The volume of a gas in a container varies inversely as the pressure on the gas. If a gas has a volume of 356 cubic inches under a pressure of 6 pounds per square inch, what will be its volume if the pressure is increased to 7 pounds per square inch? Round your answer to the nearest integer if necessary.

Answer:

[tex]\large \boxed{{y=18}}[/tex]

Step-by-step explanation:

[tex]1(y+3)=2(y+-4)+- 7[/tex]

Expand brackets.

[tex]y+3=2y-8+- 7[/tex]

Simplify.

[tex]y+3=2y-15[/tex]

Add -y and 15 on both sides.

[tex]y+3-y+15=2y-15-y+15[/tex]

Simplify.

[tex]3+15=2y-y[/tex]

[tex]18=y[/tex]

Answer:

18

Step-by-step explanation:

● 1 (y+3) = 2 (y+(-4) )+ (-7)

When you multiply by 1 you get the same result.

● y+3 = 2 (y+(-4))+(-7)

When you have a + sign with a - sign write -.

● y+3 = 2(y-4)-7

Multiply 2 by (y-4) and simplify

● y+3 = (2y-8)-7

● y+3 = 2y -8-7

● y+3 = 2y -15

Add 15 to both sides

● y +3+15 = 2y-15 +15

● y + 18 = 2y

Sibstract y from both sides

● y +18 - y = 2y -y

● 18 = y

Answer:

x = 58

Step-by-step explanation:

The exterior angle is equal to the sum of the opposite interior angles

90  = 32+x

Subtract 32 from each side

90-32 = x

58 =x

Answer:

(a) 1.341

(b) -2.539

(c) -2.160 and 2.160

Step-by-step explanation:

(a) We have to find the critical​ value(s) for a​ right-tailed test of a population mean at the alpha = 0.10 level of significance with 15 degrees of freedom. ​

Since the degrees of freedom are included here, so we will use t table here for a population mean test.

In the table there are two values given, one is the degrees of freedom and another is the value of P.

P is the level of significance at which the critical values are calculated.

So, here the degrees of freedom (n - 1) = 15 and the level of significance for a right-tailed test is 0.10, i.e. P = 10%

Now, looking in the t table with P = 10% and [tex]\nu[/tex] = 15, we get the critical value of 1.341.

(b) We have to find the critical​ value(s) for a​ left-tailed test of a population mean at the alpha = 0.01 based on a sample size of n = 20. ​

Since the degrees of freedom are included here, so we will use t table here for a population mean test.

In the table there are two values given, one is the degrees of freedom and another is the value of P.

P is the level of significance at which the critical values are calculated.

So, here the degrees of freedom (n - 1) = 20 - 1 = 19 and the level of significance for a left-tailed test is 0.01, i.e. P = 1%

Now, looking in the t table with P = 1% and [tex]\nu[/tex] = 19, we get the critical value of 2.539. But since it is a left-tailed test, so the critical value will be -2.539.

(c) We have to find the critical​ value(s) for a​ two-tailed test of a population mean at the alpha = 0.05 level of significance based on a sample size of n = 14. ​

Since the degrees of freedom are included here, so we will use t table here for a population mean test.

In the table there are two values given, one is the degrees of freedom and another is the value of P.

P is the level of significance at which the critical values are calculated.

So, here the degrees of freedom (n - 1) = 14 - 1 = 13 and the level of significance for a two-tailed test is [tex]\frac{0.05}{2}[/tex] is 0.025, i.e. P = 2.5%.

Now, looking in the t table with P = 2.5% and [tex]\nu[/tex] = 13, we get the critical value of -2.160 and 2.160 for a two-tailed test.

Answer:

(a)

dependent

(b)

x = -3t - 12

y = -5t - 16

z = t

Step-by-step explanation:

2x - 3y - 9z = 24       Eq. 1

x + 3z = -12                Eq. 2

-3x + y - 4z = 20        Eq. 3

      2x - 3y - 9z = 24

(+)  -9x + 3y - 12x = 60     3 * Eq. 3

--------------------------------

     -7x           -21z = 84     Eq. 4

       7x + 21z = -84          7 * Eq. 2

(+)    -7x - 21z = 84            Eq. 4

-----------------------------

                  0  = 0

(a) The system is dependent.

