The ratios are 1. Current ratio = 2.90, 2. Acid-test ratio = 2.22, 3. Inventory turnover ratio = 3.57, 4. Debt to equity ratio = 0.77, 5. Return on equity ratio = 15%.
The ratios to be computed are:
1. Current ratio
2. Acid-test (quick) ratio
3. Inventory turnover ratio
4. Debt to equity ratio
5. Return on equity ratio
1. Current ratio = Current assets / Current liabilities
Current assets = Cash + Accounts receivable + Inventory = $17,205 + $80,290 + $68,820 = $166,315
Current liabilities = Accounts payable = $57,350
Current ratio = $166,315 / $57,350 = 2.90
2. Acid-test (quick) ratio = (Cash + Accounts receivable) / Current liabilities
Acid-test ratio = ($17,205 + $80,290) / $57,350 = 2.22
3. Inventory turnover ratio = Cost of goods sold / Average inventory
Average inventory = (Beginning inventory + Ending inventory) / 2
Beginning inventory = $57,350
Ending inventory = $68,820
Average inventory = ($57,350 + $68,820) / 2 = $63,085
Inventory turnover ratio = $225,600 / $63,085 = 3.57
4. Debt to equity ratio = Total liabilities / Total equity
Total liabilities = Accounts payable + Mortgage payable = $57,350 + $114,700 = $172,050
Total equity = Common stock + Retained earnings = $160,580 + $63,085 = $223,665
Debt to equity ratio = $172,050 / $223,665 = 0.77
5. Return on equity ratio = Net income / Average equity
Average equity = (Beginning equity + Ending equity) / 2
Beginning equity = Common stock + Retained earnings = $137,640 + $45,880 = $183,520
Ending equity = Common stock + Retained earnings + Net income - Dividends = $160,580 + $63,085 + $31,100 - $21,700 = $232,065
Average equity = ($183,520 + $232,065) / 2 = $207,793
Return on equity ratio = $31,100 / $207,793 = 0.15 or 15%
Therefore, the ratios are:
1. Current ratio = 2.90
2. Acid-test ratio = 2.22
3. Inventory turnover ratio = 3.57
4. Debt to equity ratio = 0.77
5. Return on equity ratio = 15%
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David is setting up camp with his friend Xavier. David and Xavier want to place their tents equal distance to the ranch where the mess hall is. A model is shown, where points D and X represent the location
tents and point R represents the ranch. DR = (12.3z + 12.4) meters (m) and XR= (10.5z+34) m.
D
X
R
What is the distance Xavier and David are from the ranch?
The distance from Xavier and David to the ranch can be found using the distance formula:
distance = sqrt((change in x)^2 + (change in y)^2 + (change in z)^2)
In this case, we are given the distances DR and XR, which represent the change in x, y, and z coordinates between the tents and the ranch. We know that the tents are located at equal distances from the ranch, so the change in x, y, and z coordinates for both David and Xavier will be the same.
Let's call the distance from each tent to the ranch "d", then we have:
DR = XR = d
Substituting the given values, we get:
12.3z + 12.4 = 10.5z + 34
Solving for z, we get:
z = 6.8
Now we can find the distance from each tent to the ranch using the formula:
distance = sqrt((change in x)^2 + (change in y)^2 + (change in z)^2)
For David's tent:
distance = sqrt((12.3z)^2 + 0^2 + (12.4)^2) = sqrt((12.3*6.8)^2 + (12.4)^2) = 87.9 meters (rounded to one decimal place)
For Xavier's tent:
distance = sqrt((10.5z)^2 + 0^2 + (34)^2) = sqrt((10.5*6.8)^2 + (34)^2) = 95.6 meters (rounded to one decimal place)
Therefore, David and Xavier are 87.9 meters and 95.6 meters away from the ranch, respectively.
A tree’s cross sectional area is called its basal area and is measured in square inches. Tree growth can be measured by the growth of the tree’s basal area. The initial base area of tree observed by a biologist is 154 square inches and annual growth rate is 6%. What will be the basal area after 10 years of growth?
