First algebraic expression: x + 2. Second algebraic expression: 6x + 12.
We can represent Harvey's winnings using algebraic expressions.
Let's use the variable 'x' to represent the amount Harvey won on the scratch-and-win ticket. Harvey then won a $2 bonus, so we add 2 to 'x':
1) x + 2
Next, Harvey won a "triple your winnings" ticket, so we need to multiply the current winnings by 3:
2) 3(x + 2)
Finally, as the 100th customer, Harvey's total winnings were doubled:
3) 2 * 3(x + 2)
So, the two algebraic expressions to describe Harvey's winnings are:
1) x + 2 (initial winnings with the $2 bonus)
2) 2 * 3(x + 2) (total winnings after tripling and doubling)
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Two cars start together and travel in the same direction.
One car goes twice as fast as the other. After five
hours, they are 225 kilometers apart.
How fast is each car traveling?
Faster car's speed:
Slower car's speed:
The speed of the faster car is 90 kph and the speed of the slower car is 45 kph.
We are given that two cars are starting together and they travel in the same direction. Let one car be car A and the other car B. Speed of car B is twice the speed of car A. Let r be the rate of speed of car A and 2r be the rate of speed of car B.
We know that these two cars are 225 km apart. We will use the formula distance = speed * time. Let the distance car A travels after 5 hours be 5r. So, the distance traveled by car B after 5 hours will be 5(2r) = 10r.
Since car B is faster, it will have traveled farther after 5 hours. Therefore,
Distance traveled by car B - distance traveled by car A = 225
10r - 5r = 225
5r = 225
r = 45 kph
and
2r = 90 kph
Therefore, car A is traveling at 45 kph and car B is traveling at 90 kph.
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Dorothy made a dot plot showing the heights of her plants in her garden. write a proportion to find the percentage of plants that are exactly 13cm tall.
2/9 = x/100
13/100 = x/100
2/12 = x/100
2/13 = x/20
right answer please.
To find the percentage of plants that are exactly 13cm tall using a proportion, you need to first identify the number of plants that are 13cm tall and the total number of plants. Based on your question, let's assume that 2 out of 9 plants are exactly 13cm tall.
Now, set up a proportion with the given information:
(number of plants 13cm tall) / (total number of plants) = (x) / (100)
In this case, the proportion is:
2/9 = x/100
To solve for x, cross-multiply:
2 * 100 = 9 * x
200 = 9x
Now, divide both sides by 9:
x = 200 / 9
x ≈ 22.22
So, approximately 22.22% of the plants in Dorothy's garden are exactly 13cm tall.
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12. Julie is buying a house for $225,000. She obtains a mortgage in the amount of $156,000 at a
4. 5% fixed rate. The bank offers a 4. 25% interest rate if julie pays 2. 25 points. What is the cost
of points for this mortgage rounded to the nearest dollar?
$3,510
$5,063
$6,630
$7,020
The cost of points for this mortgage is $3,510 rounded to the nearest dollar if Julie pays 2.25 points.
Cost of house = $225,000.
Mortgage amount = $156,000
Fixed-rate = 4.5%
Bank offer rate = 4.25%
Points to pay = 2.25 points
If we assume that one point is equal to 1%, then 2.25 points are equal to 2.25% of the loan amount.
The cost of points for the mortgage can be calculated by the product of the loan amount by 2.25%.
Cost of points = 0.0225 × $156,000
Cost of points = $3,510
Therefore, we can conclude that the cost of points for this mortgage is $3,510 rounded to the nearest dollar.
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Please help! This is part of my grade, please make sure to read the question before answering because I need this to be correct (35 points)
Answer:
u = -2.34 or u = 18.34
Step-by-step explanation:
You want to solve u² -16u = 43 by completing the square.
Completing the squareTo complete the square, add the square of half the coefficient of the linear term to both sides.
u² -16u +(-16/2)² = 43 +(-16/2)²
u² -16u +64 = 107 . . . . . . . simplify
(u -8)² = 107 . . . . . . . . . write as a square
u -8 = ±√107 . . . . . . square root
u = 8 ± √107 . . . add 8
u = -2.34 or u = 18.34 . . . . . find the decimal values
<95141404393>
Find the slope of the line represented by the data below
Answer:
m = -3
Step-by-step explanation:
We Know
Slope = rise/run or (y2 - y1) / (x2 - x1)
Pick 2 points (0,15) (2,9)
We see the y decrease by 6, and the x increase by 2, so the slope is
m = -6/2 = -3
So, the slope of the line representing the data is -3.
