Answer:
c. number of items - discrete; total time - continuous
Step-by-step explanation:
The question is incomplete due to the lack of the following options:
to. number of items - continuous; total time - discrete
b. number of items - continuous; total time - continuous
c. number of items - discrete; total time - continuous
d. number of items - discrete; total time - discrete
Knowing this, the type of variables recorded by managers of the home improvement store are,
c. number of items - discrete; total time - continuous
Discrete variables are those that are well defined and in the finite set of values and continuous variables are variables that can take a value between any of the other two values.
Find the Laplace transform F(s)=L{f(t)} of the function f(t)=sin2(wt), defined on the interval t≥0. F(s)=L{sin2(wt)}= help (formulas) Hint: Use a double-angle trigonometric identity. For what values of s does the Laplace transform exist? help (inequalities)
The Laplace transform of the function [tex]\frac{1}{2} (\frac{1}{s} - \frac{s}{s^2 + 4w^2} )[/tex] .
The Laplace transform exist when s > 0 .
Here, the given function is f(t) = sin²(wt) .
The Laplace transform of the the function f(t),
F(s) = f(t) = { [tex]{\frac{1}{2} \times 2sin^2(wt) }[/tex] }
F(s) = { [tex]\frac{1}{2} \times (1- cos2wt)[/tex] }
F(s) = { [tex]\frac{1}{2} - \frac{1}{2} \times cos(2wt)\\[/tex] }
F(s) = [tex]\frac{1}{2} (\frac{1}{s} - \frac{s}{s^2 + 4w^2} )[/tex]
Next,
The above Laplace transform exist if s > 0 .
Know more about Laplace transform,
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AC =
Round your answer to the nearest hundredth.
с
6
B
40°
А
Answer:
5.03
Step-by-step explanation:
Answer:
5.03 = AC
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp/ adj
tan 40 = AC /6
6 tan 40 = AC
5.034597787 = AC
To the nearest hundredth
5.03 = AC
Find the area of a triangle that has the base of 5 inches and a height of 3 3/4 inches
Answer:
9.375 in^2
Step-by-step explanation:
The top figure in the composite figure is called a . And What is the volume?
Answer:
Triangular Prism
volume 748
Find the equation of the line.
Use exact numbers.
y=
Answer:
y = 2x+4
Step-by-step explanation:
First we need to find the slope using two points
(-2,0) and (0,4)
m = (y2-y1)/(x2-x1)
m = (4-0)/(0--2)
= 4/+2
= 2
we have the y intercept which is 4
Using the slope intercept form of the line
y = mx+b where m is the slope and b is the y intercept
y = 2x+4
All math teachers are smart. Ms. Smith is your math teacher, so she is smart. What type of reasoning is this? inductive or deductive
Answer:
I believe it is Inductive Reasoning.
Step-by-step explanation:
Inductive Reasoning is a type of logical thinking that involves forming generalizations based on specific incidents you've experienced, observations you've made, or facts you know to be true or false.
Deductive Reasoning is a basic form of valid reasoning.
An elementary school is offering 3 language classes: one in Spanish, one in French, and one in German. The classes are open to any of the 100 students in the school. There are 28 students in the Spanish class, 26 in the French class, and 16 in the German class. There are 12 students who are in both Spanish and French, 4 who are in both Spanish and German, and 6 who are in both French and German. In addition, there are 2 students taking all 3 classes. If two students are randomly chosen, what is the probability that at exactly one of them does exactly two language classes.
Answer:
The probability that at exactly one of them does exactly two language classes is 0.32.
Step-by-step explanation:
We can model this variable as a binomial random variable with sample size n=2.
The probability of success, meaning the probability that a student is in exactly two language classes can be calculated as the division between the number of students that are taking exactly two classes and the total number of students.