The basal area of the tree after 10 years of growth would be approximately 279.7 square inches.
Given the initial basal area of a tree, which is 154 square inches, and the annual growth rate, which is 6%. To find out what the basal area of the tree will be after 10 years of growth.
By using the formula for compound interest, which can be applied to the growth of the basal area over time. The formula is:
A = P(1 + r)ⁿ
where:
A is the final amount
P is the initial amount
r is the annual growth rate
n is the number of years
To find A, the final basal area of the tree after 10 years of growth. We know that P is 154 square inches, r is 6% or 0.06 and n is 10.
By applying these values in the formula, we get:
A = 154(1 + 0.06)¹⁰
A = 154(1.06)¹⁰
A = ≈ 279.7
Therefore, the basal area of the tree after 10 years of growth would be approximately 279.7 square inches.
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√x+3
a.3x^1/2
b.(x+3)^1/2
c.x^1/2+3
d.(3x)^1/2
Answer:
b
Step-by-step explanation:
The expression √x+3 means the square root of x+3. We can rewrite this as (x+3)^(1/2), using the exponent rule that says taking the square root is the same as raising to the power of 1/2.
So the options become:
a. 3x^(1/2)
b. (x+3)^(1/2)
c. x^(1/2) + 3
d. (3x)^(1/2)
None of the other options match the given expression. So the correct answer is (b) (x+3)^(1/2).
What is the image of the point (-3,8) after a rotation of 180 counterclockwise about the origin
The image of point (-3, 8) after a rotation of 180 counterclockwise about the origin is (3, -8)
What is transformation?Transformation is the movement of a point in the coordinate plane from one location to another. Transformation can either be reflection, rotation, translation and dilation.
Rotation is the flipping of a figure about a point in the coordinate plane; this point of rotation is usually origin.
(x, y) → (-x, -y) represents a rotation 180° counterclockwise.
The image of point (-3, 8) after a rotation of 180 counterclockwise about the origin is (3, -8)
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what is the measure of the unknown segment? pls help i keep getting bots :(
To determine the measure of the unknown segment, it's essential to first gather information about the given problem, such as the context, any provided measurements, and any relationships between the segments or angles involved. Once you have this information, you can utilize relevant geometric principles and theorems to establish connections and solve for the unknown value.
For example, if the unknown segment is a side in a triangle, you may apply the Pythagorean theorem, triangle inequality theorem, or trigonometric functions such as sine, cosine, or tangent to calculate its length. If the unknown segment is part of a circle, you might use the properties of arcs, chords, or the circumference to determine its measure. In cases where the unknown segment is part of a polygon, you can consider properties like diagonals, perimeter, or area to derive its length.
After identifying the appropriate method and relationships, you can set up equations and solve for the unknown variable. To verify the solution, you can plug it back into the original problem to ensure it satisfies all given conditions. In conclusion, finding the measure of an unknown segment involves understanding the problem's context, applying relevant geometric concepts, and using mathematical techniques to solve for the desired value.
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Question 4 of 15
Cryshel is mailing pillows with a total volume of 9. 5 ft3. She needs a mailing
box that has a volume greater than 9. 5 ft.
• Box A: length = 3 ft, width = 2 ft, height = 1. 5 ft
• Box B: length = 2. 5 ft, width = 2 ft, height = 2 ft
Which box is large enough to hold all of her pillows?
O
A. Neither box
B. Both box A and box B
ОО
C. Box B
D. Box A
Answer:
C. Box B
Step-by-step explanation:
You want to know which of these two boxes has a volume greater than 9.5 ft³:
Box A: 3 ft by 2 ft by 1.5 ftBox B: 2.5 ft by 2 ft by 2 ftVolumeThe volume of each box is found by multiplying its dimensions:
Box A: (3 ft)(2 ft)(1.5 ft) = 9 ft³
Box B: (2.5 ft)(2 ft)(2 ft) = 10 ft³
Only box B is large enough, choice C.
