$2.50 is found to be the proportionality constant for the relationship between the length of track (in inches) and the cost in dollars.
Define the term constant of proportionality?The ratio connecting two given numbers in what is regarded as a proportional relationship is the constant of proportionality. Constant ratio, consistency index, unitary rate, constant variable variation, and even rate of change are other names for said constant of proportionality.Direct proportionality is represented by the equation y = kx.
Where:
dependent variable = yx = unrelated variableK is the proportionality constant.The price of the track is the dependent variable in this situation.
The tracks' length is an independent variable.
$16 = 6.4k
k = 16 / 6.4
k = $2.5
Thus, the constant of proportionality for the relationship between the length of track (in inches) and the cost in dollars is found as $2.5.
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The mean of a set of normally distributed data is 600 with a standard deviation of 20. What percent of the data is between 580 and 620?.
We know that 68.26% of data is between 580 and 620 using a normal distribution table.
What is a normal distribution?A data set must (when graphed) follow a bell-shaped, symmetrical curve that is centered around the mean in order to be regarded as having a normal distribution.
Additionally, it must follow the empirical rule that shows the proportion of the data set that lies within (plus or minus) 1, 2, and 3 standard deviations of the mean.
So, we know that:
μ = 600
σ = 20
Use the equation:
z - score = x-μ/σ
580 in the data's Z-score:
= 580-600/20
= -20/20
= -1
While the data's z-score in 620:
= 620-600/20
= 20/20
= 1
Using a table of the normal distribution:
P(580 < z) = 0.1587
Also, P(620 > z) = 0.8413
As a result, the percent of the data that falls between 580 and 620 is given by: P(620 > z) - P(580 z).
= 0.8413 - 0.1587
= 0.6826
= 68.26 %
Therefore, we know that 68.26% of the data is between 580 and 620 using a normal distribution table.
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An 8-ounce container of yogurt is on sale for $1.12. What is the cost of 1 ounce of yogurt?
Answer: $0.14
Step-by-step explanation: All we have to do is divide $1.12 by 8 to get our answer, that being $0.14.
HELP SOLVE!
name the property if 3x= 4 and 4=z then 3 =z
The name of the property is transitive property if 3x= 4 and 4=z then 3 =z.
What is a transitive property?According to the transitive property, "if two quantities are equal to the third quantity, then we can claim that all quantities are equal to each other." The term transitive refers to the act of transferring something. If a, b, and c are three quantities and an is connected to b by some rule and b is related to c by the same rule, then a and c are related to each other by the same rule; this is known as the transitive property of equality.
The transitive property of equality states that if a = b and b = c for any values of a, b, and c, then a = c. In other words, because a and c are both equal to the same item (in this case, b), they must be equal as well.
Given,
3x=4 and 4=z then 3=z
Here a=3, b=4, c=z
The name of the property is transitive property
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professional tennis players may constitute a(n) group for an amateur tennis player who identifies with certain players by imitating their behavior whenever possible despite the fact that the amateur tennis player does not qualify for membership as a professional tennis player because he/she has neither the skills nor the opportunity to compete professionally.
Professional tennis players may constitute a(n) symbolic group for an amateur tennis player
A symbolic group is one in which a person is unlikely to be accepted even if they act like a member by emulating their beliefs, attitudes, and behaviors. For young people, cricket players like Sachin Tendulkar, Sourav Ganguly, etc., may serve as a representative group. By concentrating on the small scale, symbolic interactionism examines the individual within a community and their relationships with others.
Similar to this, professional tennis players may serve as a symbolic group for an amateur tennis player who identifies with certain players by mimicking their behavior whenever possible, even though the amateur tennis player does not meet the criteria for membership in the category of professional tennis players because he or she does not have the necessary skills or access to the professional circuit.
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How much mut be depoited today into the following account in order to have $35,000 in 7 year for a down payment on a houe? Aume no additional depoit are made. An account with annual compounding and an APR of 4%
$17505 must be deposited today.
What is simple interest?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.
Variable principal payments, or the portion of your mortgage payment that goes toward the loan itself rather than interest, are what give compound interest its feel.
Simple or compound interest are also possible. A loan's or deposit's initial principal serves as the foundation for simple interest.
Contrarily, compound interest is calculated based on both the principal amount and the interest that is accrued on it each period. Simple interest is simpler to calculate than compound interest because it is only applied to the principal.
