The length of each side of the hexagon is 13 units long, which is equal to length of the park.
What is the length of each side of the park?In order to determine the length of every side of the hexagon, it is necessary to compute the distance between each pair of neighboring vertices.
This can be accomplished by employing the distance formula, which is represented as follows:
d = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² ).
To facilitate the process, we will designate the vertices as A, B, C, D, E, and F in sequence, with A being the vertex at the top.
Then, the length of side AB is calculated as follows:
|AB| = √((38.5-26.5)² + (7-12)²)
|AB| = √((12)² + (-5)²)
|AB| = √(144 + 25)
|AB| = √169
|AB| = 13
Similarly, we can calculate the length of each side:
|BC| = √( (26.5-38.5)² + (2-7)² ) = 13
|CD| = √( (13.5-26.5)² + (2-2)² ) = 13
|DE| = √( (1.5-13.5)² + (7-2)² ) = 13
|EF| = √( (13.5-1.5)² + (12-7)² ) = 13
|FA| = √( (26.5-13.5)² + (12-12)² ) = 13
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Answer:
13 units
Step-by-step explanation:
d^2 = (x2 – x1)^2 + (y^2 – y^1)^2
Now we calculate the distance between 2 points:
d^2 = (6.5 – (-6.5))^2 + (5 – 5)^2
d^2 = 169
d = 13
Therefore the length of each side of the park is 13 units.
The average starting salary for an accountant is $52,338 but can vary by as much as $3,146. Which inequality could be used to determine the average salary range, if x represents the starting salary?
Answer: (x-y)
Step-by-step explanation:
To find the range you must subtract the largest number from the smallest.
The polygons below are similar, but not necessarily drawn to scale. Find the values of x and y. (Does anybody know how to do all, or at least most of the work out?)
Step-by-step explanation:
They are similar....so they are scaled
to go from side 16 on the left figure to the corresponding side 12 on the right figure ,
multiply by .75
so .75 ( y+1) = 21
.75 y + .75 = 21
y = 27
Similarly : .75 ( x-1) = 6
.75x - .75 = 6
x = 9
Please help! Algebra Math!
The number, 19/7, is what number
Answer: a rational number
3x -3 < 9 solve the inequality
Answer:
x > 6
Step-by-step explanation:
3x - 3 < 9
3x < 12
x < 4
Since x < 4 is not true, then the solution is x > 6
Suppose 3% of students drink more than 3 cups of coffee each day. To check this claim, a researcher randomly selected a sample of 133 students and found that 5 drink more than 3 cups of coffee each day. What is the sampling distribution of the sample proportion? (Round to 2 decimal places for all z-values and round all other answers to 4 decimal places, if needed.) The distribution of the sample proportion of students drinking more than 3 cups of coffee each day is approximately normal $ with a mean of and a standard deviation of Check
The sampling distribution could be represented numerically as follows: P [tex]N(0.03, 0.027^2)[/tex]
How and why are sample distributions used?A sample distribution is a statistical probability that is obtained by taking random samples from a certain population. It depicts the distribution of frequency on how dispersed certain outcomes will be for a particular population and is also referred to as a finite-sample distribution.
We utilize sample distribution because...Since they enable you to comprehend a particular sample statistic in the context of other potential values, sampling distributions are crucial for inferential statistics. Importantly, they enable you to compute probabilities related to your sample.
σ [tex]=\sqrt{[p(1-p)/n]}[/tex]
where [tex]p[/tex] is the population proportion [tex](0.03)[/tex] , n is the sample size [tex](133)[/tex], and sqrt denotes the square root function.
Substituting in the values, we have:
σ [tex]=\sqrt{ [(0.03)(1-0.03)/133] ≈ 0.027}[/tex]
Since the sample size is large [tex](n = 133)[/tex] and the population proportion is not close to [tex]0[/tex] or [tex]1[/tex], we can use the normal distribution to approximate the sampling distribution of the sample proportion. The mean of the sampling distribution is equal to the population proportion [tex](0.03)[/tex]. Therefore, the distribution of the sample proportion of students drinking more than [tex]3[/tex] cups of coffee each day is approximately normal with a mean of [tex]0.03[/tex] and a standard deviation of [tex]0.027[/tex].
