To find the margin of error that corresponds to a 95% confidence interval, we first need to calculate the critical value.
For a 95% confidence interval, the critical value is 1.96. Next, we can use the formula: Margin of error = Critical value x Standard error
Plugging in the values we have:
Margin of error = 1.96 x 0.022
Margin of error = 0.04312
Therefore, the margin of error that corresponds to a 95% confidence interval is 0.04312. To find the margin of error for a 95% confidence interval, you'll need to use the standard error and the z-score corresponding to the desired confidence level. In this case, the standard error is 0.022, and the z-score for a 95% confidence interval is approximately 1.96.
Margin of Error = Z-score × Standard Error
Margin of Error = 1.96 × 0.022
Margin of Error ≈ 0.04312
So, the margin of error that corresponds to a 95% confidence interval is approximately 0.04312, or 4.312%.
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in the year 2018, it was estimated that approximately 28,000 floridians were homeless. a social worker estimates that 78% of these people were age 18 and up. in the distribution of ages of homeless floridians, an 18 year old would be considered what percentile? group of answer choices 22nd percentile 78th percentile 28th percentile 18th percentile
The an 18-year-old homeless Floridian would be considered at the 22nd percentile in the distribution of ages of homeless Floridians.
the social worker estimated that 78% of the homeless population in Florida in 2018 were age 18 and up, which means that 22% of the homeless population were under 18 years old. Therefore, an 18-year-old would be at the 22nd percentile in the age distribution of homeless Floridians.
based on the given information, an 18-year-old homeless Floridian would be at the 22nd percentile in the age distribution of homeless Floridians.
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7 + x to the fifth power =
Answer:
Step-by-step explanation:
[tex](7+x)^5[/tex]
23. Write and factor an expression that
makes the computation for finding the
area of the shaded region.
so hmmm the larger containing circle has a radius of "x", whilst there are four small circles in it with a radius of "y".
Now, if we get the area of the containing circle and get the area of the smaller circles and subtract the area of the smaller circles from that of the containing larger circle, what's leftover is what we didn't subtract, the shaded region.
[tex]\stackrel{ \textit{\LARGE Areas} }{\stackrel{ \textit{containing circle} }{\pi x^2}~~ - ~~\stackrel{ \textit{four small circles} }{4(\pi y^2)}}\implies \stackrel{ \textit{shaded region} }{{\Large \begin{array}{llll} \pi x^2-4\pi y^2 \end{array}}}[/tex]
The pack burro race is the biggest event at Rockyville's annual Burro Days. Participants run the race with a burro, or donkey, running alongside. This year, there is a crack across the road before the finish line that some burros think is the finish line. So far, 3 of the burros stopped at the crack before finishing the race, while 5 burros finished without stopping. Based on the data, estimate how many of the remaining 85 burros will stop before the finish line. If necessary, round your answer to the nearest whole number.
Out of the remaining 85 burros, 32 burros are expected to stop before the finish line.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
3 out of the 5 + 3 = 8 burros stopped before the finishing line, hence the probability is given as follows:
p = 3/8.
Out of 85 burros, the expected number to stop before the finish line is given as follows:
3/8 x 85 = 32 burros. (rounded up).
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The mean weight for a typical bunch of bananas in grocery stores is 3.54 pounds. The owner of a grocery store will reject a shipment of bananas if the mean weight of the banana bunches is less than 3.54 pounds. The owner randomly selects and weighs 30 bunches of bananas. A significance test at an alpha level of tests the hypotheses H 0: Mu = 3.54 pounds; pounds. What is a Type II error in this situation?
Answer: Based on the sample mean, the owner concludes that the mean weight of all of the bunches of bananas is not less than 3.54 pounds when the true mean weight is actually less than 3.54 pounds.
The fourth choice in this scenario is the Type II error: (d) Using the sample mean, the owner determines that the average weight of all the banana bunches is more than 3.54 pounds even though the real average weight is lower.
