steven and jaden are solving b is either of them correct? explain your reasoning and in complete sentences.

Elena is buying cups and plates for her party. Cups are sold in packs of 8 and plates are sold in packs of 6. She wants to have

Svet_ta [14]

Answer:

For 80 people, Elena would need

14 packs of plates and 10 packs of cups

She would have at least 80 of each.

I am not completely sure of this, sorry if wrong.

Step-by-step explanation:

80 people

8 cups per pack

6 plates per pack

8, 16, 24, 32, 40, 48, 56, 64, 72, 80

6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84

LCM (least common multiple) = 24

8 0

2 years ago

Read 2 more answers

If the filling equipment is functioning properly what is the probability that the volume of oil in a randomly selected barrel wi

Sophie [7]

Answer:

$P(X>55.4)=P(\frac{X-\mu}{\sigma}>\frac{55.4-\mu}{\sigma})=P(Z>\frac{55.4-55}{0.5})=P(Z>0.8)$

$P(Z>0.8)=1-P(Z\leq 0.8)$

$P(Z>0.8)=1-0.788=0.212$

Step-by-step explanation:

Assuming this previous info : "Trucks carry barrels of crude oil from a port in Texas to a distributer in New Mexico on long trailers. Filling equipment is used to fill the barrels with the oil. When functioning properly, the actual volume of oil loaded into each barrel by the filling equipment at the port is approximately normally distributed with a mean of 55 gallons and a standard deviation of 0.5 gallons. If the mean is greater than 55.4 gallons, the filling mechanism is overfilling."

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the amount filling of a population, and for this case we know the distribution for X is given by:

$X \sim N(55,0.5)$

Where $\mu=55$ and $\sigma=0.5$

We are interested on this probability

$P(X>55.4)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

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

If we apply this formula to our probability we got this:

$P(X>55.4)=P(\frac{X-\mu}{\sigma}>\frac{55.4-\mu}{\sigma})=P(Z>\frac{55.4-55}{0.5})=P(Z>0.8)$

And we can find this probability using the complement rule:

$P(Z>0.8)=1-P(Z\leq 0.8)$

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

$P(Z>0.8)=1-0.788=0.212$

8 0

3 years ago

3/8-1/3 I rly need help and FAST

elixir [45]

Answer:

Step-by-step explanation:

1/24

6 0

3 years ago

The following data on average daily hotel room rate and amount spent on entertainment (The Wall Street Journal, August 18, 2011)

Zielflug [23.3K]

Answer:

a. Predicted Amount = $109.46

b. Confidence Interval = (94.84,124.08)

c. Interval = (110.6883,188.8517)

Step-by-step explanation:

Given

ŷ = 17.49 + 1.0334x.

SSE = 1541.4

a.

ŷ = 17.49 + 1.0334(89)

ŷ = 109.4626

ŷ = 109.46 --- Approximated

Predicted Amount = $109.46

b.

ŷ = 17.49 + 1.0334(89)

ŷ = 109.4626

ŷ = 109.46

First we calculate the standard deviation

variance = SSE/(n-2)

v = 1541.4/(9-2)

v = 1541.4/7

v = 220.2

s = √v

s = √220.2

s = 14.839

Then we calculate mean(x) and ∑(x - (mean(x))²

X --- Y -- Mean(x) --- ∑(x - (mean(x))²

148 -- 161 -- 43-- 1849

96 || 105|| -9 || 81

91 ||101 || -14 || 196

110 || 142 || 5 || 25

90 || 100 || -15 || 225

102 || ||120 ||-3|| 9

136 || 167 ||31 ||961

90 || 140 ||-15 ||225

82 || 98 ||-23 || 529

Sum 945 || 1134|| 0 ||4100

Mean (x) = 945/9 = 105

∑(x - (mean(x))² = 4100

α = 1 - 95% = 5%

α/2 = 2.5% = 0.025

tα,df = n − 2 = t0.025,7 =2.365

Confidence interval = 109.46 ± 2.365 * 14.839 √((1/9)+ (89-105)²/4100

Confidence Interval = (109.46 ± 14.62)

Confidence Interval = (94.84,124.08)

c.

ŷ = 17.49 + 1.0334(128)

ŷ = 149.7652

ŷ = 149.77

Interval = 149.77 ± 2.365 * 14.839 √((1/9)+ (128-105)²/4100

Interval = 149.77 ± 39.0817

Interval = (110.6883,188.8517)

3 0

3 years ago

What is the angular velocity of a 6–foot pendulum that takes 3 seconds to complete an arc of 14.13 feet?

son4ous [18]

First find the central angle A in degree. Perimeter circle 2Pi*R --> 360 deg Arc A = 14.13 --> x deg (360*14.13)/2Pi*R = 5086.8/37.68 = 135 deg The pendulum rotates 135 deg in 3 sec. Then, the angular velocity is : 135/3 = 45 deg/sec.

Hope this helps!

3 0

3 years ago