The exact value of tangent (19π/12) is option C: StartFraction 3 minus StartRoot 3 EndRoot Over 3 + StartRoot 3 EndRoot EndFraction.
To find the exact value of tangent (19π/12), we can use the trigonometric identity:
tangent (θ) = sin (θ) / cos (θ).
First, let's find the values of sin (19π/12) and cos (19π/12).
Using the unit circle, we can determine that sin (19π/12) = -1/2 and cos (19π/12) = -√3/2.
Now we can substitute these values into the tangent formula:
tangent (19π/12) = sin (19π/12) / cos (19π/12) = (-1/2) / (-√3/2).
Simplifying the expression by multiplying the numerator and denominator by 2/√3:
tangent (19π/12) = (-1/2) * (2/√3) / (-√3/2) = (1/√3).
To rationalize the denominator, we multiply the numerator and denominator by √3:
tangent (19π/12) = (1/√3) * (√3/√3) = √3/3.
Therefore, the exact value of tangent (19π/12) is option C: StartFraction 3 minus StartRoot 3 EndRoot Over 3 + StartRoot 3 EndRoot EndFraction.
Learn more about tangent here
https://brainly.com/question/4470346
#SPJ11
Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 14 fect and a height of 13 fect. Container B has a diameter of 12 feet and a height of 18 feet. Container A is full of water and the water is pumped into Container B until Container A is empty. After the pumping is complete. what is the volume of the empty portion of Container B, to the nearest tenth of a cubic foot?
The volume of the empty portion of Container B is given as follows:
34.6 ft³.
How to obtain the volume of the cylinder?The volume of a cylinder of radius r and height h is given by the equation presented as follows:
V = πr²h.
(the radius is half the diameter).
Hence the volume of Container A is given as follows:
V = π x 7² x 13
V = 2001.2 ft³.
The volume of container B is given as follows:
V = π x 6² x 18
V = 2035.8 ft³.
Then the volume of the empty portion of Container B is given as follows:
2035.8 - 2001.2 = 34.6 ft³.
More can be learned about the volume of a cylinder at brainly.com/question/9554871
#SPJ1
The price of a nine minute phone call is $3. 15 what is the price of a 12 minute phone call
The cost of a 12-minute phone call is $4.20.
The cost of a nine-minute phone call is $3.15. To find the cost of a 12-minute phone call, we must first determine the cost per minute. We can do this by dividing the cost of a nine-minute call by 9 minutes, which gives us the cost per minute.
3.15 ÷ 9 = $0.35 (cost per minute) Now that we know the cost per minute, we can find the cost of a 12-minute phone call by multiplying the cost per minute by the number of minutes. 12 × $0.35 = $4.20 Therefore, the price of a 12-minute phone call is $4.20.
To know more about cost visit:-
https://brainly.com/question/32660686
#SPJ11
A bedroom wall measures 11 ft x 13 ft, and features a rectangular doorway that measures 6 ft x 3 ft. How many square of paint will be needed to cover the wall only?
The wall area that needs to be painted, excluding the doorway, is 125 square feet.
The total area of the wall is obtained by multiplying its length and width:
Total area = 11 ft * 13 ft = 143 square feet.
The area of the doorway is given by multiplying its length and width:
Doorway area = 6 ft * 3 ft = 18 square feet.
To find the area of the wall that needs to be painted, we subtract the area of the doorway from the total area:
Painting area = Total area - Doorway area = 143 square feet - 18 square feet = 125 square feet.
Therefore, you will need 125 square feet of paint to cover the wall only.
Learn more about rectangles here: brainly.com/question/29123947
#SPJ11
Which estimate at a 95% confidence level most likely comes from a small sample?
A. 93% (±24%)
B. 82% (±8%)
C. 78% (±4%)
D. 87% (±6%)
The estimate at a 95% confidence level that most likely comes from a small sample is 93% (±24%). The correct option is A
What is margin of error ?The range of values that is most likely to include the true population parameter is known as the margin of error. The standard error, a gauge of the sample statistic's variability, is used to determine the margin of error.
Option A in this situation has the most margin of error of the four, at 24%. In comparison to the other options, this indicates that the true population parameter is probably within 24% of the sample statistic. This implies that option A's sample size is smaller than that of the other options.
Therefore, the estimate at a 95% confidence level that most likely comes from a small sample is 93% (±24%).
