Help me with math anyone

18 POINTS! At the AoPS office, mice vary inversely with cats, that is, mice=k/cats, for some value of k. When there are 3r-19 ca

Blizzard [7]

Answer:

k=30

Step-by-step explanation:

The number of mice vary inversely with cats. This is written as:

$Mice \propto \dfrac{1}{Cat} \\Mice = \dfrac{k}{Cat}$

When there are 3r-19 cats, there are 2r+1 mice

$2r+1 = \dfrac{k}{3r-19}\\$Cross multiply$\\k=(3r-19)(2r+1)$

When there are 6r-27 mice, there are r-5 cats.

$6r-27 = \dfrac{k}{r-5}\\$Cross multiply$\\k=(6r-27)(r-5)$

Taking the values of k above, we have:

$k=(3r-19)(2r+1) =(6r-27)(r-5)\\(3r-19)(2r+1) =(6r-27)(r-5)\\6r^2+3r-38r-19=6r^2-30r-27r+135\\$Collect like terms\\6r^2-6r^2+3r+30r-38r+27r-19-135=0\\22r-154=0\\22r=154\\$Divide both sides by 22\\r=7$

Therefore:

$k=(3r-19)(2r+1) \\=(3*7-19)(2*7+1)\\=(21-19)(14+1)\\=2*15\\k=30$

8 0

3 years ago

Which is the better value, 2 books for $18 or 6 books for $45? Explain. {hint: make two tables; compare} (1 pt.) RP.1.3 b a.2 bo

Musya8 [376]

Answer:

I am a little confused by your question but if you were getting less it would be the first but more would be the second

Step-by-step explanation:

4 0

3 years ago

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Graph this function using intercepts:<br> x–y= -10

Oksanka [162]

X-Y=10
X-y+y=-10+y
X=y-10
The answer is x=y-10

7 0

3 years ago

Write an question that helps explain the amount of racism here in society

emmasim [6.3K]

Why do people hate someone just because of the color of their skin? :(

8 0

3 years ago

A school has 200 students and spends $40 on supplies for each student. The principal expects the number of students to increase

Xelga [282]

Answer:

$\mathbf{S(t)=200(\frac{105}{100})^{x}}$

$\mathbf{A(t)=40(\frac{98}{100})^{x}}$

$\mathbf{E(t)=S(t) \cdot A(t)=200(\frac{105}{100})^{x} \cdot 40(\frac{98}{100})^{x}=8000(\frac{10290}{10000})^{x}}$

Step-by-step explanation:

<h3>The predicted number of students over time, S(t) </h3>

Rate of increment is 5% per year.

A function 'S(t)' which gives the number of students in school after 't' years.

S(0) means the initial year when the number of students is 200.

S(0) = 200

S(1) means the number of students in school after one year when the number increased by 5% than previous year which is 200.

S(1) = 200 + 5% of 200 = $200+\frac{5}{100}\time200$ = $200(1+\frac{5}{100})$ = $200(\frac{105}{100})$

S(2) means the number of students in school after two year when the number increased by 5% than previous year which is S(1)

S(2) = S(1) + 5% of S(1) = $\textrm{S}(1)(\frac{105}{100})$ = $200(\frac{105}{100})(\frac{105}{100})$ = $200(\frac{105}{100})^{2}$

.

Similarly $\mathbf{S(x)=200(\frac{105}{100})^{x}}$

<h3>The predicted amount spent per student over time, A(t) </h3>

Rate of decrements is 2% per year.

A function 'A(t)' which gives the amount spend on each student in school after 't' years.

A(0) means the initial year when the number of students is 40.

A(0) = 40

A(1) means the amount spend on each student in school after one year when the amount decreased by 2% than previous year which is 40.

A(1) = 40 + 2% of 40 = $40-\frac{2}{100}\time40$ = $40(1-\frac{2}{100})$ = $40(\frac{98}{100})$

A(2) means the amount spend on each student in school after two year when the amount decreased by 2% than previous year which is A(1)

A(2) = A(1) + 2% of A(1) = $\textrm{A}(1)(\frac{98}{100})$ = $40(\frac{98}{100})(\frac{98}{100})$ = $40(\frac{98}{100})^{2}$

.

Similarly $\mathbf{A(x)=40(\frac{98}{100})^{x}}$

<h3>The predicted total expense for supplies each year over time, E(t)</h3>

Total expense = (number of students) × (amount spend on each student)

E(t) = S(t) × A(t)

$\mathbf{E(t)=S(t) \cdot A(t)=200(\frac{105}{100})^{x} \cdot 40(\frac{98}{100})^{x}=8000(\frac{10290}{10000})^{x}}$

$\mathbf{E(t)=8000(\frac{10290}{10000})^{x}}$

(NOTE : The value of x in all the above equation is between zero(0) to ten(10).)

6 0

3 years ago

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