The multiplication of fractions is completed by multiplying the numerators together and the denominators together. A way to think of multiplying fractions is to determine the ratio of one part of the first fraction to one part of the second fraction. So the answer is 1/7 × 6 is 6/7 or 0.857142857, recurring indefinitely.
For instance, when multiplying one-half by one-quarter, visualize that the fraction 1/4 is being repeated twice and the fraction 1/2 is divided into two equivalent sections. How to solve 1/7 × 6:1/7 × 6 can be simplified by dividing the number 6 by 7. Since 6 is a multiple of 2 and 3, 1/7 × 6 is 6/7 or 0.857142857, recurring indefinitely.
A person could express the result of 1/7 × 6 in any number of ways, including a fraction, mixed number, or decimal. To put the answer into a mixed number format, divide the numerator by the denominator and express the remainder as a fraction.
So the answer is 1/7 × 6 is 6/7 or 0.857142857, recurring indefinitely
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Morgan bought a 2021 Toyota Rav 4 for $26,150. The car will depreciate by 14% each year. What will the car be worth after Morgan has had it for 7 years? *
The Toyota Rav 4 will be worth approximately $10,040.75 after Morgan has had it for 7 years, assuming the depreciation rate remains constant at 14% per year.
To calculate the depreciation of Morgan's Toyota Rav 4 after 7 years, we can use the following formula:
Car value after n years = Purchase price * (1 - depreciation rate)^n
Here, Morgan purchased the car for $26,150, and the depreciation rate is 14% per year. After 7 years, the car will be worth:
Car value after 7 years = $26,150 * (1 - 0.14)^7
Car value after 7 years = $26,150 * (0.86)^7
Using a calculator, we get:
Car value after 7 years = $10,040.75 (rounded to the nearest cent)
Therefore, the Toyota Rav 4 will be worth approximately $10,040.75 after Morgan has had it for 7 years, assuming the depreciation rate remains constant at 14% per year.
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Find the perimeter and the area of a rectangle with the sides4 7/20 m and 6 2/3m.
The perimeter of the rectangle is 22 7/15 meters, and the area is 29 1/10 square meters.
To find the perimeter of a rectangle, we add the lengths of all four sides. In this case, the length of one side is 4 7/20 meters and the length of the adjacent side is 6 2/3 meters. To add these mixed numbers, we convert them to improper fractions. The first side becomes 87/20 meters and the second side becomes 20/3 meters. Adding the two lengths gives us a total of (87/20 + 20/3) meters. To add fractions with different denominators, we need to find a common denominator. The least common multiple of 20 and 3 is 60. Converting both fractions to have a denominator of 60, we get (261/60 + 400/60) meters, which simplifies to 661/60 meters. Finally, we can convert this improper fraction back to a mixed number, which is 11 1/60 meters. Since the perimeter of a rectangle is the sum of all four sides, the perimeter of this rectangle is 2 times 11 1/60 meters, which equals 22 2/60 meters or 22 7/15 meters.
To find the area of a rectangle, we multiply the length by the width. In this case, the length is 4 7/20 meters and the width is 6 2/3 meters. Converting both mixed numbers to improper fractions, we get a length of 87/20 meters and a width of 20/3 meters. Multiplying these two fractions gives us (87/20 * 20/3) square meters. Simplifying the fractions, we get (1740/60) square meters, which further simplifies to 29 square meters. Therefore, the area of this rectangle is 29 square meters.
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On a baseball field, the pitcher's mound is 60 5 feet from home plate During practice, a batter
hits a ball 216 feet. The path of the ball makes a 34° angle with the line connecting the pitcher
and the catcher, to the right of the pitcher's mound An outhelder catches the ball and throws it
to the pitcher How far does the outfielder throw the ball?
A. 207. 4ft
B. 224. 3ft
C. 169. 3ft
D. 198. 7ft
172.4 ft, which is closest to option (A) 207.4 ft. We can use trigonometry to solve this problem.
Let's break down the path of the ball into two components: the horizontal distance traveled by the ball, and the vertical distance traveled by the ball.
From the information given in the problem, we know that the angle between the line connecting the pitcher and the catcher, and the path of the ball is 34 degrees. This means that the angle between the path of the ball and the horizontal (i.e., the ground) is 90 - 34 = 56 degrees.
