simplify. -4(2x-v) + (-6v+5x)

Answer:

It cannot be extended.

Step-by-step explanation:

Consider the function [tex]f(x,y) = \frac{x^2-y^2}{x^2+y^2}[/tex]. To extend this functions so it is continous at (0,0) we must define [tex] f(0,0) = \lim_{(x,y)\to(0,0)\frac{x^2-y^2}{x^2+y^2}[/tex]. However, this implies that the limit exists. So, we should find if the limit exists or not.

In this case, consider the case in which y =0. When y=0 then

[tex]\lim_{(x,y)\to(0,0) \frac{x^2-0^2}{x^2+0^2} = \lim_{x\to 0}\frac{x^2}{x^2}= 1[/tex]

But, when x=0, we get

[tex]\lim_{(x,y)\to(0,0) \frac{0^2-y^2}{0^2+y^2} = \lim_{y\to 0}\frac{-y^2}{y^2}=-1[/tex].

So, since the limit depends on how we approach to the point (0,0) the limit does not exist. So we can't extend f(x,y) so it is continous.

Answer:

(B)[tex]\dfrac{dA}{dt}=8-0.004A[/tex]

Step-by-step explanation:

Volume of fluid in the tank =1000 gallons

Initial Amount of Salt in the tank, A(0)= 30 pounds

Incoming brine solution of concentration 2 pounds of salt per gallon is pumped in at a rate of 4 gallons per minute.

Rate In=(concentration of salt in inflow)(input rate of brine)

[tex]=(2\frac{lbs}{gal})( 4\frac{gal}{min})=8\frac{lbs}{min}[/tex]

The resulting mixture is pumped out at the same rate, therefore:

Rate Out =(concentration of salt in outflow)(output rate of brine)

[tex]=(\frac{A(t)}{1000})( 4\frac{gal}{min})=\frac{A}{250}[/tex]

Therefore:

The rate of change of amount of salt in the tank,

[tex]\dfrac{dA}{dt}=$Rate In-Rate out\\\dfrac{dA}{dt}=8-\dfrac{A}{250}\\\dfrac{dA}{dt}=8-0.004A[/tex]

Answer:

  (x, y) = (-3, -2)

Step-by-step explanation:

Perhaps this is a system of equations you want the solution for.

Since you have an expression for y, substitution is a viable approach.

  5x +7(x+1) = -29 . . . . . . substitute for y

  12x = -36 . . . . . . subtract 7 and simplify

  x = -3 . . . . . . . . . divide by 12

  y = (-3) +1 = -2 . . . use the expression for y

The solution is (x, y) = (-3, -2).

Answer:

0.0066

Step-by-step explanation:

The x has a distribution that is approximately normal. For normal distribution the probability of x will be,

u = 12 and 18

P (12 [tex]\leq[/tex] [tex]x[/tex] [tex]\leq[/tex] 18)

P (- 2.3  [tex]\leq[/tex] [tex]x[/tex] [tex]\leq[/tex] 2.85 )

P (0.9912 - 0.9978)

= 0.0066

Answer:

[tex]slope = \dfrac{-680}{9}[/tex]

Step-by-step explanation:

We are given coordinates of two points:

Let the points be A and  B respectively:

[tex]A(\dfrac{7}{20}, \dfrac{8}{3})\\B(\dfrac{3}{8}, \dfrac{7}{9})[/tex]

To find the slope of line AB.

Formula for slope of a line passing through two points with coordinates [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] is given as:

[tex]m = \dfrac{y_2- y_1}{x_2- x_1}[/tex]

Here, we have:

[tex]x_2 = \dfrac{3}{8}\\x_1 = \dfrac{7}{20}\\y_2 = \dfrac{7}{9}\\y_1 = \dfrac{8}{3}\\[/tex]

Putting the values in formula:

[tex]m = \dfrac{\dfrac{7}{9}- \dfrac{8}{3}}{\dfrac{3}{8}- \dfrac{7}{20}}\\\Rightarrow m = \dfrac{\dfrac{7-24}{9}}{\dfrac{15-14}{40}}\\\Rightarrow m = \dfrac{\dfrac{-17}{9}}{\dfrac{1}{40}}\\\Rightarrow m = \dfrac{-17\times 40}{9}\\\Rightarrow m = \dfrac{-680}{9}[/tex]

So, the slope of line AB passing through the given coordinates is:

[tex]m = \dfrac{-680}{9}[/tex]

Answer: A

Step-by-step explanation:

Answer: A.

