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2 years ago

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Xian and his cousin Kai both collect stamps. Xian has 56 stamps, and Kai has 80 stamps. The boys recently joined different stamp

collecting clubs. Xians club will send him 12 new stamps per month. Kai’s club will send him 8 new stamps per month. After how many months will Xian and Kai have the same number of stamps? How many stamps will they each have?

1 answer:

kondaur [170]2 years ago

4 0

Answer:

all work is pictured/shown

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A certain amount of money is shared in a ratio 2:3:9. If the difference between the first and second shares is $40, then the amo

Alex787 [66]

Answer:

The amount of money shared is 360

Step-by-step explanation:

We are given that A certain amount of money is shared in a ratio 2:3:9.

Let x be the ratio

So, Shares of amount = 2x,3x and 9x

We are given that the difference between the first and second shares is $40

$\Rightarrow 3x-2x=40$

$x=40$

So, Shares are :

2x=2(40)=80

3x=3(40)=120

4x=4(40)=160

So,Total amount = 80+120+160=360

Hence the amount of money shared is 360

3 0

2 years ago

Consider the following sample of observations on coating thickness for low-viscosity paint.

Julli [10]

Answer:

a) $\bar X = \frac{\sum_{i=1}^n X_i}{n}$

And for this case if we use this formula we got:

$\bar x = 1.3538$

b) Since we have n =16 values for the sample the median can be calculated as the average between position 8th anf 9th and we got:

$Median = \frac{1.31+1.46}{2}= 1.385$

c) $P(X>a)=0.1$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.9 of the area on the left and 0.1 of the area on the right it's z=1.28. On this case P(Z<1.28)=0.9 and P(z>1.28)=0.1

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=1.28$

And if we solve for a we got

$a=1.3538 +1.28*0.3505=1.8024$

So the value of height that separates the bottom 90% of data from the top 10% is 1.8024.

d) $Median= \frac{x_{8} +x_{9}}{2}$

The variance for this estimator is given by:

$Var(\frac{x_{8} +x_{9}}{2}) = \frac{1}{4} Var(X_{8} +X_{9})$

We can assume the obervations independent so then we have:

$Var(\frac{x_{8} +x_{9}}{2}) = \frac{1}{4} (2\sigma^2) = \frac{\sigma^2}{2}$

And replacing we got:

$Var(\frac{x_{8} +x_{9}}{2})= \frac{0.3105^2}{2}= 0.0482$

And the standard error would be given by:

$Sd(\frac{x_{8} +x_{9}}{2})= \sqrt{0.0482}=0.2196$

Step-by-step explanation:

Data given:

0.86 0.88 0.88 1.07 1.09 1.17 1.29 1.31 1.46 1.49 1.59 1.62 1.65 1.71 1.76 1.83

Part a

We can calculate the mean with the following formula:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

And for this case if we use this formula we got:

$\bar x = 1.3538$

Part b

For this case in order to calculate the median we need to put the data on increasing way like this:

0.86 0.88 0.88 1.07 1.09 1.17 1.29 1.31 1.46 1.49 1.59 1.62 1.65 1.71 1.76 1.83

Since we have n =16 values for the sample the median can be calculated as the average between position 8th anf 9th and we got:

$Median = \frac{1.31+1.46}{2}= 1.385$

Part c

For this case we can assume that the mean is $\mu = 1.3538$

And we can calculate the population deviation with the following formula:

$\sigma = \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{N}}$

And if we replace we got: $\sigma= 0.3105$

And assuming normal distribution we have this:

$X \sim N (\mu = 1.3538, \sigma= 0.3105)$

For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.1$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.9 of the area on the left and 0.1 of the area on the right it's z=1.28. On this case P(Z<1.28)=0.9 and P(z>1.28)=0.1

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=1.28$

And if we solve for a we got

$a=1.3538 +1.28*0.3505=1.8024$

So the value of height that separates the bottom 90% of data from the top 10% is 1.8024.

Part d

The median is defined as :

$Median= \frac{x_{8} +x_{9}}{2}$

The variance for this estimator is given by:

$Var(\frac{x_{8} +x_{9}}{2}) = \frac{1}{4} Var(X_{8} +X_{9})$

We can assume the obervations independent so then we have:

$Var(\frac{x_{8} +x_{9}}{2}) = \frac{1}{4} (2\sigma^2) = \frac{\sigma^2}{2}$

And replacing we got:

$Var(\frac{x_{8} +x_{9}}{2})= \frac{0.3105^2}{2}= 0.0482$

And the standard error would be given by:

$Sd(\frac{x_{8} +x_{9}}{2})= \sqrt{0.0482}=0.2196$

6 0

2 years ago

Henry works at a warehouse where he earns $23.56 per hour. How much money will Henry earn after working for 37 hours and 42 minu

Burka [1]

Answer:

$888.21

Step-by-step explanation:

We'll break this problem into two chunks.

First, find the number of dollars Henry gets after working for 37 hours. Since he gets paid $23.56 per hour, all you do is multiply how many hours he's worked (37) by the rate he gets paid (23.56) which gets you $871.72.

Second, adding 42 minutes onto the 37 hours. Since there are 60 minutes in one hour, all you have to do is divide 42 minutes by 60 minutes to get how much of 42 minutes is 1 hour, which is 0.7. Multiply 0.7 by 23.56 (the rate he gets paid per hour) and you have $16.49.

Adding the two sums gets you 888.21 dollars in total.

8 0

2 years ago

A yard is equal in length to three feet. The function f(x) takes a measurement in yards (as input) and returns a measurement in

Grace [21]

If it takes yards and turns it into feet then it just multiplies it by 3

so if the input is 10.5 then you just multiply it by three

31.5 feet is the imput

3 0

2 years ago

Read 2 more answers

You are setting up a zip line in your yard. You map out your yard in a coordinate plane. An equation of the line representing th

finlep [7]

The <u>correct answer</u> is:

9.2 ft.

Explanation:

The distance from a point (m,n) to a line Ax+By+C=0 is given by the formula:
$d=\frac{|Am+Bn+C|}{\sqrt{A^2+B^2}}$

We first need to write our equation in the form Ax+By+C=0.
y=(-6/7)x+7

First we will add 6/7x to each side:
y+6/7x=(-6/7x)+7+(6/7x)
y+6/7x=7

Now we will subtract 7 from each side:
y+6/7x-7=7-7
y+6/7x-7=0

It will be easier to work with this equation if we do not have fractions. We can accomplish this by multiplying everything by the denominator of the fraction, 7:
y(7)+(6/7x)(7)-7(7)=0
7y+(42/7)x-49=0
7y+6x-49=0

Now we rearrange the terms to the x term is in front:
6x+7y-49=0

This is in the form Ax+By+C=0, where A=6, B=7 and C=-49.

Substituting these into our formula above along with our coordinates from our point (m,n)=(6, 14) we have:
$d=\frac{|Am+Bn+C|}{\sqrt{A^2+B^2}}
\\
\\d=\frac{|6(6)+7(14)-49|}{\sqrt{6^2+7^2}}
\\
\\d=\frac{|36+98-49|}{\sqrt{36+49}}
\\
\\d=\frac{|85|}{\sqrt{85}}=\frac{85}{\sqrt{85}}=9.2
$

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2 years ago