The bοat's hοrizοntal distance frοm the lighthοuse (and the shοre) is apprοximately 1592.53 feet.
What is trigοnοmetryTrigοnοmetry is οne οf the mοst impοrtant branches in mathematics that finds huge applicatiοn in diverse fields. The branch called “Trigοnοmetry” basically deals with the study οf the relatiοnship between the sides and angles οf the right-angle triangle.
Hence, it helps tο find the missing οr unknοwn angles οr sides οf a right triangle using the trigοnοmetric fοrmulas, functiοns οr trigοnοmetric identities. In trigοnοmetry, the angles can be either measured in degrees οr radians. Sοme οf the mοst cοmmοnly used trigοnοmetric angles fοr calculatiοns are 0°, 30°, 45°, 60° and 90°.
We can use trigοnοmetry tο sοlve fοr the hοrizοntal distance. Let x be the hοrizοntal distance frοm the bοat tο the lighthοuse.
Then, tan(5°) = οppοsite/adjacent = 139/x
Sοlving fοr x, we get:
x = 139/tan(5°) ≈ 1592.53 feet
Therefοre, the bοat's hοrizοntal distance frοm the lighthοuse (and the shοre) is apprοximately 1592.53 feet.
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10 of 1710 of 17 Questions
Question
Katherine bought 312
pounds of oranges for $1.45
per pound, as well as 434
pounds of potatoes that cost $1.69
for 2
pounds. She gives the cashier a $10.00
bill.
Which equation represents the situation if x
is the amount of change in dollars Katherine should receive?
A 312(1.45)+434(1.69)+x=10
3 and 1 half times 1 point 4 5 plus 4 and 3 fourths times 1 point 6 9 plus x is equal to 10
B 312(1.45)+434(1.692)+x=10
3 and 1 half times 1 point 4 5 plus 4 and 3 fourths times open paren 1 point 6 9 over 2 close paren plus x is equal to 10
C 312(1.45)+434(1.692)−x=10
3 and 1 half times 1 point 4 5 plus 4 and 3 fourths times open paren 1 point 6 9 over 2 close paren minus x is equal to 10
D (312+434)⋅(1.45+1.69)+x=10
HELP ME I WILL GIVE BRAINLIEST
Answer:
6)-56+567)-/(05(-)9
Step-by-step explanation:
Question
Katherine bought 312
pounds of oranges for $1.45
per pound, as well as 434
pounds of potatoes that cost $1.69
for 2
pounds. She gives the cashier a $10.00
bill.
Which equation represents the situation if x
is the amount of change in dollars Katherine should receive?
A 312(1.45)+434(1.69)+x=10
3 and 1 half times 1 point 4 5 plus 4 and 3 fourths times 1 point 6 9 plus x is equal to 10
B 312(1.45)+434(1.692)+x=10
3 and 1 half times 1 point 4 5 plus 4 and 3 fourths times open paren 1 point 6 9 over 2 close paren plus x is equal to 10
C 312(1.45)+434(1.692)−x=10
3 and 1 half times 1 point 4 5 plus 4 and 3 fourths times open paren 1 point 6 9 over 2 close paren minus x is equal to 10
D (312+434)⋅(1.45+1.69)+x=10
HELP ME I WILL GIVE BRAINLIEST
help plssss explainnn!!
Answer:
[tex]xy^8[/tex]
Step-by-step explanation:
Notice if you have the same base you can ADD the exponent, for example:
[tex]x^{-6} x^{7} =x^{-6+7}=x^{1 }=x[/tex]
[tex]y^{6} y^{2} =y^{6+2}=y^{8 }\\[/tex]
so the answer is
[tex]xy^8[/tex]
part b - find the internal axial force in each bar segment using the answer for the support reaction at a determ
As per the axial force, the support reaction at A is equal in magnitude to the axial force that is applied at the other end of the bar.
To determine the support reaction at A, we will draw a free-body diagram of the bar.
Since the bar is fixed at A, the support reaction at that end will be a vertical force, and we will label it as RA.
