Which ordered pair or pairs are solutions to the equation? Select ALL that apply.

The temperature, T, of a given mass of gas varies inversely with its Volume,V. The temperature of 98 cm ³ of a certain gas is 28

Naily [24]

Answer:

T₂ = 421.4 K

Step-by-step explanation:

The temperature, T, of a given mass of gas varies inversely with its Volume,V.

$T\propto \dfrac{1}{V}\\\\V_1T_1=V_2T_2$

We have,

V₁ = 98 cm³, T₁ = 28° C = (28+273) K = 301 K

V₂ = 70 cm₃

We need to find the new temperature of the gas. Using the above relation to find T₂.

$T_2=\dfrac{V_1T_1}{V_2}\\\\T_2=\dfrac{98\times 301}{70}\\\\T_2=421.4\ K$

Hence, the required temperature of the gas is 421.4 K.

4 0

2 years ago

Identify two composite numbers that each have 8 as a factor.

Lemur [1.5K]

Two composite numbers that have 8 as a factor are 16 and 24.

7 0

3 years ago

A statistics student wants to compare his final exam score to his friend's final exam score from last year; however, the two exa

yarga [219]

Answer:

$z= \frac{85-70}{10}=1.5$

$z= \frac{45-35}{5}=2$

So then the correct answer for this case is:

B) Our student, Z= 1.50; his friend, Z=2.00.

Step-by-step explanation:

Assuming this complete question:

A statistics student wants to compare his final exam score to his friend's final exam score from last year; however, the two exams were scored on different scales. Remembering what he learned about the advantages of Z scores, he asks his friend for the mean and standard deviation of her class on the exam, as well as her final exam score. Here is the information:

Our student: Final exam score = 85; Class: M = 70; SD = 10.

His friend: Final exam score = 45; Class: M = 35; SD = 5.

The Z score for the student and his friend are:

A) Our student, Z= -1.07; his friend, Z= -1.14.

B) Our student, Z= 1.50; his friend, Z=2.00.

C) Our student, Z= 1.07; his friend, Z= -1.14.

D) Our student, Z= 1.07; his friend, Z= 1.50

Step-by-step explanation:

Previous concepts

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 Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution

Let X the random variable that represent the scores for our student, and for this case we know that:

$E(X)= \mu =70, SD_X=\sigma=10$

The z score is given by:

$z=\frac{x-\mu}{\sigma}$

If we use this we got:

$z= \frac{85-70}{10}=1.5$

Let Y the random variable that represent the scores for his friend, and for this case we know that:

$E(Y)= \mu =35, SD_Y=\sigma=5$

The z score is given by:

$z=\frac{y-\mu}{\sigma}$

If we use this we got:

$z= \frac{45-35}{5}=2$

So then the correct answer for this case is:

B) Our student, Z= 1.50; his friend, Z=2.00.

3 0

3 years ago

Find the area of the shape.

Butoxors [25]

7 x 6 = 42 x 5 = 210 x 8 = 1,680 x 4 = [ 6,720 ]

4 0

3 years ago

Using algebra, solve the inequality<br> writing your answer in set notation.<br> x²-x> 20

Xelga [282]

Answer:

(-4, 0) U (1, ∞)

Step-by-step explanation:

Set each factor EQUAL to zero to find the zeroes (since it is not actually equal to zero, you will use an open circle when graphing and an open bracket when writing in interval notation).

x = 0 x-1 = 0 x + 4 = 0

x = 1 x = -4

Next, choose a value to the far left, between each of the zeroes, and to the far right to evaluate if it makes a true statement when input into the given inequality.

far left (I choose -5): -5(-5 - 1)(-5 + 4) > 0 → (-)(-)(-) > 0 → negative > 0 FALSE

- 4 to 0 (I choose -2): -2(-2 - 1)(-2 + 4) > 0 → (-)(-)(+) > 0 → positive > 0 TRUE

0 to 1 (I choose 0.5): .5(.5 - 1)(.5 + 4) > 0 → (+)(-)(+) > 0 → negative > 0 FALSE

far right (I choose 2): 2(2 - 1)(2 + 4) > 0 → (+)(+)(+) > 0 → positive > 0 TRUE

3 0

1 year ago