Patrick wants to estimate the percentage of parents who use cloth diapers. He asks a randomly selected group of 125 parents whether or not they use cloth diapers. What is the statistic?

The length of a 45° arc with a radius of 4 miles is approximately 3.14 miles, calculated using the formula for arc length.

To determine the length of a 45° arc given a radius of 4 miles, we can use the formula: Arc length = (angle measure / 360°) x 2πr, where r is the radius of the circle and π is a constant equal to approximately 3.14.

Substituting the given values into the formula, we get: Arc length = (45° / 360°) x 2π(4 mi)Arc length = (1/8) x 2π(4 mi)Arc length = (1/8) x 8π Arc length = π

The length of the 45° arc is approximately 3.14 miles.

Summary: To find the length of a 45° arc of a circle, we use the formula: Arc length = (angle measure / 360°) x 2πr. Given a radius of 4 miles, we can substitute the values into the formula to get the length of the 45° arc, which is approximately 3.14 miles.

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Answer:

The answer is 11

Step-by-step explanation:

√11 × √11 = √121 = 11

Thus, The answer is 11

Answer:

\( \sf \: \sqrt{11} \times \sqrt{11} = 11 \)

Step-by-step explanation:

Given problem,

→ √11 × √11

Let's solve the problem,

→ √11 × √11

→ √(11 × 11)

→ √(121)

→ √121 = 11

Hence, the answer is 11.

Answer:

3

Step-by-step explanation:

Answer:

C none of the answer is correct 24m³–cm³ is 2400cm³

Answer:

The coordinate of any given point can be written as (x, y), where x is the x coordinate, and y is the y coordinate.

For example, point A has an x coordinate (horizontal) of 5, and a y coordinate (vertical) of 6. So the ordered pair is (5, 6).

Similarly, for the rest we have:

B: (-5,5)

C: (-2,3)

D: (-2,-2)

E: (3,-4)

F: (3,-6)

Answer: 25/8

Step-by-step explanation:

\(\rule{300}{1}\\\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}\)

Change 3+1/8 to an improper fraction.

\(\dashrightarrow\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}\)

First, multiply the whole part (3) times the denominator (8):-

\(\bold{3\times8=24}\)

Now add the numerator:-

\(\bold{25}\)

That's the numerator of the improper fraction, and the denominator stays the same.

\(\bigstar\) Therefore, the fraction is

\(\bold{\dfrac{25}{24}}\)

\(\rule{300}{1}\)

Answer:

Chi-square distribution

Step-by-step explanation:

We want to investigate that whether best ski area is independent of skier level or not so this situation leads to test of independence. For investigating independence of two variable we usually use chi-square distribution.

Thus, for conducting the test for investigating the independence between best ski area and skier level we use chi-square distribution.

Answer:

-1 = -5

0 = -1

2 =  5

Step-by-step explanation:

In order to do this you need to follow these five (5) steps:

1) Know what each of the variables mean in an equation of a line. The equation of a line is y = mx + b where y = y-coordinate, m = slope, x = x-coordinate, and b = y-intercept. (Remember that the slope is the steepness  of a line and the y-intercept is the point where the line intersects  the y-axis. The x- and y-coordinates are values of the points on the line of y = 3x - 1.)

2) Identify the m (slope) and the b (y-intercept). The slope is 3, which can also be written as 3/1. The y-intercept is -1. (Remember that subtraction of 1 is the SAME thing as adding -1!) Since the y-intercept is a point it will be plotted at (0, -1).

3) Plot the y-intercept first. Start at the origin (intersection of the x- and y-axes) since the x coordinate is 0. Then move DOWN 1 unit since the y-coordinate is negative.

4) Use the m (slope) to plot at least three new points. The slope can also be represented as "rise/run" or the amount of units that you move UP or DOWN (vertically), then LEFT or RIGHT (horizontally). (Remember: if the numerator is positive (move UP); numerator is negative (move DOWN); denominator is POSITIVE (move RIGHT); denominator is NEGATIVE (move LEFT)). Since our slope is 3/1, and both the numerator and denominator are POSITIVE, that means we will be "rising" (moving UP) 3 units and "running" (moving RIGHT) 1 unit.