Using Newton's second law of motion, we can write the equation of equilibrium for the bar in the vertical direction:
ΣFy = 0
where ΣFy is the sum of all the forces in the vertical direction. Since there are only two forces acting on the bar, the axial force and the support reaction, we can write:
-FA + RA = 0
where FA is the axial force that is applied at one end, and RA is the support reaction at the other end.
From this equation, we can solve for RA:
RA = FA
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Complete Question:
Determine the support reaction at A
The axially loaded bar is fixed at A and loaded as shown. Draw a free-body diagram and determine the support reaction at A.
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Parallelogram ABCD is a rhombus with measure EBC = 36. What is the measure of DAE?
picture below
In an effort to figure out why application rates are slipping, your college decides to set up an experiment to determine why students who are interested in the college decide to enroll or not. The college decides to send out a questionnaire to everyone who submitted an application to the college in 2017. What's the population for this study, and what's the sample?
A. The population is all college students everywhere, and the sample is all college students interested in your school.
B. The population is all college students everywhere, and the sample is the individuals who responded to the survey.
C. The population is all students who applied to your college, and the sample is the individuals who responded to the survey.
D. The population is all college students interested in your school, and the sample is everyone who decided to enroll.
The population of interest is the group of students who submitted an application to the college in 2017.
What is sample?A sample is a subset of a population that is selected and studied in order to make inferences or conclusions about the population. The sample is usually selected to be representative of the population in some way, so that the conclusions drawn from the sample can be generalized to the population as a whole.
According to question:The correct answer is C.
The purpose of the study is to determine why students who are interested in the college decide to enroll or not. Therefore, the population of interest is the group of students who submitted an application to the college in 2017.
Option A is incorrect because the population is not all college students everywhere, only those who applied to the college in question.Option B is incorrect because the sample is not just the individuals who responded to the survey, but rather all students who submitted an application in 2017.Option D is incorrect because the sample is not just everyone who decided to enroll, but rather all students who submitted an application, regardless of whether they enrolled or not.To know more about sample visit:
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point $p$ lies inside square $abcd$ such that triangle $abp$ is equilateral. find $\angle pcd$ in degrees.
The measurement of angle PCD in equilateral triangle is 67.38°.
Let $s$ be the side length of the square $abcd$, and let $O$ be the center of the square. Then $OP = s/\sqrt{2}$.
Since triangle $ABP$ is equilateral, we have $\angle ABP = 60^\circ$ and $AP=BP=s$. Let $E$ be the foot of the perpendicular from $P$ to $AB$. Then $AE=BE=s/2$ and $EP=s\sqrt{3}/2$.
Since $EP$ is perpendicular to $AB$ and $AB$ is parallel to $CD$, we have $\angle PCD = \angle ACE$.
Since $OP$ is perpendicular to $AB$, we have $\angle OEP = \angle AEP = 30^\circ$. Also, $OE=OP/\sqrt{2}=s/2$.
Using the Pythagorean theorem in triangle $OCE$, we have
CE= [tex]\sqrt{(OE)^{2} + (OC)^{2}} = \sqrt{(s/2)^{2} + s^{2}} = s\sqrt{5}/2[/tex]
Therefore, $\sin \angle ACE = CE/CP = \sqrt{5}/2$. Thus,
∠PCD = ∠ACE = arcsin(√5/2) ≈ 67.38°
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FILL IN THE BLANK ______ can creep into a study if subjects are picked (intentionally or not) according to some criterion and not randomly.
Selection bias can creep into a study if subjects are picked (intentionally or not) according to some criterion and not randomly.
Selection bias occurs when the selection of study participants is not random and is instead influenced by certain criteria. This can result in a non-representative sample that does not accurately reflect the population being studied, leading to inaccurate conclusions. For example, if a study on the effectiveness of a medication only enrolls participants who are already known to respond well to that medication, the results may overestimate its effectiveness in the general population. To minimize selection bias, researchers should use random sampling techniques and carefully consider the inclusion and exclusion criteria .
