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UkoKoshka [18]
3 years ago
8

Given the linear equation, 2x +4= 6, find the rate, initial value, and specific value.

Mathematics
1 answer:
kap26 [50]3 years ago
4 0

Answer: B. The rate is 2, the initial value is 4, and the specific value is 6.

Step-by-step explanation:

for a linear function y = a*x + b

Rate = coefficient that is multiplicating the variable. ( a in this case)

Initial value = value taken of y, when we have x = 0 (b in this case)

Specific value = value forced on y.

In this case, we have:

y = 6 = 2*x + 4

Then:

The coefficient multiplicating x is 2, so the rate is 2.

The constant term is 4, so the initial value is 4.

The value equal to y is 6, so the specific value is 6.

The correct option is B.

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The question is given in the picture.
lorasvet [3.4K]
This is a really interesting question! One thing that we can notice right off the bat is that each of the circles has the same amount of area swept out of it - namely, the amount swept out by one of the interior angles of the hexagon. Let’s call that interior angle θ. We know that the amount of area swept out in the circle is proportional to the angle swept out - mathematically

θ/360 = a/A

Where “a” is the area swept out by θ, and A is the area of the whole circle, which, given a radius of r, is πr^2. Substituting this in, we have

θ/360 = a/(πr^2)

Solving for “a”:

a = π(r^2)θ/360

So, we have the formula for the area of one of those sectors; all we need to do now is find θ and multiply our result by 6, since we have 6 circles. We can preempt this but just multiplying both sides of the formula by 6:

6a = 6π(r^2)θ/360

Which simplifies to

6a = π(r^2)θ/60

Now, how do we find θ? Let’s look first at the exterior angles of a hexagon. Imagine if you were taking a walk around a hexagon. At each corner, you turn some angle and keep walking. You make 6 turns in all, and in the end, you find yourself right back at the same place you started; you turned 360 degrees in total. On a regular hexagon, you’d turn by the same angle at each corner, which means that each of the six turns is 360/6 = 60 degrees. Since each interior and exterior angle pair up to make 180 degrees (a straight line), we can simply subtract that exterior angle from 180 to find θ, obtaining an angle of 180 - 60 = 120 degrees.

Finally, we substitute θ into our earlier formula to find that

6a = π(r^2)120/60

Or

6a = 2πr^2

So, the area of all six sectors is 2πr^2, or the area of two circles with radii r.
5 0
3 years ago
Define the random variables X and X in words. X is the amount of time an individual waits at the courthouse to be called for ser
densk [106]

<u>Question</u>

Suppose that a committee is studying whether or not there is excessive time waste in our judicial system. It is interested in the mean amount of time individuals spend at the courthouse waiting to be called for jury duty. The committee randomly surveyed 81 people who recently served as jurors. The sample mean wait time was 4 hours with a sample standard deviation of 1.2 hours. Define the random variables X and \bar{X} in words.

Answer:

(B)

  • X is the amount of time an individual waits at the courthouse to be called for service.
  • \bar{X}  is the mean wait time for a sample of individuals.

Step-by-step explanation:

The random variable X is the amount of time for which each of the prospective juror waits at the courthouse before being called for service.

\bar{X}  is the mean wait time for a the given sample of individuals. In the case given,

5 0
3 years ago
Find the values of A, B, and C in the table.​
PilotLPTM [1.2K]

Answer:

A = 1

B = 2

C = below

Step-by-step explanation:

Zero is included in the second interval, therefore, A = 1 is a correct choice (A must be also less than 2 ).

B must be positive, so that, f(0) is above the x-axis, therefore, B = 2 is a correct choice.

f(1.5) is negative, this means that the function is <u>below</u> the x-axis, then, C = below.

8 0
3 years ago
A watermelon weighs 8,475 grams. A scale measured the weight with an error of 12% under the actual weight. What was the measured
nordsb [41]
7,458 is the answer because 12% of 8475 is 1017 8475-1017 = 7458 so being the answer.
3 0
2 years ago
HALPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP. Please no links :P
beks73 [17]

Answer:

it will be x < 2

Step-by-step explanation:

Because the circle means greater than or less than. And if the circle isn't fillied up it means it is greater than or equal to or less thanor equal to.

4 0
3 years ago
Read 2 more answers
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