The standard form of the equation of the circle with the given characteristics is[tex] {(x - 4)}^{2} + {(y - 3)}^{2} = 25[/tex]
To get the equation of the circle using the endpoints of a diameter, we have to use the standard form :
[tex](x - h) ^{2} + (y - k)^{2} = {r}^{2} [/tex]
In which (h, k) represents the middle point of the circle and r as the radius. so, we need to find the midpoint of the diameter using the endpoints (0, 0) and (8, 6).
Midpoint = ((0+8)/2, (0+6)/2) = (4, 3)
Next, we need to calculate the radius by using the distance formula to calculate the distance between the center and one of the diameter endpoints.
[tex] {r}^{2} = {(8 - 4)}^{2} + {(6 - 3)}^{2} = {4}^{2} + {3}^{2} = 16 + 9 = 25[/tex]
Now, substituting the values of (h, k) and
[tex] {r}^{2} [/tex] into the standard form equation to get the equation:
[tex] {(x - 4)}^{2} + {(y - 3)}^{2} = 25[/tex]
Therefore, the standard form equation of the circle with the given characteristics is
[tex] {(x - 4)}^{2} + {(y - 3)}^{2} = 25[/tex]
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The standard form of the given question is (x - 4)² + (y - 3)² = 25, under the condition endpoints of a diameter: (0, 0), (8, 6).
In order To write the standard form of the equation of a circle with endpoints of a diameter (0, 0), (8, 6), we first need to find the center and radius of the circle.
The diameter comprises the midpoints of the center of the circle. The midpoint of (0, 0) and (8, 6) is ((0+8)/2, (0+6)/2) = (4,3). Center point of the circle is (4,3).
Diameter = 2× radius
. The distance between (0, 0) and (8, 6) is √((8-0)² + (6-0)²)
= √(64+36)
= √100
= 10.
Then, the radius of the circle is 10/2 = 5.
Then,
(x - h)² + (y - k)² = r²
here
(h,k) = center of the circle
r = radius.
Staging in this equation
h=4,
k=3
r=5
(x - 4)²+ (y - 3)² = 25
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A square root function that has been reflected over the x-axis and move up 9
Therefore, the square root function that has been reflected over the x-axis and moved up 9 units is: g(x) = -√(x) + 9.
What is function?In mathematics, a function is a relation between two sets, called the domain and the range, that associates each element in the domain with a unique element in the range. A function is often denoted by a symbol such as f, and is defined by a rule that assigns to each element x in the domain a corresponding value f(x) in the range. Functions can have many different forms and types, depending on the nature of the rule that defines them. Some common types of functions include linear functions, quadratic functions, exponential functions, trigonometric functions, and many others.
Here,
A square root function is a function of the form f(x) = √(x), where the square root of x is taken. To reflect the function over the x-axis, we multiply the function by -1, which changes the sign of the function values.
So, the reflected square root function is g(x) = -√(x). To move the function up by 9 units, we add 9 to the function, which shifts the function vertically upwards.
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Use the properties of sigma notation and the summation formulas to evaluate the given sum: 15 [ili2 – 21 +1) – 4] i=1
The sum is equal to 18600.
How to find summation?
Let's first simplify the expression inside the brackets:
(i^2 - 21 + 1) - 4 = i^2 - 24
Now we can write the sum using sigma notation:
15 Σ (i^2 - 24), i=1
Using the summation formulas of the first n squares, we have:
Σ i^2 = n(n+1)(2n+1)/6
So, substituting n = 1 to 15, we get:
15 Σ i^2 = 15 Σ n(n+1)(2n+1)/6
Now, let's use the formula for the sum of the first n integers:
Σ i = n(n+1)/2
Substituting n = 1 to 15, we get:
Σ i = 1 + 2 + ... + 15 = 15(15+1)/2 = 120
Substituting these formulas into our original expression, we have:
15 Σ (i^2 - 24), i=1
= 15 [Σ i^2 - 24Σ i], i=1
= 15 [15(15+1)(2(15)+1)/6 - 24(120)]
= 15 [1240]
= 18600
Therefore, the sum of 15 (i^2 - 24) from i = 1 to 15 is equal to 18600.
