When you went apple picking, you got a total of 25 apples.
However, 10 of the apples weren't edible because they were
rotten. What percent of apples that you picked were edible?
%

To calculate the cliff's elevation in 10 millennia, we need to use a little bit of math.

Since the cliff is losing elevation at a rate of 5% every millennium, we know that after one millennium, the cliff's elevation will be 95% of its current elevation. Therefore, we can use this formula to calculate the cliff's elevation after three millennia:
1,519 meters * 0.95^10 = 601.83 meters
So, after 10 millennia, the cliff's elevation will be approximately 601.83 meters. This means that the cliff will have lost approximately 917 meters of elevation over the course of 10,000 years due to erosion.

Finally, by applying the formula, we can determine the cliff's elevation in 10 millennia. After doing the calculation, we find that the final elevation will be approximately 744.29 meters.

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The value of the surface integral or flux is \(\(2\pi\)\) for the given vector field \(\(\mathbf{f}\)\) across the surface defined by the unit sphere centered at the origin.

To properly solve the problem, let's consider a specific example. Suppose we have the vector field \(\(\mathbf{f}(x, y, z) = x^2\mathbf{i} + y^2\mathbf{j} + z^2\mathbf{k}\)\), and we want to calculate the surface integral or flux of \(\(\mathbf{f}\)\) across the surface \(\(S\)\) defined by the unit sphere centered at the origin.

Using the divergence theorem, the surface integral can be calculated as follows:

\(\[\iint_S \mathbf{f} \cdot d\mathbf{S} = \iiint_V \nabla \cdot \mathbf{f} \, dV\]\)

Since \(\(\nabla \cdot \mathbf{f} = \frac{\partial}{\partial x}(x^2) + \frac{\partial}{\partial y}(y^2) + \frac{\partial}{\partial z}(z^2) = 2x + 2y + 2z\)\), the triple integral becomes:

\(\[\iiint_V (2x + 2y + 2z) \, dV\]\)

Considering the unit sphere as the volume \(\(V\)\), we can switch to spherical coordinates with \(\(x = \rho\sin\phi\cos\theta\), \(y = \rho\sin\phi\sin\theta\), and \(z = \rho\cos\phi\), and \(\rho\) ranging from 0 to 1, \(\phi\) ranging from 0 to \(\pi\), and \(\theta\) ranging from 0 to \(2\pi\).\)

To further solve the problem, let's evaluate the triple integral using the given limits and spherical coordinates:

\(\[\iiint_V (2x + 2y + 2z) \, dV\]\)

In spherical coordinates, the volume element \(\(dV\) becomes \(\rho^2 \sin \phi \, d\rho \, d\phi \, d\theta\)\).

Substituting the coordinates and limits into the triple integral, we have:

\(\iiint_V (2x + 2y + 2z) \, dV &= \int_0^{2\pi} \int_0^{\pi} \int_0^1 (2\rho\sin\phi\cos\theta + 2\rho\sin\phi\sin\theta + 2\rho\cos\phi) \rho^2 \sin \phi \, d\rho \, d\phi \, d\theta \\\)

\(&= \int_0^{2\pi} \int_0^{\pi} \int_0^1 (2\rho^3\sin^2\phi\cos\theta + 2\rho^3\sin^2\phi\sin\theta + 2\rho^2\sin\phi\cos\phi) \, d\rho \, d\phi \, d\theta \\\)

\(&= \int_0^{2\pi} \int_0^{\pi} \left[\frac{1}{2}\rho^4\sin^2\phi\cos\theta + \frac{1}{2}\rho^4\sin^2\phi\sin\theta + \frac{2}{3}\rho^3\sin\phi\cos\phi\right]_0^1 \, d\phi \, d\theta \\\)

\(&= \int_0^{2\pi} \int_0^{\pi} \left(\frac{1}{2}\sin^2\phi\cos\theta + \frac{1}{2}\sin^2\phi\sin\theta + \frac{2}{3}\sin\phi\cos\phi\right) \, d\phi \, d\theta\end{aligned}\]\)

