Which system of equations represent the matrix shown below?

1 2 -1| 8
-1 0 3| 15
1 -2 4| 18

A. x + 2y + z =8
x + y + 3z =15
x + 2y + 4z =18

B. x + 2y + z =8
x + 3z =15
x + 2y + 4z =18

C. x + 2y - z =8
-x + y + 3z =15
x - 2y + 4z =18

D. x + 2y - z =8
-x + 3z =15
x - 2y + 4z =18

Answer:

The answer is option C.

Step-by-step explanation:

- 9x - 3 > 51

Group like terms

- 9x > 51 + 3

- 9x > 54

Divide both sides by -9

x < - 6

Hope this helps you

Answer:

work is shown and pictured

The slope would be 4/3 and the y-intercept is 1

Create a table x and y and in x there is -3/4 and 0 and for the y side is 0 and 1. The line would be in the 2 quadrant with 2 points on on the y axis 1 and the other on the x axis 0.9 and that would be the graphed description of the line. Sorry if this is hard to understand i don’t have a access to draw or insert an image.

The graph of the linear equation is on the image at the end.

To do it, we need to find two points on the line, so let's evaluate it.

When x = 0

y = (4/3)*0 + 1 = 1 ----> (0, 1)

When x = 3

y = (4/3)*3 + 1 = 5 ---> (3 , 5)

Now just graph these two points and connect them with a line, that will be the graph of the linear equation.

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Answer:

Initial amount (a)= 620

Growth factor (b)= 7.8

Step-by-step explanation:

620 is the initial amount and is multiplied by 7.8 x which is the growth factor.

Answer:

y=2.2

Step-by-step explanation:

1: Distribute all numbers to get rid of all parenthesis

2: Solve

Hope this helped :) LET ME KNOW IF YOU NEED THE ANSWER IN A DIFFERENT FORM I CAN GET IT FOR YOU

We're told (and we can confirm) that [tex]v_3=2v_1-3v_2[/tex], so [tex]v_3[/tex] is a linear combination of the other two vectors.

This means H is sufficiently spanned by [tex]\{v_1,v_2\}[/tex]; no need for the third vector.

But this also means we can write either [tex]v_1[/tex] as a linear combination of [tex]\{v_2,v_3\}[/tex], and [tex]v_2[/tex] as a lin. com. of [tex]\{v_1,v_3\}[/tex]. So any set of these three vectors taken two at a time will span the subspace H. Hence all of b, c, and d are acceptable.

Answer:

The worst-case probability is 0.05

Step-by-step explanation:

The given significance level ([tex]\alpha[/tex]) = 0.05

since Probability of a type I error is [tex]\alpha[/tex]

∴ P (type I error) = 0.05

0.05 will be the worst-case probability of a type I error in at least one of the tests.

Answer:

240

Step-by-step explanation:

You should go to the value 50 °F and see the value that match it

here it's 240 students

Based on the line of best fit, the number of students who wear a jacket to school when the temperature is 50°F is 240.

A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. Usually, the line of the graph is a function that follows the graph.

Given that The graph shows a line of best fit for data collected on the number of students who wear a jacket to school and the average daily temperature in degrees Fahrenheit.

Now, Based on the line of best fit, the number of students who wear a jacket to school when the temperature is 50°F can be found by simply observing the graph when the average daily temperature is 50°F as shown below, and then looking the value of y at that temperature.

Hence,  Based on the line of best fit, the number of students who wear a jacket to school when the temperature is 50°F is 240.

