What is (2/9v - ( -1/3v + 5/9)

A particular psychological test is used to measure need for achievement. The average test score for all university students in O

Angelina_Jolie [31]

Answer:

Only B and C are always true.

Step-by-step explanation:

To analyse which statements are always true, we go through the process of finding confidence intervals for sample means, from the start.

Confidence Interval = (Sample mean) ± (Margin of error)

From this expression, it is evident that the margin of error determines how wide the confidence interval would be.

Sample Mean = 110 (given)

Margin of Error = (Critical value) × (Standard deviation of the distribution of sample means)

Since no information about the population standard deviation is provided, the critical value is obtained using t-distribution.

The critical value usually varies at different confidence levels and degree of freedoms.

The higher the confidence level, the higher the critical value and the higher the margin of error leading to a wider range.

Hence, a confidence interval of 95% will have a higher critical value than a confidence interval of 90%. Hence, statement C is proved once that 'for n = 100, the 95% confidence interval will be wider than the 90% confidence interval'.

After obtaining the critical value, we then obtain the standard deviation of the distribution of sample means or simply the standard error of the mean. This is given as

σₓ = σ/√n

where σ = standard deviation; which isn't given. The standard deviation might be high enough to guarantee that the Margin of error is high too for the confidence interval to contain 115 or low enough to ensure that the Margin of error is very small and the confidence interval will not contain 115.

Or the sample size might be high enough to make the standard error of the mean to be eventually small and lead to a small margin of error and the condidence interval will not contain 115.

The point is, it isn't always sure that the resulting interval.would contain 115. So, statement A isn't always true.

Then from σₓ = σ/√n,

n = sample size, a large sample size means a more narrow confidence interval and a small sample size means a wider sample size. This proves statement C.

The 95% confidence interval for n = 100 will be more narrow than the 95% confidence interval for n = 50.

Hence, Only B and C are always true.

Hope this Helps!!!

5 0

3 years ago

I need all three answers again please help

choli [55]

Answer:

Step-by-step explanation:

3) Sales tax rate = $\frac{42.42}{499}*100$

= 8.50

= 9%

4) Rate of commission = $\frac{1400}{28000}*100$

= 5 %

5) Reduction = $\frac{30}{100}*5000$

=$ 1500

New price = 5000 - 1500

= $ 3500

8 0

2 years ago

After Squints gets the team banned from the pool, the guys from the Sandlot decide they need to build their own pool. They decid

pishuonlain [190]

Answer:

525 truckloads

Step-by-step explanation:

First we need to find the volume of the pool. This lets us know how much dirt must be moved.

25*19*5 = 2,375 cubic feet total.

Divide that by 4.53 cubic feet for each load, and we get 524.282 truckloads. Round up to the nearest integer for a final answer of 525 truckloads.

7 0

3 years ago

A circle is growing so that the radius is increasing at the rate of 3 cm/min. How fast is the area of the circle changing at the

Naya [18.7K]

Answer:

The area is growing at a rate of $\frac{dA}{dt} =226.2 \,\frac{cm^2}{min}$

Step-by-step explanation:

<em>Notice that this problem requires the use of implicit differentiation in related rates (some some calculus concepts to be understood), and not all middle school students cover such.</em>

We identify that the info given on the increasing rate of the circle's radius is 3 $\frac{cm}{min}$ and we identify such as the following differential rate:

$\frac{dr}{dt} = 3\,\frac{cm}{min}$

Our unknown is the rate at which the area (A) of the circle is growing under these circumstances,that is, we need to find $\frac{dA}{dt}$ .

So we look into a formula for the area (A) of a circle in terms of its radius (r), so as to have a way of connecting both quantities (A and r):

$A=\pi\,r^2$

We now apply the derivative operator with respect to time ( $\frac{d}{dt}$ ) to this equation, and use chain rule as we find the quadratic form of the radius:

$\frac{d}{dt} [A=\pi\,r^2]\\\frac{dA}{dt} =\pi\,*2*r*\frac{dr}{dt}$

Now we replace the known values of the rate at which the radius is growing ( $\frac{dr}{dt} = 3\,\frac{cm}{min}$ ), and also the value of the radius (r = 12 cm) at which we need to find he specific rate of change for the area :

$\frac{dA}{dt} =\pi\,*2*r*\frac{dr}{dt}\\\frac{dA}{dt} =\pi\,*2*(12\,cm)*(3\,\frac{cm}{min}) \\\frac{dA}{dt} =226.19467 \,\frac{cm^2}{min}\\$

which we can round to one decimal place as:

$\frac{dA}{dt} =226.2 \,\frac{cm^2}{min}$

4 0

3 years ago

Question 9 (10 points)

Slav-nsk [51]

The length is 5cm long

5 0

3 years ago