The 6th term is -487 i.e, option(a)
What is a Sequence ?
A sequence is an ordered list of objects (or events). Like a set, it contains members (also called elements, or terms). The number of ordered elements (possibly infinite) is called the length of the sequence.
There are 4 types of sequence, arithmetic sequences, geometric sequences, quadratic sequences and special sequences.
Given, the 1st term = -3
According to question, we get the term by multiplying the previous term by 3 and then adding 2.
Now, calculate the other terms.
so, the 2nd term will be
-3 * 3 + 2 = -7
3rd term
-7 * 3 + 2 = -19
4th term
-19 * 3 + 2 = - 55
5th term
-55 * 3 + 2 = -163
6th term
-163 * 3 + 2 = -487
Hence, the 6th term is -487 i.e, option(a)
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two cards are drawn without replacement from a well-shuffled deck of 52 playing cards. what is the probability that the first card drawn is a diamond and the second card drawn is not a diamond? a) 0.1875 b) 0.1912 c) 0.0577 d) 0.0588 e) 0.7500 f) none of the above.
The correct answer is Option 'B'.
We are drawing cards without replacement,
So first card is a diamond is 13/52 and
Second not a diamond is 39/51
51 because we have picked 1 card in the first draw.
so final answer is
(13/52) *(39/51) = 0.1912.
Therefore, the probability that the first card drawn is a diamond and the second card drawn is not a diamond is 0.1912.
Probability refers to possibility. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain occurrences. The degree to which something is likely to happen is essentially what probability means.
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A factory produces 270000 000 sweets every
week. How many sweets does the factory
produce in a year? Give your answer in
standard form
The factory produced 1.404 x 10⁶ sweets in a year
How to calculate the number of sweets the factory produce in a year?
Standard form is a way of writing very large numbers or very small numbers in a simpler form. It is also called scientific notation
Given that: The factory produces 270000000 sweets every
week.
To know how many sweets the factory produces in a year, we will multiply the quantity produced in a week by 52 since there are 52 weeks in a year. Thus:
Number of sweet in a year = Weekly production x 52
= 270000000 x 52 = 14040000000 sweets
To express 140400000000 in standard form, we will move the position of the decimal point to the back of the first number(1) and take note of the number of steps we take to get there. The number of steps will then be used as the power of 10:
14040000000 = 1.404 x 10⁶
Therefore, the number of sweets produced by the factory in a year in standard form is 1.404 x 10⁶ sweets
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Triangle DEF with coordinates D(0, 0), E(3, 1), and F(3, 0) is similar to triangle EGH. If G has
coordinates (9, 3), what are the coordinates for H?
The coordinates for H are (9,2)
What are the coordinates?
A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.
Here, we have
D(0, 0), E(3, 1), and F(3, 0) is similar to triangle EGH.
coordinates are (x,y) = (x+6,y+2)
F's coordinate is (3,0)
using the coordinates we get (9,2)
Hence, the coordinates of H are (9,2)
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How many kilometres is 6.5cm
Answer:
0.000065 km
Step-by-step explanation:
To get from cm to km you need to divide 6.5 by 0.000001 which equals 0.000065km
Hudson goes to a store an buys an item that costs a dollars. He has a coupon for 20%
off, and then a 5% tax is added to the discounted price. Write an expression in terms
of a that represents the total amount that Hudson paid at the register.
An expression that represents the total amount (a) that Hudson paid is
a-a/10×2+{(a/10×2)/20}.
What do we mean by expressions?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.So, the expression that represents the total amount Hudson paid:
We know that,
Hudson has a coupon for 20% off.A 5% tax is added to the discounted price.Then, the expression can be as follows:
a - (a/100×20) + {(a/100×20)/100 × 5}a - a/10 × 2 + {(a/10×2)/20}Therefore, an expression that represents the total amount (a) that Hudson paid is a - a/10 × 2 + {(a/10×2)/20}.
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a variable t follows a uniform probability distribution where t is between 0 and 8 what is the probability that the random variable has a value greater than 5?
There is a 1/3 chance that random variable will have a value higher than 5.
Define the term random variable?A random variable is called with an unknown value or a function that gives values to each of the results of an experiment. Random variables are similarly defined by letters and fall into one of two categories: continuous variables, which can take on any value within a continuous range, or discrete variables, which have specified values.For the variable t, which follows uniform probability distribution.
0 ≤ t ≤ 8
Total variables = 9.
For the probability of value greater than 5 for the random variable.
