how many moles of ammonia (nH4) are there in 405 liters of ammonia at STP?

The slope of the line that represents the relationship between x and y is 3.33.

What is positive and negative slope?

The slope of a line, which in mathematics is a measure of how steep it is, is the ratio of the change in the y-coordinate to the change in the x-coordinate between two points on a line. In contrast to a line with a negative slope, which is travelling downhill from left to right, a positive slope line is moving uphill from left to right. The y-coordinate rises as the x-coordinate rises in a positive slope, whereas the y-coordinate falls as the x-coordinate rises in a negative slope, to put it another way.

The slope of the line is given as:

slope = (change in y) / (change in x)

Substituting the points (0, 0) and (0.3, 1).

slope = (1 - 0) / (0.3 - 0) = 1 / 0.3 = 3.33

Hence, the slope of the line that represents the relationship between x and y is 3.33.

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To find the distance between the boat and lighthouse B, we can use the Law of Cosines. The boat is approximately \(3.33\) km away from Lighthouse B.

Here are the steps:

1. Identify the given information: - Side a = \(5.1\) km (distance from lighthouse A to the boat) - Side b = 7.2 km (distance between lighthouse A and B, west of A) - Angle C\(=180\)°\(-\)(\(90\)° \(+65\)° \(10')\)

\(=180\)° \(-155\)° \(10'\)

\(=24\) \(50'\)

(angle between sides a and b, where 90° represents the west direction and \(65\)°\(10'\) is the bearing from B)

2. Apply the Law of Cosines to find the side \(c\) (the distance between the boat and lighthouse B): \(c^{2} = a^{2} + b^{2} - 2ab * cos(C)\)

\(c^{2} = (5.1^{2} ) + (7.2^{2} ) - 2(5.1)(7.2) * cos\)(\(24\)°\(50'\))

\(c^{2} = 25.81 + 51.84 - 73.44 * 0.9063\)

\(c^{2}= 77.65 - 66.59\)

\(c^{2} =11.06 3\).

Find the square root to get the value of \(c\):

\(c = \sqrt{11.06}\)

\(c = 3.33\) km

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Answer:

Step-by-step explanation:

so u have (2, 14) and (5, 20) those two are (x,y) ur gonna put it over each other by doing it like this y^2-y^1 and x^2-x^1 so like this over each other but its y first then x (2x^1, 14y^1) (5x^2, 20y^2) then subtract those and simplify ur final answer!

y=2x+10

find slope by doing y2-y1 over x2-x1

then choose a point to plug into y=mx+b (I chose 2,14)

after that solve for b using pemdas

the you get 10 as b

Answer: $ 55

Step-by-step explanation:

When interest is compounded continuously, the final amount will be

\(A=Pe^{rt}\)

When interest is compounded daily, the final amount will be

\(A=P(1+\dfrac{r}{365})^{365t}\)

, where P= Principal , r = rate of interest , t = time

For Hunter , P= $750, r = \(6\dfrac{5}{8}\%=\dfrac{53}{8}\%=\dfrac{53}{800}=0.06625\)

t = 18 years

\(A=750e^{0.06625(18)}=\$2471.48\)

For London , P= $750, r = \(6\dfrac{1}{2}\%=\dfrac{13}{2}\%=\neq \dfrac{13}{200}=0.065\)

t = 18 years

\(A=750(1+\dfrac{0.065}{365})^{18(365)}=\$2416.24\)

Difference = $ 2471.48 - $ 2416.24 =$ 55.24≈$ 55

Hence, Hunter would have $ 55 more than London in his account .

The length of the radius AB is 6 units.

The angle ∠BAC is 90 degrees. The length of arc BC is 3π. The length of  

radius AB can be found as follows:

Hence,

length of arc = ∅ / 360 × 2πr

where

Therefore,

length of arc = 90 / 360 × 2πr

3π = 1 / 4 × 2πr

cross multiply

12π = 2πr

divide both sides by 2π

r = 6 units

Therefore,

radius AB = 6 units

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The integral by reversing the order of integration is \(\frac{1}{14}\left[e^{49}-1}\right]\).

In the given question, we have to evaluate the integral by reversing the order of integration.

The given integration is \(\int_{0}^{1}\int_{7y}^{7}e^{x^2}dxdy\).

The given integral is in the form of dxdy. We must create an integral of order dydx in order to shift the order of integration. This indicates that x is the outer integral's variable. Its bounds must be fixed and match the complete range of x over the area D.