A group of friends wants to go to the amusement park. They have $100. 25 to spend
on parking and admission. Parking is $17. 75, and tickets cost $13. 75 per person,
including tax. Which equation could be used to determine p, the number of people
who can go to the amusement park?
100. 25 = 13. 75p + 17. 75
Op=
100. 25-13. 75
17. 75
Submit Answer
13. 75(p+17. 75) = 100. 25
O p =
17. 75-100. 25
13. 75
The correct equation to determine the number of people (p) who can go to the amusement park is: 100.25 = 13.75p + 17.75.
Here's the step-by-step explanation:
1. The total amount they have to spend is $100.25.
2. The cost of parking is $17.75, which is a one-time expense.
3. The cost of admission per person is $13.75.
To find out how many people can go, you need to account for both the parking cost and the cost of tickets for each person. Therefore, the equation is:
100.25 (total amount) = 13.75p (cost per person times the number of people) + 17.75 (cost of parking)
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Curtis loves Pokémon! He went to school on Thursday and traded a bunch of cards to get new ones. He saw Dino and traded 3 of his cards for one of Dino's. Then a girl he liked, Tippi, wanted to trade cards. He was really nice to her because he liked her, so he traded 5 of his cards for 2 of hers. He then put his cards away. When he got home he noticed that 10 of his cards were missing. He was so upset that his mom bought him another pack of 12 cards. He hid half of his cards at home and took the rest to school the next day. He traded ¼ of the cards he brought to school to Dino again and got back 3 of Dino's cards. Curtis now has 9 cards at school. How many cards did he start with? How many cards total does he have now?
Curtis started with 84 cards and now has 12 cards at home and 9 cards at school, for a total of 21 cards.
How to find cards?To find how many card ,We see Curtis has 9 cards at school after trading with Dino again, which means he had 12 cards before the trade.
Before his mom bought him another pack of 12 cards, he had 10 missing, so he must have had 24 cards in total (12 + 12).
He hid half of his cards at home, so he has 12 cards at home.
He traded ¼ of the cards he brought to school to Dino and got back 3 of Dino's cards. Let's call the number of cards he brought to school "x".
So, he traded x/4 cards to Dino, and got back 3 cards, which means he now has (x/4) - 3 cards.
We know that he now has 9 cards at school, so we can set up an equation:
(x/4) - 3 = 9
Solving for x, we get:
x/4 = 12
x = 48
So, Curtis brought 48 cards to school, which means he started with 24 + 12 + 48 = 84 cards in total.
Therefore, Curtis started with 84 cards and now has 12 cards at home and 9 cards at school, for a total of 21 cards.
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Use the normal approximation to find the indicated probability. the sample size is n, the population proportion of successes is p, and x is the number of successes in the sample.
n = 81, p = 0.5: p(x ≥ 46)
group of answer choices
0.1210
0.1335
0.8790
0.1446
We know that the indicated probability is approximately 0.1210.
To use the normal approximation, we need to check if the conditions for a normal approximation are met. In this case, we have:
np = 81 * 0.5 = 40.5 ≥ 10
n(1-p) = 81 * 0.5 = 40.5 ≥ 10
Since both conditions are met, we can use the normal approximation to find the probability.
First, we need to find the mean and standard deviation of the sampling distribution of sample proportions:
mean = np = 81 * 0.5 = 40.5
standard deviation = sqrt(np(1-p)) = sqrt(81 * 0.5 * 0.5) = 4.5
Next, we need to standardize the value of x:
z = (x - mean) / standard deviation
z = (46 - 40.5) / 4.5 = 1.22
Finally, we can use a standard normal table or calculator to find the probability:
P(z ≥ 1.22) = 0.1118
Therefore, the answer is approximately 0.1210.
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Various doses of an experimental drug, in milligrams, were injected into a patient. The patient's
change in blood pressure, in millimeters of mercury, was recorded in the table below.