When the null hypothesis—in this case,
The average weight of the banana bunches is 3.54 pounds—is not accepted despite being erroneous, a Type II mistake takes place.
In other words, despite the cargo of bananas not meeting the requisite weight criteria, the owner fails to reject it. In this case, the owner may experience a loss in sales or reputation as a result of the poor quality of the bananas, as well as losses from selling the underweight bananas at a loss or even throwing them away.
The probability of making a Type II error can be minimized by increasing the sample size or decreasing the significance level (alpha level) of the test. However, a Type II error can never be completely eliminated.
Therefore, the correct option is d.
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Patricio deposits $800 in a savings account that pays 2.5% simple interest. He does not withdraw any money from the account, and he makes no other deposits. How much money does Patricio have in the savings account after 4 years?
Answer: The formula for simple interest is:
I = Prt
Where:
I is the interest earned
P is the principal (the initial amount deposited)
r is the interest rate (as a decimal)
t is the time period in years
Using this formula, we can calculate the interest earned by Patricio after 4 years:
I = Prt
I = 800 * 0.025 * 4
I = 80
So, after 4 years, Patricio will have earned $80 in interest. Adding this to the initial deposit of $800, the total amount of money he will have in the account is:
Total = P + I
Total = 800 + 80
Total = $880
Therefore, Patricio will have $880 in the savings account after 4 years.
Step-by-step explanation:
can you help me pleass
Answer:
A. y = 1/2x + 7/2
Step-by-step explanation:
Slope intercept form: y = mx + b
y + 2 = 1/2 (x + 11) use distributive property.
y + 2 = 1/2x + 5.5
-2 = -2 subtract 2 from both sides
y = 1/2x + 3.5
(3.5 in fraction is 7/2)
y = 1/2x + 7/2
A tabletop in the shape of a trapezoid has an area of 4,732 square centimeters. Its longer base measures 123 centimeters, and the shorter base is 85 centimeters. What is the height? The height of the tabletop is centimeters.
The height of the tabletop is 45.5 centimeters.
How to calculate the area of a trapezoid?In Mathematics and Geometry, the area of a trapezoid can be calculated by using this mathematical equation (formula):
Area of trapezoid, A = ½ × (a + b) × h
Where:
a and b represent the base areas of a trapezoid.
h represent the height of a trapezoid.
By substituting the given side lengths into the formula for the area of a trapezoid, we have the following:
4,732 = ½ × (85 + 123) × h
4,732 = 104h
Height, h = 4732/104
Height, h = 45.5 cm.
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John recently scored 113 on a particular standardized achievement test. The scores on the test are distributed with a mean of 100 and a standard deviation of 10. His cousin, Brandon, took a different standardized test and scored 263. The scores on Brandon's test have a mean of 250 and a standard deviation of 25. Which student did relatively better on his particular test? A) John did better on his test. B) Brandon did better on his test. C) They both performed equally as well on their respective tests. D) It is impossible to tell since they did not take the same test. E) It is impossible to tell since the number of students taking the test is unknown.
The correct answer is: A) on his particular test, John did better on his test.
To determine which student performed relatively better on their respective test, we need to compare their scores in relation to the mean and standard deviation of their respective tests.
For John, his score of 113 is above the mean of 100 and deviates by (113 - 100) / 10 = 1.3 standard deviations from the mean.
For Brandon, his score of 263 is above the mean of 250 and deviates by (263 - 250) / 25 = 0.52 standard deviations from the mean.
Since John's deviation from the mean is larger than Brandon's, we can conclude that John performed relatively better on his particular test.
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Mrs. B tutors outside of her normal
teaching job. She charges $60 for one
hour sessions and $40 for half hour
sessions. One week she can work a
maximum of 12 hours, but hopes to make
more than $800 tutoring. Graph a system
of inequalities below to determine how
many one hour sessions (x) and half hour
sessions (y) she could possibly teach to
reach her goals. Is it possible for Mrs.
