In hypothesis testing, if the test value is in the critical region, the researcher should fail to reject the null hypothesis. The given statement is true.
What is hypothesis testing?Hypothesis testing is a statistical process used to determine the validity of a statement that is made about a population. It's a statistical procedure that aids in making inferences about population parameters from sample data. It's used to test the null hypothesis against the alternative hypothesis, which determines whether or not a sample statistic and the claim made by a population parameter are in agreement.
The null hypothesis is that the population parameter is equal to a particular value, while the alternative hypothesis is that it is different from that value.
In a hypothesis test, the calculated value of a test statistic is compared to a critical value. The null hypothesis is rejected if the calculated value exceeds the critical value, implying that the alternative hypothesis is correct. However, if the calculated value of the test statistic falls within the critical region, the null hypothesis cannot be rejected, implying that there is insufficient evidence to support the alternative hypothesis.
Thus, the given statement is true.
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A function that converts an input of letters and numbers into an encrypted output of a fixed length. The links in the blockchain that is created using an algorithm.
A function that converts an input of letters and numbers into an encrypted output of a fixed length is called hash. The links in the blockchain that is created using an algorithm.
A hash is a mathematical function that changes an input of any length into an encrypted output of a specific length. Therefore regardless of the quantity of raw data involved or the size of the file, its unique hash is always the same size. Also, a hash cannot be used to "reverse engineer" an input from a hash output, because hash functions are "one-way" (like a meat grinder; you don't can't put ground beef back into a steak). However, if you use such a function on the same data, its hash will be the same, so you can confirm that the data is the same (i.e., unchanged) if you already know its hash.
Hashes are used in various parts of the blockchain system. Each block header contains the hash of the previous block, ensuring nothing has been tampered with as new blocks are added. Cryptocurrency blockchains use hashes to secure information and make the ledger immutable.
It refers to the technique of making an input element of arbitrary length reflect an output element of definite length. For blockchain applications in cryptocurrencies, variable duration transactions are processed by specific hashing algorithms and all produce fixed length outputs. This is true regardless of the duration of the input transaction.
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Complete Question:
Fill in the blanks,
A function that converts an input of letters and numbers into an encrypted output of a fixed length is called ________. The links in the blockchain that is created using an algorithm.
Suppose you are investigating the relationship between two variables, traffic flow and expected lead content, where traffic flow is a predictor of lead content. you find the 95% ci for expected lead content when traffic flow is 15, based on a sample of n 10 observations, is (461.7, 598.1) what parameter is this interval estimating?a. beta the average change in lead content with a change in traffic flow.b. key u lead content!traffic flow = 15 the average lead content when traffic flow is 15. oc. u lead content the average lead content.
The confidence interval provides an estimate of the population mean of lead content when the traffic flow is 15, which is denoted by the symbol μ.
The confidence interval (461.7, 598.1) estimates the true population parameter of the expected lead content when traffic flow is 15. In this case, the parameter being estimated is the population mean of lead content at a specific level of traffic flow, which is denoted by the symbol μ.
Option (c) "μ lead content, the average lead content" is the correct option, as the confidence interval provides an estimate of the true population mean of lead content when the traffic flow is at a specific level (in this case, 15).
Option (a) "β, the average change in lead content with a change in traffic flow" is not applicable here since the confidence interval is estimating the mean lead content at a specific level of traffic flow, not the change in lead content with a change in traffic flow.
Option (b) "μ lead content traffic flow = 15, the average lead content when traffic flow is 15" is partially correct, but it is important to note that this is a conditional mean, which is the mean of lead content given that the traffic flow is 15. The confidence interval estimates the true population mean of lead content at a specific level of traffic flow, regardless of whether that traffic flow is 15 or any other value.
In summary, the confidence interval provides an estimate of the population mean of lead content when the traffic flow is 15, which is denoted by the symbol μ.
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I don't understand this could someone help I will give brainliest!
