Fraction 4 5/6 -2 2/7

Otrada [13]

$\huge\color{pink}\boxed{\colorbox{black}{Answer ☘}}$

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1 )

$(8 + 5) {}^{2} + (14 - 18 \div 6) \\ = > (13) {}^{2} + (14 - 3) \\ = > 169 + 11 \\ = > 180$

2)

$(14 + 24 - 6) \div 16 - 2 {}^{2} \\ = > 32 \div 16 - 4 \\ = > 2 - 4 \\ = > - 2$

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8 0

2 years ago

Read 2 more answers

In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal dist

WARRIOR [948]

Answer:

(a) The probability that more than 180 will take your free sample is 0.1056.

(b) The probability that fewer than 200 will take your free sample is 0.9997.

(c) The probability that a customer will take a free sample and buy the product is 0.2184.

(d) The probability that between 60 and 80 customers will take the free sample and buy the product is 0.8005.

Step-by-step explanation:

We are given that about 56% of all customers will take free samples. Furthermore, of those who take the free samples, about 39% will buy what they have sampled.

The day you were offering free samples, 303 customers passed by your counter.

Firstly, we will check that it is appropriate to use the normal approximation to the binomial, that is;

Is np > 5 and n(1-p) > 5

In our question, n = sample of customers = 303

p = probability that customers will take free sample = 56%

So, np = $303 \times 0.56$ = 169.68 > 5

n(1-p) = $303 \times (1-0.56)$ = 133.32 > 5

Since, both conditions are satisfied so it is appropriate to use the normal approximation to the binomial.

Now, mean of the normal distribution is given by;

Mean, $\mu$ = $n \times p$ = 169.68

Also, the standard deviation of the normal distribution is given by;

Standard deviation, $\sigma$ = $\sqrt{n \times p \times (1-p)}$

= $\sqrt{303 \times 0.56 \times (1-0.56)}$ = 8.64

Let X = Number of people who will take your free sample

The z score probability distribution for normal distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

(a) The probability that more than 180 will take your free sample is given by = P(X > 180) = P(X > 180.5) {Using continuity correction}

P(X > 180.5) = P( $\frac{X-\mu}{\sigma}$ > $\frac{180.5-169.68}{8.64}$ ) = P(Z > 1.25) = 1 - P(Z < 1.25)

= 1 - 0.8944 = 0.1056

(b) The probability that fewer than 200 will take your free sample is given by = P(X < 200) = P(X < 199.5) {Using continuity correction}

P(X < 199.5) = P( $\frac{X-\mu}{\sigma}$ < $\frac{199.5-169.68}{8.64}$ ) = P(Z < 3.45) = 0.9997

(c) We are given in the question that of those who take the free samples, about 39% will buy what they have sampled, this means that we have;

P(Buy the product / taken a free sample) = 0.39

So, Probability(customer will take a free sample and buy the product) = P(customer take a free sample) $\times$ P(Buy the product / taken a free sample)

= 0.56 $\times$ 0.39 = 0.2184

(d) Now our mean and standard deviation will get changed because the probability of success now is p = 0.2184 but n is same as 303.

So, Mean, $\mu$ = $n \times p$ = $303 \times 0.2184$ = 66.18

Standard deviation, $\sigma$ = $\sqrt{n \times p \times (1-p)}$

= $\sqrt{303 \times 0.2184 \times (1-0.2184)}$ = 7.192

Now, the probability that between 60 and 80 customers will take the free sample and buy the product is given by = P(60 < X < 80) = P(59.5 < X < 80.5) {Using continuity correction}

P(59.5 < X < 80.5) = P(X < 80.5) - P(X $\leq$ 59.5)

P(X < 80.5) = P( $\frac{X-\mu}{\sigma}$ < $\frac{80.5-66.18}{7.192}$ ) = P(Z < 1.99) = 0.9767

P(X $\leq$ 59.5) = P( $\frac{X-\mu}{\sigma}$ $\leq$ $\frac{59.5-66.18}{7.192}$ ) = P(Z $\leq$ -0.93) = 1 - P(Z < 0.93)

= 1 - 0.8238 = 0.1762

Therefore, P(59.5 < X < 80.5) = 0.9767- 0.1762 = 0.8005.

4 0

3 years ago

What is the area, in square millimeters, of a right triangle with a hypotenuse of 68 millimeters and a leg of 60 millimeters?

Paladinen [302]

First, we have to solve the sides of the right triangle by using the Pythagorean theorem: a² + b² = c² where c is the length of the hypotenuse. Then, we can use the legs as length and height of the triangle and find the area by 1/2(base x height).

x² + 60² = 68²
x² + 3600 = 4624
x² = 1024
x = √1024
x = 32 = length of the other side

A = (1/2)(32) (60) = 960 mm²

6 0

3 years ago

Sophie has 5 pieces of string that are 4 yards each. She uses 3 pieces that are each 3 feet long. How much string does Sophie ha

stich3 [128]

Alright, lets get started.

Sophie has 5 pieces of string that are 4 yards each.

1 yards = 3 feet,

So, 4 yards = $4 * 3 =12$ feet

Total number of string she has = 5 piece

So, total length she has = $5*12 = 60$ feet

It means she had 60 feet string in starting.

Now, She uses 3 pieces that are each 3 feet long, means

She uses = $3*3 = 9$ feet

So, remaining string length will be = $60 - 9 = 51$ feet

Means 51 feet string does Sophie have. : Answer

Hope it will help :)

5 0

3 years ago

Read 2 more answers

Find the unit rate. round to the nearest hundred if necessary

Lina20 [59]

360÷60=60 60 miles per hour 6840÷45=152 152 costumes per day 45.5÷13=3.5 rounded to nearest hundred= 4 4 meters per second $7.40÷5=$1.48 rounded to nearest hundred = 1 $1 per pound

3 0

3 years ago

Fraction 4 5/6 -2 2/7 - 1 3/14 ​

Fraction 4 5/6 -2 2/7 - 1 3/14