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4 years ago

Determine which package of laundry soap is the better buy: 65 ounces for 6.99 of 120 ounces of 12.99

1 answer:

3 0

65 oz for 6.99....
6.99/65 = 0.107

120 oz for 12.99..
12.99 / 120 = 0.108

well...if u rounded them, they would cost the same.....but actually, 65 oz is about 1/1000 cheaper....I would probably say they cost about the same because I dont think that 1/1000 difference is gonna make that much of a difference

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A university found that 20% of its students withdraw without completing the introductory statistics course. Assume that 20 stude

Mkey [24]

Answer:

(a) Probability that 2 or fewer will withdraw is 0.2061.

(b) Probability that exactly 4 will withdraw is 0.2182.

(c) Probability that more than 3 will withdraw is 0.5886.

(d) The expected number of withdrawals is 4.

Step-by-step explanation:

We are given that a university found that 20% of its students withdraw without completing the introductory statistics course.

Assume that 20 students registered for the course.

The above situation can be represented through binomial distribution;

$P(X =r) = \binom{n}{r} \times p^{r} \times (1-p)^{n-r};x=0,1,2,3,......$

where, n = number of trials (samples) taken = 20 students

r = number of success

p = probability of success which in our question is probability

that students withdraw without completing the introductory

statistics course, i.e; p = 20%

Let X = Number of students withdraw without completing the introductory statistics course

So, X ~ Binom(n = 20 , p = 0.20)

(a) Probability that 2 or fewer will withdraw is given by = P(X $\leq$ 2)

P(X $\leq$ 2) = P(X = 0) + P(X = 1) + P(X = 2)

= $\binom{20}{0} \times 0.20^{0} \times (1-0.20)^{20-0}+ \binom{20}{1} \times 0.20^{1} \times (1-0.20)^{20-1}+ \binom{20}{2} \times 0.20^{2} \times (1-0.20)^{20-2}$

= $1 \times1 \times 0.80^{20}+ 20 \times 0.20^{1} \times 0.80^{19}+ 190\times 0.20^{2} \times 0.80^{18}$

= 0.2061

(b) Probability that exactly 4 will withdraw is given by = P(X = 4)

P(X = 4) = $\binom{20}{4} \times 0.20^{4} \times (1-0.20)^{20-4}$

= $4845\times 0.20^{4} \times 0.80^{16}$

= 0.2182

(c) Probability that more than 3 will withdraw is given by = P(X > 3)

P(X > 3) = 1 - P(X $\leq$ 3) = 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3)

= $1-(\binom{20}{0} \times 0.20^{0} \times (1-0.20)^{20-0}+ \binom{20}{1} \times 0.20^{1} \times (1-0.20)^{20-1}+ \binom{20}{2} \times 0.20^{2} \times (1-0.20)^{20-2}+\binom{20}{3} \times 0.20^{3} \times (1-0.20)^{20-3})$

= $1-(1 \times1 \times 0.80^{20}+ 20 \times 0.20^{1} \times 0.80^{19}+ 190\times 0.20^{2} \times 0.80^{18}+1140\times 0.20^{3} \times 0.80^{17})$

= 1 - 0.4114 = 0.5886

(d) The expected number of withdrawals is given by;

E(X) = $n\times p$

= $20 \times 0.20$ = 4 withdrawals

3 0

4 years ago

Write an expression for 35 minus b.

aalyn [17]

Answer:

35-b

Step-by-step explanation:

the answer is 35-b

8 0

3 years ago

Solve for x. ax + b = r

fomenos

Answer:

ax+b=r

ax=r-b

x = r-b/a

8 0

3 years ago

22: A 2.0 kg object moves along the x-axis under the influence of an unknown force. Its potential energy due to the force is U(x

aleksandr82 [10.1K]

Answer: a) -13.25 N, b) 1.78 m/sec

Step-by-step explanation:

Since we have given that

$U(x)=ax^4+bx^2$

where

$a=2.5\ J/m^4\\\\b=12\ J/m^2$

As we know that

$F=\dfrac{-dU}{dx}=-(4ax^3+2bx)$

Here, x= 0.5 m

So, it becomes,

$F=-(4\times 2.5\times (0.5)^3+2\times 12\times 0.5)=-13.25\ N$

Now, we need to find the velocity when it crosses the origin,

$F=mg\\\\F=m\dfrac{dv}{dt}\\\\F=mv\dfrac{dv}{dx}\\\\-(4ax^3+2bx)dx=mvdv\\\\\int\limits^{0.5}_0 {-(4ax^3+2bx)} \, dx =\int\limits {mv} \, dv\\\\ \dfrac{-4ax^4}{4}+\dfrac{2bx^2}{2}|_0^{0.5}=\dfrac{mv^2}{2}\\\\ax^4+bx^2|_0^{0.5}=\dfrac{mv^2}{2}\\\\2.5(0.5)^4+12(0.5)^2=\dfrac{2v^2}{2}\\\\0.15625+3=v^2\\\\3.15625=v^2\\\\\sqrt{3.15625}=v\\\\v=1.78$

Hence, a) -13.25 N, b) 1.78 m/sec

7 0

4 years ago

I need helppppp I forgot how to do this :(

Otrada [13]

a=associates / p=partners

1a= $800 / 1p= $1500

(6)a + (2)p = 800 x 6 + 1500 + 2 = $7800

(x)a + (y)p = $z

hope this helps :)

7 0

3 years ago