(a) Therefore, the z-value for an area of 0.08 to the right of z is -1.41. (b) Therefore, the z-value for an area of 0.025 to the right of z is -1.96. (c) Therefore, the z-value for an area of 0.05 to the right of z is -1.64. (d) Therefore, the z-value for an area of 0.10 to the right of z is -1.28.
To answer this question, we need to use the standard normal distribution table (also called the z-table or appendix table). This table gives the area under the standard normal curve to the left of a given z-value.
(a) To find the z-value for an area of 0.08 to the right of z, we can subtract the area from 1 (since the total area under the curve is 1) to get the area to the left of z:
1 - 0.08 = 0.92
Using the standard normal distribution table, we can find the z-value that corresponds to an area of 0.92 to the left of z. This value is approximately 1.41.
(b) Following the same process, for an area of 0.025 to the right of z, we find:
1 - 0.025 = 0.975
Looking at the standard normal distribution table, we find that the z-value corresponding to an area of 0.975 to the left of z is approximately 1.96.
(c) For an area of 0.05 to the right of z, we get:
1 - 0.05 = 0.95
The z-value corresponding to an area of 0.95 to the left of z is approximately 1.64.
(d) Finally, for an area of 0.10 to the right of z, we have:
1 - 0.10 = 0.90
The z-value corresponding to an area of 0.90 to the left of z is approximately 1.28.
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What is 131 divided by 1.5?
Answer:
87.3
Step-by-step explanation:
131 ÷ 1.5 = 87.3
The answer will be 87.3 repeat.
131 divided by 1.5 is equal to 8 with a remainder of 11, or 8.7333 (rounded to four decimal places).
We have,
To divide 131 by 1.5, we can perform the division operation as follows:
131 ÷ 1.5
To make the calculation easier, we can convert 1.5 to an equivalent fraction with a denominator of 10.
We can multiply both the numerator and denominator by 10 to get 15.
So, the division becomes:
131 ÷ 15
When we divide 131 by 15, we get a quotient of 8 with a remainder of 11.
Therefore,
131 divided by 1.5 is equal to 8 with a remainder of 11, or 8.7333 (rounded to four decimal places).
131 ÷ 1.5 is approximately equal to 8.7333.
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James has completed 3/4 of his homework. Marcus has completed 2/3 of his homework. Draw 2 number lines to represent these fractions . Who has more homework left to complete
The two number lines to represent these fractions are shown in the image attached below.
Marcus has more homework left to complete.
What is a number line?In Mathematics and Geometry, a number line simply refers to a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).
For James, he has completed 3x/4 of his homework while Marcus has completed 2x/3 of his homework and as such, Marcus has more homework left to complete.
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use the formula for the sum of the first n integers to evaluate the sum given below. 3+6+9+12+....+150
The sum of the numbers 3+6+9+12+....+150 is 3825. To find the sum of an arithmetic series, you can use the formula:
Sum = (n * (a1 + an)) / 2
where n is the number of integers, a1 is the first integer, and an is the last integer.
In this case, the series is 3, 6, 9, ..., 150, and it's an arithmetic series with a common difference of 3. To find the number of integers (n) in the series, use the formula:
n = ((an - a1) / common difference) + 1
n = ((150 - 3) / 3) + 1 = (147 / 3) + 1 = 49 + 1 = 50
Now, use the sum formula:
Sum = (n * (a1 + an)) / 2
Sum = (50 * (3 + 150)) / 2
Sum = (50 * 153) / 2
Sum = 7650 / 2
Sum = 3825
So the sum of the given series is 3825.
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A company has installed a generator to back up power in case there is a power failure. The probability that there will be a power failure during a snowstorm is .30. The probability that the generator will stop working during a snowstorm is .09. What is the probability that during a snowstorm the company will lose both sources of power? Note that the two sources are independent.
The probability that during a snowstorm the company will lose both sources of power is 2.7%.
To find the probability that during a snowstorm the company will lose both sources of power, we need to multiply the probabilities of each event happening. Since the two sources are independent, we can use the formula: P(A and B) = P(A) * P(B).