(b)

z = t

x + 3z = -12                Eq. 2

x + 3t = -12

x = -3t - 12

2x - 3y - 9z = 24       Eq. 1

2(-3t - 12) - 3y - 9t = 24

-6t - 24 - 3y - 9t = 24

-3y - 15t = 48

-y - 5t = 16

-y = 5t + 16

y = -5t - 16

x = -3t - 12

y = -5t - 16

z = t

Answer:

Tran family's sprinkler was used for 20 hours

Green's  family's sprinkler was used for 30 hours

Step-by-step explanation:

Let the hours for which Tran family's sprinkler used is x hours

water output rate for the Tran family's sprinkler = 35L per hour

water output from  Tran family's sprinkler in x hours = 35*x L = 35x

Let the hours for which Green family's sprinkler used is y hours

water output rate for the Green family's sprinkler = 40L per hour

water output from  Green family's sprinkler in x hours = 40*y L = 40y

Given

The families used their sprinklers for a combined total of 50 hours

thus

x + y = 50 -------------------equation 1

y = 50-x

total water output of 1900L

35x+40y = 1900  -------------------equation 1

using  y = 50-x in equation 2, we have

35x + 40(50-x) = 1900

35x + 2000 - 40x = 1900

=> -5x = 1900 - 2000 = -100

=> x = -100/-5 = 20

y = 50-20 = 30

Thus,

Tran family's sprinkler was used for 20 hours

Green's  family's sprinkler was used for 30 hours

Answer:

The​ z-score for 1880 is 1.34.

The​ z-score for 1190 is -0.88.

The​ z-score for 2130 is 2.15.

The​ z-score for 1350 is -0.37.

And the z-score of 2130 is considered to be unusual.

Step-by-step explanation:

The complete question is: A standardized​ exam's scores are normally distributed. In recent​ years, the mean test score was 1464 and the standard deviation was 310. The test scores of four students selected at random are ​1880, 1190​, 2130​, and 1350. Find the​ z-scores that correspond to each value and determine whether any of the values are unusual. The​ z-score for 1880 is nothing. ​(Round to two decimal places as​ needed.) The​ z-score for 1190 is nothing. ​(Round to two decimal places as​ needed.) The​ z-score for 2130 is nothing. ​(Round to two decimal places as​ needed.) The​ z-score for 1350 is nothing. ​(Round to two decimal places as​ needed.) Which​ values, if​ any, are​ unusual? Select the correct choice below​ and, if​ necessary, fill in the answer box within your choice. A. The unusual​ value(s) is/are nothing. ​(Use a comma to separate answers as​ needed.) B. None of the values are unusual.

We are given that the mean test score was 1464 and the standard deviation was 310.

Let X = standardized​ exam's scores

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

                          Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = mean test score = 1464

           [tex]\sigma[/tex] = standard deviation = 310

S, X ~ Normal([tex]\mu=1464, \sigma^{2} = 310^{2}[/tex])

Now, the test scores of four students selected at random are ​1880, 1190​, 2130​, and 1350.

So, the z-score of 1880 =  [tex]\frac{X-\mu}{\sigma}[/tex]

                                      =  [tex]\frac{1880-1464}{310}[/tex]  = 1.34

The z-score of 1190 =  [tex]\frac{X-\mu}{\sigma}[/tex]

                                =  [tex]\frac{1190-1464}{310}[/tex]  = -0.88

The z-score of 2130 =  [tex]\frac{X-\mu}{\sigma}[/tex]

                                =  [tex]\frac{2130-1464}{310}[/tex]  = 2.15

The z-score of 1350 =  [tex]\frac{X-\mu}{\sigma}[/tex]

                                =  [tex]\frac{1350-1464}{310}[/tex]  = -0.37

Now, the values whose z-score is less than -1.96 or higher than 1.96 are considered to be unusual.

According to our z-scores, only the z-score of 2130 is considered to be unusual as all other z-scores lie within the range of -1.96 and 1.96.

Answer:

The angle [tex]\theta[/tex] at which the sun is hitting the ground is:

[tex]\theta\approx 59.74^o[/tex]

Step-by-step explanation:

You can use right angle trigonometry to solve this, since the man (6 ft tall) and the shadow on the ground (3.5 ft long) form a right angle triangle as shown on the attached image.

