Solve for x.

3.4>x+2/3
i need it in fraction form please.

Answer:

gotchu.

c = 36

Step-by-step explanation:

First add five to each side.

c/4 = 9

then you multiply by four:

c=36

15 bottles of Mango juice cost AED 30

Will this solve this question by the unitary method

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

What would he pay for 15 bottles of mango juice if 8 bottles cost AED 16?

so,

The unitary method's formula is to identify the value of a single unit, then multiply that value by the number of units to obtain the required value.

8 bottle=AED16 So I bottle of mango juice costs AED 2.

2x15=30

So,15 bottles of Mango juice cost AED 30

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In this scenario, the financial administrator is interested in determining whether the average cost of tuition plus room and board at small private liberal arts colleges is higher than the reported value of $9,350 per term. To test this hypothesis, we can set up a hypothesis test with the following null and alternative hypotheses:

Null Hypothesis (H₀): The average cost is 9,350 per term.

Alternative Hypothesis (H₁): The average cost is higher than $9,350 per term.

To perform the hypothesis test, we can use the Z-test since we have the population standard deviation. The formula for the Z-test is given by:

where is the sample mean, is the population mean (in this case,   is the population standard deviation  and n is the sample size (350). Using the given values, we can calculate the Z-score:

The next step is to compare the calculated Z-score with the critical value or find the corresponding p-value. Based on the significance level (α) chosen by the administrator, we can make a decision to reject or fail to reject the null hypothesis. Since the significance level  is not provided in the question, we cannot determine the final decision without this information. The choice of α is crucial in hypothesis testing as it determines the level of confidence required to reject the null hypothesis.

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Answer:

3rd choice

a rotation of 90° counterclockwise about the origin and a translation down 1 unit

Step-by-step explanation:

This is just asking you what operations you need to perform to get figure N from figure M. Such a set of operations is called a transformation.

In this case we see that to get figure N we have to rotate figure M 90° in a counterclockwise direction. That would be the first transformation

From the choices you can eliminate the first two choices which deal only with clockwise rotation

Translation transformation is one where the figure is shifted horizontally or vertically

All we have to do is figure out if, after 90° counterclockwise rotation of M whether it was shifted 1 unit up or 1 unit down

Look at the point (-3, 1) in figure M.

When a figure is rotated 90° counterclockwise, each if its original coordinates (x, y) become new coordinates (-y, x)

In other words the coordinates are interchanged in the transformed figure and the sign of the new x-coordinate is changed from the original y value

So (-3, 1) should become (-1, -3)

But in figure N, that point has become (-1, -4) which is (-1, -3-1). This indicates the figure has been shifted down which corresponds to a translation down by 1 unit

Answer: 3rd choice

a rotation of 90° counterclockwise about the origin and a translation down 1 unit

The two images I have attached may help you understand better. First one is just the rotation of M. Second one is the rotated figure shifted down which results in figure N

The decimal 1.0227 is a rational number. First of all, it is a terminating decimal, which means that the decimal has a definite ending point.

The Laplace Transform of f(t) isL{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...

                            = (1/s^2) + e^{−πs}(1/s^2) − e^{-2πs}(1/s^2) + ...= (1/s^2)[1 + e^{−πs} − e^{−2πs} + ...]

Given function is,f(t) ={ t, 0 < t < π π < t < 2π}

where f(t + 2 π) = f(t)

Let's take Laplace Transform of f(t)

                     L{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...f(t + 2π) = f(t)

∴ L{f(t + 2 π)} = L{f(t)}⇒ e^{2πs}L{f(t)} = L{f(t)}

     ⇒ [e^{2πs} − 1]L{f(t)} = 0L{f(t)} = 0

when e^{2πs} ≠ 1 ⇒ s ≠ 0

∴ The Laplace Transform of f(t) is

                       L{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...

                               = (1/s^2) + e^{−πs}(1/s^2) − e^{-2πs}(1/s^2) + ...

                              = (1/s^2)[1 + e^{−πs} − e^{−2πs} + ...]

The Laplace Transform of f(t) isL{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...

                            = (1/s^2) + e^{−πs}(1/s^2) − e^{-2πs}(1/s^2) + ...= (1/s^2)[1 + e^{−πs} − e^{−2πs} + ...]

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The formula for Average Fixed Cost (AFC) is: AFC = FC / Q. Where FC represents the total fixed costs incurred by a firm and Q represents the quantity of output produced by the firm.

AFC is a per-unit measure of the fixed cost of production, and represents the amount of fixed cost that is attributed to each unit of output. As the quantity of output increases, the AFC decreases, since the fixed costs are spread out over a larger number of units. AFC is an important concept in economics and business, as it is used to calculate other cost measures such as average total cost and average variable cost.

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The activation energy of the reaction is approximately 126.8 kJ/mol. The calculation was done using the Arrhenius equation and the natural logarithm of the rate constants at the two temperatures.

To calculate the activation energy of a reaction, we can use the Arrhenius equation:

k = A * e⁽⁻ᴱᵃ/ᴿᵀ⁾

where k is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin.

We have two rate constants at different temperatures, so we can set up two equations:

k₁ = A * e⁽⁻ᴱᵃ/ᴿᵀ₁⁾

k₂ = A * e⁽⁻ᴱᵃ/ᴿᵀ₂⁾

We want to solve for Ea, so we can take the natural logarithm of both sides of each equation:

ln(k₁) = ln(A) - Ea/RT₁

ln(k₂) = ln(A) - Ea/RT₂

We can subtract the second equation from the first to eliminate ln(A):

ln(k₁) - ln(k₂) = Ea/R * (1/T₂ - 1/T₁)

Now we can solve for Ea:

Ea = -R * (ln(k₁) - ln(k₂)) / (1/T₂ - 1/T₁)

Plugging in the given values, we get:

Ea = -8.314 J/mol/K * (ln(6.20 x 10⁻⁴) - ln(2.39 x 10⁻²)) / (1/760 K - 1/700 K)

Ea ≈ 126.8 kJ/mol

Therefore, the activation energy of the reaction is approximately 126.8 kJ/mol.

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(a) we are saying that the probability of rejecting a null hypothesis that is actually true is 0.001 or 0.1%.

(b) we are saying that the probability of rejecting a null hypothesis that is actually true is 0.05 or 5%.

(c) we are saying that the probability of rejecting a null hypothesis that is actually true is 0.10 or 10%.

a. If α is assigned the value 0.001, we are setting a very low significance level for the hypothesis test. This means that we are willing to accept only a very small probability of making a Type I error. Specifically, we are saying that the probability of rejecting a null hypothesis that is actually true is 0.001 or 0.1%.

b. If α is assigned the value 0.05, we are setting a standard significance level for the hypothesis test. This means that we are willing to accept a probability of up to 0.05 or 5% of making a Type I error. Specifically, we are saying that the probability of rejecting a null hypothesis that is actually true is 0.05 or 5%.

c. If α is assigned the value 0.10, we are setting a relatively high significance level for the hypothesis test. This means that we are willing to accept a probability of up to 0.10 or 10% of making a Type I error. Specifically, we are saying that the probability of rejecting a null hypothesis that is actually true is 0.10 or 10%.

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The proof for the statement "For all sets A, B, and C, if A ⊆ B and B ∩ C = ∅, then A ∩ C = ∅" follows a proof by contradiction approach. By assuming the negation of the desired conclusion and deriving a contradiction, it is shown that the original statement holds true.

The proof begins by assuming the negation of the statement, which states that there exist sets A, B, and C such that A ⊆ B, B ∩ C = ∅, and A ∩ C ≠ ∅.

Then, it is argued that if A ∩ C ≠ ∅, there must exist an element x that belongs to both A and C, denoted as x ∈ A ∩ C.

Next, using the fact that A ⊆ B, it is concluded that x ∈ B because any element in A must also be in B. Additionally, it is known that x ∈ C.

By the definition of intersection, it follows that x ∈ B ∩ C.

Then, using the definition of the complement, it is stated that (A ∩ C)c (the complement of A ∩ C) is equal to the universal set U.

From the definition of intersection, it can be deduced that x ∈ A and x ∈ C.

Assuming A = U by the definition of intersection, it leads to the contradiction that x ∈ B and x ∈ C, but B ∩ C = ∅.

This contradiction disproves the assumption that A ∩ C ≠ ∅, and therefore, the original statement holds true.

In conclusion, the proof establishes that for all sets A, B, and C, if A ⊆ B and B ∩ C = ∅, then A ∩ C = ∅.

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If we want to find the value of f(x) at x = -2, we simply put "-2" into the given function. Shown below:

The procedure which is deemed to be the type of sample in discuss is; representative sample are free of bias.

Representative sampling and random sampling are two techniques used to help ensure data is free of bias. A representative sample on the other hand is a group or set chosen from a larger statistical population according to specified characteristics. A random sample is a group or set chosen in a random manner from a larger population.

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Answer:

Step-by-step explanation:

y = (1/12)x + 20

Answer:

ummmm 5 ..............

Answer:

Step-by-step explanation:

Let the time of the complete race be x.

