They walk 810 m on 21 day and 1,200 m on 60th day.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
She has decided to walk 10 m more every day on day 20 she walked 800 m.
Now,
Since, She has decided to walk 10 m more every day on day 20 she walked 800 m.
Hence, The amount of meters she walk everyday can be given as a linear function, and, the rate of variation is a constant (10 m/day):
⇒ 10 m / day
This constant (10 m/day) is the slope of the linear function.
And, We know that;
One point of the linear function (D(20) = 800) and the slope, so we can calculate the y-intercept:
⇒ D (t) = 10t + b
⇒ 800 = 10 × 20 + b
⇒ 800 - 200 = b
⇒ b = 600
So, The equation become;
⇒ D (t) = 10t + 600
Hence, For day t = 21;
⇒ D (21) = 10 x 21 + 600
⇒ D (21) = 810 m
And, For day t = 60;
⇒ D (60) = 10 x 60 + 600
⇒ D (60) = 1,200 m
Thus, They walk 810 m on 21 day and 1,200 m on 60th day.
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Which of the following correctly describes the steps to find the volume of a cylinder?
A. Find the circumference of the base and multiply it by the height of the cylinder.
B. Find the area of the base and multiply it by the height of the cylinder.
C. Square the area of the base and multiply it by the height of the cylinder.
D. Find the area of the base and add it to the height of the cylinder.
Answer:
B. Find the area of the base and multiply it by the height of the cylinder.
Step-by-step explanation:
πr^2h is the formula for finding the volume of a cylinder.
You find the area of the base by squaring the radius, then do pi times base area times height to get the volume.
The following matrix is in reduced row echelon form. Decode from the matrix the solution of the corresponding system of linear equations or state that the system is inconsistent. (If the system is dependent assign the free variables the parameters s and t. If the system is inconsistent, enter INCONSISTENT.) 1 0-4 5 2 0 1 2 -9 3 10 -4 5 21 o 0 00 0 (xi, X2, X3, x4)- X1, X2, X3, X4) =
The solution of the corresponding system of linear equations is: (X1, X2, X3, X4) = (-9s, 10s, -4s, t).
The reduced row echelon form of the matrix is:
1 0 0 -9
0 1 0 10
0 0 1 -4
0 0 0 0
This tells us that the system of linear equations has the following solution:
X1 = -9X4
X2 = 10X4
X3 = -4X4
The system is dependent, so we assign the free variables the parameters s and t:
X1 = -9s
X2 = 10s
X3 = -4s
X4 = t
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use interval notation to express the set of real numbers $x$ that satisfies the inequality $(x 2)(x-5) < 0$.
x -2 and x 5 provide the solution to the system of inequalities.
A collection of equations with the same variables is known as a system of equations. The only difference is that you're working with inequalities rather than equations in a system of inequalities. Finding the variable values that will make each inequality true simultaneously is necessary to solve a system like this.
(x+2)(x-5) 0, according to the inequality formula.
The inequality's zeros will be provided by the inequality's zeros, as demonstrated:
(x+2)(x-5) < 0.
(x+2) < 0
x < -2
Similarly;
x - 5 < 0
x < 5
Thus, x -2 and x 5 provide the solution to the system of inequalities.
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There are 1,295 students attending a small university. There are 714 women enrolled. What percentage of student are women?
Answer:
55.13 I'm sure is the answer
There are 714 women out of the total 1295 students:
[tex]\dfrac{714}{1295}\approx0.551351351351351[/tex]
About 55.14% of the students are women.
Find the area and the circumference of a circle with radius 3cm.
Use the value 3.14 for π, and do not round your answers. Be sure to include the correct units in your answers.
Area: [tex]3.14*3^2=28.26 cm^2\\[/tex]
Circumference: [tex]2*3.14*3=18.84cm[/tex]
develop a least squares estimated regression line. (round your numerical values to five decimal places.)
The least squares estimated regression line is 0.5x+1.667
If your data shows a linear relationship between the X and Y variables, you will want to find the line that best fits that relationship. That line is called a Regression Line and has the equation ŷ= a + b x. The Least Squares Regression Line is the line that makes the vertical distance from the data points to the regression line as small as possible. It’s called a “least squares” because the best line of fit is one that minimizes the variance (the sum of squares of the errors).
Data rarely fit a straight line exactly. Usually, it is satisfactory with rough predictions. Typically, you have a set of data whose scatter plot appears to “fit” a straight line. This is called a Line of Best Fit or Least-Squares Line.
