Answer:
a6 = 4/243
Step-by-step explanation:
We can represent the geometric sequence with [tex]a_n=4(\frac{1}{3})^{n-1}[/tex], so the 6th term would be [tex]a_6=4(\frac{1}{3})^{6-1}=\frac{4}{243}[/tex].
Find the coordinates of the circumcenter of AABC with vertices A(9,-4), B(5,-2), and C(0, -1).
The coordinates of the circumcenter are
Coordinates of the circumcenter are (7.7, -6.6)
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
we first need to find the midpoint of each side, and then find the intersection of the perpendicular bisectors of each side.
Midpoint of AB is (7, -3)
Midpoint of BC is (2.5, -1.5)
Midpoint of AC is (4.5, -2.5)
The slope of the line passing through A and B is:
m= (-4 - (-2))/(9 - 5) = -1/2
the slope of the perpendicular bisector is 2
By point slope form
y - (-3) = 2(x - 7)
y = 2x - 17
And the equation of the perpendicular bisector of AC is:
y - (-2.5) = -1/2(x - 4.5)
y = -1/2x + 5
Now 2x - 17 = -1/2x + 2.25
2.5x = 19.25
x = 7.7
Substituting x = 7.7 into the equation for the perpendicular bisector of AB, we get:
y = 2(7.7) - 17
y = -6.6
Hence, coordinates of the circumcenter are (7.7, -6.6)
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The measure of angle DEF is ___ degrees.
Because of the SSS postulate for proving triangles congruent, you can say that triangles DEG and FEG are congruent. Corresponding parts of congruent triangles are congruent (CPCTC) means that angles DEG and FEG are congruent, which means their measures are equal. So 3y + 4 = 5y - 10.
4 = 2y - 10
14 = 2y
7 = y
The measure of angle DEF is 50 degrees
What is the volume of each hemisphere in the picture below? (Use 3.14 for)
Answer:
The answer is C.
106.0 in^3
Answer:
106.0 in^3
Step-by-step explanation:
5) After surveying a sample of high school teachers, Enrique concluded that
adults like to eat dinner at The Bistro more than other restaurants in town.
Terry disagreed with Enrique's conclusion, saying that Enrique's population
was too specific for such a broad question. Which question would have
been more appropriate for Enrique's survey of high school teachers?
The question that would be more appropriate for Enrique's survey of high school teachers is Among high school teachers, what is the most popular restaurant to eat dinner at in town?
The appropriate question for Enrique's survey of high school teachersEnrique's conclusion about adults liking to eat dinner at The Bistro more than other restaurants in town may not be accurate since his survey was only limited to high school teachers.
To make his conclusion more reliable, Enrique could have asked a more specific question that is relevant to high school teachers. Here are a few examples of more appropriate questions for Enrique's survey of high school teachers:
Among high school teachers, what is the most popular restaurant to eat dinner at in town?
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A rectangular aquarium 7 m long, 1 m wide, and 1 m deep is full of water. Find the work needed to pump the top half of the water out of the aquarium by raising it over the top of the aquarium. (Use the facts that the density of water is 1000 kg/m3 and g ≈ 9.8 m/s2.)
The work needed to pump the top half of the water out of the aquarium by raising it over the top of the aquarium is 34,300 J.
How to find the work needed to pump the top half of the water out of the aquarium?First we need to calculate the total amount of water that needs to be lifted and the height it needs to be lifted to.
The volume of water in the aquarium is given by:
V = 7 m * 1 m * 1 m = 7 m^3
Since we need to pump out the top half of the water, the volume of water that needs to be lifted is:
V = (1/2) * 7 m^3 = 3.5 m^3
The mass of the water can be calculated as:
m = V * density of water = 3.5 m^3 * 1000 kg/m^3 = 3500 kg
The height that the water needs to be lifted to is equal to the height of the aquarium, which is 1 m.
The work needed to lift the water can be calculated using the formula:
W = m * g * h
where
M is the mass of the water G is the acceleration due to gravity (9.8 m/s^2) H is the height the water needs to be lifted toSo, the work needed is:
W = 3500 kg * 9.8 m/s^2 * 1 m = 34,300 J (joules)
Therefore, the work needed to pump the top half of the water out of the aquarium by raising it over the top of the aquarium is 34,300 J.