The notation for the sampling distribution can be written as follows:
P [tex]N(0.03, 0.027^2)[/tex]
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Part 1
At a factory, two machines pack bottles into boxes for shipping. Machine A can pack 8 boxes per minute, and Machine B can pack 11 boxes per minute. Both machines have been packing boxes for some time, and the difference between the number of boxes that Machine B has packed and the number of boxes that Machine A has packed is less than 200. Write and solve an inequality to find the possible lengths of time to the nearest second that the machines have been working. Describe the possible solutions.
Machines A and B worked for 66 minutes and 6 seconds.
What are inequalities:An inequality is a mathematical statement that compares two quantities using one of the inequality symbols: "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).
Inequalities can be solved just like equations, with the goal of finding the set of values that satisfy the inequality.
Here we have
Machine A can pack 8 boxes per minute, and Machine B can pack 11 boxes per minute.
Let Machines A and B work for 'x' minutes
Number of boxes packed by Machine A = 8x
Number of boxes packed by Machine B = 11x
The difference between the number of boxes that Machine B has packed and the number of boxes that Machine A has packed is less than 200.
=> | 11x - 8x| < 200
=> 3x < 200
Divide by 3 into both sides
=> 3x/3 < 200/3
=> x < 66.67
=> x < 66.6
Therefore,
Machines A and B worked for 66 minutes and 6 seconds.
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Work out the equation of the straight line that passes through (5, 4) and (8, 19). Give your answer in the form y = mx + c, where m and c are integers or fractions in their simplest forms.
Answer:
y = 5x - 21
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (5, 4 ) and (x₂, y₂ ) = (8, 19 )
m = [tex]\frac{19-4}{8-5}[/tex] = [tex]\frac{15}{3}[/tex] = 5 , then
y = 5x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (5, 4 ) , then
4 = 5(5) + c = 25 + c ( subtract 25 from both sides )
- 21 = c
y = 5x - 21 ← equation of line
To schedule enough drivers for an upcoming week. a local pizza shop manager recorded the number of deliveries each day from the previous week 38,54,44,61,97,103,124.
Based on the deliveries of each day, the total number of deliveries made by the drivers is 521.
What is the total number of deliveries?In order to determine the total deliveries, add the number of deliveries for each day together.
The addition is determining the total value or summing two or more numbers. The addition is one of the four basic operations in mathematics. The other basic operations are subtraction, multiplication and division. The sign that represents addition is +.
Total deliveries = 38 + 54 + 44 + 61 + 97 + 103 + 124 = 521Here is the complete question: To schedule enough drivers for an upcoming week. a local pizza shop manager recorded the number of deliveries each day from the previous week 38,54,44,61,97,103,124. What is the total number of deliveries?
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Ken lives at the point between the school and the pet shop, How far away is Ken’s house from the park
The answer to this question is that it depends. The distance of Ken’s house from the park cannot be determined without knowing the distance of the school and the pet shop from the park, and other factors such as terrain, local roads, and traffic can also affect the distance between Ken’s house and the park.
What is distance?Distance is the amount of space between two points. It is a physical quantity that can be measured in various units such as meters, kilometers, miles and light-years. Distance can be calculated using the formula d = s × t, where d is the distance, s is the speed, and t is the time.
Ken lives at a point between the school and the pet shop, so it is impossible to answer this question without knowing how far away the school and the pet shop are from the park. If the park is close to the school or the pet shop, then Ken’s house would be close to the park, but if the park is further away from the school or the pet shop, then Ken’s house would be further away from the park. Therefore, the distance of Ken’s house from the park cannot be determined unless the distances of the school and the pet shop from the park are known.
In addition, other factors such as terrain, local roads, and traffic can also affect the distance between Ken’s house and the park. For example, if there is a hilly terrain between Ken’s house and the park, then the distance between them may be greater than if the terrain were flat.
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An investor has an account with stock from two different companies. Last year, his stock in Company A was worth $2000 and his stock in Company B was worth $4240. The stock in Company A has increased 1% since last year and the stock in Company B has increased 5%. What was the total percentage increase in the investor's stock account? Round your answer to the nearest tenth (if necessary).
The total percentage increase in the investor's stock account is 3.7%.
What is percentage?a percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
According to given information :The initial total value of the investor's stock account was $2000 + $4240 = $6240.
