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ludmilkaskok [199]
3 years ago
6

Fresh cut flowers need to be in at least 4in of water. A spherical vase is filled until the surface of the water is a circle of

5in in diameter. Is the water deep enough for the flowers? Explain.
Mathematics
1 answer:
Aleks [24]3 years ago
8 0

Answer:

No. The depth of the water is less than the required depth(2.5 inches<4 inches)

Step-by-step explanation:

-The deepest point of the half-filled vase is the point perpendicular to the sphere's midpoint.

-This point is equivalent to the extreme end of the radius.

-Since, the diameter is 5 inches, the radius is:

D=2r\\\\r=D/2\\\\=5/2\\\\=2.5 \ inches

2.5inches<4 inches

Hence, the water is not deep enough for the flowers.

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Sam wants to buy 8 pencils and 6 pens, which cost a total of $8.50. He realizes he doesn't have enough cash and instead takes on
Diano4ka-milaya [45]
X = pencils, y = pens

8x + 6y = 8.50
4x + 4y = 5.....multiply by -2
----------------
8x + 6y = 8.50
-8x - 8y = -10 (result of multiplying by -2)
-----------------add
-2y = - 1.50
y = -1.50 / -2
y = 0.75 <=== pens cost 0.75

4x + 4y = 5
4x + 4(0.75) = 5
4x + 3 = 5
4x = 5 - 3
4x = 2
x = 2/4
x = 0.50 <== pencils cost 0.50
8 0
3 years ago
In a recent study on world​ happiness, participants were asked to evaluate their current lives on a scale from 0 to​ 10, where 0
uysha [10]

Answer:

a) A response of 8.9 represents the 92nd ​percentile.

b) A response of 6.6 represents the 62nd ​percentile.

c) A response of 4.4 represents the first ​quartile.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 5.9

Standard Deviation, σ = 2.2

We assume that the distribution of response is a bell shaped distribution that is a normal distribution.

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

a) We have to find the value of x such that the probability is 0.92

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P( X < x) = P( z < \displaystyle\frac{x - 5.9}{2.2})=0.92

Calculation the value from standard normal z table, we have,  

P(z

\displaystyle\frac{x - 5.9}{2.2} = 1.405\\x = 8.991 \approx 8.9

A response of 8.9 represents the 92nd ​percentile.

b) We have to find the value of x such that the probability is 0.62

P(X < x)  

P( X < x) = P( z < \displaystyle\frac{x - 5.9}{2.2})=0.62

Calculation the value from standard normal z table, we have,  

P(z

\displaystyle\frac{x - 5.9}{2.2} = 0.305\\x = 6.571 \approx 6.6

A response of 6.6 represents the 62nd ​percentile.

c) We have to find the value of x such that the probability is 0.25

P(X < x)  

P( X < x) = P( z < \displaystyle\frac{x - 5.9}{2.2})=0.25

Calculation the value from standard normal z table, we have,  

P(z

\displaystyle\frac{x - 5.9}{2.2} = -0.674\\x = 4.4172 \approx 4.4

A response of 4.4 represents the first ​quartile.

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Step-by-step explanation:

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