Evaluating the inner integral with respect to \(\(\phi\)\), we get:

\(\[\int_0^{\pi} \left(\frac{1}{2}\sin^2\phi\cos\theta + \frac{1}{2}\sin^2\phi\sin\theta + \frac{2}{3}\sin\phi\cos\phi\right) \, d\phi = \frac{\pi}{2}\]\)

Substituting this result into the outer integral with respect to \(\(\theta\)\), we have:

\(\[\int_0^{2\pi} \frac{\pi}{2} \, d\theta = \pi \cdot 2 = 2\pi\]\)

Therefore, the value of the surface integral or flux is \(\(2\pi\)\) for the given vector field \(\(\mathbf{f}\)\) across the surface defined by the unit sphere centered at the origin.

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Answer:

how we supposed to know its unfinished cuz we never knew how much molly had

Step-by-step explanation:

Answer:

p(t) = 200(2)^t

Step-by-step explanation:

an exponential function is in the form a(b)^x.

a is the initial value. the initial value is 200 in the problem, so a = 200.

b is the growth/decay rate. because it doubles, b = 2.

therefore, the function is p(t) = 200(2)^t

The linearized equation for the non-linear equation z = x² + 4xy + 6xy² in the region defined by 8 ≤ x ≤ 10, 2 ≤ y ≤ 4 is given by :

z ≈ 244 + 20(x - 8) + 128(y - 2).

When using the linearized equation to calculate the value of z at x = 8, y = 2, the error is 0.

1.1. To linearize the equation in the given region, we need to find the partial derivatives of z with respect to x and y:

∂z/∂x = 2x + 4y

∂z/∂y = 4x + 6xy

At the point (x₀, y₀) = (8, 2), we substitute these values:

∂z/∂x = 2(8) + 4(2) = 16 + 8 = 24

∂z/∂y = 4(8) + 6(8)(2) = 32 + 96 = 128

The linearized equation is given by:

z ≈ z₀ + ∂z/∂x * (x - x₀) + ∂z/∂y * (y - y₀)

Substituting the values, we get:

z ≈ z₀ + 24 * (x - 8) + 128 * (y - 2)

1.2. To find the error when using the linearized equation to calculate the value of z at x = 8, y = 2, we substitute these values:

z ≈ z₀ + 24 * (8 - 8) + 128 * (2 - 2)

= z₀

Therefore, the linearized equation gives the exact value of z at x = 8, y = 2, and the error is 0.

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The objective function in this scenario would be to maximize the exposure of Diamond Jeweler's while staying within their weekly advertising budget of $10,000.

The correct answer is (c) Maximize 7000T + 8500N + 3000R

Maximize 7000T + 8500N + 3000R where T represents the number of TV ads, N represents the number of newspaper ads, and R represents the number of radio ads. By maximizing the audience reached through each medium, Diamond Jeweler's can ensure that they are getting the most out of their advertising budget and reaching as many potential customers as possible.

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17. The matrix A for counterclockwise rotation through the angle π/2 about the origin in R^2 is:

A = [ 0 -1 ]

   [ 1  0 ]

The eigenvalues are complex conjugate pair λ = ±i, indicating that the matrix A represents a rotation by 90 degrees, which has no stretching or compressing effect on vectors. The eigenvectors are any non-zero vector in R^2.

19. The matrix A for orthogonal projection of R^2 onto the X2-axis is:

A = [ 0 0 ]

   [ 0 1 ]

The eigenvalues are λ1 = 0 and λ2 = 1, and the eigenvectors are [1 0]^T and [0 1]^T, respectively. The geometric meaning of the eigenvectors is that they represent the directions of the axes of the projection. The eigenvalue λ1 = 0 indicates that the matrix A collapses all vectors in the direction of the X1-axis to the origin, while leaving vectors in the direction of the X2-axis unchanged. This means that the projection matrix A reduces the dimension of the vector space from 2 to 1, projecting all vectors onto the X2-axis.

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Answer:

134.4

Step-by-step explanation:

134.4432966

Just find the Square Root of 18,075 (I punched it into my calculator.)

