One coterminal angle to 30 degrees is -330 degrees. 150 degrees and 510 degrees are coterminal angles. Similarly, any angle that differs by a multiple of 360 degrees from the given angle is coterminal with it.
Coterminal angles are angles that have the same initial side and the same terminal side. They can be either negative or positive, and they can have any degree measure. Coterminal angles are determined by adding or subtracting 360 degrees (or 2π radians) from the given angle as many times as necessary until the resulting angle falls between 0 and 360 degrees.
Here are the steps to determine coterminal angles: Add or subtract 360 degrees from the given angle. Keep adding or subtracting 360 degrees as many times as necessary to obtain an angle between 0 and 360 degrees. For example, consider the given angle of 150 degrees.150 degrees + 360 degrees = 510 degrees510 degrees - 360 degrees = 150 degreesThe angle 510 degrees is coterminal with 150 degrees. However, it is a very large angle that is difficult to visualize on the coordinate plane.
Therefore, we can find the smallest positive coterminal angle to 150 degrees by subtracting 360 degrees from 510 degrees as many times as necessary until we get an angle between 0 and 360 degrees.510 degrees - 360 degrees = 150 degrees (already between 0 and 360 degrees). Any angle that differs by a multiple of 360 degrees from the given angle is coterminal with it. For example, 870 degrees, 1230 degrees, and -330 degrees are all coterminal with 150 degrees.
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A jar contains 4 red marbles numbered 1 to 4 and 12 blue marbles numbered 1 to 12. A marble is drawn at random from the jar. Find the probability of the given event. (a) The marble is red
Your answer is :
(b) The marble is odd-numbered
Your answer is :
(c) The marble is red or odd-numbered
Your answer is :
(d) The marble is blue and even-numbered
Your answer is :
a) The probability of drawing a red marble is 1/4.
b) There is a 3/8 chance of drawing an odd-numbered stone.
c) There is a 7/16 chance of drawing a red or odd-numbered marble.
d) The odds of drawing the blue, even-numbered marble are 3/8.
(a) The ratio of red marbles to all other marbles in the jar represents the likelihood of drawing a red marble.
(4) red marbles are present.
(4) + (12) = (16) marbles total
As a result, there is a 4/16 or 1/4 chance of drawing a red marble.
(b) The proportion of odd-numbered marbles to all marbles in the jar determines the likelihood of drawing an odd-numbered marble.
6 odd-numbered marbles make up the total (red marbles numbered 1 and 3, and blue marbles numbered 1, 3, 5, and 7)
There are 16 marbles in total.
The likelihood of drawing an odd-numbered stone is therefore 6/16 or 3/8.
(c) The likelihood of drawing a red or odd-numbered marble is calculated as the product of the odds of drawing each type of marble, less the likelihood of drawing a red or odd-numbered stone (i.e., marble number 1).
a red marble's chances of being drawn = 1/4
Probability of drawing an odd-numbered marble = 3/8
Probability of drawing a marble that is both red and odd-numbered = 1/16
Therefore, the probability of drawing a red or odd-numbered marble is (1/4) + (3/8) - (1/16) = 7/16.
(d) The proportion of blue and even-numbered marbles to all other marbles in the jar determines the likelihood that a blue and even-numbered marble will be drawn.
Six blue and even-numbered marbles make up the total (blue marbles numbered 2, 4, 6, 8, 10, and 12)
Total number of marbles = 16
Probability of drawing the marble is blue and even-numbered = 6/16 or 3/8
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Question 1 You have noticed that it seems that men attend fewer group counseling sessions than women. As a result, you are curious whether they actually differ in a significant way or not. You collect data on the number of counseling sessions attended and determine that the mean number of sessions attended by men is 7 and the mean number of sessions attend by women is 17 . The grouped standard deviation is 5 . You are assuming a normal distribution of your variables.Xmen =7Xwomen =17SD grouped =51. What is the null hypothesis? 2. Would you reject the null for a: a. Two-tailed.05test? b. One-tailed.05test? c. Two-tailed.01test? d. One-tailed.01test? (challenge yourself on this one to find the appropriate critical value for a one-tailed.01test) 3. What does it mean to reject and to accept the null hypothesis in Question 2a-d? In your answer, refer to how much risk and confidence you have. 4. Indicate whether you could have made a Type I or Type II error in Q2a-d. 5. Conceptually, what does it mean for something to be significant?
