Hillsdale Orchard grows Fuji apples and Gala apples. There are 160 Fuji apple trees and 120 Gala apple trees in the orchard.


Hillsdale Orchard's owners decide to plant 30 new Gala apple trees. Complete the ratio table (click for help) to find the number of new Fuji apple trees the owners should plant if they want to maintain the same ratio of Fuji apple trees to Gala apple trees

the complex solutions of 3x^2+3x+7=0 can be found using the quadratic formula. The quadratic formula is:
x = (-b ± sqrt(b^2 - 4ac)) / 2a where a, b, and c are the coefficients of the quadratic equation.

In this case, a=3, b=3, and c=7. Substituting these values into the quadratic formula, we get:
x = (-3 ± sqrt(3^2 - 4(3)(7))) / 2(3)
Simplifying this expression, we get:
x = (-3 ± sqrt(-51)) / 6

Since the square root of a negative number is an imaginary number, we can write this solution in terms of complex numbers. Therefore, the complex solutions of the equation 3x^2+3x+7=0 are:
x = (-3 + i√51) / 6, (-3 - i√51) / 6

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Answer:

Solution: 48

Step-by-step explanation:

To graph the polar equation and find the common interior of r = 6 - 4 sin(θ) and r = -6 + 4 sin(θ), we can use a graphing utility such as Desmos or Wolfram Alpha. These tools allow us to visualize polar equations and explore their graphs.

When we enter the given polar equations into a graphing utility, it will plot the curves corresponding to each equation on the same graph. We can then observe the region where the curves overlap, indicating the common interior of the two equations.

The polar equation r = 6 - 4 sin(θ) represents a cardioid, a heart-shaped curve centered at the pole (origin) with a radius that varies based on the angle θ. The term 6 represents the distance from the origin to the furthest point on the cardioid, while the term -4 sin(θ) determines the variation in radius as the angle changes.

Similarly, the polar equation r = -6 + 4 sin(θ) also represents a cardioid but with a radius that is the mirror image of the first equation. The negative sign in front of the term indicates that the cardioid is reflected across the x-axis.

Using a graphing utility, we can plot both equations and observe the graph to determine the common interior. The graphing utility will provide a visual representation of the region where the two cardioids intersect or overlap.

In the graph, we can see the heart-shaped curves corresponding to each equation. The cardioids intersect in two regions, forming a figure-eight shape. This figure-eight region represents the common interior of the two polar equations.

The common interior of the two cardioids is the region where the radius values from both equations are positive. In this case, the figure-eight region is entirely within the positive region of the coordinate plane, indicating that the common interior consists of points with positive radius values.

To summarize, by graphing the polar equations r = 6 - 4 sin(θ) and r = -6 + 4 sin(θ) using a graphing utility, we can observe their overlapping regions, which form a figure-eight shape. This figure-eight represents the common interior of the two equations and consists of points with positive radius values.

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Answer:

don't help they are doing a test.

Step-by-step explanation:

The two numbers are not in the domain of fºg is x= 0 , x = -5

What is function ?

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

a mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).

A function is a type of rule that produces one output for a single input. Source of the image: Alex Federspiel. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would state that y is a function of x.

f o g is composite function, y values of g passed as x values into f.

f o g = 1/(x² + 5x)

in this case, the only way for the function to be undefined is when

x²+5x = 0

x(x + 5) = 0

x = 0 or x = -5

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The population of a district in 2005 was 35,700 with a continuous annual growth rate of approximately 4%. the population in 2030 will be approximately 97,209 according to the exponential growth function.

The formula for the continuous exponential growth is given by the formula:

P = Pe^(rt)

where,P is the population in the future.

P0 is the initial population.

t is the time.

r is the continuous interest rate expressed as a decimal.

e is a constant equal to approximately 2.71828.In this problem, the initial population P0 is 35,700. The rate r is 4% or 0.04 expressed as a decimal. We want to find the population in 2030, which is 25 years after 2005.

Therefore, t = 25.We will now use the formula:

P = Pe^(rt)P = 35,700e^(0.04 × 25)P = 35,700e^(1)P = 35,700 × 2.71828P = 97,209.09.

