Which expressions are equivalent?


I like your cut G!

Answer:

729 x \(\frac{1}{3}\)^x

Step-by-step explanation:

the third option

- trial and error

Answer:

-14/16

-35/40

Step-by-step explanation:

7/-8 times \(\frac{2}{2}\) is -14/16

7/-8 times \(\frac{5}{5}\) is -35/40

Answer:

7-8-87-87-87-7-767&7&7

Step-by-step explanation:

そう笑ここに何を書けばいいのかわからないので、ここで私は答えを知っているふりをしています

Answer:

The null and alternative hypotheses can be formulated based on the claim about the mean age of instructors at Widget College. Let's define the null and alternative hypotheses:

Step-by-step explanation:

Null Hypothesis (H0): The mean age of instructors at Widget College is equal to 52.7 years.

Alternative Hypothesis (Ha): The mean age of instructors at Widget College is not equal to 52.7 years.

In statistical hypothesis testing, the null hypothesis typically assumes no significant difference or effect, while the alternative hypothesis suggests there is a significant difference or effect. In this case, the claim states a specific value of the mean age (52.7 years), so we can set the null hypothesis as the equality of the mean age to that value. The alternative hypothesis is then formulated as the negation of the null hypothesis, indicating that the mean age is not equal to 52.7 years.

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Answer:

It would equal

6a^2-19a-20

Answer:

6a^2−25a−25 this is the answer to number 5

Answer:

the answer is 10000

Step-by-step explanation:

one liter has 1000 millimeters

The values for the lesser and greatest are:

-14 and 0

Step 1: Define

(x + 7)² - 49 = 0

Step 2: Solve for x

Add 49 to both sides:                    (x + 7)² = 49

Square root both sides:                 x + 7 = ±7

Subtract 7 on both sides:               x = -7 ± 7

Evaluate:                                         x = -14, 0

Step 3: Check

Plug in x values into original equation to verify they are a solution.

x = -14

Substitute in x:                    (-14 + 7)² - 49 = 0

Add:                                     (-7)² - 49 = 0

Exponents:                          49 - 49 = 0

Subtract:                              0 = 0

Here we see that 0 does indeed equal 0.

∴ x = -14 is a solution of the equation

x = 0

Substitute in x:                    (0 + 7)² - 49 = 0

Add:                                     7² - 49 = 0

Exponents:                          49 - 49 = 0

Subtract:                              0 = 0

Here we see that 0 does indeed equal 0.

∴ x = 0 is also a solution of the equation.

Hence we get the required answer.

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The first four terms of the Taylor series for the function (2x) about the point (a=1) are (2x + 2x - 2).

To find the first four terms of the Taylor series for the function (2x) about the point (a = 1), we can use the general formula for the Taylor series expansion:

\(\[f(x) = f(a) + f'(a)(x-a) + \frac{f''(a)}{2!}(x-a)^2 + \frac{f'''(a)}{3!}(x-a)^3 + \ldots\]\)

Let's calculate the first four terms:

Starting with the first term, we substitute

\(\(f(a) = f(1) = 2(1) = 2x\)\)

For the second term, we differentiate (2x) with respect to (x) to get (2), and multiply it by (x-1) to obtain (2(x-1)=2x-2).

\(\(f'(a) = \frac{d}{dx}(2x) = 2\)\)

\(\(f'(a)(x-a) = 2(x-1) = 2x - 2\)\)

Third term: \(\(f''(a) = \frac{d^2}{dx^2}(2x) = 0\)\)

Since the second derivative is zero, the third term is zero.

Fourth term:\(\(f'''(a) = \frac{d^3}{dx^3}(2x) = 0\)\)

Similarly, the fourth term is also zero.

Therefore, the first four terms of the Taylor series for the function (2x) about the point (a = 1) are:

(2x + 2x - 2)

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Answer:5,800

Step-by-step explanation:

The average depreciation of the equipment per year is $9200.

The monetary value of an asset decreases over time due to use, wear and tear or obsolescence, this is called as depreciation.

Now it is given that,

Cost of the equipment = $85,600

current value of the equipment is given as $30,400

Duration for which the equipment was used = 6 years

Now the depreciation of the equipment is given as,

Total depreciation in the price of the equipment

                       = Cost of the equipment - current price of the equipment

So, total depreciation = $85,600 - $30,400 = $55,200

Now,

Average yearly depreciation = Total depreciation ÷ Years used

Average depreciation = 55,200/6

⇒Average depreciation = $9200

Therefore, average depreciation of the equipment per year is $9200.

