maria had $150 in gift certificates to use in a record store.she bought fewer than 20 recordings.each tape cost $5.95 and each cd cost $8.95. how many of each type of recordings might she have bought(it has to be graphed so i need points to plot)

Answer: 15

Step-by-step explanation:

Answer:

2 ounces of clay is left in the bucket

Step-by-step explanation:

Total amount of clay in the bucket = 12 ounce

Ari used 1/6th of the clay in the bucket and Greg used 2/3 of the clay in the bucket

Hence, the remaining clay in the bucket

12 - 1/6 *12 - 2/3 * 12

12 - 2-8

2

The value of f(a) is \(9a^2 + 7\). The value of f(a+h) is \(9(a+h)^2 + 7\). The difference quotient (f(a+h) - f(a))/h simplifies to 18a + 9h for the function \(f(x) = 9x^2 + 7.\)

Let's break down the calculations step by step. First, to find f(a), we substitute a into the function: \(f(a) = 9(a^2) + 7 = 9a^2 + 7\).

Next, to find f(a+h), we substitute (a+h) into the function: \(f(a+h) = 9(a+h)^2 + 7\). Expanding the square, we get \(f(a+h) = 9(a^2 + 2ah + h^2) + 7 = 9a^2 + 18ah + 9h^2 + 7\).

Lastly, to calculate the difference quotient, we subtract f(a) from f(a+h) and divide by h: \((f(a+h) - f(a))/h = [(9a^2 + 18ah + 9h^2 + 7) - (9a^2 + 7)]/h = (18ah + 9h^2)/h.\)

Simplifying further, we can cancel out h from the numerator, giving us the final result: 18a + 9h.

Therefore, the difference quotient (f(a+h) - f(a))/h simplifies to 18a + 9h for the function \(f(x) = 9x^2 + 7.\)

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Find percent -> 2nd month.

4264*.25==1066 phone calls+=4264

==5330 for 2nd month.

for 2nd -> 3rd

6396==5330*x, solve algebraically to get .20  == 20% increase from 2nd month to 3rd month.

The coefficient of correlation can be determined using the coefficient of determination, which is given as the square of the correlation coefficient. In this case, the coefficient of determination is 0.81, indicating that 81% of the variability in the dependent variable (y) can be explained by the independent variable (x).

To find the coefficient of correlation, we take the square root of the coefficient of determination. Taking the square root of 0.81 gives us 0.9. However, the coefficient of correlation can be positive or negative, depending on the direction of the relationship between the variables.

Looking at the given regression line y^= -2.88 + 1.77x, the positive slope of 1.77 indicates a positive relationship between x and y. Therefore, the coefficient of correlation would also be positive.

Hence, the answer is (c) +0.90, indicating a positive correlation between the variables.

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The graph of the function is added as an attachment

From the question, we have the following parameters that can be used in our computation:

f(x) = 4x + 17

f(x) = -2

Also, we have the interval to be

f(x) = 4x + 17 for x <-3

f(x) = -2 for x > 0

The above expression is a piecewise function

Next, we plot the graph and the intervals

See attachment for the graph of the equations

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Answer:

Either of the following square values:

\(8^{2} =64 \,\,in^2\\15^2= 225\,\,in^2\\17^2=280\,\,in^2\)

Step-by-step explanation:

The three possible answers correspond to the square of the sides of the triangles via the Pythagorean theorem. And these are:

\(8^{2} =64 \,\,in^2\\15^2= 225\,\,in^2\\17^2=280\,\,in^2\)

Answer:

y + 9 = -2(x - 10)

The correct answer is d.

The standard matrix of a linear transformation T can be found by using the formula A = [T(e1) T(e2) ... T(en)], where A is the standard matrix, e1, e2, ..., en are the columns of the identity matrix, and T(e1), T(e2), ..., T(en) are the images of the identity matrix columns under the transformation T.

1. For the first transformation, the standard matrix of T can be found by using the formula A = [T(e1) T(e2)] = [(3,1,3,1) (-5,2,0,0)] = [[3 -5] [1 2] [3 0] [1 0]]. Therefore, the standard matrix of T is [[3 -5] [1 2] [3 0] [1 0]].

2. For the second transformation, the standard matrix of T can be found by using the formula A = [T(e1) T(e2) T(e3)] = [(1,3) (4,-7) (-5,4)] = [[1 4 -5] [3 -7 4]]. Therefore, the standard matrix of T is [[1 4 -5] [3 -7 4]].

3. For the third transformation, the standard matrix of T can be found by using the formula A = [T(e1) T(e2)] = [cos(31/2) -sin(31/2) sin(31/2) cos(31/2)], where cos(31/2) and sin(31/2) are the cosine and sine of 31/2 radians, respectively. Therefore, the standard matrix of T is [cos(31/2) -sin(31/2) sin(31/2) cos(31/2)].

4. For the fourth transformation, the standard matrix of T can be found by using the formula A = [T(e1) T(e2)] = [cos(-1/4) -sin(-1/4) sin(-1/4) cos(-1/4)], where cos(-1/4) and sin(-1/4) are the cosine and sine of -1/4 radians, respectively. Therefore, the standard matrix of T is [cos(-1/4) -sin(-1/4) sin(-1/4) cos(-1/4)].

5. For the fifth transformation, the standard matrix of T can be found by using the formula A = [T(e1) T(e2)] = [(1,0) (2,1)] = [[1 2] [0 1]]. Therefore, the standard matrix of T is [[1 2] [0 1]].

6. For the sixth transformation, the standard matrix of T can be found by using the formula A = [T(e1) T(e2)] = [(1,0) (3,1)] = [[1 3] [0 1]]. Therefore, the standard matrix of T is [[1 3] [0 1]].

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We can take advantage of the integrand's symmetry over the y-axis to employ symmetry to evaluate the integral [-8, 8] (3 + x + x2 + x3) d.

As a result, the integral across the range [-8, 8] can be divided into two equally sized pieces, [-8, 0] and [0, 8].

Taking into account the integral throughout the range [-8, 0]: [-8, 0] (3 + x + x² + x³) dx

The integral of an odd function over a symmetric interval is zero because the integrand is an odd function (contains only odd powers of x). The integral over [-8, 0] hence evaluates to zero.

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To find the radius of the circle covered by the lawn sprinkler, we can use the formula for the circumference of a circle: C = 2πr, where C is the circumference and r is the radius.

Given that the distance around the circle is 64π feet, we can equate this to the circumference of the circle: 64π = 2πr.

By canceling out the π terms on both sides of the equation, we get

64 = 2r.

Dividing both sides of the equation by 2, we find that the radius of the circle is r = 32 feet.

Therefore, the radius of the circle covered by the lawn sprinkler is 32 feet.

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Answer:

Step-by-step explanation:

Answer is 30

Answer:

a=5

Step-by-step explanation:

4a−3−2a=2a+7−2a

2a−3=7

2a−3+3=7+3

2a=10

2a /2 = 10 /2

a=5

Step-by-step explanation:

the FH seems to be option b.6.0

........

Answer:

#4 should be C

You can use substitution to solve this system.

since y = x, you can plug in that in the place of x

New equation: x + x = 4

x = 2

Now plug in x for the original equation

y = 2

so the answer is 2,2

:)

Answer

linear

nonproportional

Step-by-step explanation:

Since for each equal change in time (1 week), there is an equal change in weight (5 lb), the situation is linear.

At time zero, the first week, the weight was not zero. It was 60 lb, so it is not proportional.

Answer:

linear

nonproportional

Answer:

\(\displaystyle f'(1) = 6\)

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Multiplied Constant]:                                                           \(\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)\)

Derivative Property [Addition/Subtraction]:                                                         \(\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]\)  

Basic Power Rule:

Step-by-step explanation:

Step 1: Define

Identify

\(\displaystyle f(x) = 5x - 1 + \ln x\)

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Answer:

25896

Step-by-step explanation:

Answer:

below

Step-by-step explanation:

The steps to solve this are:

The perimeter of a rectangle is given by p=2(l+w) where p is the perimeter, l is the length and w is the width. We are told the length of the field is 10 times the width so l=10w. Using this in the formula above we get:

2090=2(10w+w)

22w=2090

w=95 ft

l=950 ft

Answer:

Step-by-step explanation:4

yes. the hikers will ever be the same elevation.6+1=7  the same elevation.

Y = 6x + 1

FIll the value of y in this equation

3x + 4​= 6x + 1

3x=4-1

x=3/3=1

Y = 6x + 1

FIll the value of x in this equation

6+1=7. The height above or below a specified reference point, most frequently a reference geoid, which is a mathematical representation of the Earth's sea level as an equipotential gravitational surface, determines a location's elevation. In most cases, elevation is used to describe locations on the surface of the Earth, whereas altitude or geopotential height is used to describe locations above the surface, such as those of flying airplanes or orbiting satellites, and depth is used to describe locations below the surface. Elevation should not be confused with the angular separation from the Earth's center. The summits of Mount Everest and Chimborazo have the highest elevation and greatest geocentric distance, respectively, because of the equatorial bulge.

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Answer: x=64 y=43

Step-by-step explanation:

Answer:

Area of circle bounded by a 135 ° arc is 4.71 m ²

Step-by-step explanation:

Radius of circle, r = 2 m

Angle of the circle , θ = 135 °

Area of circle bounded by a 135 ° arc.

Using Formula

Area of circle = θ/ 360 × π × r ²

substitute the values,

Area of circle = 135 /360 × 3.14 × ( 2 m) ²

solve it

Area = 27 / 72 × 3.14 × 4 m ²

Area = 27 / 18 × 3.14

Area = 1.5 × 3.14

Area = 4.71 m ²

Therefore, Area of circle bounded by a 135 ° arc is 4.71 m ²

Answer:

it's 3/2pi

Step-by-step explanation:

.

