Answers
a) Yes , the variable y varies directly with x
b) The constant of variation is k = 1/3
c) The function rule is given by the equation y = x/3
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be A
Now , the values of x are in set P = { 57 , 63 , 66 }
The values of y are in the set Q = { 19 , 21 , 22 }
a)
From the data set of P and Q , we can see that when the value of y increase the value of x also increases
Therefore , the value of variable y varies directly with x
And , y ∝ x
b)
The value of variable y varies directly with x
And , y ∝ x
So , y = kx
Substituting the value for x and y from the data set , we get
The equation will be
y = kx
19 = 57k
Divide by 57 on both sides of the equation , we get
k = 19 / 57
k = 1/3
Therefore , the constant of variation k is 1/3
c)
The function rule is given by the equation
y = kx
Substituting the value for k in the equation , we get
y = ( 1/3 ) x
y = x/3
Hence ,
a) Yes , the variable y varies directly with x
b) The constant of variation is k = 1/3
c) The function rule is given by the equation y = x/3
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Answer:
its six hundred men
Step-by-step explanation:
its Six hundred men, six hundred men under my command
With only one goal in mind
Make it back alive to our homeland
Six hundred men, six hundred miles of open sea
But the problem's not the distance
It's what lies in between
And Ithaca's waiting Ithaca's waiting
My kingdom is waiting The kingdom is waiting
Penelope's waiting for me
So full speed ahead, full speed ahead
Related Questions
If cos of Ф = 2/5, find sin Ф/2 and cos Ф/2. Assume the angles are in the 1st quartile
Answers
a. The trigonometric ratio sin(Ф/2) = +√(3/10)
b. The trigonometric ratio cos(Ф/2) = +√(7/10)
What are trigonometric ratio?Trigonometric ratios are the ratios of the sides of a right-angled triangle. They include
sinФ, cosФ, tanФ etcwhere Ф is the angle between the sides
a. How to find the trigonometric ratio sin(Ф/2)?Given that cosФ = 2/5, we use the trigonometric identity
cosФ = 1 - 2sin²(Ф/2)
Making sin(Ф/2) subject of the formula, we have
sin(Ф/2) = ±√(1 - cosФ)/2
So, susbstituting the value of cosФ = 2/5 into the equation, we have
sin(Ф/2) = ±√(1 - cosФ)/2
sin(Ф/2) = ±√(1 - 2/5)/2
sin(Ф/2) = ±√[(5 - 2)/5]/2
sin(Ф/2) = ±√(3/[5 × 2])
sin(Ф/2) = ±√(3/10)
Since Ф is in the first quartile, sin(Ф/2) = +√(3/10)
b. How to find the trigonometric ratio sin(Ф/2)?Given that cosФ = 2/5, we use the trigonometric identity
cosФ = 2coss²(Ф/2) - 1
Making sin(Ф/2) subject of the formula, we have
coss(Ф/2) = ±√(1 + cosФ)/2
So, susbstituting the value of cosФ = 2/5 into the equation, we have
coss(Ф/2) = ±√(1 + cosФ)/2
cos(Ф/2) = ±√(1 + 2/5)/2
cos(Ф/2) = ±√[(5 + 2)/5]/2
cos(Ф/2) = ±√(7/[5 × 2])
cos(Ф/2) = ±√(7/10)
Since Ф is in the first quartile, cos(Ф/2) = +√(7/10)
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2x^2 – 4x + 3 = 0 Solve using the quadratic formula
Please help i tried twice im so confused, nobody has the answer.
Answers
Answer: d = -8
Step-by-step explanation: look at the attached link
F and H are sets of real numbers defined as follows.
F = { v l v < 4}
H = { v l v ≥ 7}
Write F ∩ H and F ∩ H using interval notation. If the set is empty, write ∅.
Answers
The final interval notation is F ∩ H = [7, 4] & F ∪ H = [-∞, ∞].
What is the interval notation?
A set of real numbers known as an interval in mathematics contains all real numbers falling inside any two of the set's numbers. For instance, the interval containing 0, 1, and all integers in between is the set of values x satisfying 0 x 1.
We have,
F and H are sets of real numbers defined as follows.
F = { v l v < 4}
H = { v l v ≥ 7}
F is the set of all real numbers that are less than or equal to 4. H is the set of real numbers greater than 7.
F U H is the union (or combination) of the two sets, so it is the set of all real numbers that are less than equal to 3 or greater than 6:
F ∩ H is the set of real numbers that are in both sets; but since F is less than or equal to 4 and H is greater than 7, there are no numbers that are in both sets. Hence the answer is the empty set, Ø:
F ∩ H = Ø
F ∩ H = [7, 4]
F ∪ H = [-∞, ∞]
Hence, the final interval notation is F ∩ H = [7, 4] & F ∪ H = [-∞, ∞].
