Answers
Given the above conditions with regard to Rolle's Theorem, the answers are:
Therefore, the solution is:
F(0) = 0
f(4) = (-8) e^4
C = 1
What is the explanation for the above response?
To find F(0), we can simply substitute x=0 into the expression for f(x):
f(0) = (0^2 - 4(0)) e^0 = 0
To find f(4), we can substitute x=4:
f(4) = (4^2 - 4(4)) e^4 = (-8) e^4
Next, we need to find the critical point(s) of f(x) on the interval [0,4]. To do this, we find the derivative of f(x) and set it equal to zero:
f'(x) = (2x-4) e^x + (x^2-4x) e^x = (x^2-2x) e^x
Setting f'(x) equal to zero, we have:
(x^2-2x) e^x = 0
Since e^x is never zero, we can divide both sides by e^x to get:
x^2 - 2x = 0
Factoring out x, we have:
x(x-2) = 0
Therefore, the critical points on [0,4] are x=0 and x=2.
Since both critical points are in the open interval (0,4), Rolle's Theorem applies. This means there exists a number c in (0,4) such that f'(c) = 0. To find this value of c, we can simply take the average of the critical points:
c = (0 + 2)/2 = 1
Therefore, the solution is:
F(0) = 0
f(4) = (-8) e^4
C = 1
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Related Questions
Camila saved 4/5% of her allowance. What is this percent expressed as a fraction and as a decimal
Answers
4/5% would easily be represented as 80%. In decimal form, this could be represented as 0.80 or 0.8 if you needed to simplify.
Answer:
Decimal: 0.8
Fraction:4/5
Percent: 80%
Statistical measures are shown for the number of hours per week spent doing homework by the students in two classes. Class 1: mean number of hours spent doing homework = 20,mean absolute value deviation = 2. Class 2: mean number of hours spent doing homework = 24, mean absolute value deviation = 2. The difference between the means of the two data sets is ___
Answers
The difference between the means of the two data sets is 4.
How to determine the difference between the means of the two data sets?
Statistical measures are used to describe, analyze, and interpret data. There are several measures that are commonly used in statistics, such as mean, median, mode, standard deviation, etc.
The mean, also known as the average, is the sum of all the values in a dataset divided by the total number of values. It represents the central tendency of the data.
The difference between the means of the two data sets is:
difference between the means = (Class 2 mean) - (Class 1 mean)
difference between the means = 24 - 20 = 4
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The grocery store is Two Thirds of a mile from John’s office. His house is One and Two Thirds miles from the office in the opposite direction. How many miles is his house from the grocery store
Answers
John's home is thus two kilometers away from the supermarket.
What does the distance calculation mean?the algebraic equation known as the distance formula, which provides the distances between two locations as an expression of their coordinates. (see coordinate system). The distance formulas for locations in rectangular coordinates in two- and multidimensional Euclidean spaces are founded on the theorem known as Pythagorean.
To find how many miles John's house is from the grocery store, we need to add the distance from John's house to the office and the distance from the office to the grocery store.
Distance from John's house to the office = 1 and 2/3 miles
Distance from the office to the grocery store = 2/3 miles
Total distance from John's house to the grocery store = (1 and 2/3) + (2/3) = 2 miles
Therefore, John's house is 2 miles from the grocery store.
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Find the area of the parallelogram.
Answers
Answer: 33.34
Step-by-step explanation: first we have to cut this shape up like you would a pizza
2 triangles and 1 rectangle, we know that the rectangle is 10 by 3 cm, but we don't have all the measurements for the triangle.
Find the last side using this equation:
3.2 squared = 10.24
3 squared = 9
subtract
1.24
square root of 1.24 = 1.11
Area of rectangle:
10 x 3 = 30
Area of triangle:
1.11 x 3 ≈ 1.67
Final Area:
30 + 1.67x2 = 33.34
Find the length of the segment indicated. Round your answer to the nearest tenth if necessary. (Please show step by step on how to figure this out! I want to understand!)
Answers
The length segment of the circle indicated is 6 units.
How to find the radius of a circle?A circle is a round-shaped figure that has no corners or edges. Therefore, let's find the length segment of the circle.
Therefore, the diameter of a circle is the line that passes through the centre and meets the circumference at opposite ends.
Therefore, the radius of a circle is the distance from the centre of the circle to any point on it's circumference.
