Answer:
a: 0.9544 9 within 8 units)
b: 0.9940
Step-by-step explanation:
We have µ = 300 and σ = 40. The sample size, n = 100.
For the sample to be within 8 units of the population mean, we would have sample values of 292 and 308, so we want to find:
P(292 < x < 308).
We need to find the z-scores that correspond to these values using the given data. See attached photo 1 for the calculation of these scores.
We have P(292 < x < 308) = 0.9544
Next we want the probability of the sample mean to be within 11 units of the population mean, so we want the values from 289 to 311. We want to find
P(289 < x < 311)
We need to find the z-scores that correspond to these values. See photo 2 for the calculation of these scores.
We have P(289 < x < 311) = 0.9940
Answer:
(C)18 units
Step-by-step explanation:
- Point G is the centroid of triangle ABC.
- C is a vertex of the triangle
- D is the midpoint of the side opposite the vertex.
From Centroid Theorems, we know that the distance from the centroid to the vertex is twice as long as the distance from the centroid to the midpoint of the side opposite the vertex.
Therefore:
CG=2DG
Let the length of segment DG =x
The length of segment CG is 6 units greater, therefore: CG=x+6
Substituting into CG=2DG:
x+6=2x
2x-x=6
x=6 Units
Therefore:
CD=CG+GD
=6+6+6
=18 Units
<u><em>The correct option is C.</em></u>
By knowing how much Mark deposits, how much he deducts and what is his initial balance, we can know what the final balance is.
We will see that the balance at the end of the month is $2224.
We know that:
Mark deposited:
$450, $312, $125, and $432.
<u>The total deposit</u> is: $450 + $312 + $125 + $432 = $1319
The deductions are:
$205 and $123
<u>The total deductions</u> are: $205 + $123 = $328
<u>The initial balance</u> is $1233.
The final balance will be equal to the initial balance plus what Mark deposits minus what Mark deducts, this is:
Final balance = $1233 + $1319 - $328 = $2224
We can conclude that the balance at the end of the month is $2224
If you want to learn more, you can read:
brainly.com/question/19245500
ANSWER
M=(−3,72)
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