<span>Given that Kate
is constructing an equilateral triangle and she has already used her
straightedge to construct a line segment AB.
What Kate should do for her next step is "</span><span>Place the point of the compass on point A and draw an arc, using AB as the width for the opening of the compass".</span>
Answer:
Hope it helps....!!!!!
Step-by-step explanation:
AB = c = 38
BC = a = 29
AC = b
Angle ABC = 63 degrees
Solving for AC "b":
Cosine rule: c^2 = a^2 * b^2 -2ab * cos C
38^2 = 29^2 * b^2 - (2* 29) * b * (cos 38)
1444 = 841 * b^2 - 58 * b * 0.955
(1444 + 58)/0.955 = b^2 * b
1572.77486911 = b^3
11.62935 = b
11.63 = b (rounded to two decimal places)
Now solving for angle A:
Sine rule: a/sinA = b/sinB
29/sinA = 11.63/sin(63)
sinA/29 = sin(63)/11.63
sin A = (sin(63)/11.63) * 29
sin A = 0.41731
A = sin^-1 (0.41731)
A = 24 degrees 39 minutes 53 seconds
Now solving for angle C:
Sine rule: c/sinC = b/sinB
38/sinC = 11.63/sin(63)
sinC/38 = sin(63)/11.63
sin C = (sin(63)/11.63) * 38
sin C = 0.54682
C = sin^-1 (0.54682)
C = 33 degrees 8 minutes 56 seconds
X = 56% * 48
x = 56/100 * 48
x = 28/50 * 48
x = 14/25 * 48
x = 672/25
x = 26.88
<span>56% of 48 is </span>26.88<span>.</span>
Answer:
Step-by-step explanation:
1) Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Let X the random variable that represent the scores, and for this case we know the distribution for X is given by:
And let represent the sample mean, the distribution for the sample mean is given by:
On this case
2) Calculate the probability
We want this probability:
The best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
Answer: -19x
Step-by-step explanation: In this problem, we're asked to simplify the expression.
The two parts of this expression, -8x and 11x are called terms. The numbers in front of the variables are called coefficients.
Because the variables, x and x are identical, the terms get a special name and they're called like terms.
To subtract like terms, we simply subtract their coefficients and add the variable on to the difference of the two numbers.
Since -8 (-11) is -19, -8x - 11x simplifies to -19x.