which number has the greatest absolute value 15,5,0,-25

Answer:

2^(-4).

Step-by-step explanation:

f^2(x) = (2x^3)^2

f^2(1/2) = (2(1/2)^3))^2

             = (2 * 1/8)^2

             = (1/4)^2

             = 1/16

             = 2^(-4)

Answer:

\(\dfrac{1}{2^4}\\\\\textrm{or}\\\\2^{-4}\)

Step-by-step explanation:

\(f\left(\dfrac{1}{2}\right) = 2\left(\dfrac{1}{2}\right) ^3\\\\= 2\times \dfrac{1^3}{2^3}\\\\=2\times \dfrac{1}{8}\\\\= \dfrac{1}{4}\\\\f^2\left(\dfrac{1}{2}\right) =\left[ f(\dfrac{1}{2})\right] ^2 = \left(\dfrac{1}{4}\right)^2\\\\= \dfrac{1}{16}\\\\16 = 2^4\\\\\rm Hence \\f^2\left(\dfrac{1}{2}\right)= \dfrac{1}{2^4}\\\\\textrm {which can be written as }2^{-4}\)

since \(\dfrac{1}{a^m} = a^{-m}\)

Answer:

D. an = 40. (1)-0•40(n-1)

Step-by-step explanation:

Simplifying the formula, we have:

an = 40 - 0 * 40 * (n-1)

an = 40 - 0

an = 40

Answer:

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Step-by-step explanation:Please help me important question in image

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Answer:

The equation a=0.003x^2+21.3 models the average ages of women when they first married since the year 1940 in the United States. In this equation, a represents the average age and x represents the years since 1940. To estimate the year in which the average age of brides was the youngest, we need to find the minimum value of the quadratic function a=0.003x^2+21.3. This can be done by using the formula x=-b/2a, where b is the coefficient of x and a is the coefficient of x^2. In this case, b=0 and a=0.003, so x=-0/(2*0.003)=0. This means that the average age of brides was the lowest when x=0, which corresponds to the year 1940. The value of a when x=0 is a=0.003*0^2+21.3=21.3, so the average age of brides in 1940 was 21.3 years old. This is consistent with the historical data, which shows that the median age of women at their first wedding in 1940 was 21.5 years old. The average age of brides has been increasing since then, reaching 28.6 years old in 2021.

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Answer:

x = 5

Step-by-step explanation:

x is the length of the hypotenuse of this triangle.  The length of one of the legs of the triangle is 3" and that of the other leg is 4".

Applying the Pythagorean Theorem:  x^2 = 3^2 + 4^2, or 25

Thus, the length x is +√25, or 5.

x = 5

The surface area of the cylinder is 948m²

The area occupied by a three-dimensional object by its outer surface is called the surface area. The surface of a cylinder is expressed as ;

SA = 2πr(r+h)

Where r is the radius of the base and h is the height of the cylinder.

r =8m

h = 4m

SA = 2 × 3.14 × 8 (8+4)

SA = 78.96 × 12

SA = 947.52 m²

to the nearest whole number

SA = 948 m²

therefore the surface area of the cylinder is 948 m²

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Law of cosines:

For the given triangle:

Solve x from the equation above:

Note that the coordinates of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4). (Option B)

To rotate a point 90 degrees  clockwise about a given point,we can follow these steps -

Translate the coordinates   of the given point so that the center of rotation is at the origin.   In this case,we subtract the coordinates   of the center (0,1) from the coordinates of point A (5,4) to get (-5, 3).

Perform the rotation by swapping the x and y coordinates and changing the sign of the   new x coordinate. In this case,we  swap the x and y coordinates of (-5, 3)   to  get (3, -5).

Translate the coordinates back to their original position   by adding the coordinates of the center (0,1)  to the result from step 2. In   this case, we add (0,1) to (3, -5) to get (3, -4).

Therefore, the coordinates   of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4).

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In probability function, the value of b = \(\frac{\pi}{2}\).

What is Probability?

Probability is the measure of the likelihood of a given event occurring. It is usually expressed as a number between 0 and 1, where 0 indicates an impossibility of the event occurring and 1 indicates a certainty that the event will occur. Probability theory is an important part of mathematics, and is used in a variety of applications, from predicting weather patterns to assessing the risk of a financial investment.

For f(x) to be a probability density function, the total area under the graph of the function should be equal to 1. This implies that the integral of f(x) from 1 to 3 should be equal to 1. This gives us the equation

\(\int1^3 (x^2 - b) dx = 1\)

Solving the integral, we get b = 4.