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Your family decides they have $400 per month to spend towards remodeling their house. the bank offers them a ten year(120 months) home equity loan for $30,000 with an interest rate of 6.5%. use p = p v ( i 1 − ( 1 + i ) − n ) to determine if your family can afford the monthly payment.
The monthly payment for the loan is $328.05. So we can determine that the family can afford the monthly payment.
Money spend = $400
Time = 120 months
Loan amount = $30,000
Interest rate = 6.5%.
The formula is given P = [tex]PV*(i / (1 - (1+i)^{-n}))[/tex]
The interest should be calculated at the monthly rate. So, we can divide the interest rate by 12.
i = 0.065/12 = 0.00541667
Substituting the values into the formula,
P = [tex]30000 * 0.00541667 / (1 - (1+0.00541667)^{-120})[/tex]
P = $328.05
Therefore, we can conclude that the monthly payment for the loan is $328.05.
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The number of males of a species of whale in Antarctic feeding grounds is w(x) when x million squid are present. Squid availability in the feeding grounds changes according to the surface temperature of the water so that the number of available squid is x(t) when the water is t°F. In December, when water temperature is near 32°F, there are an estimated 710 million deep-water squid in the feeding grounds, with the number of squid increasing by approximately 3 million squid per degree. At the same time, there are 6,000 adult male whales in the Antarctic feeding grounds, with the number of male whales increasing by 4 whales per million squid. Evaluate each of the following expressions when the surface temperature of the ocean is 32°F, and write a sentence interpreting each value. (a) Evaluate x(t). x(32) = million squid Write a sentence interpreting the value. When water temperature is near 32°F, the squid population is million squid. (b) Evaluate w(x). w(710) = whales Write a sentence interpreting the value. When there are 710 million squid there are adult male whales in the Antarctic feeding grounds. (C) Evaluate x million squid per degree Write a sentence interpreting the value. When water temperature is near 32°F, the squid population is increasing by million squid per degree. (d) Evaluate dw dw whales per million squid dx x = 710 Write a sentence interpreting the value.
The number of adult male whales in Antarctic feeding grounds, w(x), depends on the number of million squid available, x(t). At a surface temperature of 32°F, x(32) = 710 million squid, and w(710) = 6000 whales. The population of squid is increasing by 3 million per degree, and the population of whales is increasing by 4 whales per million squid.
The following expressions when the surface temperature of the ocean is 32°F is
(a) To evaluate x(t) when t=32°F, we use the given information that "there are an estimated 710 million deep-water squid in the feeding grounds, with the number of squid increasing by approximately 3 million squid per degree." Thus, at 32°F, we have:
x(32) = 710 + 3(32-32) = 710 million squid
Interpretation: When the water temperature is near 32°F, there are approximately 710 million deep-water squid in the feeding grounds.
(b) To evaluate w(x) when x=710 million squid, we use the given information that "there are 6,000 adult male whales in the Antarctic feeding grounds, with the number of male whales increasing by 4 whales per million squid." Thus, at 710 million squid, we have:
w(710) = 6,000 + 4(710-710) = 6,000 adult male whales
Interpretation: When there are approximately 710 million deep-water squid in the feeding grounds, there are approximately 6,000 adult male whales in the Antarctic feeding grounds.
(c) To evaluate dx/dt when t=32°F, we use the given information that "the number of available squid is x(t) when the water is t°F, with the number of squid increasing by approximately 3 million squid per degree." Thus, at 32°F, we have:
dx/dt = 3 million squid per degree
Interpretation: When the water temperature is near 32°F, the population of deep-water squid in the feeding grounds is increasing by approximately 3 million squid per degree.
(d) To evaluate dw/dx when x=710 million squid, we use the given information that "the number of male whales increases by 4 whales per million squid." Thus, at 710 million squid, we have:
dw/dx = 4 whales per million squid
Interpretation: For every additional 1 million deep-water squid that are present in the feeding grounds, the number of adult male whales in the Antarctic feeding grounds increases by approximately 4 whales.
