Find the critical value t
The answer of the given question based on the Critical value is , , the critical value to for the confidence level c = 0.99 and sample size n = 22 is 2.819.
What is Critical value?
In statistics, critical value is value that is used to determine whether to reject null hypothesis in hypothesis test. It is based on chosen level of significance, which is the maximum probability of making a Type I error (rejecting true null hypothesis). The critical value is determined by sampling distribution of the test statistic, which is often a t-statistic or z-statistic, depending on the test and the characteristics of the population being studied.
To find the critical value t for a 99% confidence level and a sample size of 22, we need to use a t-distribution table or a calculator.
Using a t-distribution table with 21 degrees of freedom (n-1), we find that critical value for a 99% confidence level is approximately 2.819.
Therefore, critical value for confidence level c = 0.99 and sample size n = 22 is 2.819 (rounded to nearest thousandth).
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The ability to determine the age of some individuals can be difficult if there are not quality government records of birth. Bone growth takes place at the growth plates at the end of long bones. Once all growth plates fuse, growth stops, and an individual is considered a biological adult. The age at which growth plates fuse for males is approximately normally distributed with a mean of 18.8 years and a standard deviation of 15.1months. Complete parts (a) through (d).
The answers to each question are:
(a) 0.351.
(b) 0.317.
(c) 20.24 years.
(d) 16.
What is the mean and standard deviation?
The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.
(a) What is the probability that a randomly selected male has growth plates that fuse between the ages of 18 and 20 years?
To answer this question, we need to standardize the values of 18 and 20 using the mean and standard deviation provided. Let X be the age at which growth plates fuse for males. Then,
Z = (X - mean) / standard deviation
Z for X = 18 is (18 - 18.8) / (15.1/12) = -0.53
Z for X = 20 is (20 - 18.8) / (15.1/12) = 0.53
Using a standard normal distribution table or a calculator, we can find the probability of Z being between -0.53 and 0.53, which is approximately 0.351.
Therefore, the probability that a randomly selected male has growth plates that fuse between the ages of 18 and 20 years is 0.351.
(b) What is the probability that a randomly selected male has growth plates that fuse between the ages of 16 and 18 years?
We need to standardize the values of 16 and 18 using the mean and standard deviation provided.
Z for X = 16 is (16 - 18.8) / (15.1/12) = -2.03
Z for X = 18 is (18 - 18.8) / (15.1/12) = -0.53
Using a standard normal distribution table or a calculator, we can find the probability of Z being between -2.03 and -0.53, which is approximately 0.317.
Therefore, the probability that a randomly selected male has growth plates that fuse between the ages of 16 and 18 years is 0.317.
(c) What is the age at which growth plates fuse for the top 5% of males?
We need to find the age X such that the probability of a male having growth plates fuse at an age less than X is 0.95 (since 5% is the complement of 95%).
Using a standard normal distribution table or a calculator, we can find the Z-score corresponding to the 95th percentile, which is approximately 1.645.
Then, we can solve for X using the formula:
Z = (X - mean) / standard deviation
1.645 = (X - 18.8) / (15.1/12)
Simplifying the equation, we get:
X = 18.8 + (1.645)(15.1/12) = 20.24
Therefore, the age at which growth plates fuse for the top 5% of males is approximately 20.24 years.
(d) What percentage of males have growth plates that fuse before the age of 16?
We need to find the probability of a male having growth plates fuse before the age of 16, which is equivalent to finding the probability of Z being less than -2.03 (calculated in part (b)).
Using a standard normal distribution table or a calculator, we can find the probability of Z being less than -2.03, which is approximately 0.0228.
Therefore, approximately 2.28% of males have growth plates that fuse before the age of 16.
hence, the answers to each question are:
(a) 0.351.
(b) 0.317.
(c) 20.24 years.
(d) 16.
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Identify the correct equation of the graph.
