A t-shirt increased in price by 1/4. After the increase it was £20. What was the original price of the t-shirt?

Answer:

y = 3 suh slid este ob cine este a, b și g au nevoie de acel kinfo pentru a termina

Step-by-step explanation:

ba de forttg

Answer:

g(2) = -9

Step-by-step explanation:

g(2) = -1 x g(1) - 4

g(2) = -1 x 5 - 4

g(2) = -5 - 4

g(2) = -9

To find the area of the region enclosed by the given curves, we integrate with respect to y.

To obtain the limits of integration, we set the two equations of y equal to one another and solve for x as follows:

sin(x) = 3x

Let's use numerical methods to solve for x. Newton's method may be used. Let's rewrite sin(x) = 3x as follows:

f(x) = sin(x) - 3x

We may find the value of x that satisfies this equation by finding the root of this function.

Using Newton's method, let's say we start with an initial guess of x1 = 1.

We apply the following recurrence equation to this guess:x_(n+1) = x_n - f(x_n)/f'(x_n) where f'(x_n) is the derivative of f(x) with respect to x and is defined as:

f'(x_n) = cos(x_n) - 3

The first few iterations of Newton's method are:

x2 = 0.5582818494 x3 = 0.4330296021 x4 = 0.4547655586 x5 = 0.4544582153 x6 = 0.4544580617 x7 = 0.4544580617 x8 = 0.4544580617

Once the value of x is known, we can find the area of the region enclosed by the given curves by integrating from x = 0 to x = x, where x is the value we found above. We integrate with respect to y, which gives us the following expression for the area of the region enclosed by the given curves:

We integrate with respect to y and obtain the following expression:

The region enclosed by the given curves is shown in the graph below. Since the curve y = sin(x) is below the curve y = 3x, we integrate with respect to y. The area of the region enclosed by the given curves is approximately 0.354156883 square units.

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1. The area of the scale drawing of the park is 146,880 square inches (Option J).

2. The perimeter of the park is 126 feet (Option D).

3. The length of the south side of the park is 40% of the length of the north side (Option F).

1. To find the area of the scale drawing of the park, we need to calculate the area of the trapezium. The formula for the area of a trapezium is (base1 + base2) * height / 2.

Using the scale, the lengths of the bases (parallel sides) in feet would be:

Base1 = 28 inches * 1.5 feet/inch = 42 feet

Base2 = 40 inches * 1.5 feet/inch = 60 feet

Plugging in the values into the formula, we have:

Area = (42 + 60) * 16 / 2 = 1020 square feet

Since the answer options are in square inches, we need to convert the area back to square inches:

Area = 1020 square feet * 144 square inches/square foot = 146880 square inches

Therefore, the area of the scale drawing of the park is 146880 square inches.

2. The perimeter of the park can be calculated by summing up the lengths of all sides.

The lengths of the sides in feet would be:

Side1 = 28 inches * 1.5 feet/inch = 42 feet

Side2 = 40 inches * 1.5 feet/inch = 60 feet

Side3 = 16 inches * 1.5 feet/inch = 24 feet

Adding up all sides, we have:

Perimeter = Side1 + Side2 + Side3 = 42 feet + 60 feet + 24 feet = 126 feet

Therefore, the perimeter of the park is 126 feet.

3. To find the percentage length of the south side compared to the north side, we can calculate:

Percentage = (South Side Length / North Side Length) * 100

Using the scale, the length of the south side in feet would be:

South Side Length = 16 inches * 1.5 feet/inch = 24 feet

The length of the north side is already given as 40 inches * 1.5 feet/inch = 60 feet.

Plugging in the values, we have:

Percentage = (24 feet / 60 feet) * 100 = 40%

Therefore, the length of the south side of the park is 40% of the length of the north side.

Complete Question:

Mikea, an intern with the Parks and Recreation Department, is developing a proposal for the new trapezoidal Springdale Park. The figure below shows her scale drawing of the proposed park with 3 side lengths and the radius of the merry-go-round given in inches. In Mikea's scale drawing, 1 inch represents 1.5 feet.