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I need your help please with this problem of math.
(14+8²)÷2-10
Answers
Answer: 29
Step-by-step explanation: your welcome
20. ASSESS REASONABLENESS Your friend says that when the pool in Exercise 19 is more than 8 feet deep, you will win the race. Is your friend's claim reasonable? Explain your reasoning. pls hurry
Answers
Answer:
Step-by-step explanation:
No because the deepness of an pool doesnt affect how fast you will swim during the race
No because the deepness of an pool doesnt affect how fast you will swim during the race.
What is the depth?
Depth refers to a type of vertical distance, where vertical distance is the difference between two vertical positions. One of the most common everyday examples of depth is its use in reference to water.
Here given that,
Your friend says that when the pool in Exercise [tex]19[/tex] is more than [tex]8[/tex] feet deep, you will win the race.
Our swimming speed will never change it does not depend on the depth of the pool.
Hence, depth of the pool does not effect the speed of swimmer.
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pythagorean theorem number search activity
Answers
Step-by-step explanation:
1). Red
x² = 98² - 44² = 9604 - 1936 = 7668
x =√7668 = 6√213
2) orange
X² = 31²+30² = 1861
x = √1861
can someone help me please?
Answers
let's consider two numbers for this case, hmmm say
x = 13
y = 17
so yes, 13 < 17
also true, 13 + 2 < 17 + 2
also true that 2(13) < 2(17)
now, -13 < -17? well, not quite
reason being, the on the negative side of the number line, the closer to 0, the larger the number, for that case, -1 is much much larger than -1,000,000.
Four scenarios of statistical studies are given below. Decide which study uses a sample statistic.
Answers
Based on the four scenarios of statistical studies given, a study which uses a sample statistic is: D. As part of her senior project, Kaisa asked 84 of her classmates if they voted in the last presidential election, 39 said yes.
What is a sample statistic?In Mathematics and Statistics, a sample statistic can be defined as a small piece of statistical information that is obtained by a researcher or scientist from the sample of a population.
This ultimately implies that, a sample statistic simply refers to any numerical quantity (figure) or data that is generated from the sample of a population by a researcher or scientist.
In this context, we can reasonably infer and logically deduce that 84 of Kaisa's classmates represent the sample of the total population while the 39 classmates who answered yes represent the sample statistic.
In conclusion, the statistical study that was conducted by Kaisa is a study that represent the sample statistic.
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Complete Question:
Four scenarios of statistical studies are given below. Decide which study uses a population parameter.
The average finish time for the Ironman, Kona was 11:32 for the 1883 finishers, with an average swim time of 1:14, an average bike time time of 4:14.
Lakeside Family Dentistry reported that 6 of the 15 patients who came in for a regular cleaning one day had at least one cavity.
Of 351 dog owners who were surveyed, 70 reported owning two dogs.
As part of her senior project, Kaisa asked 84 of her classmates if they voted in the last presidential election, 39 said yes.
A number is between 41 and46. It has prime factor of 2 and 11. What is the number?
Answers
Answer:
The required number lies between 41 and 46 and has prime factors of 2, and 11 is 44.
Step-by-step explanation:
The number lies between 41 and 46 are 42, 43, 44, and 45. From the straightforward observation and according to the condition that must be divisible by 2 and 11 there is only one number that is divisible by both 2 and 11 is 44.
I really need help on this!
Answers
The common ratio of given geometric sequence is r = - (1/2)
What is geometric sequence?A geometric sequence is a set of integers that follows a pattern where each term is multiplied by a fixed number called the common ratio, or r, to find the following term.
solution:
a3 = - (3/8)
a8 = 3/256
common ratio = a3 / a8
= - (3/8) / 3/256
common ratio = - (1/32)
a8/a3 = (ar^7) / (ar^2)
= r^5
r^5 = - (1/32)
r = - (1/2)
Hence the common ratio of given geometric sequence is r = - (1/2)
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How many solutions does the system of equations have?
Answers
Answer: IT can have simultaneous solutions
Step-by-step explanation:
You need to go through the cubic units and count them to get the answer
Answer:
2 solutions
Step-by-step explanation:
The solutions of the system of equations are the points of intersection of the two graphs, the red line and the blue parabola. Since there are two points of intersection, there are 2 solutions.
Answer: 2 solutions
What is the r2 value for the following data to three decimal places?
0.783 0.278 0.611 0.885
Answers
Answer:
0.783
Step-by-step explanation: got it right :)
How do you simplify the square ro
ot of 180 and how do you know that it is in simplest form?
