Which expression is equivalent to 45w2 - 27?

Answer:

Step-by-step explanation:

You take the 15 he had and subtract 9.52 from that which would look like this

15 - 9.52 = 5.48

Now with our new value 5.48 we divide it by two.

5.48 / 2 = 2.74

So he saved $2.74

1/4

To learn more about function,Given function is (sqrt(x + 1) - 2) / (x - 3).

To find the value of lim as x approaches 3, let's first calculate the value of the function at x = 3.

Plug x = 3 in the given function:

= (sqrt(3+1)-2)/(3-3) = 0/0

As we can see, we get 0/0 which is an indeterminate form. Let's find the derivative of the function f(x) using the formula:

f(x) = (sqrt(x + 1) - 2) / (x - 3)

f'(x) = [(1/2) * (x + 1)^-0.5 * 1] * (x - 3) - [(sqrt(x + 1) - 2) * 1] / (x - 3)^2

We can simplify the above equation as:

f'(x) = (2 - sqrt(x + 1)) / (2 * (x - 3)^2)

Let's now calculate the value of the derivative at x = 3:

f'(3) = (2 - sqrt(3+1)) / (2 * (3 - 3)^2) = (2 - 2) / (2 * 0) = undefined

Since f'(3) is undefined, let's now use L'Hopital's rule to find the value of the limit of the function as x approaches 3.

Taking the derivative of the numerator and denominator separately and then solving the limit, we get:

lim as x approaches 3 [(sqrt(x + 1) - 2) / (x - 3)] = lim as x approaches 3 [((1/2) * (x + 1)^-0.5 * 1) / 1] / [-1] = - 1 / 4

Hence, the value of the limit of the function as x approaches 3 is 1/4.

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The perimeter of the drawing is 22 inches.

The perimeter of the actual garden is 770 inches.

The effect on the perimeter of the garden is that it becomes 35 times larger than the original perimeter.

What is perimeter ?

Perimeter is the total length of the sides or edges of a two-dimensional shape, such as a polygon or a circle. It is the distance around the outside of the shape.

For example, the perimeter of a square is the sum of the lengths of all four sides of the square. If the side length of a square is "s", then the perimeter of the square is:

Perimeter = 4s

According to the question:

(a) Perimeter of the drawing:

The garden is rectangular, so we can use the formula for perimeter:

P = 2L + 2W

where L is the length and W is the width.

In the drawing, the length is 7 inches and the width is 4 inches. Substituting these values into the formula, we get:

P = 2(7) + 2(4) = 14 + 8 = 22 inches

Therefore, the perimeter of the drawing is 22 inches.

(b) Perimeter of the actual garden:

We are told that the actual garden is 35 times larger than the drawing. This means that the length and width of the actual garden are 35 times the length and width in the drawing, respectively.

The length of the actual garden is:

L_actual = 35L_drawing = 35(7) = 245 inches

The width of the actual garden is:

W_actual = 35W_drawing = 35(4) = 140 inches

Using the formula for perimeter again, we get:

P_actual = 2L_actual + 2W_actual

= 2(245) + 2(140)

= 490 + 280

= 770 inches

Therefore, the perimeter of the actual garden is 770 inches.

(c) Effect on the perimeter of the garden when the dimensions are multiplied by 35:

When the dimensions of the garden are multiplied by 35, the perimeter of the garden also increases by a factor of 35. This is because the perimeter depends on the length and width of the garden, and both of these dimensions are being multiplied by 35.

Therefore, the effect on the perimeter of the garden is that it becomes 35 times larger than the original perimeter.

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Answer: 7. 50%         8. 30%         9. 60%          10. 25%

Step-by-step explanation: That is the answer for the first page ohh and can you type the other page so it is easier to solve?

The power of the test will increase when you increase alpha. It is true when the probability of rejecting the null hypothesis.

In statistics, a statistical test is a formal procedure that is used to make an inference about the population based on the information provided by a sample.

When you increase alpha, the power of the test will increase.

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Answer:

x is equal to 12

x = 12

The solution of the quadratic equation using method of factorization is given by x = 5/2 or x = -4

Quadratic equation is equals to ,

2x^2 + 3x - 20 =0

Factorization of the quadratic equation  required two numbers that multiply to -40 and add up to 3.

