Answer:
(g ○ f )(x)
Step-by-step explanation:
(g ○ f )(x) means substitute f(x) into g(x) , that is
g( \(\frac{1}{x-2}\) )
= \(\frac{1}{x-2}\) + 5
Answer:
(g ○ f )(x)
Step-by-step explanation:
The speed(S) of a car varies partly directly as its mass(M) and partly directly as the quantity (Q) of fuel in it. When the speed is 80km/hr, the mass is 220kg and the quantity of fuel is 30litres, when the speed is 60km/hr, the mass is 300kg and the quantity of fuel is 40 litres. Find the volume of fuel if the speed is 100km/hr and the mass 250kg
Answer:
S varies partly directly as M and Q.
S=C.
S=KMQ+C.
For the first one...
speed=80,m=220,Q=30.
80=K20×30+C.
80=600K+C......(I).equation one.
For the second one....
speed=60,m=300,Q=40.
60=K300×40+C.
60=12000K+C.....(ii). equation two.
Minus eqtn(I) from eqtn(ii).
80=600K+C.
- 60=12000K+C.
K=0.01754~0.018.
Substitute K=0.018 into eqtn(I).
80=600K+C
80=600×0.018+C.
80=10.8+C.
C=80-10.8=69.2.
The relation is S=0.018MQ+69.2
when speed is 100 and mass is 250 find the volume.
100=0.018×250×Q+69.2.
100=4.5Q+69.2.
4.5Q=100-69.2
4.5Q=30.8.
Q=30.8/4.5.
Q=6.8~7litres.
What are the Examples of Adding Fractions with Unlike Denominators
2/3 + 1/4 = 11/12
Fractions are very important in many areas such as math, physics, engineering, chemistry and many more, understanding how to add fractions with unlike denominators is a fundamental skill that will help you in many aspects of your life.
Adding fractions with unlike denominators can be a bit tricky, but with the right understanding and techniques, it's definitely doable.
When we add fractions with unlike denominators, we need to first find a common denominator. A common denominator is a number that is a multiple of both denominators. Once we have a common denominator, we can add the fractions as usual by adding the numerators and keeping the denominator the same.
Here are a few examples of adding fractions with unlike denominators:
2/3 + 1/4
We can find a common denominator by finding the least common multiple (LCM) of 3 and 4. The LCM of 3 and 4 is 12.
So, we can convert 2/3 to 8/12 by multiplying the numerator and denominator by 4.
We can convert 1/4 to 3/12 by multiplying the numerator and denominator by 3.
Now we can add the fractions by adding the numerators: 8/12 + 3/12 =
1/5 + 2/7
We can find a common denominator by finding the least common multiple (LCM) of 5 and 7. The LCM of 5 and 7 is 35.
So, we can convert 1/5 to 7/35 by multiplying the numerator and denominator by 7.
We can convert 2/7 to 10/35 by multiplying the numerator and denominator by 5.
So, we can convert 3/4 to 9/12 by multiplying the numerator and denominator by 3.
We can convert 1/3 to 4/12 by multiplying the numerator and denominator by 4.
Now we can add the fractions by adding the numerators: 9/12 + 4/12 = 13/12
So, 3/4 + 1/3 = 13/12
It's important to note that when adding fractions, it's also important to simplify the final result if possible.
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Farhan bought one dozen bananas for $2.40. What is the rate ( cost ) of each banana?
Answer:
20 cents
Step-by-step explanation:
12 divided by 2.40
The average age of 6 men is 35 years and the average age of four of them is 32 year.
Find the ages of the remaining two ment one is 3 years older than the other.
Let's denote the ages of the two remaining men as x and x + 3 (since one is 3 years older than the other).
We know that the average age of 6 men is 35 years. So, the sum of their ages is 6 * 35 = 210 years.
We also know that the average age of four of them is 32 years. So, the sum of their ages is 4 * 32 = 128 years.
To find the sum of the ages of the two remaining men, we subtract the sum of the ages of the four men from the sum of the ages of all six men:
210 - 128 = 82 years.
Now, we can set up an equation to solve for the ages of the remaining two men:
x + (x + 3) = 82.
Combining like terms, we get:
2x + 3 = 82.
Subtracting 3 from both sides:
2x = 79.
Dividing both sides by 2:
x = 39.5.
So, one of the remaining men is 39.5 years old, and the other is 39.5 + 3 = 42.5 years old.
please help me..... asap
Answer:
collect a sample bacteria from the lake
Answer:
A- collect a sample of bacteria from the lake.