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A baseball pitcher records 153 strikeouts in
his first year pitching. Since then, the
number of strikeouts for this pitcher has
decreased by 31% per year. If this trend
continues, what is an upper limit on the total
of strikeouts over the pitcher's lifetime?
If a baseball pitcher records 153 strikeouts in his first year pitching with the number of strikeouts decreasing by 31% yearly, and if the trend continues, the upper limit on the total of strikeouts over the pitcher's lifetime is 153.
What is the upper limit?The upper limit refers to the maximum value possible.
The initial number of recorded strikeouts = 153
The annual decay rate = 31%
Decay factor = 0.69 (1 - 0.31)
Let the number of strikeouts in the year = y
Let the number of years of pitching = x
Equation:y = 153(0.69)^x
For instance, if x = 3, y = 153(0.69)^3
y = 50
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Which expression is equivalent to 16 + 2 x 36?
Answer choices:
The correct expression equivalent to 16 + 2 x 36 is 88.
To simplify the expression, we need to follow the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). In this case, we have multiplication and addition.
Using the order of operations, we first need to perform the multiplication:
2 x 36 = 72
Then, we add 16 to the product:
16 + 72 = 88
Therefore, 16 + 2 x 36 is equivalent to 88.
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Stephanie took her family out to Texas Roadhouse and is getting ready to pay the dinner bill. The bill is $57. 50. If she plans on leaving an 18% tip, what is the total dinner cost?
To calculate the total dinner cost, we need to add the bill amount to the tip amount.
The tip amount is 18% of the bill amount:
Tip = 0.18 x $57.50 = $10.35
Therefore, the total dinner cost is:
Total Cost = Bill Amount + Tip Amount
Total Cost = $57.50 + $10.35
Total Cost = $67.85
So, the total dinner cost including the 18% tip is $67.85.
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Determine the intervals on which the function is concave up or down and find the points of inflection f(x) = 2x^3 - 11x^2 + 7. (Give your answer as a comma-separated list of points in the form (* . *). Express numbers in exact form. Use symbolic notation and fractions where needed.)
points of inflection: ______.
Points of inflection: (11/6, -10.37).
To determine the intervals of concavity and find the points of inflection, we first need to find the second derivative of the function f(x) = 2x^3 - 11x^2 + 7.
1. First derivative:
f'(x) = 6x^2 - 22x
2. Second derivative:
f''(x) = 12x - 22
Now, we need to find the critical points by setting the second derivative equal to zero:
12x - 22 = 0
x = 11/6
The point of inflection occurs at x = 11/6. Now, let's find the intervals of concavity:
1. f''(x) > 0 (concave up):
12x - 22 > 0
x > 11/6
2. f''(x) < 0 (concave down):
12x - 22 < 0
x < 11/6
Finally, we need to find the y-coordinate for the point of inflection:
f(11/6) = 2(11/6)^3 - 11(11/6)^2 + 7 ≈ -10.37
So, the point of inflection is (11/6, -10.37).
Points of inflection: (11/6, -10.37).
Your answer: The function is concave up on the interval (11/6, ∞) and concave down on the interval (-∞, 11/6). The point of inflection is (11/6, -10.37).
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√4x^2 BRAINLIEST IF CORRECT!!!!!!!!!
Answer:
Step-by-step explanation:
√4x^2=2x
Suppose that 6 thank-you notes are written and 6 envelopes are addressed. Accidentally, the notes are randomly inserted into the envelopes and mailed without checking the addresses. What is the probability that all the notes will be inserted into the correct envelopes? The probability is (Type an integer or decimal rounded to six decimal places as needed.) A county park system rates its 20 golf courses in increasing order of difficulty as bronze, silver, or gold. There are only two gold courses and twice as many bronze as silver courses. Complete parts (A) and (B) below. (A) If a golfer decides to play a round at a silver or gold course, how many selections are possible? There is/are possible selection(s). (Type a whole number.) (B) If a golfer decides to play one round per week for 3 weeks, first on a bronze course, then silver, then gold, how many combined selections are possible? There is/are possible selection(s). (Type a whole number.)