Start by listing the factors of -40 as,

-1, 40

-2, 20

-4, 10

-5, 8

Out of these pairs, the only one whose sum is 3 is -5 and 8.

Rewrite the quadratic equation using factorization method as,

2x^2 + 3x - 20  = 0

⇒ 2x^2 - 5x + 8x - 20 =0

Now factor it by grouping,

⇒ (2x^2 - 5x) + (8x - 20) = 0

⇒ x(2x - 5) + 4(2x - 5) = 0

⇒ (2x - 5)(x + 4) = 0

⇒ x = 5/2 or x = -4

Therefore, the solutions of the quadratic equation 2x^2 + 3x - 20 by factorization  are x = 5/2 or x = -4.

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The above question is incomplete , the complete question is:

Solve by factorization

2x^2 +3x-20

Answer:

B

Step-by-step explanation:

The number line starts at twelve to positive infinity but the circle around point twelve is not shaded thus it is not included. Therefore

[tex]x > 12[/tex]

another way of writing this is ;

[tex]x€(12; \infty )[/tex]

The conditions have been met for inference with a confidence interval for the difference in population means is (A) Yes, all conditions have been met.

A confidence interval is a range of values that specifies the degree of uncertainty associated with an estimate. It is used to estimate population parameters based on sample statistics.

In a confidence interval, a population parameter is estimated to fall within a certain range of values with a specific degree of confidence.

The population distribution is approximately normal or the sample size is larger than 30.

In this case, the data has been collected using a random sample of 75 people with chronic headaches, with 38 being randomly assigned to medication R and 37 being assigned to medication S.

The sample mean times were calculated for each medication.

Therefore, all of the conditions have been met for inference with a confidence interval for the difference in population means.

Hence, the answer is (A) Yes, all conditions have been met.

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The first number is x = 5, and the second number is y = -2 when the difference between the square of a number and four times the square of another number is 9.

Let's start by assigning variables to the two unknown numbers. Let x be the first number, and let y be the second number. We are given two conditions:

The difference between the square of x and four times the square of y is 9:

[tex]x^2 - 4y^2 = 9[/tex]

The sum of x and twice y is 1:

[tex]x + 2y = 1[/tex]

We can use the second equation to solve for one of the variables in terms of the other. Solving for x, we get:

[tex]x = 1 - 2y[/tex]

Substituting this expression for x into the first equation, we get:

[tex](1 - 2y)^2 - 4y^2 = 9[/tex]

Expanding the left-hand side, we get:

[tex]1 - 4y + 4y^2 - 4y^2 = 9[/tex]

Simplifying, we get:

[tex]-4y + 1 = 9[/tex]

Subtracting 1 from both sides, we get:

[tex]-4y = 8[/tex]

Dividing both sides by -4, we get:

[tex]y = -2[/tex]

Substituting this value of y into the expression we derived for x, we get:

[tex]x = 1 - 2y = 1 - 2(-2) = 5[/tex]

Therefore, the first number is x = 5, and the second number is y = -2.

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Answer:

18

Step-by-step explanation:

To find the least common multiple (LCM) of 6 and 9, we can list their multiples and find the smallest multiple they have in common:

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, ...

Multiples of 9: 9, 18, 27, 36, 45, 54, ...

We can see that 18 is the smallest multiple that both 6 and 9 have in common, so the LCM of 6 and 9 is 18. Therefore, the answer is 18.

C. Calculate the mass of a gallon of milk and multiply it by the volume in cubic centimeters.

Density is the measure of an object's mass per unit volume. Kilograms per cubic meter (kg/m3) is the SI unit for density.

We must divide a substance's mass by its own volume to determine its density. In this instance, we are aware that one gallon of milk is there, yet we have to determine its mass. Hence, we can weigh a milk container, which weighs about 3.78 kilos, on a scale to determine its mass (or 8.34 pounds).

The volume of a gallon, which equals 3,785.41 cubic centimeters, can then be calculated. Lastly, we may calculate the density of milk in grammes per cubic centimeter (g/cm³) by dividing the mass of a gallon of milk by the quantity of cubic centimeters in a gallon. The volume of milk is around 1.03 g/cm³, though it can vary somewhat based on other factors, such as the fat content.

