Combining these, we have[tex]$6 \times 6 = \boxed{36}$[/tex] different arrangements of the numbers [tex]${}1,$ ${}2,$ ${}3,$ ${}4,$ ${}5,$ $6$[/tex] in a row where the sum of any adjacent numbers is even.
What are the fundamental products?Products intended for exporting after processing into goods or processed products are referred to as "basic products," as are goods planned for export after processing. Samples 1 - 3 Samples 2 - 3.
We may start by noting that at minimum one of the neighboring numbers must be even for the sum of both numbers to be even. This means that a even numbers (2, 4, 6) as well as the odd numbers (1, 3, 5) should be arranged in the appropriate positions.
Let's start by thinking about the even positions. The second, fourth, and sixth places are the only even positions. We can choose any variant of the 3 even numbers to occupy these spots, giving us[tex]$3! = 6$[/tex] ways.
Let's now think about the unusual positions. The first, third, and fifth positions are the only ones that are odd. We have an additional [tex]$3! = 6$[/tex]ways to fill these spots by using any combination of the 3 odd numbers.
Consider the odd locations now. The first, third, and fifth places are the three odd positions. We have an additional[tex]$3! = 6$[/tex]ways by using any permutation of the three odd numbers to fill these positions.
Together, this give us [tex]$6 \times 6[/tex] = [tex]\boxed{36}$[/tex] different ways to arrange the numbers [tex]${}1,$ ${}2,$ ${}3,$ ${}4,$ ${}5,$ $6$[/tex]in a row so that the sum of any two adjacent numbers is even.
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Complete the recursive formula of the arithmetic sequence -16, -33, -50, -67,. −16,−33,−50,−67,. Minus, 16, comma, minus, 33, comma, minus, 50, comma, minus, 67, comma, point, point, point. C(1)=c(1)=c, left parenthesis, 1, right parenthesis, equals
c(n)=c(n-1)+c(n)=c(n−1)+c, left parenthesis, n, right parenthesis, equals, c, left parenthesis, n, minus, 1, right parenthesis, plus
The following is the recursive formula for the arithmetic sequence in this issue:
c(1) = -16.
c(n) = c(n - 1) - 17.
An arithmetic sequence is a series of numbers where each term is obtained by adding a fixed constant, known as the common difference, to the previous term. For example, in the sequence 2, 5, 8, 11, 14, 17, each term is obtained by adding 3 to the previous term.
The formula for finding the nth term of an arithmetic sequence is: a(n) = a(1) + (n-1)d, where a(1) is the first term, d is the common difference, and n is the term number. For example, to find the 10th term of the sequence 2, 5, 8, 11, 14, 17, we would use the formula a(10) = 2 + (10-1)3 = 29. Arithmetic sequences have many practical applications, such as in finance, where they can be used to calculate the interest earned on an investment over time.
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A straw that is 15cm long leans against the inside of a glass. The diameter of a glass is
5cm, and has a height of 8cm. How far past the edge of the glass would the straw extend?
Round your answer to the nearest tenth.
The straw will extend past the edge of the glass in a straight line. To find the answer, subtract the diameter of the glass (5cm) from the length of the straw (15 cm): 15 cm - 5 cm = 10 cm. This is the distance the straw will extend past the edge of the glass. To round to the nearest tenth, round 10.0 up to 10.1. Therefore, the straw will extend past the edge of the glass 10.1 cm.
At the book store, you purchased some $3 clearance mystery books and $8 regular-priced science fiction books. How many of each did you buy if you spent a total of $77?
Answer:
we bought 12 $3 clearance mystery books and 5 $8 regular-priced science fiction books.
Step-by-step explanation:
The ratio between two supplementary angle is 13:7. What are the measures of the angles?
Answer: The two angles are 117 degrees and 63 degrees.
Step-by-step explanation:
Supplementary angles are two angles whose sum is 180 degrees. Let the two angles be 13x and 7x, where x is a constant of proportionality.
