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2 years ago

Write in standard form 3.15x10^4

Mathematics

2 answers:

Alenkasestr [34]2 years ago

8 0

Your answer will be 31500

hope it helps

krok68 [10]2 years ago

4 0

Standard form would be 31500.

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A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 421 gram setting. It is

Anastaziya [24]

Answer:

The p-value is approximately 0.0508

Step-by-step explanation:

The given parameters are;

The expected mass of banana chips bag filled by the machine, μ = 421 gams

The number of bags in the sample of bags filled by the machine, n = 26 bags

The mean mass of the bags in the sample, $\overline x$ = 413 grams

The standard deviation of the mass in the bags, s = 24 grams

The level of significance, α = 0.02

The null hypothesis, H₀; μ = 421 grams

The alternative hypothesis, Hₐ; μ < 421 grams

The test statistic is given as follows;

$t=\dfrac{\bar{x}-\mu }{\dfrac{s}{\sqrt{n}}}$

We get;

$t=\dfrac{413-421 }{\dfrac{24}{\sqrt{26}}} \approx -1.6996731712$

The t-value = -1.6996731712

The degrees of freedom df = n - 1 = 26 - 1 = 25

From an online source, we get the critical-t = 2.166587

The p-value is obtained using an online source as p(t ≤ -1.6996731712) = 0.0508

From the p-value table, we get

0.05 < p < 0.1

3 0

2 years ago

What’s the domain and range of:<br> log(√(2x-1) + 3 )<br> Please explain how you got it too!!

Radda [10]

Two main facts are needed here:

1. The logarithm $\log x$ , regardless of the base of the logarithm, exists for $x>0$ .

2. The square root $\sqrt x$ exists for $x\ge0$ .

(in both cases we're assuming real-valued functions only)

By (2) we know that $\sqrt{2x-1}$ exists if $2x-1\ge0$ , or $x\ge\dfrac12$ .

By (1), we know that $\log(\sqrt{2x-1}+3)$ exists if $\sqrt{2x-1}+3>0$ , or $\sqrt{2x-1}>-3$ . But as long as the square root exists, it will always be positive, so this condition will always be met.

Ultimately, then, we only require $x\ge\dfrac12$ , so the function has domain $\left[\dfrac12,\infty)$ .

To determine the range, we need to know that, in their respective domains, $\sqrt x$ and $\log x$ increase monotonically without bound. We also know that $x=\dfrac12$ at minimum, at which point the square root term vanishes, so the least value the function takes on is $\log3$ . Then its range would be $[\log3,\infty)$ .