Describe the solutions of the following system in parametric vector form,and provide a geometric comparison with the solution set .

x1 + 3x2- 5x3 = 4
x1+ 4x2 - 8x3 = 7
-3x1- 7x2 +9x3 =6

Answer:

51.5m

Step-by-step explanation:

half 8.1 to get the radius (4.05)

then times pi by 4.05 squared

your answer is 51.5 (rounded)

Answer:

Top prism = 262 in.² Bottom prism = 478 in.²

Step-by-step explanation:

top prism:

front + back: 5 x 3 = 15

sides: 19 x 4 x 2 = 152

bottom: 19 x 5 = 95

15 + 152 + 95 = 262

bottom prism:

front + back: 5 x 6 x 2 = 60

sides: 19 x 6 x 2 = 228

top + bottom: 19 x 5 x 2 = 190

60 + 228 + 190 = 478

Answer:

So first subtract 14 from 32

That means that -6y+4y = 18

Simplify the left side 4-6=-2

-2y = 18

Divide by -2

-9 = y

Step-by-step explanation:

Answer:

-9

Step-by-step explanation:

-6y+14+4y=32

Combine like terms

-2y +14 = 32

Subtract 14 from each side

-2y +14-14 = 32-14

-2y =18

Divide each side by -2

-2y/-2 = 18/-2

y = -9

Answer:

80 km/h

Step-by-step explanation:

2 h 30 min = 2.5 h

Average speed = distance/time= 200 km/2.5 h = 80 km/h

Answer:

GH¢.37480.36

Step-by-step explanation:

Let the amount invested at 12% per annum =GH¢.x

He  invested 580.00 more than the first at 14%.

Therefore:

The amount invested at 14% =GH¢.(x+580)

For each investment option:

Amount Accrued =Principal + Simple Interest

Amount Accrued at 12%

[tex]=x+x*0.12\\=1.12x[/tex]

Amount Accrued at 14%

[tex]=(x+580)+0.14(x+580)\\=x+580+0.14x+81.2\\=1.14x+661.2[/tex]

Mr. Azu had total accumulated amount of  GH42,358.60

Therefore:

1.12x+1.14x+661.2=42,358.60

2.26x=42,358.60-661.2

2.26x=41697.4

x=GH¢.18450.18

Therefore:

The amount invested at 12% per annum= GH¢.18450.18

The amount invested at 14% per annum= GH¢.18450.18+580

=GH¢.19030.18

Mr Azu's Total Investment = 18450.18 +19030.18

=GH¢.37480.36

Answer:

Where is the diagram?

Step-by-step explanation:

Answer:

OC and OE are apposite rays so the Answer is yes

Answer:

D

Step-by-step explanation:

This is the veritcal angles theorem

Answer: choice A

Step-by-step explanation:

by rearranging the initial inequality you’ll get

[tex]\frac{3}{2} x\leq 5-\frac{1}{3}[/tex]

which equals

[tex]\frac{3}{2} x\leq\frac{14}{3}[/tex]

then multiply both sides by 2/3

[tex]x\leq \frac{28}{9}[/tex]

Answer:

8 + 15i

Step-by-step explanation:

(-2 + 3i) + 2(5 + 6i) =

= -2 + 3i + 10 + 12i

= 8 + 15i

Answer:

30%

Step-by-step explanation:

fat ÷ total

15 ÷ 50

.3

30%

Answer:

30%

Step-by-step explanation:

To find the percent from fat, take the calories from fat and divide by the total

15/50

.3

Multiply by 100%

30%

Answer:

3,360

Step-by-step explanation:

We calculate the number of permutations for this problem where the order in which we accommodate people matters to us as follows:

[tex]P=\frac{n!}{(n-r)!}[/tex]

where n is the total number of options we have; the total number of members: [tex]n=16[/tex]

and r is the number of places or positions we are considering which in this case are the President position, the Vice president position and the treasurer position ⇒ 3 positions in total ⇒ [tex]r=3[/tex]

substituting n and r in the formula:

[tex]P=\frac{16!}{(16-3)!} \\\\P=\frac{16!}{13!} \\\\P=3,360[/tex]

A president, a Vice President, and a treasurer can be selected from the members in 3,360 ways

Answer:

5 inches is 5 times as big as 1 inch

Answer:

a)0.2240

b)0.5768

Step-by-step explanation:

Given:

µ=3

Poison probability is given by :

[tex]f_k=\frac{\mu^ke^-^\mu}{k!}[/tex]

a) Evaluating at k=3

[tex]f(3)=\frac{3^3e^-^3}{3!} \approx 0.2240[/tex]

b)Evaluating at k=0,1,2:

[tex]f(0)=\frac{3^0e^-^3}{0!} \approx 0.0498[/tex]

[tex]f(1)=\frac{3^1e^-^3}{1!} \approx 0.1494[/tex]

[tex]f(2)=\frac{3^2e^-^3}{2!} \approx 0.2240[/tex]

Use complement rule:

P(x≥3)= 1 - f(0) - f(1) - f(2)= 1- 0.0498 - 0.1494 - 0.2240 =0.5768

Answer:

A

Step-by-step explanation:

The combinations of decisions and true states of nature for a test of​ hypothesis is given below:

Note that when [tex]H_o[/tex] is False, then the Alternate Hypothesis, [tex]H_a[/tex] is True.

Therefore Option A gives the possible combinations.

The possible choices in Option A are ordered below to correspond to the results above.

Answer:

The 95% confidence interval for the mean number of ounces of ketchup bottle is (23.8, 24.2).

Step-by-step explanation:

The complete question is:

Suppose that a restaurant chain claims that its bottles of ketchup contain 24 ounces of ketchup on average, with a standard deviation of 0.8 ounces. If you took a sample of 49 bottles of ketchup, what would be the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample?

Solution:

The (1 - α)% confidence interval for the population mean is:

[tex]CI=\bar x\pm z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}}[/tex]

The information provided is:

[tex]\bar x=24\\\sigma=0.8\\n=49\\\text{Confidence Level}=95\%[/tex]

The critical value of z for 95% confidence level is:

[tex]z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96[/tex]

*Use a z-table.

Compute the 95% confidence interval for the mean number of ounces of ketchup per bottle as follows:

[tex]CI=\bar x\pm z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}}[/tex]

     [tex]=24\pm1.96\cdot \frac{0.80}{\sqrt{49}}\\\\=24\pm 0.224\\\\=(23.776, 24.224)\\\\\approx (23.8, 24.2)[/tex]

Thus, the 95% confidence interval for the mean number of ounces of ketchup bottle is (23.8, 24.2).

Answer:

Plan A would be the least expensive

Step-by-step explanation:

Plan A= $0.45x100= 45, 45+40=$85

Plan B= $0.35x100= 35, 35+70= %105

(Each plan is for 100 minutes)

Step-by-step explanation:

a rectangle has reflectional symmetry when reflected over the line through the midpoints of its opposite sides

Answer: A square always has a four reflection symmetry no matter the size.

Answer:

true

Step-by-step explanation:

Answer:

22%

Step-by-step explanation:

Car's price is reduced by 8% or 0.92 times a year

after 3 years it will make:

or

Answer:

Hello!

Here is your answer:

22%

I hope I was able to help you.  If not, please let me know!

Step-by-step explanation:

Answer:

  see below

Step-by-step explanation:

The way the problem is worded, we expect "n" to represent the year number we're at the beginning of. That is the initial balance is that when n=1, and the balance at the beginning of year 5 (after interest accrues for 4 years) is the value of obtained when n=5.

After compounding interest for 4 years, the balance will be ...

  500·1.04^4 = 584.93

The matching answer choice is shown below.

Answer:

b

Step-by-step explanation:

Answer:

72°

Step-by-step explanation:

This is called an isosceles triangle. This means that the 2 angles related to the equal sides, are also equal. Hence, the answer is 72°

Answer:

A

Step-by-step explanation:

Since it is isosceles triangle (two equal sides) therefore, there are 2 equal angles too which at the base (72°)

The total angle of triange is 180°

So 180-72-72=36°

Answer:

  parallel lines both have slope 1/3; non-parallel lines both have length 5

Step-by-step explanation:

It generally works well to follow instructions.

A graph of the points shows you that the parallel sides are RA and PT. The difference between the end points of these segments are ...

  A - R = (6, 8) -(-3, 5) = (9, 3) = (Δx, Δy)

So, the slope of RA is Δy/Δx = 3/9 = 1/3

And the other difference and slope are ...

  P -T = (9, 4) -(-3, 0) = (12, 4)   ⇒   Δy/Δx = 4/12 = 1/3

The slope of RA is the same as the slope of PT, so those segments are parallel.

__

The length of segment TR can be found from the differences of the end point coordinates:

  R - T = (-3, 5) -(-3, 0) = (0, 5)

Since these points are on the same vertical line, this tells us the segment length is 5.

The other difference of coordinates is ...

  A - P = (6, 8) -(9, 4) = (-3, 4)

The distance formula tells us the length of AP is then ...

  AP = √((-3)² +4²) = √25 = 5

Non-parallel sides TR and AP have the same lengths, so the trapezoid is isosceles.

Answer:

8+8=16

Step-by-step explanation:

Lets say you have 8 apples and your friend gives you 8 more apples. So, you count 9,10,11,12,13,14,15,16 which was 8 times.

Hope this helps.

Answer:

The maximum height reached by the rocket is of 938.56 feet.

Step-by-step explanation:

The height y, after x seconds, is given by a equation in the following format:

[tex]y(x) = ax^{2} + bx + c[/tex]

If a is negative, the maximum height is:

[tex]y(x_{v})[/tex]

In which

[tex]x_{v} = -\frac{b}{2a}[/tex]

In this question:

[tex]y(x) = -16x^{2} + 230x + 112[/tex]

So

[tex]a = -16, b = 230, c = 112[/tex]

Then

[tex]x_{v} = -\frac{230}{2*(-16)} = 7.1875[/tex]

[tex]y(7.1835) = -16*(7.1835)^{2} + 230*7.1835 + 112 = 938.56[/tex]

The maximum height reached by the rocket is of 938.56 feet.

