A grocery store sells 3 pounds of Granny Smith apples for $6.27. It sells 5 pounds of Red Delicious apples for $9.95. Which costs more per pound?​

Answer:

The change is a decrease of 87%

Answer:

the change of decrease is 87%

Step-by-step explanation:

Answer:

Justin is 23 years old, and Aimee is 42 years old.

Step-by-step explanation:

Let Marcella's age be represented by x, and Justin's age by t.

Given that Justin is 2 years older than one third Marcella's age.

t = \(\frac{1}{3}\) x + 2

t = \(\frac{x}{3}\) + 2 ........... 1

Also, Aimee is four years younger than 2 times Justin's age.

Aimee = 2 x t - 4

Aimee = 2t - 4 .......... 2

But, Marcella's age is 63 years, so that from equation 1;

Justin's age =  \(\frac{x}{3}\) + 2

                    = \(\frac{63}{3}\) + 2

                    = 21 + 2

                    = 23

Justin is 23 years.

From equation 2,

Aimee = 2 x 23 - 4

           = 46 - 4

           = 42

Aimee is 42 years.

Therefore,

Marcella is 63 years old, Justin is 23 years old, and Aimee is 42 years old.

Answer:

38 minutes per day

Step-by-step explanation:

Divide 114 to 3

114 ÷ 3 = 38

Divide 304 to 8

304 ÷ 8 = 38

Answer:

1 day = 38 minutes

Step-by-step explanation:

3 days = 114 minutes

=> 1 day = 38 minutes

=> 8 days = 38 x 8 minutes.

Her rate is 1 day = 38 minutes. Hoped this helped.

Answer: the equation would be a-1

If you use the correct formula, you can solve the hardest questions in math

Answer:11486.34

Step-by-step explanation:

p is semiperimeter

p=(a+b+c)/2

p=(174+138+188)/2

For Heron equation,

S=\(\sqrt{p*(p-a)*(p-b)*p-c}\)

so, it is 11487.34

Answer:

  11,486.3 square units

Step-by-step explanation:

You want the area of the triangle with side lengths a=174, b=138, c=188.

The area of a triangle can be found from the lengths of the three sides using Heron's formula:

  A = √(s(s -a)(s -b)(s -c)) . . . . . . . where s = (a+b+c)/2, the "semiperimeter"

The calculation is shown in the second attachment.

  s = (174 +138 +188)/2 = 500/2 = 250

  A = √(250(250 -174)(250 -138)(250 -188)) = √(250(76)(112)(62))

  A = √131936000 ≈ 11486.3

The area of the triangle is about 11486.3 square units.

__

Additional comment

An effectively equivalent way to find the area is to use the Law of Cosines to find an angle, then use the trig formula for the area.

  C = arccos((a²+b²-c²)/(2ab)) = arccos(13976/48024) ≈ 73.080899°

  Area = 1/2(ab·sin(C)) = 1/2(24012·0.9567166) ≈ 11486.3

We say this is "effectively equivalent" not only because it gives the same area, but because using the relation between cos(C) and sin(C), you can demonstrate that this formula gives Heron's formula for the area.

The solution of the given initial-value problem is y(t) = t + 1.

The given initial-value problem is:

y'' + 2y' + y = 0, y(0) = 1, y'(0) = 0

To solve the above initial-value problem using the Laplace transform, we will first apply the Laplace transform to both sides of the given differential equation. Using the linearity property of the Laplace transform and taking into account the derivative property of the Laplace transform,

we get

\(L[y'' + 2y' + y] = L[0]L[y''] + 2L[y'] + L[y] = 0s^2L[y] - s*y(0) - y'(0) + 2[sL[y] - y(0)] + L[y] = 0s^2L[y] - s + 2sL[y] + L[y] = s^2L[y] + 2sL[y] + L[y] = s^2 + 2s + 1L[y] = 1/s^2 + 2/s + 1\)

Taking the inverse Laplace transform of both sides, we gety(t)

\(= L^-1[1/s^2 + 2/s + 1]y(t) = t + 1.\)

We can now find the value of the constant of integration using the initial conditions: y(0) = 1 => 0 + c = 1 => c = 1y'(0) = 0 => 1 + b = 0 => b = -1Therefore, the solution of the given initial-value problem is y(t) = t + 1.

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The expressions that means "five factors of 3 is \(3^{5}\), option D.

The concept that will be used is the factor: A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.

It should be noted that Factors of 3 that can be found are (1 and 3).

