Determine whether each statement makes sense or does not make sense, and explain your reasoning. I'm working with a true conditional statement, but when I reverse and negate the antecedent and the consequent, my new conditional statement is no longer true.

The table shows Emma's midyear exam results. The exam results for each subject are normally distributed with the mean $\mu$ and standard deviation $\sigma$ shown in the table.

$$\begin{matrix} \text{Subject} & \text{Emma's score} & {\mu} & {\sigma}\\ \text{English} & \text{48} & \text{40} & \text{4.4}\\ \text{Mandarin} & \text{81} & \text{60} & \text{9}\\ \text{Geography} & \text{84} & \text{55} & \text{18}\\ \text{Biology} & \text{68} & \text{50} & \text{20}\\ \text{Maths} & \text{84} & \text{50} & \text{15}\\ \end{matrix}$$

Arrange Emma's subjects from 'best' to 'worst' in terms of the z-scores.

(a.) What is meant by tangent line approximation? (b.) Define the terms propagated error, relative error, and percentage error.

Determine whether the given random variable X is discrete or continuous. X measures the living area of a randomly selected house in your neighborhood.

Southside Landscapes proposes to plant the flower beds for the historic Earle House gardens. The company uses four patterns. Pattern I uses 40 tulips, 25 daffodils, and 6 boxwood. Pattern II uses 25 tulips, 50 daffodils, and 4 boxwood. Pattern III uses 30 tulips, 40 daffodils, and 8 boxwood. Pattern IV uses 45 tulips, 45 daffodils, and 2 boxwood. The profit for each pattern is $48 for Pattern I,$45 for Pattern II, $55 for Pattern III, and$65 for Pattern IV. Southside Landscape has 1250 tulips, 1600 daffodils, and 195 boxwood available. How many of each pattern should be used to maximize profit?

Write the word sentence as an inequality. $y+5 \gt 8 ; y=1$

Simplify.

$$\sqrt [ 3 ] { 32 }$$

To be rescued from the roof of a burning building, a 70-kg man must be able to jump straight up and catch hold of a rope ladder hanging from a helicopter. He has to raise his center of mass 2.00 m above the roof to do so. (a) If he crouches down such that his center of mass is 0.50 m above the roof and his feet leave the roof when his center of mass is 1.05 m above the roof, what minimum force must he exert on the roof to reach the ladder? (b) A typical candy bar contains about 850 kJ of food energy. How many candy bars does this jump require?

Calculate. $\int{\dfrac{dx}{1-\sqrt{x}}}$

Claim: The mean pulse rate (in beats per minute, or bpm) of adult males is equal to 69 bpm. For the random sample of 153 adult males the mean pulse rate is 69.6 bpm and the standard deviation is 11.3 bpm. Make subjective estimates to decide whether results are significantly low or significantly high, then state a conclusion about the original claim. For example, if the claim is that a coin favors heads and sample results consist of 11 heads in 20 flips, conclude that there is not sufficient evidence to support the claim that the coin favors heads (because it is easy to get 11 heads in 20 flips by chance with a fair coin).

In a drama club, 7 of the 20 girls are seniors, and 4 of the 14 boys are seniors. What is the probability of randomly selecting a boy or a senior to represent the drama club at an arts symposium?

Some water is placed in a coffee cup calorimeter. When 1.0 g of an ionic solid is added, the temperature of the solution increases from $21.5 ^ { \circ } \mathrm { C }$ to $24.2 ^ { \circ } \mathrm { C }$ as the solid dissolves. For the dissolving process, what are the signs for $\Delta S _ {sys}, \Delta S _ {surr},$ and $\Delta S _ {univ}?$

Let P(x) be the cumulative distribution function for the household income distribution in the US in 2009. Values of P(x) are in the following table:

Income x (thousand $): 20, 40, 60, 75, 100 P(x) (%): 29.5, 50.1, 66.8, 76.2, 87.1

Is the statement "More than one-third of households made between$40,000 and $75,000" true or false?

If a function f has no limit as x approaches c, then we say that $\lim _{x \rightarrow c} f(x)$ _____ _____ _____.