We know that the sum of the angles is 180 degrees, so:
13x + 7x = 180
Combining like terms, we get:
20x = 180
Dividing both sides by 20, we get:
x = 9
So the measures of the angles are:
13x = 13(9) = 117 degrees
7x = 7(9) = 63 degrees
Therefore, the two angles are 117 degrees and 63 degrees.
part c question consider two groups of randomly selected peppers, where neither group has all big or all small peppers. a mean difference of zero indicates the peppers are well distributed between the two groups.a. true b. false
False. A mean difference of zero does not necessarily indicate that the peppers are well distributed between the two groups.
What is number?Number is a mathematical object used to count, measure, and label. It is one of the most fundamental concepts in mathematics and is used to describe a wide variety of physical, logical, and abstract objects. Numbers are used to represent quantities, lengths, temperatures, money, and many other measurements. They are also used to represent abstract ideas, such as the number of days in a year or the number of colors in a rainbow.
Although the mean may be equal between the two groups, the distribution of the peppers could be skewed and not evenly distributed. For example, one group could have all large peppers and the other all small peppers and the mean would be equal. This would not be considered well distributed. To ensure the peppers are evenly distributed, one should check the standard deviation or range of the data to see if the peppers are spread across both groups.
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Answer: A mean difference of zero indicates the peppers
are not well distributed between the two groups.
Why: Part B Answers
What do large differences of the means of each group indicate? Select the correct answer.
The peppers with different weights aren’t properly distributed between the two groups.
So they arent distributed well
Solve the system of equations shown below using graphing and substitution. y=2x+3 and y=15-x
Answer: -17x+3
Step-by-step explanation:
y=2x+3 and y=15-x
15x-2x+3
-17x+3
you can try this
Write an equation of the line that is parallel to y = 12
x + 3 and passes through the point (10, -5).
Answer:
y = 12x - 125
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 12x + 3 ← is in slope- intercept form
with slope m = 12
• Parallel lines have equal slopes , then
y = 12x + c ← is the partial equation
to fond c substitute (10, - 5 ) into the partial equation
- 5 = 12(10) + c = 120 + c ( subtract 120 from both sides )
- 125 = c
y = 12x - 125 ← equation of parallel line
suppose you start at the origin, move along the x-axis a distance of 7 units in the positive direction, and then move downward a distance of 6 units. what are the coordinates of your position? (x, y, z)
The coordinates of your position If we start at the origin, we are moving only along the x-axis of a distance of 7 units in positive direction and then only in the negative y-axis direction and z-coordinate is zero are (7,-6,0).
The origin is the point in space that has a position of (0, 0, 0), which represents the point where the x, y, and z axes intersect.
The first step is to move 7 units in the positive x direction. The positive x direction is the direction in which x values increase. Therefore, we move to the right along the x-axis to the point (7, 0). This means that we have moved 7 units along the x-axis, and our position is now (7, 0, 0).
The second step is to move downward a distance of 6 units. Since we are not moving in the x direction, we are only changing our position along the y-axis. Moving downward in the y direction means decreasing our y-coordinate. Therefore, we move 6 units downward from our current position to the point (7, -6, 0).
Therefore, the coordinates of our position are (7, -6, 0)
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Will make you brainlist!
Answer:
x = -2 , y = 2
Step-by-step explanation:
label your equations (1) and (2) the question mention to use elimination method and make x the same for both. To do that multiply equation (1) by 2. than label it (3)so 3x becomes 6x adding the equation (2)+(3) cancels out -6x and 6x so you can find value of yuse value of y to find xhope this helps :)
Kate plans to save 5% of her income. She just earned 80.Howmuchmoneyshouldsheputintosavings?
$4
Multiply 80 by 0.05 to get the answer of $4
Answer:
4 (insert the currency needed)
Step-by-step explanation:
To find our answer we have to find 5% of Kate's wages and to do this we have to do 5 divided by 100. Then that answer is multiplied by 80!
5 ÷ 100 = 0.0580 × 0.05 = 4This means she has to put £4 into her savings!
Hope this helps, have a lovely day! :)
what is the value of y in the solution to the system of equations below.
y=-x+6
2x-y=-9
Answer:
I gave a couple solutions as I wasn't sure if you were asking for graphing purposes or substituting y=-x+6 into the second equation 2x-y=-9. So I gave both solutions just in case.
for the first equation y=-x+6, y intercept is (0,6)
for equation two 2x-y=-9, y intercept is (0,9)
In both of the equations the x value is 1.
