MATHEMATICS HIGH SCHOOL

A storeowner applies a 15% markup to a lamp costing $159. What is the retail price of the lamp

Answers

Answer 1

Answer: 182.85 is the answer.
159 * .15 = 23.28
23.4+159=182.85

Answer 2

Answer:

182.85

Step-by-step explanation:

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Hi, I need help with this equation x²+y²-4x-6x+9=0

Answers

$x^2+y^2-4x-6y+9=0\n\n x^2-4x+16+y^2-6y+9-16=0\n\n(x-4)^2+(y-3)^2=16\n\nthis\ is\ the\ equation\ of\ a\ circle:\ \ (x-a)^2+(y-b)^2=r^2\n\ncenter\ \ S=(4;3)\ \ \ and\ \ \ radius\ \ r =4$

The half-life of Po-214 is 0.001 seconds. How much of a 10g sample is left after the 0.003 seconds. Also, create an exponential function to model its decay.

Answers

$\bf \textit{Amount for Exponential Decay using Half-Life} \n\n A=P\left( (1)/(2) \right)^{(t)/(h)}\qquad \begin{cases} A=\textit{accumulated amount}\n P=\textit{initial amount}\dotfill &10\n t=\textit{elapsed time}\dotfill &0.003\n h=\textit{half-life}\dotfill &0.001 \end{cases} \n\n\n A=10\left( (1)/(2) \right)^{(0.003)/(0.001)}\implies A=10\left( (1)/(2) \right)^3\implies A=1.25$

Final answer:

After 0.003 seconds, we would have 1.25g of the initial 10g Po-214 left. The decay process can be modeled with the exponential function: N = 10 * $(1/2)^{(0.003/0.001)$ , where N is the final amount, N0 is the initial amount, t is time, and T is the half-life.

Explanation:

The subject matter pertains to the concept of half-life in physics which interprets the decay of a radioactive material. In radioactive decay, the number of atoms in a radioactive sample decreases exponentially over time. This time is taken into consideration in the form of their half-lives. In the case of Po-214, the half-life is given as 0.001 seconds.

Before finding how much of Po-214 is left after 0.003 seconds, let's first understand the calculation. After one half-life (0.001 second), half of the sample will be left, i.e., 10g/2 = 5g. After another half-life (another 0.001 second), half of this 5g will be left, i.e.,5g/2 = 2.5g. After the third half-life (the remaining 0.001 second), we will have 2.5g/2 = 1.25g left. So, after 0.003 seconds, we would have 1.25g of Po-214 remaining from the initial 10g.

The decay process can be modeled with an exponential function N = N0 * $(1/2)^{(t/T)$ , where N is the final amount, N0 is the initial amount, t is time, and T is the half-life. For this problem, the equation would be: N = 10 * (1/2)^(0.003/0.001).

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Rick used 4-2-3 yards to sew 3-1-2 shirts what is the unit rate of cloth he used in terms of yards per shirt Mathematics 7th grade

Answers

If Rick used 4 2/3 yards of fabric to sew 3 1/2 shirts. The unit rate of cloth he used in terms of yards per shirt will be 4/3.

What is an arithmetic operation?

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

It is given that, Rick used 4 2/3 yards of fabric to sew 3 1/2 shirts.

We'll apply division by Splitting into equal halves or groups, the division may be used to decide how to distribute a dish of cookies evenly among a group.

The unit rate of cloth he used in terms of yards per shirt is found by dividing the 3 1/2 shirts by 4 2/3 yards,

$= 4 (2)/(3) / 3 (1)/(2) \n\n = (14)/(3) / (7)/(2) \n\n = (14)/(3) * (2)/(7) \n\n = (4)/(3)$

Thus, if Rick used 4 2/3 yards of fabric to sew 3 1/2 shirts. The unit rate of cloth he used in terms of yards per shirt will be 4/3.

The question is incomplete

The complete question is"Rick used 4 2/3 yards of fabric to sew 3 1/2 shirts. What is the unit rate of cloth he used in terms of yards per shirt?"

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A quantity m varies jointly with p and r. If m is 1, p is 2, and r is 4. What is the constant of variation?1/8
1/2
2
8

Answers

m vaires jointly as with p and r
m=kpr
m=1
p=2
r=4
sub
1=k*2*4
1=k*8
divide both sides by 8
1/8=k

answer is contatnt is 8

Answer:

A) 1/8

Step-by-step explanation:

Given:

A quantity "m" varies jointly with "p" and "r".

Now we have to form the equation.

m = kpr, where "k" is the constant.

Now we have to plug in the given values; m =1, p = 2 and r = 4 and find the value of k.

1 = k.2.4

1 = 8k

Divide both sides by 8, we get

8k/8 = 1/8

k = 1/8.

Compare partial products and regrouping how the methods are alike and different

Answers

Answer:

We get the same answer from both processes.In the end, it is a multiplication process. In partial product we take the values of ones, tens, hundreds in each step and then add them together. In regrouping same thing happens but we do not break them down to processes.

Step-by-step explanation:

In Partial products we multiply the numbers partially and add them together to get the answer. It is easier to explain with an example, lets say we multiply 47 by 3

1) 47

×3

--------

2) 47

×3

---------

120 ( $(3*40)$

3) 3 8

×3

----------

+21

120

-----------

141

In Regrouping we add the partial products to the next tens,hundreds and so on. We don not write them down and then add later. Lets take the same example and do the multiplication with Regrouping method.

1)2 --------> ( $3*7=21$ write the number in tenth place here)

×3

___

__1 --------> ( $3*7=21$ write the number in ones place here)

2)47

×3

___

141 ( $3*4=12$ then add the 2 above to get 14)

Partial products are different in regrouping in terms of how numbers are clustered from a set equation as a whole delivering it individual but naturally to all the numbers involved in the set.
Regrouping is just like the commutative or associative property of numbers.
Associative property of addition is used when you want to group addends. This is mainly used to cluster set of numbers or in this case, addends. How do you use the associative property when you break apart addends? Simple you group them using the open and closed parentheses or brackets. Take for an example 1 + 1 + 2 = 4. Using the associative property you can have either (1 + 1) + 2 = 4 or 1 + (1 + 2) = 4 clustered into place.

A stack of paper contains 400 sheets. The volume of the stack is 140.25 cubic inches. Each sheet of paper is identical, with a length of 11 inches and a width of 8.5 inches. Find the height of each sheet of paper. Please put the process.