Start at the y-intercept  of (0, -1) and move up 3 units and to the right 1 unit. You should be at (1, 2). Plot a point here. Then do it again. You should now be at (2, 5). Plot another point. Now, do it one more time. You should now be at (3, 8). Plot your last point. (If you wish to continue plotting additional points, feel free to do so.)

Answer:

Given line:

The table has x-values and asks to find f(x) for each x.

f(x) is same as y, plug in x- values to get f(x):

Answer:

A = 121π

General Formulas and Concepts:

Pre-Algebra

Geometry

Step-by-step explanation:

Step 1: Define

C = 22π

Step 2: Find radius r

Step 3: Find Area

And we have our final answer!

Answer: 18(a)-89=217

Step-by-step explanation:

If a = 17 then you substitute/replace the a with the 17. Making 18(a) into 18(17). 18(17)= 306 - 89 = 217.

Hope this helped.

Answer:217

Step-by-step explanation:

putting the value of a in the equation.

18×17-89= 217

1) Polynomial of 4 terms.

2) The rational roots of the function are,

x = - 2, 1

3) The zeroes of the function are,

x = - 2, - 3, 2

4) The zeroes of the function are,

x = 1, - 1, 2i, - 2i

5) The correct function which shows the cubic equation is, option 1.

We have to given that;

1) Function is,

⇒ 3x⁵ + 5x⁴ - 7x³ + 15

Clearly, There are 4 terms in function.

Hence, Polynomial of 4 terms.

2) Function is,

⇒ x⁴ + 5x³ + 7x² - 3x - 10 = 0

The correct rational roots are satisfy the function,

Hence, We get;

Plug x = 1,

⇒ x⁴ + 5x³ + 7x² - 3x - 10 = 0

⇒ 1⁴ + 5(1)³ + 7 (1)² - 3(1) - 10 = 0

⇒ 0 = 0

Plug x = - 2;

⇒ x⁴ + 5x³ + 7x² - 3x - 10 = 0

⇒ 2⁴ + 5(2)³ + 7 (2)² - 3(2) - 10 = 0

⇒ 0 = 0

Thus, The zeroes of the function are,

x = - 2, 1

3) Function is,

⇒ y = (x + 3) (x + 2) (x - 2)

Hence, The zeroes of the function are,

x = - 3

x = - 2

x = 2

4) Function is,

⇒ 3x² - 4 = - x⁴

⇒ x⁴ + 3x² - 4 = 0

⇒ x⁴ + 4x² - x² - 4 = 0

⇒ x² (x² + 4) - 1 (x² + 4) = 0

⇒ (x² - 1) (x² + 4) = 0

⇒ x² - 1 = 0

⇒ x² = 1

⇒ x = ±1

⇒ x² + 4 = 0

⇒ x² = - 4

⇒ x = ±2i

Hence, The zeroes of the function are,

x = 1, - 1, 2i, - 2i

5) By given graph the  correct function which shows the cubic equation is, Option 1.

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Answer:

24

multiply them

Step-by-step explanation:

1s-1t-1n

1s-2t-1n

1s-3t-1n

1s-4t-1n

1s-1t-2n

1s-1t-3n

2s-1t-1n

2s-2t-1n

2s-3t-1n

2s-4t-1n

2s-1t-2n

2s-1t-3n

3s-1t-1n

3s-2t-1n

3s-3t-1n

3s-4t-1n

3s-1t-2n

3s-1t-3n

Answer:

-6,-2 is the answer!!

Step-by-step explanation:

The coordinate of A' would be (-6, -2)

Dilation is a transformation technique that changes the size of an object by a scale factor "k"

From the diagram shown, the measure of the coordinate point is given as (-3, -1).

If the coordinate A is dilated by a factor of 2, the resulting coordinate A' will be given as:

A' = (2(-3), 2(-1)) = (-6, -2)

Hence the  coordinate of A' would be (-6, -2)

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The extremas of the function f(x) = x³ - 7x² + 10x are given as follows:

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Answer:

168

Step-by-step explanation:

Answer:

Liam would save $168.

What I did:

Multiply the $12 and the 14 weeks. this will give you $168.

