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Mekhanik [1.2K]

2 years ago

12

To order tickets online to a hockey game, there is a processing fee plus the cost per ticket. The cost for 5 tickets is $174.45.

The codt for 8 tickets is $271.95. Write and solve a linear equation to find the total cost to order 13 tickets.

1 answer:

xeze [42]2 years ago

3 0

Wouldn’t the total for 13 tickets be $446.40 ? We already know the cost for 5 and 8 just add it up .... js

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A sailboat is sitting at rest near its dock. A rope attached to the bow of the boat is drawn in over a pulley that stands on a p

irina [24]

Answer:

The boat is approaching the dock at rate of 2.14 ft/s

Step-by-step explanation:

The situation given in the question can be modeled as a triangle, please refer to the attached diagram.

A rope attached to the bow of the boat is drawn in over a pulley that stands on a post on the end of the dock that is 5 feet higher than the bow that means x = 5 ft.

The length of rope from bow to pulley is 13 feet that means y = 13 ft.

We know that Pythagorean theorem is given by

$x^{2} + y^{2} = z^{2}$

Differentiating the above equation with respect to time yields,

$2x\frac{dx}{dt} + 2y\frac{dy}{dt} = 2z\frac{dz}{dt}$

$x\frac{dx}{dt} + y\frac{dy}{dt} = z\frac{dz}{dt}$

dx/dt = 0 since dock height doesn't change

$y\frac{dy}{dt} = z\frac{dz}{dt}$

$\frac{dy}{dt} = \frac{z}{y} \frac{dz}{dt}$

The rope is being pulled in at a rate of 2 feet per second that is dz/dt = 2 ft/s

First we need to find z

z² = (5)² + (13)²

z² = 194

z = √194

z = 13.93 ft

So,

$\frac{dy}{dt} = \frac{z}{y} \frac{dz}{dt}$

$\frac{dy}{dt} = \frac{13.93}{13}(2)$

$\frac{dy}{dt} = 2.14$ $ft/s$

Therefore, the boat is approaching the dock at rate of 2.14 ft/s

8 0

2 years ago

An annexation suit against a county subdivision of 1200 residences is being considered by a neighboring city. If the occupants o

Sunny_sXe [5.5K]

Answer:

Probability that in a random sample of 10 at least 3 favor the annexation suit is 0.9453.

Step-by-step explanation:

We are given that an annexation suit against a county subdivision of 1200 residences is being considered by a neighboring city. The occupants of half the residences object to being annexed.

Also, a random sample of 10 residents is taken.

The above situation can be represented through Binomial distribution;

$P(X=r) = \binom{n}{r}p^{r} (1-p)^{n-r} ; x = 0,1,2,3,.....$

where, n = number of trials (samples) taken = 10 residents

r = number of success = at least 3

p = probability of success which in our question is probability that

residents favor the annexation suit, which is calculated as below;

p = $\frac{\text{Number of residents favoring the annexation suit }}{\text{Total number of residents considered } }$ = $\frac{600}{1200}$ = 0.50

<em>LET X = Number of residents favoring the annexation suit</em>

So, it means X ~ $Binom(n=10, p=0.50)$

Now, Probability that in a random sample of 10 at least 3 favor the annexation suit is given by = P(X $\geq$ 3)

P(X $\geq$ 3) = 1 - P(X < 3) = 1 - P(X $\leq$ 2)

= 1 - [P(X = 0) + P(X = 1) + P(X = 2)]

= $1- [\binom{10}{0}\times 0.50^{0} \times (1-0.50)^{10-0} + \binom{10}{1}\times 0.50^{1} \times (1-0.50)^{10-1} +\binom{10}{2}\times 0.50^{2} \times (1-0.50)^{10-2}]$

= $1-[ 1 \times 1 \times 0.50^{10}+10 \times 0.50^{1} \times 0.50^{9}+45 \times 0.50^{2} \times 0.50^{8}]$

= $1-[ 0.50^{10}+10 \times 0.50^{10}+45 \times 0.50^{10}]$

= $1-0.50^{10}[ 1+10 +45 ]$ = $1-0.50^{10} \times 56$

= 0.9453

Therefore, Probability that in a random sample of 10 at least 3 favor the annexation suit is 0.9453.

8 0

2 years ago

Caroline needs to find 15% of $128, but she doesn't have a calculator. Thoroughly explain how she can do this mentally, detailin

IrinaK [193]

Answer:

The correct answer is $19.2.

Step-by-step explanation:

Caroline needs to find 15% of $128, but she doesn't have a calculator.

Caroline should start by finding the value of 10 % of any number as it is given by dividing the number by 10. Therefore 10% of $128 is given by $\frac{128}{10}$ = $12.8.

Now she can find the value of 5% of $128 which is given by dividing the 10% value of any number by 2. Thus 5% of $128 = $\frac{12.8}{2}$ = $6.4

Thus to calculate the value of 15% of $128 is given by adding 10% of 128 and 5% of 128 = $ (12.8 + 6.4) = $ 19.2.

Thus the value of 15% of $128 is $19.2.

5 0

2 years ago

Juanita wants to buy 12.5 pounds of stones to decorate her garden. The stone normally sells for $1.80 a pound. The salesman offe

True [87]

Answer:

Juanita is saving $0.10 a pound.

Step-by-step explanation:

Find the new price that the salesman offered her, by dividing the total price by the number of pounds of stones:

21.25 / 12.5

= 1.70

This means the new price is $1.70 a pound

Then, find the difference between the new price and the original:

1.80 - 1.70

= 0.10

So, Juanita is saving $0.10 a pound

8 0

2 years ago

Read 2 more answers

The relationship between the number of days a public radio station spends fundraising per year and the number of dollars it rece

SCORPION-xisa [38]

56000
Explanation:
Using Y= and graphing you see after 7 days it will be 154000 but you have to subtract the 98000 so therefore your answer is 56000

3 0

2 years ago