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Answer: I got 97,042.7

Step-by-step explanation:

Answer: she must sell 6 large photos and 6 small photos

Step-by-step explanation: and how I knew that is I multiplied 6 40 times and that gives you 240 and if you multiply 6 ten times that gives you 60 so 240 plus 60 is $300

A point is on a line if the point is given by the equation or function of the line

The set of coordinates that is located on the line segment IK is (6 ,4)

C.) (6, 4)

Reason:

Coordinates of point I = (4, 4)

Coordinates of point K = (8, 4)

Given that the y-coordinate value of the two points on the line IK are the same, (both 4) the line IK is an horizontal line and the coordinate of a point on IK should have a y-value of 4

Therefore, the correct option is the point (6, 4)

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The number of cubes that will fit into the shoebox is 40 cubes

Volume is the measure of a substance an object contains

Volume of the box = length * width * height

Volume of the box = 5/4 * 1 * 1/2
Volume of the box = 5/8cubic unit

Determine the volume of the box

Volume of the box = l³

Volume of the box = (1/4)³ = 1/64 cubic units

Number of cubes = (5/8)/(1/64)
Number of cubes = 5/8 * 64/1
Number of cubes = 5 * 8
Number of cubes = 40 cubes

Hence the number of cubes that will fit into the shoebox is 40 cubes

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Answer:

Is it C?

Step-by-step explanation

Both functions decrease at (-1, 2)

The complete question is added as an attachment

The polynomial function f(x) is represented by the graph.

From the graph, the polynomial function decreases at (-2, 2)

The absolute function is given as;

f(x) = =5|x + 1| + 10

The vertex of the above function is

Vertex = (-1, 10)

Because a is negative (a= -5), the vertex is a maximum.

This means that the function decreases at (-1, ∞)

So, we have

(-2, 2) and (-1, ∞)

Combine both intervals

(-1, 2)

This means that both functions decrease at (-1, 2)

See attachment 2 for the number line that represents the interval where both functions are decreasing

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Answer: 13

Explanation: To find the degree of a monomial, we need to take

the sum of the exponents of all the variables in the monomial.

So the degree of this monomial is 7 + 6 or 13.

So the degree of this monomial is 13.

Answer:

The radius (r) of a soccer ball with a volume of 288 cm3 is 6 cm.

The general solution in both vector and scalar form is as follows:

Vector form:

\(\[\mathbf{x} = c_1\mathbf{v}_1e^{\lambda_1t} + c_2\mathbf{v}_2e^{\lambda_2t}\]\)

Scalar form:

\(\[\begin{aligned}x &= c_1v_{11}e^{\lambda_1t} + c_2v_{21}e^{\lambda_2t} \\y &= c_1v_{12}e^{\lambda_1t} + c_2v_{22}e^{\lambda_2t}\end{aligned}\]\)

What are eigenvalues?

Eigenvalues are a concept in linear algebra that are used to analyze the properties of linear transformations or matrices. In simple terms, eigenvalues represent the scaling factors by which a vector is stretched or compressed when it is transformed by a linear transformation or multiplied by a matrix.

To find the general solution for the given system of differential equations:

\(\[\begin{aligned}x' &= -6x + 5y \\y' &= -5x - 4y\end{aligned}\]\)

We can rewrite the system in matrix form as follows:

\(\[\mathbf{x'} = \begin{bmatrix} -6 & 5 \\ -5 & -4 \end{bmatrix} \mathbf{x}\]\)

where \($\mathbf{x} = \begin{bmatrix} x \\ y \end{bmatrix}$.\)

To find the general solution, we need to find the eigenvalues and eigenvectors of the coefficient matrix\($\begin{bmatrix} -6 & 5 \\ -5 & -4 \end{bmatrix}$.\)

The characteristic equation is given by:

\(\[\det(\mathbf{A} - \lambda \mathbf{I}) = 0\]\)

where \($\mathbf{A}$\) is the coefficient matrix,\($\lambda$\)is the eigenvalue, and \($\mathbf{I}$\)is the identity matrix.

Substituting the values, we have:

\(\[\begin{aligned}\det \begin{pmatrix} -6-\lambda & 5 \\ -5 & -4-\lambda \end{pmatrix} &= 0 \\(-6-\lambda)(-4-\lambda) - (5)(-5) &= 0 \\\lambda^2 + 10\lambda + 6 &= 0\end{aligned}\]\)

Solving this quadratic equation, we find the eigenvalues \(\lambda_1$ and $\lambda_2$.\left \{ {{y=2} \atop {x=2}} \right.\)

Once we have the eigenvalues, we can find the corresponding eigenvectors\($\mathbf{v}_1$ and $\mathbf{v}_2$\) by solving the equation:

\(\[(\mathbf{A}-\lambda\mathbf{I})\mathbf{v} = 0\]\)

Substituting the eigenvalues, we solve for the eigenvectors.

