Solve the system by using the inverse of the coefficient matrix. -3x + 9y = 9 3x + 2y = 13 Group of answer choices

Answer:

15√20/6√125

=√20/√5

=2

Step-by-step explanation:

Answer:

a) 12

b) 129

Step-by-step explanation:

a)

[tex]w, x \in \mathbb{Z}_{\ge 0}[/tex]

[tex]w>50\\x<40[/tex]

For the smallest value of [tex]w-x[/tex], we gotta figure out the smallest value for w and the highest value for x.

[tex]w>50 \Rightarrow \text{ smallest value is } 51[/tex]

For [tex]x[/tex], once [tex]-(-x)=x[/tex], we conclude that [tex]x[/tex] cannot be negative and therefore, [tex]x=39[/tex].

[tex]51-39=12[/tex]

b)

[tex]y, z \in \mathbb{Z}_{\ge 0}[/tex]

[tex]y<70\\z\leq 60[/tex]

For the largest value of [tex]y+z[/tex], we gotta figure out the highest value for y and z.

[tex]y<70 \Rightarrow \text{ highest value is } 69[/tex]

[tex]z\leq 60 \Rightarrow \text{ highest value is } 60[/tex]

[tex]y+z=69+60=129[/tex]

Answer: The difference between the estimated and real value of 55-21 is about 4 or 5

Step-by-step explanation:

Answer:

The difference between the estimate and the real value of 55-21 is that when you estimate you're giving an educated guess and the real value is when you're actually doing the work to prove your answer and not just guess.

Step-by-step explanation:

Real Value

55-21=34

 55

- 21

 34

Estimated

55-21=32

Answer:

C

Step-by-step explanation:

If two lines are parallel, their slopes are the same.

Since the slope of line l is 4/9, this means that the slope of line m must also be 4/9.

Answer:

C. 4/9

Step-by-step explanation:

Parallel lines have equal slopes.

Since line l and line m are parallel, then their slopes must be the same.

[tex]m_{l} =m_{m}[/tex]

We know that the slope of line l is 4/9

[tex]\frac{4}{9} = m_{m}[/tex]

Line l has a slope of 4/9, therefore line m must also have a slope of 4/9.

The correct answer is C. 4/9

Step-by-step explanation:

Head(H) Tails(T)

Sample space is S (HHH,HHT,HTH,THH)

Event(HHT,HTH,THH)

so the probability is 3/4

Answer:

3/4

Step-by-step explanation:

Answer:

The actress had more extreme age when winning the​ award.

Step-by-step explanation:

We are given that for all the best​ actors, the mean age is 43.4 years and the standard deviation is 8.8 years. For all best​ actresses, the mean age is 38.2 years and the standard deviation is 12.6 years.

To find who had the more extreme age when winning the​ award, the actor or the​ actress, we will use the z-score method.

Let X = age of the winner for best actor

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

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

where, [tex]\mu[/tex] = mean age = 43.4 years

            [tex]\sigma[/tex] = standard deviation = 8.8 years

It is stated that the age of the winner for best actor was 34, so;

   z-score for 34 =  [tex]\frac{X-\mu}{\sigma}[/tex]

                            =  [tex]\frac{34-43.4}{8.8}[/tex]  = -1.068

Let Y = age of the winner for best actress

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

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

where, [tex]\mu[/tex] = mean age = 38.2 years

            [tex]\sigma[/tex] = standard deviation = 12.6 years

It is stated that the age of the winner for best actress was 62, so;

   z-score for 62 =  [tex]\frac{Y-\mu}{\sigma}[/tex]

                            =  [tex]\frac{62-38.2}{12.6}[/tex]  = 1.889

Since the z-score for the actress is more which means that the actress had more extreme age when winning the​ award.

4 times 4 is 16, think of it like 4 + 4 + 4 + 4.

4 times 4 is 16, think of it like 4 + 4 + 4 + 4.

(4x-16)/3 = 36

4x-16 = 108

4x = 108+16

4x = 124

x = 124/4

x = 31

Answer:

x = 31

Step-by-step explanation:

=> [tex](4x-16)\frac{1}{3} = 36[/tex]

Multiplying 3 to both sides

=> [tex]4x-16 = 36*3[/tex]

=> 4x-16 - 108

Adding 16 to both sides

=> 4x = 108+16

=> 4x = 124

Dividing both sides by 4

=> x = 31

Answer:

[tex]19.6-2.42\frac{5.8}{\sqrt{42}}=17.43[/tex]    

[tex]19.6+2.42\frac{5.8}{\sqrt{42}}=21.77[/tex]    

And the best option for this case would be:

a. (17.5, 21.7)