Answer:

answer is 21= 5x- y

Step-by-step explanation:

y+6=5(x-3)

y+6=5x-15

y = 5x-15-6

y = 5x-21

rearrange this equation as formAx+By=C

5X - y = 21

The result of the product \((s^2+5s)(s^3+4s^2)\) is \(s^5+9s^4+20s^3\)

The product is given as:

\((s^2+5s)(s^3+4s^2)\)

Rewrite as:

\((s^2+5s)(s^3+4s^2) = (s^2+5s) \times (s^3+4s^2)\)

Expand the expression on the right-hand side

\((s^2+5s)(s^3+4s^2) = s^2\times (s^3+4s^2)+5s \times (s^3+4s^2)\)

Distribute the expressions

\((s^2+5s)(s^3+4s^2) = s^5+4s^4+5s^4+20s^3\)

Evaluate like terms

\((s^2+5s)(s^3+4s^2) = s^5+9s^4+20s^3\)

Hence, the result of the product \((s^2+5s)(s^3+4s^2)\) is \(s^5+9s^4+20s^3\)

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The coordinates of the images of the points are B'(x, y) = (0, 2), C'(x, y) = (3, 4), Z'(x, y) = (4, 3) and X'(x, y) = (4, 1), respectively.

In this problem we find four points set on Cartesian plane, each of which has to be transformed by using the following transformation rule about the origin:

(x', y') = (x · cos θ - y · sin θ, x · sin θ + y · cos θ)

Where:

(x, y) - Coordinates of the original point.

θ - Angle of rotation, in degrees.

If we know that B(x, y) = (- 2, 0), C(x, y) = (- 4, 3), Z(x, y) = (- 3, 4), X(x, y) = (- 1, 4) and θ = 90°, then the coordinates of the resulting point:

B'(x, y) = (- 2 · cos (- 90)° - 0 · sin (- 90°), - 2 · sin (- 90°) + 0 · cos (- 90°))

B'(x, y) = (0, 2)

C'(x, y) = (- 4 · cos (- 90°) - 3 · sin (- 90°), - 4 · sin (- 90°) + 3 · cos (- 90°))

C'(x, y) = (3, 4)

Z'(x, y) = (- 3 · cos (- 90°) - 4 · sin (- 90°), - 3 · sin (- 90°) + 4 · cos (- 90°))

Z'(x, y) = (4, 3)

X'(x, y) = (- 1 · cos (- 90°) - 4 · sin (- 90°), - 1 · sin (- 90°) + 4 · cos (- 90°))

X'(x, y) = (4, 1)

Finally, we proceed to graph the locations of the points, both original and resulting, by means of a graphing tool.

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a. Im(Mu) = Im(Mu + iMv)

=> 0 = bv - aiv

=> Mv = -bu + av

b. G^-1MG is equivalent to the standard rotation-dilation matrix Ca,b.

a. We have the complex eigenvector u + iv with eigenvalue a - bi. By applying the matrix M to this eigenvector, we get:

Mu = M(u + iv) = Mu + iMv

Since M is a real matrix, the real and imaginary parts must be equal:

Re(Mu) = Re(Mu + iMv)

=> Mu = au + biv

Similarly,

Im(Mu) = Im(Mu + iMv)

=> 0 = bv - aiv

=> Mv = -bu + av

b. Let's consider the matrix G = [u | v], where the columns are u and v in that order. Multiplying this matrix by M, we have:

MG = [Mu | Mv] = [au + bv | -bu + av]

On the other hand, let's compute GCa,b:

GCa,b = [u | v] Ca,b = [au - bv | bu + av]

Comparing these two expressions, we can see that MG = GCa,b.

c. To show that u and v are linearly independent, we assume that there exist real numbers r and s such that ru + sv = 0. Applying the matrix M to this equation, we get:

0 = M(ru + sv) = rMu + sMv

0 = r(au + bv) + s(-bu + av)

0 = (ar - bs)u + (br + as)v

Since u and v are complex eigenvectors with distinct eigenvalues, they cannot be proportional. Therefore, we have ar - bs = 0 and br + as = 0. Solving these equations simultaneously, we find that r = s = 0, which implies that u and v are linearly independent.

d. Since u and v are linearly independent, the matrix G = [u | v] is invertible. Let's denote its inverse as G^-1. Now, we can show that G^-1MG = Ca,b:

G^-1MG = G^-1 [au + bv | -bu + av]

= [G^-1(au + bv) | G^-1(-bu + av)]

= [(aG^-1)u + (bG^-1)v | (-bG^-1)u + (aG^-1)v]

= [au + bv | -bu + av]

= Ca,b

Therefore, we conclude that G^-1MG is equivalent to the standard rotation-dilation matrix Ca,b.

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True, Monte Carlo simulation is used for statistical sampling where larger number of trials are used for the precise result.

Step by Step Explanation:

Therefore, it is true to have more number of trials in Monte Carlo simulation  statistical sampling for precise result.

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