A new spiral notebook contains 30 more sheets of paper than a new memo book. The total number of sheets of paper in 3 new spiral notebooks and 5 new memo books is
810. Which system of equations can be used to find s, the number of sheets of paper in one new spiral notebook, and m, the number of sheets of paper in one new memo book?

The amount of money that each student has saved is between $ 4418 and $ 4982

Given data ,

To find the margin of error, we need to use the formula:

Margin of error = z (standard deviation / square root of sample size)

where z is the z-score associated with the desired confidence level.

For a 95% confidence level, the z-score is 1.96

On simplifying , we get

Margin of error = 1.96 (1300 / √(84))

Margin of error ≈ 282.3

Therefore, we can say with 95% confidence that the true mean amount of money that each student has saved is between 4700 - 282 = 4418 dollars and 4700 + 282 = 4982 dollars

Hence , the margin of error is solved

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Answer:

2,000 pages.

Step-by-step explanation:

The heat teacher has 60 notebooks in total. If the teacher evenly distributed the notebooks among the 6 students, then that would be

60 ÷ 6 = 10 notebooks to each student.

Now let's say a kid named Ethan found out each of his notebooks contains 200 pages. Ethan has 10 notebooks in total so he needs to do

10 × 200 = 2,000 pages in total.

We do 10 × 200 since Ethan has 10 notebooks, and each of his notebooks have 200 pages.

Thus 2,000 is the answer.

Answer:

A = (1/2)(3)(2/3) = 1 square foot

Answer:

[tex]\frac{1}{7^6}[/tex]

Step-by-step explanation:

When we have a negative exponent in the form a^-x, this is equal to 1/a^x.

We can apply this here, where a = 7, and x = 6.

Hence, 7^-6 = 1/(7^6)

average formula : sum of all numbers/how many numbers in list

= (16+50+14+20+40)/5

= 140/5

= 28

∴, the average of the numbers is A, 28

The average of 16, 50, 14, 20, and 40 is 28 (option A).

To find the average of a set of numbers, you add up all the numbers and then divide the sum by the total count of numbers. Let's calculate the average of 16, 50, 14, 20, and 40:

Average = (16 + 50 + 14 + 20 + 40) / 5

Now, add up the numbers in the parentheses:

Average = 140 / 5

Now, perform the division:

Average = 28

Therefore, the average of 16, 50, 14, 20, and 40 is:

A. 28

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The narrative techniques used in this story are:

The theme of this narrative is to never give up and to always follow your curiosity.

In the narrative, the climax is the most challenging part because it was the point where the story reached its highest level.

I noticed the locked door that I passed every day was slightly ajar as I walked by it. Curiosity got the better of me, and I pushed the door open, eager to see what was inside.

The room was dark, but as my eyes adjusted to the dim light, I realized I'd found a forgotten storage room. The room was cluttered with old boxes and furniture, but as I rummaged through it, I discovered a small locked chest.

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Answer:

60 friends

Step-by-step explanation:

If Noah has 184 apples and only gave away 60 I would be assuming that he has 60 friends. You didn't give a good question and this is my best guess.

- Hope this helps

If queen bee has a colony of 2000 drones and 18000 worker bees, One-sixth (1/6) of the worker bees in the queen bee's colony are drones.

The total number of bees in the queen bee's colony is the sum of drones and worker bees. Therefore, we can calculate the total number of bees as follows:

Total number of bees = number of drones + number of worker bees

Total number of bees = 2000 + 18000

Total number of bees = 20000

Out of the total number of worker bees (18000), 6000 are foragers. Therefore, the number of worker bees that are not foragers is:

Number of worker bees that are not foragers = 18000 - 6000

Number of worker bees that are not foragers = 12000

Now we can find the part of worker bees that are drones by dividing the number of drones by the total number of bees that are not foragers:

Part of worker bees that are drones = number of drones / number of worker bees that are not foragers

Part of worker bees that are drones = 2000 / 12000

Part of worker bees that are drones = 1/6

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Answer:

Step-by-step explanation:i need you to add

Since the black and white areas are equal, the folded sheet has four congruent right triangles with legs x and \frac{6}{2x}.  This is the same as the area of the unfolded sheet, so x satisfies the equation x^2 + (\frac{6}{2x})^2 = 6. Simplifying, we get x^4 - 6x^2 + 9 = 0$. This factors as (x^2 - 3)^2 = 0, so x^2 = 3. Therefore, a is \sqrt{3} centimeters from its original position.

We're given that the square sheet of paper has an area of 6 cm². To find the side length of the square, we'll take the square root of the area:

Side length = √(area) = √6 cm

Now let's focus on the folding part. When point A is folded onto the diagonal, a smaller square is formed with one of its vertices at point A. Let's call the side length of this smaller square x cm.