All the answers related to null hypothesis are explained below.
What is null hypothesis?Null hypothesis is used to test if there is any statistical significance between the two groups being compared.
1. The null hypothesis is that there is no difference in the number of counseling sessions attended by men and women.
2a. For a two-tailed .05test, you would reject the null hypothesis if the absolute value of the t-statistic is greater than the critical value of 1.96.
2b. For a one-tailed .05test, you would reject the null hypothesis if the t-statistic is greater than the critical value of 1.645.
2c. For a two-tailed .01test, you would reject the null hypothesis if the absolute value of the t-statistic is greater than the critical value of 2.58.
2d. For a one-tailed .01test, you would reject the null hypothesis if the t-statistic is greater than the critical value of 2.33.
3. Rejecting the null hypothesis means that the data is statistically significant and you are confident that the difference in the number of counseling sessions attended by men and women is not due to chance.
4. For a two-tailed test, a Type I error occurs when the null hypothesis is rejected when it should not have been. For a one-tailed test, a Type I error occurs when the null hypothesis is rejected when the difference between the two groups is not greater than the critical value.
5. Conceptually, something is considered to be statistically significant when it is unlikely that the observed results were due to chance.
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i sell a car for £6502 making a 22% profit. how much did i buy it for originally
Answer:
£5329.51
Step-by-step explanation:
Knowing that £6502 is the price with 22% profit, we can understand that £6502 is 122% of the original price meaning that the individual would have had to multiply their original value by 1.22 to get £6502!
To find our answer we, therefore, have to do the inverse...
6502 ÷ 1.22 = 5329.5082Turning the value into money we round to 2d.p leaving our answer as...
£5329.51Hope this helps, have a lovely day! :)
A diet plan claims that women have a mean weight of 145 lbs. Assume that the weights of women have a standard deviation of 30. 86 lb. A sample of 40 weights of women has a mean weight of 153. 2 lb. Find the P-value and, using a 0. 05 significance level, state the conclusion about the null hypothesis
The null hypothesis is that the mean weight of women is 145 lbs.The P-value is 0.0145. At a 0.05 significance level, the null hypothesis can be rejected. This suggests that the mean weight of women is not 145 lbs.
The null hypothesis is that the mean weight of women is 145 lbs. To test the hypothesis, we need to calculate the P-value. The mean of the sample of 40 weights is 153.2 lbs, with a standard deviation of 30.86 lb. The P-value is calculated using a z-score formula which is (153.2-145)/(30.86/sqrt(40)) = 0.0145. Since the P-value is less than 0.05, this suggests that the mean weight of women is not 145 lbs. Therefore, at a 0.05 significance level, the null hypothesis can be rejected.
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G
3
X
You are traveling by car to New York City. The map you will use for your journey is
below.
Seattle
• San Jose
• Los Angeles
1 unit
1 unit = 557 miles
Denver
El Paso
Chicago
Houston
a) What is the scale factor on the map? (1 point)
Memphis
New York
Jacksonville
grup
The scale factor given in the map to measure the distance is 1 unit = 557 miles.
What is scale factor?
The scale factor of a shape refers to the amount by which it is increased or shrunk. It is applied when a 2D shape, such as a circle, triangle, square, or rectangle, needs to be made larger.
The map is given for United States of America.
The map shows different states with their locations.
The maps say that 1 unit measures 557 miles.
The scale factor is the means to measure the distance on the map.
The scale factor mentioned in the map is 1 unit.
The value of 1 unit is given as 557 miles.
Therefore, the scale factor is 1 unit = 557 miles.
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simplify the expression if m = -7 and n = 4: 5m + 9n
Answer:
If m = -7 and n = 4, then we can substitute these values into the expression:
5m + 9n = 5(-7) + 9(4)
= -35 + 36
= 1
Therefore, 5m + 9n simplifies to 1 when m = -7 and n = 4.
Step-by-step explanation:
(2x-3y)(x+5y)=0 where x>0 and y>0
find the ration x:y
Give your answer in its simplest form
The ratio of x:y is -9:5 or 3:-2.
The given equation is 2x-3y=0 and x+5y=0.
