The interval where y increases for the function f(x) = (4x² - 1)/(x² + 1) is (-∞, -0.5) U (0.5, ∞) is 0.5-(-∞) = ∞.
To find the intervals where the function f(x) = (4x² - 1)/(x² + 1) increases, we need to find its derivative and determine its sign. The derivative of f(x) can be found using the quotient rule:
f'(x) = [(8x)(x² + 1) - (4x² - 1)(2x)]/(x² + 1)²
Simplifying this expression, we get:
f'(x) = (12x - 4x³)/(x² + 1)²
To find the critical points, we need to solve the equation f'(x) = 0:
12x - 4x³ = 0
4x(3 - x²) = 0
This gives us the critical points x = 0 and x = ±√3. We can now test the intervals between these critical points to determine the sign of f'(x) in each interval.
Testing x < -√3, we choose x = -4, and we get f'(-4) = (-224)/(17²) < 0. Therefore, f(x) is decreasing on this interval.
Testing -√3 < x < 0, we choose x = -1, and we get f'(-1) = (16)/(2²) > 0. Therefore, f(x) is increasing on this interval.
Testing 0 < x < √3, we choose x = 1, and we get f'(1) = (16)/(2²) > 0. Therefore, f(x) is increasing on this interval.
Testing x > √3, we choose x = 4, and we get f'(4) = (-224)/(17²) < 0. Therefore, f(x) is decreasing on this interval.
Hence, the interval where f(x) increases is (-∞, -0.5) U (0.5, ∞). Therefore, the answer is 0.5 - (-∞) = ∞.
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Eva signs up for dance classes. She pays a onetime registration fee and then the same monthly tuition. Eva pays $110 the first month and at the end of 9 months has paid $670 in all. Which equation can be used to model the tuition and registration fees?
Answer: (670 -110)/8
Step-by-step explanation:
Months: 110 the first month
*Now since she paid 670 in total she subtracts the 110 from the first month which is 560, and now there is an event amound paid in the other months so you divide 560 by 8 since 8 months are left over resulting in $70 each month.
January,
February,
March,
April,
May,
June,
July,
August,
The faces of a rectangular prism have areas of 9, 9, 25, 25, 49, and 49 square meters. Find the volume of the rectangular prism, in cubic meters
The volume of the rectangular prism is 105 cubic meters.
To find the volume of the rectangular prism, we can use the formula V = lwh, where V is the volume, l is the length, w is the width, and h is the height.
Since there are three pairs of congruent faces, we can deduce that the areas of the three pairs of faces represent the three dimensions of the rectangular prism. The areas are 9, 25, and 49 square meters, which are the squares of the sides' lengths.
Take the square root of each area to find the corresponding side lengths:
√9 = 3 meters
√25 = 5 meters
√49 = 7 meters
Now, apply the formula to find the volume:
V = lwh = 3 × 5 × 7 = 105 cubic meters.
The volume of the rectangular prism is 105 cubic meters.
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Problem 68 An outdoor adventure club has 35 members, who are all either rock climbers or skiers. There are 3 more rock climbers than
there are skiers. How many climbers are there?
WHOEVER ANSWERS FIRST GETS BRAINLIEST AND ANSWER FAST FOR WHOEVER GOTS THE HIGHEST BRAILIEST I WILL GIVE THEM THE BRAINLIEST POINT
Answer: 14.5 climbers technically 14 because 1/2 a person is wrong
Step-by-step explanation:
Pls help. And please actually answer the question
Answer: y= |x-1| -1
Step-by-step explanation:
Explanation:
This is an absolute value function.
The parent function looks like: y=|x| When transformations take place, we use this function to describe those transformations:
y = a|x-h|+k
where (h, k) is your new vertex
"a" is your stretch
and a - would be placed in the front if there was a reflection
Solution:
Your equation has a new vertex at (1, -1)
There is no stretch and no reflection
Plug into equation:
y= |x-1| -1
Add. Hint: Use the place value blocks to help solve
8
+
7
8+78, plus, 7. 8
+
7
=
8+7=start color #0c7f99, 8, end color #0c7f99, plus, start color #ca337c, 7, end color #ca337c, equals
The answer of addition is 94.
