MATHEMATICS COLLEGE

Explain how you know 437,160 is greater than 43,716

Answers

Answer 1

Answer: 437160 has more numbers than 43716

Answer 2

Answer:

Answer:

Because 437,160 is greater than 43,716

Step-by-step explanation:

It has more numbers and on the number line, 437,160 is greater than 43,716

Think about it this way:

Suppose a company has a profit of $437,160 this spring.

And another one has $43,716 this spring.

Now, the question is:

Which company has a larger profit?

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Answers

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In a city known for many tech start-ups, 311 of 800 randomly selected college graduates with outstanding student loans currently owe more than $50,000. In another city known for biotech firms, 334 of 800 randomly selected college graduates with outstanding student loans currently owe more than $50,000. Perform a two-proportion hypothesis test to determine whether there is a difference in the proportions of college graduates with outstanding student loans who currently owe more than $50,000 in these two cities. Use α=0.05. Assume that the samples are random and independent. Let the first city correspond to sample 1 and the second city correspond to sample 2. For this test: H0:p1=p2; Ha:p1≠p2, which is a two-tailed test. The test results are: z≈−1.17 , p-value is approximately 0.242

Answers

Answer:

Null hypothesis: $p_(1) - p_(2)=0$

Alternative hypothesis: $p_(1) - p_(2) \neq 0$

$z=\frac{0.389-0.418}{\sqrt{0.403(1-0.403)((1)/(800)+(1)/(800))}}=-1.182$

$p_v =2*P(Z<-1.182)=0.2372$

Comparing the p value with the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say that we don't have significant difference between the two proportions.

Step-by-step explanation:

1) Data given and notation

$X_(1)=311$ represent the number college graduates with outstanding student loans currently owe more than $50,000 (tech start-ups)

$X_(2)=334$ represent the number college graduates with outstanding student loans currently owe more than $50,000 ( biotech firms)

$n_(1)=800$ sample 1

$n_(2)=800$ sample 2

$p_(1)=(311)/(800)=0.389$ represent the proportion of college graduates with outstanding student loans currently owe more than $50,000 (tech start-ups)

$p_(2)=(334)/(800)=0.418$ represent the proportion of college graduates with outstanding student loans currently owe more than $50,000 ( biotech firms)

z would represent the statistic (variable of interest)

$p_v$ represent the value for the test (variable of interest)

$\alpha=0.05$ significance level given

2) Concepts and formulas to use

We need to conduct a hypothesis in order to check if is there is a difference in the two proportions, the system of hypothesis would be:

Null hypothesis: $p_(1) - p_(2)=0$

Alternative hypothesis: $p_(1) - p_(2) \neq 0$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_(1)-p_(2)}{\sqrt{\hat p (1-\hat p)((1)/(n_(1))+(1)/(n_(2)))}}$ (1)

Where $\hat p=(X_(1)+X_(2))/(n_(1)+n_(2))=(311+334)/(800+800)=0.403$

3) Calculate the statistic

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.389-0.418}{\sqrt{0.403(1-0.403)((1)/(800)+(1)/(800))}}=-1.182$

4) Statistical decision

Since is a two sided test the p value would be:

$p_v =2*P(Z<-1.182)=0.2372$

6.Write the equation in slope-intercept form for the line that passes through the given pointand is perpendicular to the given equation.5x + 3y = -21 and passes through (-5, 1)

Answers

Let us first solve for the slope (m) of the perpendicular line.

$\text{ 5x + 3y = -21}$ $\text{ 3y = -5x - 21}$ $\text{ y =}\frac{-5x\text{ -21}}{3}$ $\text{ y = -}(5)/(3)x-7$

The slope of the perpendicular line is -5/3.

Thus, for the slope of the line, we get,

$\text{ m}_(\perp)\text{ = }(-5)/(3)$ $\text{ m = }(3)/(5)$

Let us solve for the value of b with the given value of slope (m) = 3/5 and (x,y) = (-5,1).

