The grade point average for college students is based on a weighted mean computation. For most colleges, the grades are given the following data values: A (4), B (3), C (2), D (1), and F (0). After 60 credit hours of course work, a student at State University earned 6 credit hours of A, 15 credit hours of B, 31 credit hours of C, and 8 credit hours of D.
a. Compute the student's grade point average. Round your answer to two decimal places.
b. Students at State University must maintain a 2.5 grade point average for their first 60 credit hours of course work in order to be admitted to the business college. Will this student be admitted?

The tables that show a valid probability density function, are tables 1 to 3

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

Table of values

For a table to show a valid probability density function, the following must be true

Sum of P(X = x) = 1

Using the above as a guide, we have the following:

Table 1: Sum = 0.37  + 0.06 + 0.01 + 0.56 = 1

Table 2: Sum = 3/8 + 3/8 + 1/4 = 1

Table 3: Sum = 1/8 + 1/8 + 1/8 + 3/8 + 1/4 = 1

Table 4: Sum = 0.03 + 0.01 + 0.61 + 0.31 + 0.21 = 1.17

Table 5: Sum = 1/10 + 3/10 + 4/5 + 1/5 = 1.4

Hence, the tables are tables 1 to 3

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The value of sin -1(square root 2/2) is π/4 or 45 degrees.

Inverse sine, also known as arcsine, is a trigonometric function that is the inverse of the sine function. It is denoted as sin^-1(x), where x is a number between -1 and 1.

The inverse sine function is used to find the angle in a right triangle that has a given sine value. In other words, if we know the ratio of the length of the side opposite an angle to the length of the hypotenuse in a right triangle, we can use the inverse sine function to find the measure of that angle.

The inverse sine function returns an angle in radians, which can be converted to degrees if needed. It has a domain of -1 ≤ x ≤ 1 and a range of -π/2 ≤ sin^-1(x) ≤ π/2.

Like other inverse trigonometric functions, the inverse sine function is a multivalued function. This means that for a given value of x, there can be multiple angles that satisfy sinθ = x. To address this, the principal value of the inverse sine function is defined as the angle between -π/2 and π/2 that satisfies sinθ = x.

The inverse sine function has many applications in mathematics, physics, engineering, and other fields. It is used in the calculation of angles in a variety of contexts, such as in the design of structures and in the analysis of wave phenomena. It is also used in calculus and other advanced mathematics courses to solve integrals and differential equations.

To see why, we can use the definition of the inverse sine function, which gives us the angle whose sine is equal to the input value. In this case, we have:

sin -1(square root 2/2) = θ

where sin(θ) = square root 2/2.

We know that the sine of 45 degrees (or π/4 radians) is also equal to square root 2/2. Therefore, we have:

sin(45 degrees) = square root 2/2

Taking the inverse sine of both sides gives us:

sin -1(square root 2/2) = 45 degrees = π/4

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There are 16 sweets that are fizzy and orange and the fraction is 4/15

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

Fizzy = 2/5

Orange = 4/6 of Fizzy

So, we have

Orange = 2/5 * 4/6

Orange = 4/15

Using (a) as a guide, we have

Fizzy and orange​ = 4/15 * 60

Fizzy and orange​ = 16

Hence, the fizzy and orange​ is 16

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The original number that satisfies the condition the square of a non-zero number is equal to 68% of the original number is 1.68.

Variables and constants are used to create algebraic expressions using a variety of techniques.

It is a mathematical expression made up of terms and includes variables, constants, and algebraic operations like addition, subtraction, etc. When operations like addition, subtraction, multiplication, division, etc. are performed on any variable, the resulting equations are called algebraic expressions.

An algebraic expression (or variable expression) is the name given to a grouping of terms that have undergone operations including addition, subtraction, multiplication, and division.

Let us suppose a non zero number = x.

Given that, the square of a non-zero number is equal to 68% of the original number.