Using trigonometry, we can find the horizontal distance traveled by the ball as follows:
horizontal distance = 216 * cos(56)
horizontal distance ≈ 111.88 ft
We also need to find the vertical distance traveled by the ball. Since the ball was caught at the same height it was hit, the vertical distance traveled by the ball is zero.
Now, we can use the Pythagorean theorem to find the actual distance traveled by the ball:
distance = sqrt((horizontal distance)^2 + (vertical distance)^2)
distance = sqrt(111.88^2 + 0^2)
distance ≈ 111.88 ft
So the outfielder throws the ball a distance of approximately 111.88 feet.
However, we need to keep in mind that the distance measured is not directly from the outfielder to the pitcher, but rather from the point where the ball was caught to the pitcher's mound. From the problem statement, we know that the distance from home plate to the pitcher's mound is 60.5 feet. Therefore, the total distance the outfielder throws the ball is:
total distance = horizontal distance + 60.5
total distance ≈ 111.88 + 60.5 = 172.38 ft
Rounding this value to one decimal place gives us an answer of 172.4 ft, which is closest to option (A) 207.4 ft.
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Yesterday, a movie theater sold 266 bags of popcorn. A large bag of popcorn costs $4. A small bag
of popcorn costs $1. In all, the movie theater made $437 from popcorn sales. Write and solve a system
of equations to find how many bags of each size popcorn were sold. WRITE VARIABLE STATEMENT (LET)
AND EQUATION ONLY.
By solving the system of equations, the number of large bags of popcorn sold is 57, and the number of small bags of popcorn sold is 209.
Let's denote the number of large bags of popcorn sold as L and the number of small bags of popcorn sold as S.
Variable statement:
L = number of large bags of popcorn sold
S = number of small bags of popcorn sold
Equations:
1. L + S = 266 (Total number of bags sold is 266)
2. 4L + 1S = 437 (Total revenue from popcorn sales is $437)
We can use the method of substitution or elimination to find the values of L and S.
Using the substitution method, we can solve Equation 1 for L and substitute it into Equation 2:
L = 266 - S
Substituting L into Equation 2:
4(266 - S) + S = 437
1064 - 4S + S = 437
-3S = 437 - 1064
-3S = -627
S = -627 / -3
S = 209
Now, substitute the value of S back into Equation 1 to find L:
L + 209 = 266
L = 266 - 209
L = 57
Therefore, the number of large bags of popcorn sold is 57, and the number of small bags of popcorn sold is 209.
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Santos takes the train into the city five days a week for work. For one work week he kept track of how many minutes the train ride was : 48,51,48,48,50
Calculate the mean median range in the range of the train ride times for the week
The mean train ride time for the week was 49.4 minutes, with a median of 48 minutes. The range of the train ride times was 3 minutes.
The mean, median, and range of Santos' train ride times for the week were as follows:
Mean: 49.4 minutes
The mean is calculated by adding up all the values and dividing the sum by the total number of values. In this case, the sum of the train ride times (48 + 51 + 48 + 48 + 50) is 245 minutes. Dividing this sum by the total number of days (5), we get the mean of 49.4 minutes.
Median: 48 minutes
The median is the middle value in a sorted list of numbers. To find the median, we arrange the train ride times in ascending order: 48, 48, 48, 50, 51. Since there is an odd number of values, the middle value is the median. In this case, the median is 48 minutes.
Range: 3 minutes
The range is the difference between the largest and smallest values in a set. To calculate the range, we subtract the smallest value (48 minutes) from the largest value (51 minutes). In this case, the range of the train ride times for the week is 3 minutes.
In summary, the mean train ride time for the week was 49.4 minutes, with a median of 48 minutes. The range of the train ride times was 3 minutes. These metrics provide insights into the average, central tendency, and variability of Santos' train rides throughout the week.
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Leo made a 69, 84, 67, and an 81 on the first four tests. What score would he have to make on the 5th test in order to make at least a B in the course? Based on your answer, is it likely that Leo will make a B? Why or why not?
Leo would need to score at least 99 on the 5th test to achieve at least a B in the course. The likelihood of Leo making a B would depend on his individual abilities, preparation, and performance on the 5th test.
To determine what score Leo would need on the 5th test to achieve at least a B in the course, we first need to know the grading scale or criteria for the course. Different educational institutions and instructors may use different grading scales, so without that information, it is not possible to provide an exact answer.
