Evaluate the following.

If the principal, interest rate, or time in a simple interest problem is doubled, and the other two quanities remain constant, h

Alex17521 [72]

one would say that the simple interest doubles if the period of time is specified in the contract and the contract is still valid, if the interest amount is available anitime and so on.

So if the amount doubles let's say at half time for which the principal was awarded to the bank, by the end of the contract , the interest amount can be double × just increased by 1.5

8 0

3 years ago

A college chemistry instructor thinks the use of embedded tutors will improve the success rate in introductory chemistry courses

Yuliya22 [10]

Answer:

Step-by-step explanation:

Hello!

The chemistry instructor tested the hypothesis that the proportion of students that passed the introductory chemistry class is better with an embedded. If the known proportion for this population is 65%, the tested hypothesis is:

H₀: p=0.65

H₁: p>0.65

The calculated statistic is Z=2.52 and the associated p-value: 0.0059

Remember:

The p-value is defined as the probability corresponding to the calculated statistic if possible under the null hypothesis (i.e. the probability of obtaining a value as extreme as the value of the statistic under the null hypothesis).

In this case:

P(Z≥2.52)=0.0059

There is no significance level, the most common one is α: 0.05 so I'll use it as an example.

To make a decision using the p-value you have to compare it to the α.

If p- value>α then you support the null hypothesis (In this case, you can say that there is no change in the proportion of students that passed the introductory chemistry class with an embedded tutor.)

If p-value≤α your decision will be to reject the null hypothesis (In this case, there is significant evidence to say that there is an improvement in the success rate of the introductory chemistry class with an embedded tutor?

Since the p-value:0.0059 is less than the significance level 0.05, you will decide to reject the null hypothesis.

I hope you have a SUPER day!

8 0

3 years ago

Sally has a discount card that reduces the price of her grocery bill in a certain grocery store by 6%. If c represents the cost

Nitella [24]

Answer:

Step-by-step explanation:

c - 0.06c = 0.94c

total bill = 0.94c

8 0

2 years ago

Consider a set of one-dimensional points: 6, 12, 18, 24, 30, 42, 48.

Vinvika [58]

Answer:

1) With initial centroids 10-40, final clusters are

first cluster (6,12,18,24,30)

second cluster (42,48)

And the Sum of Squared Errors (SSE) for the clustering result is 378

2) With initial centroids 10-20, final clusters are

first cluster (6,12,18,24)

second cluster (30,42,48)

And the Sum of Squared Errors (SSE) for the clustering result is 348

Step-by-step explanation:

K-means works as follows

the points will be clustered according to their distance to the centroids.
Then centroids are updated as the cluster means.
This process continues until clusters doesn't change anymore

1) initial centroids 10-40

first cluster (6,12,18,24) mean:15

second cluster (30,42,48) mean:40

new centroids 15-40

first cluster (6,12,18,24,30) mean:18

second cluster (42,48) mean:45

final centroids 18-45

first cluster (6,12,18,24,30) mean:18

second cluster (42,48) mean:45

Sum of Squared errors = $(18-6)^{2}$ + $(18-12)^{2}$ + $(18-18)^{2}$ + $(18-24)^{2}$ + $(18-30)^{2}$ + $(45-42)^{2}$ + $(45-48)^{2}$ =378

2)initial centroids 10-20

first cluster (6,12) mean:9

second cluster (18,24,30,42,48) mean:32.4

new centroids 9-32.4

first cluster (6,12,18) mean:12

second cluster (24,30,42,48) mean:36

new centroids 12-36

first cluster (6,12,18,24) mean:15

second cluster (30,42,48) mean:40

final centroids 15-40

first cluster (6,12,18,24) mean:15

second cluster (30,42,48) mean:40

Sum of Squared errors = $(15-6)^{2}$ + $(15-12)^{2}$ + $(15-18)^{2}$ + $(15-24)^{2}$ + $(40-30)^{2}$ + $(40-42)^{2}$ + $(40-48)^{2}$ =348

6 0

3 years ago

The population f(x), in millions, of State A of a country after x years is represented by the function shown below:

OverLord2011 [107]

Option 1 is correct. The correct solution about these functions is that The original population of State A was double of the original population of State B.

<h3>How to solve for the solution</h3>

The function in the question is given as

For A:

$F(x) = 4*(1.08)^x$

For B

$g(x) = 2*(1.08)^x$

The exponential growth equation that is used to solve this is

$h(x) = A(r)^x$

such that A is the initial and r is the rate of growth.

f(x) and g(x) are at the same rate but the exponential function is known to grow faster.

Hence the correct option is The original population of State A was double of the original population of State B.

<h3>Complete question:</h3>

Which conclusion is correct about the population of State A and State B? 1. The original population of State A was double of the original population of State B.

2. The original population of State A was half of the original population of State B.

3. The original population of State B was one-fourth of the original population of State A.

4. The original population of State A was one-fourth of the original population of State B.