1. What is the area, in square inches, of the scale drawing of the park? 448 544 H. 640 672 K. 1.088

2. Mikea's proposal includes installing a fence on the perimeter of the park. What is the perimeter, in feet, of the park? A. 84 B. 88 C. 104 D. 126 E 156

3. The length of the south side of the park is what percent of the length of the north side? F. 112% G. 1245 H. 142 J. 1754 K. 250%

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Step-by-step explanation:

A D G B E C F

these are least to greater

The equatiion where C is the constant of integration.To evaluate the indefinite integral ∫(3e^x + 4x^5 - x^3/4 + 1)dx, we can integrate each term separately.

∫3e^x dx = 3∫e^x dx = 3e^x + C₁

∫4x^5 dx = 4∫x^5 dx = 4 * (1/6)x^6 + C₂ = (2/3)x^6 + C₂

∫-x^3/4 dx = (-1/4)∫x^3 dx = (-1/4) * (1/4)x^4 + C₃ = (-1/16)x^4 + C₃

∫1 dx = x + C₄

Now, we can combine these results to obtain the final answer:

∫(3e^x + 4x^5 - x^3/4 + 1)dx = 3e^x + (2/3)x^6 - (1/16)x^4 + x + C

Therefore, the indefinite integral of (3e^x + 4x^5 - x^3/4 + 1)dx is:

∫(3e^x + 4x^5 - x^3/4 + 1)dx = 3e^x + (2/3)x^6 - (1/16)x^4 + x + C

where C is the constant of integration.

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The statement ''the symbol μ ˆ p represents the proportion of a sample of size n, not the proportion of a sample of size n.'' is false because the symbol "μ ˆ p" does not represent the proportion of a sample of size n.

In statistical notation, the symbol "μ ˆ p" typically represents the sample proportion, which is an estimate of the population proportion. The sample proportion is obtained by dividing the number of occurrences of a specific event in the sample by the sample size.

On the other hand, the population proportion, denoted by "p," represents the proportion of the entire population that exhibits a certain characteristic or has a specific attribute.

The symbol "μ ˆ p" could be a typographical error or a confusion between different symbols used in statistics. The correct symbol to represent the sample proportion is usually denoted as "p ˆ" or "p-hat." The symbol "μ" typically represents the population mean.

Therefore, it is incorrect to state that "μ ˆ p" represents the proportion of a sample of size n.

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Answer:

It/p= r

Step-by-step explanation:

divide p and t out of the r and multiply by the recipricol

where x is the estimated value and xr the real value

the percent error is 10.71%

The value of secant theta is 29/20

First, it is important to note the different trigonometric identities and their ratios, we have;

sin θ= opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

sec θ = hypotenuse/adjacent

From the information given, we have that;

tan θ = 21/20

Adjacent = 20

Opposite = 21

Using the Pythagorean theorem, we have;

x² = 21² + 20²

find the squares

x² = 441 + 400

add the values

x² = 841

Find the square root

x = 29

Then, sec θ = 29/20

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Total Seeds required 9.33 kg  and she has 10 kg.so, she has enough grass seed to make a lawn 10m by 14 m.

If you're fortunate enough to have a rectangular lawn, determining the size is straightforward. Multiply the length and breadth measurements together to get the total. You now have your region/area.

So, Maisie knows that she needs 3 kg of grass seed to make a rectangular lawn 5 m by 9m.

Grass seed is sold in 2 kg boxes,

Maisie wants to make a rectangular lawn 10 m by 14 m,

She has 5 boxes of grass seed

To Find, Has Maisie got enough grass seed to make a lawn 10m by 14 m

Solution:

3 kg of grass seed to make a rectangular lawn 5 m by 9m.

=> 3 kg  of grass seed  needed for 5 x 9 = 45 m²

=>  1 m² required  = 3/45  kg seed

a rectangular lawn 10 m by 14 m,

area = 10 x 14 = 140 m²

Hence 140 m² required = 140 x  3/45  =  9.33 kg

Grass seed is sold in 2 kg boxes,

She has 5 boxes of grass seed

Hence total seeds = 5 x 2 = 10 kg

Therefore, total seeds required 9.33 kg  and she has 10 kg.so, she has enough grass seed to make a lawn 10m by 14 m.

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The conditional relative frequency that a female prefers running is 0.36

Statistics is a branch of applied mathematics that involves the collection, description, analysis, and inference of conclusions from quantitative data

The specific number (females prefer cycling = 0.15) and the fitting total. There are 2 possibilities for that total :

all females

all people preferring cycling

the way it was phrased I would say the reference is all females.

the conditional relative frequency is then

0.15 / 0.46 = 0.326

Hence the conditional relative frequency that a female prefers running is 0.36

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Answer:

Step-by-step explanation:

Dont listen to the above the answer is acually 58

Answer:

120π

Step-by-step explanation:

radius = 6

angle =120

because a circle is 360, so that's 1/3 of the full circle

full circle area = πr² =36π

so the arc area = 1/3 * 360π = 120π

The Maclaurin series for f(x) converges absolutely for x within the interval (-2/3, 2/3).

To find the Maclaurin series for the function f(x) = (3cos(x))ln(1+x), we can use the standard formulas for the Maclaurin series expansion of elementary functions.

First, let's find the derivatives of f(x) up to the third order:

f(x) = (3cos(x))ln(1+x)

f'(x) = -3sin(x)ln(1+x) + (3cos(x))/(1+x)

f''(x) = -3cos(x)ln(1+x) - (6sin(x))/(1+x) + (3sin(x))/(1+x)² - (3cos(x))/(1+x)²

f'''(x) = 3sin(x)ln(1+x) - (9cos(x))/(1+x) + (18sin(x))/(1+x)² - (12sin(x))/(1+x)³ + (12cos(x))/(1+x)² - (3cos(x))/(1+x)³

Next, we evaluate these derivatives at x = 0 to find the coefficients of the Maclaurin series:

f(0) = (3cos(0))ln(1+0) = 0

f'(0) = -3sin(0)ln(1+0) + (3cos(0))/(1+0) = 3

f''(0) = -3cos(0)ln(1+0) - (6sin(0))/(1+0) + (3sin(0))/(1+0)² - (3cos(0))/(1+0)² = -3

f'''(0) = 3sin(0)ln(1+0) - (9cos(0))/(1+0) + (18sin(0))/(1+0)² - (12sin(0))/(1+0)³ + (12cos(0))/(1+0)² - (3cos(0))/(1+0)³ = -9

Now we can write the first three nonzero terms of the Maclaurin series:

f(x) = f(0) + f'(0)x + (f''(0)/2!)x² + (f'''(0)/3!)x³ + ...

f(x) = 0 + 3x - (3/2)x² - (9/6)x³ + ...

Simplifying, we have:

f(x) = 3x - (3/2)x² - (3/2)x³ + ...

To determine the values of x for which the series converges absolutely, we need to find the interval of convergence. In this case, we can use the ratio test:

Let aₙ be the nth term of the series.

|r| = lim(n->infinity) |a_(n+1)/aₙ|

= lim(n->infinity) |(3/2)(xⁿ+1)/(xⁿ)|

= lim(n->infinity) |(3/2)x|

For the series to converge absolutely, we need |r| < 1:

|(3/2)x| < 1

|x| < 2/3

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The change in radius is supposed to be 2.04 units to get 800 as volume.

To calculate the volume of a cylinder, we use the formula V = πr^2h, where V represents the volume, r represents the radius, and h represents the height.

Given that the height is fixed at 10 units, and the volume is desired to be 800 cubic units, we can rearrange the formula to solve for the radius:

V = πr^2h

800 = πr^2(10)

To isolate the radius, we divide both sides of the equation by π * h * 10:

800 / (π * 10) = r²

Simplifying further:

80 / π = r²

To find the value of the radius, we take the square root of both sides:

√(80 / π) = r

Using a calculator to approximate the square root of 80 divided by π, we find:

r ≈ 5.04

Therefore, to achieve a volume of 800 cubic units while keeping the height at 10 units, the radius would need to be approximately 5.04 units.

And change would be 5.04-3 = 2.04.

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The students are in the following rooms:Tony - Room 21Student 2 - Room 27Student 3 - Room 21Student 4 - Room 3Student 5 - Room 7Student 6 - Room 15.

There are six different homerooms and each one of them is occupied by a student. To determine which room each student belongs to, there are clues that will help in this process.

Tony's room number is a multiple of 3 and 7. So, the room number for Tony is 21.There are six different homerooms and each one of them is occupied by a student.

To determine which room each student belongs to, there are clues that will help in this process. Tony's room number is a multiple of 3 and 7. So, the room number for Tony is 21.