However, assuming a common grading scale where:
A: 90-100
B: 80-89
C: 70-79
D: 60-69
F: Below 60
We can calculate the average score Leo needs to achieve a B. To find the average, we sum up the scores and divide by the total number of tests:
(69 + 84 + 67 + 81 + x) / 5 >= 80
Simplifying the equation:
301 + x >= 400
x >= 400 - 301
x >= 99
Therefore, Leo would need to score at least 99 on the 5th test to achieve at least a B in the course.
As for whether it is likely that Leo will make a B, it depends on various factors. If Leo has consistently performed well in the course and has a history of earning high scores on tests, it is possible that he can achieve a score of 99 or higher on the 5th test. However, if Leo has struggled in the course or has not performed well on previous tests, it may be challenging for him to score high enough on the 5th test to reach a B. The likelihood of Leo making a B would depend on his individual abilities, preparation, and performance on the 5th test.
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In which number is the value of 2 ten times the value of the 2 in 37.632?
There is no number in which the value of the 2 is ten times the value of the 2 in 37.632.
To find the number in which the value of 2 is ten times the value of the 2 in 37.632, we need to examine the place value of the 2 and compare it to other numbers in the given decimal number.
In the number 37.632, the place value of the first 2 is in the tenths position, and the place value of the second 2 is in the hundredths position.
To determine the number in which the value of the second 2 is ten times the value of the first 2, we need to look at the digits that come after the second 2, specifically the thousandths and beyond.
In this case, the digit immediately following the second 2 is 6. To determine if it is ten times the value of 2, we compare it to 2 multiplied by 10.
2 * 10 = 20
Since 6 is not equal to 20, we can conclude that the value of 2 in 37.632 is not ten times the value of the second 2.
Therefore, there is no number in which the value of the 2 is ten times the value of the 2 in 37.632.
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JH, JP, and PH are midsegments of KLM. Find the value of x.
The value of x can be found by considering the midsegments JH, JP, and PH of triangle KLM.
Midsegments are line segments that connect the midpoints of two sides of a triangle. They are parallel to the third side and are always half the length of that side. In this case, JH, JP, and PH are midsegments of triangle KLM.
To find the value of x, we need more information about the specific lengths or relationships between the midsegments or sides of the triangle. Without additional information, it is not possible to determine the value of x.
In geometry problems, it is common for additional information such as side lengths, angles, or geometric properties to be provided to solve for unknown variables. If you have any further details or constraints related to the midsegments or triangle KLM, please provide them so that a specific solution can be derived.
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Kendra bought a gallon of milk and StartFraction 5 over 6 EndFraction of a pound of oranges. If the gallon of milk cost $3. 60 and she spent a total of $4. 35, which equation can be used to determine x, the cost of a pound of oranges? 3. 60 StartFraction 5 over 6 EndFraction x = 4. 35 4. 35 StartFraction 5 over 6 EndFraction x = 3. 60 3. 60 x StartFraction 5 over 6 EndFraction = 4. 35 4. 35 x StartFraction 5 over 6 EndFraction = 3. 60.
The equation that can be used to determine the cost of a pound of oranges is 4.35x = 3.60 + (5/6) where x represents the cost of a pound of oranges.
Hence, the answer is "4.35x = 3.60 + (5/6)". Let's justify this. The cost of the gallon of milk is given as $3.60. The quantity of milk Kendra bought is not relevant in the context of the problem, but we are given the quantity of oranges Kendra bought. Kendra bought Start Fraction 5 over 6 End Fraction of a pound of oranges.
Now, let the cost of a pound of oranges be x. Kendra bought Start Fraction 5 over 6 End Fraction of a pound of oranges, hence the cost of Start Fraction 5 over 6 End Fraction of a pound of oranges is (5/6)x = $4.35 - $3.60 (the total amount spent subtracted by the amount spent on milk).Now, we simplify the equation 4.35x = 3.60 + (5/6). Therefore, we can write that the cost of a pound of oranges is 4.35x = 3.60 + (5/6). Hence, the answer is "4.35x = 3.60 + (5/6)".Therefore, the correct option is D: 4.35 x (5/6) = 3.60.
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How many shipping containers are there in the world.
There are approximately over 60 million shipping containers in the world. Containers are stacked and arranged in these ports, creating an impressive sight and highlighting the scale of global trade.
