Answers
As k₁ = k₂ = k₃, the table represents a linear relation whose constant of variation is - 4.
Does the table represent a linear relation?
A table between two variables represents a linear relation if and only if every pair of values (x, y) have the same constant:
k = y/x (1)
Now we proceed to check the existence of the constant of variation:
k₁ = 8/(- 2) = - 4
k₂ = (- 16)/4 = - 4
k₃ = (- 36)/9 = - 4
As k₁ = k₂ = k₃, the table represents a linear relation whose constant of variation is - 4.
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Related Questions
QUESTION 2
Which of the following is a quantitative variable?
Amount in fluid ounce of coffee
Name of a cell phone carrier
O Occupation
Anxiety rating (highly anxious, moderately anxious, or relaxed)
Answers
Answer:
Step-by-step explanation:
Amount in fluid ounce of coffee
Its the only one that deals with numbers
A sports center offers party packages. They advertise a flat rate of $325 for the first 10 guests. They charge $15 per person for each additional guest. A formula for the cost of the party is:
C = 325 + 15p
where p is the number of guests more than 10. (For example, if 12 people come to the party, p = 2.) Suppose you want to have a huge birthday celebration this year. However, you have budgeted $600 for your party. How many guests can you invite if you decide to have your party at this sports center?
Answers
Using the given linear equation, we conclude that you can invite a maximum number of 21 guests.
How many guests can you invite if you decide to have your party at this sports center?Here the function is:
C(p) = 325 + 15*p
Where p is the number of guests minus 10, now we know that your budget is $600, then the maximum value of guests allowed is such that:
C(p) = 600 = 325 + 15*p
Now we can solve this equation for p:
600 - 325 = 15*p
275 = 15*p
175/15 = p = 11.67
Then the maximum whole number that p can take is p = 11
This means that the maximum number of guest that you can have is:
Guests = 10 + p = 10 + 11 = 21.
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Henry wants to laminate the tabletop in his study room. The tabletop is the shape of an isosceles trapezoid shown here. If laminating costs $4 per square foot, what is the total cost to laminate the tabletop?
A trapezoid with a height of 3 feet and bases of 6 feet and 10 feet is shown.
Answers
The total cost to laminate the tabletop is $96.
What is the total cost to laminate the tabletop?The first step is to determine the area of the trapezoid.
Area of the trapezoid = 0.5 (sum of parallel sides) x height
0.5 x (6 + 10) x 3 = 24 feet²
The total cost of laminating = cost per square feet x area
$4 x 24 = $96
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Which ordered pair below is a solution to the following system of equations? x + 2y = 7 2x − y = -1
Answers
Answer: (1,3)
Step-by-step explanation:
Let's solve this system of equations by elimination. We will multiply one or both equations such that when we combine the equations, one of the variables will completely cancel out.
Let's multiply the whole first equation by -2 to achieve this:
[tex]-2(x+2y=7)[/tex] now becomes [tex]-2x-4y=-14[/tex]
Now let's add both equations
[tex]-2x-4y=-14[/tex]
[tex]2x-y=-1[/tex]
[tex]-5y= -15[/tex]
Since we got y into a form we can solve it for, lets divide both sides by -5 to isolate it.
[tex]\frac{-5y}{-5} = \frac{-15}{-5}[/tex]
[tex]y=3[/tex]
Now that we have the value of y, we can substitute it into any equation to solve for x. Only if we have both x and y can we make an ordered pair. Let's use the second equation and substitute 3 for y.
[tex]2x-3=-1[/tex]
We can now solve for x.
[tex]2x=2[/tex] [Adding 3 to both sides]
[tex]x=1[/tex] [Dividing by 2 on both sides]
We now have both x and y, so we can put it in an ordered pair to answer the question.
[tex](1,3)[/tex]
what percent of 74.39 is 8 %
Answers
Answer:
5.9512
Step-by-step explanation:
1. Convert the percentage to decimal
8% = 8/100 = 0.08
2. Multiply the decimal by the quantity to be extracted
(0.08)(74.39) = 5.9512
Hope this helps
Graph the parabola.
y=x^2
Plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex.
Then click on the graph-a-function
button.
Answers
Answer:
Vertex: (0,0)
Left 2 points: (-1,1) , (-2,4)
Right 2 points: (1,1) , (2,4)
Step-by-step explanation:
i know i just posted two in a row but im slow and im doing a test so expect more later
Answers
Answer:
D. is the answer of your questions
Combine like terms to simplify the following polynomial.
