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3 years ago

Factor using ac-method, 15y+6y²-21= ________

Mathematics

1 answer:

Sunny_sXe [5.5K]3 years ago

3 0

$15y+6y^2-21=\\
6y^2+15y-21=\\
3(2y^2+5y-7)=\\
3(2y^2-2y+7y-7)=\\
3(2y(y-1)+7(y-1))=\\
3(2y+7)(y-1)
$

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Twenty percent of drivers driving between 10 pm and 3 am are drunken drivers. In a random sample of 12 drivers driving between 1

Lesechka [4]

Answer:

(a) 0.28347

(b) 0.36909

(d) 0.9806

Step-by-step explanation:

Given information:

n=12

p = 20% = 0.2

q = 1-p = 1-0.2 = 0.8

Binomial formula:

$P(x=r)=^nC_rp^rq^{n-r}$

(a) Exactly two will be drunken drivers.

$P(x=2)=^{12}C_{2}(0.2)^{2}(0.8)^{12-2}$

$P(x=2)=66(0.2)^{2}(0.8)^{10}$

$P(x=2)=\approx 0.28347$

Therefore, the probability that exactly two will be drunken drivers is 0.28347.

(b)Three or four will be drunken drivers.

$P(x=3\text{ or }x=4)=P(x=3)\cup P(x=4)$

$P(x=3\text{ or }x=4)=P(x=3)+P(x=4)$

Using binomial we get

$P(x=3\text{ or }x=4)=^{12}C_{3}(0.2)^{3}(0.8)^{12-3}+^{12}C_{4}(0.2)^{4}(0.8)^{12-4}$

$P(x=3\text{ or }x=4)=0.236223+0.132876$

$P(x=3\text{ or }x=4)\approx 0.369099$

Therefore, the probability that three or four will be drunken drivers is 0.3691.

(c)

At least 7 will be drunken drivers.

$P(x\geq 7)=1-P(x$

$P(x\leq 7)=1-[P(x=0)+P(x=1)+P(x=2)+P(x=3)+P(x=4)+P(x=5)+P(x=6)]$

$P(x\leq 7)=1-[0.06872+0.20616+0.28347+0.23622+0.13288+0.05315+0.0155]$

$P(x\leq 7)=1-[0.9961]$

$P(x\leq 7)=0.0039$

Therefore, the probability of at least 7 will be drunken drivers is 0.0039.

(d) At most 5 will be drunken drivers.

$P(x\leq 5)=P(x=0)+P(x=1)+P(x=2)+P(x=3)+P(x=4)+P(x=5)$

$P(x\leq 5)=0.06872+0.20616+0.28347+0.23622+0.13288+0.05315$

$P(x\leq 5)=0.9806$

Therefore, the probability of at most 5 will be drunken drivers is 0.9806.

5 0

3 years ago

PLS HELP ME 6, 7, and 8 (SHOW WORK!!) + LOTS OF POINTS + THANKS! + BRAINLIEST IF POSSIBLE!

julsineya [31]

6. $1 \frac{1}{2} = \frac{6}{4}$ since $\frac{1}{4} = 4$ feet. Then 6*4=24 So the answer is C

7. 1200 m/8 cm = C. 1 cm = 150 m

8. A. Since 1 in = 3 feet then 6 inches = 18 feet (6*3=18) and 4 inches = 12 feet (4*3=12) so the dimensions of her room are 16'x12'.

B. A=lxw so 16*12= 216 $m^{2}$

Hope that helps

6 0

3 years ago

Read 2 more answers

The vertices of quadrilateral PQRS are P(4, 5), Q(6, 6), R(9, 4), and S(7, 2). Write a paragraph proof to determine whether quad

Svetlanka [38]

The vector PQ is Q-P = (2, 1). The vector SR is R-S = (2, 2). One is not a multiple of the others, so the vectors are not parallel. In a parallelogram, these vectors would be identical. PQRS is not a parallelogram.

5 0

3 years ago

X+y=5 3x-4y=8 please i need the steps

grandymaker [24]

Answer:

x + y = 5

3x - 4y = 8

3x + 3y = 15

3x - 4y = 8 -

7y = 7

y = 1

x + y = 5

x + 1 = 5

x = 4

x = 4

y = 1

Hope it helps!

6 0

2 years ago

Can someone help me with this? I am a little confused

arsen [322]

28 .to explain they want to know the missing side and the triangles are equal to each-other just one is projected smaller than the other . So the one with 16 16 and 24 is the smaller one . The difference between 24-16 is 8 . And In the bigger one the sides 20 and 20 where given so since the smaller one is equal to the bigger one you just do 20+8=28

4 0

2 years ago