Solving for y without graphing. Y=9+2x
and x=-1
Step-by-step explanation:substitute i
HOWEVER, if you are saying that the top equation is the value of y, then you substitute it into the bottom equation. 2x--x+6=-9 which would be x=-5
It really depends on what is expected of the question. I wasn't sure which one, so I gave a couple different approaches. If you could give more information, such as, are you graphing, that would be great. I'll keep an eye out for any comments.
Use the following function to find d(0)
d(x)=-x+-3
d(0)=
Answer:
d(0) = -3
Step-by-step explanation:
d(x) = -x + -3 d(0)
d(0) = 0 - 3
d(0) = -3
So, the answer is d(0) = -3
Find the particular solution of the first-order linear differential equation for x > 0 that satisfies the initial condition. Differential Equation Initial Condition y' + y tan x = sec X + 9 cos x y(0) = 9 y = sin x + 9x cos x +9
Previous question
Answer: Differential Equation Initial Condition y' + y tan x = sec X + 9 cos x y(0) ... linear differential equation for x > 0 that satisfies the initial condition.
Step-by-step explanation:
A coffee maker is on sale for 45$. If the sales tax is 7%, how much will the buyer spend altogether?
Answer: 38 I think if it's not right I'm sorry I'm bad at math that's like the only thing I suck at
Step-by-step explanation:
What is the answer I keep getting 32
Answer:
2 9/14
Step-by-step explanation:
Guidance Missile System A missile guidance system has seven fail-safe components. The probability of each failing is 0.2. Assume the variable is binomial. Find the following probabilities. Do not round intermediate values. Round the final answer to three decimal places, Part: 0 / 4 Part 1 of 4 (a) Exactly two will fail. Plexactly two will fail) = Part: 1/4 Part 2 of 4 (b) More than two will fail. P(more than two will fail) = Part: 214 Part: 2/4 Part 3 of 4 (c) All will fail. P(all will fail) = Part: 3/4 Part 4 of 4 (d) Compare the answers for parts a, b, and c, and explain why these results are reasonable. Since the probability of each event becomes less likely, the probabilities become (Choose one smaller larger Х 5
The probability of all will fail is the lowest.
The given problem states that a missile guidance system has seven fail-safe components, and the probability of each failing is 0.2. The given variable is binomial. We need to find the following probabilities:
(a) Exactly two will fail.
(b) More than two will fail.
(c) All will fail.
(d) Compare the answers for parts a, b, and c, and explain why these results are reasonable.
(a) Exactly two will fail.
The probability of exactly two will fail is given by;
P(exactly two will fail) = (7C2) × (0.2)2 × (0.8)5
= 21 × 0.04 × 0.32768
= 0.2713
Therefore, the probability of exactly two will fail is 0.2713.
(b) More than two will fail.
The probability of more than two will fail is given by;
P(more than two will fail) = P(X > 2)
= 1 - P(X ≤ 2)
= 1 - (P(X = 0) + P(X = 1) + P(X = 2))
= 1 - [(7C0) × (0.2)0 × (0.8)7 + (7C1) × (0.2)1 × (0.8)6 + (7C2) × (0.2)2 × (0.8)5]
= 1 - (0.8)7 × [1 + 7 × 0.2 + 21 × (0.2)2]
= 1 - 0.2097152 × 3.848
= 0.1967
Therefore, the probability of more than two will fail is 0.1967.
(c) All will fail.
The probability of all will fail is given by;
P(all will fail) = P(X = 7) = (7C7) × (0.2)7 × (0.8)0
= 0.00002
Therefore, the probability of all will fail is 0.00002.
(d) Compare the answers for parts a, b, and c, and explain why these results are reasonable.
The probability of exactly two will fail is the highest probability, followed by the probability of more than two will fail. And, the probability of all will fail is the lowest probability. These results are reasonable since the more the number of components that fail, the less likely it is to happen. Therefore, it is reasonable that the probability of exactly two will fail is higher than the probability of more than two will fail, and the probability of all will fail is the lowest.
