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OLEGan [10]
3 years ago
12

Use the distributive property to find an expression that is equivalent to 2x(x + 7)-(3x +1)

Mathematics
1 answer:
zaharov [31]3 years ago
7 0

Given expression:

     2x(x + 7)-(3x +1);

To distribute implies to spread a process equally in an expression. Often times, the distributive property is used for expressions inside parentheses;

  2x(x + 7)-(3x +1)  

  Distribute 2x over the first parentheses;

   the negative sign distributes over the second part

    = (2x² + 14x)  - 3x -1

    = 2x² + 14x -3x -1

    Add like terms;

    = 2x² + 11x -1

This expression  2x² + 11x -1 is equal to the given one

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3 years ago
Two 5-year girls, Alyse and Jocelyn, have been training to run a 1-mile race. Alyse's 1 mile time A is approximately Normally di
tatyana61 [14]

Answer:

1.7 × 10⁻⁴

Step-by-step explanation:

The question relates to a two sample z-test for the comparison between the means of the two samples  

The null hypothesis is H₀:  μ₁ ≤ μ₂

The alternative hypothesis is Hₐ: μ₁ > μ₂

z=\dfrac{(\bar{x}_1-\bar{x}_2)-(\mu_{1}-\mu _{2} )}{\sqrt{\dfrac{\sigma_{1}^{2} }{n_{1}}-\dfrac{\sigma _{2}^{2}}{n_{2}}}}

Where;

\bar {x}_1 = 13.5

\bar {x}_2 = 12

σ₁ = 2.5

σ₂ = 1.5

We set our α level at 0.05

Therefore, our critical z = ± 1.96

For n₁ = n₂ = 23, we have;

z=\dfrac{(13.5-12)-(0)}{\sqrt{\dfrac{2.5^{2} }{23}-\dfrac{1.5^{2}}{23}}} = 3.5969

We reject the null hypothesis at α = 0.05, as our z-value, 3.5969 is larger than the critical z, 1.96 or mathematically, since 3.5969 > 1.96

Therefore, there is enough statistical evidence to suggest that Alyse time is larger than Jocelyn in a 1 mile race on a randomly select day and the probability that Alyse has a larger time than Jocelyn is 0.99983

Therefore;

The probability that Alyse has a smaller time than Jocelyn is 1 - 0.99983 = 0.00017 = 1.7 × 10⁻⁴.

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3 years ago
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Answer:

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Step-by-step explanation:

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3 years ago
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3 years ago
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