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2 years ago

The sum of 2 consecutive whole numbers is 206. What are the 2 numbers

Mathematics

2 answers:

vlabodo [156]2 years ago

8 0

Answer:

There are no two consecutive whole numbers that sum to 206 (See proof below)

Step-by-step explanation:

let the first number be x

since the numbers are whole and consecutive, the second number must be (x + 1)

we are given that the number sum to 206

hence,

x + (x+1) = 206

x + x + 1 = 206

2x + 1 = 206 (subtract 1 from both sides)

2x = 206 - 1

2x = 205 (divide both sides by 2)

x = 205/2 = 102.5 (NOT A WHOLE NUMBER)

if x = 102.5, then the second number must be

x + 1 = 102.5 + 1 + 103.5 (ALSO NOT A WHOLE NUMBER)

Anni [7]2 years ago

5 0

Answer:

102.5, 103.5

Step-by-step explanation:

a+a+1=206

2a+1=206

2a=205

a=102.5

103.5

I think there is a bug here. They can't be whole numbers.

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A sample of size =n72 is drawn from a population whose standard deviation is =σ25. Part 1 of 2 (a) Find the margin of error for

kherson [118]

Answer:

a) margin of error ME = 5.77

b) Margin of error becomes smaller

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

x+/-ME

Where margin of error ME = zr/√n

Given that;

Mean = x

Standard deviation r = 25

Number of samples n = 72

Confidence interval = 95%

z(at 95% confidence) = 1.96

Substituting the values we have;

ME = 1.96(25/√72)

ME = 1.96(2.946278254943)

ME = 5.774705379690

ME = 5.77

For n = 89

ME = 1.96(25/√89)

ME = 1.96(2.649994700015)

ME = 5.193989612031

ME = 5.19

5.19 is smaller than 5.77 in a) above. So,

Margin of error becomes smaller

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2 years ago

Write 1.0315x10^6 in standard form

lapo4ka [179]

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3 years ago

A turtle is 20 5/6 inches below the surface of a pond. It dives to a depth of 32 1/4 inches. What is the change in the turtle’s

Naddik [55]

Change=new-original
change=32 and 1/4-20 and 5/6
32 and 1/4-20 and 5/6=
32+1/4-(20+5/6)=
32+1/4-20-5/6=
32-20+1/4-5/6=
1/4 and 5/6
LCD=12
1/4 times 3/3=3/12
5/6 times 2/2=10/12

32-10+3/12-10/12=
12-7/12=
11+12/12-7/12=
11+5/12
the turtle went down so the change is negative

the change is -11 and 5/12 inches

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3 years ago

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Stels [109]

Answer:

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3 years ago

Find the absolute extrema of the function over the region R. (In each case, R contains the boundaries.) Use a computer algebra s

algol [13]

f(x, y) = x ² - 4xy + 5

has critical points where both partial derivatives vanish:

∂f/∂x = 2x - 4y = 0 ==> x = 2y

∂f/∂y = -4x = 0 ==> x = 0 ==> y = 0

The origin does not lie in the region R, so we can ignore this point.

Now check the boundaries:

• x = 1 ==> f (1, y) = 6 - 4y

Then

max{f (1, y) | 0 ≤ y ≤ 2} = 6 when y = 0

max{f (1, y) | 0 ≤ y ≤ 2} = -2 when y = 2

• x = 4 ==> f (4, y) = 12 - 16y

Then

max{f (4, y) | 0 ≤ y ≤ 2} = 12 when y = 0

max{f (4, y) | 0 ≤ y ≤ 2} = -4 when y = 2

• y = 0 ==> f (x, 0) = x ² + 5

Then

max{f (x, 0) | 1 ≤ x ≤ 4} = 21 when x = 4

min{f (x, 0) | 1 ≤ x ≤ 4} = 6 when x = 1

• y = 2 ==> f (x, 2) = x ² - 8x + 5 = (x - 4)² - 11

Then

max{f (x, 2) | 1 ≤ x ≤ 4} = -2 when x = 1

min{f (x, 2) | 1 ≤ x ≤ 4} = -11 when x = 4

So to summarize, we found

max{f(x, y) | 1 ≤ x ≤ 4, 0 ≤ y ≤ 2} = 21 at (x, y) = (4, 0)

min{f(x, y) | 1 ≤ x ≤ 4, 0 ≤ y ≤ 2} = -11 at (x, y) = (4, 2)

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