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4 years ago

Which of the following is a solution for x/4 > 10?

Mathematics

1 answer:

Simora [160]4 years ago

3 0

Answer: $x>40$

Step-by-step explanation:

For this exercise it is important to remember the Multiplication property of inequality. This states that:

If $c>0$ and $a>b$ , then $ac>bc$

If $c>0$ and $a$ , then $ac$

If $c$ and $a>b$ , then $ac$

If $c$ and $a$ , then $ac>bc$

Then, given the following inequality:

$\frac{x}{4}>10$

You need to apply Multiplication property of inequality and multiply both sides of the inequality by 4.

Then, the solution is:

$(\frac{x}{4})(4)>(10)(4)\\\\x>40$

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Answer:

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Nina knows that the average of the x-intercepts represents the line of symmetry for a quadratic function through the x-axis. Whi

Romashka [77]

Answer:

$\bf \displaystyle\frac{5+1}{2}=\displaystyle\frac{6}{2}=3$

Step-by-step explanation:

The x-intercepts are the values of x for which y=0, that is f(x)=0.

The x-intercepts of

$\bf f(x)=4x^2-24x+20$

are the values of x such that

$\bf 4x^2-24x+20=0$

Divide both sides by 4 to simplify a little

$\bf x^2-6x+5=0$

Solve the quadratic equation

$\bf x=\displaystyle\frac{-(-6)\pm\sqrt{(-6)^2-4*1*5}}{2*1}=\displaystyle\frac{6\pm\sqrt{36-20}}{2}=\\\\=\displaystyle\frac{6\pm\sqrt{16}}{2}=\displaystyle\frac{6\pm4}{2}$

and you get the 2 x-intercepts

x =10/2 and x = 2/2

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3 years ago

Read 2 more answers

ACT mathematics score for a particular year are normally distributed with a mean of 27 and a standard deviation of 2 points.

mel-nik [20]

Answer:

A: 16%

B: 95%

C: 97.5%

Step-by-step explanation:

According to the empirical rule:

68% of a normal distribution is between -1 and +1 standard deviations.

95% of a normal distribution is between -2 and +2 standard deviations.

99.7% of a normal distribution is between -3 and +3 standard deviations.

Given μ = 27 and σ = 2.

Part A

29 is one standard deviation above the mean. We can show this by calculating the z-score:

z = (x − μ) / σ

z = (29 − 27) / 2

z = 1

We know that 68% is between -1 and +1 standard deviations. Since normal distributions are symmetrical, we can also say that 34% is between 0 and +1 standard deviations.

P(0 < Z < 1) = 68%/2 = 34%

We can also say that 50% is less than 0 standard deviations.

P(Z < 0) = 50%

Therefore, P(Z < 1) = 34% + 50% = 84%.

Which means P(Z > 1) = 100% − 84% = 16%.

Part B

Like before, calculate the z-scores:

z₁ = (23 − 27) / 2

z₁ = -2

z₂ = (31 − 27) / 2

z₂ = 2

From the empirical rule, we know this is 95% of the normal distribution.

Part C

We found in part B that the z-score is 2.

P(0 < Z < 2) = 95%/2 = 47.5%

P(Z < 2) = 50% + 47.5% = 97.5%

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