Answer:
15 = 3 × 5
40 = 2 × 2 × 2 × 5
100 = 2 × 2 × 5 × 5
LCM of 15, 40, and 100:
2 × 2 × 2 × 3 × 5 × 5 = 600
The three signals will beep at the same time every 600 seconds (10 minutes). So in one hour (60 minutes), the three signals will beep at the same time 6 times.
the ratio of the surface areas of two similar right cylinders is 36:121. what is the ratio of their volumes?
To find the ratio of the volumes of two similar right cylinders, we need to know the ratio of their heights and radii. We can use the fact that the ratio of their surface areas is 36:121 to determine this. So, the ratio of the volumes of the two right cylinders is 216:1331.
Let the height and radius of the first cylinder be h1 and r1, respectively, and the height and radius of the second cylinder be h2 and r2, respectively. Then, we can write:
(2πr1h1)/(2πr2h2) = 36/121
Simplifying this equation, we get:
r1h1/r2h2 = 18/121
Since the cylinders are similar, we know that their ratios of heights and radii are equal. So, we can write:
r1/r2 = h1/h2 = x
Substituting this into our equation above, we get:
x^2 = 18/121
x = √(18/121) = 3/11
Therefore, the ratio of the volumes of the two cylinders is:
(r1^2h1)/(r2^2h2) = (r1/r2)^2(h1/h2) = (3/11)^2 = 9/121
In other words, the volume of the second cylinder is 121/9 times the volume of the first cylinder. Answer more than 100 words.
The ratio of the surface areas of two similar right cylinders is 36:121. To find the ratio of their volumes, we can use the fact that when two similar solids have a ratio of their surface areas (A1:A2), the ratio of their volumes (V1:V2) is the cube of the ratio of their corresponding linear dimensions (L1:L2).
First, let's find the ratio of the linear dimensions:
√(A1/A2) = √(36/121) = 6/11
Now, cube the ratio of the linear dimensions to find the ratio of their volumes:
(6/11)^3 = (6^3)/(11^3) = 216/1331
So, the ratio of the volumes of the two right cylinders is 216:1331.
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A student claims that statistics students at her school spend, on average, an hour doing statistics homework each night. In an attempt to substantiate this claim, she selects a random sample of 6 of the 62 students that are taking statistics currently and asks them how much time they spend completing statistics homework each night. Here are the data (in hours): 0.75, 0.75, 0.75, 0.5, 1, 1.25. She would like to know if the data provide convincing statistical evidence that the true mean amount of time that statistics students spend doing statistics homework each night is less than one hour. The student plans to test the hypotheses, H0: μ = 1 versus Ha: μ < 1, where μ = the true mean amount of time that statistics students spend doing statistics homework each night. Are the conditions for inference met?
Answer: Yes, all conditions for inference are met.
Answer:
0.1 is the correct answer of this questions
When a survey question contains assumptions that may or may not be true, it has
A randomness
B bias
C an outlier
D bivariate data
An arc of length 80 inches is subtended by an angle of 3.2 radians . What is the length of the diameter of the circle ?
The length of the diameter of the circle is 50 inches.To find the length of the diameter of the circle, we can use the formula that relates the length of an arc to the angle it subtends and the radius of the circle.
The formula is: arc length = radius * angle
In this case, we are given that the arc length is 80 inches and the angle is 3.2 radians. Let's assume the radius of the circle is 'r'.
Plugging in the given values, we have:
80 = r * 3.2
To solve for 'r', we divide both sides of the equation by 3.2:
r = 80 / 3.2 = 25
So, the radius of the circle is 25 inches.The diameter of a circle is twice the radius, so:
Diameter = 2 * radius = 2 * 25 = 50 inches.
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If the correlation coefficient is 0.3, find the percentage of variation in the dependent variable explained by the variation in the independent variable. - 0.09% 3% 9% 30%
Answer:
The correct answer is 9%.
