The ratios of successive numbers in the Fibonacci sequence eventually get closer to a. 1.61
In mathematics, the Fibonacci sequence is a sequence in which each number is the sum of the two preceding ones. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted Fn . The sequence commonly starts from 0 and 1, although some authors start the sequence from 1 and 1 or sometimes (as did Fibonacci) from 1 and 2.
The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones, usually starting with 0 and 1 (0, 1, 1, 2, 3, 5, 8, 13, ...). When you take the ratio of successive numbers in the sequence (e.g., 5/3 or 8/5), it converges to approximately 1.618, also known as the Golden Ratio or Phi.
The closest option in your list is 1.61, which is option (a).
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A restaurant owner rejects his produce shipment if he finds more than 3 crates with any bruised
or spoiled food in it. The probability that a crate has bruised or spoiled food in it is 0.11. What
is the probability that he will reject a shipment of 15 crates?
Find the probability of at least one failure in five trials of a binomial experiment in which the probability of success is %30
The probability of having at least one failure in five trials is approximately 0.83193 or 83.193%.
To calculate the probability of at least one failure, we first need to find the probability of having zero failures in five trials, which is equal to (0.3)^5 or 0.00243. Then, we subtract this value from 1 to obtain the probability of having at least one failure. This is because the sum of the probabilities of all possible outcomes should be equal to 1.
In this case, we can see that the probability of having at least one failure in five trials is quite high, at approximately 83%. This means that it is more likely than not that there will be at least one failure in a series of five trials with a success rate of 30%.
The probability of having at least one failure in five trials of a binomial experiment with a success rate of 30% can be calculated as follows:
1 - (probability of having zero failures in five trials)
= 1 - (0.7)^5
= 1 - 0.16807
= 0.83193
Therefore, the probability of having at least one failure in five trials is approximately 0.83193 or 83.193%.
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Find the highest common factor (HCF) of 12x^12 and 16x^16
Answer:
Step-by-step explanation:
To find the highest common factor (HCF) of 12x^12 and 16x^16, we need to factor both expressions.
12x^12 = 2^2 * 3 * (x^2)^6
16x^16 = 2^4 * (x^2)^8
The common factors of 12x^12 and 16x^16 are 2^2 and (x^2)^6. To find the HCF, we take the product of these common factors:
HCF = 2^2 * (x^2)^6 = 4x^12
Therefore, the highest common factor (HCF) of 12x^12 and 16x^16 is 4x^12.
they're surprised to see that final stores the value 0.7999999999999999 instead of 0.8. what is the best explanation for that result?
The limited precision of floating-point arithmetic in computers can cause rounding errors, leading to unexpected results such as the value 0.7999999999999999 instead of 0.8. This occurs because certain decimal values cannot be accurately represented in binary form.
This is due to the way floating-point numbers are represented in the computer's memory.
Binary floating-point arithmetic cannot represent every decimal value exactly, so sometimes small rounding errors can occur.
In this case, the value 0.8 cannot be represented exactly in binary floating-point format, so the closest approximation is used, resulting in a slightly different value.
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What is the lateral area of the cone to the nearest whole number? The figure is not drawn to scale.
*
Captionless Image
34311 m^2
18918 m^2
15394 m^2
28742 m^2
Answer:
π(70)(√(70^2 + 50^2)) = π(700√74) m^3
= 18,918 m^3
Kennedy makes $7 per hour babysitting. Hours (h) dollars (d) 1 7 2 14 3 21 4 28 which equation represents the amount kennedy makes babysitting? 7 = hd h = 7d d = 7h h = d
The correct equation represents the amount Kennedy makes babysitting is,
⇒ d = 7h
We have to given that,
Kennedy makes $7 per hour babysitting.
Let us assume that,
'h' represent the number of hours
And, d represent amount in dollars.
Hence, By given condition, we get;
⇒ d = 7h
Thus, The correct equation represents the amount Kennedy makes babysitting is,
⇒ d = 7h
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The formula that Kennedy uses to calculate how much money she makes babysitting is:d = 7h
We have,
Kennedy makes $7 per hour babysitting.
let "d" represents the amount of dollars Kennedy makes, and "h" represents the number of hours she babysits.
