2. Lucy opens a savings account with $300 that pays 2.45% interest compounded quarterly.
Part A. Write an equation to represent the balance of Lucy's saving account after tt years.
Part B. How much money will be in Lucy's savings account after 15 years?
3. Felipe signs up for a new airline credit card that has 24% annual interest rate. If he doesn't pay his monthly
statements, interest on his balance would compound daily. If Felipe never pays his statements for a full year, what
would be the actual percentage rate he would pay the credit card company?

The composite functions  are (A + B)(x) = x² + 2x + 4. and (AB)(x) = 2x³ - x² + 10x - 5.

To find (A + B)(x), we add the two functions A(x) and B(x):

(A + B)(x) = A(x) + B(x)

So, we have

= x² + 5 + 2x - 1 (substituting the given expressions for A(x) and B(x))

= x² + 2x + 4

Therefore, (A + B)(x) = x² + 2x + 4.

To find (AB)(x), we multiply the two functions A(x) and B(x):

(AB)(x) = A(x)B(x)

= (x² + 5)(2x - 1) (substituting the given expressions for A(x) and B(x))

= 2x³ - x² + 10x - 5

Therefore, (AB)(x) = 2x³ - x² + 10x - 5.

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To find the area of the shaded region subtract the unshaded region from the total area, so we got 87.

Square Area equals Side x Side. The square's size is therefore equal to side square units. and a square's circumference equals four side units.

To find the area of the shaded region first we need to find the sum of the area of all quadrilaterals and then subtract the area of the unshaded region.

Area of first quadrilateral A1  = [tex]16^{2}[/tex] = 256

Area of first quadrilateral A2  = [tex]3^{2}[/tex] = 9

Area of first quadrilateral A3  = [tex]3^{2}[/tex] = 9

Area of first quadrilateral A4  = [tex]19^{2}[/tex] = 361

To find the area of the shaded region subtract the unshaded region from the total area = Area of first quadrilateral A4 - (Area of first quadrilateral A1  + Area of first quadrilateral A2 + Area of first quadrilateral A3)

= 361 - (9 + 9 + 256)

=87

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The total possible outcomes are 36 and the probability of rolling a 5 and a 6 is 2.78 approximately.

What is dice?

Dice are small objects with different numbers of dots or pips on each side used in games of chance or strategy. Most commonly, dice are cubes with each of the six faces marked with a different number of pips from one to six. When rolled, the number that appears on the top face of the die is used to determine the outcome of the game or the action of the player.

Dice are used in a wide variety of games, including board games, tabletop games, role-playing games, and gambling games. They can also be used for randomization in decision-making or statistical analysis. Some games use dice with more or less than six sides, with various shapes and markings, or even electronic versions that simulate rolling.

When rolling two six-sided dice, the total number of possible outcomes is 6 x 6 = 36, as there are 6 possible outcomes for each die.

To determine the probability of rolling a 5 and a 6, we first need to determine the number of ways this outcome can occur. There is only one way to roll a 5 and a 6, which is to have one die show a 5 and the other die show a 6.

So, the probability of rolling a 5 and a 6 is

P(rolling a 5 and a 6) = number of ways to roll a 5 and a 6 / total number of possible outcomes

= 1 / 36

Therefore, the probability of rolling a 5 and a 6 is 1/36, or approximately 0.0278, or about 2.78%.

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The 99% confidence interval for the proportion of GSU Juniors who believe that they will, immediately, be employed after graduation is (0.835, 0.866), option B.

In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts. So, it may be concluded that there is a 95% likelihood that the real value falls within that range if a point estimate of 10.00 is produced using a statistical model with a 95% confidence interval of 9.50 - 10.50.

Confidence intervals are used by statisticians and other analysts to comprehend the statistical significance of their estimates, conclusions, or forecasts. One cannot reasonably assert that a result from data produced by testing or experimentation is to be ascribed if a confidence interval involves the value of zero.

Confidence interval for Population Proportion is given as below:

Confidence Interval = [tex]p \pm Z\sqrt{\frac{p(1-p)}{n} }[/tex]

Where, p is the sample proportion, Z is critical value, and n is sample size.