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Answer:

Where's the qn

Step-by-step explanation:

pls mrk me brainliest i need to get the next rank

Answer:    D

Step-by-step explanation:

For perpendicular lines, you must find the slope that matches the slope of the graph. This graph has a slope of 2 high and 1 left meaning 2/1 which also equals 2. The only answer choice with 2 as the slope is D meaning your answer is D.

Therefοre , the sοlutiοn οf the given prοblem οf vοlume cοmes οut tο be the clοsest pοssible respοnse is 7.09, οr 0.28 in3, sο the cοrrect respοnse is:0.28 in3.

The vοlume οf a three-dimensiοnal οbject, which is measured in cubic units, describes hοw much rοοm it οccupies. Litre and in3 are the emblems fοr cubic measurements. The bulk οf an οbject, hοwever, can be used tο estimate its measurements. Usually, the οbject's weight is transfοrmed intο mass units like grammes and kilοs.

Here,

Each cοin's vοlume is calculated by multiplying its base area by its height:

=> V = πr²h

=> 3.14 x 1.2 x 0.0625 x 0.02835

=>0.02835 cubic inches (rοunded tο five decimal places)

The sum οf the weights οf all the cοins is:

=> Tοtal vοlume = V * 250, οr

=>  V * 0.02835 * 250, οr

=> 7.0875 cubic inches (rοunded tο fοur decimal places)

The cοins therefοre οccupy abοut 7.09 cubic inches οf the treasure chest (rοunded tο the nearest hundredth).

The clοsest pοssible respοnse is 7.09, οr 0.28 in³, sο the cοrrect respοnse is: 0.28 in³

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The value of the length of side HI of the right triangle is 46.40 cm.

In the given right angles triangle.

cos Ф = base / hypotenuse

cos 23.5° = HI/50.6

HI = 50.6* cos23.5°

HI = 46.40

Thus, the value of the length of side HI of the right triangle is 46.40 cm.

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Answer:

2/4

Step-by-step explanation:

if you follow the line it goes up 2 and over 4.

the slope is 1

Step-by-step explanation:

slope is found by the formula y2-y1÷x2-x1

so (4,4) and (8,8) will equal 1

Answer:6

Step-by-step explanation:

Answer:

the answer is 23

all angles in a triangle add up to 180

Answer: 113 5/6 - 11115 6/8 = -11001.9166667

Step-by-step explanation: 1. Simplify the expression

More Icon

1135/6-111156/8

Perform any multiplication or division, from left to right:

1135/6-111156/8

189.167-111156/8

189.167-13894.5

Calculate any addition or subtraction, from left to right.

189.167-13894.5

-13705.333

The best estimate of the average change in mood rating linked with an additional hour spent playing sports is 1.5 points, according to the presented linear function.

A linear function is modeled by:

[tex]y = mx + c[/tex]

In which:

m is the slope, which is the rate of change of y when x changes by 1.

c is the y-intercept, which is the value of y when x = 0.

x is the number of hours they spent playing sports.

y be their mood rating.

Therefore, the equation will be:

[tex]y=1.5x+5[/tex]

The best estimate of the average change in mood rating linked with a 1 hour increase in hours spent doing sports is 1.5 points because the slope is m= 1.5.

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The arrangement of the rose plants on the triangular plot is such that they form a series, or progression that is defined.

What is the arithmetic sequence?

An arithmetic sequence is an ordered set of numbers that have a common difference between each consecutive term. For example in the arithmetic sequence 3, 9, 15, 21, 27, the common difference is 6. An arithmetic sequence can be known as an arithmetic progression.

Let's denote the number of rows in Dodie's triangular plot as n. Since there are n rows, the number of plants in the first row is 1, the number of plants in the second row is 1 + 5, the number of plants in the third row is 1 + 2(5), and so on.