The correlation coefficient r is a measure of the linear relationship between two variables. It can range from -1 to 1. A value of 0 means that there is no linear relationship between the variables. A positive value of r means that the variables are positively correlated, i.e., as one variable increases, the other variable also increases. A negative value of r means that the variables are negatively correlated, i.e., as one variable increases, the other variable decreases.
The square of the correlation coefficient, r^2, is called the coefficient of determination. It is a measure of the percentage of variation in the dependent variable that is explained by the variation in the independent variable. In this case, r = 0.3, so r^2 = 0.09. This means that 9% of the variation in the dependent variable is explained by the variation in the independent variable.
The other answers are incorrect. 0.09% is too small, 3% is too large, and 30% is much too large.
Step-by-step explanation:
Simplify.
410 x 45 ÷ 49 = 4[?]
Hello !!
kᵃ x kᵇ = kᵃ⁺ᵇ
kᵃ ÷ kᵇ = kᵃ⁻ᵇ
4¹⁰ x 4⁵ ÷ 4⁹
= 4¹⁰⁺⁵ ÷ 4⁹
= 4¹⁵ ÷ 4⁹
= 4¹⁵⁻⁹
= 4⁶
in a randomly selected 100 students in a large college, 20 of them had at least one sibling. does this provide strong evidence that more than 15% of college students in america have at least one sibling? when you test using what type of error might you have committed?
a) Yes, this provide strong evidence that more than 15% of college students in America have at least one sibling
b) Type of error might you have committed is type 1 error.
We can use the sample proportion of students with at least one sibling (20/100 = 0.2) to calculate a test statistic, which measures how far the sample proportion is from the null hypothesis. In this case, we can use a one-sample proportion z-test to calculate the test statistic:
z = (p1 - p) / √(p * (1 - p) / n)
where p1 is the sample proportion, p is the null hypothesis proportion, and n is the sample size.
Using the values from your question, we get:
z = (0.2 - 0.15) / √(0.15 * 0.85 / 100) ≈ 1.18
We can use a standard normal distribution to find the p-value, which is the probability of getting a test statistic as extreme as the one we observed, assuming the null hypothesis is true. The p-value can be calculated as:
p-value = P(Z > z)
where Z is a standard normal random variable.
Using a calculator or a table of standard normal probabilities, we can find that the p-value is approximately 0.12.
To make a decision about whether to reject or fail to reject the null hypothesis, we compare the p-value to a significance level, which is a threshold that we set to determine how much evidence we need to reject the null hypothesis.
The most common significance level is 0.05, which means that we are willing to accept a 5% chance of rejecting the null hypothesis when it is actually true.
In this case, the p-value (0.12) is greater than the significance level (0.05), so we fail to reject the null hypothesis. This means that we do not have strong evidence to conclude that more than 15% of college students in America have at least one sibling based on this sample.
Now, let's talk about the type of error that we might have committed when testing the hypothesis. In hypothesis testing, there are two types of errors: type I error and type II error.
A type I error occurs when we reject a true null hypothesis, and a type II error occurs when we fail to reject a false null hypothesis.
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brian wants to sell t-shirts for the crosstown showdown. he purchases the shirts for $6 and plans to sell them to uc basketball fans for $10. he has to pay a service fee of $300 to be able to sell them on campus. assume there is no value for any t-shirts that are unsold before the start of the game. the payoff, if he orders 1000 and demand is 850, is
Brian orders 1000 t-shirts, and demand is 850, resulting in a $2200 profit after expenses and revenue.
To calculate the payoff for Brian if he orders 1000 t-shirts and the demand is 850, we need to consider the costs and revenues involved.
Costs:
Brian purchases each t-shirt for $6, so the cost of ordering 1000 t-shirts is 1000 * $6 = $6000.
Additionally, Brian incurs a service fee of $300.
Revenues:
Brian plans to sell each t-shirt for $10.
If the demand is 850, he will be able to sell 850 t-shirts.