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4. On a reality TV show, there were 13 participants, 7 males and 6 females. Two teams of 6
are to be randomly selected. The first team of 6 will be selected from all 13 participants, and
the second team of 6 will be picked from the remaining 7 participants. Assume the order in
which the players are picked does not matter.
a. What is the probability that the first team will be a team of all males?
b. What is the probability the second team is all females, given the first team is all males?
Answer:
What is Probability ?Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can vary from 0 to 1, with 0 being an impossibility and 1 denoting a certainty. For pupils in Class 10, probability is a crucial subject since it teaches all the fundamental ideas of the subject. One is the probability of every event in a sample space.
Probability of event to happen P(E) = Number of favourable outcomes/Total Number of outcomes
Three main categories of probability exist:
Theoretical ProbabilityExperimental ProbabilityAxiomatic ProbabilityThe first team will be a team of all males :
Total number of Outcomes = 13C6 = 1716
Number of favourable outcomes = 7C6 = 7
Probability that all member of the first team will be male is =
Number of favourable outcomes/Total number of Outcomes
= 7/1716
the second team is all females, given the first team is all males
Total number of Outcomes = 7C6= 7
Number of favourable outcomes = 1
the probability the second team is all females, given the first team is all males = (Number of favourable outcomes/Total number of Outcomes)
= 1/7.
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The universities budget covers cost for nine months what is Amy’s monthly budget for textbooks in course supplies? What is her monthly budget for rent on utilities and food? What is your monthly budget for a personal and miscellaneous cost? what is her total monthly budget?
Amy’s monthly budget for textbooks equals $900.00
Amy's monthly budget for rent, utilities and food equals $12,798.
Her monthly budget for a personal & miscellaneous cost equals $2,259.
Her total monthly budget equals $15,957.
What does Budget mean?A budget is refers to an estimation of the revenue and expenses over a specified future period of time and is usually compiled and re-evaluated on a periodic basis.
Budget for textbooks:
= $900.00
Budget for rent, utilities and food:
= $12,798.
Budget for personal and miscellaneous cost:
= $2,259.
Total monthly budget:
= $900 + $12,798 + $2,259
= $15,957
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which statement is true about the graphed function? F(x) < 0 over the intervals (–[infinity], –2.5) and (–0.75, 0.75).
F(x) > 0 over the intervals (–[infinity], –2.5) and (–0.75, 0.75).
F(x) < 0 over the intervals ( –2.5, –0.75) and (–0.75, [infinity]).
F(x) > 0 over the intervals ( –2.5, –0.75) and (0.75, [infinity]).
F(x) > 0 over the intervals (–∞, –2.5) and (–0.75, 0.75).
Lets explain the graph to answer the problem
- When we ask about f(x) we means the values of y
- f(x) > 0 means the graph is over the x-axis because over the x-axis
y is positive
- f(x) < 0 means the graph is under the x-axis because under the x-axis
y is negative.
* Lets describe each part of the graph
- The graph intersect the x-axis at :
x = -2.5 , x = -0.75 , x = 0 , x = 0.75
- The graph is over the x-axis between -∞ and -2.5 and between
-0.75 and 0.75
At x = -2.5 f(x) = 0 , at x = -0.75 f(x) = 0 , at x = 0.75 f(x) = 0
∴ x = (-∞ , -2.5) and (-0.75 , 0.75)
∴ f(x) > 0 over the intervals (-∞ , -2.5) and (-0.75 , 0.75)
- The graph is under the x-axis between -2.5 and -0.75 and between
0.75 and ∞
At x = -2.5 f(x) = 0 , at x = -0.75 f(x) = 0 , at x = 0.75 f(x) = 0
∴ x = (-2.5 , -0.75) and (0.75 , ∞)
∴ f(x) < 0 over the intervals (-2.5 , -0.75) and (0.75 , ∞)
* The true statement in the answer is;
F(x) > 0 over the intervals (–∞, –2.5) and (–0.75, 0.75).
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A college statistics professor has office hours from 9.00 AM: to 10.30 AM. daily sample of waiting times to see the professor (in minutes 10, 12,20, 15,17,10, 28,35, 28, 19,27, 25,22, 33, 37,14,21,20 Assuming & = 7.84, find the 99.74% confidence interval for the population mean. Round to two decima places_ a. 20.55 to 24.05 minutes b. 17.05 to 27.55 minutes c. 18.8 to 25.8 minutes d. 19.5 to 35. minutes
We are given the following data set:
10, 12,20, 15,17,10, 28,35, 28, 19,27, 25,22, 33, 37,14,21,20
Standard deviation = 8.043
Confidence level = 1 - Significance Level = 1 - 99.74% = 4.56% = 0.0456
The water in the swimming pool was as blue as the sky.