The new value of the stock in Company A is 1% more than last year's value, which means it is worth 1/100 * $2000 = $20 more than last year. Therefore, its new value is $2000 + $20 = $2020.
The new value of the stock in Company B is 5% more than last year's value, which means it is worth 5/100 * $4240 = $212 more than last year. Therefore, its new value is $4240 + $212 = $4452.
The new total value of the investor's stock account is $2020 + $4452 = $6472.
To calculate the percentage increase, we need to find the difference between the new and old values and express it as a percentage of the old value:
Percentage increase = ((New value - Old value) / Old value) x 100%
= (($6472 - $6240) / $6240) x 100%
= 3.7% (rounded to one decimal place)
Therefore, the total percentage increase in the investor's stock account is 3.7%.
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Rhonda kept track of the cats at a shelter where she volunteers. She measured how many times per day each cat ate, and she also ranked their activity level on a scale from 1 to 10 each day. She found the line of best fit for the data has the equation y=0. 23x+4. 1, where x represents the activity level and y represents the number of meals eaten.
If a cat had an activity level of about 9, then it's likely to have eaten about _[blank]_ meals.
Enter the value that correctly fills in the blank.
Round to the nearest whole number, if necessary, like this: 42
A cat would probably have consumed about 6 meals if its activity level had been around 9.
A linear equation is a relation between two variables in which one is dependent on the other in such a manner that changing one of the variables causes the change in another variable "linearly".
The above statement can be represented mathematically as,
y=mx+b
where m represents the rate of the change and c is the initial value of the equation.
Let x stand for activity level and y for the number of meals consumed. Therefore:
y = 0.23x + 4.1
For an activity level of 9, we will put x as 9:
y = 0.23(9) + 4.1 = 6.17
Thereby, we can say that If a cat had an activity level of about 9, then it's likely to have eaten about 6 meals.
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Use a calculator to find the approximate value of the expression. cot−1(−2.1) cot−1(−2.1)≈ (Type your answer in radians. Type an integer or decimal rounded to two decimal places as needed.) Let f(x)=sinx,−2π≤x≤2π and g(x)=cosx,0≤x≤π. Find the exact value of the composite function. g−1(f(4π)) g−1(f(4π))= (Simplify your answer, including any radicals. Type an exact answer, using π as needed. Use integers or fractions for any numbers in the expression.)
cot⁻¹(-2.1) ≈ -1.068 radians
g⁻¹(f(4π)) = π/2.
When answering questions on the Brainly platform, it is important to be factually accurate, professional, and friendly. Additionally, it is important to be concise and not provide extraneous amounts of detail. Irrelevant parts of the question should be ignored, and any typos should be corrected as necessary. When answering a question, it is helpful to repeat the question in your answer to ensure that the answer is clear and understandable. A step-by-step explanation should be provided in your answer to help the student understand the solution. Finally, when using specific terms in your answer, it is important to define them and use them accurately.
Now, let's answer the given questions:
1. Use a calculator to find the approximate value of the expression.
cot−1(−2.1) cot−1(−2.1)≈
To find the approximate value of cot⁻¹(-2.1), we can use a calculator.
Using a calculator, we get:
cot⁻¹(-2.1) ≈ -1.068
Therefore, cot⁻¹(-2.1) ≈ -1.068 radians (rounded to two decimal places).
2. Let f(x)=sinx, −2π ≤ x ≤ 2π and g(x)=cosx, 0 ≤ x ≤ π. Find the exact value of the composite function.
g⁻¹(f(4π)) g⁻¹(f(4π))= (Simplify your answer, including any radicals. Type an exact answer, using π as needed. Use integers or fractions for any numbers in the expression.)
We know that f(x) = sin(x) and g(x) = cos(x).
Therefore,
f(4π) = sin(4π) = 0
Now, we need to find g⁻¹(0).
Since g(x) = cos(x), we know that g⁻¹(x) = cos⁻¹(x).
Therefore, g⁻¹(0) = cos⁻¹(0)
We know that cos(π/2) = 0, so cos⁻¹(0) = π/2 or 90°.
Therefore, g⁻¹(f(4π)) = g⁻¹(0) = cos⁻¹(0) = π/2.
Thus, g⁻¹(f(4π)) = π/2.