Step-by-step explanation:
It will not help to get bacteria from a RIVER since the scientist wants to learn about the LAKE. Also, getting all the lake bacteria will cause no more bacterial life to thrive, which is bad- but just a single bacteria cell isn't good either since we don't know how it reproduces and one is usually not enough.
the measure of an angle is 6 less than 5 times its complement. what is the complement.
Answer:
90−74=16∘.
Step-by-step explanation:
If x is the measure of the angle, then 90−x is the measure of the complement, both in degrees
The amunt of money that college students spend on rent each month is usually between $300 and $600. However, there are a few students who spend $1,300. What measure of spread would be most appropriate to measure the amount of money that college student spend on rent per month? Explain in detail why or why not one of the below measures would be used.
A. Median
B. Range
C. Standard Deviation
D. Inquartile Range
The range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.
To measure the amount of money college students spend on rent per month, the most appropriate measure of spread would be the range. The range is the simplest measure of spread and is calculated by subtracting the lowest value from the highest value in a data set. In this case, the range would be $1,300 - $300 = $1,000.
The median would not be the best choice in this scenario because it only represents the middle value in a data set. It does not take into account extreme values like the $1,300 rent expense.
Standard deviation would not be the most appropriate measure of spread in this case because it calculates the average deviation of each data point from the mean. However, it may not accurately represent the spread when extreme values like the $1,300 rent expense are present.
The interquartile range (IQR) would not be the best choice either because it measures the spread of the middle 50% of the data set. It does not consider extreme values and would not accurately represent the range of rent expenses in this scenario.
In summary, the range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.
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A circle of radius 10cm has a rectangle ABCD inscribed in the first quadrant. Find |AC| (ignore blue pen)
According to the Pythagorean theorem, |AC| = 10 * sqrt(5/3)
What is the theory of the Pythagorean Theorem?The Pythagorean Theorem states that the square on the tangent line (the side across from the right angle) of a right triangle, or, in standard algebraic form, a2 + b2, are equal to a square just on legs.
What practical applications of the Pythagorean Theorem exist?The following are some significant applications of the Pythagoras theorem in daily life: used in architecture and building. used to determine the shortest distance in two-dimensional navigation.
Since the diagonals of a rectangle are identical, the Pythagorean theorem states that AB = CD and BC = AD.
Using the Trigonometry once more, but this times with the edges of the rectangle, we can get d.
Lastly, by applying the right triangle's sides to the Pythagorean theorem, we may determine AC. ACD:
\(AC=\frac{500}{3}=10*\frac{5}{3}\)
Therefore, |AC| = 10*(5/3)
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Find the area of the following composite figure please
Step-by-step explanation:
answer is in photo above
A 35 ft ladder reaches a window that is 25 feet high. What is the angle of elevation the ladder forms with the ground? A. 44.4 C. 35 B 54.5 D. 45.6
Answer:
D
Step-by-step explanation:
Sin(x)=25/35=5/7
=> x = 45.6
1.) Sam raked 4 bags of
leaves in 22 minutes. If
he continues to work at
the same rate, about
how long will it take
him to rake 7 bags?
Answer: 38.5 minutes, aka 38 minutes and 30 seconds, round up, unless ur teacher wants the exact time.
Answer:
38.5 minutes or if rounded up it would be 39 minutes.
Step-by-step explanation:
22 divided by 4 bags would get you 5.5. This means it would take you 5.5 minutes to rake 1 bag. Since, they already raked 4 bags that would be 22 minutes, plus the other 3 bags it would be, 5.5 x 3 = 16.5 minutes. Add it together and you get 22 minutes + 16.5 minutes = 38.5 minutes to rake 7 bags. Hope this helped!
Recall the scenario about Eric’s weekly wages in the lesson practice section. Eric's boss has been very impressed with his work. He has given him a $2 raise and now Eric earns $12 an hour. His boss also has increased Eric’s work hours to 10 to 25 hours per week. The restrictions remain the same; he needs to work a full-hour in order to get the hourly wage (i.e. working 1.5 hour does not pay him for 1.5 hours but for one hour).
1.) function equation
2.) domain of the function in the set notation
3.) range of the function in the et notation
Answer:
f(x)= 12x where x is the number of hours worked (only whole numbers)
Domain= {10,11,12,13,.............., 25}
Range = { $ 120, $ 132, $ 144,$ 156 ,$ 168, $ 180, $ 192, $ 204, $ 216, $ 228, $ 240, $ 252, $ 264, $ 276, $ 288, $ 300}
Step-by-step explanation:
Let x be the number of hours worked then the function will be
f(x)= 12 (x) for {x=10,11,12,13,.............., 25}
x cannot taken any fractional value or decimal value.