For h(x) to be a probability density function, the total area under the graph of the function should be equal to 1. This implies that the integral of h(x) from -b to b should be equal to 1. This gives us the equation

\(\int-b^b cos x dx = 1\)

Solving the integral, we get b = \(\frac{\pi}{2}\).

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Step-by-step explanation:

A randomized experiment with order, replacement, and no repetition is one in which the order of the outcomes matters, the same outcome can occur multiple times, and no outcome can occur more than once.

For example, drawing a card from a deck and then flipping a coin would be a random experiment with order, replacement, and no repetition. The order of the results is important because the outcome of the coin toss will depend on the outcome of the card draw.

The same result can occur multiple times because the same card can be drawn twice, and no result can occur more than once because the coin can only land heads or tails once.

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Random experiment with order, replacement and without repetition

Sphenathi and the other matriculants must travel at an average speed of approximately 107 km/h to reach Uptington by 09:45.

To determine the average speed at which Sphenathi and the other matriculants must travel to reach Uptington by 09:45, we need to calculate the time available for the journey and the distance between the two locations.

The time available is from 07:25 to 09:45, which is a total of 2 hours and 20 minutes. We need to convert this time to hours by dividing by 60:

2 hours + 20 minutes / 60 = 2.33 hours

Now, let's calculate the distance between Bloemfontein and Uptington. Suppose the distance is 'd' kilometers.

We can use the formula for average speed: average speed = distance / time

In this case, the average speed should be such that the distance divided by the time is equal to the average speed.

d / 2.33 = average speed

Now, let's assume that Sphenathi and the other matriculants must travel a distance of 250 kilometers to reach Uptington. We'll substitute this value into the equation:

250 / 2.33 = average speed

To find the average speed to the nearest km/h, we'll calculate the result:

average speed ≈ 107.3 km/h

Therefore, Sphenathi and the other matriculants must travel at an average speed of approximately 107 km/h to reach Uptington by 09:45.

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Step-by-step explanation:

Since the lines are parallel, they got equal slopes

m1 = m2

First, what's the slope of the first line y = ¾x - 4

y = ¾x - 4 compared to y = mx + c

yh, m = ¾ [I hope u understand that... That's coefficient]

m1 = ¾

Then, m1 = m2 = ¾ [parallel lines]

Yh, we use:

y - y1 = m(x - x1)

y - 5 = ¾( x - (-3) )

4(y - 5) = 3(x + 3)

4y - 20 = 3x + 9

4y = 3x + 29

y = ¾x + 29/4

The equation is y = ¾x + 29/4

Answer:

\(y=\dfrac{3}{4}x+\dfrac{29}{4}\)

Step-by-step explanation:

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Given line:

\(y=\dfrac{3}{4}x-4\)

The given line is in slope-intercept form. Therefore:

The slopes of parallel lines are the same.

Therefore, the slope of a line parallel to the given line is also 3/4.

Given the parallel line passes through the point (-3, 5), substitute this and the found slope into the slope-intercept formula and solve for b:

\(\implies y=mx+b\)

\(\implies 5=\dfrac{3}{4}(-3)+b\)

\(\implies 5=-\dfrac{9}{4}+b\)

\(\implies 5+\dfrac{9}{4}=-\dfrac{9}{4}+b+\dfrac{9}{4}\)

\(\implies b=5+\dfrac{9}{4}\)

\(\implies b=\dfrac{20}{4}+\dfrac{9}{4}\)

\(\implies b=\dfrac{20+9}{4}\)

\(\implies b=\dfrac{29}{4}\)

Therefore, the equation of the line that passes through the given point and is parallel to the given line in slope-intercept form is:

\(y=\dfrac{3}{4}x+\dfrac{29}{4}\)

Answer:

Height of the pole = 9.17 chi.

Length of the rope = 12.17 chi.

Step-by-step explanation:

Given that the rope is hanging from the top of a pole having height x chi and the portion of the rope lying on the ground is 3 chi.

So, the length of the rope= x + 3 chi.

Let AB represents the pole in the figure, and one end of the rope is at point A.

When the rope is tightly stretched, let C be the other end of the rope as shown in the triangle.

The length of the rope = AC.

\Rightarrow AC=x+3 chi.

Distance from the bottom of the pole, point A, to the other end of the pole, point B, is 8 chi.

So, BC=8 chi.

As the triangle ABC is a right-angled triangle, so by using Pythagoras theorem,

\(AC^2= AB^2+BC^2\)

\(\Rightarrow (x+3)^2=x^2+8^2\)

\(\Rightarrow x^2+6x+9=x^2+64\)

\(\Rightarrow 6x=64-9=55\)

\(\Rightarrow x=55/6=9.17\) chi.

