Answers
The component form and magnitude of the vector are;
v = ⟨-5, 3⟩ and ||v|| = √(34)
How can the component form of the vector be found?The difference between the points on the graph can be used to express the vector in component form as follows;
The component of the vectors are the horizontal and the vertical component
The horizontal component is; -(2 - (-3))·i = -5·i·
The vertical component is; ((5 - 2)·j = 3·j
The component form of the vector is therefore; v = ⟨-5, 3⟩
The magnitude of the vector is; ||v|| = √((-3 - 2)² + (5 - 2)²) = √(34)
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Related Questions
6) Find the range of values for x using the
Triangle Inequality Theorem.
X
15.4
7.6
Answers
Using this theorem, we can find the range of values for x in the given triangle:
x + 7.6 > 15.4
x > 7.8
x + 15.4 > 7.6
x > -7.8
Therefore, the range of values for x is:
7.8 < x < 7.8
Two events, A and B, are mutually exclusive and each has a nonzero probability. If event A is known to occur, the probability of the occurrence of event B is
a. any positive value
b. one
c. any value between 0 to 1
d. zero
Answers
Given that event A is known to occur and both events A and B have nonzero probabilities, we can conclude that the probability of event B occurring is zero. So, the correct answer to your question is: d. zero
If events A and B are mutually exclusive, it means that they cannot occur at the same time. So, if we know that event A has occurred, we can safely say that event B cannot occur. Therefore, the probability of the occurrence of event B given that event A has occurred is zero. Therefore, the correct answer is d) zero.
Mutually exclusive events are a fundamental concept in probability theory. It means that the occurrence of one event excludes the occurrence of another event. For example, when flipping a coin, the event of getting heads is mutually exclusive with the event of getting tails. It is impossible to get both heads and tails at the same time.
Understanding mutually exclusive events is important because it helps us to calculate the probability of combined events. For mutually exclusive events, we can simply add their probabilities to get the probability of their union. However, if events are not mutually exclusive, we need to subtract the probability of their intersection to avoid counting the same outcome twice.
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Let A = {1,2,3,4}, give an example of a relation on A|| that is • reflexive and symmetric but not transitive. You may give your example in the form R = {(x,y),(y,w), (w,y), ... } or draw a directed graph reflexive and transitive but not symmetric. You may give your example in the form R = {(x,y),(y,w),(w,y),... } or draw a directed graph
Answers
For the first part of the question, let R = {(1,1), (2,2), (3,3), (4,4), (1,2), (2,1), (2,3), (3,2)}. This relation is reflexive because every element in A is related to itself, and it is symmetric because if (x,y) is in R, then (y,x) is also in R. However, it is not transitive because (1,2) and (2,3) are in R, but (1,3) is not in R.
For the second part of the question, let R = {(1,1), (2,2), (3,3), (4,4), (1,2), (2,3), (3,4), (1,3), (2,4)}. This relation is reflexive because every element in A is related to itself, and it is transitive because if (x,y) and (y,z) are in R, then (x,z) is also in R. However, it is not symmetric because (1,2) is in R, but (2,1) is not in R.
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HELP ME TODAY PLEASE
Answers
Answer: answer is 3
Step-by-step explanation:
The current of a system is defined as the following function i(t) = Ae-1-1-1 Evaluate the rate of change of the current at time t = 0.01s and A = 20 0 28.79 O 18.79 O 10.79 O None 0 20.79
Answers
The rate of change of the current is -19.79.
You provided the function i(t) = Ae^(-t) and you'd like to evaluate the rate of change of the current at time t = 0.01s with A = 20.
Step 1: Find the derivative of the function i(t) with respect to time (t). This will give us the rate of change.
di/dt = -Ae^(-t)
Step 2: Substitute the given values for A and t into the derivative equation.
di/dt = -20e^(-0.01)
Step 3: Evaluate the expression.
di/dt ≈ -20 * 0.99004983 ≈ -19.79
So, the rate of change of the current at time t = 0.01s and A = 20 is approximately -19.79.
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A tin contains 5 cookies. Only 1 of them is chocolate flavoured. Noah picks a cookie at random from the tin. What is the probability that it is chocolate flavoured? Give your answer as a decimal.
