There are eight wires which need to be attached to a circuit board. A robotic device will attach the wires. The wires can be attached in any order, and the production manager wishes to determine which order would be fastest for the robot to use. Use the multiplication rule of counting to determine the number of possible sequences of assembly that must be tested.

No, the rank of the product of two n by n square matrices A and B, denoted as AB, cannot be less than n-1 if both A and B have ranks of n-1.

According to the Rank-Nullity theorem, for any matrix M, the sum of its rank and nullity is equal to the number of columns in M. In this case, the number of columns in AB is n, so the sum of the rank and nullity of AB must be n.

If rank(A) = rank(B) = n-1, it means that both A and B have nullity 1. The nullity of a matrix is the dimension of its null space, which consists of all vectors that get mapped to the zero vector when multiplied by the matrix. Since both A and B have rank n-1, their null spaces consist only of the zero vector.

Now, considering AB, if the rank of AB were less than n-1, it would mean that the nullity of AB is greater than 1.

However, this would violate the Rank-Nullity theorem since the sum of the rank and nullity of AB must be n, which is the number of columns.

Therefore,  if rank(A) = rank(B) = n-1, the rank of AB cannot be less than n-1.

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If you were to close your eyes and pick a ball then the probability of picking a green ball is 3 / 14.

To find the probability of picking a green ball, the formula is :

= Number of green balls / Number of total balls

The number of green balls would be 3 balls.

The number of total balls is 14 balls.

The probability of picking a green ball is therefore :

= 3 / 14

This is the simplest form.

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Answer:

f(36)

Step-by-step explanation:

f(3)=5(3)²-9(3)+18

f(3)=5(9)-27+18

f(3)=45-27+18

f(3)=36

Answer:

360

Step-by-step explanation:

if you rotate it at 90 it will be of same shape but diffeemt position but if it is 360 the result will be same position and same shape

Answer: 360 degrees

Step-by-step explanation:

I took the test, and it is a full rotation back to the og spot.

Answer:

c) 108

Step-by-step explanation:

All angles of a regular polygon are the same.

Answer:

\(1.2 + 2.3 + 1.8 = 5.3 \: \\ so \: they \: bouhgt \: about \: 5 \: pouns \: together.\)

\(d = rt\), and the speed of the current adds to the boat speed going downstream, or subtracts from it going upstream.

Let's say I'm in a 10 mph current in a canoe. If I can row 2 mph, I can go 12 mph downstream, or if I try to go upstream, I'm gonna actually be going backward 8 mph \((2 - 10 = -8)\).

\(4(b - c) = 128\)

\(2(b + c) = 128\)

\(b - c = 32\)

\(b + c = 64\)

\(2b = 96\)

b = 48 mph

\(48 + c = 64\)

c = 16 mph

Answer:

The model is \(V(t)=2239+249\sin(\frac{\pi}{2}t)\).

Step-by-step explanation:

Consider the given information.

The volume of air inside the lungs increases or decreases so for this we will use the basic sine function \(B(t)=d+a\sin[b(t+ \frac{c}{a})]\) as our parent function.

Let us assume that the phase shift is 0 it means \(\frac{c}{b}=0\).

The air that moves into and out of the lungs is about 498 mL.

It means the amplitude of the function will vary by 249(half of 498).

The reserve and residual volumes of air that remains in the lungs occupy about 1990 mL which is the minimum air in the lungs.

So, the max air will be: 1990+498 =2488 mL

And the average will be d=1990+249=2239 ml

The horizontal stretch will be  \(b=\frac{2\pi}{4}=\frac{\pi}{2}\) as we know that period of \(y=\sin t\) is \(2\pi\) and respiratory cycle for an average human takes about 4 seconds.

Hence, the model is \(V(t)=2239+249\sin(\frac{\pi}{2}t)\).

There is no significant difference between the mean scores of Education and Nursing students in mathematics.

Null hypothesis (H₀): There is no significant difference between the mean scores of Education and Nursing students in mathematics.

Alternative hypothesis (H₁): There is a significant difference between the mean scores of Education and Nursing students in mathematics.

We will use significance level (α) of 0.01.

Given:

Sample mean for Education students (x₁) = 88.50

Sample mean for Nursing students (x₂) = 90.25

Standard deviation for the Education student sample (s₁) = 7.5

Standard deviation for the Nursing student sample (s₂) = 8.2

Sample size for Education students (n₁) = 25

Sample size for Nursing students (n₂) = 29

The t-test statistic for two independent samples is:

t = (x1₁ - x2) / sqrt((s₁² / n₁) + (s₂² / n₂))

t = (88.50 - 90.25) / sqrt((7.5² / 25) + (8.2² / 29))

t ≈ -0.8187

In this case, df = 24.