Since x is greater than 0 and y is greater than 0, we can solve the equations for x and y
2x = 3y
x = 3/2y
and
x = -5y
Substituting x = 3/2y in the second equation,
-5y = 3/2y
-10y = 3
y = -3/10
Substiuting y = -3/10 in the first equation,
2x = 3(-3/10)
x = -9/5
Therefore, the ratio of x:y is -9:5. In the simplest form, the ratio can be written as -9:5 or 3:-2.
2x - 3y = 0
x + 5y = 0
2x = 3y
x = 3/2y
-5y = 3/2y
-10y = 3
y = -3/10
2x = 3(-3/10)
x = -9/5
Therefore, x:y = -9:5 or 3:-2
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a car moves at a speed of 90 meters per minute. what is its speed in meters per second?
Answer:
There are 60 seconds in a minute, so to convert meters per minute to meters per second, we need to divide by 60.
90 meters per minute ÷ 60 = 1.5 meters per second
Therefore, the car's speed is 1.5 meters per second.
Step-by-step explanation:
Step-by-step explanation:
There are 60 in a minute, so to convert meters per minute to meters per second, we need to divide by 60
90 meters per minute ÷ 60 = 1.5 meters per second
Twelve students are going to listen to a talk. The group consists of 3 chemistry majors, 2 business majors, 3 political science majors and 4 journalism majors. In how many ways can these students sit in their twelve seats if they must be grouped by major?
There are 1,728 ways for the 12 students to sit in their assigned seats while maintaining the grouping by major.
How to find how many ways can these students sit in their twelve seats if they must be grouped by majorThere are four groups based on major: chemistry, business, political science, and journalism. We need to find the number of ways the 12 students can sit in their assigned seats while maintaining the grouping by major.
We can approach this problem by first considering the number of ways each group can be seated separately, and then multiply the results together to get the total number of arrangements.
For the chemistry group, there are 3 students who can be seated in any order.
For the business group, there are 2 students who can be seated in any order.
For the political science group, there are 3 students who can be seated in any order.
Finally, for the journalism group, there are 4 students who can be seated in any order.
Therefore, the total number of arrangements for the 12 students is:
3! * 2! * 3! * 4! = 6 * 2 * 6 * 24 = 1,728
Therefore, there are 1,728 ways for the 12 students to sit in their assigned seats while maintaining the grouping by major.
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55 /10
45/10
20/4
4/0.8
please convert into whole numbers
Converting into whole number:
a. 5 5/10 = 5 1/2
b. 4 5/10 = 4 1/2
c. 5
d. 4/8 = 1/2
Converting fraction into whole numbers?To convert a fraction into a whole number, you need to perform the division indicated by the fraction and express the result as a mixed number or a whole number.
Example: 55/10 means that 55 is divided by 10. When we divide 55 by 10, we get 5 with a remainder of 5. Therefore, we can express 55/10 as a mixed number: 5 5/10. However, we usually simplify the mixed number by reducing it to its lowest terms, which in this case is 5 1/2.
Similarly, we can convert the other fractions into whole numbers:
45/10 = 4 5/10 = 4 1/2
20/4 = 5
4/0.8 can be simplified first by dividing both the numerator and denominator by 0.8, which gives 5. Then we can express 5 as a fraction with a denominator of 10 by multiplying both the numerator and denominator by 2, which gives 5/10. Finally, we can reduce this fraction to its lowest terms, which is 1/2. Therefore, 4/0.8 = 1/2.
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The fine for an overdue library book is. 75 for the first day and. 50 for each additional day. Rewrite the expression. 75 +. 5(d-1) for the fine as a sum of two terms where d represents the number of days overdue
The expression can be written as the sum of two terms as 74.5 + 0.5d
Mathematical expressions:Mathematical expressions are combinations of numbers, variables, and operators (such as +, -, ×, ÷, =) that represent a mathematical relationship or computation.
To write the given expression as the sum of two terms simplify the expression by multiplying and adding or subtracting like terms.
Here we have
The expression 75 + 0.5(d - 1) represents the fine for an overdue library book, where d is the number of days overdue.
Simplify expression as shown below
=> 75 + 0.5(d - 1)
= 75 + 0.5d - 0.5
= 0.5d + 74.5
Now the expression is in the form of the sum of two terms
Therefore
The expression can be written as the sum of two terms as 74.5 + 0.5d
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Find d. Round to the nearest tenth.