Since Kennedy earns $7 per hour, the equation can be written as
d = 7h
which relates the dollars earned (d) to the number of hours worked (h).
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The domain in a set of ordered pairs is always the y-coordinate.
True or False
Answer: False
Step-by-step explanation: It is false because the y-coordinate is the range.
Write the equation for shifting the parent function of the absolute value function 3 units down.
The vertex will be at (0, -3), and the graph will be lower than the parent function by 3 units at every point. The parent function of the absolute value function is f(x) = |x|.
To shift this function 3 units down, we need to subtract 3 from the function's output (y) at every point on the graph. This can be expressed as:
f(x) = |x| - 3
The absolute value function is symmetric around the y-axis, which means that any shifts to the left or right do not affect the shape of the graph, only its position on the coordinate plane.
However, a vertical shift up or down will change the location of the vertex, the point where the graph changes direction. In this case, the vertex will be at (0, -3), and the graph will be lower than the parent function by 3 units at every point.
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Estimate the radius of the object. Round to the nearest hundredth if necessary.
C = 8. 9 mm
radius: about
mm
The estimated radius of the object is about 1.42 mm.
The given information is that the circumference( C) of the object is8.9 mm.
We know that the formula for the circumference of a circle is given by
C = 2πr
where r is the compass of the circle.
To estimate the compass, we can rearrange the formula as
r = C/ 2π
Substituting the given value of C, we get
r = 8.9/ 2π
we can estimate this expression to get
r ≈1.42 mm( rounded to two decimal places)
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25) When (x + 1)2 is divided by x - 2, the quotient is 16 and the remainder is x - 3. Find the possible values of x.
Answer:
x = 3 or x = 12
Step-by-step explanation:
You want the possible values of x that make it true that ...
(x +1)²/(x -2) = 16 +(x -3)/(x -2)
Division expressionThe given division expression can be written in terms of quotient and remainder as ...
p/q = a +r/q ⇒ p = aq +r
ApplicationHere, this means ...
(x +1)² = 16(x -2) +(x -3)
x² +2x +1 = 16x -32 +x -3
x² -15x = -36
x² -15x +56.25 = 20.25 . . . . . complete the square
(x -7.5)² = 4.5²
x = 7.5 ± 4.5 . . . . . . . . . . . . . take the square root, add 7.5
x = 3 or 12
__
Additional comment
The given quotient-remainder equation has a vertical asymptote at x = 2. When we write it as f(x) = 0, the graph of f(x) is symmetrical about the point (2, -11).
The lengths of the sides of a triangle are given. Classify each triangle as acute,
right, or obtuse.
19. 3, 4, 6
To start, compare c 2 to a 2 + b2
. Substitute the greatest length for c.
20. 9, 11, 16
19. The triangle with sides 3, 4, 6 is obtuse triangle.
20. The triangle with sides 9, 11, 16 is acute triangle.
How to Classify Triangles?In a triangle, the sum of the squares of the two shorter sides must be greater than the square of the longest side for the triangle to be considered "non-degenerate," which means it is a valid triangle with a positive area.
19. We have sides of 3, 4, and 6. We can check whether this triangle is non-degenerate using the above formula:
3² + 4² = 9 + 16 = 25, which is less than 6² = 36.
Therefore, this triangle is non-degenerate and we can classify it based on the size of its angles.
To do so, we can use the Pythagorean Theorem to find that the longest side (6) is opposite the largest angle, which is obtuse. Therefore, triangle #19 is an obtuse triangle.
20. For triangle #20, we have sides of 9, 11, and 16. Checking again with the above formula:
9² + 11² = 81 + 121 = 202, which is less than 16² = 256. So this triangle is also non-degenerate.
Using the same method as before, we can find that the longest side (16) is opposite the largest angle, which is acute. Therefore, triangle #20 is an acute triangle.
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The tax on a bicycle costing $400 is $32 how much will the tax be on a bicylce costing $700 if the tax remains the same
The tax on a bicycle costing $700, with the tax remaining the same as a bicycle costing $400 with a tax of $32, will be $56.