The domain of the function is the input values
Domain= {10,11,12,13,.............., 25}
Now range of the function is the set of all possible output values
f(10)= 12 *10= $ 120
f(11)= 12 *11= $ 132
f(12)= 12 *12= $ 144
f(13)= 12 *13= $ 156
f(14)= 12 *14= $ 168
f(15)= 12 *15= $ 180
f(16)= 12 *16= $ 192
f(17)= 12 *17= $ 204
f(18)= 12 *18= $ 216
f(19)= 12 *19= $ 228
f(20)= 12 *20= $ 240
f(21)= 12 *21= $ 252
f(22)= 12 *22= $ 264
f(23)= 12 *23= $ 276
f(24)= 12 *24= $ 288
f( 25) = 12*25= $ 300
Range = { $ 120, $ 132, $ 144,$ 156 ,$ 168, $ 180, $ 192, $ 204, $ 216, $ 228, $ 240, $ 252, $ 264, $ 276, $ 288, $ 300}
Witch two ratios represent quantity's that are pro proportional?
9/5 and 19/10
4/6 and 10/16
25/35 and 20/24
15/10 and 21/14
Answer:
15/10 and 21/14
Step-by-step explanation:
Simplify:
9/5 and 19/10
Simplified; not proportional.
Simplify:
4/6 and 10/16
2/3 and 5/8
Simplified; not proportional.
Simplify:
25/35 and 20/24
5/7 and 5/6
Simplified; not proportional.
Simplify:
15/10 and 21/14
3/2 and 3/2
Simplified; proportional.
1+1=1268934457687423456779052436869867543?
Answer:
2
Step-by-step explanation:1+1=2 its 2 okay its 2 not 1268934457687423456779052436869867543
What value for x will make the equation −3x+1=2(4x−5)true?
given supermarket customer sequences. using the aprioriall algorithm, find length-k sequential patterns. <{1, 8} {2} {3} {4} > <{1} {3} {4} {3, 8}> <{1} {2} {3} {4}>
<{1} {3} {8}>
<{4} {8}>
The Aprioriall algorithm is a method for finding length-k sequential patterns in a set of customer sequences.
To use this algorithm, we need to first specify the minimum support and minimum confidence thresholds. These thresholds determine which patterns will be considered significant. Once the thresholds have been set, the algorithm will iterate over the customer sequences and look for length-k sequential patterns that meet the minimum support and confidence thresholds. In this case, the algorithm would look for length-k sequential patterns in the given customer sequences:
<{1, 8} {2} {3} {4} >
<{1} {3} {4} {3, 8}>
<{1} {2} {3} {4}>
<{1} {3} {8}>
<{4} {8}>
For example, if the minimum support threshold is set to 50% and the minimum confidence threshold is set to 80%, the algorithm might find the following length-2 sequential pattern:
<{1} {3}>
This pattern has a support of 60% (3 out of 5 customer sequences contain this pattern) and a confidence of 100% (all customer sequences that contain the first item in the pattern, {1}, also contain the second item, {3}). Other possible length-2 sequential patterns that the algorithm might find include <{1} {2}>, <{1} {4}>, and <{3} {4}>. The specific patterns found by the algorithm will depend on the specific values of the minimum support and minimum confidence thresholds.
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2 apples cost 2 dabloons.
How much does 1 apple cost
Steel sheet length 2400 mm, wide 1200 mm, how many number of pieces 300 mm×200 mm for cutting.
6 12 24 48
The correct answer is 48 pieces.
To determine the number of pieces that can be cut from the steel sheet, we need to divide the dimensions of the steel sheet by the dimensions of each piece to see how many can fit.
Calculate the number of pieces along the length:
The length of the steel sheet is given as 2400 mm, and each piece has a length of 300 mm. By dividing the total length by the length of each piece, we get 2400 mm ÷ 300 mm = 8. This means we can cut 8 pieces along the length of the steel sheet.
Calculate the number of pieces along the width:
The width of the steel sheet is given as 1200 mm, and each piece has a width of 200 mm. By dividing the total width by the width of each piece, we get 1200 mm ÷ 200 mm = 6. This means we can cut 6 pieces along the width of the steel sheet.
Calculate the total number of pieces:
To find the total number of pieces, we multiply the number of pieces along the length by the number of pieces along the width: 8 pieces × 6 pieces = 48 pieces.