Answer: c
Step-by-step explanation:
The most appropriate measure of center for this data is the .
The mean is the most appropriate measure of center for the given data. While the median and mode were also calculated, the mean provides the best representation of the data's central tendency. The geometric mean was not applicable in this case.
Option A) Mean: To calculate the mean, we add up all the values and divide by the total number of values.
Mean = (20 + 6 + 42 + 13 + 15 + 10 + 9 + 12 + 12) / 9
Mean = 16.222
Option B) Median: To calculate the median, we need to arrange the values in order and find the middle value.
After arranging the values in ascending order: 6, 9, 10, 12, 12, 13, 15, 20, 42
The median is 12.
Option C) Mode: To calculate the mode, we need to find the most frequently occurring value. In this case, there is no value that occurs more than once, so there is no mode.
Option D) Geometric Mean: The geometric mean is used to calculate the average rate of change or growth. It is not suitable for this data set.
Therefore, option A) mean is the most appropriate measure of center for this data.
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Complete question:
The most appropriate measure of center for this data is the.
20, 6, 42, 13, 15, 10, 9, 12, 12
A) mean
B) median
C) mode
D) geometric mean
Answer:
median, A, 65
Step-by-step explanation:
.....
5. we know that the true relative risk of an association between a selected exposure and outcome is 1.5 in the entire population of a city x. a study conducted to examine the same association, but in a small sample of participants from city x, with a certain degree of measurement bias, yielded a relative risk of 4.0. what type of error would you expect in this study?
The study has a measurement bias due to the small sample size and the likely difference between the population of city x and the sample used in the study, resulting in a Type I Error (false positive) of 1.67, meaning an overestimation of the true relative risk of the association by 67%.
In this case, the study has a measurement bias due to the small sample size and the likely difference between the population of city x and the sample used in the study. As a result, we can expect the relative risk to be overestimated. This is known as a Type I Error (false positive) and can be calculated using the formula:
Type I Error = (4.0 – 1.5) / 1.5 = 1.67
In other words, the study overestimated the true relative risk by 67%. This is an example of an inflated relative risk due to a lack of representativeness of the sample population.
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Find the area and circumference of a circle with diameter 7 feet use the value 3.14 for pi
Answer:
Circumfrance= 21.991
area= 38.48
Step-by-step explanation:
2piR
R=3.5
:)
Somebody please please please help me
Answer:
a₅ = 11
Step-by-step explanation:
using the recursive rule [tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 2 , with a₁ = 3 , then
a₂ = a₁ + 2 = 3 + 2 = 5
a₃ = a₂ + 2 = 5 + 2 = 7
a₄ = a₃ + 2 = 7 + 2 = 9
a₅ = a₄ + 2 = 9 + 2 = 11
Write the equation of the hyperbola using the given information, The hyperbola has vertices (-2,9) and (-2,3) and foci (-2,13) and (-2,-1)
The center of the hyperbola is the midpoint between the vertices, which is (-2,6).
The distance between the center and each vertex is 3, so the distance between the center and each focus is c = 7.
The distance between each vertex and focus is a = 4.
The equation of the hyperbola with center (h,k) is:
(x - h)^2 / a^2 - (y - k)^2 / b^2 = 1
where b^2 = c^2 - a^2.
Plugging in the values we have:
- Center: (h,k) = (-2,6)
- a = 4
- c = 7
- b^2 = c^2 - a^2 = 49 - 16 = 33
So the equation of the hyperbola is:
(x + 2)^2 / 16 - (y - 6)^2 / 33 = 1
The graph above shows quadrilateral ABCD. Which set of vertices represents a rotation? a glide reflection? a translation? a similarity transformation? Write a rule for each of these transformations. 1. A'(-3, 1), B'(-1, 4), C'(-3, 6), D'(-6, 3) 2. A'(-5, -5), B'(-3, -8), C'(-5, -10), D'(-8, -7) 3. A'(-8, 0), B'(-4, -6), C'(-8, -10), D'(-14, -4) 4. A'(1, -3), B'(4, -1), C'(6, -3), D'(3, -6) 5. A'(-1, -3), B'(-4, -1), C'(-6, -3), D'(-3, -6) 6. A'(6, 1), B'(8, 4), C'(6, 6), D'(3, 3)
Note that the transformation for the above vertices are given as follows.
