We are interested in the population proportion of drivers who claim they always buckle upa.i. x = 320 ii. n = 400 iii. p′ = 0.8
b. The random variable X represents the number of drivers out of the sample of 400 who claim they always buckle up, while P′ represents the sample proportion of drivers who claim they always buckle up.
c. The distribution to use for this problem is the normal distribution because the sample size is large enough (n=400) and the population proportion is not known.
d. i. The 95% confidence interval for the population proportion who claim they always buckle up is (0.7709, 0.8291).
ii. The graph is a normal distribution curve with mean p′ = 0.8 and standard deviation σ = sqrt[p′(1-p′)/n].
iii. The error bound is 0.0291.
e. Three difficulties the insurance companies might have in obtaining random results from a telephone survey are:
Selection bias: The survey might not be truly random if the telephone numbers selected are not representative of the population of interest.
Nonresponse bias: People may choose not to participate in the survey or may not be reached, which could bias the results.
Social desirability bias: Respondents may give socially desirable answers rather than their true opinions, which could also bias the results.
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Jennifer bought 14.75 gallons of gasoline for her car at a cost of $2.95 a gallon. which is closest to the amount she paid for the gasoline?
The total amount paid by Jennifer for 14.75 gallons of gasoline at the cost of $2.95 per gallons is equal to $43.51.
Total gallons of gasoline bought by Jennifer for her car = 14.75 gallons
Cost of gasoline per gallons= $2.95
The total amount Jennifer paid for the gasoline is equal to, amount paid by Jennifer= number of gallons of gasoline* cost per gallon
substitute the value in the formula we get, = amount paid by Jennifer= 14.75 gallons* $2.95/gallon= $43.51
Therefore, the closest amount Jennifer paid for the gallons of gasoline is equal to $43.51.
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A man deposited sh. 600,000 to a savings account in a bank that offers an interest rate of 15% p.a. What amount will be on his account after 8months
We can start by calculating the interest earned by the man over 8 months.
First, we need to convert the annual interest rate of 15% to a monthly rate by dividing it by 12:
15% / 12 = 1.25%
Next, we can use the formula for simple interest to calculate the interest earned:
Interest = Principal x Rate x Time
where:
Principal = sh. 600,000 (the amount deposited)
Rate = 1.25% (the monthly interest rate)
Time = 8/12 (8 months is 2/3 of a year)
Plugging in the values, we get:
Interest = 600,000 x 1.25% x 8/12
Interest = 5,000
Therefore, the man will earn sh. 5,000 in interest over 8 months.
To find the total amount in his account after 8 months, we simply add the interest earned to the initial deposit:
Total amount = Principal + Interest
Total amount = 600,000 + 5,000
Total amount = sh. 605,000
Therefore, the amount on the man's account after 8 months will be sh. 605,000.
Which of the options below are inequalities? Choose all of the correct answers. 3h-7-19 h≥14 h=60 3h +12 < 18 20=h+h 8> h
All the equation shown as inequalities:
3h-7-19 ; h≥14 ; h=60 ; 3h +12 < 18 ; 20=h+h ; 8> h
Explain about the inequalities of the numbers?When resolving an inequality, you can do one of the following:
Add the same amount to each side; •Subtract the same amount from each side;Multiply but rather divide both side with a single positive amount. You must flip the inequality sign if you multiply as well as divide each side from a negative number. On a number line, inequalities are represented by making a straight path and designating the end points through an open or closed circle. An empty circle indicates that the value is not included. A closed circle indicates that the value is included.Thus, all the equation shown as inequalities:
3h-7-19 ; h≥14 ; h=60 ; 3h +12 < 18 ; 20=h+h ; 8> h
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The complete question is-
Which of the options below are inequalities? Choose all of the correct answers.
3h-7-19 ; h≥14 ; h=60 ; 3h +12 < 18 ; 20=h+h ; 8> h
Please help me with my math!!
Answer:
5
Step-by-step explanation:
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To find the current that supplies the maximum wattage, we need to take the derivative of the power function with respect to I, set it equal to zero, and solve for I. The derivative of the power function is:
dW/dI = 120 - 24I
Setting this equal to zero and solving for I, we get:
120 - 24I = 024I = 120I = 5
Therefore, the current that supplies the maximum wattage is 5 amps. We can verify that this is a maximum by checking the second derivative of the power function with respect to I. The second derivative is:
d^2W/dI^2 = -24Since the second derivative is negative, the function has a maximum at I = 5.