The radius is half of a diameter.
Therefore, the length x is the radius of the circle and it is 6 units.
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FIND THE SIZE OF XYZ
Answers
The angle of XYZ is approximately 87.6 degrees.
To find the angle of XYZ, you need to use the Law of Cosines, which states that c² = a² + b² - 2ab cos(C), where c is the side opposite the angle C. Given the side lengths of the triangle XYZ, you can find the measure of angle XYZ as follows:
First, use the Pythagorean Theorem to find the length of side XY: XY² = 5² + 12² = 169, so XY = √169 = 13.
Next, use the Law of Cosines to find the measure of angle YXZ: 13² = 7² + 8² - 2(7)(8)cos(YXZ), which simplifies to 169 = 113 - 112cos(YXZ). Solving for cos(YXZ), you get cos(YXZ) = (113 - 169) / (278) = -0.125.
Finally, take the inverse cosine (cos⁻¹) of -0.125 to find the measure of angle YXZ in degrees: YXZ ≈ 102.4°.
Therefore, the measure of angle XYZ is 180° - 90° - 102.4° = 87.6°.
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(13 points)
A gardener would like to add to their existing garden to make more flowers available for the butterflies that visit the garden. Her current garden is 45 square feet. If she added another rectangular piece with vertices located at (−21, 7), (−23, 7), (−21, 12), and (−23, 12), what is the total area of the garden?
A: 10 ft2
B: 55 ft2
C: 225 ft2
D: 450 ft2
no image
Answers
Total area of garden after adding rectangular piece will be 55 ft² i.e. B.
What exactly is a rectangle?
A rectangle is a two-dimensional geometric shape that is characterized by having four sides and four right angles. Opposite sides of a rectangle are parallel and equal in length, while opposite angles are equal. The area of a rectangle can be calculated by multiplying its length by its width, while its perimeter is the sum of the lengths of all its sides. Rectangles are commonly used in many fields, such as architecture, engineering, and mathematics.
Now,
The rectangle has a length of |-21 - (-23)| = 2 and a width of |7 - 12| = 5. Therefore, the area of the new rectangular piece is 2 x 5 = 10 square feet.
Adding this to the area of the existing garden gives a total area of 45 + 10 = 55 square feet.
Therefore, the answer is (B) 55 ft².
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a trapezoid is shown with bases AD and BC. if slopCe of AD is 1/2, what is the slope of BC
Answers
The slope of BC is 1/2, since the slope of AD is 1/2. This is because the rise and run of the two bases are the same.
What is slope?The slope of a line is defined as the ratio of the vertical change (the rise) to the horizontal change (the run).
In the case of an isosceles trapezoid, the two bases (AD and BC) are parallel and of equal length. Therefore, the slope of the two bases is the same.
Given that the slope of AD is 1/2, the slope of BC is also 1/2.
This is because the rise and run of the two bases are the same. Therefore, the ratio of rise to run is the same and the slope of both bases is 1/2.
To understand this better, let us consider the rise and run of the two bases:
AD: Rise = y² − y1, Run = x² − x1
BC: Rise = y² − y1, Run = x² − x1
Therefore,
Slope of AD = (y² − y1)/(x² − x1)
Slope of BC = (y² − y1)/(x² − x1)
Since the rise and run of the two bases are the same, the slope of the two bases is also the same.
Therefore, the slope of BC is 1/2, since the slope of AD is 1/2.
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A square is graphed in a coordinate plane, with vertices at S(−3,0)
, H(2,0)
, A(2,5)
, and Q(−3,5)
. The square is then reflected across the x-axis to form the image S′H′A′Q′
.
Which statement is true?
S′H′¯¯¯¯¯¯¯¯¯¯¯
is parallel to S′Q′¯¯¯¯¯¯¯¯¯¯
.
H′A′¯¯¯¯¯¯¯¯¯¯¯
is parallel to H′S′¯¯¯¯¯¯¯¯¯¯¯
.
A′Q′¯¯¯¯¯¯¯¯¯¯
is parallel to S′Q′¯¯¯¯¯¯¯¯¯¯
.
Q′S′¯¯¯¯¯¯¯¯¯¯
is parallel to A′H′¯¯¯¯¯¯¯¯¯¯¯
.
Answers
The statement "S′H′ is parallel to S′Q′" is true.