5a²b+7ab² +9c+ 11a²b-3ab² - 9c
Answers
Answer:
5a²b + 7ab² + 9c + 11a²b - 3ab² - 9c
= (5a²b + 11a²b) + (7ab² - 3ab²) + (9c - 9c)
= 16a²b + 4ab²
to shift the graph of an equation a certain number of units down, you need to ______ the function equation
Answers
Answer:
Step-by-step explanation:
...You need to subtract that number of units from the function equation.
Example: given y = x^2, and wanting to shift the entire graph down 3 units, we subtract 3 from y = x^2, obtaining y = x^2 - 3.
Find the decimal. _. _ _ _ Clues: (a) The digits 0, 1 and 2 are not used in the decimal. (b) The digit in the ones place is the greatest 1-digit number. The hundredths digit is smaller than 5. The difference between the tenths digit and the ones digit is the hundredths digit. (c) (d) (e) (f) The thousandths digit is greater than 5 and is an odd number. All the digits are different.
Answers
Answer:
Step-by-step explanation:
143
or
121
We are accepting
does any of this help
first prime factor....
Answers
Answer:
The first 10 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.
The sum of the digits of a two-digit number is 5. If nine is subtracted from the number, the digits will be reversed. Find the number.
Answers
The number whose sum of the digits of a two-digit number is 5. If nine is subtracted from the number, the digits will be reversed is 32
Equationx = tens digit y = ones digitthe number can be expressed as 10x + y
x + y = 5
nine is subtracted from the number(10x+y) - 9
= 10y+x
x + y = 5
9x - 9y = 9
x + y = 5
x - y = 1
Add the equations
2x = 6
x = 6/2
x = 3
substitute into
x + y = 5
3 + y = 5
y = 5 - 3
y = 2
Therefore, the unknown number is 32.
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27. Which is wrongly spelt? A. reliable B. sociable C. viable D. avialable
Answers
Answer:
D. Avialable
Step-by-step explanation:
the correct spelling is available :)
The answer is D.
The correct spelling of the word in the given option is : Available
Instead, here the places of a and i have been interchanged, causing it to be misspelt.
The graph shows f(x)and its transformation(x).
Enter the equation for g(x) in the box.
g(x) =
Answers
Using translation concepts, the equation for function g(x) given in the graph is:
[tex]g(x) = 2^{x + 2}[/tex]
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
The parent function for this problem is given as follows:
[tex]f(x) = 2^x[/tex]
From the graph, function g(x) was shifted 2 units left, hence x -> x + 2 and the definition is:
[tex]g(x) = 2^{x + 2}[/tex]
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mrs.kingsleys has 102 inches of ribbon for her crafts she cut the ribbon into 8 pieces of equal length which statment best explains how mrs. kingsley cut the ribbon
Answers
Mrs Kingsley cut the ribbon into a length of 12.75 inches each.
How did Mrs Kingsley cut the ribbon?
Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷.
Length of each ribbon = 102 / 8 = 12.75 inches
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Mathematics word problem
Answers
75 miles per hour is the rate of train.
what is the formula of speed?Formula of speed = distance/time
let,
s1 , speed of A train = s
s2, Speed of B train = s
t1, time of travel for train A = 2.5h
t2, time of travel for train B = 4 h
d1, distance traveled by train A
distance travel by train A = speed*time
= s1*t1
d2, distance traveled by train B
distance travel by train A = speed*time
= s2*t2
Total distance between station A and station B = 562.5 mi
d1+d2=562.5 mi
s1t1+s2t2=562.5
s(2.5)+s(4)=562.5
6.5 s = 562.5
s = 562.5/6.5
s = 86.5 mph
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75 miles per hour is the rate of the train.
what is the rate of the train?Given:
Train A and Train B leave a central station at the same time.They travel at the same speed, but in opposite directions, with train A heading towards station A.Train B heading towards station B.Train A reaches station A after 2 and 1/2 hours.Train B reaches station B after 4 hours.Station A and Station B are 585 mi apart.Find:
Rate of the trains.Solution:
Formula of speed = distance/time
Let us consider
Speed of A train(s1) = s
Speed of B train(s2) = s
Time of travel for train A(t1) = 2.5h
Time of travel for train B(t2) = 4 h
Distance traveled by train A(d1)
= speed*time
= s1*t1
Distance traveled by train B(d2)
= speed*time
= s2*t2
The total distance between station A and station B = 562.5 mi
d1+d2=562.5 mi
s1t1+s2t2=562.5
s(2.5)+s(4)=562.5
6.5 s = 562.5
s = 562.5/6.5
s = 86.5 mph
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What is the solution of p - 12 > -18
p> -30
p<-6
p> -6
p < -30
Answers
Answer:
p > -6
Step-by-step explanation:
1) Add 12 to both sides.
p > -18 + 12
2) Simplify -18 + 12 to -6.
p > -6
Which of the following are equations for the line shown below? Check all that
apply.
