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faltersainse [42]
2 years ago
13

The length of a living room is 12 feet and its width is 10.5 feet. The length of the room is being expanded by x feet.

Mathematics
1 answer:
I am Lyosha [343]2 years ago
3 0

Answer:

A) A= 10.5(12 +x)

B) A= 10.5x +126

Step-by-step explanation:

A) Length of living room= 12 ft

Width= 10.5 ft

Since the length expanded by x ft,

New length of living room= (12 +x) ft

Area= length ×width

Let the new area of the living room be A ft².

A= 10.5(12+x)

B) To expand the expression, multiply 10 to each term and constant in the bracket on the right hand side of the equation.

A= 10.5(12 +x)

A= 10.5(12) +10.5x

A= 126 +10.5x

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Solve the system of equations using the substitution method.<br> -5x − 3y = 16<br> y = x
max2010maxim [7]

Answer:

-5x - 3x = 16

-8x = 16

x = -2

y = x

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
The Empirical Rule The following data represent the length of eruption for a random sample of eruptions at the Old Faithful geys
ad-work [718]

Answer:

(a) Sample Standard Deviation approximately to the nearest whole number = 6

(b) The use of Empirical Rule to make any general statements about the length of eruptions is empirical rules tell us about how normal a distribution and gives us an idea of what the final outcome about the length of eruptions is.

(c) The percentage of eruptions that last between 92 and 116 seconds using the empirical rule is 95%

(d) The actual percentage of eruptions that last between 92 and 116 seconds, inclusive is 95.45%

(e) The percentage of eruptions that last less than 98 seconds using the empirical rule is 16%

(f) The actual percentage of eruptions that last less than 98 seconds is 15.866%

Step-by-step explanation:

(a) Determine the sample standard deviation length of eruption.

Express your answer rounded to the nearest whole number.

Step 1

We find the Mean.

Mean = Sum of Terms/Number of Terms

= 90+ 90+ 92+94+ 95+99+99+100+100, 101+ 101+ 101+101+ 102+102+ 102+103+103+ 103+103+103+ 104+ 104+104+105+105+105+ 106+106+107+108+108+108 + 109+ 109+ 110+ 110+110+110+ 110+ 111+ 113+ 116+120/44

= 4582/44

= 104.1363636

Step 2

Sample Standard deviation = √(x - Mean)²/n - 1

=√( 90 - 104.1363636)²+ (90-104.1363636)² + (92 -104.1363636)² ..........)/44 - 1

= √(199.836777 + 199.836777 + 147.2913224+ 102.7458678+ 83.47314049+ 26.3822314+ 26.3822314+ 17.10950413+17.10950413+ 9.836776857+ 9.836776857, 9.836776857+9.836776857+ 4.564049585+ 4.564049585+ 4.564049585+ 1.291322313+ 1.291322313+ 1.291322313+ 1.291322313+ 1.291322313+ 0.01859504133+ 0.01859504133+ 0.01859504133+ 0.7458677685+ 0.7458677685+ 0.7458677685+ 3.473140497+ 3.473140497+ 8.200413225+ 14.92768595+ 14.92768595+ 14.92768595+ 23.65495868+ 23.65495868+ 34.38223141+ 34.38223141+34.38223141+ 34.38223141+ 34.38223141+47.10950414+ 78.56404959+ 140.7458677+ 251.6549586) /43

= √1679.181818/43

= √39.05073996

= 6.249059126

Approximately to the nearest whole number:

Mean = 104

Standard deviation = 6

(b) On the basis of the histogram drawn in Section 3.1, Problem 28, comment on the appropriateness of using the Empirical Rule to make any general statements about the length of eruptions.

The use of Empirical Rule to make any general statements about the length of eruptions is empirical rules tell us about how normal a distribution and gives us an idea of what the final outcome about the length of eruptions is .

(c) Use the Empirical Rule to determine the percentage of eruptions that last between 92 and 116 seconds.