According to our question-
In order to calculate compound interest, we would use the formula A = P(1+r/n)nt.
Where A = the account's total balance at the end of t years, and r is the interest rate.
The periodic interval at which it was compounded is represented by n.
P stands for the principal, or the initial deposit amount.
Since it was compounded once a year, A = 30000 r = 8% = 8/100 = 0.08 and n = 1 according to the information provided.
t = year
In light of this, 30000 = P(1 + 0.08/1)1 7 30000 = P(1.08)7 30000 = 1.7138P
P = 30000/1.7138 \s P = $17505
Hence, $17505 must be deposited today
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what must be true for any direction if the instantaneous rate of change from (1,3,2) is equal to 0? what shape is formed by the collection of these vectors? (be as specific as you can.)
The instantaneous rate of change is the change in the rate at a particular instant and it is same as the change in derivative value at a specific point.
From the above given data, the following solution is given below:
Given:
Let f(x,y,z) = x³z - yz²
To find the partial derivatives of f
Here the directional derivative of a function f(x,y,z) is given by:
(df/dx , df/dy, df/dz)
df/dx = 3x²
df/dy = -z²
df/dz = x³ - 2yz
at points(1,3,2)
(df/dx)₍₁,₃,₂₎ = 3(1)² = 3
| (df/dx)₍₁,₃,₂₎ | = 3
(df/dy)₍₁,₃,₂₎ = -2² = 4
| (df/dy)₍₁,₃,₂₎ | = 4
(df/dz)₍₁,₃,₂₎ = 1³ - 2*3*2 = 1-12 = -11
| (df/dz)₍₁,₃,₂₎ | = 11
As we got the maximum modulus of derivative in direction of x. Since, therefore we should move into z direction to maximize the directional derivative.
(df/dz)₍₁,₃,₂₎ = -11
Hence, the instantaneous rate of change is the change in the rate at a particular instant and it is same as the change in derivative value at a specific point.
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The instantaneous rate of change is the change in the rate at a particular instant and it is same as the change in derivative value at a specific point | (∂f/∂z)₍₁,₃,₂₎ | = 11.
What is instantaneous rate of change?
The derivative value change at a particular point is the same as the instantaneous rate of change, which is the change in rate at a specific instant. The tangent line slope and the instantaneous rate of change at a given point on a graph are the same. That is, the slope is curved.
From the given data, the solution is given below:
Given:
Let f(x, y, z) = x³z - yz²
To find the partial derivatives of f
Here the directional derivative of a function f(x, y, z) is given by:
(∂f/∂x , ∂f/∂y, ∂f/∂z)
∂f/∂x = 3x²
∂f/∂y = -z²
∂f/∂z = x³ - 2yz
at points(1,3,2)
(∂f/∂x)₍₁,₃,₂₎ = 3(1)² = 3
| (∂f/∂x)₍₁,₃,₂₎ | = 3
(∂f/∂y)₍₁,₃,₂₎ = -2² = 4
| (∂f/∂y)₍₁,₃,₂₎ | = 4
(∂f/∂z)₍₁,₃,₂₎ = 1³ - 2*3*2 = 1-12 = -11
| (∂f/∂z)₍₁,₃,₂₎ | = 11
As we got the maximum modulus of derivative in direction of z. Since, therefore we should move into z direction to maximize the directional derivative.
(∂f/∂z)₍₁,₃,₂₎ = -11
Hence, The instantaneous rate of change is the change in the rate at a particular instant and it is same as the change in derivative value at a specific point.
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Complete question:
Complete question is attached below.
Solve: -5/6 + m = -3 1/6
m= -4
m= -2
m= -2 1/6
m= -2 1/3
Answer: -2 1/3
Step-by-step explanation:
Okay
A particle accelerates from rest with an acceleration of 3 ms2 to a speed V. It continues at
this speed for time T and then decelerates to rest at 1.5 ms. The total time for the motion
is 1 minute, and the total distance travelled is 1 km. Find a value for V.