Let A be the event that there is a power failure during a snowstorm, with a probability of 0.30.
Let B be the event that the generator will stop working during a snowstorm, with a probability of 0.09.
Then, the probability of both events happening together is:
P(A and B) = P(A) * P(B)
P(A and B) = 0.30 * 0.09
P(A and B) = 0.027 or 2.7%
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Find the slope of the line tangent to the following polar curve at the given point. At the point where the curve intersects the origin (if this occurs), find the equationn of the tangent line in polar coordinates. r = 9 + 7 cos theta; (16,0) and (2, pi) Find the slope of the line tangent to r = 9 + 7 cos theta at (16,0). Select the correct choice below and fill in any answer boxes within your choice. Find the slope of the line tangent to r = 9 + 7 cos theta at (2, pi). Select the correct choice below and fill in any answer boxes within your choice. At the point where the curve intersects the origin (if this occurs), find the equationn of the tangent line in polar coordinates. Select the correct choice below and fill in any answer boxes within your choice. The equationn of the tangent line when the curve intersects the origin is The curve does not intersect the origin.
To find the slope of the line tangent to the polar curve r = 9 + 7 cos(theta) at the point (16, 0), we can use the formula:
dy/dx = (dy/dtheta) / (dx/dtheta) = (r' sin(theta) + r cos(theta)) / (r' cos(theta) - r sin(theta))
where r' = dr/dtheta.
First, we need to find r' by taking the derivative of r with respect to theta:
r' = dr/dtheta = -7 sin(theta)
Then, we can plug in the given values to find the slope at (16, 0):
dy/dx = [(r' sin(theta) + r cos(theta)] / [r' cos(theta) - r sin(theta)]
= [(-7 sin(0) sin(0) + (9 + 7 cos(0)) cos(0))] / [(-7 sin(0) cos(0)) - (9 + 7 cos(0)) sin(0))]
= (9 + 7) / (-9) = -2
Therefore, the slope of the line tangent to the polar curve r = 9 + 7 cos(theta) at the point (16, 0) is -2.
To find the slope of the line tangent to the polar curve r = 9 + 7 cos(theta) at the point (2, pi), we can use the same formula as above:
dy/dx = (r' sin(theta) + r cos(theta)) / (r' cos(theta) - r sin(theta))
First, we need to find r' by taking the derivative of r with respect to theta:
r' = dr/dtheta = -7 sin(theta)
Then, we can plug in the given values to find the slope at (2, pi):
dy/dx = [(r' sin(theta) + r cos(theta)] / [r' cos(theta) - r sin(theta)]
= [(-7 sin(pi) sin(2) + (9 + 7 cos(pi)) cos(2))] / [(-7 sin(pi) cos(2)) - (9 + 7 cos(pi)) sin(2))]
= (-2) / (7)
Therefore, the slope of the line tangent to the polar curve r = 9 + 7 cos(theta) at the point (2, pi) is -2/7.
The polar curve r = 9 + 7 cos(theta) intersects the origin when r = 0, which occurs when cos(theta) = -9/7, which is not possible since the range of cosine function is [-1, 1]. Therefore, the curve does not intersect the origin.
Since the curve does not intersect the origin, the answer is "The curve does not intersect the origin" for the equation of the tangent line in polar coordinates.
Evaluate the expression 2x^2 + 5xy - 3y^2 for x = 2 and y = -1
The answer for the value of the expression 2x² + 5xy - 3y², which is a quadratic equation, for x = 2 and y=-1, is 1.
The values of the unknown variable x that satisfy the equation are known as the roots or zeros of a quadratic equation. A quadratic equation of the type:
ax² + bx + c = 0 with a 0 can have solutions found using the quadratic formula. Given in the question, solutions are given as x= 2 and y=-1.
To evaluate the expression 2x² + 5xy - 3y² for x = 2 and y = -1, we substitute these values into the expression and simplify:
2x² + 5xy - 3y²
= 2(2)² + 5(2)⁻¹ - 3(-1)²
= 8 - 10 + 3
= 1
Therefore, the value of the expression 2x² + 5xy - 3y² for x = 2 and y = -1 is 1.