True or false. The author uses this figurative language to help the reader understand the color of the water.
True
False
Answer:
true
Step-by-step explanation:
the author compares the color of the water to the color of the sky. so that makes it figurative language.
hope this helps.
Avis Company earns $2.50 per share. Today, the stock is trading at $18.99. The company pays an annual dividend of $.25.
a. Calculate the price-earnings ratio. (Round your answer to the nearest whole number.)
b. Calculate the yield on the stock. (Round your answer to the nearest tenth percent.)
If Avis Company earns $2.50 per share and today, the stock is trading at $18.99. the price-earnings ratio. is 7.6 and yield on the stock is 0.013.
How to find the Price-earnings ratio?a. Price-earnings ratio
Using this formula to find the Price-earnings ratio
Price-earnings ratio =Share price/ Earning per share
Let plug in the formula
Price-earnings ratio = $18.99/ $2.50 per share
Price-earnings ratio = 7.596
Price-earnings ratio = 7.6 (Approximately)
b. Yield on stock
Using this formula to find the yield on stock
Yield on stock = Annual divided / Stock price per share
Let plug in the formula
Yield on stock = $0.25 / $18.99
Yield on stock = 0.013
Therefore the Price-earnings ratio is 7.6 and yield on stock is 0.013.
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A doctor wants to determine if a new medication for cholesterol is more effective than the previous medication. The doctor asks her patients if they would like to take part in a study for a new medication, and 30 patients currently taking medication for cholesterol volunteer to participate. Which of the following would be an appropriate procedure for this experiment?
ANSWER IS A
A) The doctor needs to randomly assign 15 patients to the new medication and 15 to the original medication to even out the variability between the patients.
B) The doctor needs to assign the first 15 patients to the new medication and 15 to the original medication to even out the variability between patients.
C) The doctor needs to let the 30 patients choose which medication they are going to take through use of a survey to determine whether they want to participate in the experiment.
D) The doctor needs to randomly assign the 30 patients to the new medication to even out the variability between the patients and to determine if their cholesterol level is lowered.
The option that would be an appropriate procedure for this experiment is option A) The doctor needs to randomly assign 15 patients to the new medication and 15 to the original medication to even out the variability between the patients.
How does random assignment work?Random assignment is seen as a method of assigning participants from your sample to various groups in experimental research by using randomization. By using this technique, each sample member has a known or equal chance of being assigned to either the control group or the experimental group.
Note that with the goal of making the groups equal at the start of the study, random assignment is a method used in experiments to divide participants into multiple study groups that include those who share similar traits.
Therefore, in regards to the work of the doctor in the above case, any observed differences in the two groups' cholesterol levels would most likely be brought on by the new medication because the subjects' variability would be evenly distributed between the two groups. Hence option A is correct.
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In a previous poll, 28% of adults with children under the age of 18 reported that their family ate dinner together seven nights a week. Suppose that, in a more recent poll, 291 of 1122 adults with childron under the age of 18 reported that their family ate dinner together seven nights a week. Is there sufficient evidence that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has decreased? Use the a 0.1 signiflicance level. Because npo (1- Po) 226 2> 10 and the sample size is less than 5% of the population size, and the sample %3D can be reasonably assumed to be random, the requirements for testing the hypothesis paysges (papaou se 0oejd jeupop auo oi puno) What are the null and altemative hypotheses?
There is insufficient evidence to say that the population proportion has decreased from 28%.
"Information available from the question"
In the question:
The significance level, α =.01
The sample size, n = 1122
The number of success, x = 291
What are the null and alternative hypotheses?
Now, According to the question;
Let's know:
Significance Level:
The significance level is the area of the rejection region in the hypothesis test. The larger the significance level, the easier is to reject the null hypothesis. The most common significance level used is 5% but in cases where high precision is required significance level is reduced.
