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1 year ago

Two fifths of the candies in a bag are mint. There are 34 mint candies.

1 answer:

6 0

So 2/5 are mint. that should mean if you divide 34 with 2, you will get 1/5 of the candy. SO! Divide 34 with 2 and you will get 17. The muiltiply with 5 then you will get the answer...

85 candies!!!

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Tahari is shopping for a new car. She is making her decision based on brand, color, and style. She can choose from 4 brands, 5 c

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If she chose the color she would have 12 options left.

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1 year ago

Read 3 more answers

A probability calculator is required on this problem; answer to six decimal places. Suppose we will spin the wheel pictured 400

KiRa [710]

Answer:

$P(90< X< 110)= P(\frac{90-80}{8}$

And we can find this probability with this difference:

$P(90< X< 110)=P(z$

And we can find the real value with the following excel code using the binomial distribution:

"=BINOM.DIST(110,400,0.2,TRUE)-BINOM.DIST(89,400,0.2,TRUE)"

And we got 0.118 a very close value from the value obtained using the normal approximation

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=400, p=0.2)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

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

We need to check the conditions in order to use the normal approximation.

$np=400*0.2=80 \geq 10$

$n(1-p)=400*(1-0.2)=320 \geq 10$

So we see that we satisfy the conditions and then we can apply the approximation.

If we appply the approximation the new mean and standard deviation are:

$E(X)=np=400*0.2=80$

$\sigma=\sqrt{np(1-p)}=\sqrt{400*0.2(1-0.2)}=8$

So then we can approximate the random variable as $X \sim N(\mu = 80, \sigma = 8)$

And we want this probability:

$P(90< X< 110)$

We can use the z score formula given by:

$z = \frac{x -\mu}{\sigma}$

And replacing we got:

$P(90< X< 110)= P(\frac{90-80}{8}$

And we can find this probability with this difference:

$P(90< X< 110)=P(z$

And we can find the real value with the following excel code using the binomial distribution:

"=BINOM.DIST(110,400,0.2,TRUE)-BINOM.DIST(89,400,0.2,TRUE)"

And we got 0.118 a very close value from the value obtained using the normal approximation

8 0

1 year ago

walnut grower estimates from past records that if 20 trees are planted per acre, then each tree will average 60 pounds of nuts p

laila [671]

Answer:

5 trees should be planted to maximize the yield per acre,

The maximum yield would be 1250

Step-by-step explanation:

Given,

The original number of trees per acre = 20,

Average pounds of nuts by a tree = 60,

Let x be the times of increment in number of trees,

So, the new number of trees planted per acre = 20 + x

∵ for each additional tree planted per acre, the average yield per tree drops 2 pounds,

So, the new number of pounds of nut = (60 - 2x)

Thus, the total yield per acre,

$Y(x) = (20+x)(60-2x)$

Differentiating with respect to t ( time ),

$Y'(x) = (20+x)(-2) + 60 - 2x = -40 - 2x + 60 - 2x = 20 - 4x$

Again differentiating with respect to t,

$Y''(x) = -4$

For maxima or minima,

$Y'(x) = 0$

⇒ 20 - 4x = 0

⇒ 20 = 4x

⇒ x = 5,

For x = 5, Y''(x) = negative,

Hence, Y(x) is maximum for x = 5,

And, maximum value of Y(x) = (20+5)(60 - 10) = 25(50) = 1250,

i.e. 5 trees should be planted to maximize the yield per acre,

and the maximum yield would be 1250 pounds

4 0

1 year ago

an employer will do a 50% match on your investment to a 401k retirement plan. If you decide to contribute a monthly amount of $2

faltersainse [42]

Answer:

The amount that should be in the account after 15 years is $95,321.85

Step-by-step explanation:

According to the given data, we have the following:

monthly amount of $220=R

interest rate is fixed at 2.05%. We require the monthly ineterest rate, hence monthly interest rate= 2.05%/12=0.1708%=0.0017

t=15years×12=180 months

In order to calculate how much should be in the account after 15 years, we would have to use the following formula:

Ap=R(1-(1+i)∧-t)

Ap=220(1-(1+0.0017)∧-180)

0.0017

Ap=162,04

0.0017

Ap=$95,321.85

The amount that should be in the account after 15 years is $95,321.85

6 0

1 year ago

Marissa buys a licorice candy rope to share with some friends. The rope is 30 and two thirds inches long. She begins to cut the

adell [148]

9!
3.33 x 9 =(about)= 29.97

4 0

1 year ago