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Katyanochek1 [597]
1 year ago
15

Use the euclidean algorithm to find integers $x$ and $y$ such that $164x + 37y = 1,$ with the smallest possible positive value o

f $x$. state your answer as a list with $x$ first and $y$ second, separated by a comma.
Mathematics
1 answer:
Advocard [28]1 year ago
8 0

Well, let's use the Euclidean algorithm:

164 = 4×37 + 16

37 = 2×16 + 5

16 = 3×5 + 1

Then working backwards,

1 = 16 - 3×5

1 = 16 - 3×(37 - 2×16) = 7×16 - 3×37

1 = 7×(164 - 4×37) - 3×37 = 7×164 - 31×37

so that x = 7 and y = -31.

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A prism is dilated by a factor of 1.5. How many times larger is the volume of the resulting prism than the volume of the origina
Margarita [4]
By the term dilated we mean to say that the dimensions of the new polyhedron is increase to a certain size by that times. For the volume, this dilation scale should be cubed in order to determine the number of times the volume of new figure is larger than the original.
                                    r = (1.5)³
                                      = 3.375
Thus, the volume of the new prism is 3.375 times larger than the volume of the original prism. 
6 0
3 years ago
Read 2 more answers
a bowl contains 4 peaches and 4 apricots. Maine randomly selects one, puts it back, and randomly selects another. what is the pr
almond37 [142]
1/4 or 25% because...

The probability that Maine picks an apricot is 4/8

The probability that Maine picks an apricot after putting the first apricot back is still 4/8

4/8 x 4/8 = 16/64 = 1/4
4 0
2 years ago
1. Find the 90% Cl for the population mean if sample
Elden [556K]

Answer:

The answer is below

Step-by-step explanation:

1)

mean (μ) = 12, SD(σ) = 2.3, sample size (n) = 65

Given that the confidence level (c) = 90% = 0.9

α = 1 - c = 0.1

α/2 = 0.05

The z score of α/2 is the same as the z score of 0.45 (0.5 - 0.05) which is equal to 1.65

The margin of error (E) is given as:

E=Z_{\frac{\alpha}{2} }*\frac{\sigma}{\sqrt{n} } =1.65*\frac{2.3}{\sqrt{65} } =0.47

The confidence interval = μ ± E = 12 ± 0.47 = (11.53, 12.47)

2)

mean (μ) = 23, SD(σ) = 12, sample size (n) = 45

Given that the confidence level (c) = 88% = 0.88

α = 1 - c = 0.12

α/2 = 0.06

The z score of α/2 is the same as the z score of 0.44 (0.5 - 0.06) which is equal to 1.56

The margin of error (E) is given as:

E=Z_{\frac{\alpha}{2} }*\frac{\sigma}{\sqrt{n} } =1.56*\frac{12}{\sqrt{45} } =2.8

The confidence interval = μ ± E = 23 ± 2.8 = (22.2, 25.8)

8 0
3 years ago
HELP PLS i’ll mark as brainliest if correct
Vlada [557]

Answer:

I believe the answer is the second one

Step-by-step explanation:

7 0
3 years ago
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A rectangular flowerbed at a city park has an area of 126 square meters.the width of the flowerbed is 3 meters.what is the perim
Alona [7]

First we need to find the length. So we do 126/3 to get 42. The length is 42. Now to find perimeter we do 2(42)+2(3) or 42+42+3+3.

Both ways are right ways. The perimeter is 90 meters.

Hope that helps!!

6 0
3 years ago
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