Guys i need help!!!!

(a) The inverse matrix A⁻¹ is:

| -9/2   5/2 |

|  1     -1 |

(b) The solution to the system is x = -9/2 and y = 1. z is undetermined.

(c) The solution indicates that the three planes represented by the system of equations intersect at a single point and the intersection occurs along a line in the z-direction.

(a) The coefficient matrix, A, is given by:

A = | 2  10   42 |

     | 4  18   10 |

We can use matrix inversion. A matrix is invertible if its determinant is non-zero. Let's calculate the determinant of matrix A:

det(A) = (2 * 18) - (10 * 4) = 36 - 40 = -4

Since the determinant is non-zero (-4 ≠ 0), the matrix A is invertible. Now, we can find the inverse of A:

A⁻¹ = (1/det(A)) * adj(A)

Where adj(A) denotes the adjugate of matrix A. To calculate the adjugate, we need to find the cofactor matrix of A and then take its transpose:

Cofactor matrix of A:

| 18   -4 |

| -10   2 |

Transpose of the cofactor matrix:

| 18  -10 |

| -4    2 |

Now, divide the transpose by the determinant:

A⁻¹ = (1/-4) * | 18  -10 |

                 | -4    2 |

Simplifying:

A⁻¹ = | -9/2   5/2 |

        |  1     -1 |

Therefore, the inverse matrix A⁻¹ is:

| -9/2   5/2 |

|  1     -1 |

(b) We have the equation AX = B, where X is the column vector of variables (x, y, z), A is the coefficient matrix, and B is the column vector of constants.

The coefficient matrix A is:

A = | 2  10   42 |

     | 4  18   10 |

The column vector B is:

B = | 1 |

      | 0 |

Now, we can solve for X using A-1:

X = A⁻¹ * B

Substituting the values:

X = | -9/2   5/2 | * | 1 |

          | 1    -1 |      | 0 |

Multiplying the matrices:

X = | (-9/2 * 1) + (5/2 * 0) |

        | (1 * 1) + (-1 * 0) |

Simplifying:

X = | -9/2 |

        |   1   |

Therefore, the solution to the system is x = -9/2 and y = 1. The value of z is not determined from this calculation.

(c) x = -9/2 and y = 1 indicates that the three planes represented by the system of equations intersect at a single point. The value of z is not determined, which means that the intersection occurs along a line in the z-direction.

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Answer:

1. D

2. B

3. C

4. A

Step-by-step explanation:

just know when the sentence says "each" or "per" next to a number, there need to be an x next to it.

In other words, I kinda just winged it :P

Answer:

13 + x ≤ 22

x ≤ 9

Step-by-step explanation:

Total players = 22

Players available = 13

Players remaining = x

The inequality can be written as:

Players available + Players remaining ≤ Total players

13 + x ≤ 22

x ≤ 22 - 13

x ≤ 9

Answer:

The answer is J

Step-by-step explanation:

If you start from Quinn's location (8,7), and move south 3 units, you get to (8,4). Then you move to the west 4 units and that gets you to (4,4).

hope this helped! :)

Answer:

5

Step-by-step explanation:

The winnings are in G.P. : 1, 2, 4, ..... till 10 toss.

[tex]$a_n = 1 \times 2^{n-1}\ \ \ \forall \ n = 1,2,3,4,....,10$[/tex]

[tex]$a_n$[/tex] denotes the winnings on the [tex]$n^{th}$[/tex] toss.

The probability of earning amount [tex]$a_n$[/tex] on the [tex]$n^{th}$[/tex] toss is = [tex]$\left(\frac{1}{2}\right)^n$[/tex]

∴ [tex]$E(X) = \sum_{n=1}^{10} \ a_n \times \left(\frac{1}{2}\right)^n $[/tex]

            [tex]$=\sum_{n=1}^{10} \ 1 \times \frac{2^{n-1}}{2^n} $[/tex]

           [tex]$=\sum_{n=1}^{10} \ \frac{1}{2}$[/tex]

Sum of the 1st n terms of the A.P. is :

[tex]$=\frac{n}{2}[2a+(n-1)d] $[/tex]

[tex]$=\frac{10}{2}[2\times \frac{1}{2}+(10-1)\times 0] $[/tex]

= 5

Therefore, E(X) = 5

Hence the expected value of the game is 5

Answer:

6. D

7. F

8.A

9. B

10 C

13.Question- Write an expression using division and subtraction with a difference of 3.

answer-  (12 divide 3) -1

  Twelve divided by three is four. Four minus 1 is three.

