What is the area of a circle with a radius of 1.5 centimeters? Use 3.14 as an approximation for pi.

The length of a rectangle is 12 units longer than the width. The perimeter is 7 times the width. Find the length and the width o

katen-ka-za [31]

Log explanation below; answer is at bottom.

If the length, l, is 12 units longer than the width, w, then w = l - 12. If the perimeter, p,

p = 2l +2w,

is 7 x w, then

w = p/7

When two things are set equal to the same variable, they are equal to each other, so,

l - 12 = p/7

Now you need to get rid of the p so you are only working with one variable. To do this you plug in whatever p is equal to for p, so,

l - 12 = (2l + 2w)/7 now to get rid of the w do the same thing we did with p just for w. So,

l - 12 = (2l + 2(l - 12))/7

To solve this you want to multiply both sides by 7 first to get rid of the fraction.

7l - 84 = 2l + 2(l - 12)

Next you want to distribute the 2 over the l and the 12.

7l - 84 = 2l + 2l - 24

Next you want to combine like terms on each side.

7l - 84 = 4l - 24

Next add 84 and subtract 4l from sides to isolate the variable.

3l = 60

Now divide each side by 11 to get your answer.

l = 20.

To find the width,

w = l - 12

Just plug in and solve.

w = 20 - 12

w = 8

So your length and width are 20 and 8.

l = 20

w = 8

7 0

3 years ago

Sam Kramer earns an annual salary of $38,900. He is paid semimonthly. His personal exemptions total $4826. The state income tax

Alisiya [41]

Step-by-step explanation:

we pay taxes of the income without the exemptions.

so, the tax-interresting amount is

38,900 - 4826 = $34,074

2% of the first $1000 = $20

$34,074 - 1000 = $33,074

3% of the next $3000 = $90

$33,074 - 3000 = $30,074

3.5% of the next $3000 = $105

$30,074 - 3000 = $27,074

4% of $27,074 = $1,082.96

so, in total he pays state taxes over a year

20+90+105+1082.96 = $1,297.96

now, he gets paid semimonthly, that means twice a month.

his salary but also his deductions (incl. tax deductions) are all split across these 24 paychecks per year.

so, each state income tax deduction is then

$1,297.96 / 24 = $54.08 on every paycheck.

8 0

2 years ago

Paul owes Paula 3535 cents and has a pocket full of 55-cent coins, 1010-cent coins, and 2525-cent coins that he can use to pay h

Ray Of Light [21]

Paul owes paula 35 cents...she has a pocket full of nickels,dimes,and quarters.

largest number of coins would be : 7 nickels (7 coins)
smallest number of coins would be : 1 quarter and 1 dime (2 coins)

the difference is : 7 - 2 = 5 coins <=

4 0

3 years ago

Dinosaur fossils are often dated by using an element other than carbon, like potassium-40, that has a longer half life (in this

Firlakuza [10]

The amount of substance left of a radioactive element of half life, $t_{\frac{1}{2}}$ after a time, t, is given by:

$N(t)=N_0\left( \frac{1}{2} \right)^ \frac{t}{t_{ \frac{1}{2} }}$

Given that <span>potassium-40 has a half life of approximately 1.25 billion years.

The number of years it will take for 0.1% of potassium-40 to remain is obtained as follows:

$0.1=100\left( \frac{1}{2} \right)^ \frac{t}{1.25}} \\ \\ \Rightarrow\left( \frac{1}{2} \right)^ \frac{t}{1.25}}=0.001 \\ \\ \Rightarrow\frac{t}{1.25}\ln\left( \frac{1}{2} \right)=\ln(0.001) \\ \\ \Rightarrow \frac{t}{1.25}= \frac{\ln(0.001)}{\ln\left( \frac{1}{2} \right)} =9.966 \\ \\ t=9.966(1.25)=12.5$

Therefore, </span><span>the maximum age of a fossil that we could date using 40k is 12.5 billion years.</span>

3 0

3 years ago

While visiting the 200, Elijah, Alda, and Chris create a triangle by standing at its vertices. They are the same distance away f

trapecia [35]

Answer:

Circumcenter

Step-by-step explanation:

The circumcenter of a triangle is the point that has same distance from the three vertices of the triangle.

The snake exhibit is in the circumcenter of the triangle.

5 0

2 years ago