In my class, everyone studies French or German, but not both languages.



One third of the girls and the same number of boys study German.



Twice as many boys as girls study French.



Which of these could be the total number of boys and girls in my class?

Answer:

b^(-6)

Step-by-step explanation:

The numerator of this fraction is b^(-11).  The -11 is the sum of -4 and -7.  

The denominator is b^(-5).

Recall that b^a / b^c = b^(a - c).  Thus, b^(-11) / b^(-5) = b^(-6)

Answer:

Ice melting

Step-by-step explanation:

Think about ice for a moment. After ice melts into liquid water, you can refreeze it into solid ice if the temperature drops. Freezing and melting are physical changes. The substances produced during chemical changes however cannot easily change back into the original substances.

The actual dimension of the distance is approximately 0.0046667 cm.

To compute the actual dimension of a distance given a drawing measurement and a scale, you can use the following formula:

Actual Dimension = Drawing Measurement × Scale Factor

In this case, the given drawing measurement is 28 cm, and the scale is 1:60 m.

To calculate the scale factor, we need to convert the scale to the same unit as the drawing measurement. Since the drawing measurement is in centimeters (cm), we need to convert the scale from meters (m) to centimeters (cm).

1 meter = 100 centimeters

So, the scale factor is:

Scale Factor = 1:60 m = 1 cm : 60 cm = 1 : 6000 cm

Now we can calculate the actual dimension:

Actual Dimension = Drawing Measurement × Scale Factor

Actual Dimension = 28 cm × 1/6000

Actual Dimension = 28/6000 cm

Simplifying the fraction, we get:

Actual Dimension ≈ 0.0046667 cm

Therefore, the actual dimension of the distance is approximately 0.0046667 cm.

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Given sequence is geometric sequence and common ratio between consecutive term is

In Arithmetic sequence , common difference between consecutive terms should be equal.

In Geometric sequence, common ratio between consecutive terms should be equal.

Given sequence, 16, 8, 4, ...

Since, common difference = 8 - 16 ≠ 4 - 8 , this is not arithmetic sequence.

Common ratio = T2/T1 = T3/T2 = 8/16 = 4/8 = 1/2 Because common ratio is are equal. Thus, given sequence is geometric sequence.

Hence the sequence is a geometric sequence and the common ratio = 1/2

Answer:

wat thing?

Step-by-step explanation:

Rounding to the nearest whole number, we get x = 2524.

a. Using the standard normal distribution table, we can find the corresponding z-score for the given probability:

P(X ≤ x) = P((X-μ)/σ ≤ (x-μ)/σ) = P(Z ≤ (x-μ)/σ) = 0.9382

From the standard normal distribution table, the closest probability to 0.9382 is 0.9382, which corresponds to a z-score of 1.56. Therefore:

(x - μ) / σ = 1.56

Substituting in the given values for μ and σ, we get:

(x - 2500) / 800 = 1.56

Solving for x, we get:

x = 2500 + 1.56 * 800 = 2728

Rounding to the nearest whole number, we get x = 2728.

b. Again, using the standard normal distribution table, we can find the corresponding z-score for the given probability:

P(X > x) = P((X-μ)/σ > (x-μ)/σ) = P(Z > (x-μ)/σ) = 0.025

From the standard normal distribution table, the closest probability to 0.025 is 0.0249979, which corresponds to a z-score of -1.96. Therefore:

(x - μ) / σ = -1.96

Substituting in the given values for μ and σ, we get:

(x - 2500) / 800 = -1.96

Solving for x, we get:

x = 2500 - 1.96 * 800 = 1144

Rounding to the nearest whole number, we get x = 1144.

c. We can use the same approach as in part (a), but this time we need to find the z-score for the probability between two values:

P(2500 ≤ X ≤ x) = P((X-μ)/σ ≤ (x-μ)/σ) - P((X-μ)/σ ≤ (2500-μ)/σ) = P(Z ≤ (x-μ)/σ) - P(Z ≤ -0.63) = 0.1217

