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3 years ago

Alex is 22 years older than Lana. Four years ago Lana’s age was one-half of Alex’s current age. How old was Alex four years ago?

Mathematics

2 answers:

katen-ka-za [31]3 years ago

7 0

Answer:

Step-by-step explanation

22 divided by 2 is 11

it says four years ago so add 11 and 4 and that equals 15

she is 15 right now. then add 22 which is 37 and subtract 4 which your answer would be 33

icang [17]3 years ago

3 0

22 divided by 2 is 11

it says four years ago so add 11 and 4 and that equals 15

she is 15 right now. then add 22 which is 37 and subtract 4 which your answer would be 33

33 is the answer.

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The test scores on a 100-point test were recorded for 20 students:71 93 91 86 7573 86 82 76 5784 89 67 62 7277 68 65 75 84a. Can

Dafna11 [192]

Answer: a. Yes

b. mean = 76.65

standard deviation = 10.04

c. 76.65 ± 4.4

Step-by-step explanation:

a. Stem and leaf Plot shows the frequencies with which classes of value occur. To create this plot, we divide the set of numbers into 2 columns: stem, the left column, which contains the tens digits; leaf, the right column, which contains the unit digits.

Normal distribution is a type of distribution: it's a bell-shaped, symmetrical, unimodal distribution.

A stem and leaf plot displays the main features of the distribution. If turned on its side, we can see the shape of the data.

The figure below shows the stem and leaf plot of the 100-point test score. As we can see, when turned, the plot resembles bell-shaped distribution. So, this test scores were selected from a normal population.

b. Mean is the average number of a data set. It is calculated as the sum of all the data divided by the quantity the sample has:

mean = $\frac{\Sigma x}{n}$

For the 100-point test score:

mean = $\frac{71+93+91+...+65+75+84}{20}$

mean = 76.65

Standard Deviation determines how much the data is dispersed from the mean. It is calculated as:

$s=\sqrt{\frac{\Sigma (x-mean)^{2}}{n-1} }$

For the 100-point test score:

$s=\sqrt{\frac{[(71-76.65)+(93-76.65)+...+(84-76.65)]^{2}}{20-1} }$

s = 10.04

The mean and standard deviation of the scores are 76.65 and 10.04, respectively.

c. Confidence Interval is a range of values we are confident the real mean lies.

The calculations for the confidence interval is

mean ± $z\frac{s}{\sqrt{n} }$

where

z is the z-score for the 95% confidence interval, which is equal 1.96

Calculating interval

76.65 ± $1.96.\frac{10.04}{\sqrt{20} }$

76.65 ± 4.4

The 95% confidence interval for the average test score in the population of students is between 72.25 and 81.05.

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3 years ago

Two complex numbers are represented by c + di and , where c, d, e, and f are positive real numbers. In what two quadrants may th

myrzilka [38]

Answer: In quadrant 1 or quadrant 2.

Step-by-step explanation:

We have the numbers:

x = c + di

y = e + fi

where c, d, e and f are real positive numbers.

the product of these numbers is:

x*y = (c + di)*(e + fi) = c*e + c*fi + d*ei ´+d*f*i^2

x*y = c*e - d*f + (c*f + d*e)i

where I used that i^2 = -1

knowing that c,f, d and e are positive numbers, then the imaginary part of the product must be always positive.

For the real part, we have c*e - d*f, that can be positive o negative depending on the values of c, e, d, and f.

So we have that the product must lie always in one of the upper two quadrants, quadrant 1 or quadrant 2 because the imaginary part is always positive and the real part can be positive or negative.

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