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2 years ago

7

Rachel read 30 minutes for every 10 minutes that she spent watching television. Nicolas read 45 minutes for every 15 minutes tha

t he watched television. The ratio of time that Rachel and Nicolas spent reading to the time they spent watching television is

2 answers:

Ainat [17]2 years ago

6 0

Answer:

Answer:

Both 3:1

Step-by-step explanation:

30:10 Divide by 10

3:1

45:15 Divided by 15

3 : 1

Click to let others know, how helpful is it

Step-by-step explanation:

k0ka [10]2 years ago

3 0

Answer:

Both 3:1

Step-by-step explanation:

30:10 Divide by 10

3:1

45:15 Divided by 15

3 : 1

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The box plot shows the number of sit-ups done by students in a gym class. What is the

Nikitich [7]

The box plot shows the number of sit-ups done by students in a gym class. What is the range of the data?

A)15 is the answer.

7 0

1 year ago

Three data entry specialists enter requisitions into a computer. Specialist 1 processes 42 percent of the requisitions, speciali

suter [353]

Answer:

The probabilities are 0.480;0.077 and 0.443 respectively

Step-by-step explanation:

This is a conditional probability exercise.

Let's define conditional probability :

Given two events A and B :

$P(A/B)=\frac{P(A,B)}{P(B)} \\P(B) > 0$

P(A,B) = P(A∩B) = P(B∩A) = P(B,A) : Is the probability that event A and event B occur at the same time.

We define the following events :

S1 : ''Specialist 1 processes requisitions''

S2 : ''Specialist 2 processes requisitions''

S3 : ''Specialist 3 preocesses requisitions''

I : ''Incorrect entered requisitions''

In our exercise :

$P(S1)=0.42\\P(S2)=0.27\\P(S3)=0.31\\P(I/S1)=0.04\\P(I/S2)=0.01\\P(I/S3)=0.05$

We are ask to find

$P(S1/I) ;P(S2/I);P(S3/I)$

We write the conditional equations :

$P(I/S1)=\frac{P(I,S1)}{P(S1)} \\0.04=\frac{P(I,S1)}{0.42} \\P(I,S1)=0.0168$

$P(I/S2)=\frac{P(I,S2)}{P(S2)} \\0.01=\frac{P(I,S2)}{0.27} \\P(I,S2)=0.0027$

$P(I/S3)=\frac{P(I,S3)}{P(S3)} \\0.05=\frac{P(I,S3)}{0.31} \\P(I,S3)=0.0155$

We also define

P(A∪B) = P(A) + P(B) - P(A∩B)

P(I) = P [(I,S1)∪(I,S2)∪(I,S3)]

$P(I) =P(I,S1) +P(I,S2)+P(I,S3)\\P(I)=0.0168+0.0027+0.0155\\P(I)=0.035$

There is no intersection between (I,S1);(I,S2) and (I,S3) because they are mutually exclusive events.

$P(S1/I)=\frac{P(I,S1)}{P(I)} =\frac{0.0168}{0.035} =0.480\\P(S2/I)=\frac{P(I,S2)}{P(I)} =\frac{0.0027}{0.035} =0.077\\P(S3/I)=\frac{P(I,S3)}{P(I)} =\frac{0.0155}{0.035} =0.443$

5 0

2 years ago

The mini muffins company bakes 1872 muffins the large mini muffin boxes hold a dozen muffins how many large boxes are needed to

lilavasa [31]

Answer:

To pack 1872 muffins the mini muffins company needs 156 large boxes.

Step-by-step explanation:

Number of muffins baked by the mini muffins company = 1872.

the large mini muffin boxes hold a dozen muffins that is the large box contains 12 muffins.( 1 Dozen = 12 )

We have to find the number of large boxes needed to pack 1872 muffins.

Using unitary method,

12 muffins is contained in 1 large box.

1 muffin is contained in $\frac{1}{12}$ large box.

1872 muffins contained in $\frac{1}{12} \times 1872=156$ large boxes.

Hence, To pack 1872 muffins the mini muffins company needs 156 large boxes.

6 0

2 years ago

In a science-fiction story, a spaceship travels 3 times faster each minute than it traveled during the minute before. If the shi

JulijaS [17]

The expression is:

$speed(minutes)=3\frac{km}{h} ^{minutes} \\\\speed(15minutes)=(3^{15})\frac{km}{4} =14348907\frac{km}{g}$

Why?

From the statement we know that the spaceship travels 3 times faster each minute that it traveled during the minute before, it can be expressed using an exponential function, its base will be the starting speed (during the first minute).

The expression will be:

$speed(minutes)=(3^{minutes})\frac{km}{h} \\\\speed(15minutes)=(3^{15})\frac{km}{h}=14348907\frac{km}{h}$

Have a nice day!

6 0

1 year ago

preliminary sample of 100 labourers was selected from a population of 5000 labourers by simple random sampling. It was found tha

VladimirAG [237]

Answer:

$n=\frac{0.4(1-0.4)}{(\frac{0.05}{1.96})^2}=368.79$

n=369

Step-by-step explanation:

1) Notation and definitions

$X=40$ number of the selected labourers opt for a new incentive scheme.

$n=100$ random sample taken

$\hat p=\frac{40}{100}=0.4$ estimated proportion of the selected labourers opt for a new incentive scheme.

$p$ true population proportion of the selected labourers opt for a new incentive scheme.

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

2) Solution tot he problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.05$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

And replacing into equation (b) the values from part a we got:

$n=\frac{0.4(1-0.4)}{(\frac{0.05}{1.96})^2}=368.79$

And rounded up we have that n=369

8 0

1 year ago