Tutor profile: Patrick D.
Subject: Basic Math
Pat is running a marathon (26.2 miles). He begins by running his the first 7 miles of the race in 45 minutes. The next 8 miles of the race are downhill and Pat picks up the pace and averages this portion in 10 miles per hour. By mile 15, Pat is worn out and runs the next ten miles in 1.5 hours. Finally with just 1.2 miles left, Pat sprints to the finish at 5 minutes per mile pace. What time did Pat finish his marathon in?
To answer the question we need to convert all of the different portions of the race to minutes and add them up to get the total time it took Pat to run the race. Each of these conversions can be calculate by using the rate equation of rate = distance/time For the first portion we don't need to do anything since we are told it took him 45 minutes. The next portion is 8 miles and is completed at 10 miles per hour. To calculate the amount of time Pat ran this portion we must rearrange the rate equation to calculate for time ( time = distance/ rate). The time of this portion can be calculated by dividing distance (8 miles) by rate (10 miles/hour). This calculation gives a value of 0.8 hours. To convert this to minutes we simply need to multiply by 60 minutes ($$0.8*60=40$$ minutes). This portion took Pat 40 minutes. The third portion is basically given to us. All we have to do is convert to minutes. Again we complete this conversion by multiplying 1.5 hours by 60 minutes ($$1.5*60=90$$ minutes). This portion took Pat 90 minutes. Finally, the last 1.2 miles were run at 5 minutes per mile. We need to rearrange the rate equation again to be time = distance/ rate. This time the calculation will be $$1.2 * 5 = 6$$ minutes. To answer the question we need to add each of the portions. $$45 + 40 + 90 + 6 = 181$$ minutes or 3 hours and 1 minute.
Subject: Basic Chemistry
48 grams of methane (CH4) combusts with oxygen (O2) to form water (H2O) and carbon dioxide (CO2). How much oxygen was needed in grams for this reaction to occur to completion?
The first step to answer this question will be to write out the equation for the chemical reaction and balance it so that the elements on either side of the reaction are equal. In this case the reaction is CH4 + 2 O2 --> CO2 + 2 H2O Now that everything is set up, all that is needed is some simple stoichiometry to answer the question. Firstly, we must calculate how many moles of CH4 are inputed into the reaction. The molar mass of methane can be calculated by breaking out your periodic table and adding up the molar mass of carbon (12g) and 4 parts hydrogen (4g) for a total of 16 g/mol. To calculate how many moles of methane 48g is we only need to divide 48g by 16 g/mol to get that we have 3 moles of methane. Next we use this number to see how many moles of O2 is needed to complete this reaction. In this reaction for every mole of methane, 2 moles of oxygen are used. This means that if we use 3 moles of methane, then 6 moles of oxygen are used. Finally, the last step is to convert the 6 moles of O2 to grams. To complete this conversion we must multiply the 6 moles of oxygen by the molar mass of O2 (16 g/mol) to receive a value in grams. Multiplying 6 x 16 gives us an answer of 96 grams. This means that for 48 grams of methane to be combusted, there must be 96 grams of oxygen.
A family has a history of a genetic disorder resulting in poor coagulation. In the family, the father and all of his daughters do not have the disorder. However, the mother and all of the sons are afflicted with the disorder. 1.)What is a possible mode of inheritance of the disorder and why? A) Autosomal Dominant B) Autosomal Recessive C) X-Linked Dominant D) X-Linked Recessive
This disorder must be (D) X-linked-recessive. This means that the gene for this disorder is located on the X chromosome. This also means that to display the disorder one must have two copies of the mutated gene (homozygous recessive) if they are female and 1 copy of the mutated gene (hemizygous recessive) if they are male. The answer to this question can be determined by noticing a couple of key details. Firstly, because the disorder seems to be sex-related, where all male offspring and no female offspring are afflicted, it would be highly unlikely for this disorder to be autosomal-linked (Non X-related). This sex-relatedness of X-linked inheritance comes from the fact that males receive only one X chromosome copy from their mother, where females receive a copy from their mother and father. Because males receive only one copy of the chromosome it makes the chances that they display X-linked disorders more common. Secondly, The disorder must also be recessive instead of dominant. This is because none of the female offspring are afflicted. In the case of a x-linked dominant scenario where the mother is afflicted, 50% of the female offspring would receive a copy of the mutated X and have the disorder if the mother is heterozygous. 100% of the female offspring would receive a copy of the mutated X and have the disorder if the mother is homozygous mutant. Being that the disorder is recessive, the afflicted mother must be homozygous recessive and 50% of the female offspring will receive one copy of the mutant gene. However, since it is recessive, none of the females will actually have the disorder phenotype since they only have one copy of the mutant gene.
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