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Write the equation in standard form for the circle with center (-10, 0) passing through
(-12,3/2)
Answer:
Step-by-step explanation:
the standard equation for the circle is:
(x-a)²+(y-b)² = r²
the center is : A(a,b) and ridus r
you have : a= -10 and b=0 r²= (-12+10)²+(3/2-0)²= 4+ 9/4
r² = 25/4 so : r = 5/2
the standard equation for the circle is:
(x+10)²+y² =25/4
Find the shaded area of 12ft 5ft 9ft 18ft 5ft
The area of the shaded region is 180 square feet.
What is the shaded area?The figiure in the image is a triangle inscribed in a rectangle.
To get area of the shaded region, we subtract the area of the triangle from the area of the rectangle.
For the triangle:
Base = 18 - (5+5) = 8ftHeight = 9ftFor the rectangle:
Length = 18 ftWidth = 12 ftHence:
Area of the shaded region = Area of rectangle - Area of triangle
Area of the shaded region = ( length × width ) - ( 1/2 × base × height )
Area of the shaded region = ( 18ft × 12ft ) - ( 1/2 × 8ft × 9ft )
Area of the shaded region = 216ft ²- 36ft²
Area of the shaded region = 180ft²
Therefore, the area is 180ft².
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In right triangle DOG with the right angle O
find OG if DG = 4√5 and DO = 4.
The calclated length of segment OG is 8 units
Calculating the length OGFrom the question, we have the following parameters that can be used in our computation:
DG = 4√5
DO = 4.
The length OG is calculated as
OG^2 = DG^2 - DO^2
substitute the known values in the above equation, so, we have the following representation
OG^2 = (4√5)^2 - 4^2
Evaluate
OG^2 = 64
So, we have
OG = 8
Hence, the solution is 8
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the jenkins family is having a family reunion. 15 people are each bringing 2 tables each. there are the same amount of people sitting at each table. if 90 people attend the reunion how many people will sit at each table
If 15 people are each bringing 2 tables, then there will be a total of 30 tables at the family reunion.
Since there are the same amount of people sitting at each table, we can divide the total number of people (90) by the total number of tables (30).
90 ÷ 30 = 3
Therefore, there will be 3 people sitting at each table.
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Factorise completely 49xy+56x
Answer:
[tex]49xy + 56x = 7x(7y + 8)[/tex]
Determine the number of solutions that 5x^2 + 3x + 8 has without solving the equation.
The number of solutions that the quadratic equation, 5x² + 3x + 8 can have without solving the equation using discriminant is 0.
Given equation is,
5x² + 3x + 8
This is a quadratic equation.
It can have atmost 2 solutions.
So there can't be any solutions, there can be one solution or 2 solutions.
We can find the discriminant to know this.
Discriminant = √(b² - 4ac)
Here,
discriminant = √(3² - (4 × 5 × 8)) = √(9 - 160) = √(-154)
Discriminant is less than 0.
So there are no solutions.
Hence the number of solutions is 0.
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Find the 8th term of the geometric sequence 4,-12,36
The 8th term of the geometric sequence [tex]4,-12, 36[/tex] is [tex]-8748[/tex].
How to find the 8th term of the geometric sequence?We must find common ratio by dividing the term by its preceding term. By dividing second term (-12) by the first term (4), this gives us:
= -12 / 4
= -3
So, the common ratio is -3.
The formula for the nth term of geometric sequence to find the 8th term is : an = a1 * r^(n-1) where an = nth term, a1 = first term, r = common ratio and n = term number
a8 = 4 * (-3)^(8-1)
a8 = 4 * (-3)^7
a8 = 4 * (-2187)
a8 = -8748.
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Question 9 of 10
The vertex of this parabola is at (2, -4). When the y-value is -3, the x-value is
-3. What is the coefficient of the squared term in the parabola's equation?