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Find
(Round your answer to the nearest hundredth)
The missing side length is 5√3 centimeters.
We can use the Pythagorean theorem to find the missing side length. The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. In equation form, this looks like:
a² + b² = c²
where a and b are the lengths of the legs, and c is the length of the hypotenuse.
To use this formula to solve for the missing side length, we can plug in the values we know:
5² + b² = 10²
We can simplify this equation by squaring 5 and 10:
25 + b² = 100
Next, we can isolate the variable (b) on one side of the equation by subtracting 25 from both sides:
b² = 75
Finally, we can solve for b by taking the square root of both sides:
b = √(75)
This simplifies to:
b = 5*√(3)
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Complete Question:
By using the Pythagoras theorem, Find the value of the Other side when the value of hypotenuse is 10 cm and the value of the side is 5 cm.
Find f
f’’(θ) = sin (θ) +cos (θ), f(0) = 2, f’(0) = 4
F(θ) =
Substituting these values into the expression for f(θ), we get:
f(θ) = -sin(θ) - cos(θ) + 5θ + 4
To find f, we need to integrate f''(θ) twice.
First, we integrate sin(θ) + cos(θ) with respect to θ to get f'(θ):
f'(θ) = -cos(θ) + sin(θ) + C1
where C1 is the constant of integration.
Next, we integrate f'(θ) with respect to θ to get f(θ):
f(θ) = -sin(θ) - cos(θ) + C1θ + C2
where C2 is the constant of integration.
Using the initial conditions given, we can solve for C1 and C2:
[tex]f(0) = -1 - 1 + C2 = 2[/tex]
C2 = 4
f'(0) = -1 + 0 + C1 = 4
C1 = 5
Substituting these values into the expression for f(θ), we get:
f(θ) = -sin(θ) - cos(θ) + 5θ + 4
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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.
what’s the inverse of f(x) for f(x)=4x-3/7
Answer:
x/4 + 3/28 = y
Step-by-step explanation:
To find the inverse, switch the x's and y's (note that f(x) is y) and solve for y:
x = 4y - 3/7
x + 3/7 = 4y
x/4 + 3/28 = y
Answer:
−1(x) = 3√2(x+7) 2 f - 1 (x) = 2 (x + 7) 3 2 is the inverse of f (x) = 4x3 − 7 f (x) = 4 x 3 - 7.
Find dx/dy, if x=sin^3t,y=cos^3t.
dx/dy = -sin(t)/cos(t) when x = sin^3(t) and y = cos^3(t).
To find dx/dy, we first need to find dx/dt and dy/dt, and then we can use the chain rule.
Given x = sin^3(t) and y = cos^3(t),
dx/dt = d(sin^3(t))/dt = 3sin^2(t) * cos(t) (using the chain rule)
dy/dt = d(cos^3(t))/dt = -3cos^2(t) * sin(t) (using the chain rule)
Now, we can find dx/dy by dividing dx/dt by dy/dt:
dx/dy = (dx/dt) / (dy/dt) = (3sin^2(t) * cos(t)) / (-3cos^2(t) * sin(t))
Simplify the expression:
dx/dy = -sin(t)/cos(t)
So, dx/dy = -sin(t)/cos(t) when x = sin^3(t) and y = cos^3(t).
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Sam has 42 pencils and 56 pens.he will give all of them to a group of his classmates. each classmate will receive the same number of each item. what is the greatest number of classmates sam can give pencils and pens to? how many of each item will each classmate receive?
Sam can give pencils and pens to 14 classmates, with each classmate receiving 3 pencils and 4 pens (since 42 divided by 14 is 3, and 56 divided by 14 is 4).
Sam has 42 pencils and 56 pens, and he wants to distribute them equally among his classmates. To find the greatest number of classmates, we need to find the greatest common divisor (GCD) of 42 and 56.