Hence, the height of the pole, \(AB=x=9.17\) chi,

and the length of the rope, \(x+3=9.17+3=12.17\) chi.

Answer:

Step-by-step explanation:

Apr is 248  the customer has to pay 248 dollars every month for 30 years he has to pay 7,440 dollars to the bank or he will lose the house.

It is possible to translate the parent function f(x) = x using various transformations including vertical and horizontal translations. Each transformation will result in
the graph intersecting the x- or y-axis at a different point.

Function is an operation that takes an input, performs some processing on it, and returns a result. It is a set of instructions that performs a specific task. Functions are typically used to perform repetitive tasks, like finding the sum of two numbers, adding two strings together, or finding the maximum of a list of numbers. Functions are essential to programming and can be used to make code more organized, reusable, and efficient.


The function f(x) = x is the parent function for linear equations. This equation is generally used to graph a line with a slope of 1 and a y-intercept of (0, 0). In order to translate this parent function, different transformations are applied to it.

A vertical translation down 4 units would be represented by the equation f(x) = x - 4. This transformation would shift the graph of the parent function down 4 units on the y-axis. This would result in the graph intersecting the y-axis at the point (0, -4).

A horizontal translation right 4 units would be represented by the equation f(x) = x + 4. This transformation would shift the graph of the parent function right 4 units on the x-axis. This would result in the graph intersecting the x-axis at the point (4, 0).

A horizontal translation left 4 units would be represented by the equation f(x) = x - 4. This transformation would shift the graph of the parent function left 4 units on the x-axis. This would result in the graph intersecting the x-axis at the point (-4, 0).

Finally, a vertical translation up 4 units would be represented by the equation f(x) = x + 4. This transformation would shift the graph of the parent function up 4 units on the y-axis. This would result in the graph intersecting the y-axis at the point (0, 4).

In conclusion, it is possible to translate the parent function f(x) = x using various transformations including vertical and horizontal translations. Each transformation will result in the graph intersecting the x- or y-axis at a different point.

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In geometry, a great circle is a circle on a sphere whose center is also the sphere's center.

The largest circle that can be drawn on a sphere is called a great circle. It divides the sphere into two equal halves, and its center coincides with the center of the sphere. A small circle is any circle that is not a great circle.

Great circles are important in navigation and are used to determine the shortest distance between two points on the surface of a sphere. The equator and all longitude lines are examples of great circles. In contrast, small circles are tilted with respect to the equator and do not divide the sphere into two equal halves.

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Answer:

w=3

Step-by-step explanation:

Answer:

W=3

Step-by-step explanation:

What’s ur insta?

Answer:

Hi! The slope is  -3/2

Y intercept  2.5

(0,2.5)

Step-by-step explanation:

I hope this helps!

Answer:

The slope is \(\frac{-3}{2}\)

The y - intercept is 2 1/2

The y-intercept point is (0, 2 1/2)

Step-by-step explanation:

If you start at the point on the left to get to the lower point on the right, you need to go down 3 units and to the right 2 units.  This is the slope.  Going down represents a negative number and going right represents a positive number.  The slope is \(\frac{-3}{2}\)

The y -intercpet is where the graph is cross the y axis.  It looks like it is crossing between 2 and 3.  So, 2 1/2 is a good estimate.  Actually, I did calculate the y-intercept and it is in fact 2 1/2.

The point of the y-intercept is when x = 0

(0, 2 1/2)

Helping in the name of Jesus.

Given:

We have

Required:

Select correct option.

Explanation:

We can check from D option

Answer:

Option D is correct.

The equation of the function is f(x) = 1200(0.95)^x

From the question, we have the following parameters that can be used in our computation:

Initial value, a = 1200

Rate of decrement, r = 5%

Using the above as a guide, we have the following:

f(x) = a *(1 - r)^x

Substitute the known values in the above equation, so, we have the following representation

f(x) = 1200(1 - 5%)^x

So, we have

f(x) = 1200(0.95)^x

Hence, the function is f(x) = 1200(0.95)^x

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Answer:

1

Step-by-step explanation:

The maximum of f(x) = sin(x) is 1. The sine function has a range of -1 ≤ sin(x) ≤ 1. The sine function oscillates between -1 and 1, reaching a maximum of 1 when x = π/2 and a minimum of -1 when x = -π/2.  If you look at a graph of

y = sin(x) you can see this.  