Answers
Two monomials are shown below. 28x²y 34x y What is the greatest common factor (GCF) of these monomials? A
7xy B
4x²y
C2xy
D2x²y
I need an answer asap
Answers
Answer: 2xy
Step-by-step explanation:
you need the biggest factor that goes into
Shannon’s Ice Cream Shop, Shenanigans, sells three types of ice cream: Peanut Butter Cup, Coffee Cream and Oreo. Last week Shenanigans sold a total of 489 ice cream cones that were either Coffee Cream or Oreo. In total, they sold 711 ice cream cones last week. What is the probability Shenanigan’s will sell a Peanut Butter Cup cone next? Express your answer as a percent.
Answers
The probability of Shenanigans selling a Peanut Butter Cup cone next is approximately 31.22%.
To calculate the probability of Shenanigans selling a Peanut Butter Cup cone next, we need to determine the number of cones sold that were not Peanut Butter Cup cones and divide that by the total number of cones sold.
Given that Shenanigans sold a total of 711 ice cream cones last week and 489 of those were either Coffee Cream or Oreo, we can subtract 489 from 711 to find the number of cones that were not Coffee Cream or Oreo;
Number of cones that were not Coffee Cream or Oreo = 711 - 489 = 222
So, out of the total 711 cones sold, 222 were not Coffee Cream or Oreo cones. Therefore, the remaining cones must be Peanut Butter Cup cones.
Now, we can calculate the probability of selling a Peanut Butter Cup cone next by dividing the number of Peanut Butter Cup cones by the total number of cones sold, and then multiplying by 100 to find the result as a percentage;
Probability of selling a Peanut Butter Cup cone next = (Number of Peanut Butter Cup cones / Total number of cones sold) × 100
Probability of selling a Peanut Butter Cup cone next = (222 / 711) × 100
≈ 31.22%
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Hey can anyone help me
Answers
Answer: 12 units
Step-by-step explanation:
Since in this situation we're going by units it will be easier. First to create the rectangle just fill in 3 boxes horizontally and 4 units vertically. connect the squares together.
Then to find the area, the formula for that is Base x Height so all you have to do is multiply 4*3 and that's 12.
Ricardo has a square pyramid with a base side length of 19 inches and a height of 5 inches. Frido has a square pyramid with a volume of 4873.5 in^3.
Use this information to choose all the correct statements below:
A.
Ricardo’s pyramid has a volume of 601.7 in^3.
B.
Ricardo’s pyramid has a volume of 31.7 in^3.
C.
Frido’s pyramid is 8.1 times larger than Ricardo’s.
D.
Frido’s pyramid is 153.7 times larger than Ricardo’s.
E.
Frido's pyramid is 27% larger than Ricardo's.
F.
Frido’s pyramid is 810% larger than Ricardo’s.
Answers
Answer: A, C, and F
Step-by-step explanation:
v=1/3 x B(not b to get B do bxb)xh
V=1/3(19x19)(5)=1/3(361)(5)=1/3(1805)
1805/3=601.7^3
Frido has V=4873.5
601.7x8.1=4873.5
8.1 as a percent is 8.1x100=810%
So the answers are
A.
Ricardo’s pyramid has a volume of 601.7 in^3.
C.
Frido’s pyramid is 8.1 times larger than Ricardo’s.
F.
Frido’s pyramid is 810% larger than Ricardo’s.
The only correct statements are:
Ricardo’s pyramid has a volume of 601.7 in³.
Frido’s pyramid is 8.1 times larger than Ricardo’s.
Options A and C are the correct answer.
We have,
The volumes of square pyramids.
V = (1/3) x s² x h
For Ricardo's pyramid,
s = 19 inches
h = 5 inches.
Substituting these values into the formula, we get:
V = (1/3) x 19² x 5
V ≈ 601.7 in³
Therefore, statement A is correct.
We do not have enough information to determine the volume of Frido's pyramid directly using the given formula.
However, we can use the fact that the volume of a pyramid is proportional to the cube of its linear dimensions (i.e., the length of its sides).
So if Frido's pyramid has a volume that is k times larger than Ricardo's, then the ratio of their corresponding linear dimensions (i.e., side lengths) will be:
(k)^(1/3)
Using this information, we can compare the volumes of the two pyramids:
Frido's pyramid / Ricardo's pyramid = k
(Frido's pyramid / Ricardo's pyramid)^(1/3) = (k)^(1/3)
We are given that Frido's pyramid has a volume of 4873.5 in³.
so,
k = Frido's pyramid / Ricardo's pyramid
k = 4873.5 / 601.7
k = 8.1
Therefore, statement C is correct.