12. Question- Write an expression using multiplication and addition with a sum of 16.

answer- There are many answers for this and this is one of them:

Y=4(3+1)

Y=16

or

Y=2(6+2)

Y=16

11.  Question- Sam bought two CDs for $13 each. Sales tax for both CDs was $3. Write an expression to show how much Sam paid in all.

answer- Expression- (13*2)(3*2)=$32

This is the answer because Sam bought two CD's for 13, 13*2, and the sales tax was $ 3, so 3*2=6

Answer:

C = 4π in

Step-by-step explanation:

We require to find the radius r of the circle

Given the area is 4π , then

πr² = 4π ( divide both sides by π )

r² = 4 ( take the square root of both sides )

r = [tex]\sqrt{4}[/tex] = 2

Then

C = 2πr = 2π × 2 = 4π inches

Answer:

4π in

Step-by-step explanation:

The formula for area is πr². We will work backwards from 4π. First, I will do √4 so I can find r.

√4 = 2

Now, I know that r = 2. Next, I will substitute r into the circumference formula which is 2πr.

2π(2) - I know r is 2 from my previous set.

Now, I will simplify.

2 · 2 π = 4π

Since the question is asking in terms of π, I will not simplify all the way, and leave pi as is.

a: 550-n×55

Step-by-step explanation:

because she withdraws every week 55 then the equation is that

Answer:

Explanation:

so the equation is: A = 550 - (n55)

A = 550 - (7×55)

A = 550 - 385

A = $165.00

Answer:

A

Step-by-step explanation:

The critical z value for a confidence level of 85% is approximately 1.44.

To understand this better, let's delve into the concept of confidence level. A confidence level is a measure of the uncertainty or margin of error associated with an estimation. In this case, we are given a confidence level of 85%, which means that we want to be 85% confident that the true population parameter falls within a specific range.

To find the critical z value, we need to determine the z value that leaves a certain percentage in the tails of the standard normal distribution. Since the confidence level is 85%, we divide this value by 2 to get a/2, which is 0.85/2 = 0.425. This value corresponds to the area under the curve in one tail of the distribution.

Using a standard normal distribution table or a statistical software, we can find the z value that corresponds to a cumulative probability of 0.425. The closest z value to this probability is approximately 1.44. Therefore, the critical z value for a confidence level of 85% is approximately 1.44.

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Answer:

37 pounds of apples.

Step-by-step explanation:

you add together the amount of apples that both people have gathered, which in this case would be 33+4 which makes 37, so your answer would be 37 apples.

Answer:

The discount was 24%.

Step-by-step explanation:

24% of 50 is 12.

Answer:

0.5, 0, -1/4, -1

Answer: 55

Step-by-step explanation:

Since lines m and n are parallel, angle 55 would be the same for the measure of angle 1.

Answer:

2/b

Step-by-step explanation:

9 yards

Answer:

you got this

Step-by-step explanation:

I believe in you

Answer:

(1,1)

Step-by-step explanation:

Since both the equations equal y, we can replace one of them with y.

y=-3x + 4

3x - 2 = -3x + 4

Add 3x to both sides.

6x - 2 = 4

Add 2 to both sides of the equation.

6x = 6

x = 1

Now that we know what x is, we can plug that value into one of the original equations.

y = 3x -2

= 3(1) - 2

= 3 - 2

= 1

Answer:

The tree is 8 foot long

hope this helps

good day mate

Answer:

8

Step-by-step explanation:

12:6 = x:4

2:1 = x:4

x=8

Answer:

1. false

2. false

3. true

Step-by-step explanation:

Answer:

The answer is a...............

Answer:

the answer is C

Step-by-step explanation:

As the number of days increases, the number of daily visitors at the visual arts exhibit levels off to a lower amount than the number of daily visitors at the sculpture exhibit.

As the number of days increases, the number of daily visitors at the visual arts exhibit levels off to a lower amount than the number of daily visitors at the sculpture exhibit.

The correct option is C.

A function is a law that relates a dependent and an independent variable.

The function representing the Visual Arts Exhibit is

V(n) = (800/x) +120

V(10) = 80+120 = 200

V( 50) = 16+120 = 136

V(100) = 8 +120 = 128

V(120) = 6.67 + 120 = 128.67

V(200) = 4 +120 = 124

The number of visitors in the Visual Arts Exhibit is decreasing with increasing number of days.

Therefore correct option is C .

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Answer:

turtle biscuit believes in you

Answer:

3600 Liters

Step-by-step explanation:

The given rate is 2L and we have to find how much water will flow in 1/2 hours at the same rate

1/2 hour is the same thing as 30 mins

multiply by 60 to convert minutes to seconds

[tex]3omin * \frac{60sec}{1min} = 1800 s[/tex]

since the rate is 2L per second we multiply 1800 by 2 and get 3600 Liters

Answer:

who?