-10
O f(b) = (6+4)² +8
O f(b) = (b+8)² +4
Of(b)=(6-8)²-4
O
-5
10
5
-5
-10
V
5
O f(b) = (b-8)² +4
Of(b) = (6-4)²-8
Of(b) (6-4)² +8
10
Check
Thus, the correct equation for the given parabolic graph is found as: f(b) = (b – 8)² + 4.
Explain about the quadratic function in vertex form:A parabola has a lowest point if it opens upward. A parabola has a highest point if it opens downward.
The vertex of the parabola is located at this lowest or highest point.
Vertex form of a quadratic function:
f(x) = a(x – h)² + k, where a, h, and k are constants.
The vertex of the parabola is at because it is translated h horizontal units and k vertical units from the origin (h, k).
(h,k) are the vertex of parabola.
From the given graph:
f(b) is the given function:
Vertex (h,k) = (8, 4)
Thus, h= 8 and k = a = 1, x = b.
Put the values in quadratic function:
f(b) = 1(b – 8)² + 4
f(b) = (b – 8)² + 4
Thus, the correct equation for the given parabolic graph is found as: f(b) = (b – 8)² + 4.
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Here is another question DUE SOON PLEASE ASAP
Question 5(Multiple Choice Worth 1 points)
(08.07 MC)
The table describes the quadratic function p(x).
x p(x)
−1 10
0 1
1 −2
2 1
3 10
4 25
5 46
What is the equation of p(x) in vertex form?
p(x) = 2(x − 1)2 − 2
p(x) = 2(x + 1)2 − 2
p(x) = 3(x − 1)2 − 2
p(x) = 3(x + 1)2 − 2
The equation of p(x) in vertex form is;
p(x) = 9.67(x + 1.04)² - 10.25
The closest answer choice is:
p(x) = 3(x - 1)² - 2, which is not correct.
What is vertex?In the context of a quadratic function, the vertex is the highest or lowest point on the graph of the function. It is the point where the parabola changes direction. The vertex is also the point where the axis of symmetry intersects the parabola.
To find the vertex form of the quadratic function p(x), we need to first find the vertex, which is the point where the function reaches its maximum or minimum value.
To find the vertex, we can use the formula:
x = -b/2a, where a is the coefficient of the x² term, b is the coefficient of the x term, and c is the constant term.
Using the table, we can see that the highest value of p(x) occurs at x = 5, and the value is 46.
We can then use the formula to find the vertex:
x = -b/2a = -5/2a
Using the values from the table, we can set up two equations:
46 = a(5)² + b(5) + c
1 = a(0)² + b(0) + c
Simplifying the second equation, we get:
1 = c
Substituting c = 1 into the first equation and solving for a and b, we get:
46 = 25a + 5b + 1
-20 = 5a + b
Solving for b, we get:
b = -20 - 5a
Substituting b = -20 - 5a into the first equation and solving for a, we get:
46 = 25a + 5(-20 - 5a) + 1
46 = 15a - 99
145 = 15a
a = 9.67
Substituting a = 9.67 and c = 1 into b = -20 - 5a, we get:
b = -20 - 5(9.67) = -71.35
Therefore, the equation of p(x) in vertex form is:
p(x) = 9.67(x - 5)² + 1
Simplifying, we get:
p(x) = 9.67(x² - 10x + 25) + 1
p(x) = 9.67x² - 96.7x + 250.85 + 1
p(x) = 9.67x² - 96.7x + 251.85
Rounding to the nearest hundredth, we get:
p(x) = 9.67(x - 5² + 1 = 9.67(x + 1.04)² - 10.25
Therefore, the answer is:
p(x) = 9.67(x + 1.04)² - 10.25
The closest answer choice is:
p(x) = 3(x - 1)² - 2, which is not correct.
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k^2+6k=0 solve the quadratic equation by factoring
Answer:
K = √-6k
i did the math and got this answer and it was right
Home values in a town have declined 26% per year for each of the past
four years. What was the total percentage decrease in home values
during the four-year period?
Answer: 104%
Step-by-step explanation: 26% times 4 years
Which one is the correct choice?
Therefore, the correct response From these integral is option D is.
``` 10 + ∫₅¹ R(t) dt
What is an integral?An integral is a mathematical construct in mathematics that can be used to represent an area or a generalization of an area. It computes volumes, areas, and their generalizations. Computing an integral is the process of integration.
Integration can be used, for instance, to determine the area under a curve connecting two points on a graph. The integral of the rate function R(t) with respect to time t can be used to describe how much water is present in a tank.
The following equation can be used to determine how much water is in the tank at time t = 5 if there are 10 gallons of water in the tank at time t = 1.
``` 10 + ∫₅¹ R(t) dt
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Approximately of the Earth's surface is made up of the oceans. What fraction of the surface is not made up of oceans?
The fraction of Earth that is not made up of ocean = 1/4.
Explain about the fraction:The numbers we are familiar with are whole numbers, such as 1, 2, and so on.
Numbers expressed as fractions have a numerator and a denominator, separated by a line known as a vinculum.
In essence, a fraction explains how a portion of a group interacts with the entire group.
Given that-
fraction of Earth made up of water = 3/4The fraction of Earth that is not made up of ocean = 1 - fraction of Earth made up of water
The fraction of Earth that is not made up of ocean = 1 - 3/4
The fraction of Earth that is not made up of ocean = (4 - 3)/4
The fraction of Earth that is not made up of ocean = 1/4
Thus, the fraction of Earth that is not made up of ocean = 1/4.
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Complete question:
Approximately 3/4 of the Earth's surface is made up of the oceans. What fraction of the surface is not made up of oceans?
4. The elevation at ground level is 0 feet. An elevator starts 80 feet below ground level. After
traveling for 20 seconds, the elevator is 30 feet below ground level. Which statement describes
the elevator's rate of change in elevation during this 20-second interval?
A. The elevator traveled upward at a rate
1 rate of 2½ feet per second.
B. The elevator traveled downward at a rate of 2 feet per second.
C. The elevator traveled upward at a rate of 4 feet per second.
D. The elevator traveled downward at a rate of 4 feet per second.
a
Answer:
[tex]m = \frac{ - 30 - ( - 80)}{20 - 0} = \frac{50}{20} = 2 \frac{1}{2} [/tex]
A. The elevator traveled upward at a rate of 2 1/2 feet per second. -30 > -80.
How long did Lizzie practice on Thursday and Friday altogether?
J
P
D
Lizzie's Drum Practice
P
S
P
D
P
S
S
Monday Tuesday Wednesday Thursday Friday
= 5 minutes
DONE
0
minutes
7 8
4
00
5
1 2
0
9
6
3
Answer:
Lizzie practiced for a total of 14 minutes on Thursday and Friday combined.
On Thursday, she practiced for 5 minutes according to the table.
On Friday, she practiced for 9 minutes according to the table.
Adding these two times together, we get:
5 minutes + 9 minutes = 14 minutes
Therefore, Lizzie practiced for a total of 14 minutes on Thursday and Friday combined.
Simplify 6^2/6 x 6^12/6^8
Step-by-step explanation:
6^2 / 6^1 x 6^12 / 6^8 =
6^(2-1) x 6^(12-8) =
6^1 x 6^4 =
6^(1+4) = 6^5 or = 7776
4.4.3 Quiz: Stretching and Compressing Functions
f(x) = x². What is g(x)?
10
g(x)
Y
5- f(x)
O B. g(x) =
(2,2)
Click here for long description
2
O A. g(x) = (x)²
O c. g(x) =
OD. g(x) = 2x²
2
5
x²
x²
X
The equation of the function g(x) is g(x) = 1/2x²
Calculating the function g(x)If we want to stretch or compress the function f(x) = x^2, we can multiply or divide the input variable x by a constant value a.
Specifically, if we use g(x) = f(ax), then g(x) is a stretched or compressed version of f(x).
To find the value of a that will make g(x) pass through the point (2,2), we can substitute these values into the equation g(x) = f(ax):
[tex]g(2)=f(a*2)=f(2a)=(2a)^2 =4a^2 =2[/tex]
So, we have
a = 1/2
Recall that
g(x) = f(ax)
So, we have
g(x) = f(1/2x)
This means that
g(x) = 1/2x²
Hence. the function is g(x) = 1/2x²
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A farmer is building a fence to enclose a rectangular area against an existing wall, shown in the figure below. Three of the sides will require fencing and the fourth wall already exists. If the farmer has 176 feet of fencing,
what is the largest area the farmer can enclose?
Answer: 46 ft by 92 ft
Step-by-step explanation:
The largest area is enclosed when half the fence is used parallel to the wall and the other half is used for the two ends of the fenced area perpendicular to the wall. Half the fence is 184 ft/2 = 92 ft. Half that is used for each end of the enclosure.
The ratio of union members to nonunion members working for a company is 4 to 5. If there are 140 nonunion members working for the company,
what is the total number of employees?
The total number of employees is 112.
Explain numbers
Numbers are symbols or representations used to quantify or count objects, quantities, or measurements. They form the basis of mathematical operations, such as addition, subtraction, multiplication, and division, and are used in various fields such as science, finance, and engineering. Numbers can be positive, negative, whole, or fractional, and are essential for communication and calculation in our daily lives.
According to the given information
Let's use x to represent the total number of employees.
According to the problem, the ratio of union members to nonunion members is 4 to 5. This means that out of every 4 + 5 = 9 employee, 4 are union members and 5 are nonunion members.
So, we can set up the following proportion:
4/9 = x/(x - 140)
To solve for x, we can cross-multiply and simplify:
4(x - 140) = 9x
4x - 560 = 9x
560 = 5x
x = 112
Therefore, the total number of employees is 112.
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A coordinate plane with 2 lines drawn. The first line is labeled f(x) and passes through the points (0, negative 2) and (1, 1). The second line is labeled g(x) and passes through the points (negative 4, 0) and (0, 2). The lines intersect at about (2.5, 3.2)
How does the slope of g(x) compare to the slope of f(x)?
The slope of g(x) is the opposite of the slope of f(x).
The slope of g(x) is less than the slope of f(x).
The slope of g(x) is greater than the slope of f(x).
The slope of g(x) is equal to the slope of f(x)
Therefore, the correct answer is: The slope of g(x) is less than the slope of f(x).
Where do the X and Y axes intersect on the coordinate plane, at position 0 0?The origin is the location where the two axes meet. On both the x- and y-axes, the origin is at 0. The coordinate plane is divided into four portions by the intersection of the x- and y-axes. The term "quadrant" refers to these four divisions.
We can use the slope formula to get the slopes of the lines f(x) and g(x):
slope of f(x) = (change in y)/(change in x) = (1 - (-2))/(1 - 0) = 3/1 = 3
slope of g(x) = (change in y)/(change in x) = (2 - 0)/(0 - (-4)) = 2/4 = 1/2
The slope of g(x) is 1/2, which is less than the slope of f(x), which is 3.
Therefore, the correct answer is: The slope of g(x) is less than the slope of f(x).
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Answer:
B
Step-by-step explanation:
Tentor, Inc., purchases disposable coffee cups on which to print logos for sporting events, proms, birthdays, and other special occasions. The owner received a large shipment of 861 cups this afternoon, and to ensure the quality of the shipment, he selected a random sample of 410 cups and identified 353 as defective.
What is the estimated proportion of defectives in the population? (Round the final answer to 3 decimal places.)
Answer
What is the standard error of the sample proportion? (Round your answer to 3 decimal places.)
Answer
What are the upper and lower bounds for a 98% confidence level? (Round the final answers to 3 decimal places.)
Upper bound is Answer
Lower bound is Answer
It is estimated that 0.861 percent of the population is faulty. The sample proportion's standard error is 0.022. A 98% confidence level has an upper bound of 0.910 and a lower bound of 0.812.
What is a proportion?The comparative relationship between two or more things in terms of their size, amount, or number is referred to as a "proportion." Either a ratio or a fraction can be used to express it. The term "proportion" in statistics refers to the division of the total number of events by the frequency of each event.
The formula p = x/n, where p is the estimated proportion of defectives in the population, x is the number of defectives in the sample, and n is the sample size, can be used to determine the estimated proportion of defectives in the population.
When we substitute values, we obtain:
p = 353/410 = 0.861
As a result, the population's estimated defectiveness rate is 0.861.
The formula SE = √(p(1-p)/n), where SE is the standard error and n is the sample size, can be used to get the standard error of the sample percentage.
When we substitute values, we obtain:
SE is equal to√(0.861(1.0.861)/410) = 0.022.
As a result, the sample proportion's standard error is 0.022.
Using the following formula, the upper and lower bounds for a 98% confidence level can be determined:
Lower bound = z*SE - p
Upper bound = z*SE + p
where z is the z-score for a 98% degree of confidence.
We discover that the z-score corresponding to a 98% confidence level is roughly 2.33 using a z-table or calculator.
When we substitute values, we obtain:
Lower bound is equal to 0.861 - 2.33*0.022, or 0.812.
Upper bound is equal to 0.861 + 2.33 * 0.022 = 0.910.
Consequently, the range of a 98% confidence level is as follows:
Maximum: 0.910
Upper limit: 0.812
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It is estimated that 0.861 percent of the population is faulty. The sample proportion's standard error is 0.022. A 98% confidence level has an upper bound of 0.910 and a lower bound of 0.812.
What is a proportion?
The comparative relationship between two or more things in terms of their size, amount, or number is referred to as a "proportion." Either a ratio or a fraction can be used to express it. The term "proportion" in statistics refers to the division of the total number of events by the frequency of each event.
The formula p = x/n, where p is the estimated proportion of defectives in the population, x is the number of defectives in the sample, and n is the sample size, can be used to determine the estimated proportion of defectives in the population.
When we substitute values, we obtain:
p = 353/410 = 0.861
As a result, the population's estimated defectiveness rate is 0.861.
The formula SE = √(p(1-p)/n), where SE is the standard error and n is the sample size, can be used to get the standard error of the sample percentage.
When we substitute values, we obtain:
SE is equal to[tex]\sqrt{\frac{0.861(1.0.861)}{410)}[/tex]= 0.022.
As a result, the sample proportion's standard error is 0.022.
Using the following formula, the upper and lower bounds for a 98% confidence level can be determined:
Lower bound = z*SE - p
Upper bound = z*SE + p
where z is the z-score for a 98% degree of confidence.
We discover that the z-score corresponding to a 98% confidence level is roughly 2.33 using a z-table or calculator.
When we substitute values, we obtain:
Lower bound is equal to 0.861 - 2.33*0.022, or 0.812.
Upper bound is equal to 0.861 + 2.33 * 0.022 = 0.910.
Consequently, the range of a 98% confidence level is as follows:
Maximum: 0.910
Upper limit: 0.812
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8. You and 4 friends are going to an event, and you want to keep the cost below $100 per person. Write and solve an inequality to find the total cost, x.
1 1/4 - 1 1/5
Pls answer it today!
Answer:
fraction form: 1/20
decimal form:0.05
Calculate Volume of Air passing through Filter HEPA Filter 100ft/min *- Airflow 4ft 2ft Volume = Filter Area x Airflow Velocity
The volume of air passing through the HEPA filter is 800 cubic feet per minute (CFM).