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Answer:
We can find the current that supplies the maximum wattage by finding the value of I that maximizes the power function W(I) = 120I - 12I^2.
To do this, we can take the derivative of W with respect to I and set it equal to zero:
dW/dI = 120 - 24I = 0
Solving for I, we get:
I = 5
Therefore, the current that supplies the maximum wattage is 5 amps.
Answer: b. 5
Are the given functions y1 and y2 linearly independent or linearly dependent on the interval (0, 1) and why? Choose the correct statement below. Yi = cscº(t) - cot? (t), y2 = 9a. Since yi = - 42 on (0, 1), the functions are linearly independent on (0,1). b. Since yı = 5y2 on (0,1), the functions are linearly independent on (0,1). c. Since yı = 3y2 on (0,1), the functions are linearly dependent on (0,1). d. Since yi = - Žy2 on (0, 1), the functions are linearly dependent on (0,1).
The given functions [tex]y_1[/tex] and [tex]y_2[/tex] are linearly dependent on the interval (0, 1)
(a) Since [tex]y_1 = -42[/tex] on (0,1), the functions are linearly independent on (0,1).
This option does not make sense because [tex]y_1[/tex] is not always -42 on the interval (0,1).
(b) Since [tex]y_1 = 5y_2[/tex] on (0,1), the functions are linearly independent on (0,1).
This option is not correct because if we substitute y1 with 5y2 in the equation [tex]c_1 y_1 + c_2 y_2 = 0[/tex], we get [tex]5c_2 y_2 + c_2 y_2 = 0,[/tex] which means we can write [tex]y_1[/tex]as a constant times [tex]y_2[/tex], so they are dependent.
(c) Since [tex]y_1 = 3y_2[/tex] on (0,1), the functions are linearly dependent on (0,1)."
To see why, we can substitute [tex]y_1[/tex] with [tex]3y_2[/tex] in the equation [tex]c_1 y_1 + c_2 y_2 = 0[/tex]:
[tex]c_1 (3y_2) + c_2 y_2 = 0[/tex]
Simplifying this, we get:
[tex](3c_1 + c_2) y_2 = 0[/tex]
Since [tex]y_2[/tex] is not equal to 0 for any value of t in the interval (0,1), this means that [tex]3c_1 + c_2[/tex] must equal 0. This is a non-trivial solution for [tex]c_1[/tex] and [tex]c_2[/tex], which means that [tex]y_1[/tex] and[tex]y_2[/tex] are linearly dependent on the interval (0,1).
(d) Since[tex]y_1 = -1/2 y_2[/tex]on (0,1), the functions are linearly dependent on (0,1).
This option is also correct because if we substitute [tex]y_1[/tex] with -1/2 y2 in the equation [tex]c_1 y_1 + c_2 y_2 = 0,[/tex] we get [tex]-1/2 c_2 y_2 + c_2 y_2 = 0[/tex], which means we can write[tex]y_1[/tex]as a constant times [tex]y_2[/tex], so they are dependent.
Therefore, the correct answer is either option d, and the functions [tex]y_1[/tex] and [tex]y_2[/tex] are dependent on the interval (0,1).
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A number is decreased by 40% and the result is 54. What is the number?
A. 94
B. 90
C. 75.6
D. 21.6
E. 14
Answer:
B. 90
Step-by-step explanation:
Let x be the original number.
We know that the number is decreased by 40%, which means we need to subtract 40% of the original number from the original number:
x - 0.4x = 54
Simplifying this equation, we get:
0.6x = 54
Dividing both sides by 0.6, we get:
x = 90
Therefore, the original number is 90.
So, the answer is B) 90.
Drag the term to the corresponding probability. Each term may be used only once. CertainLikelyUnlikelyImpossible Probability Term Probability < 12 Probability = 0 Probability = 1 Probability > 12
Thus, the probability are Zero represents the impossibility.
1/2 equals probable and unlikely
1 = event happens.
Because we don't know how something will turn out, we might talk about the probability of one outcome or the potential for several outcomes.
Typically, the likelihood is stated as the proportion of favourable events to all other potential outcomes in the sample space.
The probability of an event is calculated using the formula P(E) = (Number of favourable outcomes) (Sample space).
Given that probability can only be a number between 0 and 1,
The zeroth value is the impossible.
so there is a 50% chance for both likely and unlikely.