The GCD of 42 and 56 is 14. Therefore, the greatest number of classmates Sam can give pencils and pens to is 14.
Each classmate will receive:
- 42 pencils / 14 classmates = 3 pencils per classmate
- 56 pens / 14 classmates = 4 pens per classmate
So, each of the 14 classmates will receive 3 pencils and 4 pens.
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Find the indicated length
Answer:
y = 32/3 or 10.67 units------------------------------
The two smaller right triangles are similar by AA property.
Use ratios of corresponding sides to get:
8/y = 6/8Simplify and solve for y:
8/y = 3/4y = 8*4/3y = 32/3 ≈ 10.67Select the expressions that are equivalent to 3v+2v. A. V*5
B. V+5
C. V+5v
D. V+v+v+v+v
The expression that is equivalent to 3v+2v is:
D. v+v+v+v+v
How to write equivalent expressions?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we substitute the same value(s) for the variable(s).
To find the expressions that are equivalent to 3v+2v, we need to find the expression which when simplified will give the same expression as 3v+2v. That is: 3v + 2v = 5v
v*5 = 5v
v+5 = v + 5
v+5v = 6v
v+v+v+v+v = 5v
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Mike has some candies. he gave some to his friend. then, his mom gave him twice as much as he had in the beginning. how much did he have in the beginning if he has a total of 60 candies now?
According to given question Mike has 25 candies in the beginning.
Let's assume that Mike had "x" candies in the beginning.
After giving 15 candies to his friend, he would have had (x - 15) candies left.
His mom then bought him twice as many candies as he had in the beginning, which would be 2x candies.
So, the total number of candies Mike has now is (x - 15) + 2x = 60.
Combining like terms, we get 3x - 15 = 60.
Adding 15 to both sides, we have 3x = 75.
Finally, dividing both sides by 3, we find that x = 25.
Therefore, Mike had 25 candies in the beginning.
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The complete question is Mike had some candies. He gave 15 of them to his friend. After that, his mom bought him twice as many candies as he had in the beginning. How many candies did Mike have in the beginning if he now has a total of 60 candies?
The diagram below shows the radius of the circular opening of a Ice cream cone.
Which of the following Is closest to the circumference of the opening in inches.
Dina has a mass of 50 kilograms and is waiting at the top of a ski slope that’s 5 meters high. the maximum kinetic energy she can reach when she skis to the bottom of the slope is joules. use pe = m × g × h and g = 9.8 m/s2. ignore air resistance and friction.
Dina can reach a maximum kinetic energy of 2450 Joules when she skis to the bottom of the slope.
How much kinetic energy can Dina reach?Potential energy (PE) = m x g x h
where m = mass, g = acceleration due to gravity, and h = height
Here, Dina's mass (m) = 50 kg, height (h) = 5 m, and acceleration due to gravity (g) = 9.8 m/s².
So, PE = 50 x 9.8 x 5
PE = 2450 Joules
When Dina skis down the slope, all of her potential energy will be converted into kinetic energy (KE) at the bottom of the slope, neglecting any losses due to friction and air resistance.
Thus, the maximum kinetic energy (KE) Dina can reach at the bottom of the slope is also 2450 Joules.
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The maximum kinetic energy she can reach when she skis to the bottom of the slope is 2452 joules
To find the maximum kinetic energy that Dina can reach when she skis to the bottom of the slope, we need to use the principle of conservation of energy, which states that the total energy of a system remains constant.
At the top of the slope, Dina has potential energy due to her position relative to the ground. This potential energy is given by:
PE = m × g × h
where m is Dina's mass (50 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the slope (5 m).
PE = 50 kg × 9.8 m/s^2 × 5 m = 2450 J
When Dina skis to the bottom of the slope, all of her potential energy is converted into kinetic energy, which is given by:
KE = 1/2 × m × v^2
where v is her velocity at the bottom of the slope.