Since the visible black area is equal to the visible white area, that means the area of the smaller square is equal to half of the total area:

Area of smaller square = (1/2) * 6 cm² = 3 cm²

Now we can find the side length of the smaller square:

x = √(area of smaller square) = √3 cm

Since the smaller square is formed by folding, its diagonal is equal to the side length of the original square (√6 cm). We can now use the Pythagorean theorem to find the distance of point A from its original position:

Diagonal² = (side length of smaller square)² + (distance of A from original position)²

(√6 cm)² = (√3 cm)² + (distance of A from original position)²

6 cm² = 3 cm² + (distance of A from original position)²

3 cm² = (distance of A from original position)²

√3 cm = distance of A from the original position

So the distance of point A from its original position is √3 cm.

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13 weeks.

Our equation is [tex]y=-24x + 379[/tex].
x is the amount of weeks that has passed. x is being multiplied by -24. The +379 is our y-intercept. This means that per week, the account loses $24. The y-intercept also means that the account started with having $379 in it.

Finally, y is the output of the equation. This means that when you plug in the number of weeks, we see how much money is in the bank account with the y-value.

For example, if we solve for 2 weeks;

[tex]y=-24(2)+379=-48+379=331[/tex]. So after 2 weeks, the account will have $331 left.

Now to find the answer. We can plug in the final amount that we are given ($67) and then solve from there.

[tex]67=-24x+379[/tex]

Next we isolate x and its coefficient:

[tex]67-379=-24x+379-379[/tex]

[tex]-312=-24x[/tex]

Multiply both by -1 to get positive numbers:

[tex]-312*-1=-24x*-1[/tex]

[tex]312=24x[/tex]

Now divide both sides by 24 to completely isolate x.

[tex]\frac{312}{24}=\frac{24x}{24}[/tex]

[tex]13=x[/tex]

OR

[tex]x=13[/tex].

This means that when x = 13, y = 67. When 13 weeks pass, the amount of money in the account is equal to $67.

Therefore, the amount of time it takes for the account to be depleted to $67 is 13 weeks.

The total amount of sales in dollars for this year is $162500.

It is given that Sales person has $250,000 sales last year which is 65% of the sales she had this year.

We can write the equation to determine the value of {x} as -

{x} = 65% of 250000

{x} = 65/100 x 250000

{x} = 65 x 2500

{x} = 162500

Therefore, the total amount of sales in dollars for this year is $162500.

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The total amount in the account at the end of 8 years, if no deposits or withdrawals were made, at 3.5 percent simple interest is $384

The simple interest on an amount is; I  = P × R × T

Where;

I = The simple interest on the amount

P = The principal amount saved

R = The interest rate.

The amount or principal deposited in the account, P = $300

The interest rate on the account, R = 6.5% simple interest

The number of years, which is the time duration of the deposit, or savings, T = 8 years

The interest earned on the account after 8 years is therefore;

Interest, I = $300 × (3.5/100)/year × 8 years = $84

The amount in the account after 8 years, A = P + I

Therefore;

The total amount in the account, A = $300 + $84 = $384

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The solution of x in the intersecting lines l, m, and n forming a triangle is 70

From the question, we have the following parameters that can be used in our computation:

The intersecting lines l, m, and n that form a triangle.

Using the sum of opposite internal angles of a triangle, we have the following equation

x = 30 + 40

Evaluate the sum of the expressions

So, we have the following representation

x = 70

Hence, the calculated measure of the angle x is 70 degrees

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Answer:

  $5.33

Step-by-step explanation:

You want to know Matthew's change from a $10 bill if he bought 6 donuts for $0.35 each, and a Coke for $2.57.

The amount of change is the difference between the amount tendered and the value of the purchase(s):

  10 - (6×0.35 +2.57) = 5.33

Matthew received $5.33 in change.

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Answer:

It is not specified in the question how many rolls of fabric Mary used, so we can't calculate the total length of the fabric she used.

Answer:

-23\2h+3\2 i.e. option A is the answer

Answer: (x + 9)^2 = x^2 + 18x + 18

Step-by-step explanation:

A neat trick that can help you get this answer is the box method, Draw a box with 4 smaller boxes in it. Then on the right of the box, but the first box(outside on the right) x, bottom from there, but 9. At the top of the box(first square) put x again and beside it, another 9, we do this because when a variable is with a constant inside parentheses, they can't combine, so you do what's outside the parentheses, in this case its the exponent of 2. Then we do the math, x + x is x squared, x * 9 is 9x(when you multiply a variable and constant,  you can combine those), 9 + 9 is 18, then you should get x^2 + 9x + 9x + 18, next you combine "Like Terms"(same values). They only Like Terms here would be 9x and 9x, when combining Like Terms, you must only add, don't multiply, 9x + 9x would be 18x. Then you got quadratic to standard.

(x + 9)^2   ---)   x^2 + 18x + 18.