Learn more about margin of error here : brainly.com/question/30760332
#SPJ1
Write it as a fact family
12. 4-3. 2=9. 2
The fact family 12, 4, 3, 2, and 9 demonstrates the relationship between addition and subtraction. In this fact family, when we subtract 3 from 4, the result is 1. If we then add 2 to 1, we get 3. Furthermore, when we subtract 2 from 9, the result is 7. If we add 7 and 2 together, the sum is 9.
In the given fact family, the numbers 4 and 3 are related through subtraction. When we subtract 3 from 4, we get 1. This is represented by the equation 4 - 3 = 1.
On the other hand, the numbers 2 and 1 are related through addition. If we add 2 to 1, the sum is 3. This is represented by the equation 1 + 2 = 3.
Similarly, the numbers 9 and 2 are related through subtraction and addition. When we subtract 2 from 9, we get 7, represented by the equation 9 - 2 = 7. By adding 7 and 2 together, the sum is 9, represented by the equation 7 + 2 = 9.
Therefore, the fact family 12, 4, 3, 2, and 9 demonstrates the relationship between addition and subtraction within the given numbers.
Learn more about addition here : brainly.com/question/29464370
#SPJ11
which statement is true about this comparison
0.739 > 0.7380
The statement that is true about this comparison is that they differ in the thousandths place, with 0.739 being greater than 0.7380.
The statement that is true about the comparison
0.739 > 0.7380
is that they differ in the thousandths place. The difference between the two numbers is
0.001 or 1/1000,
which is why we can say that they differ in the thousandths place. This difference is very small, but it is enough to make
0.739 greater than 0.7380.
The comparison between
0.739 and 0.7380
is true in that the former is greater than the latter by a small margin. The two numbers differ in the thousandths place, with 0.739 having a value of
0.739 and 0.7380
having a value of 0.738.
The difference between the two values is
0.001 or 1/1000,
which is very small.
However, this difference is enough to make 0.739 greater than 0.7380.
Therefore, the statement that is true about this comparison is that they differ in the thousandths place, with
0.739 being greater than 0.7380.
To know more about thousandths visit:
https://brainly.com/question/297733
#SPJ11
A population of 1000 alligators has a birthrate of 400 per year. Each year, 150 alligators die, and 150 leave the population to look for new territory, but 30 alligators arrive from other territories to join the population. What is the annual population growth rate per thousand animals
The annual population growth rate per thousand animals in this scenario is 130.
In the given population of 1000 alligators, the birthrate is 400 per year. This means that 400 new alligators are born each year. However, there are also factors that decrease the population. Each year, 150 alligators die and 150 leave the population to search for new territory. On the other hand, 30 alligators arrive from other territories to join the population.
To calculate the annual population growth rate per thousand animals, we can subtract the total number of deaths and departures (150 + 150) from the total number of births and arrivals (400 + 30). This gives us a net increase of 130 alligators.
To calculate the growth rate per thousand animals, we divide the net increase (130) by the initial population size (1000) and multiply the result by 1000. This gives us a growth rate of 130/1000 * 1000 = 130.
Therefore, the annual population growth rate per thousand animals in this scenario is 130.
Learn more about growth rate here:
https://brainly.com/question/7414993
#SPJ11
Identify the expression as an equation containing factors, a fractional equation, or a proportion.
2x/x+7 - x/x+3 = 1 + 1/x^2+10+21
A. Proportion
B. Fractional Equation
C. Equation containing fractions
The given expression is an equation containing fractions.
Given expression is:
[tex]$$\frac{2x}{x+7} - \frac{x}{x+3} = 1 + \frac{1}{x^2+10x+21}$$[/tex]
We can rewrite the given expression as follows:
[tex]$$\frac{2x(x+3)-x(x+7)}{(x+7)(x+3)}=\frac{x^2+10x+22}{(x+3)(x+7)}$$[/tex]
Simplifying the numerator and denominator of the above expression,
we get:[tex]$$\frac{x^2-4x-21}{(x+7)(x+3)} = \frac{x^2+10x+22}{(x+7)(x+3)}$$[/tex]
On simplifying, we get the following equation:
[tex]$$x^2-4x-21=x^2+10x+22$$[/tex]
Simplifying the above equation, we get:
$$14x=-43$$
On dividing by 14 on both sides,
we get:[tex]$${x=-\frac{43}{14}}$$[/tex]
To know more about denominator visit:
https://brainly.com/question/32621096
#SPJ11
James, Gilbert, Matthew, and Simon ran in a relay race. Their times are
listed in the chart below.
