How many months are equivalent to 4 years?

Answer:

D)  $ 300

Step-by-step explanation:

Here, the cost ( in dollars ) of x products is defined by the function,

[tex]C=0.25x^2-80x+300[/tex]

Since, if the no units are produced,

x = 0,

Hence, the cost would be,

[tex]C=0.25(0)^2-80\times 0+300[/tex]

[tex]=0-0+300[/tex]

[tex]=\$ 300[/tex]

Option D is correct.

The cost is $300 if no units are produced.

To find the cost when no units are produced, which are shown by x and we need to evaluate the cost function C at x = 0. The cost function is given by [tex]C = 0.25x^2 - 80x + 300.[/tex]

Let's substitute x = 0 into the function:

[tex]C(0) = 0.25(0)^2 - 80(0) + 300[/tex]

[tex]C(0) = 0 - 0 + 300[/tex]

[tex]C(0) = 300[/tex]

Therefore, the cost when no units are produced is $300.

This corresponds to the constant term in the cost function, which represents the fixed costs that are incurred regardless of the number of units produced.

Answer:

the answer is A

Step-by-step explanation:

Answer:

C The pre-image will be congruent to the image.

Step-by-step explanation:

Answer: The solution is g = 4, -8.

Step-by-step explanation: We are given to solve the following algebraic equation.

[tex]g^2+4g-32=0.[/tex]

Since the above algebraic equation is quadratic, so it will have two solutions.

The solution by the method of factorization is as follows:

[tex]g^2+4g-32=0\\\\\Rightarrow g^2+8g-4g-32=0\\\\\Rightarrow g(g+8)-4(g+8)=0\\\\\Rightarrow (g-4)(g+8)=0\\\\\Rightarrow g-4=0,~~~g+8=0\\\\\Rightarrow g=4, -8.[/tex]

Thus, the required solution is  g = 4, -8.

To determine the time it takes for the computer to sort 10 objects, substitute x with 10 in the given function, resulting in 0.52 seconds, rounded to the nearest hundredth.

The student's question involves determining how long it takes a computer to sort 10 objects, given the function t = 0.005x² + 0.002x, where x is the number of objects and t is the time in seconds. To find out the time it takes to sort 10 objects, we substitute x with 10 into the function.

So, we have:

t = 0.005(10)² + 0.002(10)

t = 0.005(100) + 0.002(10)

t = 0.50 + 0.02

t = 0.52 seconds

Therefore, it takes the computer approximately 0.52 seconds to sort 10 objects, when the result is rounded to the nearest hundredth of a second.

The diameter is increasing at a rate of approximately 100 / 300π cm/s when the radius is 5 cm.

To find the rate at which the diameter is increasing, we need to differentiate the formula for the volume of a sphere with respect to time:

V = (4/3)πr^3

Where V is the volume and r is the radius.

Let's differentiate V with respect to t:

dV/dt = (4/3)π(3r^2)(dr/dt)

We know dV/dt = 100 cm^3/s and r = 5 cm, so plug in these values:

100 = (4/3)π(3(5^2))(dr/dt)

Simplifying the equation gives us:

dr/dt = 100 / (4π(3(5^2)))

dr/dt ≈ 100 / 300π

So, the diameter is increasing at a rate of approximately 100 / 300π cm/s when the radius is 5 cm.

4.32*10^5

To write scientific number must be greater than one but less than 10

The number 4.24 in its decimal form is already a simplified numerical value, it does not require conversion to a simplified radical form, unless it's interpreted as the square root of 4.24.

The student is wanting to know the simplified radical form of 4.24. The student's proposed answer of 106/25 indicates that they are interpreting the number as a fraction. As the number 4.24 is already a decimal, which is a form of a simplified numerical expression, it does not need conversion to a simplified radical form or fraction. A number in radical form typically denotes the square root of a number, for which 4.24 does not have a simple whole number equivalent.

In summary, 4.24 in its decimal expression is already a simplified numerical value. Unless it is interpreted as the square root of 4.24, which represents an entirely different value and is not commonly presented in radical form when it's a decimal.

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The number 4.24 can be simplified to 106/25.

No, actually, you're right!  The decimal number 4.24 can be expressed as the simplified fraction 106/25.

Here is how:

1. First, express the number 4.24 as a fraction, understanding that the number after the decimal point stands for hundredths. Thus, we can write it as 424/100.

2. Next, we need to simplify the fraction. To do that, we find the greatest common divisor (GCD) of 424 and 100. The gcd of 424 and 100 is 4.

3. Now we divide both the numerator and the denominator by the gcd. So, 424 divided by 4 is 106, and 100 divided by 4 is 25.

4. Now we write the simplified fraction as 106/25.

However, it seems there's a misunderstanding in the question. The term 'radical form' usually refers to the square root of a number which we can only do in contrast to perfect square numbers (those whose square root is a whole number). However, the decimal number 4.24 doesn't have a perfect square root, so it can't be expressed in 'radical form'. But, as per your query, 106/25 is the simplified fractional form of 4.24.

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Final answer:

Using equivalent ratios is like adding fractions with unlike denominators as it involves finding a common value to work with.

Explanation:

Using equivalent ratios is similar to adding fractions with unlike denominators because both involve finding a common value to work with. When adding fractions, we look for a common denominator so that we can add the numerators. With equivalent ratios, we find a common multiplier to scale the ratios, which allows us to compare or combine the quantities represented by the ratios.

Here's a step-by-step process:

Convert the given ratios to fractions by writing them as a fraction with the given quantities as the numerator and denominator.

Find a common denominator for the fractions. This involves identifying the least common multiple (LCM) of the denominators.

Multiply the numerators and denominators of the fractions by the appropriate multiples to get equivalent fractions with the same denominator.

Compare or combine the quantities represented by the equivalent fractions.

Answer:

Option B. $155

Step-by-step explanation:

Jay Ward has already been taxed on his earning on $107,600.

So on this paycheck only  ($110,100 - $107,600) = $2,500 of his earnings are taxable for social security tax.

Social security tax rate = 6.2%

Hence, social security tax amount = 6.2% × 2500

                                                         = 0.062 × 2500

                                                         = $155

Option B. $155 is the answer.

Final answer:

The probability of rolling a number less than or equal to 8 with two dice, given at least one die shows a 6, is 5/36, considering all the valid dice combinations that meet the criteria.

Explanation:

The probability of rolling a number less than or equal to 8 with two dice, given at least one must be a 6, is calculated by considering the possible combinations of dice that adhere to these conditions. First, we determine how many outcomes include at least one 6:

If the first die is a 6, the other die can be 1, 2, or a 3 (since 6+4 is already 10, which is greater than 8).

If the second die is a 6, the first die can again be 1, 2, or 3.

Both dice can be 6, which adds one more outcome.

These are mutually exclusive events, therefore we add their probabilities. There are 5 outs of 36 possible rolls (3+3) when the numbers can sum up to less than or equal to 8 with at least one die showing a 6 (1+6, 2+6, 3+6, 6+1, 6+2, 6+3).

The probability of rolling a number less than or equal to 8, given that at least one die shows a 6, is 5/36.

The probability of rolling a number less than or equal to 8 with two dice, given that at least one die shows a 6, is [tex]\( \frac{10}{11} \).[/tex]

To find the probability of rolling a number less than or equal to 8 with two dice, given that at least one of the dice must show a 6, we can use conditional probability.

Let's consider the outcomes where at least one die shows a 6:

- (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)

- (1, 6), (2, 6), (3, 6), (4, 6), (5, 6)

Out of these 11 outcomes, the ones where the sum of the two dice is less than or equal to 8 are:

- (6, 1), (6, 2), (6, 3), (6, 4), (6, 5)

- (1, 6), (2, 6), (3, 6), (4, 6), (5, 6)

So, there are 10 favorable outcomes out of 11 possible outcomes when at least one die shows a 6.

Therefore, the probability of rolling a number less than or equal to 8 with two dice, given that at least one of the dice must show a 6, is [tex]\( \frac{10}{11} \).[/tex]

Answer: the correct answer is D.

Step-by-step explanation:

The total cost of a movie ticket for club members is $20 ($15 membership fee + $5 ticket price) and for non-members it is $8.

To find the total cost of a movie ticket for club members and non-members, we need to consider the membership fee and the ticket price. Let's break it down:

For club members:

For non-members:

To calculate the total cost for club members, we add the membership fee to the ticket price: $15 + $5 = $20.

To find the total cost for non-members, we simply use the ticket price: $8.

The system of equations representing the total cost for a club member (y) and a nonmember (y) after viewing x movies is given by:

y = 15 + 5x

y = 8x

Let's break down the system of equations. For a club member, the total cost (y) is the sum of the membership fee ($15) and the product of the ticket price $5 and the number of movies viewed (x). This relationship is represented by the equation y = 15 + 5x.

On the other hand, for a nonmember, the total cost (y) is solely the product of the ticket price for nonmembers $8 and the number of movies viewed (x), as there is no membership fee. This is expressed by the equation y = 8x.

To find the number of movies (x) after which the total cost (y) for a club member equals the cost for a nonmember, we set the two equations equal to each other:

15 + 5x = 8x

Now, solving for x, we can determine the point at which the total cost for a club member is the same as the cost for a nonmember. This helps in understanding the break-even point where joining the movie club becomes financially advantageous, factoring in the membership fee and the reduced ticket price for club members.

The complete question of the above answer is:

Certainly, here is the complete question:

It costs $15 for a yearly membership to a movie club at a movie theater. A movie ticket costs $5 for club members and $8 for nonmembers.

a. Write a system of equations that you can use to find the number x of movies viewed after which the total cost y for a club member, including the membership fee, is the same as the cost for a nonmember.

Answer:

Its a triangle

The beam reaches approximately 23 feet up the wall.

Given that, a wooden beam is 24 feet in length and makes an angle of 71° with the ground.

We need to determine how high does it touches the wall,

To find the height up the wall reached by the wooden beam, we can use trigonometry.

Let's denote the height as "h".

In a right triangle formed by the wooden beam, the height "h" represents the opposite side, and the length of the beam (24 feet) represents the hypotenuse.

The angle between the ground and the beam is given as 71°.

We can use the sine function to solve for "h" since sine is defined as the ratio of the opposite side to the hypotenuse in a right triangle.

sin(71°) = h / 24

To find "h," we rearrange the equation:

h = sin(71°) × 24

Calculating this, we get:

h ≈ 0.9511 × 24 ≈ 22.8264

Rounding to the nearest foot, the beam reaches approximately 23 feet up the wall.

Learn more about trigonometry click;

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