What is the transformation for the above vertices ?From the given graph, we can determine the transformations as follows:
A'(-3, 1), B'(-1, 4), C'(-3, 6), D'(-6, 3) - This set of vertices represents a reflection across the line y = 3. Rule: (x, y) -> (x, 6 - y)A'(-5, -5), B'(-3, -8), C'(-5, -10), D'(-8, -7) - This set of vertices represents a glide reflection. Rule: (x, y) -> (x - 2, -y)A'(-8, 0), B'(-4, -6), C'(-8, -10), D'(-14, -4) - This set of vertices represents a translation. Rule: (x, y) -> (x - 4, y - 4)A'(1, -3), B'(4, -1), C'(6, -3), D'(3, -6) - This set of vertices represents a rotation of 270 degrees counterclockwise about the origin. Rule: (x, y) -> (y, -x)A'(-1, -3), B'(-4, -1), C'(-6, -3), D'(-3, -6) - This set of vertices represents a reflection across the line y = -2. Rule: (x, y) -> (x, -4 - y)A'(6, 1), B'(8, 4), C'(6, 6), D'(3, 3) - This set of vertices represents a similarity transformation (rotation and dilation). Rule: (x, y) -> (2x - 9, 2y + 1)Learn more about transformation at:
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Full Question:
Although part of your question is missing, you might be referring to this full question: See attached image.
Question 1 (if someone answers this I give 15 points)
The net for a cylindrical candy container is shown.
net of a cylinder with a diameter of both circles labeled 1.8 inches and a rectangle with a height labeled 0.8 inches
The container was covered in plastic wrap during manufacturing. How many square inches of plastic wrap were used to wrap the container? Write the answer in terms of π.
7.92π square inches
7.2π square inches
3.06π square inches
2.34π square inches
(no rush at all these are for my notes)
The amount of plastic wrap used to wrap the container is 3.06π square inches.
What is cylinder ?
A cylinder is a multi object used in geometry that has a round base, a curving surface rising from it, and another circular shape at the top or lid. One way to visualize a cylinder is as a stack of infinitely thin circular discs stacked one on top of the other. The height and radius of a cylinder, which measure the distance from the base to the top and the edge of the circular base, respectively, determine the shape of the object.
The plastic wrap covers the entire surface area of the cylinder. The formula for the surface area of a cylinder is:
Surface area of cylinder = 2πr² + 2πrh
where r is the radius of the circular base of the cylinder, and h is the height of the cylinder.
We can use the given diameter of the circular base, which is 1.8 inches, to find the radius r:
r = d/2 = 1.8/2 = 0.9 inches
We are also given the height of the rectangle, which is 0.8 inches.
Now we can substitute the values of r and h into the formula for the surface area of the cylinder:
Surface area of cylinder = 2π(0.9)² + 2π(0.9)(0.8)
Surface area of cylinder = 2π(0.81) + 2π(0.72)
Surface area of cylinder = 1.62π + 1.44π
Surface area of cylinder = 3.06π square inches
Therefore, the amount of plastic wrap used to wrap the container is 3.06π square inches.
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Help! I have a take home test due Tommorow please give me answers
This is the simplified ratio of lengths DE:EF as (2/√(29))√(34) : 1.
What is ratio?A ratio is a relationship between two or more quantities that indicates how many times one quantity is contained in another. It is a way of comparing quantities of the same kind, such as lengths, areas, volumes, or numbers. A ratio is usually expressed as a fraction or a colon (:). Ratios can be simplified by dividing both terms of the ratio by their greatest common factor (GCF). Ratios are used in many fields such as mathematics, finance, science, engineering, and statistics, among others. They are used to compare different quantities, to express proportions or rates, and to solve various mathematical problems.
