In the proportion, the cost of 0.7kg apple is Rs.62.65 .
What is proportion?
A percentage is created when two ratios are equal to one another. We write proportions to construct equivalent ratios and to resolve unclear values. a comparison of two integers and their proportions. According to the law of proportion, two sets of given numbers are said to be directly proportional to one another if they grow or shrink in the same ratio.
Here cost of 1kg apples = 89.50
Then cost of 0.7 kg apple = x.
Now using proportion,
=> 1 = 89.50
0.7= x
=> x = [tex]\frac{89.50\times0.7}{1}[/tex]
=> x = 62.65.
Hence the cost of 0.7kg apple is Rs.62.65 .
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Hudson is designing a new board game, and is trying to figure out all the possible
outcomes. How many different possible outcomes are there if he spins a spinner with
three equal-sized sections labeled Walk, Run, Stop and spins a spinner with 5 equal-
sized sections labeled Monday, Tuesday, Wednesday, Thursday, Friday?
There are 15 different possible outcomes when Hudson spins both spinners in his board game.
To determine the total number of possible outcomes when Hudson spins both spinners, you need to multiply the number of outcomes on the first spinner (Walk, Run, Stop) by the number of outcomes on the second spinner (Monday, Tuesday, Wednesday, Thursday, Friday).
Step 1: Determine the number of outcomes on the first spinner. There are 3 outcomes: Walk, Run, and Stop.
Step 2: Determine the number of outcomes on the second spinner. There are 5 outcomes: Monday, Tuesday, Wednesday, Thursday, and Friday.
Step 3: Multiply the number of outcomes from both spinners. 3 outcomes on the first spinner multiplied by 5 outcomes on the second spinner equals 15 total possible outcomes.
So, there are 15 different possible outcomes when Hudson spins both spinners in his board game.
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the expression x^2-8x+6 can be written in the form (x-p)^2+q
Answer:(x-4)^2-10
Step-by-step explanation:
How might the graph be redrawn to emphasize the difference between the cost per doctor visit for each of the three plans? The scale on the y-axis could be changed to 0–100. The scale on the y-axis could be changed to 25–40. The interval of the y-axis could be changed to count by 5s. The interval of the y-axis could be changed to count by 20s.
To emphasize the difference between the cost per doctor visit for each of the three plans, you can change the scale on the y-axis to either 0–100 or 25–40 and adjust the interval of the y-axis to count by 5s.
To emphasize the difference, you can consider the following adjustments to the graph:
1. Change the scale on the y-axis to 0–100. This adjustment will give a wider range for the costs, making it easier to see the differences between the three plans.
2. Alternatively, change the scale on the y-axis to 25–40. This change will focus more on the specific cost range that the three plans fall into, magnifying the differences between them.
3. Change the interval of the y-axis to count by 5s. This alteration will increase the number of increments on the y-axis, giving a more detailed view of the cost differences between the plans.
4. On the other hand, changing the interval of the y-axis to count by 20s might not be the best option. It will decrease the increments on y-axis and make it harder to visualize the cost differences between the plans.
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Six friends are selling crafts at a flea market. they each need to pay $7. 20 to pay
for the table rental. they each sell 3 items. if every item is the same price, and the
6 friends make a total profit of $25. 20, what was the sale price of each item?
To find the sale price of each item, we need to use some basic algebra. Let's call the sale price of each item "x".
First, we need to find the total cost of the table rental for all six friends. Since each friend needs to pay $7.20, the total cost of the table rental is 6 * $7.20 = $43.20.
Next, we need to find the total revenue from selling the items. Each friend sells 3 items, so the total number of items sold is 6 * 3 = 18. The total revenue is the number of items sold multiplied by the sale price, so the total revenue is 18x.
We know that the total profit is $25.20, which is the total revenue minus the total cost of the table rental. So we can set up the equation:
18x - $43.20 = $25.20
Simplifying this equation, we get:
18x = $68.40
Dividing both sides by 18, we get:
x = $3.80
Therefore, the sale price of each item is $3.80.