If 1, the event must take place.
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What is the image of (-2, 6) after a dilation by a scale factor of 1/2 centered at the
origin?
The image of (-2, 6) after a dilation by a scale factor of 1/2 centered at the origin is given as follows:
(-1, 3).
What is a dilation?A dilation is a transformation that changes the size of a figure, but not its shape. Specifically, a dilation is a type of similarity transformation that involves multiplying the coordinates of each point in a figure by a scale factor. This causes the figure to either enlarge or reduce in size.
The scale factor in the context of this problem is given as follows:
1/2.
The coordinates of the original point are given as follows:
(-2, 6).
Multiplying the coordinates of the original point by the scale factor, the coordinates of the image are given as follows:
(-1,3).
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Say my population is USA voters. If I interviewed people in front of a major grocery supermarket. Making sure that I selected supermarkets in high median salary areas. What type of sampling best fits my experiment?
The sampling method that best fits your experiment is convenience sampling.
Describe Sampling?Sampling is the process of selecting a subset of individuals or items from a larger population in order to gather information and draw conclusions about the entire population. Sampling is often used in scientific research, market research, and other fields where it is impractical or impossible to measure the entire population.
There are many different types of sampling methods, including random sampling, stratified sampling, cluster sampling, and convenience sampling. Each method has its own advantages and disadvantages, and the choice of sampling method depends on the specific research question and the resources available.
The sampling method that best fits your experiment is convenience sampling. Convenience sampling is a non-probability sampling method that involves selecting individuals who are readily available and accessible to the researcher. In your case, you are selecting individuals who are present in front of a major grocery supermarket, which is a convenient location. Convenience sampling is often used in situations where it is difficult or impractical to obtain a random sample, and is commonly used in market research and pilot studies.
However, it is important to note that convenience sampling has some limitations. Since the sample is not randomly selected, it may not be representative of the population as a whole. In your case, selecting supermarkets in high median salary areas may introduce bias into the sample, as it may not accurately represent the entire population of USA voters. Additionally, the sample size and characteristics may be affected by factors such as time of day, day of the week, and other factors that may affect who is present in front of the supermarket at a given time. Therefore, the results obtained from this sampling method may not be generalizable to the entire population of USA voters.
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which of the following are presentation methods? (select all that apply)multiple select question. reciprocal training traditional classroom instruction audiovisual training distance learning
There are four presentation methods to choose from. These include reciprocal training, traditional classroom instruction, audiovisual training, and distance learning. The multiple selection question format asks which presentation methods are included.
What is a presentation method?
A presentation method refers to a way to deliver information to a group of individuals. Presentation methods are often used to teach concepts, inform, or persuade the audience. Various presentation methods are available for different types of information, such as traditional classroom instruction, audiovisual training, and distance learning. These methods vary in how information is presented and how participants engage with the material.Presentation methods that are available Reciprocal Training, Reciprocal Training, often known as reciprocal teaching, is a technique that involves individuals exchanging roles as teachers and learners. This method has been shown to be effective in developing students' comprehension of academic material.Traditional Classroom Instruction, Traditional classroom instruction, also known as classroom instruction, is a technique that has been used for centuries. A teacher is in front of a group of students, who are expected to engage with the material and participate in activities.Audiovisual Training Audiovisual training refers to the use of video, audio, and other visual aids in the delivery of instruction. This approach is thought to be more engaging and memorable than other teaching methods.Distance Learning Distance learning, or online learning, is a form of education that is delivered via the internet. This allows individuals to learn from any location, as long as they have access to the internet. This type of education is often more cost-effective than traditional classroom instruction.Therefore, all of the above presentation methods are effective.
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Here are two employment adds from a newspaper. Use them to solve the problem.
Driver needed for hauling service.
Must have phone & current
driver's license. $14/hr to start.
$18/hr after 28 days. Call Jerry
777-555-7314
What is the hourly wage that the driver will be paid during the first 18 days? Write your answer in dollar amt. ($8.00)
For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac).
BIUS
Paragraph
Arial
10pt
✓E V
Nurse needed for long-term care
facility. RN $21.50/hr. LPN $14/hr.
Paid Bonus: 1 wk. vacation after 6
mos. + medical benefits. Call
Peggy 777-555-3433
AVA
>
I % 0
Based on the information, it can be inferred that the hourly wage that the driver will receive during the first 18 days would be 14/h.
