Find the value of x.

A. 6
B. 7
C. 4
D. 5

Answer:

[tex]m^3+m^2[/tex]

Step-by-step explanation:

=> [tex]2m^2-m^2(7-m)+6m^2[/tex]

Collecting like terms and expanding the brackets

=> [tex]2m^2+6m^2-7m^2+m^3[/tex]

=> [tex]8m^2-7m^2+m^3[/tex]

=> [tex]m^2+m^3[/tex]

=> [tex]m^3+m^2[/tex]

Answer:

critical point of the given function f(x,y) = x²+y²+2xy is from line y = -x is the critical point of the function f(x0,y0) = 0

and it local minimum.

Step-by-step explanation:

Let the given function be;

f(x,y) = x²+y²+2xy

From above function, we can locate relative minima, maxima and the saddle point

f(x,y) = x²+y²+2xy = (x+y)²

df/dx = 2x+2y = 0 ---- (1)

df/dy =2y+2x = 0 ---- (2)

From eqn 1 and 2 above,

The arbitrary point (x0,y0) from line y = -x is the critical point of the function f(x0,y0) = 0

Then, from f(x,y) >= 0 for arbitrary (x,y) € R^n, the arbitrary point from the line x = -y is local minima of the function f.

Answer: a) Mean = [tex]=37.80[/tex]

Standard deviation=[tex]=1.9442[/tex]

b) Mean = [tex]56.00[/tex]

Standard deviation=[tex]4.0988[/tex]

c) Mean = [tex]=24[/tex]

Standard deviation=[tex]2.4495[/tex]

Step-by-step explanation:

To compute Mean and standard deviation , we use following formula:

Mean = [tex]n\pi[/tex]

Standard deviation=[tex]\sqrt{n\pi(1-\pi)}[/tex]

a. [tex]n=42,\ \pi=0.90[/tex]

Mean = [tex]42\times0.90=37.80[/tex]

Standard deviation=[tex]\sqrt{42(0.90)(0.10)}=\sqrt{3.78}\approx1.9442[/tex]

b. [tex]n=80,\ \pi=0.70[/tex]

Mean = [tex]80\times0.70=56.00[/tex]

Standard deviation=[tex]\sqrt{80(0.70)(0.30)}=\sqrt{16.8}\approx4.0988[/tex]

c. [tex]n=32,\ \pi=0.75[/tex]

Mean = [tex]32\times0.75=24[/tex]

Standard deviation=[tex]\sqrt{32(0.75)(0.25)}=\sqrt{6}\approx2.4495[/tex]

Step-by-step explanation:

Unit rate = 24 ÷ 8 = 3 tires

Answer:

Step-by-step explanation:

24 tires/8hours

Question:

Which of the following values cannot be probabilities? 3 / 5,  2,  5 / 3,  1.39, −0.57,  1,  0,  0.04 Select all the values that cannot be probabilities.

A. 0

B. 2

C. 3 / 5

D. − 0.57

E. 0.04

F. 1.39

G. 5 / 3

H. 1

Answer:

B, D, F, G

Step-by-step explanation:

The probability, P(A), of an event A occurring is given by;

0 ≤ P(A) ≤ 1

This means that the probability of an event happening is always between 0 and 1 (both inclusive).

Therefore;

=> 3 / 5 is a valid probability value as;

0 ≤ 3/5 ≤ 1

=> 2 is NOT a valid probability value as 2 is not within the range 0 and 1

=> 5 / 3 is NOT a valid probability value as 5 / 3 = 1.6667 is not withing the range 0 and 1

=> 1.39 is NOT a valid probability value

=> -0.57 is NOT valid. Probability values are not and cannot be negative.

=> 1 is a valid probability value. This just means that the probability that an event will occur is 100% likely.

=> 0 is a valid probability value. This just means that the probability that an event will occur is 0% likely.

=> 0.04 is valid as;

0 ≤ 0.04 ≤ 1

Answer:

The missing side is [tex]B = 6.0\ cm[/tex]

The missing angles are [tex]\alpha = 56.2[/tex] and [tex]\theta = 93.8[/tex]

Step-by-step explanation:

Given

[tex]A = 10\ cm[/tex]

[tex]C = 12\ cm[/tex]

[tex]\beta = 30[/tex]

The implication of this question is to solve for the missing side and the two missing angles

Represent

Angle A with [tex]\alpha[/tex]

Angle B with [tex]\beta[/tex]

Angle C with [tex]\theta[/tex]

Calculating B

This will be calculated using cosine formula as thus;

[tex]B^2 = A^2 + C^2 - 2ACCos\beta[/tex]

Substitute values for A, C and [tex]\beta[/tex]

[tex]B^2 = 10^2 + 12^2 - 2 * 10 * 12 * Cos30[/tex]

[tex]B^2 = 100 + 144 - 240 * 0.8660[/tex]

[tex]B^2 = 100 + 144 - 207.8[/tex]

[tex]B^2 = 36.2[/tex]

Take Square root of both sides

[tex]B = \sqrt{36.2}[/tex]

[tex]B = 6.0[/tex] (Approximated)

Calculating [tex]\alpha[/tex]

This will be calculated using cosine formula as thus;

[tex]A^2 = B^2 + C^2 - 2BCCos\alpha[/tex]

Substitute values for A, B and C

[tex]A^2 = B^2 + C^2 - 2BCCos\alpha[/tex]

[tex]10^2 = 6^2 + 12^2 - 2 * 6 * 12 * Cos\alpha[/tex]

[tex]100 = 36 + 144 - 144Cos\alpha[/tex]

Collect Like Terms

[tex]100 - 36 - 144 = -144Cos\alpha[/tex]

[tex]-80 = -144Cos\alpha[/tex]

Divide both sides by -144

[tex]\frac{-80}{-144} = Cos\alpha[/tex]

[tex]0.5556 = Cos\alpha[/tex]

[tex]\alpha = cos^{-1}(0.5556)[/tex]

[tex]\alpha = 56.2[/tex] (Approximated)

Calculating [tex]\theta[/tex]

This will be calculated using cosine formula as thus;

[tex]C^2 = B^2 + A^2 - 2BACos\theta[/tex]

Substitute values for A, B and C

[tex]12^2 = 6^2 + 10^2 - 2 * 6 * 10Cos\theta[/tex]

[tex]144 = 36 + 100 - 120Cos\theta[/tex]

Collect Like Terms

[tex]144 - 36 - 100 = -120Cos\theta[/tex]

[tex]8 = -120Cos\theta[/tex]

Divide both sides by -120

[tex]\frac{8}{-120} = Cos\theta[/tex]

[tex]-0.0667= Cos\theta[/tex]

[tex]\theta = cos^{-1}(-0.0667)[/tex]

[tex]\theta = 93.8[/tex] (Approximated)

Answer:

14 and 9

Step-by-step explanation:

Y values are always the second number in the parenthesis. The X value is the first one. I like to think of Y being dependent on X, so X goes first, then Y.

Answer:

Step-by-step explanation:

The statement

3x less than two times the sum of 2X and one is written as

2( 2x + 1) - 3x

the sum of 2 and 5 is written as

2 + 5

Equate the two statements

We have

2( 2x + 1) - 3x = 2+5

Expand

4x + 2 - 3x = 7

Simplify

4x - 3x = 7 - 2

We have the final answer as

Hope this helps you

Answer:

pay the 11 AM ticket

Step-by-step explanation:

Note that the flight last for 12 hours, and assuming the freelance developer can still work (have access to the internet) on the airplane throughout the flight, he stand to earn $960 ($80*12), which will still cover the cost of the flight with a profit of $60 ($960-900).

However, if he decides to pay the $11 flight ticket and there is no Internet on boards; there by losing a day of work, he stand to have lost working time which would earn with $900.

Therefore, the best choice is to pay the 11 AM ticket.

x² - 8x + 12 = 0

First of all we need to find the roots

Δ = b² - 4.a.c

Δ = (-8)² - 4 . 1 . 12

Δ = 64 - 4. 1 . 12

Δ = 16

Has 2 real roots

x = (-b +- √Δ)/2a

x' = (--8 + √16)/2.1    

x'' = (--8 - √16)/2.1

x' = 12 / 2    

x'' = 4 / 2

x' = 6    

x'' = 2

So our equation can be solved with x = 6 and x = 2, therefore we can create two other equations with the same roots

x - 6 = 0

and

x - 2 = 0

Answer:

(x – 4)2 = 4

Step-by-step explanation:

Answer:

1112

Step-by-step explanation:

6458 + 2994  = 9452

7013  - 6945  = 68

9452/68 = 139

139 * 8 = 1112

​

Answer:

y = 1.8

Step-by-step explanation:

Question 39).

Let the operation which defines the relation between a and b is O.

Relation between a and b has been given as,

a O b = [tex]\frac{(a+b)}{(a-b)}[/tex]

Following the same operation, relation between 3 and y will be,

3 O y = [tex]\frac{3+y}{3-y}[/tex]

Since 3 O y = 4,

[tex]\frac{3+y}{3-y}=4[/tex]

3 + y = 12 - 4y

3 + y + 4y = 12 - 4y + 4y

3 + 5y = 12

3 + 5y - 3 = 12 - 3

5y = 9

[tex]\frac{5y}{5}=\frac{9}{5}[/tex]

y = 1.8

Therefore, y = 1.8 will be the answer.

Answer:

90/x=70/100 that's my answer

[tex]90 \x = 70 \100[/tex]

Answer:

90/x = 70/100

Step-by-step explanation:

Is means equals and of means multiply

90 = 70% *x

Changing to decimal form

90 = .70x

Changing to fraction form

90 = 70/100 *x

Divide each side by x

90/x = 70/100

Answer:

Five-number summary in ascending order: [tex] 0.58, 0.89, 0.98, 1.26, 1.42 [/tex]

Step-by-step Explanation:

The number summary, in ascending order, includes the minimum value, maximum value, median value, upper quartile and lower quartile.

To find each of the above values, first, order the data set in ascending order. Our values given, when ordered, would be:

0.58, 0.59, 0.89, 0.96, 0.97,| 0.98|, 1.07, 1.14, 1.26, 1.28, 1.42

1.The minimum value (the least value or lower value in the given data set).

From the ordered data set, minimum value = 0.58

2. The maximum value is the highest value in the data set = 1.42

3. Median value is the middle value of the data set. The middle value is the 6th value = 0.98.

The median value divides the data set into lower and upper region, as shown below.

0.58, 0.59, 0.89, 0.96, 0.97,|0.98|, 1.07, 1.14, 1.26, 1.28, 1.42

4. Lower Quartile (Q2) is the middle value of the lower region = 0.89, as shown below,

0.58, 0.59, [0.89], 0.96, 0.97,|0.98|, 1.07, 1.14, 1.26, 1.28, 1.42

5. Upper Quartile (Q3) is the middle value of the upper region = 1.26, as shown below.

0.58, 0.59, 0.89, 0.96, 0.97,|0.98|, 1.07, 1.14, [1.26], 1.28, 1.42

: this is the middle value of lower region, after our median divides the data set into two.

0.58, 0.59, 0.89, 0.96, 0.97,|0.98|, 1.07, 1.14, 1.26, 1.28, 1.42

Therefore, the five-number summary in ascending order is as follows: [tex] 0.58, 0.89, 0.98, 1.26, 1.42 [/tex]

Min = 0.58

Q1 = 0.89

Median = 0.98

Q3 = 1.26

Max = 1.42

A box plot has been constructed using the five-number summary. Check the attachment below.

The min value is represented by the whisker that starts from your left and connects to the rectangular box.

The max value is indicated at the extreme end of the other whisker that you have from the end of the rectangular box to your far right.

The median value is indicated by the vertical line that divides the rectangular box into 2.

The lower quartile is indicated at the beginning of the rectangular box, while the upper quartile is located at the end of the rectangular box.

Answer:

answer D

Step-by-step explanation:

Lets have a look to the graph and to the  each of given functions.

As we can see in graph it intersects X in points (-3;0) and (-6;0) that means the function has the roots x1=-3 and x2=-6

Function A  has the roots x1=+3 and x2=+6 => doesn' t fit

Function B has only 1 root x=2 , so can be factorized y=(x-2)^2 => doesn' t fit

Function C has 2 roots  x1=4  and x2=-5 => doesn' t fit

Function D can be factotized as y=(x+6)*(x+3) so has 2 roots x1=-6 x2=-3 => exactly what we need!!!

We can also notice that the coefficient near x²  is equal to 1  and is positive.

That means the legs of the graph directed up,- this is exactly like in our graph. It gives us extra argument why we choose D.

Answer:

200 N/m

Step-by-step explanation:

Rearranging the formula F = kx, you find that k = F/x. For the first spring,

F = 36 N and x = 0.06 m (6 cm). So the spring constant, F/x, is 36N/0.06m = 600 N/m

For the second spring, F = 36 N and x = 0.09 m. F/x = 36N/0.09m = 400 N/m

The difference between these values is 200 N/m, and that's the answer.

Answer:

6

Step-by-step explanation:

10 - 4 = 6

16 - 10 = 6

22 - 16 = 6

Answer:6

Step-by-step explanation:

1) 10-4=6

2) 16-10=6

3) 22-16=6

Answer:

Step-by-step explanation:

To find the length of BC we use tan

tan ∅ = opposite / adjacent

From the question

AC is the opposite

BC is the adjacent

So we have

tan 61 = AC / BC

tan 61 = 47/BC

BC = 47/tan 61

Hope this helps you

Step-by-step explanation:

a. z = 5.5

25 ^( 5.5 - 4 ) = 125

25 ^ (1.5) = 125

125 = 125

z = 5.5

PlZzzzz follow me

Answer:

its 14/C

Step-by-step explanation:

i got i right on edg U^U

Answer:

16

Step-by-step explanation:

i did edge test yea dont  be imma fake :***    

Answer:

you will start to ascend at the rate of 1.6

Step-by-step explanation:

Walking south, it's the negative part of a coordinate, so the unit vector at this point is; u = (0,-1)

We are told that the equation z = 1600 − 0.005x² − 0.01y²

Therefore, we have;

∇z = ((δ/δx)i + (δ/δx)j)(1600 − 0.005x² − 0.01y²)

This gives;

∇z = -0.005(2x)i - 0.01(2y)j

∇z = <-0.01x - 0.02y>

coordinates are (120, 80, 1464).

Thus;

∇z(120, 80, 1464) = <-0.01(120), - 0.02(80)> = <-1.20, -1.60>

D_uf = <-1.20, -1.60> × <0, - 1>

D_uf = 0 + 1.6

D_uf = 1.6

So, you will start to ascend at the rate of 1.6

Answer:

undefined! one cannot divide by 0

Step-by-step explanation:

Answer:

undefined!

Step-by-step explanation:

Answer:

14.05

Step-by-step explanation:

We have the following:

Current Dividend = D0 = $ 1.40

g = growth rate = 2%

r = discount rate = 13%

Dividend in Year 5

= D5 = D0 * (1 + g) ^ 5

= $ 1.40 * (1 + 2%) ^ 5

= $ 1.40 * (1.02) ^ 5

Firm Stock Price at the end of year 4 = Dividend in Year 5 / (r - g)

= $ 1.40 * (1.02) ^ 5 / (13% -2%)

= $ 1.40 * (1.02) ^ 5 / (0.13 - 0.02)

Therefore, firm stock at the end of year 4 is

P4 = $ 1.40 * (1.02) ^ 5 / (0.13 - 0.02) = 14.05

Answer:

-21/5 = -4.2

Step-by-step explanation:

-21.87 / 4.79 = -4.5657.....

So, the quotients is -4

Now, Let's see who's quotient is equal to think one:

-21/4 = -5.25

-21/5 = -4.2

-40/4 = -5

-20/5 = 4

Answer:

-21/5 = -4.2

Step-by-step explanation:

Answer:

83.0

Step-by-step explanation:

We have all three sides and the only thing we're missing is the X angle. And that's okay!

All you have to do is plug in the numbers into each variable. In this case if you are going to solve for X, you should use this equation.

[tex]x^2=y^2+z^2-2yzcosX[/tex]

x = 17ft

y = 8ft

x = 16fi

Then you can algebraically solve for cosX, and then use the inverse of cosx to get the angle.

Answer:

[tex]\Large \boxed{\sf \ \ 4\sqrt{a^2+b^2} \ \ }[/tex]

Step-by-step explanation:

Hello,

You can use Pythagoras in the 4 right triangles.

For one triangle it comes [tex]\sqrt{a^2+b^2}[/tex].

Then for the polygon it gives [tex]4\cdot \sqrt{a^2+b^2}[/tex].

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

-3x^2 -5x +2

Step-by-step explanation:

-2x(x+3)-(x+1)(x-2)=

Distribute

-2x^2 -6x  -(x+1)(x-2)

Foil

-2x^2 -6x  -(x^2 -2x +x -2)

Combine like terms

-2x^2 -6x  -(x^2 -x  -2)

Distribute the minus sign

-2x^2 -6x  -x^2  +x +2

Combine like terms

-2x^2  -x^2  -6x +x +2

-3x^2 -5x +2

Answer:

[tex]\huge\boxed{-2x(x+3)-(x+1)(x-2)=-3x^2-5x+2}[/tex]

Step-by-step explanation:

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

Use the distributive property: a(b + c) = ab + ac

and FOIL: (a + b)(c + d) = ac + ad + bc + bd

[tex]=(-2x)(x)+(-2x)(3)-\bigg[(x)(x)+(x)(-2)+(1)(x)+(1)(-2)\bigg]\\\\=-2x^2-6x-\bigg(x^2-2x+x-2\bigg)=-2x^2-6x-x^2-(-2x)-x-(-2)\\\\=-2x^2-6x-x^2+2x-x+2[/tex]

Combine like terms:

[tex]=(-2x^2-x^2)+(-6x+2x-x)+2=-3x^2+(-5x)+2\\\\=-3x^2-5x+2[/tex]

Answer:

Step-by-step explanation:

a) Given cos2theta=28/53 and 0degrees< theta < 90degrees

From cos2theta=28/53

[tex]2\theta = cos^{-1}\frac{28}{53}[/tex]

[tex]2\theta = cos^{-1}0.5283\\ \\2\theta = 58.12\\\\Dividing\ both \ sides\ by \ 2\\\\\frac{2\theta}{2} = \frac{58.12}{2}\\ \\\theta = 29.06^0[/tex]

b) Given

[tex]sin\theta = \frac{-\sqrt{7} }{5} \\\\\theta = sin^{-1} \frac{-\sqrt{7} }{5}\\\\\\\theta = sin^{-1} \frac{-2.6458}{5}\\\\\theta = sin^{-1} -0.5292\\\\\theta = -31.95^0[/tex]

If cos theta [tex]\gneq[/tex] 0, this means we need to look for the quadrant where sin is negative and cos is positive. That will be the fourth quadrant. In the fourth quadrant, theta = 360 - 31.95° = 328.05°

2theta = 2 * 328.05

2theta = 656.1°

c) Given tan x=2 and cos x<0, lets find the angle of x first.

If tan x = 2

x = tan^-1 2

x = 63.4°

Sine cos is less than 0, then we need to find the angle of x where tan is positive and cos is negative. That will be the third quadrant. In the third quadrant, ew value of x = 180+63.4

x = 243.4°

Since we are to find 2x,

2x = 2(243.4)

2x = 486.8°

Answer:

Step-by-step explanation:

children=c

adults=a

c+a=359

a=359-c

2.75c+6a=1621

2.75  c+6(359-c)=1621

2.75 c+2154-6c=1621

-3.25 c=1621-2154

-3.25 c=-533

[tex]-\frac{325}{100} c=-533\\-\frac{13}{4} c=-533\\c=-533 \times \frac{-4}{13} =41 \times 4=164 \\children=164\\adults=359-164=195[/tex]

Notice that C has a clockwise orientation. By Green's theorem, we have

[tex]\displaystyle\int_C\mathbf F(x,y)\cdot\mathrm d\mathbf r=-\iint_D\left(\frac{\partial(xy+x\cos x)}{\partial x}-\frac{\partial(y\cos x-xy)}{\partial y}\right)\,\mathrm dx\,\mathrm dy[/tex]

where D is the triangule region with C as its boundary, given by the set

[tex]D=\{(x,y)\mid0\le x\le2\land0\le y\le8-4x\}[/tex]

So we have

[tex]\displaystyle\int_C\mathbf F(x,y)\cdot\mathrm d\mathbf r=-\int_0^2\int_0^{8-4x}((y+\cos x-x\sin x)-(\cos x-x\sin x))\,\mathrm dy\,\mathrm dx[/tex]

[tex]\displaystyle\int_C\mathbf F(x,y)\cdot\mathrm d\mathbf r=-\int_0^2\int_0^{8-4x}y\,\mathrm dy\,\mathrm dx=\boxed{-\dfrac{64}3}[/tex]