Answer:

-134.44 and 134.44.

Step-by-step explanation:

There are 2 numbers +/- √18,075

= +/- 134.44

Failure to include some units, or entire portions, of the defined survey population in the actual operational sample frame represents: a noncoverage error.

One of the components of coverage error that results from a flawed sample frame that excludes a certain percentage of the population is noncoverage.

Sampling errors need to be controlled and reduced to a level at which their presence does not defeat or obliterate the usefulness of the final sample results.

The difference between the observed values of a variable and the long-run average of the observed values in repetitions of the measurement is the sampling error.

Noncoverage, another word for these frames, inadequate coverage is also known as undercoverage.

Sampling errors can be decreased by increasing the sample size.

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Answer:

Step-by-step explanation:

a - 7 = 3(b + 2)

a - 7 = 3b + 2*3

a - 7 = 3b + 6           {Subtract 6 from both sides}

a - 7 - 6 = 3b

a - 13  = 3b         {Divide both sides by 3}

\(b =\frac{a-13}{3}\)

the equation of the normal plane to the curve at the point (0, 1, 3) is 2x + 6z - 18 = 0.

To find the equation of the normal plane, we first calculate the gradient vector of the curve at the given point. The gradient vector is obtained by taking the partial derivatives of the curve with respect to each variable: ∇r = (dx/dt, dy/dt, dz/dt) = (2cos(2t), 2sin(2t), 6).

At the point (0, 1, 3), the parameter t is 0. Therefore, the gradient vector at this point becomes ∇r = (2cos(0), 2sin(0), 6) = (2, 0, 6).

The normal vector of the plane is the same as the gradient vector, so the normal vector is (2, 0, 6). Since the normal vector represents the coefficients of x, y, and z in the equation of the plane, the equation of the normal plane becomes:

2(x - 0) + 0(y - 1) + 6(z - 3) = 0.

Simplifying the equation, we have:

2x + 6z - 18 = 0.

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Explanation:

There are 5 letters, so there would be 5! = 5*4*3*2*1 = 120 different permutations; however, there are 2 letter 'o's meaning we have double counted. To correct this, divide by 2 to get 120/2 = 60.

If there was a way to tell the two 'o's apart, then the answer would be 120.

The total number of ways the letter in the word "spoon" can be arranged is 120 and this can be determined by using the given data.

Given :

Word  --  Spoon

The following steps can be used in order to determine the total number of ways the letter in the word spoon is arranged:

Step 1 - According to the given data, the word is 'spoon'.

Step 2 - The total number of letters in the word 'spoon' is 5.

Step 3 - So, the total number of ways the letter in the word "spoon" can be arranged is:

\(= 5 \times 4\times 3\times 2 \times 1\)

Step 4 - Simplify the above expression.

= 120

Therefore, the correct option is D).

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Answer:

it's c the slop is 3 your welcome

Answer:

The equation of a circle centred at the origin is

with r² = 42.25 ( take the square root of both sides )

\(\rm\sf{r = 42.25}\) = \(\sf\red{6.5}\)

Answer:

I can help!

Step-by-step explanation:

Is the total length 85? and the small triangle 10? if that is then i can help.

Answer:

a. Letting m represent the number of additional miles driven, we have .35m.

b. Devon paid $43 for additional mileage.

Step-by-step explanation:

For part b: $421 - ($54 × 7)

= $421 - $378 = $43

The algebraic expression to represent the amount Devon paid for additional mileage only is 0.35m and Devon pays for additional mileage if he paid a total of $421 for the rental car is $43.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

During a long weekend, Devon paid a total of x dollars for a rental car so he could visit his family. He rented the car for 7 days at a rate of $54 per day.

For part (a):

Write an algebraic expression to represent the amount Devon paid for additional mileage only.

The amount Devon paid for additional mileage only = 0.35m

For part (b):

Devon pays for additional mileage if he paid a total of $421 for the car rental is:

= $421 - ($54 × 7)

= $43

Thus, the algebraic expression to represent the amount Devon paid for additional mileage only is 0.35m and Devon pays for additional mileage if he paid a total of $421 for the rental car is $43.