[tex]H_0[/tex] : p [tex]\geq[/tex] 0.28
[tex]H_\alpha[/tex] : p < 0.28
The significance level, α =.01
The sample size, n = 1122
The number of success, x = 291
So,
The sample proportion:
p(cap) = x/ n
= 291/1122
= 0.2594
Test Statistics:
z = [tex]\frac{p_c_a_p - p }{\sqrt{p\frac{(1-p)}{n} } }[/tex]
z = [tex]\frac{0.2594 - 0.28}{\sqrt{0.28\frac{(1-0.28)}{1122} } }[/tex]
z = -0.0206/0.0003396
z = -0.2591
Decision rule:
Reject the null if,
p- value [tex]\leq[/tex] [tex]\alpha[/tex]
We can use a z-distribution table, an online tool, or the following excel command to calculate the p-value using excel.
p - value = P(z < -0.2591)
= 0.79635
p - value ≈ 0.79635 > [tex]\alpha[/tex] = 0.01
Fail to reject the null.
Conclusion:
There is insufficient evidence to say that the population proportion has decreased from 28%.
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Three CDs cost 52.17 If each CD costs the same, how much did one CD cost?
If the cost of 3 CDs is 52.17 then the cost of 1 CD is 17.723.
What do you mean by cost?
Cost is the sum of money needed to produce, market, and sell goods and services or to purchase assets. A cost is added to expense when something is sold or consumed.
Let the cost of 1 CD be x
Then the cost of three CDs will be equal to 3x,
And the cost of three CDs is equal to 53.17.
Equating the costs,
3x = 53.17
x = 53.17/3
x = 17.723
Therefore, the cost of 1 CD is 17.723.
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A sphere-shaped beach ball is 16 inches in diameter. How many cubic inches of air will the ball hold when it is fully inflated? Use 3.14 for π. Round your answer to the nearest cubic inch.
A.5,461 in^3
B. 17,149 in^3
C.2,144 in^3
D.683 in^3
The sphere with 16 inches diameter would hold 2144in^3 of air.
What is a sphere?A sphere is a three-dimensional object that is round in shape. The sphere is defined in three axes, i.e., x-axis, y-axis and z-axis. This is the main difference between circle and sphere. A sphere does not have any edges or vertices, like other 3D shapes.
The points on the surface of the sphere are equidistant from the center. Hence, the distance between the center and the surface of the sphere are equal at any point.
The radius of spere = diameter / 2 which is 16/2
radius = 8 inches.
The volume(V) of a sphere is 4/3 πr^3
where r = radius of sphere, π = constant = 3.14
V = 4/3 x 3.14 x (8)^3
V = 2144 in^3
In conclusion the sphere can hold 2144in^3 of air
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the cholesterol levethe cholesterol levels (in milligrams per deciliter) of 32 adults are listed below: 100 100 105 105 106 106 107 107 109 110 110 112 112 112 114 114 114 115 116 117 118 118 118 118 118 119 120 121 122 125 128 134 find the interquartile range for the data.ls (in milligrams per deciliter) of 32 adults are listed below: 100 100 105 105 106 106 107 107 109 110 110 112 112 112 114 114 114 115 116 117 118 118 118 118 118 119 120 121 122 125 128 134 find the interquartile range for the data.
Since the upper value is 104.75 + 1.5 * 13.75 = 125.37500, the last observation, 130, is an outlier.
What is data ?A collection of information, whether numerical or not, can take any shape and is referred to as data in mathematics. Calculable information, such as student test scores, employee salaries, football team member heights, etc., is known as numerical data and is always gathered in numerical form.
here the explanation,
Five points in brief
Min=91, Q1=94, Q2=99, and Q3=104.75, with a maximum of 130 B] Outlier values are those that are either below or above Q1-1.5*IQR (IQR = Q3-Q1=104.75-91=13.75).
Reduced value: 94-1.5*13.75 = 73.37500
Since the upper value is 104.75 + 1.5 * 13.75 = 125.37500, the last observation, 130, is an outlier.
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What happens to standard deviation when outliers are removed?; How does outliers affect standard deviation?; When the outliers are removed How does this mean change?; How will a high outlier affect the mean and median?; Which data set has an outlier?
Answer:
Before we declare what happens, we must have an understanding of outliers and standard deviation. Outliers are certain points that are x deviations away from the mean. Standard deviation is a measurement of dispersion in relations to the mean you are identifying. Given this information, when outliers are removed, the standard deviation becomes a lower amount, because you have to think of standard deviation as a population measurement in a way. So imagine the outliers are a prestigious group of people, and if they leave the community, the population is indeed lower. Outliers affect deviation by a measure of extremity. The more extreme an outlier, the more or less a standard deviation will be affected. When outliers are removed, they will lower the standard deviation, which changes the data in respect to population. A high outlier, however, will increase both mean and median no matter what.
Hope this helps!
- 14 + x = 42, x = is 56 a solution
[tex]\fbox{x=56}[/tex]
Simplify:
[tex]x-14=42[/tex]
Add 14 to both sides:
[tex]x-14+14=42+14[/tex]
[tex]x=56[/tex]
Determine the period.
Enter
The period is the time interval after curves repeat their behavior thus time period of the given curve will be 4.
What is a graph?The graph is a geometrical representation of a function and can be plotted by taking x's and y's corresponding values within the interval.
For example plot of y = x³ ,y = sinx.
As per the given graph of a function,
The time period is the time interval after curves repeat their behavior.
The given graph repeats after 1 + 1 + 1 + 1 = 4 thus period will be 4.
Hence "The period is the time interval after curves repeat their behavior thus time period of the given curve will be 4".
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Tia has 28 yards of fabric. If each project needs 3 and one half yards of fabric, how many projects can she complete?
Answer:
8
Step-by-step explanation:
28/3.5=8
Please help witht this ones. I need help
28. The pair of angles is classified as: alternate exterior angles.
29. The pair of angles is classified as: alternate interior angles.
30. The measure of the larger angle is of: 160º.
How to classify the pair of angles?In both items 28 and 29, we have that two parallel lines are cut by a transversal, hence the angles are classified as follows:
3 and 6: alternate exterior angles, as they are on the opposite side of the transversal line, and both are outside the region between the two parallel lines.2 and 7: alternate interior angles, as they are between the two parallel lines, on the opposite side of the transversal.What are linear pairs?Two angles are called linear pairs if they are supplementary, that is, if the sum of their measures is of 180º.
In this problem, we have that two angles form a linear pair, hence:
x + y = 180º.
The measure of the greater angle is eight times the measure of the smaller angle, hence:
x = 8y.
Thus:
8y + y = 180
9y = 180
y = 20º.
Then the measure of the larger angle is of:
x = 8y = 8 x 20 = 160º.
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Amy got a part-time job working 15 hours a week $12 per hour. How much will she make each week?How many weeks per month will she need to work to cover her monthly expenses?
hmmm let's recall from https://brainly.com/question/30111897 that's she needs 625 bucks to make it monthly.
so her part-time at 15h at $12 per hour, well, that's just 15*12 = 180 bucks weekly, how many weeks she needs to work? well, 625 ÷ 180 ≈ 3.47, so pretty much 3 weeks and about 7 hours more, not quite kinda, 3 weeks and 7 hours is really 624, well if she saves a buck somewheres and get a buck that'll do it =), hmmm so one can say 3 weeks and 8 hours I guess, that's 636 bucks, to cover the 625 expenses.
which equation can be used to solve the problem? 60 percent of what number is 30?; which fraction is equivalent to one-eighth?
The equation that can be used to solve the first problem is [tex]0.60 x = 30\\[/tex] and the equation that can be used to solve the second problem is [tex]\frac{x}{y} = \frac{1}{8}[/tex].
There are two problems given to us -
(a) 60 percent of what number is 30
(b) which fraction is equivalent to one-eighth
We have to find out the equations that can be used to solve the two problems.
(a) Let us say that the number to be considered is x
According to the information given for the first problem, we can say that -
60% of x = 30
[tex]= > \frac{60}{100} x = 30\\ = > 0.60 x = 30\\[/tex]
We can now solve the equation to find out the value of x as -
[tex]0.60 x = 30\\= > x = 50[/tex]
Thus, the problem of "60 percent of what number is 30?" can be represented by the equation [tex]0.60 x = 30\\[/tex].
(b) Let us say that the fraction to be considered is represented as [tex]\frac{x}{y}[/tex].
According to the information given for the second problem, we can say that -
[tex]\frac{x}{y} = \frac{1}{8}\\= > y = 8x[/tex]
For every value of the numerator x, the value of denominator y can be found out through the above equation and vice-versa.
Thus, the problem of "which fraction is equivalent to one-eighth?" can be represented by the equation [tex]\frac{x}{y} = \frac{1}{8}[/tex].
Therefore, the equation that can be used to solve the first problem is [tex]0.60 x = 30\\[/tex] and the equation that can be used to solve the second problem is [tex]\frac{x}{y} = \frac{1}{8}[/tex].
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Please help
Find the value of x
Answer:
75
Step-by-step explanation:
60+55+x=180
All triangles equal 180 so if you add 60 and 55 you get 105 then subtract that from 180 to get 75.
Answer:
x = 65
Step-by-step explanation:
= 60 +55 =115 ( exterior < property)
x = 180 -115 = 65 (linear pair)
Mathematics department is holding an election for department chair… rest of question is below.
Answer:
Step-by-step explanation:
Your question
Hi can someone please help me Im struggling with this!!!
Hence, the measure of the angles are
∠q = 65°
∠r = 65°
∠s = 50°
∠t = 65°
∠b = 64°
Calculating the measure of anglesFrom the question, we are to determine the measure of the angles.
Calculating the measure of angle q
∠q + 65° + (180° - 130°) = 180° (Sum of angles in a triangle)
∠q + 65° + 50° = 180°
∠q + 115° = 180°
∠q = 180° - 115°
∠q = 65°
Calculating the measure of angle r
∠r = ∠q (Corresponding angles)
Therefore,
∠r = 65°
Calculating the measure of angle s
∠s + ∠r + 65° = 180° (Sum of angles on a straight line)
∠s + 65° + 65° = 180°
∠s + 130° = 180°
∠s = 180° - 130°
∠s = 50°
Calculating the measure of angle t
∠t = ∠r (Vertically opposite angles)
Therefore,
∠t = 65°
Second diagram
Calculating the measure of angle b
∠b = ∠a (Corresponding angles)
Therefore,
∠b = 64°
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a hungry statistician analyzed nutritional information from 77 food items available for purchase at a popular coffee shop (seattle's worst). the statistician produces a multiple regression model with response variable calories, and three predictors.
For given regression model, the number 59.89 in the table tells us that for every food item which is sandwich there is a corresponding 59.89-unit increase in Calories.
In this question we have been given a summary of regression model.
We need to explain the meaning of the number 59.89 in the table.
For given regression model, to view the results of the model, we can use the summary() function in R programming.
In given summary consider the 'Coefficients' table.
The first row gives the estimates of the y-intercept, and the second row gives the regression coefficient of the model.
The 'Estimate' column is the estimated effect, also called the regression coefficient or r² value.
The number 59.89 in the table is coefficient for IsSandwich.
This number tells us that for every food item which is sandwich there is a corresponding 59.89-unit increase in Calories.
Therefore, the meaning of the number 59.89 in the table: for every food item which is sandwich there is a corresponding 59.89-unit increase in Calories.
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The complete question is as shown in the following image
The accompanying data, or the length in centimeters and girths (in centimeters) of 12 harbor seals. Find the equation of the regression line. Then construct a scatterplot of the data and draw the regression line. Then use the regression equation to predict the value of Y for each of the given X values, if meaningful, if the X value is not meaningful to predict the value of y, explain why not.
The equation of the regression line is defined as follows:
y = 0.71x + 8.27.
The estimates are given as follows:
a) x = 140 cm: 107.67 cm.
b) x = 172 cm: 130.39 cm.
c) x = 164 cm: 124.71 cm.
d) x = 158 cm: 120.45 cm.
How to obtain the linear regression equation?The linear regression equation is obtained inserting the points of the data-set into a linear regression calculator.
From the table given in this problem, the points are given as follows:
(138, 106), (168, 130), (151, 116), (144, 105), (160, 124), (159, 119), (125, 103), (137, 103), (154, 120), (147, 110), (146, 108), (147, 110).
Inserting these points into a calculator, the equation is given as follows:
y = 0.71x + 8.27.
Then the estimates are obtained replacing x into the equation and obtaining the value of y, for example, for x = 140 cm:
y = 0.71(140) + 8.27 = 107.67 cm.
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Which function is represented in this graph?
y= cos x
y = arccos x
y = arcsin x
y = tan x
The function that is represented on the given graph is;
y = arccos x
How to Interpret Trigonometric graphs?
We know in trigonometry that sine and cosine are expressed as;
cos 0 = 1
cos (π/2) = 0
cos π = -1
cos (π/4) = 0.7071
sin 0 = 0
sin (π/2) = 1
sin π = 0
sin (π/4) = 0.7071
Looking at the graph attached, we see that when x = 1, y = 0 and from earlier we saw that cos 0 = 1.
Similarly, on the graph, when x = 0, y = π/2 which fits with cos (π/2) = 0. Thus, it is clear that the graph is the inverse of cosine which is arc cos x
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