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What does 9x5 equal to
Answer:
Step-by-step explanation:
9 groups with 5 in each equals to
45
Answer: 9 x 5 = 45
Step-by-step explanation:
9
18
27
36
45
54
63
72
81
90
99
108
The first is kept by the albatross, which first lands in our region. The second occurs every night in shooting, swimming, fighting, singing and others. Separately, they would reveal many to you. Together, they will reveal only one to you. And whose one is it?
Based on the information provided, it is not clear what "they" refer to. However, it seems that there are two distinct events or phenomena being described here.
The first involves the albatross, which is known to be a migratory bird that visits certain regions at certain times of the year. It is unclear what exactly is being "kept" by the albatross, but it could be some sort of information or knowledge that is unique to this bird.
The second event or phenomenon is described as happening every night and involving various activities such as shooting, swimming, fighting, and singing.
It is unclear what this refers to exactly, but it could be some sort of nightly ritual or tradition that takes place in a particular community or region.
The statement that "separately, they would reveal many to you" suggests that each of these phenomena has its own unique insights or knowledge to offer.
However, the statement that "together, they will reveal only one to you" implies that there is some sort of deeper connection or meaning between these two events that is not immediately apparent.
The question of "whose one is it?" suggests that there is some sort of ownership or responsibility associated with this revelation.
It is unclear who this refers to, but it could be interpreted as asking who is responsible for uncovering the deeper meaning or connection between these two phenomena.
In summary, the information provided is somewhat cryptic and open to interpretation. However, it seems that there are two distinct events or phenomena being described, and that there is some sort of deeper connection or meaning between them that is not immediately apparent.
The question of who is responsible for uncovering this connection remains unanswered.
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A store sells a coat in three sizes: small, medium, and large. The coat comes in red, navy, and tan. Sales from a given day are displayed in the table
What is the experimental probability that the next coat sold is a medium, navy coat? Round your answer
to the nearest whole percent.
The probability of the next coat being sold as a medium navy coat is 11 / 95 when a store sells a coat in three sizes: small, medium, and large. The coat comes in red, navy, and tan.
We need to find the probability that the next coat sold as a medium navy coat. To find the probability we need to find the total number of coats and the number of medium navy coats,
Given data:
Medium navy coat = 22
Total Number of small coats = 18 + 24 +19 = 61
Total Number of medium coats = 21 + 22 + 25 = 68
Total Number of large coats = 19 + 20 + 22 = 61
From the given data the total number of coats is = 61 + 68 + 61 = 190
The probability that the next coat sold as a medium navy coat = a number of medium navy coats / total number of coats.
= 22 / 190
= 11 / 95
Therefore, the probability of the next coat being sold as a medium navy coat is 11 / 95
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y = 49 - 4x y = 73 - 7x
The solution of the system of equation
x = 8 and y = 17
How to solve system of equation?System of equation can be solved using different method such as elimination method, substitution method and graphical method. Let's solve the system of equation by substitution method.
Therefore,
y = 49 - 4x
y = 73 - 7x
Hence, using substitution,
73 - 7x = 49 - 4x
73 - 49 = -4x + 7x
24 = 3x
divide both sides of the equation by 3
x = 24 / 3
x = 8
Therefore,
y = 73 - 7(8)
y = 73 - 56
y = 17
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An airplane flies at 500 mph with a direction of 135* relative to the air. The plane experiences a wind that blows 60 mph with a direction of 60*
The plane's new velocity is 421.4 mph with a direction of 63.43 degrees relative to the air.
To solve this problem, we need to use vector addition. Let's first draw a diagram to represent the situation.
First, we need to break down the velocity of the plane and the velocity of the wind into their horizontal and vertical components.
The velocity of the plane can be broken down into a horizontal component of 500*cos(135) mph and a vertical component of 500*sin(135) mph.
The velocity of the wind can be broken down into a horizontal component of 60*cos(60) mph and a vertical component of 60*sin(60) mph.