We are given

x = number of items/observations of interest = 3010

n = sample size = 3539

Best Point Estimate = p = x/n

= 3010/ 3539

= 0.850522747

Confidence level = 99%

Critical Z value = 2.5758

(We can find this z-value by using R, excel, z-table, Ti-83/84 calculator, software, etc.)

[Excel command: =NORMSINV(1 - (1 - 0.99)/2)]

Confidence Interval = [tex]p \pm Z\sqrt{\frac{p(1-p)}{n} }[/tex]

Confidence Interval = [tex]0.850522747 \pm 2.5758 \sqrt{\frac{0.850522747(1-0.850522747)}{3539} }[/tex]

Confidence Interval = 0.850522747 ± 2.5758 x 0.0060

Confidence Interval = 0.850522747 ± 0.015

Lower limit = 0.850522747 - 0.015 = 0.835

Upper limit = 0.850522747 + 0.015 = 0.866

Confidence interval = (0.835, 0.866)

B. (0.835, 0.866).

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Complete question:

The ability to find a job after graduation is very important to GSU students as it is to the students at most colleges and universities. Select one answer 10 points Suppose we take a poll (random sample) of 3539 students classified as Juniors and find that 3010 of them believe that they will find a job immediately after graduation What is the 99% confidence interval for the proportion of GSU Juniors who believe that they will, immediately, be employed after graduation A. (0.839, 0.862) B.O(0.835, 0.866) C. (0.845, 0.857) D.O(0.841, 0.86)

Answer:

The ladder is approximately 9.75ft from the building

Step-by-step explanation:

We can use Pythagoras theorem:

[tex]c^2=a^2+b^2[/tex]

where:

[tex]c =[/tex] it's the size of the ladder, 12ft

[tex]b=[/tex] it's the top of the ladder above the ground, 7ft

so:

[tex]c^2-b^2=a^2\\\implies a=\sqrt{c^2-b^2}\\ a=\sqrt{(12)^2-(7)^2}\\a=\sqrt{95}\\ a\approx 9.75ft[/tex]

[tex]\text{-B$\mathfrak{randon}$VN}[/tex]

Answer: a. x ≤7 b. x<6

Step-by-step explanation:

a. 6x-3≤4x+11

6x-4x≤11+3

2x≤14

x≤7

b. x<-x+12

x+x<12

2x<12

x<6

Answer:

Step-by-step explanation:

We are given that the quadratic function has the equation:

y = a(x + 6)(x - 2)

To find the value of a, we can use the fact that the function passes through the point (3, 36). This means that when x = 3, y = 36. Substituting these values into the equation, we get:

36 = a(3 + 6)(3 - 2)

36 = 9a

a = 4

Therefore, the value of a is 4.

The musical theater group should charge $14.25 per ticket to maximize revenue. To find the ticket price that maximizes revenue, we need to determine the revenue function and then differentiate it with respect to the ticket price to find the critical points.

We can then evaluate the revenue at these points to determine the maximum. Let x be the number of dollars charged for admission above the base price of $7.75, and let y be the number of tickets sold at that price. Then, the revenue function is given by:

R(x) = (1200 - 50x)(7.75 + x)

Expanding this expression, we get:

R(x) = 9300 + 650x - 50x^2

To find the ticket price that maximizes revenue, we need to find the critical points of the revenue function. We can do this by differentiating the revenue function with respect to x and setting the derivative equal to zero:

R'(x) = 650 - 100x = 0

Solving for x, we get:

x = 6.5

This means that the additional charge above the base price that maximizes revenue is $6.50. Therefore, the ticket price that maximizes revenue is:

7.75 + 6.50 = $14.25

So, the musical theater group should charge $14.25 per ticket to maximize revenue.

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Answer:

A

Step-by-step explanation:

If bottles of soda are marked S, and one bottle costs $1,75

And slices of pizza - P, and one slice costs $3,5

Then the equation would be:

3,50p + 1,75s = 35,00

Answer:

25°, 65°, and 90°

Step-by-step explanation:

To form a triangle the 3 angles must sum to 180 degrees.

Answer:

Both are correct as we can transform one from the other.

Step-by-step explanation:

The equations describe the relation between the distance(m)  speed (9) and time (h),

distance = speed * time

m = 9h

Divide both sides by 9:

m/9 = h

h = (1/9) m

This value of x doesn't satisfy the Equation we set up earlier (59 + 2x = 360). So, we must conclude that this value of x is incorrect, and the value we found earlier (x = 150.5) is the correct one.