Keesler to teach 5 one hour sessions and
14 half hour sessions? Explain.
Let x be the number of one hour sessions that Mrs. B teaches and let y be the number of half hour sessions that she teaches per week. Then we can write the following system of inequalities to represent her goals:
60x + 40y > 800 (She hopes to make more than $800 tutoring)
x + y <= 12 (She can work a maximum of 12 hours per week)
To determine how many one hour sessions and half hour sessions she can teach, we need to graph these inequalities on a coordinate plane. The graph should show the shaded region that satisfies both inequalities.
To graph the inequality 60x + 40y > 800, we can first rewrite it as:
3x + 2y > 40
Then we can graph the line 3x + 2y = 40 by plotting the points (0,20) and (13.33,0) and drawing a line through them. Since we want to graph the inequality 3x + 2y > 40, we need to shade the region above the line.
To graph the inequality x + y <= 12, we can simply graph the line x + y = 12 by plotting the points (0,12) and (12,0) and drawing a line through them. Since we want to graph the inequality x + y <= 12, we need to shade the region below the line.
The shaded region that satisfies both inequalities is the region that is above the line 3x + 2y = 40 and below the line x + y = 12. This region is a triangle with vertices at (0,12), (8,4), and (13.33,0).
To determine if Mrs. B can teach 5 one hour sessions and 14 half hour sessions, we can plug these values into the inequalities and see if they are satisfied:
60(5) + 40(14) = 860 > 800 (This inequality is satisfied)
5 + 14 = 19 <= 12 (This inequality is not satisfied)
Since the second inequality is not satisfied, it is not possible for Mrs. B to teach 5 one hour sessions and 14 half hour sessions.
sometimes two variables are statistically correlated, but there is actualy a third variable that is driving this relationship. an example provided in class was the correlation between ice cream sales and violent crimes, where the third variable was temperature. what is the name of this type of correlation
The type of correlation that occurs when two variables are statistically correlated due to the influence of a third variable is called a spurious correlation.
A spurious correlation is a type of correlation that occurs when two variables are statistically related to each other, but the relationship is not causal. Instead, the relationship is driven by the influence of a third variable that is related to both variables. This type of correlation can be misleading and can lead to incorrect conclusions if not properly understood.
For example, consider the relationship between ice cream sales and violent crime. Studies have found a positive correlation between these two variables, meaning that as ice cream sales increase, so do violent crimes. However, it is unlikely that there is a causal relationship between these two variables. Instead, the real cause of the correlation is likely the temperature. As the temperature increases, people are more likely to buy ice cream and to be out and about, which increases the opportunity for violent crime to occur. Thus, the temperature is the third variable that is driving the spurious correlation between ice cream sales and violent crime.
It is a type of correlation where there is no causal relationship between the two variables that are correlated. Instead, the correlation is driven by the influence of a third variable that is related to both variables. In the example given, the correlation between ice cream sales and violent crimes is spurious, as the real cause of the correlation is the temperature, which influences both variables.
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Biologists studying horseshoe crabs want to estimate the percent of crabs in a certain area that are longer than 35 centimeters. The biologists will select a random sample of crabs to measure.
Which of the following is the most appropriate method to use for such an estimate?
a A one sampe z-interval for a population proportion
b A one sampe z-interval for a sample proportion
c A one sampe z-interval for a population proportion
d A one sampe z-interval for a difference between population proportions
e A one sampe z-interval for a difference between sample proportins
The most appropriate method to use for estimating the percent of horseshoe crabs longer than 35 centimeters in a certain area would be a one-sample z-interval for a population proportion (Option C).
In this scenario, the biologists want to estimate a percentage or proportion (percent of crabs longer than 35 centimeters) for a specific population (horseshoe crabs in a certain area). A one-sample z-interval for a population proportion is used when estimating a single population proportion based on a random sample. It allows for determining a confidence interval for the true proportion in the population using the sample data.
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For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 90 N acts on a certain object, the acceleration of the object is 10 m/s² . If the force is changed to 81N , what will be the acceleration of the object?
Answer:
9 1/10th m/s2 :)
Step-by-step explanation:
The reason it is 1/10 is because the Number is 81 not 80, therefore 1/10 because there it is 1 left in 80 making it a fraction not a whole :) i hope this helps sorry if the explanation is too complicated...
A map of three airstrips labeled
A, B, and C is shown below. About
how far is airstrip C from airstrip A
Answer:
192.17 mi
Step-by-step explanation:
a tank contains 100 gal of pure water inirially. a solution containing zib salt /gal enters into the tank at the vate of 3 gal/min. also a drain is open so that qhe volume of the solution is constant. tow much after salt is in the tank after 60 mins?
To determine the amount of salt in the tank after 60 minutes, we need the concentration of salt in the solution entering the tank.
The information provided, which is the salt concentration in terms of "zib salt /gal," is incomplete and does not specify the actual value of zib.
If you can provide the concentration of salt in the solution entering the tank (in terms of a specific numerical value), I can help you calculate the amount of salt in the tank after 60 minutes.
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a tank contains 100 gal of pure water inirially. a solution containing zib salt /gal enters into the tank at the vate of 3 gal/min. also a drain is open so that qhe volume of the solution is constant. tow much after salt is in the tank after 60 mins?
What is the vertex of the parabola is the vertex a maximum or minimum
NEED HELP WITH MATH GEOMETRY
The value of angle m∠FCG is 27.5.
x = 25
x = 35
We have,
1.
GCH and ECD are alternate angles.
This means,
GCH = 125 = ECD
And,
ECG and DCH are alternate angles.
This means,
ECG = DCH = x
Now,
GCH + ECD + ECG + DCH = 360
125 + 125 + x + x = 360
250 +2x = 360
2x = 360 - 250
2x = 110
x = 55
Now,
ECG = ECF + FCG
55 = ECF + FCG
ECF and FCG are equal.
So,
m∠FCG = 55/2 = 27.5
2.
The straight angles are formed by (5x + 20) and (2x - 5).
So,
5x + 10 + 2x - 5 = 180
7x + 5 = 180
7x = 180 - 5
7x = 175
x = 25
3.
2x + 43 and 2x - 3 are on the same side of the parallel lines.
So,
2x + 43 + 2x - 3 = 180
4x + 40 = 180
4x = 180 - 40
4x = 140
x = 35
Thus,
The value of angle m∠FCG is 27.5.
x = 25
x = 35
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Can someone solve these two questions for me step by step? (In scientific notation)
The values of the equations are 1) 3 × 10⁴ and 2) 8.132 × 10⁵.
Given that are equations in scientific notation, we need to simplify them,
1) 2.4 × 10⁴ + 5.57 × 10³
So,
= 2.4 × 10 × 10³ + 5.57 × 10³
= 24 × 10³ + 5.57 × 10³
= 10³(24+5.57)
= 10³(29.57)
= 10³ × 29.57 × 10 / 10
= 2.957 × 10⁴
≈ 3 × 10⁴
2) 8.14 × 10⁵ - 7.8 × 10²
= 8.14 × 10³ × 10² - 7.8 × 10²
= 8140 × 10² - 7.8 × 10²
= 10²(8140-7.8)
= 10²(8132.2)
= 8132.2 × 10²
= 8132.2 × 10² × 10³ / 10³
= 8.132 × 10⁵
Hence the values of the equations are 1) 3 × 10⁴ and 2) 8.132 × 10⁵.
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biologists want to determine the number of raccoons in a particular area. they captured 16 raccoons, tagged them, and released them back into the area. the next week, 40 raccoons were caught, of which 9 were tagged. what is the best estimate of the number of raccoons in the area?
The best estimate of the number of raccoons in the area is approximately 71.
The best estimate of the number of raccoons in the area can be obtained using the mark and recapture method, also known as the Lincoln-Petersen index.
The formula for the Lincoln-Petersen index is:
Estimated population size = (Number of marked individuals in first sample * Total number of individuals in second sample) / Number of marked individuals recaptured in second sample
In this case, 16 raccoons were initially captured and tagged, and in the subsequent sample of 40 raccoons, 9 were found to be tagged.
Using the formula, the estimated population size would be:
Estimated population size = (16 * 40) / 9 = 71.11
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The table and graph below give the age (in weeks) and weight (in ounces) of a purebred chihuahua.
The graph and table show weight changes of two Chihuahua puppies over time; B's weight can be expressed as a function of A's weight plus 3 ounces.
The graph and table show the weight of two Chihuahua puppies, A and B, over a 10-week period. We can use the graph to determine the change in weight of Puppy B from week 2 to week 9.
This change in weight can be expressed in various ways, including as the rate at which Puppy B gained weight per week
(B(9) - B(2) divided by 7),
the amount of weight Puppy B gained in ounces during the seven-week interval ending at
t=9 (B(9) - B(2)),
or simply as the difference in height between the two points on the graph representing weeks 2 and 9.
The equation B(t) = A(t) + 3
It represents the relationship between Puppy B's weight and Puppy A's weight at any given time t. Specifically, Puppy B weighs three more ounces than Puppy A at time t.
This equation can be used to calculate Puppy A's weight at any given time if we know Puppy B's weight, or vice versa.
It can also be used to compare the weights of the two puppies at any given time, as the difference between their weights will always be
3 ounces.
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observations consisting of pairs of variable data are required to construct a ________ chart.
Observations consisting of pairs of variable data are required to construct a scatter plot chart. A scatter plot chart is a graphical representation of the relationship between two variables.
One variable is plotted on the horizontal axis, while the other variable is plotted on the vertical axis. Each point on the chart represents an observation or data point consisting of a pair of values for the two variables being plotted. The scatter plot chart is useful for identifying patterns, trends, and relationships between the variables. It can also be used to detect outliers or unusual observations that do not follow the general pattern of the data.
The scatter plot chart can be enhanced by adding regression lines or trend lines, which provide a visual representation of the linear relationship between the two variables. Overall, the scatter plot chart is a powerful tool for analyzing and understanding the relationship between two variables in a dataset.
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Observations consisting of pairs of variable data are required to construct a scatter chart.
A scatter chart is a graphical representation of a set of observations where one variable is plotted on the x-axis and the other variable is plotted on the y-axis. Scatter charts are useful in identifying patterns and relationships between the two variables. The strength and direction of the relationship between the variables can be determined by examining the pattern of the scatter chart. If the data points are tightly clustered around a straight line, then there is a strong linear relationship between the two variables. On the other hand, if the data points are scattered without any pattern, then there is no relationship between the two variables. Scatter charts are commonly used in scientific research, marketing analysis, and other fields where two variables need to be analyzed simultaneously.
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manova tests whether mean differences among groups on a combination of dvs is ... if there is at least 20 cases in the smallest cell the test is robust to ...
Manova (Multivariate Analysis of Variance) tests whether mean differences among groups on a combination of dependent variables (DVs) are statistically significant. If there is at least 20 cases in the smallest cell, the test is robust to violations of the assumption of multivariate normality.
In Manova, multiple dependent variables are analyzed simultaneously to determine if there are significant differences among groups. The test examines whether the mean vectors of the groups are equal across the DVs. The assumption of multivariate normality implies that the data should follow a multivariate normal distribution.
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what factor should -8-7i be multiplied by to find the quotient? enter any complex numbers in the form .