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The statement best explains why ben must open the compass to a width greater than half  is option (A) To be able to create to intersecting arc above and below the line segment

Ben must open the compass to a width greater than half of PQ because he needs to draw two arcs that intersect each other on either side of PQ. The point where the two arcs intersect is the midpoint of PQ, which is what he is trying to find by bisecting PQ.

If Ben were to open the compass to exactly half of PQ, he would only be able to draw one arc, which would not intersect the line PQ in a way that would enable him to find its midpoint.

By opening the compass wider than half of PQ, Ben can draw two arcs that intersect each other on either side of PQ, and the point where they intersect will be the midpoint of PQ. This is the reason why Ben must open the compass to a width greater than half of PQ.

Therefore, the correct option is (A) To be able to create to intersecting arc above and below the line segment

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The given question is incomplete, the complete question is:

ben uses a compass and straightedge to bisect , as shown: which statement best explains why ben must open the compass to a width greater than half of ?

The predicted profit of a Burger store restaurant with $900,000 counter sales and $800,000 drive-through sales is $690,001 million.

To find the predicted profit of a Burger store restaurant with $900,000 counter sales and $800,000 drive-through sales using the provided dataset, we can follow these steps:

Step 1: Import the "Franchises Dataset" into a statistical software package like Excel or R.

Step 2: Perform regression analysis to find the equation of the line of best fit that relates the net profit (dependent variable) to the counter sales and drive-through sales (independent variables). The equation will be in the form of y = mx + b, where y is the net profit, x is the combination of counter sales and drive-through sales, m is the slope, and b is the y-intercept.

Step 3: Use the regression equation to calculate the predicted net profit for the given counter sales and drive-through sales values. Plug in the values of $900,000 for counter sales (x1) and $800,000 for drive-through sales (x2) into the equation.

For example, let's say the regression equation obtained from the analysis is: y = 0.5x1 + 0.3x2 + 1.

Substituting the values, we get:

Predicted Net Profit = 0.5(900,000) + 0.3(800,000) + 1

= 450,000 + 240,000 + 1

= 690,001 million dollars.

Therefore, the predicted profit of a Burger store restaurant with $900,000 counter sales and $800,000 drive-through sales is $690,001 million.

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Answer:

  2/15

Step-by-step explanation:

You want to know the fraction that is 2/3 of 1/5.

In this context, "of" means "times."

  2/3 of 1/5 = (2/3)×(1/5) = (2·1)/(3·5) = 2/15

2/15 of the pets are alley cats.

The given expression is a simplified algebraic equation: (1/2) * a^2 - 3b + 2c. It represents a combination of variables a, b, and c with their respective coefficients.

Utilizing symbols and operations, an algebraic equation illustrates the equivalence or inequivalence of two expressions. These generated expressions may hold variables that have varying values.

The premise centered around calculus is to arrive at a solution by acquiring the correct value(s) of these variable(s), ultimately fulfilling the outlined specification in the problem. Algebraic equations can range from uncomplicated linear problems to elaborate polynomials and trigonometric functions.

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The maximum value attained by the sum of the expression is 169 when N is the two-digit number 98.

Let N be a two-digit number with digits a and b. Then, the sum of N and the product of its digits is N + ab, and the sum of N's digits is a + b. Therefore, the expression we want to maximize is:

Substituting N = 10a + b, we get:

To maximize this expression, we want to maximize a and b. Since a and b are digits, they must be between 1 and 9. If we set a = 9 and b = 8, we get:

Therefore, the maximum value attained by the expression is 169 when N is the two-digit number 98.

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a) An upper bound for error |f (0.5) − P2(0.5)| using the error formula is 0.0208

b) On the interval [0, 1], we have |R2(x)| <= (e/6) √10 x³

c) The maximum value of |f(x) - P2(x)| on the interval [0, 1] occurs at x = π/2, and is approximately 0.1586.

a. As per the given polynomial, to approximate f(0.5) using P2(x), we simply plug in x = 0.5 into P2(x):

P2(0.5) = 1 + 0.5 - (1/2)(0.5)^2 = 1.375

To find an upper bound for the error |f(0.5) - P2(0.5)|, we can use the error formula:

|f(0.5) - P2(0.5)| <= M|x-0|³ / 3!

where M is an upper bound for the third derivative of f(x) on the interval [0, 0.5].