Now, we can add these components together to get the resultant velocity.
The horizontal component of the resultant velocity is 500*cos(135) + 60*cos(60) = -189.28 mph. The negative sign indicates that the velocity is in the opposite direction of the plane's original direction.
The vertical component of the resultant velocity is 500*sin(135) + 60*sin(60) = 374.28 mph.
Using the Pythagorean theorem, we can find the magnitude of the resultant velocity:
|v| = sqrt((-189.28)^2 + (374.28)^2) = 421.4 mph.
Finally, we can find the direction of the resultant velocity using the inverse tangent function:
θ = tan^-1(374.28/-189.28) = -63.43 degrees.
So the plane's new velocity is 421.4 mph with a direction of 63.43 degrees relative to the air.
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What kind of triangle is this?
A. Equilateral
B. Isosceles but not equilateral
C. Scalene
Answer:
C. Scalene
Step-by-step explanation:
Equilateral triangle has all sides equal.
Isosceles triangle has exactly 2 sides equal.
All side lengths in a Scalene triangle are distinct.
Pleasee help
f(x) = 3x² - 7x + 4
f(2)= [?]
Answer:
f(2) = 2
Step-by-step explanation:
We are given
f(x) = x² - 7x + 4
To find f(2), just plug in 2 wherever you see an x and simplify
f(2) = 3 · 2² - 7 · 2 + 4
= 3 · 4 - 7 · 2 + 4
= 12 - 14 + 4
= 2
3. Jumal and Jabari are helping Jumal's father with a construction project. He needs to build a triangular frame as a piece to be used in the whole project, but he has not been given all the information he needs to cut and assemble the sides of the frame. He is even having a hard time envisioning the shape of the triangle from the information he has been given. Here is the information about the triangle that Jumal's father has been given.
Side a 10.00 meters
Side b= 15.00 meters
Angle A = 40.0°
Jumal's father has asked Jumal and Jabari to help him find the measure of the other two angles and the missing side of this triangle. Carry out each student's strategy as described below. Then draw a diagram showing the shape and dimensions of the triangle that Jumal's father should construct.
The triangles created using the law of sines and the law of cosines for Jumal's approach and Jabari's approach are attached
What is the Law of Sines?The Law of Sines states that the ratio of a sine of an angle to the length of the side facing the angle is the same for the three sides of the triangle.
Jumal's approach
a. The measure of the angle B can be found as follows;
sin(40)/10 = sin(B)/15
B = 15 × arcsine(sin(40)/10) ≈ 74.6°
b. The measure of angle C can be found using the angle sum property of a triangle as follows;
∠C = 180 - (40 + 74.6) = 65.4°
c. The length of the side c is therefore;
sin(40)/10 = sin(65.4)/c
c = sin(65.4) × 10/sin(40) ≈ 14.1
The length of the side c is about 14.1 meters
The triangle can be obtained by using the specified and obtained dimensions as shown in the attached drawing
Jabari's Approach
a. The Law of Cosines indicates; a² = b² + c² - 2·b·c·cos(A)
Therefore;
100 = 225 + c² - 2 × 15 × c × cos(40)
10² = 15² + c² - 23·c
c² - 23·c + 125 = 0
c = (23 ± √(29))/2
c = 14.2 and 8.8
c. Please find attached then possible drawings based on the calculated dimensions, created with MS Word
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Can someone help me asap? It’s due today!!
Based on the information provided, James would have 20 different waffle options.
How many options will James have?Since each waffle cone can hold two scoops of ice cream and James must choose a different flavor for each scoop, we can approach this problem by using the multiplication principle of counting.
There are 5 different ice cream flavors to choose from for the first scoop, and 4 different flavors remaining for the second scoop. This is because James must choose a different flavor for each scoop.
Therefore, the number of different waffle cone options that James has is:
5 x 4 = 20
So, James has 20 different waffle cone options if he chooses a different flavor of ice cream for each scoop.
