Mateo wants to make a toy sailboat. he has two pieces of wood to choose from.
his first piece of wood is a block that measures 18'' x 10" x 8". it weighs 46.65 lbs.
his second piece of wood is a log of wood measuring 21" long, with an average circumference of 25.12". it weights 39.25 lbs.
the sailboat needs to float, but both blocks of wood are denser than wood usually is, and he's not sure either piece of wood will float. he doesn't want to get the water wet before he's applied a sealant, so he isn't willing to just drop them in the water to find out.
2a. which common solid can he use to represent the block? which common solid can he use to represent the log? (2 points)
2b. what is the density of the block in pounds per cubic inch? give the formula for density and show your work. (3 points)
2c. what is the density of the log in pounds per cubic inch? give the formula for density and show your work. use 3.14 for π. (hint: you can determine the radius from the circumference.) (3 points)
2d. water has a density of about 0.0361 pounds/cubic inch. anything rarer will float, and anything denser will sink. which of the pieces of wood are suitable for making a toy boat that will float? (2 points)

2

step-by-step explanation:

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

positive

step-by-step explanation:

the quadrant is facing upwards

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.