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Which of the following is the biconditional statement for the conditional statement below?

If today is Saturday or Sunday, then it is the weekend.
1. It is the weekend if and only if it is Saturday or Sunday.
2. If is not the weekend, then it not Saturday or Sunday.
3. If it is not Saturday or Sunday, then it is not the weekend.
4. It is not Saturday or Sunday if and only if it is the weekend.
Grade 10 Problem Solving Strategies CCSS: HSN-Q.A.1
Grade 10 Problem Solving Strategies CCSS: HSN-Q.A.1
Using dimensional analysis, the following calculation can be performed to convert between 3 pounds and its equivalent in grams (using the rate of 1 oz equals 28.3 g).

$(3 \ "lb")/1 xx (16 \ "oz") / (1 \ "lb") xx (28.3 \ "g")/(1 \ "oz") = 1,358.4 \ "g"$

Mathematically, why can 3 be multiplied by the factors $(16 \ "oz") / (1 \ "lb")$ and $(28.3 \ "g")/(1 \ "oz") ?$
1. Because this is dimensional analysis, regular rules of math do not apply.
2. Since the necessary units cancel out, there is no problem.
3. Because each of these factors is equal to one (the numerator and denominator are equal, but in different units).
4. By the Multiplicative Property of Equality.
Grade 10 Problem Solving Strategies CCSS: HSN-Q.A.2
A moving company chargers $65 per hour, plus a fee that depends on the distance between where the objects are being moved ($35 for every mile). What variable(s) would be good to define if one were to create an expression that would determine the total cost of moving?
1. One variable: C, the cost of moving.
2. One variable: t, for the amount of time.
3. Two variables: C, for the total cost, and t, for the amount of time.
4. Two variables: t, for the amount of time, and d, for the distance traveled.
Given the statement: "If you eat all your vegetables, then you will grow," which of the following choices is its converse?
1. If you grow, then you will eat all of your vegetables.
2. If you do not eat all of your vegetables, then you will not grow.
3. If you do not grow, then you will not eat all of your vegetables.
Grade 10 Problem Solving Strategies CCSS: HSN-Q.A.2
There is a leak in the ceiling of Kara's room. She puts a bucket underneath the drip. After an hour, there's about a half liter of water. She checks back in another 3 hours, and there is about 2 liters of water. If she wants to determine how much water there will be in 12 hours, what quantity or quantities would she need to determine?
1. The rate of the water's increase, in liters per hour.
2. The amount of water in the bucket, in liters.
3. The amount of water in the bucket in liters and the amount of time that has passed in hours.
4. The size of the bucket in liters and the rate of the drip in liters per hour.
Given the statement: "If you eat all your vegetables, then you will grow," which of the following choices is its inverse?
1. If you grow, then you will eat all of your vegetables.
2. If you do not grow, then you will not eat all of your vegetables.
3. If you do not eat all of your vegetables, then you will not grow.
Grade 10 Problem Solving Strategies CCSS: HSN-Q.A.1
Near the end of class, Jillian's physics teacher writes a formula up on the board. Jillian quickly writes it down before leaving. Later that night while doing homework, she is unsure if she correctly copied the formula. What she wrote is:
$d = d_0 + v_0t + 1/2 at^2$
where $d, d_0$ are distances measured in meters; $v_0$ is velocity, measured in meters per second; $t$ is time, measured in seconds; and $a$ is acceleration, measured in meters per second squared.

She decides she will use dimensional analysis to determine if it is correct or not. She reasons that each term has to have the same units, and since the term on the left side of the equation and the first term on the right side of the equation are in meters, the other two terms need to be as well. The second term on the right side of the equation is

$"m"/"s" *"s"/1 = "m"$

and the last term is

$"m"/"s"^2 * "s"^2/1 = "m"$.

Since all terms are in meters, she decides that the equation she wrote down is right. Is she correct, and if not, what mistake did she make?
1. Yes, she is correct.
2. No. She assumed that all terms need to have the same units, when all terms need to be without units.
3. No. Although the variable $t$ is squared, the units are not. Therefore, the units of the last term are m/s, which are different than the rest of the terms.
4. No. Jillian did the dimensional analysis incorrectly. The units of the second term on the right side come out to $"m"//"s"^2$ and the units of the last term are $"m"//"s"^4$.
On Wednesdays we wear pink.
It is Wednesday.
Therefore
1. we are wearing pink.
2. we are not wearing pink.
3. we don't have to wear pink.
4. there is not enough information given.