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Select the correct answer.
Rita is making a beaded bracelet. She has a collection of 160 blue beads, 80 gray beads, and 240 pink beads. What is the estimated probability that Rita will need to pick at least five beads before she picks a gray bead from her collection?
Use the table of randomly generated outcomes to answer the question. Each letter represents the first letter of the bead color.
Outcomes
PBBB GPBP PBPP GGGG BPBP GBPB GPBP GBPB
PBPP PPGP PBGG GPPB PPPG BPPP PPPG BPGP
GGGG PGPG PPPP PPPP BBBG PPGB BBBG PPGB
PBPB BPPG PBBG BPBB PGPP PBPP PPPP PBPP
PPBP PPBB PGBP BPPB PPPB PPPB PGGB BBBB
A.
0.05
B.
0.10
C.
0.45
D.
0.55
The estimated probability that Rita will need to pick at least five beads before she picks a gray bead from her collection is 0.45 which is denoted as option C.
What is Probability?
This is referred to as a number that indicates how likely the event is to occur.
Probability for drawing at least 5 beads before she picks a grey bead from her collection
= 1-Probability for drawing at least one grey bead in the first 5 draws.
No of grey beads drawn in first 5 trials = (5, 80/80+160+240)
= (5, 1/6)
Probability for drawing at least one grey bead in the first 5 draws.
=1 - Prob of no grey
Required probability = P(X=0 in first 5 draws) = (1/6)⁵ = 0.4018 and th nearest value is therefore 0.45.
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the product of 5/8 x 6/15
Answer: 1/4
Step-by-step explanation:
To find the product of two fractions, you simply multiply the numerators together and multiply the denominators together. That is:
(5/8) x (6/15) = (5 x 6) / (8 x 15)
Simplifying the numerator and denominator by dividing both by their greatest common factor, which is 2, we get:
(5 x 6) / (8 x 15) = 30 / 120
Further simplifying the fraction by dividing both the numerator and denominator by their greatest common factor, which is 30, we get:
30 / 120 = 1 / 4
Therefore, the product of 5/8 and 6/15 is 1/4.
Answer:
To multiply two fractions, you simply multiply their numerators (top numbers) and denominators (bottom numbers), respectively.
So, 5/8 x 6/15 = (5 x 6) / (8 x 15) = 30 / 120
To reduce this fraction to its simplest form, we can divide both the numerator and denominator by their greatest common factor, which is 30.
30 / 120 = (30 ÷ 30) / (120 ÷ 30) = 1/4
Therefore, the product of 5/8 x 6/15 is 1/4
The brass section of a middle school jazz band has 4 trumpets and 3 trombones. What is the ratio of trombones to all the brass section members?
7/3
, 7:3, or 7 to 3
4/7
, 4:7, or 4 to 7
4/3
, 4:3, or 4 to 3
3/7
, 3:7, or 3 to 7
The ratio of trombones to all the brass section members is 3:7.
What is Ratio?A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.
Given:
Number of Trumpets = 4
Number of Trombones= 3
Total = 4 + 3= 7
So, the ratio of trombones to all the brass section members
= Number of Trombones/ Total
= 3 /7
= 3:7
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PLEZ HELP WILL MARK Brainliest WITH ALL OF THEM DUE TONIGHT!!!!
Answer:
the answer you are looking for here is 3/7
Answer:
3/7
Step-by-step explanation:
6/7 ×1/2 = 6×1 × 7×2 = 6/14 ÷ 2 = 3/7
x[tex]x^{2} =[/tex]-81
Answer:
[tex]x=\pm\,9i[/tex]
Step-by-step explanation:
[tex]x^2=-81\\x=\pm\,9i[/tex]
a first time homebuyer is given the choice of two loans: loan a: 390,000, 15 year-fixed, 4 discount points, M=$3,509.71. loan b: 390,000, 15 year-fixed, 0 discount points, M=3,659.86. how much does the hole buyer save in total by choosing loan A? a) 27,027 b) 11,427 c) 26,351.02 d) 42,627.05
The amount the the home buyer saves in total by choosing Loan A is most closest to $11,427. The Option B is correct.
