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SCORPION-xisa [38]
2 years ago
7

Carla was trying to decide what to do Saturday evening. She has $100 available to spend for the evening. She has narrowed her ch

oices down to these events: Braves game, a concert of an artist she likes, or the Georgia Aquarium. Admission to the Braves game is $25, hot dogs cost $10, sodas cost $5. The concert costs $25 for admission, $20 for a souvernir t-shirt, and $10 for a soda. The Georgia Aquarium has the show of a lifetime with an all you can eat and drink that costs $100. Carla does not want to take any driving chances, so in addition to the cost of the aquarium, she will also need to pay for her Uber/Lyft, which is $15 each way. Which option should Carla choose if she wants to spend the least? Based on that choice, what then is Carla's oppotunity cost? Fully explain your answer in at least one paragraph.
Mathematics
2 answers:
Alja [10]2 years ago
8 0

Answer:

If Carla wants to choose the least spendable option, she can go with Braves game.

Step-by-step explanation:

Carla has $100 available to spend for the evening.

She has narrowed her choices down to these events:

1. Braves game - Admission to the Braves game is $25, hot dogs cost $10, sodas cost $5. So, total spent will be25+10+5=40 dollars

2. A concert - $25 for admission, $20 for a souvernir t-shirt, and $10 for a soda. So, total spent will be = 25+20+10=55 dollars

3. Georgia Aquarium - Total cost will be = 100+15(2)=130 dollars

Now, we can neglect the third choice as $130 will be spent and Carla does not have that much.

Now comparing the above two options, we can say that if Carla wants to choose the least spendable option, she can go with Braves game.

Carla can still go t the concert but not to the aquarium.

hjlf2 years ago
3 0

Answer:


Step-by-step explanation:

If carla wants to spend the least amount of money she should go to the Braves game because it has one of the lowwest admission and the food is cheaper than any where else. Yes, the concert admission is the same price but the tee-shirts and soda costs more.

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The length of time a full length movie runs from opening to credits is normally distributed with a mean of 1.9 hours and standar
Llana [10]

Answer:

a) The probability that a random movie is between 1.8 and 2.0 hours = 0.2586.

b) The probability that a random movie is longer than 2.3 hours is 0.0918.

c) The length of movie that is shorter than 94% of the movies is 1.4 hours

Step-by-step explanation:

In the above question, we would solve it using z score formula

z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation

a) A random movie is between 1.8 and 2.0 hours

z = (x-μ)/σ,

x1 = 1.8,

x2 = 2.0

μ is the population mean = 1.9

σ is the population standard deviation = 0.3

z1 = (1.8 - 1.9)/0.3

z1 = -1/0.3

z1 = -0.33333

Using the z score table

P(z1 = -0.33) = 0.3707

z2 = (2.0 - 1.9)/0.3

z1 = 1/0.3

z1 = 0.33333

p(z2 = 0.33) = 0.6293

= P(- 0.33 ≤ z ≤ 0.33)

= 0.6293 - 0.3707

= 0.2586

The probability that a random movie is between 1.8 and 2.0 hours = 0.2586

b) A movie is longer than 2.3 hours

z = (x-μ)/σ,

x1 = 2.3

μ is the population mean = 1.9

σ is the population standard deviation = 0.3

z = (2.3 - 1.9)/0.3

z = 4/0.3

z = 1.33333

P(z = 1.33) = 0.90824

P(x>2.3) = = 1 - 0.90824

= 0.091759

≈ 0.0918

The probability that a random movie is longer than 2.3 hours is 0.0918.

3) The length of movie that is shorter than 94% of the movies.

z = (x-μ)/σ

Probability (z ) = 94% = 0.94

Movie that is shorter than 0.94

= P(1 - 0.94) = P(0.06)

Finding the P (x< 0.06) = -1.555

≈ -1.56

μ is the population mean = 1.9

σ is the population standard deviation = 0.3

-1.56 = (x - 1.9)/ 0.3

Cross multiply

-1.56 × 0.3 = x - 1.9

- 0.468 + 1.9 = x

= 1.432 hours

≈ 1.4 hours

Therefore, the length of movie that is shorter than 94% of the movies is 1.4 hours

