Answer: 259/260 or 0.99615 (depending on which answer format your teacher wants)
There are 10 numbers in the set {0, 1, 2, ..., 9}. There are 26 letters in the set {A, B, C, ..., Z}. Multiply those values: 10*26 = 260. So there are 260 ways to pick a number followed by a letter. One example is 7P.
There is only one way Matthew can get the correct answer, and there are 260 - 1 = 259 ways to get the wrong answer. We divide 259 over 260 to get the probability of getting the incorrect answer, which is 259/260.
If you need this fraction in decimal form, then use a calculator to find that 259/260 = 0.99615 approximately
1. The additive identity is 0. This is because adding 0 to anything leads to the same value. Example: 0+3 = 3.
2. An equation is where you have two expressions separated by an equal sign. In your case it would be "a mathematical sentence whose verb is 'equal' (=)"
3. The multiplicative identity is 1. Multiply 1 with any number and the result is that same number. Example: 1*7 = 7.
4. An open sentence is an equation that contains one or more variables. An example would be x+2 = 4. The reason why we call it open is because the true or false nature of the sentence is up in the air until we know what x is. If we knew that x = 3 for instance, then x+2 = 4 would be false since 3+2 = 4 is false. If we nailed down what x was then it would go from open to closed.
5. The symmetric property is that if a = b then b = a. Think of a mirror how the image reverses.
Answer:
The answer is 5525710
Step-by-step explanation:
Answer:
-2, 8/3
Step-by-step explanation:
You can consider the area to be that of a trapezoid with parallel bases f(a) and f(4), and width (4-a). The area of that trapezoid is ...
A = (1/2)(f(a) +f(4))(4 -a)
= (1/2)((3a -1) +(3·4 -1))(4 -a)
= (1/2)(3a +10)(4 -a)
We want this area to be 12, so we can substitute that value for A and solve for "a".
12 = (1/2)(3a +10)(4 -a)
24 = (3a +10)(4 -a) = -3a² +2a +40
3a² -2a -16 = 0 . . . . . . subtract the right side
(3a -8)(a +2) = 0 . . . . . factor
Values of "a" that make these factors zero are ...
a = 8/3, a = -2
The values of "a" that make the area under the curve equal to 12 are -2 and 8/3.
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<em>Alternate solution</em>
The attachment shows a solution using the numerical integration function of a graphing calculator. The area under the curve of function f(x) on the interval [a, 4] is the integral of f(x) on that interval. Perhaps confusingly, we have called that area f(a). As we have seen above, the area is a quadratic function of "a". I find it convenient to use a calculator's functions to solve problems like this where possible.
