Answer:
False
Step-by-step explanation:
Without a graph, figure, or any other context the cost of grapefruit in 1995 in not related to the other years by any other facts or figures.
42. (a) find the unit vectors that are parallel to the tangent line to the curve y − 2 sin x at the point sy6, 1d. (b) find the unit vectors that are perpendicular to the tangent line. (c) sketch the curve y − 2 sin x and the vectors in parts (a) and (b), all starting at sy6, 1d.
Vectors is a quantity that has both magnitude and direction as well. A vector that has 1 magnitude is called unit vector. Unit vector is represented by the symbol '^'.
To find a Unit vector we divide the vector by its magnitude.
First find the slope of the tangent line, slope of a tangent line for a point f(x) is given by f'(x). Hence at point (π/6,1) where x = π/6, the slope of the tangent line is :
[tex]f(x)=2sinx\\f'(x)=2cosx\\f'(\pi /6)=2cos(\pi /6)=2.\frac{\sqrt{3} }{2}=\sqrt{3}[/tex]
The slope of the tangent line at this point is [tex]m=\sqrt{3}[/tex]
Finding a unit vector parallel to the tangent line. since slope is the ratio y and x then we can set an arbitrary vector with slope 4 by letting x=1 and y = √3 or v=[1,√3]. this vector has slope √3 and this is parallel to the tangent line, However this is not unit vector because its magnitude is not equal to 1 so we can divide this vector by its magnitude to find the unit vector.
[tex]u_v=\frac{v}{|v|} =\frac{1 \sqrt{3} }{\sqrt{1^{2}+(\sqrt{3})^2 } } \\=\frac{1}{\sqrt{4} } ,\frac{\sqrt{3} }{\sqrt{4} } =\frac{1}{2}, \frac{\sqrt{3} }{2} =[\frac{1}{2},\frac{\sqrt{3} }{2} ][/tex]
If a line has slope of m then all lines perpendicular of it will have a slope of -1/m
So we are looking for a unit vector of slope of -1/√3
Using the same logic we have unit vector that are perpendicular to the tangent line are [tex][\frac{\sqrt{3} }{2},-\frac{1}{2} ][/tex]
To learn more about vector,
brainly.com/question/28527185
#SPJ4
Mary used 10 2/3 yards of fabric to make 4 identical curtain panels.
What equation can be used to model the total number of yards of fabric, y. needed to make x curtain panels? Write the equation in the form
The equation that can be used to model the total number of yards of fabric, y. needed to make x curtain panels is y = (10 2/4 ÷ 4) × x
How to compute the expression?It should be noted that Mary used 10 2/3 yards of fabric to make 4 identical curtain panels.
Therefore, the equation that can be used to model the total number of yards of fabric, y. needed to make x curtain panels will be:
y = (10 2/4 ÷ 4) × x
where
y = number of yards
x = number of panels
Therefore, the equation is y = (10 2/4 ÷ 4) × x
Learn more about equations on:
brainly.com/question/2972832
#SPJ1
Answer quick please :)
Select the correct answer.
The first term of a geometric series is -3, the common ratio is 6, and the sum of the series is -4, 665. Using a table of values, how many terms
are in this geometric series?
OA 6
OB. 5
OC. 10
OD. 4
This geometric progression has 5 terms
This is a geometric progression or geometric series whose sum of n terms is given by the formula
Sn = a[([tex]r^{n\[/tex] – 1)/(r – 1)]
Where Sn is sum of n terms of geometric progression, a is the first term of the series , r is the common ratio
Here we are required to find the number of terms in the geometric progression whose first term is -3 and common ratio is 6
-4665 = -3 [( [tex]6^{n}[/tex]-1)/(6-1)
1555=( [tex]6^{n}[/tex]-1)/5
7775= [tex]6^{n}[/tex]- 1
7776 = [tex]6^{n}[/tex]
[tex]6^{5}[/tex] = [tex]6^{n}[/tex]
So, n=5
Therefore this geometric progression has 5 terms
To know more about geometric progression - https://brainly.com/question/4853032
#SPJ9
a couple decides to have 4 children. if they succeed in having 4 children and each child is equally likely to be a boy or a girl, what is the probability that they will have exactly 2 girls and 2 boys?
3/8 is the probability that they will have exactly 2 girls and 2 boys.
What does a probability mean?
The probability serves as a gauge for how likely an event is to occur. It gauges how likely an event is. P(E) = Number of Favorable Outcomes/Number of Total Outcomes is the formula for probability.Got to have 4 children
Boy and Girl are equally likely
Hence, P( boy) = P( girl) = 1/2
This is like performing binomial distribution.
P( excatly 2 boys and 2 girls)
=4C2(1/2)^2 (1/2)^2
=6/16
=3/8
Learn more about probability
brainly.com/question/11234923
#SPJ4
HELPS!!! WILL MARK BRAINLIEST!!!!
20x+50=150
Find x
Answer:
x = 5
Step-by-step explanation:
The table shows the results of an experiment in which three coins were tossed.
What is the experimental probability that all three of the coins will be heads? The theoretical probability?
The experimental probability that all three of the coins will be head is 1 / 10.
The theoretical probability that all three of the coins will be head is 1/8.
What are the probabilities?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.
Experimental probability is based on the result of an experiment that has been carried out multiples times.
Experimental probability = number of times all heads is gotten / total number of tosses
5/50 = 1/10
Theoretical probability = number of times all heads can be gotten / total number of possible outcomes
1/8
Please find attached the complete question. To learn more about probability, please check: https://brainly.com/question/13234031
#SPJ1
Which table represents a linear function?
An airplain flys and altitide of 30,000 feet to avoid the storm .
A. what integer represents the airplains change to avoid the storm ?
B.what integer represents the airplane s the change in altitude immedeitly after the passing the storm
A. The integer that represents the change of altitude to avoid the storm is 8,000
B. The integer representing the altitude after passing the storm is 30,000
How to illustrate the information?A. We are given that the initial altitude of the plane was 30,000 ft. The plane flew at at altitude of 38,000 feet
Change of altitude = final altitude - initial altitude
Change of altitude = 38,000 - 30,000 = 8,000 ft
Therefore, the integer representing the change of altitude to avoid the storm is 8,000
B. After the storm:
We know that, after the storm, the plane returned to its initial altitude. Given that the initial altitude is 30,000 ft, this would mean that the integer representing the altitude after passing the storm is 30,000
Learn more about integers on:
https://brainly.com/question/17695139
#SPJ1
Directions: Find the next five terms, then write a conjecture.
7. ⬆️,➡️,⬇️
Conjecture:
The next five terms are ← ↑ → ↓ ← and the conjecture is each arrow is rotated 90 degrees clockwise to get the next
How to find the next five terms, then write a conjecture?The first three terms are given as
↑ → ↓
From the above pattern, we have the following highlights:
Each arrow is rotated 90 degrees clockwise to get the next
Using the above as a guide, we have the next five terms to be:
← ↑ → ↓ ←
Also, we have the conjecture to be:
Each arrow is rotated 90 degrees clockwise to get the next
Read more about pattern at
https://brainly.com/question/16544803
#SPJ1
5. Susan is selling raffle tickets for $4. She collects a total of
$284. How mary tickets did she sell?
Bro each ticket is 4$. You just divide the money she earned with how much a ticket costs;
284/4 = 71 tickets
R
The following transformations are to be performed, in order, on the parallelogram.
• Translate 2 units in a positive y-direction.
. Translate 6 units in a positive x-direction.
• Reflect about the x-axis.
Which of the following describes the location of vertex Q after the transformations?
OA (2,-4)
B. (-2,-8)
C. (2,-8)
OD. (-2,4)
Determine the correct METRIC length of the cockroach in this image.
A 1.0 in
B 2.5 cm
C 7.5 cm
D 3.0 in
Answer:
B
Step-by-step explanation:
7.5cm - 5cm = 2.5cm
So it is B :)
Find the product of 3.2 x 1012 and 4.25 x 109. Write the final answer in scientific notation.
The product of the numbers written as a scientific notation is 1.36 × 10²²
Product of numbersFrom the question, we are to determine the product of the given numbers
The given numbers are
3.2 x 10¹² and 4.25 x 10⁹
The product of the numbers can be determined as shown below
3.2 × 10¹² × 4.25 × 10⁹
= 3.2 × 4.25 × 10¹² × 10⁹
= 13.6 × 10¹² ⁺ ⁹
= 13.6 × 10²¹
= 1.36 × 10¹ × 10²¹
= 1.36 × 10¹ ⁺ ²¹
= 1.36 × 10²²
Hence, the product of the numbers written as a scientific notation is 1.36 × 10²²
Learn more on Product of numbers here: https://brainly.com/question/28426966
#SPJ1
Write a method called listlength() that takes in a list of strings and returns a list of their lengths as integers. you must create a new list for your answer.
Following are examples of the listlength() methods -
listLength(list("Guava" "apple", "orange", "pineapple")) -> list(0, 1, 2, 3)listLength(list("HI")) -> list(2)listLength(list()) -> list()What is the function of listlength() method?It counts the string characters.
What are the different methods to get string length in python?Len(), a built-in method in Python, may be used to determine a list's size or length. The iterable that is accepted as an input by the len() function counts and returns the number of elements that are present in the list.Using a for loop in a Python program to determine the length of the list is seen as an antiquated or simple approach.The length hint() method in the Python operator module may be used to determine the total number of entries in a list.To learn more about string methods from given link
https://brainly.com/question/28290531
#SPJ4
The tangent function has asymptotes at where and where? and they occur every
? radians around the circle.
There are two vertical asymptotes at angles of 0.5π radians and 1.5π radians and it occurs every π radians.
What are the family of vertical asymptotes of the tangent function?
Tangent function is a kind of trigonometric function, that is, a kind of transcendent function. This function has a period of π radians and for f(x) = tan x, the vertical asymptotes are contained in the points:
x = 0.5π + i · 2π, where i is an integer.
Hence, there are two vertical asymptotes at angles of 0.5π radians and 1.5π radians and it occurs every π radians.
To learn more on tangent function: https://brainly.com/question/22161213
#SPJ1
Find the product (2x + 9) (9x + 11)
Answer:
Step-by-step explanation:
18x^2 + 22x + 81x + 99
18x^2 + 103x + 99
Awat Withdrawals $18 from his bank account once each day for five days what integer represents the change in amount in the account used pencil and paper find the true that would represent the changing them out the account if awat deposit $18 into his bank once each day for five days explain the difference between the integer for the withdraws and the integers for the deposit
-90
90
Since it is withdrawing, we are taking away -$18 every day for 5 days.
(-18)*5 = -90
Since it is a deposit, we are adding to the amount in her account, +$18 for 5 days.
18*5 = 108
The difference is that one is taking away and one is adding each day, resulting in negative or positive change.
An agreement with a bank to retain money and maintain transaction records. a plan for working with a firm on a regular basis. a set-up where a person uses a specific company's email or Internet services. The word "account" typically alludes to a ledger or record-keeping activity. In the financial sector, it can be used in a wide variety of ways. An account in banking is a contract whereby a company, generally a bank or credit union, takes a customer's financial assets and retains them on the customer's behalf at the customer's choice.
Savings accounts are one type of account that consumers can open to help them amass liquid assets.
To learn more about account form the given link:
https://brainly.com/question/22917325
#SPJ9
Find the coordinates of the midpoint of a segment with the given endpoints.
