Answer:
£500
Step-by-step explanation:
ratio of money = 3 : 1 = 3x : x ( x is a multiplier )
winner receives £250 more than the runner up, that is
3x = x + 250 ( subtract x from both sides )
2x = 250 ( divide both sides by 2 )
x = 125
total prize money = 3x + x = 4x = 4 × 125 = £500
Answer is C => 4(80+20)-12 => 4(100)-12 =>400-12 => 388
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y=cos(2x)
<span>dy/dx=-2sin(2x) </span>
<span>dy/dx at the point x=pi/4 is </span>
<span>dy/dx=-2sin(2*pi/4) </span>
<span>dy/dx=-2 sin(pi/2) </span>
<span>dy/dx=-2 </span>
<span>therefore the slope of the tangent is -2
</span>
using this slope find the equation of the line
<span>(y-y')=m(x-x') </span>
<span>(y-0)=-2(x-pi/4) </span>
<span>y=-2(x-pi/4)</span>
Answer:
D) In geometry, deductive rules can be used to prove conjectures.
Step-by-step explanation:
Geometry is the part of mathematics that deals with the relationships between lines, angles and surfaces. On the other hand, deductive rules refers to argument forms where true premises result in a conclusion that must be true and are called valid arguments. Deductive arguments that are not in a valid form are called invalid arguments. What is important here is that If I assume the premises are true, is it possible that the conclusion could be false? If the answer "yes" then the argument is invalid and valid if you answer "no".
So, we can use deductive rules to prove conjectures. A conjecture is a theory based on information that is not complete. Thus, we can use the question If I assume the premises are true, is it possible that the conclusion could be false? to get valid or invalid arguments.
Answer:
The probability that a randomly selected compact car gets at least 40 miles per gallon is about 1.74%
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation , the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
The probability that a randomly selected compact car gets at least 40 miles per gallon is about?
This is 1 subtracted by the pvalue of Z when X = 40. So
has a pvalue of 0.9826
1 - 0.9826 = 0.0174
The probability that a randomly selected compact car gets at least 40 miles per gallon is about 1.74%