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 = 104, Standard deviation = 6

For 68% μ - σ = 104 - 6 = 98, μ + σ = 104 + 6 = 110

For 95% μ – 2σ = 104 -2(6) = 104 - 12 = 92

μ + 2σ = 104 +2(6) = 104 + 12 = 116

Therefore, the percentage of eruptions that last between 92 and 116 seconds is 95%

(d) Determine the actual percentage of eruptions that last between 92 and 116 seconds, inclusive.

We solve for this using z score formula

The formula for calculating a z-score is is z = (x-μ)/σ

where x is the raw score, μ is the population mean, and σ is the population standard deviation.

Mean = 104, Standard deviation = 6

For x = 92

z = 92 - 104/6

= -2

Probability value from Z-Table:

P(x = 92) = P(z = -2) = 0.02275

For x = 116

z = 92 - 116/6

= 2

Probability value from Z-Table:

P(x = 116) = P(z = 2) = 0.97725

The actual percentage of eruptions that last between 92 and 116 seconds

= P(x = 116) - P(x = 92)

= 0.97725 - 0.02275

= 0.9545

Converting to percentage = 0.9545 × 100

= 95.45%

Therefore, the actual percentage of eruptions that last between 92 and 116 seconds, inclusive is 95.45%

(e) Use the Empirical Rule to determine the percentage of eruptions that last less than 98 seconds

The empirical rule formula:

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

For 68% μ - σ = 104 - 6 = 98,

Therefore, 68% of eruptions that last for 98 seconds.

For less than 98 seconds which is the Left hand side of the distribution, it is calculated as

= 100 - 68/2

= 32/2

= 16%

Therefore, the percentage of eruptions that last less than 98 seconds is 16%

(f) Determine the actual percentage of eruptions that last less than 98 seconds.

The formula for calculating a z-score is z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation.

For x = 98

Z score = x - μ/σ

= 98 - 104/6

= -1

Probability value from Z-Table:

P(x ≤ 98) = P(x < 98) = 0.15866

Converting to percentage =

0.15866 × 100

= 15.866%

Therefore, the actual percentage of eruptions that last less than 98 seconds is 15.866%

4 0
3 years ago
What is the value of the following expression?
monitta

The expression (−81)(−9)  will give the value of 729.

<u>Step-by-step explanation:</u>

The given expression is (−81)(−9) .

The both numbers in the expression are negative numbers and they are given inside the brackets.

This means that, the negative numbers must be multiplied to get a final value.

<u>The rules in multiplication are :</u>

  • Positive number × Positive number = positive number
  • Negative number × Positive number = negative number
  • Positive number × Negative number = negative number
  • Negative number × Negative number = positive number

From the rules, it can be determined that the result of any two negative numbers will be a positive number.

So, eliminate option A) and B) because they have negative sign.

The expression (−81)(−9) = -81 × -9

⇒ 729.

Therefore, the option C) and D) are not in match with 729. None of the options are not the value of the given expression (−81)(−9).

6 0
3 years ago
1/2x-2 <br> One half multiply negative 2
sattari [20]

Answer:

Step-by-step explanation:

11

5 0
2 years ago
Read 2 more answers
I need help with 12-14. One answer will get thanks. The highest amount of answers will get brainliest.
boyakko [2]
12. Make equation and plug in

13. Proportion

14. Finding a constant rate, and then manipulate




12. Where x is miles driven, and y is answer, and z is days
      19.95z+0.15x=y
      Plug in two values
      19.95 x 2 + 0.15 x 250 = y
      39.93+37.5 = y
      y=77.43

13. 5:2 as 175:x 
      5/2 = 175/x
      x = 70
      70+175=245

14. 260:5 = x:1
      260/5=x/1
      x = 52
      
      52:1 = y:9
      52/1 = y/9
      y = 468

I hope you understand the process.


7 0
3 years ago
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