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3 years ago

Multiple choice please answer please

Mathematics

1 answer:

Gemiola [76]3 years ago

5 0

Answer:

C. $AC = \frac{3}{\tan 35\degree}$

Step-by-step explanation:

$\tan 35\degree= \frac{BC}{AC}\\\\\tan 35\degree= \frac{3}{AC}\\\\AC = \frac{3}{\tan 35\degree}$

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Two–thirds of the children in the fourth–grade class are girls. If there are 18 girls, what is the total number of children in t

RUDIKE [14]

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3 0

3 years ago

Read 2 more answers

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

A certain flight arrives on time 8484 percent of the time. Suppose 143143 flights are randomly selected. Use the normal approxim

Troyanec [42]

Answer:

a) P(x=108)=0.0020

b) P(x≥108)=0.9980

c) P(x<124)=0.7794

d) P(124≤x≤128)=0.1925

Step-by-step explanation:

We know the population proportion, that is p=0.84.

We take a sample of size n=143.

We will use the normal approximation to the binomial distribution to model this problem.

The mean and standard deviation of the normal approximation to the binomial distribution will be:

$\mu=np=143*0.84=120.12\\\\\sigma=\sqrt{np(1-p)}=\sqrt{143*0.84*0.16}=\sqrt{19.22}=4.38$

a) We have to calculate the probability that exactly 108 flights are on time.

As the normal distribution considers the random variable to be continous, we have to apply the continuity correction factor.

In this case, the probability of 108 flights on time can be calculated as P(107.5<x<108.5):

$P(x=108)=P(107.5$

b) Now we have to calculate that at least 108 flights are on time.

As the probability includes 108, the continuity factor will indicates that we calculate P(x>107.5). The z-value for x=107.5 has been already calculated in point a:

$P(x\geq108)=P(x>107.5)=P(z>-2.88)=0.9980$

c) We have to calculate the probability that fewer than 124 flights are on time. According to the continuity factor, we have to calculate the probability P(x<123.5), as the flight number 124 is not included in the interval.

$P(x$