Match each system of equations to the inverse of its coefficient matrix, A^-1and the matrix of its solution, X.

Answer:

0.7888 = 78.88% probability that the first machine produces an acceptable cork.

0.9772 = 97.72% probability that the second machine produces an acceptable cork.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

First machine:

Mean 3 cm and standard deviation 0.08 cm, which means that [tex]\mu = 3, \sigma = 0.08[/tex]

What is the probability that the first machine produces an acceptable cork?

This is the p-value of Z when X = 3.1 subtracted by the p-value of Z when X = 2.9. So

X = 3.1

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{3.1 - 3}{0.08}[/tex]

[tex]Z = 1.25[/tex]

[tex]Z = 1.25[/tex] has a p-value of 0.8944

X = 2.9

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{2.9 - 3}{0.08}[/tex]

[tex]Z = -1.25[/tex]

[tex]Z = -1.25[/tex] has a p-value of 0.1056

0.8944 - 0.1056 = 0.7888

0.7888 = 78.88% probability that the first machine produces an acceptable cork.

What is the probability that the second machine produces an acceptable cork?

For the second machine, [tex]\mu = 3.04, \sigma = 0.03[/tex]. Now to find the probability, same procedure.

X = 3.1

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{3.1 - 3.04}{0.03}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a p-value of 0.9772

X = 2.9

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{2.9 - 3.04}{0.03}[/tex]

[tex]Z = -4.67[/tex]

[tex]Z = -4.67[/tex] has a p-value of 0

0.9772 - 0 = 0.9772

0.9772 = 97.72% probability that the second machine produces an acceptable cork.

Answer:

Solution given:

B: 9x - 4/x^2 - 4

Step-by-step explanation:

.k

You will purchase some cds and dvds. If you purchase 13 cds and 5 dvds, it will cost you $96.70; if you purchase 5 cds and 12 dvds, it will cost you $134.50. Write and solve a system of equations to solve for the cost of each cd and the cost of each dvd.

Cost of cd = $3.72

Cost of dvd = $9.66

Let the cost of a cd be c

Let the cost of a dvd be d

From the second statement:

If you purchase 13 cds and 5 dvds, it will cost you $96.70

This means that

13c + 5d = 96.70            ----------------(i)

Also, from the third statement:

if you purchase 5 cds and 12 dvds, it will cost you $134.50

This means that;

5c + 12d = 134.50            ---------------------(ii)

The equations to solve are equations (i) and (ii)

13c + 5d = 96.70

5c + 12d = 134.50

Multiply the first equation by 5 and the second equation by 13. i.e

5 x (13c + 5d = 96.70)

13 x (5c + 12d = 134.50)

This will give

65c + 25d = 483.5

65c + 156d = 1748.5

Find the difference of the two equations

    65c + 25d = 483.5

-

    65c + 156d = 1748.5

    0   -  131d   = - 1265

This gives;

-131d = -1265

Divide both sides by -131

[tex]\frac{-131d}{-131} = \frac{-1265}{-131}[/tex]

d = 9.66

This means that the cost of a dvd which is d = $9.66

Now substitute the value of d = 9.66 into equation (i) as follows;

13c + 5(9.66) = 96.70  

Expand the above and solve for c

13c + 48.3 = 96.70

13c = 48.4

c = [tex]\frac{48.4}{13}[/tex]

c = 3.72

This means that the cost of a cd which is c = $3.72

Answer:

(0, -6)

Step-by-step explanation:

Given the following systems of linear equations;

3x - 2y = 12 ...... equation 1

16x - 4y = 24 ........ equation 2

We would solve for the solution using the elimination method;

Multiplying eqn 1 by 2, we have;

2 * (3x - 2y = 12)

6x - 4y = 24

16x - 4y = 24

Subtracting the two equations, we have;

(6x - 16x) + (-4y -[-4y]) = (24 - 24)

-10x - 0 = 0

-10x = 0

x = -0/10 = 0

Next, we would find the value of y;

3x - 2y = 12

3(0) - 2y = 12

0 - 2y = 12

-2y = 12

y = -12/2

y = -6

Check:

3x - 2y = 12

3(0) - 2(-6) = 12

0 - (-12) = 12

12 = 12

Note: the options provided for this questions are incorrect or inappropriate.

Answer:

maybe the answer is 63cm...