How to calculate the hourly wage that the driver will receive during the first 18 days?To calculate the hourly wage that the driver will receive during the first 18 days, we must carefully read the information in the advertisement. In this case, the hourly wage is posted there.
Based on this information, we can infer that the driver's salary would be $14/hour for the first 28 days. Additionally, then his salary would increase to $18/hour.
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The perimeter of a rectangle is 3.5 times the length. The width is 2.5 cm less than the length. What is the width?
It is 7.5
the steps are in the photo
In culinary class, you made fudge brownies and peanut butter brownies. Each batch of fudge brownies makes 1 pan. Each batch of peanut butter brownies makes 9 pans. The class made 5 batches and ended up with 29 pans. How many batches of each type of brownie were made?
Answer: 4 batches of fudge brownies and 1 batch of peanut butter brownies were made.
Step-by-step explanation:
Let x be the number of batches of fudge brownies made, and y be the number of batches of peanut butter brownies made.
From the problem, we can write two equations based on the information given:
Each batch of fudge brownies makes 1 pan: x = number of pans of fudge brownies.
Each batch of peanut butter brownies makes 9 pans: 9y = number of pans of peanut butter brownies.
We also know that the class made 5 batches in total, and ended up with 29 pans:
x + 9y = 29 (total number of pans)
We can now solve for x and y by using a system of two equations:
x + 9y = 29 (equation 1)
x + y = 5 (equation 2)
Solving for x in equation 2 and substituting into equation 1, we get:
(5 - y) + 9y = 29
Simplifying and solving for y:
8y = 24
y = 3
Substituting y = 3 into equation 2, we get:
x + 3 = 5
x = 2
Therefore, the class made 2 batches of fudge brownies (2 pans) and 1 batch of peanut butter brownies (9 pans), for a total of 29 pans. Alternatively, we can say that the class made 4 batches of fudge brownies (4 pans) and 1 batch of peanut butter brownies (9 pans) for a total of 29 pans.
If the mean of 8 9 x and 12 is 10 find the range and its coefficient
As per the given mean value, the coefficient of range is 40%.
We know that the mean of these numbers is 10, which means that if we add them all up and divide by 4 (since there are 4 numbers in the set), the result will be 10. Using algebra, we can set up the following equation:
(8 + 9 + x + 12) / 4 = 10
If we simplify this equation, we get:
(29 + x) / 4 = 10
Multiplying both sides by 4, we get:
29 + x = 40
Subtracting 29 from both sides, we get:
x = 11
So we now know that the four numbers are 8, 9, 11, and 12. To find the range, we simply subtract the lowest value (8) from the highest value (12):
12 - 8 = 4
Therefore, the range of the numbers is 4.
To find the coefficient of range, we use the formula:
Coefficient of range = (Range / Mean) x 100%
Plugging in the values we just found, we get:
Coefficient of range = (4 / 10) x 100%
Coefficient of range = 40%
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HELP PLS combine the like terms 3x+5-x+3+4x
Answer:
3x, 4x | 5, 3
Step-by-step explanation:
Determine whether the set StartSet left bracket Start 3 By 1 Matrix 1st Row 1st Column 1 2nd Row 1st Column 0 3rd Row 1st Column negative 3 EndMatrix right bracket comma left bracket Start 3 By 1 Matrix 1st Row 1st Column negative 3 2nd Row 1st Column 1 3rd Row 1st Column 6 EndMatrix right bracket comma left bracket Start 3 By 1 Matrix 1st Row 1st Column 1 2nd Row 1st Column negative 1 3rd Row 1st Column 0 EndMatrix right bracket EndSet 1 0 −3 , −3 1 6 , 1 −1 0 is a basis for set of real numbers R cubedℝ3. If the set is not a basis, determine whether the set is linearly independent and whether the set spans set of real numbers R cubedℝ3. Which of the following describe the set?
The set [1 0 −3 , −3 1 6 , 1 −1 0] is not a basis for set of real numbers R cubed(ℝ3).
The reason why it is not a basis is because it is not linearly independent. However, the set does span set of real numbers R cubed(ℝ3).To determine if the given set is a basis for set of real numbers R cubed(ℝ3), we need to test for linear independence and for span.Linear independence
The given set is said to be linearly independent if and only if the only solution to the equation a[1 0 −3] + b[−3 1 6] + c[1 −1 0] = [0 0 0] is the trivial solution where a, b and c are constants.If the given set is linearly independent then it is a basis for R3; if it is not linearly independent, it is not a basis for R3.
