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Leokris [45]
3 years ago
10

Multiply and simplify.

Mathematics
2 answers:
Rasek [7]3 years ago
6 0
Expand the following:
(2 x - 3) (x^2 + 4 x - 6)

 | | | | 2 x | - | 3
 | | x^2 | + | 4 x | - | 6
 | | | | -12 x | + | 18
 | | 8 x^2 | - | 12 x | + | 0
2 x^3 | - | 3 x^2 | + | 0 | + | 0
2 x^3 | + | 5 x^2 | - | 24 x | + | 18:

Answer: 2 x^3 + 5 x^2 - 24 x + 18
kupik [55]3 years ago
5 0
Hello there!

(2x - 3)(x² + 4x - 6)

Start by using the distributive property

=(2x)(x²) + (2x)(4x) + (2x)(-6) + (-3)(x²) + (-3)(4x) + (-3)(-6)

= 2x³ + 8x² - 12x - 3x² - 12x + 18

= 2x³ + 5x² - 24x + 18


As always, it is my pleasure to help students like you!
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A test was given to a group of students. The grades and gender are summarized below
faust18 [17]

Answer:

<h3>★ <u>11/</u><u>3</u><u>0</u> is the right answer. ★</h3>

Step-by-step explanation:

  • Number of male students who got 'A' in the test is 11
  • Number of female students who got 'A' in the test is 19
  • Total students who got 'A' in the test is 30
  • Probability that the male student got an 'A' is P(A | male) = (Number of male students who got 'A' in the test)/(Number of total students who got 'A' in the test) = <em><u>11/</u></em><em><u>3</u></em><em><u>0</u></em>
4 0
3 years ago
HELP QUICK LOTS OF POINTS
Bad White [126]

Answer:

  see attached

Step-by-step explanation:

When the sequence of sides (shortest to longest, for example) remains the same (CW or CCW), then the number of reflections is even, possibly zero. The figure will have been <em>translated</em> if all of the corresponding sides retain their original direction, otherwise <em>rotation</em> is involved.

If the sequence is reversed, as in the upper right and lower left figures, then <em>reflection</em> is involved. The line of reflection will be the line through the midpoints of the segments connecting corresponding vertices.

6 0
3 years ago
Read 2 more answers
Let X denote the length of human pregnancies from conception to birth, where X has a normal distribution with mean of 264 days a
Kaylis [27]

Answer:

Step-by-step explanation:

Hello!

X: length of human pregnancies from conception to birth.

X~N(μ;σ²)

μ= 264 day

σ= 16 day

If the variable of interest has a normal distribution, it's the sample mean, that it is also a variable on its own, has a normal distribution with parameters:

X[bar] ~N(μ;σ²/n)

When calculating a probability of a value of "X" happening it corresponds to use the standard normal: Z= (X[bar]-μ)/σ

When calculating the probability of the sample mean taking a given value, the variance is divided by the sample size. The standard normal distribution to use is Z= (X[bar]-μ)/(σ/√n)

a. You need to calculate the probability that the sample mean will be less than 260 for a random sample of 15 women.

P(X[bar]<260)= P(Z<(260-264)/(16/√15))= P(Z<-0.97)= 0.16602

b. P(X[bar]>b)= 0.05

You need to find the value of X[bar] that has above it 5% of the distribution and 95% below.

P(X[bar]≤b)= 0.95

P(Z≤(b-μ)/(σ/√n))= 0.95

The value of Z that accumulates 0.95 of probability is Z= 1.648

Now we reverse the standardization to reach the value of pregnancy length:

1.648= (b-264)/(16/√15)

1.648*(16/√15)= b-264

b= [1.648*(16/√15)]+264

b= 270.81 days

c. Now the sample taken is of 7 women and you need to calculate the probability of the sample mean of the length of pregnancy lies between 1800 and 1900 days.

Symbolically:

P(1800≤X[bar]≤1900) = P(X[bar]≤1900) - P(X[bar]≤1800)

P(Z≤(1900-264)/(16/√7)) - P(Z≤(1800-264)/(16/√7))

P(Z≤270.53) - P(Z≤253.99)= 1 - 1 = 0

d. P(X[bar]>270)= 0.1151

P(Z>(270-264)/(16/√n))= 0.1151

P(Z≤(270-264)/(16/√n))= 1 - 0.1151

P(Z≤6/(16/√n))= 0.8849

With the information of the cumulated probability you can reach the value of Z and clear the sample size needed:

P(Z≤1.200)= 0.8849

Z= \frac{X[bar]-Mu}{Sigma/\sqrt{n} }

Z*(Sigma/\sqrt{n} )= (X[bar]-Mu)

(Sigma/\sqrt{n} )= \frac{(X[bar]-Mu)}{Z}

Sigma= \frac{(X[bar]-Mu)}{Z}*\sqrt{n}

Sigma*(\frac{Z}{(X[bar]-Mu)})= \sqrt{n}

n = (Sigma*(\frac{Z}{(X[bar]-Mu)}))^2

n = (16*(\frac{1.2}{(270-264)}))^2

n= 10.24 ≅ 11 pregnant women.

I hope it helps!

6 0
3 years ago
Find the coordinates for the midpoint of the segment with endpoints given. (12, 4) and (-8, 8) (2, 6) (10, 6) (2, 2)
cluponka [151]
The given coordinates are:
p1: (12,4) and p2: (-8,8)

Th x coordinate of the midpoint is calculated as follows:
Xmidpoint = (x1+x2) / 2 = (12+-8) / 2 = 4/2 = 2

The y coordinate of the midpoint is calculated as follows:
Ymidpoint = (y1+y2) / 2 = (4+8) / 2 = 12/2 = 6

Based on the above calculations, the midpoint of the segment with the given coordinates is (2,6)
8 0
3 years ago
joe spends $8 on lunch and $6.50 on dry cleaning. He also buys 2 shiets that cost the same amount. joe spendes a total of $52. w
ANEK [815]
X=amout the shirts cost
52=8+6.50+2x
add 8 and 6.5
52=14.5+2x
subtract 14.5 from 52
37.5=2x
divide 37.5 by 2
x=18.75
It cost $18.75 for each shirt.
4 0
3 years ago
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