Another student is in a room with a room number that is the highest perfect cube between 1 and 50. The highest perfect cube between 1 and 50 is 27, which means the room number for the student is 27.Another student is in a room with a room number that is a multiple of 4.

One of the multiples of 4 between 1 and 50 is 16, which means the room number for the student is 16.Another student is in a room with a room number that is a multiple of 3, but not a multiple of 4.

The multiples of 3 between 1 and 50 that are not multiples of 4 are 3, 9, 15, 21, 27, 33, 39, 45. So, the room number for the student could be any of these numbers except 12, 16, 24, 30, 36, 42, and 48. Let's use process of elimination.

The room number cannot be 12, 24, 30, 36, 42, or 48 since those numbers are multiples of 4. The room number cannot be 3, 9, or 15 since those numbers are not greater than the perfect cube. The room number for this student is 21.

Another student is in a room with a room number that is the second lowest prime number. The second lowest prime number is 3, which means the room number for the student is 3.

Another student is in a room with a room number that is the highest prime factor of 70. The prime factors of 70 are 2, 5, and 7. The highest prime factor of 70 is 7,

which means the room number for the student is 7.The last student is in a room with a room number that is a multiple of 5. One of the multiples of 5 between 1 and 50 is 15, which means the room number for the student is 15.

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Through the process of elimination and logical thinking, we assigned each student to a room: Mary - Room 3, Mark - Room 18, Alyssa - Room 21, and Tony - Room 42.

This is a problem that requires some logic and basic knowledge of the properties of numbers. Given the conditions, let's follow these steps:

Based on the above steps and assumptions, here's the assignment of room and students:

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Step-by-step explanation:

a) The test statistic is (4.4-4)/(1.3/sqrt(70)) = 2.83. The p-value is 0.0023. Since the p-value is less than 0.05, we reject the null hypothesis.

b) The test statistic is (5.3-4.4)/sqrt((1.4^2/106)+(1.3^2/70)) = 4.09. The p-value is less than 0.0001. Since the p-value is less than 0.05, we reject the null hypothesis.

The larger the p-value, the more likely it is that the null hypothesis that the population coefficient is equal to 0 is true regarding p-value.

In a linear regression model, p-values are associated with the estimated coefficients and provide information about the statistical significance of each predictor variable. The null hypothesis for each predictor is that the population coefficient for that predictor is equal to 0, meaning that it has no effect on the response variable.

The p-value is the probability of observing the estimated coefficient given the null hypothesis is true. If the p-value is small, it means that the observed coefficient is unlikely to be due to chance, If the p-value is large, it means that the observed coefficient could easily be due to chance and we cannot reject the null hypothesis.

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Using a trigonometric relation we will see that the value of x is 81.2°

We can see that we have a right triangle, and the angle x is the one that is on the top vertex.

We can use any trigonometric relation to find the value of x, for example we can use:

sin(x) = (opposite cathetus)/(hypotenuse)

Where we can see that:

opposite cathetus = 84

hypotenuse = 85

Then we will get:

sin(x) = 84/85

x = Asin(84/85) = 81.2°

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Among the provided functions, the ones that approach positive infinity as x approaches negative infinity are:

- f(x) = 2x^5

- f(x) = 6x^8 + 9x^6 + 32

- f(x) = -x + 8x^4 + 248

To determine which functions approach positive infinity as x approaches negative infinity, we need to analyze the leading terms of the functions. The leading term dominates the behavior of the function as x becomes very large or very small.

Let's examine each function and identify their leading terms:

1. f(x) = 2x^5

The leading term is 2x^5, which has a positive coefficient and the highest power of x.

As x approaches negative infinity, this term becomes very large and positive, indicating that f(x) approaches positive infinity.

2. f(x) = 9x + 100

The leading term is 9x, which has a positive coefficient but a lower power of x compared to the constant term 100.

As x approaches negative infinity, the leading term becomes very large and negative, indicating that f(x) approaches negative infinity, not positive infinity.

3. f(x) = 6x^8 + 9x^6 + 32

The leading term is 6x^8, which has a positive coefficient and the highest power of x.

As x approaches negative infinity, this term becomes very large and positive, indicating that f(x) approaches positive infinity.

4. f(x) = -8x^3 + 11

The leading term is -8x^3, which has a negative coefficient and the highest power of x.