From the standard normal distribution table, the closest probability to 0.1217 is 0.1217, which corresponds to a z-score of 1.17. Therefore:

(x - μ) / σ = 1.17

Substituting in the given values for μ and σ, we get:

(x - 2500) / 800 = 1.17

Solving for x, we get:

x = 2500 + 1.17 * 800 = 3056

Rounding to the nearest whole number, we get x = 3056.

d. We can use the same approach as in part (a):

P(X ≤ x) = P((X-μ)/σ ≤ (x-μ)/σ) = P(Z ≤ (x-μ)/σ) = 0.4840

From the standard normal distribution table, the closest probability to 0.4840 is 0.4838, which corresponds to a z-score of 0.03. Therefore:

(x - μ) / σ = 0.03

Substituting in the given values for μ and σ, we get:

(x - 2500) / 800 = 0.03

Solving for x, we get:

x = 2500 + 0.03 * 800 = 2524

Rounding to the nearest whole number, we get x = 2524.

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Answer:

F(5)= 21

Step-by-step explanation:

Plug in the 5 for x...

F(5)=6+3(5)

F(5)=6+15

F(5)=21

Step-by-step explanation:

F(5) = 6 +(3 ×5)

= 6 + 15 = 21

Step-by-step explanation:

what is the difference between the x- values ?

and what is the difference between the y- values ?

a transformation means a simple shift. so, addition of subtraction. no multiplication or such.

1 to -1 ? -2

-1 to -3 ? -2

5 to 3 ? -2

6 to 6 ? 0

3 to 3 ? 0

-2 to -2 ? 0

so, the transformation is (-2, 0)

it is true that  0.5% of 200 is 10.

True.

To find 0.5% of a number, we need to multiply the number by 0.5/100, which can be simplified to 5/100 or 1/20. This is because "percent" means "per hundred", so 0.5% is equivalent to 0.5 per 100 or 0.5/100.

Multiplying the number by 5/100 is the same as multiplying it by 0.5/100, so it will give us the correct result.

For example, if we want to find 0.5% of 200, we can multiply 200 by 5/100 or 0.5/100:

\(0.5% of 200 = 200 \times 5/100 = 10\)

Therefore, it is true that  0.5% of 200 is 10.

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Therefore, the expression for each wk in terms of the dataset (x1, y1), ..., (xM, yM) and W1, ..., Wk-1, Wk+1, ..., WM is: wk = (Σ (xij * yj) - Σ (wk' * xij^2), for j = 1 to N and k' ≠ k) / Σ xij^2, for j = 1 to N

The expression for each coefficient wk can be derived by taking the partial derivative of the OLS objective function J(w) with respect to wk and setting it equal to zero:

dJ(w)/dwk = 2 * Σ (xij * (wk * xij - yj)), for j = 1 to N

Setting this equal to zero and solving for wk, we get:

wk = (Σ (xij * yj) - Σ (wk' * xij^2), for j = 1 to N and k' ≠ k) / Σ xij^2, for j = 1 to N

Therefore, the expression for each wk in terms of the dataset (x1, y1), ..., (xM, yM) and W1, ..., Wk-1, Wk+1, ..., WM is: wk = (Σ (xij * yj) - Σ (wk' * xij^2), for j = 1 to N and k' ≠ k) / Σ xij^2, for j = 1 to N

The solution for this problem involves taking the partial derivative of the objective function J(w) with respect to each w_k and setting it to zero. This will give us a set of M normal equations, one for each coefficient w_k (1 ≤ k ≤ M).

The general expression for each w_k can be written as:

w_k = (Σ(x_i(k)y_i) - Σ(x_i(k)Σ(x_i(j)w_j)) / Σ(x_i(k)^2) for 1 ≤ j ≤ M, j ≠ k

Here, the summations run over all data points in the dataset D. The expression calculates w_k by considering the relationship between the k-th input variable x_i(k) and the output variable y_i, while taking into account the contribution of other coefficients w_j.