How to find the correct statement?To find the image of the square after reflection across the x-axis, we need to flip each point of the square over the x-axis. The coordinates of the reflected points will have the same x-coordinate, but the y-coordinate will have the opposite sign.
The coordinates of the original square are:
S(−3,0)
H(2,0)
A(2,5)
Q(−3,5)
The coordinates of the reflected square are:
S′(−3,0)
H′(2,0)
A′(2,−5)
Q′(−3,−5)
Now, we can find the slopes of the sides of the reflected square to determine which sides are parallel.
S′H′¯¯¯¯¯¯¯¯¯¯¯: The slope of S′H′¯¯¯¯¯¯¯¯¯¯¯ is 0, since both points have the same y-coordinate. Therefore, S′H′¯¯¯¯¯¯¯¯¯¯¯ is parallel to the x-axis.
S′Q′¯¯¯¯¯¯¯¯¯¯: The slope of S′Q′¯¯¯¯¯¯¯¯¯¯ is 0, since both points have the same y-coordinate. Therefore, S′Q′¯¯¯¯¯¯¯¯¯¯ is also parallel to the x-axis.
H′A′¯¯¯¯¯¯¯¯¯¯¯: The slope of H′A′¯¯¯¯¯¯¯¯¯¯¯ is undefined, since the two points have the same x-coordinate. Therefore, H′A′¯¯¯¯¯¯¯¯¯¯¯ is parallel to the y-axis.
H′S′¯¯¯¯¯¯¯¯¯¯¯: The slope of H′S′¯¯¯¯¯¯¯¯¯¯¯ is also undefined, since the two points have the same x-coordinate. Therefore, H′S′¯¯¯¯¯¯¯¯¯¯¯ is parallel to the y-axis.
A′Q′¯¯¯¯¯¯¯¯¯¯: The slope of A′Q′¯¯¯¯¯¯¯¯¯¯ is 0, since both points have the same y-coordinate. Therefore, A′Q′¯¯¯¯¯¯¯¯¯¯ is parallel to the x-axis.
Q′S′¯¯¯¯¯¯¯¯¯¯: The slope of Q′S′¯¯¯¯¯¯¯¯¯¯ is 0, since both points have the same y-coordinate. Therefore, Q′S′¯¯¯¯¯¯¯¯¯¯ is also parallel to the x-axis.
Based on these calculations, we can see that S′H′¯¯¯¯¯¯¯¯¯¯¯ is parallel to S′Q′¯¯¯¯¯¯¯¯¯¯ (both are parallel to the x-axis). Therefore, the statement "S′H′¯¯¯¯¯¯¯¯¯¯¯ is parallel to S′Q′¯¯¯¯¯¯¯¯¯¯" is true.
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A 500g packet of beans costs £1.55
A 125g packet of the same beans costs £0.36
Which packet is better value for money?
Answers
The packet is better value for money is a 125 g packet of beans which costs £0.36.
The better value for money of packet of beans can be calculated as follows?The first step we can check on the first packet value for money by calculating the costs of 1 g of beans as follows :
[tex](1/500) \times \£1.55 = \£0,003[/tex]
The second step we can check on the second packet value for money by calculating the costs of 1 g of beans as follows :
[tex](1/125) \times \£0.36 = \£0,0028.[/tex]
Hence, the better value for money between those two packet of beans is the second packet of beans which given by 125 g and costs £0.36.
Answer:
125g
Step-by-step explanation:
Find 1g of beans for both packets
500g /500 = 1
£1.55 / 500 = £0.0031 per gram
125 / 125 = 1
£0.36 / 125 = £0.00288 per gram
0.00288 < 0.0031
125g packet is better value for money
I need help with this please
Answers
The total amount of sugar that was consumed by Kylie in the past nine (9) days is equal to 3 units of sugar.
What is a line plot?In Mathematics and Statistics, a line plot refers a type of graph that is used to graphically represent a data set above a number line, while using crosses, dots, or any other mathematical symbol.
Based on the data and information provided in the line plot shown in the image attached above, we can calculate the total amount of sugar that was consumed by Kylie in the past nine (9) days as follows:
Total sugar consumed = (1/8 + 1/8 + 1/8) + 1/4 + (3/8 + 3/8 + 3/8) + (5/8 + 5/8)
Total sugar consumed = 3(1/8) + 1/4 + 3(3/8) + 2(5/8)
Total sugar consumed = 3/8 + 1/4 + 9/8 + 10/8
Total sugar consumed = 22/8 + 1/4
Total sugar consumed = (22 + 2)/8
Total sugar consumed = 24/8
Total sugar consumed = 3 units of sugar.