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Answer:

Miss Pepper Mills

Credit Card Statement for the month of April:

a. Average Daily Balance:

Average balance = $618.66/5 = $123.73

b. Calculation of Miss Pepper Mill's Finance Charge for the month of April:

Finance charge

= 18.5% of $20.55 x 1/12

= $0.32

Step-by-step explanation:

a) Data and Calculations:

Activity on the credit card statement for April

Beginning balance = $342.57

Date    Activity    Location       Amount     Daily Balance

04/01  Balance                                           $342.57

04/05 Payment  Payment     $200.00       $142.57

04/15  Charge    Gas               $26.37        $116.20

04/22 Charge    Macy's        $105.42          $10.78

04/25 Charge    Starbuck's     $4.24          $6.54

30 days   Total =                                       $618.66

Average balance = Total of the daily balances divided by 30 days

= $618.66/30 = $20.55

The value of the average daily balance and the finance charge for Miss pepper mills are $123.732 and $0.32 respectively.

The average daily balance :

Sum of balances = (342.57+ (342.57-200) +(342.57 - 200 - 26.37) +(342.57-200-26.37-105.42) + (342.57-200-26.37-105.42-4.24)) = $618.66

Average daily balance :

Finance charge for April :

Average balance × daily rate

Therefore, the average daily balance and finance charge are $123.732 and $0.32 respectively

Learn more : 149.9448066146972668163077278862934016

Answer:

Given that

radius of circle =5units

So, circumference of circle=2πr

=2×π×5

=10π units

hope it helps u...

plz mark as brainliest...

Answer:

[tex]\boxed{Circumference = 10\pi \ units}[/tex]

Step-by-step explanation:

Circumference = [tex]2\pi r[/tex]

Where r = 5

=> Circumference = 2π(5)

=> Circumference = 10π units

Answer:

The correct option is a

Step-by-step explanation:

From the question we are told that

    The sample size is n =  415

    The sample proportion is  [tex]\r p = 0.49[/tex]

Now

     The null hypothesis is  [tex]H_o : p = 0.3[/tex]

     The alternative hypothesis is [tex]H_a : p \ne 0.3[/tex]

The test statistics is mathematically evaluated as

      [tex]t = \frac{\r p - p }{ \frac{\sqrt{ p (1- p )} }{n} }[/tex]

substituting values

      [tex]t = \frac{0.49 - 0.3 }{ \sqrt{ \frac{0.3 (1- 0.3 ) }{415} }}[/tex]

     [tex]t = 8.446[/tex]

Answer:

90°

Step-by-step explanation:

Circumcenter of a triangle is obtained by drawing perpendicular bisectors of the sides of a triangle. Hence GE is perpendicular to AC.

Therefore, m∠GEA = 90°

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Let's solve this step by step.

[tex]2^x + 4^x + 8^x = -14[/tex]

              ↓

In order to factor an integer, we need to repeatedly divide it by the ascending sequence of primes (2, 3, 5...).

The number of times that each prime divides the original integer becomes its exponent in the final result.

    Prime number 2 to the power of 2 = 4                

[tex]2^x + (2^2)^x + (2^3) ^x = -14[/tex]

                    ↓

Prime number 2 to the power of 3 = 8

[tex]2^x + 2^2x + 2^3x = -14[/tex]

                    ↓

We need to exponentiate the power.

The following rule is applied:

           [tex](A^B) ^C = A^BC[/tex]

In our example,

   A is equal to 2,

   B is equal to 2 and

   C is equal to x.

[tex]( 2^x + 2^2x + 2^3x ) + 14 = -14 + 14[/tex]

                         ↑

In order to solve this non-linear equation, we need to move all the terms to the left side.

In our example,

- term −14, will be moved to the left side.

Notice that a term changes sign when it 'moves' from one side of the equation to the other.

___________________

We need to get rid of expression parentheses.

If there is a negative sign in front of it, each term within the expression changes sign.

Otherwise, the expression remains unchanged.

In our example, there are no negative expressions.