(-2,-5)
(2,5)
A. y + 5 = 2.5(x+2)
B. y-5=2.5(x-2)
C. y-2=2.5(x - 5)
D. y+2=2.5(x+5)
Answers
Answer:
A
Step-by-step explanation:
A small company has 6 employees with associate degrees, 2 employees with bachelor's degrees, and 8 employees with master's degrees. If a single employee is picked at random, what is the probability that he or she has a bachelor's or a master's degree
Answers
Using it's concept, there is a 0.625 = 62.5% probability that he or she has a bachelor's or a master's degree.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
The company has 6 + 2 + 8 = 16 employees, out of which 2 + 8 = 10 have a bachelor's or a master's degree, hence the probability is:
p = 10/16 = 0.625.
0.625 = 62.5% probability that he or she has a bachelor's or a master's degree.
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find the lcm of 48,64,72,96,108
Please help me fast i will give you50 pts
Answers
2|48,64,72,96,108
2|24,32,36,48,54
2|12,16,18,24,27
2|6,8,9,12,27
2|3,4,9,6,27
2|3,2,9,3,27
3|3,1,9,3,27
3|1,1,3,1,9
3|1,1,1,1,3
LCM
2⁶×3⁴64×815184en una fiesta hay 16 personas de las cuales el 25% son mujeres, luego llegan mas mujeres a la fiesta, de tal manera que ahora los hombres son el 60% ¿cuantas mujeres llegan a la fiesta?
Answers
Answer:
English (Ingles):
10 Women come to the party.
Spanish (Espanol):
10 Las mujeres vienen a la fiesta.
Step-by-step explanation:
English (Ingles):
We know that there are 16 people there at the start. 25% of those people are women. We can work out by subtracting 100 by 25 that 75% of the p-eople there are men. We need to do 25% of 16 so we can work out how many men and women there are there.
So we find 10% of 16 which is 1.6 then we take off 5% of 1.6 which is 0.08. We then double 1.6 to get 20% which gives us 3.2. We now add on the 5% to make it 25% which gives us 4.
This means 25% of 16 is 4.
This tells us that there are 4 women at the party and 12 men as 16 - 4 = 12.
It now says that more women arrive which makes the percentage for men go down to 60%. We now need to add 5% on to the 25% of women there are which will tell us how many more women there are now and it will let us work out how many women and men there are in total now.
As we can't do this without it giving us 4.8, we know that 25% of people is 4 women which means 50% of people would be 8 women and we make an estimate of how many women have joined which gives us 6 people which means the total amount of women at the party is 10.
Spanish (Espanol):
Sabemos que hay 16 personas allí al principio. El 25% de esas personas son mujeres. Podemos calcular restando 100 por 25 que el 75% de las personas son hombres. Necesitamos hacer el 25% de 16 para poder calcular cuántos hombres y mujeres hay allí.
Así que encontramos el 10 % de 16, que es 1,6, luego quitamos el 5 % de 1,6, que es 0,08. Luego duplicamos 1,6 para obtener el 20%, lo que nos da 3,2. Ahora sumamos el 5% para convertirlo en 25%, lo que nos da 4.
Esto significa que el 25% de 16 es 4.
Esto nos dice que hay 4 mujeres en la fiesta y 12 hombres como 16 - 4 = 12.
Ahora dice que llegan más mujeres lo que hace que el porcentaje de hombres baje al 60%. Ahora necesitamos agregar un 5% al 25% de mujeres que hay, lo que nos dirá cuántas mujeres más hay ahora y nos permitirá calcular cuántas mujeres y hombres hay en total ahora.
Como no podemos hacer esto sin que nos dé 4.8, sabemos que el 25% de las personas son 4 mujeres, lo que significa que el 50% de las personas serían 8 mujeres y hacemos una estimación de cuántas mujeres se han unido, lo que nos da 6 personas que significa que la cantidad total de mujeres en la fiesta es 10.
you can correct your mistake.
