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3 years ago

10

What is the solution to x - 9 > -15?

2 answers:

ella [17]3 years ago

7 0

Answer:

x> -6

Step-by-step explanation:

x - 9 > -15

Add 9 to each side

x - 9+9 > -15+9

x> -6

valina [46]3 years ago

4 0

Answer:

x:-6

Step-by-step explanation:

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Please help!!!!!!! multiple choice question in the picture

marishachu [46]

Answer:66

Step-by-step explanation:

4 0

3 years ago

Sixty percent of the eligible voting residents of a certain community support the incumbent candidate. If eight of the residents

il63 [147K]

By the binomial theorem we know that

$1 = (.4 + .6)^8 \\ = {8 \choose 0} (.4)^{8} (.6)^{0} + {8 \choose 1} (.4)^{7} (.6)^{1} +{8 \choose 2} (.4)^{6} (.6)^{2} + {8 \choose 3} (.4)^{5} (.6)^{3} + {8 \choose 4} (.4)^{4} (.6)^{4} \\ + \quad {8 \choose 5} (.4)^{3} (.6)^{5} + {8 \choose 6} (.4)^{2} (.6)^{6} + {8 \choose 7} (.4)^{1} (.6)^{7} + {8 \choose 8} (.4)^{0} (.6)^{8}$

The probability that exactly 5 of 8 support the incumbent is the term

${8 \choose 5} (.4)^{3} (.6)^{5}$

So at least five of eight support is the sum of this term and beyond,

$p={8 \choose 5} (.4)^{3} (.6)^{5} + {8 \choose 6} (.4)^{2} (.6)^{6} + {8 \choose 7} (.4)^{1} (.6)^{7} + {8 \choose 8} (.4)^{0} (.6)^{8}$

No particularly easy way of calculating that except popping it into Wolfram Alpha which reports

$p = \dfrac{ 46413}{78125}$

Shouldn't half the terms work out to .6 ? Interestingly it's not exactly .6 but pretty close at .594.

6 0

4 years ago

For a hyperbolic mirror the two foci are 42 cm apart. The distance of the vertex from one focus is 6 cm and from the other focus

navik [9.2K]

Answer:

$\dfrac{y^2}{225} -\dfrac{x^2}{216}=1$

Step-by-step explanation:

For a hyperbolic mirror the two foci are 42 cm apart.

The distance between the foci = 2c.

Therefore:

2c=42
c=21

The distance of the vertex from one focus = 6 cm

The distance of the vertex from the other focus = 36 cm

2a=36-6=30

a=15

Now:

$c^2=a^2+b^2\\21^2=15^2+b^2\\b^2=21^2-15^2\\b^2=216\\b=6\sqrt{6}$

If the transverse axis lies on the y-axis, and the hyperbola is centered at the origin. Then the hyperbola has an equation of the form:

$\dfrac{y^2}{a^2} -\dfrac{x^2}{b^2}=1$

Therefore, the equation of the hyperbola is:

$\dfrac{y^2}{225} -\dfrac{x^2}{216}=1$

4 0

4 years ago

Select the equivalent expression.

denpristay [2]

Answer:

$\boxed{\bold{[C] \ \ \ \ \frac{1}{3^5} } }}$

Explanation:

Apply Exponent Rule: $\bold{\:a^{-b}=\frac{1}{a^b}}$

$\bold{3^{-5}: \ \frac{1}{3^5} }$

5 0

3 years ago

What is the value of x?<br><br><br><br> Enter your answer in the box.

spayn [35]

Answer:

x = 75

Step-by-step explanation:

The parallel lines FS and DY divide their transversals into proportional segments. That is ...

... x/50 = 63/42

Multiplying by 50 gives x:

... 63/42·50 = x = 75

3 0

3 years ago