Answers
Step-by-step explanation:
[tex] \sqrt{180 } = 6 \sqrt{5} [/tex]
because 6² = 36 and 36×5 = 180
I don't think there's any simple way to do it
What is the rate of change of the function?
Enter your answer as a number, like this: 42
Answers
Answer:
-2
Step-by-step explanation:
1. Identify two points with integer (not fraction or decimal) coordinates:
Ex: (0,5) and (3,-1)
2. subtract the y-coordinates: -1-5 = -6
and the x- coordinates (IN THE SAME ORDER): 3-0 = 3
3. divide the difference in y (-6) by the difference in x (3): -6/3 = -2
A college is currently accepting students that are both in-state and out-of-state. They plan to accept four times as many in-state students as out-of-state, and they only have space to accept 100 out-of-state students. Let x = the number of out-of-state students and y = the number in-state students. Write the constraints to represent the incoming students at the college.
x > 0 and y > 0
0 < x ≤ 100 and 0 < y ≤ 400
0 < x ≤ 100 and y > 400
0 < x and y < 100
Answers
The constraints to represent the incoming students at the college are -
0 < x ≤ 100 and 0 < y ≤ 400
What is an Inequality? What is a expression? What is a mathematical equation?An inequality in mathematics compares two values or expressions, showing if one is less than, greater than, or simply not equal to another value.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.We have a college is currently accepting students that are both in-state and out-of-state. They plan to accept four times as many in-state students as out-of-state, and they only have space to accept 100 out-of-state students
Now -
[x] = the number of out-of-state students
[y] = the number in-state students
y = 4x
0 < x ≤ 100
and the range of [y] will be -
0 < y ≤ (4 x 100)
0 < y ≤ 400
Therefore, the constraints to represent the incoming students at the college are -
0 < x ≤ 100 and 0 < y ≤ 400
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A coordinator will select 7 songs from a list of 11 songs to compose an event's musical entertainment lineup. How many different lineups are possible?
Answers
Answer:
Step-by-step explanation:
= 604800
The lines passing through which pairs of points have a positive y-intercept? Select all that apply. A (- 3, 10) and (1, 2) B (- 1, 6) and (0, 2) C (1, 2) and (3, 4) D (0, - 4) and (3, - 2) E (3, 1) and (5, 2)
Answers
The lines passing through points A (- 3, 10) and (1, 2) , B (- 1, 6) and (0, 2) , and C (1, 2) and (3, 4) has positive y-intercept.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
As we know, the slope formula is:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
A (- 3, 10) and (1, 2)
m = (2-10)/(1+3)
m = -8/4 = -2
y = mx + c
y = -2x + c
Plug (- 3, 10)
10 = -2(-3) + c
c = 10 - 6 = 4 (positive y-intercept)
Similarly, for the other points:
B (- 1, 6) and (0, 2)
y = -4x + 2 (positive y-intercept)
C (1, 2) and (3, 4)
y = x + 1 (positive y-intercept)
D (0, - 4) and (3, - 2)
y = 0.667x - 4 (negative y-intercept)
E (3, 1) and (5, 2)
y = 0.5x -0.5 (negative y-intercept)
Thus, the lines passing through points A (- 3, 10) and (1, 2) , B (- 1, 6) and (0, 2) , and C (1, 2) and (3, 4) has positive y-intercept.
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What two ways could you describe the shape pattern below?
ΔΟΔΟΔΟ
Answers
Answer:
The pattern is a repeated triangle and circle.
So, the next shape would be a triangle and a circle.
Step-by-step explanation:
If XY=16, XZ=14, JQ=6, and the radius of the circumscribed circle of triangle XYZ is 10, find QK
Answers
Check the picture below.
What is the probability that a point chosen at random in the triangle is also in the blue square?
Answers
Answer:
[tex]\dfrac{1}{3}[/tex]
Step-by-step explanation:
Divide the area of the square by the area of the triangle.
[tex]\dfrac{A_{\textrm{square}}}{A_{\textrm{triangle}}} = \dfrac{3^2}{(9\times 6)\div 2}[/tex]
And simplify.
[tex]= \dfrac{9}{54 \div 2}[/tex]
[tex]= \dfrac{9}{27}[/tex]
[tex]=\dfrac{1}{3}[/tex]
help meeeeeeeeeeeeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeee
Answers
Answer:
The quickest answer is to take the number 72 and divide it by the rate of interest. In this case, it would take approximately 72/6, or 12 years to double.
Step-by-step explanation:
here is the image of triangle ABC and its dilation using Center D and scale factor 2. Why is B'C' on the same line as its corresponing side segment BC
Answers
Since only the lengths increase by scale factor, B'C' on the same line as its corresponding side segment BC .
What is the Dilation?
Math definition of dilation Resizing an object is accomplished through a change called dilation. The objects can be enlarged or shrunk via dilation. A shape identical to the source image is created by this transformation. The size of the form does, however, differ.
The following are the properties of dilation of the triangle:
1)measures of the angles will not change
2)The sides of the image of the triangle are multiplied by the scale factor 2.
So,
A'B'=2AB
B'C'=2BC
A'C'=2AC
Since only the lengths increase by scale factor, B'C' on the same line as its corresponding side segment BC .
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638 divided by 34 long division
Answers
Answer:
18 R26
Step-by-step explanation:
[tex]\ \ \ \ \ \ \,\,\, 18 \textrm{ R}26\\{34\ \overline{\smash{)}\ 638}}\\\textrm{ } \ \ \ \underline{-34}\\\textrm{ } \ \ \ \ \ \, 298\\\textrm{ } \: \, \ \ \underline{-272}\\\textrm{ } \ \ \ \ \ \ \: \, 26[/tex]
5. Gary has walked 5 miles
already and continues
walking at a pace of 2
miles per hour. Write an
expression to represent
how many miles he has
walked.
Answers
Answer:210 miles
Step-by-step explanation:Gary walking in opposite directions will calculate how long it takes for him to be a given distance apart.
25 = 10x - 5
What’s the answer
Answers
Answer:
the answer would be x=3.
Step-by-step explanation:
when the x is supplemented for the 3, it comes out to 30. by then taking 5 from that, it brings the the number to 25.
Answer:
x = 3
Step-by-step explanation:
25 = 10x - 5
What’s the solution?
25 = 10x - 5
30 = 10x
x = 30 : 10
x = 3
----------------------
Check
25 = 10 x 3 - 5
25 = 30 - 5
25 = 25
the answer is good
Find the missing angle:
RPQ:________
Answers
The missing angle RPQ between the intersected chord is 115 degrees.
How to find the angle between intersected chord?The intersecting chords theorem is a statement in elementary geometry that describes a relation of the four line segments created by two intersecting chords within a circle
If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.
Therefore,
∠RPQ = 1 / 2 (arc angle RQ + arc angle SA)
arc angle RQ = 175 degrees
arc angle SA = 55 degrees
Hence,
∠RPQ = 1 / 2 (175 + 55)
∠RPQ = 1 / 2 (230)
∠RPQ = 115 degrees.
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Divide €45 between Sharon and Louise in the ratio of 4: 5.
Answers
Answer:
€20 for Sharon
€25 for Louise
Step-by-step explanation:
For a ratio of 4:5, you add 4+5 = 9.
You need 4 out of 9 parts for Sharon, and 5 out of 9 parts for Louise.
4/9 × €45 = €20 for Sharon
5/9 × €45 = €25 for Louise
Levi invested $8,500 in an
account paying an interest rate of 3.4%
compounded continuously. Assuming no deposits or withdrawals are
made, how much money, to the nearest ten dollars, would be in the
account after 18 years?
Answers
The amount of money after 18 years when the interest is compounded continuously is $15725.
What is compound interest?The process of calculating interest and reinvesting it in an account's balance over an infinite number of periods is known as continuous compounding.
Given that Levi invested $8,500 in an account paying an interest rate of 3.4% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest ten dollars?
The compound interest will be calculated as
[tex]P(t) = P_oe^{rt}[/tex]
[tex]P(t) = 8500\times e^{0.034\times 18}[/tex]
P(t) = 8500 x 1.85
P(t) = $15725
Therefore, the amount of money after 18 years when the interest is compounded continuously is $15725.
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Answer:15670
Step-by-step explanation:
What is the solution to the equation?
1/2n+3=6
n = 18
n = 9
n = 6
n=3/2
Answers
start by plugging them in to thr problem
1/2n+3-3=6-3
1/2n=3
n=6
Hope this helps
Avery earned a score of 310 on Exam A that had a mean of 350 and a standard deviation of 20. She is about to take Exam B that has a mean of 550 and a standard deviation of 40. How well must Avery score on Exam B in order to do equivalently well as she did on Exam A? Assume that scores on each exam are normally disturbed.
Answers
The score that Avery must get on Exam B is given as follows:
470.
What is the z-score formula?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.
For exam A, the mean and the standard deviation are given as follows:
[tex]\mu = 350, \sigma = 20[/tex]
She scored 310, hence the z-score of her grade is given as follows:
Z = (310 - 350)/20
Z = -2.
For exam B, the mean and the standard deviation are given as follows:
[tex]\mu = 550, \sigma = 40[/tex]
To do as well as on exam A, she needs a z-score of -2, hence the grade X is obtained as follows:
-2 = (X - 550)/40
X - 550 = -80
X = 470.
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