Let's start with the given information: we have two arc measures and an angle measure. We know that the sum of the arc measures is equal to the total circumference of the circle, which is 360 degrees. So, we can set up an equation:

59 + 2x = 360

Solving for x, we get:

2x = 301

x = 150.5

So, the value of x that makes one arc measure 2x and the other arc measure 59, and the angle measure 15, is 150.5.

Now, let's think about why this makes sense. The sum of the arc measures is equal to the total circumference of the circle, which means that the angle formed by those two arcs must be half of the central angle that intercepts them. In other words, the angle formed by the 59-degree arc and the 2x-degree arc is (59 + 2x)/2. We also know that the angle formed by the 15-degree angle and the same arc is equal to half of the angle formed by the two arcs. So:

(59 + 2x)/2 = (180 - 15)/2

59 + 2x = 165

2x = 106

x = 53

However, this value of x doesn't satisfy the equation we set up earlier (59 + 2x = 360). So, we must conclude that this value of x is incorrect, and the value we found earlier (x = 150.5) is the correct one.

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

The first number within the the x axis.

The second number is the y axis.

the point you're looking is where they both intersect,

Do that for the 3 points, and you get 3 dots.

Make a line connecting each other in order.

And you made a shape.

Happy Solving

the price per ticket that will give maximum revenue is $6.5, and the maximum revenue in dollars per ticket is $2.925.

As given,If club members charge $3 admission to a classic car show, 1000 people will attend, and for each $1 increase in price, 100 fewer people will attend.

We need to determine the price that will give the maximum revenue for the show and the maximum revenue in dollars per ticket.

Let the number of $1 increases in price be x. Then the number of people attending will be (1000 - 100x), and the price per ticket will be $(3 + x).The total revenue will be:

Revenue = Price × Quantity= $(3 + x) × (1000 - 100x)= $3000 - $100(x^2 + 7x)

The revenue function is quadratic, with the coefficient of the x^2 term being negative. Hence the graph of the function is a parabola which opens downwards, with a maximum at the vertex of the parabola.To find the value of x that will give maximum revenue, we first find the x-coordinate of the vertex.

For a quadratic function of the form f(x) = ax^2 + bx + c, the x-coordinate of the vertex is given by x = -b / (2a).In this case, a = -100, and b = -100(7) = -700. Therefore, the x-coordinate of the vertex is:x = -b / (2a)= 7/2= 3.5

Therefore, the value of x that will give maximum revenue is 3.5. Substituting this value of x in the revenue function, we get:Revenue = $3000 - $100(x^2 + 7x)= $3000 - $100(3.5^2 + 7(3.5))= $2925

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When it is said that the null hypothesis was rejected in a hypothesis test, it means that the sample data has given strong evidence against the null hypothesis and in favor of the alternative hypothesis.

What is a hypothesis?

A hypothesis is a statement that proposes a potential relationship between two variables. It's a conjecture about the nature of the relationship between the two variables that a researcher might test.In hypothesis testing, the null hypothesis is always the hypothesis being tested. A null hypothesis is a statement that assumes there is no relationship between the variables being studied. It is denoted by H0.The alternative hypothesis is a statement that negates the null hypothesis. It suggests that there is a relationship between the variables being studied. It is denoted by Ha.When it is said that the null hypothesis was rejected in a hypothesis test, it means that the sample data has given strong evidence against the null hypothesis and in favor of the alternative hypothesis. As a result, the researcher may conclude that the alternative hypothesis is true with a certain level of confidence.If the null hypothesis is not rejected in a hypothesis test, it means that there is insufficient evidence to support the alternative hypothesis. As a result, the researcher cannot conclude that the alternative hypothesis is true with a certain level of confidence.

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Answer:

Step-by-step explanation:(10,4)=10.9.8.7/4.3.2.1=210

The number of different samples of size 4 that can be taken from a finite population of size 10, without replacement, is 210.

The formula for calculating the number of different samples of size r that can be taken from a finite population of size n without replacement is given by the combination formula: nCr = n! / (r! * (n-r)!), where n! denotes n factorial (n × (n-1) × (n-2) × … × 1).

