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2 years ago

7

Simon and greg shared pencils in the ratio 7:5. if simon gives away 30 pencils and greg gets 30 more pencils, they will have the

same number of pencils. how many did each of them have in the beginning?

1 answer:

Dafna1 [17]2 years ago

7 0

Simon has 210 pencils
Greg has 150 pencils

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Shawn has 4 nickles. How many walnuts can he buy if he spends all 4 nickels?

Roman55 [17]

Answer:

This really depends.

Step-by-step explanation:

If a walnut costs 10 cents, he can buy 2 walnuts.

If a walnut costs 5 cents, he can buy 4.

If a walnut costs 20 cents, he can buy 3.

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2 years ago

The following model can be used to study whether campaign expenditures affect election outcomes: voteA = β0 + β1log(expendA) + β

rosijanka [135]

Answer:

(i) It represents change in expenditure by candidates A; (ii) $H_0:\beta_1+\beta_2=0$

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1 year ago

Suppose that only 20% of all drivers come to a complete stop at an intersection having flashing red lights in all directions whe

Lina20 [59]

Answer:

a) 91.33% probability that at most 6 will come to a complete stop

b) 10.91% probability that exactly 6 will come to a complete stop.

c) 19.58% probability that at least 6 will come to a complete stop

d) 4 of the next 20 drivers do you expect to come to a complete stop

Step-by-step explanation:

For each driver, there are only two possible outcomes. Either they will come to a complete stop, or they will not. The probability of a driver coming to a complete stop is independent of other drivers. So we use the binomial probability distribution 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.

20% of all drivers come to a complete stop at an intersection having flashing red lights in all directions when no other cars are visible.

This means that $p = 0.2$

20 drivers

This means that $n = 20$

a. at most 6 will come to a complete stop?

$P(X \leq 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)$

In which

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

$P(X = 0) = C_{20,0}.(0.2)^{0}.(0.8)^{20} = 0.0115$

$P(X = 1) = C_{20,1}.(0.2)^{1}.(0.8)^{19} = 0.0576$

$P(X = 2) = C_{20,2}.(0.2)^{2}.(0.8)^{18} = 0.1369$

$P(X = 3) = C_{20,3}.(0.2)^{3}.(0.8)^{17} = 0.2054$

$P(X = 4) = C_{20,4}.(0.2)^{4}.(0.8)^{16} = 0.2182$

$P(X = 5) = C_{20,5}.(0.2)^{5}.(0.8)^{15} = 0.1746$

$P(X = 6) = C_{20,6}.(0.2)^{6}.(0.8)^{14} = 0.1091$

$P(X \leq 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) = 0.0115 + 0.0576 + 0.1369 + 0.2054 + 0.2182 + 0.1746 + 0.1091 = 0.9133$

91.33% probability that at most 6 will come to a complete stop

b. Exactly 6 will come to a complete stop?

$P(X = 6) = C_{20,6}.(0.2)^{6}.(0.8)^{14} = 0.1091$

10.91% probability that exactly 6 will come to a complete stop.

c. At least 6 will come to a complete stop?

Either less than 6 will come to a complete stop, or at least 6 will. The sum of the probabilities of these events is decimal 1. So

$P(X < 6) + P(X \geq 6) = 1$

We want $P(X \geq 6)$ . So

$P(X \geq 6) = 1 - P(X < 6)$

In which

$P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.0115 + 0.0576 + 0.1369 + 0.2054 + 0.2182 + 0.1746 = 0.8042$

$P(X \geq 6) = 1 - P(X < 6) = 1 - 0.8042 = 0.1958$

19.58% probability that at least 6 will come to a complete stop

d. How many of the next 20 drivers do you expect to come to a complete stop?

The expected value of the binomial distribution is

$E(X) = np = 20*0.2 = 4$

4 of the next 20 drivers do you expect to come to a complete stop

4 0

2 years ago

what is f(x) = 2x2 28x – 5 written in vertex form? f(x) = 2(x 7)2 – 19 f(x) = 2(x 7)2 – 103 f(x) = 2(x 14)2 – 14 f(x) = 2(x 14)2

Katarina [22]

Hello,
++++++++++++++++++++++
Answer B
++++++++++++++++++++++

2x²+28x-5=2(x²+2*7x+49)-5-2*48
=2(x+7)²-103

++++++++++++++++++++++++++++++

4 0

2 years ago

Read 2 more answers

Henry is 3 times older than Julia. Rhianna is 1/2 as old as Julia. What formula shows the relationship between Henry and Rhianna

Sedbober [7]

The answer is A because if you make up an age for Julia for example Julia is 6 years old. In that case we multiply her age by 3 to figure out Henry's age which is 18. Rhianna is half as old as Julia is so that would make her 3 years old. In order for Henry which he is 18 years old to get to Rhianna's age which is 3 years old. you just divide 18 by 3 which is 6 years old. therefore the answer is A

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1 year ago