The total number of plants can be expressed as the sum of an arithmetic sequence:

160 = 1 + (1 + 5) + (1 + 2(5)) + ... + [1 + (n-1)(5)]

Simplifying this expression, we get:

160 = [n(1 + 1 + (n-1)(5))] / 2

160 = [n(5n + 4)] / 2

320 = n(5n + 4)

5n² + 4n - 320 = 0

Using the quadratic formula, we can solve for n:

n = (-4 ± √(4² - 4(5)(-320))) / (2(5))

n = (-4 ± √(6404)) / 10

n = (-4 ± 80) / 10

Since we are looking for the positive value of n, we take:

n = (-4 + 80) / 10 = 7.6

Hence, n must be a whole number, and the maximum number of rows Dodie's plot can have is 7. Therefore, the answer is 7 rows.

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The second option has the best value for money. It is $0.014 cheaper.

First we know that a 80 ml bottle is priced at  £55, then the price per ml will be given by the quotient:

p = 55/80 = 0.689

In the other case a 50ml bottle costs  £45 and a second one of 50ml comes by half of that at £22.5

Then the price for 100ml is £67.5

Then the value for money here is:

q = 67.5/100 = 0.675

Then the second option has the best value for money by $0.014. Being cheaper.

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The distance between Sudbury and Stratford in Ontario, Canada is approximately 250 kilometers

Assuming you are referring to Sudbury in Ontario, Canada, and Stratford in Ontario, Canada, the distance between the two cities is approximately 250 kilometers (155 miles) by car, taking about 2.5 hours to drive without traffic.

There are several routes you can take to travel between Sudbury and Stratford, but the most direct and commonly used route is to take Highway 69 south from Sudbury, then merge onto Highway 400 south and continue on until you reach Highway 7. From there, head east until you reach Stratford. Along the way, you will pass through scenic areas like the Muskoka region, Orillia, and the Kitchener-Waterloo area.

Alternatively, you can take public transportation such as a bus or train, but the travel time and distance may vary depending on the specific route and schedule.

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The given question is incomplete, the complete question is:

Write down the distance from Sudbury to Stratford.

The area of a circle in polar coordinates can be calculated as an integral, where r = 4sinθ is  2π.

The region encircled by a circle with radius r is known as r2 in geometry. Here, the Greek letter stands for the constant proportion of a circle's circumference to its diameter, which is roughly equivalent to 3.14159.

We know that the area of a polar curve can be calculated using the formula:

A = ½ ∫ [f(θ)]² dθ

where f(θ) is the radial function.

In this case, the radial function is r = 4 sin θ. Substituting this into the formula, we get:

A = ½ ∫ [4 sin θ]²dθ

= ½ ∫ 16 sin² θ dθ

= ½ [8θ - 4 sin 2θ] from 0 to π/2

= 2π

Therefore, the area of the circle r = 4 sin θ is 2π.

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Answer:

Step-by-step explanation:

Given: y³ - (18x⁴)³xy²y' = 0. Let's solve this equation step by step:

Rearrange the given equation to y³ = (18x⁴)³xy²y'

Rearrange to y' on one side: y' = y³/((18x⁴)³xy²)

Now separate variables: y²dy = 1/((18x⁴)³)dx. Integrate both sides∫y²dy = ∫1/((18x⁴)³)dx⇒ y³/3 + C = ∫1/((18x⁴)³)dx.

Let c be the constant of integration.∫1/((18x⁴)³)dx = 1/3(2/3)³∫1/u³du [where u = 18x⁴]∫1/u³du = -1/6u² + c₂∫1/u³du = -1/6(18x⁴)² + c₂∫1/u³du = -1/6(324x⁸) + c₂∫1/u³du = -54x⁸ + c₂.

Now substitute values back into the previous equation: y³/3 + C = -54x⁸ + c₂. Solving for y: y = [3(-54x⁸ + c₂) - C]^(1/3). Let c be the constant of integration, y = [3(-54x⁸ + c) - C]^(1/3) is the required solution.

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The y-coordinate is the time in minutes since the start of the race that she finished the task, and the x-coordinate is the station number. (1, 2), (2, 4), (3, 8), (4, 16) (4, 16)

Part a: The data appears to model an exponential function.

Part b: The function that represents the data is y = [tex]2^x[/tex].

Part c: The average rate of change between station 2 and station 4 is 6 minutes per station.