In this case, we want to find the number of different samples of size 4 that can be taken from a population of size 10, so we use the combination formula with n=10 and r=4:

10C4 = 10! / (4! × (10-4)!) = (10987) / (4321) = 210

Therefore, there are 210 different samples of size 4 that can be taken from a population of size 10 without replacement.

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The distance around the equator is 40,820 km, when the Earth's diameter is approximately 13000km. The distance around the Earth is the circumference.

The Earth is nearly a perfect sphere, but not quite. Astronomers utilized the diameter of the Earth as their primary measuring tool to gauge the extent of the solar system during the 18th and 19th centuries. Today's astronomers typically don't need to be aware of the Earth's size for their regular research tasks.

Nonetheless, the Earth's diameter continues to be the starting point for us, the inhabitants of this planet, in our quest to comprehend the cosmic distance scale. Eratosthenes measured the polar radius, and the number he obtained using the conversion of 0.15 km/stadium sits halfway between the polar and equatorial values.

Given:

Diameter = 13,000 km

Circumference = pi x diameter

Circumference = 3.14 x 13,000 = 40,820 km

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Answer:

90.6°

Step-by-step explanation:

It is given that x represents the number of minutes. You are solving for 8 minutes. Therefore, plug in 8 for x in the given equation, and simplify:

[tex]y = 8.2x + 25\\y = 8.2(8) + 25[/tex]

Simplify. Remember to follow PEMDAS. PEMDAS is the order of operations and stands for:

Parenthesis

Exponent (& Root)

Multiplication

Division

Addition

Subtraction

~

First, multiply 8.2 with 8:

[tex]y = (8.2 * 8) + 25\\y = (65.6) + 25\\[/tex]

Next, add:

[tex]y = 65.6 + 25\\y = 90.6[/tex]

90.6 is your answer.

~

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Answer: 60

Step-by-step explanation:

To form a 3-digit positive integer using the digits 1, 3, 5, 7, and 9 without repeating any digit, we can use the counting principle.

There are 5 choices for the first digit (hundreds place) since any of the 5 digits (1, 3, 5, 7, or 9) can be placed there.

5 (choices for the first digit) × 4 (choices for the second digit) × 3 (choices for the third digit) = 60

There are 60 ways to write a 3-digit positive integer using the digits 1, 3, 5, 7, and 9 without using any digit more than once.

Answer:

She was supposed to DIVIDE the amount of money by the amount of eggs in the carton.

Step-by-step explanation:

12 egg carton = $2.40, 1 egg = $2.40 ÷ 12 = 0.2c
18 egg carton = $3.40, 1 egg = $3.40 ÷ 18 = 0.188 (1.9)

The 18 egg carton was more affordable by about 1.22 cents. Nikki was supposed to divide the amount of money it was worth by the quantity in it.

Answer:

8 cherries

Step-by-step explanation:

Let r represent the number of cherries Rua was given

24 - r - 5 = 1.5r - 1

Simplify and solve for r.

19 - r = 1.5r - 1

-2.5r = -20

r = 8

So Liz gave Rua 8 cherries at the start.

Answer:

The probability that she has breast cancer if she gives a positive test result is P=0.16

Step-by-step explanation:

And according to the Bayes theorem I got 0.16

The probability that the woman who underwent routine screening and has a positive test has breast cancer is 0.017.

Let A denote the event that the woman has breast cancer, and let B denote the event that she has a positive test result. Then we need to find P(A|B), the probability that A occurs given that B has occurred. By Bayes' theorem, we have:

P(A|B) = P(B|A)P(A) / [P(B|A)P(A) + P(B|not A)P(not A)]

where P(not A) = 1 - P(A) is the probability that the woman does not have breast cancer.

From the problem statement, we have:

P(A) = 1/101, P(B|A) = 0.8, and P(B|not A) = 0.05.

Therefore,

P(not A) = 100/101,

and

P(A|B) = (0.8 x 1/101) / [(0.8 x 1/101) + (0.05 x 100/101)] = 0.017 (to three decimal places).

Therefore, the probability that the woman who underwent routine screening and has a positive test has breast cancer is 0.017.

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The following are answers to the probability questions;

1. 2/3 or 0.67 or 0.7 chances

2. 2/3 or 0.67 or 0.7 chances

3. No probability is greater than the other. They are both 2/3.

4.  There are 36 possible outcomes

5. 3/36 or 1/12

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain.