For the first question:
There are 6 notes and 6 envelopes, so there are 6! (or 720) possible ways to insert the notes into the envelopes. Only one of these ways will result in all notes being inserted into the correct envelopes. Therefore, the probability is 1/720 or 0.001389.
For the second question:
(A) There are 2 gold courses and twice as many bronzes as silver courses, so there are 2 + 2x + x = 20 courses in total, where x is the number of silver courses. Solving for x, we get x = 6. Therefore, there are 2 + 6 + 12 = 20 possible courses to select from if the golfer decides to play a round at a silver or gold course.
(B) If the golfer decides to play one round per week for 3 weeks, there are 12 possible combinations of courses to play. To see why, consider the following cases:
Week 1: bronze, Week 2: silver, Week 3: gold
Week 1: bronze, Week 2: gold, Week 3: Silver
Week 1: silver, Week 2: bronze, Week 3: gold
Week 1: silver, Week 2: gold, Week 3: bronze
Week 1: gold, Week 2: bronze, Week 3: Silver
Week 1: gold, Week 2: silver, Week 3: bronze
Each case has 2 possible choices for the bronze course, 6 possible choices for the silver course, and 2 possible choices for the gold course, for a total of 2 x 6 x 2 = 24 possible combinations. However, since the order of the courses doesn't matter, we must divide by 3! (or 6) to get rid of the extra permutations. Therefore, there are 24/6 = 4 possible combinations for each case, giving a total of 6 x 4 = 24 possible combinations of courses to play.
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a) Calculate the scale factor from shape A to shape B.
b) Find the value of t.
Give each answer as an integer or as a fraction in its simplest form.
A
5 cm
15 cm
7cm
B
12 cm
4cm
t cm
a). The scale factor of shape A to B is 4/5
b) The value of t is 5.6cm
What is scale factor?The scale factor is a measure for similar figures, who look the same but have different scales or measures.
Scale factor = dimension of new length/ dimension of old length
= 4/5 = 12/15
therefore the scale factor of from shape A to shape B is 4/5.
b) 4/5 = t/7
5t = 28
divide both sides by 5
t = 28/5
t = 5.6 cm
therefore the value of t is 5.6cm
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Solve the given differential equation 3 4ydx - 4xdy + x³dx = 7dx The solution is= (Type an equation.)
The solution of the given differential equation is y = x + Cx⁴ - x²/4, where C is a constant.
We begin by rearranging the terms as follows:
(4y + x³ - 7)dx = (4x)dy
Integrating both sides, we get:
4xy + (1/4)x⁴ - 7x = 2y² + C
where C is the constant of integration.
Next, we can rearrange this equation to solve for y:
y² = 2xy + (1/8)x⁴ - (7/2)x - C/2
y² - 2xy = (1/8)x⁴ - (7/2)x - C/2
We can complete the square to obtain a more useful expression:
(y - x)² = (1/8)x⁴ - (7/2)x - C/2 + x²
y - x = ±sqrt((1/8)x⁴ - (7/2)x - C/2 + x²)
Simplifying this expression, we get:
y = x ±sqrt(Cx⁴ - (1/4)x⁴ + 7x - C)
Taking the positive sign for simplicity, we get the final solution as:
y = x + sqrt(Cx⁴ - (1/4)x⁴ + 7x - C)
where C is the constant of integration.
We can also simplify this solution further by using the identity (a + b)² = a² + 2ab + b² to get:
y = x + Cx⁴ - x²/4
where C is a constant, as desired.
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A net of a rectangular prism is shown. A net of a rectangular prism with dimensions 4 and one-half centimeters by 3 centimeters by 8 and one-half centimeters. What is the surface area of the prism?
77.25 cm2
154.5 cm2
225 cm2
309 cm2
If net of a rectangular prism with dimensions 4 and one-half centimeters by 3 centimeters by 8 and one-half centimeters, the surface area of the rectangular prism is 154.5 cm². So, correct option is B.
A rectangular prism has six faces, and the surface area is the sum of the area of each face. To find the surface area of the prism given in the net, we need to calculate the area of each face and then add them together.
The rectangular prism has three pairs of identical faces, each of which has an area of length x width. Therefore, we can calculate the surface area of each pair of identical faces by multiplying the length and width dimensions of the prism.
The first pair of identical faces has dimensions 4.5 cm x 3 cm.
The area of one face = (4.5 cm) x (3 cm) = 13.5 cm².
So, the area of both faces = 2 x 13.5 cm² = 27 cm².
The second pair of identical faces has dimensions 4.5 cm x 8.5 cm.
The area of one face = (4.5 cm) x (8.5 cm) = 38.25 cm².
So, the area of both faces = 2 x 38.25 cm² = 76.5 cm².
The third pair of identical faces has dimensions 3 cm x 8.5 cm.
The area of one face = (3 cm) x (8.5 cm) = 25.5 cm².
So, the area of both faces = 2 x 25.5 cm² = 51 cm².
To find the total surface area, we add up the areas of all the faces:
Surface area = 27 cm² + 76.5 cm² + 51 cm² = 154.5 cm².
So, correct option is B
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The bubba corp had earnings before taxes of 206,000 and sales of 2,060,000. If it is in the 53 tax bracket
The Bubba Corp would owe $109,180 in taxes based on its earnings before taxes of $206,000 and sales of $2,060,000.
How much tax does Bubba Corp owe?To determine the taxes owed by the Bubba Corp, we first need to calculate its taxable income. Taxable income is equal to earnings before taxes minus deductions and exemptions. Assuming no deductions or exemptions, the taxable income for the Bubba Corp would be:
Taxable income = Earnings before taxes = $206,000
Next, we need to calculate the amount of taxes owed. The Bubba Corp is in the 53% tax bracket, which means that it owes 53 cents on every dollar of taxable income. Therefore, the amount of taxes owed would be:
Taxes owed = Taxable income x Tax rate
= $206,000 x 0.53
= $109,180
In summary, the Bubba Corp would owe $109,180 in taxes based on its earnings before taxes of $206,000 and sales of $2,060,000, assuming no deductions or exemptions.
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What is the scale factor for the similar figures below?
The value of the scale factor for the similar figures is 1/3
What is the scale factor for the similar figures?From the question, we have the following parameters that can be used in our computation:
The similar figures
The corresponsing sides of the similar figures are
Original = 12
New = 4
Using the above as a guide, we have the following:
Scale factor = New /Original
substitute the known values in the above equation, so, we have the following representation
Scale factor = 4/12
Evaluate
Scale factor = 1/3
Hence, the scale factor for the similar figures is 1/3
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What is the area of the figure?
Answer: 27 inches sq.
Step-by-step explanation:
3*3=9
2*9=18
18+9=27
Determine the equation of the circle with center (-3, -8) containing the point (-11, -23).
The equation of the circle with center (-3, -8) containing the point (-11, -23) is x²+y²+6x+16y=216.
The general form of the equation of the circle is (x-h) ²+(y-k) ²=r².
Here, (h, k) indicates the circle's center, and r indicates the circle's radius.
In the given question, (-3, -8) is the center of the circle.
Here, h = -3, k = -8.
Now, we need to find the radius of the circle.
Radius is the distance between the center of the circle and the given point (-11, -23).
Distance formula = √(x2-x1) ²+(y2-y1) ²
√ (-11-(-3)) ² + (-23-(-8)) ²
√ (-11+3) ² + (-23+8) ²
√64+225
√289
17.
So, the radius of the circle is 17.
Now, we can find the equation of the circle by substituting in the formula.
(x-h) ² + (y-k) ² = r²
(x-(-3)) ² + (y - (-8)) ² = 17²
(x+3) ² + (y+8) ² = 289.
x²+6x+9+y²+16y+64=289
x²+y²+6x+16y=216.
Therefore, the equation of the circle is x²+y²+6x+16y=216.
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In a class of students, the following data table summarizes how many students have a brother or a sister. What is the probability that a student chosen randomly from the class has a brother?
Has a brother Does not have a brother
Has a sister 4 2
Does not have a sister 12 10
The probability that a student chosen randomly from the class has a brother is approximately 0.143 or 14.3%.
What is the probability that a student chosen randomly from the class has a brother?To find the probability that a student chosen randomly from the class has a brother, we need to look at the number of students who have a brother and divide it by the total number of students in the class.
From the given data table, we see that there are a total of 4+2+12+10=28 students in the class. Out of these, 4 students have a brother. Therefore, the probability that a student chosen randomly from the class has a brother is:
P(having a brother) = Number of students having a brother / Total number of students
= 4 / 28
= 1/7
≈ 0.143
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Drag each tile to the correct box. arrange the samples in order starting with the sample that gives the least variation from the expected value and ending with the sample that gives the greatest variation. tiles sample a: a sample of 10 peoplesample b: a sample of 50 peoplesample c: a sample of 100 peoplesample d: a sample of 20 people sequence , , ,
The correct sequence for the samples in order of least variation to greatest variation is:
Sample A: A sample of 10 people
Sample D: A sample of 20 people
Sample B: A sample of 50 people
Sample C: A sample of 100 people
The reason for this sequence is that larger sample sizes tend to provide more accurate estimates of the population parameters, while smaller sample sizes are more prone to random fluctuations and sampling error.
Therefore, sample A (with the smallest sample size of 10) is likely to have the greatest variation from the expected value, while sample C (with the largest sample size of 100) is likely to have the least variation from the expected value.
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An engineer is using computer-aided design (CAD) software to design a component for a space shuttle. The scale of the drawing is 1 cm: 60 in. The actual length of the component is 12. 75 feet. What is the length of the component in the drawing?
The length of the component in the drawing is 2.125 centimeters.
How to find the length of the component represented in a CAD?To find the length of the component in the drawing, we convert the given length from feet to inches. Since 1 foot is equal to 12 inches, the actual length of 12.75 feet is equivalent to 12.75 x 12 = 153 inches.
Next, we apply the scale of the drawing, which is 1 cm: 60 in. This means that for every 60 inches in reality, the drawing represents it as 1 centimeter. To find the length in centimeters, we set up a proportion:
1 cm / 60 in = x cm / 153 in
Cross-multiplying and solving for x, we get:
x = (1 cm * 153 in) / 60 in = 2.55 cm
Rounding to three decimal places, the length of the component in the drawing is approximately 2.125 centimeters.
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I’m confused as to what the solution is if I follow the first step
Answer:
x = 4, y = 1, z = 5
Step-by-step explanation:
z + x =9....(3) we can say it's x + z = 9
x - z = - 1
x + z = 9
______ -
- 2z= - 10
z = 10/2
z = 5
if z + x = 9
5 + x = 9
x = 9 - 5
x = 4
if x + y = 5
4 + y = 5
y = 5 - 4
y = 1
#CMIIWA tabletop in the shape of a trapezoid has an area of 7,701 square centimeters. its longer base measures 119 centimeters, and the shorter base is 85 centimeters. what is the height?
please just give me the answer, don't send me a link i have to open
The height of the given trapezoid-shaped tabletop is 75.5 centimeters.
The height of the trapezoid-shaped tabletop. To calculate the height, we can use the formula for the area of a trapezoid: A = (1/2)(b1 + b2)h, where A is the area, b1 and b2 are the lengths of the bases, and h is the height.