Then we have the following equation:

Answer: 6 1/4 minutes

Step-by-step explanation:

Statements are False: 1. interchanging rows changes determinant. 2. determinant zero not implies specific rows. 3. determinant not product of diagonal entries. 4. determinant is scalar not matrix.

What is matrix ?

A matrix is a rectangular array of numbers or other mathematical objects, typically arranged in rows and columns. Matrices are often denoted using capital letters, such as A, B, and C. Each element of a matrix is identified by its row and column indices,

1) False, If two row interchanges are made in succession, the determinant of the new matrix is the negative of the determinant of the original matrix.

2) False, If the determinant of a matrix is zero, it does not necessarily mean that two rows or two columns are the same or a row or column is zero, it only means that the matrix is singular, i.e. non-invertible and it also can mean that the matrix is linearly dependent.

3) False, The determinant of a matrix is not always equal to the product of the diagonal entries, it is a scalar value calculated through a specific method called matrix expansion which is based on the entries of the matrix and it depends on the size of the matrix.

4) False, The determinant of a matrix is a scalar value, it cannot be equal to another matrix.

Statements are False: 1. interchanging rows changes determinant. 2. determinant zero not implies specific rows. 3. determinant not product of diagonal entries. 4. determinant is scalar not matrix.

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Analyzing the given data, it cab be concluded that Option D, that is, mL3 = 126° is most likely being shown by the proof.  

It can be observed from the given diagram, angle 1 and angle 2 are complementary. By the definition of complementary angles, we get the sum of angle 1 and angle 2 equal to 90°.

=> mL1 + mL2 = 90°

The value of angle 1 is given as 36.

=> mL1 = 36⁰

Using the first observed condition and the value of angle 1, we can obtain the value of angle 2.

=> 36⁰ + mL2 = 90°

=> mL2 = 90 - 36 = 54°

Therefore, the value of angle 2 is obtained as 54°.

From the diagram given in the question, it can also be inferred that angle 2 and angle 3 form a linear pair. Using the linear pair theorem, we get the sum of angle 2 and angle 3 as 180°.

=> mL2 + mL3 = 180°

Previously, we have obtained the value of angle 2 as 54°.

Hence, by substituting the value of angle 2 in the above equation, we get,

54° + mL3 = 180°

=> mL3 = 180 - 54 = 126°

Therefore, By researching all the data and the results, we can conclude that all other options are discarded and the correct option is option D.

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To determine the z-score(s) that cover the "middle 98%" of the normal curve and represent the 98% confidence level (CL), we can use the properties of the standard normal distribution.

The "middle 98%" refers to the area under the normal curve between the z-scores that enclose the central 98% of the distribution. In a standard normal distribution, the mean is 0 and the standard deviation is 1.

Since the distribution is symmetric, we need to find the z-score(s) that correspond to the area of (1 - 0.98) / 2 = 0.01 on each tail of the distribution. The remaining 0.02 is split equally between the two tails.

To find the z-score(s), we can use a standard normal distribution table or a calculator.

Looking up the value of 0.01 in the z-table, we find that the z-score that corresponds to the lower tail is approximately -2.33. This means that 1% of the area lies to the left of z = -2.33.

To find the z-score for the upper tail, we use the symmetry of the distribution. The z-score that corresponds to the upper tail is the negative of the z-score for the lower tail, so it is approximately 2.33.

Therefore, the z-scores that cover the "middle 98%" of the normal curve and represent the 98% confidence level (CL) are approximately -2.33 and 2.33.

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Answer:

To determine whether (1, 5) is a solution of a given system, you need to substitute these values into the equations of the system and check whether the resulting statements are true.

For example, if the given system is represented by the equations y = 2x + 1 and y = x - 3, then you would substitute 1 for x and 5 for y in each equation and check whether the resulting statements are true.

Substituting these values into the first equation, we get:

5 = 2(1) + 1

5 = 2 + 1

5 = 3

This statement is not true, so (1, 5) is not a solution of this system.

On the other hand, if the given system is represented by the equations y = 2x + 1 and y = 5, then substituting the values (1, 5) into both equations would result in true statements, so (1, 5) would be a solution of this system.

I hope this helps! Let me know if you have any more questions.

Step-by-step explanation:

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

Work Shown:

Let's call the "height" to be the "width".

The area of a rectangle is

area = length*width

We're told the width is 8.5 feet

If the length is some unknown variable L, then

area = length*width

area = L*8.5

area = 8.5L

We want the area to be at least 76.5 square feet

This means 8.5L is either equal to 76.5, or larger than it

\(\text{ area } \ge 76.5\\\\\\8.5L \ge 76.5\\\\\\\frac{8.5L}{8.5} \ge \frac{76.5}{8.5} \ \ \text{ ... divide both sides by 8.5}\\\\\\L \ge 9\\\\\\\)

This shows the length can be 9 feet or larger.

In other words, the minimum length is 9 feet.

The selection chances and the required probability for 9 women and 6 men is given by ,

Different groups of applicants selection = 3003

Selection of trainee entirely of women = 126

Probability of selection of entirely women from 15 people = 4.19%

Total number of women = 9

Total number of men = 6

Total = 9 + 6

        = 15

The total number of groups of applicants that can be selected for the positions can be calculated using the combination formula,

nCr = n! / r!(n-r)!

where n is the total number of applicants (15),

And r is the number of positions to be filled (5).

Number of different groups of applicants that can be selected for the positions is,

15C5

= (15! )/(15-5)!5!

=(15! )/(10)!5!

= 3003

Number of different groups of trainees that consist entirely of women can be calculated by selecting 5 women from the 9 available,

9C5

= (9! )/(9-5)!5!

=(9! )/(4)!5!

= 126

Probability of selecting a group of five trainees ,

Consist entirely of women can be calculated by dividing the number of different groups of all-women trainees (126) by the total number of different groups of trainees (3003),

Required probability

= 126/3003

≈ 0.0419

Probability that the trainee class will consist entirely of women is approximately 0.0419, or 4.19% (rounded to four decimal places).

Therefore, for a group of 15 people,

Selection of different groups of people = 3003

Selection of trainee represents entirely women =126

probability of selecting entirely women = 4.19%

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The domain of the given function is the one in option A,

Domain = 4 ≤x ≤13

To identify this, just look at the horizontal axis (which is the axis of the inputs, and we know that the domain is the set of the inputs of the function), here we can see that the graph (which is the bell-shaped curve) starts at 4 and ends at 13.

Then the domain is the set of all values between these two, we can write this as:

Domain = 4 ≤x ≤13

Thus the correct option is A.

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Answer:

Triangle A is correct since 87° + 23° + 70° = 180°.

Answer:

approx. 68%

Step-by-step explanation:

this is a normal distribution.

in a normal distribution, approximately 68% of the data is within one standard deviation of the mean (we also have 95% of data is within two standard deviations of the mean, and 99.7% of data is within three standard deviations of the mean).

one standard deviation in our question is 113.

315 is one standard deviation below the mean because 428 - 113 = 315.

541 is one standard deviation above the mean because 428 + 113 = 541.

so we expect approx. 68% of the data to be between 315 and 541.

Answer:

i think it's D. because 55% isn't enough, but very close, and 0.625% is waaaay too little, and the same for 1.60.

Step-by-step explanation:

estimation.

The percentage of Janet's money does Emma have is D. 62.5%.

Given that,

Based on the above information, the calculation is as follows:

\(= \$25 \div \$40\)

= 62.5%

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Answer:

1.2 ft

Step-by-step explanation:

2*0.6 ft=1.2 ft

The degrees of freedom (df) for the within-groups scenario is 27.

In the F-test, which is used to compare variances between groups, the degrees of freedom consist of two components: the numerator df and the denominator df. The numerator df corresponds to the number of groups being compared, while the denominator df represents the total number of observations minus the number of groups.

In the given scenario, F(2,27) = 8.80 indicates that the F-test is comparing variances between two groups. The numerator df is 2, representing the number of groups being compared.

To determine the within-groups df, we need to calculate the denominator df. The denominator df is calculated as the total number of observations minus the number of groups. Since the denominator df is given as 27, it implies that the total number of observations is 27 + 2 = 29, considering the two groups being compared.

Therefore, the within-groups df is 27, as it represents the total number of observations minus the number of groups in the F-test.

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Answer:

Option B: 0.4

Step-by-step explanation:

We have 20 dots.

Such that each column represents the repetitions for each proportion.

So:

0.1 -> 3 times

0.2 -> 1 time

0.3 -> 4 times

0.4 -> 6 times

0.5 -> 3 times

0.6 -> 3 times

Now we can compute the mean of these values, and that will be the best estimation we can make with the given data.

Remember that for a set of N values:

{x₁, x₂, ..., xₙ}

The mean is:

\(M = \frac{x_1 + x_2 + ... + x_n}{N}\)

In this case we have the set of 20 points described above, then the mean is:

\(M = \frac{3*0.1 + 1*0.2 + 4*0.3 + 6*0.4 + 3*0.5 + 3*0.6}{20} = 0.37\)

Rounding to the first place after the decimal point, we get:

M = 0.4

Then the correct option is option B.