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TEA [102]
2 years ago
3

A boat on the ocean is 44 mi from the nearest point on a straight​ shoreline; that point is 1515 mi from a restaurant on the sho

re. A woman plans to row the boat straight to a point on the shore and then walk along the shore to the restaurant. Complete parts​ (a) and​ (b) below. A straight shoreline runs from left to right. A boat is 4 miles from a point on the shoreline. A restaurant is 15 miles to the right of that point. A dashed line segment extends from the boat and falls from left to right to a point on the shore between the nearest point on the shore and the restaurant. A dashed horizontal line segment extends from this point on the shore to the restaurant. 4 mi 15 mi a. If she walks at 3​ mi/hr and rows at 2​ mi/hr, at which point on the shore should she land to minimize the total travel​ time? Let x be the distance between the nearest point on shore and the point she lands on shore. If T is the time it takes her to get to the​ restaurant, what is the objective​ function?
Mathematics
1 answer:
Jobisdone [24]2 years ago
8 0
The dadhd segments eeeds to have a sepcific bumber and length kease pseicofy
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A factory received a shipment of 38 sprockets, and the vendor who sold the items knows there are 5 sprockets in the shipment tha
weeeeeb [17]

Answer:

a) 0.00019923%

b) 47.28%

Step-by-step explanation:

a) To find the probability of all sockets in the sample being defective, we can do the following:

The first socket will be in a group where 5 of the 38 sockets are defective, so the probability is 5/38

The second socket will be in a group where 4 of the 37 sockets are defective, as the first one picked is already defective, so the probability is 4/37

Expanding this, we have that the probability of having all 5 sockets defective is: (5/38)*(4/37)*(3/36)*(2/35)*(1/34) = 0.0000019923 = 0.00019923%

b) Following the same logic of (a), the first socket have a chance of 33/38 of not being defective, as we will pick it from a group where 33 of the 38 sockets are not defective. The second socket will have a chance of 32/37, and so on.

The probability will be (33/38)*(32/37)*(31/36)*(30/35)*(29/34) = 0.4728 = 47.28%

5 0
2 years ago
Select all of the answers below that are equivalent to T = {Tinkey-Winky, Laa-Laa,
stepan [7]

Answer:

  • {thermometer, fridge, rusty nail, deoderant}
  • {credit card, face wash, tweezers, shovel}
  • {clothes, glass, car, greeting card}

Step-by-step explanation:

The options that will be equivalent to T will have to be the options that have the same Cardinality as T. Cardinality refers to the number of elements in a set and in the set T, there are 4 elements being Tinkey-Winky, Laa-Laa,  Dipsy, Po so the Cardinality is 4.

The equivalent sets would therefore be sets with a cardinality of 4 as well and those are;

  • {thermometer, fridge, rusty nail, deoderant}
  • {credit card, face wash, tweezers, shovel}
  • {clothes, glass, car, greeting card}
3 0
2 years ago
A waitress works 1.75 hours less in the afternoon than in the evening. If she works 5      1/8
gayaneshka [121]
Let x be the number of hours that the waitress works in the evening.

We know for our problem that she works 5 \frac{1}{8} in the afternoon and that she works <span>1.75 hours less in the afternoon than in the evening, so:
</span>x=5 \frac{1}{8} -1.75
<span>Since </span>\frac{1}{8} =0.125, we can rewrite our expression:
x=5.125-1.75
x=3.375

We can conclude that she works 3.375 hours in the evening, or expressed as a mixed fraction: 3 \frac{3}{8} hours.
3 0
2 years ago
Budget planners in two towns, Alphaville and Betaville, developed models to determine the budget surplus (in dollars) for a year
kramer

Answer:

(a)-3x^2+150x-10000

(b)-\$16,863,760,000

Step-by-step explanation:

Alphaville's Budget Surplus Model is -2x^2+ 500x

Betaville's Budget Surplus Model is x^2- 100x + 10000.

We want to determine the expression that shows how much greater Alphaville’s annual budget surplus is than Betaville’s for a particular amount of tax revenue.

  • To do this, we subtract Betaville's Model from Alphaville's model.

-2x^2+ 500x-(x^2- 100x + 10000)\\

Opening the brackets

-2x^2+ 500x-x^2+100x - 10000\\

Collect like terms and simplify

-2x^2-x^2+100x + 500x- 10000\\=-3x^2+150x-10000

The expression that shows how much greater Alphaville's Budget is:

-3x^2+150x-10000

(b) If the tax revenue that year in each town is $75,000

We want to evaluate the expression derived above when the tax revenue that year in each town is $75,000 i.e.at x=75000

-3x^2+150x-10000\\=-3(75000)^2+150(75000)-10000\\=-\$16,863,760,000

3 0
2 years ago
mark has a cabinet door in his kitchen with the dimensions shown below. he creates a scale drawing where the width of the cabine
laiz [17]

Answer:

h^{*} = 25\,in

Step-by-step explanation:

Let consider that door has a height of 5 feet and a width of 3 feet. The scale factor is:

n = \frac{15\,in}{3\,ft}

n = 5\,\frac{in}{ft}

The height of the cabinet is:

h^{*} = n \cdot h_{door}

h_{*} = \left(5\,\frac{in}{ft}  \right)\cdot (5\,ft)

h^{*} = 25\,in

6 0
2 years ago
Read 2 more answers
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