Answer:

sqrt(601)/2 ft

Step-by-step explanation:

The legs of the right triangle are 12 and 2.5. by the Pythagorean Theorem, the length of the ladder is sqrt(12^2 + 2.5^2) = sqrt(150.25). Simplified is sqrt(601)/2 ft.

The length of ladder used is 12.25 ft.

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse .

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

example:

The hypotenuse of a right-angled triangle is 16 units and one of the sides of the triangle is 8 units. Find the measure of the third side using the Pythagoras theorem formula.

Solution:

Given : Hypotenuse = 16 units

Let us consider the given side of a triangle as the perpendicular height = 8 units

On substituting the given dimensions to the Pythagoras theorem formula

Hypotenuse^2 = Base^2 + Height^2

16^2 = B^2 + 8^2

B^2 = 256 - 64

B = √192 = 13.856 units

Therefore, the measure of the third side of a triangle is 13.856 units.

given:

base=  2.5 ft,  

perpendicular= 12 ft

Using Pythagoras theorem,

H² =  B² + P²

H² = 2.5² + 12²

H² = 6.25+ 144

H= 12.25 ft

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11, - 6, -1, 4, 9, 14, 19, ... are mapped onto 4. ... A;-l = (-ltQn (mod N),. (A5.34) ... 131 2, 14, 34, 38, 42, 78, 90, 178, 778, 974(1000).

Step-by-step explanation:

the nearest .1/2 incp, we say the 'unit 131/2 incl. 1.4 a measUrement is-stated tp- be 546 inch, this UM= the

(i)  The partial fraction decomposition of\(100/(x^7 * (10 - x))\) is\(100/(x^7 * (10 - x)) = 10/x^7 + (1/10^5)/(10 - x).\) (ii) The expression for t in terms of x is t = 10 ± √(100 + 200/x).

(i) To express the rational function 100/(\(x^7\) * (10 - x)) in partial fractions, we need to decompose it into simpler fractions. The general form of partial fractions for a rational function with distinct linear factors in the denominator is:

A/(factor 1) + B/(factor 2) + C/(factor 3) + ...

In this case, we have two factors: \(x^7\) and (10 - x). Therefore, we can express the given rational function as:

100/(\(x^7\) * (10 - x)) = A/\(x^7\) + B/(10 - x)

To determine the values of A and B, we need to find a common denominator for the right-hand side and combine the fractions:

100/(x^7 * (10 - x)) = (A * (10 - x) + B * \(x^7\))/(\(x^7\) * (10 - x))

Now, we can equate the numerators:

100 = (A * (10 - x) + B * \(x^7\))

To solve for A and B, we can substitute appropriate values of x. Let's choose x = 0 and x = 10:

For x = 0:

100 = (A * (10 - 0) + B * \(0^7\))

100 = 10A

A = 10

For x = 10:

100 = (A * (10 - 10) + B *\(10^7\))

100 = B * 10^7

B = 100 / 10^7

B = 1/10^5

Therefore, the partial fraction decomposition of 100/(\(x^7\) * (10 - x)) is:

100/(\(x^7\) * (10 - x)) = 10/\(x^7\) + (1/10^5)/(10 - x)

(ii) Given the differential equation: dx/dt = (1/100) *\(x^2\) * (10 - x)

We are also given x = 1 when t = 0.

To solve this equation and obtain an expression for t in terms of x, we can separate the variables and integrate both sides:

∫(1/\(x^2\)) dx = ∫((1/100) * (10 - x)) dt

Integrating both sides:

-1/x = (1/100) * (10t - (1/2)\(t^2\)) + C

Where C is the constant of integration.

