Determine the amount of aninvestment if $400 is invested at
an annual interest rate of 7.25%
for 7 years. Round to the nearest
penny.
$[ ? ]

In the simplified form the expression is x+4

Answer:

x+4

Step-by-step explanation:

Answer:

Step-by-step explanation:

Recall that an elementary matrix of a matrix operation is obtained by applying the matrix operation to the identity matrix.  In this case, by replacement, it means changing the whole row of a matrix and replacing it with a the same row multiplied by a number k.

In this case, the solution is

What is the determinant of an elementary row replacement matrix?

An elementary n xn row replacement matrix is the same as the n x n identity matrix with Exactly one of the 1's replaced with some number k.This means this is the triangular matrix and so its determinent is product of its diagonal entries. Thus, the determinant of an elementary row replacement matrix is a number. Especifically, the number k we used to replace the one

1. Exactly one,atleast one

2. 1's or 0's

3. Identity matrix,invertible matrix, triangular matrix or zero matrix.

4. Product or sum  

5. A number

Answer:

8 counselors and 12 aids

Step-by-step explanation:

minimum number of staff to run camp = 20

Ratio of counselors to aids to work together = 2:3

To get the multiply factor = 20 / (2 counselors + 3 aids) = 20 / 5 =4

minimum number of counselors needed = 4 x 2 = 8 counselors

minimum number of aids needed = 4 x 3 = 12 aids

Answer:

8.5 or 8 1/2.

Step-by-step explanation:

To find the product of 2 5/6 and 3, you can multiply the two numbers together.

2 5/6 x 3 is equal to 8.5, therefore, the product of these two numbers is 8 1/2.

The transformations of f(x) = - 2lx - 3| + 1 from the parent function f(x) =|x|

Horizontal Shift: Right 3 Units

Vertical Shift: Up 1 Units

Reflection about the x-axis: Reflected

Vertical Stretch: Stretched

What is Transformation equation ?

Transformation of an equation into another equation whose roots are. reciprocals of the roots of a given equation we replace x→x1. 2.

Given,

Parent function f(x) = |x|

f(x) = - 2 lx - 3| + 1

Assume that f(x) = |x| is y = |x|  and,

f(x) = - 2 lx - 3| + 1 is g(x) = - 2 lx - 3| + 1

The transformation from the first equation to the second one can be found by finding a, h, and k

y = a |x−h| + k

find a, h, k in f(x) = - 2lx - 3| + 1

a = -2, h = -3, k = 1

Horizontal shift depends on the value of h,

g(x) = f(x + h) ---- The graph is shifted to the left h units.

g(x) = f(x - h) ---- The graph is shifted to the right h units.

so, h = -3 then horizontal shift will be right 3 units

The vertical shift depends on the value of k,

g(x) = f(x) + k  -------  The graph is shifted up k units.

g(x) = f(x) - k   --------  The graph is shifted down k units.

so, k = 1 then the vertical shift will be 1 unit up

The sign of a describes the reflection across the x-axis,

−a means the graph is reflected across the x-axis.

Reflection about x-axis is reflected

The value of a describes the vertical stretch or compression of the graph

a > 1,  vertical stretch will be narrower

a < 1, vertical stretch will be wider

so, vertical stretch is Stretched

Hence, The transformations of f(x) = - 2lx - 3| + 1 from the parent function f(x) =|x|

HorizontalShift: Right 3 Units

Vertical Shift: Up 1 Units

Reflection about the x-axis: Reflected

Vertical Stretch: Stretched

The graph is given below ↓

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Answer:

Step-by-step explanation:

As the base is a square so the length is a, width is a and the height is h.

According to the question,

a + a + h = 96

h = 96 - 2a     .... (1)

Volume of the box, V = length x width x height

V = a x a x h

V = a² (96 - 2a)    from equation (1)

V = 96a² - 2a³

Differentiate both sides

Now put it equal to zero.

192 a - 6a² = 0

a = 32 in

h = 96 - 2 x 32

h = 32 in

Thus, the length and the width os teh base is 32 in and the height is 32 in.

Final answer:

A square-based box with the greatest volume under a restriction of the sum of length, width, and height not exceeding 96 inches must have each dimension equal to 32 inches. Therefore, its volume will be 32x32x32 = 32,768 cubic inches.

Explanation:

A square-based box with the greatest volume that can fit the airline's restrictions would have each side (length, width, height) be exactly one third of the total permitted sum, namely 32 inches each, because the volume of a square-based box (a cube in this specific case) is calculated by cubing the edge length. This is due to the nature of a cube, where all sides are equal.

So, the volume of the box would be 32in x 32in x 32in = 32,768 cubic inches. This is the maximum volume because the mathematical principle that for a given sum S of width, length & height, a cube always takes up the most volume.

Learn more about Optimization in Mathematics here:

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