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I am in my room (State 1). There is a 65% chance that I stay here and do my work like I am supposed to. There is a 35% chance I go get a snack and procrastinate (State 2). Once I have gone to get the snack, there is a 15% chance that I go back to work (go back to State 1), and there is an 85% chance that I get another snack and procrastinate further (stay in State 2).
Create a diagram and a transition matrix for this case.
Answer:
Here is a diagram and transition matrix for this case:
Diagram:
+---(0.65)---> State 1 (work)
|
Start ---+
|
+---(0.35)---> State 2 (procrastinate)
|
+---(0.15)---> State 1 (work)
|
+---(0.85)---> State 2 (procrastinate)
Transition matrix:
| State 1 | State 2 |
----------+-----------+-----------+
State 1 | 1.00 | 0.00 |
----------+-----------+-----------+
State 2 | 0.15 | 0.85 |
----------+-----------+-----------+
In the transition matrix, the rows represent the starting state and the columns represent the ending state. The entries in the matrix represent the probabilities of transitioning from the starting state to the ending state. For example, the entry in row 1 and column 2 (0.00) represents the probability of transitioning from State 1 to State 2, which is 0.00.
of the following people, who would be included in the survey conducted by the bureau of labor statistics?
The people who are included in the survey conducted by Bureau of Labor Statistics are (a) certain unpaid workers, (b) part-time workers and (c) workers on vacation, the correct option is (d).
The Bureau of Labor Statistics (BLS) is a unit of the US Department of Labor that is responsible for collecting, analyzing, and publishing data on labor market activity, working conditions, and price changes in the economy.
The Bureau of Labor Statistics (BLS) considers individuals to be employed if they meet any of the given criteria:
(i) Worked at least one hour as paid employees
(ii) Worked at least 15 hours as unpaid workers in a family-owned enterprise
(iii) Were temporarily absent from their regular jobs due to illness, vacation, strike, etc.
⇒ This means that certain unpaid workers, such as family members working in a family-owned business, would be considered employed by the BLS.
⇒ Part-time workers, who work less than 35 hours per week but are paid for their work, are also included in the employed category.
⇒ The Workers on vacation are considered employed by the BLS because they are temporarily absent from their job.
Therefore, all the options are correct , which is Option(d).
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The given question is incomplete, the complete question is
Who of the following are included in the Bureau of Labor Statistics "employed" category?
(a) certain unpaid workers
(b) part-time workers
(c) workers on vacation
(d) All of the above are correct.
any point on the parabola can be labeled (x,y), as shown. a parabola goes through (negative 3, 3)
The correct standard form of the equation of the parabola is:
[tex]y = -x^2 - 1[/tex].
To find the standard form of the equation of the parabola that passes through the given points (-3, 3) and (1, -1), we can use the general form of the equation of a parabola:
[tex]y = ax^2 + bx + c[/tex] ___________(1)
Substituting the coordinates of the two given points into this equation, we get a system of two equations in three unknowns (a, b, and c):
[tex]3 = 9a - 3b + c[/tex]
[tex]-1 = a + b + c[/tex]
To solve for a, b, and c, we can eliminate one of the variables using subtraction or addition. Subtracting the second equation from the first, we get:
[tex]4 = 8a - 4b[/tex]
Simplifying this equation, we get:
[tex]2 = 4a - 2b[/tex]
Dividing both sides by 2, we get:
[tex]1 = 2a - b[/tex]___________(2)
Now we can substitute this expression for b into one of the earlier equations to eliminate b. Using the first equation, we get:
[tex]3 = 9a - 3(2a - 1) + c[/tex]
Simplifying this equation, we get:
[tex]3 = 6a + c + 3[/tex]
Subtracting 3 from both sides, we get:
[tex]0 = 6a + c[/tex]
Solving for c, we get:
c = -6a __________(3)
Substituting this expression for c into the second equation, we get:
[tex]-1 = a + (2a - 1) - 6a[/tex]
Simplifying this equation, we get:
[tex]-1 = -3a - 1[/tex]
Adding 1 to both sides, we get:
[tex]-3a =0[/tex]
Solving for a, we get:
[tex]a = 0[/tex]
Substituting this value of a into the equation(3) for c, we get:
c = 0
Substituting a = 0 into the equation(2) for b that we found earlier, we get:
[tex]1 = 0 - b[/tex]
Solving for b, we get:
[tex]b = -1[/tex]
Putting the values of a, b and c in (1), we get
[tex]y = -x^2 - 1[/tex]
Therefore, the equation of the parabola that passes through the given points (-3, 3) and (1, -1) is:
[tex]y = -x^2 - 1[/tex]
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Complete question:
A parabola goes through (-3, 3) & (1, -1). A point is below the parabola at (-3, 2). A line above the parabola goes through (-3, 4) & (0, 4). A point on the parabola is labeled (x, y).
