True or False:
There are an infinite number of answers for this equation:
63 - X = 34

Answer:

  B. The graph of K has a greater y-intercept

  D. The graph of J has a greater slope.

Step-by-step explanation:

Given a table for function J and an equation for function K, you want to know which has the greater slope, and which has the greater y-intercept.

The y-intercept is the value of the function when x=0. We see from the table that y=2 corresponds to x=0 for function J.

We see from the equation for function K that the constant is 8. This is the value of y when x=0.

Function K has the greater y-intercept (8 vs. 2).

The slope is the change in y-value when x increases by 1 unit. We see from the table that y=7 when x=1, so the change in y from x=0 to x=1 is 7-2 = 5. The slope of function J is 5.

The equation for function K has an x-coefficient of 3. This means a change in x of 1 unit will result in a change in y of 3 units. The slope of function K is 3.

Function J has the greater slope (5 vs. 3).

Additional comment

Both functions are graphed in the attachment. The y-intercepts have their points labeled. The graph with the steeper slope is the blue line, function J.

Answer:

0.475

Step-by-step explanation:

Given that :

We are to calculate the true positive :

True POSITIVE (TP) = 70% = 0.7

False POSITIVE (CP = 30% = 0.3

True Negative = 30% = 0.3

Number arrested = 4

(1/n * TP) / [(1/n * TP) + (n-1 /n * FP)

= (1/4 * 0.7) / [(1/4 * 0.7) + (3/4 * 0.3)

= 0.175 / (0.175 + 0.225)

= 0.175 / 0.4

= 0.475

Answer:

y=1.5

x=-3.5

Our answer is (-3.5,1.5)

Step-by-step explanation:

y-5=x

x=-2-y

y=?

--------

Using substitution,

y-5=-2-y

Solve:

2y-5=-2

2y=3

y=1.5

We can enter 1.5 into the equation:

1.5-5=x

-3.5=x

Answer:

3840

Step-by-step explanation:

1.12 times 25 is 28

1.28 times 3000

The ratio of the new volume to the old volume will be 3:1, the correct option is D.

We are given that;

The measurements= 9 cm*5 cm*3 cm

Now,

To find the volume of a rectangular prism, we can use the formula V = lwh, where l is the length, w is the width, and h is the height. Using the given dimensions, we get:

V = lwh V = 9 * 5 * 3 V = 135 cm^3

To find the new volume after tripling the width, we can use the same formula but replace w with 3w. We get:

V’ = l * 3w * h V’ = 9 * 3 * 5 * 3 V’ = 405 cm^3

To find the ratio of the new volume to the old volume, we can divide V’ by V and simplify. We get:

V’ / V = (405 cm^3) / (135 cm^3) V’ / V = 3

To write the ratio in the form of a fraction, we can use 1 as the denominator of V. We get:

V’ / V = 3 / 1

Using these steps, I found that the ratio of the new volume to the old volume will be 3:1.

Therefore, by the given rectangular prism the answer will be 3:1.

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The form of association that would be found in the variables would be:

As the number of hours spent playing a video game increases, the player is likely to reach higher levels within the game. So positive association.

The number of letters in a person's name and the last digit of their phone number are likely to be unrelated and randomly distributed. There is no association.

As the temperature of the drink decreases, the number of ice cubes in the drink is likely to increase, and vice versa. This is therefore negative association.

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Answer:

dont know sos

Step-by-step explanation:

The length of the image of the AB when dilated by a scale factor of 6 is \(24\sqrt{2}\)

The coordinates are given as:

A = (-2,-5)

B = (2,-9)

The distance AB is calculated using:

\(AB = \sqrt{(x_2 - x_1)^2 + (y_2 -y_1)^2}\)

So, we have:

\(AB = \sqrt{(-2 - 2)^2 + (-5 + 9)^2}\)

Evaluate

\(AB = \sqrt{32}\)

Express as a root of 2

\(AB = 4\sqrt{2}\)

The distance of the image is calculated using:

A'B = k* AB

Where k is the scale factor.

