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brilliants [131]
2 years ago
9

You and a friend each have a collection of tokens. Initially, for every 8 tokens you had, your friend had 3. After you give half

of your tokens to your friend, your friend now has 18 more tokens than you. Initially, how many more tokens did you have than your friend?
Mathematics
1 answer:
vlada-n [284]2 years ago
3 0
If your friend now has 18 that means you had 48, as mentioned above, you had given half of your tokens, half of 48 is 24. =24
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The monthly cost of driving a car depends on the number of miles driven. Lynn found that in May her driving cost was $380 for 48
andrezito [222]

Answer:

y=0.2x+284

Step-by-step explanation:

Let  x be the distance driven, d-distance and C our constant.

Our information can be presented as:

y=mx+c\\\\450=830x+C\ \ \ \ \ \ \ \ \ eqtn 1\\\\380=480x+C\ \ \ \ \ \ \ \ \ eqtn 2

#Subtracting equation 2 from 1:

70=350x\\x=0.2

Hence the fixed cost per mile driven,x is $0.20

To find the constant,C we substitute x in any of the equations:

450=830x+C\ \ \ \ \ \ \ X=0.2\\\therefore C=450-830\times0.2\\=284

Now, substituting our values in the linear equation:

y=0.2x+284       #y=cost of driving, x=distance driven

Hence the linear equation for the cost of driving is y+0.2x+284

7 0
2 years ago
Raj’s bathtub is clogged and is draining at a rate of 1.5 gallons of water per minute. The table shows that the amount of water
timurjin [86]

Raj’s bathtub is clogged and is draining at a rate of 1.5 gallons of water per minute. The table shows that the amount of water remaining in the bathtub, y, is a function of the time in minutes, x, that it has been draining.

What is the range of this function?

all real numbers such that y ≤ 40

all real numbers such that y ≥ 0

all real numbers such that 0 ≤ y ≤ 40

all real numbers such that 37.75 ≤ y ≤ 40

5 0
2 years ago
Read 2 more answers
Anonymous 3 years ago
amm1812
Two angles are said to be complementary, if the sum of the measures of the to angles is equal to 90 degrees.

Thus, given that HFG is complementary to ACB, them mHFG + mACB = 90 degrees.

From the figure, given that the line from point F meats line CE at point P, then HFG = CFP.
But mCFE = 90 degrees and mCFE = mCFP + mPFE
Also PFE = DFH

Thus, mCFE = mCFP + mPFE = mHFG + mDFH = 90 degrees

Recall that mHFG + mACB = 90 degrees

Thus, mHFG + mACB = mHFG + mDFH

Therefore, mACB = mDFH.
5 0
3 years ago
Based on a study of population projections for 2000 to​ 2050, the projected population of a group of people​ (in millions) can b
Olegator [25]

Answer:

(a) 0.107 million per year

(b) 0.114 million per year

Step-by-step explanation:

A(t) = 11.19(1.009)^t

(a) The average rate of change between 2000 and 2014 is determined by dividing the difference in the populations in the two years by the number of years. In the year 2000, t=0 and in 2014, t=14. Mathematically,

\text{Rate}=\dfrac{A(2014) - A(2000)}{2014-2000}=\dfrac{11.19(1.009)^14-11.19(1.009)^0} {14}

A(0)=\dfrac{12.69-11.19}{14}=\dfrac{1.5}{14}=0.107

(b) The instantaneous rate of change is determined by finding the differential derivative at that year.

The result of differentiating functions of the firm y=a^x (where a is a constant) is \dfrac{dy}{dx}=a^x\ln a. Let's use in this in finding the derivative of A(t).

A\prime(t) = \dfrac{A}{t}=11.19\cdot1.009^t\ln1.009

In the year 2014, t=14.

A\prime(14) =11.19\cdot1.009^14\ln1.009=0.114

6 0
3 years ago
Ralph’s average score for 5 tests was 82. on four of the tests his scores were 85, 73, 92, 66. what was the fifth test score?
SCORPION-xisa [38]

Answer:

94

Step-by-step explanation:

Let the unknown number be denoted by the variable, x. Also note that, the average can be found by adding all values together and dividing by the amount of values there are.

Set the equation:

(85 + 73 + 92 + 66 + x)/5 = 82

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Simplify first by combining like terms, and then do the opposite of PEMDAS.

PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& roots)

Multiplications

Divisions

Additions

Subtractions.

Combine like terms:

(85 + 73 + 92 + 66 + x)/5 = 82

(316 + x)/5 = 82

Next, isolate the x, by multiplying 5 to both sides of the equation:

(316 + x)/5 * 5 = (82) * 5

316 + x = 82 * 5

316 + x = 410

Lastly, subtract 316 from both sides of the equation:

x + 316 = 410

x + 316 (-316) = 410 (-316)

x = 410 - 316

x = 94

94 is the final test score.

5 0
2 years ago
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