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Triss [41]
3 years ago
6

A big ship drops its anchor.The variable l models the anchor's elevation (in meters) relative to the water's surface t seconds a

fter the ship drops its anchor.l=−2.4t+75What is the initial height of the anchor?
Mathematics
1 answer:
vivado [14]3 years ago
5 0

Answer:

Step-by-step explanation:

l = -2.4t + 75

what this equation is saying is that the initial height of the anchor is 75 meters (thats also ur y intercept), and it drops at a rate of 2.4 meters per second.

another way u could look at it is the initial height is before u drop the anchor....0 seconds...meaning sub in 0 for t

l = 2.4(0) + 75

l = 0 + 75

l = 75 meters <=====

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A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 50 pounds each, and the small boxes
Arturiano [62]

Answer: 50 large box

Step-by-step explanation:

First, "boxes of two sizes" means we can assign variables:

Let x = number of large boxes

y = number of small boxes

"There are 115 boxes in all" means x + y = 115 [eq1]

Now, the pounds for each kind of box is:

(pounds per box)*(number of boxes)

So,

pounds for large boxes + pounds for small boxes = 4125 pounds

"the truck is carrying a total of 4125 pounds in boxes"

(50)*(x) + (25)*(y) = 4125 [eq2]

It is important to find two equations so we can solve for two variables.

Solve for one of the variables in eq1 then replace (substitute) the expression for that variable in eq2. Let's solve for x:

x = 115 - y [from eq1]

50(115-y) + 25y = 4125 [from eq2]

5750 - 50y + 25y = 4125 [distribute]

5750 - 25y = 4125

-25y = -1625

y = 65 [divide both sides by (-25)]

There are 65 small boxes.

Put that value into either equation (now, which is easier?) to solve for x:

x = 115 - y

x = 115 - 65

x = 50

There are 50 large boxes.

Check (very important):

Is 50+65 = 115 ? [eq1]

115 = 115 ?yes

Is 50(50) + 25(65) = 4125 ?

2500 + 1625 = 4125 ?

4125 = 4125 ? yes

4 0
3 years ago
Who can help me please
aalyn [17]
1.) 32
2.)42
3.)67
4.)78
5.) 13
6.)67
7.)23
8.80
5 0
4 years ago
the larger of two numbers is six less than twice the smaller number. if the sum of the number is 42 , find the number
USPshnik [31]

42-6=? (Answer) 36

I have to write 20 characters

4 0
3 years ago
A study was done to determine the average number of homes that a homeowner owns in his or her lifetime. For the 50 homeowners su
ipn [44]

Answer:

The 95% confidence interval for the true average number of homes that a person owns in his or her lifetime is (4,6.2).

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So

df = 50 - 1 = 49

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 49 degrees of freedom(y-axis) and a confidence level of 1 - \frac{1 - 0.95}{2} = 0.975. So we have T = 2.0096

The margin of error is:

M = T\frac{s}{\sqrt{n}} = 2.0096\frac{3.8}{\sqrt{50}} = 1.1

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 5.1 - 1.1 = 4

The upper end of the interval is the sample mean added to M. So it is 5.1 + 1.1 = 6.2.

The 95% confidence interval for the true average number of homes that a person owns in his or her lifetime is (4,6.2).

7 0
3 years ago
In New York, state sales tax rates vary by county. In Allegany County, the sales tax rate is 8 1 2 %. a. A book costs $12.99, an
ArbitrLikvidat [17]

Answer:

$ 2.30

Step-by-step explanation:

Given that the sales tax rate = 8\frac{1}{2}\%=8.5\%

The cost of the book is $ 12.99.

So, the tax on the book= 8.5% of 12.99

= \frac {8.5}{100}\times 12.99

=1.10

So, the sales tax on the book is $ 1.10.

The cost of the video game is $ 39.99.

So, the tax on the book= 8.5% of 39.99

= \frac {8.5}{100}\times 39.99

=3.30

So, the sales tax on the book is $ 3.40.

The difference of taxes on both the items = $ 3.40-$ 1.10=$ 2.30

So, the tax on the video game is $ 2.30 more than then tax on the book.

3 0
3 years ago
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