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yKpoI14uk [10]
2 years ago
4

Solve the system of equations below x - y = 5 2x - 3y = 4

Mathematics
1 answer:
dusya [7]2 years ago
4 0

Answer:

x=11 y=6

Step-by-step explanation:

making x the subject in the first equation we get

x=y+5 put that in the second equation we also get

2(y+5)-3y=4

2y+10-3y=4

-y=4-10

-y=-6

y=6 use that to also find x from the equation x=y+5 we get

x=6+5

x=11

therefore x=11 y=6

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The lifespans of lions in a particular zoo are normally distributed. The average lion lives 12.512.512, point, 5 years; the stan
zaharov [31]

This question was not written properly

Complete Question

The lifespans of lions in a particular zoo are normally distributed. The average lion lives 12.5 years; the standard deviation is 2.4 years. Use the empirical rule (68-95-99.7\%)(68−95−99.7%) to estimate the probability of a lion living between 5.3 to 10. 1 years.

Answer:

Thehe probability of a lion living between 5.3 to 10. 1 years is 0.1585

Step-by-step explanation:

The empirical rule formula states that:

1) 68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ.

2) 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ.

3) 99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ.

Mean is given in the question as: 12.5

Standard deviation : 2.4 years

We start by applying the first rule

1) 68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ.

μ - σ

12.5 -2.4

= 10.1

We apply the second rule

2) 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ.

μ – 2σ

12.5 - 2 × 2.4

12.5 - 4.8

= 7.7

We apply the third rule

3)99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ.

μ - 3σ

= 12.5 - 3(2.4)

= 12.5 - 7.2

= 5.3

From the above calculation , we can see that

5.3 years corresponds to one side of 99.7%

Hence,

100 - 99.7%/2 = 0.3%/2

= 0.15%

And 10.1 years corresponds to one side of 68%

Hence

100 - 68%/2 = 32%/2 = 16%

So,the percentage of a lion living between 5.3 to 10. 1 years is calculated as 16% - 0.15%

= 15.85%

Therefore, the probability of a lion living between 5.3 to 10. 1 years

is converted to decimal =

= 15.85/ 100

= 0.1585

8 0
2 years ago
How to factor quadratics like <br> 2<br> 3x^+31x+36
anzhelika [568]

Answer:

3(x32+12)

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
Abel is making brownies for a bake sale. The recipe shows the amount of each ingredient needed to make 9 brownies. Complete each
mixas84 [53]

Answer:

In order to make 45 brownies, Abel needs 25 cups of flour, 20 cups of sugar, 10 cups of cocoa powder and 5 eggs.

Step-by-step explanation:

As the recipe is missing in this question, the recipe is found online which given following information

  • Abel needs 5 cups of flour to make brownies.
  • If Abel uses 4 cups of sugar.
  • he will need to use 2 cups of cocoa powder.
  • The recipe will make brownies if Abel uses only 1 egg.

Abel has to make 45 brownies for the sale, this is also missing in this question, however is given in the reference question linked here.

This recipe is to make 9 brownies. Now for 45 brownies the multiplier is found as 45/9=5. So by multiplying quantity of all the ingredients by 5, Abel will be able to make 45 brownies.

Now  in order to make 45 brownies

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  • If Abel uses 5*4=20 cups of sugar.
  • he will need to use 5*2=10 cups of cocoa powder.
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So in order to make 45 brownies, Abel needs 25 cups of flour, 20 cups of sugar, 10 cups of cocoa powder and 5 eggs.

5 0
2 years ago
Noah received a $500 signing bonus when he accepted a job as a paralegal. If he makes $28 an hour, which equation models Noah's
sveta [45]
A. Y= 28x + 500

The answer is A
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2 years ago
A sphere has a diameter of 14 ft. Which equation finds the volume of the sphere?
aev [14]

Answer:

The volume of the sphere is 1436 in³

The equation is    

V = ⁴⁄₃ * 3.14 * (7ft)³

Step-by-step explanation:

radius = half of diameter

d = 14ft

r = 14ft / 2 = 7ft

To calculate the volume of a sphere we have to use the following formula:

V = volume

r = radius  = 7ft

π = 3.14

V = ⁴⁄₃πr³

we replace with the known values

V = ⁴⁄₃ * 3.14 * (7ft)³

V = 4.187 * 343 in³

V = 1436 in³

The volume of the sphere is 1436 in³

6 0
2 years ago
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