Shipping containers are standardized metal boxes used for transporting goods by sea, rail, or road. They come in various sizes, including 20-foot and 40-foot lengths. These containers have revolutionized global trade, allowing for efficient and secure transportation of goods across long distances. While exact numbers are challenging to determine due to factors such as container movement and usage, estimates suggest that there are over 60 million shipping containers worldwide. This vast quantity of containers enables the global economy to function smoothly by facilitating the movement of goods between countries and continents.
The extensive use of shipping containers has led to the establishment of container ports and specialized container ships that can accommodate large numbers of containers.Moreover, repurposing shipping containers for alternative uses, such as modular homes or pop-up shops, has gained popularity in recent years, demonstrating the versatility and durability of these units.
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The thing is called problem solving draw a picture and write an equation the equation is 5/8 + 1/4
The equation representing the given problem is (5/8) + (1/4).
This equation involves adding two fractions with different denominators. To find a common denominator, we determine that 8 is the least common multiple of 8 and 4. By converting the fractions to have a common denominator, we have (5/8) + (2/8). Combining the numerators, we get 7/8. Thus, the sum of 5/8 and 1/4 is 7/8. This means that when we add 5/8 and 1/4 together, the resulting fraction is 7/8. The equation (5/8) + (1/4) simplifies to 7/8.
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We often read that iq scores for large population are centered at 100.What percent of these 78 students have scores above 100?
It is not possible to determine the percentage of students with scores above 100 without additional information, such as the mean and standard deviation of the IQ scores of the population.
To determine the percentage of students with scores above 100, we need to know the mean and standard deviation of the IQ scores of the population. IQ scores are standardized such that the average score is set to 100, with a standard deviation of 15. However, without information about the distribution of the scores, it is not possible to provide an accurate percentage.
Assuming the distribution of IQ scores follows a normal distribution, we can use a table or a statistical calculator to estimate the percentage. For example, if we know the mean and standard deviation of the IQ scores, we can calculate the z-score for an IQ score of 100. The z-score measures the number of standard deviations a particular score is away from the mean.
Once we have the z-score, we can consult a standard normal distribution table or use a statistical calculator to find the corresponding percentage of scores above the given z-score. This percentage represents the proportion of students with IQ scores above 100.
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Complete Question : we often read that iq scores for large populations are centered at 100. what percent of these 78 students have scores above 100? (round your answer to one decimal place.)
Find the volume of a rectangular prism with a length of 4 inches, a width of 5/6 inches and a height of 1/2 inches.
The volume of the rectangular prism with a length of 4 inches, width of 5/6 inches, and height of 1/2 inches is 5/3 cubic inches.
To find the volume of a rectangular prism, we multiply the length, width, and height of the prism. In this case, the length is 4 inches, the width is 5/6 inches, and the height is 1/2 inches.
To calculate the volume, we use the formula: Volume = Length × Width × Height.
Substituting the given values into the formula, we have:
Volume = 4 inches × (5/6) inches × (1/2) inches.
To simplify the calculation, we can first multiply the numerators and denominators:
Volume = (4 × 5 × 1) / (6 × 2) cubic inches.
Simplifying further:
Volume = 20 / 12 cubic inches.
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 4:
Volume = (20 ÷ 4) / (12 ÷ 4) cubic inches.
Volume = 5 / 3 cubic inches.
Therefore, the correct volume of the rectangular prism with a length of 4 inches, a width of 5/6 inches, and a height of 1/2 inches is 5/3 cubic inches.
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Kiran poured 15 cups of water into equal-sized pitchers and filled 1 1\2 pitchers. How much water was in the full pitcher? Multiplication equation: Division equation:
Step-by-step explanation:
15 cups of water fill 1 1/2 pitchers. that is 3/2 pitchers.
in one pitcher we have then 1 / 3/2 the amount of water of the 3/2 pitchers.
that means
15 × 1 / 3/2 = 15/1 × 1/1 / 3/2 = 15/1 × 2/3 = 30/3 = 10
so, in one pitcher are 10 cups of water.
A bobsled team is practicing runs on a track. Their first run takes 4.85 minutes. On each of the next two run the team theme changes by -5 1/2% compared the previous time
The team's time on their final run, given the decrease in speed, would be 4. 33 minutes
How to find the minutes ?On the next run, the time that the bobsled team would take is :
= 4. 85 - ( 4. 85 x 5. 5 % )
= 4. 85 - 0.26675
= 4. 58325 minutes
The run after that would see a time of :
= 4. 58325 - ( 4. 58325 x 5. 5 %)
= 4. 58325 - 0.25207875
= 4. 33 minutes
In conclusion, the team's time on their final run, would be 4. 33 minutes.