                                  ↓

            [tex]2^x + 2^2x + 2^3x + 14 = 0[/tex]

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Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀

Answer:

9.941*10^-6

Step-by-step explanation:

Probability of at most 1 means not more than 1 defective= probability of 1 or probability of 0

Probability of 1 = 50C1(0.25)(0.75)^49

Probability= 50(0.25)*7.55*10^-7

Probability= 9.375*10^-6

Probability of 0

= 50C0(0.25)^0(0.75)^50

= 1(1)(0.566*10^-6)

= 0.566*10^-6

Total probability

= 9.375*10^-6+ 0.566*10^-6

= 9.941*10^-6

Answer:

The transformations needed to obtain the new function are horizontal scaling, vertical scaling and vertical translation. The resultant function is [tex]z'(x) = \frac{1}{2} + \frac{9}{2} \cdot \cos \left(\frac{\pi\cdot x}{90^{\circ}} \right)[/tex].

The domain of the function is all real numbers and its range is between -4 and 5.

The graph is enclosed below as attachment.

Step-by-step explanation:

Let be [tex]z (x) = \cos x[/tex] the base formula, where [tex]x[/tex] is measured in sexagesimal degrees. This expression must be transformed by using the following data:

[tex]T = 180^{\circ}[/tex] (Period)

[tex]z_{min} = -4[/tex] (Minimum)

[tex]z_{max} = 5[/tex] (Maximum)

The cosine function is a periodic bounded function that lies between -1 and 1, that is, twice the unit amplitude, and periodicity of [tex]2\pi[/tex] radians. In addition, the following considerations must be taken into account for transformations:

1) [tex]x[/tex] must be replaced by [tex]\frac{2\pi\cdot x}{180^{\circ}}[/tex]. (Horizontal scaling)

2) The cosine function must be multiplied by a new amplitude (Vertical scaling), which is:

[tex]\Delta z = \frac{z_{max}-z_{min}}{2}[/tex]

[tex]\Delta z = \frac{5+4}{2}[/tex]

[tex]\Delta z = \frac{9}{2}[/tex]

3) Midpoint value must be changed from zero to the midpoint between new minimum and maximum. (Vertical translation)

[tex]z_{m} = \frac{z_{min}+z_{max}}{2}[/tex]

[tex]z_{m} = \frac{1}{2}[/tex]

The new function is:

[tex]z'(x) = z_{m} + \Delta z\cdot \cos \left(\frac{2\pi\cdot x}{T} \right)[/tex]

Given that [tex]z_{m} = \frac{1}{2}[/tex], [tex]\Delta z = \frac{9}{2}[/tex] and [tex]T = 180^{\circ}[/tex], the outcome is:

[tex]z'(x) = \frac{1}{2} + \frac{9}{2} \cdot \cos \left(\frac{\pi\cdot x}{90^{\circ}} \right)[/tex]

The domain of the function is all real numbers and its range is between -4 and 5. The graph is enclosed below as attachment.

Answer:

Step-by-step explanation:

pt=700 is basically evaluate it form the bottom to the top and u must mark me as brainly

Answer:

C. acute angle

Step-by-step explanation:

As you know ,right angle is equal to 90 degrees so half of 90 degrees is 45 degree which is an acute angle (acute angles are the angles which are less than 90 degrees)

Hope this helps and pls mark as brainliest :)

Answer: acute

Step-by-step explanation:

An angle that is less than 90 degrees

Answer:

1024

Step-by-step explanation:

4 * 4 * 4 * 4 * 4

the answer is x=-2

and y=12

Answer:

The probability is  [tex]P(X \ge 20 ) = 0.3707[/tex]

Step-by-step explanation:

From the the question we are told that

    The population proportion is  p =  0.60

    The sample size is  n  =  31

The  mean is evaluated as

       [tex]\mu = n * p[/tex]

substituting values  

       [tex]\mu = 31 *0.60[/tex]

       [tex]\mu = 18.6[/tex]

The standard deviation is evaluated as

    [tex]\sigma = \sqrt{n * p * (1- p )}[/tex]

substituting values  

    [tex]\sigma = \sqrt{31 * 0.6 * (1- 0.6 )}[/tex]