Answer:
d=50.3
Step-by-step explanation:
cos(29)/1=44/d
cos29d/cos29=44/cos29
d=50.31
d=50.3
please help there’s 3 different parts..a,b,and c.
The values of g(x) for the given values of x are g(0) = 4, g(-7) = 3, g(-4) = 0
Describe Function?Functions can be used to model a wide range of real-world phenomena, such as physical laws, economic relationships, or biological processes. They are a fundamental concept in mathematics and play a central role in many fields, including engineering, physics, computer science, and statistics.
Functions can be represented graphically, algebraically, or numerically, and can be manipulated and analyzed using a variety of mathematical tools and techniques. By understanding how functions work and how to use them, people can solve problems, make predictions, and gain insights into a wide range of mathematical and real-world phenomena.
To evaluate the piecewise function at each value of the independent variable, we need to substitute the given value of x into the appropriate expression for g(x):
a. To find g(0), we use the first expression since 0 is greater than or equal to -4:
g(0) = 0 + 4
g(0) = 4
b. To find g(-7), we use the second expression since -7 is less than -4:
g(-7) = -(-7 + 4)
g(-7) = -(-3)
g(-7) = 3
c. To find g(-4), we need to consider both expressions since -4 is exactly equal to -4:
g(-4) = -(-4 + 4) (using the second expression)
g(-4) = 0 (simplifying)
or
g(-4) = -4 + 4 (using the first expression)
g(-4) = 0 (simplifying)
So, g(-4) is equal to 0 using both expressions.
Therefore, the values of g(x) for the given values of x are:
g(0) = 4
g(-7) = 3
g(-4) = 0
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The right hexagonal pyramid has a base with equal length sides. The lateral faces of the pyramid are all triangles (that are exact copies of one another) with heights of 15 ft. Find the surface area of the pyramid
The surface area of the pyramid is 105.6 square feet.
To find the surface area of this pyramid, we need to calculate the area of all its faces and add them up.
Since all sides of our hexagon are equal, we can simplify this formula to:
Surface Area of Hexagon = 6 x (3√3 / 2) x (Side length)²
Total Surface Area = Surface Area of Base + Surface Area of Triangular Faces
Total Surface Area = 6 x (3√3 / 2) x (Side length)² + 6 x (Side length x 15) / 2
We can simplify this expression further by factoring out 6 x (Side length)² from both terms:
Total Surface Area = 6 x (Side length)² x [(3√3 / 2) + 15]
To find the surface area of a right hexagonal pyramid with equal-length sides and triangular faces of height 15 ft, we use the formula above:
Total Surface Area = 6 x (Side length)² x [(3√3 / 2) + 15]
When the value of side length is 1, then total surface area is
=> Total Surface Area = 6 x (1)² x [(3√3 / 2) + 15] = 105.6 square feet.
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which is cheaper paint by numbers charges a flat rate of $100 and $16 per hour paint it right charges $24 per hour and $38 flat rate
Answer:
To determine which is cheaper, we need to consider the total cost for a certain amount of time. Let's say we want to paint a picture that will take 5 hours to complete.
For Paint by Numbers:
Flat rate = $100
Hourly rate = $16/hour x 5 hours = $80
Total cost = Flat rate + Hourly rate = $100 + $80 = $180
For Paint it Right:
Flat rate = $38
Hourly rate = $24/hour x 5 hours = $120
Total cost = Flat rate + Hourly rate = $38 + $120 = $158
Therefore, Paint it Right is cheaper for this particular job. However, if the amount of time required for the job is different, the cost comparison may change.
make a table for the function d = 3t which gives the distance traveled at the rate of 3 mi per hr. then graph the function
The table for the function d = 3t is
t (hours) d = 3t (miles)
0 0
1 3
2 6
How to make a table for the functionThe equation of the function is given as
d= 3t
The above is a linear function
To make a table for the function d = 3t, we can choose some values of t and then calculate the corresponding values of d using the given equation.
Since the equation represents distance traveled at a rate of 3 miles per hour, we can assume that t represents time in hours and d represents distance in miles.