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Tori's loss from the stock will be $28.29 and her rate of return will be -84.75%.

Since Tori bought one share of Macy's stock on Nov 1, 2016 for $33.38 and she sold it and the closing price for that day was $5.09, her loss will be;

= $5.09 - $33.38

= -$28.29

Her rate of return will be:

= -28.29/33.38 × 100

= -84.75%

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The revision that corrects the misplaced modifier in the paragraph is option A. Last Saturday morning, while riding my bicycle down the street, I saw a horse.

In English grammar, a modifier is a word or group of words that provides more information about another word in a sentence. It can either modify a noun, a verb, or another modifier.

Modifiers that describe or provide more information about a noun are called adjectives. For example, in the sentence "The yellow sun is shining," "yellow" is an adjective modifying the noun "sun." Modifiers that describe or provide more information about a verb are called adverbs. For example, in the sentence "She sings beautifully," "beautifully" is an adverb modifying the verb "sings."

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Answer:

not similar

Step-by-step explanation:

The original price of the bracelet, before tax $0.68

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

Amount = $0.72

Sales tax = 6%

Using the above as a guide, we have the following:

Amount = Original amount * (1 + Sales tax)

Substitute the known values in the above equation, so, we have the following representation

0.72 = Original amount * (1.06)

So, we have

Original amount = 0.68

Hence, the original amount = 0.68

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Answer:

3:2 , 3/2,  3 to 2

Step-by-step explanation:

The best one is 3:2 cause it is the most used way to write a ratio. 3:2 also means 3 divided by 2 or 3 out of 2 so that's why you would use the other 2.

The interpretation of the straight line graph of the gallons of gas to distance in miles are as follows;

(a) After 100 miles, the equation for the graph and the graph indicates that Linda's car will have more gas

Linda's car will have 1 gallon more gas than Shen's car.

(b) Linda and Shen will have the same amount of gas in their cars after 150 miles

The graph indicates that Shen's car will have less gas than Linda's car before reaching 150 miles

A straight line graph is a graph of a linear equation.

The points on the graphs are;

Linda; (0, 14), (150, 8)

Shen; (0, 11), (150, 8)

The equation for the amount of gas remaining in Linda's car can be found as follows;

Slope of the line = (8 - 14)/(150 - 0) = -6/150 = -1/25 = -0.004

Equation of the line is therefore;

y - 14 = (-1/25)(x - 0)

The slope of the graph of the equation of Shen's car = (8 - 11)/(150 - 0) = -0.02

The equation of the line is; y - 11 = -0.02·x

After 100 miles we get;

Gas left in Linda's car = -0.04 × 100 + 14 = 10

Gas left in Shen's car = -0.02 × 100 + 11 = 9

Therefore, Linda's car will have more gas after 100 miles

Her car will have 10 gallons of gas

(b) From the graph, at the point x = 150, the tanks of Linda and Shen will contain the same amount of gas

If the miles driven is less than 150 miles, the graph indicates that Shen's car will have less gas than Linda's car

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In general, in the case of two independent events X and Y,

Therefore, in our case,

To calculate the gain on the sale of the office furniture, we need to determine the asset's book value and compare it to the sale price.

First, let's calculate the accumulated depreciation on the furniture. The furniture was purchased on January 1, 2014, and the straight-line depreciation method is used over 10 years with a salvage value of $80,200.

Depreciation per year = (Cost - Salvage Value) / Useful Life

Depreciation per year = ($746,800 - $80,200) / 10 years

Depreciation per year = $66,160

Next, we need to calculate the accumulated depreciation for the period from January 1, 2014, to May 1, 2021 (the date of the sale). This is approximately 7.33 years.

Accumulated Depreciation = Depreciation per year × Years

Accumulated Depreciation = $66,160 × 7.33 years

Accumulated Depreciation = $484,444.80

Now, we can calculate the book value of the furniture:

Book Value = Cost - Accumulated Depreciation

Book Value = $746,800 - $484,444.80

Book Value = $262,355.20

Finally, we can calculate the gain on the sale:

Gain on Sale = Sale Price - Book Value

Gain on Sale = $300,000 - $262,355.20

Gain on Sale = $37,644.80

Therefore, the gain that should be recognized on the sale of the office furniture is approximately $37,644.80.

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The gain that should be recognized on the sale of the office furniture is $84,080.

The gain is calculated by subtracting the equipment's book value from the sale price. This gain will be reported on the company's income statement. Here is how to calculate the gain:First, find the equipment's book value using the straight-line method of depreciation.

Straight-line depreciation is calculated by taking the difference between the equipment's original cost and its salvage value, and then dividing it by the number of years the equipment is used. The annual depreciation expense is then multiplied by the number of years the equipment is used to find the equipment's book value at the end of its useful life.

For this question, the book value of the equipment at the time of sale is:Cost of equipment: $746,800Salvage value: $80,200Depreciable cost: $746,800 - $80,200 = $666,600Annual depreciation: $666,600 ÷ 10 years = $66,660Book value at the end of 2020: $666,600 - ($66,660 x 7) = $156,420

Next, subtract the equipment's book value from the sale price to find the gain:Sale price: $300,000Book value: $156,420Gain: $143,580Finally, round the gain to the nearest dollar:$143,580 ≈ $143,580.00So the gain that should be recognized on the sale of the office furniture is $84,080.

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Answer 2.05

Step-by-step explanation: hope this helps

Answer:

B (1/2,-2)

Step-by-step explanation:

4b + 13c = -24 --(1)

12b - 5c = 16 --(2)

(1)x3

12b + 39c = -72 --(3)

(3)-(2)

12b + 39c - 12b + 5c = -72-16

c = -2

Sub c = -2 into (1)

4b = -24 - 13(-2)

b = 1/2

Answer:

b

Step-by-step explanation:

In a complete metric space X, if {Sn} is a family of decreasing non-empty closed subsets with a limit of 0, then (a) Sn is not empty and (b) Sn contains only one element.


(a) To prove that Sn is not empty, we assume the contrary and suppose there exists an n for which Sn is empty.

However, since Sn is a closed set, its complement in X is open. By the decreasing function property, the complement contains all points beyond Sn, which contradicts the limit of 0. Hence, Sn is non-empty.

(b) To prove that Sn contains only one element, we consider two distinct elements x and y in Sn.

Since Sn is closed, it contains all its limit points. However, the limit of Sn is 0, so x and y cannot be distinct. Therefore, Sn contains only one element.

(c) If X is not complete, the validity of (a) depends on the completeness of X. If X is not complete, it is possible to have a decreasing family of non-empty closed subsets Sn with a limit of 0, where Sn can be empty for some n.

In such cases, (a) does not hold.

The properties (a) and (b) hold in a complete metric space, ensuring that the decreasing non-empty closed subsets Sn have at least one element and contain only one element.

However, the completeness of X is crucial for the validity of these properties.

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Answer: (4,-7) is the solution to this system of equations.

Step-by-step explanation:

y = 2x − 15;4x + 3y = −5

Step: Solve y= 2x − 15 for y:

Step: Substitute 2x − 15 for y in 4x + 3y = −5:

4x + 3y = −5

4x + 3(2x−15) = −5

10x − 45 = −5 (Simplify both sides of the equation)

10x − 45+45 = −5+45 (Add 45 to both sides)

10x = 40

10x/10 = 40/10 (Divide both sides by 10)

x = 4

Step: Substitute 4 for x in y = 2x − 15:

y = 2x − 15

y = (2) (4) − 15

y = −7 (Simplify both sides of the equation)

I hope this helps!

the potential at the center of the equilateral triangle is 3kq√3 / a.To find , we can use the formula for the electric potential due to a point charge:

V = kq / r

where k is the Coulomb constant, q is the charge, and r is the distance between the point charge and the center of the triangle.