James
2/3
Gilbert
11/12
Matthew
5/6
Simon
7/12
1. Find the difference between the fastest boy’s time and the slowest
boy’s time
The difference between the fastest boy's time and the slowest boy's time can be found by comparing their respective times and calculating the difference.
To determine the fastest and slowest times among James, Gilbert, Matthew, and Simon, we examine their recorded times: 2/3, 11/12, 5/6, and 7/12.
To compare these fractions, we need to find a common denominator. In this case, the least common multiple of the denominators 3, 12, 6, and 12 is 12.
Converting the fractions to have a denominator of 12, we get:
James: 2/3 = 8/12
Gilbert: 11/12 (already in terms of 12)
Matthew: 5/6 = 10/12
Simon: 7/12 (already in terms of 12)
Now, we can clearly see that the fastest time is 8/12 (James) and the slowest time is 11/12 (Gilbert).
To find the difference between these two times, we subtract the slowest time from the fastest time:
8/12 - 11/12 = -3/12 = -1/4
Therefore, the difference between the fastest boy's time and the slowest boy's time is -1/4, or in other words, the fastest boy is 1/4 of a unit of time faster than the slowest boy.
To learn more about fractions: -brainly.com/question/10354322
#SPJ11
Is the following event Independent or Dependent:Yolanda grabs 2 red checkers, replacing between.
The correct answer is that the event you described is dependent.
When Yolanda grabs 2 red checkers and replaces them between each draw, the outcome of the first draw affects the probability of the second draw. This is because replacing the checkers means that the probability of drawing a red checker remains the same for each individual draw, but the overall probability changes after each draw.
Let's break it down:
In the first draw, Yolanda has a certain probability of drawing a red checker.
After the first draw, if Yolanda indeed drew a red checker, there is one less red checker in the pool and the total number of checkers has decreased.
In the second draw, Yolanda now has a different probability of drawing a red checker compared to the first draw because the pool of available checkers has changed.
Therefore, the outcome of the first draw affects the probability of the second draw, making the event dependent.
Learn more about probability here:
https://brainly.com/question/15124899
#SPJ11
Which histogram depicts a higher standard deviation.
Histograms visualize the distribution and spread of data. A higher standard deviation implies greater variability in the data points. In a histogram, a wider shape indicates a larger spread of data and thus a higher standard deviation. Therefore, the histogram with a broader shape depicts a higher standard deviation.
To determine which histogram depicts a higher standard deviation, we need to look for the histogram with a greater spread or dispersion of data. In a histogram, a higher standard deviation indicates that the data points are more spread out or have a larger variability. This means that the values are more scattered from the mean. Therefore, the histogram with a wider and more spread-out shape would depict a higher standard deviation, as it indicates a greater variability in the data.
learn more about histograms here:
https://brainly.com/question/16819077
#SPJ11
Alexa is designing a paper airplane whose final shape, when viewed from the top or bottom, is a trapezoid. A sketch of her plane, viewed from the top, is shown on the left.
A trapezoid has a base of 6 centimeters, a height of 3 centimeters, and a top side length of 2 centimeters
The dimensions of one of the identical triangular pieces of the paper airplane are A. 2 cm base, 3 cm height
How to find the dimensions ?From the given information, the paper airplane is designed in the shape of a trapezoid when viewed from the top. The trapezoid has a base of 6 centimeters, a height of 3 centimeters, and a top side length of 2 centimeters.
When we divide the trapezoid along the height, we get two congruent triangles. These triangles have the same shape and size, making them identical. The height of the triangle corresponds to the same height as the trapezoid, which is 3 centimeters.
Therefore, the dimensions of one of the identical triangular pieces of the paper airplane are a base of 2 centimeters and a height of 3 centimeters.
Find out more on trapeziums at https://brainly.com/question/21625730
#SPJ4
Full question is:
Alexa is designing a paper airplane whose final shape, when viewed from the top or bottom, is a trapezoid. A sketch of her plane, viewed from the top, is shown on the left.
What are the dimensions of one of the identical triangular pieces of the plane?