What is addition?The phrase "the addition" refers to combining two or more numbers. Adding two numbers is indicated by the plus sign (+), therefore adding three is written as three plus three.
To add 8 and 78, we can start by adding the ones place digits, which are 8 and 7.
8 + 7 = 15
Since 15 is greater than 10, we need to regroup 10 ones as 1 ten and carry it over to the tens place. We can represent this with place value blocks by moving a rod of 10 ones from the ones place to the tens place.
So we have:
8
+78
---
```
8
+78
---
16 (write 6 in the ones place and carry 1 to the tens place)
```
Now we can add the tens place digits, which are 1 (carried over) and 8:
1 + 8 = 9
So the final result is:
8
+78
-----
86
Therefore, 8 plus 78, plus 7 is:
```
8
+78
+ 7
---
94
```
So the answer of addition is 94.
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Please answer the question correctly and neatly. Please find the
exact answer. Will upvote if correct.
Find the volume of the solid obtailed by rotating the region bounded by the given curves about the specified axis. y= x, y = 1 about y = 3
The region bounded by the given curves is a triangle with vertices at (0,0), (1,1), and (1,0). When this region is revolved around the line y=3, we obtain a solid with a hole in the middle.
To find the volume of this solid, we can use the method of cylindrical shells. Imagine slicing the solid into thin cylindrical shells with radius r and height Δy. The volume of each shell is approximately 2πrΔy times the thickness of the shell.
The distance between the axis of rotation (y=3) and the line y=1 is 2 units. Therefore, the radius of each cylindrical shell is r = 3 - y. The height of each shell is Δy = dx, where x is the distance from the y-axis.
To set up the integral, we need to express x in terms of y. Since the region is bounded by y=x and y=1, we have x=y for 0<=y<=1. Therefore, the integral for the volume of the solid is:
V = ∫[0,1] 2π(3-y)x dx
= 2π ∫[0,1] (3-y)y dx
Evaluating this integral, we get:
V = 2π [3y^2/2 - y^3/3] from 0 to 1
= 2π (3/2 - 1/3)
= 2π/3
Therefore, the volume of the solid obtained by rotating the region bounded by y=x, y=1 about y=3 is (2/3)π cubic units.
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(co 4) from a random sample of 85 teens, it is found that on average they spend 31.8 hours each week online with a population standard deviation of 5.91 hours. what is the 90% confidence interval for the amount of time they spend online each week?
The 90% confidence interval for the amount of time that teens spend online each week is (30.761, 32.839) hours
To find the 90% confidence interval for the amount of time that teens spend online each week, we can use the following formula
CI = x ± z*(σ/√n)
where
x is the sample mean
σ is the population standard deviation
n is the sample size
z is the z-score associated with the desired confidence level
In this case, we have
x = 31.8 hours
σ = 5.91 hours
n = 85
z = 1.645 (for a 90% confidence level, using a z-table or calculator)
Plugging in these values, we get
CI = 31.8 ± 1.645*(5.91/√85)
Simplifying, we get
CI = 31.8 ± 1.039
We can interpret this interval as saying that if we were to take many random samples of 85 teens and compute the confidence interval for each sample, about 90% of these intervals would contain the true population mean.
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The box plots show a summary of push–up scores for Group A and Group B in the same gym class. Both groups have the same number of students. Determine whether each statement is true based on these box plots. Select True or False for each statement. True False At least 50% of students in each group scored more than 165 push–ups. The median score of push–ups of Group A is 10 points greater than the median score of push–ups of Group B. The scores of Group A have less variability than the scores of Group B
Statement 2 is false because while the median score of Group A is higher than Group B, it is not 10 points greater as claimed.
Statement 1 is false because the box plots provide limited information, making it impossible to determine whether at least 50% of students in each group scored more than 165 push-ups.
Statement 3 is false because Group A has more variability in push-up scores than Group B, as indicated by the larger interquartile range (IQR) of Group A.
Looking at the box plots, we can see that the median score of Group A is higher than Group B, but it is not 10 points greater. Therefore, statement 2 is False.
We cannot determine whether at least 50% of students in each group scored more than 165 push-ups. The box plots only show us the quartiles and the minimum and maximum values, so we do not know the exact number of students who scored above 165 push-ups. Therefore, statement 1 is False.