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HELP MEEEEEEEE
20 POINTS
Answer: 61 N
Step-by-step explanation:
18+15+28=61
An angle measuring (468n)° is in standard position. For which value of n will the terminal side fall on the x-axis?
n = 4
n = 5
n = 6
n = 7
Answer:
n=5
Step-by-step explanation:
Standard Position of the Angle =(468 n)°
We have to find that value of, n for which terminal side will fall on X axis, that is the angle should be multiple of 180°.
You must be thinking why not multiple of ,360°, because factors of 360 are , 90,180,and 360, in which , multiple of 90 falls on x and y axis ,and multiple of 180 ,falls on X axis only.So, instead of taking factors of 90 or 360, you should take multiple of 180° for which terminal side fall on the x-axis.
The Unit Digit of , (468 n)°,should be equal to 0, as it is divisible by number 180°.
For, n=5,
→468° × 5=2340°
So, 2340° , is divisible by 180°.
For, n=5, the terminal side ,the angle having Measure (468 n)°,will fall on the X axis.
The arithmetic calculations and statistical procedures for (a) the test of homogeneity and (b) the test of independence are the same.
a) Explain in a few sentences what distinguishes these two hypothesis tests.
b) To illustrate your answer in part (a), make up an example of a research question that would require a test of homogeneity, and an example that would require a test of independence. Briefly describe the aspects of your examples that illustrate the distinguishing characteristics you mentioned in part (a).
a) These two hypothesis tests differ in terms of their research questions, assumptions, and the types of variables that are involved in each test.
The arithmetic calculations and statistical procedures for (a) the test of homogeneity and (b) the test of independence are not the same. They are different from each other. These two hypothesis tests differ in terms of their research questions, assumptions, and the types of variables that are involved in each test. This is because they deal with different types of data. Below are the examples of a research question that would require a test of homogeneity and an example that would require a test of independence. These examples show the distinguishing characteristics that are involved in each of these tests. Research question that would require a test of homogeneity: A researcher would like to determine whether there is any significant difference between the proportions of men and women who voted for the two main political parties in an election. The research question can be framed as follows: Are the proportions of men and women who voted for the two main political parties homogenous or different? Assumptions: Samples are independent, observations are nominal or categorical, and the variable of interest has more than two categories (i.e., nominal or ordinal).Test of homogeneity:It is used to determine whether two or more populations have the same proportion or distribution of a nominal or categorical variable.Example that would require a test of independence:A researcher is interested in knowing whether there is any relationship between gender and drug addiction among high school students in a particular area. The research question can be framed as follows: Is there a relationship between gender and drug addiction among high school students?Assumptions:Samples are independent, observations are nominal or categorical, and the variable of interest has only two categories (i.e., nominal).Test of independence: It is used to determine whether there is any relationship between two nominal or categorical variables.
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The answer to this question pls
The equation of the line is y = (-1/3)x + 2.
This is the equation of the line in slope-intercept form, where the slope is -1/3 and the y-intercept is 2.
What is the equation of the line?
A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.
The place on the x-axis where the line crosses. This is the x-intercept of the linear function.
If the line is horizontal (and not the x-axis), the linear function will have no x-intercept.
Here, the line crosses the x-axis at 6.
The place on the y-axis where the line crosses. This is the y-intercept of the linear function
Here, the line crosses the y-axis at 2.
If a line crosses the x-axis at the point (6,0), it means that the line intersects the x-axis when the y-coordinate is 0 and the x-coordinate is 6. Similarly, if the line crosses the y-axis at the point (0,2), it means that the line intersects the y-axis when the x-coordinate is 0 and the y-coordinate is 2.
We can use these two points to find the equation of the line using the slope-intercept form:
y = mx + b
where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).
To find the slope, we can use the two points (6,0) and (0,2):
m = (y2 - y1) / (x2 - x1)
m = (2 - 0) / (0 - 6)
m = -1/3
To find the y-intercept, we can use the point (0,2):
y = mx + b
2 = (-1/3)(0) + b
b = 2
Therefore, the equation of the line is y = (-1/3)x + 2.
This is the equation of the line in slope-intercept form, where the slope is -1/3 and the y-intercept is 2.