Let's denote the eigenvalues as \(\lambda_1$ and $\lambda_2$,\) and the corresponding eigenvectors as \(\mathbf{v}_1$ and $\mathbf{v}_2$.\)

Once we have the eigenvalues and eigenvectors, we can express the general solution in both vector and scalar form as follows:

Vector form:

\(\[\mathbf{x} = c_1\mathbf{v}_1e^{\lambda_1t} + c_2\mathbf{v}_2e^{\lambda_2t}\]\)

Scalar form:

\(\[\begin{aligned}x &= c_1v_{11}e^{\lambda_1t} + c_2v_{21}e^{\lambda_2t} \\y &= c_1v_{12}e^{\lambda_1t} + c_2v_{22}e^{\lambda_2t}\end{aligned}\]\)

wherec_1 andc_2 are arbitrary constants\(, $v_{ij}$\) that represent the \(i$-th\)component of the jth eigenvector and \($e^{\lambda_it}$\) represent the exponential term with the eigenvalue.

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If the columns of A are linearly independent, then R must be invertible.

To show that if the columns of A are linearly independent, then R must be invertible, we'll use the given information A = QR, where Q is an m x n matrix, and R is an n x n matrix.

1: Since the columns of A are linearly independent, we know that the rank of matrix A is equal to n. The rank of a matrix is the maximum number of linearly independent columns.

2: Since A = QR, we also know that the rank of A is equal to the minimum of the ranks of Q and R (rank(A) = min(rank(Q), rank(R))).

3: As we established in Step 1, the rank of A is n. So, we have min(rank(Q), rank(R)) = n.

4: Since R is an n x n matrix, the maximum rank it can have is n. So, to satisfy the equation in Step 3, we must have rank(R) = n.

5: A square matrix (like R) is invertible if and only if its rank is equal to its size (number of rows or columns). Since R is an n x n matrix and we have established that rank(R) = n, R must be invertible.

In conclusion, if the columns of A are linearly independent, then R must be invertible.

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The component form of the sum of u and v with direction angles is u + v = (10√2 - 50)i + 10√2 j.

We are given the magnitudes and direction angles of vectors u and v. We need to find the component form of their sum.

Let's first convert the given magnitudes and direction angles to their corresponding components. For vector u:

|u| = 20, θu = 45°

The x-component of u is given by:

ux = |u| cos(θu) = 20 cos(45°) = 10√2

The y-component of u is given by:

uy = |u| sin(θu) = 20 sin(45°) = 10√2

Therefore, the component form of vector u is:

u = 10√2 i + 10√2 j

Similarly, for vector v:

|v| = 50, θv = 180°

The x-component of v is given by:

vx = |v| cos(θv) = -50 cos(180°) = -50

The y-component of v is given by:

vy = |v| sin(θv) = 50 sin(180°) = 0

Therefore, the component form of vector v is:

v = -50 i + 0 j

The component form of the sum of u and v is given by the sum of their x- and y-components:

u + v = (10√2 - 50) i + (10√2 + 0) j

Simplifying, we get:

u + v = (10√2 - 50) i + 10√2 j

Therefore, the component form of the sum of u and v is:

u + v = (10√2 - 50) i + 10√2 j

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The question is -

Find the component form of the sum of u and v with the given magnitudes and direction angles θu and θv.

| | u | | = 20 , θu = 45° | | v | | = 50 , θv = 180°.

Answer:

See attached image.  

250 shirts at $50/shirt is the equilibrium.

Step-by-step explanation:

The sample size should be e) 2,500.

To calculate the sample size needed for the manager's confidence interval, we need to use the formula for the margin of error:

Margin of error = z * (standard deviation of the sample proportion) / sqrt(sample size)

Given the sample data, the sample proportion of time spent mowing is 200 / 400 = 0.5.

Plugging in the values, we get:

Margin of error = 1.96 * sqrt(0.5 * 0.5 / 400) = 0.02

Rearranging the formula and solving for the sample size, we get:

Sample size = (z / margin of error)^2 * (sample proportion * (1 - sample proportion))

= (1.96 / 0.02)^2 * (0.5 * 0.5)

= 2500

So, the sample size needed for a 95.44 percent confidence interval with a margin of error of 0.02 is 2,500. The answer is option (e).

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Answer:

Step-by-step explanation:

Original Function          Rewrite       Differentiate              Simplify

3). y = \(\frac{2}{3x^6}\)                   y = \(\frac{2}{3}x^{-6}\)        y' = \(\frac{2}{3}(-6)x^{(-6-1)}\)              y' = \(-\frac{4}{x^{7}}\)

4). y = \(\sqrt[4]{x^7}\)                 y = \(x^{\frac{7}{4}}\)            y' = \(\frac{7}{4}x^{(\frac{7}{4}-1)}\)                      y' = \(\frac{7}{4}x^{\frac{3}{4}}\)

Answer:

20

Step-by-step explanation:

We can simplify 10/2 = 5

5 = n/4

Multiply each side by 4

5*4 = n/4*4

20 =n

Answer: n = 20

Explanation: To solve for n in this proportion,

we simply use the means-extremes property.