$\text{ y = mx + b}$ $1\text{ = (}(3)/(5))(-5)+b$ $1\text{ = -1 + b ; b = 1 + 1 = }2$

Let's now make the equation of the line using Slope-Intercept Form,

Given, m = 3/5 and b = 2

$\text{ y = mx+b}$ $\text{ y = (}(3)/(5))x\text{ + 2}$

$\text{ y = }(3)/(5)x\text{ +2}$

Jacqueline buys 2 fourths yard of green ribbon and 1 fourths yard of pink ribbon. How many yards of ribbon does she buy?

Answers

Answer:

3/4

Step-by-step explanation:

What is the probability of first drawing a red card, then a face card, and then a black card? Do not round your intermediate computations. Round your final answer to four decimal places.

Answers

Answer:

[ 26 / 425 ] ≈ 0.0612

Step-by-step explanation:

Solution:-

- First we will describe the standard deck of 52 cards in terms of black, red and face cards found in a standard deck

- Following is a table of distribution of colored and face card found in a standard deck:

Type Number of cards

1 - 10 40

Black 26

Red 26

Face 12

- The numerical cards from digit ( 1 to 10 ) are found in all 4 suits ( Clubs, Diamonds, Spades, and Hearts ). Hence, 10 x 4 = 40

- The entire deck is split in two colors ( Red and Black ) equally. So, the number of Black and Red cards are = 52 / 2 = 26 cards.

- The face cards are of three types ( King, Queen and Jack ). These three face cards are found in each of the 4 suits. Hence, Total number of face cards are = 4 * 3 = 12

- We will now consider the probabilities asscociated with each type. We will define 3 events and write down their proability as expressed:

Event ( A ): First draw is a red card.

- The probability of this event can be determined with the help of the table given above. There are a total of 26 red card in a standard deck of 52 cards. Hence,

p ( A ) = [ Number of red cards ] / [ Total cards in a deck ]

p ( A ) = [ 26 ] / [ 52 ]

p ( A ) = 1 / 2

- After we make the first draw of a red card. Our deck distribution is changed to Number of Red cards remaining = 25 and total deck now has 51 cards remaining.

- We will define the next event as:

Event ( B ): The second draw is a face card.

- The probability of this event can be determined with the help of the table given above. There are a total of 12 face cards in a standard deck of 52 cards which is now down to 51 cards. Hence,

p ( B ) = [ Number of face cards ] / [ Total cards in a deck ]

p ( B ) = [ 12 ] / [ 51 ]

p ( B ) = 4 / 17

- After we make the first draw of a face card. Our deck distribution is changed to Number of Face cards remaining = 11 and total deck now has 50 cards remaining.

- We will define the next event as:

Event ( C ): The third draw is a black card.

- The probability of this event can be determined with the help of the table given above. There are a total of 26 black cards in the deck. The total number of cards are down to 50 cards only. Therefore,

p ( C ) = [ Number of black cards ] / [ Total cards in a deck ]

p ( C ) = [ 26 ] / [ 50 ]

p ( C ) = 13 / 25

- The entire drawing process consists of 3 events which are dependent on each draw. However, for the overall event to occur i.e drawing a red card , then a face card, and then a black card. We will multiply all three outcomes as follows:

p ( T ) = p ( A ) * p ( B ) * p ( C )

p ( T ) = [ 1 / 2 ] * [ 4 / 17 ] * [ 13 / 25 ]

p ( T ) = [ 26 / 425 ] ≈ 0.0612

Final answer:

The overall probability of first drawing a red card, then a face card, and then a black card from a standard deck of cards is 0.0124.

Explanation:

This question is related to the concept of probability in Mathematics. A standard deck of cards consists of 52 cards - 26 red (diamonds and hearts) and 26 black (clubs and spades). There are 12 face cards (King, Queen, and Jack of each suit).

For the first draw, the probability of picking a red card is 26/52, which simplifies to 1/2.

After picking a red card, we are left with 51 cards. So, for the second draw, the probability of picking a face card is 12/51.

Then, having picked a red and face card, we are left with 50 cards. For the third draw, the probability of picking a black card is 26/50 which simplifies to 13/25.

We multiply these probabilities together to get the overall probability, therefore (1/2) * (12/51) * (13/25) = 0.012418. Rounding this to four decimal places, we get 0.0124.