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The function composition exists an operation " ∘ " that brings two functions f and g, and has a function h = g ∘ f such that h(x) = g(f(x)).

Let the functions be f(x) = 4x² + 1 and g(x) = x² - 3

The correct answer is (f o g)(x) = 4x⁴ - 96x + 37 and

(g o f)(x) = 16x⁴ + 8x² - 2.

The function composition exists an operation " ∘ " that brings two functions f and g, and has a function h = g ∘ f such that h(x) = g(f(x)). In this operation, the function g exists used for the outcome of applying the function f to x.

Given:

f(x) = 4x² + 1 and g(x) = x² - 3

a) (f o g)(x) = f[g(x)]

f[g(x)] = 4(x² - 3)² + 1

substitute the value of g(x) in the above equation, and we get

    = 4(x⁴ - 24x + 9) + 1

simplifying the above equation

    = 4x⁴ - 96x + 36 + 1

    = 4x⁴ - 96x + 37

(f o g)(x) = 4x⁴ - 96x + 37

b) (g o f)(x) = g[f(x)]

substitute the value of g(x) in the above equation, and we get

g[f(x)] = (4x² + 1)²- 3

      = 16x⁴ + 8x² + 1 - 3

simplifying the above equation

      = 16x⁴ + 8x² - 2

(g o f)(x) = 16x⁴ + 8x² - 2.

Therefore, the correct answer is (f o g)(x) = 4x⁴ - 96x + 37 and

(g o f)(x) = 16x⁴ + 8x² - 2.

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Answer:

-11

Step-by-step explanation:

f(x)=-2x-5

Let x = 3

f(3) = -2 *3 -5

     = -6 -5

     = -11

Answer:

y = \(\frac{1}{2}\)

Step-by-step explanation:

Given y is inversely proportional to x then the equation relating them is

y = \(\frac{k}{x}\) ← k is the constant of variation

To find k use the condition y = 5 when x = 7, then

5 = \(\frac{k}{7}\) ( multiply both sides by 7 )

35 = k

y = \(\frac{35}{x}\) ← equation of variation

When x = 70, then

y = \(\frac{35}{70}\) = \(\frac{1}{2}\)

Answer:

The slope of the graph is 5, and the y-intercept is (0, -3).

Step-by-step explanation:

Let's start by finding the y-intercept.

The y-intercept is the point where the line intercepts the y-axis.

Looking at the graph, we can determine that the y-intercept is (0, -3).

The slope of a graph can be found using two points on the line.

Let's use (0, -3) and (1, 2):

\(Slope=\frac{Rise}{Run}=\frac{y_2-y_1}{x_2-x_1}=\frac{2-(-3)}{1-0}=\frac{5}{1}=5\)

Therefore the slope of the graph is 5, and the y-intercept is (0, -3).

Step-by-step explanation:

(+4)+(-7)

=4-7

=-3

Hope it will help you..

Answer:

The answer choice is D.

Step-by-step explanation:

Multiply 5 and 8

= 40

Then put d to 40

=40d

And also multiply 6 with 5

which equals to 30.

Now the expression would be: 40d + 30

Answer:

Step-by-step explanation: i think in my own word x+3<12 is A because it said julie only 3 notebook togerther it make itt less than 12notebook

a) The probability that a battery lasts more than four hours can be calculated by converting four hours (240 minutes) into a standard score and finding the area under the normal distribution curve to the right of that score.

First, we calculate the z-score using the formula:

z = (x - μ) / σ

where x is the value (240 minutes), μ is the mean (265 minutes), and σ is the standard deviation (50 minutes).

z = (240 - 265) / 50

z = -0.5

Next, we look up the corresponding area under the normal distribution curve for a z-score of -0.5. This can be found using a standard normal distribution table or a calculator. The area to the right of -0.5 is equal to the area to the left of 0.5, which is approximately 0.3085.

Therefore, the probability that a battery lasts more than four hours is 1 - 0.3085 = 0.6915, which rounds to 0.692.

The probability that a battery in a laptop computer lasts more than four hours is approximately 0.692.

b) To find the quartiles of battery life, we need to calculate the values corresponding to the 25th and 75th percentiles of the normal distribution.

The 25th percentile corresponds to a z-score of -0.674. We can use the formula mentioned earlier to calculate the value:

x = μ + (z * σ)

x = 265 + (-0.674 * 50)

x = 231.3

Therefore, the 25th percentile value (Q1) is approximately 231 minutes.

The 75th percentile corresponds to a z-score of 0.674. Again, using the formula:

x = μ + (z * σ)

x = 265 + (0.674 * 50)

x = 298.7

Therefore, the 75th percentile value (Q3) is approximately 299 minutes.

The quartiles of battery life in a laptop computer are 231 minutes (Q1) and 299 minutes (Q3), rounded to the nearest integer.

c) To find the value of battery life in minutes that is exceeded with 95% probability, we need to find the z-score that corresponds to a cumulative probability of 0.95.

Using a standard normal distribution table or a calculator, we find that the z-score corresponding to a cumulative probability of 0.95 is approximately 1.645.

Using the formula mentioned earlier, we can calculate the value:

x = μ + (z * σ)

x = 265 + (1.645 * 50)

x = 344.25

Therefore, the value of battery life in minutes that is exceeded with 95% probability is approximately 344 minutes.

With 95% probability, the battery life in a laptop computer exceeds approximately 344 minutes.

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Answer:

80.2

Step-by-step explanation:

Answer:80.2

Step-by-step explanation:

i did the test so yeh edg 2023

Answer:

49 +1 =50 is the answer you are looking for

To find out the percent change in profit between the two years, you need to use the percent change formula, which is given as: Percentage Change = (New Value − Old Value) / Old Value × 100Where Old Value = Profit of the previous year = birr 880,000New Value = Profit of this year = birr 970,000Now we will substitute these values in the formula and solve for the percentage change:

Percentage Change = (New Value − Old Value) / Old Value × 100Percentage Change = (970,000 − 880,000) / 880,000 × 100Percentage Change = 90,000 / 880,000 × 100Percentage Change = 0.102 × 100Percentage Change = 10.2%Therefore, the percentage change in profit between the two years is 10.2%. The company earned 10.2% more profit this year than last year.

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The probability of coffee or cookies is 0.456, and the probability of tea given that it contains mugs is 0.727.

The probability of an event occurring is the number of successful outcomes divided by the total number of possible outcomes. In this case, we are asked to find the probability of two different combinations: coffee or cookies, and tea given that it contains mugs.

Part 1 of 3:

(a) Coffee or cookies

To find the probability of coffee or cookies, we need to add the probability of coffee and the probability of cookies, and then subtract the probability of both occurring. The probability of coffee is 16/79, and the probability of cookies is 20/79.

The probability of both occurring is 0, since there are no gift baskets that contain both coffee and cookies. So, the probability of coffee or cookies is:

P(coffee or cookies) = P(coffee) + P(cookies) - P(coffee and cookies)
P(coffee or cookies) = 16/79 + 20/79 - 0
P(coffee or cookies) = 36/79
P(coffee or cookies) ≈ 0.456

Part 2 of 3:

(b) Tea, given that it contains mugs

To find the probability of tea given that it contains mugs, we need to use the formula for conditional probability:

P(A|B) = P(A and B)/P(B)
In this case, A is the event of tea, and B is the event of mugs. The probability of tea and mugs is 16/79, and the probability of mugs is 22/79. So, the probability of tea given that it contains mugs is:

P(tea| mugs) = P(tea and mugs)/P(mugs)
P(tea| mugs) = (16/79)/(22/79)
P(tea| mugs) = 16/22
P(tea| mugs) = 8/11
P(tea| mugs) ≈ 0.727

Therefore, the probability of coffee or cookies is 0.456, and the probability of tea given that it contains mugs is 0.727.

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Answer:

Step-by-step explanation:

28