Here,
We can use the distance formula to find the lengths DE and EF, and then calculate their ratio:
Length DE = √[(xE - xD)² + (yE - yD)²]
= √[(10 - 4)² + (15 - 4)²]
= √(6² + 11²)
= √(136)
= 2√(34)
Length EF = √[(xF - xE)² + (yF - yE)²]
= √[(12 - 10)² + (20 - 15)²]
= √(2² + 5²)
= √(29)
Therefore, the ratio of lengths DE:EF is:
DE:EF = (2√(34)) : (√(29))
We can simplify this ratio by dividing both sides by √(29):
DE:EF = (2√(34))/√(29) : (√(29))/√(29)
= (2/√(29))√(34) : 1
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PLEASE HELPPP!!!
Solve the system of equations using elimination
Answer:
the answer is 3,9
Step-by-step explanation:
-3x+2y=9
3(x+y=12)
-3x+2y=9
3x+3y=36
5y=45
_ __
5 5
y=9
x+y=12
x+9=12
-9 -9
_______
x=3
What series of transformations would carry the rectangle onto itself?
O(x+0,y-4), 180° rotation, reflection over the y-axis
O(x+0, y-4), 180° rotation, reflection over the x-axis
O (x-4, y+0), 90° counterclockwise rotation, reflection over the x-axis
O (x-4, y+0), 90° counterclockwise rotation, reflection over the y-axis
The answer of the given question based on the graph transformations is option (c): (x-4, y+0), 90° counterclockwise rotation, reflection over the x-axis.
What is Reflection?Reflection is a transformation that flips an object over a line, plane, or point. The line, plane, or point is called the "line of reflection", the "plane of reflection", or the "point of reflection", respectively. Reflection is a fundamental concept in geometry, and it has applications in various fields of mathematics, physics, and engineering. It is often used in symmetry analysis, transformation geometry, and computer graphics.
The series of transformations that would carry the rectangle onto itself is option (c): (x-4, y+0), 90° counterclockwise rotation, reflection over the x-axis.
To see why, we can analyze each transformation and its effect on the rectangle:
(x-4, y+0) translates the rectangle left by 4 units.
90° counterclockwise rotation preserves the right angles and parallel sides of the rectangle.
Reflection over the x-axis preserves the right angles of the rectangle and also preserves the orientation of its parallel sides.
Therefore, the final image after all three transformations would be congruent to the original rectangle, i.e., the rectangle would be carried onto itself.
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a cylinder is leaking water at an unknown rate. the cylinder has a height of 6 meters and a radius of 5 meters. find the rate at which the volume of water in the tank is changing if the rate at which the height is decreasing is 8 centimeters per minute when the height is 4 meters.
The rate at which the volume of water in the tank is changing is 58π(dr/dt).
To find the rate at which the volume of water in the tank is changing if the rate at which the height is decreasing is 8 centimeters per minute when the height is 4 meters, we need to use the formula for the volume of a cylinder, which is given by:
V = πr²hwhere V is the volume of the cylinder, r is the radius, and h is the height.
We also need to differentiate the formula for the volume of a cylinder with respect to time to get an equation for the rate of change of the volume of the cylinder. Differentiating the formula for the volume of a cylinder with respect to time, we get:
dV/dt = πr²dh/dt + 2πrhdr/dt
where dV/dt is the rate of change of the volume of the cylinder, dh/dt is the rate of change of the height of the cylinder, and dr/dt is the rate of change of the radius of the cylinder.
Substituting the given values into the formula and simplifying, we get:
dV/dt = π(5²)(-8/100) + 2π(5)(6)(dr/dt) = -2π + 60π(dr/dt) = 58π(dr/dt)
Therefore, the changes in water volume in the tank is 58π(dr/dt).