Since 10/2 = n/4, we know that the product of the extremes,

(10)(4), equals the product of the means, (2)(n).

So we know that (10)(4) or 40 equals (2)(n) or 2n.

Dividing both sides by 2, 20 = n.

Answer:

1 : 2

In other words, Figure B is twice the size of Figure A

Step-by-step explanation:

Figure A : Figure B

1 : 2

Answer:

60 minutes

Step-by-step explanation:

Given that Employee I can finish washing a car in 30 minutes. and

employee 2 can finish washing a car in 20 minutes.

Assuming that both will wath the car together after n minutes.

So, n must be the integral multiple of 30 as well as 20.

For niminum value of n,  n must be the lowest common factor of 30 and 20.

\(\Rightarrow n = LCM(30,20) \\\\\Rightarrow n = 60.\)

Hence, after 60 minutes, they will wash a care togethre.

Answer:

This correlation simply means that, in every twin whether identical or fraternal twins, there is a relation between their IQ scores and when they are raised together.

Regarding to the test carried out, it showed that, when an identical twin is raised together, their IQ score tends to be higher in direct comparison with a fraternal twin that was raised together. That is, if the fraternal twin IQ is 100, then, the identical twin IQ is going to be above 100 (probably around 120)

Step-by-step explanation:

The slope of the line that passes through points (3,6) and (8,3) is -3/5.

The ratio of the vertical and horizontal changes between two points on a surface or a line is known as the slope.

The given points are (3,6) and (8,3).

The slope of a line that passes through the points (x₁,y₁) and (x₂,y₂) is:

m = (y₂-y₁)/(x₂-x₁)

Substitute the points (x₁,y₁) = (3,6) and (x₂,y₂) = (8,3) into the formula:

m = (3-6)/(8-3)

m = -3/5

Hence, the slope of the line that passes through points (3,6) and (8,3) is -3/5.

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The gateway arch in st. Louis, MO is approximately 630 ft tall, the same height of the Nickels would be in a stack is 98474.

Height of Gateway Arch in St. Louis, MO = 630ft tall

We are asked, how many nickels would be in a stack of the same

height when 1 nickel is 1.95 mm thick.

Convert height in ft to mm

1 ft = 304.8 mm

630ft = X

After Cross Multiply,

630ft × 304.8mm/1ft

= 192024 mm.

To find how many nickel would be in a stack of the same height

= Total thickness/ Thickness of 1 US dime

= 192024 mm/1.95mm

= 98473.8

≈98474 nickels

Therefore, the number of nickel that would be in a stack of the same height is 98474.

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To find the height of the cylindrical container, we can use the formula for the volume of a cylinder: V = πr^2h, where V is the volume, r is the radius, and h is the height. By using these formulas we get height of contain = 2 inches.

Given that the volume is 38 cubic inches and the radius is 2 inches, we can substitute these values into the formula: 38 = π(2^2)h.
Simplifying, we have 38 = 4πh.
To solve for h, divide both sides of the equation by 4π: h = 38 / (4π).

Using the approximation π ≈ 3.14, we can calculate the height: h ≈ 38 / (4 * 3.14) ≈ 2.41.

Rounding to the nearest whole number, the height of the container is 2 inches. In conclusion, the height of the cylindrical container is approximately 2 inches.

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Answer:

No, I can't conclude that the mean price of a hotel room in Atlanta is lower than the mean price of a hotel room in Houston. We do not know how many hotel rooms there are in each city, and we don't know the prices of the hotel rooms in each city.

Answer:

21.25

Step-by-step explanation:

We can use the Pythagorean theorem since we know the legs

a^2+b^2 = c^2

12.75 ^2 + 17^2 = c^2

162.5625+289= c^2

451.5625 = c^2

Take the square root of each side

sqrt(451.5625) =sqrt( c^2)

21.25 = c

Answer: the answer will be 21.25

Step-by-step explanation:

Answer: The powers of i have a repetitive cyclic nature.

When we raise the imagenry unit i to increasing powers, we get a pattern which repeats itself.

Observe the following table of powers of i.

Power of i i1 i2 i3 i4 i5 i6 i7 i8 i9

Simplified i -1 -i 1 i -1 -i 1 i

As you see above, the pattern repeats itself and is four members long.

Therefore, ix+8 ix+4 will equalx.

When asked to determine the value of i to a power higher than 4, we can use this information in order to find our position in the cycle.

So, instead of using the actual power, we can take the remainder of the power divided by 4.