To find the maximum velocity, we can use the fact that the total energy of the system remains constant:
PE = KE
2450 J = 1/2 × 50 kg × v^2
v^2 = 98 m^2/s^2
v = sqrt(98) = 9.90 m/s
Finally, we can substitute this velocity into the kinetic energy equation to find the maximum kinetic energy that Dina can reach:
KE = 1/2 × 50 kg × (9.90 m/s)^2 = 2452 J
Therefore, Dina can reach a maximum kinetic energy of 2452 Joules when she skis to the bottom of the slope.
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Patricia bought 4 apples and 9 bananas for $12. 70. Jose bought 8 apples and 11 bananas for $17. 70 at the same grocery store. What's the price of one apple?
The price of one apple is $0.70, obtained by solving the system of equations 4x + 9y = 12.70 and 8x + 11y = 17.70 using elimination.
How much would Patricia pay for each apples?Let's use a system of equations caculation the problem.
Let x be the price of one apple and y be the price of one banana.
From the first sentence, we know that:
4x + 9y = 12.70
From the second sentence, we know that:
8x + 11y = 17.70
Now we can solve for x by using either substitution or elimination.
Let's use elimination.
We can multiply the first equation by 11 and the second equation by -9, then add them together:
44x + 99y = 139.70
-72x - 99y = -159.30
-28x = -19.60
Dividing both sides by -28, we get:
x = 0.70
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Tina is selling tickets for a fundraiser.
She wants to sell more than $300 worth
of tickets. The inequality 12t> 300 can
be used to determine the number of
tickets, t, she must sell in order to meet
her goal. Which number line represents
the solution to this inequality? (6. 9B |
6. 1A, 6. 1B, 6. 10, 6. 1F)
10
20
30
B
to
10
20
30
+
С
+o
+
10
20
30
D
+
10
O
20
30
The number line that represents the solution to this inequality is 6.10, with an open circle at 25 and shading to the right.
To solve the inequality 12t > 300, we need to isolate t on one side of the inequality. We can do this by dividing both sides by 12:
12t/12 > 300/12
t > 25
This means that Tina must sell more than 25 tickets in order to meet her goal of selling more than $300 worth of tickets.
To represent this solution on a number line, we can start by plotting a point at 25. Since the inequality is greater than (>) and not greater than or equal to (≥), we use an open circle at 25.
Then, we need to shade the area to the right of 25 to represent all the possible values of t that satisfy the inequality. This is because any value of t greater than 25 will make 12t greater than 300.
Out of the answer choices given, the number line that represents the solution to this inequality is 6.10, with an open circle at 25 and shading to the right.
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A pond of fish starts with 200 fish. The pond can sustain 460 fish, 40% of the fish die each year while the number of births is 60% of the current population. – 3.04174E+07 fish are harvested from the pond each year. Write a differential equation that models the problem
The differential equation that models the problem is: dN/dt = 0.2*N(t) - 3.04174E+07.
Let's denote the current number of fish in the pond by N(t), where t is time in years.
The rate of change of N(t) is given by the difference between the number of births and deaths, minus the number of fish harvested from the pond:
dN/dt = (0.6N(t)) - (0.4N(t)) - (3.04174E+07)
The first term represents the number of births, which is 60% of the current population N(t). The second term represents the number of deaths, which is 40% of the current population N(t). The third term represents the number of fish harvested from the pond each year.
Therefore, the differential equation that models the problem is:
dN/dt = 0.2*N(t) - 3.04174E+07
Note that we have simplified the expression (0.6-0.4)N(t) to 0.2*N(t) for simplicity.
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Identify the point (x1, y1) from the equation: y 8 = 3(x – 2)
The point (2, 8) is the point (x1, y1) identified from the equation y - 8 = 3(x - 2
Identify (x1, y1) the equation: y 8 = 3(x – 2)The equation y - 8 = 3(x - 2) is in point-slope form, which is y - y1 = m(x - x1), where (x1, y1) is the point on the line and m is the slope of the line. In this case, the slope of the line is 3, which means that for every increase of 1 in the x-coordinate, the y-coordinate increases by 3.Comparing the given equation with the point-slope form, we can see that x1 = 2 and y1 = 8. Therefore, the point (2, 8) is the point identified from the equation.Learn more about equation
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Find the surface area of the composite figure.