    [tex]\sigma = 2.73[/tex]

The  the probability that at least 20 of them have looked at their score in the past six months is mathematically represented as

     [tex]P(X \ge 20) = 1- P(X < 20)[/tex]

 applying normal approximation we have that

     [tex]P(X \ge 20) = 1- P(X < (20-0.5))[/tex]

   Standardizing

         [tex]1 - P(X < 20) = 1 - P(\frac{X - \mu }{\sigma} < \frac{19.5 - \mu }{\sigma } )[/tex]

         [tex]1 - P(X < 20) = 1 - P(Z < \frac{19.5 - 18.6 }{2.73 } )[/tex]

         [tex]1 - P(X < 20) = 1 - P(Z < 0.33)[/tex]

Form the standardized normal distribution table we have that

      [tex]P(Z < 0.0512)[/tex] = 0.6293

=>   [tex]P(X \ge 20 ) = 1- 0.6293[/tex]

=>   [tex]P(X \ge 20 ) = 0.3707[/tex]

Answer:

The plane is 388 miles far from the airport.

Step-by-step explanation:

We know that, the angle between southeast and south directions is [tex]135^\circ[/tex].

The plane travels as per the triangle as shown in the attached image.

A is the location of airport.

First it travels for 210 miles southeast from A to B and then 210 miles south from B to C.

[tex]\angle ABC = 135^\circ[/tex]

To find:

Side AC = ?

Solution:

As we can see, the [tex]\triangle ABC[/tex] is an isosceles triangle with sides AB = BC = 210 miles.

So, we can say that the angles opposite to the equal angles in a triangle are also equal. [tex]\angle A = \angle C[/tex]

And sum of all three angles of a triangle is equal to [tex]180^\circ[/tex].

[tex]\angle A+\angle B+\angle C = 180^\circ\\\Rightarrow \angle A+135^\circ+\angle A = 180^\circ\\\Rightarrow \angle A = \dfrac{1}{2} \times 45^\circ\\\Rightarrow \angle A =22.5^\circ[/tex]

Now, we can use Sine Rule:

[tex]\dfrac{a}{sinA} = \dfrac{b}{sinB}[/tex]

a, b are the sides opposite to the angles [tex]\angle A and \angle B[/tex] respectively.

[tex]\dfrac{210}{sin22.5^\circ} = \dfrac{b}{sin135^\circ}\\\Rightarrow \dfrac{210}{sin22.5^\circ} = \dfrac{b}{cos45^\circ}\\\Rightarrow b = 210\times \dfrac{1}{\sqrt2 \times 0.3826}\\\Rightarrow b = 210\times \dfrac{1}{0.54}\\\Rightarrow b \approx 388\ miles[/tex]

So, the answer is:

The plane is 388 miles far from the airport.

Answer:

x is 2

Step-by-step explanation:

To solve this you have to use the Pythagoram theorem A^2+B^2=C^2. So 9+16=C^2.

25=C^2

c=5

Than since u know the radius of the circle is 3, its 5-3 so x is 2.

Step-by-step explanation:

. 345,000 cm³.

b. 124,300 hl.

c. 9,000 cm³.

d. 32.5 dm³.

Step-by-step explanation:

To solve this problem you must apply the proccedure shown below:

a. 3,450 deciliters to cubic decimeters:

1 deciliter=100 cubic decimeters

(3,450dl)(\frac{100cm^{3}}{1dl})=345,000cm^{3}(3,450dl)(

1dl

100cm

3

)=345,000cm

3

b. 124.3 hectoliters to deciliters:

1 hectoliter=1,000 deciliters

(124,3hl)(\frac{1,000dl}{1hl})=124,300hl(124,3hl)(

1hl

1,000dl

)=124,300hl

c. 9 liters to cubic centimeters:

1 liter=1,000 cubic centimeters

(9L)(\frac{1,000cm^{3}}{1L})=9,000cm^{3}(9L)(

1L

1,000cm

3

)=9,000cm

3

d. 32.5 liters to cubic decimeters:

1 liter=1 cubic decimeter

32.5L=32.5dm^{3}32.5L=32.5dm

3

your answer follow me plzzz

Answer:

The first one is 345,000 cm³.