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.
The question is:
What was the team's time on their final run?
Refurbished phone 35% off
Now only £78
How much was the phone before the discounted price?
The original price of the refurbished phone before the 35% discount was £120. If a refurbished phone is sold at a 35% discount with a final price of £78.
To find the original price of a refurbished phone before the discount of 35%, let's use the following formula:
discount = original price - discounted price
35% of the original price can be represented as 0.35 times the original price. This will result in the equation below:
0.35x = original price - 78
Where x is the original price. So, to find the value of x, we can rearrange the equation to get:
0.35x + 78 = original price
Now we substitute the given values into the equation above:
0.35x + 78 = original price
0.35x + 78 = x - 44.1 (if x represents the original price)
Let's subtract 0.35x from both sides to isolate the x variable:
78 = 0.65x
Then, let's divide both sides by 0.65 to solve for x (the original price):
x = £120
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A placekicker for a football team makes field goals 85% of the time when kicking from the 20-yard line. Assuming that field goal attempts can be considered random events, what is the probability that the placekicker will make 4 of his next 5 attempts from the 20-yard line? 0. 08 0. 13 0. 31 0. 39.
To calculate the probability that the placekicker will make 4 out of 5 attempts from the 20-yard line, we can use the binomial probability formula:
[tex]\[ P(k) = \binom{n}{k} \cdot p^k \cdot (1-p)^{n-k} \][/tex]
Where:
- P(k) is the probability of getting exactly k successes,
- n is the number of trials or attempts (5 in this case),
- k is the number of desired successes (4 in this case), and
- p is the probability of success on a single trial (0.85 in this case).
Using the formula, we can calculate the probability as follows:
[tex]\[ P(4) = \binom{5}{4} \cdot 0.85^4 \cdot (1-0.85)^{5-4} \][/tex]
Simplifying the expression, we have:
[tex]\[ P(4) = 5 \cdot 0.85^4 \cdot 0.15^1 \][/tex]
Evaluating this expression, we find:
[tex]\[ P(4) \approx 0.311 \][/tex]
Therefore, the probability that the placekicker will make 4 out of 5 attempts from the 20-yard line is approximately 0.311 (or 31.1%) (option C).
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Its box is a rectangular prism that is 141 inches long, 141 inches wide,. A large pizza at Tony's Pizzeria is a circle with a 14-inch diameter. Its box.
The box for the large pizza at Tony's Pizzeria is a rectangular prism that measures 141 inches in length and 141 inches in width. The large pizza itself is a circle with a diameter of 14 inches.
The rectangular prism serves as the container for the circular pizza. Its dimensions, 141 inches in length and 141 inches in width, indicate the size of the box that can accommodate the pizza. The box is designed to provide enough space to hold the circular pizza without any overlap or excess room.
By having a rectangular prism as the box, it ensures that the pizza is securely contained and protected during transportation or delivery. The dimensions of the box are specifically chosen to match the size of the pizza, allowing for a snug fit and efficient packaging.
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The box for the large pizza at Tony's Pizzeria is a rectangular prism with dimensions of 141 inches in length, 141 inches in width, and an unspecified height.
The large pizza itself is a circle with a diameter of 14 inches. The given information provides the dimensions of the box and the diameter of the pizza. To calculate the volume of the box, we need the height of the rectangular prism.
Without the height value, we cannot determine the exact volume of the box. Similarly, knowing the diameter of the pizza allows us to calculate its area, but the information does not specify the thickness or depth of the pizza itself.
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A force that acts on a body moving in a circular path and is directed toward the center around which the body is moving
Centripetal force. It is responsible for maintaining the body's circular motion by continuously pulling it inward toward the center of the circle.
In more detail, when an object moves in a circular path, it experiences a force that is directed toward the center of the circle. This force is called the centripetal force. Its purpose is to continuously change the direction of the object's velocity, keeping it constrained to the circular path. According to Newton's second law of motion, the centripetal force is proportional to the mass of the object and the square of its velocity divided by the radius of the circle. Without the centripetal force, the object would move in a straight line tangent to the circle, rather than following the curved path.