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5.9 rounded to the nearest tenth
Answers
Step-by-step explanation & Answer
5.9 roundest to the nearest ten is:
5.9 .9 is a tenth which can be rounded
But since you said nearest tenth answer is
= 5.9
Look at picture :)
Thus the answer to your problem is, 5.9
Which of the following equations are equivalent? Select three options.
2 + x = 5
x + 1 = 4
9 + x = 6
x + (negative 4) = 7
Negative 5 + x = negative 2
Answers
Simplify the following expression. Write your answer using positive exponents.
Answers
After simplifying the given expression we can write answer using positive exponent [tex]7^3 * 6^30[/tex].
What is expression?
In mathematics, an expression is a combination of numbers, variables, and symbols that are grouped together to represent a mathematical relationship or quantity. It can be a single term, or a combination of terms separated by mathematical operations such as addition, subtraction, multiplication, and division.
When we raise a power to another power, we need to multiply the exponents. So we can simplify the expression as follows:
[tex]7^3(6^6)^5 = 7^3 * 6^(6*5) = 7^3 * 6^30[/tex]
so we write the answer using positive exponents as:
[tex]7^3 * 6^30[/tex]
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bob left his grandmothers house at 5:00 he drove for 2 hours and 22 minutes
Answers
Answer:
7:22
Step-by-step explanation:
Given: 2 hours and 22 minutes
5:00 + 2 hours
5 + 2 = 7
7:00 + 22 minutes
7:22
P=$4655, R= 13.83% per year, T=42 months
Answers
Answer:
6,908.25$
Step-by-step explanation:
First, convert R to a decimal.
So R=0.1383
Next, 42 months = 3.5 years
A=4655(1+(0.1383 * 3.5)) = 6,908.25275
Calculate the arithmetic mean of these numbers. -12 and 7
Answers
Answer:
The arithmetic mean is the simplest and most widely used measure of a mean, or average. It simply involves taking the sum of a group of numbers, then dividing that sum by the count of the numbers used in the series.
Step-by-step explanation:
Therefore, the arithmetic mean of -12 and 7 is -2.5
Helppp please
A population of bacteria is growing according to the equation p(t)=1000e^0.21t
Use a graphing calculator to estimate when the population will exceed 2627.
t =------------
Answers
The population will exceed 2627 when t is greater than approximately 6.05.
What is inequality?Inequality is a mathematical cοncept that expresses a relatiοnship between twο values οr expressiοns, indicating that οne is greater than, less than, οr nοt equal tο the οther. An inequality is usually represented using symbοls such as < (less than), > (greater than), ≤ (less than οr equal tο), ≥ (greater than οr equal tο), and ≠ (nοt equal tο).
To solve for the value of t when the population exceeds 2627, we can set up the inequality:
p(t) > 2627
Substituting the given equation for p(t), we get:
1000[tex]e^{0.21t}[/tex] > > 2627
Dividing both sides by 1000, we get:
[tex]e^{0.21t}[/tex] > 2.627
Taking the natural logarithm of both sides, we get:
0.21t > ln(2.627)
Solving for t, we get:
t > ln(2.627)/0.21 ≈ 6.05
Therefore, the population will exceed 2627 when t is greater than approximately 6.05.
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Select the coordinates A′ and B′ after dilation of the line segment AB with a scale factor of 4, centered at the origin where the endpoints are A(−2,−3) and B (−4,−5).(1 point)
Answers
Answer: A'(-8,-12); B'(-16,-20)
Step-by-step explanation:
Since the line is scaled about the origin, simply multiplying the points (x,y) by 4 will give you A' and B'.
Integers a and b are such that
[tex](a + 3 \sqrt{5} ) {}^{2} + a - b \sqrt{5} = 51 [/tex]
Find the possible values of a and the corresponding values of b.
(Answers are a= -3 , 2 and b= -18 , 12. But I don't know how to show the working so please help, thx)
Answers
The possible values of a and the corresponding values of b are; a= -3, 2 and b= -18, 12.