Now, we can substitute the initial condition x = 1 and t = 0 into the equation to find the value of C:

-1/1 = (1/100) * (10*0 - (1/2)*\(0^2\)) + C

-1 = 0 + C

C = -1

Plugging in the value of C, we have:

-1/x = (1/100) * (10t - (1/2)\(t^2\)) - 1

To solve for t in terms of x, we can rearrange the equation:

1/x = -(1/100) * (10t - (1/2)\(t^2\)) + 1

Multiplying both sides by -1, we get:

-1/x = (1/100) * (10t - (1/2)\(t^2\)) - 1

Simplifying further:

1/x = -(1/100) * (10t - (1/2)\(t^2\)) + 1

Now, we can isolate t on one side of the equation:

(1/100) * (10t - (1/2)t^2) = 1 - 1/x

10t - (1/2)t^2 = 100 - 100/x

Simplifying the equation:

(1/2)\(t^2\) - 10t + (100 - 100/x) = 0

At this point, we have a quadratic equation in terms of t. To solve for t, we can use the quadratic formula:

t = (-(-10) ± √((-10)^2 - 4*(1/2)(100 - 100/x))) / (2(1/2))

Simplifying further:

t = (10 ± √(100 + 200/x)) / 1

t = 10 ± √(100 + 200/x)

Therefore, the expression for t in terms of x is t = 10 ± √(100 + 200/x).

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Answer:

Below

Step-by-step explanation:

32/2 x 100% = 1600 %

A normal distribution has a mean of 50 and a standard deviation of 3 , the probability P(X ≤ 44) = P(Z ≤ -2) = 0.0241  option a) 0.025.

In probability theory, normal distribution is also known as Gaussian distribution. It is a probability distribution that is symmetrical, bell-shaped, and a continuous probability distribution. It's also a part of continuous probability distribution that describes real-valued random variables whose probability density function is affected by two parameters: the mean μ and the variance σ².

Let us consider the problem. Suppose a normal distribution has a mean of 50 and a standard deviation of 3. Firstly, we need to standardize the random variable X that is to convert it to the standard normal distribution. We use the following formula for this Z = (X - μ) / σwhere X is the random variable and μ is the mean, σ is the standard deviation of the population.

So in this case, we can write this as Z = (44 - 50) / 3 = -2

We have now obtained the standard score or standard deviation for the random variable X.

Now we need to calculate the probability P(X ≤ 44) = P(Z ≤ -2).

The probability of Z being less than -2 is denoted by the area under the standard normal curve to the left of Z = -2.

Using the standard normal table we look for the probability that corresponds to -2 and the closest we find is 0.0228.

This probability represents the area under the standard normal distribution to the left of Z = -2.

To calculate the area to the left of Z = -2, we add the area to the left of the next integer, which is -3, which we find from the standard normal table as 0.0013, 0.0228 + 0.0013 = 0.0241.

Therefore, the probability P(X ≤ 44) = P(Z ≤ -2) = 0.0241 or 0.025 (rounded to three decimal places)Therefore, the answer is option A. 0.025.

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The sum of the scores is equal to 160.

In Mathematics, a mean is sometimes referred to as an average and it can be defined as a ratio of the sum of the total number in a data set (population) to the frequency of the data set.

Mathematically, the mean for this set of scores can be calculated by using the following formula:

Mean = [F(x)]/n

For the total number of scores (data set), we have;

∑x = 20 + 60 + 30 + 50

∑x = 160.

Mean = [F(x)]/n = 160/4 = 40.

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Answer:

40 degrees

Step-by-step explanation:

the bottom angles are 70 each because you can find one of them by subtracting 110 from 180 (110 is an exterior angle to one of the bottom sides). The other is also 70 because the triangle is an isosceles. Then, subtract 70*2 from 180 to get 40 degrees for x (the remaining side).

Answer:

Barts total cost is (c)213.36

Step-by-step explanation:

First, you subtract 6% from $219

=204.92

add shipping,

+7.50

=213.36

Hope this helps <3

Answer:

C. $213.36

Step-by-step explanation:

The original price is $219 and the discount is 6% which is equal to $13.14

$219 - $13.14 + $7.50 (shipping cost) = $213.36

Complete Question:

Last year Mr. Petersen’s rectangular garden had a width of 5 meters and an area of 20 square meters.  This year he wants to make the garden three times as long and two times as wide.  

Last year, Mr. Petersen had a fence all the way around his garden. He can reuse all of the fence he had around the garden last year, but he needs to buy more fencing to go around this year’s garden.  

How many more meters of fencing is needed for this year’s garden than last year’s?

