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3 years ago

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Please help, thanks! Ok so, you pick a card at random, put it back, and then pick another card at random. There are FIVE cards a

nd they are numbered like this: 1, 2, 3, 4, 5. What is the probability of picking a number greater than 1 and then picking a number less than 2? Write the answer as a fraction or whole number. Thank you!

1 answer:

tatyana61 [14]3 years ago

6 0

Answer:

$P(x > 1\ and\ x < 2) = \frac{4}{25}$

Step-by-step explanation:

Given

$S = \{1,2,3,4,5\}$

$n(S) = 5$

Required

$P(x > 1\ and\ x < 2)$

$P(x > 1\ and\ x < 2)$ is calculated as:

$P(x > 1\ and\ x < 2) = P(x > 1) * P(x < 2)$

Since it is a probability with replacement, we have:

$P(x > 1\ and\ x < 2) = \frac{n(x > 1)}{n(S)} * \frac{n(x < 2)}{n(S)}$

For x > 1, we have:

$x > 1 = \{2,3,4,5\}\\$

$n(x > 1) = 4$

For x < 2, we have:

$x < 2 = \{1\}$

$n(x < 2) = 1$

$P(x > 1\ and\ x < 2) = \frac{n(x > 1)}{n(S)} * \frac{n(x < 2)}{n(S)}$

becomes

$P(x > 1\ and\ x < 2) = \frac{4}{5} * \frac{1}{5}$

$P(x > 1\ and\ x < 2) = \frac{4}{25}$

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I need help with these please

notsponge [240]

Answer:

1a - no

1b - yes

1c - no

2 - 1.5 grams of protein

3 - a solution to this equation tells us how many grams of protein/fat there could be depending on how many grams of the other there are. a solution to this is 6 grams of protein and 4 grams of fat.

Step-by-step explanation:

1a

4(5)+9(2)=60

20+18=60

38=60

the equation is false

1b

4(10.5)+9(2)=60

42+18=60

60=60

the equation is true

1c

4(8)+9(4)=60

32+36=60

68=60

the equation is not true

2

plug in 6 for the f value

4p+9(6)=60

4p+54=60

subtract 54 from both sides

4p=6

divide both sides by 4 to get p alone

p=1.5

3

a possible solution can be seen by graphing the equation using the intercepts. the intercepts for this equation are (15,0) and (0,6.6). attached is an image of the graph. the points where the line crosses are possible solutions. the line crosses the point (6,4) on the graph, which represents 6 grams of protein and 4 grams of fat. you can also check this by plugging these values into the equation.

4 0

3 years ago

There are 5 different coloured cups in a row.

Marizza181 [45]

There are 12 possible arrangements.

------------------------

Considering that the blue cup has to be on one end, we consider the number of arrangements possible with the other 4 cups, then multiply by 2(considering the blue on each end).

------------------------

Considering green and yellow before red and purple, there are $2 \times 2 = 4$ outcomes(G-Y-R-P, G-Y-P-R, Y-G-R-P and Y-G-P-R).
Another two possible outcomes are yellow-purple and green-red, or vice-versa, thus 4 + 2 = 6 outcomes.
To account for the blue on the end, multiplying by 2. $2 \times 6 = 12$
There are 12 possible arrangements.

A similar problem is given at brainly.com/question/24617788

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3 years ago

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3 years ago

A sample of 100 workers located in Atlanta has an average daily work time of 6.5 hours with a standard deviation of 0.5 hours. A

Readme [11.4K]

Answer:

$t=\frac{6.5-6.7}{\sqrt{\frac{0.5^2}{100}+\frac{0.7^2}{110}}}}=-2.398$

$df = n_1 +n_2 -2= 100+110-2= 208$

Since is a bilateral test the p value would be:

$p_v =2*P(t_{208}$

Comparing the p value with the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we can reject the null hypothesis, and we have significant differences between the two groups at 5% of significance.

Step-by-step explanation:

Data given and notation

$\bar X_{1}=6.5$ represent the sample mean for Atlanta

$\bar X_{2}=6.7$ represent the sample mean for Chicago

$s_{1}=0.5$ represent the sample deviation for Atlanta

$s_{2}=0.7$ represent the sample standard deviation for Chicago

$n_{1}=100$ sample size for the group Atlanta

$n_{2}=110$ sample size for the group Chicago

t would represent the statistic (variable of interest)

$\alpha=0.01$ significance level provided

Develop the null and alternative hypotheses for this study?

We need to conduct a hypothesis in order to check if the meanfor atlanta is different from the mean of Chicago, the system of hypothesis would be:

Null hypothesis: $\mu_{1}=\mu_{2}$

Alternative hypothesis: $\mu_{1} \neq \mu_{2}$

Since we don't know the population deviations for each group, for this case is better apply a t test to compare means, and the statistic is given by:

$t=\frac{\bar X_{1}-\bar X_{2}}{\sqrt{\frac{s^2_{1}}{n_{1}}+\frac{s^2_{2}}{n_{2}}}}$ (1)

t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

Calculate the value of the test statistic for this hypothesis testing.

Since we have all the values we can replace in formula (1) like this:

$t=\frac{6.5-6.7}{\sqrt{\frac{0.5^2}{100}+\frac{0.7^2}{110}}}}=-2.398$

What is the p-value for this hypothesis test?

The degrees of freedom are given by:

$df = n_1 +n_2 -2= 100+110-2= 208$

Since is a bilateral test the p value would be:

$p_v =2*P(t_{208}$

Based on the p-value, what is your conclusion?

Comparing the p value with the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we can reject the null hypothesis, and we have significant differences between the two groups at 5% of significance.

3 0

3 years ago

Read 2 more answers

Can someone help me with this task please? !!

viva [34]

Answer:

we need to get your brain thinking in this way. that you begin to understand how to do these things.

airways to say that your brain is not working that way, is not a valid excuse. we need to change that. your brain needs to get used to this way of thinking.

so, please, please, PLEASE go through the explanations below and tell me, where exactly in these explanations you stopped understanding what I was saying. so that I can better explain to you what is happening.

1. (0, -2)

2. 4

3. a geometric sequence. the common ratio is -2.0

4. the third option

5. the fourth option

Step-by-step explanation:

1. as x increases, y decreases. until, suddenly after x=0, this tendency reverses, and with increasing x also y increases. so, this is a turning point.

2. look at the line. it only starts with x>0 (it looks like x is around 1).

"input" is all the values of x the function has a defined result for (y = result values).

so, as there is no line for negative x, we can eliminate the first 2 answers.

x=0 is no valid answer either (as mentioned above, the line only starts well after x=0).

in the answer options the only x value having an y value above or below this x value is x=4.

3. look at the difference between 2 numbers next to each other in the sequence.

2.4 to -4.8

-4.8 to 9.6

and so on.

what do we need to do to get from the left to the right ?

we need to multiply by -2.

so, the relationship between "sequence item n" (an) to "sequence item n-1" (an-1) is a ratio, a multiplication factor :

an/an-1 = -2

4. it is completely simple. a function can be many things. on an x/y coordinate grid it can have gaps, it can have sharp direction changes,...

but there us one thing a function can never have : multiple different y values for one x value.

in the first graph x=2 has two different y values (-1 and -3). so, it is not clear what the result for x=2 would be. and that means, it is not a function.

in the second graph x=4 has two different y values.

in the third graph all is OK.

in the fourth graph x=-2 has two different y values.

so, only the third option is a function.

5. this function calculates the height of the thrown rock after t seconds of flight.

therefore, only the fourth answer makes sense.

4 0

3 years ago