How to calculate possible and the corresponding values?Expanding the left-hand side of the equation:
(a + 3√5)² + a - b√5 = a² + 6a√5 + 45 + a - b√5
Combining like terms:
2a² + (2a - b)√5 + 45 = 51
Simplifying further:
2a² + (2a - b)√5 = 6
Now, since √5 is irrational, the only way the left-hand side can equal 6 is if both the rational and irrational parts are equal to 0. Therefore two equations:
2a² + 2a - b = 0 (Equation 1)
2a - b = 0 (Equation 2)
Solving Equation 2 for b:
b = 2a
Substituting this into Equation 1:
2a² + 2a - 2a = 0
Simplifying:
2a² = 0
Thus, a = 0 is a solution. However, a = 0 does not satisfy the original equation, since the left-hand side would be 45, which is not equal to 51. Therefore, we can divide both sides of Equation 1 by 2a to get:
a + 1 - b/2a = 0
Multiplying both sides by 2a:
2a² + 2a - b = 0
Substituting b = 2a:
2a² + 2a - 2a = 0
Simplifying:
2a² = 0
Thus, a = 0 is a solution. However, as noted above, a = 0 does not satisfy the original equation. Therefore, we must consider the case where a ≠ 0. Dividing both sides of Equation 2 by 2:
a - b/2 = 0
Solving for b:
b = 2a
Substituting into the original equation:
(a + 3√5)² + a - 2a√5 = 51
Expanding:
a² + 6a√5 + 45 + a - 2a√5 = 51
Combining like terms:
a² + 7a√5 - 6 = 0
Using the quadratic formula:
a = (-7√5 ± √(7²√5² - 4(1)(-6))) / 2(1)
Simplifying:
a = (-7√5 ± 13) / 2
Therefore, the possible values of a are -3 and 2. For each value of a, we can use b = 2a to find the corresponding value of b. Thus, the possible values of b are -18 and 12.
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Suppose on your 21st birthday you begin saving $500 quarterly into an account that pays 12% compounded quarterly. If you continue the savings until your 51st birthday (30 years), how much money will be in the account?
Answers
Answer:$386,711.70
Step-by-step explanation:
To solve the problem, we can use the formula for the future value of an annuity:
FV = PMT x [(1 + r/n)^(n*t) - 1] / (r/n)
where:
FV = future value
PMT = payment per period
r = annual interest rate
n = number of compounding periods per year
t = number of years
First, we need to find the number of compounding periods and the interest rate per quarter:
n = 4 (quarterly compounding)
r = 0.12 / 4 = 0.03 (3% quarterly interest rate)
Next, we can plug in the values:
PMT = $500
n = 4
r = 0.03
t = 30
FV = $500 x [(1 + 0.03/4)^(4*30) - 1] / (0.03/4)
FV = $500 x [(1 + 0.0075)^120 - 1] / 0.0075
FV = $500 x [6.3207 - 1] / 0.0075
FV = $500 x 773.4234
FV = $386,711.70
Therefore, if you save $500 quarterly into an account that pays 12% compounded quarterly from your 21st to your 51st birthday, you will have approximately $386,711.70 in the account.
P = $500
r = 0.12 (12% as a decimal)
n = 4 (since interest is compounded quarterly)
t = 30 (the number of years)
Plugging in the values, we get:
A = $500(1 + 0.12/4)^(4*30)
A = $500(1 + 0.03)^120
A = $500(1.03)^120
A = $500(15.5919)
A = $7,795.96
Therefore, after 30 years of quarterly savings at a 12% interest rate compounded quarterly, there will be approximately $7,795.96 in the account.
Four part spinner is spun twice total number of possible outcomes. What is the probability of spinning pink on both spins? What is the probability of not spinning orange either spin?
Answers
Probability of spinning pink on both spins = 1/4 and Probability of not spinning orange on either spin = 9/16.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
If a four-part spinner is spun twice, there are 16 possible outcomes (4 options on the first spin, multiplied by 4 options on the second spin).