2 cm base, 3 cm height
3 cm base, 3 cm height
3 cm base, 4 cm height
3 cm base, 6 cm height
a:b = 1:5
a:c = 2:1
how many times is b bigger than c
b is 10 times bigger than c. the ratio A:b is equivalent to the ratio a:c multiplied by 5: A:b = (a:c) * 5
To determine how many times b is bigger than c, we need to compare their respective ratios.
Given:
A:b = 1:5
a:c = 2:1
To make a comparison, we can find the relative sizes of b and c by considering the ratios they have with other variables.
From the ratio A:b = 1:5, we can rewrite it as A:b = 2:10 (multiplying both sides by 2).
Comparing the ratios A:b and a:c, we can see that the ratio A:b is equivalent to the ratio a:c multiplied by 5:
A:b = (a:c) * 5
Substituting the given ratios, we have:
2:10 = (2:1) * 5
Now, we can compare the values of b and c directly:
b = 10
c = 1
Therefore, b is 10 times bigger than c.
Learn more about equivalent here
https://brainly.com/question/24734894
#SPJ11
What is the explicit formula for the sequence below?4, – 12, 36, – 108,...A.tn=(−3)n−1B.tn=4(−3)n−1C.tn=4(3)n−1D.tn=4(−3)n
The explicit formula for the given sequence 4, -12, 36, -108,... is D. tn = 4(-3)n. Option D
In the given sequence, each term is obtained by multiplying the previous term by -3. This indicates an exponential decay pattern with a common ratio of -3.
To derive the explicit formula, we start with the initial term 4 and observe that each subsequent term can be obtained by multiplying the previous term by -3:
Term 1: 4
Term 2: -3 × 4 = -12
Term 3: -3 ×(-12) = 36
Term 4: -3 × 36 = -108
We can generalize this pattern by using the formula tn = ar^(n-1), where tn represents the nth term, a is the initial term, and r is the common ratio. In this case, a = 4 and r = -3. Thus, the explicit formula for the sequence is tn = 4(-3)n which matches option D.
learn more about explicit formula here:
https://brainly.com/question/25094536
#SPJ11
Eva drove to work in rush hour traffic, going just 30 miles in 1 hour and 18 minutes. Later that day, she left work early to avoid the rush and was able to take the same route home in 31 minutes. What was Eva's average speed overall?
Hence, Eva's average speed overall is 35.29 miles per hour
The given information can be tabulated as follows: Distance, Time, Speed
Eva drove to work30 miles1 hour 18 minutes1.18 hours
Eva drove to work30 miles1.18 hours
Eva left work31 minutes0.52 hours
Eva left work30 miles0.52 hours
It is given that Eva drove to work in rush hour traffic, going just 30 miles in 1 hour and 18 minutes, i.e. 1.18 hours.
Her speed during this time can be calculated as follows:
Speed = Distance / Time
Speed = 30 / 1.18 = 25.42 miles per hour
Similarly, when Eva left work early to avoid the rush and was able to take the same route home in 31 minutes, i.e. 0.52 hours.
Her speed during this time can be calculated as follows:
Speed = Distance / Time
Speed = 30 / 0.52 = 57.69 miles per hour
Therefore, Eva's average speed overall can be calculated as follows:
Average speed = Total distance / Total time
Total distance = 30 + 30 = 60 miles
Total time = 1.18 + 0.52 = 1.7 hours
Average speed = 60 / 1.7 = 35.29 miles per hour
to know more about average speed visit:
https://brainly.com/question/17661499
#SPJ11
Elizabeth’s credit card computes her finance charges using the previous balance method and a 30-day billing cycle. The table below shows Elizabeth’s credit card transactions in July. Date Amount ($) Transaction 7/1 969. 26 Beginning balance 7/3 45. 00 Payment 7/10 67. 48 Purchase 7/12 20. 00 Payment 7/28 85. 00 Payment If Elizabeth has an APR of 14. 61%, how much will her July finance charge be? a. $9. 97 b. $12. 62 c. $11. 80 d. $10. 80.
To calculate Elizabeth's finance charge using the previous balance method, we need to determine the average daily balance and then apply the APR (Annual Percentage Rate) to calculate the finance charge.