Answer: 720 possible passwords

Step-by-step explanation:

good luck!

Vinny made a password consisting of 3 digits, and since none of the digits are the same, the first digit can be any number from 1 to 9, the second digit can be any number from 0 to 9 excluding the first digit, and the third digit can be any number from 0 to 9 excluding the first two digits. Therefore, the possibility of passwords Vinny could choose from is: 9 x 9 x 8 = 648 possible passwords.

Vinny made a password consisting of 3 unique digits. To determine the number of possible passwords, we need to consider the available options for each digit.
For the first digit, Vinny can choose any of the 10 digits (0-9), but since the leading digit cannot be 0, there are 9 choices (1-9). For the second digit, Vinny has 9 options remaining (10 digits minus the first digit). And for the third digit, there are 8 options left (10 digits minus the first two digits).
To calculate the total number of possible passwords, simply multiply the options for each digit: 9 (first digit) * 9 (second digit) * 8 (third digit) = 648 possible passwords.
So, Vinny had 648 possible passwords to choose from.

Vinny made a password consisting of 3 digits, and since none of the digits are the same, the first digit can be any number from 1 to 9, the second digit can be any number from 0 to 9 excluding the first digit, and the third digit can be any number from 0 to 9 excluding the first two digits. Therefore, the number of possible passwords Vinny could choose from is:
9 x 9 x 8 = 648 possible passwords.

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Answer:

B

Step-by-step explanation:

given 2 similar triangles with ratios of sides a : b , then

ratio of areas = a² : b²

here the ratio of sides = 3 : 1 , then

ratio of areas = 3² : 1² = 9 : 1

The ratio of the area of the larger to the area of the smaller triangle is B. 9:1

From the question, we have the following parameters that can be used in our computation:

The triangles

The triangles are similar triangles

So, we have

Ratio = 3 : 1

The area ratio is the square of the length ratio

So, we have

Area Ratio = 3^2 : 1^2

Evaluate

Area Ratio = 9 : 1

Hence, the Area Ratio = 9 : 1

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Solving the system of equations by elimination gives (-4, 1)

Given that

f(x) = |x| and g(x) = 12|x - 7|

Next, it is translated right by 7 units

Given that

x - 9y = -13

2x + y = -7

Multiply (1) by 2

2x - 18y = -26

2x + y = -7

Subtract the equations

-19y = -19

So, we have

y = 1

Recall that

2x + y = -7

So, we have

2x + 1 = -7

This gives

2x = -8

Evaluate

x = -4

Hence, the solution is (-4, 1)

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The equation of the conic section  is x² + y² + 10x + 2y - 20 = 0

The equation of a circle is x^2 + y^2 - 4y - 21 = 0

A circle is a two-dimensional geometric shape that consists of a set of points in a plane that are equidistant from a fixed point called the center. The distance from the center to any point on the circle is called the radius.

A circle can be defined by its center point and radius or by its circumference, which is the distance around the perimeter of the circle. The circumference of a circle can be calculated using the formula:

C = 2πr

where C is the circumference, r is the radius, and π (pi) is a mathematical constant approximately equal to 3.14.

The center of the circle is (-5,-1) and its radius is the distance from the center to any point on the circle. Using the distance formula, we can find the radius:

r = √((0 - (-1))² + (-10 - (-5))²) = √(1 + 25) = √(26)

So, the equation of the circle in standard form is:

(x + 5)² + (y + 1)² = 26

Alternatively, in general form, it can be written as:

x² + y² + 10x + 2y - 20 = 0

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Answer:

To evaluate the function of f(x) for x=-2 we substitute-2 for x in the expression of the function

F(-2)= 20(-2)-4

F (-2)=-40 -4

F(-2) = -44

Therefore f(-2) = -44 when x= - 2

To evaluate the function f(x) for x =8 we substitute 8 for x in the express of the function

F(8)=20(8)-4

F(8) = 160-4

F(8)= 156

Therefore f(8) = 156 when x = 8

The investment will be worth approximately $633.96 in 20 years if it is invested at a rate of 5% per year and compounded quarterly.

The interest you earn on interest is known as compound interest. Simple maths can be used to demonstrate this: if you have $100 and it earns 5% interest annually, you will have $105 at the end of the first year.

We can use the compound interest formula to calculate the future value (A) of the investment:

[tex]A = P(1 + r/n)^{(n*t)[/tex]

where:

P = the principal amount (initial investment) = $300

r = the annual interest rate = 5% = 0.05 (decimal)

n = the number of times the interest is compounded per year = 4 (quarterly)

t = the number of years the money is invested for = 20

Plugging in the values, we get:

[tex]A = 300(1 + 0.05/4)^{(4*20)[/tex]

A = 300(1.0125)⁸⁰

A = 300(2.1134)

A = $633.96

Therefore, the investment will be worth approximately $633.96 in 20 years if it is invested at a rate of 5% per year and compounded quarterly.