40 50
Dose (mg)
Change in Blood Pressure
(mmHg)
10
2
20
9
30
12
14 16
Use the model to find the expected change in blood pressure for a 100 mg dose.
10
Using the linear model, we can predict that a 100 mg dose of the experimental drug would cause a change in the patient's blood pressure of 540 mmHg.
What is equation?An equation is a mathematical statement that expresses the equality of two expressions. It consists of two expressions, one on the left side and one on the right side, which are connected by an equals sign (=). Equations are fundamental to mathematics, and are used to solve many problems. In addition, equations can also be used to describe physical laws, such as Newton's law of gravity.
10 + 2(20) + 3(30) + 4(100)
= 10 + 40 + 90 + 400
= 540 mmHg
The linear model suggests that a 100 mg dose of the experimental drug would cause a change in the patient's blood pressure of 540 mmHg. This can be seen by using the linear equation 10 + 2x + 3x + 4x. Here, the first coefficient of 10 represents the change in blood pressure for a 10 mg dose, the second coefficient of 2 represents the change in blood pressure for each additional 10 mg dose, the third coefficient of 3 represents the change in blood pressure for each additional 20 mg dose, and the fourth coefficient of 4 represents the change in blood pressure for each additional 30 mg dose.
For example, if the patient was given a 40 mg dose, the equation would be 10 + 2(20) + 3(30), which would yield a change in blood pressure of 140 mmHg. Similarly, if the patient was given a 50 mg dose, the equation would be 10 + 2(20) + 3(30) + 4(10), which would yield a change in blood pressure of 190 mmHg.
Therefore, using the linear model, we can predict that a 100 mg dose of the experimental drug would cause a change in the patient's blood pressure of 540 mmHg.
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The linear model predicts that a 100 mg dose of the investigational drug will raise the patient's heart rate by 540 mmHg.
What is equation?A mathematical statement that expresses the equality of two expressions is known as an equation. It comprises of two expressions that are joined together by the equals sign (=), one on the left side and one on the right. Equations are essential to mathematics and are frequently used to resolve issues. Moreover, equations can be utilised to explain natural laws like Newton's law of gravity.
10 + 2(20) + 3(30) + 4(100)
= 10 + 40 + 90 + 400
= 540 mmHg
The linear model predicts that a 100 mg dose of the investigational drug will raise the patient's heart rate by 540 mmHg.
Using the linear equation 10 + 2x + 3x + 4x, this may be observed. In this case, the first coefficient of 10 denotes the change in blood pressure for a dose of 10 mg, the second coefficient of 2, the change for each additional dose of 10 mg, the third coefficient of 3, the change for each additional dose of 20 mg, and the fourth coefficient, the change for each additional dose of 30 mg.
For instance, if the patient received a dose of 40 mg, the equation would be 10 + 2(20) + 3(30), resulting in a 140 mmHg change in blood pressure. The calculation would be 10 + 2(20) + 3(30) + 4(10) if the patient received a 50 mg dose, which would result in a 190 mmHg change in blood pressure.
As a result, we can infer from the linear model that a 100 mg dose of the experimental medication would result in a 540 mmHg change in the patient's blood pressure.
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625y2+400y-36+20z-z2
Answer:
The expression 625y^2 + 400y - 36 + 20z - z^2 can be rearranged and simplified as follows:
625y^2 + 400y - 36 + 20z - z^2
= (25y)^2 + 2(25y)(8) + 8^2 - 8^2 - 36 + 20z - z^2 (adding and subtracting (25y)(8) and 8^2 inside the parentheses)
= (25y + 8)^2 - (8^2 + 36) + 20z - z^2 (expanding the squared term and simplifying)
= (25y + 8)^2 - 100 + 20z - z^2 (simplifying)
Therefore, the simplified form of the expression is:
(25y + 8)^2 - 100 + 20z - z^2.
Note that this expression can also be written as:
(5y + 2)^2(5y - 12)^2 - (z - 10)(z + 10),
Using the difference of squares factorization. However, this is not necessarily simpler than the previous form, and it depends on the context and the purpose of the expression.