Step-by-step explanation:

A composition of reflections over two parallel lines is equivalent to a translation.

Answer:

0.6

Step-by-step explanation:

3+2=5

P (white) = 3/5 = 0.6

(Hopefully this works, if not, on hearty maths you can go back to your assigned tasks page and go back onto the task to get a new question if that makes sense)

Answer:

5/12

Step-by-step explanation:

The probability of rolling a number greater than 1 is 5/6, because 5 numbers on a 6-sided dice are greater than 1.

The probability of rolling an even number is 3/6, because 3 numbers on a 6-sided dice are even numbers.

[tex]5/6 \times 3/6[/tex]

[tex]=15/36[/tex]

[tex]=5/12[/tex]

Answer:

Step-by-step explanation:

133 is the product of -19 and n

Translate to an equation is:

133 = -19n

then:

n = 133/-19

n = -7

Check:

133 = -19*7

Answer:

[tex]-14x^4+71x^3-61x^2+30x-6[/tex]

Step-by-step explanation:

All we are doing is distributing each number of the 1st equation to the 2nd equation to get our answer. Once we do so, we combine like terms and we get our answer.

Answer:

32 feet

Step-by-step explanation:

area of square is given by side^2

Perimeter of  square is given by 4*side

_______________________________

Given

area of square = 64 sq feet

side^2 = 64

side^2 = 8^2

side = 8

thus side = 8 feet

_______________________________________

The dog pen is fenced with chain, hence chain will be fence at the edge of square and at the perimeter.

Thus, length of chain required will be same as the Perimeter of  square.

Perimeter of given dog pen with side length 8 feet = 4*8 = 32 feet.

Thus, 32 feet of chain fence is required.

Answer:

Q = (- 3, 5 )

Step-by-step explanation:

Given the 2 equations

3y - 2x = 21 → (1)

4y + 5x = 5 → (2)

Multiplying (1) by 5 and (2) by 2 and adding will eliminate the x- term.

15y - 10x = 105 → (3)

8y + 10x = 10 → (4)

Add (3) and (4) term by term to eliminate x

23y = 115 ( divide both sides by 23 )

y = 5

Substitute y = 5 into either of the 2 equations and solve for x

Substituting into (2)

4(5) + 5x = 5

20 + 5x = 5 ( subtract 20 from both sides )

5x = - 15 ( divide both sides by 5 )

x = - 3

Solution is (- 3, 5 )

Answer:

Step-by-step explanation:

An isosceles triangle is a triangle in which two of its sides are equal. This also means that in the triangle, two angles are equal. The angles are usually the base angles. Looking at the given triangle ABC, the base angles are angle Angle A and Angle B, thus angle A = ang B

Therefore, the statement that can be used in the proof is

Angle CAB = angle CBA

Answer: 2 1/2 or 2.5 hours

Step-by-step explanation:

Add 360 and 330

360 + 330 = 690

Divide 1,725 by 690

1,725 / 690 = 2.5

The two planes will meet in 2.5 hours

The speed is the distance covered by an object at a particular time. The time it will take for the two planes to meet is 2.5 hours.

The speed is the distance covered by an object at a particular time. Therefore, it is the ratio of distance and time.

[tex]\rm{Speed = \dfrac{Distance}{Time}[/tex]

Given that the speed of the two planes is 360 km/hr and 330 km/hr. Therefore, the relative speed of the two planes with respect to each other is,

Relative speed = 360 km/hr + 330 km/hr

                         = 690 km/hr

Now, since the total distance between the two cities is 1725 km. Therefore, the time it will take for two planes to meet is,

Time = Distance /Speed

         = 1725 km / 690 km/hr

         = 2.5 hour

Hence, the time it will take for the two planes to meet is 2.5 hours.

Learn more about Speed:

https://brainly.com/question/15100898

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Answer:

12,780

Step-by-step explanation:

Initial population = 9000

grows 7% of 9000= 630 people in a year

after 6 yrs, number of added people = 630× 6=3780 ...... totally, population = 9000+ 3780

= 12,780

The population of the town after 6 years will be 13506.

Thus, the population of the town after 6 years will be 13506.

Learn more about population here:

https://brainly.com/question/20115298

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Answer:

yes

Step-by-step explanation:

y = 19+ 3x

Let x = 3 and y = 28

28 = 19 + 3*3

28 =19+9

28 = 28

This is true so the point is one the line

Answer:  0.627 or 62.7 %

Step-by-step explanation:

The probability that shipment will be rejected P(rejected) = 1- probability that shipment will be accepted.

P(rejected)= 1-P(accepted)

P(accepted) is equal to probability when all 10 watches are not defective.

The probability that 1st one randomly selected watches are not defective is 51/60  (51 watches are not defective and 9 are defective)

The probability that 2-nd one randomly selected watches are not defective is  50/59 ( because the total number of the watches now is 1 unit less 60-1=59, and the total number of not defective watches is 1 unit less 51-1=50 units)

The probability that 3rd one randomly selected watches are not defective is 49/58  (49 watches are not defective total number of watches is 58)

Similarly P(4th)= 48/57  P(5th)=47/56   P(6th)=46/55  P(7th)=45/54

P(8th)=44/53  P(9th)=43/52  P(10th)=42/51

So P(accepted)= P(1st)*P(2nd)*P(3rd)*P(4th)*P(5th)*P(6th)*P(7th)*P(8th)*P(9th)*P(10th)=

=51*50*49*48*47*46*45*44*43*42/(60*59*58*57*56*55*54*53*52*51)=

= approx= 0.373

So P(rejected)=1-0.373=0.627

Answer:

(a) 2.3

(b) 0.5245

(c) 0.7242

(d) 0.5245

Step-by-step explanation:

The data provided is:

S = {180.5, 181.7, 180.9, 181.6, 182.6, 181.6,  181.3, 182.1, 182.1, 180.3, 181.7, 180.5}

(a)

The formula to compute the sample range is:

[tex]\text{Sample Range}=\text{max.}_{x}-\text{min.}_{x}[/tex]

The data set arranged in ascending order is:

S' = {180.3 , 180.5 , 180.5 , 180.9 , 181.3 , 181.6 , 181.6 , 181.7 , 181.7 ,, 182.1 , 182.1 , 182.6}

The minimum value is, 180.3 and the maximum value is, 182.6.

Compute the sample range as follows:

[tex]\text{Sample Range}=\text{max.}_{x}-\text{min.}_{x}[/tex]

                       [tex]=182.6-180.3\\=2.3[/tex]

Thus, the sample range is 2.3.

(b)

Compute the sample variance as follows:

[tex]S^{2}=\frac{1}{n-1}\sum(x_{i}-\bar x)^{2}[/tex]

     [tex]=\frac{1}{12-1}\times [(180.5-181.41)^{2}+(181.7-181.41)^{2}+...+(180.5-181.41)^{2}]\\\\=\frac{1}{11}\times 5.7692\\\\=0.524473\\\\\approx 0.5245[/tex]

Thus, the sample variance is 0.5245.

(c)

Compute the sample standard deviation as follows:

[tex]s=\sqrt{S^{2}}[/tex]

  [tex]=\sqrt{0.5245}\\\\=0.7242[/tex]

Thus, the sample standard deviation is 0.7242.

(d)

Compute the sample variance using the shortcut method as follows:

[tex]S^{2}=\frac{1}{n-1}\cdot [\sum x_{i}^{2}-n(\bar x)^{2}][/tex]

     [tex]=\frac{1}{12-1}\cdot [394913.57-(12\times (181.41)^{2}]\\\\=\frac{1}{11}\times [394913.57-394907.80]\\\\=\frac{5.77}{11}\\\\=0.5245[/tex]

Thus, the sample variance is 0.5245.

Answer:

An independent sample.

Step-by-step explanation:

In this scenario, to compare the production techniques used by foreign and local firms in Brazil, a random sample of 80 foreign firms and a random sample of 80 local firms are selected. We can safely conclude that this study uses an independent sample design.

An independent sample design can be defined as a research method that usually involves the use of multiple experimental groups (two or more). The samples or participants are only in one group and as such each group has no relationship with the other. This simply means that, the samples in a particular group is having no relationship with the other samples in another group.

Ultimately this implies, each samples are independent and satisfies only one condition of the independent sample design during the experiment to compare the production technique used by foreign and local firms in Brazil.

Hence, the researcher would use only two variables or conditions: a random sample of 80 foreign firms and a random sample of 80 local firms are selected.

Answer:

nx^(n-1)

Step-by-step explanation:

Answer:

2.598 and -2.598.

Step-by-step explanation:

f(x) = 2 cos x + sin 2x

f'(x) = -2 sin x + 2 cos 2x = 0   for turning points.

cos 2x =  1 - 2 sin^2 x so we have

-2 sin x + 2 - 4 sin^2 x = 0

4sin^2 x + 2 sin x - 2 = 0

2(2 sin^2 x + sin x - 1) = 0

2(2sinx - 1)(sinx + 1) = 0

sin x  = 0.5, -1   when  f(x) is at a turning point.

x = π/6,  -π/2, 5pi/6

The second derivative is  2 cos x + 2 * -2 sin 2x

= 2 cos x - 4 sin 2x

When x = π/6, this is negative , when x = -π/2 it is positive

so x = π/6 gives a maximum f(x) and x = -π/2 gives 0 so this is a point of inflection

When x = π/6 , f(x) = 2.598

When x = 5pi/6,  f(x) = -2.598.

Answer:

a. P-value = 0.1589

b. P-value = 0.0016

Step-by-step explanation:

a. This is a hypothesis test for the difference between populations means.

The claim is that the two types of steel have different true average fracture toughness values.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0[/tex]

The significance level is α=0.05.

The sample 1, of size n1=100 has a mean of 60.7 and a standard deviation of 1.  The sample 2, of size n2=100 has a mean of 60.5 and a standard deviation of 1.

The difference between sample means is Md=0.2.

[tex]M_d=M_1-M_2=60.7-60.5=0.2[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2+\sigma_2^2}{n}}=\sqrt{\dfrac{1^2+1^2}{100}}\\\\\\s_{M_d}=\sqrt{\dfrac{2}{100}}=\sqrt{0.02}=0.1414[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{0.2-0}{0.1414}=\dfrac{0.2}{0.1414}=1.4142[/tex]

The degrees of freedom for this test are:

[tex]df=n_1+n_2-2=100+100-2=198[/tex]

This test is a two-tailed test, with 198 degrees of freedom and t=1.4142, so the P-value for this test is calculated as (using a t-table):

[tex]P-value=2\cdot P(t>1.4142)=0.1589[/tex]

As the P-value (0.1589) is greater than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the two types of steel have different true average fracture toughness values.

b. As the sample size changes, the standard error and the degress of freedom change.

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2+\sigma_2^2}{n}}=\sqrt{\dfrac{1^2+1^2}{500}}\\\\\\s_{M_d}=\sqrt{\dfrac{2}{500}}=\sqrt{0.004}=0.0632[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{0.2-0}{0.0632}=\dfrac{0.2}{0.0632}=3.1623[/tex]

The degrees of freedom for this test are:

[tex]df=n_1+n_2-2=500+500-2=998[/tex]

This test is a two-tailed test, with 998 degrees of freedom and t=3.1623, so the P-value for this test is calculated as (using a t-table):

[tex]P-value=2\cdot P(t>3.1623)=0.0016[/tex]

As the P-value (0.0016) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the two types of steel have different true average fracture toughness values.

Answer:

3/4

Step-by-step explanation:

Use [tex]\frac{rise}{run}[/tex]. From the bottom red point, you have to go up 3 and left 4 to get to the top point. That's your answer.

Answer:

41.67%  probability of the sum of the dots indicate a sum less than or equal to 6

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes:

In this problem, we have these possible outcomes:

Format(Dice A, Dice B)

(1,1), (1,2), (1,3), (1,4), (1,5),(1,6)

(2,1), (2,2), (2,3), (2,4), (2,5),(2,6)

(3,1), (3,2), (3,3), (3,4), (3,5),(3,6)

(4,1), (4,2), (4,3), (4,4), (4,5),(4,6)

(5,1), (5,2), (5,3), (5,4), (5,5),(5,6)

(6,1), (6,2), (6,3), (6,4), (6,5),(6,6)

There are 36 possible outcomes.

Desired outcomes:

Sum of 6 or less. They are:

(1,1), (1,2), (1,3), (1,4), (1,5), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (4,1), (4,2), (5,1)

15 desired outcomes

15/36 = 0.4167

41.67%  probability of the sum of the dots indicate a sum less than or equal to 6

Answer:

there is no inequality..

Step-by-step explanation:

Answer:

???

Step-by-step explanation:

Answer:

no supplement

Step-by-step explanation:

Supplementary angles add to 180 degrees,

This angle is larger than 180 degrees by itself, so it has no supplement

Answer:

$1,06

Step-by-step explanation:

Calculation for dividend per share of common stock for board of directors of Midwest Foods

First step is to find the amount of dividends due to the preferred shareholders

Using this formula

Total Dividend =Dividend- (Preferred stock *Per share of preferred stock )

Let plug in the formula

Total Dividend =$3,500,000-($300,000*$2.85)

Total Dividend =$3,500,000-$855,000

Total Dividend =$2,645,000

The second step is to find Dividend per share of common stock

Using this formula

Dividend per share of common stock=Total dividend/Shares of common stock

Let plug in the formula

Dividend per share of common stock=$2,645,000/$2,500,000

Dividend per share of common stock=$1.06

Therefore the dividend per share of common stock for board of directors of Midwest Foods will be $1.06

Answer:

891

Step-by-step explanation:

x has to be 1001 and y has to be 11 * 10 = 110 so x - y = 1001 - 110 = 891.

Answer:

891

Step-by-step explanation:

[tex]$1001$ is the smallest integer greater than $1000$. It also happens to be a multiple of $11$, since $1001 = 11 \cdot 91$. So $1001$ is the smallest multiple of $11$ greater than $1000$ and thus $x = 1001$.The greatest multiple of $11$ that is less than $11^2 = 11 \cdot 11$ is$$11 \cdot (11 - 1) = 11 \cdot 10 = 110$$Thus $y = 110$, and we compute$$x - y = 1001 - 110 = \boxed{891}$$[/tex]

Hope this helped! :)

Answer:

coefficient of variation = 7.108%

Step-by-step explanation:

From the given information:

The objective is to determine the  coefficient of variation for the prices of tickets purchased 30 days in advance is ____%

The mean [tex]\overline x[/tex] = [tex]\dfrac{250+286+305+256+288+282+254}{7}[/tex]

The mean [tex]\overline x[/tex] = [tex]\dfrac{1921}{7}[/tex]

The mean [tex]\overline x[/tex] = 274.4285714

The standard deviation also can be computed as follows:

[tex]\sigma =\sqrt{ \dfrac{\sum (x_i-\mu)^2}{N}}[/tex]

[tex]\sigma =\sqrt{ \dfrac{ (250-274.43)^2+(286-274.43)^2+(305-274.43)^2+...+(254-274.43)^2}{7}}[/tex][tex]\sigma =19.507[/tex]

Finally; the coefficient of variation can be calculated with the formula:

coefficient of variation = [tex]\dfrac{\sigma}{\overline x}[/tex]

coefficient of variation = [tex]\dfrac{19.507}{274.43}[/tex]

coefficient of variation = 0.07108

coefficient of variation = 7.108%