We can also use this value of k to compare the sizes of the two pyramids in other ways:
Frido's pyramid is 7.1 times larger than Ricardo's (k - 1 = 8.1 - 1 = 7.1).
so statement D is incorrect.
Frido's pyramid is approximately 80.5% larger than Ricardo's.
[(k - 1) x 100%
= (8.1 - 1) x 100%
= 750%,
so statement E is incorrect.
Frido's pyramid is approximately 710% larger than Ricardo's
= k x 100%
= 810%
so statement F is incorrect.
Therefore,
The only correct statements are:
Ricardo’s pyramid has a volume of 601.7 in³.
Frido’s pyramid is 8.1 times larger than Ricardo’s.
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what is the best way to solve ratios
Answers
When looking at a ratio problem, the key pieces of information that you need are what the ratio is, whether you have been given the whole amount or a part of the whole and what you are trying to work out.
If you have been given the whole amount you can follow these steps to answer the question:
Add together the parts of the ratio to find the total number of shares.
Divide the total amount by the total number of shares.
Multiply by the number of shares required.
If you have been been given a part of the whole you can follow these steps:
Identify which part you have been given and how many shares it is worth.
Use equivalent ratios to find the other parts.
Use the values you have to answer your problem.
If you have $50,000 today and deflation is 5% each year. How much would you need in 20 years to have the same buying power?
Use the formula: A=P(1-r)1^
A 103,946,41
B 23,164,56
C 132,664,89
D 17,924,30
Answers
You would need about $17,924.30 in 20 years to have the same buying power as $50,000 today, assuming a 5% annual deflation rate.
Option D is the correct answer.
We have,
To calculate the future value of money adjusted for deflation, we can use the formula:
A = P(1 - r)^n
Where:
A = future value of money
P = present value of money
r = deflation rate
n = number of years
Plugging in the given values, we get:
A = 50,000(1 - 0.05)^20
Simplifying the expression inside the parentheses:
A = 50,000(0.95)^20
A ≈ 17,924.30
Therefore,
You would need about $17,924.30 in 20 years to have the same buying power as $50,000 today, assuming a 5% annual deflation rate.
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"In each case suppose R"" has usual norm. Decide whether the statement is true and give a reason for your answer: (a) In R, 2 € B.(-2) (b) In R. -1.5 € B (0) c) In R(1,5,0.5) € B.(-1,0) (d) In R."
Answers
This statement is incomplete and does not make sense. It cannot be evaluated as true or false without more information.
(a) In R, 2 € B.(-2)
False.
Explanation: The statement means that 2 is an element of the closed ball centered at -2 with radius 1. But this is not true since the distance between 2 and -2 is greater than 1 (|2 - (-2)| = 4).
(b) In R, -1.5 € B(0)
True.
Explanation: The statement means that -1.5 is an element of the closed ball centered at 0 with radius 1. Since the distance between -1.5 and 0 is less than 1 (|-1.5 - 0| = 1.5 < 1), the statement is true.
(c) In R(1,5,0.5) € B(-1,0)
False.
Explanation: The statement means that (1,5,0.5) is an element of the closed ball centered at (-1,0) with radius 1. But the distance between these two points is greater than 1, since
d((1,5,0.5), (-1,0)) = √[(1-(-1))^2 + (5-0)^2 + (0.5-0)^2] = √[4+25+0.25] = √29.25 > 1.
(d) In R.
True.
Explanation: This statement is incomplete and does not make sense. It cannot be evaluated as true or false without more information.
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How would you describe the following events, of randomly drawing a RED card OR a card with a NUMBER?
Question 6 options:
Independent
Conditional
Mutually Exclusive
Overlapping
Answers
The description of the statement is (b) inclusive.
Here, we have,
to describe the events:
The events are given as:
Drawing a red card
A card with a number
A red card can have a number and a numbered card can be a red card.
This means that
n(Red and Numbered) ≠ 0
Events that have similar features are referred to as inclusive events
Hence, the description of the statement is (b) inclusive
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The camp cook made 7 1/2 pints of baked beans. Each serving of beans is 5/6 of a pint. How many servings of beans did the cook make?
Answers
The cook made 9 servings of baked beans.
We have,
To find the number of servings of beans, we need to divide the total amount of baked beans by the number of baked beans per serving.
Total amount of baked beans = 7 1/2 pints
Amount of baked beans per serving = 5/6 pint
Number of servings of beans = (7 1/2) ÷ (5/6)
Converting 7 1/2 to an improper fraction:
7 1/2 = (2 × 7) + 1 = 15/2
Number of servings of beans = (15/2) ÷ (5/6)
To divide fractions, we can multiply by the reciprocal of the divisor:
Number of servings of beans = (15/2) × (6/5)
Number of servings of beans = 45/5
Number of servings of beans = 9
Therefore,
The cook made 9 servings of baked beans.
