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posledela
2 years ago
6

Five consecutive positive integers are chosen at random. If the average of the five integers is odd, what is the remainder when

the largest of the five integers is divided by 4?
Mathematics
1 answer:
kupik [55]2 years ago
4 0

Answer:

The remainder would be 1 or 3

Step-by-step explanation:

Consider the 5 consecutive positive integers are,

x,  x + 1,  x + 2,  x + 3,  x + 4,

Average =\frac{\text{Sum of all observation}}{\text{Number of observations}}

Since, the average of these 5 numbers = \frac{x+x+1+x+2+x+3+x+4}{5}

=\frac{5x+10}{5}

= x + 2

If x + 2 = odd,

⇒ x = odd - 2 = odd - even = odd

⇒ x + 4 = odd + even = odd

∵ an odd number is represented by '2n + 1'

Where, n = 0, 1, 2, 3, ........

Now, 2n + 1 = 1( mod 4) if n = even

While, 2n + 1 = 3( mod 4) if n = odd,

Hence, when the largest of the five integers is divided by 4 remainder would be 1 or 3.

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there are red and white roses in a vase 30% are red .there are 21 white roses.how many are there in total
jarptica [38.1K]

Answer:

Step-by-step explanation:

21 roses are white so that is 70%

so that would be 70/100 and can reduce to 7/10

and the percent of red would be 3/10

so we can do 21 divided by 7 which equals 3

then we can do 3 x 3 because 3/10 which equals 9

then you do 21 + 9= 30

so the answer is 30.

3 0
2 years ago
1) What is the first x in x + 3x = 16?
Lyrx [107]
1. x=22/5
2. x=4
3. x=4
5 0
2 years ago
A sample size of 500 is sufficiently large enough to conclude that the sampling distribution of the sample proportions is a norm
Paha777 [63]

In a statistical test, the null hypothesis to be made is that the sample proportions do not have any significant differences, which means an equal distribution. This is only rejected when the estimate is equal or less than 0.95. But since in this case it is >0.95, so therefore the null hypothesis is not rejected. Therefore:

<span>False</span>

7 0
3 years ago
While surveying Overlook Cave, Mike measures the angle of elevation from his line of sight to the top of a rock formation as 22°
Kaylis [27]

Answer:

The rock formation is approximately 7 feet tall.

Step-by-step explanation:

<em>We can visualize this situation as a triangle and know that the bottom side is </em><em>10</em><em> and the angle of elevation (the angle created by Mike and the ground, looking to the top of a rock). With this information, we can use tangent to solve.</em>

<em>x = the height of the rock formation</em>

tan(22°) = x/10

10 tan(22°) = x

x = ~4.04 feet

<em>We also have to add the </em><em>3 feet</em><em> to it because it is being measured 3 feet above the floor.</em>

x + 3 = 7.04 feet

7 0
2 years ago
What is the length of an arc with a central angle of 54π radians and a radius of 34 cm?
zvonat [6]
The formula in solving the length of an arc is shown below:
Length of an Arc = 2pi*r (central angle/360°)
Central angle = 54pi * (180°/pi) 
r = 34 cm

Solving for an arc length"
Arc length = 2*3.14*34((54*180)/360)
Arc length = 5,765.04 cm

The answer is 5,765.04 cm.
4 0
3 years ago
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