So, we have:

\(A'B' = 6 * 4\sqrt{2}\)

This gives

\(A'B' = 24\sqrt{2}\)

Hence, the length of the image of the AB is \(24\sqrt{2}\)

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The values of {m} that is greater than 4.6 represent the solution of the given inequality.

An inequality is used to compare two or more expressions or numbers.

For example -

2x > 4y + 3

x + y > 3

x - y < 6

The given inequality is -

5m - 7 > 16

Adding 7 on both sides, we get -

5m - 7 + 7 > 16 + 7

5m > 23

m > 23/5

m > 4.6

Therefore, the values of {m} that is greater than 4.6 represent the solution of the given inequality.

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Answer:

1.5 or 1 1/2

Step-by-step explanation:

2x+7=10 (subtract 7 from both sides)

2x=10-7

2x=3 (divide both sides by 2)

X=3/2  

Simplify

X= 1.5 or 1 1/2

The standard error represents the average deviation of the sample means from the true population mean. Rounding this value to four decimal places, the standard error of X¯¯¯ is approximtely 0.6500 mpg.

A smaller standard error indicates that the sample means are more likely to be close to the population mean.To calculate the standard error of X¯¯¯, the mean from a random sample of 25 fill-ups by one driver, we can use the formula:

Standard Error (SE) = σ / sqrt(n),

where σ is the standard deviation and n is the sample size.

In this case, the standard deviation (σ) is given as 3.25 mpg, and the sample size (n) is 25.

Plugging in these values into the formula, we have:

SE = 3.25 / sqrt(25).

Calculating the square root of 25, we get:

SE = 3.25 / 5.

Performing the division, we find:

SE ≈ 0.65.

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The simplified form of the given expression, 6 × 10⁻³ / 8 × 10⁻⁶, is 3/4  × 10³

From the question, we are to simplify the given expression

The given expression is

6 × 10⁻³ / 8 × 10⁻⁶

Simplifying the expression

6 × 10⁻³ / 8 × 10⁻⁶

This can be written as

6/8 × 10⁻³/10⁻⁶

Reduce the fraction

3/4  × 10⁻³/10⁻⁶

Apply the division law of indices

3/4  × 10⁻³ ⁻ ⁽⁻⁶⁾

3/4  × 10⁻³ ⁺ ⁶

3/4  × 10³

Hence, the value is 3/4  × 10³

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The approximate surface area of the package is approximately 245.05 square inches.

The best model for the package is a cylinder.

To calculate the approximate surface area of the package, we need to find the lateral surface area of the cylinder and the area of the circular base.

The lateral surface area of a cylinder can be calculated using the formula:

Lateral Surface Area = 2πrh

where r is the radius of the base and h is the height.

The area of the circular base can be calculated using the formula:

Area of Base = \(πr^2\)

Given that the diameter of the bottom is 9 inches, the radius (r) would be half of that, which is 4.5 inches.

Using the given height of 13 inches, we can now calculate the surface area:

Lateral Surface Area = 2πrh = 2π(4.5)(13) ≈ 117.81 square inches

Area of Base = \(πr^2 = π(4.5)^2 ≈ 63.62\) square inches

To find the total surface area, we add the lateral surface area and the area of the base:

Total Surface Area = Lateral Surface Area + 2 × Area of Base = 117.81 + (2 × 63.62) ≈ 245.05 square inches

Therefore, the approximate surface area of the package is approximately 245.05 square inches.

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Answer:

Rate=6

Step-by-step explanation:

First multiply the interest by 100

50.40×100=5040

then multiply the investment by the number of years

210×4=840

then divide the two answers together

5040÷840=6

Answer:

θ= 60° or 120°Step-by-step explanation: if im wrong im srry

The value of f(g(x))=\(\frac{7x}{1-x}\) and g(f(x))=\(6(\frac{7x}{6-7x})\). The function f(g(x)) = g(f(x)) are inverse of each other.

In mathematics, an argument of a function is a value provided to obtain the function's result. It is also called an independent variable.

1. To find the f(g(x)), we need to substitute g(x) into the expression for f(x):

\(f(g(x))= \frac{(f(x))}{(6+g(x))} \\f(g(x)) =\frac{(6x/(1-x))}{6+(6x)/(1-x)} \\f(g(x))=\frac{(7x)}{(1-x)}\)

To find g(f(x)), we need to subsititute f(x) into the expression for g(x):

\(g(f(x))= \frac{6(f(x))}{(1-f(x))} \\g(f(x)) =\frac{6((x/6)+x)}{(1-((x/6)+6)} \\g(f(x)) =\frac{6(7x/6)}{(1-(7x/6))} \\g(f(x))=\frac{6(7x)}{(6-7x)}\)

2. The fact that f(g(x)) = g(f(x)) tells us that these two functions are inverses of each other. This means that if we apply f and then g to a number, we get back the same number, and if we apply g and then f to a number, we also get back the same number.

In other words, these two functions "undo" each other's operations.

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a. f(g(x)) = x/(1 - x) and g(f(x)) = x/(1 - x/6)

b. f(x) and g(x) are not inverses of one another.

What is function?

In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range.

(a)

To find f(g(x)), we substitute g(x) into f(x) in place of x:

f(g(x)) = g(x)/6 + g(x) = [(6x)/(1 - x)]/6 + (6x)/(1 - x) = x/(1 - x)

To find g(f(x)), we substitute f(x) into g(x) in place of x:

g(f(x)) = (6f(x))/(1 - f(x)) = (6[x/6 + x])/(1 - [x/6 + x]) = x/(1 - x/6)

(b)

Comparing f(g(x)) = x/(1 - x) and g(f(x)) = x/(1 - x/6), we can see that they are not the same expression. Therefore, f(x) and g(x) are not inverses of one another. In fact, we can verify that:

f(g(x)) ≠ x

g(f(x)) ≠ x

Thus, there is no inverse relationship between the two functions.

When f(g(x)) = g(f(x)) = x, it means that the functions f(x) and g(x) are inverse functions of each other. This implies that composing one function with its inverse function results in the identity function. However, this is not the case for the functions f(x) and g(x) given in this question.

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If we restrict the domain of the function to the portion of the graph with a positive slope, the domain of the inverse function will be the range of the original function for values of x greater than 4, and its range will be all real numbers greater than or equal to 4.

The given function f(x) = |x – 4| + 6 is a piecewise function that contains an absolute value. The absolute value function has a V-shaped graph, and the slope of the graph changes at the point where the absolute value function changes sign. In this case, that point is x=4.

If we restrict the domain of f(x) to the portion of the graph with a positive slope, we are essentially considering the piece of the graph to the right of x=4. This means that x is greater than 4, or x>4.

The domain of the inverse function, f⁻¹(x), will be the range of the original function f(x) for values of x greater than 4. This is because the inverse function reflects the original function over the line y=x. So, if we restrict the domain of f(x) to values greater than 4, the reflected section of the graph will be the range of f⁻¹(x).

The range of f(x) is all real numbers greater than or equal to 6 because the absolute value function always produces a positive or zero value and when x is greater than or equal to 4, we add 6 to that value. The range of f⁻¹(x) will be all real numbers greater than or equal to 4, as this is the domain of the reflected section of the graph.

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Answer:

  y = -x +3

Step-by-step explanation:

You want the slope-intercept equation of the line with the same intercept as -3y = -9 +3x, and the same slope as -2x -2y = -8.

The slope-intercept form of the equation of a line is ...

  y = mx +b . . . . . where m is the slope, and b is the y-intercept

For the given equations, we can put them in this form to find the desired parameters.

  -3y = -9 +3x

  y = -x +3 . . . . . . . . . . divide both sides by -3

We observe that the y-intercept is +3, which we will need for our answer.

The slope-intercept form of the second equation is ...