The factor that -8 - 7i should be multiplied by to find the quotient is 1 + 2i and the quotient is (-22 - 23i) / 5.
When dividing complex numbers of the form a + bi by another complex number of the form c + di, we use the following method:
Multiplying both the numerator and denominator by the conjugate of the denominator, c - di, we get:
(a + bi)(c - di)/(c + di)(c - di) = [(ac + bd) + (bc - ad)i]/(c² + d²)
where a, b, c, and d are real numbers and i is the imaginary unit with the property i² = -1.
In the given question, the denominator is 1 - 2i, so its complex conjugate would be 1 + 2i. Therefore, we need to multiply -8 - 7i by 1 + 2i in both numerator and denominator to get the quotient: (-8 - 7i)(1 + 2i) / (1 - 2i)(1 + 2i) = (-8 - 23i - 14) / (1 + 4) = (-22 - 23i) / 5
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PLEASE HELP:)))
1 In a triangle labelled ABC, ∠C = 90°, A= 44°, and AC = 27.3 cm. Calculate the length of BC.
2 In a triangle labelled ABC, ∠C= 90°, AB = 17 mm, and BC= 15 mm. Calculate
∠A.
3 in a non-right-angled triangle labelled PQR, ∠P = 124°, ∠R = 32°, and =
37.5 m. Calculate the length of
4 In a non-right-angled triangle labelled PQR, = 52.9 m, = 10.4 m, and =
47.6 m. Calculate the size of ∠R to the nearest degree.
SHOW ALL WORK PLEASE
In the triangle;
1. /BC/ = 26.4 m
2. <A = 41 degrees
3. The parameters in the question are incomplete
4. The parameters in the question are incomplete.
What is the triangle?The triangle is a three-sided geometric shape that has three angles, three vertices, and three sides. It is one of the basic shapes in geometry and is commonly studied in mathematics, physics, and engineering.
[tex]/BC/ = x\\Thus;\\Tan 44 = x/27.3\\x = 27.3 * Tan 44\\= 26.4 cm[/tex]
2)
[tex]Tan A = 15/17\\A = Tan-1(15/17)[/tex]
A = 41 degrees
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Ade and ola share a sum of 4000in the ratio of 3ratio5. Find the amount ade received
A ratio is a comparison of two or more quantities expressed as a fraction. For example, if we say that the ratio of apples to oranges is 2:3, it means that for every two apples, there are three oranges. Ade received an amount of 1500 from the total sum of 4000 .
In order to find out the amount Ade received, we need to first understand the concept of ratio. A ratio is a comparison of two or more quantities expressed as a fraction. For example, if we say that the ratio of apples to oranges is 2:3, it means that for every two apples, there are three oranges.
In this problem, we are given that Ade and Ola share a sum of 4000 in the ratio of 3:5. This means that the total ratio is 3+5 = 8.
To find out the amount Ade received, we need to first find the fraction of the total sum that belongs to Ade. We can do this by dividing Ade's ratio by the total ratio.
Ade's ratio is 3, so the fraction of the total sum that belongs to Ade is 3/8.
Now, we can find the amount Ade received by multiplying this fraction by the total sum:
Amount Ade received = (3/8) x 4000 = 1500.
1.Add the ratio parts: 3 (Ade's part) + 5 (Ola's part) = 8 total parts.
2. Divide the total sum (4000) by the total parts (8): 4000 ÷ 8 = 500. This gives us the value of one part.
3. Multiply Ade's ratio part (3) by the value of one part (500): 3 × 500 = 1500.
So, Ade received an amount of 1500 from the total sum of 4000.
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Whats one more expression that can be used for this?
Using exponents three more expressions whose value is 216 are;
6⁴ ÷ 6 = 216
6² x 2¹ x 3¹ = 216
6 ÷ 6⁻² = 216
What is an exponent?The exponent of a number says how many times to use the number in a multiplication.
Also, exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.