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Two groups of volunteers are cleaning up the football stadium after the Homecoming game. Volunteers from the Band Booster Club have already cleaned 5 rows of bleachers and will continue to clean at a rate of 3 rows per minute. The leadership class has completed 6 rows and will continue working at 2 rows per minute. Once the two groups get to the point where they have cleaned the same number of rows, they will take a break and decide how to split up the remaining work. How long will that take? How many minutes will each group have cleaned by then?
1) The time it will take for both to have cleaned the same number of rows is: 1 minute
2) The number of rows cleaned by then is: 16 rows
How to solve Algebra word problems?We are told that Volunteers from the Band Booster Club have already cleaned 5 rows of bleachers and will continue to clean at a rate of 3 rows per minute. If the number of minutes is x, then the equation here is:
3x + 5
Similarly, the leadership class has completed 6 rows and will continue working at 2 rows per minute. If the number of minutes is x, then the equation here is:
2x + 6
The point at which they have cleaned the same number of rows will be:
3x + 5 = 2x + 6
3x - 2x = 6 - 5
x = 1 minute
Thus, after 1 minute they would have cleaned 8 + 8 = 16 rows of bleachers
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Work out the size of angle A
around 85 degrees. I did it with a protractor.
A recipe uses 3/4 teaspoon of baking soda and 3 teaspoons of salt write the ratio of baking soda to salt then find the value of the ratio
Answer:
Step-by-step explanation:
To write the ratio of baking soda to salt, we need to compare the amount of baking soda to the amount of salt in the recipe.
The recipe uses 3/4 teaspoon of baking soda and 3 teaspoons of salt, so the ratio of baking soda to salt is:
3/4 : 3
To simplify this ratio, we can divide both numbers by the greatest common factor (GCF) of 3 and 4, which is 1.
3/4 divided by 1 = 3/4
3 divided by 1 = 3
So the simplified ratio of baking soda to salt is:
3/4 : 3 = 3: 12
To find the value of the ratio, we can divide both the numerator and denominator by 3:
3/3 : 12/3 = 1: 4
Therefore, the value of the ratio of baking soda to salt is 1:4.
The nineteenth term in an arithmetic
sequence is 243, and the eleventh term is 147.
What is the value of the eighty-sixth term?
Answer:
1047
Step-by-step explanation:
a_n = a_1 + (n - 1)d
a_19 = 243
a_11 = 147
243 = a_1 + (19 - 1)d
147 = a_1 + (11 - 1)d
243 = a_1 + 18d
147 = a_1 + 10d
a_1 = 243 - 18d
a_1 = 147 - 10d
243 - 18d = 147 - 10d
-8d = -96
d = 12
a_1 = 147 - 10d
a_1 = 147 - 10(12)
a_1 = 27
The first term is 27. The common difference is 12.
a_86 = a_1 + (n - 1)d
a_86 = 27 + 85(12)
a_86 = 1047
Martin is a hair stylist. He averages a weekly wage of $240 and
usually gets another $356 in tips. What is his average total
income?
To find Martin's average total income, we need to add his average weekly wage to his average weekly tips:
$240 (weekly wage) + $356 (weekly tips) = $596 (average total income)
Therefore, Martin's average total income is $596 per week.
Hi pls solve this and make sure your answer is original and whoever does this will get brainless
Answer:
because he is wittery hitting da gwity
Erik just found an old set of reference books his grandfather gave him years ago. There are 12 same-sized books in the set, each being 6 inches long and 3 4 of an inch wide. The books are packed in a case shaped like a rectangular prism that fits them perfectly. The case has a volume of 432 cubic inches. How tall are the books?
Thus, each book has an 8-inch height.
What are some math examples of volume?
The quantity of space taken up by a three-dimensional object can also be used to describe volume. By determining the number of units cubes it contains, the volume of such a solid like such a cube or cuboid can be determined.
