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Tanzania [10]
3 years ago
12

Solve (10b+7b^2-6b^3)-(12b^2-3b^3)

Mathematics
1 answer:
MrRa [10]3 years ago
3 0

Answer:

-3b³ - 5b² + 10b

General Formulas and Concepts:

<u>Pre-Algebra</u>

  • Distributive Property

<u>Algebra I</u>

  • Combining Like Terms

Step-by-step explanation:

<u>Step 1: Define Expression</u>

(10b + 7b² - 6b³) - (12b² - 3b³)

<u>Step 2: Simplify</u>

  1. Distribute negative:                   10b + 7b² - 6b³ - 12b² + 3b³
  2. Combine like terms (b³):            -3b³ + 10b + 7b² - 12b²
  3. Combine like terms (b²):            -3b³ - 5b² + 10b
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A random sample of 20 recent weddings in a country yielded a mean wedding cost of $ 26,388.67. Assume that recent wedding costs
Makovka662 [10]

Answer:

a) 95% confidence interval for the mean​cost, μ​, of all recent weddings in this country = (22,550.95, 30,226.40)

.The​ 95% confidence interval is from $22,550.95 to $30,226.40.

b) For the interpretation of the result, option D is correct.

We can be​ 95% confident that the mean​ cost, μ​, of all recent weddings in this country is somewhere within the confidence interval.

c) Option B is correct.

The population mean may or may not lie in this​ interval, but we can be​ 95% confident that it does.

Step-by-step explanation:

Sample size = 20

Sample Mean = $26,388.67

Sample Standard deviation = $8200

Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample mean) ± (Margin of error)

Sample Mean = 26,388.67

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error of the mean)

Critical value will be obtained using the t-distribution. This is because there is no information provided for the population mean and standard deviation.

To find the critical value from the t-tables, we first find the degree of freedom and the significance level.

Degree of freedom = df = n - 1 = 20 - 1 = 19.

Significance level for 95% confidence interval

(100% - 95%)/2 = 2.5% = 0.025

t (0.025, 19) = 2.086 (from the t-tables)

Standard error of the mean = σₓ = (σ/√n)

σ = standard deviation of the sample = 8200

n = sample size = 20

σₓ = (8200/√20) = 1833.6

99% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]

CI = 26,388.67 ± (2.093 × 1833.6)

CI = 26,388.67 ± 3,837.7248

99% CI = (22,550.9452, 30,226.3948)

99% Confidence interval = (22,550.95, 30,226.40)

a) 95% confidence interval for the mean​cost, μ​, of all recent weddings in this country = (22,550.95, 30,226.40)

.The​ 95% confidence interval is from $22,550.95 to $30,226.40.

b) The interpretation of the confidence interval obtained, just as explained above is that we can be​ 95% confident that the mean​ cost, μ​,of all recent weddings in this country is somewhere within the confidence interval

c) A further explanation would be that the population mean may or may not lie in this​ interval, but we can be​ 95% confident that it does.

Hope this Helps!!!

4 0
3 years ago
A ramp is to be built beside the steps to the campus library. Find the angle of elevation of the 23​-foot ​ramp, to the nearest
Usimov [2.4K]

Answer:

the angle of elevation is 12.56°

Step-by-step explanation:

the height of the ramp represents the opposite side and the length of the ramp the hypotenuse

we see that it has (angle, hypotenuse, opposite)

well to start we have to know the relationship between angles, legs and the hypotenuse

a: adjacent

o: opposite

h: hypotenuse

sin α = o/h

cos α= a/h

tan α = o/a

we choose the one with opposite and hypotenuse

sin α = o/h

sin α = 5ft / 23ft

sin α = 5/23

α = sin^-1 ( 5/23)

α = 12.56°

the angle of elevation is 12.56°

3 0
3 years ago
What is the equation of the line which includes points (1, 1) and (1, 5)?
Allisa [31]
Equation of the line that includes points (1, 1) and (1, 5) is a vertical line given by x = 1.
6 0
3 years ago
I need an answer asap
bezimeni [28]

Answer:

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to solve the system of equations below, Becca isolated x^2 in the firs equation and then substituted it into the second equation
bija089 [108]

The resulting equation if Becca isolated x² in the first equation and then substituted it into the second equation is (9-y²) / 25 - y²/36 = 1

<h3>Equation</h3>

x² + y² = 9

x²/25 - y²/36 = 1

From (1)

x² = 9 - y²

substitute x² = 9 - y² into (2)

x²/25 - y²/36 = 1

(9-y²) / 25 - y²/36 = 1

Therefore, the resulting equation is option C; (9-y²) / 25 - y²/36 = 1

Learn more about equation:

brainly.com/question/4172455

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4 0
1 year ago
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