If 6³ = 216, using exponents, we can write three more expressions whose value is 216 as shown below;
6³ = 6 x 6 x 6 = 216
6⁴ ÷ 6 = 6³ × 6⁰ = 1296 ÷ 6 = 216
6² x 2¹ x 3¹ = 216
6 ÷ 6⁻² = 6 × 36 = 216
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Please solve (Will give brainliest!)
There are 7 multiples of 3 in the range 100₃ to 1000₃
Calculating the number of multiples of 3 in the rangeFrom the question, we have the following parameters that can be used in our computation:
Multiples of 3 from 100₃ to 1000₃
Convert the numbers to base ten using the product rule
Such that each digit is multipled by the 3 to the exponent of the position of the number
And the sum of each product is taken
So, we have
100₃ = 1 * 3² = 0 * 3¹ + 0 * 3⁰ = 9
1000₃ = 1 * 3³ + 0 * 3² + 0 * 3¹ + 0 * 3⁰ = 27
The multiples of 3 from 9 to 27 are
9, 12, 15, 18, 21, 24 and 27 i.e. 7 numbers
Hence, the number of multiples of 3 in the range are 7
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30 = 2(x + 6) solve for x
Answer:
x = 9
Step-by-step explanation:
30 = 2(x +6)
30 = 2x +12
Subtract 12 from both sides.
18 = 2x
divide both sides by 2.
9 = x
First, we can simplify the equation by dividing both sides by 2:
30/2 = x + 6
This gives us:
15 = x + 6
Now we can solve for x by subtracting 6 from both sides:
15 - 6 = x
Therefore, the solution is:
x = 9.
P has coordinates (-9, 7)
Q has coordinates (11, 12)
M is the point on the line segment PQ such that PM: MQ=2:3
Line L is perpendicular to the line segment PQ.
L passes through M.
Find an equation of L.
The calculated equation of the line L is y = -4x + 5
Finding the equation of line L.Given that
P has coordinates (-9, 7)Q has coordinates (11, 12)We have the partition to be
m : n = 2 : 3
The coordinate is then calculated as
M = 1/(m + n) * (mx₂ + nx, my₂ + ny₁)
So, we have
M = 1/5 * (2 * 11 + 3 * -9, 2 * 12 + 3 * 7)
Evaluate
M = (-1, 9)
The slope of line PQ is
Slope = (12 - 7)/(11 + 9)
So, we have
Slope = 1/4
The slopes of perpendicular lines are opposite reciprocals
So, the slope of L is
m = -4
The equation of line L is then calculated s
y - 9 = -4(x + 1)
So, we have
y = -4(x + 1) + 9
Evaluate
y = -4x + 5
Hence, the equation of line L is y = -4x + 5
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a bucket full of water is in the form of a frustum of a cone. the bottom at the top radius are 18 cm and 28 cm representively and the Vertical depth is 30 cm.if the water is poured into an empty cylinder container with base radius 20 cm.
find the depth of the water in the container
(take π=22÷7)
Answer:
9.8596
Step-by-step explanation:
The depth of the water in the cylinder container is 120.9inches.
Given:
The frustum's vertical depth (h) is 30 cm.
Top frustum radius (r1) = 18 cm
Frustum's bottom radius (r2) is 28 cm.
The following formula determines the volume of a cone's frustum:
[tex]V = \frac{1}{3}* \pi * h * (r1^2 + r2^2 + (r1 * r2))[/tex]
calculating the frustum's volume
V=[tex]\frac{1}{3} *\pi *30(18^2+28^2+18*28)\\[/tex]
V=50642.5[tex]in^3[/tex].
The following formula determines a cylinder's volume:
Volume of cylinder = [tex]\frac{1}{3} \pi r^2h[/tex]
[tex]50642.5 = (1/3) *\pi *20^2*h[/tex]
h=[tex]50642.5*\frac{3}{\pi *20^2}[/tex]
h= 120.9 inches
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