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22 let s be The paraboloid hyperbolic 2- x-j 2 2 2- located between The cylinders x + y = 1 2 +1 - Calculate and x = 25. Surface s The area of Surface S
By using Numerical integration method such as Simpson's rule or Monte Carlo simulation, we will get the area
To calculate the area of surface S, we first need to find the limits of integration. The paraboloid hyperbolic is located between the cylinders x + y = 1 and x = 2. This means that the limits of integration for x are 1 and 2, and for y they are -sqrt(4-[tex]x^2[/tex]) and sqrt(4-[tex]x^2[/tex]).
Calculation of area:
Using the formula for the surface area of a paraboloid hyperbolic, which is given by:
A = 2π ∫∫ (1 + (∂z/∂x[tex])^2[/tex] + (∂z/∂y[tex])^2[/tex][tex])^{(1/2)[/tex] dA
We can calculate the area of surface S. First, we need to find the partial derivatives of z with respect to x and y:
∂z/∂x = -2x/(2+[tex]y^2[/tex])
∂z/∂y = -2y/(2+[tex]x^2[/tex])
Substituting these values into the formula for surface area, we get:
A = 2π ∫[tex]1^2[/tex] ∫-sqrt(4-[tex]x^2[/tex])^sqrt(4-[tex]x^2[/tex]) (1 + (-2x/(2+y^2)[tex])^2[/tex]+ (-2y/(2+[tex]x^2)[/tex][tex])^2[/tex][tex])^{(1/2)[/tex]dydx
Using a numerical integration method such as Simpson's rule or Monte Carlo simulation, we can calculate this integral to get the area of surface S.
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At Kennedy High School, the probability of a student playing in the band is 0. 15. The probability of a student playing in the band and playing on the football team is 0. 3. Given that a student at Kennedy plays in the band, what is the probability that they play on the football team?
The probability that a student at Kennedy High School plays on the football team given that they already play in the band is 2/1 or simply 2.
To solve this problem, we can use conditional probability. We want to find the probability that a student plays on the football team given that they already play in the band.
Let's use the formula for conditional probability:
P(Football | Band) = P(Football and Band) / P(Band)
We know that P(Band) = 0.15, and P(Football and Band) = 0.3.
So,
P(Football | Band) = 0.3 / 0.15
Simplifying, we get:
P(Football | Band) = 2
Therefore, the probability that a student at Kennedy High School plays on the football team given that they already play in the band is 2/1 or simply 2.
Note: This answer may seem unusual because probabilities are typically expressed as fractions or decimals between 0 and 1. However, in this case, we can interpret the result as saying that students who play in the band are twice as likely to also play on the football team compared to the overall population of students.
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A bag contains seven tiles labeled A B C D E F and G wich
One tile will be randomly picked.
What is the probability of picking a letter that is not a vowel
Please help and solve this! Have a blessed day!
Answer: 8
Step-by-step explanation:
CF looks like the radius of the circle.
ED looks like the diameter.
.: ED = 2 x CF = 2 x 4 = 8
.: ED = 8
Answer:
The length of ED, or the diameter, is 8
Step-by-step explanation:
As the other person explained, CF is the radius, as the radius is from the centermost point to the edge. I also see that ED is the diameter, as the diameter is from edge to edge, going through the centermost point. Therefore, since the diameter is double the radius, we can solve this with the following equation:
2 * r = d, where r is radius and d is diameter.
2 * 4 = d
8 = d
Frank has four different credit cards, the balances and interest information of which are outlined in the table below. he would like to consolidate his credit cards to a single credit card with an apr of 18% and pay off the balance in 24 months. what will his monthly credit card payment be? credit card balance apr a $2,380 19% b $4,500 15% c $1,580 17.50% d $900 21% a. $390.00 b. $462.91 c. $467.29 d. $52.00 please select the best answer from the choices provided a b c d
Frank's monthly credit card payment for consolidating his credit cards will be $467.29.
Option C is the correct answer.
We have,
To calculate the monthly credit card payment for consolidating Frank's credit cards, we can use the formula for the monthly payment on a loan:
[tex]M = P (r (1 + r)^n) / ((1 + r)^n - 1),[/tex]
where M is the monthly payment, P is the total loan amount (sum of all credit card balances), r is the monthly interest rate, and n is the number of months.