The limit of y and x is;

0 ≤ y ≤ 1; 7y ≤ x ≤ 7; dA = dxdy

Now changing the order of integration

0 ≤ x ≤ 7; 0 ≤ y ≤ x/7; dA = dydx

I = \(\int_{0}^{7}\int_{0}^{x/7}e^{x^2}dydx\)

Now integrating with respect to dy

I = \(\int_{0}^{7}t[y]_{0}^{x/7}e^{x^2}dydx\)

I = \(\int_{0}^{7}t[x/7 - 0]e^{x^2}dydx\)

I = \(\frac{1}{7}\int_{0}^{7}xe^{x^2}dx\)

Now integrating again

I = \(\frac{1}{14}\left[e^{x^2}\right]_{0}^{7}\)

I = \(\frac{1}{14}\left[e^{(7)^2}-e^{(0)^2}\right]\)

I = \(\frac{1}{14}\left[e^{49}-1}\right]\)

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The complete question is:

Evaluate the integral by reversing the order of integration.

\(\int_{0}^{1}\int_{7y}^{7}e^{x^2}dxdy\)

The only number that is 10 times as much as 72 is 720.

To find the numbers that are 10 times as much as 72 or 1/10 of 72, we can perform the following calculations:

10 times 72 = 720

1/10 of 72 = 7.2

So, the numbers that are 10 times as much as 72 are 720.

The number 67 is not 10 times as much as 72 or 1/10 of 72. Therefore, it is not one of the numbers we are looking for.

On the other hand, 1/10 of 72 is 7.2, which is not one of the numbers we are looking for either.

Therefore, the only number that is 10 times as much as 72 is 720.

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complete question

Select all the numbers that are 10 times as much as 72, 67, or 1/10 of 72.

- 67

-46

-720

-480

To determine the significance of the slope in regression, perform a hypothesis test by calculating the t-value, degrees of freedom, and P-value.

If the P-value is less than the significance level, the slope is considered significant, indicating a meaningful relationship between the independent and dependent variables.

To determine the significance of the slope in regression, we need to conduct a hypothesis test using the following terms:
Null hypothesis (H0):

The null hypothesis states that there is no significant relationship between the independent and dependent variables, meaning the slope is zero (β1 = 0).
Alternative hypothesis (H1):

The alternative hypothesis states that there is a significant relationship between the independent and dependent variables, meaning the slope is not equal to zero (β1 ≠ 0).

Test statistic:

The test statistic is calculated using the sample data to determine if we should reject or fail to reject the null hypothesis. In the case of regression, the test statistic is the t-value, calculated as:
t-value = (b1 - β1) / standard error of b1
where b1 is the sample slope, and the standard error of b1 measures the precision of the slope estimate.
Degrees of freedom (df): Degrees of freedom is the number of independent observations in the sample that are available for estimating the slope.

In a simple linear regression, the degrees of freedom is calculated as:
df = n - 2
where n is the sample size.
P-value:

The P-value is the probability of obtaining a test statistic as extreme or more extreme than the observed one, assuming the null hypothesis is true.

If the P-value is less than the chosen significance level (e.g., α = 0.05), we reject the null hypothesis and conclude that the slope is significant.

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When comparing two sample means, we can safely reject the null hypothesis if the calculated test statistic exceeds the critical value corresponding to the chosen significance level.

In hypothesis testing, when comparing two sample means, we typically perform a t-test or z-test depending on the characteristics of the data and assumptions. The null hypothesis assumes that there is no significant difference between the means of the two samples.

To determine whether we can reject the null hypothesis and conclude that there is a significant difference, we calculate a test statistic. The specific test statistic (t or z) depends on factors such as sample size and whether population parameters are known.

Next, we compare the calculated test statistic to the critical value. The critical value is determined based on the chosen significance level (commonly denoted as α). If the calculated test statistic exceeds the critical value, we reject the null hypothesis, indicating that there is evidence to support a significant difference between the two sample means.

The significance level determines the threshold for rejecting the null hypothesis and is typically set at 0.05 (5%) or lower, depending on the desired level of confidence.

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Answer:

\(Option C) 120cm^{3}\)

Step-by-step explanation:

As we know the formula to find the volume is,

\(V=LXBXH\)

\(V=5cm x 3cmx8cm\)

\(V=120cm^{3}\)

Hope it helps you

Answer:

-5

Step-by-step explanation:

-11-(-6)

-11+6

-5

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The left-hand limit and the right-hand limit both do not exist, the limit of sin(1/x) as x approaches 0 does not exist.

(i) To show that the limit of (1/x^2) as x approaches 0 does not exist, we need to show that the limit from the left-hand side and the right-hand side are not equal or they both go to infinity. Let's consider the right-hand limit:

lim x→0+ (1/x^2) = +∞ (the limit goes to infinity)

Now let's consider the left-hand limit:

lim x→0- (1/x^2) = +∞ (the limit goes to infinity)

Since the left-hand limit and the right-hand limit are both infinite and not equal, the limit does not exist.

(ii) To show that the limit of (1/√x^2) as x approaches 0 does not exist, we need to show that the limit from the left-hand side and the right-hand side are not equal or one or both of them goes to infinity. Let's consider the right-hand limit:

lim x→0+ (1/√x^2) = lim x→0+ (1/|x|) = +∞ (the limit goes to infinity)

Now let's consider the left-hand limit:

lim x→0- (1/√x^2) = lim x→0- (1/|x|) = -∞ (the limit goes to negative infinity)

Since the left-hand limit and the right-hand limit are not equal, the limit does not exist.

(iii) To show that the limit of (x+(x)) as x approaches 0 does not exist, we need to show that the limit from the left-hand side and the right-hand side are not equal or one or both of them goes to infinity. Let's consider the right-hand limit:

lim x→0+ (x+(x)) = 0+0 = 0

Now let's consider the left-hand limit:

lim x→0- (x+(x)) = 0+0 = 0

Since the left-hand limit and the right-hand limit are equal, the limit exists and equals 0.

(iv) To show that the limit of sin(1/x) as x approaches 0 does not exist, we need to show that the limit from the left-hand side and the right-hand side are not equal or one or both of them goes to infinity. Let's consider the right-hand limit:

lim x→0+ sin(1/x) does not exist

This is because sin(1/x) oscillates infinitely many times between -1 and 1 as x approaches 0 from the right-hand side, and the limit does not approach any single value.

Now let's consider the left-hand limit:

lim x→0- sin(1/x) does not exist

This is because sin(1/x) oscillates infinitely many times between -1 and 1 as x approaches 0 from the left-hand side, and the limit does not approach any single value.

Since the left-hand limit and the right-hand limit both do not exist, the limit of sin(1/x) as x approaches 0 does not exist.

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a. 12 out of 20 is 60%

b 62 out of 80 is 77.5%

a. 12% of 125 is 15

b. 18.3% of 28 is 5.12.

The percentage can be found by dividing the value by the total value and then multiplying the result by 100.

Hence, let's find the percentage of the following:

a.

12 / 20 × 100 = 1200 / 20 = 60%

b.

62 / 80 × 100 = 6200 / 80 = 77.5%

Therefore,

12% of 125 = 12 / 100 × 125 = 1500 / 100 = 15

18.3% of 28 = 18.3 / 100 × 28 = 512.4 / 100 = 5.12

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The 90% confidence interval is: (2.51, 3.22)

It is a boundary of values which is eventually to comprise a population value with a certain degree of confidence. It is usually shown as a percentage whereby a population means lies within the upper and lower limit of the provided confidence interval.

We have the following information :

The level of significance is calculated as:

\(\alpha =1-c\\\\\alpha =1-0.90\\\\\alpha =0.10\)

The degrees of freedom for the case is:

df = n - 1

df = 15 - 1

df = 14

The 90% confidence interval is calculated as:

=x(bar) ±\(t_\frac{\alpha }{2}\), df \(\frac{s}{\sqrt{n} }\)

= 2.86 ±\(t_\frac{0.10 }{2}\), 14 \(\frac{0.78}{\sqrt{15} }\)

= 2.86 ± 1.761 × \(\frac{0.78}{\sqrt{15} }\)

= 2.86 ± 0.3547

= (2.51, 3.22)

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9b²+30b+25

Step-by-step explanation:

15b+25+9b²+15b

9b²+30b+25

Answer:

115 lbs = 52.16 kilograms

Step-by-step explanation:

115 pounds is a little over 52kg

Answer:

24

Step-by-step explanation:

Multiples of 16 are \(16,32,48,64,80,...\)

Find product of each of the multiple of 16 until a number is obtained, the product of whose digits is a multiple of 12.

\(16=1(6)=6\\32=3(2)=6\\48=4(8)=32\\64=6(4)=24\)

Here, 24 is a multiple of 12.

So,

24 is the least positive integer such that it is a multiple of 16 and the product of its digits is a multiple of 12.

The answer to the given linear programming problem, which is solved using the simplex method, is as follows:

The optimal solution to minimize the objective function Z = X1 + 2X2 is X1 = 20 and X2 = 0, with the objective function value Z = -100.

To solve the problem, we'll first convert the inequalities to equations by introducing slack and surplus variables. Then we'll set up the initial simplex tableau and iterate through the simplex algorithm until we reach an optimal solution.

⇒ Convert the inequalities to equations:

A. X1 + 3X2 + S1 = 90 (where S1 is the slack variable)

B. 8X1 + 2X2 + S2 = 160 (where S2 is the slack variable)

C. 3X1 + 2X2 + S3 = 120 (where S3 is the slack variable)

D. X2 + S4 = 70 (where S4 is the surplus variable)

⇒ Set up the initial simplex tableau:

        | X1 | X2 | S1 | S2 | S3 | S4 | RHS |

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

Z       | -1 | -2 |  0 |  0 |  0 |  0 |  0  |

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

S1      |  1 |  3 |  1 |  0 |  0 |  0 | 90  |

S2      |  8 |  2 |  0 |  1 |  0 |  0 | 160 |

S3      |  3 |   2 |  0 |  0 |  1 |  0 | 120 |

S4      |  0 |   1 |  0 |  0 |  0 | -1 | 70  |

⇒ a) Select the most negative coefficient in the Z row, which is -2. Choose the corresponding column as the pivot column (X2 column).

b) Find the pivot row by selecting the minimum ratio of the RHS value to the positive values in the pivot column. The minimum ratio is 70/1 = 70. Thus, the pivot row is S4.

c) Perform row operations to make the pivot element (1 in S4 row) equal to 1 and eliminate other elements in the pivot column:

  - Divide the pivot row by the pivot element (1/1 = 1).

  - Replace other elements in the pivot column using row operations:

    - S1 row: S1 = S1 - (1 * S4) = 90 - 70 = 20

    - Z row: Z = Z - (2 * S4) = 0 - 2 * 70 = -140

    - S2 row: S2 = S2 - (0 * S4) = 160

    - S3 row: S3 = S3 - (0 * S4) = 120

d) Update the tableau with the new values:

        | X1 | X2 | S1 | S2 | S3 | S4 | RHS |

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

Z       | -1 |  0 |  0 |  0 |  2 | -2 | -140|

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

S1      |  1 |  3 |  1 |  0 |  

0 |  0 | 20  |

S2      |  8 |  2 |  0 |  1 |   0 |  0 | 160 |

S3      |  3 |  2 |  0 |  0 |   1 |  0 | 120 |

S4      |  0 |  1 |  0 |  0 |   0 | -1 | 70  |

e) Repeat steps a to d until all coefficients in the Z row are non-negative.

  - Select the most negative coefficient in the Z row, which is -1. Choose the corresponding column as the pivot column (X1 column).

  - Find the pivot row by selecting the minimum ratio of the RHS value to the positive values in the pivot column. The minimum ratio is 20/1 = 20. Thus, the pivot row is S1.

  - Perform row operations to make the pivot element (1 in S1 row) equal to 1 and eliminate other elements in the pivot column.

  - Update the tableau with the new values.

f) The final simplex tableau is:

        | X1 | X2 | S1 | S2 | S3 | S4 | RHS |

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

Z       |  0 |  0 |  0 |  0 |  1 | -3 | -100|

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

X1      |  1 |  3 |  1 |  0 |  0 |  0 | 20  |

S2      |  0 | -22 | -8 |  1 |  0 |  0 | 140 |

S3      |  0 | -7 | -3 |  0 |  1 |  0 | 60  |

S4      |  0 |  1 |  0 |  0 |  0 | -1 | 70  |

⇒ Read the solution from the final tableau:

The optimal solution is X1 = 20 and X2 = 0, with the objective function value Z = -100.

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Answer:

24%

Step-by-step explanation:

we subtract to see how much it increased

62-50=12

Now divide 12 by 50 to get percent

12/50

0.24

0.24x100

24%

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The equation of the red graph, g(x) is g(x) =1/3x²

From the question, we have the following parameters that can be used in our computation:

The functions f(x) and g(x)

In the graph, we can see that

This means that

g(x) = 1/3f(x)

Recall that

f(x) = x²

This means that

g(x) =1/3x²

This means that the equation of the red graph is g(x) =1/3x²

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The data to develop an empirical discrete probability distribution for x is 1 and the probabilities of the discrete probability distribution are all non-negative. Therefore, the distribution is valid. and the probability distribution satisfies the conditions for a valid discrete probability distribution, it is necessary to check that the probabilities sum to 1 and that they are all non-negative

a. The empirical discrete probability distribution for the random variable x is given as shown below:

Time with Current Employer (years)                     Number of College Graduates 1                                                                                               500 2                                                                                               388 3                                                                                               308 4                                                                                               216 5                                                                                               580

Let X denote the number of years worked for a current employer and let f(x) denote the corresponding empirical probability distribution of X. The empirical probability distribution f(x) is found by dividing the number of graduates who have worked for x years by the total number of graduates.

Thus, f(1) = 500/2000 = 0.25, f(2) = 388/2000 = 0.194, f(3) = 308/2000 = 0.154, f(4) = 216/2000 = 0.108 and f(5) = 580/2000 = 0.29b. To show that the probability distribution satisfies the conditions for a valid discrete probability distribution, it is necessary to check that the probabilities sum to 1 and that they are all non-negative:

∑f(x) = f(1) + f(2) + f(3) + f(4) + f(5) = 0.25 + 0.194 + 0.154 + 0.108 + 0.29 = 0.996 Since ∑f(x) = 0.996, which is very close to 1. This is because of rounding off to 3 decimal places. So, ∑f(x) ≈ 1. The distribution is, therefore, valid.The probabilities of the discrete probability distribution are all non-negative. Therefore, the distribution is valid.

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Answer:

C is the anser on edege

Step-by-step explanation:

Answer:

2 3 5 on edge

Step-by-step explanation:

Answer:

Multiply the second equation by -3 to get -3x - 9y = -30.

Step-by-step explanation:

When eliminating, you need to find a term with the negative of that term to combine so that they cancel each other out. An example would be 3x in the first equation and (-3x) in another equation so that when added, it becomes: 3x-3x = 0.

In the second equation, you see that there is already an x there and you just need to make it become (-3x). Thus, you multiply the entire second equation by -3 to make -3x. Once you have done that, you can combine the two equations and eliminate 3x from the first equation.

3x + 5y = 30

-3x - 9y = -30

3x + 5y -3x - 9y = 30 + (-30)

0 - 4y = 30 - 30

-4y = 0

You can find y and then x later on from here.

The expressions are simplified to give;

7. 4n³(3n² + 4)

8. -3x(3x² - 4)

9. 5(k² - 8k + 2)

10. -10(6 + 6n² + 5n³)

11. 3(6n³ - 4n - 7)

12. 9(7n³ + 9n + 2)

Algebraic expressions are defined as mathematical expressions that are composed of variables, coefficients, terms, factors and constants.

These algebraic expressions are also made up of arithmetic operations, such as;

To factorize the expressions, we have;

12n⁵ + 16n³

Find the common term

4n³(3n² + 4)

-9x³ - 12x

find the common term

-3x(3x² - 4)

5k² - 40k + 10

find the common terms

5(k² - 8k + 2)

-60 + 60n² + 50n³

find the common term

-10(6 + 6n² + 5n³)

18n³ -12n - 21

find the common term

3(6n³ - 4n - 7)

63n³ + 81n + 18

Find the common term

9(7n³ + 9n + 2)

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Answer:

Step-by-step explanation:

1. 2(12x6.5)=156 (This equation is for the bottom squares.)

2. 2(6.5x25)=325 (This equation is for the side rectangles.)

3. 2(12x25)=600 (This equation is for the front rectangles.)

4. Now we need to add everything together.

5. 156+325+600=1081

6. The surface area of the prism is 1081 cm².

(If you can, please give me brainliest! It would really help!)

Answer:

1,752,000

Step-by-step explanation:

1.  First you have to take the 7% and multiply that by the years whish is 17 so      that way you know your total percentage of growth which is 119%

2.  Second you then need to find how much 1% is to find out our total growth in population so you take 800,000 and divide that by 100 since there's only 100% and you get 8,000.

3.  Now you take the 8,000 and multiply that by the percentage of the growth that you have which is 8,000*119 and you get 952,000

4.  Lastly all you have to do is add the growth of the population to the population you already have so 800,000+952,000=1,752,000

It will take Emily 12.1 hours to mow 5 acres

Variation is the relation between a set of values of one variable and a set of values of other variables

Let T and A represent the time and area respectively

Since the time it takes Emily to mow a lawn is proportional to its area. We can write:

T α A

T = kA (where k is constant of proportionality)

It takes her about 30 minutes to mow 1,000 square yards. That is:

T = 30 and A = 1,000

T = kA

30 = 1000k

k = 30/1000

k = 0.03

Time for 5 acres:

5 acres = 5 × 4840 = 24200 square yards   (1 acre = 4840 square yards)

T = kA

T = 0.03 × 24200

T = 726 minutes     (divide by 60 to get time in hours)

T = 12.1 hours

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