P(t > 5) = P(t = 6) + P(t = 7) + P(t = 8)
P(t > 5) = 1/9 + 1/9 + 1/9
P(t > 5) = 3/9
P(t > 5) = 1/3
Thus, there is a 1/3 chance that random variable will have a value higher than 5.
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someone pls help this is the last question im begging you im gonna cry
Answer:
x = 10
Step-by-step explanation:
48 = x + 8 + 2x + x
48 = 4x + 8
-8 -8
40 = 4x
divide both sides by 4
10 = x or x =10
A store owner bought dog bowls for $6 and sold them for $8.10. What is the mark-up, as a percentage?
Answer:I am not fully going to do it for you, but here is the best way i can explain, it if not i am sorry.
Step-by-step explanation: Simply take the sales price minus the unit cost, and divide that number by the unit cost. Then, multiply by 100 to determine the markup percentage. For example, if your product costs $50 to make and the selling price is $75, then the markup percentage would be 50%: ( $75 – $50) / $50 = . 50 x 100 = 50%.
PLEASE HELP ASAPPPPP ILL GIVE BRAINLIEST PLEASEEEEEE
Rewrite x³y + xy²
x³y +
xy(x² +5y)
xy² using a common factor.
xy(3x² +15y)
xy(x² +5y)
1x³y² (y + 5x)
Answer:
[tex] \frac{1}{6} {x}^{3} y + \frac{5}{6} x {y}^{2} \\ \frac{1}{6} xy( {x}^{2} + 5y)[/tex]
option 3 is correct
HELP ASAP !!!! Use the equation one fourth plus s equals 18 over 20 to answer the questions.
Part A: Determine two numbers that the solution to the equation is between. Support your answer using the correct vocabulary. (2 points)
Part B: Solve for the variable. Show your work. (2 points)
a. The two numbers between which the solution to the equation lies are 0 and 1.
b. The value of the variable "s" is 13/20.
How to solve Algebra Word Problems?The equation given to us is one fourth plus s equals 18 over 20. This can be expressed as;
¹/₄ + s = ¹⁸/₂₀
s = ¹⁸/₂₀ - ¹/₄
s = (18/20) - (5/20)
s = (18 - 5)/20
s = 13/20
The solution is a rational number. A rational number is defined in mathematics as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.
We can determine two rational numbers such that the solution is in between them. A rational number smaller than the solution is 0. A rational number larger than the solution is 1. Hence, the solution lies between 0 and 1.
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a haunted house claims that 80% of customers are scared speechless. if this is true, what is the probability that 60% or less out of a group of 50 customers will be scared speechless?
Answer: The probability of 60% or less scared speechless out of a group of 50 customers (i.e. 30 customers) is 0.0932% or 0.000932.
Step-by-step explanation: Given problem meets all criteria for application of a binomial distribution with the probability of success; p=0.8 or 80% (which makes probability of failure; q=0.2 or 20%) and the total number of trials; n=50.
Let probability of 30 or less people scared (30 is 60% of 50 people) be P(x≤30), where x≤30 encapsulates all possibilities from 0 to 30 people scared speechless.
Then, by binomial distribution,
P(x≤30) =r=030nCr*pr*q(n-r)
Now we can substitute given values and find the desired probability,
P(x≤30) =r=03050!(50-r)!r!*(0.8)r*(0.2)(50-r)
P(x≤30) =r=03050!(50-r)!r!*(0.8)r*(0.2)-r*(0.2)50
P(x≤30) =(0.2)50*r=03050!(50-r)!r!*(0.8)r*(0.2)-r
P(x≤30) =(0.2)50*r=03050!(50-r)!r!*4r
The first value on the right hand side of equation is a very small number while the summation factor on second is a relatively larger number.
P(x≤30) = 0.000932
Thus, there is a 0.09% chance of 30 or less people scared speechless out of a group of 50.
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What is the value of z where distance of between two point R(6, - 1, - 3) and S(3, 3, z) is 13?
Answer:
-15, 9
Step-by-step explanation:
Substituting into the distance formula,
[tex]\sqrt{(6-3)^2+(-1-3)^2+(-3-z)^2}=13 \\ \\ \sqrt{25+(3+z)^2}=13 \\ \\ 25+(3+z)^2=169 \\ \\ (3+z)^2=144 \\ \\ 3+z=\pm 12 \\ \\ z=-3 \pm 12 \\ \\ z=-15, 9[/tex]
18. a rectangular page is to contain 42 square inches of printable area. the margins at the top and bottom of the page are each 1 inch, one side margin is 1 inch, and the other side margin is . what should the dimensions of the page be so that the least amount of paper is used?
