Use the dot product to determine whether v and w are orthogonal.

v=-i-j, w=-i+j

Select the correct choice below and fill in the answer box to complete your choice.

O A. The vectors v and w are not orthogonal because their dot product is ___

O B. The vectors v and w are orthogonal because their dot product is ___

The complete question is;

The polynomial P(x) = 5x²(x − 1)³(x + 9) has degree ____. It has zeros 0, 1, and ____. The zero 0 has multiplicity ____ , and the zero 1 has multiplicity ____

Answer:

A) degree = 6

B) -9 is also a zero of the polynomial

C) 0 has multiplicity of 2

1 has multiplicity of 3

Step-by-step explanation:

A) To find the degree of the polynomial, we will first have to identify each term [term is for example (x - 1)³]. Thus, to find the degree of each term we will add the exponents.

The terms are;

5x², (x - 1)³, (x + 9)

The exponents are, 2, 3 and 1 respectively.

Thus, degree = 2 + 3 + 1 = 6

B) A zero of a polynomial is the value of x that causes the polynomial function to equal 0.

Since 0 and 1 are zeros, looking at the polynomial P(x) = 5x²(x − 1)³(x + 9), we can tell that when the term which when x = 0 makes the polynomial 0 is 5x².

Similarly, the term which when x = 1 makes the polynomial 0 is (x - 1)³

Thus,we are left with the term (x + 9)

So for the polynomial to be zero, (x + 9) = 0

Thus,x = -9

So -9 is a zero of the polynomial

C) The zero 0 is from the term 5x².

Thus,the multiplicity is the highest power of x which is 2.

The zero 1 is from the term (x - 1)³. Thus, the multiplicity is the highest power of x which is 3

Answer:

  16%

Step-by-step explanation:

The difference between the time of interest (339 days) and the mean (336 days) is 3 days, which is exactly 1 standard deviation.

The 68-95-99.7 rule tells you that 68% of pregnancies will be within 1 standard deviation. The remaining 32% will be evenly split between pregnancies that are longer than 339 days and ones that are shorter than 333 days. So, half of 32%, or 16%, will be longer than 339 days.

Answer:

6x-3=21

6x=24

x=4

........

6x+27=39

6x=39-27

6x=12

x=2

........

8x-10=14

8x=24

x=3

.........

6+6x=22

6x=22-6

x=3

......

12x-2=28

12x=26

x=3

.....

8-4x=16

-4x=8

x=-2

.....

4x-24=3x-3

4x-3x=24-3

x=21

....

9x+6=6x+12

9x-6x=12-6

3x=6

x=2

Answer:

Step-by-step explanation:

1. 3(2x - 1) = 21

 = 6x - 3 = 21

 = 6x = 24

 = x = 24/6 = 4

------------------------------

2. 3(2x+9) = 39

   = 6x + 27 = 39

   = 6x = 39 - 27

   = 6x = 12

   = x = 12/6 = 2

--------------------------------

3. 2(4x - 5) = 14

  = 8x - 10 = 14

  = 8x = 14+10

 = x = 3

-------------------------------

Answer:

[tex] \begin{cases} (x - 2)^2 + (y - 2)^2 = 25 \\ y = 5 \end{cases} [/tex]

Solutions: x = 6, y = 5   or   x = -2, y = 5

Step-by-step explanation:

Use a graph.

Plot point (-2, 5). That will be a point on a circle with radius 5.

From point (-2, 5), go right 4 and down 3 to point (2, 2). (2, 2) is the center of the circle.

You now need the equation of a circle with center (2, 2) and radius 5.

Use the standard equation of a circle:

[tex] (x - h)^2 + (y - k)^2 = r^2 [/tex]

where (h, k) is the center and 5 is the radius.

The circle has equation:

[tex] (x - 2)^2 + (y - 2)^2 = 25 [/tex]

To have a single solution, you need the equation of the line tangent to the circle at (-2, 5), but since you want more than one solution, you need the equation of a secant to the circle. For example, use the equation of the horizontal line through point (2, 5) which is y = 5.