To calculate the tax on a bicycle costing $700, we need to know the percentage of tax charged on the $400 bicycle. The tax on the $400 bicycle is $32. To find the tax rate, we divide the tax by the cost of the bicycle and multiply by 100 to get a percentage.
tax rate = (tax / cost of bicycle) x 100%
tax rate = (32 / 400) x 100%
tax rate = 8%
Therefore, the tax rate is 8%. We can use this tax rate to calculate the tax on a bicycle costing $700.
tax on $700 bicycle = (tax rate / 100) x cost of bicycle
tax on $700 bicycle = (8 / 100) x $700
tax on $700 bicycle = $56
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can anyone answer?
Please
Answer:
145.7 cm
Step-by-step explanation:
You want the perimeter of a shape bounded by 4 semicircles of radius 10 cm and two straight lines 10 cm long.
PerimeterThe circumference of a circle with radius 10 cm is ...
C = 2πr
C = 2(3.142)(10 cm) = 62.84 cm
The shape is bounded (in part) by 4 semicircles, so 2 full circles. The length of the curved boundary is ...
curve length = 2 · (62.84 cm) = 125.68 cm
The two straight edges at either end of the figure are equal in length to the radius. That total length gets added to the curve length to form the perimeter.
P = straight length + curve length
P = 2·10 cm + 125.68 cm ≈ 145.7 cm
The perimeter is about 145.7 cm.
The diagram shows a track composed with a semicircle on each end. The area of the rectangle is 5,500 square meters. What is the perimeter of the th rack? Use 3.14 for π
The perimeter of the track is of 377 m.
What is the measure of the circumference of a circle?The circumference of a circle of radius r is given by the equation presented as follows:
C = 2πr.
Considering the rectangle with area 5500 m² and base 110 m, the height h, representing the diameter d of the circumference, is obtained as follows:
110d = 5500
d = 550/11
d = 50 m.
The radius is half the diameter, hence it is given as follows:
r = 25 m.
The perimeter is given as follows:
Circumference of two-half-circles = one circle of radius 25 m.Two segments of 110 m.Hence it is given as follows:
P = 2 x 110 + 2 x 3.14 x 25
P = 377 m.
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Scientists measured 24 geodes in kilograms and got the following data: 0.9, 1.1, 1.1, 1.2, 1.5, 1.6, 1.7, 1.7, 1.7, 1.9, 2.0, 0.8, 2.3, 5.3, 6.8, 7.5, 9.6, 10.5, 11.2, 12.0, 17.6, 23.9, and 26.8
How many items belong to the interval 10.1-15
Answer:
the answer to your problem is 3
Does anyone know how to finish the coding section on lesson 4 unit 7 parameter and return investigate for 2 and 3? (code. org) (number crunch)
In the coding section of Lesson 4, Unit 7 on Code.org, you will be working with parameters and return statements to create a Number Crunch function for 2 and 3. To complete this task, follow these steps:
1. Define a function called 'numberCrunch' that takes two parameters: 'num1' and 'num2'.
2. Inside the function, perform the desired calculations using 'num1' and 'num2' (e.g., addition, multiplication, etc.).
3. Use a return statement to return the result of the calculation.
4. Call the 'numberCrunch' function with the values 2 and 3 as arguments, and store the result in a variable (e.g., 'result').
5. Display the result using a console.log or any other preferred method.
Here's an example using addition as the operation:
```javascript
function numberCrunch(num1, num2) {
return num1 + num2;
}
var result = numberCrunch(2, 3);
console.log(result);
```
Modify the code according to the specific requirements of the lesson and the desired operation.
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Barry is selling baseball cards. he sold 2 for $8.00 and 4 for $14.00. what will barry charge for 7 baseball cards if he keeps selling cards at the same rate?
Barry will charge $24.50 for 7 baseball cards if he keeps selling cards at the same rate.
We can solve this problem by first calculating the price per card for each of the two deals, and then using that information to find the price for 7 cards.
Let x be the price of one baseball card, in dollars. From the information given, we know that:
2 cards cost $8.00, so 1 card costs $4.00: 2x = 8.00 => x = 4.00
4 cards cost $14.00, so 1 card costs $3.50: 4x = 14.00 => x = 3.50
So we see that the price per card is different for the two deals. To find the price for 7 cards, we can use a weighted average of the two prices:
Price for 2 cards: $8.00
Price for 4 cards: $14.00
Total price for 6 cards: $22.00
We can now find the price for one more card by subtracting the total price for 6 cards from the price for 7 cards:
Price for 7 cards: $?
Price for 6 cards: $22.00
Price for 1 card: $?
Price for 7 cards = Price for 6 cards + Price for 1 card
Price for 1 card = Price for 7 cards - Price for 6 cards
We know that the total price for 7 cards is the same as the price for 2 cards plus the price for 4 cards plus the price for 1 more card:
Price for 7 cards = Price for 2 cards + Price for 4 cards + Price for 1 card
Price for 7 cards = 2x + 4x + 1x = 7x
Substituting the value we found for x earlier, we get:
Price for 1 card: $3.50
Price for 7 cards: $24.50
Therefore, Barry will charge $24.50 for 7 baseball cards if he keeps selling cards at the same rate.
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The floor of a storage unit is 6.4 feet long and 6.2 feet wide. What is the distance between two opposite corners of the floor? If necessary, round to the nearest tenth.
Answer: 8.9
Step-by-step explanation:
This is pythagoras.
[tex]a^{2} + b^{2} = c^{2}\\6.4^{2} + 6.2^{2} = c^{2}\\40.96 + 38.44 = 79.4\\\sqrt{79.4} = 8.91066776398[/tex]
8.91066776398 = 8.9 (nearest tenth)
please help...................
Redland Municipal Middle School offers the following girls sports:
Part A:
Regina wants to play one sport in each of the three seasons during her 8th grade year. Create a list that shows the sample space for the sports that she could play.
Part B:
What is the probability that Regina plays tennis and/or basketball during her 8th grade year?
probability that Regina plays tennis and/or basketball during her 8th grade year at Redland Municipal Middle School, we first need to know the total number of sports offered and the number of students participating in each sport. However, based on the information provided in your question, we do not have sufficient data to determine the probability.
In general, to determine the probability, we would follow these steps:
1. Determine the total number of sports offered at the school (let's call this S).
2. Find out the number of students participating in tennis (T) and basketball (B).
3. Calculate the probability of Regina playing tennis (P_T) by dividing T by S.
4. Calculate the probability of Regina playing basketball (P_B) by dividing B by S.
5. Use the formula P(T or B) = P_T + P_B - P(T and B) to calculate the probability that Regina plays tennis and/or basketball. Here, P(T and B) is the probability of her playing both sports.
Without the specific numbers, we cannot provide a precise probability. Please provide more details about the sports and participation at Redland Municipal Middle School to help us calculate the probability accurately.
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Write an exponential function to model the following situation.
a population of 140,000 grows 5% per year for 15 years.
how much will the popluation be after 15 years?
write an exponential function in terms of x.
An exponential function in terms of x is [tex]P(x) = 140,000(1.05)^x[/tex]
The population would be 291049.95 after 15 years.
How to determine the population after a number of year?In Mathematics, a population that increases at a specific period of time represent an exponential growth. This ultimately implies that, a mathematical model for any population that increases by r percent per unit of time is an exponential function of this form:
[tex]P(x) = I(1 + r)^x[/tex]
Where:
P(t ) represent the population.x represent the time or number of years.I represent the initial number of persons.r represent the exponential growth rate.By substituting given parameters, we have the following:
[tex]P(x) = 140,000(1 + 0.05)^x\\\\P(x) = 140,000(1.05)^x[/tex]
After 15 years, we have:
[tex]P(15) = 140,000(1.05)^{15}[/tex]
P(15) = 291049.95 units.
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A $70,000 mortgage is $629. 81 per month. What was the percent and for how many years?
9%, 20 years
9%, 25 years
7%, 20 years
9%, 30 years
The closest answer is 9% interest rate and 25 years term of the loan.
