Answer:
66.42° between height and hypotenuse
23.58° between base and hypotenuse
Step-by-step explanation:
Using the concept of cosine and sine, we know that cosine of an angle is equal to the adjacent divided by hypotenuse.
Similarly, sine of an angle is given by opposite divided by hypotenuse
Tangent is given by opposite divided by adjacent
In rhis case, we use cosine
Therefore, the angle between the hypotenuse and height is 66.42°
To find the angle between base and hypotenuse, since it is a right angle triangle then the other angle will be 90-66.42=23.58°
x is case of almonds and y is case of walnuts.
Almonds are packaged 15 bags per case and walnuts are packaged 17 bags per case.
H-E-B orders no more than 200 bags of almonds and walnuts at a time.
So,
x + y < 200
where x and y refers to the number of bags
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H-E-B pays $24 per case of almonds and $27 per case of walnuts, but will not order more than $300 total at any one time.
But keep in mind that : Almonds are packaged 15 bags per case and walnuts are packaged 17 bags per case.
So,
24 * (x/15) + 27 * (y/17) < 300
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The constraints are:
x + y < 200
(24/15) x + (27/17) y < 300
So, the graph of the previous constraints is as following :
Answer:
54.80 MPa to 55.92 MPa
Step-by-step explanation:
Sample mean fracture strength (x) = 55.36 MPa
Sample standard deviation (s) = 3.99 MPa
Sample size (n) = 196.
The upper and lower bounds for a 95% confidence interval are given by:
The upper and lower bounds of the confidence interval are;
The 95% confidence interval for true average fracture strength is 54.80 MPa to 55.92 MPa
Answer: See explanation
Step-by-step explanation:
We will use the formula for an arithmetic sequence which will be:
a + (n - 1)d
where a = unknown
n = 6
d = 4
We then slot them into the formula
a + (6 - 1)4 = 12
a + 5(4) = 12
a + 20 = 12
a = 12 - 20
a = -8
The 6 numbers are
1st term = -8
2nd term = -8 + 4 = -4
3rd term = -4 + 4 = 0
4th term = 0 + 4 = 4
5th term = 4 + 4 = 8
6th term = 8 + 4 = 12
I assume by starting value, you mean y-intercept. The y-intercept is 15
To find this, we need to use slope intercept form and the given information to find it.
y = mx + b ----> plug in the known values
9 = -3/4(8) + b
9 = -6 + b
15 = b
Therefore, the starting value is 15.