Answer:

[tex] \orange{ \bold{\frac{dy}{dx} =\frac{ 5{x}^{2} + 3 }{3\sqrt[3]{(1 + {x}^{2})^{2} } }}}[/tex]

Step-by-step explanation:

[tex]y = x \sqrt[3]{1 + {x}^{2} } \\ assuming \: log \: both \: sides \\log y = log(x \sqrt[3]{1 + {x}^{2} } ) \\ \therefore log y = logx + log(\sqrt[3]{1 + {x}^{2} } ) \\ \therefore log y = logx + \frac{1}{3} log({1 + {x}^{2} } ) \\ differentiating \: both \: sides \: w.r.t.x \\ \frac{1}{y} \frac{dy}{dx} = \frac{1}{x} + \frac{1}{3} . \frac{1}{(1 + {x}^{2}) } (0 + 2x) \\ \frac{1}{y} \frac{dy}{dx} = \frac{1}{x} + \frac{2x}{3(1 + {x}^{2}) }\\ \frac{1}{y} \frac{dy}{dx} =\frac{3(1 + {x}^{2}) + 2 {x}^{2} }{3x(1 + {x}^{2}) }\\ \frac{1}{y} \frac{dy}{dx} =\frac{3 + 3{x}^{2} + 2 {x}^{2} }{3x(1 + {x}^{2}) }\\ \frac{1}{y} \frac{dy}{dx} =\frac{3 + 5{x}^{2} }{3x(1 + {x}^{2}) }\\ \frac{dy}{dx} =\frac{y(3 + 5{x}^{2} )}{3x(1 + {x}^{2}) } \\ \\ \frac{dy}{dx} =\frac{x \sqrt[3]{1 + {x}^{2} } (3 + 5{x}^{2} )}{3x(1 + {x}^{2}) }\\ \\ \frac{dy}{dx} =\frac{(3 + 5{x}^{2} )\sqrt[3]{1 + {x}^{2} } }{3(1 + {x}^{2}) }\\ \\ \purple{ \bold{\frac{dy}{dx} =\frac{ 5{x}^{2} + 3 }{3\sqrt[3]{(1 + {x}^{2})^{2} } }}}[/tex]

Answer:

17

Step-by-step explanation:

12+5

Answer:

Step-by-step explanation:

The amount of money the store makes selling ice by the same ratio will be $340.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

As per the given,

The store sells 800 bags of ice, making $3,400.

Ratio = 3400/800

With the same ratio,

The store sells x amount of bags of ice,

x/80 = 3400/800

x = $340

Hence "The store will make $340 from selling ice using the same ratio".

For more information about ratios and proportions,

brainly.com/question/26974513

#SPJ2

Answer:

is there anymore to the question because this doesn't make sense

Step-by-step explanation:

Answer:

8. cos(58) = 20/x

x · cos(58) = 20

x = 20/cos(58)

= 37.742

≈ 37.7

9. tan(69) = 324/x

x · tan(69) = 324

x = 324/tan(69)

= 124.372

≈ 124.4

Answer:

Volume of cone = 686π/3 or 718.67 in³

Step-by-step explanation:

Given the following data;

Radius, r = 7 in

Height, h = 14 inches

From the diagram, we can see that the object is a cone

To find the volume of a cone;

Mathematically, the volume of a cone is given by the formula;

[tex] V = \frac{1}{3} \pi r^{2}h[/tex]

Where;

V is the volume of the cone.

r is the radius of the base of the cone.

h is the height of the cone.

Substituting into the equation, we have;

[tex] Volume = \frac{1}{3} * \frac {22}{7} *7^{2}*14 [/tex]

[tex] Volume = \frac{1}{3} * 22 * 7 * 14 [/tex]

[tex] Volume = \frac{1}{3} * 2156 [/tex]

[tex] Volume = 718.67 [/tex]

Volume of cone = 718.67 in³ or 686π/3 in³

Answer:

because i decided that

Step-by-step explanation:

Answer:

4.5

Step-by-step explanation:

18 divided by 4 equals 4.5

Answer:

Parent's share would be : 28%

Step-by-step explanation:

Cost of the computer = $2000

Anya's share = $1200

Brother's share = $240

Parents paid rest. That will be : 2000 - 1200 - 240 = $560

Percentage of parents share :

                                             [tex]\frac{560}{2000} \times 100 = 28 \%[/tex]

Answer:

1/4= 3/12 & 2/6 = 4/12

Step-by-step explanation:

Answer:

Its simply B

Step-by-step explanation:

If we are to express both ratios in their simplest form, we will have the ratio of Michael’s lemonade is 1:4 and that of Sondra is 1:3. The denominator that can be used in order to compare the ratios is that which can be divided by both ratios. For example, we have 12 as a denominator. The ratios can be expressed as 3/12 and 4/12. Also, the denominator can be 24 such that the ratios can be expressed as 6/24 and 8/24.

Answer:

0.872

Step-by-step explanation:

Given that :

P(cloudy) = P(C) = 0.94

P(cloudy and rainy) = P(C n R) = 0.82

Probability that a given day will be rainy if it is cloudy ; this is a conditional probability problem:

Recall ; P(A|B) = P(AnB) / P(B)

P(R|C) = P(C n R) / P(C) = 0.82 / 0.94 = 0.872

Answer:

[tex]a_5 = 120[/tex]

Step-by-step explanation:

Given

[tex]a_1 = 1[/tex]

[tex]a_n = n(a_{n-1})[/tex]

Required

[tex]a_5[/tex]

This is calculated as:

[tex]a_5 = 5(a_{5-1})[/tex]

[tex]a_5 = 5*a_4[/tex]

Calculate [tex]a_4[/tex]

[tex]a_4 =4(a_{4-1})[/tex]

[tex]a_4 =4*a_3[/tex]

Calculate [tex]a_3[/tex]

[tex]a_3 =3*a_2[/tex]

Calculate [tex]a_2[/tex]

[tex]a_2 = 2 * a_1[/tex]

[tex]a_2 = 2 * 1[/tex]

[tex]a_2 = 2[/tex]

So:

[tex]a_3 =3*a_2[/tex]

[tex]a_3 = 3 * 2 = 6[/tex]

So:

[tex]a_4 =4*a_3[/tex]

[tex]a_4 = 4 * 6 =24[/tex]

Lastly;

[tex]a_5 = 5*a_4[/tex]

[tex]a_5 = 5 * 24[/tex]

[tex]a_5 = 120[/tex]

Answer:

9.74418019cm=h

~ 9.7442

Step-by-step explanation:

volume of a cylinder=πr²h

radius=½of diameter

=½×140cm

=70cm

1l=1000cm³

150l=150l/1l×1000cm³

=150000cm³

150000cm³=π(70cm)²×h

150000cm³=15393.8040cm²h

150000cm³/15393.8040cm²=15393.8040cm²h/15393.8040cm²

150000cm³/15393.8040cm²=h

9.74418019cm=h

Answer:

slope of the line is 0

Step-by-step explanation:

given points are:

(-3 , 2)=(x1 , y1)

(4 , 2)=(x2 , y2)

slope =y2 - y1/x2 - x1

=2-2/4-(-3)

=0/4+3

=0/7

=0

Answer:

the ordered list is x, x+2, x+4, x+6, x+8, x+10

formula is Tn = 2n - 2

Answer:

338π

Step-by-step explanation:

[tex]2\pi rh+2\pi r^2[/tex]

[tex]2\pi *7*20+2\pi *7^2=240\pi +98\pi[/tex]

Answer:

x = 8

Step-by-step explanation:

m<PQR = (2x + 6)°

m<RPQ = (x - 7)°

m<QRS = (5x - 17)°

<PQR and <RPQ are interior angles opposite to the exterior angle <RPQ.

Therefore,

m<PQR + m<RPQ = m<QRS (Exterior Angle Theorem of a Triangle)

Substitute in the values

2x + 6 + x - 7 = 5x - 17

Add like terms

3x - 1 = 5x - 17

Collect like terms

3x - 5x = 1 - 17

-2x = -16

-2x/-2 = -16/-2

x = 8

The answer to this question is B) 44.78

Answer:

Step-by-step explanation:

x = 44.78

Answer:

x =74

Step-by-step explanation:

540 degrees is the sum of all the angles

90 +90 + 2x+10 + x + 2x-20 = 540

Combine like terms

5x+170=540

Subtract 170 from each side

5x = 370

Divide by 5

5x/5 = 370/5

x =74

Answer:

1)x=−3/5y+17/5  

2)x=−3/8y+−9/8

Step-by-step explanation:

Let's solve for x.

5x+3y=17

Step 1: Add -3y to both sides.

5x+3y+−3y=17+−3y

5x=−3y+17

Step 2: Divide both sides by 5.

5x/5=−3y+17/5

x=−3/5y+17/5

Answer:

x=−3/5y+17/5  

Let's solve for x.

−8x−3y=9

Step 1: Add 3y to both sides.

−8x−3y+3y=9+3y

−8x=3y+9

Step 2: Divide both sides by -8.

−8x/−8=3y+9/−8

x=−3/8y+−9/8

Answer:

x=−3/8y+−9/8

I HOPE THIS IS CORRECT IF NOT TELL ME AND ILL FIX IT.

Answer:

dh/dt =  0.4 m/min

Step-by-step explanation:

The volume of the cone is:

V(c) = (1/3)*r² *h              if always  h = 3r    then    r = h/3

The volume of the cone as a function of h will be:

V(h)  =  (1/3)* (h/3)²*h

V(h) =  (1/27)*h³

The increasing rate of the volume is equal to the rate of sand added the:

D(V)/dt   = (1/27)*3*h²*dh/dt

D(v) / dt  =  10 m³/min

h =  15 m      and   dh/dt is the rate of increasing of the height

By substitution

10 m³/min  = ( 1/9)* 225 * dh/dt  (m²)

dh/dt =  90 / 225   m/min

dh/dt =  0.4 m/min