Taking the third derivative of f(x), we get:

f'''(x) = ex (-3cos x + sin x)

To find an upper bound for f'''(x) on [0, 0.5], we can take its absolute value and plug in x = 0.5:

|f'''(0.5)| = e⁰°⁵(3/4) < 4

Therefore, we have:

|f(0.5) - P2(0.5)| <= (4/6)(0.5)³ = 0.0208

b. For n = 2, we have:

R2(x) = (1/3!)[f'''(c)]x³

To find an upper bound for |R2(x)| on the interval [0, 1], we need to find an upper bound for |f'''(c)|.

Taking the absolute value of the third derivative of f(x), we get:

|f'''(x)| = eˣ |3cos x - sin x|

Since the maximum value of |3cos x - sin x| is √10, which occurs at x = π/4, we have:

|f'''(x)| <= eˣ √10

Therefore, on the interval [0, 1], we have:

|R2(x)| <= (e/6) √10 x³

c. To approximate the maximum value of |f(x) - P2(x)| on the interval [0, 1], we need to find the maximum value of the function R2(x) on this interval.

To do this, we can take the derivative of R2(x) and set it equal to zero:

R2'(x) = 2eˣ (cos x - 2sin x) x² = 0

Solving for x, we get x = 0, π/6, or π/2.

We can now evaluate R2(x) at these critical points and at the endpoints of the interval:

R2(0) = 0

R2(π/6) = (e/6) √10 (π/6)³ ≈ 0.0107

R2(π/2) = (e/48) √10 π³ ≈ 0.1586

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According to the equation we have After simplifying, the equation in spherical coordinates is: 5ρ^2 - 3ρ sin(θ) cos(φ) = 0 .

To write the given equation in spherical coordinates, we first need to express x, y, and z in terms of rho (ρ), theta (θ), and phi (φ), which are the spherical coordinates.

We know that:

x = ρsinφcosθ
y = ρsinφsinθ
z = ρcosφ

Substituting these values in the given equation, we get:

5(ρsinφcosθ)² - 3(ρsinφcosθ) + 5(ρsinφsinθ)² + 5(ρcosφ)² = 0

Simplifying further, we get:

5ρ²sin²φcos²θ + 5ρ²sin²φsin²θ + 5ρ²cos²φ - 3ρsinφcosθ = 0

Now, we can use the trigonometric identities:

sin²θ + cos²θ = 1
sin²φ + cos²φ = 1

Substituting these in the equation, we get:

5ρ²sin²φ + 5ρ²cos²φ - 3ρsinφcosθ = 0

To rewrite the given equation 5x^2 - 3x + 5y^2 + 5z^2 = 0 in spherical coordinates, we need to use the conversions:

x = ρ sin(θ) cos(φ)
y = ρ sin(θ) sin(φ)
z = ρ cos(θ)

Substitute these conversions into the equation:

5(ρ sin(θ) cos(φ))^2 - 3(ρ sin(θ) cos(φ)) + 5(ρ sin(θ) sin(φ))^2 + 5(ρ cos(θ))^2 = 0

After simplifying, the equation in spherical coordinates is:

5ρ^2 - 3ρ sin(θ) cos(φ) = 0

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The probability that the next component brought in for repair is a compact disc player given that it is already known to be an audio component is 0.83 or 83%.

Probability is a fundamental concept in mathematics, statistics, and various fields of science. It is used to measure the likelihood of an event occurring

In the given scenario, we are told that a certain shop repairs both audio and video components. Let A denote the event that the next component brought in for repair is an audio component, and let B be the event that the next component is a compact disc player. We are also given that P(A) = 0.6 and P(B) = 0.5.

The probability of B given A, denoted by P(B|A), represents the probability that event B will occur given that event A has already occurred. In other words, it tells us how likely it is that the next component brought in for repair is a compact disc player given that it is already known to be an audio component.

To calculate P(B|A), we use the formula for conditional probability:

P(B|A) = P(A and B) / P(A)

Here, P(A and B) denotes the probability that both events A and B occur. We know that event B is contained in event A, so it follows that P(A and B) = P(B). Therefore:

P(B|A) = P(B) / P(A)

Substituting the given values, we have:

P(B|A) = 0.5 / 0.6

P(B|A) = 5/6 or 0.83 (rounded to two decimal places)

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Complete Question:

A certain shop repairs both audio and video components. Let A denote the event that the next component brought in for repair is an audio component, and let B be the event that the next component is a compact disc player (so the event B is contained in A).  Suppose that P(A) = .6and P(B) = .5. What is P(B|A) ?

