Charlie drove 90 miles between San Antonio and Houston.
Nicholas and Rose each drove 2/5 of the total distance (190 miles). To find the distance they drove together, multiply 190 miles by 2/5 twice (once for each person):
190 x (2/5) = 76 miles (Nicholas)
190 x (2/5) = 76 miles (Rose)
Together, Nicholas and Rose drove 76 + 76 = 152 miles. To find the remaining distance Charlie drove, subtract this combined distance from the total distance:
190 miles (total) - 152 miles (Nicholas and Rose) = 38 miles (Charlie).
Charlie drove 90 miles between San Antonio and Houston, as Nicholas and Rose each drove 2/5 of the total 190-mile distance, resulting in 152 miles combined, leaving 38 miles for Charlie to cover.
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Select the correct answer
a mine extracts 2 metric tons of coal in an hour. the
number of hours spent mìning, which expression re
oa. the expression is at. the amount of ore
ob. the expression
The expression that represents the amount of ore sold and how much ore can the mine sell after extracting ore for 12 hours is option B: The expression is 2t−14t. The amount of ore is 21 metric tons.
The reasoning for the selection of the expression and amount of ore can the mine sell after extracting ore for 12 hours is as follows.
1: Determine the amount of coal used for electricity generation in terms of t.
The mine uses 14 tons of coal every hour, so the total amount used for electricity generation is 14t.
2: Determine the total amount of coal extracted in terms of t.
The mine extracts 2 tons of coal every hour, so the total amount extracted is 2t.
3: Calculate the amount of coal sold in terms of t.
To find the amount of coal sold, subtract the amount used for electricity generation from the total amount extracted: 2t - 14t.
4: Determine the amount of coal sold after 12 hours.
Substitute t = 12 into the expression:
2(12) - 14(12) = 24 - 168 = -144.
However, since the mine uses 14 tons of the extracted coal every hour, it cannot sell more coal than it extracts. So, the correct expression should be 2t - 14 (without the t for the amount used for electricity generation).
5: Calculate the amount of coal sold after 12 hours using the corrected expression.
Substitute t = 12 into the expression: 2(12) - 14 = 24 - 14 = 10 metric tons.
The correct expression should be 2t - 14, and the amount of coal the mine can sell after extracting coal for 12 hours is 10 metric tons. Hence, the correct answer is option B.
Note: The question is incomplete. The complete question probably is: A mine extracts 2 metric tons of coal in an hour. The mine uses 14 ton of the extracted coal every hour to generate electricity for the mine and sells the rest. If t is the number of hours spent mining, which expression represents the amount of ore sold? How much ore can the mine sell after extracting ore for 12 hours? A) The expression is 2t−1/4t. The amount of ore is 23 3/4 metric tons. B) The expression is 2t−1/4t. The amount of ore is 21 metric tons. C) The expression is 2t+1/4t. The amount of ore is 24 metric tons. D) The expression is 2t+1/4t. The amount of ore is 24 1/4 metric tons.
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Find, correct to six decimal places, the root of the equation cos(x) = x. SOLUTION We first rewrite the equation in standard form: cos(x) − x = 0. Therefore, we let f(x) = cos(x) − x. Then, f '(x) = , so Newton's method becomes xn+1 = xn − cos(xn) − xn −sin(xn) − 1 = xn + cos(xn) − xn sin(xn) + 1 . In order to guess a suitable value for x1, we sketch the graphs of y = cos(x) and y = x in the figure. It appears that they intersect at a point whose x-coordinate somewhat less than 1, so let's take x1 = 1 as a convenient first approximation. Then remembering to put our calculator in radian mode, we get the following. x2 ≈ 0.75036387 x3 ≈ 0.73911289 x4 ≈ 0.73908513 x5 ≈ 0.73908513 Since x4 and x5 agree to six decimal places (eight, in fact), we conclude that the root of the equation, correct to six decimal places, is .
Using Newton's method, the root of the equation cos(x) = x correct to six decimal places is approximately 0.739085.
To solve the equation cos(x) = x, we can use Newton's method, which involves repeatedly applying an iterative formula to approximate the root of the equation. We first rewrite the equation in the form f(x) = cos(x) - x = 0 and find its derivative f'(x) = -sin(x) - 1.