3 cm
5 cm
4 cm
8 cm
10 cm
SA =
8 cm
5 cm
7 cm
[?] cm²
If you'd like,
you can use a
calculator.
Enter please help I don’t want to fail!
The surface area of the composite figure is given as follows:
446 cm².
What is the surface area of a rectangular prism?The surface area of a rectangular prism of height h, width w and length l is given by:
S = 2(hw + lw + lh).
This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas.
The figure is this problem is given by the composition of two rectangular prisms, with dimensions given as follows:
5 cm, 10 cm and 7 cm.8 cm, 4 cm and 3 cm.Hence the surface area is given as follows:
S = 2 x (5 x 10 + 5 x 7 + 10 x 7) + 2 x (8 x 4 + 8 x 3 + 4 x 3)
S = 446 cm².
Missing InformationThe prism is given by the image presented at the end of the answer.
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Help asap
what is the measure of angle oac if major arc ab measures 220 degrees?
a. 55
b. 70
c. 110
d. 140
pls explain/show work
The measure of angle OAC if major arc AB measures 220 degrees is 110 degrees. Therefore, the correct option is C.
To find the measure of angle OAC, we need to use the central angle theorem which states that the measure of an inscribed angle is equal to half the measure of the intercepted arc.
Here, we are given that the major arc AB measures 220 degrees. So, the measure of angle AOB (the central angle) is 220 degrees.
Since angle OAC is an inscribed angle that intercepts arc AB, its measure is half the measure of arc AB.
Therefore, measure of angle OAC = (1/2) * 220 = 110 degrees.
So, the correct answer is option (c) 110.
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HELP FAST PLEASEEEEEE I NEED HELPPPPP
The median means that as many as friends have less than A. 1. 5 pets as those that have more than A. 1. 5 pets.
What does the median mean ?The median is a measure of central tendency in statistics that represents the middle value of a dataset when it is ordered from smallest to largest. The median is often used as a more robust measure of central tendency than the mean, because it is less affected by extreme values in the dataset.
From the box plot, the data set of friends with pets would be:
0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, ,2 ,2, 2, 2, 2, 3, 4, 4, 7.
The median here is:
= ( 10 th position + 11 th position ) / 2
= ( 1 + 2 ) / 3
= 1. 5
This therefore means that as many friends have more than 1. 5 pets as those with less than 1. 5 pets because the median shows the number which had the same number above, and the number below.
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One day, Bill at the candy shop sold 210 bottles of cherry soda and grape
soda for a total of $230. 30. If the cherry soda costs $1. 15 and the grape
soda costs $0. 99, how many of each kind were sold?
Bill sold 140 bottles of cherry soda and 70 bottles of grape soda.
Let's assume that x is the number of bottles of cherry soda sold and y is the number of bottles of grape soda sold. We can set up a system of equations to represent the given information:
x + y = 210 (equation 1: the total number of bottles sold is 210)
1.15x + 0.99y = 230.30 (equation 2: the total cost of the sodas is $230.30)
We can use the first equation to solve for y in terms of x:
y = 210 - x
Substituting this expression for y into the second equation, we get:
1.15x + 0.99(210 - x) = 230.30
Simplifying and solving for x, we get:
1.15x + 207.9 - 0.99x = 230.30
0.16x = 22.4
x = 140
So Bill sold 140 bottles of cherry soda. Substituting this value into equation 1, we get:
140 + y = 210
y = 70
Therefore, Bill sold 140 bottles of cherry soda and 70 bottles of grape soda.
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Appreciate if somebody answered this question
Thank you
A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
A probability can be classified as experimental or theoretical, as follows:
Experimental -> calculated after previous trials.Theoretical -> calculate before any trial.Over a small number of trials, these two probabilities can be different, but over a large number of trials, their values get closer.