Then the  ''Five factors of 3''  can be interpreted as =( 5 times the factor of 3) and this can be written as \(3^{5}\)

Therefore, Five factors of 3  can be expressed as \(3^{5}\)

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To find the inverse function of F(x) = 2x - 3, we replace F(x) with y, swap the positions of x and y, and solve for y. The inverse function is f⁻¹(x) = (x+3)/2.

To find the inverse function of F(x) = 2x - 3, follow these steps

Replace F(x) with y. The equation now becomes y = 2x - 3.

Switch the positions of x and y, so the equation becomes x = 2y - 3.

Solve for y in terms of x. Add 3 to both sides: x + 3 = 2y.

Divide both sides by 2 (x + 3)/2 = y.

Replace y with the notation for the inverse function, f⁻¹(x): f⁻¹(x) = (x + 3)/2.

So, the inverse function of F(x) = 2x - 3 is f⁻¹(x) = (x + 3)/2.

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--The given question is incomplete, the complete question is given

" How do I find the inverse function of F(x) = 2x - 3"--

Answer:

Slope of green line:

\(m = \frac{ - 3 - 3}{4 - ( - 4))} = - \frac{6}{8} = - \frac{3}{4} \)

Slope of red line:

\(m = \frac{3 - ( - 5)}{3 - ( - 3)} = \frac{8}{6} = \frac{4}{3} \)

The slopes of these two lines are negative reciprocals of each other.

Therefore, the correct answer is True (A).

Step-by-step explanation:

(x + 2)(x + 3) = 12

x² + 5x + 6 = 12

x² + 5x - 6 = 0

(x + 6)(x - 1) = 0

By zero product rule, we have (x + 6) = 0 or (x - 1) = 0.

=> x = -6 or x = 1. (A)

The probability that there will be no accidents during the first 2 weeks of January is calculated to be approximately 0.778 or 77.8%.

The first two weeks of January consist of 14 days, so we want to find the probability that no accidents occur in 14 days given that the probability of an accident occurring on any given day is 30/365. We can use the binomial distribution to solve this problem.

Let X be the number of accidents in 14 days. Then X follows a binomial distribution with n = 14 and p = 30/365. The probability of no accidents in 14 days is P(X = 0), which is given by the formula:

P(X = 0) = (n choose 0) x p⁰ x (1-p)⁽ⁿ⁻⁰⁾

where "n choose 0" is the number of ways to choose 0 accidents out of n days, which is simply 1.

Substituting n = 14 and p = 30/365, we get:

P(X = 0) = (1) x (30/365)⁰ x (1 - 30/365)⁽¹⁴⁻⁰⁾ ≈ 0.778

Therefore, the probability that there will be no accidents during the first 2 weeks of January is approximately 0.778 or 77.8%.

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Answer: It should be 3 and 5

Step-by-step explanation: I hope this helps <33

The graph that represents Ramon's initial step is, On a coordinate plane, the point (0, 3) is graphed.

The ordinate and abscissa of the x coordinate, along with two values specified in parentheses in a specific order, make up an ordered pair.

Pair in Order = (x, y) where x represents the abscissa, the measure of a point's separation from the main axis, and y represents the ordinate, the measure of a point's separation from the secondary axis.

Given, Ramon is graphing the function f(x) = 3 + (4)x.

We know the initial value of a function is determined when the independent variable is set to zero.

Here the independent variable is 'x'.

Now, at x = 0,

f(0) = 3 + (4)(0).

f(0) = 3.

So, The ordered pair is (0, 3).

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Answer:

a

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Point slope Formula: y2-y1/x2-x1

10+2/7-4

=4

Answer:

$40

Step-by-step explanation:

You have two sweatshirts that cost $30 more the day after.

First, you do \(340 -(2*30)\)

Second, you divide what you got above ($280), by 7 and voila, you have $40 per sweatshirt.

Answer:

Robert got 35 problems right if he received an 87.5% oh his test.

Step-by-step explanation:

As Robert got right 87.5% on his test.

so the expression becomes

87.5% × 40

= 87.5/100 × 40

= 0.875 × 40

= 35

Therefore, Robert got 35 problems right if he received an 87.5% oh his test.

The Jacobi iteration scheme for the matrix problem in part (e) can be described as follows:

1. Start with an initial vector \(\phi ^{(0)} = [1, 1]^T\).

2. For each iteration, calculate the updated values of \(\phi^{(k+1)\) using the formula:

 \(\phi^{(k+1)}_i = (b_i - \sum (A_{ij} * \phi^{(k)}_j)) / A_{ii}, for\ i = 0, 1.\)

3. Repeat the iteration process until convergence is achieved.

The Jacobi iteration scheme is an iterative method used to approximate solutions to linear systems of equations. In this case, it can be applied to solve the matrix problem described in part (e).

