To find the length of the entire perimeter of the region inside r = 7 sin Ф but outside r = 2, we first need to determine the boundaries of the region.
The equation r = 7 sin Ф represents a curve that forms a flower-like shape, while the equation r = 2 represents a circle with radius 2.
To find the region inside r = 7 sin Ф but outside r = 2, we need to find the points where these two curves intersect.
Setting the two equations equal to each other, we get:
7 sin Ф = 2
Solving for sin Ф, we get:
sin Ф = 2/7
Using a calculator, we can find the two values of Ф that satisfy this equation to be approximately 0.304 and 2.837 radians.
Thus, the region inside r = 7 sin Ф but outside r = 2 is bounded by the angles 0.304 and 2.837 radians.
To find the length of the entire perimeter of this region, we need to integrate the length element around this curve:
L = ∫(from 0.304 to 2.837) √[r² + (dr/dФ)²] dФ
Using the equation r = 7 sin Ф, we can substitute and simplify the expression under the square root:
L = ∫(from 0.304 to 2.837) √[49sin²(Ф) + 49cos²(Ф)] dФ
L = ∫(from 0.304 to 2.837) 7 dФ
L = 7(2.837 - 0.304)
L = 16.1
Therefore, the length of the entire perimeter of the region inside r = 7 sin Ф but outside r = 2 is approximately 16.1 units.
To find the length of the entire perimeter of the region inside r = 7 sin Ф but outside r = 2, we must first identify the points of intersection between the two curves.
1. Set the equations equal to each other:
7 sin Ф = 2
2. Solve for Ф:
sin Ф = 2/7
Ф = arcsin(2/7)
Now, we must determine the length of the perimeter of each curve in the region of interest:
3. Length of the perimeter of r = 7 sin Ф (half of the curve, since it's within the specified region):
For a polar curve r = f(Ф), the arc length L is calculated using the formula L = ∫√(r² + (dr/dФ)²) dФ.
In this case, f(Ф) = 7 sin Ф, so dr/dФ = 7 cos Ф. Integrating over the range [0, arcsin(2/7)], we can find the half-length of this curve.
4. Length of the perimeter of r = 2 (portion of the circle outside the region):
Since we know the points of intersection from step 2, we can find the central angle of the circular segment using Ф. The central angle is 2 * arcsin(2/7), and the circumference of the circle is 2π * 2. The portion of the perimeter is given by the ratio of the central angle to 2π, multiplied by the circumference.
Finally, add the lengths obtained in steps 3 and 4 to get the total length of the entire perimeter of the region.
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b) During the first market day, Fatuma bought 30 oranges and 12 mangoes and paid Ksh. 936 for all the fruits. In the second market day, the price of an orange increased by 20% while that of a mango reduced in the ratio 3:4. Fatuma bought 15 oranges and 20 mangoes and paid Ksh. 780 for all the fruits. Given that the cost of an orange and that of a mango during the first market day was Ksh. x and Ksh. y respectively: (i) Write down simultaneous equations to represent the information above. (2 marks) (ii) Use matrix in (a) above to find the cost of an orange and that of a mango in the first market day. (4 marks) (iii) Fatuma sold all the fruits bought on the second market day at a profit of 10% per orange and 15% per mango. Calculate the total amount of money realized for the sales. (2 marks)
Answer:Let the cost of an orange and that of a mango during the first market day be Ksh. x and Ksh. y respectively.
From the first market day:
30x + 12y = 936
From the second market day:
15(1.2x) + 20(3/4y) = 780
Simplifying the second equation:
18x + 15y = 780
(ii) Using matrix to find the cost of an orange and that of a mango in the first market day:
Rewriting the equations in matrix form:
|30 12| |x| |936|
|18 15| x |y| = |780|
Multiplying the matrices:
|30 12| |x| |936|
|18 15| x |y| = |780|
|30x + 12y| |936|
|18x + 15y| = |780|
Using matrix inversion:
| x | |15 -12| |936 12|
| y | = | -18 30| x |780 15|
|x| |270 12| |936 12|
| | = |-360 30| x |780 15|
|y|
Simplifying the matrix multiplication:
|x| |1194| |12|
| | = | 930| x |15|
|y|
Therefore, the cost of an orange in the first market day was Ksh. 39 and the cost of a mango in the first market day was Ksh. 63.
(iii) Calculation of the total amount of money realized for the sales:
On the second market day, Fatuma bought 15 oranges and 20 mangoes.
Cost of 15 oranges = 15(1.2x) = 18x
Cost of 20 mangoes = 20(3/4y) = 15y
Total cost of fruits bought on the second market day = 18x + 15y = 18(39) + 15(63) = Ksh. 1629
Profit earned on 15 oranges at 10% = 1.1(1.2x)(15) - (1.2x)(15) = 0.18x(15) = 2.7x
Profit earned on 20 mangoes at 15% = 1.15(3/4y)(20) - (3/4y)(20) = 0.15y(20) = 3y
Total profit earned = 2.7x + 3y
Total amount of money realized for the sales = Total cost + Total profit
= Ksh. 1629 + 2.7x + 3y.
Step-by-step explanation:
What is the area of the following circle?
Either enter an exact answer in terms of π or use 3.14 for π and enter your answer as a decimal.
The area of the circle whose diameter is 14 is approximately 153.94 square units or 49π square units..
The area of a circle is given by the formula A = πr², where r is the radius of the circle. Since the diameter of the circle is given as d = 14, we know that the radius is half of the diameter, which is r = d/2 = 7.
Substituting the value of the radius in the formula, we get:
A = πr² = π(7)² = π(49) ≈ 153.94 (rounded to two decimal places using 3.14 for π)
Therefore, the area of the circle is approximately 153.94 square units. Alternatively, the exact answer can be left in terms of π, which would be A = 49π square units.
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Which name best describes the polygon with
vertices (0,0), (4,8), (12,8), and (16,0)?
The polygon described by the given vertices is a trapezoid.
Why is the polygon is given vertices a trapezoid?
A trapezoid is a quadrilateral with at least one pair of parallel sides. In this case, the sides with endpoints (0,0) and (16,0) are parallel to each other, and the sides with endpoints (4,8) and (12,8) are parallel to each other. Therefore, the polygon described by the given vertices is a trapezoid.
In addition to having parallel sides, a trapezoid can have various other properties, such as being isosceles (having two equal sides) or having perpendicular diagonals. However, based solely on the given vertices, we can determine that the polygon is a trapezoid.
A trapezoid has various properties, including having one pair of parallel sides, having one pair of non-parallel sides, and having two pairs of adjacent angles that add up to 180 degrees. It can also be isosceles if the non-parallel sides are equal in length.
The trapezoid is a commonly studied shape in geometry because of its simple properties and its appearance in many real-world applications, such as in architecture and engineering. Trapezoids are used in the design of roofs, bridges, and other structures that require stable, load-bearing shapes.
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Consider the series Σ(1) с (where c is a constant). For which values of c will the series converge, and for which it diverge? Justify your answer, and show all your work. (Hint: Use the root test)
To determine whether the series Σ(1) с converges or diverges, we can use the root test. The root test states that if the limit of the absolute value of the nth root of the terms of the series approaches a value less than 1, then the series converges. If the limit approaches a value greater than 1, the series diverges. If the limit equals 1, the test is inconclusive and another test should be used.
Using the root test, we have:
lim┬(n→∞)〖|1^(1/n) c| = lim┬(n→∞)|c| = |c|〗
If |c| < 1, then the limit approaches a value less than 1 and the series converges. If |c| > 1, then the limit approaches a value greater than 1 and the series diverges. If |c| = 1, then the test is inconclusive.
Therefore, the series Σ(1) с converges if |c| < 1, and diverges if |c| > 1. If |c| = 1, then another test should be used to determine convergence or divergence.
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how would you work the image attached out
The ratio of a : b : c : d is 3 : 7 : 2 : 7.
What are the ratios?The ratios are determined as follows from the data given.
The given data is:
7a = 2b
b = (7/2)a.
a and b have no common factors, thus a must be even and b must be odd.
c : d is 2 : 7
For an integer x, c = 2x and d = 7x
a : d is 3 : 1
So for an integer y, a = 3y and d = y
Substituting into 7a = 2b:
7(3y) = 2(7/2)y a
21y = 7y * b
b = 3a
Substituting these expressions for a and b into c : d = 2:7, we get:
2x : 7x = 3 : 1
2x = 3y and 7x = y
y = 14x/3
a : b : c : d = 3y : 7y : 2x : 7x
a : b : c : d = 3(3y) : 3(7y) : 3(2x) : 3(7x)
a : b : c : d = 9y : 21y : 6x : 21x
a : b : c : d = 3 : 7 : 2 : 7
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Only a small percentage of Americans owned cars before the 1940s. By 2017, there were nearly 250 million vehicles for 323 million people, significantly increasing the need for roadways. In 1960, the United States had about 16,000 km of interstate highways. Today, the interstate highway system includes 77,000 km of paved roadways. What percent increase does this represent?
A. 381 percent
B. 792 percent
C. 38 percent
D. 79 percent
The percent increase in the interstate highway system from 1960 to now is 381%.
option A.
What is the percent increase?The percent increase from 16,000 km to 77,000 km is difference between the old value and new value divided by the old value expressed in 100%.
percent increase = 100% x (new value - old value) / old value
percent increase = 100% x (77,000 - 16,000) / 16,000
percent increase = 100% x 61,000 / 16,000
percent increase = 381.25%
Thus, the percent increase in the interstate highway system from 1960 to now is approximately 381%, which is option A.
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Is the expression (x + 18) a factor of x² - 324?
Answer: We can check whether the expression (x + 18) is a factor of x² - 324 by dividing x² - 324 by (x + 18) using polynomial long division or synthetic division.
Using polynomial long division:
x + 18 │x² + 0x - 324
-x² - 18x
----------
18x - 324
18x + 324
----------
0
Since there is no remainder, we can see that (x + 18) is indeed a factor of
x² - 324.
Dai orders milk with her meal. The server asks her if she wants regular or chocolate. Dai can choose from skim, 2%, or whole, and from small, medium, or large. If all of the choices are equally likely to be ordered, what is the probability that Dai orders a regular, medium milk? Write a whole number or fractions
The probability of Dai ordering a regular, medium milk is 1/18.
What is the probability of an event? Calculate the total number of possible milk orders.There are 2 types of milk (regular and chocolate), and 3 sizes (small, medium, and large), and 3 levels of fat content (skim, 2%, and whole). So the total number of possible milk orders is:
2 (types of milk) x 3 (sizes) x 3 (fat content) = 18
Calculate the number of ways Dai can order a regular, medium milk.Dai needs to choose regular milk and medium size, so there is only one way she can order this combination.
Calculate the probability of Dai ordering a regular, medium milk.The probability of Dai ordering a regular, medium milk is the number of ways she can order a regular, medium milk divided by the total number of possible milk orders:
1 (number of ways to order a regular, medium milk) / 18 (total number of possible milk orders) = 1/18
So the probability that Dai orders a regular, medium milk is 1/18 or approximately 0.056 (rounded to three decimal places).
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Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval. If the interval of convergence is an Interval, enter your answer using interval notation. If the Interval of convergence is a finite set, enter your answer using set notation.)
Sum = (n!(x+5)^n) / 1 . 3 . 5 ...... (2n-1)
To find the interval of convergence of the power series, we can use the ratio test:
lim (n->inf) |((n+1)!(x+5)^(n+1)) / (1.3.5....(2n+1))| / |(n!(x+5)^n) / (1.3.5....(2n-1))|
= lim (n->inf) |(x+5)(2n+1)| / (2n+2) = |x+5| lim (n->inf) (2n+1)/(2n+2) = |x+5|
So the series converges if |x+5| < 1, and diverges if |x+5| > 1. Thus the interval of convergence is (-6, -4).
To check for convergence at the endpoints, we can use the limit comparison test with the divergent series:
1/1.3 + 1/1.3.5 + 1/1.3.5.7 + ... = sum (2n-1) terms = inf
At x = -6, we have:
sum (n=0 to inf) (n!(-1)^n)/(1.3.5....(2n-1)) = 1/1 - 1/1.3 + 1/1.3.5 - 1/1.3.5.7 + ... = inf
Since the series diverges at x = -6, the interval of convergence is (-6, -4] using set notation.
At x = -4, we have:
sum (n=0 to inf) (n!(1)^n)/(1.3.5....(2n-1)) = 1/1 - 1/1.3 + 1/1.3.5 - 1/1.3.5.7 + ... = 1 - 1/3 + 1/15 - 1/105 + ...
This is an alternating series that satisfies the conditions of the alternating series test, so it converges. Thus the interval of convergence is (-6, -4] using set notation, or [-6, -4) using interval notation.
To find the interval of convergence of the power series, we'll use the Ratio Test, which states that if the limit L = lim(n→∞) |aₙ₊₁/aₙ| < 1, then the series converges. Here, the series is given by:
Σ(n!(x+5)^n) / 1 . 3 . 5 ... (2n-1)
Let's find the limit L:
L = lim(n→∞) |(aₙ₊₁/aₙ)|
= lim(n→∞) |((n+1)!(x+5)^(n+1))/(1 . 3 . 5 ... (2(n+1)-1)) * (1 . 3 . 5 ... (2n-1))/(n!(x+5)^n)|
Now, simplify the expression:
L = lim(n→∞) |(n+1)(x+5)/((2n+1))|
For the series to converge, we need L < 1:
|(n+1)(x+5)/((2n+1))| < 1
As n approaches infinity, the above inequality reduces to:
|x+5| < 1
Now, to find the interval of convergence, we need to solve for x:
-1 < x + 5 < 1
-6 < x < -4
The interval of convergence is given by the interval notation (-6, -4). To check the endpoints, we need to substitute x = -6 and x = -4 back into the original series and use other convergence tests such as the Alternating Series Test or the Integral Test. However, the power series will diverge at the endpoints, as the terms do not approach 0. Therefore, the interval of convergence remains (-6, -4).
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If a sample of 32 runners is taken from a population of 201 people what if the means of how many runners times
201 could refer to the mean of how many runners' times. The Option C is correct.
Could sample refer to the mean of runner times?The sample of 32 runners, as given, does not refer to the mean of how many runners' times. The sample size refers to the number of individuals selected from the population while population size refers to the total number of individuals in the population.
Data:
The population of 201 people is given.
The sample of 32 runners is taken from the population.
So, the mean of the runners' times would be calculated using all 201 runners in the population, not just the 32 in the sample. Therefore, the Option C is correct.
Full question "If a sample of 32 runners were taken from a population of 201 runners, could refer to the mean of how many runners' times ? A. Both 32 and 201 B. Neither 32 nor 201 C. 201 D. 32"
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I need help ASAP (will give brainliest)
Answer:
92°
Step-by-step explanation:
All angles should add up to 360°
Opposite angles are equal so that means two angles are 88°
88+88=176
360 - 176 = 184
184 / 2 = 95
Measure of angle A is 92°
HELP PLEASE, DUE IN 17 MINUTES!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
A bag of paper clips contains:
. 9 pink paper clips
• 7 yellow paper clips
• 5 green paper clips
• 4 blue paper clips
A random paper clip is drawn from the bag and replaced 50 times. What is a
reasonable prediction for the number of times a yellow paper clip will be
drawn?
A. 5
B. 8
C. 10
D. 12
A rectangle with length n is inscribed in a circle of radius 9. Find an expression for the area of the rectangle in terms of n
Using pythagorean theorem the area of the rectangle in terms of n is given by A = n√(324 - n^2).
In the given scenario, we have a circle with a diameter that is twice the length of the radius, which is stated as 18. The diagonal of the rectangle is also the diameter of the circle, so it measures 18. Let's assume the width of the rectangle as 'w'. By applying the Pythagorean theorem, we can establish the following relationship:[tex]n^2 + w^2 = 18^2[/tex] = 324, where 'n' represents the length of the rectangle.
To solve for 'w', we rearrange the equation: [tex]w^2 = 324 - n^2.[/tex] This equation allows us to calculate the width 'w' of the rectangle when we know the length 'n'.
The area of the rectangle, denoted as 'A', is given by the formula A = nw, where 'n' is the length and 'w' is the width of the rectangle. By substituting the expression for w^2, we obtain: A =[tex]n\sqrt(324 - n^2).[/tex]
This equation represents the relationship between the length 'n' and the area 'A' of the rectangle, taking into account the given information about the diameter of the circle, which is also the diagonal of the rectangle. By solving for 'n' and substituting it into the formula, we can determine the area of the rectangle.
Let the width of the rectangle be w, then by the Pythagorean theorem, we have:
[tex]n^2 + w^2 = 18^2[/tex] = 324
Solving for w, we get: [tex]w^2 = 324 - n^2[/tex]
The area of the rectangle is given by:
A = nw
Substituting the expression for w^2, we get:
A =[tex]n\sqrt(324 - n^2)[/tex]
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SOMEONE HELPP , giving brainlist to anyone who answers
Answer:
[tex]2( {3}^{x} ) = 258280326[/tex]
[tex] {3}^{x} = 129140163[/tex]
[tex]x = \frac{ ln(129140163) }{ ln(3) } = 17[/tex]
n = 17 + 1 = 18
[tex]s = \frac{2( 1 - {3}^{18} )}{1 - 3} = 387420488[/tex]
The sum of this finite geometric series is 387,420,488.
Prove that if G is a cyclic group of order m and d | m, then G must have a subgroup of
order d
Since G is a cyclic group of order m, there exists an element g in G such that the subgroup generated by g contains all elements of G. We denote this subgroup by <g>. The order of <g> is equal to the order of g, which is a divisor of m. Hence, there exists an integer k such that m = kg.
Now, consider the element [tex]g^{(k/d)[/tex]. Since ([tex]g^k[/tex]) generates G and d is a divisor of k, ([tex]g^k/d[/tex]) is an element of <g>. Therefore, the subgroup generated by [tex]g^{(k/d)[/tex] is a subgroup of <g> with order d.
To show that this subgroup has order d, suppose that there exists an integer r such that [tex](g^{(k/d)})^r[/tex] = [tex]g^{(kr/d)[/tex] = e, where e is the identity element of G. This means that kr/d is an integer multiple of k, which implies that r is a multiple of d. Thus, the order of [tex]g^{(k/d)[/tex] is d, and the subgroup generated by [tex]g^{(k/d)[/tex] has order d.
Therefore, we have shown that if G is a cyclic group of order m and d | m, then G must have a subgroup of order d, which is generated by an element of the form [tex]g^{(k/d)[/tex], where g is a generator of G and m = kg.
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If $8000 is invested at 4. 25%, compounded continuously, how long will it take to double?
Round the nearest tenth of a
year
The formula for continuously compounded interest is:
A = Pe^(rt)
Where A is the ending amount, P is the principal, e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate as a decimal, and t is the time in years.
If we want to find how long it takes for the investment to double, we need to solve for t when A = 2P:
2P = Pe^(rt)
Dividing both sides by P and simplifying, we get:
2 = e^(rt)
Taking the natural logarithm of both sides, we get:
ln(2) = rt ln(e)
ln(2) = rt
t = ln(2) / r
Substituting the given values, we get:
t = ln(2) / 0.0425
t ≈ 16.3 years
So it will take approximately 16.3 years for the investment to double. Rounded to the nearest tenth of a year, the answer is 16.3 years.
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Can you use addition or mulipulcation for solving 100000 x 1/100000
Using multiplication to solve 100000 x 1/100000, the answer would be 1.
You should use multiplication to solve the problem 100000 x 1/100000.
When you multiply 100000 by 1/100000, you're essentially multiplying 100000 by a fraction that represents "one part out of 100000.". The step by step explanation is:
1. Write down the given problem: 100000 x 1/100000
2. Perform the multiplication: 100000 x (1/100000)
3. Simplify the expression: 1
Mathematically, this can be written as:
So, 100000 x 1/100000 equals 1.
You wouldn't typically use addition to solve this particular problem, as it involves multiplication of a fraction rather than adding two numbers together. However, you could use addition to solve related problems.
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the diagram shows a polygon composed of rectangles
Answer:
210 feet
Step-by-step explanation:
Refer the attached figure
LK = 22 ft
KH=JI = 18 ft.
HG=14 ft.
CD=FE=16 ft.
AL=15 ft.
GF=CB = 5ft.
KJ=HI=10 ft.
CF=CB+BG+GF=5+15+5=25 ft. =DE
AB= LK+KH+HG=22+18+14= 54 ft.
Perimeter of polygon = Sum of all sides
Perimeter of polygon=AL+LK+KJ+JI+HI+HG+GF+FE+DE+CD+CB+BA
=15+22+10+18+10+14+5+16+25+16+5+54
=210
Hence the perimeter of the polygon is 210 feet.
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Use the Picard-Lindeloef iteration to find the first few elements of a sequence {yn}n=0 of approximate solutions to the initial value problem y(t) = 5y(t)+1, y(0) = 0
To use the Picard-Lindelöf iteration to find a sequence of approximate solutions to the initial value problem y'(t) = 5y(t) + 1, y(0) = 0, we start with the initial approximation y_0(t) = 0. Then, for each n ≥ 0, we define y_{n+1}(t) to be the solution to the initial value problem y'(t) = 5y_n(t) + 1, y_n(0) = 0. In other words, we plug the previous approximation y_n into the right-hand side of the differential equation and solve for y_{n+1}.Using this procedure, we can find the first few elements of the sequence {y_n} as follows:y_0(t) = 0y_1(t) = ∫ (5y_0(t) + 1) dt = ∫ 1 dt = ty_2(t) = ∫ (5y_1(t) + 1) dt = ∫ (5t + 1) dt = (5/2)t^2 + ty_3(t) = ∫ (5y_2(t) + 1) dt = ∫ (5(5/2)t^2 + 5t + 1) dt = (25/6)t^3 + (5/2)t^2 + tTherefore, the first few elements of the sequence {y_n} are y_0(t) = 0, y_1(t) = t, y_2(t) = (5/2)t^2 + t, and y_3(t) = (25/6)t^3 + (5/2)t^2 + t.
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To use the Picard-Lindelöf iteration method to find the first few elements of a sequence {y_n} of approximate solutions to the initial value problem y'(t) = 5y(t) + 1, y(0) = 0, we first set up the integral equation for the iteration:
y_n+1(t) = y(0) + ∫[5y_n(s) + 1] ds from 0 to t
Since y(0) = 0, the equation becomes:
y_n+1(t) = ∫[5y_n(s) + 1] ds from 0 to t
Now, let's calculate the first few approximations:
1. For n = 0, we start with y_0(t) = 0:
y_1(t) = ∫[5(0) + 1] ds from 0 to t = ∫1 ds from 0 to t = s evaluated from 0 to t = t
2. For n = 1, use y_1(t) = t:
y_2(t) = ∫[5t + 1] ds from 0 to t = 5/2 s^2 + s evaluated from 0 to t = 5/2 t^2 + t
3. For n = 2, use y_2(t) = 5/2 t^2 + t:
y_3(t) = ∫[5(5/2 t^2 + t) + 1] ds from 0 to t = ∫(25/2 t^2 + 5t + 1) ds from 0 to t = 25/6 t^3 + 5/2 t^2 + t
These are the first few elements of the sequence {y_n} of approximate solutions to the initial value problem using the Picard-Lindelöf iteration method.
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A consumer group is investigating two brands of popcorn, R and S. The population proportion of kernels that will pop for Brand R is 0. 90. The population proportion of kernels that will pop for Brand S is 0. 85. Two independent random samples were taken from the population. The following table shows the sample statistics. Number of Kernels in Samples Proportion from Sample that Popped Brand R 100 0. 92 Brand S 200 0. 89 The consumer group claims that for all samples of size 100 kernels from Brand R and 200 kernels from Brand S, the mean of all possible differences in sample proportions (Brand R minus Brand S) is 0. 3. Is the consumer group’s claim correct? Yes. The mean is 0. 92−0. 89=0. 3. Yes. The mean is 0. 92 minus 0. 89 equals 0. 3. A No. The mean is 0. 92+0. 892=0. 905. No. The mean is the fraction 0. 92 plus 0. 89 over 2 equals 0. 905. B No. The mean is 0. 92−0. 892=0. 15. No. The mean is the fraction 0. 92 minus 0. 89 over 2 equals 0. 15. C No. The mean is 0. 90+0. 852=0. 875. No. The mean is the fraction 0. 90 plus 0. 85 over 2 equals 0. 875. D No. The mean is 0. 90−0. 85=0. 5
The mean of all possible differences in sample proportions (Brand R minus Brand S) is given by:
mean = pR - pS,
where pR is the population proportion of kernels that will pop for Brand R, and pS is the population proportion of kernels that will pop for Brand S.
Substituting the given values, we get:
mean = 0.90 - 0.85 = 0.05
However, the consumer group claims that the mean of all possible differences in sample proportions is 0.3. This claim is not supported by the calculations above.
Therefore, the correct answer is:
C) No. The mean is 0.90+0.85/2=0.875. No. The mean is the fraction 0.90 plus 0.85 over 2 equals 0.875.
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Without using a protractor, estimate the measure of the angle below. Explain how you made your estimate.
Let the function f be defined by
f(x) = x² + 28. If f(3y) = 2f(y), what is the one possible
value of y?
A) -1
B) 1
C) 2
D) -3
The one possible value of y, will be 2. Option C is correct.
We have f(x) = x² + 28, and f(3y) = 2f(y). Substituting 3y for x in the definition of f, we get;
f(3y) = (3y)² + 28 = 9y² + 28
Substituting y for x in the definition of f, we get;
f(y) = y² + 28
Using the given equation, we have;
2(y² + 28) = 9y² + 28
Expanding and simplifying, we get;
0 = 7y² - 56
Dividing by 7, we get:
y² - 8 = 0
Factoring, we get;
(y + 2)(y - 2) = 0
So y = -2 or y = 2. Since we are looking for only one possible value of y is 2.
Hence, C. is the correct option.
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36 A bicycle rental company charges a fixed rental fee for the first
30 minutes and a cost per minute for each additional minute. The
table shows the linear relationship between the total cost in dollars
to rent a bicycle and the number of additional minutes a bicycle
is rented.
Bicycle Rental
Number of Additional Minutes Total Cost (dollars)
15
3.05
20
$0.17 per min
$0.35 per min
$0.07 per min
$0.56 per min
35
55
3.40
4.45
5.85
What is the rate of change of the total cost in dollars with respect to
the number of additional minutes?
Answer:
C
Step-by-step explanation:
Since the rate is linear, we can subtract a larger amount of minutes by a smaller one and a larger cost by a smaller one.
For example:
20 - 15 = 5
3.40 - 3.05 = 0.35
Since you want to find the amount it takes per minute, you divide the 5 by 5 to make it one minute. You also divide the 0.35 by 5 in which you get 7.
which of the following groups of numbers is ordered from least to greatest?
A. 1/5, 3/8, 4/10, 0.45, 0.6
B. 1/5, 3/8, 0.45, 4/10, 0.6
C. 0.6, 0.45, 4/10, 3/8, 1/5
D. 0.6, 4/10, 0.45, 1/5, 3/8
ans.(a) is correct
only in option (a) numbers are arranged from least to greatest.
Tell which property the statement illustrates.
(x + 2) + 5 = x + (2 + 5)
The given statement:
(x + 2) + 5 = x + (2 + 5)
illustrates the associative property of addition.
There are three properties of addition : Associative, commutative and identity.
The associative property of addition states that : (a+b)+c = a + (b+c)
The commutative property of addition states that : a + b = b + a
The identity property of addition states that : a + 0 = a.
Therefore, the statement is illustrating the associative property of addition.
What is the slope of the linear function that models the data in the table?
The slope of the linear function that models the data in the table is -1.5. It was calculated by using the formula for slope (change in y divided by change in x) and plugging in the given coordinates. This means that for every increase of 2 in the x-value, the y-value decreases by 3.
To find the slope of the linear function that models the data in the table, we can use the slope formula
slope = (change in y)/(change in x)
We can choose any two points from the table to calculate the slope. Let's choose the points (-2,6) and (0,3)
change in y = 3 - 6 = -3
change in x = 0 - (-2) = 2
So the slope is
slope = (-3)/(2) = -1.5
Therefore, the slope of the linear function that models the data in the table is -1.5.
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--The given question is incomplete, the complete question is given
" What is the slope of the linear function that models the data in the table? "--
John has a pepper shaker in the shape of a cylinder. It has a radius of 9 mm and a height of 32 mm. John wants to cover the pepper shaker with tape, How much tape is needed? Round to the hundredths
John needs approximately 1,814.4 mm² of tape to cover the pepper shaker. Rounded to the hundredths, the answer is 1,814.40 mm².
To calculate the amount of tape needed to cover the pepper shaker, we need to find the lateral area of the cylinder. This is given by the formula L = 2πrh, where r is the radius and h is the height.
Substituting the values given, we get L = 2π(9 mm)(32 mm) = 1,814.4 mm².
Therefore, John needs approximately 1,814.40 mm² of tape to cover the pepper shaker.
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The buying and selling rate of U. S. Doller ($) in a day are Rs 115. 25 and Rs 116. 5 respectively. How many dollar should be bought and sold to have the profit of $ 10 ? Find it
To earn a profit of $10, we need to buy and sell 10 dollars.
The difference between the buying and selling rates is the profit margin for the currency exchange. Here, the profit margin is 116.5 - 115.25 = 1.25 Rs per dollar.
To make a profit of $10, we need to buy and sell enough dollars to earn a profit of 1.25*10 = 12.5 Rs.
Let's assume we buy and sell x dollars. Then the cost of buying x dollars is 115.25x Rs, and the revenue from selling x dollars is 116.5x Rs.
So, the profit from buying and selling x dollars is (116.5x - 115.25x) = 1.25x Rs.
We need to find x such that 1.25x = 12.5, which gives x = 10.
Therefore, we need to buy and sell 10 dollars to earn a profit of $10.
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what is 5 less than the square of a number in an algebraic expression
Answer:
let x be the no.
So, 5 less than the square of a number in an algebraic expression is:
x^2 - 5
Consider the following acceleration d^2s/dt^2, initial velocity, and initial position of an object moving on a number line. Find the object's position
at time t.
a = 9.8, v(0) = - 15, s(0) =
s(t) = -15t + 4.9t^2 This equation represents the object's position at time t on the number line.
To find the object's position at time t, we need to use the equation for displacement:
s(t) = s(0) + v(0)t + 1/2at^2
Plugging in the given values, we get:
s(t) = s(0) + v(0)t + 1/2at^2
s(t) = -15(0) + 1/2(9.8)(t^2)
s(t) = 4.9t^2
Therefore, the object's position at time t is given by the equation s(t) = 4.9t^2.
To find the object's position at time t, we can use the following formula:
s(t) = s(0) + v(0)t + 0.5at^2
Given the values a = 9.8, v(0) = -15, and s(0) = 0, we can substitute them into the formula:
s(t) = 0 + (-15)t + 0.5(9.8)t^2
s(t) = -15t + 4.9t^2
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