Find the area of the trapezoid with bases 12 cm and 14 cm and height 9 cm

8,431.62709 which digit is in the ten-thousand place?

Sergeu [11.5K]

6 is in the ten thousand place

6 0

3 years ago

For the hypothesis test H0: μ = 10 against H1: μ >10 and variance known, calculate the Pvalue for each of the following test

Basile [38]

Answer:

a) $p_v =P(Z>2.05)=1-P(z$

b) $p_v =P(Z>-1.84)=1-P(z$

c) $p_v =P(Z>0.4)=1-P(z$

Step-by-step explanation:

Some previous concepts

The p-value is the probability of obtaining the observed results of a test, assuming that the null hypothesis is correct.

A z-test for one mean "is a hypothesis test that attempts to make a claim about the population mean(μ)".

The null hypothesis attempts "to show that no variation exists between variables or that a single variable is no different than its mean"

The alternative hypothesis "is the hypothesis used in hypothesis testing that is contrary to the null hypothesis"

Hypothesis

Null hypothesis: $\mu=10$

Alternative hypothesis: $\mu >10$

If the random variable is distributed like this: $X \sim N(\mu,\sigma)$

We assume that the variance is known so the correct test to apply here is the z test to compare means, the statistic is given by the following formula:

$z_o=\frac{\bar X -\mu}{\sigma}$

Since we have the values for the statistic already calculated we can calculate the p value using the following formulas:

Part a

$p_v =P(Z>2.05)=1-P(z$

And in order to find the answer using excel we can use the following code:

"=1-NORM.DIST(2.05,0,1,TRUE)"

Part b

$p_v =P(Z>-1.84)=1-P(z$

And in order to find the answer using excel we can use the following code:

"=1-NORM.DIST(-1.84,0,1,TRUE)"

Part c

$p_v =P(Z>0.4)=1-P(z$

And in order to find the answer using excel we can use the following code:

"=1-NORM.DIST(0.4,0,1,TRUE)"

Conclusions

If we use a reference value for the significance, let's say $\alpha=0.05$ . For part a the $p_v$ so then we can reject the null hypothesis at this significance level.

For part b the $p_v>\alpha$ so then we FAIL to reject the null hypothesis at this significance level.

For part c the $p_v>\alpha$ so again we FAIL to reject the null hypothesis at this significance level.

3 0

3 years ago

40 POINTS AND BRAINLIEST!! I NEED THIS DONE ASAP

inna [77]

(a) Answer: One solution.

Explanation: two lines that have same slope with opposite sign will necessarily cross each other at a single point, as one is "pointing uphill" and the other "downhill."

(b) Answer: Infinitely many solutions.

Explanation:

2x + 3y = 5.5

4x + 6y = 11 | divide by 2

-->

2x + 3y = 5.5

--> equations are identical.

2x + 3y = 2x + 3y

so any (x,y) will satisfy this equation. This means infinitely many solutions.

(c) Answer: One solution

Explanation:

Continuing the two lines it becomes obvious they will cross at one point (the solution)

(d) Answer: No solution

Explanation: If the two lines are parallel, they will never cross (by definition of "parallel"). Therefore there will be no solution to the corresponding linear system.

8 0

3 years ago

Solve the system of equations below by graphing.

Katen [24]

(0.5, 1.3) is the correct answer

Step-by-step explanation:

Given equations are:

$y = 4x-0.8\ \ \ Eqn1\\2x+y-2.3=0\ \ \ Eqn2$

As we can see that the given equations are linear equations which are graphed as straight lines on graph. The solution of two equations is the point of their intersection on the graph.

We can plot the graph of both equations using any online or desktop graphing tool.

We have used "Desmos" online graphing calculator to plot the graph of two lines (Picture Attached)

We can see from the graph that the lines intersect at: (0.517, 1.267)

Rounding off both coordinates of point of intersection to nearest tenth we get

(0.5, 1.3)

Hence,

(0.5, 1.3) is the correct answer

Keywords: Linear equations, variables

Learn more about linear equations at:

#LearnwithBrainly

8 0

3 years ago

Read 2 more answers

The question is given in the picture.

lorasvet [3.4K]

This is a really interesting question! One thing that we can notice right off the bat is that each of the circles has the same amount of area swept out of it - namely, the amount swept out by one of the interior angles of the hexagon. Let’s call that interior angle θ. We know that the amount of area swept out in the circle is proportional to the angle swept out - mathematically

θ/360 = a/A

Where “a” is the area swept out by θ, and A is the area of the whole circle, which, given a radius of r, is πr^2. Substituting this in, we have

θ/360 = a/(πr^2)

Solving for “a”:

a = π(r^2)θ/360

So, we have the formula for the area of one of those sectors; all we need to do now is find θ and multiply our result by 6, since we have 6 circles. We can preempt this but just multiplying both sides of the formula by 6:

6a = 6π(r^2)θ/360

Which simplifies to

6a = π(r^2)θ/60

Now, how do we find θ? Let’s look first at the exterior angles of a hexagon. Imagine if you were taking a walk around a hexagon. At each corner, you turn some angle and keep walking. You make 6 turns in all, and in the end, you find yourself right back at the same place you started; you turned 360 degrees in total. On a regular hexagon, you’d turn by the same angle at each corner, which means that each of the six turns is 360/6 = 60 degrees. Since each interior and exterior angle pair up to make 180 degrees (a straight line), we can simply subtract that exterior angle from 180 to find θ, obtaining an angle of 180 - 60 = 120 degrees.

Finally, we substitute θ into our earlier formula to find that

6a = π(r^2)120/60

Or

6a = 2πr^2

So, the area of all six sectors is 2πr^2, or the area of two circles with radii r.

5 0

3 years ago