The number of students that are taking exactly two classes is equal to the sum of the number of students that are taking two classes, minus the number of students that are taking the three classes:
[tex]N_2=F\&S+S\&G+F\&G-F\&S\&G=12+4+6-2=20[/tex]
Then, the probabilty of success p is:
[tex]p=20/100=0.2[/tex]
The probability that k students are in exactly two classes can be calcualted as:
[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{2}{k} 0.2^{k} 0.8^{2-k}\\\\\\[/tex]
Then, the probability that at exactly one of them does exactly two language classes is:
[tex]P(x=1) = \dbinom{2}{1} p^{1}(1-p)^{1}=2*0.2*0.8=0.32\\\\\\[/tex]
Which is the better buy?. Store A $180 at 1/3 off Or Store B $110 at 10% off
Answer: Store B
Step-by-step explanation:
180 / 3 = 60. 180 - 60= $120. Store A cost is $120.
110 * 0.9 = $99. Store B's cost is $99.
Answer:
Store B
Step-by-step explanation:
Store A the price would be about $120.60
Store B price would be about $99
To find store a price, you first find the discount, so
0.33 x 180 = 59.40
Then subtract this from the original price to know the total after the discount
180-59.40=120.60
Do the same thing with the other Store
110 x 0.10 = 11
110-11=99
When $\frac{1}{1111}$ is expressed as a decimal, what is the sum of the first 40 digits after the decimal point?
Answer:
90
Step-by-step explanation:
1/1111= 0. (0009) cycles of 0009 after decimal point (one 9 per 4 digits)
Number of digits 9:
40/4= 1010*9= 90Answer:
90
Step-by-step explanation:
Insurance companies track life expectancy information to assist in determining the cost of life insurance policies. AIB Insurance randomly sampled 100 recently paid policies and determined the average age of clients in this sample to be 77.7 years with a standard deviation of 3.6. The 90% confidence interval for the true mean age of its life insurance policy holders is
A. (76.87, 80.33)
B. (72.5, 82.9)
C. (77.1, 78.3)
D. (74.1, 81.3)
E. (74.5, 80)
Answer:
[tex]77.7-1.66\frac{3.6}{\sqrt{100}} =77.102[/tex]
[tex]77.7+1.66\frac{3.6}{\sqrt{100}} =78.30[/tex]
And the best option would be:
C. (77.1, 78.3)
Step-by-step explanation:
Information given
[tex]\bar X=77.7[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
s=3.6 represent the sample standard deviation
n=100 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom are given by:
[tex]df=n-1=100-1=99[/tex]
Since the Confidence is 0.90 or 90%, the significance would be [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and the critical value for this case would be [tex]t_{\alpha/2}=1.66[/tex]
And replacing we got:
[tex]77.7-1.66\frac{3.6}{\sqrt{100}} =77.10[/tex]
[tex]77.7+1.66\frac{3.6}{\sqrt{100}} =78.30[/tex]
And the best option would be:
C. (77.1, 78.3)
Rasheeda sees a garden in a book. She changes the scale because she wants a garden with different dimensions. The figure below shows both scales and a scale drawing of the garden.
Book scale: 1 inch = 2 feet. Rasheeda's Scale: 2 inches = 3 feet. A rectangle with length A of 18 inches and width B of 6 inches.
Which statements about the gardens are true? Select three options.
Answer:
B. Length A of Rasheeda’s garden is 27 ft.
C. Length B of the book’s garden is 12 ft.
E. Length A of the book’s garden is 9 ft longer than length A of Rasheeda’s garden.
Step-by-step explanation:
step 1
Find the dimension of the book's garden
we know that
Book scale: 1 inch = 2 feet
That means
1 inch in the drawing represent 2 feet in the actual
To find out the actual dimensions, multiply the dimension in the drawing by 2
so
Length A of the book’s garden
Width B of the book’s garden
step 2
Find the dimension of Rasheeda’s garden
we know that
Rasheeda's Scale: 2 inch = 3 feet
That means
2 inch inches the drawing represent 3 feet in the actual
To find out the actual dimensions, multiply the dimension in the drawing by 3 and divided by 2
so
Length A of Rasheeda's garden
Width B of Rasheeda's garden
Verify each statement
A. Length A of the book’s garden is 18 ft.
The statement is false
Because, Length A of the book’s garden is 36 ft (see the explanation)
B. Length A of Rasheeda’s garden is 27 ft.
The statement is true (see the explanation)
C. Length B of the book’s garden is 12 ft
The statement is true (see the explanation)
D. Length B of Rasheeda’s garden is 6 ft.
The statement is false
Because, Length B of Rasheeda’s garden is 9 ft. (see the explanation)
E. Length A of the book’s garden is 9 ft longer than length A of Rasheeda’s garden.
The statement is true
Because the difference between 36 ft and 27 ft is equal to 9 ft
F. Length B of the book’s garden is 3 ft shorter than length B of Rasheeda’s garden.
The statement is false
Because, Length B of the book’s garden is 3 ft greater than length B of Rasheeda’s garden.