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Answer: $810.45

Step-by-step explanation:

Step-by-step explanation:

For a right triangle  

 sinΦ = opposite leg/x

sin 30 = sqrt (11) / x

x = sqrt (11) / sin 30 =  = 2 sqrt (11) = 6.6 units

Answer:

x=4,-10

Step-by-step explanation:

Move all terms to the left side and set equal to zero. Then set each factor equal to zero.

Answer: x=4 or  x=-10

Step-by-step explain: Factoring  x2+6x-40

The first term is,  x2  its coefficient is  1 .

The middle term is,  +6x  its coefficient is  6 .

The last term, "the constant", is  -40

Step-1 : Multiply the coefficient of the first term by the constant   1 • -40 = -40

Step-2 : Find two factors of  -40  whose sum equals the coefficient of the middle term, which is   6 .

     -40    +    1    =    -39

     -20    +    2    =    -18

     -10    +    4    =    -6

     -8    +    5    =    -3

     -5    +    8    =    3

     -4    +    10    =    6    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -4  and  10

                    x2 - 4x + 10x - 40

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-4)

             Add up the last 2 terms, pulling out common factors :

                   10 • (x-4)

Step-5 : Add up the four terms of step 4 :

                   (x+10)  •  (x-4)

            Which is the desired factorization

A) 122 degrees because it's an obtuse angle so the inner layer numbers is the ones you need to pick.

Answer: number 3 is the answer!!!

Step-by-step explanation:

number 3!!!

1) To find the missing ordered pair of a rectangle, we can use the fact that opposite sides of a rectangle are parallel and equal in length. This means that the x-coordinate of D must be equal to the x-coordinate of A, and the y-coordinate of D must be equal to the y-coordinate of C. Therefore, D(-3, -3).

2) Similarly, we can use the fact that opposite sides of a rectangle are parallel and equal in length. This means that the x-coordinate of H must be equal to the x-coordinate of E, and the y-coordinate of H must be equal to the y-coordinate of F. Therefore, H(0, 0).

3) To find the missing ordered pair of a square, we can use the fact that all sides of a square are equal in length and all angles are right angles. This means that the distance between J and K must be equal to the distance between K and L, which is 4 units. Therefore, the distance between L and M must also be 4 units. Since L has an x-coordinate of 2, M must have an x-coordinate of 2 + 4 = 6. Similarly, since L has a y-coordinate of -2, M must have a y-coordinate of -2 + 4 = 2. Therefore, M(6, 2).

4) To find the missing ordered pair of an isosceles right triangle, we can use the fact that two sides of an isosceles triangle are equal in length and two angles are equal in measure. This means that the distance between P and Q must be equal to the distance between Q and R, which is 6 units. Therefore, R must be 6 units away from Q along the x-axis. Since Q has an x-coordinate of 0, R must have an x-coordinate of 0 + 6 = 6. Similarly, since Q has a y-coordinate of 6, R must have a y-coordinate of 6 - 6 = 0. Therefore, R(6, 0).

The above table of 3 by 3 grid of 9 numbers where 5 numbers are present, the product value of missing numbers in table, i.e, ABCD is equals to the [tex]12 \sqrt{3} .[/tex]

We have a table of 3 by 3 grid of 9 numbers present in above figure. That is table consists 3 rows (horizontal) and 3 columns (vertical). Five numbers are present out of 9 numbers in table. The missing numbers represented by A,B,C and D. We have to determine the product of ABCD. Now, product of the numbers in each row and in each column is the same, so

[tex]2A\sqrt{3 } = AB\sqrt{3}[/tex]

=> B = 2

[tex]6 \sqrt{6} = BC \sqrt{6} [/tex]

=> BC = 6

[tex]2CD \sqrt{3} = D \times 6 \sqrt{3} [/tex]

=> C = 3

Now, the statement that product of the numbers in each row and in each column is the same is valid for all rows and columns. So,

from first two equality, [tex]A = \frac{ 6\sqrt{6}}{2\sqrt{3}}[/tex]

=> [tex] A = 3\sqrt{2}[/tex]

From last two equality, [tex] 6 \sqrt{3} = 2 \sqrt{3} \times CD[/tex]

=> D = 1

Therefore, A = 2√3, B = 2, C =3, D = 1, so compute the product of numbers, ABCD

= [tex] 2×3×1×2 \sqrt{3} = 12 \sqrt{3} [/tex]

Hence, required value is [tex] 12 \sqrt{3} [/tex].

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Complete question:

The above table complete the question. the table above is A 3 by 3 grid of 9 numbers, 5 of which are given. the 4 numbers that are not given are denoted by A, B, C, and D. the product of the numbers in each row and in each column is the same for all rows and columns. what is the value of the product ABCD?