Answer: The Maximum Value of f(x)=sin(x) is 1 , when x=90°.

Step-by-step explanation:

Property of Sine function:

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The value of integral is 3.

Let's evaluate the integral over the positive half of the interval:

∫[0 to π] (cos(x) / √(4 + 3sin(x))) dx

Let u = 4 + 3sin(x), then du = 3cos(x) dx.

Substituting these expressions into the integral, we have:

∫[0 to π] (cos(x) / sqrt(4 + 3sin(x))) dx = ∫[0 to π] (1 / (3√u)) du

Using the power rule of integration, the integral becomes:

∫[0 to π] (1 / (3√u)) du = (2/3) . 2√u ∣[0 to π]

Evaluating the definite integral at the limits of integration:

(2/3)2√u ∣[0 to π] = (2/3) 2(√(4 + 3sin(π)) - √(4 + 3sin(0)))

(2/3) x 2(√(4) - √(4)) = (2/3) x 2(2 - 2) = (2/3) x 2(0) = 0

So, the value of integral is

= 3-0

= 3

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Answer:

\(3-\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3 \sin x}}\; \text{d}x\approx 0.806\; \sf (3\;d.p.)\)

Step-by-step explanation:

First, compute the indefinite integral:

\(\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x\)

To evaluate the indefinite integral, use the method of substitution.

\(\textsf{Let} \;\;u = 4 + 3 \sin x\)

Find du/dx and rewrite it so that dx is on its own:

\(\dfrac{\text{d}u}{\text{d}x}=3 \cos x \implies \text{d}x=\dfrac{1}{3 \cos x}\; \text{d}u\)

Rewrite the original integral in terms of u and du, and evaluate:

\(\begin{aligned}\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=\int \dfrac{\cos x}{\sqrt{u}}\cdot \dfrac{1}{3 \cos x}\; \text{d}u\\\\&=\int \dfrac{1}{3\sqrt{u}}\; \text{d}u\\\\&=\int\dfrac{1}{3}u^{-\frac{1}{2}}\; \text{d}u\\\\&=\dfrac{1}{-\frac{1}{2}+1} \cdot \dfrac{1}{3}u^{-\frac{1}{2}+1}+C\\\\&=\dfrac{2}{3}\sqrt{u}+C\end{aligned}\)

Substitute back u = 4 + 3 sin x:

                            \(= \dfrac{2}{3}\sqrt{4+3\sin x}+C\)

Therefore:

\(\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x= \dfrac{2}{3}\sqrt{4+3\sin x}+C\)

To evaluate the definite integral, we must first determine any intervals within the given interval -π ≤ x ≤ π where the curve lies below the x-axis. This is because when we integrate a function that lies below the x-axis, it will give a negative area value.

Find the x-intercepts by setting the function to zero and solving for x in the given interval -π ≤ x ≤ π.

\(\begin{aligned}\dfrac{\cos x}{\sqrt{4+3\sin x}}&=0\\\\\cos x&=0\\\\x&=\arccos0\\\\\implies x&=-\dfrac{\pi }{2}, \dfrac{\pi }{2}\end{aligned}\)

Therefore, the curve of the function is:

So to calculate the total area, we need to calculate the positive and negative areas separately and then add them together, remembering that if you integrate a function to find an area that lies below the x-axis, it will give a negative value.

Integrate the function between -π and -π/2.

As the area is below the x-axis, we need to negate the integral so that the resulting area is positive:

\(\begin{aligned}A_1=-\displaystyle \int^{-\frac{\pi}{2}}_{-\pi} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=- \left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{-\frac{\pi}{2}}_{-\pi}\\\\&=-\dfrac{2}{3}\sqrt{4+3 \sin \left(-\frac{\pi}{2}\right)}+\dfrac{2}{3}\sqrt{4+3 \sin \left(-\pi\right)}\\\\&=-\dfrac{2}{3}\sqrt{4+3 (-1)}+\dfrac{2}{3}\sqrt{4+3 (0)}\\\\&=-\dfrac{2}{3}+\dfrac{4}{3}\\\\&=\dfrac{2}{3}\end{aligned}\)

Integrate the function between -π/2 and π/2:

\(\begin{aligned}A_2=\displaystyle \int^{\frac{\pi}{2}}_{-\frac{\pi}{2}} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&= \left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{\frac{\pi}{2}}_{-\frac{\pi}{2}}\\\\&=\dfrac{2}{3}\sqrt{4+3 \sin \left(\frac{\pi}{2}\right)}-\dfrac{2}{3}\sqrt{4+3 \sin \left(-\frac{\pi}{2}\right)}\\\\&=\dfrac{2}{3}\sqrt{4+3 (1)}-\dfrac{2}{3}\sqrt{4+3 (-1)}\\\\&=\dfrac{2\sqrt{7}}{3}-\dfrac{2}{3}\\\\&=\dfrac{2\sqrt{7}-2}{3}\end{aligned}\)

Integrate the function between π/2 and π.