How much does the buyer save by choosing Loan A?In order to compare the total cost of each loan, we need to consider both the monthly payment and the discount points.
For Loan A, we have Loan amount: $390,000, Loan term: 15 years, Discount points: 4 and Monthly payment: $3,509.71. For Loan B, we have Loan amount: $390,000, Loan term: 15 years Discount points: 0 and Monthly payment: $3,659.86.
The total cost of Loan A is the sum of the discounted upfront cost (discount points) and the total of all monthly payments over the life of the loan:
= (4% of $390,000) + ($3,509.71 x 180)
= $15,600 + $631,948.80
= $647,548.80
The total cost of Loan B is the total of all monthly payments over the life of the loan:
= ($3,659.86 x 180)
= $658,574.80
Now, the amount saved by choosing Loan A over Loan B is the difference between their total costs which equals:
= Total cost of Loan B - Total cost of Loan A
= $658,574.80 - $647,548.80
= $11,026
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Quadrilateral QRST is shown, with side lengths in inches (in.) and angle measurements in degrees.
2 in.
R
135°
3 in.
√18 in.
45°
S
5 in.
Lynn draws quadrilateral WXYZ, which is similar to quadrilateral QRST, with WX = 5 in
Enter values in the blank boxes to make the statement true.
The length of WZ is
2
degrees.
inches and the measure of angle Y is
Answer:
Y will be 65°
Step-by-step explanation:
Since angle S is 65°, angle Y will also be 65°
What are similar shape ?
Similar shapes are shapes that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
Since quadrilateral QRST is similar to quadrilateral WXYZ, then angle Q = angle W , angle R = angle X and angle S = angle Y and angle T = angle Z.
Since angle S is 65° from the diagram shown, angle will be measured as 65°.
What is the average cost of living for a retiree per year?
O around $50,000
O around $60,000
O around $70,000
O around $80,000
We can infer from the foregoing description that the typical annual cost of living for a retiree is (A) around $50,000.
Who is a retiree?One who has retired is known as a retiree.
Many seniors underestimate their retirement income by not accounting for inflation.
Wages, a gauge of the income that retirees must replace, will be the basis for benefits.
One who has retired is known as a retiree.
According to the U.S. Bureau of Labor Statistics most recent Consumer Expenditure Survey, the typical retiree household—one that is headed by a person 65 or older—spends $50,220 annually.
Comparatively, the average yearly household expenditure is $63,036.
So, from the above description, we can state that the average cost of living for a retiree per year is (A) around $50,000.
Therefore, we can infer from the foregoing description that the typical annual cost of living for a retiree is (A) around $50,000.
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Complete question:
What is the average cost of living for a retiree per year?
A. around $50,000
B. around $60,000
C. around $70,000
D. around $80,000
What is the square root rule?
The square root function involves the square root symbol √ which is mostly read as "square root of", the rule says that the square root of a number 'x' is a number 'y' such that y² = x.
We know that the square root of a number can be either positive or negative, but while defining the square root function, we restrict its range to be the set of all positive real numbers and hence making all square roots possible to be positive.
If the range for the square root of a number is set to be positive as well as negative it wont be a function that is why there is a restriction to the range of this set allowing only positive real numbers.
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Describe the type and degree of association in the scatter plot and what it means in terms of the time the player spent practicing and the number of points he scored in the game.
As the time a basketball player practices increases, the number of points scored in a game increases with a strong linear association.
As the time a basketball player practices increases, the number of points scored in a game increases with a strong nonlinear association.
As the time a basketball player practices increases, the number of points scored in a game decreases with a weak linear association.
As the time a basketball player practices increases, the number of points scored in a game decreases with a weak nonlinear association.
As the time a basketball player practices increases, the number of points scored in a game decreases with a weak nonlinear association
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Given a scatter plot in terms of the time the player spent practicing and the number of points he scored in the game.
A scatter plot uses dots to represent values for two different numeric variables.
The position of each dot on the horizontal and vertical axis indicates values for an individual data point.