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solve 2x-7=13 what is x
Answer:x = 10
Step-by-step explanation:
13+7=20
2 x 10 = 20
x=10
Answer:
x = 10
Step-by-step explanation:
[tex]2x-7=13[/tex]
First, add 7 to both sides.
[tex]2x-7 + 7=13 + 7[/tex]
This cancels the -7 on the left side because [tex]-7 + 7 = 0[/tex].
[tex]2x=20[/tex]
Then, we can divide both sides by 2 to isolate one multiple of x.
[tex]2x=20\\\overline{\ 2\ } \ \ \ \ \overline{\, 2 \: }[/tex]
[tex]\boxed{x = 10}[/tex]
4.02 Lesson check ! (8)
The difference is not constant, the sequence is not arithmetic.
What exactly is an algebraic sequence?An arithmetic sequence is a set of integers where each term is created by multiplying the preceding term by a fixed constant value (known as the common difference). A constant rate of change is modelled by arithmetic sequences in fields like engineering, physics, and financial computations.
For the given series we need to determine if the sequence is arithmetic, by checking difference between consecutive terms is constant.
9 - 7 = 2
12 - 9 = 3
16 - 12 = 4
Since the difference is not constant, the sequence is not arithmetic.
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The actual values of the mean, variance, and standard deviation of a population are called: O regressed standardized scores O population Z scores population parameters sample statistics You wish to survey the interests of students in your statistics class. You enter the names of all students onto an excel spreadsheet. You then use a computer program to generate a list of random names. This is called: O computerized selection sampling selection O simple random selection haphazard selection In a population with a mean of 50, what is the deviation score for X = 45? O 5 05 45 O cannot be determined without more information In systematic sampling O A random sample is taken from each pre-selected subgroup. O Every Kth member of the population is included in the sample. Every member in a well-delineated area is sampled. Every member in the population is included in the sample
Population parameters are the real values of the variance, mean, and standard deviation of a population. These parameters are often unknown but can be estimated from a sample of the population.
When conducting a survey, it is important to select participants in a way that avoids bias and represents the population as accurately as possible. Simple random selection, in which individuals are selected randomly and every individual has an equal chance of being selected, is one way to achieve this.
Deviation score is the difference between an individual score and the mean of the population or sample. In this case, the deviation score for X = 45 in a population with a mean of 50 is -5.
In systematic sampling, every Kth member of the population is selected, making it a more efficient way of sampling compared to random sampling, but it requires that the population is well-ordered and homogeneous.
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Lesson Review Directions: Simplify the following expressions. Refer to the rules for signed numbers in solving these problems. Example: - 4 + 5 = +1 (the signs are different, take the difference (subtract) and place the sign of the larger number) 1. + 6 - (+3) = 2. + 10 + (-10) = 3. - 3 + (-3 ) = 4. + 24 - 21 = 5. - 48 - (-44) = 6. -12 - (-4 ) + 3 = 7. + 16 -(-15) = 8. - 35 - (-36) = 9. -6 * 10 = 10. -10 * -10 = 11. + 7 * - 7 = 12. -4 / -4 = 13. -6 * - 5 = 14. -10 * + 7 = 15. -4 * - 7 =
The simplified form of the following expression's is: +3, 0, -6, +3, -4, -11, +31, +1, -60, +100, -49, +1, +30, -70, +28.
What is expression?Any mathematical statement that includes numbers, variables, and an arithmetic action between them is known as an expression or algebraic expression. In the expression 4m + 5, for instance, the words 4m and 5 are separated from the variable m by the arithmetic symbol +.
