2x ≡ 6(mod 4)

Determine the lowest common multiple (LCM) of the following 4𝑥2𝑦2 , 6𝑥𝑦 , 10𝑥𝑦2 
 

Find all zero divisors of z_81

A nonhomogeneous second-order linear equation and a complementary function $y_c$ are given. Find a particular solution of the equation.
${\displaystyle 4x^{2}y{ }^{″}-4x{y}^{\prime }+3y=8x^{\frac{3}{4}}}$

A simple random sample of pulse rates of 25 women from a normally distributed population results in a standard deviation of 12.7 beats per minute. The normal range of pulse rates of adults is typically given as 60 to 100 beats per minute. If the range rule of thumb is applied to that normal range, the result is a standard deviation of 10 beats per minute. Use the sample results with a 0.10 significance level to test the claim that pullse rates of women have a standard deviation equal to 10 beats per minute. Complete parts (a) through (d) below.
a. Identify the null and alternative hypotheses. Choose the correct answer below.
A. ${\displaystyle H_0:\sigma \ne 10}$ beats per minute, ${\displaystyle H_1:\sigma =10}$ beats per minute
B. ${\displaystyle H_0:\sigma =10}$ beats per minute, ${\displaystyle H_1:\sigma \ne 10}$ beats per minuteSNKC. ${\displaystyle H_0:\sigma =10}$ beats per minute, ${\displaystyle H_1:\sigma <10}$ beats per minute
D. ${\displaystyle H_0:\sigma \ge 10}$ beats per minute, ${\displaystyle H_1:\sigma <10}$ beats per minute
b. Compute the test statistic.
${\chi }^2=\square$
(Round to three decimal places as needed.)
c. Find the P-value of the test statistic.
The P-value of the test statistic is $\square$
(Round to three decimal places as needed.)
d. State the conclusion.
'Reject'/'Fail to reject' ${\displaystyle H_0}$ 'is'/'is not' sufficiert evidence to warrant rejection of the claim that pulse rates of women have a standard deviation equal to 10 beats per minute.

Show that $\sqrt[3]{\pi }$ is transcendental

In a family of 6, what is the probability of getting 1 boy and 5 girls