As the time a basketball player practices increases, the number of points scored in a game decreases with a weak nonlinear association.
Hence, As the time a basketball player practices increases, the number of points scored in a game decreases with a weak nonlinear association
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QUICKK!! Which sentence is correct? A. -4 > 3 B. -4< -6 C. -4 > -7 D. -5 > -4
Answer:
C
Step-by-step explanation:
-4 is greater than -7
Samantha has two anthills in her yard. The first anthill has 982 ants. The second PLEASE HELP QUICKLY // anthill has one and one-third the amount of ants of the first hill. Which statement correctly compares the two anthills?
The first anthill is one and one-third times as many than the second anthill.
The first anthill is equal in size to the second anthill.
The second anthill is one and one-third times as many than the first anthill.
The second anthill is one and one-third times fewer ants than the first anthill.
The statement that correctly compares the two anthills is "the second anthill is one and one-third times as many ants as the first anthill."
Which statement correctly compares the two anthills?From the question, we have the following parameters that can be used in our computation:
The first anthill has 982 antsThe second anthill has one and one-third the amount of ants of the first hillUsing the above as a guide, we have the following:
First = 982
Second = 1 1/3 * First
This means that "the second anthill is one and one-third times as many ants as the first anthill."
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i just need the equation
Answer:
The decimal 6.25 would be 6 25/100 as a mixed number. In lowest terms, it would be 6 1/4.
Convert the Cartesian equation 2 xy = 1 in polar equation form.
The Cartesian equation 2xy = 1 has the following polar equation r²·sen2θ = 1.
To convert the Cartesian equation 2xy = 1 into polar equation form, we need to use the relationships between Cartesian coordinates and polar coordinates. The relationships are as follows:
x = r cos θy = r sin θSubstituting these relations in the Cartesian equation, we proceed to solve:
2 (r·cosθ)(r·sinθ) = 1
2r²·cosθ·sinθ = 1
r²·(2cosθ·sinθ) = 1
r²·sen2θ = 1
In conclusion, the polar equation has the following form: r²·sen2θ = 1.
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what is a congruent triangles worksheet
A congruent triangles worksheet is a type of educational resource that provides practice problems and exercises for students to work on to help them understand and apply the concept of congruent triangles.
The worksheet typically includes a variety of problems, such as identifying pairs of congruent triangles, determining congruent sides and angles, and applying congruence postulates or theorems to solve problems. The problems may involve using the side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), or hypotenuse-leg (HL) congruence criteria.
Congruent triangles are triangles that have the same size and shape. In other words, they are identical in every way except for their position and orientation in space. Understanding congruent triangles is important in geometry, as it can help students to solve problems involving triangles, as well as more complex geometric figures.
Worksheets are a useful tool for students to practice and reinforce their understanding of congruent triangles, and can be used in the classroom or as homework assignments.
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Kristen has 5 dozen pencils.She wants to put them in equal groups so that the number of groups is at least 3, but less than 11. What are all the possible equal sized groups she can make with the pencils? *There are 12 item in a dozen*
The possible number of equal sized group is given by set N = 5 groups
What is union and intersection of sets?The union of two sets A and B is the set of all those elements which are either in A or in B, i.e. A ∪ B, whereas the intersection of two sets A and B is the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B
The union of two sets is a new set that contains all of the elements that are in at least one of the two sets
The intersection of two sets is a new set that contains all of the elements that are in both sets
Given data ,
Let the total number of pencils be represented as n = 5 dozen = 60 pencils
The number of equal groups should be at least 3 and less than 11
So , the groups are represented by sets A , B , C , D , E
where the value of set A is
Set A = { 6 , 6 , 6 , 6 , 6 , 6 , 6 , 6 , 6 , 6 }
The set A contains 6 pencils of 10 groups
Set B = { 10 , 10 , 10 , 10 , 10 , 10 }
The set B contains 10 pencils of 6 groups
Set C = { 12 , 12 , 12 , 12 , 12 }
The set C contains 12 pencils of 5 groups
Set D = { 15 , 15 , 15 , 15 }
The set D contains 15 pencils of 4 groups
Set E = { 20 , 20 , 20 }
The set E contains 20 pencils of 3 groups
Therefore , the total number of sets N = 5 sets
Hence , the sets are solved
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The rectangular floor of a classroom is 24 feet in length and 40 feet in width. A scale drawing of the floor has a length of 6 inches. What is the area, in square inches, of the floor in the scale drawing?
