it’s kinda hard to read soo

A lake near The Arctic Circle is covered by a thick sheet of ice during the cold winter months. When spring arrives, the warm air gradually melts the ice, causing it’s thickness to decrease at a rate of 0.2m per week. After 7 weeks, the sheet is only 2.4m thick.

Let y represent the ice sheets thickness (in meters) after x weeks.

Complete the equation for the relationship between the thickness a number of weeks.

Answer:

x > 25.5

Step-by-step explanation:

2.5 < \(\frac{1}{3}\) (x - 18 ) ← multiply both sides by 3 to clear the fraction

7.5 < x - 18 ( ad 18 to both sides )

25.5 < x , then

x > 25.5

To find the coordinates of the centroid for the region bounded by the curves y=16x, y=9/x, y=0, and x=10, we need to calculate the x-coordinate and y-coordinate of the centroid separately. First, let's find the x-coordinate of the centroid.

We can use the formula: x-bar = (1/A) ∫[a,b] xf(x) dx, where A is the area of the region. The intersection points of the curves y=16x and y=9/x can be found by setting the equations equal to each other: 16x=9/x.

Solving this equation, we get x=±√(9/16)=±3/4. Since the region is bounded by x=10, we take the positive value x=3/4. To find the area A, we integrate the difference between the curves: A=∫[3/4,10] (16x-9/x) dx. Evaluating this integral, we find A=400-9ln(10).

Now we can calculate the x-coordinate of the centroid: x-bar=(1/A) ∫[3/4,10] x(16x-9/x) dx. Simplifying the integral and evaluating it, we get x-bar=(8160-36ln(10))/(400-9ln(10)). Next, let's find the y-coordinate of the centroid.

Since the region is symmetric about the x-axis, the y-coordinate of the centroid will be y-bar=0. Therefore, the exact coordinates of the centroid for the given region are: (x-bar, y-bar)=((8160-36ln(10))/(400-9ln(10)), 0).

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Answer:

The skater slows down, then gains speed quickly. The speed begins to slow until it becomes constant .

Step-by-step explanation: answer on edge

Answer:-83/25 and 27/40

The mean, median and mode of the data sets are as follows:

The median is the middle value in a list ordered from smallest to largest.

The mode is the most frequently occurring value on the list.

The mean is the average of the distribution.

Therefore,

1. 1, 2, 3, 4, 5

mean = 1 + 1 + 2+ 3 + 4 + 5 / 6 = 16 / 6 = 2.7

median = 2 + 3 / 2 = 5 / 2  = 2.5

mode = 1

2, 2,3,4,5,6,6

mean = 2+2+3+4+5+6+6 / 7 = 28 / 7 = 4

median = 4

mode = 2 and 6

2,3, 4, 5, 5, 5,6, 6,7

mean = 3+6+7+5+4+5+6+2+5 / 9 = 43 / 9 = 4.8

median = 5

mode = 5

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The first five terms in the recursive sequence are: 2, 3, 6, 18, 108.

First five terms of the recursive sequence defined by a1 = 2, a2 = 3, and an = an-2 * an-1.
1. First term (a1): Given as 2.
2. Second term (a2): Given as 3.
3. Third term (a3): To find a3, use the formula an = an-2 * an-1. In this case, n = 3, so a3 = a1 * a2 = 2 * 3 = 6.
4. Fourth term (a4): Similarly, to find a4, use the formula with n = 4. So a4 = a2 * a3 = 3 * 6 = 18.
5. Fifth term (a5): Finally, to find a5, use the formula with n = 5. So a5 = a3 * a4 = 6 * 18 = 108.
The first five terms in the recursive sequence are: 2, 3, 6, 18, 108.