The interquartile range (IQR) of Group A is greater than the IQR of Group B, indicating that Group A has more variability in push-up scores than Group B. Therefore, statement 3 is False.
Hence, All the statement are False.
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I need help finding the decimal for these equations.
Answer:
Carlos=1.5041
Mykala=2.6991
William=4.1350
Emily=4.1773
Small baskets of tomatoes are sold at a vegetable stand for $3 per basket. Large
baskets of tomatoes are sold at the stand for $5 per basket. Only whole numbers of
baskets may be purchased.
A customer purchases a total of 8 baskets of tomatoes and pays $36.
A. Write and solve a system of equations that models the number of small
baskets (x) and the number of large baskets () that the customer purchases.
Show or explain all your work.
The customer purchased 2 small baskets and 6 large baskets.
Let x be the number of small baskets and y be the number of large baskets that the customer purchases.
We can set up a system of two equations based on the information given:
Equation 1: x + y = 8 (The total number of baskets purchased is 8)
Equation 2 3x + 5y = 36: (The total amount paid for the baskets is $36)
To solve this system, we can use either substitution or elimination method.
Using substitution method:
From Equation 1, we have x = 8 - y.
Substitute this into Equation 2:
3(8 - y) + 5y = 36
24 - 3y + 5y = 36
2y = 12
y = 6
Now, we can substitute y = 6 back into Equation 1 to find x:
x + 6 = 8
x = 2
Therefore, the customer purchased 2 small baskets and 6 large baskets.
Using elimination method:
We can multiply Equation 1 by 3 and subtract it from Equation 2 to eliminate x:
3x + 5y = 36
- (3x + 3y = 24)
2y = 12
y = 6
Now, we can substitute y = 6 back into either Equation 1 or Equation 2 to find x. Let's use Equation 1:
x + 6 = 8
x = 2
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James weighs 8712 pounds. he has 2 dogs that each weigh 1314 pounds. how many more pounds does james weigh than both of his dogs combined?
James weighs 6084 more pounds than both of his dogs combined.
To find out how many more pounds James weighs than both of his dogs combined, we first need to calculate the total weight of the dogs. Since he has two dogs that weigh 1314 pounds each, we can find the total weight of the dogs by multiplying 1314 by 2, which gives us 2628 pounds.
Next, we can add the weight of both dogs together to get the total weight of the dogs, which is 2628 pounds. We can then subtract the weight of the dogs (2628 pounds) from James' weight (8712 pounds) to find out how many more pounds James weighs than both of his dogs combined.
Therefore, James weighs 6084 more pounds than both of his dogs combined. This can be calculated by subtracting the weight of the dogs (2628 pounds) from James' weight (8712 pounds), which gives us 6084 pounds.
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¿Como la gastronomia puede ayudarnos a convivir armoniosamente?
Gastronomy is a way of promoting understanding among different cultures, and of bringing people and traditions closer together.
The practise of choosing, preparing, presenting, and consuming exquisite cuisine. The foundation of gastronomy lies in the connections between food, culture, and tradition. Gastronomy has emerged through time as a more potent cultural force than language or other influences among the peoples of the world.
Molecular gastronomy is a relatively recent branch of science that studies the physical and chemical changes that take place during cooking. Molecular cuisine is the name of the new culinary movement based on this emerging discipline.
Nowadays, the world may be broken down into separate gastronomic zones, where different cuisines are popular and similar cooking techniques are used. Throughout much of Southeast Asia, rice is the main food. The abundant and creative use of spices to give meals an extra flavour is what makes Indian and Indonesian cuisine unique. The prevalent ingredient in Mediterranean recipes is olive oil.
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Complete question:
How can gastronomy help us live harmoniously?
Barak is going to buy 550 nails from one of these companies.
Nail Company
50 nails
£4. 15 plus VAT at 20%
Hammer Company
25 nails
£2. 95
Special offer
Buy 100 get 25 free
He wants to buy the nails at the cheaper cost.
Where should he buy the nails, from the Nail Company or the Hammer Company?
Barak should buy the nails from the Hammer Company as it is cheaper than buying from the Nail Company.
Let's first calculate the cost of buying 550 nails from each company:
Nail Company:
Cost of 1 nail = £4.15 + (20% of £4.15) = £4.15 + £0.83 = £4.98 (rounded to 2 decimal places)
Cost of 50 nails = £4.98 x 50 = £249
Cost of 550 nails = £249 x 11 = £2739
Hammer Company:
Cost of 1 nail = £2.95/25 = £0.118 (rounded to 3 decimal places)
Cost of 75 nails (buy 100 get 25 free) = 100 x £0.118 x 3 = £35.40
Cost of 550 nails = 550 x £0.118 = £64.90
Therefore, Barak should buy the nails from the Hammer Company as it is cheaper than buying from the Nail Company.
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T and I Construction is paving a rectangular-shaped parking lot with Hot Asphalt Mix. The parking lot is 100 yards by 44 yards and will have a 9-inch base. If the Hot Asphalt Mix has a density of 140 pounds per cubic foot, about how many tons of mix will be needed to pave the parking lot?
A. ) 77
B. ) 91
C. ) 2079
D. ) 2772
The approximate amount of Hot Asphalt Mix needed to pave the parking lot is 2772 tons. (D)
To calculate the required amount of Hot Asphalt Mix, follow these steps:
1. Convert the dimensions of the parking lot to feet: 100 yards x 3 (feet/yard) = 300 feet and 44 yards x 3 (feet/yard) = 132 feet.
2. Convert the base thickness to feet: 9 inches / 12 (inches/foot) = 0.75 feet.
3. Calculate the volume of the parking lot: 300 feet x 132 feet x 0.75 feet = 29,700 cubic feet.
4. Find the weight of the Hot Asphalt Mix: 29,700 cubic feet x 140 pounds/cubic foot = 4,158,000 pounds.
5. Convert the weight to tons: 4,158,000 pounds / 2000 (pounds/ton) = 2079 tons.
However, the answer options provided do not match the calculated value of 2079 tons. In this case, the closest answer would be option D, 2772 tons.
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Prove the following two properties of the Huffman encoding scheme. (a) If some character occurs with frequency more than 2=5, then there is guaranteed to be a codeword of length 1. (b) If all characters occur with frequency less than 1=3, then there is guaranteed to be no codeword of length 1
(a) Since the character occurs with a frequency higher than 2=5, it is guaranteed to be merged with another character with the same frequency or a lower frequency. Therefore, there is guaranteed to be a codeword of length 1 for this character. (b) Since all symbols occur with a frequency less than 1=3, the root of the tree will have a frequency less than 1=3. Therefore, there is guaranteed to be no codeword of length 1 for any symbol in this case.
(a) Let's assume that some character occurs with frequency more than 2=5.
The two nodes with the lowest frequency are merged into a single node, with the sum of their frequencies as the frequency of the new node.
This process is repeated until all the nodes are merged into a single node, which becomes the root of the tree.
Since the character occurs with a frequency higher than 2=5, it is guaranteed to be merged with another character with the same frequency or a lower frequency.
Therefore, there is guaranteed to be a codeword of length 1 for this character.
(b) Let's assume that all characters occur with frequency less than 1=3.
Consider the binary tree created by the Huffman algorithm. The root of the tree corresponds to the least frequent symbol, which will be assigned the longest codeword.
Since all symbols occur with a frequency less than 1=3, the root of the tree will have a frequency less than 1=3.
This means that the corresponding codeword for the root will be longer than 1 bit. Therefore, there is guaranteed to be no codeword of length 1 for any symbol in this case.
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Write two numbers that multiply to the value on top and add to the value on bottom.
Answer:
-17 and -5
Step-by-step explanation:
-5 x -17 = 85
-5 + -17 = -22
Can you find continuous function & so that when an = f(n) we have SIGMA an = ∫ f(x)dx
[tex]SIGMA an = 1 + 2 + 3 + ... + n = n(n+1)/2 = ∫_1^n f(x)dx = ∫ f(x)dx[/tex]
f(x) = x is indeed a continuous function that satisfies the given condition.
Yes, we can find a continuous function f(x) such that when an = f(n), we have SIGMA an = ∫ f(x)dx.
One such function is f(x) = x.
To see why this works, let's consider a few terms of the series SIGMA an.
When n = 1, we have a1 = f(1) = 1, so the series starts with 1.
When n = 2, we have a2 = f(2) = 2, so the series becomes 1 + 2. When n = 3, we have a3 = f(3) = 3, so the series
becomes 1 + 2 + 3. And so on.
Notice that this series is just the sum of the first n positive integers, which we know is equal to n(n+1)/2.
But if we take the derivative of f(x) = x, we get f'(x) = 1, which means that the integral of f(x) from 1 to n is just n.
So we have:
[tex]∫ f(x)dx = ∫ xdx = 1/2 x^2 + C[/tex]
[tex]∫_1^n f(x)dx = (1/2 n^2 + C) - (1/2 (1)^2 + C) = 1/2 n^2 - 1/2[/tex]
And therefore:
[tex]SIGMA an = 1 + 2 + 3 + ... + n = n(n+1)/2 = ∫_1^n f(x)dx = ∫ f(x)dx[/tex]
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Caleb has
coins (nickels, dimes, and quarters) in a jar, totaling. He has three more nickels than dimes. How many quarters does Caleb have?
Caleb has 30 quarters.
What is arithmetic?
Mathematical arithmetic is the study of the properties of the standard operations on numbers, such as addition, subtraction, multiplication, division, exponentiation, and root extraction.
Here, we have
Given: Caleb has 51 coins (nickels, dimes, and quarters) in a jar, totaling $9. He has three more nickels than dimes.
We have to find out how many quarters Caleb has.
Let x be nickel,
y be dimes and
z be quarters
x + y + z = 51.....(1)
1 quartes = 25 cents
1 dimes = 10 cents
1 nickel = 5 cents
Now, the total dollar is $9,
5x/100 + 10y/100 + 25z/100 = 9
5x + 10y + 25z = 900
x + 2y + 5z = 180....(2)
and
y + 3 = x...(3)
Solving equation(1) and (2), we get
From (1)
x + x-3 + z = 51
2x + z = 54....(4)
From (2)
x + 2(x -3) + 5z = 180
3x + 5z = 186...(5)
Now, by solving equations (4) and (5), we get
x = 12
z = 30
Now,
y + 3 = x
y + 3 = 12
y = 9
Hence, Caleb has 30 quarters.
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Which is true about the relationship between 1 inch and 1 foot?
A. 1 inch is 12 times as long as 1 foot. B. 1 foot is 12 times as long as 1 inch. C. 1 foot is 6 times as long as 1 inch. D. 1 inch is 6 times as long as 1 foot
Option B is true about the relationship between 1 inch and 1 foot.
What is conversation?
A unit's use depends on the context; for example, a room's area is expressed in meters, yet a pencil's length and thickness are expressed in centimeters and millimeters, respectively. Therefore, converting one unit to another is necessary. We must first understand the link between units in order to comprehend the concept of unit conversion. When addressing many problems in mathematics, unit conversion is necessary. Mathematical conversions are necessary to perform the necessary calculations.
There are 12 inches in 1 foot. This means that 1 foot is 12 times longer than 1 inch. Therefore, option B is correct. Option A is incorrect because it states that 1 inch is 12 times as long as 1 foot, which is the opposite of the correct relationship. Option C is incorrect because it states that 1 foot is 6 times as long as 1 inch, which is half of the correct relationship. Option D is incorrect because it states that 1 inch is 6 times as long as 1 foot, which is the opposite of the correct relationship.
Hence, Option B is true about the relationship between 1 inch and 1 foot.
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One tire manufacturer claims that his tires last an average of 44000 miles with a standard deviation of 7650 miles. A random sample of 120 of his tires is taken. What is the probability that the average of this sample of tires will last longer than 45000 miles
The probability of a randomly selected tire from this sample having a lifespan greater than 45,000 miles is approximately 0.0639 or 6.39%.
We can use the central limit theorem to approximate the distribution of the sample mean.
In this case, the population mean is 44,000 miles and the population standard deviation is 7,650 miles. We are taking a sample of 120 tires, so the standard deviation of the sample mean is:
σ/√n = 7,650/√120 = 698.68
To find the probability that the sample mean will be longer than 45,000 miles, we need to standardize the sample mean using the formula:
z = (x - μ) / (σ / √n)
where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
Plugging in the values, we get:
z = (45,000 - 44,000) / (7,650 / √120) = 1.527
We can then look up the probability corresponding to a z-score of 1.527 in a standard normal distribution table or using a calculator. The probability of a randomly selected tire from this sample having a lifespan greater than 45,000 miles is approximately 0.0639 or 6.39%.
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put the measuraments from greatest to least
The measurements from greatest to least would be ordered as follows:
6 yards 2 1/2 feet 45 inchesHow to order the measurements ?First, we need to convert all the units to the same unit. Let's convert everything to inches, since that is the smallest unit.
6 yards = 6 x 3 = 18 feet
18 feet = 18 x 12 = 216 inches
2 1/2 feet = 2 x 12 + 6 = 30 inches
So now we have:
6 yards = 216 inches
2 1/2 feet = 30 inches
45 inches = 45 inches
Putting these in order from greatest to least, we have:
216 inches, 45 inches, 30 inches
Therefore, the measurements from greatest to least would be ordered as follows:
6 yards, 45 inches, 2 1/2 feet
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The full question is:
Put the measurements from greatest to least. 45 inches, 6 yards, and 2 1/2 feet
A hot water pipe needs to be insulated to prevent heat loss. The outer pipe has a diameter D = 48.7 cm (correct to 3 significant figures). The inner pipe has a diameter d = 19.25 cm (correct to 2 decimal places). Work out the upper and lower bound of the cross-sectional area of the insulation, A (the shaded area between the inner and outer pipes) in cm2 to the nearest whole number. Give your answer in interval form, using A as the variable.
The upper and lower bound of the cross-sectional area of the insulation, would be A = [ 3129, 3137 ] cm².
How to find the upper and lower bond ?The upper and lower bound of A would be found by the formula :
A = π x ( R ² - r ² )
The upper bound is therefore:
= π x (( 48. 75 / 2) ² - ( 19.2 45 / 2) ²)
= π x ( 1183. 0625 - 184. 857025 )
= π x 998. 205475
= 3, 137 cm²
The lower bound will then be:
= π x ( ( 48. 65 / 2 ) ²- (19. 255 / 2) ²)
= π x ( 1180. 9225 - 184. 963025)
= π x 995. 959475
= 3, 129 cm²
The interval form is therefore A = [ 3129, 3137 ] cm²
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Choose the diagram that shows the graph of the inequality.
Answer: C
Step-by-step explanation:
In 2010, Keenan paid $2,826 in federal income tax, which is 70% less than he paid in 2009. How much did he pay in 2009?
Based on the above, Keenan paid $9,420 in federal income tax in 2009.
What is the income tax?Let X be the amount Keenan paid in taxes in 2009.
According to the problem, Keenan paid 70% less in 2010 than he did in 2009. This means that he paid only 30% of what he paid in 2009, since 100% - 70% = 30%.
We can express this mathematically as:
0.30X = 2,826
To solve for X, we can divide both sides of the equation by 0.30:
X = 2,826 ÷ 0.30
X = 9,420
Therefore, Keenan paid $9,420 in federal income tax in 2009.
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What is 0.50 divided by 0.25
Answer:
2
Step-by-step explanation:
0.50/0.25 = 50/25
= 2
Dividing 0.50/0.25 no. is same as 50/25 when we multultiply by 100/ 100 so it is 2
ans. = 2
0.50 / 0.25
5/10 x 100/5
=2
Calcula los siguientes lÃmites página. 115 ejercicio
a) lim n = +[infinity] infinito 6-4n²
----------
2(n)²
b) lim n = +[infinity] infinito 4n²+3n-2
--------------
2n ³ -4n
c) lim n = +[infinity] infinito 2n ³ -4n
---------------
4n
d) lim x = +[infinity] infinito -8x4 +2
------------
2x² +4
a) Para calcular este límite, podemos dividir tanto el numerador como el denominador por n² y luego aplicar la regla de L'Hôpital:
lim n → ∞ [(6 - 4n²)/(2n²)]
= lim n → ∞ [6/(2n²) - (4n²)/(2n²)]
= lim n → ∞ [3/n² - 2]
= -2
Por lo tanto, el límite es -2.
b) Podemos dividir tanto el numerador como el denominador por n³ para simplificar el límite:
lim n → ∞ [(4n² + 3n - 2)/(2n³ - 4n)]
= lim n → ∞ [(4/n + 3/n² - 2/n³)/(2/n² - 4/n²)]
= lim n → ∞ [(4 + 3/n - 2/n²)/(2 - 4/n)]
= lim n → ∞ [(4n + 3 - 2n²)/(2n² - 4)]
= lim n → ∞ [-2n²/(2n² - 4)]
= -1
Por lo tanto, el límite es -1.
c) Podemos dividir tanto el numerador como el denominador por n³ para simplificar el límite:
lim n → ∞ [(2n³ - 4n)/(4n)]
= lim n → ∞ [(2n² - 4)/(4)]
= lim n → ∞ [(n² - 2)/2]
= +∞
Por lo tanto, el límite es +∞.
d) Podemos dividir tanto el numerador como el denominador por x⁴ para simplificar el límite:
lim x → ∞ [-8x⁴ + 2]/[2x² + 4]
= lim x → ∞ [-8 + 2/x⁴]/[2/x² + 4/x⁴]
= -4/1
= -4
Por lo tanto, el límite es -4.
The tops of two vertical poles of heights 20 m and 15 m joined by a taut wire 12 m long. What is the angle of slope of the wire?
The angle of the tops of two vertical poles of heights 20 m and 15 m joined by a taut wire 12 m long slope of the wire = 24.6 °
Height of the 1st vertical pole = 20m
Height of the second vertical pole = 15m
Difference of their height = 5 m
Length of the taut wire = 12m
Using trigonometry ratio of sin we get
Perpendicular = 5 m
Hypotenuse = 12 m
Sin A = Perpendicular/ hypotenuse
Sin A = 5/12
A = [tex]sin^{-1} (5/12)[/tex]
A = 24.6 °
The angle of slope of the wire = 24.6°
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If r is the annual interest rate of the bank account, then at the end of the year the balance in the account is multiplied by a growth factor of x = 1 + r.
Answer:
Step-by-step explanation:
Yes , that is correct. The growth factor for the balance in the account at the end of the year is calculated by adding 1 to the annual interest rate, which is expressed as a decimal, and multiplying the result by the balance. This gives the formula:
Ending balance = Beginning balance * (1 + r)
where r is the annual interest rate as a decimal.
Davis spent 25 minutes working on math problems. Carl worked on math problems for m fewer minutes.
Drag a number and symbols to represent the amount of time Carl worked on problems.
X
M
25
The amount of time Carl represent is 25-m on the problems.
The statement "Davis spent 25 minutes working on math problems. Carl worked on math problems for m fewer minutes" means that Carl spent some amount of time working on math problems, but that amount is m minutes less than what Davis spent.
To represent the amount of time Carl worked on math problems, we can use the variable X. We know that X is equal to the amount of time Carl worked on math problems, and that X is equal to 25 minus m.
This is because Davis spent 25 minutes on math problems, and Carl worked on them for m fewer minutes. So if we subtract m from 25, we get the amount of time Carl worked on math problems.
Therefore, the equation X = 25 - m represents the amount of time Carl worked on math problems, where X is the amount of time in minutes and m is the number of minutes Carl worked less than Davis.
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Find the coordinates of point P along the directed line segment cap A cap b$AB$AB so that cap A cap p$AP$AP to cap p cap b$PB$PB is the given ratio.
cap A times open paren negative 7 comma negative 5 close paren
The coordinates of point P along the directed line segment AB with a ratio of 1:4 are (-5, -2).
Since the ratio of AP to PB is 1:4, we can use the midpoint formula to find the coordinates of point A. The midpoint formula is
((x₁ + x₂)/2, (y₁ + y₂)/2)
Plugging in the coordinates of points P and B, we get:
((4(-7) - 2)/5, (4(-5) + 0)/5) = (-30/5, -20/5) = (-6, -4)
we can use the point-slope formula to find the equation of the line segment AB:
(y - (-4)) = (1/5)(x - (-6))
Simplifying this equation, we get:
y = (1/5)x + 2
Finally, we can use the given ratio of 1:4 to find the coordinates of point P. Since the ratio of AP to PB is 1:4, we can use the ratio formula to find the coordinates of point P:
(x, y) = (4(-5) + (-2))/5, (4(-2) - (-4))/5) = (-30/5, 12/5) = (-6, 2.4)
Rounding off to one decimal place, we get the coordinates of point P as (-5, -2).
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