on solving x/2 +5/3=_1/2 we get x=​

PROOF:

[tex]y^4-(y^2-9)(y^2+9)\\=y^4 -(y^4-81)\\=y^4-y^4+81\\=81[/tex]

And 81 is ALWAYS divisible by 9

Answer:

Its 9*9

Step-by-step explanation:

The equation equals 81 and 9*9=81.

Have a great day! :)

Answer:

3

Step-by-step explanation:

8-(3a+8)

8-(11a)

8-11a

a=11-8

a=3

Answer:

0

Step-by-step explanation:

8-(3a+8)=0

8-3a-8=0

-3a=0

a=0

Answer:

D

Step-by-step explanation:

shifting 4 units to the right means that the new root = old root + 4

what that means is that the equation must have a transformation such that it equates to 0 with the root being 4 larger.

the root/vertex for x^4 is at x=0

we want the root to be at x=4

so that means we can subtract 4 from x

and get (x-4)^4

Answer:

The answer would 177.06 centimeters

Answer19/40=x/3.6

By cross multiplication

19*3.6=40*x

68.4 =40x

x=68.4/40

x=1.71

x=

Answer: C

Step-by-step explanation:

[tex]\frac{19}{40} = \frac{x}{3.6}[/tex]     solve by cross product

40x = 68.4   Divide both sides by 40

x =  1.71

Answer:

8x/5

There’s a 1 in front of the x also remember to always simplify

3/5x + 1x

Answer:8x/5

Step-by-step explanation:

Answer:

73 mph

Step-by-step explanation:

The question seems to be incomplete because the model is missing, I found a similar question with the addition of the model, so if we can solve it (see attached image).

We have that the model would be:

y = 43.81 - 0.395 * x

We need to solve for x, if y = 15

Replacing:

15 = 43.81 - 0.395 * x

Solving for x we have:

0.395 * x = 43.81 - 15

0.395 * x = 28.81

x = 28.81 / 0.395

x = 72.9

We are asked to round to the nearest number therefore x = 73.

The car will average 15 miles per gallon at the speed of 73 miles per hour.

Answer:

difference in area = 16 ft²

if you use 8 the difference in length between Jack patio and his neighbor patio will be will be 15 - 13 = 2 ft

if you use 13 the difference i length will be 25 - 18 = 7 ft

Step-by-step explanation:

Jacks rectangular patio

width = a

length = 2a - 1

area = lw

where

l = length

w = width

area = 120 ft²

a(2a - 1)

2a² - a - 120 = 0

(a - 8) (2a + 15)

a = 8 or -15/2

Ron's rectangular patio

width = a

length = a + 5

area = lw

area = 104 ft²

a (a + 5) = 104

a² + 5a -104 = 0

(a + 8)  (a - 13)

a = -8 or 13

How many square feet longer is jack patio longer than Ron's patio is the difference in their area. Therefore,

120 - 104 = 16 ft²

The value 8 or 13 can be used for a since the width a have to be the same.

if you use 8 the difference in length between Jack patio and his neighbor patio will be will be 15 - 13 = 2 ft

if you use 13 the difference i length will be 25 - 18 = 7 ft

Answer:

Step-by-step explanation:

Idk

Answer:

£149.5

Step-by-step explanation:

[tex]100 + 15 = 115\\115/100 = 1.15\\130 * 1.15 = 149.5[/tex]

Answer:

if you go around a track one time thats 400 meters but if you go around 4 times thats 1600 meters, you dont need to use 3.14 pi for this " no offense", i do track and field myself and i do the short distance, which is 100 meters and 200 meter but for for long distance runners they go around the track 4- 8 times so it is 1600 meters is ur answer. and when u go around 8 times, thats 3200 meters.

Step-by-step explanation:

Answer:

(a) Probability distribution is prepared below.

(b) The probability that two or fewer heads are observed in three tosses is 0.875.

(c) The probability that at least one head is observed in three tosses is 0.875.