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Answer:

44%

Step-by-step explanation:

Total number of students = 100

Number of girls = 49

So,

Number of boys = Total number of students - Number of girls = 100 - 49 = 51

Number of girls liking biology the best = 22

Number of girls liking chemistry = 21

Total number of students liking chemistry = 35

So,

Number of boys liking chemistry = 35 - 21 = 14

Number of boys liking Physics = 15

Number of boys liking biology = Total number of boys - Number of boys liking Physics - Number of boys liking Chemistry = 51 - 14 -15 = 22

Total number of students (girls and boys) liking biology the best =  Number of boys liking Biology +  Number of girls liking Biology = 22 + 22 = 44

Percentage of students who prefer bio = \(\frac{44}{100} \times 100 = \bold{44\%}\)

The probability of the die showing any given output is 1/6.

Then, the probability of showing a 1 on the first turn is 1/6.

On the second turn, the probability of showing an even number is 1/2 because half of the output numbers are even.

To find the probability of showing a 1 on the first turn and an even number on the second turn, multiply the probabilities of each event:

Therefore, the probability of showin a 1 on the first roll and an even number in the second roll is 1/12.

The equation of the surface in words is described as follows: The given equation `ρ^2 - 3ρ + 2 = 0` is a quadratic equation in `ρ`, the radial distance from the origin.

It's a sphere with radius `ρ = 1` and the center at `ρ = 2` in the Cartesian coordinate system. When the equation is rearranged to standard form, we get `(ρ - 2) (ρ - 1) = 0`. The equation of the surface in words is described as follows:

The given equation `ρ^2 - 3ρ + 2 = 0` is a quadratic equation in `ρ`, the radial distance from the origin. It's a sphere with radius `ρ = 1` and the center at `ρ = 2` in the Cartesian coordinate system. When the equation is rearranged to standard form, we get `(ρ - 2) (ρ - 1) = 0`.Therefore, the surface represented by the given equation is a sphere with radius `ρ = 1` and the center at `ρ = 2` in the Cartesian coordinate system.

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Answer:

I think the answer would be 0.35, 7/20, 35%

Step-by-step explanation:

They are all the same its just different form

Answer:

0

Step-by-step explanation:

7 - (63 ÷ 9)^2/7 = ?

(63 ÷ 9) = 7^2 = 49/7 = 7

then the equation would be 7 - 7 = 0

We can write the given algebraic expression as a function of \(\theta\) as: \(f(\theta) = 9|\tan\theta|\)

We are given the algebraic expression:

\(\sqrt{x^2 - 81}\)

We are also given the substitution:

\(x = 9\sec\theta\)

We can substitute x  with \(9\sec\theta\) in the given expression:

\(\sqrt{x^2 - 81} = \sqrt{(9\sec\theta)^2 - 81}\)

Simplifying the expression inside the square root:

\(\sqrt{(9\sec\theta)^2 - 81} = \sqrt{81\sec^2\theta - 81} = \sqrt{81(\sec^2\theta - 1)}\)

Recall that \(\sec^2\theta - 1 = \tan^2\theta .\)

Substituting this into the expression:

\(\sqrt{81(\sec^2\theta - 1)} = \sqrt{81\tan^2\theta} = 9|\tan\theta|\)

Finally, we can write the given algebraic expression as a function of \(\theta\) as:

\(f(\theta) = 9|\tan\theta|\)

Note that the absolute value is used because the substitution \(x = 9\sec\theta\)  only holds for \(0 < \theta < \frac{\pi}{2}\), but \(\tan\theta\) can be negative in the second quadrant. The absolute value ensures that the function is always non-negative.

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Answer:

2 -5

Step-by-step explanation:

The slope and y-intercept are 2 and -5 after comparing them with the standard equation.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

It is given that:

The inequality is y > 2x-5

The above inequality represents the linear graph

After drawing on the graph:

On comparing:

y = mx + c

The slope m = 2

The y-intercept c = -5

Thus, the slope and y-intercept are 2 and -5 after comparing them with the standard equation.

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The graph of a function can be used to find solutions to equations and to identify important properties of the function, such as its domain, range, intercepts, and asymptotes.