The scheme starts with an initial guess for the solution and iteratively updates the solution until convergence is reached.

To calculate each iteration, the scheme uses the formula where the updated value of each element \(\phi_i^{(k+1)\) is determined by subtracting the sum of the products of the matrix elements \(A_{ij\) with the corresponding elements \(\phi_j^{(k)\) in the previous iteration from the right-hand side vector \(b_i\), and then dividing the result by the diagonal element \(A_{ii\).

The spectral radius of the iteration matrix, denoted by ρ, can be calculated by finding the maximum absolute eigenvalue of the matrix.

The convergence of the Jacobi iteration method is determined by the value of the spectral radius.

If ρ is less than 1, the method converges. If ρ is equal to 1, the convergence is uncertain, and if ρ is greater than 1, the method diverges.

By performing one iteration starting with the given initial vector \(\phi^{(0)} = [1, 1]^T\), the updated solution \(\phi^{(1)\) can be obtained.

The error of the initial approximate solution \(\epsilon_0\) can be calculated as the absolute difference between \(\phi^{(0)\) and the exact solution \(\phi^{(e)\).

Similarly, the error of the solution after one iteration \(\epsilon_1\) can be calculated as the absolute difference between \(\phi^{(1)\) and \(\phi^{(e)\).

The convergence of the Jacobi iteration method is closely related to the spectral radius. If the spectral radius is less than 1, the method is more likely to converge quickly.

However, if the spectral radius is close to 1 or greater than 1, the convergence may be slower or the method may not converge at all.

The Jacobi iteration scheme is just one of several iterative methods used to solve linear systems of equations.

Other methods, such as Gauss-Seidel and Successive Overrelaxation (SOR), can also be employed depending on the specific problem and its characteristics.

Convergence analysis and spectral radius calculation play important roles in determining the effectiveness and efficiency of iterative methods.

Understanding these concepts can help identify suitable methods for solving matrix problems and assess their convergence properties.

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To find the area between the x-axis and the elliptical curve defined by the parametric equations x(t) = t^2 and y(t) = e^t, where t ranges from 0 to some value, we need to integrate the absolute value of y(t) with respect to x(t) over the given interval.

The area can be calculated as:

A = ∫|y(t)| dx = ∫|e^t| (2t) dt

Since the parameter t ranges from 0 to some value, we integrate with respect to t. The absolute value of e^t simplifies to e^t since e^t is always positive. Therefore, the integral becomes:

A = ∫e^t (2t) dt

Evaluating this integral will give us the area between the x-axis and the elliptical curve.

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Answer:

270 cm

Step-by-step explanation:

LA = (6+6+6)15

LA = 18(15)

LA = 270

Answer:

To calculate the surface area and volume of a cylinder, we can use the following formulas:

a) Surface Area of a Cylinder:

The surface area of a cylinder consists of two circles (top and bottom) and the curved surface area.

The formula for the surface area of a cylinder is:

SA = 2πr² + 2πrh

Where:

SA = Surface Area

r = Radius of the base (half the diameter)

h = Height of the cylinder

Given that the diameter is 16 yards, the radius is half of that, so r = 8 yards. The height is 20 yards.

Substituting the values into the formula, we get:

SA = 2π(8)² + 2π(8)(20)

= 2π(64) + 2π(160)

= 128π + 320π

= 448π

So, the surface area of the cylinder is 448π square yards.

b) Volume of a Cylinder:

The formula for the volume of a cylinder is:

V = πr²h

Using the same values for the radius (r = 8 yards) and height (h = 20 yards), we can calculate the volume:

V = π(8)²(20)

= 64π(20)

= 1280π

The volume of the cylinder is 1280π cubic yards.

Answer:

k=1/4

Step-by-step explanation:

1/4x1=1/4

0x1/4=0

-1x1/4=-1/4

-2x1/4=-1/2

Very easy

Answer:

K=0.25

Step-by-step explanation:

Well the realationship in the problem y=kx. so now we substitute the numbers so that the equation is now -1/2=-2k

-1/2=-2k

-1/2/-2=k

0.25 or 1/4=k

Answer:

\(\huge\boxed{\sf y = 4x - 5}\)

Step-by-step explanation:

Given that,

Slope = m = 4

Y-intercept = b = -5

Put the above values.

y = 4x + (-5)

\(\rule[225]{225}{2}\)

Answer:

-7 = m

Step-by-step explanation:

5m − 7 = 6m

Subtract 5m from each side

5m-5m − 7 = 6m-5m

-7 = m

Answer:

They both have the same slope of 2. Their y-intercepts are different. One is -2 and the other is -3/2.