What is the correct standard form of the equation of the parabola?
The figure is in the image attached below
type the correct words in the blanks. two radicals are said to be radicals if they have the same and the radicand.
Two radicals are said to be radicals if they have the same indices and the radicand.
In mathematics, a radicand is an expression, a number, or a variable that is enclosed in a root symbol. The factor for which we are determining the root is quantity. As we study exponents and roots, the word "radicand" is utilised. Therefore, the radicand in 2 has a value of 2. Following are some radicand examples:
3√(pq) → pq is the radicand
√(a+b) → a + b is the radicand
4√15 → 15 is the radicand
A radical is a symbol used to represent a number's root. It is symbolised as. The word or phrase that appears after the radical symbol is known as the radicand. Hence, it may be claimed that the radical represents the radicand. Alternatively said, the radicand sign is √.
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Complete question:
Type the correct words in the blanks:
Two radicals are said to be radicals if they have the same and the radicand.
Question 4
Let us assume an original starting value of $4 trillion in 2033, but that the actual rate of
decline after 2033 was 10% greater than the 7.6% rate. (Notice that this refers to a 10%
relative increase over the 7.6% rate of decline that was originally estimated in the
lesson, and not an absolute increase of 10 percentage points.) In the questions below,
consider how this would affect the estimated value of the funds in 2038?
What is the new estimated value of the trust funds in 2038? Round to the nearest
The new estimated value of the trust funds in 2038 would be $2.5 trillion.
What is funds?Funds are resources of monetary value that can be used to acquire goods, services, or to meet financial obligations. They are usually obtained through the sale of goods and services or by borrowing. Funds can come from a variety of sources, including individuals, businesses, governments, and other organizations. Funds can be used to purchase assets such as stocks, bonds, real estate, or other forms of investments.
This is because a 10% relative increase over the original estimated 7.6% rate of decline means that the actual rate of decline is 8.36% (7.6% x 1.10 = 8.36%). Applying this rate to the original starting value of $4 trillion, the value of the trust funds in 2038 would be $4 trillion x 0.9164 (which is the equivalent of 1 - 0.0836) = $2.5 trillion.
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The new estimated value of the trust funds in 2038 would be $2.4 trillion.
What is trust fund?A trust fund is a legal arrangement in which a person or organization (the trustor) transfers assets to another person or organization (the trustee) to be managed and distributed for the benefit of a third party (the beneficiary). The trustor sets out a set of instructions (the trust deed) on how the trust funds should be handled, managed, and distributed. The trustee is legally bound to abide by these instructions, and is responsible for the management and distribution of the trust funds according to the trust deed. Trust funds can be used for a variety of purposes, such as providing for a beneficiary's education, medical care, or retirement.
This is because a 10% increase in the rate of decline would result in a rate of decline of 8.36% (7.6% plus 10% of 7.6%).
Using this new rate of decline, the value of the trust funds in 2038 would be $4 trillion multiplied by (1 - 0.0836)⁵,
which is equal to $2.4 trillion.
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What is the smallest possible average of five distinct positive even integers?
A. 10
B. 8
C. 6
D. 4
E. 0
Answer:
The smallest possible average of five distinct positive even integers will occur if we choose the five smallest even integers. Since we want the integers to be distinct, we start with 2 and add the next four even integers:
2, 4, 6, 8, 10
The average of these five integers is:
(2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6
Therefore, the smallest possible average of five distinct positive even integers is 6, which is answer choice C.
Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table.
In response to the stated question, we may state that As a result, the overall probability of an accurately picked drive-thru order across all chains is roughly 0.929, or 92.9%.
What is probability?Probability theory is an area of mathematics that calculates the likelihood of an occurrence or a proposition being true. A risk is a number in the range of 0 and 1, whereas 1 implies certainty and a probability of roughly 0 indicates how likely an event seems to be to occur. Probability is a mathematical expression of the chance or chances that a given event will occur. Probabilities can alternatively be stated as integers between 0 and 1 or as % from 0% to 100%. the ratio of occurrences among equally likely choices that result in a certain event in comparison to all other outcomes.
Using the data in the table, we can compute the likelihood of a correct drive-thru order for each fast food chain, as well as the overall chance of an accurate order across all chains.
Divide the number of accurate orders by the total number of orders to find the chance of a randomly picked order being accurate at each chain:
P(accurate order) = 1246 / 1300 = 0.958 for McDonald's
P(accurate order) = 1020 / 1100 = 0.927 Taco Bell
P(accurate order) = 708 / 800 = 0.885 for Burger King
P(accurate order) = 940 / 1000 = 0.94 for Wendy's
P(adequate overall order) = 0.3 * 0.958 + 0.25 * 0.927 + 0.2 * 0.885 + 0.25 * 0.94 = 0.929
As a result, the overall likelihood of an accurately picked drive-thru order across all chains is roughly 0.929, or 92.9%.
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I need help with this
Answer:
D.
Step-by-step explanation:
Consider two agents, Alice and Bob, who have utility functions 0.3x3 + 0.72A if xa > XB (0.314 +0.72B if XB > XA UA(2A, 2B) = UB(XA, XB) 4X A – 32B if XB > IA -0.32A + 1.3xB if x A > XB If Alice is the dictator in the dictator game with a $10 endowment, then she will offer Bob (A) $0; (B) $5; (C) $2; (D) $10.
The utility that maximizes the possible utility of both the agents Alice and Bob is equal to option D. $10.
Compare Alice's utility from each option and choose the one that maximizes her utility.
Let us consider each option,
If Alice offers Bob $0, her utility will be,
If XA > XB then
UA (XA , XB )= 0.3x3 + 0.72A
UA(10,0)
= 0.3(10)³ + 0.72(10)
= 307.2
If Alice offers Bob $5, Bob's utility will be,
UB(10,5)
= 0.314 + 0.72(5)
= 0.314 + 3.6
= 3.914
And Alice's utility will be,
UA(5,10)
= -0.32(5) + 1.3(10)
= 11.4
Total utility for both Alice and Bob will be,
UA(5,10) + UB(10,5)
= 11.4 + 3.914
= 15.314
If Alice offers Bob $2, Bob's utility will be,
UB(10,2)
= 0.314 + 0.72(2)
= 1.754
And Alice's utility will be,
UA(2,10)
= -0.32(2) + 1.3(10)
= 12.4
So the total utility for both Alice and Bob will be,
UA(2,10) + UB(10,2)
= 12.4 + 1.754
= 14.154
If Alice offers Bob $10, Bob's utility will be,
UB(10,10)
= 0.314 + 0.72(10)
= 7.514
And Alice's utility will be,
UA(10,10)
= 0.3(10)³ + 0.72(10)
= 307.2
So the total utility for both Alice and Bob will be,
UA(10,10) + UB(10,10)
= 307.2 + 7.514
= 314.714
Therefore, utility which maximizes the total utility for both Alice and Bob is given by option (D) $10.
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-51+((-5+(-4)) all calculation
Answer:
the answer to that is -31
Which function represents the following graph?
Oy=√√x-3+3
Oy=√√x+3+3
O y=3√√x-3+3
Oy-3√x+3+3
The correct option b) [tex]\rm y = \sqrt{x+ 3} + 3[/tex] is a function of the given graph.
What particular graph best illustrates a function?The graph οf a relatiοn is said tο reflect a functiοn if a vertical line drawn anywhere οn the graph οnly intersects the graph οnce. In the event when a vertical line can graph is nοt a representatiοn οf a functiοn if there are mοre than twο pοints οn it.
The graphs coordinate is at (-3, 3)
Lets put the value in all the given function to find the correct function
a. [tex]\rm y = \sqrt{x - 3} + 3[/tex]
Using (-3, 3) as x and y
[tex]\rm 3 = \sqrt{(-3) - 3} + 3[/tex]
[tex]\rm 3 = \sqrt{9} + 3[/tex]
[tex]\rm 3 \neq 3 + 3[/tex]
[tex]\rm y = \sqrt{x - 3} + 3[/tex] is not a function of graph.
b. [tex]\rm y = \sqrt{x+ 3} + 3[/tex]
Using (-3, 3) as x and y
[tex]\rm 3 = \sqrt{-3+ 3} + 3[/tex]
[tex]\rm 3 = \sqrt{0} + 3[/tex]
[tex]\rm 3 = 0 + 3[/tex]
[tex]\rm 3 = 3[/tex]
[tex]\rm y = \sqrt{x+ 3} + 3[/tex] is a function of the given graph.
The other two options are no the functions as cube root is used and the value of x wont satisfy there.
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Is this a quadrilateral, parallelogram, rectangle,rhombus,square or trapezoid 
As all the sides of the closed figure are equal to each other, the quadrilateral here is a square.
What is a square?A square is a closed, two-dimensional (2D), object with four corners. With four sides and four vertices, a quadrilateral is referred to as a square. All four sides of a square are equal and parallel.
In other words, a square is a polygon or quadrilateral with four sides. An equiangular quadrilateral is a shape in which all of the angles are of equal size.
Here in the given figure, we can see a quadrilateral is given.
We can see that all the sides of the quadrilateral are given to be equal to each other.
We can conclude from the observation that the quadrilateral is a square as the sides are all equal to each other.
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Letsha wants to produce 80 pages information books for school project. She can have this done at local printing company at R0.35 per page.
Answer:
if u want total price then,
=Rs.35×80=Rs.2800
There are two types of trees to plant in the yard type A trees are 36 inches tall and grows 8 inches per year type B are 18 inches tall but grow 10 inches per year when will the trees be the same height
As a result, both varieties of trees will be the same height after 9 years. We can change both equations to a = 9 to verify this: Height of the type A tree is 36 + 8(9) or 36 + 72 inches, whereas the height of the type B tree is 18 + 10(9) or 18 + 90 inches.
What function do height and distance serve in everyday life?Trigonometry includes heights and distances, and it has numerous uses in practical daily life. It utilised to compute height of towers, structures, mountains, etc., and distance between any two objects such celestial bodies others. ,sys,s tos.as to .... and.
Let's use "a" to denote the number of years after planting the trees.
A type A tree will reach the following height after "a" years:
Height of type A tree = 36 + 8a
After "a" years, the height of a type B tree will be:
Height of type B tree = 18 + 10a
We must set the two types of trees' heights equal to one another and solve for "a" to determine when they will reach the same height:
36 + 8a = 18 + 10a
Subtracting 8a from both sides, we get:
36 = 18 + 2a
Subtracting 18 from both sides, we get:
18 = 2a
Dividing both sides by 2, we get:
a = 9
Therefore, after 9 years, both types of trees will be the same height.
To check this, we can substitute a = 9 into both equations:
Height of type A tree = 36 + 8(9) = 36 + 72 = 108 inches
Height of type B tree = 18 + 10(9) = 18 + 90 = 108 inches
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Question:
You have two types of trees to plant in your yard: type A trees are 36 inches tall and grow 8 inches per year, while type B trees are 18 inches tall and grow 10 inches per year. At what point in time will the trees be the same height? How tall will the trees be at that time?
Find any critical numbers of the function.
Answer:
(1, 2) and (-1, -2). or. (±1, ±2)
Step-by-step explanation:
[tex]{ \sf{f(x) = \frac{4x}{ {x}^{2} + 1 } }} \\ [/tex]
- Simply, a critical number or critical point is gotten by differentiating the function.
From Quotient rule;
[tex]{ \sf{ {f}^{l}(x) = \frac{4( {x}^{2} + 1) - (2x)(4x)}{ {( {x}^{2} + 1)}^{2} } }} \\ \\ { \sf{f {}^{l}(x) = \frac{ {4x}^{2} + 4 - {8x}^{2} }{ {( {x}^{2} + 1) }^{2} } }} \\ \\ { \sf{f {}^{l}(x) = \frac{4(1 - {x}^{2}) }{ {( {x}^{2 } + 1) }^{2} } }}[/tex]
Then equate this derivative to zero;
[tex]{ \sf{0 = \frac{4(1 - {x}^{2} )}{ {( {x}^{2} + 1) }^{2} } }} \\ \\ { \sf{4(1 - {x}^{2} ) = 0}} \\ \\ { \sf{4 - {4x}^{2} = 0}} \\ \\ { \sf{4 {x}^{2} = 4}} \\ \\ { \sf{x = \sqrt{1} }} \\ \\ { \sf{ \underline{ \: x = \pm 1 \: }}}[/tex]
Substitute for x in f(x)
For x = 1
[tex]{ \sf{f(1) = \frac{4(1)}{ {(1)}^{2} + 1} = \frac{4}{2} = 2 }} \\ [/tex]
For x = -1
[tex]{ \sf{f( - 1) = \frac{4( - 1)}{ {( - 1)}^{2} + 1 } = \frac{ - 4}{2} = - 2 }} \\ [/tex]
Therefore points are;
(1, 2) and (-1, -2)
Problem 2 (Vector and Matrix Refresh) Seven data points are arranged as columns of a data matrix X given as follows: 2 1 0 0 -1 0 -2 X = 2 0 1 0 0 -1 -2 a) Draw all data points on a 2D plane by hand. Properly label the two axes. Clearly provide important tick values to facilitate a precise graphical description of the data. b) Consider each point as a vector. Calculate the angle in between (2 27 and the five other points (excluding [0 07), respectively, using the inner/dot product formula that involves the angle. Note that the angle between two vectors can be negative. c) Calculate the matrix outer product for X, namely, R = XXT. Show the intermediate steps of calculating each element of the 2-by-2 matrix R. d) The matrix outer product can also be calculated via R =
a) The drawing of all data points on a 2D plane is illustrated below.
b) The angle in between the five other points is 27
c) The matrix outer product for X is R = XXT.
d) The matrix outer product can also be calculated via R is (2,27)
The data matrix X is a 2-by-7 matrix, where each column represents a data point with two components. We can visualize each data point as a vector in a two-dimensional plane, where the horizontal axis represents the first component and the vertical axis represents the second component.
To draw all data points on a 2D plane, we can plot each column of X as a vector starting from the origin. Proper labeling of the two axes and providing important tick values will facilitate a precise graphical description of the data.
Next, we can use the inner product formula to calculate the angle between the first data point (2, 27) and the other five data points, respectively.
The inner product, also known as the dot product, is a way to measure the similarity between two vectors by multiplying their corresponding components and summing the products.
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PLEASE HURRY!!
Curious about people's recycling behaviors, Sandra put on some gloves and sifted through some recycling and trash bins. She kept count of the plastic type of each bottle and which bottles are properly dispensed.
What is the probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle? Please show your work.
The probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle is 0.25 or 25%
What is Conditional probability?
Conditional probability is the probability of an event occurring given that another event has occurred or is known to have occurred. It is denoted by P(A|B), which reads as "the probability of A given B."
The formula for conditional probability is:
P(A|B) = P(A and B) / P(B)
where P(A and B) is the probability of both events A and B occurring, and P(B) is the probability of event B occurring.
The total number of Plastic #2 bottles is 8 (correctly placed) + 5 (incorrectly placed) = 13.
The total number of Plastic #4 bottles is 5 (correctly placed) + 2 (incorrectly placed) = 7.
The probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle is given by:
(number of Plastic #4 bottles correctly placed) / (total number of bottles)
So the probability is:
5/20 = 1/4 = 0.25
Therefore, the probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle is 0.25 or 25%.
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How do you find the slope of (-4, 8) and (4, 2)
To find the slope of a line that passes through two points, you can use the slope formula. The slope formula is:
Slope = (y2 - y1) / (x2 - x1)
Using the points given in your question, the slope formula to find the slope of the line is:
Slope = (2 - 8) / (4 - (-4))
Using the order of operations, the calculation of the slope formula is as follows:
Slope = -6 / 8
Therefore, the slope of the line passing through (-4, 8) and (4, 2) is -3/4.
Last years freshman class at big state university totaled 5,303 students
URGENT
The 1,262 students who received a merit scholarship, the amount they received varied per student and totaled an average of $3,458 ($454). That amount is 78.2% of the full tuition cost of $4,400.
What is merit?Merit is a term used to describe the quality of something or someone that makes them worthy of recognition or respect. It is an indicator of worthiness and is usually based on a person's ability, effort, or accomplishments. Merit is often used when evaluating an individual or a group for a promotion, hiring, or award. Merit is subjective, as different people have different standards for what merits recognition.
Therefore, 21.8% of the students who received a merit scholarship did not receive enough to cover full tuition. Therefore, the percentage of students who received a merit scholarship and did not receive enough to cover full tuition is 21%.
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1. A living room measures 4.75 m by 5.2 m. a. What is the area of the living room? 24.7m b. The area of the game room is one and a half times that of the living room. Fi the living room and the game room.
The area of the living room is 24.7 m², and the area of the game room is 37.05 m².
What is area?Area is the measure of the two-dimensional space occupied by a figure or an object. It is usually expressed in square units such as cm2, m2, or in2. It is used to measure the size of a figure or object, and can also be used to calculate the amount of material required for a project.
The area of a living room measuring 4.75 m by 5.2 m can be calculated using the formula A = l × w, where A is the area, l is the length and w is the width. In this case, A = 4.75 m × 5.2 m = 24.7 m².
To calculate the area of the game room, we must multiply the area of the living room by 1.5. Therefore, the area of the game room is 1.5 × 24.7 m² = 37.05 m².
The area of the living room is 24.7 m², and the area of the game room is 37.05 m².
The area of a room can be used to determine how much furniture can fit in the room or how much floor space is available for activities. Knowing the area of a room is also important for calculating the cost of painting, wallpapering, carpeting, and other flooring materials.
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If the gradient of the equation 2x-ay+2=0 is 1. Then find the value of a.
Step-by-step explanation:
2x + ay + 2 = 0
the gradient or slope of the line is the factor m of x in the form
y = mx + b
so let's transform the given equation into that form :
ay = -2x - 2
y = (-2/a)x - 2/a
we know that m = 1.
so,
-2/a = 1
-2 = a
Let A and B be events with P(A) = 0.3, P(B) = 0.6, and P(A and B) = 0.03. Are A and B mutually exclusive? Explain why or why not.
Answer:
A and B are not mutually exclusive
Step-by-step explanation:
A and B are not mutually exclusive because P(A and B) > 0. If A and B were mutually exclusive, then they would have no outcomes in common and the probability of their intersection would be zero. However, in this case, they do share some outcomes, since P(A and B) is greater than zero.
generally, cold fronts move fast er than warm fronts generally, cold fronts have steeper slopes generally, precipitation cover s a much broader area with a cold front especially in winter, cumuliform clouds are more often associated with cold fronts
Cold fronts generally move faster than warm fronts because cold air is denser and thus, moves more quickly. Precipitation with a cold front typically covers a broader area, especially during the winter.
On the other hand, warm fronts move more slowly as they are characterized by the gradual lifting of warm air over colder air. Cold fronts also typically have steeper slopes than warm fronts. This is because the leading edge of a cold front is more abrupt.
With a steep rise in the cold air mass. In contrast, the leading edge of a warm front has a gentler slope as the warm air gradually rises over the colder air.
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