Answer:

-8

Step-by-step explanation:

For a system to have infinitely many solutions the two equations must be the same line. We can simplify the first and second equations by dividing them by 3 and 2 respectively to get:

y + 4 = 2x

y = 2x + b/2 → y -b/2 = 2x

Since the constants must be equal, 4 = -b/2 which means b = -8.

Answer:

b=-8

Step-by-step explanation:

The transformation matrix for the mapping T is the matrix T such that

[tex]\mathbf T(\vec x)=T\,\vec x[/tex]

where

[tex]T=\begin{bmatrix}1&4&0&0\\0&0&0&0\\0&3&0&1\\0&1&0&-1\end{bmatrix}[/tex]

The correct matrix A is

[tex]A=\left[\begin{array}{cccc}1&4&0&0\\0&0&0&0\\0&3&0&1&0&1&0&-1\end{array}\right][/tex]

To find the matrix A that represents the linear transformation T, we need to determine the coefficients that map the input vector (X₁, X₂, X₃, X₄) to the output vector (x₁ +4x₂, 0, 3x₂ +x₄, x₂ -x₄)

By comparing the corresponding entries in the input and output vectors, we can determine the coefficients of the matrix A.

The first row of A will have the coefficients for X₁ and X₂, which are 1 and 4 respectively. The second row will have all zeros since the output vector has a zero in the second position. The third row will have the coefficient 3 for X₂ and 1 for X₄. Finally, the fourth row will have the coefficient 1 for X₂ and -1 for X₄.

Thus, the matrix A that implements the mapping T is:

[tex]A=\left[\begin{array}{cccc}1&4&0&0\\0&0&0&0\\0&3&0&1&0&1&0&-1\end{array}\right][/tex]

Learn more about linear transformation here:

brainly.com/question/13595405

#SPJ2

Answer:

Percentage of all samples of three men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.20 kg = 78.5%

The sampling error is 0.08083, in terms of the sampling error, 78.5% of samples of three men will have mean brain weights within (1.24×sampling error) of the mean.

Step-by-step explanation:

Complete Question

According to one study, brain weights of men are normally distributed with mean = 1.20 kg and a standard deviation = 0.14 kg.

Determine the percentage of all samples of three men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.20 kg. Interpret your answer in terms of sampling error.

Solution

The Central limit theorem allows us to say

The mean of sampling distribution is approximately equal to the population mean.

μₓ = μ = 1.20 kg

And the standard deviation of the sampling distribution is given as

σₓ = (σ/√N)

σ = population standard deviation = 0.14 kg

N = sample size = 3

σₓ = (0.14/√3) = 0.08083

Percentage of all samples of three men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.20 kg, that is, percentage of all samples of three men with mean brain weights within 1.10 kg and 1.30 kg.

P(1.10 ≤ x ≤ 1.30)

We first normalize or standardize 1.10 and 1.30

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

For 1.10 kg

z = (x - μₓ)/σₓ = (1.10 - 1.20)/0.08083 = -1.24

For 1.30 kg

z = (x - μₓ)/σₓ = (1.30 - 1.20)/0.08083 = 1.24

To determine the required probability

P(1.10 ≤ x ≤ 1.30) = P(-1.24 ≤ z ≤ 1.24)

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

P(1.10 ≤ x ≤ 1.30) = P(-1.24 ≤ z ≤ 1.24)

= P(z ≤ 1.24) - P(z ≤ -1.24)

= 0.89251 - 0.10749

= 0.78502 = 78.502%

The sampling error is 0.08083, in terms of the sampling error, 78.5% of samples of three men will have mean brain weights within (1.24×sampling error) of the mean.

Hope this Helps!!!

Answer:

plot a point at 6 up from (0,0) and then go down one and over three places then plot another point- and so on - and so on

Step-by-step explanation:

To graph the line using the slope and intercept, first understand what the slope and intercept mean:

Slope is how steep or flat the line appears on the graph.

The y-intercept is the point at which the line hits the y-axis. In this equation, the line hits the y-axis at positive 6, which means that the point is (0, 6).

You can use a method called "rise over run" to graph. The slope is negative one over three, so the line will "rise" negative one units after "running" three units.

So, for every one unit down, the line will travel three units to the right.

Graph this from the point (0, 6), your y-intercept, and plot the points according to the slope:

Answer:

This has multiple answers, A, C, And D

Step-by-step explanation:

Answer:

It is definitely A, C, and D.

Step-by-step explanation:

I just answered this question and got it right. I hope this helps and please mark brainliest!

Answer:

  14

Step-by-step explanation:

Opposite angles in a rhombus are congruent. Even if you didn't know that, adding up the angles in this quadrilateral would tell you that ...

  (5x)° = 70°

  x = 70/5 = 14 . . . . . divide by 5

The value of x is 14.