Multiply. - 4.3 x - 3.2 =
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-4.3 x -3.2 = 13.76
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If x > y and y > z, then x > z. This describes which ordinal scale preference? A. Asymmetry B. Transitivity C. Negative transitivity D. None of the above
If grade point average rises as number of hours watching tv falls, the correlation between GPA and TV is
Joe's taxable income is $67,825. Use this tax schedule to calculate the total amount he owes in taxes.1. $8,993.752. $13,380.003. $12,348.80
Compute the odds in favor of rolling a sum of 10 in a single roll of two fair dice
−14.4
−5.625
5.625
14.4
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Answer:
Step-by-step explanation:
First thing, let's call f(x) "y". So y varies directly with x^2 looks like this:
y = kx^2
k is our constant of variation. We need to solve for k before we can find what we are asked to find.
Filling in:
10 = k(-4)^2 and
10 = 16 k so
k = 5/8 (reduced)
Now we will use that value of k along with the given of x = 3 to find y:
y = (5/8)(3)^2 and
y = (5/8)(9)
y = 45/8 which simplifies to
y = 5.625
Final answer:
The function f(x) varies directly with x2. First, find the constant of variation, then use this constant to find the value of the function at the desired x value. The value of f(x) when x = 3 is 5.625.
Explanation:
The phrase 'f(x) varies directly with x2' implies that there is a linear relationship between f(x) and x2. That is to say, the formula will be something like f(x) = kx2 where k is the constant of variation. We can solve for k using the given condition f(x) = 10 when x = -4. By substituting these values into the equation, we get 10 = k(-4)2, which simplifies to 10 = 16k. Solving for k, we find k = 10 / 16 = 0.625.
To find the value of f(x) when x = 3, we substitute x = 3 into the formula f(x) = 0.625x2, which results in f(3) = 0.625 * 9 = 5.625.
Learn more about Direct Variation here:
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B. 3p + 11
C. –3p + 11
D. 3p + 7
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=
=
=
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So, I guess
Choice: C
Answer:
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x=32a+30=58b+44 where a and b are the quotients you get on dividing x by 32 and 58.
Simplifying this equation you get 16a+15=29b+22
16a= (16+13)b+22-15 or 16a=16b+13b+7
16(a-b)=13b+7
Now I have to find a value for b where 13b+7 is divisible by 16. The least common multiple of these numbers can be found bygoing through the multiplication tables of 13 and 16 and 13x13+7=176,while 16x11 is also 176.
Now that the value of b is found to be 13, we can substitute it in our first equation, x=58b+44=58x13+44=798.
Now find the least common multiple of 58 and 32
LCM (n,m)=nm/GCD (n,m) where GCD is the greatest common divisor of n and m
LCM (58, 32)=58x32/2 as 2 is the GCD of 58 and 32
LCM (58, 32)= 1856/2= 928
Add this LCM to the previous answer, ie, 798 to get the next answer in the series. 798+928=1726
Add the LCM again to the last answer to get the final answer, that is less than 3000=1726+928=2654
Final answer:
The query is a mathematical problem about diophantine equations and the Chinese Remainder Theorem. By setting up the equations 32n + 30 and 58m + 44, we search for a number that fits both conditions and is less than 3000. That number is 1978.
Explanation:
The problem described is a common type of question in number theory, specifically in the field of diophantine equations. In mathematics, a diophantine equation is a polynomial equation where the solutions are sought in integers. This problem consists in finding a common remainder when dividing by different numbers, which is the essence of the Chinese Remainder Theorem.
We can set up the equations as follows: the number can be written as 32n + 30 (this gives a remainder of 30 when divided by 32) and as 58m + 44 for some integers n and m (this gives a remainder of 44 when divided by 58). Now, we check for possible solutions less than 3000 by trying out different values of 'n' and 'm'.
After checking several possibilities one by one, the smallest positive number that satisfies both equations is 1978.
Learn more about Diophantine Equations here:
#SPJ11
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Answer:
30%
Step-by-step explanation:
Answer:
65%
Step-by-step explanation:
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Answer: The 60th term of the arithmetic sequence -29, -49, -69, … is -1209.
Step-by-step explanation:
The given arithmetic sequence is -29, -49, -69, …
To find the 60th term of this sequence, we need to use the formula for the nth term of an arithmetic sequence:
a_n = a_1 + (n - 1)d
where a_n is the nth term of the sequence, a_1 is the first term of the sequence, n is the number of terms in the sequence, and d is the common difference between consecutive terms.
In this case, a_1 = -29 and d = -20 (since each term is 20 less than the previous term). We want to find a_60, so we substitute n = 60 into the formula:
a_60 = -29 + (60 - 1)(-20) = -29 + 59(-20) = -29 - 1180 = -1209
Therefore, the 60th term of the arithmetic sequence -29, -49, -69, … is -1209.
Please let me know if you have any other questions!