Use the exchange rate £1 = €1.11 to convert €222 into £.

3.In 1995, the Educational Testing Service in Princeton, New Jersey (which administers SAT exam) re-centered the scores so that

Travka [436]

Answer:

38.22% probability that of 10 randomly selected students, lessthan four will be between 900 and 1,100

Step-by-step explanation:

For each student, there are only two possible outcomes. Either they score between 900 and 1,100, or they score outside this range. The probability of a student scoring between 900 and 1,100 is independent from other students. 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.

About 40 percent of these students’ scores were between 900 and 1,100.

This means that $p = 0.4$ .

a)Based on this estimate, what is the probability that of 10 randomly selected students, lessthan four will be between 900 and 1,100?

This is $P(X < 4)$ when $n = 10$ . So

$P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)$

In which

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

$P(X = 0) = C_{10,0}.(0.4)^{0}.(0.6)^{10} = 0.0060$

$P(X = 1) = C_{10,1}.(0.4)^{1}.(0.6)^{9} = 0.0403$

$P(X = 2) = C_{10,2}.(0.4)^{2}.(0.6)^{8} = 0.1209$

$P(X = 3) = C_{10,3}.(0.4)^{3}.(0.6)^{7} = 0.2150$

$P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0060 + 0.0403 + 0.1209 + 0.2150 = 0.3822$

38.22% probability that of 10 randomly selected students, lessthan four will be between 900 and 1,100

8 0

4 years ago

Factor to solve: x² + 18x +27 = 8x +3

patriot [66]

Answer: $x=-4$ $or$ $x=-6$

Subtract 8x+3 from both sides

$x^2+18x+27-(8x+3)=8x+3-(8x+3)$

$x2+10x+24=0$

Factor left side of equation

$(x+4)(x+6)=0$

Set factors equal to 0

$x+4=0$ $or$ $x+6=0$

Final Answer: $x=-4$ $or$ $x=-6$

3 0

4 years ago

URGENTLY NEED THIS ASAP PLZ TYSM

Kazeer [188]

Answer:

fifth option

Step-by-step explanation:

Given

- 2(x - 5) ≤ 6x + 18 ← distribute left side

- 2x + 10 ≤ 6x + 18 ( subtract 6x from both sides )

- 8x + 10 ≤ 18 ( subtract 10 from both sides )

- 8x ≤ 8

Divide both sides by - 8, reversing the sign as a result of dividing by a negative quantity, thus

x ≥ - 1

3 0

4 years ago

Helllp i give brainliest

Sergeu [11.5K]

Answer:

50 is the right answer

Step-by-step explanation:

please mark me as brainliest answer

4 0

3 years ago

Read 2 more answers

A trebuchet launches a projectile from a hilltop 30 feet above ground level on a parabolic arc at a velocity of 40 feet per seco

erica [24]

Answer:

t = 3.1 seconds

Step-by-step explanation:

Set the equation h = -16t^2 + 40t + 30 equal to 0 (0 represents ground level).

Then h = -16t^2 + 40t + 30 = 0

Applying the quadratic formula with a = -16, b = 40 and c = 30,

-40 ± √( 1600 - 4[-16][30] )

t = -----------------------------------------

2(-16)

-40 ± √ 3520

t = -------------------------

-32

-40 - 59.33

Only the positive t value makes sense. It is t = ------------------

-32

t = 3.1 seconds

8 0

3 years ago