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Archy [21]
3 years ago
8

Jose asks his friends to guess the higher of two grades he received on his math tests. He gives them two hints. The difference o

f the two grades is 16. The sum of one-eighth of the higher grade and one-half of the lower grade is 52. The system that represents his scores is below. x – y = 16 StartFraction 1 over 8 EndFraction x plus StartFraction one-half EndFraction y equals 52.x + StartFraction one-half EndFraction x plus StartFraction one-half EndFraction y equals 18.y = 52 What is the higher grade of Jose’s two tests?
Mathematics
1 answer:
tatyana61 [14]3 years ago
8 0

Answer : 96

x – y = 16 --------> equation 1

1/8 x + 1/2 y = 52

x is the higher grade and y is the lower grade

We solve the first equation for y

x - y = 16

-y = 16 -x ( divide each term by -1)

y = -16 + x

Now substitute y in second equation

1/8 x + 1/2 ( -16 + x ) = 52

1/8x - 8 + 1/2 x = 52

1/8x + 1/2x - 8 = 52

Take common denominator to combine fractions

1/8x + 4/8x -8 = 52

5/8x - 8 = 52

Add 8 on both sides

5/8x = 60

Multiply both sides by 8/5

x = 96

We know x is the higher grade

96 is the higher grade of Jose’s two tests.

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A pair of Descartes jeans costs $120. If the tax is 13%, how much does the pair of jeans cost including tax?
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$135.60

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120*13%=15.6

15.60+120.00=$135.60

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Determine the domain of the function (fog)(x) where f(x)=3x-1/x-4 and g(x)=x+1/x
Katarina [22]

Answer: (-∞,-1) ∪ (0,+∞)

Step-by-step explanation: The representation fog(x) is a representation of composite function, meaning one depends on the other.

In this case, fog(x) means:

fog(x) = f(g(x))

fog(x) = 3(x+\frac{1}{x} )-\frac{1}{x+\frac{1}{x} } -4

fog(x)=3x+\frac{3}{x} -\frac{1}{\frac{x^{2}+x}{x} } -4

fog(x)=3x+\frac{3}{x} -\frac{x}{x^{2}+x} -4

fog(x)=\frac{3x^{2}(x^{2}+x)+3(x^{2}+x)-x-4x(x^{2}+x)}{x(x^{2}+x)}

fog(x)=\frac{3x^{4}+3x^{3}+3x^{2}+3x-x-4x^{3}+4x^{2}}{x(x^{2}+x)}

fog(x)=\frac{3x^{4}-x^{3}-x^{2}+2x}{x(x^{2}+x)}

This is the function fog(x).

The domain of a function is all the values the independent variable can assume.

For fog(x), denominator can be zero, so:

x(x^{2}+x) \neq 0

If x = 0, the function doesn't exist.

x^{2}+x \neq0

x(x+1) \neq0

x+1\neq0

x\neq-1

<u>Therefore, the domain of this function is: </u><u>-∞ < -1 or x > 0</u>

5 0
3 years ago
What is the probability that a randomly selected male will have a foot length between 8 and 12.5 inches? P(8 &lt; r &lt; 12.5)=
melisa1 [442]

Answer:

0.8185 or 81.85%

Step-by-step explanation:

The mean length (μ) of an adult foot is 11 and the standard deviation (σ) is 1.5.

The z score is a measure in statistic used to determine the amount of standard deviation by which the raw score (x) is above or below the mean. If the raw score is above the mean, the z score is positive  and if the raw score is below the mean the z sore is negative. It is given by:

z=\frac{x-\mu}{\sigma}

To calculate the probability that a randomly selected male will have a foot length between 8 and 12.5 inches, we first calculate the z score for 8 inches and then for 12.5 inches.

For 8 inches:

z=\frac{x-\mu}{\sigma}=\frac{8-11}{1.5}=-2

For 12.5 inches:

z=\frac{x-\mu}{\sigma}=\frac{12.5-11}{1.5}=1

From the normal distribution table, The probability that a randomly selected male will have a foot length between 8 and 12.5 inches = P(8 < x < 12.5) = P(-2 < z < 1) = P(z < 1)  - P(z < -2) = 0.8413 - 0.0228 = 0.8185 = 81.85%

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