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2 years ago

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When the phone rings at home, I never let it ring fewer than three times or more than 4 times. Today my little sister, who likes

to count everything, told me that the phone rang 17 times and that I answered all the calls. How many times did I answer the phone?

2 answers:

sukhopar [10]2 years ago

8 0

You either answered it 4 times or 5 times.

vagabundo [1.1K]2 years ago

6 0

You answer the phone 5 times:
x=number of calls
17/3.5=x
4.85=x that rounds into 5

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In circle O, central angle AOB measures StartFraction pi Over 3 EndFraction radians. Circle O is shown. Line segments A O and B

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Answer:

6(pie)

Step-by-step explanation:

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2 years ago

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Which could be the dimensions of a rectangular prism whose surface area is greater than 140 square feet? Select three options,

ElenaW [278]

Answer:

These are the rectangular prisms that have a surface area greater than 140 square feet

6 feet by 5 feet by 4 feet

7 feet by 6 feet by 4 feet

8 feet by 3 feet by 7 feet

Step-by-step explanation:

The formula to find the surface area of a rectangular prism is SA=2(wl+hl+hw)

All you have to do is go through all the options given to you to figure out which retangular prisms have a surface area greater than 140 square feet.

6 feet by 2 feet by 3 feet

SA = 2((2)(6)+(3)(6)+(3)(2))

SA = 2(12 + 18 + 6)

SA = 2(36)

SA = 72

6 feet by 5 feet by 4 feet

SA = 2((6)(5) + (4)(5) + (4)(6))

SA = 2(30 + 20 + 24)

SA = 2(74)

SA = 148

7 feet by 6 feet by 4 feet

SA = 2((7)(6) + (4)(6) + (4)(7))

SA = 2(42 + 24 + 28)

SA = 2(94)

SA = 188

8 feet by 3 feet by 7 feet

SA = 2((8)(3)+(7)(3)+(7)(8))

SA = 2(24 + 21 + 56)

SA = 2(101)

SA = 202

8 feet by 4 feet by 3 feet

SA = 2((8)(4)+(3)(4)+(3)(8))

SA = 2(32 + 12 + 24)

SA = 2(68)

SA = 136

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2 years ago

A sports company wants to package a ball with a 1.5-inch radius in sets of two. They have two options: a cylinder or a square pr

guajiro [1.7K]

Step 1

Find the Volume of the two balls

we know that

the Volume of a sphere is equal to

$V=\frac{4}{3} \pi r^{3}$

In this problem we have

$r=1.5\ in$

Substitute

$V=\frac{4}{3} \pi 1.5^{3}=4.5\pi\ in^{3}$

so

the volume of the two balls is equal

$V=2*4.5\pi=9 \pi\ in^{3}$

Step 2

Find the volume of a cylinder

we know that

The Volume of a cylinder is equal to

$V=\pi r^{2}h$

In this problem we have

$r=1.5\ in$

$h=4*r=4*1.5=6\ in$

Substitute

$V=\pi (1.5^{2})(6)=13.5 \pi\ in^{3}$

Step 3

Find the amount of wasted space in the cylinder

Subtract the volume of the two balls from the volume of the cylinder

$13.5\pi\ in^{3}-9\pi\ in^{3}=4.5\pi\ in^{3}=14.14\ in^{3}$

Step 4

Find the volume of the square prism

The volume of the prism is equal to

$V=Bh$

where

B is the area of the base of the prism

h is the height of the prism

In this problem we have

$B=(2*1.5)^{2}=9\ in^{2}$ -----> the base is equal to the diameter

$h=4*r=4*1.5=6\ in$

Substitute

$V=9*6=54\ in^{3}$

Step 5

Find the amount of wasted space in the prism

Subtract the volume of the two balls from the volume of the prism

$54\ in^{3}-9\pi\ in^{3}=25.73\ in^{3}$

Step 6

Compare the amount of wasted space

the amount of wasted space in the cylinder is $14.14\ in^{3}$

the amount of wasted space in the prism is $25.73\ in^{3}$

Find the difference

$25.73\ in^{3}-14.14\ in^{3}=11.59\ in^{3}=11.6\ in^{3}$

The package that has the least amount of wasted space is the cylinder

therefore

<u>the answer is the option</u>

the cylinder because it has approximately 11.6 in.3 less wasted space than the prism

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2 years ago

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in a group of 140 adults, 92 watch tennis, 81 play a sport and 40 do neither. find the probability that an adult chosen at rando

coldgirl [10]

Step-by-step explanation:

27.7%

Step-by-step explanation:

Let's call:

n: the number of adults interviewed

t: number of adults who watch tennis

d: number of adults who practice some sport

x: number of adults who watch tennis and do not practice a sport

The probability that a randomly chosen adult watches tennis and does not play any sports is calculated as follows:

- We calculate the probability that a selected adult will see tennis.

