Answer:
sin 5x cos x - cos 5x sin x = sin(4x)
Step-by-step explanation:
Given that the trigonometric expression,
sin 5x cos x - cos 5x sin x
Here we use the "sum and difference formulas"
Sum and Difference Formulas
sin(A+B)=sin A cos B + cos A sin B
sin(A-B)=sin A cos B - cos A sin B
cos(A+B)=cos A cos B - sin A sin B
cos(A-B)=cos A cos B + sin A sin B
So,
sin 5x cos x - cos 5x sin x = sin (5x - x)
sin 5x cos x - cos 5x sin x = sin(4x)
That's the final answer.
Answer:
Step-by-step explanation:
Given
Jar contains 4 white and 4 black marbles
We randomly select 4 marbles out of which 2 are white and 2 are black
Probability that 2 white and 2 black marbles are selected is


The process is continue for n trails until we choose the correct order
i.e. we have to fail in n-1 trails
For exact n selection Probability is given by


Answer:
92.9997<
<99.5203
Step-by-step explanation:
Using the formula for calculating the confidence interval expressed as:
CI = xbar ± Z * S/√n where;
xbar is the sample mean
Z is the z-score at 90% confidence interval
S is the sample standard deviation
n is the sample size
Given parameters
xbar = 96.52
Z at 90% CI = 1.645
S = 10.70.
n = 25
Required
90% confidence interval for the population mean using the sample data.
Substituting the given parameters into the formula, we will have;
CI = 96.52 ± (1.645 * 10.70/√25)
CI = 96.52 ± (1.645 * 10.70/5)
CI = 96.52 ± (1.645 * 2.14)
CI = 96.52 ± (3.5203)
CI = (96.52-3.5203, 96.52+3.5203)
CI = (92.9997, 99.5203)
<em>Hence a 90% confidence interval for the population mean using this sample data is 92.9997<</em>
<em><99.5203</em>
Answer:
231 cubed centimeters
Step-by-step explanation:
Find the area of the base of the pyramid
18 x 7=126 divided by 2= 63 cm
Next, make sure to the remember the formula is 
1/3(63)(11)=
21(11)=231
231 cubed centimeters is the answer.
1. archaic
2. evangelists
3. Norman’s
4. John Wycliffe
5. Vulgar