power companies severely trim trees growing near their lines to avoid power failures due to falling limbs in storms. applying a chemical to slow the growth of the trees is cheaper than trimming, but the chemical kills some of the trees. suppose that one such chemical would kill 20% of sycamore trees. the power company tests the chemical on 250 sycamores. consider these an srs from the population of all sycamore trees. what is the standard deviation?

population at 1992 = 3590

Population after Seven years (1999) = 4500

Given two points (t1, P1) and (t2, P2), the slope of the line m can be found.

p1 = (1992, 3590) and p2 = (1999, 4500)

m= ΔP/Δt

m= ((4500-3590))/((1999-1992))

m = 910/7

m=130 is the slope

The linear population function P(t) is

P(t)=130t + P0

Find the Y-Intercept P0

The population function P(t) is measured since the year 1990, year zero. The first moose population was measured in 1992, one year later. This provides an initial condition P (1) = 4500.

P (1) =130 (1) + P0 = 4500

P0 = 4370

P(t)=20t+4630

The moose population P(t) changes linearly year after year. The population function P(t) is measured in terms of t years since 1990.

t= 1990, P (0) =4370

t =1992, P (1) =130 (1) + 4370 = 4500 matches data

t=1999, P (2) = 130(2) + 4370 = 4630

t=2006, P (3) = 130(3) + 4370 = 4760

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Here's a Scheme function that checks whether a matrix is symmetric or not:

```scheme

(define (is-symmetric-matrix matrix)

 (define (get-element matrix i j)

   (if (null? matrix)

       #f

       (if (= i 0)

           (if (null? (car matrix))

               #f

               (if (= j 0)

                   (car (car matrix))

                   (get-element (cdr matrix) i (- j 1))))

           (get-element (cdr matrix) (- i 1) j))))

 (define (is-matrix-symmetric-helper matrix i j)

   (if (null? matrix)

       #t

       (if (equal? (get-element matrix i j)

                   (get-element matrix j i))

           (is-matrix-symmetric-helper matrix i (+ j 1))

           #f)))

 (if (null? matrix)

     #t

     (is-matrix-symmetric-helper matrix 0 0)))

```

The function `is-symmetric-matrix` takes a matrix as an input, which is represented as a list of lists. It uses a helper function called `is-matrix-symmetric-helper` to compare each element of the matrix with its corresponding element in the transposed position. The `get-element` function is used to retrieve the element at position `(i, j)` in the matrix.

The `is-matrix-symmetric-helper` function recursively iterates over the matrix, comparing each element with its transposed element. If any pair of corresponding elements is found to be different, it immediately returns `#f` (False), indicating that the matrix is not symmetric. If it reaches the end of the matrix without finding any differences, it returns `#t` (True), indicating that the matrix is symmetric.

Finally, the main `is-symmetric-matrix` function first checks if the matrix is empty. If it is, it immediately returns `#t` since an empty matrix is considered symmetric. Otherwise, it calls the helper function with the initial indices `(0, 0)` and returns its result.

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Answer:

87

Step-by-step explanation:

1x0=97x1x0xratio=87

The decision variables of a model are also known as the controllable inputs. The correct answer is B.

Decision variables are parameters used in the formulation of a mathematical model to depict, in mathematical terms, an entity's objectives or constraints.

These variables are critical in modeling and optimization because they are the inputs that can be varied or altered to enhance system output or performance.

Controllable inputs are variables that the modeler can manage or manipulate. In a mathematical or quantitative model, these variables are used to optimize the output or performance of the model. They are also called decision variables because they reflect a modeler's choices and can be altered to improve the model's output or performance.

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Answer:

Step-by-step explanation:

To find the volume of the composite figure, we need to find the volumes of the half-sphere and the cylinder separately, and then add them together.

The volume of the half-sphere is given by the formula:

V_half_sphere = (2/3)πr^3

where r is the radius of the half-sphere. In this case, the radius is 3 cm, so we have:

V_half_sphere = (2/3)π(3)^3

V_half_sphere = (2/3)π(27)

V_half_sphere = 18π

The volume of the cylinder is given by the formula:

V_cylinder = πr^2h

where r is the radius of the base of the cylinder, h is the height of the cylinder. In this case, the radius is 3 cm and the height is 10 cm, so we have:

V_cylinder = π(3)^2(10)

V_cylinder = 90π

To find the volume of the composite figure, we add the volumes of the half-sphere and the cylinder:

V_composite = V_half_sphere + V_cylinder

V_composite = 18π + 90π

V_composite = 108π

Therefore, the exact volume of the composite figure is 108π cubic centimeters.