The set of points (x,y) in the xy-plane that satisfy the equation of a function defined by an equation in xx and yy is called the graph of the function. Graphing an equation allows one to identify patterns in the data and draw conclusions about the relationship between variables. The graph of a function is created by plotting points (x,y) on the coordinate plane and connecting them with a line or curve.

Each point on the graph represents a pair of inputs and outputs that satisfy the equation of the function. The graph provides a visual representation of the behavior of the function over a given domain.

For example, consider the function f(x) = x^2. The graph of this function is a parabola that opens upwards, as shown below:graph of function f(x) = x^2The input values are represented by the x-coordinates on the graph, and the output values are represented by the y-coordinates. The graph of a function can be used to find solutions to equations and to identify important properties of the function, such as its domain, range, intercepts, and asymptotes.

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Answer:

Shares

Step-by-step explanation:

PLS GIVE BRAINLIEST

The equation of the tangent line represents a straight line that passes through the point of tangency and has a slope of -16.

The slope of the tangent line to the graph of the function y = x^4 - 10x^2 + 9 at x = 1 can be found by taking the derivative of the function and evaluating it at x = 1. The equation of the tangent line can then be determined using the point-slope form.

Taking the derivative of the function y = x^4 - 10x^2 + 9 with respect to x, we get:

dy/dx = 4x^3 - 20x

To find the slope of the tangent line at x = 1, we substitute x = 1 into the derivative:

dy/dx (at x = 1) = 4(1)^3 - 20(1) = 4 - 20 = -16

Therefore, the slope of the tangent line is -16.

To find the equation of the tangent line, we use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Given that the point of tangency is (1, y(1)), we substitute x1 = 1 and y1 = y(1) into the equation:

y - y(1) = -16(x - 1)

Expanding the equation and simplifying, we have:

y - y(1) = -16x + 16

Rearranging the equation, we obtain the equation of the tangent line:

y = -16x + (y(1) + 16)

To find the slope of the tangent line, we first need to find the derivative of the given function. The derivative represents the rate of change of the function at any point on its graph. By evaluating the derivative at the specific value of x, we can determine the slope of the tangent line at that point.

In this case, the given function is y = x^4 - 10x^2 + 9. Taking its derivative with respect to x gives us dy/dx = 4x^3 - 20x. To find the slope of the tangent line at x = 1, we substitute x = 1 into the derivative equation, resulting in dy/dx = -16.

The slope of the tangent line is -16. This indicates that for every unit increase in x, the corresponding y-value decreases by 16 units.

To determine the equation of the tangent line, we use the point-slope form of a linear equation, which is y - y1 = m(x - x1). We know the point of tangency is (1, y(1)), where x1 = 1 and y(1) is the value of the function at x = 1.

Substituting these values into the point-slope form, we get y - y(1) = -16(x - 1). Expanding the equation and rearranging it yields the equation of the tangent line, y = -16x + (y(1) + 16).

The equation of the tangent line represents a straight line that passes through the point of tangency and has a slope of -16.

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Regardless of what the Inspector chooses, the Owner's expected payoff is the same (33.33). The Owner does not have a better option than waiting for the Inspector to choose container B.

This problem can be modeled as a game of incomplete information. The Inspector and Owner are players in the game, and each has two possible strategies: either choose container B, or switch to container C. The payoffs for each player depend on the strategy they choose and which container contains the counterfeit goods.

To solve this game, we can use backward induction. We start by considering the final decision point: whether to switch to container C after seeing that container A does not contain the counterfeit goods. Let's consider the two cases:

If the counterfeit goods are in container B, then the Inspector knows that container C also does not have the counterfeit goods. In this case, the payoff for choosing container B is 100 (if they find the counterfeit goods) or -100 (if they do not).

If the counterfeit goods are in container C, then the Inspector knows that container B does not have the counterfeit goods. In this case, the payoff for switching to container C is 100 (if they find the counterfeit goods) or -100 (if they do not).