taffy927x2 and 22 more users found this answer helpful
Answer:
B. Length A of Rasheeda’s garden is 27 ft.
C. Length B of the book’s garden is 12 ft.
E. Length A of the book’s garden is 9 ft longer than length A of Rasheeda’s garden.
(second, third, and fifth choices)
Explanation: I did the quiz and got it right.
Hope this Helps!
Where is my phone? I seem to have lost my phone. I know where I last saw it but it has been moved since then and I need help to locate it. It started at the following coordinates A (14, -12); B (14, -19); C (10, -19); D (10, -14); E (13, -14); F (13, -12). My Mom told me she translated it 6 units to the left Then my little brother said he had reflected it over the Y-axis My friend many found it and translated it 9 units up Dad said he tripped over it and reflected it over the X-axis My sister then rotated it 900 clockwise Uncle Jose translated it 5 units left and 4 units down Cousin Michelle then said she rotated it 900 clockwise Finally my dog picked it up and translated it 5 units down and 10 units to the right Where is my phone? Using the scenario on this page do the following. Graph the preimage using the given points. Label points (A, B, C, ...) Transform the objects using the information provided. Show each transformation and label. (A', B', C', ...) Determine the final location. Write a 2 to 3 sentence explain on how you found the phone location.
Answer:
see attached
Step-by-step explanation:
The attachments show the initial (brown) and final (blue) positions of the phone. The spreadsheet shows all the intermediate locations and the formulas used to determine them.
The two reflections cancel the total of 180° of CW rotation, so the net result is simply a translation. That translation is up by 9 units.
__
Translation up adds to the y-coefficient; translation right adds to the x-coefficient. Down or left use negative values.
90° CW does this: (x, y) ⇒ (y, -x)
Reflection across y does this: (x, y) ⇒ (-x, y)
Reflection across x does this: (x, y) ⇒ (x, -y)
A study conducted at a certain college shows that "53%" of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that among 6 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating. 0.989 0.978 0.927 0.167 0.530
Answer:
0.989
Step-by-step explanation:
For each graduate, there are only two possible outcomes. Either they find a job in their chosen field within a year after graduation, or they do not. The probability of a graduate finding a job is independent of other graduates. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
A study conducted at a certain college shows that "53%" of the school's graduates find a job in their chosen field within a year after graduation.
This means that [tex]p = 0.53[/tex]
6 randomly selected graduates
This means that [tex]n = 6[/tex]
Probability that at least one finds a job in his or her chosen field within a year of graduating:
Either none find a job, or at least one does. The sum of the probabilities of these outcomes is 1. So
[tex]P(X = 0) + P(X \geq 1) = 1[/tex]
We want [tex]P(X \geq 1)[/tex]
So
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{6,0}.(0.53)^{0}.(0.47)^{6} = 0.011[/tex]
So
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.011 = 0.989[/tex]
B
Round your answer to the nearest hundredth.
A
9
B
5
Answer:
56.25°
Step-by-step explanation:
The definition of the cosine function tells you that
cos(B) = BC/BA
B = arccos(BC/BA) = arccos(5/9)
B ≈ 56.25°
If the legs of a right triangle are 10 and 24, then the
hypotenuse is
26.
Step-by-step explanation:
To figure out the missing side of a right triangle, we will use the Pythagorean theorem. This is...
[tex]a^2+b^2=c^2[/tex]
With this Pythagorean theorem, a and b will always be the legs and the c will always be the hypotenuse, no matter what. Now knowing this, we can plug the legs into the equation.
[tex]10^2+24^2=c^2[/tex]
[tex]100+576=c^2[/tex]
Add the legs together.
[tex]676=c^2[/tex]
Now, since c is squared we will have to find the square root of 676.
[tex]\sqrt{676}[/tex]
= 26
A triangular window has an area of 594 square meters. The base is 54 meters. What is the height?
Answer:
22 m
Step-by-step explanation:
Use the formula for the area of a triangle. Fill in the known values and solve for the unknown.
A = (1/2)bh
594 m^2 = (1/2)(54 m)h
h = (594 m^2)/(27 m) = 22 m
The height of the window is 22 meters.
Solve for x: −3x + 3 < 6
Answer:x>-1
Step-by-step explanation:
Step 1: Subtract 3 from both sides.
-3x+3-3<6-3
-3x<3
Step 2: Divide both sides by -3.
-3x/-3<3/3
X>-1
Please help !! Correct and first answer I’ll give you brainesttttt ! What is the equation of the line?
Step-by-step explanation:
can u give image PlZzzzz ....
Answer:
Hey!
Your answer should be Y=2x+4
Step-by-step explanation:
Hope this helps!
A game popular in Nevada gambling casinos is Keno, which is played as follows: Twenty numbers are selected at random by the casino from the set of numbers 1 through 80. A player can select from 1 to 15 numbers; a win occurs if some fraction of the player’s chosen subset matches any of the 20 numbers drawn by the house. The payoff is a function of the number of elements in the player’s selection and the number of matches. For instance, if the player selects only 1 number, then he or she wins if this number is among the set of 20, and the payoff is $2.20 won for every dollar bet. (As the player’s probability of winning in this case is , it is clear that the "fair" payoff should be $3 won for every $1 bet). When the player selects 2 numbers, a payoff (of odds) of $12 won for every $1 bet is made when both numbers are among the 20.A) What would be the fair payoff in this case? Let P, k denote the probability that exactly k of the n numbers chosen by the player are among the 20 selected by the house. B) Compute Pn, k.C) The most typical wager at Keno consists of selecting 10 numbers. For such a bet, the casino pays off as shown in the following table. Compute the expected payoff.
The missing part in the question;
and the payoff is $2.20 won for every dollar bet. (As the player’s probability of winning in this case is [tex]\dfrac{1}{4}[/tex]........
Also:
For such a bet, the casino pays off as shown in the following table.
The table can be shown as:
Keno Payoffs in 10 Number bets
Number of matches Dollars won for each $1 bet
0 - 4 -1
5 1
6 17
7 179
8 1299
9 2599
10 24999
Answer:
Step-by-step explanation:
Given that:
Twenty numbers are selected at random by the casino from the set of numbers 1 through 80
A player can select from 1 to 15 numbers; a win occurs if some fraction of the player’s chosen subset matches any of the 20 numbers drawn by the house
Let assume X to represent the numbers of player chooses which are in the Casino-selected-set of 20.
Let assume the random variable X has a hypergeometric distribution with parameters N= 80 and m =20.
Then, the probability mass function of a hypergeometric distribution can be defined as:
[tex]P(X=k)=\dfrac{(^m_k)(^{N-m}_{n-k})}{(^N_n)}, k =1,2,3 ... n[/tex]
Now; the probability that i out of n numbers chosen by the player among 20 can be expressed as:
[tex]P(X=k)=\dfrac{(^{20}_k)(^{60}_{n-k})}{(^{80}_n)}, k =1,2,3 ... n[/tex]
Also; given that ; When the player selects 2 numbers, a payoff (of odds) of $12 won for every $1 bet is made when both numbers are among the 20
So; n= 2; k= 2
Then :
Probability P ( Both number in the set 20) [tex]=\dfrac{(^{20}_2)(^{60}_{2-2})}{(^{80}_2)}[/tex]
Probability P ( Both number in the set 20) [tex]= \dfrac{20*19}{80*79}[/tex]
Probability P ( Both number in the set 20) [tex]=\dfrac{19}{316}[/tex]
Probability P ( Both number in the set 20) [tex]=\dfrac{1}{16.63}[/tex]
Thus; the payoff odd for [tex]=\dfrac{1}{16.63}[/tex] is 16.63:1 ,as such fair payoff in this case is $16.63
Again;
Let assume X to represent the numbers of player chooses which are in the Casino-selected-set of 20.
Let assume the random variable X has a hypergeometric distribution with parameters N= 80 and m =20.
The probability mass function of the hypergeometric distribution can be defined as :
[tex]P(X=k)=\dfrac{(^m_k)(^{N-m}_{n-k})}{(^N_n)}, k =1,2,3 ... n[/tex]
Now; the probability that i out of n numbers chosen by the player among 20 can be expressed as:
[tex]P(n,k)=\dfrac{(^{20}_k)(^{60}_{n-k})}{(^{80}_n)}, k =1,2,3 ... n[/tex]
From the table able ; the expected payoff can be computed as shown in the attached diagram below. Thanks.
Consider the graph of the line of best fit, y = 0.5x + 1, and the given data points. A graph shows the horizontal axis numbered negative 4 to positive 4 and the vertical axis numbered negative 4 to positive 4. Points show an upward trend. Which is the residual value when x = 2? –2 –1 1 2
Answer
its -1
Step-by-step explanation:
ED 2020 boiiiii
The residual value of the line of the best fit when x = 2 is -1
How to determine the residual value?The equation of the line is given as:
y = 0.5x + 1
When x = 2, we have:
y = 0.5 * 2 + 1
Evaluate
y = 2
The residual is the difference between the actual value and the predicted value.
From the complete graph, the actual value is 1.
So, we have:
Residual = 1 - 2
Evaluate
Residual = -1
Hence, the residual value when x = 2 is -1
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Approximately 8% of all people have blue eyes. Out of a random sample of 20 people, what is the probability that 2 of them have blue eyes? Round answer to 4 decimal places. Answer:
Answer:
27.11% probability that 2 of them have blue eyes
Step-by-step explanation:
For each person, there are only two possible otucomes. Either they have blue eyes, or they do not. The probability of a person having blue eyes is independent of any other person. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
8% of all people have blue eyes.
This means that [tex]p = 0.08[/tex]
Random sample of 20 people:
This means that [tex]n = 20[/tex]
What is the probability that 2 of them have blue eyes?
This is P(X = 2).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{20,2}.(0.08)^{2}.(0.92)^{18} = 0.2711[/tex]
27.11% probability that 2 of them have blue eyes
The probability that 2 of them have blue eyes is 27.11%.
Given that,
Approximately 8% of all people have blue eyes.
Out of a random sample of 20 people,
We have to determine,
What is the probability that 2 of them have blue eyes?
According to the question,
People having blue eyes p = 8% = 0.08
Sample of people n = 20
For each person, there are only two possible outcomes. Either they have blue eyes, or they do not.
The probability of a person having blue eyes is independent of any other person.
The probability that 2 of them have blue eyes is determined by using a binomial probability distribution.
[tex]\rm P (X = x) =n_C_x\times p^x \times (1-p)^{n-x}}[/tex]
Therefore,
The probability that 2 of them have blue eyes is,
[tex]\rm P (X = x) =n_C_x\times p^x \times (1-p)^{n-x}}\\\\ \rm P (X = x) = \dfrac{n!}{(n-x)! \times x!} \times p^x \times (1-p)^{n-x}}\\\\[/tex]
Substitute all the values in the formula,
[tex]\rm P (X = 2) = \dfrac{20!}{(20-2)! \times 2!} \times (0.08)^2 \times (1-0.08)^{20-2}}\\\\ P (X = 2) = \dfrac{20!}{(18)! \times 2!} \times (0.0064) \times (0.92)^{18}}\\\\ P (X = 2) = \dfrac{19\times 20}{ 2} \times (0.0064) \times (0.222)\\\\ P(X = 2) = {19\times 10}\times (0.00142)\\\\P(X = 2) = 0.2711\\\\P(X = 2) = 27.11 \ Percent[/tex]
Hence, The required probability that 2 of them have blue eyes is 27.11%.
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Imagine you have a rectangular wooden block with dimensions of 10 cm x 3 cm x 8 cm (L x W x H). Required:a. What is the volume of your wooden block?b. What is the density of this wooden block if it has a mass of 168 g?
Answer:
a) The volume of the wooden block is 240 cm^3.
b) The density of the wooden block is 0.7 g/cm^3.
Step-by-step explanation:
The volume of the rectangular wooden block can be calculated as the multiplication of the length in each dimension: length, wide and height.
With dimensions 10 cm x 3 cm x 8 cm, the volume is:
[tex]V=L\cdot W\cdot H = 10\cdot 3\cdot 8=240[/tex]
The volume of the wooden block is 240 cm^3.
If we know that the mass of the wooden block is 168 g, we can calculate the density as:
[tex]\rho = \dfrac{M}{V}=\dfrac{168}{240}=0.7[/tex]
The density of the wooden block is 0.7 g/cm^3.
Prove your work what is 1/12 of a dozen Branliest
Answer:
1/12 of a dozen is 1
Step-by-step explanation:
One dozen means 12. If you ask for 1/12 of 12, you multiply 12 and 1/12. You should get 1 as your answer.
Please answer this correctly I want genius expert or ace people to answer this correctly as soon as possible as my work is due today
Answer:
25%
Step-by-step explanation:
The last percentile always contains 25% of the observations.
Alessandro wrote the quadratic equation -6=x2+4x-1 in standard form. What is the value of c in his new equation? c=-6
Answer:
5
Step-by-step explanation:
To put the equation in standard form, add 6 to both sides.
x^2 +4x -1 +6 = -6 +6
x^2 +4x +5 = 0
The new value of "c" (the constant) is 5.
Answer:
C or 5 for me
Step-by-step explanation:
Solve for x. 9x-2c=k
what is the recursiveformula for this geometric sequence? 4,-12,36,108
Answer:
a[1] = 4
a[n] = -3·a[n-1]
Step-by-step explanation:
The sequence given is not a geometric sequence, since the ratios of terms are -3, -3, 3 -- not a constant.
If we assume that the last given term is supposed to be -108, then the common ratio is -3 and each term is -3 times the previous one. That is expressed in a recursive formula as ...
a[1] = 4 . . . . . . . . . . . first term is 4
a[n] = -3·a[n-1] . . . . . each successive term is -3 times the previous one
Which division sentence is related to the product of a/3 (a/3) when A is not equal to 0?
Answer:
Option 4.
Step-by-step explanation:
Reciprocal of the second fraction turns the product into the division of the two fractions, which equals to 1.
[tex]a/3(a/3)[/tex]
[tex]a/3 \div 3/a=1[/tex]
Two fractions are said to be the reciprocal or multiplicative inverse of each other, if their product is 1.
Answer:
D. a/3 divided by 3/a = 1
Step-by-step explanation:
edge
explain why the solution to the absolute value inequality |4x-9|>-12 is all real numbers
Answer:
Step-by-step explanation:
Hello,
by definition the absolute value is always positive
so |4x-9| >= 0
so the equation |4x-9| > -12 is always true
so all real numbers are solution of this equation
hope this helps
A student walk 60m on a bearing
of 028 degree and then 180m
due east. How is she from her
starting point, correct to the
nearest whole number?
Answer:
d = 234.6 m
Step-by-step explanation:
You can consider a system of coordinates with its origin at the beginning of the walk of the student.
When she start to walk, she is at (0,0)m. After her first walk, her coordinates are calculated by using the information about the incline and the distance that she traveled:
[tex]x_1=60cos28\°=52.97m\\\\y_1=60sin28\°=28.16m[/tex]
she is at the coordinates (52.97 , 28.16)m.
Next, when she walks 180m to the east, her coordinates are:
(52.97+180 , 28.16)m = (232.97 , 28.16)m
To calculate the distance from the final point of the student to the starting point you use the Pythagoras generalization for the distance between two points:
[tex]d=\sqrt{(x-x_o)^2+(y-y_o)^2}\\\\x=232.97\\\\x_o=0\\\\y=28.16\\\\y_o=0\\\\d=\sqrt{(232.97-0)^2+(28.16-0)^2}m=234.6m[/tex]
The displacement of the student on her complete trajectory was of 234.6m