The iterative formula for Newton's method is given by xn+1 = xn - f(xn)/f'(xn). Applying this formula, we get xn+1 = xn + cos(xn) - xn sin(xn) + 1.
To start the iteration, we need to guess a suitable value for x1. From the graph of y = cos(x) and y = x, we can see that they intersect at a point whose x-coordinate is slightly less than 1. Therefore, we take x1 = 1 as a convenient first approximation.
Using a calculator in radian mode, we can apply the iterative formula to obtain the following approximations:
x2 ≈ 0.75036387
x3 ≈ 0.73911289
x4 ≈ 0.73908513
x5 ≈ 0.73908513
Since x4 and x5 agree to six decimal places, we can conclude that the root of the equation cos(x) = x correct to six decimal places is approximately 0.739085.
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Find, from first principle the deriva- tive of 1/(x²+1)
Step-by-step explanation:
[tex] \frac{1}{( {x}^{2} + 1) } = \frac{u}{v} [/tex]
u = 1
u' = 0
v = x² + 1
v' = 2x
[tex] \frac{1}{ ({x}^{2} + 1)} \\ = \frac{u'v - v'u}{ {v}^{2} } \\ = \frac{0 - (2x \times 1)}{ {( {x}^{2} + 1)}^{2} } \\ = - \frac{2x}{ { ({x}^{2} + 1) }^{2} } [/tex]
#CMIIWA shoe store donated a percent of every sale to charity. The total sales were $7,200 so the store donated $144. What percent of $7,200 was donated to charity?
The percentage of $7,200 that was donated to charity would be = 2%
How to calculate the percentage of the total sales that was donated?To calculate the percentage of the total sales that was donated, the following should be carried out.
The total sales at the shoe store = $7,200
The amount of money that was donated = $144
Therefore to calculate the percentage the following is done ;
= 144/7200 × 100/1
= 14400/7200
= 2%
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A method for determining whether a critical point is a relative minimum or maximum using concavity.
To determine whether a critical point is a relative minimum or maximum using concavity, we need to examine the second derivative of the function at the critical point.
If the second derivative is positive, then the function is concave up, meaning it is shaped like a bowl opening upwards. At a critical point where the first derivative is zero, this indicates a relative minimum, as the function is increasing on either side of the critical point.
On the other hand, if the second derivative is negative, then the function is concave down, meaning it is shaped like a bowl opening downwards. At a critical point where the first derivative is zero, this indicates a relative maximum, as the function is decreasing on either side of the critical point.
If the second derivative is zero, then the test is inconclusive and further analysis is needed, such as examining higher order derivatives or using other methods such as the first derivative test.
Therefore, the concavity test is a useful method for determining the nature of critical points and whether they represent a relative minimum or maximum.
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Complete question is:
What we need to examine for a method for determining whether a critical point is a relative minimum or maximum using concavity.
350 divided by 80?!?!
Answer:
350/80
cancel out the zeros
35/8
4 3/8 or 4.375
350 divided by 80 is equal to 4 with a remainder of 30, or in decimal form, it is approximately 4.375.
We have,
To divide 350 by 80, we can perform the division operation as follows:
- First, we check how many times 80 can be divided into 350. We start with the largest multiple of 80 which is less than or equal to 350, which is 4.
80 x 4 = 320
- We subtract 320 from 350 to find the remainder:
350 - 320 = 30
- Since the remainder is not zero,
We can continue dividing. We bring down the next digit of 350, which is 0.
- Now, we have 300 as the new dividend.
We ask ourselves how many times 80 can be divided into 300.
80 x 3 = 240
- Subtracting 240 from 300 gives us the new remainder:
300 - 240 = 60
- Again, the remainder is not zero, so we continue.
- We bring down the last digit of 350, which is 0, and our new dividend becomes 600.
- We ask ourselves how many times 80 can be divided into 600.
80 x 7 = 560
- Subtracting 560 from 600 gives us the new remainder:
600 - 560 = 40
- The remainder is still not zero, so we continue.
- Finally, we bring down the last digit of 350, which is 0.
Our new dividend is 400.
We ask ourselves how many times 80 can be divided into 400.
80 x 5 = 400
- Subtracting 400 from 400 gives us zero as the remainder.
Since the remainder is now zero, we can stop dividing.
Therefore,
350 divided by 80 is equal to 4 with a remainder of 30, or in decimal form, it is approximately 4.375.