P(t) = 92/140 = 0.657

- We calculate the probability that an adult plays a sport:

P(d) = 81/140 = 0.5786

- We calculate the probability that an adult will see tennis and play some sport (See diagram attached)

P (t ∩ d) = 0.657 (0.5786) = 0.3802

Finally the probability that an adult who sees tennis does not play any sport is:

P(x) = P(t) - P(t ∩ d) = 0.657 - 0.3802

P(x) = 0.277

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2 years ago

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Leicester City Fanstore (LCF) will be selling the "new season jersey" for the 2018-2019 season. The regular price of the jersey

andrew-mc [135]

Complete Question

Leicester City Fanstore (LCF) will be selling the "new season jersey" for the 2018-2019 season. The regular price of the jersey is $80. Each jersey costs $40. Leftover jerseys will be sold at the end of the season (or later) at $30. Since jerseys are produced in China and lead time is long, Puma wants LCF to decide the quantity right now (December 2017).

a. After some analysis using historic data, LCF expects that the demand will follow a Normal distribution with a mean 40,000 and a standard deviation of 8,000 due to uncertainty in team performance. How many jerseys should LCF order?

b. If a customer cannot buy the jersey from LCF (in the case of a stock-out), they may leave the store disappointed and use other channels (such as Puma stores or puma.com) in future. LCF thinks that the lost customer goodwill is around $10. Should LCF change their decision in part (a)? If yes, please state the number of jerseys LCF should order.

c. Please state whether the following statement is always true, and give a brief explanation. If $C_o =C_i$ , the news vendor solution is the mean.

Answer:

a

$N = 46728$

b

$n = 47728$

c

Yes it is always true

Step-by-step explanation:

From the question we are told that

The regular price of the jersey is $P_r = \$ 80$

The cost of producing a jersey is $C= \$ 40$

The left-over price of the jersey is $P_o = $ 30$

The mean is $\mu = 40000$

The standard deviation is $\sigma = 8000$

The cost of lost customer goodwill is $C_g = \$ 10$

Generally the fund that LCF will loss for one jersey if they order for too many jersey (i.e more than they need )is mathematically represented

$C_o = P_o - C$

=> $C_o = 40 - 30$

=> $C_o = \$ 10$

Generally the fund that LCF will loss for one jersey if they order lesser amount jersey (i.e less than they need )is mathematically represented

$C_i = P_r - C$

=> $C_i = 80 - 40$

=> $C_i = \$ 40$

Generally the critical ratio is mathematically represented as

$Z = \frac{C_i }{ C_i + C_o}$

=> $Z = \frac{40}{ 40 + 10}$

=> $Z = 0.8$

Generally the critical value of $Z = 0.8$ to the right of the normal curve is

$z = 0.841$

Generally the optimal quantity of jersey to order is mathematically represented as

$N = \mu * [z * \sigma]$

=> $N = 40000 * [0.841 * 8000]$

=> $N = 46728$

Considering question b

Generally considering the factor of customer goodwill the fund that LCF will loss for one jersey if they order lesser amount jersey (i.e less than they need )is mathematically represented as

$C_k = C_i + C_g$

=> $C_k = 40 + 10$

=> $C_k = \$ 50$

Now the critical ratio is mathematically represented as

$Z = \frac{C_k }{ C_k + C_o}$

=> $Z = \frac{50}{ 50 + 10}$

=> $Z = 0.833$

Generally the critical value of $Z = 0.833$ to the right of the normal curve is

$z = 0.966$

Generally the optimal quantity of jersey to order is mathematically represented as

$n = \mu * [z * \sigma]$

=> $n = 40000 * [0.966 * 8000]$

=> $n = 47728$

Considering question c

When $C_o =C_i$ then

The critical ratio is mathematically represented as

$Z = \frac{C_k }{ C_k + C_k}$

=> $Z = \frac{1}{ 2}$

=> $Z = 0.5$

Generally the critical value of $Z = 0.5$ to the right of the normal curve is

$z = 0$

So

The optimal quantity of jersey to order is mathematically represented as

$n = \mu * [z * \sigma]$

=> $n = 40000 * [0* 8000]$

=> $n = 40000 = \mu$

Hence the statement in c is true

4 0

2 years ago