Answer:

26 meters of fencing needed

Step-by-step explanation:

Given

Last Year:

\(Width = 5m\)

\(Area = 20m^2\)

This Year:

\(Length = 3\ times\ longer\)

\(Width = 2\ times\ wider\)

Required

Determine how many more meters is needed

Represent last year's length of Fence with L and last year's width with W

First, we need to calculate L

\(Area = L * W\)

Where

\(Area = 20m^2\)

\(W = 5m\)

\(20m^2 = L * 5m\)

Divide both sides by 5m

\(\frac{20m^2}{5m} = \frac{L * 5m}{5m}\)

\(\frac{20m^2}{5m} = L\)

\(L = \frac{20m^2}{5m}\)

\(L = 4m\)

So, we have that:

For Last Year

\(Length = 4m\) and \(Width = 5m\)

For this year:

\(Length = 3\ times\ longer\)

\(Length = 3 * 4m\)

\(Length = 12m\)

\(Width = 2\ times\ wider\)

\(Width = 2 * 5m\)

\(Width = 10m\)

So, for this year, we have:

\(Length = 12m\) and \(Width = 10m\)

Next, we calculate perimeter of fencing in both years.

\(Perimeter = 2 * (Length + Width)\)

Last Year:

\(Perimeter = 2 * (4m + 5m)\)

\(Perimeter = 2 * 9m\)

\(Perimeter = 18m\)

This Year:

\(Perimeter = 2 * (12m + 10m)\)

\(Perimeter = 2 * 22m\)

\(Perimeter = 44m\)

To get the meters of fencing needed this year, we simply calculate the difference in the calculated perimeters.

\(Difference = 44m - 18m\)

\(Difference = 26m\)

Hence, there are 26 meters of fencing needed

Answer:

The Industrial Revolution shifted from an agrarian economy to a manufacturing economy where products were no longer made solely by hand but by machines. This led to increased production and efficiency, lower prices, more goods, improved wages, and migration from rural areas to urban areas.

Step-by-step explanation:

Brainli

(i) \(\lim_{x \to \pi/3}\) f(x) = 1 + √3.

(ii) \(\lim_{x \to \frac{\pi}{4}} f(x)\) does not exist.

For λ = 2.5, the function f(x) will be continuous at x = 0.

Given the function is,

f(x) = 1.5, when x = 0

    = 1 -2 sin x, when x < π/4

    = 1 + 2 sin x, when x > π/4

    = 1 + (sin λx/sin 5x)

Now,

\(\lim_{x \to \pi/3}\) f(x) = \(\lim_{x \to \pi/3}\) (1 + 2 sin x) [Since, π/3 > π/4]

                    = 1 + 2 sin (π/3)

                    = 1 + 2√3/2 = 1 + √3

Hence, \(\lim_{x \to \pi/3}\) f(x) = 1 + √3.

Now left hand limit is,

\(\lim_{x \to \frac{\pi^+}{4}}\) f(x) = \(\lim_{x \to \frac{\pi^+}{4}}\) (1 + 2sin x) = 1 +2 sin(π/4) = 1 + 2*(1/√2) = 1 + √2

and right hand limit is,

\(\lim_{x \to \frac{\pi^-}{4}}\) f(x) = \(\lim_{x \to \frac{\pi^-}{4}}\) (1 - 2 sin x) = 1 - 2*(1/√2) = 1 - √2

Since left hand limit and right hand limit are not equal so value of \(\lim_{x \to \frac{\pi}{4}} f(x)\) does not exist.

\(\lim_{x \to 0}\) f(x) = \(\lim_{x \to 0}\) (1 + (sin λx/sin 5x)) = 1 + \(\lim_{x \to 0}\) ((sin λx/λx)/(sin 5x/5x))*(λ/5) = 1 + λ/5

Since f(x) is continuous at x = 0.

So, \(\lim_{x \to 0}\) f(x) = f(0)

1 + λ/5 = 1.5

λ/5 = 1.5 - 1 = 0.5

λ = 2.5

Hence the value of λ will be 2.5.

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The graph of the function \(f(x) = (9/4)x^2\) is a symmetric upward-opening parabola.

Overall, the graph represents a quadratic function with a positive leading coefficient, resulting in an upward-opening parabolic curve. The graph has been attached.

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