If f'(x) = 8x³ + 12x + 2 and f(1) = -4, f(-1) is equal to -18.
Given that f'(x) = 8x³ + 12x + 2, we can find the original function f(x) by integrating f'(x) with respect to x:
f(x) = 2x⁴ + 6x² + 2x + C, where C is an arbitrary constant.
We can then use the given initial condition f(1) = -4 to solve for C:
f(1) = 2(1)⁴ + 6(1)² + 2(1) + C = -4
Simplifying, we get:
C = -16
Therefore, the function f(x) is:
f(x) = 2x⁴ + 6x² + 2x - 16
To find f(-1), we substitute x = -1 into the expression for f(x):
f(-1) = 2(-1)⁴ + 6(-1)² + 2(-1) - 16 = -18
Thus, f(-1) equals -18.
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Will give brainiest answer
which pair of equations would represent lines that are perpendicular to each other?
i. 3x - 2y = 12
ii. 3x + 2y = -12
iii. 2x - 3y = -12
Answer:
Step-by-step explanation:
Two lines are perpendicular to each other if their slopes are negative reciprocals of each other. So, The equations i and ii are perpendicular to each other since their slopes are negative reciprocals of each other.
In other words, if the slope of one line is m, then the slope of the other line is -1/m.
To determine the slope of each equation, we can rewrite each equation in slope-intercept form, y = mx + b, where m is the slope and b is the
y-intercept.
i. 3x - 2y = 12
-2y = -3x + 12
y = (3/2)x - 6
The slope of this line is 3/2.
ii. 3x + 2y = -12
2y = -3x - 12
y = (-3/2)x - 6
The slope of this line is -3/2.
iii. 2x - 3y = -12
-3y = -2x - 12
y = (2/3)x + 4
The slope of this line is 2/3.
Therefore, equations i and ii are perpendicular to each other since their slopes are negative reciprocals of each other. Equation iii is not perpendicular to either of the other two equations.
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The student council wants to determine the best date for the end-of-year dance for the 350 students. They survey every 5th student who gets off the bus one morning. Eighteen students voted for May 2, 39 students voted for May 9, and 13 students voted for May 16. Which date is it likely that 105 of the 350 students would choose for the dance?
There is a probability that 105 of the 350 students would select May 9 for the dance.
What is the sample about?To solve the above we need to find the proportion of students in the sample who voted for each date and this can be done by:
May 2: 18/70
= 0.257
May 9: 39/70
= 0.557
May 16: 13/70
= 0.186
if the whole population of 350 students voted, then
May 2: 0.257 x 350
= 90
May 9: 0.557 x 350
= 195
May 16: 0.186 x 350
= 65
From the above calculation, we can see that if 105 students out of 350) were to choose a date, the most likely date that they will select is May 9, since it is the one that has the highest proportion of votes in the sample.
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part of a multiplication table is below. complete the pattern in the multiplication table. click each dot on the image to select an answer. a partial multiplication table with 3 rows and 3 columns. the first row reads 40, 45, 50. the second row reads an unknown number, 54, 60. the third row reads 56, an unknown number, 70. stuck?.
the completed multiplication table is: 40 45 50 ,72 54 60 and 56 90 70 .by using common factor logic we can solve this question.
what is common factor ?
A common factor is a number that divides evenly into two or more other numbers. For example, the common factors of 12 and 18 are 1, 2, 3, and 6, because all of these numbers divide evenly into both 12 and 18.
In the given question,
From the given table, we can see that:
The first row reads 40, 45, 50 (which are multiples of 5).
The second row has an unknown number (let's call it x), 54, and 60.
The third row reads 56, an unknown number (let's call it y), 70 (which are also multiples of 7).
To find the missing numbers, we can use the fact that multiplication is commutative, meaning that the order of the factors does not matter. Therefore, we can fill in the missing numbers by looking for factors that are common to both the row and column headers.
Starting with the second row, we can see that the common factor between x and 54 is 9, since 9 x 6 = 54 and 9 x x = ?. So, the missing number in the second row is 9 x 10 = 90.
Moving on to the first column, we can see that the common factor between 40 and 56 is 8, since 8 x 5 = 40 and 8 x 7 = 56. So, the missing number in the second row, first column is 8 x 9 = 72.
Finally, we can find the missing number in the first row, second column by finding the common factor between 45 and 60, which is 15, since 15 x 3 = 45 and 15 x 4 = 60. So, the missing number in the first row, second column is 15 x 5 = 75.