Given the area (A) is 7,701 square centimeters, the longer base (b1) measures 119 centimeters, and the shorter base (b2) is 85 centimeters, we can solve for the height (h) using the following steps:
1. Plug in the given values into the formula: 7,701 = (1/2)(119 + 85)h
2. Simplify the expression inside the parentheses: 7,701 = (1/2)(204)h
3. Multiply the two numbers inside the parentheses: 7,701 = 102h
4. Divide both sides of the equation by 102 to solve for h: h = 7,701 / 102
5. Calculate the value of h: h ≈ 75.5 centimeters
So, the height of the trapezoid-shaped tabletop is approximately 75.5 centimeters.
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3.
What does limit as x goes to infinity of the quotient of f of x and g of x equals 5 show? (4 points)
g(x) grows faster than f(x) as x goes to infinity.
f(x) and g(x) grow at the same rate as x goes to infinity.
f(x) grows faster than g(x) as x goes to infinity.
L'Hôpital's Rule must be used to determine the true limit value
The statement "limit as x goes to infinity of the quotient of f of x and g of x equals 5" means that as x gets larger and larger, the ratio of f(x) to g(x) approaches 5.
If f(x) grows faster than g(x) as x goes to infinity, then the ratio of f(x) to g(x) would approach infinity, not 5.
If f(x) and g(x) grow at the same rate as x goes to infinity, then the ratio of f(x) to g(x) would approach a constant value, not necessarily 5.
Therefore, the statement "limit as x goes to infinity of the quotient of f of x and g of x equals 5" shows that g(x) grows faster than f(x) as x goes to infinity. L'Hôpital's Rule is not necessary to determine this conclusion.
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A bridge is to be built across a small lake from a gazebo to a dock. The bearing from the gazebo to the dock is S 41° W. From a tree 100 meters from the gazebo, the bearings to the gazebo and the dock are S 74° E and S 28° E, respectively (see figure). Find the distance from the gazebo to the dock
The distance from the gazebo to the dock is approximately 120.45 meters.
The given problem can be solved using the concept of trigonometry.
let the distance from the gazebo to the dock be "d".
According to the question it is known that the bearing from the gazebo to the dock is S 41° W which means that the angle between the line from the gazebo to the dock and due south is 41°.
Hence the angle between the line from the gazebo to the tree and due south is =(74°-41°) =33°
Similarly, the angle between the line from the dock to the tree and due south is = 28°-x =28°-41°= -13°(As it is to the west of south).
Using the trigonometry law of sines we can write,
d/ sin(41°) = 100/ sin(33°)
d=(100/sin(33°))*sin(41°)
d= 120.45 meters
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Which of the following tables represent a proportional relationship
a. y/x= 40/1 76/2 112/3 148/4
Table c represents a proportional relationship because the ratio of y to x is constant at 18.
Which table represent a proportional relationship?A proportional relationship is a relationship between two quantities where their ratios always remain the same.
In option (a), the ratio of y to x is not constant. For example, y/x = 40/1 = 40, but y/x = 148/4 = 37. Therefore, this table does not represent a proportional relationship.
In option (b), the ratio of y to x is not constant either. For example, y/x = 48/2 = 24, but y/x = 192/5 = 38.4. Therefore, this table does not represent a proportional relationship.
In option (c), the ratio of y to x is constant. For example, y/x = 18/1 = 18, but y/x = 126/7 = 18. Therefore, this table represent a proportional relationship.
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Complete questionWhich of the following tables represent a proportional relationship?
a. y/x= 40/1 76/2 112/3 148/4
b. y/x= 48/2 96/3 144/4 192/5
c. y/x= 18/1 54/3 90/5 126/7
d. 24/1 21/2 18/3 15/4
On January 2, 2021, Twilight Hospital purchased a $100,000 special radiology scanner from Bella Inc. The scanner had a useful life of 4 years and was estimated to have no disposal value at the end of its useful life. The straight-line method of depreciation is used on this scanner. Annual operating costs with this scanner are $105,000. Use incremental analysis for retaining or replacing equipment decision. Approximately one year later, the hospital is approached by Dyno Technology salesperson, Jacob Cullen, who indicated that purchasing the scanner in 2021 from Bella Inc. Was a mistake. He points out that Dyno has a scanner that will save Twilight Hospital $25,000 a year in operating expenses over its 3-year useful life. Jacob notes that the new scanner will cost $110,000 and has the same capabilities as the scanner purchased last year. The hospital agrees that both scanners are of equal quality. The new scanner will have no disposal value. Jacob agrees to buy the old scanner from Twilight Hospital for $50,000. Instructions a. If Twilight Hospital sells its old scanner on January 2, 2022, compute the gain or loss on the sale. B. Using incremental analysis, determine if Twilight Hospital should purchase the new scanner on January 2, 2022. C. Explain why Twilight Hospital might be reluctant to purchase the new scanner, regardless of the results indicated by the incremental analysis in (b)
a. The hospital will incur a loss of $25,000 on the sale of the old scanner.
b. he total cost of operating the new scanner is $35,000 more than the total cost of operating the old scanner.
c. Twilight Hospital might be reluctant to purchase the new scanner because of the initial cost of $110,000, which is $10,000 more than the cost of the old scanner.
a. To compute the gain or loss on the sale, we need to calculate the book value of the old scanner on January 2, 2022, which is the cost of the scanner minus accumulated depreciation. The cost of the scanner is $100,000, and the accumulated depreciation after one year is ($100,000 ÷ 4) = $25,000. Therefore, the book value is $75,000. Since the sales price is $50,000, the hospital will incur a loss of $25,000 on the sale of the old scanner.
b. To determine if the hospital should purchase the new scanner, we need to compare the total cost of operating the old scanner for the remaining 3 years of its useful life with the total cost of operating the new scanner for its entire 3-year useful life. The total cost of operating the old scanner for 3 years is:
$105,000 × 3 = $315,000
The total cost of operating the new scanner for 3 years is:
($110,000 − $50,000) + ($80,000 × 3) = $350,000
Therefore, the total cost of operating the new scanner is $35,000 more than the total cost of operating the old scanner. Since the new scanner does not provide any additional benefits, it is not economically feasible to purchase the new scanner.
c. Twilight Hospital might be reluctant to purchase the new scanner because of the initial cost of $110,000, which is $10,000 more than the cost of the old scanner. Additionally, the hospital may not have the funds available to purchase the new scanner, or it may be concerned about the reliability and performance of the new scanner. Finally, the hospital may have to deal with the hassle of disposing of the old scanner and purchasing a new one.
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The function f(x) = 454 + 0.9x gives the cost, in dollars, of manufacturing x vinyl records. select all the true statements. the initial cost for manufacturing records depends on the quantity ordered. the initial cost for the manufacturing is $454, regardless of the number of records ordered. in addition to the initial cost, each record costs $0.90 to manufacture. in addition to the initial cost, each record costs $454 to manufacture. each record costs a total of $454.90 to manufacture.
The true statements are:
The initial cost for manufacturing records is $454, regardless of the number of records ordered.
In addition to the initial cost, each record costs $0.90 to manufacture.
Each record costs a total of $454.90 to manufacture.
As according to the question the function f(x)= 454+0.9x gives the cost, in dollars, of manufacturing x vinyl records.
Hence the incorrect statements are:
"The initial cost for manufacturing records depend on the quantity ordered".
"in addition to the initial cost, each record costs $454 to manufacture".
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Q2) For the following exercises, write the first five terms of the indicated
sequence:
The first five terms of the sequence are: 3/5, 3/4, 9/7, 3/2, 15/9.
To find the first five terms of the sequence aₙ = 3n/(n+4)
we need to substitute the values of n from 1 to 5 and solve for .
a₁ = 3×1/(1+4) = 3/5
a₂ = 3×2/(2+4) = 3/4
a₃ = 3×3/(3+4) = 9/7
a₄ = 3×4/(4+4) = 12/8 = 3/2
a₅ = 3×5/(5+4) = 15/9
Hence, the first five terms of the sequence are: 3/5, 3/4, 9/7, 3/2, 15/9.
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My bestfriend has parents that are 11 years apart. She's 12. How old are her parents?
The younger parent is at least 1 year old, and the older parent is 23 years old.
If your best friend's parents have an age gap of 11 years, then we can assume that one of them is 11 years older than the other. Let's call the younger parent "X" years old. Then the older parent must be X + 11 years old. Since your best friend is 12 years old, we know that both of her parents are older than 12. Therefore, we can set up an equation:
X + (X + 11) > 12
Simplifying this, we get:
2X + 11 > 12
2X > 1
X > 0.5
Since X must be a whole number (you can't have half a year of age), we know that X must be at least 1. Therefore, the younger parent is at least 1 year old. Using our equation, we can find the age of the older parent:
X + 11 = 12 + 11 = 23
Therefore, the younger parent is at least 1 year old, and the older parent is 23 years old.
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The original price of an item is $25, but after the discount, you only have to pay $18.50. What is the discount (as a percent)
The discount is 26%.
What is Discount?The discount equals the difference between the price paid for and it's par value. Discount is a kind of reduction or deduction in the cost price of a product.
Given:
[tex]\bold{Marked} \ \text{price} = \$25[/tex]
[tex]\bold{Selling} \ \text{price} = \$18.50[/tex]
So,
[tex]\text{Discount = MP - SP}[/tex]
[tex]\text{Discount} = 25-18.50[/tex]
[tex]\bold{Discount} = 6.50[/tex]
Now,
[tex]\text{D}\% = \dfrac{\text{D}}{\text{MP}} \times100[/tex]
[tex]\text{D}\% = \dfrac{6.5}{25} \times100[/tex]
[tex]\text{D}\% = 26\%[/tex]
Hence, the discount percent is 26%.
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Your local high school is putting on a musical. They have sold 1000 tickets. Adult tickets
were sold for $8. 50, while child tickets were sold for $4. 50. A total of $7100 was
collected from ticket sells. How many tickets of each kind were sold?
650 adult tickets and 350 child tickets were sold for the local high school musical.
To determine how many adult and child tickets were sold for the local high school musical, you can use a system of linear equations. Let's use the terms "x" for adult tickets and "y" for child tickets.
1. The total number of tickets sold is 1000, so we have:
x + y = 1000
2. The total amount collected from ticket sales is $7100, so we have:
8.50x + 4.50y = 7100
Now, let's solve this system of equations step-by-step:
Step 1: Solve the first equation for x:
x = 1000 - y
Step 2: Substitute the expression for x from Step 1 into the second equation:
8.50(1000 - y) + 4.50y = 7100
Step 3: Simplify the equation:
8500 - 8.50y + 4.50y = 7100
Step 4: Combine like terms:
-4.00y = -1400
Step 5: Divide both sides by -4.00:
y = 350
Step 6: Substitute the value of y back into the expression for x from Step 1:
x = 1000 - 350
Step 7: Calculate the value of x:
x = 650
So, 650 adult tickets and 350 child tickets were sold for the local high school musical.
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Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
The proper options provided for the required equation of a circle is
x2 + (y – 3)2 = 36x2 + (y + 8)2 = 36How to find the equation of the circleAt the center of the circle there rests a y-axis, so its x-coordinate is equal to 0.
The formula for a specified circle with coordinates (0, k) and radius r is
(x - 0)² + (y - k)² = r²
Therefore, the equation ends up categorically signified by:
x2 + (y – 3)2 = 36
x2 + (y + 8)2 = 36
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