The area of the region bounded by the curve y=sin(x) and the x-axis between x=0 and x=4pi is 0.
To find the area of the region bounded by the curve y=sin(x) and the x-axis between x=0 and x=4pi, we can use the following steps:
1. Determine the function: In this case, the function is y=sin(x).
2. Identify the interval: The interval is from x=0 to x=4pi.
3. Integrate the function over the given interval: We'll integrate y=sin(x) with respect to x from 0 to 4pi.
∫(sin(x) dx) from 0 to 4pi.
4. Find the antiderivative: The antiderivative of sin(x) is -cos(x).
-∫(cos(x) dx) from 0 to 4pi.
5. Apply the fundamental theorem of calculus: We'll evaluate the antiderivative at the upper limit (4pi) and subtract the antiderivative evaluated at the lower limit (0).
[-cos(4pi)] - [-cos(0)]
6. Calculate the values: cos(4pi) = 1 and cos(0) = 1.
[-1] - [-1]
7. Determine the area: The area is the difference between the values calculated in step 6.
[-1 - (-1)] = 0
The area of the region bounded by the curve y=sin(x) and the x-axis between x=0 and x=4pi is 0.
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The 8th grade class of City Middle School has decided to hold a raffle to raise money to fund a trophy cabinet as their legacy to the school. A local business leader with a condominium on St. Simons Island has donated a week’s vacation at his condominium to the winner—a prize worth $1200. The students plan to sell 2500 tickets for $1 each.
1) Suppose you buy 1 ticket. What is the probability that the ticket you buy is the winning ticket? (Assume that all 2500 tickets are sold. )
2) After thinking about the prize, you decide the prize is worth a bigger investment. So you buy 5 tickets. What is the probability that you have a winning ticket now?
3) Suppose 4 of your friends suggest that each of you buy 5 tickets, with the agreement that if any of the 25 tickets is selected, you’ll share the prize. What is the probability of having a winning ticket now?
4) At the last minute, another business leader offers 2 consolation prizes of a week-end at Hard Labor Creek State Park, worth around $400 each. Have your chances of holding a winning ticket changed? Explain your reasoning. Suppose that the same raffle is held every year. What would your average net winnings be, assuming that you and your 4 friends buy 5 $1 tickets each year?
1) If there are 2500 tickets sold, and you buy 1 ticket, then the probability of your ticket being the winning ticket is 1/2500 or 0.04%.
2) If you buy 5 tickets, then the probability of having a winning ticket is 5/2500 or 0.2%.
3) If you and your 4 friends each buy 5 tickets, then there will be a total of 25 tickets. The probability of having a winning ticket in this scenario is 5/25 or 20%.
4) The chances of holding a winning ticket have not changed. This is because the consolation prizes are separate from the main prize, and the probability of winning the main prize is still the same.
The addition of consolation prizes does not affect the probability of winning the main prize.
Assuming the same raffle is held every year and you and your 4 friends buy 5 tickets each year, the average net winnings would be calculated as follows:
Total cost of tickets = $1 x 5 x 5 = $25
Total prize money = $1200 + ($400 x 2) = $2000
Probability of winning = 5/2500 = 0.2%
Expected value of winning = $2000 x 0.2% = $4
Average net winnings = ($4 - $25)/year = -$21/year
This means that on average, you and your friends would lose $21 per year if you participate in the raffle every year.
However, it is important to note that this is just an average and there is a chance of winning a larger prize which would make the net winnings positive.
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A peregrine falcon can dive at the speed of 320km/h. Create a problem that you can solve by finding an equivalent rate for this speed. Then solve the problem.
If a and b are positive numbers, prove that the equation
a/x^3+2x^2-1 + b/x^3+x-2 = 0
has at least one solution in the interval (- 1, 1).
The equation has at least one solution in the interval (-1, 1).
To prove that the equation has at least one solution in the interval (-1, 1), we can use the Intermediate Value Theorem.
First, let's simplify the equation by finding a common denominator:
a(x^3+x-2) + b(x^3+2x^2-1) = 0
Now, let's define a new function f(x) = a(x^3+x-2) + b(x^3+2x^2-1). This function is continuous on the interval (-1, 1) because it is a sum of continuous functions.
Next, we will evaluate f(-1) and f(1) to see if the Intermediate Value Theorem can be applied.
f(-1) = a(-1^3-1-2) + b(-1^3+2(-1)^2-1) = -a-b < 0
f(1) = a(1^3+1-2) + b(1^3+2(1)^2-1) = a+3b > 0
Since f(-1) is negative and f(1) is positive, there must be at least one value of x in the interval (-1, 1) such that f(x) = 0, by the Intermediate Value Theorem.