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A spinner is divided into 10 equally sized sectors. The sectors are numbered 1 to 10. A randomly selected point is chosen.
What is the probability that the randomly selected point lies in a sector that is a factor of 3?
Enter your answer in the box.
Answers
Answer:
0.2 or 20%-----------------------
There are two sectors that are factors of 3:
sector 1, sector 3So out of the 10 sectors, there is a 2/10 probability that the randomly selected point lies in one of these three sectors.
Therefore, the probability is 0.2 or 20%.
Answer:
20%
Step-by-step explanation:
For this question, we must find the numbers from 1-10 that are factors of 3. A factor is a number that, when multiplied by a specific number, gives a specific whole. For instance, in 2*4=8, 2 and 4 would be factors. The number 3 only has two factors: one and itself. Since two of the ten numbers are factors of 3, that is a rate of 2/10, 0.2, or 20%.
A data has 24 subgroups. 5 measurements were made per one subgroup. The sum of the subgroup averages is 160.25. The sum of the subgroup ranges is 2.19.
(1) Determine Trial central lines / Trial control limits on X bar chart and R chart.
In case of X bar chart, two values were out-of-control points and had assignable causes ( subgroup 4 - X bar value 6.65, subgroup 20 - X bar value 6.51)
In case of R bar chart, one value is out-of-control point and not part of natural variation. (subgroup 18 - R value 0.30)
(2) Determine Revised central lines / Revised control limits on X bar chart and R chart.
(Please show your calculation process logically )
Answers
The X bar chart, two values were out-of-control points and had assignable causes is 6.68 and Revised central lines / Revised control limits on X bar chart and R chart is 6.7364.
The X-bar chart, a form of Shewhart control chart, is used in industrial statistics to track the arithmetic means of subsequent samples of fixed size, n. For variables that may be monitored on a continuous scale, such as weight, temperature, thickness, etc., this sort of control chart is employed. For instance, one might sample five shafts from the production process once per hour, measure each shaft's diameter, and then display the mean of the five diameter values for each sample on a chart.
a) Here we are given that,
k=24
n=5
The sum of the subgroup averages is 160.25.
ΣΧ =160.25
The sum of the subgroup ranges is 2.19.
ΣR = 2.19
(1) Determine Trial central lines / Trial control limits on X bar chart and R chart.
Then,
[tex]\bar{\bar{X}}= \sum k=160.25/24=6.68[/tex]
Therefore,[tex]\bar{\bar{X}}=6.68[/tex]
b) Determine Revised central lines / Revised control limits on X bar chart and R chart.
From the statistical quality control chart
we get,
For, n=5
We have,
A₂=0.58
D₃=0
D₄=2.11
Revised Control limits for X -chart is,
[tex]UCLX =\bar{\bar{X}}+A2*\bar{R}=6.69+(0.58*0.08)=6.69+0.0464=6.6436[/tex]
[tex]CLX =\bar{\bar{X}}=6.69[/tex]
[tex]LCLX =\bar{\bar{X}}-A2*\bar{R}=6.69-(0.58*0.08)=6.69-0.0464=6.7364[/tex]
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Ashley keeps track of their fuel efficiency when they buy gas. The last time, they got 16.6 gallons and had driven 385 miles. What is the fuel efficiency? Select an answer Select an answer miles/gallo
Answers
Ashley's fuel efficiency is approximately 23.19 miles per gallon. To calculate Ashley's fuel efficiency in miles per gallon, you can follow these steps:
Step:1. Fuel efficiency = Miles driven / Gallons of fuel used Step:2. Fuel efficiency = 385 miles / 16.6 gallons Step:3. Fuel efficiency = 23.193 miles/gallon (rounded to three decimal places)
Therefore, Ashley's fuel efficiency for this particular fill-up was approximately 23.193 miles per gallon. This means that for every gallon of fuel used, Ashley's car was able to travel approximately 23.193 miles. It's important to note that fuel efficiency can vary depending on factors such as driving habits, vehicle condition, and fuel quality.
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A mathematics student decides to use
355
an approximation to of
113
Calculate his percentage error in using
this value, giving your answer in
standard form.