System:

[tex] \begin{cases} (x - 2)^2 + (y - 2)^2 = 25 \\ y = 5 \end{cases} [/tex]

To solve, let y = 5 in the equation of the circle.

(x - 2)^2 + (5 - 2)^2 = 25

(x - 2)^2 + 9 = 25

(x - 2)^2 = 16

x - 2 = 4  or x - 2 = -4

x = 6 or x = -2

Solutions: x = 6, y = 5   or   x = -2, y = 5

An example of a nonlinear system that has at least two solutions, one of which is (-2,5) are,

⇒ x² + y² = 29

⇒ 3x + 4y = -2

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now, This system by starting with the equation of a circle centered at the origin with radius sqrt(29), which is,

⇒ x² + y² = 29.

Then, Added a linear equation that intersects the circle at (-2,5) to create a system with two solutions.

The entire solution set for this system is: (-2, 5) and (7/5, -19/10)

Thus, An example of a nonlinear system that has at least two solutions, one of which is (-2,5) are,

⇒ x² + y² = 29

⇒ 3x + 4y = -2

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ3

Answer:

≈ 0.2526

Step-by-step explanation:

The number of combinations of 4 out of 8:

Success factor is:

and failure factor is:

Probability:

Answer:

$ 180,000

Step-by-step explanation:

All we are being asked to do in this question is take the simple interest, given a principle value of $100,000, with 8 percent interest each year over a course of 10 years. This is given the simple interest formula P( 1 + rt ).

Simple Interest : P( 1 + rt ),

P = $ 100,000 ; r = 8% ; t = 10 years,

100,000( 1 + 0.08( 10 ) ) = 100,000( 1 + 0.8 ) = 100,000( 1.8 ) = 180,000

Therefore you will have to pay back a total of $ 180,000

Complete Question

The data represent the membership of a group of politicians. If we randomly select one politician, what is the probability of getting a Republican given that a male was selected?    

        Republican      Democrat           Independent

Male           11                  6                                   0

Female       70                  17                                  7

The probability is approximately_____?

Answer:

The  probability is  [tex]P(k) = 0.647[/tex]

Step-by-step explanation:  

From the question we are told that

   The  sample size of male is  [tex]n_m = 11 + 6 =17[/tex]

     The  number of male Republican is  [tex]k = 11[/tex]  

Generally the probability of getting a Republican given that a male was selected is

            [tex]P(k) = \frac{k}{n_m}[/tex]

substituting values

          [tex]P(k) = \frac{ 11}{17}[/tex]

          [tex]P(k) = 0.647[/tex]

Answer:

b

Step-by-step explanation:

The value of a is negative, so the vertex is a minimum.

Answer:

a. 0.36

b. 0.1296

c. No.

Step-by-step explanation:

1. Note the probability of emergency backup generators to fail when they are needed = 18% or 0.18. Thus,

a. Probability of both emergency backup generators failing = P (G1 and G2 fails) where G represents the generators.

= P (G1 falls) x P ( G2 fails)

= 0.18 x 0.18

= 0.36

b. The probability of having a working generator in the event of a power outage = G1 fails x G2 works + G2 works x G2 fails

= 0.36 x 0.18 + 0.18 x 0.36

= 0.1296

c. Looking at the probability of any of the generators working, it is not meeting safety standards as lives could be lost if the backup generators needed to perform an emergency surgery operation fails.

Answer:

x = 300 feet

Step-by-step explanation:

In the given right triangle,

Length of the string of the kite = 324 feet

Angle between the string and the ground = 68°

By applying law of Sines in the given right triangle,

[tex]\frac{\text{SinA}}{a}=\frac{\text{SinB}}{b}=\frac{\text{SinC}}{c}[/tex]

Now we substitute the values of angles and sides in the formula,

[tex]\frac{\text{Sin68}}{x}=\frac{\text{Sin90}}{324}[/tex]

[tex]\frac{\text{Sin68}}{x}=\frac{1}{324}[/tex]

x = 324 × Sin(68)°

x = 300.41 feet

x ≈ 300 feet

Therefore, measure of side x = 300 feet will be the answer.