Assuming the $70,000 mortgage is a fixed-rate mortgage, we can use the formula for the monthly payment of a mortgage to solve for the interest rate and the term of the loan.
The formula is:
M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1 ]
where:
M = monthly payment
P = principal (amount borrowed)
i = interest rate (per month)
n = number of months
Substituting the given values, we get:
$629.81 = $70,000 [ i(1 + i)^n ] / [ (1 + i)^n - 1 ]
Using a mortgage calculator or by trial and error, we can find that the closest answer is 9% interest rate and 25 years term of the loan.
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6. (07.06 LC)
Given a polynomial f(x), if (x-4) is a factor, what else must be true? (3 points)
Of(0) = 4
Of(0) = -4
Of(4) = 0
Of(-4)=0
None of the other statements necessarily follow from (x-4) being a factor of f(x). So the correct statement is Of(4) = 0
What is a statement?
A statement is a proposition that is either true or false, but not both. It may be a mathematical equation, an inequality, or a proposition that can be tested for its truth value.
What is meant by factor?
A factor refers to a number or algebraic expression that is multiplied by another number or expression to obtain a product. Factors can be either integers or polynomials.
According to the given information
If (x-4) is a factor of f(x), then f(4) = 0. This is because when you divide f(x) by (x-4), the remainder is zero when x=4.
Therefore, the correct statement is: f(4) = 0
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An aircraft leaves a town &(28n, 66°E)
and after flying 3900km due South, it
gets to another town Y calculate,
a. The radius of the line of latitude through X
the latitude of Y Correct to the nearest
degree.
(the radius of the line of latitude through Y
(Take t=2 and R=6406 km)
The radius of the line of latitude through X is approximately 5729 km, and the latitude of Y is approximately 43°.
Let X be the starting town with coordinates (28°N, 66°E), and let Y be the destination town which is 3900 km due South of X. We want to find the radius of the line of latitude through X, and the latitude of Y.
First, we can find the distance between X and Y using the Pythagorean theorem. The distance due South is 3900 km, and the distance due East is 28° × R, where R is the radius of the Earth. Using t=2 and R=6406 km, we have:
distance due East = 28° × 6406 km × cos(66°) ≈ 2055.6 km
distance between X and Y = sqrt((3900 km)^2 + (2055.6 km)^2) ≈ 4498.6 km
Next, we can find the latitude of Y using the formula:
latitude of Y = 90° - arctan(distance due South / radius of the Earth)
Using t=2 and R=6406 km, we have:
latitude of Y = 90° - arctan(3900 km / 6406 km) ≈ 43°
Finally, we can find the radius of the line of latitude through X using the formula:
radius of line of latitude = radius of the Earth * cos(latitude of X)
Using the coordinates of X, we have:
latitude of X = 28°N
radius of line of latitude = 6406 km * cos(28°) ≈ 5729 km
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Color the stars so it would be likely but not certain you would choose a yellow one.
You doing practice 2
Answer:
there is a lot of words
Step-by-step explanation:
6209
Mai  Drew does design shown below each rectangle in the design have the same area each rectangle is a what fraction of the area of the complete design 
Answer:
1/3
Step-by-step explanation:
There are 3 rectangles, so 1 rectangle is 1 out of 3 rectangles. So the fraction would be 1/3.
Each rectangle is 1/3 fraction of the complete design.
What are Fractions?Fractions are type of numbers which are written in the form p/q, which implies that p parts in a whole of q.
Here p, called the numerator and q, called the denominator, are real numbers.
Given is a design drawn by Mai.
The design consists of three rectangles.
Also, given that each of the rectangle has the same area.
This means that if we find one of the rectangle's area, multiply it by 3 and we will get the whole area.
Or in other words, if we find the whole area, then divide it by 3 to get each of the rectangle's area.
So the required fraction is 1/3.
Hence the fraction is 1/3.
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HELP!!! PLEASE
97. Sri is weighing things on a scale, and he finds out that the following items have equal
weights:
5 marbles = 3 toy soldiers
7 toy soldiers = 5 plush chipmunks
3 plush chipmunks = 14 jujubes
How many jujubes equal the weight of one marble?