Revenue from t-shirt sales:
Revenue = Selling price per t-shirt * Number of t-shirts sold
Revenue = $10 * 850 = $8500
Payoff:
The payoff is calculated by subtracting the costs from the revenues.
Payoff = Revenue - Costs
Payoff = $8500 - ($6000 + $300)
Payoff = $8500 - $6300
Payoff = $2200
Therefore, if Brian orders 1000 t-shirts and the demand is 850, his payoff would be $2200. This represents the profit he would make after accounting for the costs of purchasing the t-shirts and the service fee, and the revenue generated from selling the t-shirts.
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Assume the average amount of caffeine consumed daily by adults is normally distributed with a mean of 240 mg and a standard deviation of 49 mg. Determine the percent of adults who consume less than 240 mg of caffeine daily. Click here to view page 1 of the standard normal distribution table. LOADING. Click here to view page 2 of the standard normal distribution table. LOADING. Question content area bottom
Part 1
enter your response here% of adults consume less than 240 mg of caffeine daily. (Round to two decimal places as needed. )
We need to convert the normal distribution of caffeine consumption to a standard normal distribution using the z-score formula. We can then look up the corresponding area under the standard normal distribution curve using a z-table.
Explanation:
To convert the normal distribution of caffeine consumption to a standard normal distribution, we use the z-score formula:
z = (x - μ) / σ
where x is the value we want to convert to a z-score, μ is the mean of the normal distribution, and σ is the standard deviation of the normal distribution.
In this case, we want to find the z-score for x = 240, μ = 240, and σ = 49:
z = (240 - 240) / 49 = 0
Since the z-score is 0, we can look up the area to the left of z = 0 in the standard normal distribution table. This area represents the percentage of adults who consume less than 240 mg of caffeine daily.
From the standard normal distribution table, we can see that the area to the left of z = 0 is 0.5000. Therefore, approximately 50% of adults consume less than 240 mg of caffeine daily.
So, the percent of adults who consume less than 240 mg of caffeine daily is 50%.
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a sales boy is given a commission of 5% on all sales made. if his commission at the end of the month was GH¢150.00. find his total sales in the month
The sales boy has a sale of $142.9.
Given that the commission given to a sales boy is 5%, he earns $150, we need to find the sale he did for the month,
So,
Let the sale be x,
Therefore,
x + 5% of x = 150
x of 105% = 150
x × 1.05 = 150
x = 142.9
Hence the sales boy has a sale of $142.9.
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I just need an answer to how to give brainlist.....
and I NEED HELP ON THISWhich of the following shows parallel lines? (1 point)
Figure A has two rays connecting at a vertex. Figure B has two rays connecting at a vertex. Figure C has two lines intersecting at 90 degrees. Figure D has two lines that are the same distance apart.
a
Figure A
b
Figure B
c
Figure C
d
Figure D
Figure D, two lines that are the same distance apart :)
find the area of the part of the plane 5x + 2y + z = 10 that lies in the first octant.
The area of the part of the plane 5x + 2y + z = 10 that lies in the first octant is 5 square units.
To find the area of the part of the plane 5x + 2y + z = 10 that lies in the first octant, we need to first find the coordinates of the three points where the plane intersects the coordinate axes.
Setting x = 0, we get 2y + z = 10, so the plane intersects the y-axis at the point (0, 5, 0).
Setting y = 0, we get 5x + z = 10, so the plane intersects the x-axis at the point (2, 0, 0).
Setting z = 0, we get 5x + 2y = 10, so the plane intersects the z-axis at the point (0, 0, 5).
We can see that the triangle formed by these three points lies entirely in the first octant.
To find the area of this triangle, we can use the formula for the area of a triangle given its vertices:
A = 1/2 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|
Plugging in the coordinates of the three points, we get:
A = 1/2 * |(0)(5 - 0) + (2)(0 - 5) + (0)(0 - 0)| = 1/2 * |-10| = 5
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PLS HELP FAST
The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 195 grams of a radioactive isotope, how much will be left after 3 half-lives?