Part A:

The data does not appear to model a linear function because the y-coordinates are not increasing at a constant rate. Instead, the y-coordinates are increasing at an increasing rate. Therefore, the data appears to model an exponential function.

Part B:

We can use the form y = [tex]ab^x[/tex] to represent the data, where x is the station number and y is the time in minutes since the start of the race that she completed the task.

Using the given data points, we can create a system of equations:

2 = [tex]ab^1[/tex]

4 = [tex]ab^2[/tex]

8 = [tex]ab^3[/tex]

16 = [tex]ab^4[/tex]

Solving for a and b, we can divide the second equation by the first equation to get:

4/2 = [tex](ab^2)[/tex]/[tex](ab^1)[/tex]

2 = b

Substituting b = 2 into any of the equations above, we can solve for a:

2 = [tex]a(2^1)[/tex]

a = 1

Therefore, the function that represents the data is y = [tex]2^x[/tex].

Part C:

To determine the average rate of change between day 2 and day 4, we need to calculate the slope of the line between points (2, 4) and (4, 16).

The slope between two points can be calculated using the formula:

slope = [tex]\frac{change in y}{change in x}[/tex]

Using points (2, 4) and (4, 16):

[tex]change in y[/tex] = 16 - 4 = 12

[tex]change in x[/tex] = [tex]4-2[/tex] = 2

Therefore, the slope (or average rate of change) between day 2 and day 4 is:

slope = [tex]\frac{change in y}{change in x}[/tex]

slope = [tex]\frac{12}{2}[/tex]

slope = 6

So, the average rate of change between day 2 and day 4 is 6 minutes per station.

The complete question is:-

Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station.

The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.

(1, 2), (2, 4), (3, 8), (4, 16)

Part A: Is this data modeling a linear function or an exponential function? Explain your answer. (2 points)

Part B: Write a function to represent the data. Show your work. (4 points)

Part C: Determine the average rate of change between day 2 and day 4. Show your work. (4 points)

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Answer:

144/112 = 1.29

Step-by-step explanation:

What is 144 divided by 112? Your answer is a decimal, 1.29

The most appropriate method for calculating the margin of error for the population mean in this scenario would be the Student's t-distribution.

The sample size is small (n = 65) and the population standard deviation is known (σ = 1.9).

Additionally, the population is assumed to be skewed to the right, which makes the use of the t-distribution more appropriate than the normal z-distribution. The t-distribution is used when the sample size is small and the population standard deviation is known, whereas the normal z-distribution is used when the sample size is large and the population standard deviation is known.

To calculate the margin of error using the Student's t-distribution, we would use the following formula:

Margin of error = t * (σ / √n)

Where t is the t-value for the desired confidence level, σ is the population standard deviation, and n is the sample size.

By plugging in the known values and looking up the t-value for the desired confidence level in a t-distribution table, we can calculate the margin of error for the population mean.

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As a result, the response is (D) 4.7  because 5(4.7) = 23.5, which is not less than or equivalent to 23/5.

A set in mathematics is a grouping of unique things that are referred to as its members or elements. Any object can be one of these, including words, letters, numbers, colors, humans, animals, and other things. Typically, sets are represented by capital letters, and the components of a set are encased in curly braces. For instance, the set of all even integers can be represented by the symbols 2, 4, 6, 8, etc., while the set of all English vowels,

given

We must first solve the inequality and then determine whether each of the provided numbers satisfies the inequality in order to determine which number does not belong to the solution set of 5x 23.

5x ≤ 23

x ≤ 23/5

We can now verify each of the figures provided:

A. 0: 0 is a part of the solution set because 5(0) = 0, which is less than or equivalent to 23/5.

B. -4.7: -4.7 is not a part of the solution set because 5(-4.7) = -23.5, which is not less than or equivalent to 23/5.

C. 4.6: 4.6 is a part of the solution set because 5(4.6) = 23, which is less than or equivalent to 23/5.

D. 4.7: 4.7 is not a part of the solution set because 5(4.7) = 23.5, which is not less than or equivalent to 23/5.

As a result, the response is (D) 4.7  because 5(4.7) = 23.5, which is not less than or equivalent to 23/5.

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