To find the probability of spinning pink on both spins, we need to first determine how many outcomes result in pink on both spins. If we label the four parts of the spinner A, B, C, and D, and assume that pink is on part A, then there are four possible outcomes where pink appears on both spins: AA, AB, AC, and AD. Each of these outcomes has a probability of 1/16, since there are 16 total possible outcomes. So the probability of spinning pink on both spins is:
Probability of spinning pink on both spins = (number of outcomes where pink appears on both spins) / (total number of possible outcomes)
Probability of spinning pink on both spins = 4/16
Probability of spinning pink on both spins = 1/4
To find the probability of not spinning orange either spin, we need to determine how many outcomes do not have orange. If we assume that orange is on part B, then there are three outcomes on the first spin that do not result in orange: AB, AC, and AD. On the second spin, there are again three outcomes that do not result in orange: BA, CA, and DA. So there are a total of 3 x 3 = 9 outcomes where orange does not appear on either spin.
Again, each of these outcomes has a probability of 1/16, so the probability of not spinning orange on either spin is:
Probability of not spinning orange on either spin = (number of outcomes where orange does not appear on either spin) / (total number of possible outcomes)
Probability of not spinning orange on either spin = 9/16
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. QUESTION 8: You are 765 feet above in the air. You are descending at a rate of 12 feet per minute. Write an equation in slope intercept form to represent this situation. b: Equation:
Answers
Step-by-step explanation:
You need the line in y = mx + b form:
y = -12x + 765 where x = minutes y = height in feet
Police plan to enforce speed limits by using radar traps at four different locations within the
national limits. The radar traps at each of the locations L1, L2, L3, and L4 will be operated
40%, 20%, 30%, and 40% of the time. A person who is speeding on her way to work has
probabilities of 0.3, 0.1, 0.4, and 0.2 respectively, of passing through these locations.
Let S be the event that radar traps was set and Li be the locations i, i = 1, 2, 3 or 4.
If the person received a speeding ticket on her way to work, what is the probability
that she passed through the radar trap located at L2?Draw a tree diagram with the notation and probabilities provided
Answers
Using Bayes theorem, the probability that the person passed through the radar trap located at L2 given that she received a speeding ticket is 0.059 or 5.9%.
What is the probability that the person passed through the radar trap located at L2We can solve this problem using Bayes' theorem. Let A be the event that the person received a speeding ticket, and Bi be the event that the radar trap was set at location Li, for i = 1, 2, 3, or 4. Then we want to find the conditional probability of B22 given A, which is:
[tex]P(B_2 | A) = P(A | B_2) * P(B_2) / P(A)[/tex]
We can compute each of the probabilities on the right-hand side using the given information.
First, we have:
[tex]P(B_1) = 0.4, P(B_2) = 0.2, P(B_3) = 0.3, P(B_4) = 0.4[/tex]
Next, we have:
[tex]P(A | B_1) = 0.3, P(A | B_2) = 0.1, P(A | B_3) = 0.4, P(A | B_4) = 0.2[/tex]
Finally, we have:
[tex]P(A) = P(A | B_1) * P(B_1) + P(A | B_2) * P(B_2) + P(A | B_3) * P(B_3) + P(A | B_4) * P(B_4)\\= (0.3 * 0.4) + (0.1 * 0.2) + (0.4 * 0.3) + (0.2 * 0.4)\\= 0.34[/tex]
Plugging these values into Bayes' theorem, we get:
[tex]P(B_2 | A) = P(A | B_2) * P(B_2) / P(A)\\= (0.1 * 0.2) / 0.34\\= 0.059\\[/tex]
Therefore, the probability that the person passed through the radar trap located at L2 given that she received a speeding ticket is 0..059 or 5.9%.
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22. Morality In a recent poll, the Gallup Organization found
that 45% of adult Americans believe that the overall state of
moral values in the United States is poor. Suppose a survey of a random sample of 500 adult Americans is conducted in which they are asked to disclose their feelings on the overall state of moral values in the United States. Use the normal approximation to the binomial to approximate the probability that
(a) exactly 250 of those surveyed feel the state of morals is poor.
(b) no more than 220 of those surveyed feel the state of morals is poor.
(c) more than 250 of those surveyed feel the state of morals is poor.
(d) between 220 and 250, inclusive, believe the state of morals is poor.
(e) at least 260 adult Americans believe the overall state of
moral values is poor. Would you find this result unusual? Why?
Answers
The probability that exactly 250 of those surveyed feel the state of morals is poor is approximately 0.9918.
(To find the probability that exactly 250 of those surveyed feel the state of morals is poor, we can use the normal approximation to the binomial with mean np = 500 * 0.45 = 225 and standard deviation √(npq) = √(500 * 0.45 * 0.55) ≈ 10.42, where q = 1 - p.
Then, we can standardize the value of 250 using the formula z = (x - np) / √(npq), where x is the number of people who feel the state of morals is poor.
z = (250 - 225) / 10.42 ≈ 2.4
Using a standard normal table or calculator, we find that the probability of z being less than or equal to 2.4 is approximately 0.9918.
Therefore, the probability that exactly 250 of those surveyed feel the state of morals is poor is approximately 0.9918.
(b) To find the probability that no more than 220 of those surveyed feel the state of morals is poor, we can use the normal approximation to the binomial with mean np = 500 * 0.45 = 225 and standard deviation √(npq) = √(500 * 0.45 * 0.55) ≈ 10.42, where q = 1 - p.
Then, we can standardize the value of 220 using the formula z = (x - np) / √(npq), where x is the number of people who feel the state of morals is poor.
z = (220 - 225) / 10.42 ≈ -0.48
Using a standard normal table or calculator, we find that the probability of z being less than or equal to -0.48 is approximately 0.3146.
Therefore, the probability that no more than 220 of those surveyed feel the state of morals is poor is approximately 0.3146.
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What’s the interest?
Answers
Amount Due at Maturity a. $102,000, b. $30,100, c. $62,620, d. $42,930, e. $40,700.
Describe Interest?Interest is the cost of borrowing money, typically expressed as a percentage of the borrowed amount, called the principal. It is the amount charged by a lender to a borrower for the use of money over a certain period of time. Interest can also refer to the amount earned on money that is invested, such as in a savings account or a bond. The rate of interest depends on factors such as the level of risk associated with the loan, the length of the loan period, and the market rate of interest at the time of borrowing. The amount of interest paid or earned can be calculated using various formulas, including simple interest and compound interest.
To determine the due date and amount of interest due at maturity for each note, we can use the following formula:
Interest = Principal x Rate x Time
where Principal is the face amount of the note, Rate is the annual interest rate, and Time is the time in years (based on a 360-day year).
a. January 5, $100,000, 6%, 120 days
Due Date: May 5
Time: 120/360 = 1/3 year
Interest = $100,000 x 0.06 x 1/3 = $2,000
Amount Due at Maturity = Principal + Interest = $100,000 + $2,000 = $102,000
b. February 15, $30,000, 4%, 30 days
Due Date: March 17 (assuming non-leap year)
Time: 30/360 = 1/12 year
Interest = $30,000 x 0.04 x 1/12 = $100
Amount Due at Maturity = Principal + Interest = $30,000 + $100 = $30,100
c. May 19, $62,000, 8%, 45 days
Due Date: July 3
Time: 45/360 = 1/8 year
Interest = $62,000 x 0.08 x 1/8 = $620
Amount Due at Maturity = Principal + Interest = $62,000 + $620 = $62,620
d. August 20, $42,400, 5%, 90 days
Due Date: November 18
Time: 90/360 = 1/4 year
Interest = $42,400 x 0.05 x 1/4 = $530
Amount Due at Maturity = Principal + Interest = $42,400 + $530 = $42,930
e. October 19, $40,000, 7%, 90 days
Due Date: January 17
Time: 90/360 = 1/4 year
Interest = $40,000 x 0.07 x 1/4 = $700
Amount Due at Maturity = Principal + Interest = $40,000 + $700 = $40,700
Therefore, the due date and amount of interest due at maturity for each note are as follows:
a. Due Date: May 5, Interest: $2,000, Amount Due: $102,000
b. Due Date: March 17, Interest: $100, Amount Due: $30,100
c. Due Date: July 3, Interest: $620, Amount Due: $62,620
d. Due Date: November 18, Interest: $530, Amount Due: $42,930
e. Due Date: January 17, Interest: $700, Amount Due: $40,700
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What is the surface area of the cylinder? Approximate using π = 3.14 and round to the nearest square meter.
a cylinder with a radius labeled 2.6 meters and height labeled 6.1 meters
82 square meters
91 square meters
96 square meters
142 square meters
Answers
Answer:
142 square meters
Step-by-step explanation:
To find the Surface Area of a Cylinder you have to use the formula [tex]A= 2\pi rh+2\pi r^2[/tex]
Plug in the radius, height, and pi to get
[tex]A=(2*3.14*2.6*6.1)+(2*3.14*2.6^2)\\A= (99.6008)+(42.4528)\\A= 142.0536\\[/tex]
You can round the answer to 142
Write the prime factorization of 25 use exponents when appreciate, and order the factors from least to greatest
Answers
Answer:5^2
Step-by-step explanation:
25
/ \
5 5
Since both 5 and 5 are prime, it can't be simplified more so the answer is 5^2.
solve the equation x^3 - x^2 - 8x + 12=0
Answers
The root of this given equation is 2, -3.
What is a quadratic equation?
Any equation that can be written in standard form as where x is an unknown value, a, b, and c are known quantities, and a 0 is a quadratic equation.
Here, we have
Given: x³ - x² - 8x + 12 = 0
We have to solve this equation and find the roots.
x³ - x² - 8x + 12 = 0
= (x-2)(x²+ x - 6) = 0
= (x-2)(x² + 3x - 2x - 6)
= (x-2)(x(x+3)-2(x+3))
= (x-2)(x+3)(x-2) = 0
x = 2, -3
Hence, the root of this given equation is 2, -3.
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After solving [tex]x^3 - x^2 - 8x + 12 = 0[/tex] we get x = 1, x = √8, and x = -√8.
The equation[tex]x^3 - x^2 - 8x + 12 = 0.[/tex]
Identify the given equation.
The given equation is [tex]x^3 - x^2 - 8x + 12 = 0.[/tex]
Look for possible factorization.
In this case, we can factor the equation by grouping:
[tex]x^3 - x^2 - 8x + 12 = (x^3 - x^2) + (-8x + 12)[/tex]
Factor out the common terms in each group.
[tex]x^3 - x^2 - 8x + 12 = x^2(x - 1) - 8(x - 1)[/tex]
Factor out the common binomial.
[tex]x^3 - x^2 - 8x + 12 = (x^2 - 8)(x - 1)[/tex]
Solve the factors for x.
Set each factor to zero and solve for x:
[tex]x^2 - 8 = 0[/tex] and x - 1 = 0
[tex]x^2 = 8[/tex], x = 1
x = ±√8
The solutions to the equation [tex]x^3 - x^2 - 8x + 12 = 0[/tex] are x = 1, x = √8, and x = -√8.
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10. Patrick is walking around an amusement park looking at the following map. Use the following diagram
and the following information to calculate the desired distances. Sides of grid squares represent 500 feet.
(HINT: The statement in bold will be important when calculating your answers.) Round your answers to the
nearest hundredth.
Bumper Cars
-654-3 -2 -1
Water Slide
JA
1
-1-
23
3
Ferris Wheel
Rollercoaster
1 2 3 4 5 6
Restrooms.
a) How far must she travel from the Bumper Cars to the Ferris Wheel?
b) What is the distance from the Water Slide to the Rollercoaster?
c) How far is it from the Bumper Cars to the Restrooms?
feet
d) If Sasha gets a direct distance from the Water Slide to the Ferris Wheel, how far is it?
Answers
a) The distance from the Bumper Cars to the Ferris Wheel is 3 squares or 1500 feet or 1.5 miles. b) 1000 feet or 1 mile. c) 2000 feet or 2 miles. d) 2500 feet or 2.5 miles.
What is distance?Distance is the measurement of how far apart two points are on a surface.
a) The distance from the Bumper Cars to the Ferris Wheel is 3 squares or 1500 feet. To calculate this, we can count the number of squares (3) from the Bumper Cars to the Ferris Wheel. Each square represents 500 feet, so the total distance is 1500 feet or 1.5 miles.
b) The distance from the Water Slide to the Rollercoaster is 2 squares or 1000 feet.
To calculate this, we can count the number of squares (2) from the Water Slide to the Rollercoaster. Each square represents 500 feet, so the total distance is 1000 feet or 1 mile.
c) The distance from the Bumper Cars to the Restrooms is 4 squares or 2000 feet.
To calculate this, we can count the number of squares (4) from the Bumper Cars to the Restrooms. Each square represents 500 feet, so the total distance is 2000 feet or 2 miles.
d) The direct distance from the Water Slide to the Ferris Wheel is 5 squares or 2500 feet.
To calculate this, we can count the number of squares (5) in a straight line from the Water Slide to the Ferris Wheel. Each square represents 500 feet, so the total distance is 2500 feet or 2.5 miles.
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