Determine the value of x such that \dfrac{8^{29}-8^{28}}{7} = 2^x
.
A. 29
B. 84
C. 58
D. 56
The sum of 300 - 299 + 298 - 297 + 296 - 295 + ... - 3 + 2 - 1 is
A. 149
B. 151
C. 300
D. 150
Determine the values of three positive integers x, y, and z given that x + \dfrac{1}{y + \dfrac{1}{z} = \dfrac{38}{11}}
.
If the fraction \dfrac{5}{13}
is written in expanded decimal form, what is the 153rd digit after the decimal point?
A. 4
B. 6
C. 8
D. 1
Three consecutive integers less than 20 have a sum of 27 and a product of 720. What are the numbers?
If f(x) = \dfrac{1}{x^2 - 4}
and g(x) = \dfrac{2x}{x - 2}
, determine the value of x such that (f + g)(x) = 2
.
A. -2
B. -\dfrac{5}{2}
C. -\dfrac{9}{4}
D. \dfrac{7}{4}
How many different-sized squares can be made on a 5-by-5 geoboard?
A. 43
B. 10
C. 6
D. 8
A sequence of numbers has the terms 0.3, 0.33. 0.333, 0.3333, ... What value does the sequence approach?
A. 0.34
B. 0.4
C. \dfrac{1}{3}
D. 1
A sequence of numbers has the terms \sqrt 2, \sqrt {2 \sqrt 2}, \sqrt {2 \sqrt {2 \sqrt 2}}, \sqrt {2 \sqrt {2 \sqrt {2 \sqrt 2}}}
What is the limit of the value of the terms in the sequence?
A.2
B. 1.5
C. 3
D. 1.4
When a number is divided by 18, the remainder is 13. What is the remainder When the number is divided by 6?
A. 2
B. 1
C. 3
D. 5
The period of y = |5 sin (4x - 120^{\circ})|
is
A. 45^{\circ}
B. 90^{\circ}
C. 120^{\circ}
D. 360^{\circ}
If the number 6912 can be written in the form 2^x3^y4^z
, then the value is x^2 + y^2 + z^2
is
A. 9
B. 14
C. 33
D. 29
If y = \sqrt[3] x
, what is the value of x^{21} + 3 \sqrt 2 - y^{63}
?
If n \choose r
= \dfrac{n!}{r!(n-r)!}
where n! = n \times (n-1) \times (n-2) \times ... 3 \times 2 \times 1
determine the value of \dfrac{100 \choose 98}{2}
.
A. 4950
B. 2475
C. 9900
D. 10 540