10
10+
-10
O A. -1
OB. -5
O C. 1
DE
← PREVIOUS
(2,-4)
10
The coefficient of the squared term in the parabola's equation is 1/25.
How to determine the factored form of a quadratic equation?In this exercise, you are required to determine the factored form of the given quadratic function that passes through the points (2, -4) and (-3, -3).
In Mathematics, the vertex form of a quadratic function is represented by the following mathematical equation:
f(x) = a(x - h)² + k
Where:
h and k represents the vertex of the graph.a represents the leading coefficient.Based on the information provided above, we can determine the value of a as follows:
f(x) = a(x - h)² + k
-3 = a(-3 - 2)² - 4
-3 = 25a - 4
1 = 25a
a = 1/25
Therefore, the required quadratic function is given by:
f(x) = a(x - h)² + k
f(x) = y = 1/25(x - 2)² - 4
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Three experiments investigating the relation between need for cognitive closure and persuasion were performed. Part of the study involved administering a "need for closure scale" to a group of students enrolled in an introductory psychology course. The "need for closure scale" has scores ranging from 101 to 201. For the 72 students in the highest quartile of the distribution, the mean score was x = 175.90. Assume a population standard deviation of σ = 8.35. These students were all classified as high on their need for closure. Assume that the 72 students represent a random sample of all students who are classified as high on their need for closure. How large a sample is needed if we wish to be 99% confident that the sample mean score is within 1.5 points of the population mean score for students who are high on the need for closure? (Round your answer up to the nearest whole number.) students
Rounding up to the nearest whole number, we get a sample size of 314 students. Therefore, if we randomly select 314 students who are classified as high on their need for closure. we can be 99% confident that the sample mean score is within 1.5 points of the population mean score.
To determine the sample size needed, we can use the formula:
n = (z * σ / E)^2
Where:
z = the z-score corresponding to the desired level of confidence (in this case, 2.576 for 99% confidence)
σ = the population standard deviation (8.35)
E = the maximum allowable error (1.5)
Plugging in these values, we get:
n = (2.576 * 8.35 / 1.5)^2
n = 313.15
To determine the required sample size for a 99% confidence interval within 1.5 points of the population mean score, follow these steps:
1. Identify the given information:
- Population standard deviation (σ) = 8.35
- Desired margin of error (E) = 1.5
- Confidence level (z-score) = 2.576 (for 99% confidence interval)
2. Use the formula for sample size calculation:
n = (Z * σ / E)^2
3. Plug in the values:
n = (2.576 * 8.35 / 1.5)^2
4. Calculate the result:
n ≈ 121.22
5. Round up to the nearest whole number:
n = 122 students
So, a sample size of 122 students is needed to be 99% confident that the sample mean score is within 1.5 points of the population mean score for students who are high on the need for closure.
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The estimated marginal profit associated with producing X widgets is given by, p'(x)=-0.4x+20 where p'(x) is measured in dollars per unit per month when the level of production is X widgets per month. If the monthly fix cost for producing and selling the widgets is $80, find the maximum monthly profit.
$380 $420 $370 $460 $400
The maximum monthly profit is $420. To find the maximum monthly profit, we need to find the production level (X) that will maximize the profit.
We can do this by setting the marginal profit equation equal to zero and solving for X:
p'(x) = -0.4x + 20 = 0
0.4x = 20
x = 50
So, the production level that will maximize the profit is 50 widgets per month.
To find the maximum monthly profit, we need to calculate the total monthly revenue and subtract the fixed cost. The total monthly revenue can be calculated as the product of the price per unit and the number of units sold:
p(x) = -0.2x^2 + 20x
p(50) = -0.2(50)^2 + 20(50) = $500
So, the total monthly revenue is $500.
The maximum monthly profit can now be calculated as:
Profit = Total Revenue - Fixed Cost
Profit = $500 - $80
Profit = $420
Therefore, the maximum monthly profit is $420.
So, the answer is $420.
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plsss help!!! giving 100 B and brainliest.
29. The percentage of change is -39.66%.
30. The percentage of change is 35.29%
31. The percentage of change is 150.38%.
32. The percentage of change is -62.5%
How to calculate the percentageA percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.
The percentage of change is
= (-2300 / 5800) × 100
= -39.66%.
The percentage of change is:
= 6/17 × 100
= 35.29%
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A great egret has a wingspan of 180
centimeters. A red-tailed hawk has a
wingspan of 1,100 millimeters. Which has
bird has the greater wingspan? Explain.
The bird with the greater wingspan is the great egret
How to determine the greater wingspanTo determine the greater wingspan, we need to know the following conversion values, we have;
1 decimeter = 10 centimeters
1 decimeter = 100millimeters
1 centimeter = 10 millimeters
From the information given, we have;
The red-tailed hawk = 1,100 millimeters
The great egret = 180 centimeters
convert the millimeters to centimeters
if 1 centimeters = 10 millimeters
then, 180 centimeters = x
cross multiply
x = 1800 millimeters
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Is my answer right or wrong click to see file
The given representation is a quadratic function.
The given table can be represented in the form of equation as,
y = x²
When x = 0, y = 0
When x = 1, y = 1
When x = 2, y = 2² = 4
When x = 3, y = 3² = 9
When x = 4, y = 4² = 16
This can be written as,
y = x² + 0x + 0
This is a quadratic function.
Hence the given representation is a quadratic function.
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Practice
Example 1
Write each equation in exponential form.
1. log₁5 225 = 2
4. log3 243 = 5
10. ()³ = 343
Example 2
Write each equation in logarithmic form.
7. 27 = 128
Example 3
Evaluate each expression.
13. log2 64
16. log27 81
2. 1093 27 = -3
19. logg 512
5. log4 64 = 3
8. 3-4 = 1
11. 29 = 512
14. log100 100,000
17. 1094 32
20. log, 1
Practice
3. logs 25= -2
6. log432 = 5/2
9. 7-2 = 49
12. 643 = 16
15. log5 625
ace
18. log₁0 0.00001
21. logg 4
Answer: 546
Step-by-step explanation:
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Is vector v with an initial point of (0,0) and a terminal point of (50,120) equal to vector u with an initial point of (50,120) and a terminal point of (0,0)?
The vectors u and v are not equal because they have different direction.
If the initial point is (x₁, y₁) and terminal point is (x₂, y₂) then the vector is
Vector =(x₂-x₁)i+(y₂-y₁)j
Vector v with an initial point of (0, 0) and a terminal point of (50,120).
Vector v = 50i+120j..(1)
Vector u with an initial point of (50, 120) and a terminal point of (0,0).
Vector u = (0-50)i+(0-120)j
=-50i-120j..(2)
Hence, the vectors u and v are not equal because they have different direction.
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Sophie and Simon are peeling a pile of potatoes for lunch in the cafeteria. Sophie can peel all the potatoes by herself in 45 minutes, while it would take Simon 30 minutes to do the job working alone. If Sophie and Simon work together to peel the potatoes, how long will i
The time taken by them to complete the work is 18 minutes.
Time taken by Sophie to peel all the potatoes = 45 minutes
Time taken by Simon to peel all the potatoes = 30 minutes
Amount of work done by Sophie in one minute = 1/45
Amount of work done by Simon in one minute = 1/30
Let the time taken by both of them to complete the work together be x.
So, the time taken by them to complete the work,
1/x = (1/45) + (1/30)
x = 1350/75
x = 18 minutes
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the noise level in a restaurant is normally distributed with an average of 30 decibels. 99% of the time it is below what value?
According to the given information, the noise level in a restaurant is normally distributed with an average of 30 decibels. To find the value below which 99% of the time the noise level is, we need to use the Z-table.
We know that 99% of the area under the normal curve is below a Z-score of 2.33 (found from the Z-table).
To find the corresponding noise level value, we use the formula:
Z-score = (X - μ) / σ
where X is the noise level value we want to find, μ is the average (30 decibels), and σ is the standard deviation (which is not given in this question).
