MATHEMATICS HIGH SCHOOL

the ratio of red marbles to green marbles is 3 to 5. which situation follows this ratio? 70 red marbles and 42 green marbles 9 red marbles and 24 green marbles 51 red marbles and 85 green marbles 30 red marbles and 18 green marbles

Answers

Answer 1

Answer: 3/5 = 51/85

Therefore, 51 red marbles and 85 green marbles follows the required ratio.

Answer 2

Answer:

Answer with explanation:

Ratio of red marbles to green marbles is equal to $(3)/(5)$

Now starting from Options given

$1.(70)/(42)=(5)/(3)\n\n2.(9)/(24)=(3)/(8)\n\n3.(51)/(85)=(3)/(5)\n\n4.(30)/(18)=(5)/(3)\n\n\text{Option C}\rightarrow (51)/(85)$

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The graph shows the data points in the table and the exponential regression model associated with the data. A 2-column table with 5 rows. The first column is labeled days after treatment with entries 2, 4, 6, 8, 10. The second column is labeled number of weeds with entries 100, 26, 6, 2, 1. A graph shows days after treatment labeled 1 to 11 on the horizontal axis and number of weeds on the vertical axis. A line shows a downward trend. Based on the graph of the regression model, which is true? The number of weeds is decreasing by a multiplicative rate. The number of weeds is increasing by a multiplicative rate. The number of weeds is decreasing by an additive rate. The number of weeds is increasing by an additive rate.

A man invests a certain amount of money at 2% interest and $800 more than that amount in another account at 4% interest. At the end of one year he earned $112 in interest. How much money was invested in each account?Which of the following equations could be used to solve the problem?

A.)0.02x + 0.04(800) = 112
B.)0.02x + 0.04(x + 800) = 112
C.)0.04x + 0.02(x + 800) = 112

Answers

.02x+.04*2x=112
.02x+.08x=112
.10x=112
x=112/.10
x=$1,120 invested @ 2%.
2*1,120=$2,240 amount invested @ 4%.
Proof:
.02*1,120+.04*2,240=112
22.4+89.6=112
112=112

A.) 0.02x + 0.04(800) = 112

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Cutting a 4 foot ribbon into 7 equal parts, how long is each piece

Answers

The length of each piece will be 4/7 or 0.57

each piece would be 6.86 inches long.
pretty short must have ment the person had short hair :)

How do you convert celsius into fahrenheit?

Answers

You multiply by 9, then divide by 5, then add 32

The quantity demanded per month, x, of a certain make of personal computer (PC) is related to the average unit price, p (in dollars), of PCs by the equationx = f(p) =1009810,000 − p2It is estimated that t mo from now, the average price of a PC will be given byp(t) =4001 +18t+ 200 (0 ≤ t ≤ 60)dollars. Find the rate at which the quantity demanded per month of the PCs will be changing 16 mo from now. (Round your answer to one decimal place.)

Answers

Answer:

The value of dx/dt is $(100p)/(9√((810000-p^2))).(1600)/(√(t)\left(√(t)+8\right)^2)\n$ while the rate of change of quantity demanded per month after 16 months is 18.7.

Step-by-step explanation:

From the given data the equation of quantity demanded for average price is given as is given as

$x=f(p)=(100)/(9)√(810000-p^2)$

The equation of average price p for a given value of t is given as

$p(t)=(400)/(1+(1)/(8)√(t))+200$

Now in order to determine the rate at which the quantity demanded will be changing is given as $(dx)/(dt)$

This is found by using the chain rule as

$(dx)/(dt)=(dx)/(dp).(dp)/(dt)$

Now

$(dx)/(dp)=(d((100)/(9)√(810000-p^2)))/(dp)\n(dx)/(dp)=(100)/(9)(d)/(dp)[(810000-p^2)^(1/2)]\n(dx)/(dp)=(100)/(9)(1)/(2)[(810000-p^2)^(-1/2)](d)/(dp)[(810000-p^2)]\n(dx)/(dp)=(50)/(9)[(810000-p^2)^(-1/2)](-2p)\n(dx)/(dp)=(100p)/(9√((810000-p^2)))$

Now

$\n(dp)/(dt)=(d((400)/(1+(1)/(8)√(t))+200))/(dt)\n(dp)/(dt)=(d)/(dt)\left((400)/(1+(1)/(8)√(t))+200\right)\n(dp)/(dt)=(d)/(dt)\left((400)/(1+(1)/(8)√(t))\right)+0\n(dp)/(dt)=400(d)/(dt)\left((1)/(1+(1)/(8)√(t))\right)\n(dp)/(dt)=400(d)/(du)\left(\left(1+(1)/(8)√(t)\right)^(-1)\right)(d)/(dt)\left(1+(1)/(8)√(t)\right)\n(dp)/(dt)=-(1600)/(√(t)\left(√(t)+8\right)^2)$

So now the value of dx/dt is given as

$(dx)/(dt)=(dx)/(dp).(dp)/(dt)\n(dx)/(dt)=(100p)/(9√((810000-p^2))).(1600)/(√(t)\left(√(t)+8\right)^2)\n$

So the value of dx/dt is $(100p)/(9√((810000-p^2))).(1600)/(√(t)\left(√(t)+8\right)^2)\n$

Now for the time =16 months price is given as

$p(t)=(400)/(1+(1)/(8)√(t))+200\np(16)=(400)/(1+(1)/(8)√(16))+200\np(16)=466.67$

Now the value of x is given as

$(dx)/(dt)=(100p)/(9√((810000-p^2))).(1600)/(√(t)\left(√(t)+8\right)^2)\n\n(dx)/(dt)=(100*466.67)/(9√((810000-466.67^2))).(1600)/(√(16)\left(√(16)+8\right)^2)\n(dx)/(dt)=18.72$

So the rate of change of quantity demanded per month after 16 months is 18.72

The probability that a new spark plug is defective is 0.06. You need two new spark plugs. What is the probability that both spark plugs you buy are defective?A) 0.06
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