SpanThe given set is said to span R3 if every vector in R3 can be written as a linear combination of vectors in the given set.
If the given set spans R3, then it can be considered a basis for R3.For us to test if the given set is linearly independent, we can form a matrix by placing the three given vectors into the columns of a 3 x 3 matrix as follows:[1 0 1] [−3 1 −1] [−3 6 0]
By expanding the determinant of the matrix above, we get: det(A) = 0 - 0 - (-3) = 3
Since the determinant is non-zero, we can say that the given set is linearly independent. Since the given set is linearly independent, we can then use it to span R3. Hence the given set does not form a basis for R3 but it is linearly independent and spans R3.
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If P = 2y² + 4xy + 4
Q = − 3y² + 7 - 3xy
R=- 3xy + 8
Find P+Q=R.
Answer:
P = [tex]2y^{2}[/tex] + 4xy +4
Q = [tex]-3y^{2}[/tex] + 7 -3xy
R = -3xy +8
Step-by-step explanation:
refer to exercise 7.11. suppose that in the forest fertilization problem the population standard deviation of basal areas is not known and must be estimated from the sample. if a random sample of n = 9 basal areas is to be measured, find two statistics g1 and g2 such that p (g1 ≤ ( y - u ) ≤ g2 ) = 90
Confidence interval = (y ± t∗s/√n)g1 = y - t*s/√ng2 = y + t*s/√n Substituting the values, g1 = 26.22 - 1.860*(0.11)/√9 = 25.84g2 = 26.22 + 1.860*(0.11)/√9 = 26.59Therefore, the statistics g1 and g2 that will satisfy the required inequality are 25.84 and 26.59 respectively.
The formula for finding the confidence interval is as follows: n − 1, where t is the value of the t-distribution corresponding to the specified confidence level and the sample size minus one.
As per the given exercise 7.11, suppose that in the forest fertilization problem the population standard deviation of basal areas is not known and must be estimated from the sample.
If a random sample of n = 9 basal areas is to be measured, find two statistics g1 and g2 such that p(g1 ≤ (y - u) ≤ g2) = 90
To find the statistics g1 and g2 that will satisfy the required inequality
the following formula can be used: Confidence interval = [tex](y ± t∗s/√n)[/tex]
From the formula, we can see that the confidence interval depends on the values of y, s, t and n.
The value of y is the sample mean
the value of s is the sample standard deviation
And the value of n is the sample size.
The value of t depends on the confidence level desired and the degrees of freedom for the t-distribution. In this case, the confidence level is 90%, which means that we want to find the value of t that will give us a total area of 0.90 under the t-distribution curve with 8 degrees of freedom .Using the t-table, the value of t can be found to be 1.860, where the value for 90% and 8 degrees of freedom is 1.860.t = 1.860Now, we need to calculate the value of s, which is the sample standard deviation.
Since we do not have any information about the population standard deviation, we will use the sample standard deviation as an estimate of the population standard deviations = σ/√nσ = s*√nσ = 0.11*√9σ = 0.33Substituting the values in the confidence interval formula
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60°
d. Opposite C:
e. Adjacent C:
B
90°
1. Consider the triangle ABC. Which side is being described by the following labels?
a. Hypotenuse:
b. Opposite A:
c. Adjacent A:
30°
Side BC is the hypotenuse of the right triangle ABC. Against A: The side that is opposed to angle A is side BC. Adjacent A: Side AB is the side that faces angle A. The side that is in opposition to angle C is side AB.
What does a math hypotenuse mean?
An "opposite" side in a right triangle is the one that is across from a specific angle, while a "adjacent" side is the one that is next to a specific angle. The hypotenuse is the longest side in a right triangle. The sides of right triangles are described with particular terminology. It goes without saying that the side opposite the right angle is the hypotenuse of a right triangle.
Side BC is the hypotenuse of the right triangle ABC. Against A: The side that is opposed to angle A is side BC. Adjacent A: Side AB is the side that faces angle A. The side that is in opposition to angle C is side AB.
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five program systems are prepared so that they work independently of each other. each system has a 0.3 chance of detecting an error. find the probability that at least one program system will detect an error. use 4 decimal places.
The probability that at least one program system will detect an error is 0.8319 (approx) or 0.832 (approx).