J(-11.2,-3.4), K(-5.6,-7.8)
The coordinates of the midpoint of a segment with the given endpoints (-8.4, -5.6)
How to find the coordinates of the midpoint of a segment with the given endpoints?The endpoints are given as
J(-11.2,-3.4), K(-5.6,-7.8)
The coordinates of the midpoint is calculated as
Midpoint = 0.5(x1 + x2, y1 + y2)
So, we have
Midpoint = 0.5(-11.2 - 5.6, -3.4 - 7.8)
This gives
Midpoint = (-8.4, -5.6)
Hence, the coordinates of the midpoint of a segment with the given endpoints (-8.4, -5.6)
Read more about midpoints at:
https://brainly.com/question/5566419
#SPJ1
write a phrase as an expression of 22 and a number a
Write the phrase as an expression the quotient of 22 and a number [tex]a[/tex].The quotient of 22 and [tex]a[/tex] number = 22/[tex]a[/tex]
Given that
number = 22
quotient = [tex]a[/tex]
To find
The mathematical equation or relation between quotient of 22 and a number [tex]a[/tex].
So according the question
We have
quotient = 22
divisor = [tex]a[/tex]
For finding the relation between given quotient and divisor, let's firstly know about Dividend, Divisor, Quotient and Remainder,
In Mathematics, the dividend is the value that is divided by another value to get the result. The dividend is the base of any division method.
An integer that divides another integer to obtain a result is called a divisor. The result of this division, or quotient, is the dividend, which is the original number that was divided.
Quotient = Dividend ÷ Divisor
When we divide one number by another, the result is a quotient. As an illustration, when we divide 6 by 3, we obtain the answer 2, which is the quotient. A decimal or an integer can both be used as the quotient. When dividing exactly, as when 10 ÷5 = 2, the quotient is an integer, whereas when dividing roughly, as when 12÷ 5 = 2.4, the quotient is a decimal. Although a quotient can be greater than the divisor, it will never be greater than the dividend.
The value remaining after division is known as the Remainder. After division, we are left with a value if a number (dividend) cannot be divided entirely by another number (divisor). This value is called the remainder.
Now, from question
We have a quotient of 22 that is [tex]a[/tex].
So, 22 fully divided by [tex]a[/tex].
In mathematical form,
= 22/[tex]a[/tex]
The quotient of 22 and [tex]a[/tex] number = 22/[tex]a[/tex]
To learn more about Dividend, Divisor, Quotient and Remainder please click on link:-
https://brainly.com/question/13024189
#SPJ4
the volume 216 whats the lenght in inches
Answer:
so i the answer is 216 only
Add.
7/4 + 2/3
help pls!!
Answer: 2 5/12
Step-by-step explanation: you multiply each number to 12 as the bottom number it’s hard to explain
The 4 inch radius pizza for $3 or the 8 inch radius pizza for $14 what is the better buy
By unitary method we can say that it is better to buy the 4 inch radius pizza for $3.
According to the given question.
The price of 4 inch radius pizza = $3
And, the price of 8 inch radius pizza = $14
As we know that, the unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Therefore, by unitary method.
Cost of 1inch radius pizza, when the price of 4 inch radius pizza is $3
= 3/4
= $0.75
And the cost of 1 inch radius pizza, when the price of 8 inch radius pizza is $ 14
= 14/8
= $ 1.75
Hence, by unitary method we can say that it is better to buy the 4 inch radius pizza for $3.
Find out more information about unitary method here:
https://brainly.com/question/22056199
#SPJ4
A student performs several experiments in which he swings a pendulum for 20-second duration. He uses a string that is 27 cm long, and he tests pendulum masses of different sizes, varying from 2 to 12 grams. He records the number of swings each pendulum makes in 20 seconds. What is the independent quantity and the dependent quantity.Be sure to include the appropriate units of measure
Using it's concepts, we have that:
The independent variable is the pendulum mass.The dependent variable is the number of swings.What is the relation between a function and the dependent and independent variables?A function has the following format: y = f(x).
In which each value of y is a function of one value of x, and thus, x is the independent variable and y is the dependent variable.
That is, the input of the function is the independent variable and the output is the dependent variable.