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In ΔLMN, m = 59 inches, n = 35 inches and ∠L=82°. Find ∠N, to the nearest degree
The answer is: ∠N ≈ 33°
To find ∠N in ΔLMN, we can use the Law of Cosines which states that c² = a² + b² - 2abcos(C), where c is the side opposite angle C.
In this case, side LM (m) is opposite angle ∠N, side LN (n) is opposite angle ∠L, and side MN (x) is opposite the unknown angle.
So, we can write:
m² = n² + x² - 2nxcos(82°)
Substituting the given values:
x² = 35² + 59² - 2(35)(59)cos(82°)
Solving for x, we get:
x ≈ 64.27
Now, using the Law of Sines which states that a/sin(A) = b/sin(B) = c/sin(C), we can find ∠N:
sin(∠N)/35 = sin(82°)/64.27
sin(∠N) ≈ 0.5392
∠N ≈ sin⁻¹(0.857) ≈ 32.6344°
Therefore, ∠N ≈ 33° to the nearest degree.
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5. a space shuttle traveling at 17,581 miles per hour decreases its speed by 7,412 miles per hour. estimate the speed of the space shuttle after it has slowed down by rounding each number to the nearest hundred.
The rounding method used, the estimated speed of the space shuttle after it has slowed down is 10,200 miles per hour.
To estimate the speed of the space shuttle after it has slowed down, we round each number to the nearest hundred. The speed before the decrease is rounded to 17,600 miles per hour, and the decrease in speed is rounded to 7,400 miles per hour.
Next, we subtract the rounded decrease in speed from the rounded speed before. So, 17,600 - 7,400 = 10,200 miles per hour. This result represents the estimated speed of the space shuttle after it has slowed down.
Rounding to the nearest hundred is a way to approximate the values and make calculations simpler. However, it is important to note that rounding introduces some degree of error, and the actual speed after the decrease may differ slightly from the estimated value.
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At a noodles and company restaurant, the probability that a customer will order a nonalcoholic beverage is 48. Out of 12 customers 5 will order alcohol
The probability is that out of 12 customers, 7 will order a non-alcoholic beverage, and the remaining 5 will order an alcoholic beverage.
The likelihood that a client will arrange a non-alcoholic refreshment is given as 48%, which implies that the likelihood that a client will arrange an alcoholic refreshment is (100 - 48) = 52%.
Out of 12 customers, 5 will arrange liquor, which suggests that the remaining clients will arrange a non-alcoholic refreshment. We are able to calculate the number of clients who will arrange a non-alcoholic refreshment as takes after:
Number of clients who will arrange a non-alcoholic refreshment =
Add up to a number of clients - Number of clients who will arrange liquor
= 12 - 5
= 7
Subsequently, out of 12 clients, 7 will arrange a non-alcoholic refreshment, and the remaining 5 will arrange an alcoholic refreshment.
It is critical to note that these calculations are based on the presumption that each client will as it were arrange one refreshment.
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A school’s prom committee is composed of 10 students. Seven are girls: Kelly, Karri, Michela, Raquel, Rara, Nadya, and Neesa. Three are boys: Rio, Elke, and Kevin. If they choose a student at random, what is the probability the choose a student whose name begins with "K" P(K name)?
Question 1 options:
30%
70%
40%
50%
The probability of choosing a student whose name begins with "K" is 40%.
To find the probability of choosing a student whose name begins with "K," P(K name), we need to calculate the ratio of students with "K" names to the total number of students in the prom committee.
There are 10 students in the prom committee: 7 girls (Kelly, Karri, Michela, Raquel, Rara, Nadya, Neesa) and 3 boys (Rio, Elke, Kevin). Out of these, 4 students have names that start with "K": Kelly, Karri, Kevin, and Elke (note that Elke has been mistakenly included in the boys' list, but we'll consider it as a "K" name).
To find the probability, we'll use the formula:
P(K name) = (number of students with "K" names) / (total number of students)
P(K name) = 4 / 10 = 0.4 or 40%
So, the probability of choosing a student whose name begins with "K" is 40%.
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Customer: "Currently I am paying $60. 00 a month for my service. I would like to upgrade to the $80. 00 service package because my new employer offers a 20% discount with your company. What would be the cost difference compared to what I am paying now if I upgraded?" Employee: "With your discount you would only pay __________ a month more for the upgraded plan. "
"With your discount, you would only pay $4.00 a month more for the upgraded plan."
You are currently paying $60.00 a month for your service and you would like to upgrade to the $80.00 service package because your new employer offers a 20% discount with the company. Let's calculate the cost difference compared to what you are paying now if you upgraded.
Step 1: Calculate the discount on the $80.00 service package.
Your new employer offers a 20% discount, so to find the discount amount, multiply the original price by the discount percentage.
Discount = $80.00 * 20% = $80.00 * 0.20 = $16.00
Step 2: Subtract the discount from the original price to find the new monthly cost.
New price = Original price - Discount = $80.00 - $16.00 = $64.00
Step 3: Calculate the cost difference between your current plan and the upgraded plan.
Cost difference = New price - Current price = $64.00 - $60.00 = $4.00
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The price of a calculator is decreased by
31
%
and now is
$
189. 6. Find the original price
Answer:
274.78
Step-by-step explanation:
Let's call the original price "x".
We know that the price decreased by 31%, so the new price is
100% - 31% = 69% of the original price:
0.69x = 189.6
To solve for x, we can divide both sides by 0.69:
x = 189.6 / 0.69
Simplifying this expression, we get:
x ≈ 274.78
Therefore, the original price was approximately $274.78.
Geometry question I need help with:
We denote triangle ABC, angle A measures 90°, angle B measures 30° and angle C measures 60°.
We apply the cosine of 30 degrees, becuase m(∡A) = 90° and find the hypotenuse of triangle ABC:
cos = (adjacent side) / (hypotenuse)
⇔ cos B = AB/BC ⇔
⇔ cos 30° = 8√3/v ⇔
⇔ √3/2 = 8√3/v ⇔
⇔ √3 • v = 2 • 8√3 ⇔
⇔ v√3 = 16√3 ⇔
⇔ v = 16√3 ÷ √3 ⇔
⇔ v = 16 millimeters
Hope that helps! Good luck! :)
Given the function g(a) = 6x^3 - 9x^2 - 36x, find the first derivative, g'(x).
The first derivative of g(a) is [tex]g'(x) = 18x^2 - 18x - 36.[/tex]
To find the first derivative of g(a), we need to use the power rule and the constant multiple rule.
First, we use the power rule to take the derivative of each term:
[tex]- The derivative of 6x^3 is 18x^2
- The derivative of -9x^2 is -18x
- The derivative of -36x is -36[/tex]
Next, we use the constant multiple rule to combine these derivatives:
g'(a) = 18x^2 - 18x - 36
Therefore, the first derivative of g(a) is [tex]g'(x) = 18x^2 - 18x - 36.[/tex]
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ashley measured a line to be 3.9 inches long. if the actual length of the line is 4.1 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?
The percent error in measuring if the actual length is 4.1 cm and the measured length is 3.9 cm is 4.88%
The error refers to the estimated difference between the measured and actual measurement of an object. Error is mainly of three types systematic errors, random errors, and negligent errors.
Measured length = 3.9
Actual length = 4.1
Error = actual value - measured value
= 4.1 - 3.9
= 0.2
Error percent is the ratio of error to the actual value multiplied by 100
Error percent = [tex]\frac{0.2}{4.1}[/tex] * 100
= 4.88%
Thus, the error percent in the given question comes out to be 4.88%
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Solve for x, t, r and round to the nearest hundredth
Answer:
x = 14°
t = 12.367 ~ 12.4
r = 2.999 ~ 3
Step-by-step explanation:
1st we can find x by sum theory which is the sum of all side equal to 180° .
x + 90° + 76° = 180 °
x + 166° = 180°
x= 180° - 166°
x = 14° ... So the unknown angle is 14°
and we also can solve hypotenus t and adjecent r by using sin amd cos respectively by angle 76° .
sin(76) = 12/t
sin(76) t = 12 ....... criss cross it
t = 12 / sin(76) ....... divided both side by sin(76)
t = 12.367 ~ 12.4 ....... result
And
cos(76) = r / 12.4
r = cos(76) × 12.4 .......criss cross
r = 2.999 ~ 3 ....... amswer and i approximate it
A police unit has deployed a tracking system on a highway with a speed limit of 65 mph. A driver passes through one radar detector at 2pm and is traveling 60 mph at that moment. Then, the driver passes through a second radar detector 159 miles away at 4pm, again traveling 60 mph at that moment. However, a speeding ticket is being issued for this driver. When he asked for an explanation, the response was "Mean Value Theorem. " Explain. Your report should include:
i- Detailed explanation about the mean value theorem.
ii- Detailed calculation steps.
The Mean-Value-Theorem is being used to explain why the driver received a speeding ticket even though they were traveling at exactly 60 mph at both radar-detectors. It suggests that there must have been a moment during the trip where the driver's speed was above the speed limit.
The Mean-Value Theorem is a theorem from calculus that states that for a continuous function on a closed interval, there exists at least one point in the interval where the instantaneous rate of change (the derivative) of the function is equal to the average rate of change of the function over the interval.
In this case, the police unit used the two radar detectors to determine the average-speed of the driver between the two points. The distance between the two detectors is 159 miles, and the time it took for the driver to travel that distance was 2 hours (from 2pm to 4pm), so the average speed of the driver was 159/2 = 79.5 mph.
However, the speed-limit on the highway is 65 mph, so the driver was exceeding the speed limit and received a speeding-ticket.
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A group of friends wants to go to the amusement park. They have $207. 50 to spend on parking and admission. Parking is $5, and tickets cost $33. 75 per person, including tax. Which equation could be used to determine x x, the number of people who can go to the amusement park?
The equation that can be used to determine the number of people (x) who can go to the amusement park is:
207.50 = 5 + (33.75 × x).
To determine the number of people (x) who can go to the amusement park, we need to create an equation using the given information. We know that they have $207.50 to spend, parking costs $5, and each ticket costs $33.75 per person (including tax).
We can represent the total cost of the trip as the sum of the cost for parking and the cost of the tickets for x number of people. The equation would be:
Total Cost = Cost of Parking + (Cost of Tickets per Person × Number of People)
Since we know the total cost is $207.50, the cost of parking is $5, and the cost of tickets per person is $33.75, we can plug in these values:
207.50 = 5 + (33.75 × x)
This equation can be used to determine the value of the variable x, the number of people who can go to the amusement park. To find the value of x, simply solve the equation by isolating the variable x.
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This equation gives the light intensity, I (in lumens), in water at a depth of feet: d= -425log(I/12). I) What is the intensity of the light at a depth of 300 feet? Please show all work. Ii) At what water depth is the intensity 5 lumens? Please show all work. Iii) What is the light intensity at the surface of the water? Please show all work
i) The light intensity at a depth of 300 feet is approximately 0.131 lumens.
ii)The light intensity of 5 lumens is reached at a depth of approximately 106.6 feet.
iii)The light intensity at the surface of the water is 12 lumens.
The equation given is:
[tex]d= -425log(\frac{I}{12} )[/tex]
where d is the depth in feet, and l is the light intensity in lumens.
i)To find the intensity of light at a depth of 300 feet:
[tex]d= -425log(\frac{I}{12} )[/tex]
[tex]or, \frac{d}{-425}=log(\frac{I}{12})[/tex]
[tex]or, 10^{\frac{d}{-425}}=\frac{I}{12}[/tex]
[tex]or, 12 X 10^{\frac{d}{-425}}=I[/tex]
Given, d= 300 feet. Hence,
[tex]or, 12 X 10^{\frac{300}{-425}}=I[/tex]
or, I = 0.131 lumens (approx.)
ii) We have been given the equation :
[tex]d= -425log(\frac{I}{12} )[/tex]
when I =5 lumens
[tex]d= -425log(\frac{5}{12} )[/tex]
or, d = 106.6 feet (approx.)
iii) For finding the light intensity at the surface of the water d=0
[tex]d= -425log(\frac{I}{12} )[/tex]
Putting d = 0 we get
[tex]0= -425log(\frac{I}{12} )[/tex]
[tex]or, log(\frac{I}{12})=0[/tex]
[tex]or, \frac{I}{12} = 10^0 = 1[/tex]
or, I = 12 lumens
Therefore the light intensity at the surface of the water is 12 lumens.
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An instructor graded 200 papers and found 80 errors. If a paper is picked at
random, find the probability that it will have exactly 4 errors
The probability of a paper having exactly 4 errors can be calculated using the binomial probability formula, which is:
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
What is the probability of selecting a paper at random from 200 papers and instructor found 80 errors and the probability that a paper has exactly 4 errors?In binomial probability formula P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
n is the number of trials (in this case, the number of papers graded)
k is the number of successes (in this case, the number of papers with exactly 4 errors)
p is the probability of success (in this case, the probability that a paper has an error, which can be calculated by dividing the total number of errors by the total number of papers graded)
Calculate the probability of a paper having an errorp = 80/200 = 0.4
Calculate the probability of a paper having exactly 4 errorsP(X = 4) = (200 choose 4) * 0.4^4 * (1-0.4)^(200-4) ≈ 0.153
Therefore, the probability of picking a paper at random and finding exactly 4 errors is approximately 0.153 or 15.3%.
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please can someone help i really need help thank you
The equation of the function h(x) from the transformation is h(x) = f(x + 1)
Describing the transformation of f(x) to h(x).From the question, we have the following parameters that can be used in our computation:
The functions f(x), g(x) and h(x)
In the graph, we can see that
The graph of f(x) is the parent functionThe graph of h(x) is a shift of 1 unit leftHorizontal Shift = 1 unit left
This is represented as
h(x) = f(x + 1)
This means that the transformation of f(x) to h(x) is f(x) is shifted left 1 unit to h(x).
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At the Royal Dragon Chinese restaurant, a slip in the fortune cookies indicates a dollar amount that will be subtracted from your total bill. A bag of 10 fortune cookies is given to you from which you will select one. If six fortune cookies contain "1$ off," three contain "$3 off," and one contains "$8 off," determine the expectation of a selection.
Answer:
im sorry this makes absolutely no sense
Step-by-step explanation:
Peyton built a birdhouse in the shape of a pyramid with a square base.
The dimensions of the base were 16 in. By 16 in.
The slant height of the pyramid is 10 in.
What is the surface area of the birdhouse?
A. 262 in. 2
B. 576 in. 2
C. 640 in. 2
D. 1,280 in. 2
To find the surface area C of the birdhouse, we need to find the area of each face and add them together.
First, let's find the area of the square base:
Area of base = side^2 = 16^2 = 256 in^2
Next, let's find the area of each triangular face:
Area of each triangular face = 1/2 * base * height
Since the base is 16 in and the slant height is 10 in, the height can be found using the Pythagorean theorem:
height^2 = slant height^2 - base^2/4
height^2 = 10^2 - 16^2/4
height^2 = 100 - 64
height^2 = 36
height = 6
So the area of each triangular face is:
1/2 * 16 * 6 = 48 in^2
There are four triangular faces, so the total area of the triangular faces is:
4 * 48 = 192 in^2
Finally, we add the area of the base and the area of the triangular faces to find the total surface area:
256 + 192 = 448 in^2
Therefore, the surface area of the birdhouse is 448 square inches, which is closest to option A: 262 in^2.
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