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salantis [7]
3 years ago
8

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

ism.
The company wants to use the package that has the least amount of wasted space. The company should choose

a.)the prism because it has approximately 11.6 in.3 less wasted space than the cylinder.
b.)the prism because it has approximately 14.1 in.3 less wasted space than the cylinder.
c.)the cylinder because it has approximately 11.6 in.3 less wasted space than the prism.
d.)the cylinder because it has approximately 14.1 in.3 less wasted space than the prism.
Mathematics
2 answers:
svp [43]3 years ago
4 0

Answer:

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

Step-by-step explanation:

if you find the volumes of both shapes and subtract the volumes of the two balls and then subtract the two remaining values you get a difference of 11.6 inches. This makes the cylinder smaller and therefore uses less space.

In-s [12.5K]3 years ago
3 0

Answer:

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

Step-by-step explanation:

step 1

Find the volume of one ball

The volume of the sphere is equal to

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

we have

r=1.5\ in

V=\frac{4}{3}(3.14)(1.5)^{3}=14.13\ in^{3}

therefore

The volume of two balls is

(2)*14.13=28.26\ in^{3}

step 2

Find the volume of the cylinder

The volume of the cylinder is equal to

V=\pi r^{2}h

we have

r=1.5\ in

h=1.5*4=6\ in

substitute

V=(3.14)(1.5)^{2}(6)=42.39\ in^{3}

therefore

The wasted space with the cylinder is equal to

42.39\ in^{3}-28.26\ in^{3}=14.13\ in^{3}

step 3

Find the volume of the square prism

The volume of the square prism is equal to

V=b^{2}h

we have

b=1.5*2=3\ in

h=1.5*4=6\ in

substitute

V=(3)^{2}(6)=54\ in^{3}

therefore

The wasted space with the prism is equal to

54\ in^{3}-28.26\ in^{3}=25.74\ in^{3}

step 4

Find the difference of the wasted space

25.74\ in^{3}-14.13\ in^{3}=11.61\ in^{3}

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Answer:

Number of dolphins in zoo * number of fish per dolphin.

Step-by-step explanation:

Hansen won the raffle At the zoo and gets to feed the dolphins! The dolphin trainer gives Hansen a bucket of fish to divide evenly among five dolphins. Each dolphin gets four fish. Which equation can you use to find the number of fish F in the bucket before hansen feeds them

Given that:

Number of dolphins = 5

Fish in bucket is distributed equally ; hence, Number of fish per dolphin = 4

To obtain the initial number of fish in bucket before hansen began to feed the fishes :

Number of fish in bucket before hansen feeds then :

Number of dolphins in zoo * number of fish per dolphin.

5 * 4 = 20

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2 years ago
How do you solve this?
NNADVOKAT [17]

Answer:

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Step-by-step explanation:

The graph is positive this time, so right away you can eliminate A and B.

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2 years ago
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In a process that manufactures bearings, 90% of the bearings meet a thickness specification. A shipment contains 500 bearings. A
Marina86 [1]

Answer:

(a) 0.94

(b) 0.20

(c) 90.53%

Step-by-step explanation:

From a population (Bernoulli population), 90% of the bearings meet a thickness specification, let p_1 be the probability that a bearing meets the specification.

So, p_1=0.9

Sample size, n_1=500, is large.

Let X represent the number of acceptable bearing.

Convert this to a normal distribution,

Mean: \mu_1=n_1p_1=500\times0.9=450

Variance: \sigma_1^2=n_1p_1(1-p_1)=500\times0.9\times0.1=45

\Rightarrow \sigma_1 =\sqrt{45}=6.71

(a) A shipment is acceptable if at least 440 of the 500 bearings meet the specification.

So, X\geq 440.

Here, 440 is included, so, by using the continuity correction, take x=439.5 to compute z score for the normal distribution.

z=\frac{x-\mu}{\sigma}=\frac{339.5-450}{6.71}=-1.56.

So, the probability that a given shipment is acceptable is

P(z\geq-1.56)=\int_{-1.56}^{\infty}\frac{1}{\sqrt{2\pi}}e^{\frac{-z^2}{2}}=0.94062

Hence,  the probability that a given shipment is acceptable is 0.94.

(b) We have the probability of acceptability of one shipment 0.94, which is same for each shipment, so here the number of shipments is a Binomial population.

Denote the probability od acceptance of a shipment by p_2.

p_2=0.94

The total number of shipment, i.e sample size, n_2= 300

Here, the sample size is sufficiently large to approximate it as a normal distribution, for which mean, \mu_2, and variance, \sigma_2^2.

Mean: \mu_2=n_2p_2=300\times0.94=282

Variance: \sigma_2^2=n_2p_2(1-p_2)=300\times0.94(1-0.94)=16.92

\Rightarrow \sigma_2=\sqrt(16.92}=4.11.

In this case, X>285, so, by using the continuity correction, take x=285.5 to compute z score for the normal distribution.

z=\frac{x-\mu}{\sigma}=\frac{285.5-282}{4.11}=0.85.

So, the probability that a given shipment is acceptable is

P(z\geq0.85)=\int_{0.85}^{\infty}\frac{1}{\sqrt{2\pi}}e^{\frac{-z^2}{2}=0.1977

Hence,  the probability that a given shipment is acceptable is 0.20.

(c) For the acceptance of 99% shipment of in the total shipment of 300 (sample size).

The area right to the z-score=0.99

and the area left to the z-score is 1-0.99=0.001.

For this value, the value of z-score is -3.09 (from the z-score table)

Let, \alpha be the required probability of acceptance of one shipment.

So,

-3.09=\frac{285.5-300\alpha}{\sqrt{300 \alpha(1-\alpha)}}

On solving

\alpha= 0.977896

Again, the probability of acceptance of one shipment, \alpha, depends on the probability of meeting the thickness specification of one bearing.

For this case,

The area right to the z-score=0.97790

and the area left to the z-score is 1-0.97790=0.0221.

The value of z-score is -2.01 (from the z-score table)

Let p be the probability that one bearing meets the specification. So

-2.01=\frac{439.5-500  p}{\sqrt{500 p(1-p)}}

On solving

p=0.9053

Hence, 90.53% of the bearings meet a thickness specification so that 99% of the shipments are acceptable.

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3 years ago
A cheese wheel has a radius of 4 in. What is the circumference of the wheel? Round your answer to the nearest hundredths.
ale4655 [162]

Step-by-step explanation:

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\frac{11}{7}  \times 4

\frac{44}{7}

6 0
2 years ago
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A balloon is rising at a constant speed of 5 ftys. A boy is cycling along a straight road at a speed of 15 ftys. When he passes
Ket [755]

Answer:

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Step-by-step explanation:

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The boy is moving horizontally at 15 ft/s, so his position relative to the spot under the balloon is 15t feet after t seconds.

The balloon starts at 45 feet above the boy and is moving upward at 5 ft/s, so its vertical distance from the spot under the balloon is 45+5t feet after t seconds.

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2 years ago
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