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2 years ago

7

Mrs. Smith bought 6.5 metres of lace. She used 1.3 metre to make a dress. She used the rest to make 4 cushions of the same size.

How much lace did she use for each cushion, giving your answer in centimetres?

2 answers:

Vadim26 [7]2 years ago

5 0

Bdbdhd dbdbdbd d did

Scorpion4ik [409]2 years ago

5 0

6.5 - 1.3 = 5.2
5.2 metres = 520 centimeters
520/4 = 130 centimeters on each cushion

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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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Which inequality represents the values of that ensure triangle exists? a triangle with these side lengths: AC = 18 units, BC = 6

erastovalidia [21]

AC = 18

BC = 6x

AB = 2x + 4

Write and solve:

18 + 6x + 2x + 4

18 + 8x + 4 = 180

You can solve further:

18 + 8x = 176

8x = 158

x = 19 & 3/4

Not 100% sure what the question is asking, but hopefully this helps.

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10 mililiters per cup

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1 b
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The line with equation x + y = 0 coincides with the terminal side of an angle θ in standard position in Quadrant II .

Naya [18.7K]

Answer:

tanθ = -1

m=tanθ = -1

Step-by-step explanation:

Step 1:-

using formula m=tanθ

Given straight line is x+y=0

The given straight line is passing through the origin so y = -x

straight line is passing through the origin so y = m x

m = -1

Step3:-

The line with equation x+y=0 with the terminal side of an angle θ in standard position in Quadrant II i.e., θ = 90+45=135

m = tanθ

m = tan(90+45)

m = - cot 45

m = -1

Step4:- m =tanθ =-1

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