First, let's calculate the average daily balance:
Beginning Balance: $969.26
Days until payment: 2 (from July 1st to July 3rd)
Payment: $45.00
Days until purchase: 7 (from July 3rd to July 10th)
Purchase: $67.48
Days until payment: 2 (from July 10th to July 12th)
Payment: $20.00
Days until payment: 16 (from July 12th to July 28th)
Payment: $85.00
To calculate the average daily balance, we sum up the balances for each day and divide it by the total number of days in the billing cycle (30 days).
Average Daily Balance = (969.26 × 2 + 0 × 7 + 67.48 × 2 + 0 × 16) / 30 = $85.95
Next, we can calculate the finance charge using the APR:
Finance Charge = Average Daily Balance × (APR / 365) × Number of Days in the Billing Cycle
Finance Charge = 85.95 × (0.1461 / 365) × 30 ≈ $9.97
Therefore, Elizabeth's July finance charge will be approximately $9.97. The correct answer is option a.
Learn more about Annual Percentage Rate here -: brainly.com/question/30774234
#SPJ11
Does the table represent a function? Why or why not?
xy
3 1
4 3
5 2
6 5
6 6
A. Yes, because every x-value corresponds to exactly one y-value.
B. No, because one x-value corresponds to two different y-values.
C. Yes, because there are different y-values.
D. No, because the y-values are positive.
Option A, "Yes, because every x-value corresponds to exactly one y-value," accurately describes the situation presented in the table. Option A is the proper response, so.
The table represents a function.
A mathematical relationship known as a function is one in which every input (x-value) has exactly one corresponding output (y-value). In the given table:
xy
3 1
4 3
5 2
6 5
6 6
Every x-value in the table corresponds to exactly one y-value. There are no repeated x-values, and for each x-value, there is only one corresponding y-value. The definition of a function is met by this.
The answer given in Option A, "Yes, because every x-value corresponds to exactly one y-value," appropriately sums up the situation shown in the table. Option A is the proper response, so.
for such more question on function
https://brainly.com/question/13473114
#SPJ8
The scatter plot below shows data that were collected to compare the amount of television a student watched (hours per week ) and his or her GPA
A reasonable correlation coefficient for these data would be
The scatter plot shows a comparison between the amount of television watched by students (in hours per week) and their GPA. a reasonable correlation coefficient for these data would be close to 0, indicating a weak or negligible correlation.
Based on the scatter plot, we can observe the general trend of the data points. If the points on the plot are more closely clustered around a straight line, it indicates a stronger correlation between the two variables. Conversely, if the points are more spread out and do not follow a clear pattern, it suggests a weaker correlation. To determine the correlation coefficient, we need to assess the direction and strength of the relationship.
If the data points on the scatter plot exhibit a clear upward or downward trend, it indicates a positive or negative correlation, respectively. The correlation coefficient ranges between -1 and 1, with values closer to -1 or 1 indicating a stronger correlation. A correlation coefficient of 0 indicates no linear relationship. Given that the scatter plot does not show a clear pattern or trend, it suggests a weak or no correlation between the amount of television watched and GPA. Therefore, a reasonable correlation coefficient for these data would be close to 0, indicating a weak or negligible correlation.
Learn more about coefficient here:
https://brainly.com/question/1594145
#SPJ11
The perimeter of a rectangle is 22cm and the length of each side is a natural number. How many different areas in centimeter squared can the rectangle have?
option B is the correct answer.
The perimeter of a rectangle is 22 cmLet the length of the rectangle be 'l' and the breadth be 'b'As per the question, the perimeter of the rectangle is given by;Perimeter = 2(l + b) => 2(l + b) = 22 => l + b = 11.As we know that the area of a rectangle is given by;Area = l × b
Therefore, the different areas of the rectangle are; l × b1 × (11 - 1) = 10 cm²2 × (11 - 2) = 18 cm²3 × (11 - 3) = 24 cm²4 × (11 - 4) = 28 cm²5 × (11 - 5) = 30 cm²6 × (11 - 6) = 30 cm²7 × (11 - 7) = 28 cm²8 × (11 - 8) = 24 cm²9 × (11 - 9) = 18 cm²10 × (11 - 10) = 10 cm²Hence, there are only 8 different areas of the rectangle i.e., 10 cm², 18 cm², 24 cm², 28 cm², 30 cm².
To know more about Perimeter visit:
https://brainly.com/question/7486523
#SPJ11
for all values of x, f(x)=2x-3 and g(x)=x^2+1 find fg(x)
fg(x) is 2x³ - 3x² + 2x - 3.To find fg(x), we need to multiply f(x) and g(x).