Since the Inspector does not know which container has the counterfeit goods, they should choose the strategy with the higher expected payoff. To calculate the expected payoffs, we need to consider the probability that the counterfeit goods are in each container. Since the owner chose one container at random, each container has a 1/3 chance of containing the counterfeit goods.

If the Inspector chooses container B, the expected payoff is:

Expected payoff (choose container B) = (1/3) * 100 + (2/3) * (-100) = -33.33

If the Inspector switches to container C, the expected payoff is:

Expected payoff (switch to container C) = (1/3) * 100 + (2/3) * (-100) = -33.33

Therefore, regardless of what the Inspector chooses, their expected payoff is the same (-33.33). This means that the Inspector does not have a better option than choosing container B, and switching to container C does not improve their chances of finding the counterfeit goods.

For the Owner, if the Inspector chooses container B, then the Owner's expected payoff is:

Expected payoff (Inspector chooses container B) = (1/3) * (-100) + (2/3) * 100 = 33.33

If the Inspector switches to container C, then the Owner's expected payoff is:

Expected payoff (Inspector switches to container C) = (1/3) * (-100) + (2/3) * 100 = 33.33

Therefore, regardless of what the Inspector chooses, the Owner's expected payoff is the same (33.33). The Owner does not have a better option than waiting for the Inspector to choose container B.

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From Daniel's initial location from the campsite given the width of the

stream is 400 feet and Daniel swims to the boat ramp, we have;

1.) Please find attached the drawing of the situation

2.) 3.34 minutes

3.) 1,298.59 feet

4.) 3.69 minutes

1.) Please find attached a labelled diagram of the scenario created with MS Visio

2.) Daniel's average swimming rate (speed) = 150 feet per minute

\(The \ distance \ Daniel \ swims = \mathbf{\dfrac{400 \, feet}{sin(53^{\circ})}} \approx 500.85 \, feet\)

The time it takes him to swim to the boat ramp, t, is therefore;

3.) The distance, d₁, downstream of the boat ramp from Daniel is given as follows;

d₁ = √((500.85 feet)² - (400 feet)²) ≈ 301.41 feet

Therefore;

The distance from the boat ramp to the campsite, d₂, is therefore;

d₂ ≈ 1600 feet - 301.41 feet = 1,298.59 feet

The distance from the boat ramp to the campsite, d₂ ≈ 1,298.59 feet                              

4. The time, t₂, it will take Daniel to jog from the boat ramp to the campsite is given as follows;

\(t_2 = \mathbf{\dfrac{d_2}{v_2}}\)

Where;

v₂ = The rate at which Daniel can jog, which is 4 mph

Which gives;

\(t_2 = \mathbf{\dfrac{1298.59 \, feet}{4 \, mph}} = \dfrac{1298.59 \, feet}{4 \, mph} \approx \dfrac{1298.59 \, feet}{5.866142 \ feet/s} \approx \dfrac{221.37 \, s}{60 \, s/min} \approx 3.69 \, min\)

Therefore;

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The value of the sum of squares due to regression (SSR) is 17.43.

Certainly! In statistics, the sum of squares is a measure that quantifies the variability or dispersion of data points around a certain value. It is commonly used in regression analysis to assess how well a regression line or model fits the observed data.

The total sum of squares (SST) represents the total variability in the dependent variable, which is the sum of the squared differences between each data point and the overall mean of the dependent variable. It is a measure of the total deviation of the data points from the mean.

The sum of squares due to error (SSE), also known as the residual sum of squares, represents the unexplained variability in the dependent variable after accounting for the regression model. It is calculated by summing the squared differences between the observed values and the predicted values from the regression model.

The sum of squares due to regression (SSR), also known as the explained sum of squares, represents the variability in the dependent variable that can be attributed to the regression model. It is calculated by subtracting the SSE from the SST.

In the given scenario, the SST is 23.32 and the SSE is 5.89. By subtracting the SSE from the SST, we obtain the SSR. Substituting the values:

SSR = SST - SSE

   = 23.32 - 5.89

   = 17.43

Therefore, the value of the sum of squares due to regression (SSR) is 17.43.