The critical value for α = 0.01 and df = 24 is approximately ±2.797.

Since |-0.8187| < 2.797, the absolute value of the t-test statistic is smaller than the critical value.

Therefore, we fail to reject the null hypothesis.

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Answer:

A. 7 ft

Step-by-step explanation:

I calculated it logically

Answer: six pack of student tickets

Step-by-step explanation:

The total weight of Rice that Mark buys is given as follows:

2.5 pounds.

The total weight of Rice that Mark buys is obtained applying the proportions in the context of the problem.

The weight of each bag is given as follows:

5/8 pounds = 0.625 pounds.

The number of bags is given as follows:

4 bags.

Hence the total weight of Rice that Mark buys is given as follows:

4 x 0.625 = 2.5 pounds.

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Answer:

third option

Step-by-step explanation:

The largest power of 10 that is a factor of 1000! is 5^249, or 10^249.

(a) To find the largest power of 10 that is a factor of 50!, we need to count the number of factors of 5 in 50! since each factor of 5 contributes at least one factor of 10.

There are 10 multiples of 5 in 50!, namely 5, 10, 15, 20, 25, 30, 35, 40, 45, and 50. Each of these contributes one factor of 5. There are also 2 multiples of 25 (25 and 50), each of which contributes an additional factor of 5. Therefore, the total number of factors of 5 in 50! is 10 + 2 = 12.

Since each factor of 10 contains one factor of 5 and one factor of 2, we also need to count the number of factors of 2. It is clear that there are more factors of 2 than factors of 5, so we only need to count the factors of 5. Therefore, the largest power of 10 that is a factor of 50! is 5^12, or 10^12.

(b) To find the largest power of 10 that is a factor of 1000!, we follow the same reasoning as in part (a). The number of factors of 5 in 1000! is:

⌊1000/5⌋ + ⌊1000/25⌋ + ⌊1000/125⌋ + ⌊1000/625⌋ = 200 + 40 + 8 + 1 = 249

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Answer:

1the answer for this is easy it is 4.4

The number of degrees below zero is given by A = 56° F

Regardless of the sign, a modulus function returns the magnitude of a number. The absolute value function is another name for it.

It always gives a non-negative value of any number or variable. Modulus function is denoted as y = |x| or f(x) = |x|, where f: R → (0,∞) and x ∈ R.

The value of the modulus function is always non-negative. If f(x) is a modulus function , then we have:

If x is positive, then f(x) = x

If x = 0, then f(x) = 0

If x < 0, then f(x) = -x

Given data ,

Let the initial temperature be represented as T

Let the number of degrees below zero be A

Now , the value of T is

T = -56° F

From the modulus function , we get

The value of the modulus function is always non-negative.

So , the measure of A = | T |

A = | -56 |

A = 56° F

Hence , the number of degrees below zero is 56° F

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Answer:

p^2+n

Step-by-step explanation:

When you divide exponents, you subtract them and keep the base (the large number attached to the exponent) the same.

If we subtract two negatives (in this case it's p^-2 - p^n) the answer ends up being positive. So, the answer is p^2+n.

Hope this helped!

Answer: the parenthesis: (44-4)

Step-by-step explanation: In order of operations parenthesis are always first. Then exponents, then multiplication and division, and then addition and subtraction. (PEMDAS)

Answer:

\(\boxed {\boxed {\sf No}}\)

Step-by-step explanation:

If a triangle is a right triangle, it can satisfy Pythagorean Theorem.

\(a^2+b^2=c^2\)

where a and b are the legs and c is the hypotenuse.

12 and 84 are the legs because are they shortest. 85 is the hypotenuse because it is the longest side.

\(a= 12 \\b=84 \\c=85\)

Substitute the values into the formula.

\((12)^2+(84)^2=(85)^2\)

Solve the exponents.

\(144+7056=7225\)

Add on the right side.

\(7200\neq 7225\)

7220 is not equal to 7225, so these sides cannot be a right triangle.

Answer:

the solution to the system of equations is (x, y) = (3, -2).

Step-by-step explanation:

y = -2x + 4 (Equation 1)

y = x - 5 (Equation 2)

To solve for x, we can equate the right sides of the equations:

-2x + 4 = x - 5

Now, we can solve for x:

-2x - x = -5 - 4

-3x = -9

x = (-9) / (-3)

x = 3

Substituting the value of x back into Equation 2, we can solve for y:

y = 3 - 5

y = -2

Answer:

the angle of the car's resultant vector is approximately 52.6° (rounded to the nearest tenth) from the northward direction, towards the west.

