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3 years ago

Help me please I need help 2

Mathematics

1 answer:

djyliett [7]3 years ago

4 0

Answer:

26.6 meters

Step-by-step explanation:

Tan(x) = $\frac{opp}{adj}$

Tan(28) = $\frac{x}{50}$

x = 26.6m

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A scale drawing has a scale of 1/4in. :12ft. Find the length on the drawing for each actual length. 8ft

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The other part of your ratio is missing

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3 years ago

Sarah is a computer engineer and manager and works for a software company. She receives a

daser333 [38]

Answer:

a) Number of projects in the first year = 90

b) Earnings in the twelfth year = $116500

Total money earned in 12 years = $969000

Step-by-step explanation:

Given that:

Number of projects done in fourth year = 129

Number of projects done in tenth year = 207

There is a fixed increase every year.

a) To find:

Number of projects done in the first year.

This problem is nothing but a case of arithmetic progression.

Let the first term i.e. number of projects done in first year = $a$

Given that:

$a_4=129\\a_{10}=207$

Formula for $n^{th}$ term of an Arithmetic Progression is given as:

$a_n=a+(n-1)d$

Where $d$ will represent the number of projects increased every year.

and $n$ is the year number.

$a_4=129=a+(4-1)d \\\Rightarrow 129=a+3d .....(1)\\a_{10}=207=a+(10-1)d \\\Rightarrow 207=a+9d .....(2)$

Subtracting (2) from (1):

$78 = 6d\\\Rightarrow d =13$

By equation (1):

$129 =a+3\times 13\\\Rightarrow a =129-39\\\Rightarrow a =90$

Number of projects in the first year = 90

b)

Number of projects in the twelfth year =

$a_{12} = a+11d\\\Rightarrow a_{12} = 90+11\times 13 =233$

Each project pays $500

Earnings in the twelfth year = 233 $\times$ 500 = $116500

Sum of an AP is given as:

$S_n=\dfrac{n}{2}(2a+(n-1)d)\\\Rightarrow S_{12}=\dfrac{12}{2}(2\times 90+(12-1)\times 13)\\\Rightarrow S_{12}=6\times 323\\\Rightarrow S_{12}=1938$

It gives us the total number of projects done in 12 years = 1938

Total money earned in 12 years = 500 $\times$ 1938 = $969000

8 0

3 years ago

The South Company cash account had a balance of $1,202.50 on January 31. A deposit, made on the 31st, in the amount of $100.05 w

labwork [276]

Answer:

$1326

Step-by-step explanation:

Follow the format of the reconciliation statement

The adjusted cash balances should match

Cash balance as per the bank statement, January 31 1421.95

Add: Deposit in transit 100.05

Deduct: Outstanding checks (196)

Adjusted cash balance 1326

Balance as per depositor's record, January 31 1202.5

Subtract: NSF check (18)

Subtract: Service charges (8.5)

Add: receivable collected 150

Adjusted cash balance 1326

The reconciled amount is $1326.

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3 years ago

A dog and a cat are 200 meters apart when they see each other. The dog can run at a speed of 30 meter per second, while the cat

LenKa [72]

Answer:

They'll meet after 200 meters , if they simultaneously start running towards each other.

Step-by-step explanation:

Let x =distance travelled by dog and 200-x be the distance travelled by cat. Inorder to meet, the sum of their travelled distances shall be equal to 200 meters as they are far apart by 200 meters.

Dog: Distance =Speed x time: x=30t

Cat: Distance = 200-x

=24t

The sum of their distance travelled shall be 200 meters: 30t+ 24t= 200;54t=200;t=200/54=3.7secs

So they will meet after 3.7 seconds

To check:

Distance travelled by dog :x=30(3.7)

=111.11 meters

Distance travelled by cat: 24t=24(3.7)

=88.89 meters

Therefore since they are travelling towards each other and their distance apart is 200 meters, after 3.7 seconds they will meet because dog travelled 111.11 meters and cat travelled 88.89 meters and they covered already 200 meters as the sum of 111.11+ 88.89

=200 meters

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2 years ago

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Libby wants to make cookies for her whole class. There are 36 students in her class. The recipe Libby is going to use only makes 12 cookies. How many batches of cookies is Libby going to have to make to feed her whole class?
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