Step-by-step explanation:

Given: Nationwide, 40% of college seniors say that if they could start their college education over, they would have selected a different major. A student researcher in the education department selected a random sample of 50 seniors at Harvard and asked them if they the same question.

a. Mean is 0.40 (40%) and Standard deviation = 0.0775.

b. we cannot conclude that the percent that would have selected a different major is different at Harvard than the national average.

a. Assuming the percent of seniors at Harvard that would select a different major is consistent with the national percentage, X (the number in 50 randomly selected seniors that would select a different major at Harvard) would have an approximately normal distribution.

The mean would be the same as the population mean, which is 0.40 (40%).

The standard deviation would be calculated using the formula given below:

Standard deviation = sqrt[(p(1-p))/n], Where, p = population proportion (0.40), n = sample size (50).

Standard deviation = sqrt[(0.40 x 0.60)/50]

Standard deviation ≈ 0.0775

b. To determine if the percent that would have selected a different major is different at Harvard than the national average, we need to perform a hypothesis test.

Hypotheses:H_0: p = 0.40 (The proportion of seniors at Harvard who would have selected a different major is the same as the national percentage.)

H_a: p ≠ 0.40 (The proportion of seniors at Harvard who would have selected a different major is different from the national percentage.)

Since the sample size (50) is greater than 30 and the population standard deviation is unknown, we can use the z-test to test the hypothesis.

The formula for the test statistic is given below:

z = (p - P)/sqrt[(P(1 - P))/n], Where, p = sample proportion, P = population proportion, n = sample size.

z = (12/50 - 0.40)/sqrt[(0.40 x 0.60)/50]

z ≈ -1.84

Using a significance level of α = 0.05 and a two-tailed test, the critical values of z are ±1.96.

Since the calculated z-value (-1.84) is less than the critical value (-1.96), we fail to reject the null hypothesis.

We do not have sufficient evidence to conclude that the proportion of seniors at Harvard who would have selected a different major is different from the national percentage.

Therefore, we cannot conclude that the percent that would have selected a different major is different at Harvard than the national average.

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Answer:

[tex](4,-20)[/tex]

Step-by-step explanation:

Let [tex]P(x,y),\,Q(u,v)[/tex] be two points then midpoint of [tex]PQ[/tex] is given by [tex](\frac{x+u}{2},\frac{y+v}{2})[/tex]

Put midpoint as [tex](6,-10)[/tex] and [tex](u,v)=(8,0)[/tex]

Therefore,

[tex](\frac{x+u}{2},\frac{y+v}{2})=(6,-10)\\\\(\frac{x+8}{2},\frac{y+0}{2})=(6,-10)\\\\\frac{x+8}{2}=6,\,\frac{y}{2}=-10\\\\x+8=12,\,y=-20\\x=12-8,\,y=-20\\x=4,\,y=-20[/tex]

So, the other point is [tex](4,-20)[/tex]

Answer:

Step-by-step explanation:

We know that there are 24 white marbles in the starting.

a. How many were not chosen. => 1/6 of the white marbles.

1/6 * 24 = 4 marbles were not chosen.

b. 24 - 4 = 20 marbles were chosen

c. Not enough Info

Answer:

4,20,not enough info

Step-by-step explanation:

Answer:

Step-by-step explanation:

the area of the rectangle is : -7y² ( -2y^4+y²-1)

14y^6-7y^4+7y²   unit

The required answer is  sec θ = -√2.

Explanation:-

Part 1: Given cosine of theta is equal to radical 3 over 2 on the domain [0,[infinity]).

To determine three possible angles θ,  the cosine inverse function which is a cos and since cosine function is positive in the first and second quadrant. Therefore  conclude that, cosine function of θ = radical 3 over 2 implies that θ could be 30 degrees or 330 degrees or 390 degrees. So, θ = {30, 330, 390}.Part 2:To convert 495° to radians, multiply by π/180°.495° * π/180° = 11π/4To find sec θ, we use the reciprocal of the cosine function which is sec.

Therefore, sec θ = 1/cos θ.To find cos 11π/4,  the reference angle, which is 3π/4. Cosine is negative in the third quadrant so the final result is sec θ = -√2.

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Answer:

Step-by-step explanation:

Monday: c and p

Tuesday: 2c+p

Wednesday: 2c+p/2

Thursday: 6c+3p/2

Friday: (2c-12)+(p/2+5)

Adding them all up, you get, for Monday-Friday:  (13c-12)+(9p/2+5)

I'm not sure how to explain this to you though, you just follow the directions they gave, to multiply and subtract.

Hope this is helpful!