As the area is below the x-axis, we need to negate the integral so that the resulting area is positive:

\(\begin{aligned}A_3=-\displaystyle \int^{\pi}_{\frac{\pi}{2}} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&= -\left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{\pi}_{\frac{\pi}{2}}\\\\&=-\dfrac{2}{3}\sqrt{4+3 \sin \left(\pi\right)}+\dfrac{2}{3}\sqrt{4+3 \sin \left(\frac{\pi}{2}\right)}\\\\&=-\dfrac{2}{3}\sqrt{4+3 (0)}+\dfrac{2}{3}\sqrt{4+3 (1)}\\\\&=-\dfrac{4}{3}+\dfrac{2\sqrt{7}}{3}\\\\&=\dfrac{2\sqrt{7}-4}{3}\end{aligned}\)

To evaluate the definite integral, sum A₁, A₂ and A₃:

\(\begin{aligned}\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=\dfrac{2}{3}+\dfrac{2\sqrt{7}-2}{3}+\dfrac{2\sqrt{7}-4}{3}\\\\&=\dfrac{2+2\sqrt{7}-2+2\sqrt{7}-4}{3}\\\\&=\dfrac{4\sqrt{7}-4}{3}\\\\ &\approx2.194\; \sf (3\;d.p.)\end{aligned}\)

Now we have evaluated the definite integral, we can subtract it from 3 to evaluate the given expression:

\(\begin{aligned}3-\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3 \sin x}}\; \text{d}x&=3-\dfrac{4\sqrt{7}-4}{3}\\\\&=\dfrac{9}{3}-\dfrac{4\sqrt{7}-4}{3}\\\\&=\dfrac{9-(4\sqrt{7}-4)}{3}\\\\&=\dfrac{13-4\sqrt{7}}{3}\\\\&\approx 0.806\; \sf (3\;d.p.)\end{aligned}\)

Therefore, the given expression cannot be zero.

Answer:

276.2 rounded to the nearest 10th is 276.2.....

Step-by-step explanation:

Answer:276.2...

Step-by-step explanation:

If a basketball player has a 70% accuracy rate for making free throws. The probability that this player misses his first free throw, but makes the second one is 0.21.

The probability of making a free throw is 0.7, so the probability of missing a free throw is 0.3.

Let X be the number of trials (free throws) until the first success (a made free throw). Since we want to know the probability of missing the first free throw and making the second one, we want to find P(X = 2).

Using the geometric distribution formula, we have:

P(X = 2) = (1 - p)^(k-1) * p

where:

p is the probability of success (making a free throw)

k is the number of trials (2 in this case), and (1 - p)^(k-1) is the probability of having k-1 failures (missing the first free throw) followed by one success (making the second free throw).

Plugging in the values, we get:

P(X = 2) = (1 - 0.7)^(2-1) * 0.7

= 0.3 * 0.7

= 0.21

Therefore, the probability  is 0.21 (rounded to the hundredths place).

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Answer:

The odds would be in faver of the white marble.

Step-by-step explanation:

Hope that helps :)

Step-by-step explanation:

2y+y=180(Sum of supplementey angle)

3y=180

y=180\3

Answer:

1.24

Step-by-step explanation:

because 1.24>1.215>0.365>0.095

The y-intercept of the linear model is 211,400, which represents the estimated number of automobiles in the town in the year 2015 (when the independent variable is zero).

To find the y-intercept of the linear model, we need to determine the value of the dependent variable (the number of automobiles) when the independent variable (the number of years since 2015) is equal to zero.

Let's first find the slope of the line, which represents the rate of change of the number of automobiles per year:

slope = (change in number of automobiles) / (change in number of years)

slope = (2420 - 1890) / (2020 - 2015) = 106 automobiles per year

Now we can use the point-slope form of a linear equation to find the y-intercept:

y - y1 = m(x - x1)

where y1 is the value of the dependent variable when the independent variable is x1. In this case, x1 = 2015, y1 = 1890, and m = 106 (the slope we just calculated).

y - 1890 = 106(x - 2015)

To find the y-intercept, we can set x = 0:

y - 1890 = 106(0 - 2015)

y - 1890 = -213,290

y = 211,400

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