Step-by-step explanation:

4x-2y=4

4x - 4 = 2y

(divide 2 by both sides)

2x-2=y

-4x+2y=-3

2y=4x-3

(divide 2 both sides)

y = 2x - 3/2

For the cosecant we will get:

   \(csc(\pm \frac{pi}{4}) = \frac{1}{sin(\pm \frac{pi}{4})} = \pm \frac{2}{\sqrt{2} } = \pm \sqrt{2}\)

So the correct option is the third one.

First, we can write:

\(csc(x) = \frac{1}{sin(x)}\)

Now, remember that:

\(cos(x) = \frac{\sqrt{2} }{2} \\\\for\ x = \pm \frac{pi}{4}\)

And for the sine we have:

\(sin(pi/4) = \frac{\sqrt{2} }{2} \\\\sin(-pi/4) = -\frac{\sqrt{2} }{2} \\\)

Then the cosecant for these possible values of x gives:

\(csc(\pm \frac{pi}{4}) = \frac{1}{sin(\pm \frac{pi}{4})} = \pm \frac{2}{\sqrt{2} } = \pm \sqrt{2}\)

So the correct option is the third one.

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Another vector in the orthogonal complement L¹ is C = [0, 0, -15]. The basis for the orthogonal complement L¹ is {B, C} or {[-2, 1, 0], [0, 0, -15]}.

To find a basis for the orthogonal complement L¹ of the line L spanned by the basis vector A = [3, 6] in ℝ³, we need to find vectors that are orthogonal (perpendicular) to every vector in L.

Let's denote a vector in the orthogonal complement as B = [x, y, z]. For B to be orthogonal to A, their dot product must be zero:

A · B = 0

Substituting the values of A and B:

[3, 6] · [x, y, z] = 0

Using the dot product formula:

3x + 6y + 0z = 0

Simplifying the equation:

3x + 6y = 0

Dividing by 3:

x + 2y = 0

Now we have an equation that describes a line in the xy-plane. We can choose any value for y and find the corresponding value for x that satisfies the equation.

Let's choose y = 1. Plugging this into the equation, we have:

x + 2(1) = 0

x + 2 = 0

x = -2

Therefore, one vector in the orthogonal complement L¹ is B = [-2, 1, 0].

To obtain a basis for L¹, we can find another vector that is orthogonal to A and B. One way to do this is by taking the cross product of A and B:

C = A × B

Using the cross product formula:

C = [3, 6, 0] × [-2, 1, 0]

Expanding the cross product:

C = [0, 0, -15]

Therefore, another vector in the orthogonal complement L¹ is C = [0, 0, -15].

The basis for the orthogonal complement L¹ is {B, C} or {[-2, 1, 0], [0, 0, -15]}.

Note that the orthogonal complement is a subspace orthogonal to L, meaning any linear combination of vectors in L¹ will be orthogonal to every vector in L.

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Answer:

$3378.3

Step-by-step explanation:

P= 1500

R= 75

T= 12 years

A= P(1+R/100)^T

A= 1500(1+7/100)^12

A=1500(1.07)^12

A= $3378.3

The system of equations that can be used to solve this problem is

{h = 4 + t

{h = 6 + 0.5t

What is the system of equations?

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.

Here, we have

Given,

A birch tree that is 4 ft tall grows at a rate of 1 ft per year.

A larch tree that is 6 ft tall grows at a rate of 0.5 ft per year.

Now, we tet the variable t represents time in years and h to represent height in feet.

The calculations are as follows:

after 4 years

The system of equations is:

4 + x = 6 + 0.5x

Hence, the system of equations that can be used to solve this problem is

{h = 4 + t

{h = 6 + 0.5t

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Answer:

(C)261.12 Square Inches

Step-by-step explanation:

The diameter of the Cone Hat = 6.6 inches

Radius = Diameter/2=6.6/2=3.3 Inches

The slant height = 8.4 inches.

To determine how many square inches of construction paper did Bree need to make the three hats, we find the Curved Surface Area of the Cones.

Curved Surface Area of a Cone \(=\pi r l\)

Therefore, the area of paper used for the 3 hats

=3 X Area of One Hat

\(=3 \times \pi r l\\=3 \times 3.14\times 3.3 \times 8.4\\=261.12$ Square Inches\)

Answer:

261.12 in2

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