The page is in landscape mode with a width : height is 3: 2
Given that,
The printable area is should be 42 square inches on a rectangular page. The margins at the top and bottom of the page are each one inch, while the margins on one side are one inch and two inches, respectively.
x = length of the horizontal side of the printable area
y = length of the vertical side of the printable area
XY = 42 inch²
y = 42/x
page height = y + 1 + 1
page width = x + 1 + 2
A = area of an entire sheet of paper
= (x+3)(y+2)
= (x+3)(42/x+2)
= x(42/x+2)+3(42/x+2)
= 42+2x+126/x+6
A = 2x+126/x+48
Extremes occur when A' = 0:
A' = 0 = 2 – 126/x²
1 = 63/x²
x² = 9*7
x = 3√(7), x has to be positive
y = 42/x = 42/(3√(7)) = 14√(7)/7 = 2√(7)
What should the dimensions of the page be so that the least amount of paper is used?
page width = x + 3 = 3√(7) + 3 = 3(√(7) + 1)
page height = y + 2 = 2√(7) + 2 = 2(√(7) + 1)
So, the page is in landscape mode with width: height is 3: 2.
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10) Determine the value of 10 - t when t = 4.
11) Determine the value of 12 + m when m = 6.
12) Determine the value of a + 5.2 when a = 1.9.
13) Determine the value of 3.4 - b when b = 2.1.
Answer:
10) 6
11) 18
12) 7.1
13) 1.3
Step-by-step explanation:
all you have to do is substitute
10 - 4 = 6
12 + 6 = 18
1.9 + 5.2 = 7.1
3.4 - 2.1 = 1.3
Kermit and Miss Piggy are a part of a close group of 10 Muppets. Four of the Muppets are randomly selected to
do press for their next movie. What is the probability Miss Piggy will do press but Kermit will not?
A.4/15
B.1/15
C.1/24
D.None of the above
Answer:
d
Step-by-step explanation:
Because answer would be 4/10 or 5/10
Betsie is going to buy 250 envelopes.
Here is some information about the cost of envelopes in two shops.
Value World
Pack of 10 envelopes for £1.99
Buy 2 packs get 1 pack free
Letters2go
Pack of 25 envelopes for £3.19
Betsie wants to buy the envelopes for the best possible price.
Which shop should Betsie buy the 250 envelopes from?
You must show how you get your answer.
Betsie should buy the 250 envelopes from the shop Letter2go.
As, 250 envelopes will cost £31.9 in Shop Letter2go whereas will cost £33.17 in Shop Value World.
Given, that Betsie is going to buy 250 envelopes.
the cost of envelopes in two shops:
Value World:
Pack of 10 envelopes for £1.99
Buy 2 packs get 1 pack free
Letters2go:
Pack of 25 envelopes for £3.19
Now, if we see the cost of envelopes in shop 1 i.e. Value World
Cost of Pack of 10 envelopes = £1.99
Also, 1 pack is free for 2 packs
1 pack = £1.99
2 packs = 2×£1.99 = £3.98
Also, with 2 packs Betsie get 1 pack free
so, Betsie gets 3 packs for £3.98.
1 pack = 10 envelopes
3 packs = 30 envelopes.
Hence, In shop Value World:
30 envelopes = £3.98
1 envelope = £3.98/30
250 envelopes = (3.98/30)×250
So, 250 envelopes will cost £33.17 in Shop Value World.
And in shop Letter2go:
25 envelopes = £3.19
1 envelope = £3.19/25
250 envelopes = (3.19/25)×250
So, 250 envelopes will cost £31.9 in Shop Letter2go.
Hence, 250 envelopes will cost £33.17 in Shop Value World and £31.9 in Shop Letter2go.
So, Betsie should buy the 250 envelopes from the shop Letter2go.
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the expressions 9x+7 and 7+9x are equivalent or not equivalent? The equation has_____
Answer:
Equivalent
Step-by-step explanation:
The equation is equivalent because they are just written the other way around although if you were to rewrite them both they would both be 9x+7
Expressions 9x+7 and 7+9x are equivalent and the equation has infinitely many solutions.
What is Expression?An expression is combination of variables, numbers and operators.
The expressions 9x+7 and 7+9x are equivalent because they have the same terms, although the order of the terms is different.
Let us check their equivalence.
9x+7 = 7+9x (commutative property of addition)
9x = 9x (subtract 7 from both sides and subtract 9x from both sides)
Both expressions simplify to the same thing, which means they are equivalent.
In terms of an equation, if we set these two expressions equal to each other, we get:
9x+7 = 7+9x
Simplifying this equation gives:
9x - 9x = 7 - 7
0 = 0
This means that the equation has an infinite number of solutions, since any value of x will satisfy.
Hence, expressions 9x+7 and 7+9x are equivalent and the equation has infinitely many solutions.
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Carol wants to make a square garden with 81 plants. Each row and column will have the same number of plants. How many plants will be in each row and column?
Answer: Row: 9 Column: 9
Step-by-step explanation:
Carol wants a square garden that means the amount of plants must be square, which it is so the square root of 81 is 9 so the square is 9 by 9
What does the average rate of change represent in the context of the question? Use complete sentences.
Laura is planning to attend a soccer skills camp that will require her to complete different skills tasks in the fastest time possible. To get ready for the event, she is practicing and logging her time to complete each skills task.
The x-coordinate is the skills task number, and the y-coordinate is the time in seconds.
(1, 4), (2, 8), (3, 16), (4, 32)
The rate of change here represents the time in seconds it takes her to perform a certain number of skills task
What is the meaning of the average rate of change?The rate of change is defined as the rate at which one quantity is changing with respect to another quantity. Mathematically:
rate of change = change in y / change in x
Given that: The x-coordinate is the skills task number and the y-coordinate is the time in seconds
Thus, rate of change = time in seconds / skills task number
Therefore, the rate of change in this context represents the time in seconds it takes to perform a certain number of skills task
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What is the remainder of the following division problem?
x StartLongDivisionSymbol x + 1 EndLongDivisionSymbol. minus x to get a remainder of 0 + 1 and a quotient of 1.
x
1
0
–1
The remainder of the division problem given by the image at the end of the answer is as follows:
How to obtain the remainder of a division problem?When a division does not result in an exact term, we have that the quotient is added to the remainder.
A long division problem is represented as follows:
q(x) + (r(x)/b(x))
In which the terms are listed as follows:
q(x) is the quotient.r(x) is the remainder.b(x) is the divisor.In this problem, the division is given as follows:
(x + 1)/x.
Separating the division into two terms, we have that:
(x + 1)/x = x/x + 1/x = 1 + 1/x.
Hence:
The quotient is of x.The remainder is of 1.Missing InformationThe division in this problem is:
(x + 1)/x.
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Answer: B. 1
Step-by-step explanation:
edge 2023
Please help, I'm struggling.
I think you would just add 8 + 5, because if NO is the same length as MN, then the length from MN is 5 and NP makes up the rest of the line.
Answer: MP = 13
If f(x)=4x^3+5, then what is the remainder when f(x) is divided by x−3?
Using Remainder theorem
Answer:
113
Step-by-step explanation:
Finding a remainder seems like you should be dividing. Remember everything is a shortcut for something else in math. So first you learn Long Division, but that's too much writing, so then you learn Synthetic Division, but there's an even shorter shortcut. It is called Remainder Theorem. If you just substitute 3 (because x-3 in the question) into the function, and you calculate it, you get the remainder.
f(x) = 4x^3 + 5
f(3) = 4(3)^3 + 5
f(3) = 4(27) + 5
= 108 + 5
= 113
See image.
Triangles geometry . I neeed help pls
The value of PQ is 43.
What is an isosceles triangle?
A triangle with at least two equal-length sides is known as an isosceles triangle in geometry.
From the figure,
PQ=3x+10, QR=5x-12
Given that, PQ=QR
So, 3x+10=5x-12
Find x:
3x+10=5x-12
Separate variable terms and constants
5x-3x=10+12
2x=22
x=22/2=11
we have PQ=3x+10=3(11)+10=33+10=43
So, PQ=43
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Q1 Q2 Logic puzzles
Solve the problems.
3 paintings are for sale.
Painting A is three times the
price of painting B.
Painting B is half the price of
painting C.
Painting C costs £368.
What are the prices of paintings
A and B?
Painting A = £ I
Painting B = £
Step-by-step explanation:
so basically, because Painting C costs £368 and Painting B is half that cost, Painting B costs £184. And Painting A is three times that amount Painting A costs £552.
You're Welcome ♡.
Is 4 ÷ 3/2 the same as 4 ÷ 2/3. Explain
7. Write the equation of the line that is parallel to the line
represented by the table and passes through the point
(-3,-10).
X
0
4
8
12
Y
10
6
2
-2
The equation of the line that is parallel to the line y = -x + 10 is y = -x - 13.
Given table:
x y
0 10
4 6
8 2
12 -2
slope m = 6 - 10 / 4 - 0
= -4/4
m = -1
substitute in y=mx+c
y = -x+c passes through (0,10)
10 = -0 + c
c = 10.
y = -x + 10.
here m = -1 and passes through (-3,-10)
y = mx +c
-10 = -1(-3)+c
-10 = 3 + c
c = -13
y = -x + (-13)
y = -x - 13.
Therefore the equation of the line that is parallel to the line y = -x + 10 is y = -x - 13.
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Mr. Yi buys vegetables at a market. He purchases 6 pounds of potatoes, p, and 3 pounds of onions, n, for $18. Onions cost twice as much as potatoes. To determine the unit price for each item, his daughter sets up and solves the system of equations shown.
6p + 3n = 18 and 2n = p
6(2n) + 3n = 18
12n + 3n = 18
15n = 18; n = $1.20
Onions cost $1.20 per pound.
Analyze the daughter’s solution. Which statements are true? Check all that apply.
The equation 2n = p should be 2p = n.
The equation 6p + 3n = 18 should be
6n + 3p = 18.
The actual cost of the onions is $3.00 per pound.
Potatoes cost $0.60 per pound.
Potatoes cost $1.50 per pound.
Potatoes cost $2.40 per pound.
The correct statements are,
(1) The equation 2n = p should be 2p = n.
(2) The actual cost of the onions is $3.00 per pound.
(3) Potatoes cost $1.50 per pound.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Mr. Yi buys vegetables at a market. He purchases 6 pounds of potatoes, p, and 3 pounds of onions, n, for $18. Onions cost twice as much as potatoes.
The equation will be formed as,
6p + 3n = 18
n = 2p
Substitute the value of n = 2p in the equation,
6p + 3(2p) = 18
6p + 6p = 18
12p = 18
p = $1.5
The cost of an onion is,
n = 2p
n = 1.5 x 2
n = $3
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a random sample of size 36 is taken from a population with mean 50 and standard deviation 5. what is (the mean of the sample mean)?
With the help of standard deviation we can conclude our answer.
What is standard deviation?The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean (also known as the anticipated value) of the collection.The lower case Greek letter (sigma), for the population standard deviation, or the Latin symbol s, for the sample standard deviation, are most frequently used in mathematical texts and equations to indicate standard deviation. Standard deviation may be written as SD.acc to our question-
Calculate the z-score of 51.5 using the formula:We substitute From the standard normal distribution table, the area to the left of 1.80 is0.9641Therefore it is 0.9461learn more about standard deviation here:
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-7.3, 7 3/4, 7.23, -7 2/3. Order the following rational numbers from least to greatest.
The order of the rational numbers from the least to greatest is [tex]-7\frac{2}{3}[/tex] < -7.3 < 7.23 < [tex]7\frac{3}{4}[/tex] .
in the question ,
it is given that the rational numbers are -7.3, [tex]7\frac{3}{4}[/tex], 7.23, [tex]-7\frac{2}{3}[/tex] .
we have to arrange the rational numbers in order from least to greatest .
For arrangement we first convert all the rational numbers in decimal form .
the decimal form of the given rational numbers are as follows .
(i) -7.3 is already given in decimal form .
(ii) [tex]7\frac{3}{4}[/tex] = (7*4+3)/4 = (28+3)/4 = 31/4 = 7.75
(iii) 7.23 is already in decimal form .
(iv) [tex]-7\frac{2}{3}[/tex] = -(7*3+2)/3 = -23/3 = -7.666
the order is -7.666 < -7.3 < 7.23 < 7.75
which is [tex]-7\frac{2}{3}[/tex] < -7.3 < 7.23 < [tex]7\frac{3}{4}[/tex]
Therefore , The order of the rational numbers from the least to greatest is [tex]-7\frac{2}{3}[/tex] < -7.3 < 7.23 < [tex]7\frac{3}{4}[/tex] .
The given question is incomplete , the complete question is
Order the following rational numbers from least to greatest.
-7.3, [tex]7\frac{3}{4}[/tex], 7.23, [tex]-7\frac{2}{3}[/tex] .
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A train traveled at the same speed for 9 hours. It went 320.55 miles in all. To the nearest hundredth of a mile per hour, how fast was the train going?
The train's speed was= 56.7 miles per hour
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
Entire distance = 210 miles + 130 miles = 340 milesTotal time = 3.5 hours and 2.5 hours = 6 hoursAverage speed = distance/ time = 340 miles/ 6 hours= 56.66666666666 miles per hourRounding to the nearest tenth= 56.7 miles per hourHence, The train's speed was= 56.7 miles per hour
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