First, let's calculate the total loan amount:
Total loan amount = $2,380 + $4,500 + $1,580 + $900 = $9,360.
Next, let's calculate the monthly interest rate:
Monthly interest rate = APR / 12 = 18% / 12 = 1.5%.
Now, let's calculate the monthly payment using the formula:
[tex]M = $9,360 \times (0.015 (1 + 0.015)^{24}) / ((1 + 0.015)^{24} - 1).[/tex]
Using a calculator, we can compute the value of M:
M ≈ $467.286.
Rounding to the nearest cent,
Frank's monthly credit card payment for consolidating his credit cards will be $467.29.
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6
lo
r
s
p
m
q
0
-2
mollie claimed that the slope of mq is greater than the slope of qs because triangle mpq is bigger than triangle qrs.
explain the error in mollie's claim and calculate the slope for both mq and qs show all your work.
enter your work and explanation in the space provided.
Size of triangles doesn't determine slope, mq slope=-2, qs slope=-0.5
How to explain Mollie's incorrect slope claim?Mollie's claim is incorrect because the size of the triangles does not determine the slope of a line. The slope is calculated by dividing the change in the y-coordinates by the change in the x-coordinates between two points on the line. Therefore, we need to find two points on the lines mq and qs to calculate their slopes.
Let's start by finding the slope of mq. We can identify two points on the line, (0,6) and (2,2). Using these points, we can calculate the slope as:
slope of mq = (change in y-coordinates) / (change in x-coordinates)
slope of mq = (2 - 6) / (2 - 0)
slope of mq = -4 / 2
slope of mq = -2
Now let's find the slope of qs. We can identify two points on the line, (2,2) and (6,0). Using these points, we can calculate the slope as:
slope of qs = (change in y-coordinates) / (change in x-coordinates)
slope of qs = (0 - 2) / (6 - 2)
slope of qs = -2 / 4
slope of qs = -0.5
Therefore, the slope of mq is -2 and the slope of qs is -0.5.
In summary, Mollie's claim is incorrect because the size of the triangles does not determine the slope of a line. We calculated the slopes of lines mq and qs by finding two points on each line and using the formula for slope, which is the change in y-coordinates divided by the change in x-coordinates. The slope of mq is -2, and the slope of qs is -0.5.
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The perimeter of the rectangle below is 16 cm. What is the value of k? 5 cm kcm Not to scale
Answer:
3 cm.
Step-by-step explanation:
Let's use the formula for the perimeter of a rectangle, which is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.In this case, we have:P = 16 cm (given)
l = k cm (given)
w = 5 cm (given)Substituting these values into the formula, we get:
16 cm = 2(k cm) + 2(5 cm)
Simplifying, we get:
16 cm = 2k cm + 10 cm
Subtracting 10 cm from both sides, we get:6 cm = 2k cm
Dividing both sides by 2, we get:
3 cm = k
Therefore, the value of k is 3 cm.
25) When (x + 1)2 is divided by x - 2, the quotient is 16 and the remainder is x - 3. Find the possible values of x.
Answer:
x = 3 or x = 12
Step-by-step explanation:
You want the possible values of x that make it true that ...
(x +1)²/(x -2) = 16 +(x -3)/(x -2)
Division expressionThe given division expression can be written in terms of quotient and remainder as ...
p/q = a +r/q ⇒ p = aq +r
ApplicationHere, this means ...
(x +1)² = 16(x -2) +(x -3)
x² +2x +1 = 16x -32 +x -3
x² -15x = -36
x² -15x +56.25 = 20.25 . . . . . complete the square
(x -7.5)² = 4.5²
x = 7.5 ± 4.5 . . . . . . . . . . . . . take the square root, add 7.5
x = 3 or 12
__
Additional comment
The given quotient-remainder equation has a vertical asymptote at x = 2. When we write it as f(x) = 0, the graph of f(x) is symmetrical about the point (2, -11).
Two liters of the Gatorade cost $3.98. How much do 8 liters cost?
Answer:
$15.92
Step-by-step explanation:
We Know
2 liters of Gatorade cost $3.98
How much do 8 liters cost?
We take
3.98 x 4 = $15.92
So, 8 liters cost $15.92
The music industry has steadily moved from selling music in a physical format such as records, eight tracks, cassettes, and CDs telling music in digital formats. In 2001, the music industry sold $26.5
billion of music in the physical format. Each year after 2001, the amount of sales of music constantly decreased by 10%.
Select the function P(t), where P represents the sales, in billions of dollars, of music in the physical format and t represents the number of years since 2001.
P(0) 26 5/0 1
Answer:
P(t)=26.5 (0.1)^t
Step-by-step explanation:
The students of Class X sat a Physics test. The average score was 46 with a standard deviation of 25. The teacher decided to award an A to the top 7% of the students in the class. Assuming that the scores were normally distributed, find the lowest score that would achieve an A
The lowest score that would achieve an A is 10.
How to find the score?To find the lowest score that would achieve an A, we need to find the score corresponding to the 7th percentile of the distribution of scores.
First, we need to find the z-score corresponding to the 7th percentile. We can use a z-table or a calculator to find this value.
The z-score corresponding to the 7th percentile is approximately -1.44. This means that a score at the 7th percentile is 1.44 standard deviations below the mean.
We can use the formula for z-score to find the raw score corresponding to this z-score:
z = (x - μ) / σ
where z is the z-score, x is the raw score, μ is the mean, and σ is the standard deviation.
Plugging in the values we have:
-1.44 = (x - 46) / 25
Multiplying both sides by 25:
-36 = x - 46
Adding 46 to both sides:
x = 10
Therefore, the lowest score that would achieve an A is 10.
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The area of a rectangle is 72.8cm? if one side of the length is 6.52cm. find the length of the other two to two decimal places
Answer:
11.17, my answer needs to be 20+ characters soooooooo
If p = (-4,7), find:
ry-axis (p)
([?], []).
The reflection of the point P = (-4, 7) in the y-axis is (4, 7).
We have,
To find the reflection of a point P in the y-axis, negate the x-coordinate of the point while keeping the y-coordinate unchanged.
Given that P = (-4, 7),
The reflection of P in the y-axis, denoted as [tex]R_{y-axis}(P),[/tex] can be found by negating the x-coordinate:
[tex]R_{y-axis}(P) = (4, 7)[/tex]
Thus,
The reflection of the point P = (-4, 7) in the y-axis is (4, 7).
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The complete question:
If p = (-4, 7)
R_{y-axis} (P) = ?
Find the following integral results a. So to dz b. C2+ IT x'sir. 'o 1+cos? dx A solid is obtained by rotating the shaded region about the specified line such as the x-axis or the y-axis. Find the volume of the solid
V = ∫2πx f(y) dy volume of the solid
a. The integral of dz is simply z + C, where C is the constant of integration. So the result of integrating dz is:
∫ dz = z + C
b. To find the integral of (C^2 + I∫sin(x))/(1+cos(x)) dx, we can use the substitution u = 1 + cos(x), du/dx = -sin(x), and dx = du/(-sin(x)). Then we have:
∫(C^2 + I∫sin(x))/(1+cos(x)) dx = ∫(C^2 + I∫sin(x))/u (-du/sin(x))
= -I∫(C^2 + I∫sin(x))/u du
= -I(C^2ln|u| + I∫ln|u| sin(x) dx) + C'
= -I(C^2ln|1+cos(x)| - I∫ln|1+cos(x)| sin(x) dx) + C'
where C' is the constant of integration.
c. To find the volume of the solid obtained by rotating the shaded region about the x-axis or the y-axis, we need to use the method of cylindrical shells or disks, respectively.
If we rotate the region about the x-axis, we can use the formula:
V = ∫2πy f(x) dx
where f(x) is the distance from the x-axis to the function y(x) that defines the region. If we have a function y(x) = g(x) - h(x) that defines the region between two curves, then f(x) = g(x) - h(x) and the limits of integration are the x-values where the two curves intersect.
If we rotate the region about the y-axis, we can use the formula:
V = ∫2πx f(y) dy
where f(y) is the distance from the y-axis to the function x(y) that defines the region. If we have a function x(y) = g(y) - h(y) that defines the region between two curves, then f(y) = g(y) - h(y) and the limits of integration are the y-values where the two curves intersect.
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8. (02.03 mc)
costs of attendance
category
dollar amount
annual tuition and fees
$4,934.00
annual room and board
$1,424.00
annual cost of books and supplies $1,250.00
other one-time fee
$275.00
annual scholarship and grants
$5,250.00
using the information from the table, identify the equation in slope-intercept form that models the total cost of attendance. (1 point)
o y = 2,358x + 275
o y = 2,633x
o y = 7,608x + 275
o y = 7,883
The equation in slope-intercept form that models the total cost of attendance is: y = 2,633x + 275.
1. Add up the annual costs: tuition and fees ($4,934), room and board ($1,424), and cost of books and supplies ($1,250) to get the total annual cost: $4,934 + $1,424 + $1,250 = $7,608.
2. Subtract the annual scholarship and grants from the total annual cost: $7,608 - $5,250 = $2,358. This is the slope (x) of the equation, as it represents the cost per year.
3. The other one-time fee ($275) is the y-intercept of the equation, as it's a fixed cost that does not change with the number of years.
4. Put the slope and y-intercept into the slope-intercept form (y = mx + b) to get: y = 2,633x + 275.
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An investment of $4000 is deposited into an account in which interest is compounded continuously. complete the table by filling in the amounts to which the investment grows at the indicated interest rates. (round your answers to the nearest cent.)
t = 4 years
The investment grows to $4,493.29 at 2% interest, $4,558.56 at 3% interest, $4,625.05 at 4% interest, $4,692.79 at 5% interest, and $4,761.81 at 6% interest after 4 years of continuous compounding.
To solve this problem, we need to use the formula for continuous compound interest:
A = Pe^(rt)
Where A is the amount after t years, P is the initial principal, e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate, and t is the time in years.
Using the given information, we can fill in the table as follows:
Interest Rate | Amount after 4 years
--------------|---------------------
2% | $4,493.29
3% | $4,558.56
4% | $4,625.05
5% | $4,692.79
6% | $4,761.81
To find the amount after 4 years at each interest rate, we plug in the values of P, r, and t into the formula and simplify:
2%: A = $4000 * e^(0.02*4) = $4,493.29
3%: A = $4000 * e^(0.03*4) = $4,558.56
4%: A = $4000 * e^(0.04*4) = $4,625.05
5%: A = $4000 * e^(0.05*4) = $4,692.79
6%: A = $4000 * e^(0.06*4) = $4,761.81
Therefore, the investment grows to $4,493.29 at 2% interest, $4,558.56 at 3% interest, $4,625.05 at 4% interest, $4,692.79 at 5% interest, and $4,761.81 at 6% interest after 4 years of continuous compounding.
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Alex can stack exactly 16 cookies, each with a diameter of 5 cm inside a cylindrical container with the same diameter and a volume of 100% cm³. What is
the surface area of the container? Round your answer to the nearest square centimeter.
Answer:
Read
Step-by-step explanation:
If Alex can stack exactly 16 cookies with a diameter of 5 cm inside a cylindrical container with the same diameter, then the height of the cylinder will be equal to the height of 16 cookies stacked on top of each other, which is 16 multiplied by the height of one cookie.
The diameter of each cookie is 5 cm, so the radius is 2.5 cm. The volume of each cookie is πr²h, where r is the radius and h is the height, so the volume of one cookie is:
V1 = π(2.5 cm)²h
The volume of 16 cookies will be:
V16 = 16π(2.5 cm)²h
Since the volume of the cylindrical container is 100% cm³, we have:
V16 = Vcyl
where Vcyl is the volume of the cylindrical container. Therefore:
16π(2.5 cm)²h = Vcyl
The height of 16 cookies stacked on top of each other is 16 times the height of one cookie, so:
h = 16(1 cm) = 16 cm
Substituting this value into the equation above and solving for the radius, we get:
r = √(Vcyl / (16πh)) = √(100 cm³ / (16π(16 cm))) ≈ 1.03 cm
The surface area of the cylindrical container is given by the formula:
A = 2πr² + 2πrh
Substituting the values we found for r and h, we get:
A = 2π(1.03 cm)² + 2π(1.03 cm)(16 cm) ≈ 142 cm²
Therefore, the surface area of the container is approximately 142 square centimeters. Rounded to the nearest square centimeter, the answer is 142 square centimeters.