The second is 124,300 hl.

the Third is 9,000 cm³.

Anddd the fourth one is 32.5 dm³

:)

Answer:

15) 2.08m

Step-by-step explanation:

We kow tanA= p/b

Here, A=33°

b=3.2m

Then,

tan33°=p/3.2

0.65=p/3.2

p=0.65*3.2

p=2.08

So, The height of tree is 2.08m

14) 59.58ft

tan50°=p/b

1.19=p/50

p=59.58ft

So, The height of signpost is 59.58ft

In both of these problems, we will be using trigonometry! Remember, SOH-CAH-TOA.

14. x = 13.5950 ft

Visualization of the problem is attached below.

We want to find out the opposite side to the angle, and we know the adjacent side. Therefore, we should use the tangent function.

tan(50) = x / 50

x = tan(50) * 50

x = 13.5950 ft (round off wherever you need)

15. x = 241.0016 m

The visualization of the problem is already given. We know the same information as we need in the previous problems, an angle and an adjacent side, and we want to find the opposite side. Therefore, we should use the tangent function.

tan(33) = x / 3.2

x = tan(33) * 3.2

x = 241.0016 (round off wherever you need)

Hope this helps!! :)

Answer:

853.8cm^3

Step-by-step explanation:

[tex]h = 9.5cm\\d = 1.5cm + 9.5 = 10.7\\r =d/2=10.7/2=5.35\\\\V = \pi r^2 h\\V = 3.14 \times (5.35)^2 \times 9.5\\\\V =853.8 cm^3[/tex]

Answer:

m = 26+32

Step-by-step explanation:

To determine the total number of miles biked, add the days together

m = 26+32

Answer:

26+32=m

Step-by-step explanation:

That is the general eqaution of this, because u must add both days worth of biked miles together.

Answer:

(a) The probability that the sample mean will be more than 61 pounds is 0.0069.

(b) The probability that the sample mean will be more than 57 pounds is 0.4522.

(c) The probability that the sample mean will be between 55 and 58 pounds is 0.6112.

(d) The probability that the sample mean will be less than 55 pounds is 0.14686.

(e) The probability that the sample mean will be less than 48 pounds is 0.00001.

Step-by-step explanation:

We are given that the Aluminum Association reports that the average American uses 56.8 pounds of aluminum in a year.

A random sample of 51 households is monitored for one year to determine aluminum usage. Also, the population standard deviation of annual usage is 12.2 pounds.

Let [tex]\bar X[/tex] = sample mean

The z-score probability distribution for the sample mean is given by;

                             Z  =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = average aluminum used by American = 56.8 pounds

           [tex]\sigma[/tex] = population standard deviation = 12.2 pounds

           n = sample of households = 51

(a) The probability that the sample mean will be more than 61 pounds is given by = P([tex]\bar X[/tex] > 61 pounds)

   P([tex]\bar X[/tex] > 61 pounds) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{61-56.8}{\frac{12.2}{\sqrt{51} } }[/tex] ) = P(Z > 2.46) = 1 - P(Z [tex]\leq[/tex] 2.46)

                                                               = 1 - 0.9931 = 0.0069

The above probability is calculated by looking at the value of x = 2.46 in the z table which has an area of 0.9931.

(b) The probability that the sample mean will be more than 57 pounds is given by = P([tex]\bar X[/tex] > 57 pounds)

   P([tex]\bar X[/tex] > 57 pounds) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{57-56.8}{\frac{12.2}{\sqrt{51} } }[/tex] ) = P(Z > 0.12) = 1 - P(Z [tex]\leq[/tex] 0.12)

                                                               = 1 - 0.5478 = 0.4522

The above probability is calculated by looking at the value of x = 0.12 in the z table which has an area of 0.5478.