However, we can use the empirical rule (68-95-99.7 rule) to estimate the standard deviation. According to the rule, 99.7% of the data falls within 3 standard deviations of the mean. So, if 99% of the time the noise level is below a Z-score of 2.33, then we can estimate that the standard deviation is approximately:
(2.33 x σ) = 3
Solving for σ, we get:
σ = 3 / 2.33 = 1.29 (approx.)
Now we can use the formula above to find the noise level value below which 99% of the time the noise level is:
2.33 = (X - 30) / 1.29
X - 30 = 2.33 x 1.29
X = 33.01
So, 99% of the time, the noise level in the restaurant is below 33.01 decibels (rounded to two decimal places).
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Find the gradient of a line perpendicular to the longest side of the triangle formed by A(-3,4),B(5,2) and C(0,-3)
The gradient of the line is 2
How to solve for the gradient[tex]Distance AB = \sqrt{[(5-(-3))^2 + (2-4)^2]}= \sqrt{68} \\Distance AC = \sqrt{[(-3-0)^2 + (4-(-3))^2]} = \sqrt{58} \\Distance BC = \sqrt{[(5-0)^2 + (2-(-3))^2]}= \sqrt{50}[/tex]
mAB = (2 - 4) / (5 - (-3)) = -1/2
This is the slope of AB
-1 / (-1/2) = 2
we have to find the point that is perpendicular to AB
(-3 + 5) / 2 = 1
(4 + 2) / 2 = 3
1 , 3 are perpendicular to AB
y - 3 = 2(x - 1)
y - 3 = 2x - 2
y = 2x + 1
There fore the gradient of the line is 2
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1) Find the linearization L(x) of the function at a. f(x)= x^4 + 3x^2, a= -1
Therefore, the linearization of f(x) at a = -1 is L(x) = -10x - 6.
To find the linearization L(x) of the function f(x) = x⁴ + 3x² at a = -1, we need to use the formula:
L(x) = f(a) + f'(a)(x-a)
where f'(x) is the derivative of f(x) with respect to x.
First, we need to find f(-1) and f'(-1).
f(-1) = (-1)⁴ + 3(-1)²
= 1 + 3
= 4
f'(x) = 4x³ + 6x
f'(-1) = 4(-1)³ + 6(-1)
= -4 - 6
= -10
Now we can substitute these values into the linearization formula:
L(x) = f(-1) + f'(-1)(x - (-1))
L(x) = 4 - 10(x + 1)
L(x) = -10x - 6
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prove that the recursive algorithm for finding the reversal of a bit string that you gave in exercise 37 is correct.
To prove that the recursive algorithm for finding the reversal of a bit string is correct, let's consider the algorithm's key components: base case, recursive case, and the correctness of the algorithm
The recursive algorithm for finding the reversal of a bit string is as follows:
1. If the string is empty or has only one character, return the string as it is.
2. Otherwise, split the string into two parts: the first character (i.e., the leftmost character) and the rest of the string (i.e., all the other characters).
3. Recursively reverse the rest of the string.
4. Concatenate the reversed rest of the string with the first character.
To prove that this algorithm is correct, we need to show that it produces the correct output for any input string. We can do this by induction on the length of the string.
Base case: If the string is empty or has only one character, the algorithm returns the string as it is, which is the correct reversal.
Induction step: Suppose the algorithm correctly reverses any string of length n or less. We want to show that it also correctly reverses any string of length n+1. Let s be a string of length n+1, and let s' be the string obtained by removing the last character of s. Then we have s = s' + c, where c is the last character of s.
By the induction hypothesis, the algorithm correctly reverses s'. Let s'' be the reversed s'. Then s'' + c is the reversal of s, since the reversed s' is the reversed rest of the string, and c is the first character.
Therefore, the algorithm correctly reverses any string of length n+1, and by induction, it correctly reverses any string of any length.
