Which statements are true about the ordered pair (−1, 5) and the system of equations?

After heating a fixed volume of gas at 50 psia from 300° R to 600°R, its pressure will be:

Vadim26 [7]

Answer:

100 psia

Step-by-step explanation:

Applying,

Pressure law,

P/T = P'/T'................. Equation 1

Where P = initial pressure, P' = Final pressure, T = initial temperature, P' = Final temperature.

make P' the subject of the equation

P' = PT'/T............ Equation 2

From the question,

Given: P = 50 psia, T = 300°R = (300×5/9)K = 166.66 K, T' = 600°R = (600×5/9)K = 333.33 K

Substitute these values into equation 2

P' = (50×333.33)/166.66

P' ≈ 100 psia

P ≈ 100 psia

4 0

2 years ago

Suppose that the sample standard deviation was s = 5.1. Compute a 98% confidence interval for μ, the mean time spent volunteerin

NISA [10]

Answer:

The 95% confidence interval would be given by (5.139;5.861)

Step-by-step explanation:

1) Previous concepts

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".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

2) Confidence interval

Assuming that $\bar X =5.5$ and the ranfom sample n=1086.

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=1086-1=1085$

Since the Confidence is 0.98 or 98%, the value of $\alpha=0.02$ and $\alpha/2 =0.01$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.01,1085)".And we see that $t_{\alpha/2}=2.33$

Now we have everything in order to replace into formula (1):

$5.5-2.33\frac{5.1}{\sqrt{1086}}=5.139$

$5.5+2.333\frac{5.1}{\sqrt{1086}}=5.861$

So on this case the 95% confidence interval would be given by (5.139;5.861) We are 98% confident that the mean time spent volunteering for the population of parents of school-aged children is between these two values.

5 0

3 years ago

8 divde by 1/6 equals 48 because

nika2105 [10]

Proof:

$8\div\frac{1}{6}=\frac{8}{1}\div \frac{1}{6}=\frac{8}{1}\times\frac{6}{1}=\frac{8\times6}{1}=\frac{48}{1}=48 \\$

6 0

3 years ago

The playing time X of jazz CDs has the normal distribution with mean 52 and standard deviation 7; N(52, 7).

natita [175]

Answer:

68% of jazz CDs play between 45 and 59 minutes.

Step-by-step explanation:

The correct question is: The playing time X of jazz CDs has the normal distribution with mean 52 and standard deviation 7; N(52, 7).

According to the 68-95-99.7 rule, what percentage of jazz CDs play between 45 and 59 minutes?

Let X = playing time of jazz CDs

SO, X ~ Normal( $\mu=52, \sigma^{2} =7$ )

The z-score probability distribution for the normal distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

Now, according to the 68-95-99.7 rule, it is stated that;

68% of the data values lie within one standard deviation points from the mean.

95% of the data values lie within two standard deviation points from the mean.

99.7% of the data values lie within three standard deviation points from the mean.

Here, we have to find the percentage of jazz CDs play between 45 and 59 minutes;

For 45 minutes, z-score is = $\frac{45-52}{7}$ = -1

For 59 minutes, z-score is = $\frac{59-52}{7}$ = 1

This means that our data values lie within 1 standard deviation points, so it is stated that 68% of jazz CDs play between 45 and 59 minutes.

6 0

3 years ago

P(x)=2x 4 −x 3 +2x 2 −6P, left parenthesis, x, right parenthesis, equals, 2, x, start superscript, 4, end superscript, minus, x,

Tresset [83]

Answer:

P = -x^3 +12 / x+6

Step-by-step explanation:

Let's solve for p.

px=(2)(4)−x3+(2)(2)−6p

Step 1: Add 6p to both sides.

px+6p=−x3−6p+12+6p

px+6p=−x3+12

Step 2: Factor out variable p.

p(x+6)=−x3+12

Step 3: Divide both sides by x+6.p(x+6)

x+6

=

−x3+12

x+6

p=

−x3+12

x+6

5 0

2 years ago