Assuming the charges are all positive, the potential at the center due to each charge will be the same, so we can find the total potential by multiplying the potential due to one charge by three.

The distance from the center of the equilateral triangle to each charge is a/√3, since the height of the equilateral triangle is √3/2 times the side length.

Therefore, the potential at the center is:

V = 3(kq / (a/√3))

Simplifying:

V = 3kq√3 / a

Hence, the potential at the center of the equilateral triangle is 3kq√3 / a.

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Answer:

\(27^{\frac{1}{3}} \quad 125^{\frac{2}{3}} \quad 9^{\frac{3}{2}}\)

Step-by-step explanation:

Rewrite 9 as 3²:

\(\implies 9^{\frac{3}{2}}=\left(3^2\right)^{\frac{3}{2}}\)

\(\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:\)

\(\implies 3^{(2 \cdot \frac{3}{2})}=3^3\)

Therefore:

\(\implies 3^3= 3 \cdot 3 \cdot 3=27\)

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

Rewrite 27 as 3³:

\(\implies 27^{\frac{1}{3}}=\left(3^3\right)^{\frac{1}{3}}\)

\(\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:\)

\(\implies 3^{(3 \cdot \frac{1}{3})}=3^1\)

Therefore:

\(\implies 3^1=3\)

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

Rewrite 125 as 5³:

\(\implies 125^{\frac{2}{3}}=\left(5^3\right)^{\frac{2}{3}}\)

\(\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:\)

\(\implies 5^{(3 \cdot \frac{2}{3})}=5^2\)

Therefore:

\(\implies 5^2=5 \cdot 5=25\)

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

Solution

In order, from smallest to largest:

\(27^{\frac{1}{3}} \quad 125^{\frac{2}{3}} \quad 9^{\frac{3}{2}}\)

Answer:

44

Step-by-step explanation:

the formula for finding the perimeter of a rectangle is p=2(l+w)

Answer:

i)

Step-by-step explanation:

i) As it is a right-angle triangle,

\((x+2)^2+(4x)^2=(2x+7)^2\\x^2+4x+4+16x^2=4x^2+28x+49\\x^2+4x+4+16x^2-4x^2-28x-49=0\\13x^2-24x-45=0\\13x^2-39x+15x-45=0\\13x(x-3) + 15(x-3) =0\\(13x+15)(x-3)=0\)

ii)From the above equation we get, that x=3 is a solution

Hence, Base= 4x=12

Altitude=5

Hence, Area of a triangle = Altitude X Height X 1/2

= 12 X 5 X 1/2

=30 cm^2

Overall, randomization in randomized controlled trials helps to minimize bias and increase the generalizability of the study results, ultimately improving the validity and reliability of the findings.

Minimizes Bias: Randomization helps to minimize selection bias and confounding factors by assigning participants randomly to different treatment groups. By randomly allocating participants, the characteristics of the individuals in each group are more likely to be balanced and comparable, reducing the potential for systematic differences between groups that could affect the study results. This allows for a more accurate assessment of the treatment's effect.

Enhances Generalizability: Randomization increases the generalizability or external validity of the study findings. By randomly assigning participants to treatment groups, the study sample is more likely to be representative of the target population. This enhances the ability to generalize the study results to a larger population, increasing the reliability and applicability of the findings beyond the study sample.

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Answer:

the answer is 111

Step-by-step explanation:

\(180 - 36 - 75 = 69\)

\(180 - 69 = 111\)

Answer:

x = 111°

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

x is an exterior angle of the triangle, thus

x = 75° + 36° = 111°

Answer:

32 and 19

Step-by-step explanation:

Let's call the numbers x and y.

Write out the equations

x + y = 51

x - y = 13

Simplify the second equation

x = 13 + y

Substitute into the first equation and simplify

(13 + y) + y = 51

13 + 2y = 51

2y = 51 - 13

2y = 38

y = 19

Substitute y for 19 in the second equation

x = 13 + y

x = 13 + 19

x = 32