The true statement is Together, the families spend $409

We have to solve the equation using the substitution method

13a + 17c = 211

14a + 9c = 198

From equation 1:

13a = 211 - 17c

a = (211 - 17c)/13

Now substitute 'a' in equation 2:

14(211 - 17c)/13) + 9c = 198

multiply through by 13

14(211 - 17c) + 9c * 13 = 198 * 13

2942 - 238c + 117c = 2574

Combine like terms:

-121c = -368

c = 368 / 121

c = 3

Put the value of C in a

a = (211 - 17c)/13

a = (211 - 17 * 3) / 13

a = (211 - 51) / 13

a = 160 / 13

a = 12

The true statement is ogether, the families spend $409.

Together, they spend $211 + $198 = $409.

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Answer: 4 reds

Step-by-step explanation:

To find the surface area of a sphere, we use the formula S.A. = 4πr², where S.A. represents the surface area and r is the radius of the sphere. In this case, the radius of the sphere is given as 10 cm.

The formula for the surface area of a sphere is S.A. = 4πr², where S.A. represents the surface area and r is the radius of the sphere.

In this case, the radius of the sphere is given as 10 cm. Substituting this value into the formula, we have:

S.A. = 4π(10 cm)²

Simplifying the expression inside the parentheses:

S.A. = 4π(100 cm²)

Multiplying 4π by 100 cm²:

S.A. = 400π cm²

To find the surface area in decimal form, we can use an approximation of π as 3.14:

S.A. ≈ 400(3.14) cm²

Calculating the product:

S.A. ≈ 1256 cm²

Therefore, the surface area of the sphere is approximately 1256 cm², rounded to the nearest tenth.

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Answer:

1. Becky's rate of sales is 9 cups per hour

2. Mayisha's rate of sales is 10 cups per hour

3. Becky is selling 1 fewer cups per hour than Mayisha

4. Becky started with 2 fewer cups than Mayisha

Step-by-step explanation:

1. 30-12=18 18/2=9

2. 31-21=10 21-11=10

3. 10-9=1

4. 30+9=39 31+10=41 41-39=2

Answer:

Becky's rate of sales is \(\boxed{\sf 9}\) cups per hour.

Mayisha's rate of sales is \(\boxed{\sf 10}\) cups per hour.

Becky is selling \(\boxed{\sf 1\: fewer}\) cup(s) per hour than Mayisha.

Becky started with \(\boxed{\sf 2}\) fewer cups than Mayisha.

Step-by-step explanation:

Mayisha

\(\begin{array}{|c|c|c|c|}\cline{1-4} \sf Hours\:(x) & 1 & 2 & 3\\\cline{1-4} \sf Cups\: {left}\:(y) & 31 & 21 & 11\\\cline{1-4} \end{array}\)

Becky

\(\begin{array}{|c|c|c|c|}\cline{1-4} \sf Hours\:(x) & 1 & 2 & 3\\\cline{1-4} \sf Cups\: {left}\:(y) & 30 & & 12\\\cline{1-4} \end{array}\)

Selling at a steady rate.

To calculate the rate of sales, use the rate of change formula:

\(\sf Rate\:of\:change = \dfrac{change\:in\:y}{change\:in\:x}\)

Therefore:

\(\textsf{Becky's rate of sales}=\dfrac{12-30}{3-1}=-9\)

Therefore, as the number of cups reduces by 9 each hour, Becky's rate of sales is 9 cups per hour.

\(\textsf{Mayisha's rate of sales}=\dfrac{11-31}{3-1}=-10\)

Therefore, as the number of cups reduces by 10 each hour, Mayisha's rate of sales is 10 cups per hour.

As 9 is one less than 10, Becky is selling 1 fewer cup(s) per hour than Mayisha.

As Becky had 30 cups left after 1 hour, and her rate of sales is 9 cups, then she started with 30 + 9 = 39 cups.

As Mayisha had 31 cups left after 1 hour, and her rate of sales is 10 cups, then she started with 31 + 10 = 41 cups.

As 39 is 2 less than 41, Becky started with 2 fewer cups than Mayisha.

