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Mathematics

1 answer:

Airida [17]3 years ago

4 0

Answer:

B. $x^2+11x+24\leq 150$

Step-by-step explanation:

Step 1) Defining Sue and Jeremy's ages using x

Sue is 3 years older than Holly (h):

$h=x+3$

Jeremy is 5 years older than Sue, or 8 years older than Holly (j):

$j=x+8$

Product of Jeremy and Sue's ages is less than or equal to 150:

$hj\leq 150$

Step 2) Simplifying into a single equation

Using the equation above we can substitute Sue and Jeremy's ages:

$(x+3)(x+8)\leq 150$

Now we can simplify this equation. Use the distributive property first:

$x(x+8)=x^2+8x\\3(x+8)=3x+24$

Now add all the terms together and get the final answer:

$x^2+8x+3x+24\leq 150\\x^2+11x+24\leq 150$

Final equation: $x^2+11x+24\leq 150$

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Consider a normal distribution curve where the middle 85 % of the area under the curve lies above the interval ( 8 , 14 ). Use t

NeTakaya

Answer:

$\mu = 11$

$\sigma = 2.08$

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Middle 85%.

Values of X when Z has a pvalue of 0.5 - 0.85/2 = 0.075 to 0.5 + 0.85/2 = 0.925

Above the interval (8,14)

This means that when Z has a pvalue of 0.075, X = 8. So when $Z = -1.44, X = 8$ . So