by multiplying both sides of the equation by 12 to cancel out the division by 12 on the left side. This results in the equation 7b = 4.2 × 12. To find the value of b, we then divide both sides of the equation by 7:

Therefore, the value of b is 7.2.

To find the value of b in the equation 7b/12 = 4.2, multiply both sides by 12 and then divide by 7 to get b = 7.2. The value of b is 7.2.

The student is asking how to find the value of b in the equation 7b divided by 12 equals 4.2. To solve for b, you can follow these steps:

Therefore, the value of b is 7.2.

probability  = number of favourable outcomes / total number of outcomes

probability of spinning any number = 1/3

probability of tossing a coin = 1/2

probability of compound event = 1/3 * 1/2 * 1/3 = 1/18

probability of spinning an odd number, flipping heads, then spinning a yellow is  = 2/3*1/2*1/3 = 1/9

Each cat would get approximately 6.67 ounces of cat food, which falls between 6 and 7 ounces. The calculation is done by dividing the total amount of food (20 ounces) by the number of cats (3).

The Philips family had to split 20 ounces of cat food among their 3 cats. To find out how much food each cat gets, we need to divide the total amount of food by the number of cats. Calculating this, 20 ounces ÷ 3 cats equals approximately 6.67 ounces per cat. Even though this is a decimal, if we consider whole numbers, the amount each cat gets falls between 6 and 7 ounces, since 6.67 is more than 6 and less than 7.

When dealing with fractions and division, it's essential to understand the concept of division and be able to find averages. The task at hand may often find itself related to dividing a quantity evenly among a number of recipients, much like in scenarios where we have to split a pie or determine individual portions.

To divide 20 ounces of cat food equally among three cats, each cat gets approximately 6.67 ounces. The amount of food per cat lies between the whole numbers 6 and 7.

The question is asking how to divide 20 ounces of cat food equally among three cats. To find out how much each cat would get, you divide the total amount of cat food by the number of cats:

This calculation shows that each cat would get approximately 6.67 ounces of food. This value lies between the whole numbers 6 and 7. Therefore, when the Philips family divides the cat food, each cat gets a little more than 6 ounces but less than 7 ounces of food.

Answer: Volume of an oblique cylinder is 2011.43 sq.m.

Step-by-step explanation:

Since we have given that

Radius of a cylinder = 8 meters

Height of a cylinder = 10 meters

Cavelieri's Principle states that volume of an oblique cylinder is same as the volume of right circular cylinder with equal radius and height.

As we know the formula for "Volume of cylinder":

[tex]Volume=\pi r^2h\\\\V=\frac{22}{7}\times 8\times 8\times10\\\\V=\frac{14080}{7}\\\\V=2011.43[/tex]

Hence, Volume of an oblique cylinder is 2011.43 sq.m.

To find a recurrence relation for the number of n-digit ternary sequences in which no 1 appears anywhere to the right of a 2, we can consider two cases depending on the last digit being 0 or 2.

To find a recurrence relation for the number of n-digit ternary sequences in which no 1 appears anywhere to the right of a 2, we can break the problem down into two cases: when the last digit is 0 or when the last digit is 2. If the last digit is 0, then the number of n-digit ternary sequences is equal to the number of (n-1)-digit ternary sequences in which no 1 appears anywhere to the right of a 2. If the last digit is 2, then the number of n-digit ternary sequences is equal to the number of (n-1)-digit ternary sequences in which no 1 appears anywhere to the right of a 2, plus the number of (n-1)-digit ternary sequences in which no 1 appears anywhere to the right of a 2.

Answer:

C: y(x + 4)(x – 6)

Step-by-step explanation:

I took the test on Edge -2022

To find out the face value of a simple discount note that will provide a proceed of $24,700 with an 8% discount rate for 180 days, use the formula FV = P / (1 - (r * t)). Plug in the given values and compute the answer. The result is the required face value and should be rounded to the nearest cent.

To find out the face value of a simple discount note, we can use the formula FV = P / (1 - (r * t)) where FV represents the face value, P is the proceeds, r is the discount rate, and t is the time in years.

In the problem, P = $24,700, r = 8% or 0.08 (expressed as a decimal), and t = 180/365 because there are 365 days in a year and the note is for 180 days. Let's substitute these values into the formula:

FV = 24700 / (1 - (0.08 * (180/365))

When you calculate the expression on the right, the answer will be the face value required to get a proceed of $24,700 with an 8% discount rate for 180 days. Round to the nearest cent for your final answer.

https://brainly.com/question/37160732

#SPJ3