How to find the probabilityGiven information:
five program systems are prepared so that they work independently of each other. Each system has a 0.3 chance of detecting an error.
Find the probability that at least one program system will detect an error. Use 4 decimal places.The probability of a system detecting an error is 0.3.
The probability of a system not detecting an error is 1 - 0.3 = 0.7.
Probability that none of the five systems detects an error is, P(error not detected in any of the five systems) = P(not detected in 1st) x P(not detected in 2nd) x ... x P(not detected in 5th) = 0.7 x 0.7 x 0.7 x 0.7 x 0.7 = 0.16807.
The probability that at least one system detects an error is, P(at least one system detects an error) = 1 - P(error not detected in any of the five systems) = 1 - 0.16807 = 0.8319 (approx).
Therefore, the probability that at least one program system will detect an error is 0.8319 (approx) or 0.832 (approx).
Hence, the correct option is 0.832.
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Find the measures of one exterior angle of a regular polygon if the sum of the interior angles is 3960 degrees.
The exteriοr angle οf the pοlygοn is 15°.
What is pοlygοn?A pοlygοn has as many pairs οf interiοr and exteriοr as number οf its sides. Further each pair οf exteriοr and interiοr add up tο 180°.
Sum οf all the exteriοr angles οf any pοlygοn is 360°.
As sum οf all the interiοr angles οf the pοlygοn is 3960°.
Sum οf all pairs οf exteriοr and interiοr angles is
=> 3960°+360°=4320°
As each pair is 180° , Number οf sides οf pοlygοn = 4320/180 = 24
Sum οf exteriοr angles is always 360° and if pοlygοn is regular (i.e. all sides and angles are equal), size οf each exteriοr angle is
=> 360°/24 = 15°
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Identify the slope and y intercept for the equation y = 2x + 3
What method could have been used to collect the data
The method used to collect data will depend on the specific research question being asked and the resources available to the researcher.
One common method for collecting data is through experimentation. This involves designing a controlled experiment that allows researchers to manipulate one or more variables while keeping all other factors constant.
Observational data can be particularly useful when it is not possible or ethical to manipulate variables in an experiment.
Surveys and questionnaires are another way to collect data. These methods involve asking people to provide information about their attitudes, beliefs, and behaviors.
Other methods for collecting data include case studies, in which researchers closely examine a single individual or group, and archival research, in which data is collected from existing records, such as census data or medical records.
By carefully selecting the right method for their research, scientists can gather accurate and reliable data that can help to advance our understanding of the world around us.
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is this A.less then
b.equal too
c.more then
Answer:
A. Less than
Step-by-step explanation:
Someone please help with this? Thank you!
Table values are -3, -1, 3, 5, 13
Define the term function?A function is a mathematical object that maps each element from one set to a unique element in another set. Functions are represented using symbols and can be described using graphs, tables, or equations.
Given function is,
[tex]f(x)=2x +3[/tex]
Solve for x = -3, f(-3) = 2×(-3) + 3 = -6 + 3 = -3
f(-3) = -3
Solve for x = -2, f(-2) = 2×(-2) + 3 = -4 + 3 = -1
f(-2) = -1
Solve for x = 0, f(0) = 2×(0) + 3 = 0 + 3 = +3
f(0) = 3
Solve for x = 1, f(1) = 2×(1) + 3 = 2 + 3 = 5
f(1) = 5
Solve for x = 5, f(5) = 2×(5) + 3 = 10 + 3 = 13
f(5) = 13
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Image attached, please help.
Step-by-step explanation:
so, it is a geometric sequence (every new term is created by multiplying the previous term by a fixed constant.
in this case this constant is 2.
a1 = 3
a2 = 3×2 = 6
a3 = a2×2 = a1 × 2×2 = 3×4 = 12
so, we see
an = 3 ×2^(n-1)
or
an+1 = 3 × 2^n
Answer:
[tex]A_n=3 \cdot 2^{n-1}[/tex]
Step-by-step explanation:
A recursive formula for a sequence allows you to find the nth term of the sequence provided you know the value of the previous term in the sequence.
Given recursive rule:
[tex]\begin{cases}A_1=3\\A_{(n+1)}=2A_n\end{cases}[/tex]
According to the recursive formula, each term in the sequence is double the previous term. This means the sequence is geometric with the common ratio, r = 2.