Let's choose some values of t and calculate the corresponding values of d:
t (hours) d = 3t (miles)
0 0
1 3
2 6
3 9
4 12
5 15
The graph is attached
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Function F please help. I think that A can be one of em but I’m not sure about the rest
The true statement about the function notation are:
d(20) = d(40)d(0) = 0: Trued(80) = 60; Trued(92) = 0; TrueHow to determine the true function notationThe definition of the graph is given as
The distance vs time graph
This is represented by F = d(t)
The function notation would be determined to be true or false by observation
This is so because the graph is not drawn to scale
Using the above as a guide, we have the following:
d(20) = d(40): True, both equal 30d(0) = 0: Trued(t) = 10 when t = 20; Falsed(80) = 60; Trued(0) = 92; Falsed(92) = 0; Trued(80) < d(50); FalseRead more about function notations at
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Diego has 90 songs on his playlist. How many songs are there for each genre?
Answer: Diego's playlist has 36 songs in rock genre, 9 songs in Country genre, 27 songs in hip hop genre and 24 songs in electronica genre.
Based on the number of songs Diego has and the proportion of the genres, Diego's song classification is:
Rock = 36 songsCountry = 9 songsHip Hop = 27 songsElectronica = 18 songsThe number of songs from a particular genre is:
[tex]= \text{Total number of songs}\times\text{Percentage of genre}[/tex]
Rock:
[tex]= 40\% \times 90[/tex]
[tex]\bold{= 36 \ songs}[/tex]
Country:
[tex]= 10\% \times 90[/tex]
[tex]\bold{= 9 \ songs}[/tex]
Hip hop:
[tex]= 30\% \times 90[/tex]
[tex]\bold{= 27 \ songs}[/tex]
Electronica:
[tex]= (100\% - 40\% - 10\% - 30\%) \times 90[/tex]
[tex]\bold{= 18 \ songs}[/tex]
In conclusion, there are various genres on Diego's phone.
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Complete Question:
Diego has 90 songs on his playlist. How many songs are there for hip-hop?
40% rock
10% country
30% hip-hop
The rest is electronica
A contractor tiles a rectangular section of floor in a square room
From the given information provided, the area of the square room with rectangular section is 72 square feet.
Let's assume that the rectangular section of the floor that is tiled has length "L" and width "W". Since the area of the rectangular section is 18 square feet, we have:
L × W = 18
Since the room is square, its length and width are equal, let's say it's "x". Then, the area of the room is x².
Since the rectangular section is a part of the room, we have:
L ≤ x and W ≤ x
Therefore, we can find the minimum possible value of x by assuming that L = W = √18 (the sides of the rectangle are equal, and equal to the square root of 18), which gives:
x = √18 + √18 = 2√18
So, the area of the room is:
x² = (2√18)² = 4(18) = 72 square feet
Question - A contractor tiles a rectangular section of floor in a square room. The tiles covers 18sq. feet. What is the area of room?
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Class A has 18 pupils and class B has 24 pupils.
Both classes sit the same maths test.
The mean score for class A is 76.
The mean score for both classes is 66.
What is the mean score (rounded to 1 DP) in the maths test for class B?
Answer: 56
Step-by-step explanation:
66 x 2 = 132
132-76 = 56
(76+52) divided by 2 = 66
Hence the mean score for class B is 56.
can yall help me solve this please and thank you
Answer:
ANswer ig
Step-by-step explanation:
1/12+1/3=1/12+[4]/12=5/12
6\12. 1\2
I have to add mor but that is all so I’m writing this
Can u please teach it step by step for me...
Step-by-step explanation:
ASA stands for angle, side, angle
How is triangle ABC congruent to DEF
If any two angles and the side included between the angles of one triangle are equivalent to the corresponding two angles and side included between the angles of the second triangle, then the two triangles are said to be congruent by ASA rule.
In the diagram you shared, side BC is equivalent to line FD
Angle B = angle F
Angle C = Angle D
(Compare the markings on both triangles)
The relationship between triangle ABC and triangle DEF are congruent only by 2 angles and one side.
At the playground, the slide and its ladder form a right triangle with the ground. The distance from the bottom of the ladder to the base of the slide is 18 feet. The length of the slide is 20 feet. If b represents the height of the ladder, what is b?
The height of ladder is approximately 26.9 feet tall.
How can the hypotenuse of a right triangle with one side be determined?In order to get the length of the hypotenuse, divide the non-hypotenuse side that is close to the angle by cos(). If you prefer, you can multiply this length by tan() to obtain the length of the side that is perpendicular to the angle.