The value for speed V is 188.15 m/s
How to find a value for V?It was given that a particle accelerates from rest with an acceleration of 3 m/s² to a speed V
It continues at this speed for time T and then decelerates to rest at 1.5m/s². The total time for the motion is 1 minute, and the total distance traveled is 1 km
During acceleration:
a = 3 m/s², at rest u = 0, t = T
V = u + at
V = 0 + 3T
V = 3T
During deceleration:
a = 1.5 m/s², t = 1 minute = 60 s, distance(s) = 1 km = 1000 m
V² = u² +2as
V² = (3t)² +2(1.5×1000)
V² = (3×60)² + 3000
V² = 32400 + 3000
V² = 35400
V = √35400
V = 188.15 m/s
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a waiter earned $300 in tips during his shift on friday. on saturday, he earned $335 in tips. what is the percent increase of his tips from friday to saturday?
The percent increase of his tips from Friday to Saturday is 35/3%.
T is equal to 112/3% as a mixed percentage fraction or 35/3% as an uncommon percentage fraction (decimal fraction: 0.116667)
PREMISES
T is the proportion of a waiter's tips that increased from $300 on Friday to $335 on Saturday.
CALCULATIONS
T=($335-$300)/$300
T=[($35/$300)100]%
T=[(7/60)100]%
T=[(7×100)/60]%
T=70/6%
A mixed percentage fraction of 112/3% or a percentage fraction of 35/3% (decimal fraction: 0.116667)
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Answer the picture in 5 minutes, please
Answer:
area of the isosceles triangle is [tex]60cm^{2}[/tex]
Step-by-step explanation:
three sides are a=10, b=13, c=13
Area of Triangle:
[tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]
where,
[tex]s=\frac{a+b+c}{2}[/tex]
[tex]s=\frac{10+13+13}{2}[/tex]
s = 18
now,
[tex]A = \sqrt{18(18-10)(18-13)(18-13)}[/tex]
[tex]A =\sqrt{9(16)(5)(5)}[/tex]
A = 3x4x5
[tex]A =60cm^{2}[/tex]
2x-y=1 , if x=-1 , then y=?
Answer: y=-3
Step-by-step explanation: In order to figure out what y would be in this problem, you would subtitute -1 in for x . and ask your self " What is 2* a -1? , The answer to that question would be -2 , ok. then the next step is to take the -2 and subtract by y which in case is 1 or -1 which will get you the answer of y=-3.
Hoped that helped!
For each relation, indicate whether the relation is a partial order, a strict order, or neither. If the relation is a partial or strict order, indicate whether the relation is also a total order. Justify your answers.
(a)
The domain is the set of all words in the English language (as defined by, say, Webster's dictionary). Word x is related to word y if x appears before y in alphabetical order. Assume that each word appears exactly once in the dictionary.
The domain is the set of all words in the English language that has a partial order relation and not a total order relation.
Given:
The domain is the set of all words in the English language (as defined by, say, Webster's dictionary.
Assume,
The domain is the set of all words in the English language (as defined by, say, Webster's dictionary). Word x is related to word y if x appears as a substring of y. x is a substring of y if all the letters in x appear in consecutive order somewhere in y. For example, "logical" is a substring of "topological" because the letters l-o-g-i-c-a-l appear consecutively in the order of the word "topological". However, "local" is not a substring of "topological" because the letters l-o are separated from c-a-l by the letters g and i.
Now, x is related to y if x is a substring of y.
Considering the following points through the example:
(A) Clearly, x is a substring of itself. Therefore, x is related to x and hence it is called reflexive.
(B) If x is related to y or y is related to x then x =y and it is called antisymmetric.
(C) If x is related to y and y is related to û then we can say that x is related to û (i.e. if x is a substring of y and y is a substring of û then x is also inscribed in û. Hence, we called it transitive.
Hence, the order is not the total order relation. It is a partial order relation.
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Identify the terms and like terms in the expression. 1/2s−4+3/4s+1/8−s3
HELP ME PLEASE TvT
1/2s, -4, 3/4s, 1/8 and -s³ are the terms and 1/2s and 3/4s are the like terms of the expression. 1/2s−4+3/4s+1/8−s³
What is Expression?An expression is combination of variables, numbers and operators.
Given expression is 1/2s−4+3/4s+1/8−s³
One by two times of s minus four plus three by four times of s plus one by eight minus s cube.
In the given expression minus, plus are the operators, s is the variable,
The expression has five terms
1/2s, -4, 3/4s, 1/8 and -s³ are the terms
Like terms contain the same variable which is raised to the same power.
