Making inferences: A man quickly walks up to a street corner and looks at his watch. He turns his head and catches a glimpse of the bus pulling away just down the block. He begins running down the street, frantically waving his hands in the air. What can we infer about this situation? A) The man is late for a lunch meeting. B) The man will take a taxi. C) The man missed the bus. D) The man is friends with the driver.
Making an inference means determining information that is not stated directly based on what is clearly written. Let's go through each answer choice to determine if we can infer that information. A) The man is late for a lunch meeting. We can infer that the man is late, but we do not know whether or not it is for a lunch meeting. There are not enough details to infer a lunch meetings as there is no indication of the time of day. B) The man will take a taxi. Although this is a possible result of the situation we read about, it is only one possibility. He may wait for the next bus. There is not enough information to determine for sure he will take a taxi. C) The man missed the bus. This is the correct choice. It is not directly stated but we can infer it because he looks at his watch when he gets to the street corner, he begins chasing the bus, and he frantically waves his arms. D) The man is friends with the driver. If the man waved at the driver while standing at the corner, that would be a good inference. However, the man waved his arms frantically while chasing the bus so we can not infer he is friends with the driver.
Pythagorean Theorem word problem: A bird is in a tree that is 10 meters high. It sees a seed on the ground, 5 meters from the base of the tree. The bird wants to fly the shortest distance, a straight line, to the seed. How far, to the nearest tenth, does the bird have to fly to get the seed?
To solve this, we can use the Pythagorean theorem, a^2 + b^2 = c^2 a is the base of the triangle, b is the height, and c is the hypotenuse. The height is where the bird is in the tree (10m), the base is the distance from the tree to the seed (5m). To find the shortest distance from the bird to the see, we need to find the hypotenuse. Let's make a model to visualize the problem: The bird in the tree and the seed on the ground form a right triangle. bird / / This height is 10 m. / / / seed____________ This width is 5 m. Now, fill the values of the base and height into the equation to find the length of the hypotenuse. a^2 + b^2 = c^2 5^2 + 10^2= c^2, solve for 5*5 and 10*10 25 + 100 = c^2 125 = c^2, find the square root of 125 c=11.1803398... Finally, round to the nearest tenth (the 8 in the hundredths place will make you round the 1 in the tenths place up to 2) C=11.2 meters The bird will have to fly 11.2 meters to get the seed.
Comparing slope-intercept equations from a word problem: Sally wants to take a taxi from the airport to her hotel. Yellow Cab charges $.75 per mile and a $2 flat fee. Blue Cab charges $.50 per mile and a $5 flat fee. Sally's hotel is 10 miles from the airport, which cab company should she take to get the cheapest fare?
First of all, you need to create an equation for each cab company. Let's start with Yellow Cab: 1) Make an equation with y representing the total fare on one side of the equals sign y= 2) Then identify the rate of change which is $.75 per mile because you know that will change depending on how many miles she will travel. This will be multiplied by x. 3) Next, identify the y intercept which is $2 because even if she travels 0 miles, she will still have to pay $2. 4) Add the rate of change times x plus the y intercept to the equation y=$.75x + $2 Now let's find the equation for Blue Cab: 1) Make an equation with y representing the total fare on one side of the equals sign y= 2) Then identify the rate of change which is $.50 per mile because you know that will change depending on how many miles she will travel. This will be multiplied by x. 3) Next, identify the y intercept which is $5 because even if she travels 0 miles, she will still have to pay $5. 4) Add the rate of change times x plus the y intercept to the equation y=$.50x + $5 Finally, let's solve both equations to see which has a cheaper fare (y) for 10 miles. Replace x with 10 in both equations: Yellow Cab y=$.75(10)+ $2 y=$7.5+$2 y=$9.5, so the fare for Yellow Cab would be $9.5 Blue Cab. y=$.50(10)+ $5 y=$5+$5 y=$10, so the fare for Blue Cab is $10 Yellow Cab has the cheaper fare, so Sally should take Yellow Cab.