Answer:
60 square inches
Step-by-step explanation:
Measure of length in scale drawing = Measure of actual length
6 inches = 24 feet
∴ 1 inch = [tex]\frac{24}{6}[/tex] feet
∴Unit multiplier applied:
∴1 inch in scale drawing = 4 feet of actual measurement
Measure of width in scale drawing = Measure of actual width
x inches = 40 feet
∴ x inches = (40 feet) × ([tex]\frac{1 inch}{4 feet}[/tex])
Measure of width in scale drawing = 10 inches
Area of rectangular floor in the scale drawing = (Length) × (Width)
= (6 inches) × (10 inches)
= 60 square inches
Find the value of the variable x. If your answer is not an integer, write it in simplest radical form with
the denominator rationalized
The values of the variable are:
x is 45.
y is 18.
z is 18.
What are trigonometric identities?There are three commonly used trigonometric identities.
Sin x = Perpendicular / Hypotenuse
Cosec = Hypotenuse / Perpendicular
Cos x = Base / Hypotenuse
Sec x = Hypotenuse / Base
Tan x = Perpendicular / Base
Cot x = Base / Perpendicular
We have,
From the figure,
Sin 45 = z / (18√2)
Sin 45 = 1 /√2
So,
1/√2 =z / 18√2
z = 18
Cos 45 = y / (18√2)
1/√2 = y/18√2
y = 18
Tan x = y / z
Tan x = 18/18
Tan x = 1
x = [tex]tan^{-1}[/tex]1
x = [tex]tan^{-1}[/tex] tan 45
x = 45
Thus,
x is 45.
y is 18.
z is 18.
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how to read 2/10 net 30 ?
2/10 Net 30 represents credit given to the buyer for the sale of goods or services. 2/10 net 30 means that the customer gets a 2% discount if the outstanding balance is paid within 10 days. Otherwise, full payment is due within 30 days.
2/10 Net 30:
The terms and conditions of the transaction are set forth in the purchase order and the corresponding invoice. These terms include terms of credit between the seller (also known as the payee) and the buyer (also known as the payer). A typical net credit period of 30 means the balance must be paid within 30 days of the invoice date. 2/10 Net 30 (also known as 2 10 Net 30) means that if a buyer pays within the first 10 days, their balance will be reduced by 2%. So "2" is the discount amount (2%) and "10" is the due date (10 days).
For example, if your company purchased $500 worth of goods or services on June 1st, you have entered into a loan agreement with the seller. If your company pays the net amount between June 1st and June 10th, you get a 2% discount, bringing the total amount to $490.
This example 2/10 net 30 step by step.
Day Start counting days from the invoice date.
Quick Formula: 100% Discount % x Invoice Amount.
100% - 2% = 98% x $500 = $490.
Formula:
(immediate discount) x (invoice amount) = less payment
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Can somebody answer this question please.
The line plot which can be used to represent the teachers record of how many miles each student ran during gym class is attached.
What is a line plot?A Line plot can be defined as a graphical representation of data as points or check marks above a number line, showing the frequency of each value along a line. It is used to analyze data
Given Data:
3/4, 1/4, 1/2, 3/4, 1/2, 1/2, 1/4, 3/4, 1/4, 1/2, 1/4, 3/4
From the given Data, the frequency of
1/4 = 5
1/2 = 4
3/4 = 3
Therefore, the line plot is attached as a diagram.
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HELP PLEASE!!
Ramon is filling cups with juice. Each cup is shaped like a cylinder and has a diameter of 4.4 inches and a height of 7 inches. How much juice can Ramon pour into 6 cups? Round to the nearest hundredth and approximate using π = 3.14.
