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3 years ago

3t-7=5t, then what does 6t=

Mathematics

2 answers:

Gelneren [198K]3 years ago

8 0

$3t-7=5t \ \ \ \ \ \ \ \ \ |-3t \\
-7=2t \ \ \ \ \ \ \ \ \ \ \ \ |\times 3 \\
-21=6t \\ \\
\boxed{6t=-21}$

BartSMP [9]3 years ago

6 0

Subtract 3t from the equation to get 2t=-7. Multiply by three to find that 6t=-21.

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2 years ago

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Calcium is essential to tree growth because it promotes the formation of wood and maintains cell walls. In 2010, the concentrati

sergij07 [2.7K]

Answer:

The p-value obtained from the hypothesis test is greater than the significance level at which the test was performed, hence, we fail to reject the null hypothesis & say that there isn't enough evidence from the sample to conclude that the the calcium concentrations have changed since 2010.

Step-by-step explanation:

To perform this test, we need to first obtain the sample mean and sample standard deviation.

The data is 0.065 0.087 0.070 0.262 0.126 0.183 0.120 0.234 0.313 0.108

Mean = (sum of variables)/(sample size)

= (0.065+0.087+0.070+0.262+0.126+0.183+0.120+0.234+0.313+0.108)/10

= 0.1568 milligram per liter

Standard deviation = σ = √[Σ(x - xbar)²/N]

Σ(x - xbar)² = 0.00842724+0.00487204+0.00753424+0.01106704+0.00094864+0.00068644+0.00135424+0.00595984+0.02439844+0.00238144

= 0.0676296

σ = √[Σ(x - xbar)²/N] = √(0.0676296/10) = 0.08224 milligrams per liter

To do an hypothesis test, we need to first define the null and alternative hypothesis

The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.

For this question, the null hypothesis would be that there is no significant evidence to suggest that the the calcium concentrations have changed since 2010. That is, the calcium concentrations haven't changed since 2010.

The alternative hypothesis is that there is significant evidence to suggest that the the calcium concentrations have changed since 2010. That is, the calcium concentrations haven't changed since 2010.

Mathematically,

The null hypothesis is represented as

H₀: μ = 0.11 milligrams per liter

The alternative hypothesis is given as

Hₐ: μ ≠ 0.11 milligrams per liter

To do this test, we will use the t-distribution because no information on the population standard deviation is known

So, we compute the t-test statistic

t = (x - μ₀)/σₓ

x = sample mean = 0.1568 milligram per liter

μ₀ = the mean calcium concentrations from 2010 = 0.11 milligrams per liter

σₓ = standard error = (σ/√n)

where n = Sample size = 10

σ = Sample standard deviation = 0.08224 milligrams per liter

σₓ = (σ/√n) = (0.08224/√10) = 0.026

t = (0.1568 - 0.11) ÷ 0.026

t = 1.80

checking the tables for the p-value of this t-statistic

Degree of freedom = df = 10 - 1 = 10 - 1 = 9

Significance level = 0.05

The hypothesis test uses a two-tailed condition because we're testing in two directions. (Greater than and less than)

p-value (for t = 1.80, at 0.05 significance level, df = 9, with a two tailed condition) = 0.105391

The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.05

p-value = 0.105391

0.105391 > 0.05

Hence,

p-value > significance level

This means that we fail to reject the null hypothesis & say that there isn't enough evidence to conclude that the the calcium concentrations have changed since 2010.

Hope this Helps!!!

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3 years ago

If the same number is subtracted from both the numerator and the denominator of 1115, the result is 35. find the number.

muminat

the answer is 5/12 i hope i helped.

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3 years ago

Let f(x,y,z) = ztan-1(y2) i + z3ln(x2 + 1) j + z k. find the flux of f across the part of the paraboloid x2 + y2 + z = 3 that li

Sophie [7]

Consider the closed region $V$ bounded simultaneously by the paraboloid and plane, jointly denoted $S$ . By the divergence theorem,

$\displaystyle\iint_S\mathbf f(x,y,z)\cdot\mathrm dS=\iiint_V\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV$

And since we have

$\nabla\cdot\mathbf f(x,y,z)=1$

the volume integral will be much easier to compute. Converting to cylindrical coordinates, we have

$\displaystyle\iiint_V\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV=\iiint_V\mathrm dV$
$=\displaystyle\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=1}\int_{z=2}^{z=3-r^2}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta$
$=\displaystyle2\pi\int_{r=0}^{r=1}r(3-r^2-2)\,\mathrm dr$
$=\dfrac\pi2$

Then the integral over the paraboloid would be the difference of the integral over the total surface and the integral over the disk. Denoting the disk by $D$ , we have

$\displaystyle\iint_{S-D}\mathbf f\cdot\mathrm dS=\frac\pi2-\iint_D\mathbf f\cdot\mathrm dS$

Parameterize $D$ by

$\mathbf s(u,v)=u\cos v\,\mathbf i+u\sin v\,\mathbf j+2\,\mathbf k$
$\implies\mathbf s_u\times\mathbf s_v=u\,\mathbf k$

which would give a unit normal vector of $\mathbf k$ . However, the divergence theorem requires that the closed surface $S$ be oriented with outward-pointing normal vectors, which means we should instead use $\mathbf s_v\times\mathbf s_u=-u\,\mathbf k$ .

Now,

$\displaystyle\iint_D\mathbf f\cdot\mathrm dS=\int_{u=0}^{u=1}\int_{v=0}^{v=2\pi}\mathbf f(x(u,v),y(u,v),z(u,v))\cdot(-u\,\mathbf k)\,\mathrm dv\,\mathrm du$
$=\displaystyle-4\pi\int_{u=0}^{u=1}u\,\mathrm du$
$=-2\pi$

So, the flux over the paraboloid alone is

$\displaystyle\iint_{S-D}\mathbf f\cdot\mathrm dS=\frac\pi2-(-2\pi)=\dfrac{5\pi}2$

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3 years ago

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