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3 years ago

Which of these expressions are equivalent to 4x+2(2x−5)−(3−5x) ? Choose the TWO correct answers. 3x−13

Mathematics

1 answer:

Julli [10]3 years ago

3 0

Answer: 4x+2(2x−5)−(3−5x) = 8x-10-3+5x

Step-by-step explanation: We need to find the equivalent expression to 4x+2(2x−5)−(3−5x).

Using distributive property as follows :

a(b+c) = ab+ac

4x+2(2x−5)−(3−5x) = 4x+4x-10-3+5x

= 8x-10-3+5x

Option (e)

Hence, the correct option is (e) "8x-10-3+5x"

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Line ET is tangent to circle A at point T and the measure of angle TNG is 35.

STALIN [3.7K]

ET is tangent to circle A so ET is perpendicular to AT

So <ATE = 90°

Given <TNG = 35°

<NET = <ATE - <TNG

= 90° - 35°

= 55°

Answer is 55°

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3 years ago

1 3 9 10 TIME REI 25: Consider the function y = asin(bx), where a > 0 and b>0. Which change compresses the graph verticall

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Making the value of 'a' smaller, but still positive, will make the graph be compressed vertically.

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3 years ago

A recent study suggested that 70% of all eligible voters will vote in the next presidential election. Suppose 20 eligible voters

natita [175]

Answer:

0.0479 = 4.79% probability that fewer than 11 of them will vote

Step-by-step explanation:

For each voter, there are only two possible outcomes. Either they will vote, or they will not. The probability of a voter voting is independent of any other voter, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

70% of all eligible voters will vote in the next presidential election.

This means that $p = 0.7$

20 eligible voters were randomly selected from the population of all eligible voters.

This means that $n = 20$

What is the probability that fewer than 11 of them will vote?

This is:

$P(X < 11) = P(X = 10) + P(X = 9) + P(X = 8) + P(X = 7) + P(X = 6) + P(X = 5) + P(X = 4) + P(X = 3) + P(X = 2) + P(X = 1) + P(X = 0)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 10) = C_{20,10}.(0.7)^{10}.(0.3)^{10} = 0.0308$

$P(X = 9) = C_{20,9}.(0.7)^{9}.(0.3)^{11} = 0.0120$

$P(X = 8) = C_{20,8}.(0.7)^{8}.(0.3)^{12} = 0.0039$

$P(X = 7) = C_{20,7}.(0.7)^{7}.(0.3)^{13} = 0.0010$

$P(X = 6) = C_{20,10}.(0.7)^{6}.(0.3)^{12} = 0.0002$

$P(X = 5) = C_{20,5}.(0.7)^{5}.(0.3)^{15} \approx 0$

The probability of 5 or less voting is very close to 0, so they will not affect the outcome. Then

$P(X < 11) = P(X = 10) + P(X = 9) + P(X = 8) + P(X = 7) + P(X = 6) + P(X = 5) + P(X = 4) + P(X = 3) + P(X = 2) + P(X = 1) + P(X = 0) = 0.0308 + 0.0120 + 0.0039 + 0.0010 + 0.0002 = 0.0479$

0.0479 = 4.79% probability that fewer than 11 of them will vote

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3 years ago

Find an equation of a line through √3,1 / 2) parallel to the line:

vagabundo [1.1K]

Answer:

(a) $x=\sqrt{3}$

(b) $y=\frac{1}{2}$

(c) Answer of part a is equation of line $x=\sqrt{3}$ which is parallel to y axis and in part by equation of line is $y=\frac{1}{2}$ which is parallel to x axis

Step-by-step explanation:

We have given points are $(\sqrt{3},\frac{1}{2})$

(a) Equation of line is given x = -9

We have to find the equation of line parallel to x= -9 and passing through $(\sqrt{3},\frac{1}{2})$

x = -9 line is parallel to y axis and so slope will be infinite

Equation of line is given by $y-y_1=m(x-x_1)$

So $y-\frac{1}{2}=\frac{1}{0}(x-\sqrt{3})$

$x=\sqrt{3}$

(b) Equation of line is given $y=-\sqrt{7}$

This line is parallel to x axis so slope will be zero

So equation of line will be $y-\frac{1}{2}=0(x-\sqrt{3})$

$y=\frac{1}{2}$

(c) Answer of part a is equation of line $x=\sqrt{3}$ which is parallel to y axis and in part by equation of line is $y=\frac{1}{2}$ which is parallel to x axis

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3 years ago

A package of 5 pairs of insulated socks costs $39.45. What is the unit price of the pairs of socks?

Brums [2.3K]

Answer:

7.89

Step-by-step explanation:

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2 years ago

Read 2 more answers