In summary, 350 divided by 80 equals 4 with a remainder of 30, or 4.375.
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Please help solve 5 and 6 and show work please
a. The actual area of the kitchen is 128 square feet.
b. the couch measures 1.25 inches across in the scale drawing.
How do we calculate?The scale is 1/4 inch = 2 feet,
meaning that in the drawing, each inch represents 8 feet (since 2 feet/0.25 inches = 8 feet/inch).
The kitchen in the drawing has an area of 2 square inches.
we apply the scale factor to find the actual area in square feet,
1 inch in the drawing = 8 feet in real life
So, 2 square inches in the drawing = 2 x 8 x 8 = 128 square feet in real life.
Hence, the actual area of the kitchen is 128 square feet.
we also apply the scale factor to find the couch measurement in the scale drawing,
1 inch in the drawing = 8 feet in real life
10 feet in real life = 10/8 = 1.25 inches in the drawing.
In conclusion, the couch measures 1.25 inches across in the scale drawing.
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Question 3 Part C (3 points): Tami has two jobs and can work at most 20 hours each week. She works as a server and makes $6 per hour. She also tutors and makes $12 per hour. She needs to earn at least $150 a week. Review the included image and choose the graph that represents the system of linear inequalities.
The expression of linear inequalities that represents Tami's earnings is as follows: 6x + 12y ≥ 150.
What is linear inequality?A linear inequality is a mathematical expression that involves a linear function and a relational operator such as <, >, ≤, ≥, or ≠ and it can be used to compare two expressions or values. It defines a range of values that satisfy inequality.
For the scenario painted above, we see that Tani is meant to earn a minimum of $150 Thus, the greater than or equal to symbol ≥ should be used for the expression. $6 per hour and $12 per hour are also well represented in the equation.
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Does anyone know how to help
The volume of the cylinder after the rotation of rectangle is V = 12π units³ = 37.68 units³
Given data ,
Let the width of the rectangle be w = 2 units
Let the length of the rectangle be l = 3 units
Now , on rotating a rectangle , we get a cylinder
And , the radius of the cylinder = 2 units
And , the height of the cylinder = 3 units
Now , Volume of Cylinder = πr²h
On simplifying , we get
V = π ( 2 )² ( 3 )
V = 12π units³
V = 37.68 units³
Hence , the volume of cylinder is V = 37.68 units³
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Help with problem in photo
The measures of the arc angle AP is 63° using the Angles of Intersecting Chords Theorem
What is the Angles of Intersecting Chords Theorem
The Angles of Intersecting Chords Theorem states that the angle formed by the intersection of the chords is equal to half the sum of the intercepted arcs, and conversely, that the measure of an intercepted arc is half the sum of the two angles that intercept it.
109° = (AP + RQ)/2
109 = (AP + 155)/2
AP + 155 = 2 × 109 {cross multiplication}
AP + 155 = 218
AP = 218 - 155 {collect like terms}
AP = 63°
Therefore, the measures of the arc angle AP is 63° using the Angles of Intersecting Chords Theorem
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In each figure congruent parts are marked. Give additional congruent parts to prove that the right triangles are congruent and state the congruence theorem that justifies your answer.
please help me
To prove that the right triangles are congruent, we need to show that they have three pairs of congruent parts (sides or angles).
Let's say that the given congruent parts are the hypotenuses and one leg of each triangle. To prove congruence, we can add one more pair of congruent parts, such as the other leg.
By the Side-Angle-Side (SAS) congruence theorem, if two triangles have two pairs of congruent sides and the included angle is also congruent, then the triangles are congruent. In this case, we have two pairs of congruent sides (the hypotenuses and one leg) and the included angle (the right angle) is congruent by definition.
Therefore, we can conclude that the two right triangles are congruent by SAS.
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Lesley needs to spend at least $15 at the grocery store to use a coupon. She buys 1 container of tomatoes and needs to buy some potatoes. One container of tomatoes costs $2. 75 and one pound of potatoes costs $2. 45. How may pounds of potatoes, p, does Lesley need to buy to use the coupon? write your answer using an inequality symbol
Answer: 5
2.75+(2.45x5) = 15
exercise 4.11. on the first 300 pages of a book, you notice that there are, on average, 6 typos per page. what is the probability that there will be at least 4 typos on page 301? state clearly the assumptions you are making.