5 0
2 years ago
Solve x2 = 12x – 15 by completing the square. Which is the solution set of the equation?
Nady [450]
For this case we have the following polynomial:
 x ^ 2 = 12x - 15&#10;
 The first thing to do is to place the variables on the same side of the equation.
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 x ^ 2 - 12x = -15&#10;
 We complete the square by adding the term (b / 2) ^ 2 on both sides of the equation.
 We have then:
 x ^ 2 - 12x + (-12/2) ^ 2 = -15 + (-12/2) ^ 2&#10;
 Rewriting we have:
 x ^ 2 - 12x + (-6) ^ 2 = -15 + (-6) ^ 2&#10;&#10;x ^ 2 - 12x + 36 = -15 + 36&#10; &#10;(x-6) ^ 2 = 21
 x-6 =+/- \sqrt{21}
 Therefore, the solutions are:
 x = 6 - \sqrt{21}
 x = 6 + \sqrt{21}
 Answer:
 
the solution set of the equation is:
 
x = 6 - \sqrt{21}
 x = 6 + \sqrt{21}
3 0
2 years ago
Read 2 more answers
Marty is asked to draw triangles with side lengths of 4 units and 2 units, and a non-included angle of 30°. Select all the trian
777dan777 [17]

Answer:

The drawn in the attached figure

see the explanation

Step-by-step explanation:

<em>First case</em>

In the triangle ABC

Let

a=4\ units\\b=2/ units\\B=30^o

Applying the law of sines

Find the measure of angle A

\frac{a}{sin(A)}=\frac{b}{sin(B)}

substitute the given values

\frac{4}{sin(A)}=\frac{2}{sin(30^o)}

sin(A)=1

so

A=90^o

Find the measure of angle C

In a right triangle

we know that

B+C=90^o ----> by complementary angles

B=30^o

therefore

C=60^o

Find the length side c

Applying the law of sines

\frac{c}{sin(C)}=\frac{b}{sin(B)}

substitute the given values

\frac{c}{sin(60^o)}=\frac{2}{sin(30^o)}

c=2\sqrt{3}\ units

therefore

The dimensions of the triangle are

A=90^o

B=30^o

C=60^o

a=4\ units\\b=2\ units\\c=2\sqrt{3}=3.46\ units

<em>Second case</em>

In the triangle ABC

Let

a=4\ units\\b=2/ units\\A=30^o

Applying the law of sines

Find the measure of angle B

\frac{a}{sin(A)}=\frac{b}{sin(B)}

substitute the given values

\frac{4}{sin(30^o)}=\frac{2}{sin(B)}

sin(B)=0.25

so

using a calculator

B=14.48^o

Find the measure of angle C

we know that

The sum of the interior angles in any triangle must be equal to 180 degrees

so

A+B+C=180^o

A=30^o\\B=14.48^o

therefore

30^o+14.48^o+C=180^o

C=135.52^o

Find the length side c

Applying the law of sines

\frac{c}{sin(C)}=\frac{a}{sin(A)}

substitute the given values

\frac{c}{sin(135.52^o)}=\frac{4}{sin(30^o)}

c=5.61\ units

therefore

The dimensions of the triangle are

A=30^o

B=14.48^o

C=135.52^o

a=4\ units\\b=2\ units\\c=5.61\ units

see the attached figure to better understand the problem

4 0
2 years ago
this past Sunday, the giants scored 9 less than twice the cowboys. the packers scored 14 points more than the giants. if the tea
Grace [21]
Let the score of cowboys is x
and giants make score 9 which is twice less than the cowboys score so
giants score will be = 2x -9
and packers scored 14 more than giants that is (2x - 9) + 14
now sum of their scores is equal to 81 it means:
x + (2x - 9) + (2x -9) + 14 = 81
x + 2x - 9 + 2x - 9 + 14 = 81
5x = 81 + 4
5x = 85
x = 17
packers scored =  (2x - 9) + 14
= 2 (17) -9 + 14
=38 + 5 = 43 points

5 0
2 years ago
What is the probability of rolling an odd number and spinning "B," given the sample space below? 1 2 3 4 5 6 A A1 A2 A3 A4 A5 A6
Zielflug [23.3K]
There are 3 odd numbers out of 6 numbers and  7 B's out of  28  so

required probability =  3/6 * 7/28 = 1/2 * 1/4 = 1/8 Answer
6 0
2 years ago
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