Answer:

LIke ummmm

Step-by-step explanation:

soo like maybe umm like umm  she has 10 dollars worth of nickles and 1.60 dollars worth of quarters

Answer:

Emma has $50.40 worth of quarters

The factor that does NOT control the stability of a slope is the angle of repose for intact bedrock. The angle of repose refers to the steepest angle at which a pile of loose material remains stable without sliding. It is mainly applicable to loose materials like soil and granular substances, not intact bedrock.

Bedrock stability depends on factors such as its strength, fracturing, and geological properties, rather than the angle of repose. Factors that control the stability of a slope include whether the slope is rock or soil. Rock slopes tend to be more stable than soil slopes due to the cohesive nature of intact rock.

The amount of water in the soil also affects slope stability, as excessive water can increase pore pressure and reduce the shear strength of the soil, leading to slope failure. Additionally, the orientation of fractures, cleavage, and bedding in the rock can influence slope stability by creating planes of weakness or strength.

To summarize, while the angle of repose is a significant factor in slope stability, it is not applicable to intact bedrock. The stability of a slope is influenced by the type of material (rock or soil), the presence of water, and the orientation of fractures and bedding.

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Step-by-step explanation:

lateral surface area here = πrl

r = 10

l = √h²+r²= √ 24²+ 10² = 26

lateral surface area = 10 × 26 × π

= 260π in²

hope this will be helpful to you .

plz mark my answer as brainlist if you find it useful.

Answer:

The lateral area of cone is 260π in².

Step-by-step explanation:

\(\begin{gathered}\end{gathered}\)

\(\begin{gathered}\end{gathered}\)

\(\star{\underline{\boxed{\sf{\purple{\ell = \sqrt{{(r)}^{2} + {(h)}^{2}}}}}}}\)

\(\star{\underline{\boxed{\sf{\purple{La_{(Cone)}= \pi r\ell}}}}}\)

\(\begin{gathered}\end{gathered}\)

Finding the slant height of cone by substituting the values in the formula :

\(\begin{gathered} \qquad{\longrightarrow{\sf{\ell = \sqrt{{(r)}^{2} + {(h)}^{2}}}}}\\\\\qquad{\longrightarrow{\sf{\ell = \sqrt{{(10)}^{2} + {(24)}^{2}}}}}\\\\\qquad{\longrightarrow{\sf{\ell = \sqrt{{(10 \times 10)} + {(24 \times 24)}}}}}\\\\\quad{\longrightarrow{\sf{\ell = \sqrt{(100)+(576)}}}}\\\\\qquad{\longrightarrow{\sf{\ell = \sqrt{100 + 576}}}}\\\\\quad{\longrightarrow{\sf{\ell = \sqrt{676}}}}\\\\\quad{\longrightarrow{\sf{\ell = 26 \: in}}}\\\\\quad\star\underline{\boxed{\sf{\pink{\ell = 26 \: in}}}} \end{gathered}\)

Hence, the slant height of cone is 26 in.

\(\begin{gathered}\end{gathered}\)

Now, finding the lateral area of cone by substituting the values in the formula :

\(\begin{gathered} \qquad{\longrightarrow{\sf{La_{(Cone)} = \pi r \ell}}}\\\\\qquad{\longrightarrow{\sf{La_{(Cone)} = \pi \times 10 \times 26}}}\\\\\qquad{\longrightarrow{\sf{La_{(Cone)} = \pi \times 260}}}\\\\\qquad{\longrightarrow{\sf{La_{(Cone)} = 260\pi\: {in}^{2}}}}\\\\ \qquad{\star{\underline{\boxed{\sf{\pink{La_{(Cone)} = 260\pi \: {in}^{2}}}}}}}\end{gathered}\)

Therefore, the lateral area of cone is 260π in².

\(\rule{300}{2.5}\)

It takes approximately 1.2 minutes to move the cans to the storage area when both conveyor belts are used.

