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3 years ago

1. Which expresses the given inequality in interval notation?

Mathematics

2 answers:

kow [346]3 years ago

8 0

Answer:

The corrext answer is C.

Digiron [165]3 years ago

7 0

1) x < 4 the answer is Option C: x E(-infinity,4) (it is strict)
2) 2x +6 < 8, and 2x < 8 - 6 = 2, and x<2/2=1
the answer is 
D. x E (-infinity, 1)
3) X greater than or equal to 8 and x < - 4
X greater than 8 means x ≥ 8
so we have x ≥ 8 and x < - 4
so the answer is 
B. x E (-4,8]
 4)
7 > x + 6 or x -2 greater than or equal to 3,
7 > x + 6 or x -2 ≥ 3

7 -6> x, and 1>x

x -2 ≥ 3 x≥ 3+2=5
finally
x<1 and x≥5

the answer is
C.x E (1,5]
5)

|x+3| > 12,
|x+3| = { -(x+3) if x+3<0 or (x+3) if x+3>0}

so, it is -(x+3)>12 is equivalent to (x+3)< -12 or (x+3)>12
the answer is
B. x + 3 > 12 or x + 3 <-12

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Answer:

-1.

Step-by-step explanation:

(tanx- secx) (tanx+ secx).

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= tan^2 x - sec^2 x.

But sec^2 x = 1 + tan^2 x

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3 years ago

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Suppose that 40 percent of the drivers stopped at State Police checkpoints in Storrs on Spring Weekend show evidence of driving

lesantik [10]

Answer:

a) 0.778

b) 0.9222

c) 0.6826

d) 0.3174

e) 2 drivers

Step-by-step explanation:

Given:

Sample size, n = 5

P = 40% = 0.4

a) Probability that none of the drivers shows evidence of intoxication.

$P(x=0) = ^nC_x P^x (1-P)^n^-^x$

$P(x=0) = ^5C_0 (0.4)^0 (1-0.4)^5^-^0$

$P(x=0) = ^5C_0 (0.4)^0 (0.60)^5$

$P(x=0) = 0.778$

b) Probability that at least one of the drivers shows evidence of intoxication would be:

P(X ≥ 1) = 1 - P(X < 1)

$= 1 - P(X = 0)$

$= 1 - ^5C_0 (0.4)^0 * (0.6)^5$

$= 1 - 0.0778$

$= 0.9222$

c) The probability that at most two of the drivers show evidence of intoxication.

P(x≤2) = P(X = 0) + P(X = 1) + P(X = 2)

$^5C_0 (0.4)^0 (0.6)^5 + ^5C_1 (0.4)^1 (0.6)^4 + ^5C_2 (0.4)^2 (0.6)^3$

$= 0.6826$

d) Probability that more than two of the drivers show evidence of intoxication.

P(x>2) = 1 - P(X ≤ 2)

$= 1 - [^5C_0 (0.4)^0 (0.6)^5 + ^5C_1 (0.4)^1 (0.6)^4 + ^5C_2 * (0.4)^2 (0.6)^3]$

$= 1 - 0.6826$

$= 0.3174$

e) Expected number of intoxicated drivers.

To find this, use:

Sample size multiplied by sample proportion

n * p

= 5 * 0.40

= 2

Expected number of intoxicated drivers would be 2

7 0

3 years ago

Ac is tangent to circle o at point c what is the length of ac?

MissTica

Answer:

The Answer is 12

Step-by-step explanation:

Use Pythagorean theorem. AB=8 and BO=5 We still need to find AO

AO=AB+BO

8+5

AO=13

Now solve for AC

AC^2 + OC^2= AO^2

AC^2+5^2=13^2

AC^2+ 25=169

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5 0

3 years ago

I don’t know how to solve this

Dmitrij [34]

Answer:

y = $\frac{1}{4}$ x - 5

Step-by-step explanation:

The equation of a line in slope- intercept form is

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Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) =( 8, - 3) and (x₂, y₂ ) = (0, - 5)

m = $\frac{-5+3}{0-8}$ = $\frac{-2}{-8}$ = $\frac{1}{4}$

Note the line crosses the y- axis at (0, - 5 ) ⇒ c = - 5

y = $\frac{1}{4}$ x - 5 ← equation of line

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