The total volume in the 6 cups is 638.30 in^2
How much juice can Ramon pour into 6 cups?Remember that the volume of a cylinder of height H and radius R is:
V = pi*R^2*H
Here the diameter is 4.4 inches, then the radius is half of that:
R = 4.4in/2 = 2.2in
The height is 7 inches, then the volume of each cup is:
V = 3.14*(2.2in)^2*7in = 106.38 in^2
And in 6 cups the total volume will be:
volume = 6*106.38 in^2 = 638.30 in^2
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What is the antiderivative of 1x?
The antiderivative of 1x (or simply x) is (1/2)x² + C, where C is the constant of integration. In other words, the antiderivative of x is the function whose derivative is equal to x.
This is a basic result in calculus, and it is derived using the power rule of integration. The antiderivative of 1x (or simply x) is the function whose derivative is equal to x. This function is (1/2)x² + C, where C is the constant of integration. To find the antiderivative, one can use the power rule of integration, which states that the antiderivative of xⁿ is (1/(n+1))x⁽ⁿ⁺¹⁾ + C. In the case of x, n is equal to 1, so the antiderivative is (1/2)x² + C. The constant of integration represents the family of functions that have the same derivative, so it is added to the antiderivative to reflect this.
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The radius of a cylinder is 3 inches, and the cylinder's height is 10 inches.
What is the exact volume of the cylinder?
Responses
1. 30π in³
2. 60π in³
3. 90π in³
4. 300π in³
Given:-
[tex] \rm{radius= \bold{ 3}}[/tex][tex] \rm{height = \bold{ 10}}[/tex][tex] \: [/tex]
To find:-
[tex] \rm{volume \: of \: the \: cylinder = \: ?}[/tex][tex] \: [/tex]
By using formula:-
[tex]\underline{ \boxed{ \rm{ \red{volume \: of \: the \: cylinder = πr²h}}}}[/tex][tex] \: [/tex]
Solution:-
[tex] \rm{v = πr²h}[/tex][tex] \: [/tex]
[tex] \rm{v = π×( 3 )² × 10}[/tex][tex] \: [/tex]
[tex] \underline{\boxed{ \color{purple}{\rm{v = 90π in³}}}}[/tex][tex] \: [/tex]
The volume of the cylinder is 90π in³
[tex] \: [/tex]
hope it helps!:)
Which statements correctly describe the relationships between x and y for each table? Responses Table A represents an additive relationship because y is 2.5 more than x, and Table B represents a multiplicative relationship because y is 9.2 times x. Table A represents an additive relationship because , y, is 2.5 more than , x, , and Table B represents a multiplicative relationship because , y, is 9.2 times , x, . Both tables represent additive relationships. In Table A, y is 2.5 more than x, and in Table B, y is 8.2 more than x. Both tables represent additive relationships. In Table A, , y, is 2.5 more than , x, , and in Table B, , y, is 8.2 more than , x, . Both data sets represent multiplicative relationships. In Table A, y is 3.5 times x, and in Table B, y is 9.2 times x. Both data sets represent multiplicative relationships. In Table A, , y, is 3.5 times , x, , and in Table B, , y, is 9.2 times , x, . Table A represents a multiplicative relationship because y is 3.5 times x, and Table B represents an additive relationship because y is 8.2 more than x.
The requried statement is mentioned in C where Table A represents y = 2.5x and table B represents y = 3x describe the relationships between x and y for each table. Option C is correct.
What is proportionality?Proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.
Here,
In Table A, y is 2.5 more than x, and in Table B, y is 3 more than x. Both tables represent additive relationships. the requried statement is mentioned in C where Table A represents y = 2.5x and table B represents y = 3x describing the relationships between x and y for each table. Option C is correct.
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Jonathan can jog 3 2/5 miles in 7/8 hour. find his average speed per hour
The average speed with the given distance and time is 119/40 miles per hour.
What is the average speed?Average speed is calculated by dividing a quantity by the time required to obtain that quantity. Meters per second is the SI unit of speed. The formula S = d/t, where S is the average speed, d is the total distance, and t is the total time, is used to determine average speed.
Given that, number of miles jogged = [tex]3\frac{2}{5}[/tex] = 17/5 miles and the time taken = 7/8 hours
Here, average speed = 17/5 ÷ 7/8
= 119/40 miles per hour
Therefore, the average speed is 119/40 miles per hour.
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