Therefore, the completed multiplication table is:
40 45 50
72 54 60
56 90 70
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(5 points) For each of the following vector fields F, decide whether it is conservative or not by computing the appropriate first order partial derivatives. Type in a potential function f (that is, a function f such that V f = F). If it is not conservative, type N. A. F(x, y) = (-6x – 7y) i +(-7x + 14y)j f (x,y) = = B. F(x, y) = -3yi – 2xj f(x,y) = N. = c. F(x, y, z) = -3xi – 2yj+k f(x, y, z) = D. F(x, y) = (-3 sin y)i + (-14y – 3x cosy)j f (x,y) = E. F(x, y, z) = -3x?i – 7y?j + 7z2k f (x, y, z) = - Note: Your answers should be either expressions of x, y and z (e.g. "3xy + 2yz"), or the letter "N"
A. The partial derivatives are not equal, F is not conservative, potential function f(x, y) = N
B. The partial derivatives are equal, F is conservative, potential function f(x, y) = -3xy - [tex]x^2[/tex] + C
C. The partial derivatives are not equal, F is not conservative, potential function f(x, y, z) = N
D. The partial derivatives are not equal, F is not conservative, potential function f(x, y, z) = N
E. The partial derivatives are not equal, F is not conservative, potential function f(x, y, z) = N
How to check if F(x, y) = (-6x – 7y) i +(-7x + 14y)j is conservative?A. F(x, y) = (-6x – 7y) i +(-7x + 14y)j
To check if F is conservative, we compute the partial derivatives:
∂F/∂y = -6i - 7j
∂F/∂x = -7i + 14j
Since the partial derivatives are not equal, F is not conservative.
Potential function f(x, y) = N
How to check if F(x, y) = -3yi – 2xj is conservative?B. F(x, y) = -3yi – 2xj
To check if F is conservative, we compute the partial derivatives:
∂F/∂y = -3i
∂F/∂x = -2j
Since the partial derivatives are equal, F is conservative.
Potential function f(x, y) =[tex]-3xy - x^2 + C[/tex], where C is a constant.
How to check if F(x, y, z) = -3xi – 2yj+k is conservative?C. F(x, y, z) = -3xi – 2yj+k
To check if F is conservative, we compute the partial derivatives:
∂F/∂x = -3i
∂F/∂y = -2j
∂F/∂z = k
Since the partial derivatives are not equal, F is not conservative.
Potential function f(x, y, z) = N
How to check if F(x, y) = (-3 sin y)i + (-14y – 3x cosy)j is conservative?D. F(x, y) = (-3 sin y)i + (-14y – 3x cosy)j
To check if F is conservative, we compute the partial derivatives:
∂F/∂y = -3cosy j - 14i
∂F/∂x = -3cosy j
Since the partial derivatives are not equal, F is not conservative.
Potential function f(x, y) = N
How to check if [tex]F(x, y, z) = -3xi - 7yj + 7z^2k[/tex] is conservative?E. [tex]F(x, y, z) = -3xi - 7yj + 7z^2k[/tex]
To check if F is conservative, we compute the partial derivatives:
∂F/∂x = -3i
∂F/∂y = -7j
∂F/∂z = 14zk
Since the partial derivatives are not equal, F is not conservative.
Potential function f(x, y, z) = N
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A
Fill in the blank. If one line has a slope of 0. 5 and another distinct line has a
slope of those two lines are
A. Parallel
B. Not correlated
C. Perpendicular
e
D. Undefined
Is urgent , no link plis
If one line has a slope of 0. 5 and another distinct line has a slope of those two lines are Parallel. The correct answer is A.
Two lines are parallel if and only if they have the same slope. If two distinct lines have different slopes, then they cannot be parallel. In this case, one line has a slope of 0.5 and the other line's slope is unknown, so we cannot determine whether they are parallel or not just by looking at their slopes.
However, if the other line's slope is perpendicular to 0.5, then the lines would be perpendicular. Two lines are perpendicular if and only if the product of their slopes is -1. Therefore, if the other line's slope is -2, then the lines would be perpendicular (0.5 * -2 = -1).
If the other line's slope is undefined (i.e., the line is vertical), then the lines would not be parallel or perpendicular, but rather they would be skew lines.
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Compute the variances in dollar amount and in percentage. (round to the nearest whole percent.) indicate whether the variance is favorable (f) or unfavorable (u).
budgeted amount - expense $106.00
actual amount $100.00
dollar variance $
percent variance
%
f or u
This is an unfavorable variance.
To calculate the dollar variance, we subtract the actual amount from the budgeted amount:
Dollar variance = Budgeted amount - Actual amount = $106.00 - $100.00 = $6.00 (favorable)
The dollar variance of $6.00 suggests that the actual expenses were less than the budgeted expenses, which is a favorable variance.
To calculate the percentage variance, we use the following formula:
Percentage variance = (Budgeted amount - Actual amount) / Budgeted amount x 100%
Substituting the values, we get:
Percentage variance = ($106.00 - $100.00) / $106.00 x 100% = 5.66% (rounded to the nearest whole percent)
The percentage variance of 5.66% suggests that the actual expenses exceeded the budgeted expenses by 5.66%, which is an unfavorable variance.
It's important to note that the dollar variance and percentage variance provide different perspectives on the variance, and they should be considered together to fully understand the implications of the variance. In this case, the dollar variance is favorable, indicating that the company spent less than expected.
However, the percentage variance is unfavorable, indicating that the company's expenses were higher than budgeted. The company may use this information to identify areas where they can reduce expenses in the future or adjust their budgeting process to be more accurate.
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Find an equivalent expression using the Distributive Property.
25w+30x
Find an equivalent expression using the Distributive Property.
25w+30x
Answer: 5(5w+6)
Step-by-step explanation:
Factor out a 5: 5(5w+6)
To check our work distribute: 25w+30
Answer: 5(5w+6)
Answer:
5 ( 5w + 5x )
Step-by-step explanation:
Just find a common factor in both terms: 5
5 ( 5w + 5x )
If you multiply again, you will see that the values of both expressions are the same.
Jasmine deposited $400 in a bank that paid her 2. 15% interest every year. Assuming no deposits or withdrawals were made. How much money will she have in 5 years? round to nearest.
Help
Answer:
$444.89
Step-by-step explanation:
PV = $400
i = 2.15%
n = 5
Compound formula:
FV = PV (1 + i)^n
FV = 400 (1 +2.15%)^5
FV = $444.89 (round to nearest cents)
Nine hundred thirty six student's, 65% of the entire student body, attended the football game. find the size of the student body.
The size of the student body is approximately 1440 students.
To determine the size of the student body, we'll use the given information that 936 students represent 65% of the total number of students. We can set up a proportion to solve for the unknown total (let's call it "x"):
(65% of x) = 936
To express the percentage as a decimal, divide 65 by 100, which equals 0.65:
0.65 * x = 936
Next, to find the value of x, divide both sides of the equation by 0.65:
x = 936 / 0.65
x ≈ 1440
So, the size of the student body is approximately 1440 students. In this problem, we used the concept of percentage to find out the total number of students in the student body, knowing that 936 students (65%) attended the football game.
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44
In the expression 5 x y/7, what value of y would make a product greater than 5 ?
Explain your answer.
Answer: ⬇️⬇️
Step-by-step explanation:
In the expression 5 x y/7, the value of y that would make a product greater than 5 is 8.
HOW TO SOLVE ALGEBRAIC EXPRESSIONS?
According to this question, the following algebraic equation was given:
5 x y/7
This equation reveals that the result can only be equal to 5 when y is exactly 7.
This is because if y = 7, y/7 = 1.
Therefore, the value of y that would make a product greater than 5 is 8.
An instructor graded 200 papers and found 80 errors. If a paper is picked at
random, find the probability that it will have exactly 4 errors
The probability of a paper having exactly 4 errors can be calculated using the binomial probability formula, which is:
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
What is the probability of selecting a paper at random from 200 papers and instructor found 80 errors and the probability that a paper has exactly 4 errors?In binomial probability formula P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
n is the number of trials (in this case, the number of papers graded)
k is the number of successes (in this case, the number of papers with exactly 4 errors)
p is the probability of success (in this case, the probability that a paper has an error, which can be calculated by dividing the total number of errors by the total number of papers graded)
Calculate the probability of a paper having an errorp = 80/200 = 0.4
Calculate the probability of a paper having exactly 4 errorsP(X = 4) = (200 choose 4) * 0.4^4 * (1-0.4)^(200-4) ≈ 0.153
Therefore, the probability of picking a paper at random and finding exactly 4 errors is approximately 0.153 or 15.3%.
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Light travels 9.45 \cdot 10^{15}9.45⋅10
15
9, point, 45, dot, 10, start superscript, 15, end superscript meters in a year. There are about 3.15 \cdot 10^73.15⋅10
7
3, point, 15, dot, 10, start superscript, 7, end superscript seconds in a year.
The distance which this light travel per second is equal to 3 × 10⁸ meters per seconds.
What is speed?In Mathematics and Science, speed is the distance covered by a physical object per unit of time.
How to calculate the speed?In Mathematics and Science, the speed of any a physical object can be calculated by using this formula;
Speed = distance/time
By making distance the subject of formula, we have:
Distance, d(t) = speed × time
Distance = (9.45 × 10¹⁵ meters per year) × (1 year/ 3.15 × 10⁷ seconds)
Distance = 3 × 10⁸ meters per seconds.
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Complete Question:
Light travels 9.45 × 10¹⁵ meters in a year. There are about 3.15 × 10⁷ seconds in a year. How far does light travel per second?
Please i cant find the answer to this
Answer:
9
Step-by-step explanation:
First, let's move the variables to one side and the numbers to the other side:
[tex]\frac{2}{3}b+5=20-b\\[/tex]
subtract 5 from both sides:
[tex]\frac{2}{3}b=15-b\\[/tex]
add b to both sides:
[tex]\\1\frac{2}{3}b=15\\[/tex]
divide both sides by [tex]1\frac{2}{3}[/tex]:
[tex]b=9[/tex]
Hope this helps :)
i need help !!!!!!!!!!!!!!!!!!
Answer:
[tex]\displaystyle\textsf{a) }\binom{8}{4}\\\\\textsf{b) }\binom{-8}{4}[/tex]
Step-by-step explanation:
Given a translation vector ...
[tex]\displaystyle \binom{g}{h}[/tex]
moves g to the right and h up, you want the vectors for 8 right, 4 up, and for 8 left, 4 up.
SubstitutionWhen we have g = units to the right, and we want 8 units to the right, we know that g = 8. Similarly, h = units up, and we want 4 units up, so h = 4.
Putting these values in the vector form, we have ...
a) 8 right, 4 up matches vector ...
[tex]\displaystyle \boxed{\binom{8}{4}}[/tex]
b) Left is the opposite of right, so 8 units left will be represented by ...
g = -8
As before, 4 units up means h = 4.
[tex]\displaystyle \boxed{\binom{-8}{4}}[/tex]
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5. Rita has a circular hot tub. The hot tub has a circumference 25. 12 feet. It is 3. 5 feet deep.
a. Find the radius of the hot tub. Use 3. 14 for pi
b. How much water can the hot tub hold?
c. The hot tub manual recommends filling the hot tub to 80% of its full capacity. How
much water should rita put in the hot tub in order to follow the recommendation?
a.The radius of the hot tub is 4 feet. b. The amount of water that the hot tub can hold is 176.96 cubic feet c. The amount of water that Rita should put in the hot tub in order to follow the recommendation is 141.57 cubic feet.
a. Find the radius of the hot tub.
Given: Circumference = 25.12 feet
Formula: Circumference = 2 * pi * radius
1: Plug in the given circumference and the value of pi.
25.12 = 2 * 3.14 * radius
2: Solve for the radius.
radius = 25.12 / (2 * 3.14)
radius ≈ 4 feet
So, the hot tub's radius is 4 feet.
b. How much water can the hot tub hold?
Given: Radius = 4 feet, Depth = 3.5 feet
Formula: Volume = pi * radius^2 * depth
1: Plug in the radius, depth, and the value of pi.
Volume = 3.14 * (4^2) * 3.5
2: Calculate the volume.
Volume ≈ 176.96 cubic feet
So, the hot tub can approximately hold 176.96 cubic feet.
c. How much water should Rita put in the hot tub to follow the recommendation?
Given: Recommended capacity = 80% of full capacity
Formula: Recommended water = 0.8 * full capacity
1: Plug in the full capacity (volume) calculated in part b.
Recommended water = 0.8 * 176.96
2: Calculate the recommended water amount.
Recommended water ≈ 141.57 cubic feet
So, Rita should put approximately 141.57 cubic feet of water in the hot tub to follow the recommendation.
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Rectangle abcd was dilated to create rectangle a’b’c’d’. the area of rectangle abcd is 16in^2 and the area of the rectangle a’b’c’d’ is 64in^2. which scale factor was used to dilate the rectangle?
help asap please!!!!!
If the area of rectangle abcd is 16in² and the area of the rectangle a’b’c’d’ is 64in², the scale factor used to dilate the rectangle was 2.
When a rectangle is dilated, its dimensions are multiplied by a common factor known as the scale factor. The scale factor is the ratio of the corresponding sides of the original rectangle and the dilated rectangle.
Let the scale factor be represented by k. The area of the original rectangle is 16 in², so we can write:
length x width = 16
Let L and W represent the length and width of the original rectangle, respectively. Therefore, we have:
LW = 16
After dilation, the area of the new rectangle is 64 in². The length and width of the new rectangle are kL and kW, respectively. Therefore, we can write:
(kL)(kW) = 64
Simplifying the above equation, we get:
k²LW = 64
Substituting the value of LW from the first equation, we get:
k²(16) = 64
Solving for k, we get:
k = √4 = 2
This means that the length and width of the new rectangle are twice the length and width of the original rectangle.
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Si se tiene un recipiente en forma de prisma triangular como el de la figura B, lleno de un líquido que se vierte en otro recipiente cilindro como el de la figura A Después de esa acción, ¿Qué volumen le falta al cilindro para estar completamente lleno?
The number of cones that can be filled with the ice cream from the container is 10.
Let's start with the container. We are given that it is a right circular cylinder with a diameter of 12 cm and a height of 15 cm. To find the volume of this cylinder, we use the formula:
Volume of cylinder = πr²h
where r is the radius of the cylinder (which is half of the diameter), and h is the height. Substituting the given values, we get:
Volume of cylinder = π(6 cm)²(15 cm) = 540π cubic cm
So the container has a volume of 540π cubic cm.
Now, let's move on to the cones. We are given that the cones have a height of 12 cm and a diameter of 6 cm. The cones have a hemispherical shape on the top, so we can consider them as a combination of a cone and a hemisphere. The formula for the volume of a cone is:
Volume of cone = (1/3)πr²h
where r is the radius of the base of the cone, and h is the height. Substituting the given values, we get:
Volume of cone = (1/3)π(3 cm)²(12 cm) = 36π cubic cm
The formula for the volume of a hemisphere is:
Volume of hemisphere = (2/3)πr³
where r is the radius of the hemisphere. Substituting the given values (the radius is half the diameter of the cone, which is 3 cm), we get:
Volume of hemisphere = (2/3)π(3 cm)³ = 18π cubic cm
So the total volume of each cone is:
Volume of cone + hemisphere = 36π + 18π = 54π cubic cm
To find out how many cones can be filled with the ice cream from the container, we divide the volume of the container by the volume of each cone:
Number of cones = Volume of container / Volume of each cone Number of cones
=> (540π cubic cm) / (54π cubic cm) Number of cones = 10
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Complete Question:
A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.
Suppose f'(x) = 833 + 12x + 2 and f(1) = -4. Then f(-1) equals (Enter a number for your answer)
To find f(-1), we can use the fact that the derivative of a function f(x) gives us the slope of the tangent line to the graph of f(x) at any point x. We can use this information along with the given value of f(1) to find the equation of the tangent line at x=1, and then use that equation to find the value of f(-1).
First, we find the equation of the tangent line at x=1:
- The slope of the tangent line at x=1 is f'(1) = 833 + 12(1) + 2 = 847
- The point (1, f(1)) lies on the tangent line, so we can use the point-slope form of the equation of a line to write the equation of the tangent line:
y - (-4) = 847(x - 1)
y + 4 = 847x - 847
y = 847x - 851
Now we can use this equation to find f(-1):
- The point (-1, f(-1)) also lies on the tangent line, so we can substitute x=-1 and solve for y:
f(-1) + 4 = 847(-1) - 851
f(-1) + 4 = -1698
f(-1) = -1702
Therefore, f(-1) = -1702.
To find f(-1), we first need to determine the function f(x). We know f'(x) = 833 + 12x + 2. To find f(x), we need to integrate f'(x) with respect to x:
∫(833 + 12x + 2) dx = 833x + 6x^2 + 2x + C
Now, we use the given condition f(1) = -4 to find the constant C:
-4 = 833(1) + 6(1)^2 + 2(1) + C
Solve for C:
C = -4 - 833 - 6 - 2 = -845
Now we have the function f(x) = 833x + 6x^2 + 2x - 845. To find f(-1), plug in x = -1:
f(-1) = 833(-1) + 6(-1)^2 + 2(-1) - 845
f(-1) = -833 + 6 - 2 - 845
f(-1) = -1674
So, f(-1) equals -1674.
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The diameter of om is 68 cm and the diameter of oj is 54 cm. if the length of jk is 8 cm, what is the length of lm? lm
The length of lm is 10 cm.
To find the length of lm, we need to use the fact that om and oj are both diameters of their respective circles. We can start by finding the radius of each circle:
- The radius of om is half of its diameter, so it's 34 cm.
- The radius of oj is half of its diameter, so it's 27 cm.
Next, we can use the fact that jk is perpendicular to lm to create a right triangle:
- One leg of the triangle is jk, which we know is 8 cm.
- The other leg is half of the difference between the radii of the two circles, since lm connects the two circles. That means the other leg is (34 - 27)/2 = 3.5 cm.
Now we can use the Pythagorean theorem to find the length of lm:
lm² = jk² + (radius difference/2)²
lm² = 8² + 3.5²
lm² = 70.25
lm = 10 cm
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the population of a city with 750,000 people is devastated by a unknown virus that kills 20% of the population per day. How many people are left after 1 week
The number of people left after one week is approximately 157286.
How to find the number of people left?The population of a city with 750,000 people is devastated by a unknown virus that kills 20% of the population per day.
Therefore, each day, 20% of the people are killed by the virus.
Hence, let's find the number of people left as follows:
Therefore,
7 days = 1 week
number of people left = 750,000(1 - 20%)⁷
number of people left = 750,000(1 - 0.2)⁷
number of people left = 750,000(0.8)⁷
number of people left = 750,000(0.2097152)
number of people left = 157286.4
Therefore,
number of people left after 1 week = 157286.4
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Evaluate the following expressions. Your answer must be an angle -z/2 S 0 S in radians, written as a multiple of r. Note that r is already
provided in the answer so you simply have to fil in the appropriate multiple. E.g. if the answer is /2 you should enter 172. Do not use decimal answers.
Write the answer as a fraction or integer
Sin^-1(sin((-5t-6)
The given expression is sin⁻¹ (sin((-5t-6)). Since the argument of sin⁻¹ and sin is the same, we can simplify the expression as follows:
sin⁻¹ (sin((-5t-6))) = -5t-6
OR, -5t-6 = (-2π/π)(-5t-6/2) = -2π(2.5t+3)/π = -5π/2(2.5t+3)
Therefore, the answer is -5π/2(2.5t+3).
Given the expression: sin^-1(sin(-5t-6))
To find the angle -z/2, we can use the following properties:
1. sin⁻¹ (sin(x)) = x, if -π/2 ≤ x ≤ π/2 (i.e., x is in the range of the principal branch of the inverse sine function).
2. The sine function has a periodicity of 2π. Therefore, sin(x) = sin(x + 2nπ), where n is an integer.
Given angle: -5t - 6
We need to add 2nπ to this angle to bring it into the range of -π/2 to π/2:
⇒ -5t - 6 + 2nπ, where n is an integer.
Now, we apply the sine and inverse sine functions:
sin⁻¹ (sin(-5t - 6 + 2nπ))
Since sin^-1(sin(x)) = x when x is in the range of the principal branch, our final expression becomes:
-z/2 = -5t - 6 + 2nπ
In this expression, -z/2 represents the angle in radians, written as a multiple of r. To find the multiple, you simply have to solve for -z/2 in terms of r.
Therefore, the answer is: -z/2 = -5t - 6 + 2nπ.
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Please please help ASAP. See photo below
Central / Inscribed Angles (Algebraic)
The calculated value of x in the circle is 12.3
Calculating the value of x in the circleFrom the question, we have the following parameters that can be used in our computation:
The circle
∠QRS = 7x - 21
QS = 130
Using the theorem of intersecting chords, we have the following equation
∠QRS = 1/2 * QS
Substitute the known values in the above equation, so, we have the following representation
7x - 21 = 1/2 * 130
Evaluate
7x - 21 = 65
Evaluate the like terms
7x = 86
Divide by 7
x = 12.3
Hence, the value of x in the circle is 12.3
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Pierce Manufacturing determines that the daily revenue, in dollars, from the sale of x town chairs is R0 -0.0001 +0.042? + Ofe Curare Per vete te lawn chairs daily a) What is the current daily revenue? b) How much would revenue increase ir 3 lawn chairs were sold each day? c) What is the marginal revenue when 50 lawn chairs are sold daily d) Use the answer from part (c) to estimate R(51), R(52) and R153)
The revenue of the chairs sold as per given R(x) = 0.004x³ -0.04x² +0.6x for different conditions are,
The current daily revenue is $2646.
Increase in revenue for 92 chairs sold every day is $185.16
Marginal revenue is $90.6 per lawn chair for 92 chairs sold every day.
Estimated revenue for R(91), R(92) and R(93) is equal to $2555.4 , $2464.8, and $2374.2 respectively.
Daily revenue from sale of x chairs is,
R(x) = 0.004x³ -0.04x² +0.6x
The current daily revenue can be found by evaluating the function at x = 90,
R(90) = 0.004(90)³ - 0.04(90)² + 0.6(90)
= 2916 - 324 + 54
= $2646
Increase in revenue,
⇒ difference between the revenue from selling 92 lawn chairs and the revenue from selling 90 lawn chairs,
R(92) - R(90)
= [0.004(92)³ - 0.04(92)² + 0.6(92)] - [0.004(90)³ - 0.04(90)² + 0.6(90)]
= 3114.752 -338.56 + 55.2 - 2646
= 2831.16 - 2646
= $185.16
Revenue would increase by$185.16 if 92 lawn chairs were sold each day.
The marginal revenue is the derivative of the revenue function,
R'(x) = 0.012x² - 0.08x + 0.6
Marginal revenue when 90 lawn chairs are sold daily,
we can evaluate the derivative at x = 90,
R'(90) = 0.012(90)² - 0.08(90) + 0.6
= $90.6
When 90 lawn chairs are sold daily, the marginal revenue is $90.6 per lawn chair.
Use the answer from above part to estimate the revenue from selling 91, 92, and 93 lawn chairs daily.
Assume that the marginal revenue is approximately constant in a small interval around 90,
Use the linear approximation,
R(91) ≈ R(90) + R'(90)(1)
= $2646 + $90.6
= $2555.4
R(92) ≈ R(90) + R'(90)(2)
= $2646 + 2($90.6)
= $2464.8
R(93) ≈ R(90) + R'(90)(3)
= $2646 + 3($90.6)
= $2374.2
If 91, 92, and 93 lawn chairs were sold daily,
The estimated daily revenue would be $2555.4 , $2464.8, and $2374.2 respectively.
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The above question is incomplete, I answer the question in general according to my knowledge:
Pierce Manufacturing determines that the daily revenue, in dollars, from the sale of x town chairs is
R(x) = 0.004x³ -0.04x² +0.6x .
Currently, Pierce sells 90 lawn chairs daily.
a) What is the current daily revenue?
b) How much would revenue increase if 92 lawn chairs were sold each day?
c) What is the marginal revenue when 90 lawn chairs are sold daily
d) Use the answer from part (c) to estimate R(91), R(92) and R(93)
What is the measure of an angle of it is 160 less than 4 times it’s complement
The measure of the angle is 40 degrees.
Let x be the measure of the angle and y be its complement.
The sum of an angle and its complement is 90 degrees, so we have:
[tex]x+y=90[/tex]
Also, we know that "the measure of an angle of it is 160 less than 4 times its complement", which can be written as:
[tex]x=4y-160[/tex]
Now we can substitute the first equation into the second equation:
[tex]4y-160+y=90[/tex]
Simplifying and solving for y, we get:
5y = 250
y = 50
Substituting y = 50 into the first equation gives:
x + 50 = 90
x = 40
Therefore, the measure of the angle is 40 degrees.
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A car mechanic has a tin containing 5 litres of engine oil.
Each week they use 450 millilitres of this oil for their vehicles.
The car mechanic says
After 9 weeks I will have used over 80% of the oil in this tin.
Are they correct?
Show how you decide.
The car mechanic is correct in saying that they will have used over 80% of the oil in the tin after 9 weeks.
To determine if the car mechanic is correct, we first need to calculate how much oil they will use in 9 weeks.
450 millilitres of oil are used each week, so after 9 weeks, they will have used:
450 x 9 = 4050 millilitres
Next, we need to convert this to litres, since the oil tin is measured in litres.
There are 1000 millilitres in 1 litre, so:
4050 ÷ 1000 = 4.05 litres
Therefore, after 9 weeks, the car mechanic will have used 4.05 litres of oil.
Now we need to determine if this is over 80% of the total oil in the tin.
The tin contains 5 litres of oil, so we need to find 80% of 5:
5 x 0.8 = 4
So if the car mechanic has used more than 4 litres of oil in 9 weeks, they have used over 80% of the oil in the tin.
We know from earlier that they will have used 4.05 litres, which is slightly over 80%. Therefore, the car mechanic is correct in saying that they will have used over 80% of the oil in the tin after 9 weeks.
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(20. 60 S-AQ) To study the metabolism of insects, researchers fed cockroaches measured amounts of a sugar solution. After 2, 5, and 10 hours, they dissected some of the cockroaches and measured the amount of sugar in various tissues. Five roaches fed the sugar D-glucose and dissected after 10 hours had the following amounts (in micrograms) of D-glucose in their hindguts: Amounts of D-glucose 55. 95 68. 24 52. 73 21. 5 23. 78
The mean amount of D-glucose in cockroach hindguts is 44.24 micrograms, with a standard deviation of 26.16 micrograms. The 96% confidence interval for the mean is (20.19, 68.29) micrograms.
We will first calculate the mean, standard deviation, and then the 96% confidence interval for the given data on D-glucose amounts in cockroach hindguts.
Data: 55.95, 68.24, 52.73, 21.5, 23.78
1. The mean is calculated as follows.
Mean = (55.95 + 68.24 + 52.73 + 21.5 + 23.78) / 5 = 221.2 / 5 = 44.24
The mean amount of D-glucose in cockroach hindguts is approximately 44.24 micrograms.
2. To find the standard deviation, we calculate the variance first:
Variance = [(55.95 - 44.24)^2 + (68.24 - 44.24)^2 + (52.73 - 44.24)^2 + (21.5 - 44.24)^2 + (23.78 - 44.24)^2] / (5 - 1) = 2739.736 / 4 = 684.934
Standard Deviation = √684.934 = 26.16 (rounded to two decimal places)
The standard deviation of D-glucose in cockroach hindguts is approximately 26.16 micrograms.
3. To calculate the 96% confidence interval, we need to find the margin of error:
Margin of Error = (Critical value * Standard Deviation) / √sample size
For a 96% confidence interval, the critical value (z-score) is approximately 2.05.
Margin of Error = (2.05 * 26.16) / √5 ≈ 24.05
Now, we can find the confidence interval:
Lower limit: Mean - Margin of Error = 44.24 - 24.05 = 20.19
Upper limit: Mean + Margin of Error = 44.24 + 24.05 = 68.29
The 96% confidence interval for the mean amount of D-glucose in cockroach hindguts approximately is (20.19, 68.29) micrograms.
Note: The question is incomplete. The complete question probably is: To study the metabolism of insects, researchers fed cockroaches measured amounts of a sugar solution. After 2, 5, and 10 hours, they dissected some of the cockroaches and measured the amount of sugar in various tissues. Five roaches fed the sugar D-glucose and dissected after 10 hours had the following amounts (in micrograms) of D-glucose in their hindguts: Amounts of D-glucose 55. 95, 68. 24, 52. 73, 21. 5, 23. 78. The researchers gave a 96% confidence interval for the mean amount of D-glucose in cockroach hindguts under these conditions. The insects are a random sample from a uniform population grown in the laboratory. We therefore expect responses to be Normal. What is the mean, standard deviation, and confidence interval?
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A recent survey reveals that one of the collie owners interviewed, 54% of them regularly groom their dogs, If there are 50,000 registered poodle owners in the county, how many owners are expected to regular groom their dos
Answer:
54% × 50000= 27000, the answer is 27000
Hey, I'm struggling with this lately, please help!
The measure of the exterior angle of the triangle is 128°.
How to find the measure of the exterior angle?Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.
Trigonometric functions are the functions that denote the relationship between angle and sides of a right-angled triangle.
Sin θ = Opposite Side/Hypotenuse
Cos θ = Adjacent Side/Hypotenuse
Tan θ = Opposite Side/Adjacent
Recall that the measure of the exterior angle of a triangle is the sum of the opposite interior angles. That is:
x = 38 + 90
x = 128°
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An ice cream cone has a radius of 6 centimeters and height of 12 centimeters. What is the volume of the ice cream cone? Round your answer to the nearest centimeter
Answer: 452.39
Step-by-step explanation: R= 6, H = 12. Volume formula is V= pi*r^2*h/3. For you, the equation is V = pi*6^2*12/3. 6^2 = 36, and 12/3 = 4. V = pi*36*4. Solving, we get V = 452.39.
The South African mathematician John Kerrich, while a prisoner of war during World War II, tossed a coin10,000 times and obtained 5067 heads. (2pts)a) Is this significant evidence at the 5% level that the probability that Kerrich’scoin comes up heads is not 0. 5?Remember to specifythe null and alternative hypotheses, the test statistic, and the P-value. B) Give a 95% confidence interval to see what probabilities of heads are roughlyconsistent with Kerrich’s result
a) We can conclude that there is significant evidence that the probability of heads is not 0.5.
b) A 95% confidence interval for the true probability of heads is (0.4872, 0.5262).
a) To test whether the probability of heads is significantly different from 0.5, we can use a two-tailed z-test with a significance level of 0.05. The null hypothesis (H₀) is that the probability of heads is 0.5, while the alternative hypothesis (Hₐ) is that it is not 0.5.
The test statistic is given by:
z = (x - np) / √(np(1-p))
where x is the number of heads observed (5067), n is the total number of coin tosses (10,000), and p is the hypothesized probability of heads under the null hypothesis (0.5).
Plugging in the values, we get:
z = (5067 - 5000) / √(10,000 * 0.5 * 0.5) = 2.20
The P-value for this test is the probability of getting a z-score greater than 2.20 or less than -2.20, which is approximately 0.0287. Since the P-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is significant evidence that the probability of heads is not 0.5.
b) To find a 95% confidence interval for the true probability of heads, we can use the formula:
p ± z*√(p(1-p)/n)
where p is the sample proportion (5067/10000), n is the sample size (10,000), and z is the critical value from the standard normal distribution corresponding to a 95% confidence level (1.96).
Plugging in the values, we get:
p ± 1.96*√(p(1-p)/n) = 0.5067 ± 0.0195
So a 95% confidence interval for the true probability of heads is (0.4872, 0.5262). This means that we can be 95% confident that the true probability of heads falls within this interval based on the observed sample proportion.
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