The given functions are f(x) = 2x - 3 and g(x) = x² + 1.
We know that (f · g)(x) = f(x) · g(x).
So, (f · g)(x) = (2x - 3)(x² + 1)
(f · g)(x) = 2x³ - 3x² + 2x - 3.
Hence, the value of fg(x) is 2x³ - 3x² + 2x - 3
Given f(x) = 2x - 3 and g(x) = x² + 1
We have to find fg(x) = f(x)g(x)
= (2x - 3)(x² + 1)
We will use the distributive law of multiplication to multiply the given two functions.
(2x - 3)(x² + 1)= 2x(x² + 1) - 3(x² + 1)
Expanding further, we get the following:
2x³ + 2x - 3x² - 3=2x³ - 3x² + 2x - 3
Therefore,
fg(x) = 2x³ - 3x² + 2x - 3.
So, we get the value of fg(x) as 2x³ - 3x² + 2x - 3.
We have found that fg(x) is 2x³ - 3x² + 2x - 3 by multiplying f(x) = 2x - 3 and g(x) = x² + 1.
To know more about the functions, visit:
brainly.com/question/29120892
#SPJ11
Edgar cannot sleep because he is terribly worried about his research paper. So edgar decides to get out of bed and continue working on the paper. Although he stays up to nearly 3 a. M. , he is relieved that it is done and easily falls off to sleep. In the future, edgar will be more likely to finish his work before going to bed so that he can avoid the worry and sleeplessness. Such behavior is an example of.
To sum up, Edgar's behavior is an example of positive reinforcement as he has learned to associate finishing his work before going to bed with positive consequences.
Edgar's behavior is an example of a learning process known as operant conditioning. Operant conditioning is the concept that we learn to associate our behavior with its consequences, either positive or negative. We are motivated by rewards, such as praise, and punishments, such as criticism, that we experience as a result of our behavior.
In Edgar's case, his relief and ability to fall asleep after completing his research paper can be considered a reward. Thus, he has been conditioned to associate finishing his work before going to bed with positive consequences. This learning process is an example of positive reinforcement.
Positive reinforcement, in which a positive stimulus is used to encourage a desired behavior, is the most effective way to promote good behavior and discourage undesirable behavior. Positive reinforcement can take many forms, including praise, recognition, and tangible rewards.
By contrast, negative reinforcement, which involves removing an unpleasant stimulus, can also be used to encourage a desired behavior, but it is not as effective as positive reinforcement in the long term.
To sum up, Edgar's behavior is an example of positive reinforcement as he has learned to associate finishing his work before going to bed with positive consequences.
To know more about Positive visit :
https://brainly.com/question/23709550
#SPJ11
what is the circumference of a cylinder with the diameter of 6cm and height of 12cm
The diameter of a cylinder is given as 6 cm and the height as 12 cm. We can use the formula of the circumference of a cylinder to calculate the circumference. We know that the circumference of a circle is πd, where d is the diameter of the circle.
Now, the circumference of a cylinder is nothing but the perimeter of its circular base. Therefore, the circumference of a cylinder is 2πr where r is the radius of the circular base. In this question, the diameter is given as 6 cm, which means the radius will be half of it. Hence the radius of the circular base will be 6/2 = 3 cm. The height of the cylinder is given as 12 cm, which means the circumference will be the perimeter of the circular base times the height of the cylinder. The circumference will be:2πr = 2π(3) = 6π cm. The circumference of a cylinder with the diameter of 6 cm and height of 12 cm is 6π cm.
The circumference of a cylinder with the diameter of 6 cm and height of 12 cm is 6π cm. The diameter of a cylinder is given as 6 cm and the height as 12 cm. We can use the formula of the circumference of a cylinder to calculate the circumference. We know that the circumference of a circle is πd, where d is the diameter of the circle. Now, the circumference of a cylinder is nothing but the perimeter of its circular base. Therefore, the circumference of a cylinder is 2πr where r is the radius of the circular base. In this question, the diameter is given as 6 cm, which means the radius will be half of it. Hence the radius of the circular base will be 6/2 = 3 cm. The height of the cylinder is given as 12 cm, which means the circumference will be the perimeter of the circular base times the height of the cylinder. The circumference will be:2πr = 2π(3) = 6π cm. The circumference of a cylinder with the diameter of 6 cm and height of 12 cm is 6π cm, where π is pi and is equal to approximately 3.14.