The dice has eight sides, hence the theoretical probability of rolling a six is given as follows:
1/8 = 0.125 = 12.5%.
(each of the eight sides is equally as likely, and a six is one of these sides).
The experimental probabilities are obtained considering the trials, hence:
100 trials: 20/100 = 0.2 = 20%.400 trials: 44/400 = 0.11 = 11%.(given in the problem).
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Austin spends a winter day recording the temperature once every three hours for science class. At 9 am, the temperature was -1.9°F. Between 9am and noon, the temperature rose 11.3°F. Between noon and 3pm, the temperature dropped 7.9°F. Between 3pm and 6pm, the temperature dropped 12.7°F. What was the temperature at 6pm?
To find the temperature at 6pm, we need to start with the temperature at 9am and then add or subtract the changes in temperature that occurred during the day.
We know that the temperature at 9am was -1.9°F. Between 9am and noon, the temperature rose 11.3°F, so at noon the temperature was:
-1.9 + 11.3 = 9.4°F
Between noon and 3pm, the temperature dropped 7.9°F, so at 3pm the temperature was:
9.4 - 7.9 = 1.5°F
Between 3pm and 6pm, the temperature dropped 12.7°F, so at 6pm the temperature was:
1.5 - 12.7 = -11.2°F
Therefore, the temperature at 6pm was -11.2°F.
Evaluate the following indefinite integral si 3x^2 – 3x +1/ x^3 + 2
To evaluate the indefinite integral of 3x^2 – 3x +1/ x^3 + 2, we can use partial fraction decomposition.
First, we factor the denominator: x^3 + 2 = (x + ∛2)(x^2 – ∛2x + 2).
Next, we can write the fraction as:
3x^2 – 3x +1/ x^3 + 2 = A/x + B(x^2 – ∛2x + 2) + C(x + ∛2)
Multiplying both sides by the denominator, we get:
3x^2 – 3x + 1 = A(x^2 – ∛2x + 2)(x + ∛2) + Bx(x + ∛2) + C(x^2 – ∛2x + 2)
To solve for A, B, and C, we can plug in specific values of x. For example, if we plug in x = -∛2, we get:
-2√2 + 1 = A(4√2) + C(0)
Therefore, A = (2 – √2)/8.
If we plug in x = 0, we get:
1 = A(2√2) + B(0) + C(√2)
Therefore, C = 1/√2.
Finally, if we plug in x = 1, we get:
1 = A(3√2) + B(1 – √2) + C(1 + √2)
Therefore, B = (-1 + √2)/4.
Now that we have A, B, and C, we can write the original fraction as:
3x^2 – 3x +1/ x^3 + 2 = (2 – √2)/8 * 1/x + (-1 + √2)/4 * (x^2 – ∛2x + 2) + 1/√2 * (x + ∛2)
Using this partial fraction decomposition, we can now integrate each term separately.
Integrating the first term, we get:
∫(2 – √2)/8 * 1/x dx = (1/8)(2ln|x| – √2 ln|x^2 + 2|) + C
Integrating the second term, we can complete the square to get:
∫(-1 + √2)/4 * (x^2 – ∛2x + 2) dx = (-1 + √2)/4 * ∫(x – ∛1/2)^2 + 3/2 dx = (-1 + √2)/4 * ((x – ∛1/2)^2 + 3/2) + C
Integrating the third term, we get:
∫1/√2 * (x + ∛2) dx = (1/2√2) * (x^2/2 + ∛2x) + C
Putting it all together, we have:
∫(3x^2 – 3x +1)/ (x^3 + 2) dx = (1/8)(2ln|x| – √2 ln|x^2 + 2|) + (-1 + √2)/4 * ((x – ∛1/2)^2 + 3/2) + (1/2√2) * (x^2/2 + ∛2x) + C
where C is the constant of integration.
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