Get the volume of a single book in cubic centimeters to get things started. We can accomplish this by multiplying a book's length, width, and height:
Volume of one book = 6 inches x 3/4 inches x height
Volume of one book = 4.5 cubic inches x height
Since the 12 books are all the same size, their combined volume is:
Total volume of books = 12 books x Volume of one book
Total volume of books = 12 books x 4.5 cubic inches x height
Total volume of books = 54 cubic inches x height
Since we are aware that the case has a total volume of 432 cubic inches, we can construct the following equation:
Total volume of case = Total volume of books
432 cubic inches = 54 cubic inches x height
When we solve for height, we obtain:
height = 432 cubic inches / 54 cubic inches
height = 8 inches
Thus, each book has a height of 8 inches.
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A study on students drinking habits asks a random sample of 170 female UF students how many alcoholic beverages they have consumed in the past week. The sample reveals an average of 4.05 alcoholic drinks, with a standard deviation of 4.66. Construct a 99% confidence interval for the true average number of alcoholic drinks all UF female students have in a one week period.Group of answer choices(-7.99, 16.09)(3.13, 4.97)(3.46, 4.64)(3.35, 4.75)
The 99% confidence interval for the true average number of alcoholic drinks all UF female students have in a one week period is option (d) (3.35, 4.75)
To construct a confidence interval for the true average number of alcoholic drinks all UF female students have in a one week period, we can use the following formula
Confidence interval = sample mean ± (critical value) x (standard error)
Where the standard error is calculated as
Standard error = standard deviation / square root of sample size
We are given
Sample size (n) = 170
Sample mean (X) = 4.05
Standard deviation (s) = 4.66
Confidence level = 99%
To find the critical value, we need to look up the t-value with 169 degrees of freedom (since we are using a t-distribution because the sample size is less than 30) and a 99% confidence level. Using a t-distribution table or a calculator, we find the t-value to be approximately 2.62.
Substituting the values into the formula, we get:
Standard error = 4.66 / √170 ≈ 0.357
Confidence interval = 4.05 ± (2.62) x (0.357) ≈ (3.35, 4.75)
Therefore, the correct option is (d) (3.35, 4.75)
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24 ÷ (5 + a) when a = 3
Answer:
3
Step-by-step explanation:
do the brackets first
(5+3) = 8
24÷8=3
so the answer is 3
A certain set of plants were constantly dying in the dry environment that was provided. The plants were moved to a more humid environment where life would improve. (a) Before moving all of the plants, the rescarchers wanted to be sure the new environment was promoting lfe. The study found that 21 out of 50 of the plants were alive after the first month. What is the point estimate? 42 (b) What Is the95 confldence Interval for the population proportlon? (Use a table or technology.Rud your answers to three decimal places.) X ,1555 (c what is the 99% confidence interval for the population proportion? Use a table or technology. Round your answers to three decima places.
The 99% confidence interval for the population proportion is (0.257, 0.583).
(a) The point estimate of the population proportion of plants alive after the first month in the more humid environment is:
point estimate = x/n = 21/50 = 0.42
So, the point estimate is 0.42.
(b) To find the 95% confidence interval for the population proportion, we can use the formula:
confidence interval = point estimate ± z√(point estimate(1-point estimate)/n)
where z is the z-score corresponding to the desired confidence level, n is the sample size, and √ represents the square root.
For a 95% confidence level, z = 1.96 (from a standard normal distribution table).
Plugging in the values, we get:
confidence interval = 0.42 ± 1.96√(0.42(1-0.42)/50)
= 0.42 ± 0.127
= (0.293, 0.547)
So, the 95% confidence interval for the population proportion is (0.293, 0.547).
(c) To find the 99% confidence interval for the population proportion, we can use the same formula but with a different z-score.
For a 99% confidence level, z = 2.58 (from a standard normal distribution table).
Plugging in the values, we get:
confidence interval = 0.42 ± 2.58√(0.42(1-0.42)/50)
= 0.42 ± 0.163
= (0.257, 0.583)
So, the 99% confidence interval for the population proportion is (0.257, 0.583).