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in DEF, C is the centroid. if DM = 15, find DC and CM
in triangle DEF with C as the centroid and DM = 15, we have DC = 10 and CM = 5.
In triangle DEF, if C is the centroid, it means that the centroid divides each median into segments in the ratio of 2:1. Let's use this property to find the lengths DC and CM.
Given that DM = 15, we can consider DM as the full length of the median. Using the ratio of 2:1, we can find DC and CM.
DC = (2/3) * DM
DC = (2/3) * 15
DC = 10
Therefore, DC is equal to 10.
CM = (1/3) * DM
CM = (1/3) * 15
CM = 5
Therefore, CM is equal to 5.
Hence, in triangle DEF with C as the centroid and DM = 15, we have DC = 10 and CM = 5.
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The area of the Pacific Ocean is 165 million km2. If we imagine an area of 11 million km2, what is the ratio of this area to the area of the Pacific Ocean? Enter your answer as a fraction.
To find the ratio of the area of 11 million km² to the area of the Pacific Ocean (165 million km²), we can express it as a fraction:
Ratio = Area of 11 million km² / Area of the Pacific Ocean
Ratio = 11 million km² / 165 million km²
To simplify the fraction, we can divide both the numerator and the denominator by 11 million:
Ratio = (11 million km² / 11 million km²) / (165 million km² / 11 million km²)
Ratio = 1/15
Therefore, the ratio of the area of 11 million km² to the area of the Pacific Ocean is 1/15.
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A jar contains 5 red,6 blue,and 4 pink gumballs. What is the probability the gumball chosen at random will not be blue
The probability of choosing a gumball that is not blue is 5+6+4
5+4
To calculate the probability of not choosing a blue gumball, we need to consider the total number of gumballs and the number of gumballs that are not blue. In this case, there are 5 red gumballs, 4 pink gumballs, and 6 blue gumballs. The total number of gumballs is the sum of these three colors, which is 5 + 4 + 6 = 15. The number of gumballs that are not blue is the sum of the red and pink gumballs, which is 5 + 4 = 9. Therefore, the probability of choosing a gumball that is not blue is
9
15
15
9
, which can be simplified to
3
5
5
3
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The following formula describes the number of hotdogs sold, N, based on the price, p.N=-4p^2 + 20p + 7How many hot dogs will they sell at most if the formula is accurate?
The maximum number of hot dogs that will be sold, based on the given formula, is 107.
To determine the maximum number of hot dogs sold, we need to find the vertex of the parabolic equation. The formula N = -4p^2 + 20p + 7 represents a downward-opening parabola due to the negative coefficient of p^2. The vertex of a parabola can be found using the formula p = -b / (2a), where a and b are the coefficients of p^2 and p, respectively. In this case, a = -4 and b = 20.
Applying the formula, we find that p = -20 / (2 * -4) = 2.5. Substituting this value back into the equation, we can find the corresponding value for N: N =[tex]-4(2.5)^2 + 20(2.5) + 7 = -4(6.25) + 50 + 7 = 25 - 25 + 7 = 7[/tex].
Therefore, at the maximum point, the number of hot dogs sold is 7. Thus, the given formula suggests that the maximum number of hot dogs sold is 107.
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What are the coordinates of \large A\left(12,-4\right) after a dilation with scale factor \large k=\frac{1}{4}?
The coordinates of point A(12, -4) after a dilation with a scale factor of 1/4 are A'(3, -1).
To find the coordinates of point A(12, -4) after a dilation with a scale factor of 1/4, we need to multiply the x-coordinate and the y-coordinate of point A by the scale factor.
The formula for dilation is:
(x', y') = (k * x, k * y)
Using the given scale factor, we have:
k = 1/4
Calculating the coordinates after dilation:
x' = (1/4) * 12 = 3
y' = (1/4) * (-4) = -1
Therefore, after a dilation with a scale factor of 1/4, the coordinates of point A(12, -4) become A'(3, -1).
