geometry
algebra
statistics
surprise!
100
How do you find the measure of an interior angle in a normal polygon?
What is "subtract 2 from the total number of sides and multiply by 180"
100
The average number of students per classroom, y, at Central High School can be estimated using the equation y = 0.8636x + 27.227, where x represents the number of years since 2004. interpret the number 0.8636 in the context of the problem.
The estimated yearly increase in the average number of students per classroom
100
what is "b"
100
does the point (0, 0) satisfy the inequality x-3y>9?
what is "no"
200
prove that tanx=sinx/cosx
(o/h)(h/a)
the Hs cancel out...
o/a=tanx
200
A company’s manager estimated that the cost C, in dollars, of producing n items is C = 7n + 350. The company sells each item for $12. The company makes a profit when the total income from selling a quantity of items is greater than the total cost of producing that quantity of items. what inequality gives all possible values of n for which the manager estimates that the company will make a profit?
n > 70
200
A quality control researcher at an electronics company is testing the life of the company’s batteries in a certain camera. The researcher selects 100 batteries at random from the daily output of the batteries and finds that the life of the batteries has a mean of 342 pictures with an associated margin of error of 18 pictures. Which of the following is the most appropriate conclusion based on these data?
A) All the batteries produced by the company that day have a life between 324 and 360 pictures
B) All the batteries ever produced by the company have a life between 324 and 360 pictures.
C) It is plausible that the mean life of batteries produced by the company that day is between 324 and 360 pictures.
D) It is plausible that the mean life of all the batteries ever produced by the company is between 324 and 360 pictures.
what is "C"
200
in trapezoid ABCD, AB is parallel to CD, angle A=150, and angle B=80. find measures of angles C and D
C=100, D=30
300
prove that the angle bisectors of a triangle are concurrent. Given segment DB bisects angle ABC, and segment EC bisects angle ACB.
since F is on the bisector of angle ABC, it's equidistant from AB and BC. since it's also on the angle bisector of angle ACB, it's also equidistant from AC and BC. Therefore, I is equidistant from all three sides of the triangle.
300
Solve the equation 2^(16x)=16^(2x)
x=2/3
300
in the design of a survey, whihc of the following best explains how to minimize response bias?
A. increase sample size
B. decrease sample size
C. randomly select the sample
D. increase the number of questions in the survey
E. Carefully word and field-test survey questions
What is "E"
300
for what values of x does the product of
(x-1)(x+2)(x-5) equal 0?
what is 1, -2, 5
400
the angle bisectors of triangle ABC are perpendicular segments from G to the sides of the triangle. why is GE=GD=GF?
since G is th equidistant from the sides of triangle ABC, then GE=GD=GF
400
what is the uppermost point on the graph of
y=-x^2+5x-7?
we would complete the square to find that
y=-(x-5/2)^2-3/4
which means that the highest point of the graph is the vertex (5/2, -3/4)
which means that the maximum value that the quadratic can attain is -3/4
400
on average throughout each day, how many more contestants got less than a 3 out of 5 than at least 3 out of 5?
what is "0.67"
400
A cube is a solid figure with six faces. Each face is a square. The surface area of a cube is the total area of all the faces of the cube. When the side length of a certain cube is increased by 4, the surface area increases by 576. What is the volume of the original cube?
what is 1000?
6(x+4)^2-6x^2=576
500
in triangle ABC, AB, BC, and AC are tangent to the circle with center r. given that angle BAC=70 and BCA=50. what is the measurement of angles RCA and ARC
because the circle is tangent to all three sides of triangle ABC, it's the incircle of triangle ABC. therefore, r is the incenter of triangle ABC, and rC and RA are angle bisectors of angles BAC and BCA, respectively.
500
if f(x)=ax^4-bx^2+x+5 and f(-3)=2, then what is f(3)?
what is 8
Because f(-3)=2, we have 81a-9b-3+5=2, so 81a-9b=0. we also have f(3)=81a-9b+3+5=81a-9b+8. we already found that 81a-9b=0, so f(3)=81a-9b+8=8
500
the weight of an adult male grizzly bear in the US s approximately normally distributed with mean 500lb and standard deviation of 50lb. the weight of an average female grizzly bear in the US is also approximately distributed with mean 300lb and s.d. of 40lb. what would be the weight of a female grizzly bear with the same standardized score (z-score) as a male grizzly bear weighing 530 lb?
what is "324lb"
500
prove heron's formula
y=a-x
apply the pythagorean theroem to triangles ABX and ACX, then subtract the second equation from thefirst to find x.
x^2+h^2=c^2
h^2=c^2-x^2
apply expression from earlier into the h^2 equation. solve.
s is the semiperimeter, 2s=a+b+c.