Find a vector v that is perpendicular to the plane through the points

A=(5,−4,4), B=(−5,0,−3), and C=(−4,2,−5).
v =

Complete Question

According to a study done by a university student, the probability a randomly selected individual will not cover his or her mouth when sneezing is 0.267 Suppose you sit on a bench in a mall and observe people's habits as they sneeze

(a) What is the probability that among 18 randomly observed individuals exactly 6 do not cover their mouth when sneezing?

Answer:

[tex]P(X=6)=(0.162)[/tex]

Step-by-step explanation:

From the question we are told that:

Sample size [tex]n=18[/tex]

Probability [tex]P=0.267[/tex]

No. that do not cover their mouth when sneezing [tex]x=6[/tex]

Generally the equation for The Binomial distribution is mathematically given by

Parameters

B(18,0.267)

Therefore

[tex]P(X=x)=(18..x)(0.267)^x(1-0.267)^{18-x}[/tex]

Where

[tex]x=6[/tex]

Therefore

[tex]P(X=6)=(18..6)(0.267)^6(1-0.267)^{18-6}[/tex]

[tex]P(X=6)=(0.162)[/tex]

Let x be the number of one-striped fish and y the number of two-striped fish.

100 families each have 2 fish, so there are a total of 200 fish:

x + y = 200

x one-striped fish carry a total of x stripes, while y two-striped fish carry a total of 2y stripes. There are 273 stripes overall, so

x + 2y = 273

Solve for x and y. Subtracting the first equation from the second eliminates x :

(x + 2y) - (x + y) = 273 - 200   ==>   y = 73

Then

x + 73 = 200   ==>   x = 127

Try rounding off your answer

The triangle is formed by using the diameter as its base, so angle opposite to the diameter, i.e., ∠QRS = 90°

Given that QR and SR are equal, so it is an isosceles triangle. Hence, ∠RQS and ∠RSQ are equal. Hence, ∠RSQ = x + 6° because given that ∠RQS = x + 6°.

We know that all angles of a triangle adds up to 180°.

So, (x+6°) + (x+6°) + 90° = 180°

=> 2(x+6°) + 90° = 180°

=> 2(x+6°) = 180° - 90°

=> 2(x+6°) = 90°

=> 2x + 12° = 90°

=> 2x = 90° - 12°

=> 2x = 78°

=> x = 78°/2

=> x = 39°

Answer:

Question. Which triangle is △ABC similar to and why?

Answer.△ABC is similar to △JEL by AA Similarity Postulate.

Answer:

△ABC ≈△JEL

Step-by-step explanation:

△ABC is similar to △JEL by AA Similarity Postulate. (final answer)

Answer:

90%

Step-by-step explanation:

27/30 = 0.9

0.9x100= 90%

9514 1404 393

Answer:

Step-by-step explanation:

The total cost is the sum of products of number of items and item cost.

  (6 bags)(1.45/bag) +(2 bananas)(0.85/banana) = 8.70 +1.70 = 10.40

It would cost 10.40 for 6 bags of chips and 2 bananas.

__

Similarly, for x bags and y bananas, the cost is ...

  1.45x +0.85y

Answer:

2.35%

Step-by-step explanation:

According to the Empirical Rule,

71 - 79 and 79 - 87 are each 34% of the graph.

63 - 71 and 87 - 95 are each 13.5% of the graph.

55 - 63 and 95 - 103 are each 2.35% of the graph.

Hope this helps.

Hello!

26xy(x + 5)(y - 4) ÷ 13x(y - 4) =

= 2xy × (x + 5) × (y - 4)x × (y - 4) =

= 2x²y × (x + 5) × (y - 4) × (y - 4) =

= 2x²y × (x + 5) × (y - 4)² =

= 2 × [x × (y - 4)]² × y × (x + 5) =

= 2(xy - 4x)² × y × (x + 5) =

= (2xy + 10y) × (x²y² - 8x²y + 16x²) =

= 2x³y³ - 16x³y² + 32x³y + 10x²y³ - 80x²y² + 160x²y

Good luck! :)

Answer:

Step-by-step explanation:

Given,

[tex] \sqrt{34} \times \sqrt{y} = 34[/tex]

[tex] = > \sqrt{34y} = 34[/tex]

[tex] = > 34y = {34}^{2} [/tex]

[tex] = > 34y = 34 \times 34[/tex]

[tex] = > y = \frac{34 \times 34}{34} [/tex]

=> y = 34 (Ans)

Answer:

Step-by-step explanation:

Angle 1 and angle 2 are remote interior angles of angle 6 because angles 1 and 2 are on the inside and it is remote and across from angle six. You can also see this where angle 1 and angle 3 are remote interior angles of angle 5

So in turn angles 2 and 3 are remote interior angles of angle 4 for the same reasoning.

Answer:

Domain of piece 1: [-4, -1)

Domain of piece 2: [-1, 1)

Domain of piece 3: [1, 5]

Step-by-step explanation:

Domain means x-values, so look along the x-axis and see where each of the pieces/segments start at end in terms of x values.

Hope that helps (●'◡'●)

Step-by-step explanation:

y — yı = m(x – xı) equation of a line

Points A(1,3) and B(2,1)

Slope (m) = (y2 – y1) / (x2 – x1)

(1 –3) / (2 – 1)

–2/1

–2

Thus, y –3 = –2 (x – 1)

y – 3 = –2x + 2

y –3 + 3 = –2x + 2 + 3

y = –2x + 5

Answer:

3.2

Step-by-step explanation:

Substitute in the equation:

|(mx1-y1+b)| / √(m2 + (1)2) =

= |(0+-5+-5)| / √(9 + 1)

Sum and operate:

|-10| / √10 = 10 / √10

Exact solution is:

√10

Approximate solution is:

3.2

Answered by GAUTHMATH

Answer: the numbers are 6 and 4.

Step-by-step explanation: 6 times 4 equals 24

6 plus 4 equals 10

Answer:

I hope this will help you

Answer:

3 doors if we are excluding her own. 4 if we are not.

4, 5, 6. she does not pass 7, she enters 7.

3, 4, 5, 6. it could be argued she must first pass her own door.

that context changes the answer.

Answer:

ind the center and radius of the sphere: x2 + y2 +z2-8x + 2y + 62+1 0 2) Find an equation of the sphere that passes through the point (6,-2, 3) and has center (-1,2, 1). Find the curve in which the sphere from #2 intersects the yz-plane. For #4-11, u : ? + j-2k 4) 2u +3v 5) Iv 6) uv and v-3i-2j + k 8) Ivxu 9) comp,v 10) proju 11) Find the angle between u and v 12) Find the scalar triple product of a, b, and c. If a (3, 1,2), b (-1,1,0), and c (0,0,-4) 13) Find the values of x such that (3,2, x) and (2x, 4, x) are orthogonal 14) Find two unit vectors that are orthogonal to both j + 2k and i-2j+3k 15) Find the acute angle between two diagonals of a cube 16) Find a vector perpendicular to the plane through the points A(1,0,0), B(2,0,-1) and C(1,4,3) 17) Find parametric equations for the line through (4,-1, 2) and (1, 1, 5) 18) Find parametric equations for the line through (-2, 2, 4) and perpendicular to the plane 2x-y+5z 12 19) Find an equation of the plane through (2, 1,0) and parallel to x + 4y -3z 1 20) Find an equation of the plane through (3, -1, 1), (4, 0, 2), and (6, 3, 1). 21) Show that the planes x y-z 1 and 2x 3y + 4z 5 are neither parallel nor perpendicular. Find the angle between the planes.

Answer:

15" by 10"

Step-by-step explanation:

Use a proportion.

10'/5" = 30"/x

10x = 5 * 30

10x = 150

x = 15"

10'/5" = 20'/y

10y = 5 * 20

10y = 100

y = 10"

Answer: 15" by 10"

Answer:

(x^4-8)^45 /180 +c

Step-by-step explanation:

If u=x^4-8, then du=(4x^3-0)dx or du=4x^3 dx by power and constant rule.

If du=4x^3 dx, then du/4=x^3 dx. I just divided both sides by 4.

Now we are ready to make substitutions into our integral.

Int(x^3 (x^4-8)^44 dx)

Int(((x^4-8)^44 x^3 dx)

Int(u^44 du/4)

1/4 Int(u^44 dul

1/4 × (u^45 / 45 )+c

Put back in terms of x:

1/4 × (x^4-8)^45/45 +c

We could multiply those fractions

(x^4-8)^45 /180 +c

Answer:

157 is the 24th term.

Step-by-step explanation:

We are given that in an arithmetic sequence, -4 is the first term and 10 is the third term. And we want to find the term number of 157.

Recall that the direct formula for an arithmetic sequence is given by:

[tex]\displaystyle x_n=a+d(n-1)[/tex]

Where n is the nth term, a is the initial term, and d is the common difference.

We know that the initial term a is -4. Hence:

[tex]x_n= -4 + d(n-1)[/tex]

Since 10 is the third term, n = 3:

[tex]\displaystyle x_{3}=10=-4+d(3-1)[/tex]

Solve for the common difference:

[tex]14=2d\Rightarrow d=7[/tex]

Hence, our direct formula is:

[tex]\displaystyle x_n=-4+7(n-1)[/tex]

To find the term number of 157, let 157 equal xₙ and solve for n. Hence:

[tex]\displaystyle (157)=-4+7(n-1)[/tex]

Therefore:

[tex]\displaystyle \begin{aligned} 161 &= 7(n-1) \\ 23 & = n-1 \\ n &= 24\end{aligned}[/tex]

157 is the 24th term.

9514 1404 393

Answer:

  12.1204%

Step-by-step explanation:

The nominal annual rate is 4 times the effective quarterly rate:

  (1 +0.12/12)^3 = 1.030301

so the effective quarterly rate is 3.0301%.

The equivalent annual rate compounded quarterly is 12.1204%.

Answer:

Tell her realtor she can only receive text messages

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

1. The denominator of a fraction indicates how many (equal) pieces a quantity is divided into. When that quantity is 1 cake, and it is divided into 8 equal pieces, each piece is 1/8 of the cake, and there are 8 pieces, or 8/8 of the cake altogether. 8/8 = 1 entire.

When 2/8 of the cake is eaten, there are 8-2 = 6 pieces left, or 6/8 of the cake remains.

When an additional 4/8 of the cake is eaten, there are 6-4 = 2 pieces left, or 2/8 of the cake remains.

__

The fraction 2/8 can be written as the product of fractions ...

  [tex]\dfrac{2}{8}=\dfrac{1\cdot2}{4\cdot2}=\dfrac{1}{4}\cdot\dfrac{2}{2}[/tex]

We know that 2/2 = 1, and anything times 1 is that same thing, so the fraction 2/8 can be "reduced" to its equivalent, 1/4.

  [tex]\dfrac{2}{8}=\dfrac{1}{4}\cdot1=\dfrac{1}{4}[/tex]

As far as we can tell, this question does not ask you to reduce the fraction. Since we're counting 1/8 cake slices, and there are 2 remaining, it is reasonable to leave the fraction as 2/8.

____

2. The given fractions are 1/5 pound, so it is reasonable to think of the whole weight of the 1-pound box as 5/5 pound. Two parts are 1/5 pound each, so the part remaining after considering those is ...

  5/5 - 1/5 - 1/5 = (5 -1 -1)/5 = 3/5

The third item in the box is 3/5 pound.

Answer:

2:3 < 5:6

10:12 > 6:9

The ratios in table 1 are less than the ratios in Table 2

Step-by-step explanation:

cross multiply the ratios and you can tell which one is bigger.

For example, in the first ratio you can see that 2x6 < 5x3

Do that for the second set of ratios and you can see that the ratios in table one are smaller than the ratios in table 2.

Hope this helps

Answer:

2  :3 <  5:6

10:  12 >  6:9

Step-by-step explanation:

i took the test

Answer:

10% of the hundreds of products will be sampled, so the most effective sample method would be systematic sampling, checking every 10th product, which would avoid sources of bias such as missing a region of production where there could be some problems.

Step-by-step explanation:

Samples may be classified as:

Convenient: Sample drawn from a conveniently available pool.

Random: Basically, put all the options into a hat and drawn some of them.

Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.

Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.

Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.

In this case:

10% of the hundreds of products will be sampled, so the most effective sample method would be systematic sampling, checking every 10th product, which would avoid sources of bias such as missing a region of production where there could be some problems.

Answer:

pls post pic of question can't understand ur question

Answer:

[tex] \frac {x}{3} + 6 = 8 [/tex]

Step-by-step explanation:

Let the unknown number be x.

Quotient simply means to divide a number by another number without any remainder.

For example, a quotient of 2 simply means that a number divided by 5 would have a value that is equal to 2 without any remainder; [tex] \frac {10}{5} = 2[/tex]

Hence, translating the word problem in this scenario into an algebraic expression, we have;

[tex] \frac {x}{3} + 6 = 8 [/tex]

Simplifying further, we have;

[tex] \frac {x}{3} = 8 - 6 [/tex]

[tex] \frac {x}{3} = 2 [/tex]

Cross-multiplying, we have;

x = 3 * 2

x = 6