(c) The probability that the sample mean will be between 55 and 58 pounds is given by = P(55 pounds < [tex]\bar X[/tex] < 58 pounds)

P(55 pounds < [tex]\bar X[/tex] < 58 pounds) = P([tex]\bar X[/tex] < 58 pounds) - P([tex]\bar X[/tex] [tex]\leq[/tex] 55 pounds)    

   P([tex]\bar X[/tex] < 58 pounds) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{58-56.8}{\frac{12.2}{\sqrt{51} } }[/tex] ) = P(Z < 0.70) = 0.75804

   P([tex]\bar X[/tex] [tex]\leq[/tex] 55 pounds) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] [tex]\leq[/tex] [tex]\frac{55-56.8}{\frac{12.2}{\sqrt{51} } }[/tex] ) = P(Z [tex]\leq[/tex] -1.05) = 1 - P(Z < 1.05)

                                                               = 1 - 0.85314 = 0.14686

The above probability is calculated by looking at the value of x = 0.70 and x = 1.05 in the z table which has an area of 0.75804 and 0.85314.

Therefore, P(55 pounds < [tex]\bar X[/tex] < 58 pounds) = 0.75804 - 0.14686 = 0.6112.

(d) The probability that the sample mean will be less than 55 pounds is given by = P([tex]\bar X[/tex] < 55 pounds)

   P([tex]\bar X[/tex] < 55 pounds) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{55-56.8}{\frac{12.2}{\sqrt{51} } }[/tex] ) = P(Z < -1.05) = 1 - P(Z [tex]\leq[/tex] 1.05)

                                                               = 1 - 0.85314 = 0.14686

The above probability is calculated by looking at the value of x = 1.05 in the z table which has an area of 0.85314.

(e) The probability that the sample mean will be less than 48 pounds is given by = P([tex]\bar X[/tex] < 48 pounds)

   P([tex]\bar X[/tex] < 48 pounds) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{48-56.8}{\frac{12.2}{\sqrt{51} } }[/tex] ) = P(Z < -5.15) = 1 - P(Z [tex]\leq[/tex] 5.15)

                                                               = 1 - 0.99999 = 0.00001

The above probability is calculated by looking at the value of x = 5.15 in the z table which has an area of 0.99999.

Answer:

Graph B

Step-by-step explanation:

We are looking for a graph with a double root at x=3. In such cases, the function will "touch' the x-axis at x=3. The graph that shows such behavior is Graph B.

Answer:B

X intercepts (3,0) Y intercepts (0,9)

Answer:

Step-by-step explanation:

[tex]\frac{sin~x}{sec~x+1} =\frac{sin~x}{\frac{1}{cos~x}+1 } =\frac{sin~x~cos~x}{1+cos~x} \\=\frac{sin~x~cos~x}{1+cos~x} \times \frac{1-cos~x}{1-cos~x} \\=\frac{sin~x~cos~x(1-cos~x)}{1-cos^2 x} \\=\frac{sin~x~cos~x(1-cos~x)}{sin^2x} \\=\frac{cos~x(1-cos~x)}{sin~x} \\=cos ~x(csc~x-cot~x)\\or\\=cot~x(1-cos~x)[/tex]

Answer:

72°

Step-by-step explanation:

Given two vectors a and b, The vector i+3j will form a right angled triangle with the x-axis (i.e the horizontal axis).

The opposite side of the triangle on the Cartesian plane will be 3units along the y axis while the adjacent will be 1 unit along the x axis.

The angle between thus two vectors is expressed as tan (theta) = opp/adj

tantheta = 3/1

theta = tan^-1(3)

Theta = 71.57° ≈ 72° to nearest degree