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A small publishing company is releasing a new book. The production costs will include a one-time fixed cost for editing and an additional cost for each book
printed. The total production cost C (in dollars) is given by the function C = 750+ 16.95N, where N is the number of books.
The total revenue earned (in dollars) from selling the books is given by the function R = 33.70N.
Let P be the profit made (in dollars). Wnite an equation relating P to N. Simplify your answer as much as possible.
P =
Answer:
The profit made is given by the difference between the total revenue and the total production cost:
P = R - C
Substituting the given expressions for R and C, we get:
P = 33.70N - (750 + 16.95N)
Simplifying:
P = 16.75N - 750
Therefore, the equation relating P to N is P = 16.75N - 750
LetR=[0, 4]×[−1, 2]R=[0, 4]×[−1, 2]. Create a Riemann sum by subdividing [0, 4][0, 4] into m=2m=2 intervals, and [−1, 2][−1, 2] into n=3n=3 subintervals then use it to estimate the value of ∬R (3−xy2) dA∬R (3−xy2) dA.Take the sample points to be the upper left corner of each rectangle
The Riemann sum is:Σ(3-xᵢₖ*yᵢₖ²)ΔA, where i=1,2 and k=1,2,3.
We can create a Riemann sum to estimate the value of the double integral ∬R (3-xy²) dA over the rectangular region R=[0, 4]×[-1, 2] by subdividing [0, 4] into m=2 intervals and [-1, 2] into n=3 intervals. Then we can evaluate the function at the upper left corner of each subrectangle, multiply by the area of the rectangle, and sum all the results.
The width of each subinterval in the x-direction is Δx=(4-0)/2=2, and the width of each subinterval in the y-direction is Δy=(2-(-1))/3=1. The area of each subrectangle is ΔA=ΔxΔy=2*1=2.
Therefore, the Riemann sum is:
Σ(3-xᵢₖ*yᵢₖ²)ΔA, where i=1,2 and k=1,2,3.
Evaluating the function at the upper left corner of each subrectangle, we get:
(3-0*(-1)²)2 + (3-20²)2 + (3-21²)2 + (3-41²)*2 = 2 + 6 + 2 + (-22) = -12.
Thus, the estimate for the double integral is -12.
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What’s -9.1 times 3.75
Find the distance between each pair of points.
a. M= (0,-11) and P=(0,2)
b. A= (0,0) and B= (-3,-4)
c. C= (8,0) and D=(0,-6)
Answer:
To calculate the distance between each pair of points given, we can use the distance formula which is derived from the Pythagorean theorem. The formula is:
distance = square root of [(x2 - x1)^2 + (y2 - y1)^2]
Using this formula, we can calculate the following distances:
a. Distance between M and P = 13 units
b. Distance between A and B = 5 units
c. Distance between C and D = 10 units
what is the messure or the vertex angle of an isosceles triangle if one of its base angle measures 16 degrees
1. An Estate dealer sells houses and makes a commission of GHc3750 for the first house sold. He
receives GHc500 increase in commission for each additional house sold. How many houses must
she sell to reach a total commission of GHc6500?
If an Estate dealer sells houses and makes a commission of GHc3750 for the first house sold and receives GHc500 increase in commission for each additional house sold, for reaching a total commission of GHc6500, she must have sold 6.5 houses.
How is the number of houses sold determined?The number of houses the estate dealer sold to reach a total commission of GHc6500 can be determined using the mathematical operations of subtraction, division, and addition.
The total commission received = GHc6,500
The commission for the first house = GHc3,750
The commission for the remaining houses sold = GHc2,750 (GHc6,500 - GHc3,750)
The commission for additional sale of each house = GHc500
The number of additional houses sold = 5.5 (GHc2,750/GHc500)
The total number of houses sold = 6.5 (5.5 + 1 or the first house)
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A student takes a multiple-choice test that has 10 questions. Each question has four choices. The student guesses randomly at each answer. Round the answers to three decimal places Part 1 of2 (a) Find P(5) P(5)- Part 2 of2 (b) Find P(More than 3) P(More than 3)
A student attempts a 10-question multiple-choice test where each question presents four options, and the student makes random guesses for each answer. So the probability of (a) P(5)= 0.058 and (b) P(More than 3)= 0.093.
Part 1: Calculation of probability of getting 5 questions correct
(a) P(5)The formula used to find the probability of getting a certain number of questions correct is:
P(k) = (nCk)pk(q(n−k))
Where, n = total number of questions
(10)k = number of questions that are answered correctly
p = probability of getting any question right = 1/4
q = probability of getting any question wrong = 3/4
P(5) = P(k = 5) = (10C5)(1/4)5(3/4)5= 252 × 0.0009765625 × 0.2373046875≈ 0.058
Part 2: Calculation of probability of getting more than 3 questions correct
(b) P(More than 3) = P(k > 3) = P(k = 4) + P(k = 5) + P(k = 6) + P(k = 7) + P(k = 8) + P(k = 9) + P(k = 10)
P(k = 4) = [tex]10\choose4[/tex](1/4)4(3/4)6 = 210 × 0.00390625 × 0.31640625 ≈ 0.02
P(k = 5) = [tex]10\choose5[/tex](1/4)5(3/4)5 = 252 × 0.0009765625 × 0.2373046875 ≈ 0.058
P(k = 6) = [tex]10\choose6[/tex](1/4)6(3/4)4 = 210 × 0.0002441406 × 0.31640625 ≈ 0.012
P(k = 7) = [tex]10\choose7[/tex](1/4)7(3/4)3 = 120 × 0.00006103516 × 0.421875 ≈ 0.002
P(k = 8) = [tex]10\choose8[/tex](1/4)8(3/4)2 = 45 × 0.00001525878 × 0.5625 ≈ 0.001
P(k = 9) = [tex]10\choose9[/tex](1/4)9(3/4)1 = 10 × 0.000003814697 × 0.75 ≈ 0.000
P(k = 10) = [tex]10\choose10[/tex](1/4)10(3/4)0 = 1 × 0.0000009536743 × 1 ≈ 0
P(More than 3) = 0.020 + 0.058 + 0.012 + 0.002 + 0.001 + 0.000 + 0≈ 0.093
Therefore, the probabilities of the given situations are: P(5) ≈ 0.058, P(More than 3) ≈ 0.093.
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One number is 13 less than another number. Let x represent the greater number. What is the sum of these two numbers?
Answer:
2x - 13
Step-by-step explanation:
If x represents the greater number, then the other number is x - 13. The sum of these two numbers is:
x + (x - 13) = 2x - 13
Use the following circle to solve for x
We know that the product of lengths of the same chord is equal to the product of the other chord intersecting it.. So;
[tex] \purple{ \mathfrak{x \times 6 = 12 \times 5}}[/tex]
[tex] \large \purple{ \mathfrak{x = \frac{12 \times 5}{6}}}[/tex]
[tex] \large \purple{ \mathfrak{x = \frac{ \cancel{12} \times 5}{ \cancel6}}}[/tex]
[tex] \large \purple{ \mathfrak{x = 2 \times 5}}[/tex]
[tex] \large \boxed{ \red{ \mathfrak{x =10}}}[/tex]
I NEED ANSWERS ASAP….
Answer:
Step-by-step explanation:
It is set up
7x+5x+2y=20
7x+5x=12x
12x+2y=20
x=0
y=10
12(0)+2(10)=20
Ok so maybe this was not the same type of equation i thought it was it is not that easy!
Please help it’s for tmr
Leo has a number of toy soldiers between 27 and 54. If you want to group them four by four, there are none left, seven by seven, 6 remain, five by five, 3 remain. How many toy soldiers are there?
The answer is 48 but I need step by step explanation
Hence, 28 toy soldiers are the correct answer.
In mathematics, how is a group defined?A group in mathematics is created by combining a set with a binary operation. For instance, a group is formed by a set of integers with an arithmetic operation and a group is also formed by a set of real numbers with a differential operator.
Let's refer to the quantity of toy soldiers as "x".
We are aware that x is within the range of 27 and 54 thanks to the problem.
x can be divided by 4 without any remainders.
The residual is 6 when x is divided by 7.