Therefore, the correct answer is 48 pieces.
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Find the distance from the vector (1, 2, 3, 4) to the
subspace of R^4 spanned by the vectors (1, −1, 1, 0) and (3, 2, 2,
1).
The distance from the vector (1, 2, 3, 4) to the subspace of R^4 spanned by the vectors (1, -1, 1, 0) and (3, 2, 2, 1) can be calculated as the length of the orthogonal projection of (1, 2, 3, 4) onto the subspace.
To find the distance, we first need to determine the orthogonal projection of the vector (1, 2, 3, 4) onto the subspace spanned by (1, -1, 1, 0) and (3, 2, 2, 1).
The orthogonal projection of (1, 2, 3, 4) onto the subspace can be obtained by projecting (1, 2, 3, 4) onto each of the spanning vectors and then summing those projections. Using the projection formula, we find that the projection of (1, 2, 3, 4) onto the first spanning vector (1, -1, 1, 0) is (5/3, -5/3, 5/3, 0), and the projection onto the second spanning vector (3, 2, 2, 1) is (3/2, 1, 1, 1/2).
Next, we calculate the difference vector between (1, 2, 3, 4) and the sum of the two projections: (1, 2, 3, 4) - [(5/3, -5/3, 5/3, 0) + (3/2, 1, 1, 1/2)] = (2/6, 13/6, 7/6, 7/2).
Finally, we find the length of the difference vector, which represents the distance between (1, 2, 3, 4) and the subspace: √[(2/6)^2 + (13/6)^2 + (7/6)^2 + (7/2)^2] = √(242/9).
Therefore, the distance from the vector (1, 2, 3, 4) to the subspace of R^4 spanned by (1, -1, 1, 0) and (3, 2, 2, 1) is √(242/9).
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Please help will give brainliest
The table shows the postal charges for sending letters to Country Y.
How much does it cost to send a letter weighing 60 grams to
Country Y?
PLS HELP ASAP!!!!
Answer:
$01.70
Step-by-step explanation:
Answer:
it will cost 170 $ total ....
A cylindrical container has a diameter of 5 inches and a height of 12 inches. The container will be wrapped and delivered as a gift. What measurement is closest to the amount of wrapping paper needed to cover the container without overlap?
Answer:
Step-by-step explanation:
1. Write your formula
2. Plug it in
3. Solve
these steps will help you out with all of your surface area problems.
Like this
Since it is a diameter you have to divide the diameter by 2. That will get you your radius. Then you write your formula for a cylinder. Your formula is...
V = Bh (Pie is also known as 3.14)
your big (B) is (pie times r squared) Then you add your height.
so your formula will look like this...
V = pie times r squared...
the full formula will be...
V = (3.14) times (2.5 squared) times the height which in this case is (12)
everything together will be...
V = (3.14) (2.5^2) (12)
all you have to do is multiply all of that and you will get your answer.
The answer is...
V = 236 inches ^2 (Just a tip, the ^ sign means to the power of)
True or False:
According to the table, about 10% of customers surveyed
ordered the eggplant parmesan meal.
About 10% of customers surveyed ordered the eggplant parmesan meal is false.
We have,
Total number of orders.
= 13 + 10 + 5 + 17 + 5
= 50
Now,
The total number of eggplant orders.
= 10
Now,
The percentage of eggplant orders.
= 10/50 x 100
= 10 x 2
= 20%
Thus,
About 10% of customers surveyed ordered the eggplant parmesan meal is false.
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Work out the value of 3.1^4
Answer: It's 92.3521 Hope that helps Goodbye!
Step-by-step explanation: 3.1×3.1= 9.61× 3.1= 29.791 ×3.1 = 92.3521 because it's the power to 4 3.1×3.1×3.1×3.1 so that telling you to multiply 3.1 four times. Can you please make me Brainliest
Jeff spent $50 on gifts for his tamily. The first 2 items cost a total of $15 and then he bought 2 more for a total of $20. How many additional gifts did Jeff buy if their average cost was $10 each?
The number of additional gifts Jeff can buy with the remaining cost is 1.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
As per the given,
Total cost = $15 + $20 = $35
Total spent = $50
Remaining = $50 - $35 = $15
Since one gift cost $10
Thus, 15/10 = 1.5 since the number of gifts will be the whole number so it will be round to bottom 1 gift.
Hence "With the money still available, Jeff can purchase 1 more present".
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A line passes through the points (8, –1) and (–4, 2).