Use the calculator provided and round your answer to the nearest gram.
SHOW YOUR WORK
YOU GET THE BRAINLIEST
Answer:
24 grams
Step-by-step explanation:
You want the amount remaining of 195 grams of an isotope after 3 half-lives.
Half-lifeEach half-life leaves 1/2 of the amount there was at the beginning of that time period. After 3 half-lives, the amount is (1/2)(1/2)(1/2) = 1/2³ = 1/8 of the original amount.
(195 g)(1/8) = 24.375 g ≈ 24 g
About 24 grams of the isotope will remain after 3 half-lives.
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an irs representative claims that the average deduction for medical care is $ 1250. a taxpayer who believes that the real figure is lower samples 32 random families and comes up with a sample mean of $934 and a sample standard deviation of $619. what null and alternative hypothesis would you use to test this claim?
These tests would allow us to determine if the observed sample mean of $934 is significantly different from the claimed average of $1250, providing evidence to support or reject the alternative hypothesis.
To test the claim made by the IRS representative that the average deduction for medical care is $1250, we can formulate the null and alternative hypotheses as follows:
Null Hypothesis (H0): The average deduction for medical care is $1250.
Alternative Hypothesis (H1): The average deduction for medical care is lower than $1250.
In this case, the taxpayer who believes that the real figure is lower has collected a sample of 32 random families. The sample mean is $934, and the sample standard deviation is $619. The null hypothesis assumes that the average deduction is $1250, while the alternative hypothesis suggests that it is lower than $1250.
To statistically test these hypotheses, we can use a one-sample t-test or a z-test, depending on the sample size and whether the population standard deviation is known.
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A survey was conducted with high school students in each grade to see how many prefer math or science. Some of the data are shown below.
A 6-column table with 3 rows. The first column has no label with entries math, science, total. The second column is labeled 9 with entries blank, 40, 63. The third column is labeled 10 with entries 18, blank, 26. The fourth column is labeled 11 with entries blank, 15, 29. The fifth column is labeled 12 with entries blank, 32, 67. The sixth column is labeled total with entries 90, 95, 185.
Which statement is true about the joint frequencies in this table?
Twenty-three 9th graders and fifteen 11th graders prefer math.
Fourteen 11th graders prefer math and eight 10th graders prefer science.
Thirty-five 12th graders prefer math and nine 10th graders prefer science.
Twenty-three 9th graders and thirty-two 12th graders prefer math.
The true statement is,
⇒ The joint frequencies is that twenty-three 9th graders and fifteen 11th graders prefer math.
Now, Based on the given table, the statement that is true about the joint frequencies is that twenty-three 9th graders and fifteen 11th graders prefer math.
Since, The given table shows that in the first column, under the ninth grade row, there are 18 students who prefer math and in the third column, under the 11th grade row, there are 15 students who prefer science.
Hence, There are no joint frequencies given that add up to 23, so the only true statement among the options is the first one.
Thus, The true statement is,
⇒ The joint frequencies is that twenty-three 9th graders and fifteen 11th graders prefer math.
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Answer answer is b dont trust the otha dude
Step-by-step explanation:
Inger keeps her white and blqck chess pieces in separate bags. For each color, there are 8 pawns, 2 rooks, 2 bishops, 2 knights, 1 queen, and 1 king. Are the events of drawing a bishop from the bag of white pieces and then drawing the queen from the same bag dependent or independent events? Explain. Find the probability of this compound event.
Choose the INCORRECT statement below.
Answer:4 is incorrect
Step-by-step explanation:
Answer:
4 is incorrect
Step-by-step explanation:
.
HELP ASAP
Given the functions f(x) = –4^x + 5 and g(x) = x^3 + x^2 – 4x + 5, what type of functions are f(x) and g(x)? Justify your answer. What key feature(s) do f(x) and g(x) have in common? (Consider domain, range, x-intercepts, and y-intercepts.)
