a grading machine can grade 48 tests in 1 minute. How
long will it take the machine to grade 300 tests?

Compound interest is the interest generated overtime on a sum of money invested. The time it will take for the amount of money to double is 5.9 years

Compound interest is the interest generated overtime on a sum of money invested. The formula for calculating compound interest is expressed as:
V(t) = P(1+r/n)^nt

where:

Given the following

V(t) = 2P
r = 0.12
n = 4

Substitute
2P = P(1+0.12/4)^4t
2 =  (1.03)^4t
ln2 = 4t ln(1.03)
0.6931 = 0.1182t
t = 0.6931/0.1182
t = 5.9 years

Hence the time it will take for the amount of money to double is 5.9 years

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To find the number of miles traveled when the total cost is $51.25, subtract the base cost from the total and divide by the per-mile rate, resulting in 65 miles traveled.

The question asks how many miles were traveled if the total cost for renting a car was $51.25. According to the equation y = 35 + 0.25x, where y represents the total cost and x represents the miles traveled, we first need to subtract the base cost of $35 from the total cost to find out how much is charged for the mileage.

Here is how you calculate it:

Therefore, you were charged for traveling 65 miles.

The absolute value inequality which relates to the expression n is less than 6 units from 0 is |n|< 6

The absolute value which stand for 6 units From 0 can be expressed as :

This means that, the number n is less than 6

Therefore, the expression can be written as :

|n| < 6. This means that the absolute value of n is less than 6.

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To write an absolute value inequality when a number n is less than 6 units from 0, use the notation |n| < 6.

To write an absolute value inequality, we need to express the distance between the number n and 0 as less than 6 units. This can be done by using the absolute value notation: |n| < 6. In this inequality, the absolute value of n must be less than 6 units.

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Answer:

140 button pep club makes per hour.        

Step-by-step explanation:

Given : Pep club members are making spirit buttons. They make 490 spirit buttons in [tex]3\frac{1}{2}[/tex] hours.

To find : The number of button pep club makes per hour ?

Solution :

In  [tex]3\frac{1}{2}[/tex] hours they make 490 buttons.

i.e. In 3.5 hours they make 490 buttons.

So, In 1 hours they make [tex]\frac{490}{3.5}[/tex] buttons.

In 1 hours they make 140 buttons.

Therefore, 140 button pep club makes per hour.

Answer:

[tex]155,850 \leq  x \leq 415,850[/tex]

Step-by-step explanation:

A publisher estimates their costs of publishing a book is from $980,000 to $1,240,000.

Let x be the amount publisher can spend

So, [tex]980000\leq x \leq 1240000[/tex]

Now we are given that  So far, they have spent $824,000

So, [tex](980000-824000)\leq x \leq (1240000-824000)[/tex]

[tex]156000\leq x \leq 416000[/tex]

So, Option D is true

Hence compound inequality correctly expresses how much more the publisher can spend is [tex]155,850 \leq  x \leq 415,850[/tex]

To make 30 cupcakes Margaret needs 4.375 cups of vanilla.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

Given that,

Margaret uses 1 3/4 teaspoon of vanilla to make 12 cupcakes

So,

1 3/4 teaspoon vanilla ⇒ 12 cupcakes

(4×1 + 3)/4 teaspoon ⇒ 12 cupcakes

7/4 teaspoon vanilla ⇒  12 cupcakes

Divide by 12 into both sides,

7/(4×12)  teaspoon vanilla ⇒ 1 cupcake

Now multiply by 30 on both sides,

(7 × 30)/(4 × 12)teaspoon vanilla ⇒ 30 cupcake

30 cupcakes ⇒ 4.375 teaspoon vanilla.

Hence "To make 30 cupcakes Margaret needs 4.375 cups of vanilla".

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Answer:

C ) 35 in2

Step-by-step explanation:

i did the test

Gio should first complete the square by adding and subtracting [tex]\((\frac{3}{2})^2\)[/tex], leading to the equation [tex]\((x + \frac{3}{2})^2 = \frac{25}{4}\).[/tex]

To solve the quadratic equation [tex]\(5x^2 + 15x - 4 = 0\)[/tex] by completing the square, Gio should follow these steps:

1. Make the Coefficient of [tex]\(x^2\) 1:[/tex]

Divide the entire equation by the coefficient of [tex]\(x^2\)[/tex] to make it equal to 1. In this case, divide the equation by 5:

[tex]\[x^2 + 3x - \frac{4}{5} = 0.\][/tex]

2. Move the Constant to the Other Side:

Move the constant term to the other side of the equation:

[tex]\[x^2 + 3x = \frac{4}{5}.\][/tex]

3. Complete the Square:

  Add and subtract [tex]\((\frac{3}{2})^2\)[/tex] inside the parentheses to complete the square:

 [tex]\[x^2 + 3x + (\frac{3}{2})^2 = \frac{4}{5} + (\frac{3}{2})^2.\][/tex]

4. Factor the Perfect Square Trinomial:

  Factor the left side, which now is a perfect square trinomial:

 [tex]\[(x + \frac{3}{2})^2 = \frac{25}{4}.\][/tex]

5. Solve for (x):

  Take the square root of both sides and solve for (x):

[tex]\[x + \frac{3}{2} = \pm \frac{5}{2}.\][/tex]

6. Isolate (x):

  Isolate (x) on one side to find the solutions:

  [tex]\[x = -\frac{3}{2} \pm \frac{5}{2}.\][/tex]

Therefore, Gio should first complete the square by adding and subtracting [tex]\((\frac{3}{2})^2\)[/tex], leading to the equation [tex]\((x + \frac{3}{2})^2 = \frac{25}{4}\).[/tex]

The equation that can be used to determine how long after Car X leaves Car Y will catch up is D. 55x = 60(x - 1).

To determine when Car Y will catch up to Car X, we need to find the time it takes for Car Y to cover the same distance as Car X. Since Car Y leaves 1 hour later, it will travel for (x - 1) hours, where x represents the time Car X has been traveling. So, the equation would be:

D. 55x = 60(x - 1)

This equation accounts for the distance traveled by both cars over the same time frame, considering Car Y started an hour later.

Complete question : Car X leaves Northtown traveling at a steady rate of 55 mph. Car Y leaves 1 hour later following Car X, traveling at a steady rate of 60 mph. Which equation can be used to determine how long after Car X leaves Car Y will catch up? A. 55x=60x-1 B.55x=60x C.60x=55x(x-1) D.55x=60(x-1).

Explanation:

It is convenient to regroup the numbers, and adjust two of them to "make a ten".

  = 13 + 17 + 19 . . . . rearrange (swap the order of 17 and 19)

  = (10 + 3) + (-3 + 20) + 19 . . . . "make a ten" by adding or subtracting a small number. Here, those adjustments cancel—which is the point of doing it.

  = 10 + 20 + 19

  = 30 + 19

  = 49

The positive value of the discriminant implies that there are two real unequal roots and this can be determined by using the formula of the discriminant.

Given :

The quadratic equation is [tex](0=-2x^2+3)[/tex].

The following steps can be used in order to determine the total number of real solutions does the equation have:

Step 1 - Write the given quadratic equation.

[tex]0=-2x^2+0x+3[/tex]

Step 2 - The formula of discriminant is given below:

[tex]D = b^2-4ac[/tex]

where 'b' is the coefficient of 'x', 'a' is the coefficient of [tex]x^2[/tex], and 'c' is the constant.

Step 3 - Now, substitute the values of a, b, and c in the above formula.

[tex]D = (0)^2-4\times (-2)\times 3[/tex]

[tex]D = 24[/tex]

Step 4 - The positive value of the discriminant implies that there are two real unequal roots.

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