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3 years ago

Icated (Q#1-4). 2. Solve by substitution; x+3y + 4) 3x - 5y = 8 3 (3x+4) aytla

Mathematics

1 answer:

puteri [66]3 years ago

4 0

Answer:

See explanation

Step-by-step explanation:

Assuming your system is:

$x + 3y = 4$

$3x - 5y = 8$

Then make x the subject in the first equation to get:

$x = 4 - 3y$

Put this equation into the second equation to get:

$3(4 - 3y) - 5y = 8$

$12 - 9y - 5y = 8$

$- 9y - 5y = 8 - 12$

$-14y = - 4$

$y = \frac{ - 4}{ - 14} = \frac{2}{7}$

This means that:

$x = 4 - 3 \times \frac{2}{7}$

$x = 4 - \frac{6}{7} = \frac{22}{7}$

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How many solutions does the equation have?

Andreyy89

Answer:

Since it is a linear equation, it has one solution.

step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Is x + 10 a factor of the function f(x) = x3 − 75x + 250? Explain.

PtichkaEL [24]

Yes. When the function f(x) = x3 – 75x + 250 is divided by x + 10, the remainder is zero. Therefore, x + 10 is a factor of f(x) = x3 – 75x + 250.

According to the remainder theorem when f(x) is divided by (x+a) the remainder is f(-a).
In this case,
f(x)=x^3-75x+250
(x+a)=(x+10)
Therefore, the remainder f(-a)=f(-10)

=x^3-75x+250
=(-10)^3-(75*-10)+250
=-1000+750+250
=1000-1000
=0.
The remainder is 0. So, (x+10) is a factor of x^3-75x+250.

8 0

3 years ago

Chose 1 answer:<br> A. 5.4<br> B. 5-4<br> C. 4/5<br> D. 5/4

umka2103 [35]

Answer:

D. 5/4

Step-by-step explanation:

A. 5.4 can't be 'cause the shade did not reach 5 on number line.

B. 5 - 4 = 1 can'e be 'cause it pass 1.

C. 4 / 5 = 0.8 can't be 'cause its less than the shade.

D. 5 / 4 = 1.25 correct

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3 years ago

Genetic Defects Data indicate that a particular genetic defect occurs in of every children. The records of a medical clinic show

Dovator [93]

Complete Question

The complete question is shown on the first uploaded image

Answer:

The probability that there exist 60 or more defected children is $P(x \ge 60)=0.0901$

Looking at the value for this probability we see that it is not so small to the point that the observation of this kind would be a rare occurrence

Step-by-step explanation:

From the question we are told that

in every 1000 children a particular genetic defect occurs to 1

The number of sample selected is $n= 50,000$

The probability of observing the defect is mathematically evaluated as

$p = \frac{1}{1000}$

$= 0.001$

The probability of not observing the defect is mathematically evaluated as

$q = 1-p$

$= 1-0.001$

$= 0.999$

The mean of this probability is mathematically represented as

$\mu = np$

Substituting values

$\mu = 50000*0.001$

$= 50$

The standard deviation of this probability is mathematically represented as

$\sigma = \sqrt{npq}$

Substituting values

$= \sqrt{50000 * 0.001 * 0.999}$

$= \sqrt{49.95}$

$= 7.07$

the probability of detecting $x \ge60$ defects can be represented in as normal distribution like

$P(x \ge 60)$

in standardizing the normal distribution the normal area used to approximate $P(x \ge 60)$ is the right of 59.5 instead of 60 because x= 60 is part of the observation

The z -score is obtained mathematically as

$z = \frac{x-\mu }{\sigma }$

$= \frac{59.5 - 50 }{7.07}$

$=1.34$

The area to the left of z = 1.35 on the standardized normal distribution curve is 0.9099 obtained from the z-table shown z value to the left of the standardized normal curve

Note: We are looking for the area to the right i.e 60 or more

The total area under the curve is 1

$P(x \ge 60) \approx P(z > 1.34)$