For this problem, we have that the number of swings is dependent on the mass of the pendulum, hence:
Number of Swings = f(mass).
Thus:
The independent variable is the pendulum mass.The dependent variable is the number of swings.More can be learned about dependent and independent variables at https://brainly.com/question/1429012
#SPJ1
A number cube labeled 1 through 6 is rolled.
What is the probability of the cube landing on an even number?
Answer: 3/6 or 1/2 or 50%
Step-by-step explanation: 1, 2, 3 4, 5, 6 are each face
2, 4, and 6 are even.
3 out of the 6 are even (3/6)
reduce (1/2)
1/2 = 50%
how do you factor x^6-27x^9 completely
Answer: -x^6(3x-1)(9x^2+3x+1)
Step-by-step explanation:
x^6-27x^9=
x^6(1-27x^(9-6))=
x^6(1-27x^3)=
-x^6(27x^3-1)=-x^6(3x-1)(9x^2+3x+1)
It cost Fawzia $12.00 to send 80 text messages. How many text messages did she send if she spent $19.95?
Answer: she would have sent 133 text messages
hope this helps
consider a sample with data values of 28, 26, 24, 15, 30, 34, 20, and 26. compute the range. 19 correct: your answer is correct. compute the interquartile range. 14 incorrect: your answer is incorrect. compute the sample variance. (round your answer to two decimal places.) 34.6 correct: your answer is correct. compute the sample standard deviation. (round your answer to two decimal places.) 5.9 correct: your answer is correct.
According to the given statement the values are:
The range = 19
Interquartile Range will be = 8.25
Sample Variance =33.93
Sample Standard deviation = 5.82
What is Interquartile Range?The dispersion of your data's middle quartile is measured by the interquartile range (IQR). It is the range for your sample's middle 50%. Assess geographical variability where the majority of your numbers are by using the IQR. Larger numbers suggest a wider dispersion of your data's center region.
According to the given data:
finding the range = Maximum value + Minimum value
= 34 - 15
= 19
The range = 19When ordering the observations, we obtain:
15,20,24,26,26,27,30,34
Where ,
n = 8
Q1=(n+14)the observation's term value
=(94)the observation's term value
=(2.25)the observation's term value
=2nd observation +0.25[3rd-2nd]
=20+0.25[24-20]
=20+0.25(4)
=20+1
=21
Q3=(3(n+1)4)the observation's term value
=(3⋅94)the observation's term value
=(6.75)the observation's term value
=6th observation +0.75[7th-6th]
=27+0.75[30-27]
=27+0.75(3)
=27+2.25
=29.25
Now finding the Interquartile Range
= Q3 -Q1
= 29.25 - 21
=8.25
The Interquartile Range will be = 8.25
Sample Variance S2=∑x2-(∑x)2nn-1
=5338-(202)28/7
=5338-5100.5/7
=237.57
=33.9286
Sample Variance =33.93
Sample Standard deviationS=√∑x2-(∑x)2nn-1
=√5338-(202)28/7
=√5338-5100.5/7
=√237.5/7
=√33.9286
=5.8248
Sample Standard deviation = 5.82
To know more about interquartile range (IQR) visit:
https://brainly.com/question/1029056
#SPJ4
The decimal representation of ___________ number neither terminates nor repeats.
The numbers that neither terminate nor repeat are called irrational numbers.
What are irrational numbers?
Any real number that is not rational is called an irrational number. These numbers can not be expressed in the form of p/q, where q is not equal to 0. Sometimes, irrational numbers are also called non-terminating and non-repeating numbers.
Filling the blank with an appropriate term
The decimal representation of ___Irrational__ number neither terminates nor repeats.
Hence, the answer is irrational.
To learn more about irrational numbers, visit here:
https://brainly.com/question/17106109
#SPJ4
What is the value of the expression when a = 6, b = 4, and c = 8?
2a3b−c
A.1
B.3
C.8
D.12
Answer: 27
Step-by-step explanation:
1. Solve: -3.9 + 2.7