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2 years ago

A line intersects the point (-3,-7) and has a slope of -1/3. What is the slope intercept equation for this line? Y = -X/3 -[?]

1 answer:

7 0

First, you can plug this into the point slope formula. you will have to do that before you can get the slope intercept form. Plug in what you know. m is slope, so plug in -1/3 for m. The point given can be plugged in to the formula also. This is what it should look like:

y + 7 = -1/3(x + 3)

***** Note that the -3 and -7 become positive because it is subtracting negative numbers and 2 negatives make a positive. *************************

Now distribute the -1/3 times x and 3.

y + 7 = -1/3x - 1

Now to get y by itself, add 7 to both sides.

y = -1/3x + 6

This is your answer: y = -1/3x + 6

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2 years ago

Tensile-strength tests were carried out on two different grades of wire rod (Fluidized Bed Patenting of Wire Rods, Wire J., June

Shtirlitz [24]

Answer:

$t=\frac{(123.6-107.6)-(10)}{\sqrt{\frac{2^2}{129}+\frac{1.3^2}{129}}}=28.569$

$p_v =P(t_{256}>28.569) \approx 0$

So with the p value obtained and using the significance level given $\alpha=0.1$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the true average strength for the 1078 grade exceeds that for the 1064 grade by more than 10 kg/mm2.

Step-by-step explanation:

The statistic is given by this formula:

$t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{\sqrt{\frac{s^2_1}{n_1}+\frac{s^2_2}{n_2}}}$

Where t follows a t distribution with $n_1+n_2 -2$ degrees of freedom

The system of hypothesis on this case are:

Null hypothesis: $\mu_1 \leq \mu_2 +10$

Alternative hypothesis: $\mu_1 >\mu_2 +10$

Or equivalently:

Null hypothesis: $\mu_1 - \mu_2 \leq 10$

Alternative hypothesis: $\mu_1 -\mu_2>10$

Our notation on this case :

$n_1 =129$ represent the sample size for group AISI 1078

$n_2 =129$ represent the sample size for group AISI 1064

$\bar X_1 =123.6$ represent the sample mean for the group AISI 1078

$\bar X_2 =107.6$ represent the sample mean for the group AISI 1064

$s_1=2.0$ represent the sample standard deviation for group 1 AISI 1078

$s_2=1.3$ represent the sample standard deviation for group AISI 1064

And now we can calculate the statistic:

$t=\frac{(123.6-107.6)-(10)}{\sqrt{\frac{2^2}{129}+\frac{1.3^2}{129}}}=28.569$

Now we can calculate the degrees of freedom given by:

$df=129+129-2=256$

And now we can calculate the p value using the altenative hypothesis:

$p_v =P(t_{256}>28.569) \approx 0$

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3 years ago

Factor <img src="https://tex.z-dn.net/?f=x%5E3-4x%5E2-3x%2B18%3D0" id="TexFormula1" title="x^3-4x^2-3x+18=0" alt="x^3-4x^2-3x+18

Nata [24]

Answer:

A) (x +2)(x -3)² = 0

Step-by-step explanation:

Synthetic division by (x-3) gives the quadratic x² -x -6, which has factors (x -3) and (x +2). This is confirmed by another round of synthetic division.

The resulting factorization is ...

... (x +2)(x -3)² = 0

_____

A graph confirms a double zero at x=3 and one at x=-2.

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