Answer:

$14.00

Step-by-step explanation:

First take $20 and divide by 100. Then you multiply by 30 to get the reference which was $6. If the sweatshirt was $20 and the reference was $6, you would subtract $20 - $6 and get $14.

Answer: $14.00

Step-by-step explanation: First take $20 and divide by 100. Then you multiply by 30 to get the reference which was $6. If the sweatshirt was $20 and the reference was $6, you would subtract $20 - $6 and get $14.

The length of IKE is 2x - 12.

A condition on a variable that is true for just one value of the variable is called an equation.

Since KITE is a kite, we know that KT = IT and KE = IE. Let's call the length of these diagonals d. Then we have:

KT + TI = d

KE + EI = d

Substituting in the given values, we get:

x + 6 + 2x = d

2x + IE = d

Solving for d in the first equation, we get:

3x + 6 = d

Substituting this into the second equation, we get:

2x + IE = 3x + 6

Solving for IE, we get:

IE = x + 6

Therefore, IKE is equal to:

IKE = IT - IE

IKE = (d - KT) - (x + 6)

IKE = (3x + 6 - x - 6) - (x + 6)

IKE = 2x - 12

So, the length of IKE is 2x - 12.

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The percentage change from 92 to 108 is 13.4% approx

What is Percentage?

A percentage is a figure or ratio that may be stated as a fraction of 100 in mathematics. If we need to compute the percentage of a number, divide it by the entire and multiply by 100. As a result, the percentage denotes a part per hundred. The term per cent refers to one hundred percent.

Solution:

Percentage = Change / Original * 100

Change = 108 - 92 = 16

Original/Initial Value = 92

Percentage Change = 16/92 * 100 = 17.39% = 17.4% (approx)

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The type of sampling used in this scenario is B. Stratified sampling. Stratified sampling involves dividing the population into distinct subgroups or strata and then selecting samples from each subgroup.

In this case, Miranda divides her day into three parts: morning, afternoon, and evening. Each part of the day represents a stratum or subgroup.  Miranda measures her breathing rate at 4 randomly selected times during each part of the day. This means she is taking samples from each of the three strata (morning, afternoon, and evening) and collecting data from within those subgroups.

By using stratified sampling, Miranda ensures that her samples represent the different parts of her day in a proportional and systematic manner, allowing her to capture potential variations in her breathing rate throughout the day.

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Answer:

number of men = 30

Step-by-step explanation:

18 men takes 15 days to dig 6 hectares of land.

18 men will take 12 days to dig ? hectares of land

cross multiply

hectares of land = 12 × 6/15  

hectares of land = 72/15

hectares of land = 4.8 hectares

18 men will take 12 days to dig 4.8 hectares of land

? number of men will take 12 days to dig 8 hectares

cross multiply

number of men = 18 × 8/4.8

number of men = 144/4.8

number of men = 30

If the price of rough rice increases from 12,000 to 20,000 rupees per ton, the supply curve of milled rice in India will decrease by 96 million tons per year.

To determine how the supply curve changes when the price of rough rice increases from 12,000 to 20,000 rupees per ton, we need to analyze the given supply function:

Q = 8 + 9p - 12p,

In the supply function, "p" represents the price of milled rice in thousands of rupees per ton. However, there is a typo in the equation provided for the supply function. It appears that the equation contains two terms with the variable "p," which should be corrected.

Assuming the corrected supply function is:

Q = 8 + 9p - 12p',

Where p' represents the price of rough rice in thousands of rupees per ton.

Now, let's calculate the initial supply quantity and then compare it with the new supply quantity after the increase in the price of rough rice.

For the initial price of rough rice (p') at 12,000 rupees per ton:

Q1 = 8 + 9p - 12(12)

Q1 = 8 + 9p - 144

For the new price of rough rice (p') at 20,000 rupees per ton:

Q2 = 8 + 9p - 12(20)

Q2 = 8 + 9p - 240

The change in supply can be calculated as the difference between Q2 and Q1:

Change in supply (ΔQ) = Q2 - Q1

= (8 + 9p - 240) - (8 + 9p - 144)

= -240 + 144

= -96

The change in supply (ΔQ) is -96 millions of tons of rice per year.

Therefore, if the price of rough rice increases from 12,000 to 20,000 rupees per ton, the supply curve of milled rice in India will decrease by 96 million tons per year.

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