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let g be a function such that g(4)=8 and g’(4)=-3
let h be the function h(x)=sqrt
Answer:If (2t+1)is a factor then t=2−1 must be one of the zeroes of the given polynomial. Substituting in the given equation.
q((2−1))=4(2−1)3+4(2−1)2−(2−1)−1=4(8−1)+4(41)+(21)−1=(2−1)+1+(21)−1=0
Hence(2t+1) is a common factor of q(t)
Step-by-step explanation:
Measure angels level D. Please help
Answer: What is the measure of ∠ D?
By using the angle sum property of quadrilateral, we get the measure of angle ∠D is 76.765°.
Step-by-step explanation:
Pairs of markings a set distance apart are made on highways so that police can detect drivers exceeding the speed limit. Over a fixed distance, the speed R varies inversely with the time T. In one
particular pair of markings, R is 41 mph when Tis 8 seconds. Find the speed of a car that travels the given distance in 5 seconds.
R= ? mph (Round to the nearest whole number.)
The the speed of a car that travels the given distance in 5 seconds from the information is 65.6 mph.
How can the speed be calculated?Speed and time are two fundamental concepts in physics and mathematics that are often used together to describe the motion of objects.
Speed refers to how fast an object is moving, and is typically measured in units of distance per unit of time, such as meters per second (m/s) or miles per hour (mph). Speed can be either constant, meaning the object is moving at the same speed throughout its motion, or variable, meaning the object's speed changes over time.
Given that the speed R varies inversely with the time T
R = 41 mph T = 8 seconds
The distance can be calculated as( speed * time)
Distance = ( speed * time)
= 41 * 8 = 328miles
The total distance travel can now bw seen as 328miles, the speed of a car that travels the given distance in 5 seconds can now be calculated as
Speed =Distance / time.
= 328miles/ 5 seconds
= 65.6 mph.
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What is measurement angle S to the nearest degree?
The unknown angle in the triangle is as follows;
m∠S = 38 degrees
How to find the angle measure of a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.
In the triangle QRS,
m∠Q = 4m∠R
m∠R = 3 / 4 m∠S
Therefore, let's find the angle m∠S in the triangle as follows:
Therefore,
m∠Q + m∠R + m∠S = 180°
let
m∠R = x
4x + x + 4 / 3 x = 180
5x + 4 / 3 x = 180
15x + 4x / 3 = 180
19x / 3 = 180
19x = 180 × 3
19x = 540
x = 540 / 19
x = 28.42
Therefore,
m∠S = 4 / 3 (28.42)
m∠S = 37.8947368421
m∠S = 38 degrees
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The radius of a circle is 5 in. Find its circumference in terms of pi
The formula for the circumference of a circle is C = 2πr, where "C" is the circumference, "π" is pi (approximately equal to 3.14), and "r" is the radius.
Given that the radius of the circle is 5 inches, we can substitute this value into the formula to find the circumference:
C = 2πr
C = 2π(5)
C = 10π
Therefore, the circumference of the circle is 10π inches.
3x − 2y = –17
–x − 9y = –4
Answer: x = -5, y = 1
Step-by-step explanation:
These are simultaneous equations
I will use the substitution method
BTW [1] means the top equation, and [2] the bottom equation
Rearrange [2] for x
-x = -4 + 9y
x = 4 - 9y
Substitute 4 - 9y into [1]
3(4 - 9y) - 2y = -17
Expand the bracket
12 - 27y - 2y = -17
Simplify
12 - 29y = -17
Rarrange for y
12 = 29y - 17
29y = 12 + 17 = 29
y = 1Now substitute y into either equation to solve for x
I will use [2] as it looks easier
-x - 9(1) = -4
Expand the bracket
-x -9 = -4
-x = 5
x = -5Now lets substitute x and y into [1] to check our answer
3(-5) - 2(1) = -17
-15 - 2 = -17