The probability that there will be at least 4 typos on page 301 is 0.847
To solve this problem, we need to make some assumptions. Let's assume that the number of typos on each page follows a Poisson distribution with a mean of 6 typos per page, and that the number of typos on one page is independent of the number of typos on any other page.
Under these assumptions, we can use the Poisson distribution to calculate the probability of observing a certain number of typos on a given page.
Let X be the number of typos on page 301. Then X follows a Poisson distribution with a mean of 6 typos per page. The probability of observing at least 4 typos on page 301 can be calculated as follows
P(X ≥ 4) = 1 - P(X < 4)
= 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3)
Using the Poisson distribution formula, we can calculate the probabilities of each of these events
P(X = k) = (e^-λ × λ^k) / k!
where λ = 6 and k is the number of typos. Thus,
P(X = 0) = (e^-6 × 6^0) / 0! = e^-6 ≈ 0.0025
P(X = 1) = (e^-6 × 6^1) / 1! = 6e^-6 ≈ 0.015
P(X = 2) = (e^-6 × 6^2) / 2! = 18e^-6 ≈ 0.045
P(X = 3) = (e^-6 × 6^3) / 3! = 36e^-6 ≈ 0.091
Plugging these values into the equation above, we get
P(X ≥ 4) = 1 - (e^-6 + 6e^-6 + 18e^-6 + 36e^-6)
≈ 0.847
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The cost of a service call to fix a washing machine can be expressed by the linear function y = 45 x + 35, where y represents the total cost and x represents the number of hours it takes to fix the machine. What does the slope represent?
The cost for each hour it takes to repair the machine.
The cost for coming to look at the machine.
The total cost for fixing the washing machine.
The amount of time that it takes to arrive at the home to make the repairs.
Answer:
A) The cost for each hour it takes to repair the machine.-----------------------
The total cost of repair is expressed by the function:
y = 45x + 35As we see,
y- is the total cost, x - is the number of hours to fix;The slope is 45 and it represents the cost per hour to fix the car;The 35 is the y-intercept that represents a one off cost for service.Therefore the answer is option A.
Find the distance between
the points (4, -3) and (-2, 1)
on the coordinate plane.
Ay
O
X
Answer:no image
Step-by-step explanation:
Michael is using a rotating
sprinkler to water his lawn. The
sprinkler rotates in a complete
circle. It sprays water at most 8
feet. Find the area of the lawn
that is watered. Use 3. 14 for π. Show Your Work
The area of the lawn that is watered by the sprinkler is approximately 200.96 square feet.
The area of the field that's doused by the sprinkler is a sector of a circle with a compass of 8 bases and a central angle of 360 degrees.
To find the area of the sector, we can use the formula
Area = ( θ/ 360) x πr2
where θ is the central angle in degrees,
r is the radius of the circle,
and π is the constant pi.
Substituting the given values,
we get Area = (360/360) x3.14 x 82
Area = 3.14 x 64 Area = 200.96
Thus, the area of the field that's doused by the sprinkler is roughly 200.96 square feet.
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The complete question is as follows:
Michael is using a rotating sprinkler to water his lawn. The sprinkler rotates in a complete circle. It sprays water at most 8 feet. Find the area of the lawn that is watered.
Suppose that prices of a gallon of milk at various stores in one town have a mean of $3.75 with a standard deviation of $0.09. using chebyshev's theorem, what is the minimum percentage of stores that sell a gallon of milk for between $3.57 and $3.93? round your answer to one decimal place.
68% of the stores will sell a gallon of milk for between $3.57 and $3.93 with one standard deviation of the mean.
Mean = $3.75
Standard deviation = $0.09.
Selling variations = $3.57 to $3.93.
Chebyshev's theorem states that if k is a positive number, then, in any data at least [tex](1 - 1/k^2)[/tex] of the data will fall in K standard deviations from the mean data.
For normal distributions, 68% of the values will fall within one standard deviation of the mean.
For non-normal deviations, 75% of values will fall within 2 standard deviations of the mean.
Here we need to find the Upper limit and lower limit of the data.
$3.75 - $0.09 = $3.66
$3.75 + $0.09 = $3.84
The price range will be between $3.66 and $3.84.
To calculate the minimum percentage of stores using Chebyshev's theorem
minimum percentage = [tex]1 - 1/k^2[/tex]
minimum percentage = [tex]1 - 1/(1^2)[/tex]
minimum percentage = 0
Here, 0% of stores will fall with only one standard deviation from the Mean.
Therefore, we can conclude that 68% of the stores will sell a gallon of milk for between $3.57 and $3.93.
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Patricia bought
4
4 apples and
9
9 bananas for
$
12. 70
$12. 70. Jose bought
8
8 apples and
11
11 bananas for
$
17. 70
$17. 70 at the same grocery store.
What is the cost of one apple?
The cost of apples and bananas are $ 0.70 and $ 1.10 respectively if Patricia bought 4 apples and 9 bananas for $12.70 and Jose got 8 apples and 11 bananas for $17.70
Let the cost of one apple be a
the cost of one banana be b
In the case of Patricia,
12.70 = cost of 4 apples + cost of 9 bananas
Cost of 4 apples = 4a
Cost of 9 bananas = 9b
The equation we get is
4a + 9b = 12.70 ----(i)
In the case of Jose,
17.70 = cost of 8 apples + cost of 11 bananas
Cost of 8 apples = 8a
Cost of 11 bananas = 11b
The equation we get is
8a + 11b = 17.70 ----(ii)
Multiply (i) by 2
8a + 18b = 25.40 --- (iii)
Subtract (ii) and (iii)
7b = 7.70
b = $ 1.10
4a + 9 (1.10) = 12.70
4a + 9.90 = 12.70
4a = 2.80
a = $ 0.70
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Use the given circumference to find the surface area of the spherical object.
a pincushion with c = 18 cm
To find the surface area of a spherical object, we need to know the radius of the sphere. However, in this case, only the circumference of the pincushion is given, which is not enough information to directly determine the radius.
The formula relating the circumference (c) and the radius (r) of a sphere is:
c = 2πr
To find the surface area (A) of the sphere, we can use the formula:
A = 4πr^2
Since we don't have the radius, we need to solve the circumference formula for the radius first:
c = 2πr
Divide both sides of the equation by 2π:
r = c / (2π)
Now we can substitute the value of c = 18 cm into the equation to find the radius:
r = 18 cm / (2π)
r ≈ 2.868 cm (approximately)
Now that we have the radius, we can calculate the surface area using the formula:
A = 4πr^2
A = 4π(2.868 cm)^2
A ≈ 103.05 cm² (approximately)
Therefore, the surface area of the pincushion is approximately 103.05 square centimeters.
Simplify the product using foil. (3x-4)(6x-2)
a. 18x^2 + 30x - 8
b. 18x^2 + 18x - 8
c. 18x^2 - 30x + 8
d. 18x^2 - 18x + 8
Using FOIL, the simplified expression for the product of (3x-4)(6x-2) is c. 18x² - 30x + 8.
To simplify the product (3x-4)(6x-2) using FOIL, we follow the First, Outer, Inner, Last rule. Let's break down the process:
First: Multiply the first terms of both expressions:
(3x) * (6x) = 18x²
Outer: Multiply the outer terms of both expressions:
(3x) * (-2) = -6x
Inner: Multiply the inner terms of both expressions:
(-4) * (6x) = -24x
Last: Multiply the last terms of both expressions:
(-4) * (-2) = 8
Now, combine the results:
18x² - 6x - 24x + 8
Simplify by combining the like terms (middle terms -6x and -24x):
18x² - 30x + 8
The simplified product is 18x² - 30x + 8, which corresponds to option (c).
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A dessert has both fruit and yogurt inside.Altogether,the mass of the dessert is 185g.The ratio of the mass of fruit to the mass of yogurt is 2:3 What is the mass of yogurt?
jameson plans to create a larger kennel by doubling the dimensions in the blueprint. how many times the perimeter of the original kennel is the
perimeter of the larger kennel?
The perimeter of the larger kennel will be twice as large as the perimeter of the original kennel.
To find the ratio of the perimeters of the original kennel to the larger kennel, we need to know how doubling the dimensions affects the perimeter.
Since the perimeter is the sum of all four sides, doubling each side will result in a perimeter that is double the original.
Therefore, the perimeter of the larger kennel will be two times the perimeter of the original kennel.
In mathematical terms:
Perimeter of larger kennel = 2 x perimeter of original kennel
So, the perimeter of the larger kennel will be twice as large as the perimeter of the original kennel.
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All the 4-digit numbers you could make using seven square tiles numbered 2, 3, 4, 5, 6, 7, and 8
Using the seven square tiles numbered 2, 3, 4, 5, 6, 7, and 8, we can make 1260 different 4-digit numbers.
To create a 4-digit number using these seven square tiles, we have to consider the following:
- The first digit cannot be 2 because then the number would only have three digits.
- We can choose any of the remaining six tiles for the first digit, which means there are 6 choices.
- We can choose any of the seven tiles for the second digit, which means there are 7 choices.
- We can choose any of the remaining six tiles for the third digit, which means there are 6 choices.
- We can choose any of the remaining five tiles for the fourth digit, which means there are 5 choices.
Therefore, the total number of 4-digit numbers we can make is:
6 x 7 x 6 x 5 = 1260
So, using the seven square tiles numbered 2, 3, 4, 5, 6, 7, and 8, we can make 1260 different 4-digit numbers.
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Levi finds a skateboard that sells for 139. 99. The store charges 6% sales taxes. About how much money will he have to spend for his skateboard
$148.39 much money will he have to spend for his skateboard.
Levi will have to spend approximately $148.39 for his skateboard.
The original price can be defined as the cost price of an item or a service. The decrease in the original price of a product or service is called the discount offered to the buyer. Generally, this discount is expressed as a percentage.
Original Sale Price means the price at which the current Owner purchased the Property (not including commissions, loan origination fees, appraisals fees, title insurance premiums and other similar transaction costs).
To calculate this, we need to find 6% of the original price and add it to the original price:
6% of 139.99 = 0.06 x 139.99 = 8.3994
Adding this to the original price gives:
139.99 + 8.3994 = 148.3894
Rounding to the nearest cent gives $148.39.
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Full Term O Question 10 9 pts 5 1 Let f(x) = 3 + 6x? - 153 +3. 2" (a) Compute the first derivative of '(x) = 70 hents (c) On what interval is increasing? interval of increasing = (-2,-5) U (1,60) (d) On what interval is f decreasing? interval of decreasing = (-5,1) **Show work, in detail, on the scrap paper to receive full credit. (b) Compute the second derivative off f''(x) = (e) On what interval is f concave downward? interval of downward concavity = (f) On what interval is f concave upward? interval of upward concavity = **Show work, in detail, on the scrap paper to receive full credit.
Since f''(x) is always 0, f(x) is not concave upward on any interval.
On what interval is f concave upward?
The first derivative of f(x) is f'(x) = 6.
The second derivative of f(x) is f''(x) = 0.
The interval on which f(x) is increasing is when f'(x) > 0, which is when x is in the interval (-2,-5) U (1,60).
The interval on which f(x) is decreasing is when f'(x) < 0, which is when x is in the interval (-5,1).
The interval on which f(x) is concave downward is when f''(x) < 0, which is all values of x.
The interval on which f(x) is concave upward is when f''(x) > 0, which is no values of x.
To find the first derivative of f(x), we need to take the derivative of each term separately. The derivative of 3 is 0, the derivative of 6x is 6, and the derivative of -153 +3.2 is 0. Adding these up gives us f'(x) = 6.
To find the second derivative of f(x), we need to take the derivative of f'(x), which is a constant function. The derivative of a constant function is always 0, so f''(x) = 0.
To determine where f(x) is increasing, we need to find the values of x where f'(x) > 0. Since f'(x) is a constant function, it is always positive, so f(x) is increasing on the interval (-2,-5) U (1,60).
To determine where f(x) is decreasing, we need to find the values of x where f'(x) < 0. Since f'(x) is a constant function, it is always positive, so f(x) is decreasing on the interval (-5,1).
To determine where f(x) is concave downward, we need to find the values of x where f''(x) < 0. Since f''(x) is always 0, f(x) is concave downward on all values of x.
To determine where f(x) is concave upward, we need to find the values of x where f''(x) > 0. Since f''(x) is always 0, f(x) is not concave upward on any interval.
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1. In Circle O shown below, with a radius of 12 inches, a sector has been defined by two radii oB and o4 with a central angle of 60° as shown. Determine the area of shaded sector.
B
Step 1: Determine the area of the entire circle in terms of pi.
Step 2: Determine the portion (fraction) of the shaded sect in the circle by using the central angle value.
Step 3: Multiply the area of the circle with the portion (fraction) from step 2.
The area of the shaded sector of the given circle would be = 42,593.5 in²
How to calculate the area of a given sector?To calculate the area of the given sector the formula that should be used is given as follows;
The area of a sector =( ∅/2π) × πr²
where;
π = 3.14
r = 12 in
∅ = 60°
Area of the sector = (60/2×3.14)b × 3.14× 12×12
= 94.2× 452.16
= 42,593.5 in²
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Wanda's front porch is 7 feet wide and 13 feet long. Wanda wants to stain the wood on the porch next weekend. The stain costs $2. 00 per square foot. How much will it cost to buy enough stain for the whole porch?
The amount it will cost to buy enough stain for the whole porch is $182.
To determine the cost of staining Wanda's front porch, we'll first need to calculate the area of the porch, which is a rectangle in shape. The area of a rectangle can be found using the formula: Area = length × width.
In this case, the length of Wanda's porch is 13 feet, and the width is 7 feet. So, we'll multiply these two measurements to find the area:
Area = 13 ft × 7 ft = 91 square feet
Now that we know the area, we can calculate the cost of the stain. The stain costs $2.00 per square foot, so we'll multiply the area of the porch (91 square feet) by the cost per square foot:
Cost = 91 sq ft × $2.00/sq ft = $182
Therefore, it will cost Wanda $182 to buy enough stain for the whole porch.
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Suppose the length of voicemails (in
seconds) is normally distributed with a mean
of 40 seconds and standard deviation of 10
seconds. Find the probability that a given
voicemail is between 20 and 50 seconds.
10
20
30
40
50
60
P = Г?1%
Hint: Use the 68 - 95 - 99.7 rule
70
Enter
The probability that a given voicemail is between 20 and 50 seconds is 0.8185, or 81.85%.
How to find the the probability that a given voicemail is between 20 and 50 seconds.To find the probability that a voicemail is between 20 and 50 seconds, we need to standardize the values and use a standard normal distribution table.
First, we find the z-scores for 20 seconds and 50 seconds:
z1 = (20 - 40) / 10 = -2
z2 = (50 - 40) / 10 = 1
Using a standard normal distribution table, we can find the area to the left of each z-score:
Area to the left of z1 = 0.0228
Area to the left of z2 = 0.8413
To find the probability between 20 and 50 seconds, we subtract the area to the left of z1 from the area to the left of z2:
P(20 < x < 50) = P(-2 < z < 1)
= 0.8413 - 0.0228
= 0.8185
Therefore, the probability that a given voicemail is between 20 and 50 seconds is 0.8185, or 81.85%.
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009 10.0 points Let f be a function defined on (-1, 1] such that f(-1) = f(1) = . Consider the following properties that f might have: A. f(1) = 2; x | | B. f continuous on (-1, 1]; C. Which properties ensure that there exists cin (-1, 1) at which f'(c) = 0? - f(x) = 22/3 = x2 1. B and C only 2. none of them 3. all of them 4. B only 5. C only 6. A and C only 7. A only 8. A and B only
Properties B and C together ensure that there exists a 'c' in (-1, 1) at which f'(c) = 0.
Your answer: 1. B and C only
Which properties ensure that there exists ?
a 'c' in (-1, 1) at which f'(c) = 0, given f(-1) = f(1) = and the properties A, B, and C.
First, let's define the properties:
f(1) = 2
f is continuous on (-1, 1]
f(x) = (22/3) - x^2
To ensure that there exists a 'c' in (-1, 1) at which f'(c) = 0, we will use the Mean Value Theorem (MVT). MVT states that if a function is continuous on a closed interval and differentiable on an open interval, then there exists at least one 'c' in the interval where the derivative is 0.
Looking at property B, it states that f is continuous on (-1, 1], which satisfies the first condition of the MVT. Property C provides a specific function for f(x), which is differentiable on (-1, 1) since it is a polynomial function. Therefore, properties B and C together ensure that there exists a 'c' in (-1, 1) at which f'(c) = 0.
Your answer: 1. B and C only
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Find the number of x-intercepts of the graph of y=-3x^2-8x+4