Let's tackle this issue using the Pythagorean theorem.
According to the Pythagorean theorem, the sum of the squares of the leg lengths in a right triangle equals
The length of the slide is the other leg, the distance from the ladder's bottom to its base is one leg, and the ladder itself is the hypotenuse.
b² = 18² + 20²
b² = 324 + 400
b² = 724
b = √(724)
b ≈ 26.9
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A shopkeeper buys 300 bicycles at Rs. 1500 per bicycle. He spends Rs 75 per bicycle on transportation. He spends Rs 7500 on advertising. Then he sell all the bicycles at Rs. 1700 per piece. Find he is profit or loss. Also calculate eat as a percentage
Therefore, the shopkeeper made a profit of Rs. 30,000 and the profit percentage is 6.25%.
What is percent?Percent is a way of expressing a fraction or a proportion as a quantity out of 100. The term "percent" means "per hundred". So, when we say that something is 50 percent, we mean that it is 50 out of 100 or 50/100, which can also be simplified to 1/2. The symbol used to represent percent is "%". For example, if a store is offering a discount of 20%, it means that the customer can buy the item for 20% less than the original price, or in other words, the customer will pay only 80% of the original price. Percentages are used in many different areas of life, such as finance, mathematics, science, and statistics. They are used to represent proportions, changes, growth rates, and many other types of data.
Here,
The total cost of 300 bicycles is:
Cost of 1 bicycle = Rs. 1500
Cost of 300 bicycles = 1500 x 300 = Rs. 4,50,000
Transportation cost per bicycle is Rs. 75, so the total transportation cost for 300 bicycles is:
Transportation cost of 1 bicycle = Rs. 75
Transportation cost of 300 bicycles = 75 x 300 = Rs. 22,500
The total cost of purchasing 300 bicycles including transportation cost is:
Total cost = Cost of bicycles + Transportation cost
Total cost = Rs. 4,50,000 + Rs. 22,500 = Rs. 4,72,500
The shopkeeper spent Rs. 7500 on advertising.
So, the total cost of the shopkeeper is:
Total cost = Cost of bicycles + Transportation cost + Advertising cost
Total cost = Rs. 4,72,500 + Rs. 7500 = Rs. 4,80,000
The selling price of 1 bicycle is Rs. 1700, so the selling price of 300 bicycles is:
Selling price of 1 bicycle = Rs. 1700
Selling price of 300 bicycles = 1700 x 300 = Rs. 5,10,000
The profit or loss is calculated by subtracting the total cost from the total selling price:
Profit/Loss = Selling price - Total cost
Profit/Loss = Rs. 5,10,000 - Rs. 4,80,000 = Rs. 30,000
Since the shopkeeper made a profit of Rs. 30,000, we can calculate the profit percentage as follows:
Profit percentage = (Profit / Total cost) x 100
Profit percentage = (30,000 / 4,80,000) x 100
Profit percentage = 6.25%
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The world population is now 8 billion people and growing at 2.2% per year. At that rate, how many people will there be in 25 years?
Using percentages we know that the population after 25 years would be 12.4 billion which is 12,40,00,00,000.
What is the percentage?A % is a quantity or ratio that, in mathematics, represents a portion of one hundred.
A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.
The symbol "%" is frequently written after the number to indicate percentages.
Now, we know that:
The population is 8 billion.
The increasing percentage is 2.2%.
Then, the population after 25 years would be:
= 8000000000/100 * 2.2
= 17,60,00,000
Now, after 25 years:
= 17,60,00,000 * 25
= 4,40,00,00,000
Total population after 25 years:
4,40,00,00,000 + 8000000000 = 12,40,00,00,000
Therefore, using percentages we know that the population after 25 years would be 12.4 billion which is 12,40,00,00,000.
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2.7c-4.5=3.6c-9
solve for c
Answer:
2,7c-3,6c =-9+4,5
-0,9c=-4,5
c=5
Answer:
c=5
Step-by-step explanation:
2.7c-4.5=3.6c-9
+4.5 +4.5
2.7c = 3.6c -4.5
-3.6c -3.6c
-0.9c = -4.5
-0.9c/-0.9= -4.5/-0.9
c= 5
I honestly don't know how to do this. Please explain it to me in the easiest way possible. Thank you.