The leftover after dividing x by five is three.
These criteria allow us to construct an equation system and find x.
Firstly, we are aware that x can be divided by 4 without any residual. As a result, x needs to have a multiple of 4. We can phrase this as:
x = 4k, where k is some integer.
Secondly, we understand that the remaining is 6 when x is divided by 7. This can be stated as follows:
x ≡ 6 (mod 7)
This indicates that x is a multiple of 7 that is 6 more than. We can solve this problem by substituting x = 4k:
4k ≡ 6 (mod 7)
We can attempt several values of k until we discover one that makes sense for this equation in order to solve for k. We can enter k in to equation starting using k = 1, as follows:
4(1) ≡ 6 (mod 7)
4 ≡ 6 (mod 7)
It is not true; thus we need to attempt a next value for k. This procedure can be carried out repeatedly until the equation is satisfied for all values of k.
k = 2:
4(2) ≡ 6 (mod 7)
1 ≡ 6 (mod 7)
k = 3:
4(3) ≡ 6 (mod 7)
5 ≡ 6 (mod 7)
k = 4:
4(4) ≡ 6 (mod 7)
2 ≡ 6 (mod 7)
k = 5:
4(5) ≡ 6 (mod 7)
6 ≡ 6 (mod 7)
k = 6:
4(6) ≡ 6 (mod 7)
3 ≡ 6 (mod 7)
k = 7:
4(7) ≡ 6 (mod 7)
0 ≡ 6 (mod 7)
We have discovered that the equation 4k 6 (mod 7) is fulfilled when k = 7. Thus, we can change k = 7 to x = 4k to determine that:
x = 4(7) = 28
This indicates that there are 28 toy troops. Yet we also understand that the leftover is 3 when x is divided by 5. We don't need to take into account any other values of x because x = 28 satisfies this requirement.
28 toy soldiers are the correct response.
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CAN SOMEBODY HELP ME FACTOR AS THE PRODUCT OF TWO BINOMIALS
x²- x- 42
Answer:
(x-7)(x+6)
factor and see what works
What is the ordered pair for y=3x-3
Answer:
Step-by-step explanation:
Choose three values for
x and substitute in to find the corresponding y values.(0,−3),(1,0),(2,3)
You can choose any of these three pairs or the equation y=3x-3
The 1948 and 2018 temperatures at 197 random locations across the globe were compared and the mean difference for the number of days above 90 degrees was found to be 2.9 days with a standard deviation of 17.2 days. The difference in days at each location was found by subtracting 1948 days above 90 degrees from 2018 days above 90 degrees.
What is the lower limit of a 90% confidence interval for the average difference in number of days the temperature was above 90 degrees between 1948 and 2018?
What is the upper limit of a 90% confidence interval for the average difference in number of days the temperature was above 90 degrees between 1948 and 2018?
What is the margin of error for the 90% confidence interval?
Does the 90% confidence interval provide evidence that number of 90 degree days increased globally comparing 1948 to 2018?
Does the 99% confidence interval provide evidence that number of 90 degree days increased globally comparing 1948 to 2018?
If the mean difference and standard deviation stays relatively constant would decreasing the degrees of freedom make it easier or harder to conclude that there are more days above 90 degrees in 2018 versus 1948 globally.
If the mean difference and standard deviation stays relatively constant does lowering the confidence level make it easier or harder to conclude that there are more days above 90 degrees in 2018 versus 1948 globally.
The lower limit of a 90% confidence interval for the average difference in the number of days the temperature was above 90 degrees between 1948 and 2018 is -22.8 days and the upper limit is 28.6 days.
The margin of error for the 90% confidence interval is 25.4 days.
The 90% confidence interval does provide evidence that the number of 90-degree days increased globally comparing 1948 to 2018.
The 99% confidence interval also provides evidence that the number of 90-degree days increased globally comparing 1948 to 2018.
If the mean difference and standard deviation stay relatively constant, decreasing the degrees of freedom would make it harder to conclude that there are more days above 90 degrees in 2018 versus 1948 globally.
Lowering the confidence level would also make it harder to conclude that there are more days above 90 degrees in 2018 versus 1948 globally.
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