Alright, so we know that the race is 5 kilometers, so the equation will be 5-<some value>= <distance from finish line>. We also know that the student runs a kilometer every three minutes, so 3x=1km . Multiplying both sides by 5, we get 15y=5km (y being the number to make the equation make sense, or the slope). When the student has run 5km, the distance from the student to the finish line should be 0, so we get that 5-5=0, and plugging 15y in for 5 we get 5-15y=0. For 15x to equal 5, 3y=1 and y=1/3. Therefore, we plug that in for y, getting 5-15(1/3)=0. However, we have to make it for all times! Since 15 represents the minutes, we make that x, and since 0 represents the distance remaining, we make that the distance remaining, making it 5-(1/3)x=distance left. You can also think of y as the slope in y=mx+b - it stays constant that way.
Answer:
Step-by-step explanation:
7x - 1 + 6x - 1 = 180
13x - 2 = 180
13x = 182
x = 14
7(14) - 1 = 98 - 1= 97
6(14) - 1 = 84 - 1 = 83
<h3>Answer: Choice B) 8.57</h3>
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Explanation:
The triangles are similar through the AA (angle angle) similarity rule. Note how the angle markers correspond and match up. Example: angle C and angle F both have triple angle markers to indicate these angles are congruent.
The corresponding sides pair up to form equal fractions. AB and DE form AB/DE which is equal to AC/DF, as these two sides correspond as well.
Therefore: AB/DE = AC/DF
Let's plug in the given values and isolate x
AB/DE = AC/DF
11/7 = (15+x)/15 ...... substitution
11*15 = 7*(15+x) ....... cross multiply
11*15 = 7*15+7*x ...... distribute
165 = 105+7x
165-105 = 105+7x-105 ..... subtract 105 from both sides
60 = 7x
7x = 60
7x/7 = 60/7 ............ divide both sides by 7
x = 8.57142857142858
x = 8.57 ..... rounding to the nearest hundredth
Answer:
<u>B. There is sufficient evidence that the mean of the pressure required to open a certain valve has changed. </u>
Step-by-step explanation:
We make this conclusion based on these reasons:
- We are told that the "null hypothesis was rejected" after the <em>"manager feels that the pressure variability has changed.,</em> meaning the <u>null hypothesis was the opposite of what occurred; that is to say, it is the alternate hypothesis that proved true instead.</u>
- <em>"changes in the manufacturing process"</em> form what can be called "sufficient evidence" that the mean of the pressure required to open the valve has changed, thereby going against the null hypothesis.
It is based on the above reasons that the null hypothesis was rejected.
