What is the mass of the decoration and of each passenger car?

James paid off the loan on his motorboat in the year 2006. He originally borrowed $6,500 to buy the boat, but with simple annual

ale4655 [162]

5 years as 6500 at a rate of 7% or 455 more dollars a year has to cover a monetary gap of $2275. divide 2275 by 455 and get a nice even 5 years

7 0

3 years ago

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Tom works at a car dealership selling cars. If he makes $4000 a month and $250 per car he sells, how much did he

pogonyaev

Answer:

Answer = he made 7,000 in July and sold 10 cars in august.

Step-by-step explanation:

3 0

2 years ago

My Notes OAsk Your Tea The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at time t an

Papessa [141]

Answer:

10.96 hours will take for 85% of the lead to decay.

Step-by-step explanation:

Suppose A represents the amount of Pb-209 at time t,

According to the question,

$\frac{dA}{dt}\propto A$

$\implies \frac{dA}{dt}=kA$

$\int \frac{dA}{A}=\int kdt$

$ln|A|=kt+C_1$

$A=e^{kt+C_1}$

$A=e^{C_1} e^{kt}$

$\implies A=C e^{kt}$

Let $A_0$ be the initial amount,

$A_0=C e^{0} = C$

$\implies A=A_0 e^{kt}$

Since, the half-life of 3.3 hours.

$\implies \frac{A_0}{2}=A_0 e^{3.3k}\implies e^{3.3k}=0.5\implies k=-0.21004$

$\implies A=A_0 e^{-0.21004t}$

Here, $A_0=1\text{ gram}$

$A=(100-85)\% \text{ of }A_0=15\%\text{ of }A_0=0.15A_0$

By substituting the values,

$0.15A_0=A_0 e^{-0.21004t}$

$0.15=e^{-0.21004t}$

$\implies t\approx 10.96\text{ hour}$

6 0

3 years ago

The sum of a rational number and an irrational number is irrational.

Harman [31]

<h3>Answer: Always</h3>

Proof:

Let

A = some rational number
B = some irrational number
C = some rational number (that isn't necessarily equal to A)

We'll show that a contradiction happens if we tried to say A+B = C.

In other words, we'll show a contradiction happens for the form rational+irrational = rational.

Because A and C are rational, we can say

A = p/q

C = r/s

where p,q,r,s are integers. The q and s in the denominators cannot be zero.

So,

A+B = C

B = C - A

B = (r/s) - (p/q)

B = (qr/qs) - (ps/qs)

B = (qr-ps)/(qs)

B = (some integer)/(some other integer)

B = some rational number

But wait, we stated that B was irrational. The term "irrational" literally means "not rational". Irrational numbers cannot be written into fraction form of two integers. This is a contradiction and shows that A+B = C is never possible if A,C are rational while B is irrational.

This must lead to the conclusion that A+B must always be irrational if A is rational and B is irrational.

The template is this

rational + irrational = irrational

rational + rational = rational

8 0

3 years ago

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Two straight lengths of wire are placed on the ground, forming vertical angles. If the measure of one of the four angles formed

vitfil [10]

We have
angle 1= $72 degrees$

see the attached picture to better understand the problem

we know that
<span>Vertical angles are congruent
</span> $angle1=angle3 \\ angle2=angle4$
<span>
and

adjacent angles are supplementary
</span> $angle2+angle1=180 \\ angle3+angle4=180$
<span>
if the measure of one of the angles is </span> $72$ degrees and straight lines equal $180$ <span> degrees you have to
subtract </span> $72$ from $180$
so
$angle 2=180-72 \\ angle 2=108 degrees$

therefore
$angle 3=amgle 1 \\ angle 3=72 degrees$

$angle 4=amgle 2 \\ angle 4=108 degrees$

the answer is

the measures of the other three angles are
$108, 108 and 72 degrees$

5 0

3 years ago

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