Three fourths of a number increased by one equals what?

17) Solve the system as matrix equations using inverses. 17) A company produces three models of MP3 players, models A, B, and C.

Vinvika [58]

Answer:

Model A=30, Model B: 20, Model C: 45

Step-by-step explanation:

Let x be the amount of type A mp3 produced, and the amount of model B mp3's produced and z the amount of model C mp3 produced.

Since in total there are 303 hours for electronics work, then:

$3.2x+5.4y+2.2z=303$

Since in total there are 393 hours for assembly, then:

$2.8x+2.4y+5.8z=393$

Since in total there are 416 hours for quality assurance, then:

$4.4x+3.4y+4.8z=416$

Then, the linear system associated to the problem is

$3.2x+5.4y+2.2z=303\\2.8x+2.4y+5.8z=393\\4.4x+3.4y+4.8z=416$

with coefficient matrix $A=\left[\begin{array}{ccc}3.2&5.4&2.2\\2.8&2.4&5.8\\4.4&3.4&4.8\end{array}\right]$ and vector of constant terms $b=\left[\begin{array}{ccc}303\\393\\416\end{array}\right]$

Since the determinant of A is equal to 36.704 then A is invertible.

Then for solve the system $Ax=b$ , is enough find the inverse of A and operate

$Ax=b\\A^{-1}Ax=A^{-1}b\\x=A^{-1}b$

Using Octave we obtain that

$A^{-1}=\left[\begin{array}{ccc}-0.22&-0.50 &0.71\\0.33&0.15&-0.34\\-0.028& 0.35&-0.20\end{array}\right]$

Then

$x=A^{-1}b=\left[\begin{array}{ccc}30\\20\\45\end{array}\right]$

This means that 30 mp3's of model A, 20 of model B and 45 of model C must be produced

8 0

3 years ago

Suppose a family has a gross annual income of $39,600.

Natalka [10]

According to financial advisers,
* mortgage payment should be at most 28% of your gross monthly income
* total monthly debt should be at most 36% of your gross monthly income. Total monthly debts include mortgage payments, car payments, credit card bills, student loans, and medical debt.\

gross annual income: 39,600

gross monthly income: 39,600 / 12 = 3,300

a) maximum amount for monthly mortgage payment: 3,300 x 28% = 924

b) maximum amount for total credit obligations: 3,300 x 36% = 1,188

c) mortgage: 924 x 70% = 646.80 actual mortgage

1,188 - 646.80 = 541.20 maximum amount they could spend each month for all other debts.

8 0

3 years ago

Trigonometry Special Right Triangles Find the exact value of tan 30* + sin 90* + cot 60*.

fredd [130]

Answer:

1 + 2sqrt(3)/3

Step-by-step explanation:

tan(30) = sqrt(3)/3

sin(90) = 1

tan(60) = sqrt(3)

cot(60) = 1/sqrt(3) = sqrt(3)/3

sqrt(3)/3 + 1 + sqrt(3)/3

1 + 2sqrt(3)/3

3 0

3 years ago

C What is the missing hypotenuse length? * х 6 8

4vir4ik [10]

Step-by-step explanation:

By Pythagoras' Theorem, 6^2 + 8^2 = x^2.

x^2 = 36 + 64 = 100, x = 10.

7 0

3 years ago

Y + 8 = 2 i need help!!!!!

sergey [27]

Answer:

y = -6

Step-by-step explanation:

-6 + 8 = 2

3 0

3 years ago

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