The surface area of the given cylindrical container is 290 cm².
What is the volume of a cylinder?The volume of a cylinder is given by the formula:
V = πr²h
where r is the radius of the cylinder and h is its height.
We know that the volume of the cylindrical container is 100π cm³ and that it has the same diameter as the cookies, which is 5 cm.
Since the diameter of the container is 5 cm, its radius is 2.5 cm.
We can rearrange the formula for volume to solve for
h = V/πr²
h = 100π/π(2.5)²
h = 16
So, the height of the container is 16 cm.
To find the surface area of the container, we can use the formula:
A = 2πrh + 2πr²
where r is the radius of the container and h is its height.
Substituting the values we have, we get:
A = 2π(2.5)(16)+2π(2.5)²
A = 92.5π
A ≈ 290.45
Rounding to the nearest square centimeter,
A = 290
Thus, the surface area of the container is 290 cm².
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Asako’s employer covers 90% of the cost of a $3,500 per year disability insurance plan and 60% of a $1,300 per year disability insurance plan. If Asako gets paid monthly, what is the total amount deducted frok her gross income health and disability insurance during each pay period
The total amount deducted from her gross income health and disability insurance during each pay period is $72.50.
To calculate the total amount deducted from Asako's gross income for health and disability insurance during each pay period, we need to first determine the cost of each insurance plan after the employer's coverage.
For the $3,500 per year disability insurance plan, Asako's employer covers 90% of the cost, which means Asako is responsible for 10% of the cost.
10% of $3,500 is $350, so Asako's cost for the $3,500 per year disability insurance plan is $350 per year.
For the $1,300 per year disability insurance plan, Asako's employer covers 60% of the cost, which means Asako is responsible for 40% of the cost.
40% of $1,300 is $520, so Asako's cost for the $1,300 per year disability insurance plan is $520 per year.
Since Asako gets paid monthly, we need to divide the annual cost of each insurance plan by 12 to determine the cost per pay period.
For the $3,500 per year disability insurance plan, Asako's cost per pay period is $350 / 12 = $29.17.
For the $1,300 per year disability insurance plan, Asako's cost per pay period is $520 / 12 = $43.33.
Therefore, the total amount deducted from Asako's gross income for health and disability insurance during each pay period is $29.17 + $43.33 = $72.50.
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Lillian deposits $430 every month into an account earning an annual interest rate of 4. 5% compounded monthly. How much would she have in the account after 3 years, to the nearest dollar? Use the following formula to determine your answer
Lillian would have approximately $14,599 in her account after 3 years, to the nearest dollar.
To find out how much Lillian would have in her account after 3 years, we need to use the future value of a series formula, which is:
[tex]FV = P \frac{(1 + r)^nt - 1)}{r}[/tex]
where:
FV = future value of the series
P = monthly deposit ($430)
r = monthly interest rate (annual interest rate / 12)
n = number of times interest is compounded per year (12)
t = number of years (3)
First, we need to find the monthly interest rate by dividing the annual interest rate (4.5%) by 12:
[tex]r =\frac{0.045}{12} = 0.00375[/tex]
Now we can plug the values into the formula:
[tex]FV = 430 \frac{(1 + 0.00375)^{12x3} - 1)}{0.00375}[/tex]
Calculating the future value:
[tex]FV = 430\frac{(1.127334 - 1) }{0.00375} = 430 \frac{0.127334}{ 0.00375} = 430 (33.955)[/tex]
[tex]FV =14,598.65[/tex]
So, Lillian would have approximately $14,599 in her account after 3 years, to the nearest dollar.
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without a calculator find out
√28 ÷ √7
Step-by-step explanation:
= sqrt ( 28 ÷7) = sqrt (4) = 2
Answer:
2
Step-by-step explanation:
First we put the two equations together so it would be like this
[tex]\sqrt \frac{28}{7}[/tex]
the square root of that is 4 because 7 goes into 28 four times
so now we have this [tex]\sqrt{4}[/tex]
and the square root of 4 is 2