  -2x -2y = -8

  x + y = 4 . . . . . . . . . . divide by -2

  y = -x +4 . . . . . . . . . . subtract x

We observe that the slope (coefficient of x) is -1, which we will need for our answer.

We want the equation of the line with slope -1 and y-intercept 3. It is ...

  y = -x +3 . . . . . . . . . . same as the equation of the first line

__

Additional comment

The slope-intercept equation (green) is plotted using dots, so that you can see it is coincident with the line described by the first equation (red). Parallel lines have the same slope, so our desired line must be parallel to the blue line. (It is.)

Answer:

$45

Step-by-step explanation:

If every square is 1/5 a square foot, and ever square foot is $15, then every 5 squares is $15. which would be 45 for the kitchen, 60 for the dining room, and 90.30.

The surface area of the cube is 1536 ft².

We have,

The cube can be seen as 6 square areas in the net.

So,

The surface area of the cube.

= 6 x area of one square surface.

Now,

Side = 16 ft

Area of one square surface.

= side²

= 16²

= 256 ft²

Now,

The surface area of the cube.

= 6 x area of one square surface.

= 6 x 256

= 1536 ft²

Thus,

The surface area of the cube is 1536 ft².

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Answer:

The answer is 6

Step-by-step explanation:

Answer: 6

Step-by-step explanation: took the quiz

Answer: 76kg

Step-by-step explanation:

If the mass of sugar in one jar is 19kg, then the mass of 4 such jars of sugar can be found by multiplying the mass of one jar by 4:

Therefore, the total mass of 4 jars of sugar is 76kg.

__________________________________________________________

The mass of sugar is 19 kg. What is the total mass of 4 such jar of a sugar?

The total mass of four jars of sugar is 76 kg.

The total mass of four jars of sugar can be found by multiplying the mass of one jar by 4:

\(\large\rm{Total\: mass = 19\: kg \times 4 = \boxed{\rm{\:76\: kg\:}}}\)

\(\therefore\) The total mass of four jars of sugar is 76 kg.

- Mass is a measure of the amount of matter an object contains. It is a fundamental property of an object and is typically measured in units such as kilograms or grams. Mass is different from weight, which is the force of gravity acting on an object's mass. Mass is an intrinsic property of an object and remains constant regardless of its location, while weight can vary depending on the gravitational field it is in. Essentially, mass determines an object's resistance to acceleration or change in motion.

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The probability that the number is 6 and the letter is a consonant is 3/40.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

The probability of choosing the number 6 is 1/10, since there are 10 possible digits to choose from (0 to 9) and each is equally likely to be chosen.

The probability of choosing a consonant from the alphabet depends on the definition of "consonant". If we define consonants as all the letters in the alphabet except for A, E, I, O, and U (i.e., the vowels), then there are 21 consonants in the alphabet.

The total number of letters in the alphabet is 26, so the probability of choosing a consonant is 21/26

To find the probability that the number is 6 and the letter is a consonant, we need to multiply the probabilities of these events occurring independently:

P(number is 6 and letter is a consonant) = P(number is 6) * P(letter is a consonant)

= (1/10) * (21/26)

= 21/260

= 3/40

Therefore, the probability that the number is 6 and the letter is a consonant is 3/40.

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The result of the simplified polynomial in standard form is 26x-67-x^2.

Given that,

Based on the above information, the equation be like

= (10x - 3) - (x - 8)^2

= 10x - 3 -(x^2-16x+64)

= 10x - 3-x^2+16x-64

= 26x-67-x^2

Therefore we can conclude that the result of the simplified polynomial in standard form is 26x-67-x^2.

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The price of the share of stock in fossil oil refineries after the three-for-one split is $50.

A stock split is an event in the stock market when the company declares split of stock into multiple parts to decrease the cost per share and make it easier to purchase.