We can begin the problem by using the formula:

work = rate x time

Let's denote the rate of the first belt as R1 and the rate of the second belt as R2. Then, we can write:

R1 = 200 pounds / 2 minutes = 100 pounds per minute

R2 = 200 pounds / 3 minutes ≈ 66.67 pounds per minute

When both belts are used, they work together to move the same 200 pounds of cans. Therefore, we can add their rates to get the total rate:

R = R1 + R2 = 100 + 66.67 = 166.67 pounds per minute

To find the time it takes to move the cans to the storage area, we can rearrange the formula:

time = work / rate

The total work is 200 pounds, so we have:

time = 200 pounds / 166.67 pounds per minute ≈ 1.2 minutes

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Estimation involves using a convenient value, close to the actual value, for calculations; especially in the absence of a calculator. The estimated number of gallons she needs to get to the station is 3 gallons.

Given that:

\(Speed= 70mph\)

\(Time = 1.25hr\) ---- equivalent of 1hr 15mins

\(Rate = 30 m/gallon\)

First, she will need to estimate the distance she can cover using:

\(Distance= Speed \times Time\)

An estimate of the calculation is:

\(Distance= 70mph \times 1.5 = 105m\)

The number of gallons is then estimated as follows:

\(Gallons = D ista nce\div Rate\)

Because the estimated distance is 105 m; she can use 35 as an estimate the rate of miles per gallon; instead of 30

\(Gallons = 105m \div 35m/gallon\)

\(Gallons = 3gallon\)

So, the estimated number of gallons she needs is 3 gallons.

We can check if the estimate is true or close by calculating the actual values.

\(Distance= Speed \times Time\)

\(D i s t a n c e= 70mph \times 1.25hr=87.5m\)

\(Gallons = D ista nce\div Rate\)

\(Gallons = 87.5m \div 30m/gallon =2.92m\)

Hence, the estimated number of gallons she needs to get to the station is 3 gallons.

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Answer:

k = 2

Step-by-step explanation:

Slope Formula: \(m=\frac{y_2-y_1}{x_2-x_1}\)

Step 1: Replace variables

\(\frac{(k+3)-2}{3+1} =\frac{3}{4}\)

Step 2: Combine like terms

\(\frac{k+1}{4} =\frac{3}{4}\)

Step 3: Solve for k

k + 1 = 3

k = 2

Answer:

k=2

Step-by-step explanation:

The slope is 3/4

The slope formula is (y1-y2)/(x1-x2)

We can plug the values in

(2-k-3)/(-1-3)=3/4

Combine like terms

(-1-k)/-4=3/4

Cross multiply

-12= -4 - 4k

-8=-4k

k=2

Hope this helps!

Answer:

x=17 degrees

Step-by-step explanation:

All 3 angles = 180 degrees

So 90 + 54 + (x+19) = 180

Combine like terms

163 + x = 180

Subtract 163 from both sides

x = 180-163

x = 17

There are 9,880 possible ways to award the gold, silver, and bronze medals to the top three runners in a group of 40 people.

In this scenario, we are trying to determine the number of ways that three runners can be chosen from a group of 40 people to receive gold, silver, and bronze medals. This is an example of a combination problem.

A combination is a way of selecting items from a larger set where the order in which they are selected does not matter. In this case, we are choosing three runners out of a group of 40, and the order in which they finish the race is not important. We just need to determine which three runners will receive the top three medals.

To calculate the number of possible combinations of three runners from a group of 40, we use the formula for combinations:

C(n, r) = n! / (r! * (n-r)!),

where n represents the total number of items and r is the number of items being selected. In this case, we have n = 40 and r = 3:

C(40, 3) = 40! / (3! * (40-3)!) = 403938 / (321) = 9880

Therefore, there are 9,880 possible ways to award the gold, silver, and bronze medals to the top three runners in a group of 40 people.

In summary, when we are selecting a group of items from a larger set and the order in which they are selected does not matter, we can use the combination formula to determine the number of possible combinations. In this particular scenario, we found that there are 9,880 possible combinations of three runners who could receive the gold, silver, and bronze medals in a group of 40 people.

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The arrangement of the lengths from the least to greatest is;

CF < FD <  CE < EF < CF < CD

The arrangement of side lengths of the triangle is calculated by applying the following formula as follows;

The greater the angle opposite to side length of a triangle, the greater the measure of the side length.

angle opposite CE = 180 - ( 54 + 75 ) = 51⁰

angle opposite CD = 180 - 51⁰ = 129⁰

angle opposite FD = 180 - (22 + 129) = 29⁰

The arrangement of the lengths from the least to greatest is;

CF < FD <  CE < EF < CF < CD

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The mean of a observed values approaches the population mean more and more as the number of data points gathered rises.

The average calculated from the group members, distribution, or population is known as the population mean.

Thus, choose a population with a finite mean and a random sample of observations. The mean of a observed values approaches the population mean to a greater extent as the number of data gathered rises.

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37.

Add all the distances .

3/4 + 1/2 + 2/3 + 3/4 = 8/3 miles

To add fractions you need equal bottom numbers

find the LCM ( Least common multiple of the denominators )

4 , 2 , 3 , 4 = LCM = 12

Multiply each fraction by the same numerator and denominator, to obtain 12 as a bottom number

(3/4 * 3/3) + (1/2 * 6/6) + (2/3 * 4/4) + (3/4 * 3/3)

9/12 + 6/12 + 8/12 + 9/12

Now that all fractions have the same denominator ( bottom number) you can add them.

Add the numerators ( top numbers ) and put 12 as a denominator.

(9 + 6 + 8 + 9 ) / 12 = 32/12

Simplify ( divide both numbers by 4 )

32/12 = 8/3

Answer:

how many bags are there?

Step-by-step explanation:

Answer $100 each

Step-by-step explanation:

2500/25

Answer:  2500/25

Each member pays $100

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

Explanation:

The slash symbol means division. It's the same as saying 2500 ÷ 25

The expression 2500/25 simplifies to 100, which means that each member must pay $100. If you had 25 members paying $100 each, then 25*100 = 2500 dollars is the total amount of money paid.

So in short, you divide the total cost over the number of members.

If the variables "r" and "s" are inversely proportional and r=7 when s=6 , then when r = 10 , value of "s" will be 4.2 .

When the two variables are inversely proportional, their product is constant. That means, for two variables "r" and "s" , the it is represented in equation as :

⇒ r × s = k, where k is a constant ;

the value of variable "r" = 7 when s = 6,

First , we have to find the value of k:

⇒ k = r × s = 7 × 6 = 42 ;

So, for any value of r and s, the product "rs" will always be equal to 42.

When r = 10, we can use the equation to find s:

⇒ s = k/r = 42/10 = 4.2

Therefore , when r = 10 , the variable "s" is 4.2.

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There are 134596 ways to distribute 24 slices between 6 people

Since pizza slices are the same hence order doesn't matter and also people are distinct so it is a case of combination.

Combination in mathematics is a way of choosing or distributing selected items from a list of the total set with distinct values. It is used when there is no repetition and order doesn't matter. It can also be depicted as permutation/r!

combination = nCr =n!/(r!(n-r!)

where n is the total number of objects

r is the number of chosen objects from the total.

Now, 24c6=24!/6!18!

=24x23x22x21x20x19x18!/6!18!

=24x23x22x21x20x19/6x5x4x3x2x1

=134596

Therefore, There are 134596 ways to distribute 24 slices between 6 people

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The linear model that represents the cost of any number of candy bars can be written as: C = $1.90B + $0.95

To write the linear model that models the cost of any number of candy bars, we need to find the equation of a line that best fits the given data points. We'll use the variables B for the number of candy bars purchased and C for the total cost of the candy bars.

Looking at the given data, we can see that there is a linear relationship between the number of candy bars and the total cost. As the number of candy bars increases, the total cost also increases.

To find the equation of the line, we need to determine the slope and the y-intercept. We can use the formula for the equation of a line: y = mx + b, where m is the slope and b is the y-intercept.

First, let's find the slope (m) using two points from the given data, for example, (3, $6.65) and (25, $48.45):

m = (C2 - C1) / (B2 - B1)

 = ($48.45 - $6.65) / (25 - 3)

 = $41.80 / 22

 ≈ $1.90

Now, let's find the y-intercept (b) using one of the data points, for example, (3, $6.65):

b = C - mB

 = $6.65 - ($1.90 * 3)

 = $6.65 - $5.70

 ≈ $0.95

Therefore, the linear model that represents the cost of any number of candy bars can be written as:

C = $1.90B + $0.95

This equation represents a linear relationship between the number of candy bars (B) and the total cost (C). For any given value of B, you can substitute it into the equation to find the corresponding estimated total cost of the candy bars.

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Answer:

  $0.57 per bun

  1 3/4 buns per dollar

Step-by-step explanation:

You have a price given as $2 for 3 1/2 buns and want to know the associated unit rate.