The key feature that f(x) and g(x) have in common is that they both have a y-intercept of (0, 5). They differ in terms of their domain, range, and x-intercepts.
The function f(x) = -4^x + 5 is an exponential function, while g(x) = x^3 + x^2 - 4x + 5 is a polynomial function of degree 3.
To show that f(x) is an exponential function, we can observe that it has the form f(x) = a*b^x + c, where a = 5, b = -4, and c = 0. This function has a domain of all real numbers and a range of (0, 5). The x-intercept is not defined since the base of the exponential function is negative, and the y-intercept is (0, 1).
On the other hand, g(x) is a polynomial function of degree 3, which means that it has the form g(x) = ax^3 + bx^2 + cx + d. This function has a domain of all real numbers and a range of (-∞, ∞). The x-intercepts can be found by setting g(x) equal to zero and solving for x, while the y-intercept is (0, 5).
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what is the probability that you will be dealt a poker hand that is a full house(three cards of the same rank a pair in another rank) and includes the ace of hearts?
Thus, the probability of being dealt a full house with an Ace of Hearts is 0.0457% (rounded to 4 decimal places).
To calculate the probability of being dealt a full house with an Ace of Hearts in a standard 52-card deck, we can use the following formula:
=(number of ways to get a full house with an Ace of Hearts) / (total number of 5-card poker hands)
The total number of 5-card poker hands is C(52,5) = 2,598,960.
To count the number of ways to get a full house with an Ace of Hearts, we need to consider the following:
We choose 2 of the remaining 3 Aces from the deck: C(3,2) = 3
We choose 2 of the 12 remaining ranks for the other 2 cards: C(12,2) = 66
For each rank, we need to choose 2 cards from the 4 of that rank: C(4,2) = 6
Therefore, the number of ways to get a full house with an Ace of Hearts is 3 x 66 x 6 = 1,188.
Thus, the probability of being dealt a full house with an Ace of Hearts is:
1,188 / 2,598,960 ≈ 0.000457 = 0.0457% (rounded to 4 decimal places)
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During part of a song, the drummer in a marching band moves from (1, 4) to (5, 1). Write the component form of the vector that describes his movement.
The component form of the vector that describes the drummer's movement is <4, -3>.
The component form of a vector is given by the difference between the coordinates of the endpoints.
The initial point is (1, 4) and the final point is (5, 1).
Thus, the horizontal component is the difference between the x-coordinates, which is 5 - 1 = 4,
and the vertical component is the difference between the y-coordinates, which is 1 - 4 = -3.
Therefore, the component form of the vector that describes the drummer's movement is <4, -3>.
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use the figure below to find requested values
The measure of angles m∠QTR and m∠PTQ are 98.25° and 81.75° respectively, using the angle N between intersecting tangents.
What is an angle between intersecting tangentsThe angle between two tangent lines which intersect at a point is 180 degrees minus the measure of the arc between the two points of tangency.
61.5 = 180 - arc PS
arc PS = 180 - 61.5
arc PS = 118.5
m∠QTR = 1/2 × (118.5 + 78) {intersecting chords}
m∠QTR = 196.5/2
m∠QTR = 98.25
m∠PTQ = [360 - 2(98.25)]/2 {one of the angles at a point}
m∠PTQ = 163.5/2
m∠PTQ = 81.75
Therefore, measure of angles m∠QTR and m∠PTQ are 98.25° and 81.75° respectively, using the angle N between intersecting tangents.
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six new employees, two of whom are married to each other, are to be assigned six desks that are lined up in a row. if the assignment of employees to desks is made at randomly, what is the probability that the married couple will not have adjacent desks?
The total number of ways to assign employees to desks is 720 (6!), and the number of favorable outcomes is 144. Therefore, the probability is 144/720 = 1/5.
The total number of ways to assign six employees to six desks is 6! (6 factorial), which equals 720. Now we need to find the number of ways that the married couple will not have adjacent desks.
