Trigonometry
What is the side opposite to the 90-degree angle?
Hypotenuse
What is Experimental Probability? Describe what is taken into consideration and state the formula.
E.P = number of successful trials / total number of trials
When calculating experimental probabilities, the outcomes of an experiment or simulation are taken into consideration.
To solve, expand, and simplify binomials, there is a trick that can be used. The acronym is what is it? Tell me about it.
FOIL
First: Multiply the first term of each binomial.
Outer: Multiply the outer terms of each binomial.
Inside: Multiply the inner terms of each binomial.
Last: Multiply the last term of each binomial.
Describe the mean, the median, the mode, and the outlier when it comes to measures of central tendencies.
Mean is the sum of all the numbers. Figure out how many there are and divide by all of them. Median is the number that falls in the middle when all the numbers are lined up. To find the middle number, take the average of the two. Mode is the number that shows up most often. That's the number that comes up most often.
What are the three exponent rules? Explain them.
The product rule states that when multiplying an exponent with another, you maintain the same bases and add the exponent together. The quotient rule is the same idea, but instead of adding the multiplication, you would subtract if a division is present between the two. The final rule is the power rule, which multiplies the exponent by the outer power if the base and exponent are in brackets and raised to a power outside of them.
Describe the formulas to find sine/cosine/tangent.
SOHCAHTOA a/c b/c a/b
What is Theoretical Probability? Describe what is taken into consideration and state the formula.
T.P = number of successful outcomes / total number of possible outcomes
Theoretical probability is an additional method of determining the likelihood of an event occurring. It is the proportion of the total number of outcomes that were successful to the total number of outcomes that may have occurred.
Expand and simplify this binomial expression. (2x + 3)(x + 4)
Using FOIL:
First: 2π₯ Γ π₯ = 2π₯Β²
Outer: 2π₯ Γ 4 = 8π₯
Inner: 3 Γ π₯ = 3π₯
Last: 3 Γ 4 = 12
Now, combine these results: ( 2π₯ + 3 )( π₯ + 4 ) = 2π₯Β² +8π₯ +3π₯ +12
Finally, combine like terms: 2π₯Β² + 11π₯ + 12
How can one identify between primary and secondary sources when it comes to the process of data collection and analysis?
Primary sources are first-hand accounts of things that people have gathered or made, while secondary sources are other people's interpretations of primary sources.
Simplify the following: 19Β³ x 19βΆβΆ
19^3+66 = 19βΆβΉ
What triangles can SOHCAHTOA only be used on?
Right triangles
What is the experimental likelihood of first-throw 27 while rolling an 8-sided die with the numbers 5, 6, 3, 12, 19, 2, 30, and 27 displayed?
β or 0.125 or 12.5%
Expand and simplify this binomial expression. (5x + 7)(x + 8)
Using FOIL:
First: 5π₯ Γ π₯ = 5π₯Β²
Outer: 5π₯ Γ 8 = 40π₯
Inner: 7 Γ π₯ = 7π₯
Last: 7 Γ 8 = 56
Now, combine these results: (5π₯+7)(π₯ +8) = 5π₯Β² +40π₯ +7π₯ +56
Finally, combine like terms: 5π₯Β² + 47π₯ + 56
In many households, it is not uncommon to have no siblings or only one sibling, whereas having a large number of siblings is considered to be a rather rare occurrence. What type of distribution would emerge if we plotted this data on a histogram?
Right-Skewed Distribution
Simplify the following:
[ (4+5^2)Γ(12β3Γ2)+345β(8Γ·2) ]β°
1
What are the formulas used for Sine Law? Which do we use to find the side and angle of a triangle?
a/sineA = b/sineB = c/sineC
*looking for a side*
sineA/a = sineB/b = sineC/c
*looking for an angle*
If there are twelve small balls in a bag, eight of them are red, three are blue, and one is green, then what is the experimental probability of picking a red ball?
To find the experimental probability of picking a red ball from the bag, you divide the number of red balls by the total number of balls. Total number of balls = 12 Number of red balls = 8
So, the experimental probability of picking a red ball is: 8/12 - β - 66.7%
Factor trinomial of the form y = π₯Β² + bπ₯ + c. Factor the following: π₯Β² + 14π₯ + 48
6+8 = 14, 6x8 = 48. βΆ ( π₯ + 6 )( π₯ + 8 )
Determine the mode and median of the following set of numbers: 1,5, 23, 31, 43, 44, 56, 57, 71, and 92.
Median = (43+44) / 2 = 87/2 = 43.5
Mean = 1+5+23+31+43+44+56+57+71+92 / 10 = 423/10 = 42.3
Mode - None
Simplify the following:
( 3^-5 / 3^-8 )
3^-5-(-8) = 3^3 = 27
If the angle of elevation from a point on the ground to the top of a tree is 30 degrees, and the distance from the point to the base of the tree is 50 meters, how tall is the tree?
25 meters Using the tangent function, which relates the opposite side to the adjacent side,
tan(30) = x/a = height of the tree/50. Solving for the height gives 25 meters.
In a standard deck of playing cards, what is the theoretical likelihood of not obtaining a jack or an ace?
To find the theoretical likelihood of not obtaining a jack or an ace from a standard deck of playing cards, we first need to determine how many jacks and aces are in a deck. 52 - 4 - 4 = 44 44/52 - 11/13 - 84.6%
Quadratic relation where a=3, and the vertex is at (1,9), write the equation in standard form y=a(π₯-h)Β²+k.
H = 1, K = 9
Y = 3(π₯-1)Β² + 9
Y = 3(π₯Β²-2π₯+1)+9
Y = 3π₯Β²-6π₯+3+9
Y = 3π₯Β²-6π₯+12
What is a box-and-whisker plot? What does it display?
Data set median (second quartile): The line inside the box reflects the median (middle) value. It splits the data into 50% below and 50% above. The plot's box depicts the interquartile range (IQR), the middle 50% of the data. The box's lower and higher boundaries reflect the first and third quartiles. IQR = Q3 - Q1. Whiskers: The box's whisker lines show the data range. They usually include the smallest and largest data values within a given distance from the quartiles. Distance is usually 1.5 times IQR. Outliers beyond the whiskers are plotted separately. Outliers: Data points outside the whiskers are plotted separately. Their values are unusually high or low for the data set.
What are the first 3 answers in the table of values in the following:
y=4^π₯, π₯ = -3, -2, -1
4^-3 = 1/64, 4^-2 = 1/16, 4^-1 = ΒΌ