(d) The expected value of X is 1.5.

(e) The standard deviation of X is 2.121.

Step-by-step explanation:

The complete question is: A fair coin is tossed three times. Let X be the number of heads observed in three tosses of this fair coin.

(a) Find the probability distribution of X.

(b) Find the probability that two or fewer heads are observed in three tosses. (Round your answer to three decimal places.)

(c) Find the probability that at least one head is observed in three tosses. (Round your answer to three decimal places.)

(d) Find the expected value of X. (Round your answer to one decimal place.)

(e) Find the standard deviation of X. (Round your answer to three decimal places.)

Now, firstly the sample space obtained in three tosses of a fair coin is given as;

Sample Space (S) = {HHH, HHT, HTH, THH, HTT, TTH, THT, TTT}

(a) The Probability distribution of X is given below;

   Number of Heads (X)         P(X)            [tex]X \times P(X)[/tex]               [tex]X^{2} \times P(X)[/tex]

              0                               [tex]\frac{1}{8}[/tex] = 0.125            0                           0

              1                                [tex]\frac{3}{8}[/tex] = 0.375         0.375                     0.375  

              2                               [tex]\frac{3}{8}[/tex] = 0.375         0.75                          3

              3                               [tex]\frac{1}{8}[/tex] = 0.125          0.375                    3.375

           Total                                                    1.5                        6.75          

(b) The probability that two or fewer heads are observed in three tosses is given by = P(X [tex]\leq[/tex] 2)

      P(X [tex]\leq[/tex] 2) = P(X = 0) + P(X = 1) + P(X = 2)

                     = 0.125 + 0.375 + 0.375

                     = 0.875

(c) The probability that at least one head is observed in three tosses is given by = P(X [tex]\geq[/tex] 1)

      P(X [tex]\geq[/tex] 1) =  1 - P(X = 0)

                    =  1 - 0.125

                    =  0.875

(d) The expected value of X = E(X) =  [tex]\sum (X \times P(X))[/tex]

                                                              =  1.5

(e) The Variance of X = V(X) = [tex]E(X^{2} ) - ( E(X))^{2}[/tex]

                                      =  [tex]\sum (X^{2} \times P(X))- (\sum (X \times P(X)))^{2}[/tex]

                                      =  [tex]6.75 - 1.5^{2}[/tex]  = 4.5

Now, Standard deviation of X = [tex]\sqrt{V(X)}[/tex]

                                                  = [tex]\sqrt{4.5}[/tex]  = 2.121.

I apologize, I am stumped... I thought you would find either the centroid, circumcenter, or incenter of the triangle created but it didn't work quite right for me.

Answer:

6

Step-by-step explanation:

Let's call the number of pairs of socks he buys s.

[tex]12.50+2.50s=27.50[/tex]

Subtract 12.50 from both sides:

[tex]2.50s=15[/tex]

Divide both sides by 2.5 to isolate s:

[tex]s=6[/tex]

Hope this helps!

Answer:

13

Step-by-step explanation:

I think

Answer:

ofn

Step-by-step explanation:

Answer:

Step-by-step explanation:

Since there are 44 average people out of 80. We can do this,

Total students : 600

Checked: 80

Average: 44

Number of averaged throughout the school: 600/80 * 44

                                                                        l: 7.5 * 44

Thus it is: 330 average students

Answer:

Step-by-step explanation:

[tex]2xsin(2y)dx-(x^2+10) cosy dy =0\\\\\frac{2x}{x^2 + 10}dx= \frac{cosy}{sin(2y)}[/tex]

Take integration both side (apply substitution for the left hand side, apply sin(2y) = 2 sin(y) cos(y) for the right hand side) you will have the condition.

Problem solved

Answer:

a) [tex]t=\frac{18.4-17.5}{\frac{2.2}{\sqrt{45}}}=2.744[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=45-1=44[/tex]  

The critical value for this case is [tex]t_{\alpha}=1.68[/tex] since the calculated value is higher than the critical we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 18.4

b) [tex]p_v =P(t_{(44)}>2.744)=0.0044[/tex]  

Step-by-step explanation:

Information given

[tex]\bar X=18.4[/tex] represent the sample mean

[tex]s=2.2[/tex] represent the sample standard deviation

[tex]n=45[/tex] sample size  

[tex]\mu_o =17.5[/tex] represent the value to verify

[tex]\alpha=0.05[/tex] represent the significance level

t would represent the statistic

[tex]p_v[/tex] represent the p value

Part a

We want to test if the true mean is higher than 17.5, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \leq 17.5[/tex]  

Alternative hypothesis:[tex]\mu > 17.5[/tex]  

The statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

And replacing we got:

[tex]t=\frac{18.4-17.5}{\frac{2.2}{\sqrt{45}}}=2.744[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=45-1=44[/tex]  

The critical value for this case is [tex]t_{\alpha}=1.68[/tex] since the calculated value is higher than the critical we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 18.4

Part b

The p value would be given by:

[tex]p_v =P(t_{(44)}>2.744)=0.0044[/tex]  

Answer:

\sqrt(12) hope this helped.

Answer:

C =81.64 cm

Step-by-step explanation:

The circumference of a circle is given by

C = 2*pi*r

C = 2 * 3.14 * 13

C =81.64 cm

_______________________________

Radius(r)=13 cm

Circumference of circle=?

Now,

Circumference of circle=2 pi r

=2*3.14*13

=81.64 cm

Hope it helps..

Good luck on your assignment

________________________________

Answer:

The vector equation in terms of v1 and v2 is x₁v₁ +x₂v₂ = [296 2454]

Step-by-step explanation:

Solution

The aim is to write down a vector equation in terms of v1 and v2, when solution gives the number of days each mine should operate in order to produce 296 tons of copper and 2454 kilograms of silver.

Thus,

Suppose that b = [ 296 2454] is the corresponding vector which is representing the total needed output.

Now,

If the company operates mine 1 for x1 days and mine​ #2 for x2 days

Then,

The total output becomes x₁v₁ +x₂v₂ which is the same output to  b = [296 2454]

Hence, x₁ and x₂ should be satisfactory to the needed vector equation x₁v₁ +x₂v₂ = [296 2454]

So, the vector equation becomes  x₁v₁ +x₂v₂ = [296 2454]

Answer:

 6x^2 -2x -6

Step-by-step explanation:

f(x) = 6x^2 -4

g(x) = 2x+2

f(x) - g(x) =  6x^2 -4 - (2x+2)

Distribute the minus sign

                   6x^2 -4 - 2x-2

Combine like terms

                  6x^2 -2x -6

Answer:

b

Step-by-step explanation:

6x^2

2x

-4+2=-2

[tex]1. \: (x - y) {2} \\ = {x}^{2} - 2xy + {y}^{2} \\ 2. \: (a + b) ^{2} \\ = {a}^{2} + 2ab + {b}^{2} \\ 3. \: (2x + 3y) ^{2} \\ = {(2x)}^{2} + 2.2x.3y + (3y) ^{2} \\ = {4x}^{2} + 12xy + {9y}^{2} \\ 4.(3x - 2y) ^{2} \\ = (3x) ^{2} - 2.3x.2y + (2y) ^{2} \\ = {9x}^{2} - 12xy + {4y}^{2} \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]

Answer:

a) x^2−2xy+y^2

b) a^2 -ab+b^2

c)4x^2+12xy+9y^2

d)9x^2 -12xy+4y^2

Step-by-step explanation:

a) x^2−2xy+y^2

b) a^2 -ab+b^2

c)4x^2+12xy+9y^2

d)9x^2 -12xy+4y^2

We rewrite (x-y)^2 as (x-y) (x-y) to show and always see + sign at start for question a ) and question b)

a) x*x+x(−y)−yx−y(−y) = x^2−2xy+y^2

b) a^2 becomes a^2 -ab as a^2 -ab+b^2

c) As shown in notes attached and this will help you most.

d) the reasons we keep +4y is because -2y becomes -2y-2y and creates a plus.

Answer:

The number of female faculty in the Department with a PhD is 8.

Step-by-step explanation:

There are 14 + 30 = 44 faculty members.

Of those, x are male and y are female.

Then

x + y = 44.

The number of female faculty who do not have a PhD is 10 more than the number of females who have a PhD.

y = z + w

z is the number of females with PhD.

w is the number of females without PhD.

w = z + 10

If a third of the male faculty in the Department have a PhD

[tex]\frac{x}{3} + z = 14[/tex]

Now, we can write all variables as functions of z, which is the number of female faculty in the Department with PhD.

The objective is:

To find z from the first equation, that is:

[tex]x + y = 44[/tex]

To do this, we have to write x and y as functions of z.

Writing x and y as functions z.

[tex]\frac{x}{3} + z = 14[/tex]

[tex]\frac{x}{3} = 14 - x[/tex]

[tex]x = 3(14 - z)[/tex]

[tex]x = 42 - 3z[/tex]

And

[tex]y = z + w[/tex]

In which

[tex]w = 10 + z[/tex]

So

[tex]y = z + 10 + z[/tex]

[tex]y = 2z + 10[/tex]

Replacing:

[tex]x + y = 44[/tex]

[tex]42 - 3z + 2z + 10 = 44[/tex]

[tex]-z + 52 = 44[/tex]

[tex]z = 52 - 44[/tex]

[tex]z = 8[/tex]

The number of female faculty in the Department with a PhD is 8.

Answer:

- 3 and 3

Step-by-step explanation:

To evaluate (u ￮ w)(- 1), evaluate w(- 1) then use this value to evaluate u(x)

w(- 1) = (- 1)² + 2 = 1 + 2 = 3, then

u(3) = - 3

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

To evaluate (w ￮ u)(- 1), evaluate u(- 1) then use this value to evaluate w(x)

u( - 1) = - (- 1) = 1, then

w(1) = 1² + 2 = 1 + 2 = 3

Answer:

(x,y)= (-124/27, 41/9)

Step-by-step explanation:

1) Add the equation to eliminate x.

5y+3x=9

4y-3x=32

2) Add 5y and 4y.

5y=9

4y=32 -->  9y=41

3) Get y by itself by dividing 9 on both sides:

y=41/9

4) Substitute Value in the equation 5y+3x=9

5(41/9)+3x=9

5) solve for x

x=-124/27

Step-by-step explanation:

5y + 3x = 9

4y - 3x = 32

using elimination method

subtracting equation 1 from 2 gives

y = -23

substitute to get value of X

5(-23) + 3X = 9

-115 +3x = 9

3x= 124

x = 41.33

3/4, 6/8, 9/12, 12/16 , 15/20, 18/24, 21/28, 24/32 , 27/36, 30/40, 33/44, 36/48 , 39/52, 42/56, 45/60, 48/64 , 51/68, 54/72, 57/76, 60/80, ect..

I hope this is what you are looking for :)

Answer:

(1,-7/2)

Step-by-step explanation:

The midpoint of (9,2)(-7,-9) is (1,-7/2)

Answer:

  27/8

Step-by-step explanation:

You seem to want to evaluate ...

  [tex]\dfrac{3a^{-3}b^2}{2a^{-1}b^0}[/tex]

I like to simplify the expression first, even though the order of operations would have you evaluate it as is.

  [tex]=\dfrac{3}{2}a^{-3-(-1)}b^{2-0}=\dfrac{3b^2}{2a^2}[/tex]

Substitute the given values for "a" and "b" and do the arithmetic.

  [tex]=\dfrac{3(-3)^2}{2(-2)^2}=\dfrac{3\cdot 9}{2\cdot 4}=\boxed{\dfrac{27}{8}}[/tex]