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3 years ago

2x + 3y= 22 -2x +5y=-6

Mathematics

1 answer:

sasho [114]3 years ago

5 0

The solution is x = 8 and y = 2

<em><u>Solution:</u></em>

<em><u>Given are the system of equations</u></em>

2x + 3y = 22 -------- eqn 1

-2x + 5y = -6 ----- eqn 2

We can solve the system of equations by elimination method

Eqn 1 + Eqn 2

2x + 3y -2x + 5y = 22 - 6

0x + 3y + 5y = 16

8y = 16

Divide both sides of equation by 8

Substitute y = 2 in eqn 1

2x + 3(2) = 22

2x = 22 - 6

2x = 16

Thus the solution is x = 8 and y = 2

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In a company, 37% of 1500 employees are females.work out the number of males in the company.

a_sh-v [17]

Formula:

$y = p\% \times x$
$p = 37\% \div 100 = 0.37$
$y = 0.37 \times 1500 = 555$
so there are 555 woman working.
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3 years ago

A survey found that women's heights are normally distributed with mean 63.2 in. and standard deviation 2.4 in. The survey also

Effectus [21]

Answer: 99.51%

Step-by-step explanation:

Given : A survey found that women's heights are normally distributed.

Population mean : $\mu =63.2 \text{ inches}$

Standard deviation: $\sigma= 2.4\text{ inches}$

Minimum height = 4ft. 9 in.= $4\times12+9\text{ in.}=57\text{ in.}$

Maximum height = 6ft. 2 in.= $6\times12+2\text{ in.}=74\text{ in.}$

Let x be the random variable that represent the women's height.

z-score : $z=\dfrac{x-\mu}{\sigma}$

For x=57, we have

$z=\dfrac{57-63.2}{2.4}\approx-2.58$

For x=74, we have

$z=\dfrac{74-63.2}{2.4}\approx4.5$

Now, by using the standard normal distribution table, we have

The probability of women meeting the height requirement :-

$P(-2.58$

Hence, the percentage of women meeting the height requirement = 99.51%

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3 years ago

Shuan rides his bike at a speed of 19 mph how far in miles is shuan travel in 25 minutes

irga5000 [103]

Answer:

7.92 miles (aprox.)

Step-by-step explanation:

1 hour = 60 minutes

19mph = 19miles/hour = 19miles/60 minutes

Proportions:

19 miles ⇔ 60 minutes

W miles ⇔ 25 minutes

W = 19*25/60

W = 7.92 miles (aprox)

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2 years ago

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3 years ago

Read 2 more answers

A clothing store has a going-out-of business sale. They are selling pants for $8.99 and shirts for $3.99. You can spend as much

astraxan [27]

Answer:

Let x represents the number of pants and y represents the number of shirts.

As per the statement:

Since, a clothing store are selling pants for $8.99 and shirts for $3.99

then;

total number of Pants cost is, $8.99x and total number of Shirt cost is, $3.99

Also, it is given that: You can spend as much as $60 and want to buy at least two pairs of pants.

then, we have the equation of inequality;

$8.99x + 3.99y \leq 60$ ;......[1] where x, y are natural number.

x-intercept:

Substitute the value y= 0 in [1] and solve for x;

$8.99x + 3.99(0) \leq 60$

$8.99x \leq 60$

Simplify:

$x \leq 6.667$

Since, x is in natural number;

$x \leq 7$

Similarly.

For y-intercept:

Substitute the value x= 0 in [1] and solve for x;

$8.99(0) + 3.99y \leq 60$

$3.99y \leq 60$

Simplify:

$y \leq 15.037$

$y \leq 15$

Therefore, we have

$8.99x + 3.99y \leq 60$ ;

$2\leq x\leq 7$ and $0\leq y\leq 15$

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2 years ago