Oliver flipped a coin 10 times. The
outcomes are shown in the table below.
a) Work out the experimental probability of
the outcome being heads. Give your
answer as a decimal.
b) Using one of the options below, copy
and complete the sentence to explain how
Oliver could improve his experiment to get
a better estimate for the probability.
a)
Outcome Frequency
Heads
7
Tails
3
b) He could improve his experiment by
using a different coin
wearing a hat
flipping the coin outside
doing more coin flips
doing fewer coin flips
Answers
a) The probability of a head exists at 0.7.
b) He could improve his experiment by doing more coin flips.
What is probability?Probability signifies possibility. It exists a branch of mathematics that values the event of a random event. The value exists represented from zero to one.
Given: Coin flipped 10 times.
The Head comes T times and the tail comes 7 times.
To estimate the probability of head in the outcome.
The total number of outcomes is 10 and the head comes 7 times.
a) Probability(head) = 7/10 = 0.7
The probability of a head exists at 0.7.
b) He could improve his experiment by doing more coin flips
Therefore, the correct answer is option c) doing more coin flips.
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PLEASE HELP 100 POINTS!! Solve the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate and show ur work.
Answers
Answer: 100
Step-by-step explanation:
1. A boat drifted 15 m out into the water off Ocean Beach, where the shore drops off
at 4°. Can Brooke walk out to bring the boat back without getting water over the
tops of her hip boots which are 1 m tall? Explain your reasoning.
2. are the engineer who designed a new branch for the Mountain Railroad
Company. You sent your plans calling for 100 km of track up Bixby Mountain
taking trains 99 km east of the city of Bixby, to the City Council for approval.
But before the Council got around to looking at your plans, they passed a
regulation that no railroad tracks could go up their mountain at an angle of more
than 8°. Will your plans be approved? Why or why not?
3. The residents of Quietville, a little town 9 km from the San Francisco Airport,
insist that any plane flying over their town disturbs them if it is lower than 3 km.
Will a plane that took off at a 21° angle disturb them? Why?
4. You are an air pollution inspector, checking that factories in your city have
chimneys at least 65 m tall. Standing 50 m from the Ore Smelting Company’s
chimney, you find the angle from the ground to the chimney top is 51°. Can the
company use that chimney legally? Explain.
6. River City is offering a $3 million contract to build a bridge between points A and
C on opposite sides of City River. Along the side of the river that makes a right
angle with the line of the bridge at point C, a surveyor walked 72 m to point B
where she measured the 55° angle form B to A. Long Company will build the
bridge for $3 million if it is not more than 103 m from point A to point C. Short
Company agrees to build it if it is no more the 100 m. Which contracting firm
will be awarded the contract? Why?
7. An elderly woman is trapped 17 m up in her burning home. Can a fireman reach
her on his 26 m ladder if it has to make a 43° angle in order to clear the woman’s
greenhouse under her window? Explain your reasoning.
8. A ski lift 1000 m long goes at a 29° angle up Mt. Gentleslope. Does the lift take
skiers all of the way up to the top of the mountain where there is a snack bar at
the 500 m elevation? Explain your reasoning.
9. Mr. Johnson is a jet pilot who just moved with his family to Suburbia, 26 km
from Toledo Airport. His seven-year-old son, Eric, would like to see his father’s
plane as it flies over their new home for the first time today, but there is a layer of
clouds 5 km above the house. Will Eric be able to see his Dad’s plane if it takes
off at a 9° angle? Explain.
10.You are the cost control expert for an engineering firm designing a giant
television tower having several metal braces, each built in 21 m from the base at a
73° angle with the ground. Part of your job is to decide which standard length of
metal brace wastes less metal: the brace that comes 71 m long, or the one that is
73 m long. What is your decision?
Answers
The correct responses found using trigonometric ratios are as follows;
Brooke's cannot bring the boat back without getting water over her boots.The plan will not be approvedThe plane will not disturbThe company can not use the chimney legallyThe Long company will build the bridgeThe fireman can reach her.The lift does not take the skiers up to the bar.Eric will be able to see his Dad's plane.The 73 m. braceHow can trigonometric ratios be used to find the right responses?1. The depth of the water = 15 × tan(4°) = 1.049 m
The height of Brooke's boot = 1 m
Therefore;
Brooke's cannot bring the boat back without getting water over her boots.2. The angle of elevation of the plan = arccos(99/100) ≈ 8.110°
Given that the angle of elevation the plan, 8.110°, is more than 8° limit, we find;
The plan will not be approved.3. Height reached by the plane = 9 × tan(21°) = 3.455
Therefore;
The plane will not disturb.4. Height of the chimney at the factory = 50 × tan(51°) = 61.745
The minimum chimney height = 65 m.
Therefore;
The company can not use the chimney legally.6. Length of the bridge = 72 × tan(55°) ≈ 102.83
Therefore;
The Long company will build the bridge because it is longer than 100 m. but not more than 103 m.7. Height reached by the ladder = 26 × sin(43°) ≈ 17.7
Therefore;
The fireman can reach her.8. Height reached by the ski lift = 1000 × sin(29°) ≈ 484.8
Therefore;
The lift does not take the skiers up to the bar.9. Height reached by plane = 26 × tan(9°) ≈ 4.12
The plane flies under the cloud therefore;
Eric will be able to see his Dad's plane.10. Length required for the metal brace = 21/(cos(73°)) ≈ 71.83
Therefore;
The brace that wastes less metal is the 73 m. brace, because the 71 m. brace is not long enough and two braces will be required.Learn more about trigonometric ratios here:
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Which choice is equivalent to the product below?
√14•√10
A. 2√35
B. 4√7
C. 35
D. 4√35
Answers
Therefore, the answer is option A
Can you help me in my work
Answers
Answer:
2-2 goes with 1 - 1
10 - 7 goes with 8 - 5
4 - 3 goes with 7 - 6
8 - 2 goes with 9 - 3
9 - 5 goes with 5 - 1
Have a nice day.
I am Clara btw.
Step-by-step explanation:
As an introduction to probability, a student asked to roll a fair, six sided number cube seven times the results of those seven rolls are shown below 1,4,4,4,4,6,5 what is the standard deviation of the data?
Answers
Using it's concept, the standard deviation of the data is of 3.742.
What are the mean and the standard deviation of a data-set?The mean of a data-set is given by the sum of all values in the data-set, divided by the number of values.The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the number of values.For this data-set, the mean is:
M = (1 + 4 + 4 + 4 + 4 + 6 + 5)/7 = 4.
Hence the standard deviation is:
[tex]S = \sqrt{\frac{(1 - 4)^2 + (4 - 4)^2 + (4 - 4)^2 + (4 - 4)^2 + (4 - 4)^2 + (6 - 4)^2 + (5 - 4)^2}{7}} = 3.742[/tex]
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What is the value of the expression below when y = 4?
Answer:
6y²-7y+9
Submit Answer
Answers
We are given a Student's t distribution with d.f. = 11 and t = 1.910. We wish to find an interval containing the corresponding P-value for a two-tailed test. To do this, we will use the Critical values for Student's t Distribution. Below is an excerpt from this table.
one-tail area 0.250 0.125 0.100 0.075 0.050 0.025 0.010 0.005 0.0005
two-tail area 0.500 0.250 0.200 0.150 0.100 0.050 0.020 0.010 0.0010
d.f. \ c 0.500 0.750 0.800 0.850 0.900 0.950 0.980 0.990 0.999
⋮
9 0.703 1.230 1.383 1.574 1.833 2.262 2.821 3.250 4.781
10 0.700 1.221 1.372 1.559 1.812 2.228 2.764 3.169 4.587
11 0.697 1.214 1.363 1.548 1.796 2.201 2.718 3.106 4.437
To determine where the given t-value would fall, we look for the row with heading d.f. =
. In this row, the sample statistic t = 1.910 falls between t = 1.796 and t =
Answers
To determine where the given t-value would fall, we look for the row with heading d.f. =11. In this row, the sample statistic t = 1.910 falls between t = 1.796 and t = 2.201
How to determine the t values?The given parameters are:
Degree of freedom, df = 11Sample statistic, t = 1.910This means that
df = 11 and t = 1.910
To calculate the t value,
We check the row where the heading of the degree of freedom is 11
i.e. df = 11
On this row, the t value 1.910 would be between 1.796 and 2.201
This is because 1.910 is greater than 1.796 and it is less than 2.201
Hence, the complete statement is
To determine where the given t-value would fall, we look for the row with heading d.f. =11. In this row, the sample statistic t = 1.910 falls between t = 1.796 and t = 2.201
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Find the value of x.
helllppp
tysm
Answers
Answer:
Step-by-step explanation: