Find the equation of the line

The volume of a cylinder can is 1.54 litre and area of base is 77cm^2 Find its height

goblinko [34]

Answer:

The height is 20 cm.

Step-by-step explanation:

First, we have to know that the volume formula is V = πr²h and the base area of cylinder is a circle. So we can let πr² be 77 cm² . Then we have to substitute the following values into the formula :

$v = 1.54 \: l$

$v = 1540 \: {cm}^{3}$

$v = \pi \times {r}^{2} \times h$

Let πr² be 77,

Let v be 1540,

$1540 = 77 \times h$

$77h = 1540$

$h = 1540 \div 77$

$h = 20 \: cm$

5 0

3 years ago

The amount of syrup that people put on their pancakes is normally distributed with mean 63 mL and standard deviation 13 mL. Supp

andreyandreev [35.5K]

Answer:

(a) X ~ N( $\mu=63, \sigma^{2} = 13^{2}$ ).

$\bar X$ ~ N( $\mu=63,s^{2} = (\frac{13}{\sqrt{43} } )^{2}$ ).

(b) If a single randomly selected individual is observed, the probability that this person consumes is between 61.4 mL and 62.8 mL is 0.0398.

(c) For the group of 43 pancake eaters, the probability that the average amount of syrup is between 61.4 mL and 62.8 mL is 0.2512.

(d) Yes, for part (d), the assumption that the distribution is normally distributed necessary.

Step-by-step explanation:

We are given that the amount of syrup that people put on their pancakes is normally distributed with mean 63 mL and a standard deviation of 13 mL.

Suppose that 43 randomly selected people are observed pouring syrup on their pancakes.

(a) Let X = amount of syrup that people put on their pancakes

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

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

where, $\mu$ = mean amount of syrup = 63 mL

$\sigma$ = standard deviation = 13 mL

So, the distribution of X ~ N( $\mu=63, \sigma^{2} = 13^{2}$ ).

Let $\bar X$ = sample mean amount of syrup that people put on their pancakes

The z-score probability distribution for the sample mean is given by;

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

where, $\mu$ = mean amount of syrup = 63 mL

$\sigma$ = standard deviation = 13 mL

n = sample of people = 43

So, the distribution of $\bar X$ ~ N( $\mu=63,s^{2} = (\frac{13}{\sqrt{43} } )^{2}$ ).

(b) If a single randomly selected individual is observed, the probability that this person consumes is between 61.4 mL and 62.8 mL is given by = P(61.4 mL < X < 62.8 mL)

P(61.4 mL < X < 62.8 mL) = P(X < 62.8 mL) - P(X $\leq$ 61.4 mL)

P(X < 62.8 mL) = P( $\frac{X-\mu}{\sigma}$ < $\frac{62.8-63}{13}$ ) = P(Z < -0.02) = 1 - P(Z $\leq$ 0.02)

= 1 - 0.50798 = 0.49202

P(X $\leq$ 61.4 mL) = P( $\frac{X-\mu}{\sigma}$ $\leq$ $\frac{61.4-63}{13}$ ) = P(Z $\leq$ -0.12) = 1 - P(Z < 0.12)

= 1 - 0.54776 = 0.45224

Therefore, P(61.4 mL < X < 62.8 mL) = 0.49202 - 0.45224 = 0.0398.

(c) For the group of 43 pancake eaters, the probability that the average amount of syrup is between 61.4 mL and 62.8 mL is given by = P(61.4 mL < $\bar X$ < 62.8 mL)

P(61.4 mL < $\bar X$ < 62.8 mL) = P( $\bar X$ < 62.8 mL) - P( $\bar X$ $\leq$ 61.4 mL)

P( $\bar X$ < 62.8 mL) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ < $\frac{62.8-63}{\frac{13}{\sqrt{43} } }$ ) = P(Z < -0.10) = 1 - P(Z $\leq$ 0.10)

= 1 - 0.53983 = 0.46017

P( $\bar X$ $\leq$ 61.4 mL) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ $\leq$ $\frac{61.4-63}{\frac{13}{\sqrt{43} } }$ ) = P(Z $\leq$ -0.81) = 1 - P(Z < 0.81)

= 1 - 0.79103 = 0.20897

Therefore, P(61.4 mL < X < 62.8 mL) = 0.46017 - 0.20897 = 0.2512.

(d) Yes, for part (d), the assumption that the distribution is normally distributed necessary.

4 0

3 years ago

What are the equivalent fractions for 2 1/5 and 1 5/6 using 30 as the common denominator

Anuta_ua [19.1K]

Answer:

2 6/30 and 1 25/30

Step-by-step explanation:

First, you need to find 30÷5 and 30÷6. You do this because you need to know the multiplier when you create an equivalent fraction. 30÷5 is 6 and 30÷6 is 5. 2 1/5. You need to multiply the 1 and 5 by 6, that is 2 6/30. 1 5/6. 5 and 6 multiplied by 5 is 25 and 30. 1 5/6=1 25/30

4 0

3 years ago

Solve for x 2-3(2x-1)=-6x+5

Simora [160]

Step 1: Simplify both sides of the equation.
2
−
3
(
2
x
−
1
)
=
−
6
x
+
5
2
+
(
−
3
)
(
2
x
)
+
(
−
3
)
(
−
1
)
=
−
6
x
+
5
(Distribute)
2
+
−
6
x
+
3
=
−
6
x
+
5
(
−
6
x
)
+
(
2
+
3
)
=
−
6
x
+
5
(Combine Like Terms)
−
6
x
+
5
=
−
6
x
+
5
−
6
x
+
5
=
−
6
x
+
5
Step 2: Add 6x to both sides.
−
6
x
+
5
+
6
x
=
−
6
x
+
5
+
6
x
5
=
5
Step 3: Subtract 5 from both sides.
5
−
5
=
5
−
5
0
=
0

6 0

3 years ago

Cancel my entire subscription please

stepladder [879]

Answer:

https://faq.brainly.com/hc/en-us/articles/360011078640-Cancelling-subscription-purchased-on-website

Step-by-step explanation:

6 0

3 years ago

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