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2 years ago

10

Find the total thickness of two pieces of wood that a carpenter glued together if one is 5/16 inches and the other is 7/8 inches

thick?

1 answer:

konstantin123 [22]2 years ago

4 0

The answer is 1 3/16 inches

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A dust particle weighs 7.42 × 10-10 kilograms. What is the weight of 5 × 106 dust particles represented in scientific notation?

vova2212 [387]

5 x 106 = 530 particles

530 x 7.42x10^-10 = 3.93x10^-7

7 0

2 years ago

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A rectangular piece of plywood has a diagonal which measures two feet more than the width. The length of the plywood is twice th

icang [17]

Answer:

The length of the plywood's diagonal(to the nearest tenth) is, 3.6 and 1.4

Step-by-step explanation:

let l be the length and w be the width of the rectangle respectively;

Diagonal(D) of a rectangle is given by:

$D = \sqrt{l^2+w^2}$ ......[1]

As per the given statement we have;

Diagonal(D) = width + 2

and

$l = 2 \times w$ = 2w

Now, substitute these in [1] we have;

$\sqrt{(2w)^2+w^2} = w+5$

Squaring both the sides we get;

$4w^2+w^2 = (w+2)^2$

$5w^2 = w^2 + 4 + 4w$

or

$5w^2 -w^2 = 4w + 4$ or

$4w^2= 4w + 4$

Simplify:

$w^2-w-1 =0$ ......[2]

The quadratic equation is in the form of $ax^2+bx+c = 0$

the solution is given by: $x = \frac{-b \pm\sqrt{b^2-4ac}}{2a}$

On comparing with [1] we get

a= 1 , b = -1 and c = -1

Then the solution is:

$w= \frac{-(-1) \pm\sqrt{(-1)^2-4(1)(-1)}}{2(1)}$

$w =\frac{1 \pm\sqrt{1+4}}{2} = \frac{1 \pm\sqrt{5}}{2}$

Simplify:

$w \approx 1.62$ and $w \approx -0.62$

Then, the diagonal D = w+2

For $w \approx 1.62$

$D = 1.62 +2 \approx 3.62$

For $w \approx -0.62$

$D =-0.62 +2 \approx 1.38$

therefore, the length of the plywood's diagonal(to the nearest tenth) is, 3.6 and 1.4

5 0

2 years ago

Consider circle O below. The length of arc BA is 8.4 cm and the length of the radius is 8 cm. The measure of angle AOC is 45°. C

denis23 [38]

Answer:

i) 60°

ii) 14.7 cm

Step-by-step explanation:

length of Arc BA = 8.4 cm

length of radius = 8 cm

angle AOC = 45°

BO = AO = CO = 8 cm

<u>i) What is the measure of Angle BOA </u>

= length of Arc BA / Radius

= 8.4 / 8 = 1.05 radians = 60.16° ≈ 60°

<u>ii) what is the length of arc BAC</u>

= radius * angle BAC * $\pi /180$

angle BAC = angle AOC + angle BOA

= 45° + 60° = 105°

hence length of arc BAC

= 8 * 105 * $\pi /180$

≈ 14.7 cm

3 0

2 years ago

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Marie spends $450.00 at a department store. She has two coupons: one for a 15% discount and one for $50 off any purchase above $

VMariaS [17]

Answer:

Her first coupon ti be used is $50 off a purchase above $300

Final purchase price= $340

Step-by-step explanation:

Marie has two coupons

one for a 15% discount and one for $50 off any purchase above $300.

The stores allow the two coupons to be combined and she spends a total of $450.

Her first coupon ti be used is $50 off a purchase above $300.

So Marie have $400 now

15% off $400= 400-(0.15*400)

15% off $400 = 400-60

15% off $400 =$ 340

6 0

2 years ago

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16.A guidance counselor is planning schedules for 30 students. Sixteen students say they want to take French, 16 want to take Sp

MariettaO [177]

Answer:7

Step-by-step explanation:

This can be solved by Venn-diagram

Given there are total 5 students who want french and Latin

also 3 among them want Spanish,french & Latin

i.e. only 2 students wants both french and Latin only.

Also Student who want only Latin is 5

Thus Student who wants Latin and Spanish both only is 11-5-3-2=1

Students who want only Spanish is 8 Thus students who wants Spanish and French is 4

Similarly Students who wants Only French is 16-4-3-2=7

8 0

2 years ago

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