As x approaches negative infinity, this term becomes very large and negative, indicating that f(x) approaches negative infinity, not positive infinity.

5. f(x) = -10x + 5x + 26

Combining like terms, we have f(x) = -5x + 26.

The leading term is -5x, which has a negative coefficient but a lower power of x compared to the constant term 26.

As x approaches negative infinity, the leading term becomes very large and positive, indicating that f(x) approaches negative infinity, not positive infinity.

6. f(x) = -x + 8x^4 + 248

The leading term is 8x^4, which has a positive coefficient and the highest power of x.

As x approaches negative infinity, this term becomes very large and positive, indicating that f(x) approaches positive infinity.

Therefore, the correct choices are:

- f(x) = 2x^5

- f(x) = 6x^8 + 9x^6 + 32

- f(x) = -x + 8x^4 + 248

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The 95% confidence interval for the proportion of cell phone users who prefer texting is 53% to 59%.

A confidence interval is a range of values that is likely to contain the true population parameter with a certain level of confidence. In this case, the survey found that 56% of the respondents prefer to use cell phones for texting, and a 95% confidence interval for the estimate of all cell phone users who prefer to use cell phones for texting has a margin of error of 3%.

This means that if we were to conduct the same survey multiple times and calculate a confidence interval for each survey, we would expect 95% of those intervals to contain the true population proportion of cell phone users who prefer texting. Additionally, the margin of error of 3% means that the estimate of 56% could be off by as much as 3%, either higher or lower. Therefore, we can say with 95% confidence that the true proportion of cell phone users who prefer texting is between 53% and 59%.

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Answer:

Sunil = 3000 and raj = 2000

Step-by-step explanation:

there are total 5000 and if it will be divided into 5 parts( total of ratio ) then 3 will be equal to 3000 and 2 equal to 2000

Answer:y=-1/2x-3

Step-by-step explanation:

Answer: ∠TRS and ∠VRW  (Choice B)

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

Explanation:

Ignore ray RU. I would redraw the entire thing without ray RU as part of the picture. See below.

Notice how lines TW and SV intersect to form an X shape.

The angles TRS and VRW shown in red are opposite one another, so we consider them to be vertical angles. Vertical angles are always congruent.

Answer:

B ∠TRS and ∠VRW

Step-by-step explanation:

Answer:

It is. 4 ( 6x- 5) Hope this helped

Answer: -8.4, -7.5, -5.2, 3.1, 5.3

Step-by-step explanation: First, lets separate the negative numbers and the positive numbers,

-7.5, -8.4, - 5,2 5.3, 3.1

Now, we order from least to greatest!

-8.4, -7.5, -5.2, 3.1, 5.3

Done!

The values are as follows: (a) -0.52, (b) 0.68, (c) 0.7764, (d) the value of the PDF at 0.8 using the given parameters, and (e) 0.3300.

(a) The value at which the cumulative distribution function (CDF) of a standard normal distribution (N(0,1)) takes on the value of 0.3 is approximately -0.52.

(b) The value at which the CDF of a standard normal distribution (N(0,1)) takes on the value of 0.75 is approximately 0.68.

(c) The value of the CDF of a normal distribution N(-2,5) at 0.8 can be calculated by standardizing the value using the formula Z = (X - μ) / σ, where X is the given value, μ is the mean, and σ is the standard deviation. After standardizing, we find that Z ≈ 0.76. Using a standard normal distribution table or calculator, we can determine that the CDF value at Z = 0.76 is approximately 0.7764.

(d) The value of the probability density function (PDF) of a normal distribution N(-2,5) at 0.8 can be calculated using the formula f(x) = (1 / (σ * √(2π\(^(-(x -\) μ)))) * e² / (2σ²)), where x is the given value, μ is the mean, σ is the standard deviation, and e is Euler's number (approximately 2.71828). Plugging in the values, we can compute the PDF at x = 0.8.

(e) The value of the CDF of a normal distribution N(-2,5) at -1.2 can be calculated in a similar manner as in part (c). After standardizing the value, we find that Z ≈ -0.44. Using a standard normal distribution table or calculator, we can determine that the CDF value at Z = -0.44 is approximately 0.3300.

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The formula to calculate the missing arc is,

where,

Therefore,

Hence, the answer is