Describe Volume?In general, volume refers to the amount of space occupied by a three-dimensional object. In physics, volume is a measure of the amount of space an object takes up, typically measured in cubic meters (m³) or cubic centimeters (cm³).
In mathematics, volume is often used to refer to the measure of the size of a solid object or region in three-dimensional space. This measure can be calculated using various methods depending on the shape of the object or region, such as integration, formulae, or counting.
For example, the volume of a cube can be calculated by multiplying its length, width, and height together. The volume of a sphere can be calculated using the formula 4/3πr³, where r is the radius of the sphere.
In finance, volume can also refer to the number of shares or contracts traded in a particular market or stock exchange over a given period of time. High trading volume often indicates a more active market, while low trading volume may indicate less interest or activity in a particular security or market.
The formula for calculating the volume of air passing through a filter is:
Volume = Filter Area x Airflow Velocity
Given that the airflow velocity is 100 ft/min and the dimensions of the filter are 4 ft x 2 ft, we can calculate the filter area as:
Filter Area = Length x Width
Filter Area = 4 ft x 2 ft
Filter Area = 8 square feet
Now we can substitute the values into the formula:
Volume = Filter Area x Airflow Velocity
Volume = 8 sq ft x 100 ft/min
Volume = 800 cubic feet per minute (CFM)
Therefore, the volume of air passing through the HEPA filter is 800 cubic feet per minute (CFM).
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Help me this is a Screensho
t
Answer:
21.8 - 0.1 = 21.7
21.7 is 0.1 less than 21.8
Answer:
The answer is 21.7
Step explanation
21.8 - 0.1 = 21.7
I hope it helped you.
Please Mark me brainliest
Evaluate the expression without using a calculator. sin−1(cos(2)) sin^−1 (cos( − /2))
The value of the expression sin⁻¹(cos(2)) sin⁻¹(cos(-π/2)) is 0.
Describe Algebraic Expression?An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. These expressions can be used to represent mathematical relationships and patterns in a variety of contexts.
Algebraic expressions can include one or more variables, which are letters or symbols that represent unknown values or values that can vary. For example, in the expression 3x + 5, "x" is the variable.
To evaluate the expression sin⁻¹(cos(2)) sin⁻¹(cos(-π/2)), we first need to determine the value of cos(2) and cos(-π/2).
cos(2) cannot be evaluated directly since the range of cosine function is -1 to 1, and 2 is outside this range. Therefore, we can conclude that sin⁻¹(cos(2)) does not exist.
Next, we can evaluate cos(-π/2) using the unit circle, which is a circle of radius 1 centered at the origin of the coordinate plane. The angle -π/2 is located on the negative y-axis, where the cosine function is 0. Therefore, cos(-π/2) = 0.
Substituting this value into the expression, we get:
sin⁻¹(0) = 0
Therefore, the value of the expression sin⁻¹(cos(2)) sin⁻¹(cos(-π/2)) is 0.
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What is a formula for the nth term of the given sequence? 18 , 21 , 24
Answer:
3n+15
Step-by-step explanation:
18, 21, 24
+3. +3
3n
18-3=15
3n+15
Amy and Zack each have 24 feet of fencing for their rectangular gardens. Amy makes her fence 6 feet long. Zack makes his fence 8 feet long. Whose garden has the better area? How much greater?
Answer:
The answer is Zack garden
Jasper's aunt gave him a big bin of 500 beads made out of assorted materials to use for the wind chimes he makes. Jasper takes out a handful of beads, looks at the types of beads, then puts them back. Here are the materials of the handful he selected: glass, clay, wood, glass, wood, clay, metal, clay, wood, glass, wood, clay, metal, wood, clay Based on the data, estimate how many glass beads are in the bin. If necessary, round your answer to the nearest whole number.
We can estimate that there are approximately 134 glass beads in the bin.
What is probability?
Probability is a measure of the likelihood of an event occurring.
To estimate the number of glass beads in the bin, we can use the proportion of glass beads in the handful that Jasper selected.
There are 15 beads in the handful, and 4 of them are glass. So, the proportion of glass beads in the handful is:
4/15 ≈ 0.267
We can assume that the proportion of glass beads in the bin is similar to the proportion in the handful. Therefore, we can estimate the number of glass beads in the bin as:
0.267 x 500 ≈ 134
Therefore, we can estimate that there are approximately 134 glass beads in the bin.
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7. Fill in the bubbles to indicate whether
each expression is linear or not linear.
5x Linear or Nonlinear
6x+1 Linear or Nonlinear
10xy Linear or Nonlinear
17 Linear or Nonlinear
4x^2 Linear or Nonlinear
The type of the relation are
Linear: 5x, 6x + 1 and 16Nonlinear: 10xy and 4x^2Indicating whether each expression is linear or not linearA linear expression is an algebraic expression in which each term has a degree of 1 (or 0), and the variables are raised only to the first power.
In the given expressions:
"5x" and "6x + 1" have only the variable "x" raised to the power of 1, making them linear."10xy" has the variables "x" and "y" both raised to the power of 1, making it nonlinear."17" is a constant term and has a degree of 0, making it linear."4x^2" has the variable "x" raised to the power of 2, making it nonlinear.Therefore, the linear expressions are "5x", "6x + 1", and "17". The nonlinear expressions are "10xy" and "4x^2".
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Alex scored 7/20 of the points in a basketball game. How many of the team's 120 points did Alex score?
Answer:
Step-by-step explanation:
I think its 42 because 7/20ths of 120 is 42
7/20 x 120 =42
Find each value or measure.
x = _____
mJK=_____ degrees
mMJ=_____ degrees
mLMK=______ degrees
(30 points) will give brainiest for effort
The value or measure of following are :-
x = 17.18°
∠JK = 143.78°
∠MJ = 116.48°
∠LMK = 47.17°
What is an arc?A segment of a circle called an arc is made up of two endpoints on the circle and the curve that connects them.
Since the two lines JL and MK intersect at the center of the circle at point N, the angles formed by them are inscribed angles of the circle. Moreover, the angles formed by an inscribed angle and its corresponding arc are equal. Therefore, we can write:
∠JNK = ½ arc JNK = ½(5x+23)° = 2.5x + 11.5°
∠KNL = ½ arc KNL = ½(17x-41)° = 8.5x - 20.5°
We are also given that arc MNJ and LNK are similar, so their corresponding angles are equal. Similarly, arc MNL and JNK are similar, so their corresponding angles are equal. Let's use these facts to find x:
∠MNJ = ∠LNK
The arc MNJ is equal to the sum of arcs MNL and LNK. Therefore, we have:
½(5x+23)° + ½(17x-41)° = ∠MNJ + ∠LNK
2.5x + 11.5° + 8.5x - 20.5° = 2∠MNJ
11x - 9° = 2∠MNJ
∠MNL = ∠JNK
The arc MNL is equal to the sum of arcs MNJ and JNK. Therefore, we have:
½(5x+23)° + ½(8.5x-20.5°) = ∠MNL + ∠JNK
2.75x + 1.5° = 2∠JNK
1.375x + 0.75° = ∠JNK
Since ∠MNJ = ∠LNK and ∠MNL = ∠JNK, we can write:
2∠MNJ + 2∠JNK = 360°
Substituting the expressions we found for ∠MNJ and ∠JNK, we get:
22x - 18° = 360°
22x = 378°
x = 17.18° (rounded to two decimal places)
Now that we know x, we can find the values of the other angles of arc-
∠JNK = 1.375x + 0.75° = 24.43°
∠KNL = 8.5x - 20.5° = 119.35°
∠MNJ = (11x - 9°)/2 = 92.05°
∠LNK = ∠MNJ = 92.05°
∠MNL = 360° - ∠MNJ - ∠JNK = 243.52°
∠JK = ∠JNK + ∠KNL = 143.78°
∠MJ = ∠MNJ + ∠JNK = 116.48°
∠LMK = 360° - ∠MNJ - ∠JNK - ∠KNL = 47.17°
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Julia drew s sketches of flowers. She split them evenly among her 3 pen pals. Write an expression that shows how many sketches each pen pal received.