Step-by-step explanation:

The angle of the car's resultant vector is 37.3°.

Use the concept of the triangle defined as:

A triangle is a three-sided polygon, which has three vertices and three angles which has a sum of 180 degrees.

Given that,

The car travels 87 miles north.

The car then travels 114 miles west.

In triangle ABC

tan B = AC/AB

Here we have,

AC = 87 miles

AB = 114 miles

Therefore,

tan B = 87/114

tan B = 0.763

Take the inverse of tangent on both sides we get,

\(B = tan^{-1}(0.763)\)

B = 37.3°

Hence,

The angle is 37.3°.

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Part A. We are asked to determine the effective interest rate given the nominal interest rate. To do that we will use the following formula:

Where:

Now, since we are given that the interest rate is compounded monthly this means that the value of "n" is:

Now, the interest rate in decimal form is determined by dividing the interest rate by 100, like this:

Now, we plug in the values:

Now, we solve the operations:

In percentage form is 5.9567%

Part B. If the interest rate is compounded continuously we use the following formula:

Plugging in the values we get:

Solving the operations:

In percentage form we get 5.9715%

Answer:

f=5/6

Step-by-step explanation:

Answer: Are you giving us the answer?

Step-by-step explanation:

Are you giving us the answer.

Answer:

The inverse is,

\(f^{-1}(x) = \sqrt[5]{x} - 3\)

Step-by-step explanation:

f(x) = (x+3)^5

Finding the inverse,

\(f(x) = (x+3)^5\\or,\\y = (x+3)^5\)

We replace x with y and vice versa

so,

\(x = (y+3)^5\)

Solving for y,

the the 5th root,

\(\sqrt[5]{x} = y + 3\\y = \sqrt[5]{x} - 3\)

hence the inverse function is,

\(f^{-1}(x) = \sqrt[5]{x} - 3\)

Step-by-step explanation:

f(x)=(x+3)×5

Y=5X+15

now

interxchanging x and y we get,

x=5y+15

5y=x-15

y=x-15/5

therefor f~1(x)=x-15/5

Answer:

19+a

Step-by-step explanation:

Based on the fact that every 2 inches represented 1 foot, the graph that best represents the relationship is Graph C.

If every 2 inches of the model is 1 foot on the statue, then the following values of the model and the statue should be correct:

From the given graphs, the only graph that has these figures intersecting is graph C which means that it best shows the relationship.

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Answer:

The single decimal multiplier is 26%.

Step-by-step explanation:

Since we have given that

You use to increase by 5% followed by 20% increase.

So, the single decimal multiplier would be

Hence, the single decimal multiplier is 26%.

The inverse of the given matrix is:

( 0 1/2 -1/2 )

(-3 1 -3 )

( 1 -1 0 )

What is inverse ?

In linear algebra, the inverse of a square matrix A is another matrix A^{-1}, such that when A and A^{-1} are multiplied together, the result is the identity matrix I. In other words, A^{-1} is the "inverse" of A, and multiplying A by its inverse "undoes" the effect of A.

To find the inverse of a matrix A using the adjoint method, we follow these steps:

Find the determinant of A.

Find the adjugate of A.

Multiply the adjugate of A by 1/det(A) to get the inverse of A.

Let's follow these steps to find the inverse of the given matrix:

Step 1: Find the determinant of A.

We can use the cofactor expansion method to find the determinant:

det(A) = 1(0-2) - 2(3-0) + 1(6-0) = -2 - 6 + 6 = -2

So det(A) = -2.

Step 2: Find the adjugate of A.

The adjugate of A is the transpose of the matrix of cofactors of A. To find the matrix of cofactors, we need to compute the cofactor of each element of A. The cofactor of an element aij is (-1)i+j times the determinant of the submatrix obtained by deleting the row and column containing aij.

The matrix of cofactors is:

( 0 -6 2 )

( 2 2 -2 )

(-2 6 0 )

Taking the transpose of this matrix gives us the adjugate of A:

( 0 2 -2 )

(-6 2 6 )

( 2 -2 0 )

Step 3: Multiply the adjugate of A by 1/det(A).

We have det(A) = -2, so:

A^{-1} = adj(A)/det(A) = (1/-2)( 0 2 -2 ) ( 0 -1 1 )

(-6 2 6 ) = (-3 1 -3)

( 2 -2 0 ) ( 1 -1 0 )

Therefore, the inverse of the given matrix is:

( 0 1/2 -1/2 )

(-3 1 -3 )

( 1 -1 0 )

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