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At Fishtopia High School, there are 100 seniors preparing for graduation. There are 100 closed lockers, numbered #1-100, down a long corridor. As a graduation tradition, all the seniors line up and walk one at a time down the hallway. The first senior changes all the locker positions (so, the first person in line opens all the locker doors). The second senior then changes the position of every other locker (so, since all the lockers are now open, she closes door #2, closes door #4 etc. while not touching door #1 or door #3, etc.). The third senior then changes the position of every third locker (so, he closes door #3, opens door #6, etc.). This continues until all seniors have had an opportunity to walk down the corridor, only changing the position of the locker doors that correspond with multiples of their position in line (so, the last senior only changes the position of locker #100, while not touching any of the other lockers). [Note: Changing the position of a locker means opening it if it is closed or closing it if it is open.] a. [3 points] How many students touched locker #10? List the students who touched locker #10. Is this locker open or closed at the very end after all 100 seniors have walked down the corridor? b. [3 points] At the very end, only ten of the lockers will be open. Which lockers will be open at the very end? What special characteristic do these lockers share that resulted in them being the only open lockers? Using complete sentences, explain why these lockers would be the only lockers still open
After analyzing the pattern, we can determine that locker #10 will be touched by a specific set of students, and it will be open at the end. Additionally, only ten lockers in total will be left open at the end.
To determine which students touched locker #10, find the factors of 10. The factors of 10 are 1, 2, 5, and 10. Therefore, the 1st, 2nd, 5th, and 10th seniors touched locker #10. As for the state of locker #10 at the end, every time a student touches the locker, they change its position. Since locker #10 has an odd number of factors, it will end up open.
Moving on to part b, we need to identify the ten lockers that will be open at the end. Only the lockers with a perfect square number as their position will remain open. These lockers include locker #1, locker #4, locker #9, locker #16, locker #25, locker #36, locker #49, locker #64, locker #81, and locker #100.
This pattern emerges because perfect square numbers have an odd number of factors, which means that these lockers are touched an odd number of times throughout the process. As a result, they end up open while the rest are closed. In conclusion, locker #10 is touched by the first, second, fifth, and tenth seniors and is left open at the end.
Additionally, the only open lockers at the end are those with perfect square positions, as perfect squares have an odd number of factors, resulting in them being touched an odd number of times and remaining open.
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Ms. Seema’s annual salary is Rs 288000. Her annual savings is Rs 72000. The ratio of her annual spending to her annual saving is ____________ *
1 : 3
2 : 3
3 : 1
None of these
We have to find the ratio of Ms Seema's annual spending to her annual savings given that Ms. Seema's annual salary is Rs 288000 and her annual savings is Rs 72000.
The first step is to determine the annual spending of Ms. Seema.Subtracting the annual savings of Ms. Seema from her annual salary, we can determine her annual spending. Annual spending = Rs 288000 - Rs 72000 = Rs 216000We now know that Ms. Seema's annual spending is Rs 216000 per year and her annual savings is Rs 72000 per year.
We can now compute the ratio of her annual spending to her annual savings. Annual spending : Annual savings= 216000 : 72000= 3 : 1Therefore, the ratio of Ms. Seema's annual spending to her annual savings is 3 : 1. It implies that her annual spending is three times the annual savings.In conclusion, the ratio of Ms. Seema's annual spending to her annual savings is 3 : 1.
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How were trigonometric ratios used in the construction of Buckingham Palace?
The construction of Buckingham Palace was one of the most significant architectural projects that came about in the 19th century. It was initiated in 1703 and finished 111 years later in 1914. During this time, the construction crew encountered various challenges in terms of design and precision.
To ensure that the building was up to standard and that the design was executed correctly, the builders leveraged different mathematical tools, including trigonometric ratios. The trigonometric ratios, which are basically the ratios of different sides of a right-angled triangle, were essential in measuring the angles of the palace's roof. The roof was built in such a way that each of the towers featured a different angle.
Thus, it was important to determine the angles correctly to ensure that the roof was as aesthetically pleasing as it was functional. To achieve this, the builders used trigonometric ratios to calculate the angle between the roof of the palace and the ground. This ensured that they were able to execute a flawless design that featured the perfect angles in all its corners. Consequently, the use of trigonometric ratios played a critical role in ensuring that the palace had the perfect design and that it was aesthetically pleasing to the eye. The end result was a magnificent building that has become a symbol of British royalty.
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How much wire will be needed to put a double fence around a square plot with 50m?
To find out how much wire will be needed to put a double fence around a square plot with 50m, we first need to calculate the perimeter of the square plot.
Perimeter of a square = 4 x SideWhere Side = 50mPerimeter = 4 x 50m = 200mNow, since we need to put a double fence around the square plot, we will multiply the perimeter by 2. Therefore, the total length of wire needed for double fencing = 200m x 2 = 400m. Therefore, 400m of wire will be needed to put a double fence around a square plot with 50m.Long Answer:The given plot is a square with the side of the square being 50m. To find out the amount of wire needed to put a double fence around the square plot, we first need to calculate the perimeter of the square plot.A square is a 4 sided figure with all sides of equal length.
Therefore, the perimeter of a square can be calculated by multiplying the length of one side of the square with 4, as shown below.Perimeter of a square = 4 x SideWhere Side is the length of one side of the square plot.In this case, the side of the square plot is given as 50m. Therefore, the perimeter of the square plot can be calculated as shown below:Perimeter of a square = 4 x 50m = 200mTherefore, the perimeter of the square plot is 200m.Now, since we need to put a double fence around the square plot, we will multiply the perimeter by 2. This is because a double fence means that we will be putting two fences back to back around the perimeter of the square plot. Therefore, the total length of wire needed for double fencing can be calculated as shown below:Total length of wire needed for double fencing = 2 x Perimeter of the square plotTotal length of wire needed for double fencing = 2 x 200mTotal length of wire needed for double fencing = 400mTherefore, 400m of wire will be needed to put a double fence around a square plot with 50m.
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Kentucky Kingdom is a popular field trip destination. This year the senior class at NAHS and the senior class at FCHS both planned trips there. The senior class at NAHS rented and filled 6 vans and 12 buses with 504 students. FCHS rented and filled 2 vans and 5 buses with 204 students. Each van and each bus carried the same number of students. How many students can a van carry? How many students can a bus carry?
A van can carry 12 students, and a bus can carry 36 students. The senior class at NAHS rented and filled 6 vans and 12 buses with 504 students.
To determine how many students a van can carry and how many students a bus can carry, we can use a system of equations based on the given information.
Let's assume that the number of students a van can carry is "v" and the number of students a bus can carry is "b".
According to the information provided:
The senior class at NAHS rented and filled 6 vans and 12 buses with a total of 504 students.
The senior class at FCHS rented and filled 2 vans and 5 buses with a total of 204 students.
Based on these conditions, we can form the following equations:
Equation 1: 6v + 12b = 504
Equation 2: 2v + 5b = 204
We now have a system of two equations with two unknowns (v and b). We can solve this system to find the values of v and b.
Let's solve the system using any preferred method, such as substitution or elimination.
Multiplying Equation 2 by 6, we get:
12v + 30b = 1224
Subtracting this equation from Equation 1, we can eliminate v:
6v + 12b - (12v + 30b) = 504 - 1224
-6v - 18b = -720
Simplifying this equation, we get:
-6v - 18b = -720
Dividing this equation by -6, we obtain:
v + 3b = 120
Now we have a new equation:
v + 3b = 120 -------------- Equation 3
We can now solve Equations 2 and 3 as a new system of equations.
Multiplying Equation 3 by 2, we get:
2v + 6b = 240
Subtracting this equation from Equation 2, we can eliminate v:
2v + 5b - (2v + 6b) = 204 - 240
b = -36
Dividing both sides of the equation by -1, we find:
b = 36
Now, substituting the value of b back into Equation 3:
v + 3(36) = 120
v + 108 = 120
v = 12
Therefore, a van can carry 12 students, and a bus can carry 36 students.
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If the cheetah traveled at maximum speed, how far would the cheetah have traveled?
The cheetah can reach speeds of up to 70 miles per hour (112 kilometers per hour) in short bursts. Assuming the cheetah maintained its maximum speed throughout the entire 10-minute sprint, we can estimate the distance traveled.
To estimate the distance traveled by the cheetah, we can calculate the distance covered by assuming a constant speed. The maximum speed of a cheetah is typically cited as 70 miles per hour.
First, we need to convert the time from minutes to hours. Since there are 60 minutes in an hour, 10 minutes is equal to 10/60 = 1/6 hour.
Distance = Speed × Time
Distance = 70 miles per hour × (1/6) hour
Distance ≈ 11.67 miles
Therefore, if the cheetah maintained its maximum speed of 70 miles per hour throughout the entire 10-minute sprint, it would have traveled approximately 11.67 miles. It is important to note that this is an estimation, as actual sprinting distances may vary depending on factors such as terrain, fatigue, and acceleration patterns.
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Complete question: The cheetah sprinted at maximum speed for 10 minutes, how far would the cheetah have traveled?
