What is the difference in meaning between |-3| and -3.

A circle is centered at the point (-7,-1) and passes through the point (8,7).

cluponka [151]

<span>The radius of the circle is __17___ units.
(Enter a whole number, not decimals)

The point, (-15, _-16_ ) lies on it's circle. </span>

6 0

3 years ago

Which is the axis of symmetry of a parabola with equation x^2=-4y?

riadik2000 [5.3K]

Answer:

x = 0

Step-by-step explanation:

Given

x² = - 4y ( divide both sides by - 4 )

y = - $\frac{1}{4}$ x²

Which is a parabola opening vertically down with it's vertex at (0, 0) and symmetrical about the y- axis

Hence equation of axis of symmetry is x = 0

3 0

3 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:

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

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.

7 0

3 years ago

What is 7 1/5 written as a percent

Alla [95]

7.20% percent I think

5 0

3 years ago

How is multiplying complex number different from multiplying binomials?

Oksi-84 [34.3K]

Answer:

A complex number is any number that can be written as \greenD{a}+\blueD{b}ia+bistart color greenD, a, end color greenD, plus, start color blueD, b, end color blueD, i, where iii is the imaginary unit and \greenD{a}astart color greenD, a, end color greenD and \blueD{b}bstart color blueD, b, end color blueD are real numbers.

Step-by-step explanation:

4 0

2 years ago