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Lesson 10.1.3 - Review and Preview
ANSWERS ARE NEEDED ASAP APEPRICATED AND WILL TRY TO PUT YOU AS BRAINLIEST WHEN IM ACTIVE (FIRST ONE THAT SOLVES THE PROBLEM AND SHOWS STEPS)
The calculated volume of the prism is 104 cubic feet
From the question, we have the following parameters that can be used in our computation:
Volume of right pyramid = 312 cubic feet
The volume of the prism next to it is calculated as
Volume = 1/3 * Volume of right pyramid
Substitute the known values in the above equation, so, we have the following representation
Volume = 1/3 * 312 cubic feet
Evaluate
Volume = 104 cubic feet
Hence, the volume is 104 cubic feet
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find the lenght of side x
give your answer in simplist form
The length of side x based on the triangle given will be 26.2cm.
How to calculate the length of the triangleIt should be noted that the image of the triangle is missing, so i have attached it.
In this case, to find the value of x, we will use cosine rule;
x² = 15² + 18² - 2(15 × 18)cos105
x² = 225 + 324 - 540(-0.2558)
x² = 549 + 138.132
x² = 687.132
x ≈ 26.2 cm
Therefore, length of side x based on the triangle given will be 26.2cm.
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Part B: If Susan originally has 7 yards of fabric, how much is left over after making the aprons? Show every step of your work. (5 points).
Based on fractional values, if Susan originally has 7 yards of fabric, after making 3 aprons consuming 5⁵/₈ yards, the quantity of fabric left is 1³/₈ yards.
What are fractional values?Fractional values are the results of fractional computations.
Fractions may be proper, improper, and complex fractions, depending on the values of the denominators and the numerators.
Algebraic expressions that have fractions are stated as fractional values.
The original quantity of fabric that Susan has = 7 yards
The quantity of fabric used for the front of each apron = 1¹/₄ yards
The quantity of fabric used for the tie of each apron = ⁵/₈ yards
The total quantity of fabric used for each apron = 1⁷/₈ yards (1¹/₄ + ⁵/₈)
The total quantity of fabric used for the 3 aprons made = 5⁵/₈ yards (1⁷/₈ x 3)
Therefore, the remaining quantity of fabric that Susan has after making the 3 aprons = 1³/₈ yards (7 - 5⁵/₈).
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Question Completion:Susan first made 3 aprons using 1¹/₄ yards for the front and ⁵/₈ yards for the tie.
estimate the value(s) of c that satisfy the conclusion of the mean value theorem on the interval [2, 6]. (enter your answers as a comma-separated list. round your answers to one decimal places. if an answer does not exist, enter dne.)
The mean value theorem states that if a function f(x) is continuous on the interval [a, b] and differentiable on (a, b), then there exists a value c in (a, b) such that:
f'(c) = (f(b) - f(a))/(b - a)
In this case, the interval is [2, 6]. So, we need to find the value(s) of c that satisfy:
f'(c) = (f(6) - f(2))/(6 - 2)
We can make an estimate based on the graph of the function.
If the graph of f(x) is a straight line between (2, f(2)) and (6, f(6)), then the derivative is constant over the interval [2, 6]. In this case, we can use the formula:
f'(c) = (f(6) - f(2))/(6 - 2) = (y2 - y1)/(x2 - x1)
where (x1, y1) = (2, f(2)) and (x2, y2) = (6, f(6)).
Solving for c, we get:
c = (x1 + x2)/2 = (2 + 6)/2 = 4
This is the only value of c that satisfies the conclusion of the mean value theorem in this case.
If the graph of f(x) is not a straight line, then we cannot make a simple estimate for c based on the graph alone.
To estimate the value(s) of c that satisfy the conclusion of the Mean Value Theorem (MVT) on the interval [2, 6], you need to follow these steps:
1. Identify the function, f(x), that you're working with.
2. Ensure the function is continuous on the interval [2, 6] and differentiable on the open interval (2, 6). This is required for MVT to be applicable.
3. Calculate the average rate of change (mean value) of the function over the interval [2, 6] by using the formula (f(6) - f(2)) / (6 - 2).
4. Take the derivative of the function, f'(x).
5. Set f'(x) equal to the mean value calculated in step 3 and solve for the value(s) of x, which will give you the value(s) of c that satisfy the MVT.
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