The value of line segment AC is 8√2
What is Pythagoras theorem?Pythagoras theorem states that, in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.
If the other two sides of the right triangle are a and b and the hypotenuse is c, then mathematically l, Pythagoras theorem can be written as:
c² = a²+b²
If CD = 4 and AD = 12, then AC will be
12² = (AC)² +4²
(AC)² = 12² - 4²
(AC)² = 144-16
(AC)² = 128
AC = √128
AC = 8√2
therefore the value of the line segment AC is 8√2
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The Fashion Center made the following leather jacket purchases during the year. At the end of the year, there are 46 jackets in The Fashion Center's
inventory. Use the FIFO method to find the inventory value of the 46 remaining jackets.
$4,875
$5,000
$5,125
$4,500
March
June
September
30 jackets at $175
25 jackets at $150
35 jackets at $125
30 jackets at $100
The total value of the remaining inventory is $5,000. So correct option is B.
Describe Inventory?Inventory refers to the stock of goods or materials that a business or organization has on hand for the purpose of selling, manufacturing, or producing. It can include finished goods ready for sale, work in progress, or raw materials waiting to be processed or used. Proper management of inventory is essential to ensure that a business can meet customer demand while minimizing costs associated with carrying excess inventory or stockouts. Inventory management techniques involve tracking inventory levels, determining optimal reorder points, and controlling the flow of goods in and out of the inventory.
Using the FIFO method, we assume that the first jackets purchased are the first ones sold, so the value of the remaining inventory is calculated as follows:
The first 30 jackets are from the beginning inventory and cost $175 each.
The next 16 jackets (out of the 25 purchased in March) cost $150 each.
The next 10 jackets (out of the 35 purchased in June) cost $125 each.
The last 0 jackets (out of the 30 purchased in September) cost $100 each.
So the total value of the remaining inventory is:
30 x $175 + 16 x $150 + 10 x $125 + 0 x $100 = $5,000
Therefore, the answer is B. $5,000.
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Erin is planning on putting tile down in her
kitchen around the island. How many square feet
of tile will she need to purchase?
16 ft
16 ft
3 ft
Island
7 ft
12 ft
2 ft
4ft
10ft
Erin will need to purchase 48ft² of tile for her kitchen island.
In order to calculate the square footage of tile needed for Erin’s kitchen island, we will use the formula for the area of a rectangle: A = lw, where A is the area, l is the length, and w is the width.
The first step is to measure the length and width of the island. Let’s assume that the length is 16ft and the width is 3ft.
Next, we will use the formula to calculate the area of the island: A = lw
A = 16ft x 3ft
A = 48ft²
Finally, Erin will need to purchase 48ft² of tile for her kitchen island.
To double check our calculations, we can also calculate the area of each individual side of the island. For example, the area of the 16ft side is 16ft x 2ft = 32ft². The area of the 3ft side is 3ft x 7ft = 21 ft². When we add the areas together, 32ft² + 21ft² = 53ft². Since 53ft² is greater than 48ft², it is clear that calculating the area of the entire island is the correct solution.
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Tuiton for one year at state university is about $13,000. Devon would like to attend this University and will save money each month for the next four years. His parents will give him $5,200 for his first year of tuition. Which planet shows a minimum amount of money Devon must save to have enough money to pay for his first year tuition?
Devon needs to save at least $162.50 per month for the next four years to have enough money to pay for his first year tuition at state university.
To calculate the minimum amount of money Devon must save to have enough money to pay for his first year tuition, we need to take into account the amount of money he has available now and the amount he plans to save each month for the next four years.
First, we can calculate the total amount of money Devon will have available for his first year of tuition by adding the $5,200 his parents will give him to the amount he plans to save over the next four years. If he saves the same amount each month, he will save $x per month for 48 months, which gives him a total of $48x. Therefore, the total amount of money he will have available is:
Total = $5,200 + $48x
We want to find the minimum amount of money he must save to have enough to pay for his first year tuition, which is $13,000. So we set up an equation:
$5,200 + $48x = $13,000
Solving for x, we get:
$48x = $13,000 - $5,200
$48x = $7,800
x = $7,800 / $48
x ≈ $162.50
Therefore, Devon needs to save at least $162.50 per month for the next four years to have enough money to pay for his first year tuition at state university.
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