To prove that the given equation has at least one solution in the interval (-1, 1), we can use the Intermediate Value Theorem (IVT). Let's define the function f(x) as follows:
f(x) = a/(x^3 + 2x^2 - 1) + b/(x^3 + x - 2)
Since a and b are positive numbers, we can examine the behavior of f(x) at the endpoints of the interval (-1, 1).
f(-1) = a/((-1)^3 + 2(-1)^2 - 1) + b/((-1)^3 + (-1) - 2)
f(-1) = a/(-1) + b/(-4) < 0
f(1) = a/(1^3 + 2(1)^2 - 1) + b/(1^3 + 1 - 2)
f(1) = a/(2) + b/(0) = a/2 > 0
Since f(-1) < 0 and f(1) > 0, by the Intermediate Value Theorem, there must be at least one point c within the interval (-1, 1) where f(c) = 0. This means that the given equation has at least one solution in the interval (-1, 1).
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Find the exact location of all the relative and absolute extrema of the function (Order your answers from smallest to largest x.) (x)=2x-x+ with domain (0,3)
The location of all the relative and absolute extrema is (0, 0) (local minimum); (1, 1) (local maximum); (3, 3) (absolute maximum)
To find the relative and absolute extrema of the function f(x) = 2x - x^2 on the domain (0,3), we first take the derivative:
f'(x) = 2 - 2x
Setting this equal to zero, we find the critical point:
2 - 2x = 0
x = 1
To determine the nature of the critical point, we need to examine the second derivative:
f''(x) = -2
Since the second derivative is negative at x = 1, this critical point is a local maximum. To find the absolute extrema, we also need to examine the endpoints of the domain, x = 0 and x = 3:
f(0) = 0
f(3) = 3
So the function has an absolute maximum at x = 3 and an absolute minimum at x = 0. Therefore, the location of all the relative and absolute extrema, from smallest to largest x, is:
(0, 0) (local minimum)
(1, 1) (local maximum)
(3, 3) (absolute maximum)
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Calculate the perimeter and area of the shaded region in the drawing of two circles at right. Round to the nearest tenth. Show all work. 10 5cm 21 cm
The perimeter of the shaded region is approximately 85.67 cm The area of the shaded region is approximately 91.84 cm² (rounded to the nearest tenth).
To calculate the perimeter and area of the shaded region, we first need to find the radius of each circle.
The larger circle has a diameter of 21 cm, which means its radius is 10.5 cm (half of the diameter). The smaller circle has a diameter of 10 cm, so its radius is 5 cm.
To find the perimeter of the shaded region, we need to add the circumference of both circles and subtract the overlap (the length of the shared segment). The circumference of the larger circle is 2π(10.5) ≈ 65.97 cm, and the circumference of the smaller circle is 2π(5) ≈ 31.42 cm.
To find the length of the shared segment, we can use the Pythagorean theorem. The distance between the centers of the circles is 15 cm (the sum of the radii), so we can form a right triangle with legs of 10.5 cm and 5 cm. Using the Pythagorean theorem, we get:
c² = a² + b²
c² = 10.5² + 5²
c² ≈ 137.25
c ≈ 11.72
So the length of the shared segment is approximately 11.72 cm.
Therefore, the perimeter of the shaded region is approximately 65.97 + 31.42 - 11.72 = 85.67 cm (rounded to the nearest tenth).
To find the area of the shaded region, we need to subtract the area of the smaller circle from the area of the larger circle, and then subtract the area of the overlap (the area of the shared segment).
The area of the larger circle is π(10.5)² ≈ 346.36 cm², and the area of the smaller circle is π(5)² ≈ 78.54 cm².
To find the area of the shared segment, we can use the formula for the area of a sector of a circle:
A = (θ/360)πr²
where θ is the central angle of the sector. In this case, the sector has a central angle of 2cos⁻¹(5/10.5) ≈ 105.2°, so:
A = (105.2/360)π(10.5)²
A ≈ 91.84 cm²
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1. the elevation of death valley, california is - 282 feet. the elevation of tallahassee, florida is 203
feet. the elevation of westmorland, california is -157 feet.
compare the elevations of death valley and tallahassee using < or >
fill in the blank:
death valley (-282 feet)
tallahassee, florida (203 feet)
Based on the elevations given, Death Valley (-282 feet) < Tallahassee, Florida (203 feet).
To compare the elevations of Death Valley and Tallahassee, we'll use the inequality symbols i.e., "<" or ">" . The symbol "<" indicate less than and ">" indicate greater than.
Death Valley, California has an elevation of -282 feet, while Tallahassee, Florida has an elevation of 203 feet. Since -282 is less than 203, we use the "<" symbol.
So, the comparison is as follows:
Death Valley (-282 feet) < Tallahassee, Florida (203 feet)
This means that the elevation of Death Valley is lower than or less than the elevation of Tallahassee.
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Please help me find x. Also show me step by step
Answer: x ≅ -0.9 or -1.8
Step-by-step explanation:
[tex]3(3x+4)^2 - 6 = 0[/tex]
[tex]3(3x+4)^2 = 6[/tex]
[tex]3(9x^2+24x+16) = 6[/tex]
[tex]9x^2+24x+16 = 2[/tex]
[tex]9x^2+24x+14 = 0[/tex]
Use the quadratric formula to get:
x ≅ -0.9 or -1.8
Find the absolute maximum and minimum of the function f(x,y)=y√x−y2−x+3y on the domain 0≤x≤9, 0≤y≤8
The absolute maximum of the function f(x,y) = y√(x-y^2)-x+3y on the domain 0≤x≤9, 0≤y≤8 is 2√2, which occurs at the point (2,2).
The absolute minimum of the function is -8, which occurs at the point (0,2).
To find the absolute maximum and minimum of the function f(x,y) = y√(x-y^2)-x+3y on the domain 0≤x≤9, 0≤y≤8, we need to evaluate the function at the critical points and at the boundary of the domain.
The critical points of the function are the points where the partial derivatives with respect to x and y are both zero. Solving these equations, we get:∂f/∂x = -1 + y/(√(x-y^2)) = 0∂f/∂y = √(x-y^2) - 1 + 3 = 0Solving these equations, we get two critical points: (0,2) and (2,2). Evaluating the function at these points, we get:f(0,2) = -8f(2,2) = 2√2Next, we need to evaluate the function at the boundary of the domain. This includes the points (0,y), (9,y), (x,0), and (x,8).
Evaluating the function at these points, we get:f(0,y) = -x+3yf(9,y) = y√(9-y^2)-6f(x,0) = -xf(x,8) = 8√(x-64/9)-x+24Taking the maximum and minimum values of the function at the critical points and on the boundary of the domain, we see that the absolute maximum of the function is 2√2, which occurs at the point (2,2), and the absolute minimum of the function is -8, which occurs at the point (0,2).
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As as you approach zero from the left on a number line the integers ____ , but the absolute values of those integers ___?
As you approach zero from the left on a number line, the integers become increasingly negative, but the absolute values of those integers remain positive.
A number line is a visual representation of numbers placed in order on a straight line. It is a graphical tool used to represent the real numbers, starting from negative infinity on the left side and extending to positive infinity on the right side. The number line is divided into equal intervals, and each point on the line corresponds to a specific value or number. The distance between any two points on the number line represents the numerical difference between the corresponding numbers. The number line is a fundamental tool in mathematics for understanding the order and magnitude of numbers, as well as for performing operations such as addition, subtraction, and comparison.
As you approach zero from the left on a number line, the integers become increasingly negative, but the absolute values of those integers remain positive.
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Help me with these questions pls
The volume of the cones are;
1. 84. 78 in³
2. 564. 15 ft³
3. 4710 yd³
How to determine the value
The formula for calculating the volume of a cone is expressed as;
V = 1/3 πr²h
Given that;
r is the radius of the cone.h is the height of the coneFrom the information given, we have;
1. Volume = 1/3 × 3.14 × 3² × 9
Multiply the values and find the square
Volume = 254. 34/3
divide the values
Volume = 84. 78 in³
2. Volume = 1/3 × 3.14 × 7² × 11
Multiply the values
Volume = 1692. 46/3
Volume = 564. 15 ft³
3. Volume = 1/3 × 3.14 × 15² × 20
Multiply the values
Volume = 4710 yd³
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Find the coordinates of the absolute extrema for f(x) on the closed interval [-4, 4]
x^3 - 3x^2 - 9x + 20
The coordinates of the absolute maximum point are (4, 24), and the coordinates of the absolute minimum point are (-4, -8).
To find the absolute extrema of the function[tex]f(x) = x^3 - 3x^2 - 9x + 20[/tex] on
the closed interval [-4, 4], we need to find the maximum and minimum
values of the function within the given interval.
Find the critical points of the function f(x) within the interval [-4, 4].
To find the critical points, we need to take the first derivative of the
function and set it equal to zero.
[tex]f(x) = x^3 - 3x^2 - 9x + 20[/tex]
[tex]f'(x) = 3x^2 - 6x - 9[/tex]
Setting f'(x) = 0, we get:
[tex]3x^2 - 6x - 9 = 0[/tex]
Dividing both sides by 3, we get:
[tex]x^2 - 2x - 3 = 0[/tex]
Factoring the quadratic equation, we get:
(x - 3)(x + 1) = 0
So, the critical points of the function within the interval [-4, 4] are x = -1 and x = 3.
Find the values of the function at the critical points and at the endpoints
of the interval [-4, 4].
To find the values of the function at the critical points and at the
endpoints of the interval, we evaluate the function at each of these
values.
f(-4) = -8
f(4) = 24
f(-1) = 24
f(3) = 2
Compare the values obtained in step 2 to find the maximum and minimum values of the function.
The maximum value of the function is 24, which occurs at x = -1 and x = 4.
The minimum value of the function is -8, which occurs at x = -4.
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A lab technician is filling vitamin C capsules. He has 2.87 ounces of vitamin C and is putting 0.014 ounces of vitamin C into each capsule. How many capsules will the lab technician be able to fill with vitamin C? A. 3 B. 25 C. 402 D. 205 
Answer:
D) 205
Step-by-step explanation:
If the technician has a total of 2.87 oz, and can have a max of 0.014 oz in each capsule, we have to divide the total amount by the max amount per bottle.
2.87/0.014
=205
This means that the technician can fill 205 capsules with 0.014 oz of vitamin C.
Hope this helps!
Please hurry I need it ASAP
A 3 ox serving of roasted skinless chicken breast contain 140 cal, 24 g of protein, 2 g of fat, 11 mg of calcium, and 61 mg of sodium. One half cup of potato salad contains 160 cal, 4 g of protein, 13 g of fat, 21 mg of calcium, and 656 mg of sodium. One brooccoli spear contains 40 cal, 5 g of protein, 1 g of fat, 81 mg of calcium, and 23 mg of sodim. Use this information to complete following parts.
a) Write a 1×5 matrices, C, P, and B that represent the nutritional values of the chicken, potato salad, and broccoli, respectively. Give the nutritional values in the following order: Cal, g of protein, g of fat, mg of calcium, and mg of sodium.
C=
P=
B=
The matrices are: C = [140, 24, 2, 11, 61] P = [160, 4, 13, 21, 656] B = [40, 5, 1, 81, 23]
To represent the nutritional values of the chicken, potato salad, and broccoli in matrices, we can use a 1x5 matrix for each food, where each column represents a different nutritional value in the following order: calories, protein, fat, calcium, and sodium.
Therefore, we have:
C = [140 24 2 11 61]
P = [160 4 13 21 656]
B = [40 5 1 81 23]
In matrix C, the values are 140 calories, 24 grams of protein, 2 grams of fat, 11 milligrams of calcium, and 61 milligrams of sodium for a 3 ounce serving of roasted skinless chicken breast. In matrix P, the values are 160 calories, 4 grams of protein, 13 grams of fat, 21 milligrams of calcium, and 656 milligrams of sodium for one half cup of potato salad. In matrix B, the values are 40 calories, 5 grams of protein, 1 gram of fat, 81 milligrams of calcium, and 23 milligrams of sodium for one broccoli spear.
These matrices can be used to perform calculations and comparisons between the nutritional values of the different foods.
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The circumference of a circle is 12.56 millimeters. What is the circle's radius?
C=12.56 mm
Use 3.14 for .
The radius of the circle is 2mm
How to determine the circumferenceIt is important to note that the formula that is used for calculating the circumference of a circle is expressed with the equation.
The equation is written as;
C = 2πr
Such that the parameters are;
C is the cicumference of the circle.r is the radius of the circle.πtakes the constant value of 22/7From the information given, we have thatt;
The radius of the circle = r
The circumference = 12.56mm
Substitute the values, we have;
12. 56 = 2×3.14r
Multiply the values
r = 12. 56/6. 28
divide the values
r = 2mm
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1) Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. (If an answer does not exist, enter DNE.)
f(x, y) = 5x^2 + 5y^2; xy = 1
2) Find the extreme values of f subject to both constraints. (If an answer does not exist, enter DNE.)
f(x, y, z) = x + 2y; x + y + z = 6, y^2 + z^2 = 4
The maximum and minimum values for given function f(x, y) = 5x² + 5y² subject to xy = 1 are both 10. The extreme values of f(x, y, z) = x + 2y; x + y + z = 6, y² + z² = 4 subject to both constraints are 7 and -4.
We can use Lagrange multipliers to find the maximum and minimum values of f(x, y) subject to the constraint xy = 1.
First, we set up the Lagrange function
L(x, y, λ) = 5x² + 5y² + λ(xy - 1)
Then, we take partial derivatives of L with respect to x, y, and λ and set them equal to 0
∂L/∂x = 10x + λy = 0
∂L/∂y = 10y + λx = 0
∂L/∂λ = xy - 1 = 0
Solving these equations simultaneously, we get
x = ±√2, y = ±√2, λ = ±5/2√2
We also need to check the boundary points where xy = 1, which are (1, 1) and (-1, -1). We evaluate f at these points and compare them to the values we get from the Lagrange multipliers.
f(√2, √2) = 10, f(-√2, -√2) = 10
f(1, 1) = 10, f(-1, -1) = 10
So the maximum and minimum values of f(x, y) subject to xy = 1 are both 10.
We can use Lagrange multipliers to find the extreme values of f(x, y, z) subject to both constraints.
First, we set up the Lagrange function
L(x, y, z, λ, μ) = x + 2y + λ(x + y + z - 6) + μ(y² + z² - 4)
Then, we take partial derivatives of L with respect to x, y, z, λ, and μ and set them equal to 0
∂L/∂x = 1 + λ = 0
∂L/∂y = 2 + λ + 2μy = 0
∂L/∂z = λ + 2μz = 0
∂L/∂λ = x + y + z - 6 = 0
∂L/∂μ = y² + z² - 4 = 0
Solving these equations simultaneously, we get
x = -1, y = 2, z = 3, λ = -1, μ = -1/2
x = 3, y = -2, z = -1, λ = -1, μ = -1/2
We also need to check the boundary points where either x + y + z = 6 or y² + z² = 4. These points are (0, 2, 2), (0, -2, -2), (4, 1, 1), and (4, -1, -1). We evaluate f at these points and compare them to the values we get from the Lagrange multipliers.
f(-1, 2, 3) = 7, f(3, -2, -1) = -1
f(0, 2, 2) = 4, f(0, -2, -2) = -4
f(4, 1, 1) = 6, f(4, -1, -1) = 2
So the maximum value of f subject to both constraints is 7, which occurs at (-1, 2, 3), and the minimum value of f subject to both constraints is -4, which occurs at (0, -2, -2).
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Your parents are buying a house for $187,500. They have a good credit rating, are making a 20% down payment, and expect to pay $1,575/month. The interest rate for the mortgage is 4.65%. What must their realized income be before each month?
Be sure to include the following in your response:
the answer to the original question
the mathematical steps for solving the problem demonstrating mathematical reasoning
A bag contains 4 white, 3 blue, and 5 red marbles. Find the probability of choosing a red marble, then a white marble if the marbles were replaced.
The probability of choosing a red marble, then a white marble is 5/36
Finding the probability of choosing a red marble, then a white marbleFrom the question, we have the following parameters that can be used in our computation:
A bag contains 4 white, 3 blue, and 5 red marbles
If the marbles were replaced, then we have
P(Red) = 5/12
P(White) = 4/12
So, we have
The probability of choosing a red marble, then a white marble is
P = 5/12 * 4/12
Evaluate
P = 5/36
Hence, the probability of choosing a red marble, then a white marble is 5/36
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I'm fairly new to this concept and I'm a bit confused on these 3 questions. Please help :)
1) All the solution are,
(x, y) = (√2, 2) , (- √2, 2), (√2, -2) , (- √2, -2), (√2i, 2) , (- √2i, 2), (√2i, -2) , (- √2i, -2),
2) Solutions are,
⇒ x = 3, 3, - √3 / 2, - 5
3) All the even integers which are divisible by 5 is,
⇒ 10, 20, 30, 40, 50, ....
Given that;
1) Expression is,
⇒ x² = y, and y² = 4
2) Expression is,
⇒ (x - 3)² (2x + √3) (x + 5) = 0
Now, We can simplify as;
⇒ x² = y,
⇒ x⁴ = y²
x⁴ = 4
x⁴ - 2² = 0
(x²)² - 2² = 0
(x² - 2) (x² + 2) = 0
This gives,
x² = 2
x = ± √2
x² = - 2
x = ±√2 i
Hence, We get;
y² = 4
y = ± 2
Thus, All the solution are,
(x, y) = (√2, 2) , (- √2, 2), (√2, -2) , (- √2, -2), (√2i, 2) , (- √2i, 2), (√2i, -2) , (- √2i, -2),
Since, 2) Expression is,
⇒ (x - 3)² (2x + √3) (x + 5) = 0
Simplify as;
⇒ (x - 3)² = 0
⇒ x = 3, 3
⇒ (2x + √3) = 0
⇒ x = - √3 / 2
⇒ (x + 5) = 0
⇒ x = - 5
3) All the even integers which are divisible by 5 is,
⇒ 10, 20, 30, 40, 50, ....
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During one week, Sheila made several changes to her bank account. She made four withdrawals of 40$ each from an ATM she also used her check card for a 156$ purchase then she deposited her paycheck of $375
The amount change in her bank account during that week after withdrawals and deposit is equal to $59.
Total number of withdrawals made by Sheila = 4
Amount made at the time withdrawals using ATM = $40
Amount withdraw using check card to purchase = $156
Amount deposited using paycheck = #375
Let us calculate the total amount of money Sheila withdrew from her bank account using ATM,
4 withdrawals of $40 each
= 4 x $40
= $160
So, she withdrew $160 and made a $156 purchase, meaning she spent a total amount of,
= $160 + $156
= $316
Sheila also deposited her paycheck of $375, so the total amount of money in her account changed by is equal to,
$375 - $316 = $59
Therefore, the amount in Sheila's account increased by $59 during that week.
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The above question is incomplete, the complete question is:
During one week, Sheila made several changes to her bank account. She made four withdrawals of $40 each from an ATM. She also used her check card for a $156 purchase. Then she deposited her paycheck of $375. By how much did the amount in her bank account change during that week?
solve by completing the square x^2-14x+49=16
ANSWER:
(x+7)^2=16
Step-by-step explanation:
x^2-14x+49=16
x^2-14x+49-16=0
x^2-14x+33=0
subtract -33 on both sides
x^2-14x+33-33=-33
x^2-14x=-33
Add 49 on both sides
x^2-14x+49=-33+49
x^2-14x+49=16
x^2-7x-7x+49=16
x(x-7)-7(x-7)=16
(x-7)(x-7)=16
(x-7)^2=16
A wheel has a diameter of 40 cm, to the nearest 10 cm.
Write an inequality to show
a the lower and upper bounds for the diameter d of the wheel
b the lower and upper bounds for the circumference C of the wheel.
a) The diameter d of the wheel has bounds:
35 cm ≤ d ≤ 45 cm
b) The circumference C has bounds, using C = πd:
π * 35 cm ≤ C ≤ π * 45 cm
How to solveThe inequality representing the lower and upper bounds for the diameter d is:
35 cm ≤ d ≤ 45 cm
b) For the lower bound, we substitute the lower bound of the diameter (35 cm) into the formula:
[tex]C_l_o_w_e_r[/tex] = π * 35 cm
For the upper bound, we substitute the upper bound of the diameter (45 cm) into the formula:
[tex]C_u_p_p_e_r[/tex] = π * 45 cm
The inequality representing the lower and upper bounds for the circumference C is:
π * 35 cm ≤ C ≤ π * 45 cm
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Determine the intervals on which the given function is concave up or concave down and find the points of inflection. S(x) = (x - 10)(1 - x) (Use symbolic notation and fractions where needed. Give your answer in three decimal numbers
There are no points of inflection.
To determine the intervals on which the function S(x) = (x - 10)(1 - x) is concave up or down and find the points of inflection, we need to find the second derivative and analyze its sign.
First, find the first derivative, S'(x):
S'(x) = (x - 10)(-1) + (1 - x)(1) = -x + 10 - 1 + x = 9
Next, find the second derivative, S''(x):
S''(x) = d(S'(x))/dx = d(9)/dx = 0
Since the second derivative S''(x) is constant and equal to 0, there is no concavity, and the function is neither concave up nor concave down. There are no points of inflection.
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3
Select the correct answer.
The angle of depression between the top of a 100-foot cliff and a ship approaching the shore is 37°.
cliff top
37°
100
feet
37°
ship
d
What is the approximate distance, d, between the bottom of the cliff and the ship?
ÐÐ
166. 2 feet
OB. 60. 2 feet
ÐС.
75. 4 feet
OD.
132. 7 feet
Reset
Next
The correct answer is (D) 132.7 feet.
From the given information, we can draw a diagram as follows:
A
/|
/ |
/ | 37°
/ |
/ |
/ |
/ |
/_ _ _ _|
d B
Where A represents the top of the cliff, B represents the ship and d represents the distance between the ship and the bottom of the cliff.
Since we know that the angle of depression is 37 degrees, then the angle CAB is also 37 degrees. We also know that AB is 100 feet, which is the height of the cliff. We want to find the distance d between the bottom of the cliff and the ship.
We can use the tangent function to find d:
tan(37°) = AB/BD
tan(37°) = 100/d
d = 100/tan(37°)
Using a calculator, we can find that:
d ≈ 132.7 feet
Therefore, the correct answer is (D) 132.7 feet.
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Henry earned $850 over the summer working odd jobs. he wants to put his money into a savings account for when he is ready to buy a car. his bank offers a simple interest account at 5%, how much interest will henry have earned after 4 years?
Answer:
We can use the formula for simple interest to calculate the interest earned by Henry:
Simple Interest = (Principal * Rate * Time)
where,
Principal = $850 (initial amount)
Rate = 5% per year (as given)
Time = 4 years (as given)
Substituting the values, we get:
Simple Interest = (850 * 0.05 * 4) = $170
Therefore, Henry will have earned $170 in interest after 4 years of keeping his money in the savings account.
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Lines b and a are intersected by line f. At the intersection of lines f and b, the bottom left angle is angle 4 and the bottom right angle is angle 3. At the intersection of lines f and a, the uppercase right angle is angle 1 and the bottom left angle is angle 2.
Which set of equations is enough information to prove that lines a and b are parallel lines cut by transversal f?
Answer:
Step-by-step explanation:
To prove that lines a and b are parallel lines cut by transversal f, we need to show that the alternate interior angles are congruent. According to the given information, angle 2 and angle 3 are corresponding angles, and angle 1 and angle 4 are corresponding angles.
Therefore, the set of equations that is enough information to prove that lines a and b are parallel lines cut by transversal f is:
angle 2 = angle 3 (corresponding angles)
angle 1 = angle 4 (corresponding angles)
!!PLEASEE HELPPP!! I’m having a hard time!!
a. A customer would save $492 during the first year by switching from ElectroniSource to Intellivision. b. A customer who would save $207 in the second year. c. Intellivision's total cost of $1654.56.
Describe Algebra?Algebra is a branch of mathematics that deals with the manipulation and properties of variables, symbols, and equations. In algebra, variables represent unknown quantities, and equations represent relationships between those unknown quantities.
The fundamental operations in algebra are addition, subtraction, multiplication, and division. Algebraic equations involve variables and constants, which are combined using these operations to form algebraic expressions. These expressions can be simplified by applying algebraic rules and properties, such as the distributive property, associative property, and commutative property.
a. To calculate the savings during the first year, we need to find the total cost for each company for all three services during a year and compare them.
For ElectroniSource, the total cost for a year would be:
$42/month x 12 months = $504 for phone service
$35/month x 12 months = $420 for Internet service
$59/month x 12 months = $708 for cable TV service
Total cost for a year with ElectroniSource = $504 + $420 + $708 = $1632
For Intellivision, the flat monthly fee is $95, so the total cost for a year would be:
$95/month x 12 months = $1140
Savings during the first year = Cost with ElectroniSource - Cost with Intellivision
= $1632 - $1140
= $492
Therefore, a customer would save $492 during the first year by switching from ElectroniSource to Intellivision.
b. After the first year, Intellivision raises the rates by 25%. The new monthly fee would be:
$95 + 25% of $95 = $118.75
To calculate the savings for the second year, we need to find the total cost for each company for all three services during the second year and compare them.
For ElectroniSource, the total cost for the second year would still be:
$504 for phone service
$420 for Internet service
$708 for cable TV service
Total cost for the second year with ElectroniSource = $504 + $420 + $708 = $1632
For Intellivision, the total cost for the second year would be:
$118.75/month x 12 months = $1425
Savings during the second year = Cost with ElectroniSource - Cost with Intellivision
= $1632 - $1425
= $207
Therefore, a customer who switched from ElectroniSource to Intellivision would save $207 in the second year.
c. If Intellivision raises the rates by 16% for the third year compared to the second year, the new monthly fee would be:
$118.75 + 16% of $118.75 = $137.88
To compare the total cost for each company for the third year, we need to find the total cost for each company for all three services during the third year and compare them.
For ElectroniSource, the total cost for the third year would still be:
$504 for phone service
$420 for Internet service
$708 for cable TV service
Total cost for the third year with ElectroniSource = $504 + $420 + $708 = $1632
For Intellivision, the total cost for the third year would be:
$137.88/month x 12 months = $1654.56
Therefore, ElectroniSource is cheaper for the third year, with a total cost of $1632 compared to Intellivision's total cost of $1654.56.
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Find each arc length. Round to the nearest hundredth.
If EB = 15 cm, find the length of CD.
mCD = ____ cm.
(30 points) will give brainiest for effort
The length of arc CD, given that the radius, EB = 15 cm, is 29.31 cm
How do i determine the length of arc CD?First, we shall determine ∠CED. Details below:
∠BEC = 68°∠CED =?2∠CED + 2∠BEC = 360
2∠CED + (2 × 68) = 360
2∠CED + 136 = 360
Collect like terms
2∠CED = 360 - 136
2∠CED = 224
Divide both sides by 2
∠CED = 224 / 2
∠CED = 112°
Finally, we shall determine the length of the of arc CD. Details below:
Radius (r) = EB = 15 cmAngle (θ) = ∠CED = 112°Length of arc CD = ?Length of arc = 2πr × (θ / 360)
Length of arc CD = (2 × 3.14 × 15) × (112 / 360)
Length of arc CD = 29.31 cm
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Complete question:
See attached photo
Part A: Sydney made $18. 50 selling lemonade, by the cup, at her yard sale. She sold each cup for $0. 50 and received a $3 tip from a neighbor. Write an equation to represent this situation. (4 points) Part B: Daria made a profit of $21. 00 selling lemonade. She sold her lemonade for $0. 75 per cup, received a tip of $3 from a neighbor, but also had to buy each plastic cup she used for $0. 10 per cup. Write an equation to represent this situation. (4 points) Part C: Explain how the equations from Part A and Part B differ. (2 points
a) equation will be 0.5x + 3 = 18.50
b) equation will be (0.75x - 0.10x) + 3 = 21.00
a) Sydney made $18.50 selling lemonade.
she sold each cup for $0.50 and received a $3 tip from a neighbor.
let x be the cost of cup she sold.
equation will be 0.5x + 3 = 18.50
b) Daria made a profit of $21.00 selling lemonade
she sold her lemonade for $0.75 per cup, received a tip of $3 from a neighbor.
equation will be (0.75x - 0.10x) + 3 = 21.00
c) Sydney don't have to pay for the cups used while Daria paid.
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A. An equation to represent the situation in part A is 18.50 = (0.50) x + 3.
B. An equation to represent the situation in part B is 21.00 = (0.75) y - (0.10) y + 3.
C. The equations differ in the fact that one accounts for the cost per cup while the other does not.
What is profit?In general, the profit is defined as the amount gained by selling a product, which should be more than the cost price of the product.
Part A: Let x be the number of cups of lemonade sold.
Then, the total amount of money Sydney made is given by:
Total money = (selling price per cup) × (number of cups sold) + tip
Substituting the given values, we get:
18.50 = (0.50) x + 3
Part B: Let y be the number of cups of lemonade sold.
Then, the total profit made by Daria is given by:
Total profit = (selling price per cup) × (number of cups sold) + tip - (cost per cup) × (number of cups sold)
Substituting the given values, we get:
21.00 = (0.75) y - (0.10) y + 3
Part C: The equation for Sydney's lemonade stand only takes into account the total amount of money she made, which includes the selling price per cup and a fixed tip.
On the other hand, the equation for Daria's lemonade stand takes into account both the total profit made (which includes the selling price per cup and a fixed tip) and the cost per cup of lemonade sold. So, the equations differ in the fact that one accounts for the cost per cup while the other does not.
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Complete question is
Part A : Sydney made $18.50 selling lemonade, by the cup, at her yard sale. She sold each cup for $0.50 and received a $3 tip from a neighbour. Write an equation to represent this situation.
Part B : Daria made a profit of $21.00 selling lemonade. She sold her lemonade for $0.75 per cup, received a tip of $3 from a neighbour, but also had to buy each plastic cup she used for $0.10 per cup. Write an equation to represent this situation.
Part C: Explain how the equation from part A and part B differ.
a florida citrus grower estimates that if 60 orange trees are planted, the average yield per tree will be 400 oranges. The average yield will decrease by 4 oranges per tree for each additional tree planted on the same acreage. Express the grower's total yield as a function of the number of additional trees planted, draw the graph and estimate the total number of trees the grower should plant to maximize yield.
Answer: 80 trees
Step-by-step explanation:
YIELD = (NUMBER OF TREES)*(NUMBER OF ORANGES PER TREE)
Let's assume NUMBER OF TREES = 60 + x, where x is the number of additional trees above 60
The NUMBER OF ORANGES PER TREE will = (400-4x). Hence:
YIELD = (60+x)*(400-4x) = 24000-240x+400x-4x2 = -4x2 + 160x + 24,000
To find the maximum YIELD, take the derivative of YIELD wrt x, set it to zero, and solve for x:
d(YIELD)/dx = -8x + 160
0 = -8x +160
8x = 160
x = 20
The grower should grow 60 + 20 = 80 trees to maximize yield.
Answer: 80 trees
Step-by-step explanation: just bc it is