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MakcuM [25]
3 years ago
9

Straws are shipped into a box with dimensions of 6.0x6.0x8.0 inches. Each straw is 3/8 inches wide and 7 and 3/4 inches long. Ho

w many straws could be shipped into a box without squeezing any straws?
Mathematics
2 answers:
sattari [20]3 years ago
6 0

Answer:

256

Step-by-step explanation:

First, let's see the height of the box (8 inches) is long enough for one straw (7 inches and 3/4) but not enough for 2... so there could be only one layer.

Now the box is a prism with a square base (6 inches each side).

How many straws can we fit on one side?  We have to divide the width of the box by the width of a straw.  

row = \frac{6}{3/8} = \frac{48}{3} = 16

We can fit 16 straw per 6-side side of the box... Since the box is 6x6 inches, we can then fit 16 x 16 straws in it... 256 total.

Roman55 [17]3 years ago
6 0

Answer:

256

Step-by-step explanation:

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A company has a bonus incentive for its employees. The company pays employees an initial signing bonus of $1000 and invests that
Angelina_Jolie [31]

Since this is a compound interest, we will use this formula: A = P(1+r/n)^n*t

P = $1000 --> the amount that we start with

r = 8% --> this is the rate

n = 4 --> This is because it is compounded quarterly.

t = 5 --> the amount of years

A = 1,000.00(1 + 0.02)^(20)

So our final value after inserting those numbers in the equation is: $1,485.95.

6 0
2 years ago
Aaron tracks the time it takes him to mow lawns by writing coordinate points relating x, the time in hours it takes to mow a law
NARA [144]

Answer:

Slope of this line is given by:

<em>Aaron’s rate for mowing lawns is 0.5 acres per hour</em>

Step-by-step explanation:

It is given that time is tracked by Aaron related to x coordinate.

and the area of land mowed in acres is related to y coordinate.

Two of his points are given as:

(3, 1.5) and (5,2.5)

We know that the coordinates are represented in the form of (x,y)

i.e. first coordinate represents x coordinate and

second coordinate represents y coordinate.

So, it can be observed that:

x_1=3, y_1=1.5\\x_2=5, y_2=2.5

Change in x coordinate = x_2-x_1=5-3 = 2

i.e. total time taken is 2 hours.

Change in y coordinate = y_2-y_1=2.5-1.5 = 1

i.e. total land mowed taken is 1 acre.

In other words, <em>it takes 2 hours for Aaron to mow 1 acre of land.</em>

So, "option 1)  It takes Aaron about 1 hour to mow 2 acres." is incorrect.

<u>Rate of mowing</u> lawn is the <em>land mowed by Aaron in 1 hour</em>.

Land mowed in 2 hours = 1 acre

Land mowed in 1 hours = \frac{1}{2} acre i.e. 0.5 acre

Also, slope of a line is given as:

m = \dfrac{y_2-y_1}{x_2-x_1}

Here y_2 - y_1 = 1

x_2 - x_1 = 2

As per formula:

m = \dfrac{1}{2} = 0.5

So, option 2) Aaron’s rate for mowing lawns is 0.5 acres per hour.

6 0
3 years ago
Read 2 more answers
12. In the given figure, RS is parallel to PQ, If RS = 3 cm, PQ = 6 cm and ar(∆TRS) = 15cm³, then ar (∆TPQ) = ? (a) 70 cm² (b) 5
Gnesinka [82]

\large\underline{\sf{Solution-}}

Given that,

In <u>triangle TPQ, </u>

  • RS || PQ,

  • RS = 3 cm,

  • PQ = 6 cm,

  • ar(∆ TRS) = 15 sq. cm

As it is given that, <u>RS || PQ</u>

So, it means

⇛∠TRS = ∠TPQ [ Corresponding angles ]

⇛ ∠TSR = ∠TPQ [ Corresponding angles ]

\rm\implies \: \triangle TPQ \:  \sim \: \triangle TRS \:  \:  \:  \:  \:  \:  \{AA \}

<u>Now, We know </u>

Area Ratio Theorem,

This theorem states that :- The ratio of the area of two similar triangles is equal to the ratio of the squares of corresponding sides.

\rm\implies \:\dfrac{ar( \triangle \: TPQ)}{ar( \triangle \: TRS)}  = \dfrac{ {PQ}^{2} }{ {RS}^{2} }

\rm\implies \:\dfrac{ar( \triangle \: TPQ)}{15}  = \dfrac{ {6}^{2} }{ {3}^{2} }

\rm\implies \:\dfrac{ar( \triangle \: TPQ)}{15}  = \dfrac{36 }{9}

\rm\implies \:\dfrac{ar( \triangle \: TPQ)}{15}  = 4

\rm\implies \:ar( \triangle \: TPQ)  = 60 \:  {cm}^{2}

3 0
2 years ago
(x3 - 2x² - 1) + (x - 1)
SSSSS [86.1K]

Answer:

x^3 -2x^2 -1 + (x-1)

= x^3 -2x^2 + x -2

= (x-2)(x^2+1)

Hope this helps!

5 0
3 years ago
Solve for a<br> -8 = a(2+5)^2 +41<br> A. -1<br> B. 1<br> C. -2<br> D. 2
mario62 [17]

Answer:A

Step-by-step explanation:

-8=a(2+5)^2 + 41

-8=a x 7^2 + 41

-8=a x 7 x 7 +41

-8=49a+41

Collect like terms

-8-41=49a

-49=49a

Divide both sides by 49

-49/49=49a/49

-1=a

a=-1

5 0
3 years ago
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