An explicit formula for a sequence allows you to find the nth term of the sequence. The explicit formula for a geometric sequence is:
[tex]\boxed{A_n=A_1 \cdot r^{n-1}}[/tex]
where:
A₁ is the first term.r is the common ratio.Substituting the given value of A₁ and the found value of r into the formula, the explicit formula for the given sequence is:
[tex]A_n=3 \cdot 2^{n-1}[/tex]
This can also be written as:
[tex]A_{(n+1)}=3 \cdot 2^{n}[/tex]
Shari is drawing triangles that had the same area the base of each triangle varies inversely with the height what are the possible base and height of the second triangle if the first triangles base is 12 and its height is eight find the height of the triangle whose base is 16
If the first triangles base is 12 and its height is eight, the height of the second triangle whose base is 16 is 6.
If the area of all the triangles Shari is drawing is the same, and the base of each triangle varies inversely with the height, then we can use the formula for the area of a triangle:
A = (1/2) * b * h
where A is the area, b is the base, and h is the height.
Since the area is the same for all the triangles, we can set the equation for each triangle equal to a constant, say k:
A = k = (1/2) * b * h
If the base varies inversely with the height, then we can write:
b = k/h
We can substitute this into the equation for the area:
k = (1/2) * (k/h) * h
Simplifying, we get:
k = (1/2) * k
This implies that k = 0, which is not possible since the area of a triangle cannot be zero. Therefore, we conclude that the base of each triangle cannot vary inversely with the height.
For the second part of the question, we are given that the base of the first triangle is 12 and its height is 8. Using the formula for the area of a triangle, we can solve for the area:
A = (1/2) * 12 * 8 = 48
We can then use the same formula to solve for the height of the second triangle whose base is 16:
48 = (1/2) * 16 * h
Simplifying, we get:
h = 6
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Find the measure of the arc. *
X
42°
V
W
?
O 42 degrees
84 degrees
0 21 degrees
O 81 degrees
According to the given circle, the measure of the arc is option C. 21°.
Let's look at the figure provided. Since arc AC has a measure of 84°, we know that angle AOC, which is the central angle that subtends arc AC, has a measure of 84° as well. We can use this information to find the measure of angle AOB, which is an inscribed angle that includes angle ABC.
Since arc AC is 84°, arc AB must have a measure of 180° - 84° = 96°. This means that angle AOB, which spans arc AB, must have a measure of half of 96°, or 48°.
Now we can use the property of inscribed angles to find the measure of angle ABC. We know that angle AOB is twice the measure of angle ABC, so angle ABC must have a measure of half of 48°, or 24°.
Therefore, the answer is C. 21°.
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a relationship that is noted between two or more variables is termed
The relationship that is noted between two or more variables is termed a correlation. Correlation refers to the statistical association or relationship between two or more variables.
It indicates the degree to which the variables are related or how they are related to each other. Correlation can be positive, negative, or zero, depending on the direction and strength of the relationship between the variables.
A positive correlation indicates that as one variable increases, the other variable also increases. A negative correlation indicates that as one variable increases, the other variable decreases. Zero correlation indicates that there is no relationship between the variables.
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A regular hexagon has side lengths of 2x and has a perimeter that is equal to an isosceles triangle with legs of x + 4 and a base that is 3 less than one of the legs. Write and solve equation to find the length of one side of the hexagon.
According to the formula, the length of one side of the hexagon is 21/4 or 5.25 units.
What is the perimeter of the regular hexagon?
Let's call the length of one side of the regular hexagon "s". Since a hexagon has six sides, the perimeter of the hexagon is 6s.
According to the problem, this is equal to the perimeter of an isosceles triangle with legs of x+4 and a base that is 3 less than one of the legs.
The perimeter of the isosceles triangle is given by:
perimeter = 2(x+4) + (x+1)
where (x+1) is the length of the base (which is 3 less than one of the legs).
Setting the perimeters equal, we get:
6s = 2(x+4) + (x+1)
6s = 3x + 9
s = (3/2)x + (3/4)
We also know that the side lengths of the hexagon are 2x. Substituting this into the equation for "s", we get:
2x = (3/2)x + (3/4)
x = 3
Therefore, the length of one side of the hexagon is:
s = (3/2)x + (3/4) = (3/2)(3) + (3/4) = 9/2 + 3/4 = 21/4
So the length of one side of the hexagon is 21/4 or 5.25 units.
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