Suppose$U=\{(x,y,x+y,x-y,2x)\in {F}^{5},x,y\in F\}$ . Find a subspace $W$of ${F}^{5}$ such that ${F}^{5}=U\oplus W$.

2022-05-05

Suppose$U=\{(x,y,x+y,x-y,2x)\in {F}^{5},x,y\in F\}$ . Find a subspace $W$of ${F}^{5}$ such that ${F}^{5}=U\oplus W$.

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asked 2020-12-30

A majorette in a parade is performing some acrobatic twirlingsof her baton. Assume that the baton is a uniform rod of mass 0.120 kg and length 80.0 cm.

With a skillful move, the majorette changes the rotation ofher baton so that now it is spinning about an axis passing throughits end at the same angular velocity 3.00 rad/s as before. What is the new angularmomentum of the rod?

asked 2021-12-07

Find derivatives of the functions defined as follows: $y=-4{e}^{-0.3x}$

asked 2022-06-13

A teacher wants to know if more than 15% of her students use online resources to complete their homework assignments instead of doing the homework independently. The teacher would like to carry out a test at the 0.05 significance level of

${H}_{0}:p=0.40$

${H}_{a}:p>0.40$

where p = the true proportion of students that use online resources to complete their homework assignments. One day after school, the teacher asked the 40 students studying in her classroom if they used online resources to complete their homework assignments or if they did their homework independently. Are the conditions to perform the significance test met?

No, the students do not represent a random sample and the Large Counts condition is not satisfied.

No, the students do not represent a random sample even though the Large Counts condition is satisfied.

No, the students represent a random sample, but the Large Counts condition is not satisfied.

Yes, the students represent a random sample and satisfy the Large Counts condition.

${H}_{0}:p=0.40$

${H}_{a}:p>0.40$

where p = the true proportion of students that use online resources to complete their homework assignments. One day after school, the teacher asked the 40 students studying in her classroom if they used online resources to complete their homework assignments or if they did their homework independently. Are the conditions to perform the significance test met?

No, the students do not represent a random sample and the Large Counts condition is not satisfied.

No, the students do not represent a random sample even though the Large Counts condition is satisfied.

No, the students represent a random sample, but the Large Counts condition is not satisfied.

Yes, the students represent a random sample and satisfy the Large Counts condition.

asked 2022-07-18

Discrete Math (Logical Question)

How many arrangements of the letters in MISSISSIPPI have no consecutive S's?

Solution:

$(}\genfrac{}{}{0ex}{}{8}{4}{\textstyle )$ $\cdot (7!/4!\cdot 2!)$

How many arrangements of the letters in MISSISSIPPI have no consecutive S's?

Solution:

$(}\genfrac{}{}{0ex}{}{8}{4}{\textstyle )$ $\cdot (7!/4!\cdot 2!)$

asked 2021-09-03

Find the Laplace transform of $\mathrm{sin}ht-\mathrm{cos}ht$

asked 2021-08-06

Mass Analysis of Two Chlorine-Fluorine Samples
SampleMass of Chlorine (g)Mass of Fluorine (g)% Cl% F I13.0226.97865.1134.89 II5.7539.248??

Which statement best describes the relationship between the two samples?

A. The compound in Sample I is the same as in Sample II. Therefore, the mass ratio of Cl to F in both samples will obey the law of definite proportions.

B. The compound in Sample I is the same as in Sample II. Therefore, the mass ratio of Cl to F in both samples will obey the law of multiple proportions.

C. The compound in Sample I is not the same as in Sample II. Therefore, the mass ratio of Cl to F in both samples will obey the law of definite proportions.

D. The compound in Sample I is not the same as in Sample II. Therefore, the mass ratio of Cl to F in both samples will obey the law of multiple proportions.

Which statement best describes the relationship between the two samples?

A. The compound in Sample I is the same as in Sample II. Therefore, the mass ratio of Cl to F in both samples will obey the law of definite proportions.

B. The compound in Sample I is the same as in Sample II. Therefore, the mass ratio of Cl to F in both samples will obey the law of multiple proportions.

C. The compound in Sample I is not the same as in Sample II. Therefore, the mass ratio of Cl to F in both samples will obey the law of definite proportions.

D. The compound in Sample I is not the same as in Sample II. Therefore, the mass ratio of Cl to F in both samples will obey the law of multiple proportions.

asked 2021-03-23

A 45-g piece of ice at 0 degree C is added to a sample of water at 8 degrees C. All of the ice melts and the temperature of the water decreases to 0 degree C. How many grams of water were there in the sample?