Can someone check this out to see if I have this correct? If not can you help me out please? Thank you! The answers are on 2nd p
age.
1 answer:
Answer:
Answer 1; Angles forming a linear sum to 180°
Answer 2; Substitution
Answer 3; Definition of perpendicular lines
Step-by-step explanation:
The two column proof is presented as follows;
Statement Reason
1. ∠SWT ≅ ∠TWU Given
2. m∠SWT + m∠TWU = 180° Angles forming a linear sum to 180°
3. m∠SWT + m∠SWT = 180° Substitution
4. m∠SWT = 90° Algebra
5. ⊥
Definition of perpendicular lines
Perpendicular lines are defined as lines that are at right angles (90°) to each other, therefore given that the angle formed by the lines and
m∠SWT = 90°, therefore, the lines
and
are perpendicular to each other.
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Answer:
.0228
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem, we have that:
Find the probability that the average score of the 36 golfers exceeded 72.
This is 1 subtracted by the pvalue of Z when X = 72. So
By the Central Limit Theorem
has a pvalue of 0.9772
1 - 0.9772 = 0.0228
Answer:
Two solutions
Step-by-step explanation:
This is a quadratic equation in the form y = ax² + bx + c.
For quadratic equations, you can find solutions using the quadratic formula:
.
To find the number of solutions, <u>you only need what's inside the square root</u>. We call it the "<u>discriminant</u>" because lets us know the number of solutions without solving.
If b²- 4ac > 0, two solutions. (greater than)
If b²- 4ac < 0, no solutions. (less than)
If b²- 4ac = 0, one solution. (equal to)
y = ax² + bx + c
y = -3x² + x + 12
a = -3 b = 1 c = 12
<u>Substitute into the discriminant</u>
b²- 4ac
= 1² - 4(-3)(12)
= 1 - (-144)
= 145 > 0
b²- 4ac > 0 Discriminant greater than 0
Therefore, there are two solutions.