First, we can treat the married couple as one entity, which means we have 5 entities to assign to 6 desks. There are 6 possible ways to choose the position of the married couple in the row. For each of these positions, we can then assign the other 4 entities to the remaining 4 desks in 4! ways.
Therefore, the total number of ways to assign employees to desks without the married couple having adjacent desks is 6 x 4! = 144.
The probability of this happening is the number of favorable outcomes (144) divided by the total number of possible outcomes (720), which is 144/720 = 1/5.
The probability that the married couple will not have adjacent desks when six new employees are randomly assigned to six desks that are lined up in a row is 1/5.
We calculated this probability by first treating the married couple as one entity and then finding the number of ways to assign the remaining entities to the desks without the married couple being adjacent to each other. The total number of ways to assign employees to desks is 720 (6!), and the number of favorable outcomes is 144. Therefore, the probability is 144/720 = 1/5.
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The equation of the graphed line is 2x – y = –6.
A coordinate plane with a line passing through (negative 3, 0) and (0, 6).
What is the x-intercept of the graph?
–3
–2
2
6
The x-intercept for the given equation is x = -3.
Given is an equation 2x-y = -6, we need to find the x-intercept for the line,
So the x-intercept of a line is the point where it cuts the x-axis,
To find the x-intercept we will put y = 0,
So,
2x - 0 = -6
2x = -6
x = -3
Or, you can just see the points from which it is passing the x-values will be the x-intercept,
Hence the x-intercept of the line is x = -3.
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if y is a positive integer, for how many different values of y is a whole number?
A positive integer y is a whole number by definition, so we are essentially being asked how many positive integers there are. There are infinitely many positive integers, so the answer to the question is also infinity.
A positive integer y is a whole number if it isn't a bit or a numeric. In other words, it's a number that can be expressed without using fragments or numbers, and can be written as a finite sum of positive integers. For illustration, 2, 5, and 10 are whole figures, but3/4,1.5, and √ 2 are not. To determine how numerous different values of y are whole figures, we need to understand the parcels of whole figures.
Whole figures have two main parcels they're closed under addition and addition. This means that when you add or multiply two whole figures, the result is always a whole number. For illustration, 2 3 = 5 and 2 × 3 = 6, both of which are whole figures. To find how numerous different values of y are whole figures, we can start with the lowest possible value of y, which is 1.
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what is the slope of the line that passes through the given points (2 12) and (6 11)
The slope of the line that passes through the given points (2 12) and (6 11) is -1/4.
Two points are given: (2, 12), (6, 11).
A line's "steepness" is quantified by a quantity called the slope, which is typically represented by the letter m. It is the adjustment of y for a unit adjustment of x.
We are aware that the formula for the slope of a line using two points is
m= y2 - y1 /x2 - x1
In this instance, x1 = 2, Y1 = 12, X2 = 6, Y2 = 11.
m = 11 - 12 / 6 - 2
m = -1/4
The slope is therefore -1/4.
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Which of the following statements are true?
(1) It is okay to use the median to estimate the mean since both are a measure of the center of a distribution.
(2) It is okay to use the standard deviation to estimate the IQR since both are measures of variability.
(3) Point estimates based on a sample are sometimes far from a parameter
The statement which is true is (1) It is okay to use the median to estimate the mean since both are a measure of the center of a distribution.
While both the median and the mean provide information about the center of a distribution, they are not interchangeable. The median represents the middle value of a dataset, while the mean represents the average value. In some cases, the median may be a better estimate of the center, especially when dealing with skewed distributions or outliers.
The standard deviation and the interquartile range (IQR) are two different measures of variability. The standard deviation measures the dispersion of data around the mean, while the IQR measures the range between the first quartile (25th percentile) and the third quartile (75th percentile). They capture different aspects of the data's spread and are not interchangeable.