This can be represented algebraically as follows:

x² = x(1 + 68/100)

x² = x(1 + 0.68)

x² = x(1.68)

x = 1.68

Hence, the original number that satisfies the condition the square of a non-zero number is equal to 68% of the original number is 1.68.

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Answer:

Step-by-step explanation:

(a) To find the minimum possible mass of the four barrels, we want to arrange them in a way that minimizes the total mass. One way to do this is to put the two lightest barrels together and the two heaviest barrels together. This way, the total mass is minimized because the lighter barrels balance out the heavier ones.

So, the minimum possible mass of the four barrels is:

2(30 kg) + 2(30 kg) = 120 kg

(b) To find the maximum possible mass of the four barrels, we want to arrange them in a way that maximizes the total mass. One way to do this is to put the heaviest barrel with the lightest barrel and the other two barrels together. This way, the total mass is maximized because the heaviest and lightest barrels are paired together, making the total mass greater than if they were all paired together.

So, the maximum possible mass of the four barrels is:

30 kg + 90 kg + 30 kg + 30 kg = 180 kg

The correct equation of the table is John's

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

John: y = -6x + 510

Jim: y = 6x + 51

From the table (see below), we have the following x and y values

x = 0, 1, 2, 3, 4

y = 510  504  498 492 486

Next, we test the equations:

John: y = -6x + 510

Substitute the known values in the above equation, so, we have the following representation

y = -6(0) + 510 = 510

y = -6(1) + 510 = 504

y = -6(2) + 510 = 498

y = -6(3) + 510 = 492

y = -6(4) + 510 = 486

Jim: y = 6x + 51

y = 6(0) + 51 = 51

y = 6(1) + 51 = 57

y = 6(2) + 51 = 63

y = 6(3) + 51 = 69

y = 6(4) + 51 = 75

The above shows that John's y values corresponds to the table of values added at the end of the equation.

Jim would be correct if the table of values is:

x = 0, 1, 2, 3, 4

y = 51  57  63 69 75

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Complete question

Given the table of values

x    y

0   510

1    504

2   498

3   492

4   486

John says that the function representing the table is y = -6x + 510

Jim says that the function representing the table is y = 6x + 51

Who’s is correct?

The key features of this rational function include the following:

Domain: (-∞, 2) ∪ (2, ∞)

Range: (-∞, 1) ∪ (1, ∞)

Y-intercept: 1.

X-intercept: 2.

Vertical asymptote: x = -2.

Horizontal asymptote​: y = -1.

In Mathematics, a rational function simply refers to a type of function  which is expressed as a fraction. This ultimately implies that, a rational function is composed of two (2) main parts and these include the following:

Additionally, the vertical extent of any graph of a rational function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

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Answer:

B 16

Step-by-step explanation:

It will take 8 days to eat one carton so 2 cartons will be 16 days.

Answer: Sherry wants to buy at least 2 movies and at least 8 songs, and her gift card has a value of $25. To represent this information as a system of inequalities, we can use the following:

Let x be the number of movies Sherry buys, and y be the number of songs she buys.

The cost of buying x movies is 5.99x dollars, and the cost of buying y songs is 0.99y dollars. Since Sherry's gift card is worth $25, we have the inequality:

5.99x + 0.99y ≤ 25

In addition, Sherry wants to buy at least 2 movies, which means x must be greater than or equal to 2. She also wants to buy at least 8 songs, which means y must be greater than or equal to 8. This gives us the inequalities:

x ≥ 2

y ≥ 8

Therefore, the system of inequalities that represents the number of movies and songs that Sherry can download is:

x ≥ 2

y ≥ 8

5.99x + 0.99y ≤ 25

The answer is (A).

Step-by-step explanation:

Answer:

it dude

Step-by-step explanation:

use internet

The individual events are dependent. The probability of the combined event is of:

0.0137 = 1.37%.

The mass probability formula is presented as follows:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

As the students are chosen without replacement, the events are dependent.

The parameter values for this problem are given as follows:

N = 72 students, k = 18 seniors, n = sample size of 3.

The probability of three seniors is P(X = 3), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 3) = h(3,72,3,18) = \frac{C_{18,3}C_{54,0}}{C_{72,3}} = 0.0137[/tex]

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Using Chebyshev's Theorem, considering a standard deviation of 40, we have that at least 75% of the students scored between 360 and 520.

When we have no information about the population distribution, Chebyshev's Theorem is used. It states that:

At least 75% of the measures are within 2 standard deviations of the mean.

At least 89% of the measures are within 3 standard deviations of the mean.

An in general terms, the percentage of measures within k standard deviations of the mean is given by.

here, we have,

In this problem, considering a standard deviation of 40, we have that:

440 - 2 x 40 = 360.

440 + 2 x 30 = 520.

Within 2 standard deviations of the mean, no information about the distribution, hence, at least 75% of the students scored between 360 and 520.

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The solution to the ordinary differential equation y' - y = 3 · t is the equation [tex]y(t) = C\cdot e^{t} + A\cdot t + B[/tex], where C, A and B are real numbers.

Differential equations are equations that involves functions and its derivatives. In this case we have an example of a first order linear non-homogeneous ordinary differential equation, whose standard form is introduced below:

y' - y = 3 · t

Given the linearity of the differential equation, the solution of the differential equation is the sum of the homogeneous component and the particular component. First, we must determine the homogeneous component:

y' - y = 0

y' = y

dy / dt = y

dy / y = dt

∫ dy / y = ∫ dt

ln y = t + C

[tex]y = C \cdot e^{t}[/tex], where C is the integration constant.

Second, find the particular component:

f(t) =3 · t → yP(t) = A · t + B, where A, B are real coefficients.

Third, write the complete solution:

[tex]y(t) = C\cdot e^{t} + A\cdot t + B[/tex]

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The answer comes to $43,592.00. 28 can be wiped from the account after 20 years, leaving nothing behind.

Think about taking out a $1,000 loan with a seven-year, 10% interest rate. The first year's interest would cost you $100. You would pay $1,100 in interest the next year, which is the sum of the initial amount plus interest. Because of this, your salary for the upcoming year will be $110 (1,100 times 0.10).

Calculate the Yearly Amount (A) given the Prepaid Value (P), at interest rate I over n periods using the equation (A/P, I n).

The equation is:

[tex]A=P \frac{i(1+i)^n}{(1+i)^n-1}[/tex]

Where:

P is the Present value = $500,000

A is the monthly Amount

i is the interest rate = 0.06

20 years are the number of periods (n).

Substituting values:

[tex]A=\$ 500,000 \frac{0.06(1.06)^{20}}{(1.06)^{20}-1}=\$ 43,592.28[/tex]

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Answer:

90  berries

Step-by-step explanation:

The fraction of these 36 chemical elements that are named for women or places is 27/36 or by simplifying it, 3/4.

A fraction is defined as a mathematical concept that can be used to express a portion of a whole or a number that can be written as the ratio of two integers.

Here,
To find the fraction of the 36 chemical elements that are named for women or places, we need to add the number of elements named for women (2) and the number of elements named for places (25), and then divide by the total number of elements (36),

Fraction = (2 + 25) / 36 = 27 / 36

Therefore, the fraction of these 36 chemical elements that are named for women or places is 27/36 or simplify it, 3/4.

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Answer:

it depends on how many students?

Step-by-step explanation:

The marginal revenue at 8 units is given as follows:

MR(8) = 288 dollars per unit.

The revenue function is defined as follows:

R(q) = -7q² + 400q.

The marginal revenue function is the derivative of the revenue function, hence it is obtained as follows:

MR(q) = -14q + 400.

At 8 units, the marginal revenue is found with the numeric value of MR(q) at q = 8, hence:

MR(8) = -14(8) + 400 = 288 dollars per unit.

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Answer:

60

Step-by-step explanation:

a tringle always adds ups to 180 add them then subtract.

The values of h is v3 in span fv1; v2g and h is fv1; v2; v3g is 4.