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Answer:

| B | = - 9

Step-by-step explanation:

The determinant of a 2 by 2 matrix B = \(\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right]\) is

| B | = ad - bc

Then for

B = \(\left[\begin{array}{ccc}0&1\\9&8\\\end{array}\right]\)

| B | = (0 × 8 ) - (1 × 9 ) = 0 - 9 = - 9

Answer:

74⁰

Step-by-step explanation:

As in cyclic quadrilateral sum of opposite angles us equal to 180⁰

Therefore, the Vickers tests of the sample are approximately 959 N/mm² and 1917 N/mm² for loads of 2.5 kg and 5 kg, respectively.

Given :Load = (2.5, 5) kg . diameter of square based pyramid diamond = 0.362 mm To find: Vickers tests of the sample Solution :The Vickers hardness test uses a square pyramid-shaped diamond indenter. It is used to test materials with a fine-grained microstructure or thin layers. The formula used to calculate the Vickers hardness is :Vickers hardness = 1.8544 P/d²where,P = load applied d = average length of the two diagonals of the indentation made by the diamond Now, we can calculate the Vickers hardness using the above formula as follows: For load = 2.5 k P = 2.5 kg = 2.5 × 9.81 N = 24.525 N For load = 5 kg P = 5 kg = 5 × 9.81 N = 49.05 N For both loads, we have the same diameter of square-based pyramid diamond = 0.362 mm .Therefore, we can calculate the average length of the two diagonals as :d = 0.362/√2 mm = 0.256 mm .Now, we can substitute the values of P and d in the formula to get the Vickers hardness :For load 2.5 kg ,Vickers hardness = 1.8544 × 24.525 / (0.256)²= 958.68 N/mm² ≈ 959 N/mm²For load 5 kg ,Vickers hardness = 1.8544 × 49.05 / (0.256)²= 1917.36 N/mm² ≈ 1917 N/mm².

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Retained earnings, December 31, 2018                               $6,470,000

Add: Net income December 31, 2019                                  $4,500,000

Less: Preferred stock dividends declared and paid           $4,500,000

Less: Common stock dividends declared and paid            $1,000,000

Total adjustments                                                                  $3,500,000

Retained earnings, December 31, 2019                             $9,970,000

The statement shows changes in the balance of retained earnings account during the year. The retained earnings balance at the beginning of the year is adjusted for the net income earned during the year and for the dividends declared and paid to the shareholders.

In this case:

So, total adjustments to the retained earnings balance:

= $4,500,000 + $1,000,000 - $4,500,000.

= $3,500,000

After adjustment on net income and dividends, the retained earnings balance at December 31 2019 is:

= $6,470,000 + $4,500,000 - $3,500,000

= $9,970,000

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Check the picture below.

Answer:

  (x, y) = (6, 8) using linear combination

Step-by-step explanation:

The coefficients of the x-terms are opposites of each other (2 and -2), so the x-terms can be eliminated using a linear combination of the equations.

Adding the two equations together gives ...

  (2x -y) +(-2x +3y) = (4) +(12)

  2y = 16 . . . . . . . . simplify

  y = 8 . . . . . . . divide by 2

Substituting for y in the first equation gives ...

  2x -8 = 4

  x -4 = 2 . . . . . divide by 2

  x = 6 . . . . . . . add  4

The solution is (x, y) = (6, 8).

Answer:

okay i'll try to help

Answer:

I'll help too.

Step-by-step explanation:

Answer:

10560Feet

Step-by-step explanation:

Answer: 10560 ft

Step-by-step explanation: 2 mi conversion. a mile is a unit of distance equal to 5,280 feet or exactly 1.609344 kilometers. it is commonly used to measure the distance between places in the United States and kingdom. so you convert 2 mi to ft.

Answer:

they cant unless each wants 0.42857...

Step-by-step explanation: