Solve the system of equations

Consider the matrix

[tex]A=\begin{bmatrix}0&1&0\\1&0&0\\0&0&1\end{bmatrix}[/tex]

Multiplying A by itself has the effect of swapping the first and second rows:

[tex]A^2=\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}[/tex]

which is diagonal, while A itself is not.

Answer:

  g(x) is f(x) expanded horizontally by a factor of 2

Step-by-step explanation:

Given:

  f(x) = 16^x

  g(x) = 16^(x/2)

__

Replacing x in a function with x/k expands the graph horizontally by a factor of k. Here, it seems we have ...

  g(x) = f(x/2)

so g(x) is a horizontal expansion of f(x) by a factor of 2.

Answer:

c). The output values of g(x) are the square root of the output values of f(x) for the same value of x.

Step-by-step explanation:

Answer:

angle ABC and angle KLM

Step-by-step explanation:

Angle ABC equals to 35 degrees and KLM equals to 95 degrees. Their sum equals 135 degrees.

Answer:

The answer is B and C.

Step-by-step explanation:

When these 2 angles are added together, they form 130° :

∠ABC + ∠KLM = 35° + 95°

= 130°

Answer:

120 Blocks or letter C

Step-by-step explanation:

I did 8x5x3, because lxwxh so i got 120

Answer:

  9/23

Step-by-step explanation:

Of the 23 students, 9 play both baseball and basketball. The probability of choosing one of those is 9/23.

___

Let A represent basketball, and B represent baseball. Then ...

  P(A or B) = P(A) +P(B) -P(A and B)

Since 8 students play neither sport, we have ...

  1 -8/23 = 11/23 +13/23 -P(A and B)

  15/23 = 24/23 -P(A and B)

  P(A and B) = (24 -15)/23

  P(A and B) = 9/23

Answer:

Two triangles are said to be similar if any two corresponding sets of angles are equal and the corresponding sides are in the same ratio.

Answer:

ABC | Stock price

Q1 | $10.50

Q2 | $11.50

Q3 | $9.00

Q4 | $10.50

Step-by-step explanation:

Answer is 37 shares on AP3X

Answer:

252 inches squared

Step-by-step explanation:

(6 x 9) + (6 x 15) + (9 x 12) = 252

Answer:

2/3

Step-by-step explanation:

1/4 ÷ 3/8 = 1/4 x 8/3 = 8/12 = 2/3

Answer:

2/3

Step-by-step explanation:

to divide make sure to use the reciprocal of the 3/8 which is

1/4*8/3

reduce the numbers with the greatest common factor divisor of 4

8/4=2 then 1*3 equals 3 which is 2/3

so it is  2/3

Answer:

The answer to this question can be defined as follows:

a)

cosine: 0.707

correlation: 0

Euclidean: 3.16

b)

cosine: 1

correlation: 1

Euclidean: 0

Jaccard: 1

c)

cosine: -0.4082

correlation: 0.5774

Euclidean: 2.64

d)

cosine: -0.333

correlation:  -0.3333

Jaccard: 0.5

e)

cosine: -0.7075

correlation: 0.2132

Step-by-step explanation:

a) cosine:

[tex]x \times y( 0 \times 2+ 0 \times 2 +1 \times 2+1 \times 2) = 4\\\\ x= \sqrt{2} = 1.414\\\\y= \sqrt(16)=4\\\\\cos (x\times y) = \frac{x\times y}{x\times y}\\\\\cos (x\times y) = \frac{4}{1.414\times 4}\\\\= 0.707[/tex]

correlation:

[tex]\ corr(x,y) =[\frac{covariance (x,y)}{standec(x) \times standdev(y)}]\\X \ mean = 0.5\\Y \ mean = 2\\covariance (x,y) = 0\\standdev(x) = 0.5774\\standdev(y) = 0\\corr(x,y) = 0[/tex]

Euclidean:

[tex]d(x,y) = \sqrt((0-2)^2+(0-2)^2+(1-2)^2+(1-2)^2)\\d(x,y) = 4+4+1+1\\d(x,y)= \sqrt(10)\\d(x,y)= 3.16\\[/tex]

by applying above formula we get all the values.

b)

cosine: 1

correlation: 1

Euclidean: 0

Jaccard: 1

c)

cosine: -0.4082

correlation: 0.5774

Euclidean: 2.64

d)

cosine: -0.333

correlation: -0.3333

Jaccard: 0.5

e)

cosine: -0.7075

correlation: 0.2132

Answer:

The first option; You must work about 62 hours.

Step-by-step explanation:

The total percent that you pay in taxes is 24.9%.

That means that you keep 75.1% of the money that you earn. We can write the following equation to determine the number of hours, h, that it will take to earn 493.68.

0.751(10.65)h = 493.68

Just divide by 0.751 and 10.65 and you will get the number of hours needed. 

Answer:

A.) 62 hours

Step-by-step explanation:

I took the consumer math test :)

Answer:

63

Step-by-step explanation:

You simply just multiply the 7 and 9.

5x = 10

x = 2

2(2) + 2y = -2

4 + 2y = -2

2y = -6

y = -3

Answer:

(x−3)(x+8)

Step-by-step explanation:

Let's factor x2+5x−24

x2+5x−24

The middle number is 5 and the last number is -24.

Factoring means we want something like

(x+_)(x+_)

Which numbers go in the blanks?

We need two numbers that...

Add together to get 5

Multiply together to get -24

Can you think of the two numbers?

Try -3 and 8:

-3+8 = 5

-3*8 = -24

Fill in the blanks in

(x+_)(x+_)

with -3 and 8 to get...

(x-3)(x+8)

Answer:

(x−3)(x+8)

Hope this helps.

Answer:

0.497 < 1/2 < 0.55 < 3/5 < 6/7

Step-by-step explanation:

Order from Least to Greatest

1: Using the given inputs

2: Rewriting these inputs as decimals

3: Sorting this table by decimal values in order from least to greatest

4: Therefore, the sorted inputs in order from least to greatest is

Answer: 0.497 < 1/2 < 0.55 < 3/5 < 6/7

Hope this helps.

Step-by-step explanation:

Fig rolls = 1.08

Half price = 1.08 ÷ 2 = 0.54

Total price = 1.08 + 0.54 = 1.62

Answer:

£8.52

Step-by-step explanation:

Fig rolls: £1.08+£1.08=£2.16

Crisps: £1.59+£1.59=£3.18 £3.18x2=£6.36

Total price= £2.16+£6.36=£8.52

Answer:

  true

Step-by-step explanation:

We assume you intend your function to be ...

  [tex]F(x)=\log_{0.5}x[/tex]

A logarithm with a base less than 1 is a decreasing curve. Here, the base appears to be 0.5, a value less than 1. Hence the curve is decreasing.

Answer:

-3/4

Step-by-step explanation:

y2-y1/x2-x1

-17+2 divided by 24-4

-15/20

-3/4

Answer:

-3/4

Step-by-step explanation:

The slope of a line is given by

m = (y2-y1)/(x2-x1)

   = (-17- -2)/(24-4)

   = (-17+2)/(20)

    = -15/20

   =-3/4

Answer:

  (f -g)(2) = 14

Step-by-step explanation:

You can write the expression for the composite function as ...

  (f -g)(x) = f(x) -g(x) = (3x² +1) -(1 -x)

  (f -g)(x) = 3x² +x

Then for x = 2 ...

  (f -g)(2) = 3(2²) +2

  (f -g)(2) = 14

Answer:

[tex] y- y_o = m(x-x_o) [/tex]

For this case m represent the slope and is given by [tex]m= g'(4) = 2[/tex] and from the other condition given we know that [tex] x_o = 4, y_o =-3[/tex]. And replacing we got:

[tex] y -(-3) = 2 (x-4)[/tex]

And if we reorganize the terms we have:

[tex] y+3 = 2x -8[/tex]

And subtracting 3 in both sides we got:

[tex] y = 2x -11[/tex]

Step-by-step explanation:

For this case we have the following function y=g(x) and we want to find the tangent line to this function using the conditions: [tex] g(4) =-3, g'(4)=2[/tex]

So we need a function like this one:

[tex] y- y_o = m(x-x_o) [/tex]

For this case m represent the slope and is given by [tex]m= g'(4) = 2[/tex] and from the other condition given we know that [tex] x_o = 4, y_o =-3[/tex]. And replacing we got:

[tex] y -(-3)=2(x-4)[/tex]

And if we reorganize the terms we have:

[tex] y+3 = 2x -8[/tex]

And subtracting 3 in both sides we got:

[tex] y = 2x -11[/tex]

Answer:

hey

Step-by-step explanation:

Answer:

Correct answer is the 4th answer.

Step-by-step explanation:

By definition, a matrix is called diagonalizable if there exists some invertible matrix P and a diagonal matrix D such that AP = PD, which is equivalent to having A = PDP^-1.

We are not told that D is a diagonal matrix, hence, it could be any matrix. If A=PDP^-1 for some matrix D that is not diagonal, it doesn't imply that A is diagonalizable. Consider the following case: Let us take A a non diagonalizable matrix. Take D = A and P = identity matrix of size n. Then, this equation holds, but A is still not diagonalizable.

Answer:

-0.6

Step-by-step explanation:

3/5 is 0.6 and the negative makes it -0.6.

Answer:

-0.6

Step-by-step explanation:

Answer:

C. How tightly the molecules in a glass of water are packed together

Step-by-step explanation:

Volume of a substance is different according to the state of the matter.

So for a water molecule, the volume of the the water is definite and can be measured by the container which is the glass cup

So volume can be the measure of how tight the molecule of that substance ate together.

Answer:

1) If the manufacturer's assumptions are correct, it would reed to replace 0.621% of its batteries free

2) The company finds that it is replacing 1.07% of its batteries free of charge. It suspects that its assumption standard deviation of the life of its batteries is incorrect. A standard deviation of 6.084 results in a 1.07% replacement rate

3) Using the revised standard deviation for battery life, the percentage of the manufacturer's batteries that don't qualify for free replacement but do qualify for the prorated credit = 92%

Step-by-step explanation:

This is a normal distribution problem with

Mean = μ = 45 months

Standard deviation = σ = 5.6 months.

Batteries that fail within the first 31 months get a free replacement and batteries that fail after 31 months but within 54 months get a prorated credit toward the purchase of a new battery.

1) Percentage of batteries that'll qualify for a replacement are the batteries that fail within 31 months. That is, P(X ≤ 31)

To obtain this, we first normalize or standardize 31 months.

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ = (31 - 45)/5.6 = - 2.50

The required probability

P(X ≤ 31) = P(z ≤ -2.50)

We'll use data from the normal probability table for these probabilities

P(X ≤ 31) = P(z ≤ -2.50) = 0.00621 = 0.621%

2) The company finds that the percentage of free batteries replaced is actually 1.07%

P(X ≤ 31) = 1.07% = 0.0107

Let the z value of 31 months under this new normal distribution be z'

P(X ≤ 31) = P(z ≤ z') = 0.0107

From the normal distribution table,

z' = -2.301

z' = (x - μ)/σ

-2.301 = (31 - 45)/σ

σ = (-14) ÷ (-2.301) = 6.084 months

3) Using the revised standard deviation for battery life, what percentage of the manufacturer's batteries don't free replacement but do qualify for the prorated credit?

That is, P(31 < X ≤ 54)

We first normalize 31 and 54 using the revised standard deviation

For 31

z = (x - μ)/σ = (31 - 45)/6.084 = - 2.30

For 54

z = (x - μ)/σ = (54 - 45)/6.084 = 1.48

The required probability = P(31 < X ≤ 54)

= P(-2.30 < z ≤ 1.48)

Using the normal distribution tables

P(31 < X ≤ 54) = P(-2.30 < z ≤ 1.48)

= P(z ≤ 1.48) - P(z < -2.30)

= 0.93056 - 0.0107

= 0.91986 = 91.986% = 92% to nearest whole number.

Hope this Helps!!!!

Answer:

[tex]\Delta s_{T} = 4712.4\,m[/tex]

Step-by-step explanation:

(This exercise is written in Spanish and for this reason the response will be presented in such language).

La distancia recorrida por la mulita tras una vuelta es:

[tex]\Delta s = 2\pi\cdot (5\,m)[/tex]

[tex]\Delta s \approx 31.416\,m[/tex]

Ahora, la distancia recorrida total es directamente proporcional a la cantidad de vueltas invertidas. Este indicador se determina por regla de tres simple:

[tex]\Delta s_{T} = \frac{150}{1}\times (31.416\,m)[/tex]

[tex]\Delta s_{T} = 4712.4\,m[/tex]

Answer:

Step-by-step explanation:

As the problem is written, you have ...

  [tex]\dfrac{x}{4} =x+\dfrac{1}{5}\\\\5x=20x+4\qquad\text{multiply by 20}\\\\-15x=4\\\\x=-\dfrac{4}{15}[/tex]

__

If you add parentheses to include x in the numerator, then you have ...

  x/4 = (x +1)/5

  [tex]5x=4(x+1)\qquad\text{multiply by 20}\\\\5x -4x = 4\qquad\text{eliminate parentheses, subtract 4x}\\\\x=4[/tex]

__

Additional comment

We include the second working because it is a fairly common mistake to neglect to put parentheses around a numerator or denominator. The solutions to such problems are not often fractions, so we suspect you intend the latter form.

Answer:

4 yd

Step-by-step explanation:

If l×w×h=v, then v÷l÷w=h

84÷7÷4=h

12÷3=h

h=4

The height of the prism is 4 yards.