Raj wants to take yoga classes. There are two yoga studios that have different membership plans.

Body armor provides critical protection for law enforcement personnel, but it does affect balance and mobility. The article "Imp

yKpoI14uk [10]

Answer:

No, there is not enough evidence to support the claim that true average task time with armor is less than 2 seconds.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that true average task time with armor is less than 2 seconds.

Then, the null and alternative hypothesis are:

$H_0: \mu=2\\\\H_a:\mu< 2$

The significance level is 0.01.

The sample has a size n=52.

The sample mean is M=1.95.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=0.2.

The estimated standard error of the mean is computed using the formula:

$s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.2}{\sqrt{52}}=0.028$

Then, we can calculate the t-statistic as:

$t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{1.95-2}{0.028}=\dfrac{-0.05}{0.028}=-1.803$

The degrees of freedom for this sample size are:

$df=n-1=52-1=51$

This test is a left-tailed test, with 51 degrees of freedom and t=-1.803, so the P-value for this test is calculated as (using a t-table):

$P-value=P(t$

As the P-value (0.039) is bigger than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that true average task time with armor is less than 2 seconds.

3 0

1 year ago

A pure acid measuring x liters is added to 300 liters of a 20% acidic solution. The concentration of acid, f(x), in the new subs

Nitella [24]

Answer How many liters of a 20% acid solution should be mixed with 30 liters of 50% acid solution in order to obtain a 40% solution. ... x=15 liters 15*(.20 pure acid)=3 liters 30*(.50 pure acid)=15 liters That is 18 liters pure acid That is 45 liters solution *0.45 pure acid=18 liters.

Step-by-step explanation:

6 0

1 year ago

Read 2 more answers

Olive oil is a cooking Ingredient. The density of olive oil is 0.92 grams per cubic centimeter. An olive farmer wants to sell bo

sveticcg [70]

Answer: The volume of container that holds 460 grams of oil is 500 cm³.

Step-by-step explanation:

Density of olive oil is $0.92 grams/(centimetre )^3$

An olive farmer wants to sell bottles that contain 460 grams of oil.

Therefore

Mass of oil = 460 grams

As we know

$\text {Density}= \dfrac{\text{Mass}}{\text{Volume}} \\\\\Rightarrow 0.92= \dfrac{460}{\text{Volume}} \\\\\Rightarrow \text{Volume}= \dfrac{460}{0.92} = 500$

Hence, the volume of container that holds 460 grams of oil is 500 cm³.

7 0

1 year ago

The data set below represents the ages of 36 executives. find the percentile that corresponds to an age of 4141 years old. 2828

solong [7]

Answer:

37th percentile.

Step-by-step explanation:

We have been given a data set that represents the ages of 36 executives. We are asked to find the percentile that corresponds to an age of 41 years.

28, 29, 29, 32, 32, 33, 34, 34, 34, 34, 37, 37, 38, 41, 41, 42, 45, 45, 47, 47, 47, 48, 50, 51, 53, 56, 56, 56, 61, 61, 62, 63, 64, 64, 65, 66.

Let us count the number of data points below and at 41.

We can see that the number of data points at and below 41 is 13.

We will use percentile formula to solve our given problem.

$\text{Percentile rank of x}=\frac{\text{Number of values below x}}{\text{Total number of data points}}\times 100$

$\text{Percentile rank of 41}=\frac{13}{36}\times 100$

$\text{Percentile rank of 41}=0.361111\times 100$

$\text{Percentile rank of 41}=36.11\approx 37$

Therefore, the percentile rank that corresponds to age of 41 years old is 37th percentile.

8 0

2 years ago

O is the centre of the circle and ABC and EDC are tangents to the circle. Find the size of angle BCD. You must give reasons in y

Simora [160]

Answer:

mBCD = 28°

Step-by-step explanation:

The angle mBFD inscribes the arc mBD, so we have that:

mBFD = mBD/2

76 = mBD/2

mBD = 152°

The angle mBOD is a central angle related to the arc mBD, so we have that:

mBOD = mBD = 152°

In the quadrilateral BODC, the sum of internal angles needs to be equal to 360° (property of all convex quadrilaterals). The angles mCBO and mCDO are right angles, because EDC and ABC are tangents to the circle.

So, we have that:

mBOD + mCDO + mBCD + mCBO = 360

152 + 90 + mBCD + 90 = 360

mBCD = 360 - 90 - 90 - 152

mBCD = 28°

7 0

1 year ago