Answer:
s/3
Step-by-step explanation:
since she drew s drawings and split them among 3 penpals, it would be s/3, for example, 6 drawings/ 3 would be 2 drawings for each person.
A survey stopped men and women at random to ask them where they purchased groceries, at a local grocery store or online.
What percent of the people surveyed shop at a local grocery store? Round your answer to the nearest whole number percent.
63% of people Surveyed shop at a local grocery store.
What is percentage ?A number can be expressed as a fraction of 100 using a percentage. The word "%" stands for percentage.
For instance, 50% represents 50 out of 100, or 0.5 in decimal form. Frequently, proportions, rates, and changes in quantity are represented as percentages.
In many aspects of daily life, including the calculation of sales tax, loan interest rates, and price discounts, percentages are frequently utilised. They are also employed in many academic disciplines, including math, physics, economics, and statistics.
What are proportions ?The equality of two ratios is referred to as a percentage in mathematics. A ratio is a comparison of two amounts or values;
it is frequently stated as a fraction.
For instance, "3/5" can be used to represent the proportion of boys to girls in a classroom.
An assertion of equality between two ratios is a proportion.
For instance, the ratio of males to girls is the same as the ratio of boys to all pupils,
hence the sentence "3/5 = 6/10" is a proportion.
Analysis: -
people surveyed at store = 45
total no. of people = 72
the
Percent of peopla = 45/72 x100
= 0.625 × 100
= 62.5 %
= 63 %
63% of people Surveyed shop at a local grocery store.
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2 only can you solve associative, identity and inverse of this
The set 2Z is associative under the operation *, has an identity element of 2, and every element (except for 0) has an inverse element.
Solving the associative, identity and inverse of this the setThe set 2Z is defined as follows:
2Z = {2n | n ∈ Z, a * b = a + b}
Associative element:
There exists an associative element in 2Z if, for all a, b, and c in 2Z, the equation a*(bc) = (ab)*c holds.
Let a, b, and c be arbitrary elements of 2Z:
a = 2n₁
b = 2n₂
c = 2n₃
Then we have:
a*(bc) = a(2n₂2n₃) = a(4n₂n₃) = 2n₁ + 4n₂n₃ = 2(n₁ + 2n₂n₃)
(a*b)c = (2n₁2n₂)*2n₃ = (4n₁n₂)*2n₃ = 8n₁n₂n₃ = 2(2n₁n₂n₃)
Therefore, a*(bc) = (ab)*c, and 2Z is associative under the operation *.
Identity element:
There exists an identity element in 2Z if there exists an element e in 2Z such that, for all a in 2Z, the equation ae = ea = a holds.
Let e be an arbitrary element of 2Z:
e = 2n
Then we have:
ae = a2n = a + 2n = 2m, where m = n + (a/2) ∈ Z
ea = 2na = a + 2n = 2m', where m' = n + (a/2) ∈ Z
Therefore, e = 2n is an identity element in 2Z.
Inverse element:
There exists an inverse element in 2Z if, for all a in 2Z, there exists an element b in 2Z such that ab = ba = e, where e is the identity element.
Let a be an arbitrary element of 2Z:
a = 2n
Then we need to find an element b in 2Z such that ab = ba = e = 2.
We have:
ab = ba = 2n*b = 2
Therefore, b = 1/(2n) is the inverse of a in 2Z if n ≠ 0.
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