In the given expression 1/2s and 3/4s are the like terms
Hence, 1/2s, -4, 3/4s, 1/8 and -s³ are the terms and 1/2s and 3/4s are the like terms of the expression. 1/2s−4+3/4s+1/8−s³
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A video game store uses a markup rate of 40% on a shipment of video games. The store paid $24 for each video game in the shipment. What is the retail price of each video game?
The retail price of each video game is $33.6
How to determine the retail price of each video game?From the question, we have the following parameters that can be used in our computation:
Markup rate = 40%
Amount paid = $24
The retail price of each video game can be calculated using the following equation
Retail price = Amount paid * (1 + Markup rate)
Substitute the known values in the above equation, so, we have the following representation
Retail price = 24 * (1 + 40%)
Evaluate
Retail price = 33.6
Hence, the retail price is $33.6
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A survey conducted asked 110 people what type of pets they owned. The results showed that 72 owned a dog, 58 owned a cat, and 37 owned both a dog and a cat. What is the probability of choosing a person who owns a dog or a cat? Enter your answer as a simplified fraction
The probability of choosing a person who owns a dog or a cat will be;
⇒ 0.845
What is mean by Probability?
The term probability refers to the likelihood of an event occurring.
Given that;
Number of peoples in survey = 110
And, The results showed that 72 owned a dog, 58 owned a cat, and 37 owned both a dog and a cat.
Now,
Since, Number of peoples in survey = 110
And, Number of peoples owns a dog or a cat = 72 + 58 - 37
= 93
Thus, The probability of choosing a person who owns a dog or a cat is,
Probability = 93 / 110
= 0.845
Therefore, The probability of choosing a person who owns a dog or a cat will be;
⇒ 0.845
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Which pairs of rectangles are similar polygons? select each correct answer.
Pairs 1 &2 are not similar whereas pairs 3&4 are similar.
The term "similarities" refers to pairs of objects whose corresponding sides have the same ratio. When two figures, such as the rectangles A and B, are given:
length A/length B equals width A/width B
We enter the values of the pairs in the formula above to determine which pairs are similar:
Pair 1
169/1.3=130
49/0.7=70
130 ≠70
therefore the first pair is not similar
Pair 2
18.55/5.3=3.5
10.5/3.5=3
Pair 2 is not similar
Pair 3
120/24=5
60/12=5
this implies that pair 3 is similar
Pair 4
189/2.1=90
81/0.9=90
this means that pair 4 is similar.
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5. Identify each of the following as convex or concave polygons:
Answer:
A) convex B) convex C) concave D) concave
Step-by-step explanation:
concave means going in on itself and convex is going outwards.
In this lesson, you sketched polynomial functions using factors and rewrote them in general form.
1 Use the factors to sketch each cubic function and label the zeros. Then rewrite the function
in general form.
F(x) = (x+3)(-x + 5)2 - 2x)
Answer:
check the attached file
Step-by-step explanation:
Unit 3 Parallel & Perpendicular Lines: Homework 3
Answer:
check the attached file
Step-by-step explanation:
Help me please with my homework Find the b and r
rhambus has four equal sides
so r+l=2r-4
r=5
b-3=r+l=6
b=9
Diamond adjacent angle complementation
So (x+2x+6)=180*
3x=174
x=58
All in all r=5 b=9 x=58 4b-6r=21-4=r+l=b-3=6
2x+6=122
this is the answer thank you when you have th problem you can tell me
-4/7+2/7x-14x+4/7
please answer the question with work :))
Answer: -13.7142x ≈ -13.72x
Step-by-step explanation:
Combine like terms. (-4/7) and (4/7) cancel each other out because you are subtracting the exact number you are starting with. So you are left with 2/7x - 14x. 2/7-14 = -13.7142 so the answer is -13.7142x. Depending on how you round, the number will be slightly different. You may want to round to the nearest hundredth or tenth place.
(I left out the x in the answer in the picture but it is supposed to be after the -13.7142)
The soccer team voted on what they wanted to eat. There are 20 members on the team. Six members voted for pizza, 10 voted for chicken, and the rest voted for hot dogs.
Which ratio represents the number of votes for hot dogs to chicken?
Responses
1/5
2/5
3/5
5/2
The ratio representing the number of votes for hot dogs to chicken is 2/5.
