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sergeinik [125]
3 years ago
7

The number 4 + i is multiplied by some real number to yield 2 + one-half i. Which equation is true?

Mathematics
2 answers:
dsp733 years ago
5 0

Answer:

A

Step-by-step explanation:

1/2(4+i)=2+1/2i

Right on edge

Nesterboy [21]3 years ago
3 0

Answer:

A. (1/2)(4+i)= 2+ (1/2)i

Step-by-step explanation:

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You always need some time to get up after the alarm has rung. You get up from 10 to 20 minutes later, with any time in that inte
Mama L [17]

Answer:

a) P(x<5)=0.

b) E(X)=15.

c) P(8<x<13)=0.3.

d) P=0.216.

e) P=1.

Step-by-step explanation:

We have the function:

f(x)=\left \{ {{\frac{1}{10},\, \, \, 10\leq x\leq 20 } \atop {0, \, \, \, \, \, \,  otherwise }} \right.

a)  We calculate  the probability that you need less than 5 minutes to get up:

P(x

Therefore, the probability is P(x<5)=0.

b) It takes us between 10 and 20 minutes to get up. The expected value is to get up in 15 minutes.

E(X)=15.

c) We calculate  the probability that you will need between 8 and 13 minutes:

P(8\leq x\leq 13)=P(10\leqx\leq 13)\\\\P(8\leq x\leq 13)=\int_{10}^{13} f(x)\, dx\\\\P(8\leq x\leq 13)=\int_{10}^{13} \frac{1}{10} \, dx\\\\P(8\leq x\leq 13)=\frac{1}{10} \cdot [x]_{10}^{13}\\\\P(8\leq x\leq 13)=\frac{1}{10} \cdot (13-10)\\\\P(8\leq x\leq 13)=\frac{3}{10}\\\\P(8\leq x\leq 13)=0.3

Therefore, the probability is P(8<x<13)=0.3.

d)  We calculate the probability that you will be late to each of the 9:30am classes next week:

P(x>14)=\int_{14}^{20} f(x)\, dx\\\\P(x>14)=\int_{14}^{20} \frac{1}{10} \, dx\\\\P(x>14)=\frac{1}{10} [x]_{14}^{20}\\\\P(x>14)=\frac{6}{10}\\\\P(x>14)=0.6

You have 9:30am classes three times a week.  So, we get:

P=0.6^3=0.216

Therefore, the probability is P=0.216.

e)  We calculate the probability that you are late to at least one 9am class next week:

P(x>9.5)=\int_{10}^{20} f(x)\, dx\\\\P(x>9.5)=\int_{10}^{20} \frac{1}{10} \, dx\\\\P(x>9.5)=\frac{1}{10} [x]_{10}^{20}\\\\P(x>9.5)=1

Therefore, the probability is P=1.

3 0
3 years ago
Which shape is both rectangle and a square?
mina [271]

Step-by-step explanation:

the rhombus is both rectangle and square

8 0
2 years ago
Read 2 more answers
According to the University of Nevada Center for Logistics Management, 6% of all mer-
Fudgin [204]

Answer:

a) The point estimate of the proportion of items returned for the population of

sales transactions at the Houston store = 12/80 = 0.15

b) The 95% confidence interval for the proportion of returns at the Houston store = [0.0718 < p < 0.2282].

c) Yes.

We set an hypothesis and construct a test statistics. The test statistics result gives us:

Z calculated  = 2.2545, and this gives us the p-value = 0.0121. We assumed 95% confident interval. Hence, the level of significance (α) = 5%. Conclusively, since the p-value ==> 0.0121 is less than (α) = 5%, the test is significant. Hence, the proportion of returns at the Houston store is significantly different from the returns  for the nation as a whole.

Step-by-step explanation:

a) Point estimate of the proportion = number of returned items/ total items sold = 12/80 = 0.15.

b) By formula of confident interval:

CI(95%) = p ± Z*\sqrt{\frac{p*(1-p)}{n} }  =  0.15 \pm 1.96 *\sqrt{\frac{0.15*(1-0.15)}{80} },

CI(95%) = [0.0718 < p < 0.2282]

c) The hypothesis:

H_{0}: The proportion of returns at the Houston store is not significantly different from the returns  for the nation as a whole.

H_{a}: The proportion of returns at the Houston store is significantly different from the returns  for the nation as a whole.

The test statistics:

Z = \frac{\hat{p} - p_{0}}{\sqrt{\frac{p*(1-p)}{n} }}, where p_{0} is the proportion of nation returns.

Z calculated  = 2.2545, and this gives us the p-value = 0.0121. We assumed 95% confident interval. Hence, the level of significance (α) = 5%. Conclusively, since the p-value ==> 0.0121 is less than (α) = 5%, the test is significant. Hence, the proportion of returns at the Houston store is significantly different from the returns  for the nation as a whole.

6 0
3 years ago
The perimeter of this triangle is 25 units. An angle bisector divides one side of the triangle into lengths of 2 and 3. Find the
grin007 [14]

Answer:

   8 and 12

Step-by-step explanation:

Sides on one side of the angle bisector are proportional to those on the other side. In the attached figure, that means

  AC/AB = CD/BD = 2/3

The perimeter is the sum of the side lengths, so is ...

  25 = AB + BC + AC

  25 = AB + 5 + (2/3)AB . . . . . . substituting AC = 2/3·AB. BC = 2+3 = 5.

  20 = 5/3·AB

  12 = AB

  AC = 2/3·12 = 8

_____

<em>Alternate solution</em>

The sum of ratio units is 2+3 = 5, so each one must stand for 25/5 = 5 units of length.

That is, the total of lengths on one side of the angle bisector (AC+CD) is 2·5 = 10 units, and the total of lengths on the other side (AB+BD) is 3·5 = 15 units. Since 2 of the 10 units are in the segment being divided (CD), the other 8 must be in that side of the triangle (AC).

Likewise, 3 of the 15 units are in the segment being divided (BD), so the other 12 units are in that side of the triangle (AB).

The remaining sides of the triangle are AB=12 and AC=8.

7 0
3 years ago
Please help with this problem:
Olegator [25]
He added 8 to both sides. He did the write thing.
6 0
3 years ago
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