The use the tangent function to find the angle that the sun's rays make with the ground:

[tex]tan(\theta)=\frac{opposite}{adjacent} \\tan(\theta)=\frac{6}{3.5} \\\theta=arctan(\frac{6}{3.5})\\\theta\approx 59.74^o[/tex]

Answer:

25(4 + 3)

Step-by-step explanation:

100 = 2^2 + 5^2

75 = 3 * 5^2

GCF = 5^2 = 25

100 + 75 =

= 25 * 4 + 25 * 3

= 25(4 + 3)

Answer:

x >162

Step-by-step explanation:

x+54 > 216

Subtract 54 from each side

x+54-54 > 216 - 54

x >162

Answer:

[tex]\huge \boxed{{x>162}}[/tex]

Step-by-step explanation:

[tex]x+54 > 216[/tex]

[tex]\sf Subtract \ 54 \ from \ both \ parts.[/tex]

[tex]x+54 -54> 216-54[/tex]

[tex]x>162[/tex]

Answer:

The null hypothesis is rejected and  research hypotheses is supported

Step-by-step explanation:

From the question we are told that

    The population mean is  [tex]\mu = 30[/tex]

     The standard deviation is [tex]\sigma = 5[/tex]

      The sample size is  n =  1

      The  cutoff Z score for significance is  [tex]Z_{\alpha } = 1.96[/tex]

       The mean score is  [tex]\= x = 45[/tex]

Generally the test hypothesis is mathematically represented as

            [tex]t = \frac{\= x - \mu }{ \frac{ \sigma }{\sqrt{n} } }[/tex]

=>         [tex]t = \frac{45 - 30 }{ \frac{ 5}{\sqrt{1} } }[/tex]

=>         [tex]t = 3[/tex]

From the obtained value  we can see that [tex]t > Z_{\alpha }[/tex]

Hence the null hypothesis is rejected and  research hypotheses is supported

Answer:

B.

Step-by-step explanation:

10c + 5 ≤ 45

10c ≤ 40

c ≤ 4

Since the inequality uses the less than or equal to sign, we use a shaded circle on the number line. Since c is less than or equal to 4, your answer will be B, since the line extends infinitely to the left of 4.

Hope this helps!

Answer:

B

Step-by-step explanation:

To get the answer, you need to simplify or re-write the equation given:

Next, group the like terms together:

Now, we can apply algebra to simplify the equation further:

Now, look at your options. Only option B matches our equations. Therefore, B is the correct answer.

Answer:

d. 27 cubic feet

Step-by-step explanation:

volume of cube = s^3 = B * s

volume of pyramid = (1/3) * B * h

The volume of a pyramid is 1/3 of the area of the base multiplied by the height. The volume of a cube is the area of the base multiplied by the height. Since the volume of a pyramid has the fraction 1/3 and the volume of the cube does not, then the volume of a cube is 3 times greater than the volume of a pyramid that fits inside and has the same base area.

volume of pyramid = 9 cu ft

volume of cube = 3 * 9 cu ft = 27 cu ft

Answer: d. 27 cubic feet

Answer:

27 ft^3 (Answer d)

Step-by-step explanation:

Here the volume of the pyramid is (1/3) the volume of the cube:

Letting s represent the length of one side of the base,

(1/3)(s)^2(s) = 9 ft^3, equivalent to  s^3 = 27.

Solving for s, we get s = 3 ft.

Thus, the volume of the cube is V = s^3 = (3 ft)^3 = 27 ft^3 (Answer d)

Answer:

= - 54

Step-by-step explanation:

- 99 + 3^2•5

- 99 + 9 × 5

- 99 + 45

= - 54

Answer:

no

Step-by-step explanation:

2(4+10)+20

2(14)+20

28+20

48

Answer:

1260

Step-by-step explanation:

(7!)/ (2!times 2!)

7 factorial divided by 2factorial times 2 facotiral

The number of distinguishable ways the letters of the following word can be arranged 'MILLION' is 1260.

The different arrangements which can be made out of a given number of objects by taking out some or all at a time are called permutations.

The number of different permutations of n objects with m₁ repeated items, m₂ repeated items,...,mₙ repeated items can be calculated as;

m!/(m₁!)(m₂!)...(mₙ!)

Here, the letter of the word 'MILLION' is a total of 7 letters.

So, the number of possible arrangements will be

(7!)/ (2!times 2!)

= 1260

Therefore the number of distinguishable ways the letters of the following word can be arranged 'MILLION' is 1260.

Learn more about permutations here -

brainly.com/question/4301655

#SPJ2

Answer:

  93

Step-by-step explanation:

First differences increase by 4 each time. The given numbers are a quadratic sequence that can be described by 2n² -2n +9. The 7th term would be 93.

_____

First differences are ...

  13-9 = 4, 21-13 = 8, 33-21 = 12, 49-33 = 16, 69-49 = 20

Second differences are ...

  8-4 = 4, 12-8 = 4, 16-12 = 4, 20-16 = 4

When second differences are constant, the sequence can be represented by a second-degree polynomial function. The leading coefficient is half the value of the second differences.

Answer:

number of games each player has played

the average number of points each player's team scores per

Step-by-step explanation:

number of games each player has played

the average number of points each player's team scores per

Answer:

$13,450

Step-by-step explanation:

The fixed cost of production is $13,450, this is because a fixed cost of production is the amount of cost that does not change with an increase or decrease in the amount of the goods or services produced. Fixed cost of production are paid by companies. It is one of the two component of the total cost of goods or services along with the variable cost.

In regard to the information given in the  question, no matter how many spinners the company produces, the fixed cost will remain the same.

Assuming x is the variable cost which signifies the number of spinners produced, this literally implies that the cost to produce each spinner is $1.28 and the fixed cost which is independent  of the production is $13,450.

Hence, the  fixed cost of production is $13,450.

Answer:

The fraction [tex]\displaystyle \frac{55}{22}[/tex] is indeed a rational number.

Step-by-step explanation:

A number [tex]x[/tex] is rational if and only if there exist two integers [tex]p[/tex] and [tex]q[/tex] (where [tex]q \ne 0[/tex]) such that [tex]x = \displaystyle \frac{p}{q}[/tex].

[tex]\displaystyle \frac{55}{22}[/tex], the number in question here is already written in the form of a fraction. The two integers [tex]p = 55[/tex] and [tex]q = 22[/tex] ([tex]q \ne 0[/tex]) meet the requirement that [tex]\displaystyle \frac{55}{22} = \frac{p}{q}[/tex]. Therefore, [tex]\displaystyle \frac{55}{22}\![/tex] is indeed a rational number.

Side note: the [tex]p[/tex] and [tex]q[/tex] here ([tex]q \ne 0[/tex]) don't have to be unique. For example:

because [tex]\displaystyle \frac{55}{22} = \frac{5 \times 11 }{2 \times 11} = \fraac{5}{2}[/tex], both of the following pairs could satisfy [tex]\displaystyle \frac{55}{22} = \frac{p}{q}[/tex]:

Answer:

[tex] {(x + 1)}^{2} + {(y - 1)}^{2} = 9[/tex]

[tex] {x} ^{2} + {y} ^{2} + 2x - 2y - 7 = 0 [/tex]

*Correct Question:

Which relationships have the same constant of proportionality between y and x as the equation 3y=27x?

Answer:

A, B, C

Step-by-step explanation:

Given that [tex] 3y = 27x [/tex] , we can simplify to get a proportionality statement that exists between X and y. Thus

[tex] 3y = 27x [/tex]

Divide both sides by 3

[tex] \frac{3y}{3} = \frac{27x}{3} [/tex]

[tex] y = 9x [/tex]

Thus, we can say, y would always be 9 times the quantity of x.

From the options given, examine which options have this proportionality statement as well.

Option A, y = 9x is same as the statement.

Option B, 2y = 18x, conforms to the same statement. If we simply further, we would have y = 9x

Option C, the graph shows that when x = 1, y = 9. This also confirms to the same constant of proportionality in the given equation.

Option D and E do not have same constant of proportionality.

The right options are A, B, and C.

Answer:

The full answer is 4.40625 but rounded it would be 4.41

Answer:

203.7

Step-by-step explanation:

5% of 194 added to 194 =

= 5% * 194 + 194

= 0.05 * 194 + 194

= 9.7 + 194

= 203.7

Answer: 0.8749

Step-by-step explanation:

Given, The time, X minutes, taken by Tim to install a satellite dish is assumed to be a normal random variable with mean 127 and standard deviation 20.

Let x be the time taken by Tim to install a satellite dish.

Then, the probability that Tim will takes less than 150 minutes to install a satellite dish.

[tex]P(x<150)=P(\dfrac{x-\text{Mean}}{\text{Standard deviation}}<\dfrac{150-127}{20})\\\\=P(z<1.15)\ \ \ [z=\dfrac{x-\text{Mean}}{\text{Standard deviation}}]\\\\=0.8749\ [\text{By z-table}][/tex]

hence, the required probability is 0.8749.

Answer:

This is a geometric progresion that begins with 1 and each term is 1/3 the preceeding term

   Let Pn represent the nth term in the sequence

   Then Pn = (1/3)^n-1

   From this P14 = (1/3)^13 = 1/1594323

5. The sum of the first n terms of a GP beginning a with ratio r is given by

   Sn = a* (r^n+1 - 1)/(r - 1)

   With n = 10, a = 1 and r = 1/3, S10 = ((1/3)^11 - 1)/(1/3 - 1) = 1.500

Answer:

Measure number 2 of the tape is for the pinus  

Step-by-step explanation:

To measure, kindly place pinus next to ruler and pinus will be in line with measurement #2

Call and ask for pinus step by step

Answer:

7 and one sixteenths of an inch.

Answer:

Option C - Reject H0. We have convincing evidence that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722.

Step-by-step explanation:

First of all let's define the hypothesis;

Null hypothesis;H0; μ = $48,722

Alternative hypothesis;Ha; μ > $48,722

Now, let's find the test statistic for the z-score. Formula is;

z = (x' - μ)/(σ/√n)

We are given;

x' = 48,722

μ = 49,870

σ = 3900

n = 50

Thus;

z = (49870- 48722)/(3900/√50)

z = 2.08

So from online p-value calculator as attached, using z = 2.08 and α = 0.05 ,we have p = 0.037526

This p-value of 0.037526 is less than the significance value of 0.05,thus, we reject the claim that that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722

==================================================

Explanation:

Dividing the side lengths, the scale factor is 6/3 = 2. This means the larger figure has a side length twice as long compared to its smaller counterpart.

How can we use this to figure out how the areas are connected? By simply squaring the scale factor to get 2^2 = 2*2 = 4, then we divide the larger area over 4 to get 24/4 = 6.

The longer side is 2 times longer

The larger area is 4 times larger

--------------------

Let's say we had a 3 by 3 square. It's area would be 9.

Also, let's say we had a 6 by 6 square. It's area is 36.

Notice the ratio of areas is 36/9 = 4, so the larger square is 4 times larger than the smaller. This 4 matches with what we got earlier.

----------------------

Another example:

square A is 7 by 7 with area 49

square B is 21 by 21 with area 441

ratio of areas is 441/49 = 9, which is exactly equal to 3^2, and the 3 comes from the ratio of the sides 21/7 = 3.

------------------------

So in short, you find the linear scale factor by dividing the sides. Then you square the result to get the area scale factor, which you use to find the smaller area.

linear scale factor = (new side)/(old side)

area scale factor = (linear scale factor)^2

smaller area = (larger area)/(area scale factor)

Answer:

The largest possible weight of flour is 11.25  pounds.

Step-by-step explanation:

To start with, we will assume that the weight of 1 sack of sugar = x pounds

We will also assume that the weight of 1 sack of flour = y pounds

So, the weight of 2 sacks of sugar = 2 * (x) = 2x

Same thing goes for the weight of 3 sacks of flour  = 3 * (y) = 3y

Supposing that the weight of (2 sacks of sugar + 3 sacks of flour) ≤ 40 pounds

= 2x + 3y ≤ 40............ we'll call that equation 1.

Also, suppose that the weight of ( 1 sack of flour) ≤ 2 sacks of sugar + 5 pounds

= y ≤ 2x + 5........................ we'll call that equation 2

Therefore, we'll solve for the values of x and y in the two equations and we will get:

2x + 3y ≤ 40

y ≤  2x + 5

Now, substitute the value of y into equation 1

2x + 3y ≤ 40 ⇒ 2x + 3(2x +5) =40

⇒ 2x + 6x + 15= 40

⇒ 8x + 15 = 40

⇒ 8x = 25

⇒ x = 25/8

⇒ x = 3.12

x cannot be more than 3.12 pounds, so we solve for y

Putting the value of x into equation 2, we'll get

⇒ 2y + 5 = 2(3.12) + 5

⇒ y = 11.25 pounds.

So, n cannot be more than 11.25 pounds