Answer:

Step-by-step explanation:

To find the approximate value of y when

x = 13 and z = 195 we must first find the relationship between them

The statement

y varies jointly with x and z is written as

where k is the constant of proportionality

From the question

y = 2

x = 11

z = 110

We have

2 = 11(110)k

2 = 1210k

Divide both sides by 1210

[tex]k = \frac{1}{605} [/tex]

So the formula for the variation is

[tex]y = \frac{1}{605} xz[/tex]

When

x = 13

z = 195

y is

[tex]y = \frac{1}{605} (13)(195)[/tex]

[tex]y = \frac{507}{121} [/tex]

y = 4.1900

We have the final answer as

Hope this helps you

Answer:

7/8

Step-by-step explanation:

7/8 = 0.875

5/8 = 0.625

7/13 = 0.538

11/19 = 0.579

So 7/8 is the largest

Answer:

= 2/3

Step-by-step explanation:

10 / (5*3)

= 10/15

= 2/3

Step-by-step explanation:

Here are some examples of ten integers (in this case prime numbers) chosen from 2 to 24;

2, 3, 5, 7, 9, 15, 17, 19, 21, 23

Lets take for example the integers 15 and 21, they have a common divisor 3 which is greater than 1. Which implies that the number 3 can divide through 15 and 21 without a remainder, that is, 21 ÷ 3 = 7, 15 ÷ 3 = 5. Also note that 3 is a divisor of 9.

Therefore, we could right say that within any set of ten integers chosen from 2 through 24, there are at least two integers with a common divisor greater than 1.

Answer: 125.6 in^2

Step-by-step explanation:

First, we have that the radius of this circle is r = 10in

Now, we know that the area of a circle is:

A = pi*r^2

Now, if we got only a section of the circle, defined by an angle x, then the area of that region is:

A = (x/360°)*pi*r^2

Notice that if x = 360°, then the area is the same as the area of the full circle, as expected.

Then each shaded area has an angle of 72°.

A = (72°/360°)*3.14*(10in)^2 = 62.8 in^2

And we have two of those, both of them with the same angle, so the total shaded area is:

2*A = 2*62.8 in^2 = 125.6 in^2

Answer:

No, the owners are not having their transmissions serviced at 30,000 miles.

Step-by-step explanation:

We are given that a car dealer recommends that transmissions be serviced at 30,000 miles.

The car dealer selects a random sample of 40 customers and finds that the average mileage of the automobiles serviced is 30,456. The standard deviation of the population is 1684 miles.

Let [tex]\mu[/tex] = true average mileage of the automobiles serviced.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 30,000 miles      {means that the owners are having their transmissions serviced at 30,000 miles}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 30,000 miles      {means that the owners are having their transmissions serviced at different than 30,000 miles}

The test statistics that will be used here is One-sample z-test statistics because we know about population standard deviation;

                             T.S.  =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~  N(0,1)

where, [tex]\bar X[/tex] = sample average mileage serviced = 30,456 miles  

            [tex]\sigma[/tex] = population standard deviation = 1684 miles

            n = sample of customers = 40

So, the test statistics =  [tex]\frac{30,456-30,000}{\frac{1684}{\sqrt{40} } }[/tex]  

                                     =  1.71

The value of z-statistics is 1.71.

Also, the P-value of the test statistics is given by;

                    P-value = P(Z > 1.71) = 1 - P(Z [tex]\leq[/tex] 1.71)

                                  = 1 - 0.9564 = 0.0436

For the two-tailed test, the P-value is calculated as = 2 [tex]\times[/tex] 0.0436 = 0.0872.

Since the P-value of our test statistics is less than the level of significance as 0.0872 < 0.10, so we have sufficient evidence to reject our null hypothesis as the test statistics will fall in the rejection region.

Therefore, we conclude that the owners are having their transmissions serviced at different than 30,000 miles.

Answer:

See below.

Step-by-step explanation:

From the graph, we can see that g(x)=3 is true only when x is between 3 and 5. However, note that when x=3, the point is a closed circle. When x=5, the point is an open circle. Therefore, the solution is between 3 and 5, and it includes 3 but not 5.

In set-builder notation, this is:

[tex]\{x|x\in \mathbb{R}, 3\leq x<5\}[/tex]

In interval notation, this is:

[tex][3,5)[/tex]

Essentially, these answers are saying: The solution set for g(x)=3 is all numbers between 3 and 5 including 3 and not including 5.

Answer:

-12

Step-by-step explanation:

Answer:

36 x^3 - 32 x^2 + (x + 4) (x^2 - 6 x + 3).x^3 - 62 x + 12

Step-by-step explanation:

Answer:

x^6-2x^5-21x^4+48x^3-32x^2-62x+12

Step-by-step explanation:

Mark me as brainliest!!!!

Answer:

B: -x^2 + 4

Step-by-step explanation:

If the equation was [tex]f(x)=x^2[/tex], then the vertex would be at 0, and the "U" would be facing straight up. Here, the "U" is upside down, so that means the "x^2" would have to be a negative number ([tex]-x^2[/tex]) to get the upside-down "U". Then, we could see that the vertex is at positive 4, so that means that the parabola moved up 4 units, so the equation should end in +4.

Our answer is:

B: -x^2 + 4

Answer:

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

From the question

y = - 1/2x + 5

Comparing with the general equation above

Slope / m = -1/2

Since the lines are perpendicular to each other the slope of the other line is the negative inverse of the original line

That's

Slope of the perpendicular line = 2

Equation of the line using point (–1, –2) and slope 2 is

y + 2 = 2( x + 1)

y + 2 = 2x + 2

y = 2x + 2 - 2

We have the final answer as

Hope this helps you

Answer:

C) y = 2x

Step-by-step explanation:

I got it right in the test !!

Answer: 36 shingles can be placed on the north part of the house.

Step-by-step explanation:

Given: Length of each shingle = [tex]1\dfrac23[/tex] feet = [tex]\dfrac53[/tex] feet.

The north part of the house has a roof line that is 60 feet across.

Then, the number of  shingles can be placed  on the north part of the house = (Length of roof line in north part) ÷ (Length of each shingle)

[tex]=60\div \dfrac{5}{3}\\\\=60\times\dfrac{3}{5}\\\\=12\times3=36[/tex]

Hence, 36 shingles can be placed on the north part of the house.

Answer:

Graph is image, and equation is from the work result below:

Step-by-step explanation:

Take two points find the slope and y-intercept:

Slope = -2

Y-intercept = (0,16)

Equation =

y  =  − 2 x  +  16

check work for one point (to make sure equation works):

(2,12)

y = -2x + 16

12 = -2(2) + 16

12 = -4 + 16

12 = 12

The equation is correct: y  =  − 2 x  +  16

Image below are the points given:

Answer:

19x

Step-by-step explanation:

product means multiply

19*x

19x

Answer:

The answer is C.

Step-by-step explanation:

if a number and a variable are next to each other, it is assumed they will be multiplied.

Answer:

13 days

Step-by-step explanation:

Given that a one-way flight to europe will take 13 hours

A round trip will take = 13 hrs x 2 = 26 hours

Also given that we make one round trip per months for 12 months (1 year)

We will take a total of 12 round trips per year

Number of hours taken for 12 round trips

= 26 hours per round trip x 12 round trips

= 26 x 12

= 312 hours

Recall that there are 24 hours in a day, hence to convert 312 hours into days, we have to divide this by 24.

Number of days = number of hours ÷ 24

= 312 ÷ 24

= 13 days

Answer:

1) [tex]\boxed{p(x) = x^3-x^2+x-1}[/tex]

2) [tex]\boxed{p(x) = x^2+x-2}[/tex]

3) [tex]\boxed{p(x) =- 2x^2+2x+4}[/tex]

4) [tex]\boxed{p(x) = 2x^2+x-4}[/tex]

Step-by-step explanation:

Part (1)

[tex]p(x) = x^3-x^2+x-1[/tex]

As we have to determine it by ourselves, this is the polynomial having a degree of 3. p(x) with a degree of 3 means that the highest degree/exponent of x should be 3.

Part (2)

[tex]p(x) = x^2+x-2[/tex]

This can be the polynomial having the factor x-1 because if we put:

x - 1 = 0 =>  x = 1 in the above polynomial, it gives us a result of zero which shows us that (x-1) "is" a factor of the polynomial.

Part (3)

[tex]p(x) = -2x^2+2x+4[/tex]

This can be the polynomial for which p(0) = 4 and p(-1) = 0

Let's check:

[tex]p(0) =- 2(0)^2+2(0)+4\\p(0) = 0 + 0+4\\p(0) = 4[/tex]

[tex]p(-1)= -2(-1)^2+2(-1)+4\\p(-1) = -2(1)-2+4\\p(-1) = -2-2+4\\p(-1) = 0[/tex]

So, this is the required polynomial determined by "myself".

Part (4):

[tex]p(x) = 2x^2+x-4[/tex]

This is the polynomial having a remainder 6 when divided by (x-2)

Let's check:

Let x - 2 = 0 => x = 2

Putting in the above polynomial

[tex]p(x) = 2(2)^2+(2)-4\\Given \ that \ Remainder = 6\\6 = 2(4) +2-4\\6 = 8+2-4\\6 = 10-4\\6 = 6[/tex]

So, Proved that it has a remainder of 6 when divided by (x-2)

Answer:

The 99% confidence interval for estimating the population mean μ is ($60,112.60, $68087.40).

Step-by-step explanation:

The complete question is:

Salaries of 42 college graduates who took a statistics course in college have a​ mean, [tex]\bar x[/tex] of, $64, 100. Assuming a standard​ deviation, σ of ​$10​,016 construct a ​99% confidence interval for estimating the population mean μ.

Solution:

The (1 - α)% confidence interval for estimating the population mean μ is:

[tex]CI=\bar x\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]

The critical value of z for 99% confidence interval is:

[tex]z_{\alpha/2}=z_{0.01/2}=z_{0.005}=2.57[/tex]

Compute the 99% confidence interval for estimating the population mean μ as follows:

[tex]CI=\bar x\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]

     [tex]=64100\pm 2.58\times\frac{10016}{\sqrt{42}}\\\\=64100+3987.3961\\\\=(60112.6039, 68087.3961)\\\\\approx (60112.60, 68087.40)[/tex]

Thus, the 99% confidence interval for estimating the population mean μ is ($60,112.60, $68087.40).

Answer:

Number of levels = 2

Type of design = Repeated measure

Dependent variable = Typing Speed

Step-by-step explanation:

The number of levels in an experiment simply refers to the number of experimental conditions in which participants are subjected to. In the scenario above, the number of levels is 2. Which are ; Halfway through the class and After the class is over.

The type of designed employed is REPEATED MEASURE, this is because the participants all took part in each experimental condition.

The dependent variable is TYPING SPEED, which is the variable which is measured with respect to the independent variable. Hence the observed value depends on period that is (halfway through the class or after the class is over).

Answer:

1/2 to the power of 3= 1/8

Step-by-step explanation:

1/2*1/2=1/4

1/4*1/2=1/8

d?

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{(\dfrac{1}{2})^3}[/tex]

[tex]\mathsf{= \dfrac{1}{2}^3}[/tex]

[tex]\mathsf{= \dfrac{1}{2} \times \dfrac{1}{2} \times \dfrac{1}{2}}[/tex]

[tex]\mathsf{= \dfrac{1 \times 1 \times 1}{2 \times 2 \times 2}}[/tex]

[tex]\mathsf{\mathsf{= \dfrac{1 \times 1} {4 \times 2}}}[/tex]

[tex]\mathsf{= \dfrac{1}{8}}[/tex]

[tex]\huge\text{Therefore your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{Option\ D.\ \dfrac{1}{8}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

135 degrees

Step-by-step explanation:

3x+15 = 5x - 5 because of the alternate interior angles theorem.

20 = 2x

x = 10

3(10) + 15 = 30+15 = 45

Remember that a line has a measure of 180 degrees. So we can just subtract the angle we found from 180 degrees to get BFG.

180-45 = 135.