Answers
In a case whereby A mathematics student decides to use an approximation of π of 355/113 his percentage error in using this value, can be expressed as
How can the percentage error be calculated?Percent error (percentage error) can be described as the difference that can be established between experimental as well as theoretical value, which is been divided by theoretical value then find the multiplication by 100
The error can be calculad as (355/113 - π) / π
=8.5*10^-5
The percentage error = 8.5*10^-5*100 = 8.5*10^-6
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100 PTS solve for x ................
Answers
Answer:
x ≈ 36.2
Step-by-step explanation:
the segment from the vertex of the triangle to the base is a perpendicular bisector, then
consider the right triangle on the right with legs 15 and 33 , hypotenuse x
using Pythagoras' identity in the right triangle
x² = 15² + 33² = 225 + 1089 = 1314 ( take square root of both sides )
x = [tex]\sqrt{1314}[/tex] ≈ 36.2 ( to the nearest tenth )
Answer:
36.2
Step-by-step explanation:
The tick marks on the two sides of the triangle indicate that the sides are of equal length. Therefore, as the triangle has two sides of equal length, it is an isosceles triangle.
In an isosceles triangle, the altitude is the perpendicular bisector of the base. Therefore, the triangle is made up of two congruent right triangles with:
height = 33base = 30/2 = 15hypotenuse = xTo calculate the value of x, we can use Pythagoras Theorem:
[tex]\boxed{a^2+b^2=c^2}[/tex]
where:
a and b are the legs of the right triangle.c is the hypotenuse (longest side) of the right triangle.Substitute the values into the formula and solve for x:
[tex]\implies 15^2+33^2=x^2[/tex]
[tex]\implies 225+1089=x^2[/tex]
[tex]\implies 1314=x^2[/tex]
[tex]\implies x^2=1314[/tex]
[tex]\implies \sqrt{x^2}=\sqrt{1314}[/tex]
[tex]\implies x=36.2491379...[/tex]
[tex]\implies x=36.2\; \rm (nearest\;tenth)[/tex]
Therefore, the value of x is 36.2 units (nearest tenth).
Angle xzw ~ to angle xvy, find the perimeter of angle xzw
Answers
The perimeter of the triangle XZW is 176.4 units
Finding the perimeter of triangle XZWFrom the question, we have the following parameters that can be used in our computation:
The similar triangles
We start by calculating the missing side lengths using proportions
So, we have
YZ/32 = 28/40
So, we have
YZ = 32 * 28/40
YZ = 22.4
Next, we have
30/WZ = 40/(40 + 32)
So, we have
WZ = 30 * (40 + 32)/40
WZ = 54
The perimeter of triangle XZW is
P = 28 + 22.4 + 54 + 32 + 40
Evaluate
P = 176.4
Hence, the perimeter is 176.4 units
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Each of the following pay stubs represents two different employees use your understanding of income tax to complete the missing pieces
Answers
In most countries, including the United States, income tax is a tax imposed on an individual's income by the government. The amount of income tax paid typically depends on the amount of income earned and any deductions or credits that apply to the individual's tax situation.
A typical pay stub includes information such as the employee's gross pay (the amount earned before any deductions), the net pay (the amount received after deductions), and various taxes and deductions taken out of the employee's pay, such as federal income tax, state income tax, Social Security tax, and Medicare tax.
To complete the missing pieces on a pay stub, you will need to know the employee's gross pay and any deductions that apply to their tax situation. The amount of income tax withheld from an employee's pay depends on several factors, including their tax bracket, filing status, and any exemptions or deductions they are eligible for.
It's important to note that tax laws and regulations vary by country and even by state or province within a country, so the specific rules and calculations for income tax can differ depending on your location.
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3. Each of the following pay stubs represents two different employees. Use your understanding of income tax to complete the missing pieces.
LILY'S PAY STUB
GROSS INCOME
$865.00
FEDERAL TAXES
$110.32
=
MEDICARE (6%)
FEDERAL TAXES
$80.32
MEDICARE (6%)
SOCIAL SECURITY (1%)
SOCIAL SECURITY (1%)
$6.65
NET INCOME
MARK'S PAY STUB
GROSS INCOME
NET INCOME
in an if loop, a variable known as a counter variable is used to track the number of times a block of commands is run. true or false
Answers
True. A counter variable is often used in loops to track the number of times the loop has executed.
In programming, a counter variable is a variable that is used to keep track of the number of times a loop has executed. A counter variable is usually initialized to a starting value, and then incremented or decremented with each iteration of the loop. The loop continues to execute as long as the counter variable meets certain conditions.
The purpose of a counter variable is to allow a loop to repeat a specific number of times. For example, if you want to repeat a block of code 10 times, you can set a counter variable to 0, and then use a loop to execute the code until the counter variable reaches 10.
Counter variables are commonly used in programming languages that support loops, such as C++, Java, Python, and JavaScript. They provide a simple and effective way to repeat code without having to write the same statements over and over again.
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Which figure shows a line segment?
Answers
How does the graph of f(x) = (x − 8)^3 + 4 compare to the parent function g(x) = x^3? SHOW WORK!!!!!
Answers
Answer:
Step-by-step explanation:
g(x) = x^3 is the parent function starting at the origin (0,0)
f(x) is the translation of the g(x).
Your teacher taught you that y = (x - h)^3 + k
(h,k) is your shift.
(8,4) meaning right 8 on the x-axis and 4 up on the y-axis.
Jayclyn has 24 cupcakes. Out of the cupckaes, 1/3 of them have vanilla frosting. How many cupcakes have vanilla frosting
Answers
Answer:
8
Step-by-step explanation:
24 divided by 3 is 8
8 in each 1/3 so 8 vanilla
Make x the subject of y = 3√(x²+2) 15
Answers
The value of the equation in terms of x is x = [tex]\sqrt{\frac{y^2-270}{135}}[/tex].
Given is an equation, y = 3√(x²+2)15, we need to convert it in terms of x,
So,
y = 3√(x²+2) 15
Squaring both sides,
y² = 9 [(x²+2)15]
y² = 9 [15x²+30]
y² = 135x²+270
y²-270 = 135x²
y²-270 / 135 = x²
x = [tex]\sqrt{\frac{y^2-270}{135}}[/tex]
Hence, the value of the equation in terms of x is x = [tex]\sqrt{\frac{y^2-270}{135}}[/tex].
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A recent study found that the weight of a certain species of fish living in the Bahamas can be modeled by the function 0. 034213, where w is measured in grams and L, the length of the fish is measured in centimeters. Calculate the approximate length of a fish that weighs 250 grams. Round your answer to the nearest tenth of a centimeter.
L=____ centimeters
Answers
To solve this problem, we need to use the given function to find the length of a fish that weighs 250 grams. We can do this by setting the weight of the fish (w) to 250 grams and solving for the length of the fish (L):
w = 0.034213 L
250 = 0.034213 L
L = 250 / 0.034213
L ≈ 7304.4
Rounding to the nearest tenth of a centimeter, the approximate length of the fish is:
L ≈ 730.4 centimeters
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m=43. Given that b = -3 + (4 + m)ſ – Ã c = -9 + 12j – (3 + m)Ã , Q = (5 + m, 4,0 + m) and P = (-1,4 + m, -3). Find: a. The unit vector along the direction of a vector has Q as initial point and Pa
Answers
The unit vector along the direction from Q to P is:
(-6 - m)/√(m² + 10m + 45) i + m/√(m² + 10m + 45) j - 3/√(m² + 10m + 45) k
What is unit vector?
A unit vector is a vector that has a magnitude of 1 and is usually used to indicate a direction in a vector space.
To find the unit vector along the direction of a vector from point Q to P, we first need to find the vector from Q to P.
The vector from Q to P is given by:
P - Q = [-1 - (5 + m)]i + [4 + m - 4]j + [-3 - (0 + m)]k
= [-6 - m]i + m j - 3k
To find the unit vector along this direction, we need to divide this vector by its magnitude:
|P - Q| = √[(-6 - m)² + m² + (-3)²] = √(m² + 10m + 45)
So, the unit vector along the direction from Q to P is:
(-6 - m)/√(m² + 10m + 45) i + m/√(m² + 10m + 45) j - 3/√(m² + 10m + 45) k
(Note that we can simplify this expression by factoring out the common factor of √(m² + 10m + 45) from the numerator.)
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What is the relationship between lines a and b
Answers
The lines a and b is parallel to each other. So, the correct answer is A).
Parallel lines are two lines that are always the same distance apart and never meet, no matter how far they are extended. This means that they maintain the same distance between them at all points, and they have the same slope or gradient, but their lengths do not affect their parallel relationship.
Parallel lines are important in geometry and mathematics, and they have numerous real-world applications, such as in architecture, engineering, and design. In many practical situations, parallel lines are used to ensure that objects are straight, balanced, or level. So, the correct answer is A).
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