Answer:
y=1/4x+1
Step-by-step explanation:
Goes zdown 3 and right 12 simplified to 1/4
Answer:
Your answer is: y = -1/4x + 1
Step-by-step explanation:
Hope this helped : )
hans paid $1.50 each for programs to the game. he sold all but 20 of them for $3 each and made a profit of $15. how many programs did he buy?
50 many programs did he buy when Hans each paid $1.50 for the game's programmes. He made a profit of $15 by selling all but 20 of them for $3 each.
Given that,
Hans each paid $1.50 for the game's programmers. He made a profit of $15 by selling all but 20 of them for $3 each.
We have to find He purchased how many programmed.
We know that
Let x = number of programs he bought
Then
(x-20) = number of programs he sold
amt sold - amt paid = profit
3(x-20) - 1.5x = 15
3x - 60 - 1.5x = 15
3x - 1.5x = 15 + 60
1.5x = 75
x = 75/1.5
x = 50 programs originally bought
Therefore, 50 many programs did he buy when Hans each paid $1.50 for the game's programmes. He made a profit of $15 by selling all but 20 of them for $3 each.
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checkers cab company is trying to decide which brand of tires to use for the coming year. based on current price and prior experience they have narrowed their choice to brands, beltex and roadmaster. a recent study examined the durability of these tires by using a machine with a metallic device that wore down the tires. the time it took (in hours) for the tire to blowout was recorded. the blowout times (hours) were as follows: Beltex: 3.82, 3.11, 4.21, 2.64, 4.16, 3.91, 2.44, 4.52, 2.84, 3.26, 3.74, 3.04, 2.56, 2.58, 3.15
Roadmaster: 4.16, 3.92, 3.94, 4.22, 4.15, 3.62, 4.11, 3.45, 3.65, 3.82, 4.55. 3.82, 3.85, 3.62, 4.88
a. construct a 90% confidence interval for the difference in the mean blowout times between the two brands of tires and interpret the results.
b. can we conclude that the average blowout times are in fact not the same? Use a significance level of .10.
To compare the mean blowout times, a 90% confidence interval will be constructed, and using a significance level of 0.10, we will determine whether we can conclude about the average blowout times.
a. To construct a 90% confidence interval for the difference in the mean blowout times between the two brands of tires, we will calculate the sample mean and standard deviation for each brand. Using the formula for the confidence interval of the difference between two means, we can determine the range within which we can be 90% confident that the true difference lies. The interpretation of this confidence interval is that it provides a range of values that likely contains the actual difference in the mean blowout times between the Beltex and Roadmaster tire brands, with 90% confidence.
b. To test whether the average blowout times are significantly different between the two brands, we can perform a hypothesis test. Using a significance level of 0.10, we can compare the means of the two samples. If the p-value is less than 0.10, we can conclude that the average blowout times are significantly different. However, if the p-value is greater than or equal to 0.10, we do not have sufficient evidence to conclude that the average blowout times are different.
By analyzing the results of the hypothesis test, we can determine whether we can reject the null hypothesis that the average blowout times are the same.
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lena is going to rent a truck for one day. there are two companies she can choose from, and they have the following prices. company a charges and allows unlimited mileage. company b has an initial fee of and charges an additional for every mile driven. for what mileages will company a charge less than company b? use for the number of miles driven, and solve your inequality for .
Therefore, company A will charge less than company B for any mileage greater than 65 miles.
To help you with your question, I need the specific prices for both companies, as well as any additional information you can provide about the charges.
To solve for the mileages at which company A will charge less than company B, we can set up the following inequality:
A < B
where A is the cost of renting from company A and B is the cost of renting from company B. We can plug in the given information to get:
x ≤ A
x > B = y + 40z
where x is the number of miles driven, y is the initial fee for company B, and z is the additional cost per mile for company B.
Now we can substitute the given values to get:
x ≤ A
x > y + 40z
For company A, the cost is a flat rate with unlimited mileage, so A is just the cost listed for one day of rental. Let's say that cost is $100.
For company B, the initial fee is $50 and the additional cost per mile is $0.25. So:
y = 50
z = 0.25
Now we can plug in these values and solve for x:
x ≤ 100
x > 50 + 40(0.25)
x > 65
Therefore, company A will charge less than company B for any mileage greater than 65 miles.
To help you with your question, I need the specific prices for both companies, as well as any additional information you can provide about the charges.
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4. 18 is 80% of what?
A. 20
B. 22.5
C. 14.4
D. 9
Answer:
22.5 (B)
Step-by-step explanation: