Tanya is printing a report. There are 100 sheets of paper in the printer, and the number of sheets of paper p left after t minutes of printing is given by the function p(t) = -8t + 100. How many minutes would it take the printer to use all 100 sheets of paper?

To find the equation of the line passing through the point (-1, 4) with slope 4, we use the point-slope form. Substituting the values into the formula, we find the equation to be y = 4x + 8.

In the given question, we have a line that passes through the point (-1, 4) and has a slope of 4.

To find the equation of this line, we can use the point-slope form, which is given by y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.

Substituting the values into the formula, we get y - 4 = 4(x - (-1)). Simplifying further, we have y - 4 = 4x + 4. Rearranging the equation, we find the equation of the line to be y = 4x + 8.

Answer:

The answer is 150%

Step-by-step explanation:

Amount of pay day loan = $1460

Also given is that the payday loan for $1460 due in 15 days that charges a $90 fee.

Per day it will charge = [tex]\frac{90}{15}=6[/tex] dollars

For a year it will charge = [tex]365\times6=2190[/tex]

Thus for the due amount of $1460, it will be charged on a rate of =

[tex]\frac{2190}{1460} \times100[/tex] = 150%

Therefore, the APR is 150%.

Iron is typically alloyed for commercial uses because it reacts easily with air and water, leading to corrosion. By creating alloys such as steel with added elements like carbon and chromium, iron becomes more robust and rust-resistant, lending itself to a wider range of applications.

The reason iron is usually made into an alloy for commercial uses is that iron reacts easily with air and water, which is option C. Commercial alloys of iron, like steel, are produced by adding elements such as carbon and metals like manganese, chromium, nickel, tungsten, molybdenum, and vanadium. These elements create an alloy that is more resistant to corrosion (rusting), and they can be engineered to have different properties suitable for specific applications. For example, stainless steel contains chromium which helps in forming a protective oxide layer on the surface, thereby protecting the base iron from rusting.

While wrought iron, which is a commercially pure iron containing less than 0.2% carbon, is quite resistant to rust and is malleable and ductile, it has largely been replaced by mild steel. Mild steel, though not as corrosion-resistant as true wrought iron, is more cost-effective and widely available. Therefore, the commercial use of iron predominantly involves its transformation into alloys that benefit from enhanced strength, durability, and corrosion resistance.

The area of rectangular piece that is 21 inches long and 13 inches wide is 273 square inches

The area of rectangle is -

A = L x B

Given is a rectangular piece that is 21 inches long and 13 inches wide

We can calculate the area using the formula -

Area = Length x Width

A = 21 x 13

A = 273 square inches

Hence, the area of rectangular piece that is 21 inches long and 13 inches wide is 273 square inches

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Answer: true.

Step-by-step explanation: do you really want an explanation?

-6 + (-5) +7

just add from left to right:

 1st step:

-6 + (-5) = -11

 2nd step:

-11 +7 = -4

Answer:

D

Step-by-step explanation:

Just did it

writing this in equation form you have 160% times X = 40

so 160% * x =40

160% as a decimal = 1.60

 so 1.60 * x = 40

to find x divide both sides by 1.6

40 /1.6 = 25

 the number is 25

With equal distribution of blueberries and grapes, Mr. Rodriguez can pack maximum of 10 bags of snacks.

Ratio is a quantitative relation between two amounts showing the number of times one value contains or is contained within the other.

Given is that Mr. Rodriguez is packing bags of snacks for his children’s lunchboxes and for that he has 20 blueberries and 30 grapes.

Now, we have -

Number of blueberries = n[b] = 20 blueberries

Number of grapes = n[g] = 30

For equal distribution, there should be a ratio of → n[b]/n[g] = 20/30 = 2/3

Or we can write it as 2 : 3. This means that in each box there should be 2 blueberries and 3 grapes.

The maximum number of bags [x] that Mr. Rodriguez can pack can be calculated as -

2x + 3x = 20 + 30

5x = 50

x = 10

Therefore, with equal distribution of blueberries and grapes, Mr. Rodriguez can pack 10 bags of snacks.

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Answer:

D. There's a problem with changing the mixed number to an improper fraction, as well as changing the division problem to multiplication.

Step-by-step explanation:

We have shown work of a student to solve a division of fractions. We are asked to check student's work.

Let us check

[tex]2\frac{6}{7}\div\frac{2}{7}[/tex]

Convert mixed fraction into improper fraction:

[tex]2\frac{6}{7}\Rightarrow \frac{2\times 7+6}{7}=\frac{14+6}{7}=\frac{20}{7}[/tex]

[tex]\frac{20}{7}\div\frac{2}{7}[/tex]

Convert division problem to multiplication problem by flipping the 2nd fraction:

[tex]\frac{20}{7}\times\frac{7}{2}[/tex]

[tex]\frac{20}{1}\times\frac{1}{2}[/tex]

[tex]\frac{20}{2}[/tex]

[tex]10[/tex]

Therefore, the student made two mistakes and option D is the correct choice.

The solution for the division of 1.2 by .3 is 4. This can be visualized by considering how many times .3 fits into 1.2, or by dividing equivalent decimals.

To solve the problem 1.2 divided by .3, simply divide the numbers as you would normally. For this problem, 1.2 divided by .3 equals 4. This is because the fundamental basis of division is how many times one number fits into another. In this case, .3 'fits' into 1.2, four times.

Alternatively, you can think of this process in three steps: First, convert 1.2 to an equivalent decimal of 12 tenths. Then, divide that by .3 (or 3 tenths). The result is 4 because 3 tenths 'fits' into 12 tenths, four times.

Another way to cross-verify your result is by multiplying the divisor (.3) by the quotient (4). The product should be equal to the dividend (1.2). Here, .3 multiplied by 4 equals 1.2, hence confirming the correctness of the answer.

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Final answer:

To divide 1.2 by 0.3 in a model, first convert the decimal numbers to fractions. Then, divide the numerator by the denominator to get the answer, which is 4.

Explanation:

To divide 1.2 by 0.3 in a model, we can use a similar approach to the example given. Let's first convert the decimal numbers into fractions by using the place value of the decimal places. 1.2 is equivalent to 12/10 and 0.3 is equivalent to 3/10.

Next, we can set up a division problem where the numerator is 12 and the denominator is 3, giving us 12 ÷ 3. This can be simplified to 4, so 1.2 divided by 0.3 in the model is equal to 4.

Therefore, the answer to 1.2 divided by 0.3 in the model is 4.