Point estimates based on a sample, such as the sample mean or proportion, are subject to sampling variability. These estimates may not perfectly match the true population parameter they aim to estimate. The difference between a point estimate and the true parameter is known as sampling error, and it can be substantial, especially for small sample sizes. It is important to acknowledge and consider this potential variability when interpreting point estimates.
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the radius of a circle is increasing at a constant rate of 2/3 inches per second. at what rate in inches squared per seconnd is the area of the circle increasing at the moemnet when the circumfrence of the circle is 27/2 inches
The rate at which the area of the circle is increasing at the moment when the circumference of the circle is 27/2 inches is 9 inches squared per second.
derivative of the circle's area with respect to time.
The area of a circle is given by the formula A = πr^2, where r is the radius of the circle.
Given that the radius is increasing at a constant rate of 2/3 inches per second, we can express this as dr/dt = 2/3.
We are also given that the circumference of the circle is 27/2 inches. The formula for the circumference of a circle is C = 2πr.
Plugging in the given circumference value, we have 27/2 = 2πr. Solving for r, we get r = (27/4π) inches.
Now, we can differentiate the area formula with respect to time:
dA/dt = d/dt (πr^2)
= 2πr(dr/dt)
Substituting the values, we have:
dA/dt = 2π(27/4π)(2/3)
= (27/2)(2/3)
= 9 inches squared per second
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Perform the following area application. (Round to the nearest tenth.)
A hot water heater measures 20" in diameter. What is the area of a metal base for the water heater, assuming a two-inch overhang for the base beyond the edge of the heater?
A = _________square inches
The area of the metal base for the water heater is approximately 452.2 square inches (rounded to the nearest tenth).
The radius of the hot water heater is 10 inches (half of the diameter). To find the radius of the base, we add the 2-inch overhang to the radius of the heater: 10 + 2 = 12 inches.
Now we can calculate the area of the base using the formula for the area of a circle: A = πr²
A = π(12)² = 452.4 square inches (rounded to the nearest tenth).
Therefore, the area of the metal base for the hot water heater is 452.4 square inches.
To find the area of the metal base for the hot water heater, we need to calculate the area of a circle with a radius of 12 inches.
We get this radius by adding the 2-inch overhang to the radius of the heater, which is 10 inches. Using the formula for the area of a circle, A = πr² , we can plug in our value for r and solve for A.
After rounding to the nearest tenth, we get an area of 452.4 square inches. Therefore, the metal base needs to have an area of at least 452.4 square inches to properly support the hot water heater.
The area of the metal base for the hot water heater is 452.4 square inches, which was found by calculating the area of a circle with a radius of 12 inches (10 inch radius of the heater + 2 inch overhang). This information can be used to ensure that the base is the correct size and can properly support the hot water heater.
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If sin 27° = t express 153° in terms of t
We can begin by noting that 153° is the supplement of 27°, meaning that the sum of the two angles is 180°.
From this, we can use the fact that the sine function has a period of 360° to express the sine of 153° in terms of the sine of 27°. Specifically, we know that the sine of an angle and its supplement are equal, but the sine of an angle and its complement are not. Therefore, we can write: sin 153° = sin(180° - 27°) = sin 27°So we can say that sin 153° = t, since we were given that sin 27° = t. This result allows us to express the sine of 153° in terms of t, which was the goal of the problem. In summary, we used the fact that 153° is the supplement of 27°, and the periodicity of the sine function, to express sin 153° in terms of sin 27° = t. This led us to the solution sin 153° = t, which provides a way of expressing the value of 153° in terms of t.
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List the multiples of 6 between 6 and 54 in order from least to greatest
6 x 1 = 6
6 x 2 = 12
6 x 3 = 18
6 x 4 = 24
6 x 5 = 30
6 x 6 = 36
6 x 7 = 42
6 x 8 = 48
6 x 9 = 54
So, 12, 18, 24, 30, 36, 42, and 48.
I assume "between" means we aren't including 6 and 54.