To know more about circumference visit:
https://brainly.com/question/28757341
#SPJ11
A 3-gallon bottle of bleach costs $15.60. What is the price per quart?
We know that the bottle contains 3 gallons of bleach. More than 250 quarts can be produced from 3 gallons. Let's find out how many quarts there are in a gallon.1 US gallon is equivalent to 4 US quarts.
So 3 gallons equal 12 quarts. Hence, More than 250 quarts can be obtained from 3 gallons, since more than 250 is greater than 12.Therefore, we can find the price per quart by dividing the total cost by the total number of quarts: Price per quart = Total cost ÷ Total number of quarts Since the cost of a 3-gallon bottle of bleach is $15.60, the cost of 1 gallon would be $15.60 ÷ 3 = $5.20.The cost of one quart is $5.20 ÷ 4 = $1.30.Therefore, the price per quart is $1.30.
To know more about cost visit:
https://brainly.com/question/13945982
#SPJ11
For the past `12` school days, Mai has recorded how long her bus rides to school take in minutes. The times she recorded are shown below. `9`, `12`, `6`, `9`, `10`, `7`, `6`, `12`, `9`, `8`, `10`, `10` Find the mean for Mai's data.
The mean for Mai's data is 8.9167.
To find the mean of the data given by Mai for the past 12 school days, we need to add all the values together and then divide by the total number of values.
Here is the solution: Given data are: 9, 12, 6, 9, 10, 7, 6, 12, 9, 8, 10, 10
To find: The mean for Mai's data
To calculate the mean, we will add up all the values and then divide by the total number of values.
Mean (average) = sum of values / total number of values
Sum of values = 9 + 12 + 6 + 9 + 10 + 7 + 6 + 12 + 9 + 8 + 10 + 10= 107
Total number of values = 12
Therefore, Mean (average) = sum of values / total number of values
= 107 / 12
= 8.9167 (rounded to four decimal places)
Hence, the mean for Mai's data is 8.9167.
Know more about mean here:
https://brainly.com/question/1136789
#SPJ8
Three minus eleven times a number is more than twenty one minus five times the number (show work)
The solution to the equation is x is less than 1.
Let's assume the number as "x".
The given statement can be translated into an equation as follows:
3 - 11x > 21 - 5x
To solve this equation, we can start by simplifying both sides:
3 - 11x > 21 - 5x
Next, let's gather the terms with x on one side and the constant terms on the other side by adding 11x and subtracting 21 from both sides:
3 - 11x + 11x - 5x > 21 - 5x + 11x - 21
Simplifying further, we get:
-16x > -x
Now, we can divide both sides by -16, but since we are dividing by a negative number, we need to reverse the inequality sign:
-16x / -16 < -x / -16
x < 1
Therefore, the solution to the equation is x is less than 1.
Visit here to learn more about inequality brainly.com/question/20383699
#SPJ11
1. Use each of the Numbers once, In any order. To form at least TWO number sentences that equal the target number
TARGET NUMBER: 2
17, 5, 8, 2, 9
2. Let A=3 B=28 C=50
D=12 E=2 F=18
Write a minimum of 5 different
relationship statements for the
variables.
Ex. DE=B-2E
Using 17 + 5 - 8 + 9 - 2 = 21 and 2 + 9 - 8 + 17 - 5 = 15 as two number sentences, we can form the target number of 2.
1) 2C = BF
2) B - 3E = A
3) C - A = 2D
4) F - A + B = 47
5) 3E - B + 2A = 8
In the first statement, the variable C is multiplied by 2, and the result is equal to the product of variables B and F. In the second statement, the product of variables E and 3 is subtracted from B, and the result is equal to A.
In the third statement, the difference between variables C and A is equal to twice the value of variable D. In the fourth statement, the sum of variables F and B is subtracted from A, and the result is equal to 47.
In the fifth statement, twice the value of variable A is added to 3 times the value of variable E, and this sum is subtracted from the value of variable B, which gives 8.
Learn more about variable here:
https://brainly.com/question/29696241
#SPJ11
Plane 1 travels 450 miles south in 2 hours with a very strong tailwind. Plane 2 travels 525 miles north in 3 hours, this time against the same wind speed, with an air speed 3 times faster than plane 1.
- Plane 1 travels at a speed of 225 mph.
- Plane 2 has an airspeed of 3 times faster than Plane 1, which is 3 * 225 mph = 675 mph.
- The wind speed is 500 mph.
Let's analyze the information provided:
Plane 1:
- Distance traveled: 450 miles
- Direction: South
- Time taken: 2 hours
Plane 2:
- Distance traveled: 525 miles
- Direction: North
- Time taken: 3 hours
- Airspeed: 3 times faster than Plane 1
We can calculate the speed of Plane 1 and the wind speed by dividing the distance traveled by the time taken.
Plane 1's speed = Distance / Time = 450 miles / 2 hours = 225 miles per hour (mph)
Let's assume the speed of the wind is W mph.
For Plane 2, since it is traveling against the wind, we need to consider the effect of the wind on its speed. The effective speed of Plane 2 against the wind can be calculated as the airspeed of Plane 2 minus the wind speed.
Effective speed of Plane 2 = Airspeed of Plane 2 - Wind speed = 3 * Plane 1's speed - W
Now we can use the formula: Speed = Distance / Time to calculate the wind speed.
For Plane 2:
Effective speed of Plane 2 = Distance / Time = 525 miles / 3 hours = 175 mph
175 mph = 3 * 225 mph - W
W = 3 * 225 mph - 175 mph
W = 675 mph - 175 mph
W = 500 mph
The wind speed is calculated to be 500 mph.
Visit here to learn more about speed brainly.com/question/17661499
#SPJ11
Jen is a member of their school’s women soccer club. She noticed that the angle formed at the corner of the soccer field was similar to her lesson in Math that morning. Which type of angle is it?
An angle is a geometric figure formed by two rays or lines that share a common endpoint called the vertex.
If Jen noticed that the angle formed at the corner of the soccer field was similar to her math lesson, we can explore the different types of angles she might be referring to.
Right Angle: A right angle measures exactly 90 degrees and forms a square corner. It is a common angle found in everyday life, such as the corners of buildings or the intersection of two perpendicular lines. Right angles are often studied in geometry due to their properties and applications in various mathematical concepts.
Acute Angle: An acute angle measures less than 90 degrees. It is a smaller angle that appears sharp and pointed. Examples of acute angles can be found in triangles, where all three angles are acute.
Obtuse Angle: An obtuse angle measures more than 90 degrees but less than 180 degrees. It is a wider angle that appears larger and open. Examples of obtuse angles can be found in shapes like rectangles or triangles with one angle greater than 90 degrees.
Straight Angle: A straight angle measures exactly 180 degrees, forming a straight line. It is a flat angle that doesn't bend or deviate. Straight angles are commonly found in line segments or in shapes like straight edges of polygons.
To learn more about vertex visit;
https://brainly.com/question/32432204
#SPJ11
An IV blood administration is in place. A bag of 376 ml is hung at
1100hrs. How long will this bag take to infuse at maximum time?
The time it would take for the bag to infuse at the maximum time would be the value of 1. 5 hours.
How to find the time ?The maximum rate of infusion for an IV bag is 250 ml/hour. This means that the maximum time it would take for the bag to infuse is:
= Quantity in bag / Maximum rate of infusion
Therefore, it will take:
= 376 ml / 250 ml/hour
= 1. 5 hours to infuse the entire bag
In conclusion, the time it would take for the bag to infuse at the maximum time is 1. 5 hours.
Find out more on Blood administration at https://brainly.com/question/30748600
#SPJ4
Mark wants to buy a video game for $39.99, he has a 30% discount and then pays 5% sales tax. What is the final cost of the video game?
Given the cost of the video game is $39.99, Mark gets a discount of 30%.Content loaded means there's enough information available to solve the problem. Here's how to find out the final cost of the video game. First, calculate the discount on the cost of the video game:$39.99 × 30/100 = $11.997
This gives us the discount that Mark gets on the video game. So, the cost of the video game after discount will be: Cost of the video game = $39.99 - $11.997 = $27.993Now, let's add the sales tax. The sales tax is 5%. Thus, the sales tax will be: Sales tax = $27.993 × 5/100 = $1.39965So, the final cost of the video game will be :Final cost = $27.993 + $1.39965 = $29.39265Thus, the final cost of the video game after the discount and the sales tax is $29.39.
Learn more about discount here:
https://brainly.com/question/2730006
#SPJ11