If we have given a vector v of initial point A and terminal point B

v = ai + bj

then the components form as;

AB = xi + yj

Here, xi and yj are the components of the vector.

We are given that;

v1 and v2 are not scalar multiples to each other

So, they are not linearly dependent

Now,

1(10h -42) -3(-14 +3h) +2 (18-20) =0

10h -9h-4 =0

h = 4

Therefore, by vectors the answer will be 4 so that the vector v3 is in {v1,v2}.

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We can conclude that -

A test statistic measures the degree of agreement between a sample of data and the null hypothesis.

Given is that you are testing the claim that the mean GPA of night students is different from the mean GPA of day students

T scores (or T statistics) are used to test the difference between a

sample mean and another sample mean or some theoretical value.

So, we can write the T score as -

T{score} = 3.06 - 2.83

T{score} = 0.23

DF = 0.82 - 0.45

DF = 0.37

Level of significance = 10%

We can write the p - value as -

p - value = 0.89

Also -

The result is not significant at p < 0.10.

Therefore, we can conclude that -

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As we discovered in chapter, there is a 1/12 chance of getting a 3.

By reducing the number of successful effects by the total amount of possible outcomes, probability—the chance that a will occur—is determined. A coin toss serves as the most fundamental example. There are just two results when users flip a coin: either it shows up heads or tails.

There are 12 potential results in total because the die has 12 sides.

(1) Since there is only one side of the die with a 3 on it and all sides are equally probable, the chance of rolling the die and having the 3 face on top is 1/12.

(2) The likelihood that the die will fall on top with a 3 or a 7 is calculated as the product of the odds of rolling a 3 and a 7 minus the likelihood of simultaneously rolling a 3 and a 7. (which is zero, since the die has only one side).

As we discovered in chapter, there is a 1/12 chance of getting a 3. (1). Given that the dice only has a 7 on one side, the likelihood of getting a 7 is also 1/12. The likelihood of tossing the dice and having the 3 or 7 face up is therefore:

1/12 + 1/12 - 0 = 1/6

(3) Since the die doesn't have a face marked "15," there is no chance that tossing the die will result in a 15 face landing on top.

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Answer:

2.7 cm

Step-by-step explanation:

We have the relationship
tan 56 = 4/z

Therefore z = 4/ (tan 56) = 4/1.48256 = 2.698
= 2.7 cm correct to one decimal place

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{70})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{100}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{100}-\stackrel{y1}{70}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{2}}} \implies \cfrac{ 30 }{ 2 } \implies 15[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{70}=\stackrel{m}{ 15}(x-\stackrel{x_1}{2}) \\\\\\ y-70=15x-30\implies {\Large \begin{array}{llll} y=15x+40 \end{array}}[/tex]

The true statements about the populations of the town based on the linear equations in the table are;

A linear equation is an equation of the form; y = m·x + c, where the slope of the graph of the equation is m and the y-intercept of the graph is c.

The analysis of the equations in the table are as follows;

Equation for Pinehill is; P = 800 - 20t

The slope of the above equation is; -20 and the y-intercept is 800. The negative sign for the slope indicates that the population is decreasing;

Therefore, the initial population of 800 in Pinehill is decreasing at a rate of 20 per unit time, t

Population for Rye; P = 500 + 15t

The population of Rye is increasing at a rate of 15 per unit time

Population for Smithfield; P = 10t + 950

The population of Smithfield is increasing at a rate of 10 per unit time

Population for Troy; P = -50·t + 600

The -50 indicates that population is decreasing at a rate of 50 per unit time

The true statements are therefore;

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Answer:

------------------------------

As per question we have:

Find the required segment length using segment addition rule:

Answer:

while True:

   user_input = input("Please enter a sequence of comma-separated numbers: ")

   if user_input.replace(",", "").isdigit():

       break

   print("Invalid input! Please try again.")

num_list = user_input.split(",")

num_list = [int(num) for num in num_list]

total_sum = sum(num_list)

print("The sum of the numbers is:", total_sum)

Step-by-step explanation:

This program uses a while loop to repeatedly ask the user for input until they provide a valid sequence of comma-separated numbers (all-digit input). The .isdigit() function is used to check if the input is all-digit. If the input is valid, the program splits the input string at each ',' using the .split() function, converts each item in the resulting list into an integer using list comprehension, then adds all numbers together using the sum() function. Finally, the program outputs the total sum.

The value of the expression 3 (x - y) is 12

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

x - y = 4

Multiply both sides of the equation by 3

So, we have the following representation

3 * (x - y) = 4 * 3

Evaluate the products

This gives

3 (x - y) = 12

Hence, the soluton of 3 (x - y) is 12

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The height of the balloon is 1.3 miles above the ground.

Height is the measure of vertical distance, either how "tall" something or someone is, or how "high" the point is. For example, a person's height is typically measured using a stadiometer and is recorded in centimeters or feet and inches. The height of a mountain is usually measured in meters or feet. In aviation, height is measured from the surface of the earth, either above ground level (AGL) or above mean sea level (AMSL).

The answer to this question can be found by using the trigonometric formula of Tangent. To calculate the height of the balloon, we must find the length of the hypotenuse in the triangle formed by the two towns and the balloonist.

Using the formula for tangent, we can calculate the length of the hypotenuse. The formula is:

tan (angle) = opposite side/adjacent side

In this case, the opposite sides are the two towns, and the adjacent side is the height of the balloon.

For the first town, the formula is:

tan 36° = 1.6/x

Solving for x, we can calculate the length of the hypotenuse for the first town to be 2.8 miles.

For the second town, the formula is:

tan 32° = 1.6/x

Solving for x, we can calculate the length of the hypotenuse for the second town to be 2.9 miles.

Since the hypotenuse is the total distance between the two towns and the balloonist, the height of the balloon can be calculated by subtracting the total length of the two towns (1.6 miles) from the hypotenuse of the second town (2.9 miles).

The height of the balloon is 1.3 miles above the ground.

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Answer:

What is height?

Height:

When a rectangle is drawn with horizontal and vertical sides, the word height makes it clear which dimension is meant; height labels how high (how tall) the rectangle is. That makes it easy to indicate the other dimension—how wide the rectangle is from side to side—by using the word width. And if the side-to-side measurement is greater than the height, calling it the length of the rectangle is also acceptable, as it creates no confusion.

The answer to this question can be found by using the trigonometric formula of Tangent. To calculate the height of the balloon, we must find the length of the hypotenuse in the triangle formed by the two towns and the balloonist.

Using the formula for tangent, we can calculate the length of the hypotenuse. The formula is:

tan (angle) = opposite side/adjacent side

In this case, the opposite sides are the two towns, and the adjacent side is the height of the balloon.

For the first town, the formula is:

tan 36° = 1.6/x

Solving for x, we can calculate the length of the hypotenuse for the first town to be 2.8 miles.

For the second town, the formula is:

tan 32° = 1.6/x

Solving for x, we can calculate the length of the hypotenuse for the second town to be 2.9 miles.

Since the hypotenuse is the total distance between the two towns and the balloonist, the height of the balloon can be calculated by subtracting the total length of the two towns (1.6 miles) from the hypotenuse of the second town (2.9 miles).

The height of the balloon is 1.3 miles above the ground.

The least number of bars of soap that must be made on any given day for the factory to make a profit that day is 369 bars.

Two expressions in an equation are combined using the equal symbol ("="). The "left-hand side" and "right-hand side," respectively, of the equation refer to the two expressions that are on either side of the equals sign. Usually, we consider an equation's right side to be zero.

We have the equation ,

y = 0.84 x + 428

Let n be the least number of bars required to make a profit.

then,

2n = 0.84n + 428

dividing both sides by 2

n = 0.42n + 214

0.58n = 214

n = 368.96

n ≈ 369 bars

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