Given,

          The selling price of a stock in fossil fuel before split = $150

          After one year the stock split into three parts

         ∴ Probable prices per share = Price before split/3

                                                         = $150/3

                                                         = $50

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Answer:

Part A:

1. Computation of Basic EPS

Basic EPS = (Net Income - Preferred Dividends) / Weighted Average Shares Outstanding²

Net Income = $120,000

Preferred Dividends = 4% x $50,000 = $2,000

Weighted Average Shares Outstanding = 100,000 (assuming no change in common stock during the year)

Basic EPS = ($120,000 - $2,000) / 100,000

Basic EPS = $1.18

2. Individual dilution/anti-dilution with decision making

We need to check if any of the convertible securities or stock options are dilutive or anti-dilutive by comparing their impact on EPS with the basic EPS.

Convertible Preferred: Each preferred share can be converted into 1.9 common shares (1,900 / 1,000). The conversion would increase the common shares outstanding by 1,900 and decrease the preferred dividends by $2,000.

EPS after conversion = ($120,000 - $0) / (100,000 + 1,900)

EPS after conversion = $1.16

Since this is lower than the basic EPS of $1.18, the convertible preferred is dilutive and should be included in the diluted EPS calculation.

Stock Options - A: Each option can be exercised at $12 to buy one common share when the average market price is $11. This means that the options are out of the money and would not be exercised by the holders. Therefore, they have no impact on EPS and are anti-dilutive.

Stock Options - B: Each option can be exercised at $7 to buy one common share when the average market price is $8. This means that the options are in the money and would be exercised by the holders. The exercise would increase the common shares outstanding by 4,000 and generate cash proceeds of $28,000 ($7 x 4,000). The cash proceeds can be used to buy back some common shares at the market price of $8. The number of shares bought back is 3,500 ($28,000 / $8). The net increase in common shares outstanding is 500 (4,000 - 3,500).

EPS after exercise = ($120,000 - $2,000) / (100,000 + 500)

EPS after exercise = $1.17

Since this is lower than the basic EPS of $1.18, the stock options - B are dilutive and should be included in the diluted EPS calculation.

Convertible Bonds: Each bond can be converted into 40 common shares (40,000 / 1,000). The conversion would increase the common shares outstanding by 40,000 and decrease the interest expense by $50,000 ($1,000,000 x 5%). The interest expense is net of tax, so we need to multiply it by (1 - tax rate) to get the after-tax amount. The tax rate is 30%.

EPS after conversion = ($120,000 - $2,000 + $50,000 x (1 - 0.3)) / (100,000 + 40,000)

EPS after conversion = $1.19

Since this is higher than the basic EPS of $1.18, the convertible bonds are anti-dilutive and should be excluded from the diluted EPS calculation.

3. Ranking of potential dilutors

We need to rank the potential dilutors from the most dilutive to the least dilutive based on their impact on EPS.

The most dilutive security is the convertible preferred with an EPS of $1.16.

The second most dilutive security is the stock options - B with an EPS of $1.17.

The least dilutive security is the convertible bonds with an EPS of $1.19.

4. Step-by-step inclusion of individual dilutors to arrive at reportable EPS with decision making.

We need to include the potential dilutors in order of their dilution until we reach a point where the next security would be anti-dilutive.

The first security to include is the convertible preferred.

EPS with convertible preferred = ($120,000 - $0) / (100,000 + 1,900)

EPS with convertible preferred = $1.16

The next security to include is the stock options - B.

EPS with stock options - B = ($120,000 - $0) / (100,000 + 1,900 + 500)

EPS with stock options

The hypotenuse of a right triangle will be $561$.

What is hypotenuse?

In a right triangle, the hypotenuse is the longest side, an "opposite" side is the one across from a given angle, and an "adjacent" side is next to a given angle.

Lengths of legs of a right triangle are given that are $264$ and $495$.

According to The Pythagorean Theorem,

\(hypotenuse^{2} = lenght^{2} + lenght^{2}\\hypotenuse^{2} = 264^{2} + 495^{2}\\\\hypotenuse^{2} = 69,696 + 245,025\\ hypotenuse^{2} = 314,721\\hypotenuse = 561\)

The hypotenuse of a right triangle will be $561$.

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