a college student takes the same number of credits each semester. before beginning college, the student had some credits earned while in high school. after 2 semesters, the student had 45 credits, and after 5 semesters, the student had 90 credits. if c(t) is the number of credits after t semesters, write the equation that correctly represents this situation.

Answer:

The slope is -2 and the y-intercept is 3

Step-by-step explanation:

Answer:

Y = 25 so 25 x 4 =  100

Step-by-step explanation:

Y = 25

25 x 4 = 100

The most appropriate choice for percentage will be given by-

14 categories can be carried

What is Percentage?

Percentage is a ratio expressed as a percentage of 100.

Total area of selling space = \(2500 ft^2\)

Percentage of space used for isles = \(30\) %

Area of space used for isles = \(\frac{30}{100} \times 2500\)

                                               = \(750 ft^2\)

Area of space left = \(2500 - 750\)

                              = \(1750 ft^2\)

Area of space reserved for each category =  \(125 ft^2\)

No of categories = \(\frac{1750}{125}\)

                            = \(14\)

14 categories can be carried

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Answer:

There are 10 cards in the stack, and 5 of them are odd (1, 3, 5, 7, and 9). There are 3 cards (1, 2, and 3) that are less than 4. Since we are replacing the first card before selecting the second, the outcomes are independent and we can multiply the probabilities of each event.

The probability of selecting an odd card on the first draw is 5/10, or 1/2.

The probability of selecting a card less than 4 on the second draw is 3/10, since there are 3 cards that meet this condition out of a total of 10.

Therefore, the probability of selecting an odd card on the first draw and a card less than 4 on the second draw is:

(1/2) x (3/10) = 3/20

So the probability of selecting an odd card on the first draw and a card less than 4 on the second draw is 3/20.

Step-by-step explanation:

Answer:

3/20.

Step-by-step explanation:

To find the probability of two independent events happening together, we multiply their individual probabilities. The probability of the first card being an odd number is 5/10, because there are 5 odd numbers out of 10 cards. The probability of the second card being less than 4 is 3/10, because there are 3 cards (1, 2, and 3) that are less than 4 out of 10 cards. Therefore, the probability of the first card being an odd number and the second card being less than 4 is:

5/10 x 3/10 = 15/100

We can simplify this fraction by dividing both the numerator and denominator by 5:

15/100 = 3/20

So, the final answer is 3/20.

Received message. To find the probability of two independent events happening together, we multiply their individual probabilities. The probability of the first card being an odd number is 5/10, because there are 5 odd numbers out of 10 cards. The probability of the second card being less than 4 is 3/10, because there are 3 cards (1, 2, and 3) that are less than 4 out of 10 cards. Therefore, the probability of the first card being an odd number and the second card being less than 4 is: 5/10 x 3/10 = 15/100 We can simplify this fraction by dividing both the numerator and denominator by 5: 15/100 = 3/20 So, the final answer is 3/20.

The value of the exponent (2/5)^3 is \(\frac{8}{125}\)

In the above question, it is given that

(2/5)^3

The number of times a number has been multiplied by itself is referred to as an exponent. For instance, the expression 2 to the third (written as 2^3) signifies 2 x 2 x 2 = 8.

We need to solve it and then find the value of the exponent

(2/5)^3

= \(\frac{2}{5}\) x \(\frac{2}{5}\) x \(\frac{2}{5}\)

= \(\frac{2 . 2. 2}{5 . 5 . 5}\)

= \(\frac{8}{125}\)

Therefore the value of the exponent (2/5)^3 is \(\frac{8}{125}\)

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Answer:

4

Step-by-step explanation:

96/4 is 24.

100/4 is 25

Answer:

4

Step-by-step explanation:

4 is the greatest common factor of 96 and 100

96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

100: 1, 2, 4, 5, 10, 20, 25, 50, 100

Answer:

Three ways I experience these benefits is 1, being able to vote in free elections, 2, being able to receive an education, and 3, being able to volunteer for things.

Step-by-step explanation:

The smallest positive integer n whose positive divisors have a product of n^6 is 2^6.

To find the smallest positive integer n satisfying the given condition, we need to consider the prime factorization of n. Since the product of positive divisors is equal to n^6, each prime factor of n must appear with an exponent that is a multiple of 6.

The smallest prime number is 2. If we raise 2 to the power of 6, we get 64, which satisfies the condition. Moreover, there is no smaller prime number that meets the requirement because any smaller prime raised to the power of 6 would result in a larger product.

Therefore, the smallest positive integer n whose positive divisors have a product of n^6 is 2^6, which is equal to 64.

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Answer:

21 hours

Step-by-step explanation:

If he worked 2/3 at home you need to divide 31.5 by 3 = 10.5

Then multiply by 2 = 21

Hope this helps! Have a great day :)

Answer:

0.4 , 0.1

Step-by-step explanation:

Let number of boys be = b , number of girls = b + 4 . As total students = 20    b + b + 4 = 20  → 2b + 4 = 20 → 2b = 20 - 4 = 16 → b = 16 / 2 = 8 (boys) , so girls = 12

Prob (a random first child is a boy) = boys / total students = 8 c 1 / 20 c1, or =  8  / 20  = 0.4

Prob ( a 'Tina' out of two Tina is the last) = 2 c 1 / 20 c 1 , or = 2 / 20 = 0.1

Answer:

x = 3

Step-by-step explanation:

8x -6 = 18

Add 6 to both sides.

8x = 24

Divide both sides by 8 to isolate x.

x = 3

Answer:

72

Step-by-step explanation:

1 stamp costs 0.36 cents

Then, 200 post cards will cost 0.36 × 200 = 72

Answer:

$72 dollars

Step-by-step explanation:

200 x 0.36 = 72

Answer:

3

Step-by-step explanation:

The greatest common divisor (GCD) of two nonzero integers a and b is the greatest positive integer d such that d is a divisor of both a and b (Wikipedia)

To find out which is the GCD of 72 and 159, keep factoring both until they cannot be factored any more

Then take the factors common to both list of factors; the greatest among them is the GCD

The factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

The factors of 159 are: 1, 3, 53, 159

The common factors are 1, 3

So GCD is 3

Assuming that the main product of a business sells for 16000.25x dollars per when x units are sold each week.

Here is the explanation :

(a) The formula for total revenue as a function of x can be obtained by multiplying the selling price per unit by the number of units sold:

R(x) = (1600 - 0.25x) * x

(b) The formula for the total cost as a function of x can be obtained by adding the fixed costs to the cost per unit multiplied by the number of units produced:

C(x) = 400 + (0.7x + 1440) * x

(c) To find the break-even points, we need to determine the values of x where the total revenue equals the total cost. In other words, we need to solve the equation R(x) = C(x).

1600x - 0.25x² = 400 + (0.7x + 1440)x

Simplifying the equation:

1600x - 0.25x² = 400 + 0.7x² + 1440x

Rearranging and combining like terms:

0.95x² + 40x - 400 = 0

We can solve this quadratic equation using the quadratic formula:

\(\begin{equation}x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)

In this case, a = 0.95, b = 40, and c = -400. Plugging in these values, we can find the break-even points.

Calculating using the quadratic formula, we find:

x ≈ 15.739 and x ≈ -22.739

Since we're dealing with the number of units produced every week, we discard the negative solution. Therefore, the smaller break-even quantity is approximately 15.739 units per week.

Substituting this value of x into the revenue function R(x), we can find the corresponding revenue:

R(15.739) ≈ (1600 - 0.25 * 15.739) * 15.739 ≈ $25040.559

The larger break-even quantity is the maximum value of x, which means it occurs at the vertex of the parabolic equation. The x-coordinate of the vertex can be found using the formula x = -b / (2a). In this case, a = 0.95 and b = 40.

\(\begin{equation}x = \frac{-40}{2 \cdot 0.95} \approx 21.053\)

Substituting this value of x into the revenue function R(x), we can find the corresponding revenue:

R(21.053) ≈ (1600 - 0.25 * 21.053) * 21.053 ≈ $35336.842

Therefore, the larger break-even quantity is approximately 21.053 units per week, with corresponding revenue of approximately $35336.842 per week.

(d) The profit function can be obtained by subtracting the total cost function from the total revenue function:

P(x) = R(x) - C(x) = (1600 - 0.25x) * x - (400 + (0.7x + 1440) * x)

Simplifying further:

P(x) = 1600x - 0.25x² - 400 - 0.7x² - 1440x

P(x) = -0.95x² + 1600x - 400

(e) To find the price that maximizes profit, we need to determine the value of x that maximizes the profit function P(x). Since the coefficient of the quadratic term is negative (-0.95), the parabolic function opens downwards and has a maximum value.

The x-coordinate of the vertex of the parabolic

function can be found using the formula \(\begin{equation}x = \frac{-b}{2a}\). In this case, a = -0.95 and b = 1600.

\(\begin{equation}x = \frac{-1600}{2 \cdot -0.95} \approx 842.105\)

Substituting this value of x into the revenue function R(x), we can find the corresponding price:

Price = 1600 - 0.25 * 842.105 ≈ $1378.947

Therefore, the price that maximizes profit is approximately $1378.947 per unit.

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The maximum distance Frank can travel would be 10 miles.

What is maximum distance?

For maximum distance that is maximum range of a projectile, the angle of projectile should be 45°.

From given question,

taxicabs charge for first mile = $1.00

for each additional mile = $0.30

The cost for the first mile is $1, and for each additional mile it's $0.30, so for 10 miles it would be $1 + 9 * $0.30 = $4.70. Since Frank has only $3.50, he can travel a maximum of 10 miles.

Therefore, The maximum distance Frank can travel would be 10 miles.

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Answer:

What do uh mean?.......

A hypothesis is a statement about a population or phenomenon that is testable through experiments or observations.

In statistical hypothesis testing, we have two types of hypotheses: the null hypothesis (H0) and the alternative hypothesis (Ha or H1).

The null hypothesis is a statement that there is no significant difference or relationship between the variables being studied. It represents the default assumption that the observations are due to chance.

For example, the null hypothesis for a study examining the effect of a new drug on blood pressure might be: "The new drug has no effect on blood pressure."

The alternative hypothesis is the opposite of the null hypothesis. It represents the hypothesis that the researcher wants to test and provides evidence against the null hypothesis.

In the same example, the alternative hypothesis might be: "The new drug does have an effect on blood pressure."

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To evaluate the integral ∫7x/(1 − x^4) dx, we first need to perform partial fraction decomposition to separate it into simpler fractions. Using algebraic manipulation.

we can rewrite the integrand as: 7x/(1 − x^4) = A/(1 + x) + B/(1 − x) + C/(1 + x^2) + D/(1 − x^2), where A, B, C, and D are constants to be determined. Then, we can multiply both sides by the common denominator (1 − x^4) and solve for the constants by equating coefficients of like terms.

After performing partial fraction decomposition, we get: ∫7x/(1 − x^4) dx = ∫A/(1 + x) dx + ∫B/(1 − x) dx + ∫C/(1 + x^2) dx + ∫D/(1 − x^2) dx, Integrating each of these simpler fractions individually, we get: ∫A/(1 + x) dx = A ln|1 + x| + c1
∫B/(1 − x) dx = −B ln|1 − x| + c2
∫C/(1 + x^2) dx = C arctan(x) + c3
∫D/(1 − x^2) dx = D ln|(1 + x)/(1 − x)| + c4.

where c1, c2, c3, and c4 are constants of integration, Therefore, the final answer to the given integral is: ∫7x/(1 − x^4) dx = A ln|1 + x| − B ln|1 − x| + C arctan(x) + D ln|(1 + x)/(1 − x)| + C, where A, B, C, and D are the constants obtained from partial fraction decomposition, and C is the constant of integration.

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Answer: First Choice. 3 ( x - 5 )

Step-by-step explanation:

Concept:

When we are doing factoring, we should try to find any Greatest Common Factor (GCF) of all constants in the given expression.

The Greatest Common factor is the largest value of the values you have, that multiplied by the whole number is able to "step onto both".

Solve:

Factors of 3: 1, 3

Factors of 15: 1, 3, 5, 15

As we can see from the list above, 3 appears in both lists of factors and is the greatest for 3. Therefore, [3] is the GCF of 3 and 15

Divide 3 for both numbers to find the remaining.

Check whether or not the remaining can be divisible

Put the factored out 3 and remaining together

Hope this helps!! :)

Please let me know if you have any questions

As the number of people visiting each day is the same 404 people visited on Sunday.

We have,

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, The water park had a total of 1,212 visitors on Friday, Saturday, and Sunday and the number of people who visited on each day is the same.

As the number of visitors is same on each day and the total number of days is three each they the number of people visited is,

= (1212/3).

= 404.

So, On Sunday 404 visitors were there.

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complete question:

The water park had a total of 1,212 visitors on Friday, Saturday, and Sunday. If the same number of people visited each day, how many visitors were there on Sunday

A confidence interval is constructed to estimate the value of a parameter.

In statistics, a parameter refers to a numerical characteristic of a population, such as the population mean or population proportion. When we want to estimate the value of a parameter, we construct a confidence interval.

A confidence interval provides a range of values within which we believe the true parameter value is likely to fall, based on our sample data. It is constructed using sample statistics and takes into account the variability and uncertainty in the estimation process.

A confidence interval is constructed to estimate the value of a parameter, not a statistic.

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s = {(-5, 7)} cannot be a basis for R^2 because it does not satisfy the three requirements of a basis: having at least two linearly independent vectors, containing only linearly independent vectors, and spanning the entire vector space.

The set s = {(-5, 7)} is not a basis for R^2 (the two-dimensional real vector space) for several reasons:

Cardinality: A basis for a vector space must contain at least two linearly independent vectors. Since s contains only one vector, it cannot be a basis for R^2, which has dimension 2.