The unit rate of A per B is found by dividing the A quantity by the B quantity. This tells you the amount of A you get for 1 unit of B.

When two numbers are given and a "unit rate" asked for, it is not always clear which of the numbers is the A quantity, and which is the B quantity. The unit rate can be figured either way:

  dollars per bun = ($2)/(3 1/2 buns) = 4/7 dollars per bun ≈ $0.57 /bun

  buns per dollar = (3 1/2 buns)/($2) = 1 3/4 buns per dollar

__

Additional comment

Where time is involved, we often want the rate specified as per unit time.

Where money is involved, we often want the rate specified as currency per unit of item (dollars per bun). This helps us compare costs.

Rates with the units reversed can be just as useful for comparing costs or times: 1 3/4 buns per dollar is a better value than 1 1/3 buns per dollar, for example.

Sometimes, rates must be inverted to be useful in a given problem. A typical case is the "working together" problem, where rates are often given in terms of completion time per project. The "working together" rates can only be added in terms of projects per time, the inverse of the given rates.

The area of the square sandbox is 1,296 square inches

The area of a square is the measure of the space or surface occupied by it. It is equal to the product of the length of its two sides. Since the area of a square is the product of its two sides, the unit of the area is given in square units.

Area of a square = Side × Side

                            =  \(Side ^{2}\)

According to the question

Side of a square sandbox =  36 inches

Therefore,

The area of the square sandbox =  \(Side ^{2}\)

                                                      =  \((36)^{2}\)

                                                      =  1,296 square inches

Hence, the area of the square sandbox is 1,296 square inches

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The z-score for P(? ≤ z ≤ ?) = 0.60 is approximately 0.25.

The z-score for P(z ≥ ?) = 0.30 is approximately -0.52.

How to find the Z score

P(Z ≤ z) = 0.60

We can use a standard normal distribution table or a calculator to find that the z-score corresponding to a cumulative probability of 0.60 is approximately 0.25.

Therefore, the z-score for P(? ≤ z ≤ ?) = 0.60 is approximately 0.25.

For the second question:

We want to find the z-score such that the area under the standard normal distribution curve to the right of z is 0.30. In other words:

P(Z ≥ z) = 0.30

Using a standard normal distribution table or calculator, we can find that the z-score corresponding to a cumulative probability of 0.30 is approximately -0.52 (since we want the area to the right of z, we take the negative of the z-score).

Therefore, the z-score for P(z ≥ ?) = 0.30 is approximately -0.52.

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(a) The utility function U(x, y) = x²y is homogeneous of degree 3 because if we multiply both x and y by a positive constant λ, the utility function becomes U(λx, λy) = (λx)²(λy) = λ³x²y. The function exhibits a degree of homogeneity equal to the exponent of λ, which in this case is 3.

(b) The budget constraint can be derived by equating the total expenditure to the agent's income. The price of good 1 is 4, so the expenditure on good 1 is 4x, and the price of good 2 is 2, so the expenditure on good 2 is 2y. Therefore, the budget constraint is given by 4x + 2y = 12. To graph this constraint, we plot x on the horizontal axis and y on the vertical axis. The resulting line has a slope of -2 and intersects the x-axis at x = 3 and the y-axis at y = 6.

(c) To compute the marginal utility of good 1, we take the derivative of the utility function with respect to x, which gives us MU₁(x, y) = 2xy. Similarly, the marginal utility of good 2 is given by MU₂(x, y) = x².

(d) The agent's marginal rate of substitution (MRS) represents the rate at which the agent is willing to trade one good for another while maintaining the same level of utility. It is given by MRS = MU₁/MU₂ = 2xy/(x²) = 2y/x. The slope of the budget constraint is equal to the negative ratio of the prices of the two goods, which is -4/2 = -2.

(e) To derive the agent's optimal consumption bundle, we need to find the combination of x and y that maximizes the agent's utility while satisfying the budget constraint. This occurs at the point where the indifference curve (representing constant utility) is tangent to the budget constraint. In this case, the indifference curve is U(x, y) = x²y, and the optimal consumption bundle can be found by solving the system of equations formed by the utility function and the budget constraint. The resulting bundle will depend on the specific values of x and y obtained. By plotting the bundle on the (x, y) plane along with the budget constraint and an indifference curve, we can visually represent the optimal consumption bundle. The slope of the budget constraint represents the rate at which the agent can trade one good for another while staying within the budget constraint.

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