Define the term ratios of the number?An set of points of integers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is indeed an equation that sets two ratios at the same value.Ratios contrast two figures by ordinarily dividing them. A/B would be your formula if you were comparing each data point (A) to some other data point (B).For the stated question.
Total votes = 20.
Pizza = 6
Chicken = 10
Hot dogs = 20 - 16 = 4
Then,
Ratio = votes for hot dogs/ votes for chicken
Ratio = 4/10
Ratio = 2/5
Thus, the ratio representing the number of votes for hot dogs to chicken is 2/5.
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(t/f) true or false. with sample size greater than 30, the standard error of sample means is the same as sample standard deviation.
The standard error for sample means is equal to the sample standard deviation when the sample size is more than 30 is a "false" statement.
Define the term standard error?When comparing a population mean to a sample mean, the standard error of mean, called simply standard error, shows how dissimilar the two are likely to be.It reveals how much doing the sample mean could change if a study were to be repeated with fresh samples drawn from a single population.For the stated question-
Let's assume that our sample size is 30 and that the population standard deviation is 10.
standard error = 10/√30 = 1.83
Now let me use a sample size of 100 while keeping overall population standard deviation constant.
=10/10 = 1
It is obvious that with this sample size, the standard error will alter.
Therefore, when our sample size grows, the standard error will drop rather than stay the same.
Thus, the standard error for sample means is equal to the sample standard deviation when the sample size is more than 30 is a "false" statement.
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i nee help please and thankyou
Question 7
Using the secant-secant theorem,
[tex]4(x+4)=3(8) \\ \\ x+4=6 \\ \\ \boxed{x=2}[/tex]
Question 8
Using the intersecting chords theorem,
[tex]8(4x+2)=9(4x) \\ \\ 32x+16=36x \\ \\ 16=4x \\ \\ \boxed{x=4}[/tex]
The ratio of the number of students in the Chess Club to the number of students on the Math Team is 3:7.
There are 12 students in the chess club.
How many students are on the math team?
Answer:
28
Step-by-step explanation:
first, find out 12 / 3, which is 4
next multiply 4 by 7, which is 28
3:7 = 12:28
At a company meeting, there were 75 people in attendance. 68% of them were managers.
How many managers were in the meeting?
Answer:
There were 51 managers.
Step-by-step explanation:
First, turn the percentage into a decimal by moving the decimal point over twice to get 0.68. Then, set up this equation:
0.68 x 75 = 51 managers.
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 10 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
Kim had 4 chocolate chip cookies and 3 sugar cookies. Kim’s sister ate two of her chocolate chip cookies. Kim shared her remaining cookies with her brothers. How many cookies does one brother get?
Answer:
Your answer would be 1 chocolate chip cookie and 1.5 sugar cookie each.
Step-by-step explanation:
We know that Kim's sister ate two Chocolate Chip cookies, so: [tex]4-2 =2[/tex] and we also know that the rest of the cookies were shared by two people, so:
[tex]3[/tex] ÷ [tex]2 = 1.5[/tex] and [tex]2[/tex] ÷ [tex]2=1[/tex]
polynomial functions- Part 1
The volume of a right rectangular prism is (10x³ +21x² 25x+6) cubic meters, and the area of its base is
(10x² - 9x+2) square meters.
What is the height of the prism?
Enter your answer in the box.
meters
Answer:
Below
Step-by-step explanation:
base * height = volume
volume / base = height
divide 10x^2-9x+2 INTO 10x^3 + 21x^2 MINUS 25x +6
( you left out the minus sign in your post)
to get height = x+3
Simplify and show work
Hence, the simplification is [tex]27-18i[/tex].
What is the equation?
The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
Here given equation is
[tex](-4+i)(-6+3i)[/tex]
then,
[tex]-4(-6+3i)+i(-6+3i)\\\\=24-12i-6i+3\\\\=24-18i+3\\\\=27-18i[/tex]
Hence, the simplification is [tex]27-18i[/tex].
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In a city in Ohio, the sales tax rate is 7.25% . Complete the table.
if the sales tax is 1.16 what is the price before tax and the price including the tax
Answer: $17.16
Step-by-step explanation:
To find the cost of the untaxed money, you have to divide your sales tax amount by the tax rate.
1.16÷.0725=16
Once you have your untaxed amount, you then add your sales tax to your untaxed amount,
16+1.16=17.16