Linear independence: A basis must contain linearly independent vectors. If a vector in the basis can be written as a linear combination of the other basis vectors, it is not linearly independent, and the set cannot be a basis.

Spanning: A basis must span the entire vector space, meaning that every vector in the vector space can be written as a linear combination of the basis vectors. The set s = {(-5, 7)} does not span R^2 because it contains only one vector, and not every vector in R^2 can be written as a scalar multiple of this vector.

Therefore, s = {(-5, 7)} cannot be a basis for R^2 because it does not satisfy the three requirements of a basis: having at least two linearly independent vectors, containing only linearly independent vectors, and spanning the entire vector space.

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The probability of selecting a human character randomly in the game is \(\frac{1}{3}\)

The probability that a human character will be chosen when the player selects a character randomly can be calculated by dividing the number of human characters by the total number of available characters.

There are 8 animal characters and 4 human characters, making a total of 12 characters to choose from. Therefore, the probability of selecting a human character randomly is:

P(Human) = Number of human characters / Total number of characters

P(Human) = 4 / 12

Simplifying this fraction, we find:

P(Human) = 1 / 3

Therefore, the probability of selecting a human character randomly is 1/3 or approximately 0.333.

In the given scenario, there are a total of 8 animal characters and 4 human characters, making a total of 12 characters to choose from. When a player selects a character randomly, each character has an equal chance of being chosen. Since there are 4 human characters, the probability of selecting one of them is determined by dividing the number of human characters (4) by the total number of characters (12).

When we simplify the fraction 4/12, we find that it is equal to 1/3.

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The radius of the circle is 13 units

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

The circle

Where we have

Center = (0, 0)

Point - (-5, 12)

The radius of the circle is the distance between the point and the center

So, we have

Radius = √[(0 + 5)² + (0 - 12)²]

Evaluate

Radius = 13

Hence, the radius is 13 units

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Answer: 78 pounds

Step-by-step explanation:

10.4/4 = 2.6

2.6 * 30 = 78

Answer

The answer is 12 for sure

Step-by-step explanation:

i just solved it like any other equation

1 i added 3/4 on both sides

2 then i added 5 on both sides

3 after you equation should look like 1 1/4x = 15

4 then i divided and it should be x = 12

pls mark brainliest

The value of x is "12".

\(\to \frac{1}{2}x-5=10-\frac{3}{4}x \\\\\to \frac{1}{2}x+ \frac{3}{4}x=10+5 \\\\\to \frac{2+3}{4}x=15 \\\\\to \frac{5}{4}x=15 \\\\\to x=15 \times \frac{4}{5}\\\\\to x=3 \times 4\\\\\to x=12\)

Therefore, the final value of x is "12".

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The guy wire must be about 55 feet long and the slope of the guy wire, expressed as a fraction is 25/11.

We can use the Pythagorean Theorem to find the length of the guy wire. Let's call the length of the guy wire "g".

g^2 = 50^2 + 22^2

g^2 = 2500 + 484

g^2 = 2984

g ≈ 54.65

So the guy wire must be about 55 feet long.

The slope of the guy wire is the ratio of the vertical distance it covers to the horizontal distance it covers. In this case, the vertical distance is 50 feet (the height of the pole) and the horizontal distance is 22 feet. So the slope is

50/22 = 25/11

Therefore, the slope of the guy wire is 25/11.

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The least common denominator (LCD) of the rational expressions is (x+1)(x-1).

When adding or subtracting rational expressions, we need to find a common denominator. The least common denominator (LCD) is the smallest multiple of the denominators of the rational expressions.

To find the LCD, we follow these steps:

Let's consider an example to illustrate this process:

Example:

Find the LCD of the rational expressions:

x/(x+1) and 1/(x-1)

Step 1: Factor the denominators:

x+1 and x-1

Step 2: Identify the common factors:

There are no common factors in this case.

Step 3: Take the product of the highest powers of each common factor:

Since there are no common factors, we skip this step.

Step 4: Include any unique factors:

The unique factors are x+1 and x-1.

Step 5: Simplify the resulting expression:

The LCD is (x+1)(x-1).

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The least common denominator of the rational expressions in this problem is given as follows:

4x(x + 5).

The rational expressions for this problem are defined as follows:

9/(4x + 20), 10/(x² + 5x).

The denominators are given as follows:

The denominators can be simplified as follows:

The least common denominator is the multiplication of the unique factors, hence it is given as follows:

4x(x + 5).

The expression that completes this problem is given as follows:

9/(4x + 20), 10/(x² + 5x).

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