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3 years ago

This diagram shows the dimensions of a plastic tab used in a toy.

Mathematics

2 answers:

aniked [119]3 years ago

7 0

Answer:

2450 mm³

Step-by-step explanation:

(15×10×7) + [(40+10)×4×7]

2450

lina2011 [118]3 years ago

6 0

Answer:

The answer is 1728

Step-by-step explanation:

I just took the test

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An investment of $100 comma 000 was made by a business club. The investment was split into three parts and lasted for one year.

Artist 52 [7]

Answer:

$54000 was invested at 8% interest
$36000 was invested at 6% interest
$10000 was invested at 9% interest

Step-by-step explanation:

Total Investment = $100,000

The investment was split into three parts (say x, y and z)

x+y+z=100000

Simple Interest = Principal X Rate/100 X Time

The first part of the investment earned 8% interest

Interest on the first part = 0.08x

The second part of the investment earned 6% interest

Interest on the second part = 0.06y

The third part of the investment earned 9% interest

Interest on the third part = 0.09z

Total interest from the investments = $ 7380.

Therefore:

0.08x+0.06y+0.09z=7380

The interest from the first investment was 2 times the interest from the second.

0.08x=2 X 0.06y

0.08x=0.12y

Substituting we have:

0.12y+0.06y+0.09z=7380

0.18y+0.09z=7380

From 0.08x=0.12y

x=1.5y

Substituting x=1.5y into x+y+z=100000

1.5y+y+z=100000

2.5y+z=100000

z=100000-2.5y

Substituting z=100000-2.5y into 0.18y+0.09z=7380

0.18y+0.09(100000-2.5y)=7380

0.18y+9000-0.225y=7380

-0.045y=-1620

Divide both sides by -0.045

y=36000

Recall: x=1.5y

x=1.5 X 36000

x =54000

x+y+z=100000

54000+36000+z=100000

z=100000-(54000+36000)

z=10,000

Therefore:

$54000 was invested at 8% interest
$36000 was invested at 6% interest
$10000 was invested at 9% interest

3 0

3 years ago

Your bill at the restaurant has total of 23.50. You received fantastic service from your server and would like to leave a 20% ti

pychu [463]

Answer:

28.2

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

The surface area of a triangular pyramid is 375.2 m2. What would change if the surface area were measured in square centimeters?

Tamiku [17]

I believe that D. The surface area of the pyramid would stay the same, but the number representing the surface area would increase is correct because when you just move it to another units, it still the same but you'll need to move the decimal two places to the left and the number 37520 cm² is greater than the number of 375.2 m²

8 0

3 years ago

You must design a closed rectangular box of width w, length l and height h, whose volume is 504 cm3. The sides of the box cost 3

Charra [1.4K]

Answer:

Dimensions will be

Length = 7.23 cm

Width = 7.23 cm

Height = 9.64 cm

Step-by-step explanation:

A closed box has length = l cm

width of the box = w cm

height of the box = h cm

Volume of the rectangular box = lwh

504 = lwh

$h=\frac{504}{lw}$

Sides which involve length and width and height, cost = 3 cents per cm²

Top and bottom of the box costs = 4 cents per cm²

Cost of the sides $C_{s}$ = 3[2(l + w)h] = 6(l + w)h

$C_{s}$ = 3[2(l + w)h]

$C_{s}=6(l+w)(\frac{504}{lw} )$

Cost of the top and the bottom $C_{(t,p)}$ = 4(2lw) = 8lw

Total cost of the box C = $3024\frac{(l+w)}{lw}$ + 8lw

= $3024[\frac{1}{l}+\frac{1}{w}]$ + 8lw

To minimize the cost of the sides

$\frac{dC}{dl}=3024(-l^{-2}+0)+8w=0$

$\frac{3024}{l^{2}}=8w$

$\frac{378}{l^{2}}=w$ ---------(1)

$\frac{dC}{dw}=3024(-w^{-2})+8l=0$

$\frac{3024}{w^{2}}=8l$

$\frac{378}{w^{2}}=l$

$w^{2}=\frac{378}{l}$ -------(2)

Now place the value of w from equation (1) to equation (2)

$(\frac{378}{l^{2}})^{2}=\frac{378}{l}$

$\frac{(378)^{2} }{l^{4}}=\frac{378}{l}$

l³ = 378

l = ∛378 = 7.23 cm

From equation (2)

$w^{2}=\frac{378}{7.23}$

$w^{2}=52.28$

w = 7.23 cm

As lwh = 504 cm³

(7.23)²h = 504

$h=\frac{504}{(7.23)^{2}}$

h = 9.64 cm

6 0

3 years ago

A coin purse contains d dimes and q quarters.There are 20 coins in the purse and the total value of the coins is $4.25.which sys

mel-nik [20]

25q + 10d = 425
q + d = 20

First thing's first, picture 4 quarters. Do you know how much these 4 quarters are worth? Obviously, you'd answer one dollar, but take the time to think about how exactly you came up with this answer.

"Well, it's simple," you might think, "Multiply 0.25 by 4."

Similar to this train of thought, the first equation is formulated by doing exactly that. 'q' represents an unknown number of quarters, and 'd' an unknown number of dimes. We use 25q and 10d, because, well, we're multiplying their value by the number of coins. They're equivalent to 425 because the 20 unknown coins make $4.25 (I converted it to cents to get rid of the pesky decimals, but if you want to keep it as dollars that works too).

Because the equation states that there are 20 coins in total, we know that we can make the equation 'q + d = 20' since there are 20 quarters and dimes in total.

Let me know if you need any further explanation :)
-T.B.

3 0

3 years ago

Read 2 more answers