Why might u want to estimate by rounding each value to the nearest $1 instead of to the nearest $5

3x - 5y = 15<br> x - 4y = 12<br> Substitution method

Scorpion4ik [409]

Answer:

x=0,y=-3

Step-by-step explanation:

3x-5y=15 - equation(1)

x-4y=12 => x=12+4y -equation (2)

Replace equation (2) in equation (1)

3(12+4y)-5y=15

36+12y-5y=15

7y=15-36

7y= -21

y = -21/7

y=-3

If y=-3,then replace in equation (1) ; 3x -5(-3)=15

3x+15=15

3x=0

x=0

4 0

3 years ago

A random sample of 9 wheels of cheese yielded the following weights in pounds has a sample mean of 20.90 and a sample variance o

Ronch [10]

Answer:

$2.002 \leq \sigma^2 \leq 11.365$

Step-by-step explanation:

1) Data given and notation

s represent the sample standard deviation

$s^2$ represent the sample variance

n=9 the sample size

Confidence=90% or 0.90

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 mean or variance 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.

The Chi Square distribution is the distribution of the sum of squared standard normal deviates .

2) Calculating the confidence interval

The confidence interval for the population variance is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

On this case we need to find the sample standard deviation with the following formula:

$s=sqrt{\frac{\sum_{i=1}^9 (x_i -\bar x)^2}{n-1}}
The sample variance given was [tex]s^2=3.45$

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

$df=n-1=9-1=8$

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical values.

The excel commands would be: "=CHISQ.INV(0.05,8)" "=CHISQ.INV(0.95,8)". so for this case the critical values are:

$\chi^2_{\alpha/2}=15.507$

$\chi^2_{1- \alpha/2}=2.732$

And replacing into the formula for the interval we got:

$\frac{(9)(3.45)}{15.507} \leq \sigma \frac{(9)(3.45)}{2.732}$

$2.002 \leq \sigma^2 \leq 11.365$

7 0

3 years ago

Carys is checking her tax bill for the last year .the tax rates were as follows: no tax on the first 11000 of earnings .earnings

faust18 [17]

Answer:

$7,440.

Step-by-step explanation:

We have been given the tax rates as follows:

$0-$11,000 = No tax.

$11,000-$43,000 = 20%.

$43,000-$150,000 = 40%.

Earnings over $150,000 = 45%.

Since last year Carys earned $45,600, so we will have to find the tax paid by her for 11,000-43,000 at rate of 20%, then the tax for amount over 43,000 at the rate of 40%.

$\text{The amount of tax paid by Carys for 11000-43000}=\frac{20}{100}\times (43,000-11,000)$