+6 - (+3) = +3(subtracting the two numbers, and keep the sign of the larger number)
+10 + (-10) = 0(add a positive and negative number with equal magnitudes results in 0)
-3 + (-3) = -6(add two negative number's results in a negative sum)
+24 - 21 = +3(subtracting the two numbers, and keep the sign of the larger number)
-48 - (-44) = -4(subtract a negative number is the same as adding its positive, so -48 - (-44) becomes -48 + 44 = -4)
-12 - (-4) + 3 = -11(subtract a negative number is the same as adding its positive, so -12 - (-4) becomes -12 + 4 = -8, ten add 3 to get -11)
+16 - (-15) = +31(subtract a negative number is the same as adding its positive, so +16 - (-15) becomes +16 + 15 = +31)
-35 - (-36) = +1(subtract a negative number is the same as adding its positive, so -35 - (-36) becomes -35 + 36 = +1)
-6 * 10 = -60(multiply a negative number by a positive number results in a negative product)
-10 * -10 = +100(multiply two negative numbers results in a positive product)
+7 * -7 = -49(multiply a positive number by a negative number results in a negative product)
-4 / -4 = +1
(Dividing a negative number by a negative number results in a positive quotient)
-6 * -5 = +30(multiply two negative numbers results in a positive product)
-10 * +7 = -70(multiply a negative number by a positive number results in a negative product)
-4 * -7 = +28(multiply two negative numbers results in a positive product)
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On the day that certain crlebrity proposes marriage 10 peoplesknow aboutb it. Each day afterward the number of people who knows triples
Write a function that give the total number n(t) of people who know about the celebrity proposing t days after thecelebrity propose
N(t)=
the total number of people who know about the proposal 5 days after it was announced is 810.
The term [tex]3^ (t-1)[/tex] represents the number of people who find out about the proposal on day t, which is equal to three times the number of people who knew about it on the previous day. The initial value of 10 represents the number of people who knew about the proposal on the first day.
For example, if we want to find out how many people know about the proposal 5 days after the celebrity proposes, we can plug t=5 into the formula:
N(5) =[tex]10* 3^(5-1)[/tex] = [tex]10*3^4[/tex] = [tex]10*81[/tex] = 810
So the total number of people who know about the proposal 5 days after it was announced is 810.
the complete question is :
Assuming that the 10 people who know about the proposal on the first day do not forget or tell anyone else, we can use the following function to calculate the total number of people who know about the proposal t days after the celebrity proposes:
N(t) = [tex]10 * 3^(t-1)[/tex]
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The following chips are placed in a bucket 5 white, 1 yellow, 2 blue, and 1 green. One chip is randomly selected from the bucket.
What color chip has the best chance of getting selected?
Answer: So,
If we add them together, we get
5 + 3 + 4 + 1 = 13
Since there are 4 blue chips, the probability would be 4 out of the total number of chips, or 4/13.
Step-by-step explanation: Hope this helps! <3
When an object is dropped, it’s height h can be determined after f seconds by using the failing object model
The object will be 6.1 m from the ground after 2 seconds.
The falling object model is used to calculate the height of an object after it has been dropped for a certain period of time. The equation used is h=h0−1/2gt2, where h0 is the initial height, g is the acceleration due to gravity and t is the time elapsed.
For example, if an object is dropped from a height of 15 m and falls for 2 seconds, we can calculate the height it will be at after 2 seconds.
The equation is then h=15−1/2(9.8)22
h=15−4.9•4
h=6.1 m
Therefore, the object will be 6.1 m from the ground after 2 seconds.
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-2 -1
X=0
YA
X=3
15
4
3
2
T
y = x²
2
3
4
y = (x-3)²
5 6
M
What are the coordinates for the x-
intercepts shown above?
XA
Answer:
what are the coordinator position y
What is the exponential regression equation that fits these data?
X
y
1
4
2
8
3
27
4
85
5
250
6
600
The exponential regression equation that fits the given data points is y = [tex]4*3^(x-1).[/tex]
The exponential regression equation that fits these data is y = 4*3^(x-1). To calculate this, we need to first calculate the parameters a and b for the equation y = a*b^x. We can do this by finding the natural logarithm (ln) of both sides of the equation.
ln(y) = ln(a*b^x)
ln(y) = ln(a) + ln(b^x)
ln(y) = ln(a) + x*ln(b)
We can now calculate the parameters a and b by plotting the points (x, ln(y)) and performing a linear regression on the points.
ln(4) = 0.602
ln(8) = 2.079
ln(27) = 3.526
ln(85) = 4.443
ln(250) = 5.52
ln(600) = 6.398
The linear regression equation is ln(y) = 0.175x + 0.602. We can now solve for the parameters a and b by using the linear regression equation.
ln(a) = 0.602
a = e^0.602
a = 4
ln(b) = 0.175
b = e^0.175
b = 3
Therefore, the exponential regression equation that fits these data is y = 4*3^(x-1).