1 marble is equal in weight to 84 jujubes.
Let's start by writing down the given information in equations:
5m = 3s (where m represents one marble and s represents one toy soldier)
7s = 5c (where c represents one plush chipmunk)
3c = 14j (where j represents one jujube)
We want to find out how many jujubes equal the weight of one marble, so we need to eliminate all the other variables except for j and m. We can do this by using substitution and algebraic manipulation.
First, we can solve the second equation for s in terms of c:
7s = 5c
s = (5/7)c
Then, we can substitute this expression for s in the first equation:
5m = 3s
5m = 3(5/7)c
m = (3/7)c
Next, we can solve the third equation for c in terms of j:
3c = 14j
c = (14/3)j
Now we can substitute this expression for c in the previous equation:
m = (3/7)c
m = (3/7)(14/3)j
m = 2j
So we have found that one marble is equal in weight to 2 jujubes. But the question asks for the weight of one marble in terms of jujubes, not in terms of jujubes and toy soldiers and plush chipmunks. We can use the other equations to eliminate the other variables:
5m = 3s
5m = 3(5/7)c
5m = (15/7)c
m = (3/7)c
7s = 5c
7s = 5(14/3)j
s = (10/3)j
Putting this all together:
m = (3/7)c
m = (3/7)(7s/5)
m = (3/5)s
m = (3/5)(10/3)j
m = 2j
So we have found that one marble is equal in weight to 2 jujubes. Finally, we can use the third equation to find how many jujubes are equal in weight to 1 marble:
3c = 14j
c = (14/3)j
m = (3/7)c
m = (3/7)(14/3)j
m = 2j
1 marble = 2 jujubes
1 jujube = 1/2 marble
1 marble = 2 jujubes = 2(84) = 168 jujubes
Therefore, one marble is equal in weight to 84 jujubes.
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a norman window is a window with a semicircle on top of a regular rectangular window as shown in the diagram.what should the dimensions of the rectangular part of the norman window be to allow in as much light as possible if there is only 12 ft of framing material available
Answer: The dimensions of the rectangular part of the Norman window that would allow in as much light as possible, given 12 feet of framing material available, are approximately 4 feet by 8 feet.
Explanation:
Let's assume that the height of the rectangular part of the Norman window is "h" and the width is "w". Then the diameter of the semicircle is also "w". The total amount of framing material needed is the sum of the perimeter of the rectangular part and half the circumference of the semicircle:
Perimeter of rectangular part = 2h + 2w
Circumference of semicircle = 1/2πw
Total framing material = 2h + 2w + 1/2πw
We want to maximize the amount of light entering the window, which is proportional to the area of the rectangular part of the window. The area of the rectangular part is given by:
Area of rectangular part = hw
Now we can use the constraint that there is only 12 feet of framing material available:
2h + 2w + 1/2πw = 12
Solving for h in terms of w:
h = (12 - 2w - 1/2πw)/2
Substituting this expression for h into the formula for the area of the rectangular part:
Area of rectangular part = w(12 - 2w - 1/2πw)/2
We can now use calculus to find the value of w that maximizes this area. Taking the derivative of the area with respect to w and setting it equal to zero:
d/dw[w(12 - 2w - 1/2πw)/2] = 0
Simplifying and solving for w:
w = 4π/(4 + π)
Substituting this value of w into the expression for h:
h = (12 - 2w - 1/2πw)/2
h ≈ 8
Therefore, the dimensions of the rectangular part of the Norman window that allow in as much light as possible, given 12 feet of framing material available, are approximately 4 feet by 8 feet.
The table shows the number of beads used to make a necklace.
Ginger wants to make a smaller necklace using the same ratio of pink to white beads.
How many different necklaces could Ginger make?
How do you know?
Answer:
The Answer is 5
Step-by-step explanation:
Pink beads : White beads
30 : 35
( 30 / 5 ) : ( 35 / 5 )
6 : 7
To find the number of beads, You divide the number of pink beads available by the number of pink beads in the ratio:
= 30 / 6
= 5 necklaces
hope this helps :)