To  calculate the probability of choosing a password with no Y's and With no O's we need to consider all the combinations that do not have Y and O. There are 20 combinations with no Y's and 20 combinations with no O.

Therefore, the probability of choosing a password with no Y's or O's are 20 each. When then calculate by sating

20/30, which simplifies to 2/3 or 0.67.

The number of possible outcomes for a single number cube is as follows;

1 2 3 4 5 6

1 1,1 1,2 1,3 1,4 1,5 1,6

2 2,1 2,2 2,3 2,4 2,5 2,6

3 3,1 3,2 3,3 3,4 3,5 3,6

4 4,1 4,2 4,3 4,4 4,5 4,6

5 5,1 5,2 5,3 5,4 5,5 5,6

6 6,1 6,2 6,3 6,4 6,5 6,6

In total, there are 36 combinations.

! There are three ways to obtain a sum of 10: rolling a 4 and a 6, rolling a 6 and a 4, or rolling two 5's. Since there are 36 possible outcomes in total (as we determined earlier), the probability of rolling two numbers that have a sum equal to 10 is:

P(sum of 10) = number of outcomes that add up to 10 / total number of possible outcomes

P(sum of 10) = 3 / 36

P(sum of 10) = 1/12

So the probability of rolling two numbers that add up to 10 is 1/12.

The answers provided is based on the full questions below as seen in the picture;

12. Higher Order Thinking The table shows the sample space of picking a 2-character password using the letters Y, B, R, O, G, and P. If double letters are not allowed, what is the probability of choosing a password with no Y's? With no O's? Is one probability greater than the other? Explain.

Possible Combinations

Y, B          B, R            R, O          O, G       G, P            P. Y

Y, R          B, O           R, G           O, P       G, Y            P, B

Y, O         B, G            R, P           O, Y       G, B            P, R

Y, G         B, P            R, Y           O, B        G, R            P, O

Y, P         B, Y            R, B           O, R         G, O           P,G

13. A single number cube is rolled twice.

PART A

Determine the number of possible outcomes. Explain how you know you have found all the possible outcomes.

PART B

Find the probability of rolling two numbers that have a sum equal to 10.

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Answer:

A=240 P=64

Step-by-step explanation:

A=240 because you take lxw and that gives you the answer

P=64 because you just add 12+12+10+10

Answer: The area is 240 and the perimeter is 64

Step-by-step explanation:

To get the area you need to do 20 x 12 = 240

And to get the perimeter you need to add up all the sides;

20 + 20 + 12 + 12 = 64

The probability that exactly two balls are of the same color when drawing 3 balls with replacement from an urn containing 1 green ball, 1 red ball, 1 yellow ball and 1 white ball is 4/16 or 1/4.

There are three ways to draw two balls of the same color: two green balls and one of any other color, two red balls and one of any other color, or two yellow balls and one of any other color. Each of these ways can occur in 4 different orders (e.g. GGR, GRG, RGG, etc.) for a total of 12 possible outcomes. The probability of each of these outcomes is (1/4)^3 = 1/64. Therefore, the probability of exactly two balls being of the same color is 12/64 or simplified to 3/16, which is equivalent to 1/4.

Therefore, the probability of exactly two balls being of the same color when drawing 3 balls with replacement from an urn containing 1 green ball, 1 red ball, 1 yellow ball and 1 white ball is 1/4.

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According to the solution we have come to find that, The equation of the circle with radius 8 and center (-2,9) is [tex](x + 2)^2 + (y - 9)^2 = 64.[/tex]

What is radius?

Radius is a straight line segment that joins the center of a circle to any point on its circumference. It is half of the diameter of the circle. The length of the radius is denoted by the letter "r".

The equation of a circle with center (a,b) and radius r is given by:

[tex](x - a)^2 + (y - b)^2 = r^2[/tex]

Substituting the given values, we have:

[tex](x - (-2))^2 + (y - 9)^2 = 8^2[/tex]

Simplifying, we get:

[tex](x + 2)^2 + (y - 9)^2 = 64[/tex]

Therefore, the equation of the circle with radius 8 and center (-2,9) is [tex](x + 2)^2 + (y - 9)^2 = 64.[/tex]

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