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The following graph shows all the possible test scores when there are only 10 equally weighed problems, and no partial credit is given. Which of the following represents the domain, D, and the range, R, of this graph?
the domain is D = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, and the range is R = {0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100}.
Why is it?
The graph shows all the possible test scores when there are only 10 equally weighed problems, and no partial credit is given. The domain represents all possible values of the independent variable, which in this case is the number of correct answers. The range represents all possible values of the dependent variable, which in this case is the score.
Looking at the graph, we can see that the domain consists of all non-negative integers from 0 to 10, inclusive. So the domain can be written as:
D = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
On the other hand, the range consists of all possible scores, which range from 0 to 100. So the range can be written as:
R = {0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
Therefore, the domain is D = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, and the range is R = {0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100}.
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Jodie has c pieces of candy. She gives away 11 of the pieces. Write an expression that shows the number of pieces of candy Jodie has left
The expression which represents the number of pieces of candy left with Jodie is given by c - 11 .
Original number of pieces of candy with Jodie is equal to 'c'.
Number of pieces of candy Jodie gives away is equal to 11.
Expression used to represents the number of pieces of candy left with Jodie is written as,
Subtract 11 from the original number of candy
= ( c - 11 )
Therefore, the representation of the expression for number of pieces of candy left with Jodie after she gives away 11 candy is equal to ( c - 11 ).
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a 25-ft long ladder is leaning against the wall of a house when its base starts to slide away. the base of the ladder is moving away from the house at the rate of 2 ft/sec. how fast is the top of the ladder sliding down the wall when its base is 15 feet from the wall?
The top of the ladder is sliding down the wall at the rate of 1.5 ft/s.
Given: A ladder is 25 ft long and is leaning against the wall of a house.
The base of the ladder is sliding away from the house at the rate of 2 ft/sec.
Asked: How fast is the top of the ladder sliding down the wall when its base is 15 feet from the wall?
Let the distance of the top of the ladder from the wall be x ft.
Then we have,
x² + y² = 25² (by Pythagoras theorem)
Differentiating both sides with respect to time t,
we get, 2x(dx/dt) + 2y(dy/dt) = 0 ...(1)
Given dx/dt = 2, and x = 15 ft.
⇒ 2(15)(dx/dt) + 2y(dy/dt) = 0
⇒ 30 × 2 + 2y(dy/dt) = 0 (substituting the given values)
⇒ 2y(dy/dt) = - 60⇒ dy/dt = - 30/ y
The negative sign indicates that y is decreasing (getting smaller) with time.
The values of y are negative because it lies below the level of the ground.
Substituting the value of x = 15 in the equation x² + y² = 25², we get
15² + y² = 25²
⇒ y² = 25² - 15² = 400
⇒ y = - 20
Substituting the values of dy/dt and y in the above equation, we get,
dy/dt = - 30/ (- 20)
dy/dt = 1.5 ft/s
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Find the area of the shaded sectors. Round to one decimal place. EB = 10,4 A=4
360
A
D
A=(
E
143
B
C
The answer of the given question based on finding the area of the shaded sectors the answer is approximately 18.8 + 4.2 = 23.0 square units.
What is Angle?An angle is geometric figure formed by the two rays or lines that share common endpoint, called vertex. The rays or lines are often referred to as arms or sides of angle
We need to know the central angles of each sector. We can find these angles by using the formula:
angle = (arc length / radius) * (180/π)
where π is pi, approximately equal to 3.14.
Therefore, we can use trigonometry to find angle EOB:
sin(EOB) = EB/OA
sin(EOB) = 10.4/8
EOB = sin^-1(10.4/8)
EOB ≈ 56.7° degrees
Since angle EOA is a right angle, we know that angle AOB is 90° degrees, so angle AOE is 90 - EOB = 33.3° degrees.
Now, we can find the area of each sector using the formula:
area = (angle/360) * π * r²
Area of shaded sector ADE:
angle AOE = 33.3° degrees
radius = OA = 8
area = (33.3/360) * π * 8²
area ≈ 18.8 square units
Area of shaded sector EBC:
angle EOB = 56.7° degrees
radius = EB/2 = 5.2
area = (56.7/360) * π * 5.2²
area ≈ 4.2 square units
Therefore, the total area of the shaded sectors is approximately 18.8 + 4.2 = 23.0 square units.
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