Answer:
see the attachments for the two solutions
Step-by-step explanation:
When the given angle is opposite the shorter of the given sides, there will generally be two solutions. The exception is the case where the triangle is a right triangle (the ratio of the given sides is equal to the sine of the given angle). If the given angle is opposite the longer of the given sides, there is only one solution.
When a side and its opposite angle are given, as here, the law of sines can be used to solve the triangle(s). When the given angle is included between two given sides, the law of cosines can be used to solve the (one) triangle.
___
Here, the law of sines can be used to solve the triangle:
A = arcsin(a/c·sin(C)) = arcsin(25/24·sin(70°)) = 78.19° or 101.81°
B = 180° -70° -A = 31.81° or 8.19°
b = 24·sin(B)/sin(70°) = 13.46 or 3.64
3 blue + 3 yellow = 6 total marbles.
The probability of picking a blue one first would be 3/6 ( 3 blue out of 6 total marbles).
3/6 reduces to 1/2.
After picking the first marble, there would be 5 marbles left in the bag.
The probability of picking a yellow one would be 3/5 ( 3 yellow and 5 total marbles left).
The probability of picking a blue then a yellow then becomes:
1/2 x 3/5 = 3/10 = 0.30 = 30%
Answer:
300 divided by 6
Step-by-step explanation:
Given that;
Number of crates of apple owned by fruit seller = 3 crates
Number of apples in each crate = 100 apples
He packed 6 apples in 1 box;
Unknown:
Number of boxes needed to pack all the apples = ?
This problem is pretty straight forward;
Number boxes needed to pack all apples = 
Input the parameters and solve;
Number of boxes need to pack all apples = 
= 
So the solution is 300 divided by 6
Using the <u>normal distribution and the central limit theorem</u>, it is found that the interval that contains 99.44% of the sample means for male students is (3.4, 3.6).
In a normal distribution with mean 
and standard deviation 
, the z-score of a measure X is given by:
- It 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, which is the percentile of X.
- By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation
.
In this problem:
- The mean is of
.
- The standard deviation is of
.
- Sample of 100, hence
The interval that contains 95.44% of the sample means for male students is <u>between Z = -2 and Z = 2</u>, as the subtraction of their p-values is 0.9544, hence:
Z = -2:
By the Central Limit Theorem
Z = 2:
The interval that contains 99.44% of the sample means for male students is (3.4, 3.6).
You can learn more about the <u>normal distribution and the central limit theorem</u> at brainly.com/question/24663213