Step-by-step explanation:

Information given

[tex]\bar X= 19.6[/tex] represent the sample mean

[tex]\mu[/tex] population mean

[tex]\sigma= 5.8[/tex] represent the population deviation

n=42 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

The degrees of freedom, given by:

[tex]df=n-1=42-1=41[/tex]

Since the Confidence is 0.98 or 98%, the significance would be [tex]\alpha=0.02[/tex] and [tex]\alpha/2 =0.1[/tex], and the critical value would be [tex]t_{\alpha/2}=2.42[/tex]

Replacing we got:

[tex]19.6-2.42\frac{5.8}{\sqrt{42}}=17.43[/tex]    

[tex]19.6+2.42\frac{5.8}{\sqrt{42}}=21.77[/tex]    

And the best option for this case would be:

a. (17.5, 21.7)

Answer:

The 98% confidence interval for the population mean is between 17.5 hours and 21.7 hours.

Answer:

Hello!

________________________

5c + 16.5 = 13.5 + 10c

Exact Form:  c = 3/5

Decimal Form: c = 0.6

Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.

Hope this helped you!

Answer:

3000+3d=noods

Step-by-step explanation:

Answer: 1/52 x 1/51 x 1/50 x 1/49

= 1/ 6,497,400

Step-by-step explanation:

Answer/Step-by-step explanation:

Let x = 4 (you and 3 friends)

Ticket cost per head = $5.50

Drink cost per head = $2.50

Popcorn cost per head = $4.00

Expression representing total amount of money spent = $5.50(x) + $2.50(x) + $4.00(x)

Evaluate the expression by plugging in the value of x = 4

Total amount of money spent = $5.50(4) + $2.50(4) + $4.00(4)

= $22 + $10 + $16 = $48

Total amount of money spent = $48

Maya should Isolate the variable x² option (A) Isolate the variable x² is correct.

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

The complete question is:

Maya is solving the quadratic equation by completing the What should Maya do first? square.

4x² + 16x + 3 = 0

We have a quadratic equation:

4x² + 16x + 3 = 0

To make the perfect square

Maya should do first:

Isolate the variable x²

To make the coefficient of x² is 1.

4(x² + 4x + 3/4) = 0

x² + 4x + 3/4 = 0

x² + 4x + 2² - 2² +  3/4 = 0

(x + 2)² - 4 + 3/4 = 0

(x + 2)² = 13/4

x + 2 = ±√(13/4)

First, take the positive and then the negative sign.

x = √(13/4) - 2

x = -√(13/4) - 2

Thus, Maya should Isolate the variable x² option (A) Isolate the variable x² is correct.

Learn more about quadratic equations here:

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Answer:

96.08% probability that their mean rebuild time is less than 8.9 hours.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

[tex]\mu = 8.4, \sigma = 1.8, n = 40, s = \frac{1.8}{\sqrt{40}} = 0.2846[/tex]

Find the probability that their mean rebuild time is less than 8.9 hours.

This is the pvalue of Z when X = 2.9.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{2.9 - 2.4}{0.2846}[/tex]

[tex]Z = 1.76[/tex]

[tex]Z = 1.76[/tex] has a pvalue of 0.9608

96.08% probability that their mean rebuild time is less than 8.9 hours.

Answer:

The correct option is (A)

A. Replace row 4 by its sum with - 4 times row 3.

[tex]\left[\begin{array}{ccccc}1&-4&4&0&-2\\0&2&-6&0&5\\0&0&1&2&-4\\0&0&0&-3&15\end{array}\right][/tex]

w = 8

x = 17/2

y = 6

z = -5

Step-by-step explanation:

The given matrix is

[tex]\left[\begin{array}{ccccc}1&-4&4&0&-2\\0&2&-6&0&5\\0&0&1&2&-4\\0&0&4&5&-1\end{array}\right][/tex]

To solve this matrix we need to create a zero at the 4th row and 3rd column which is 4 at the moment.

Multiply 3rd row by -4 and add it to the 4th row.

Mathematically,

[tex]R_4 = R_4 - 4R_3[/tex]

So the correct option is (A)

A. Replace row 4 by its sum with - 4 times row 3.

So the matrix becomes,

[tex]\left[\begin{array}{ccccc}1&-4&4&0&-2\\0&2&-6&0&5\\0&0&1&2&-4\\0&0&0&-3&15\end{array}\right][/tex]

Now the matrix may be solved by back substitution method.

Bonus:

The solution is given by

Eq. 1

-3z = 15

z = -15/3

z = -5

Eq. 2

y + 2z = -4

y + 2(-5) = -4

y - 10 = -4

y = -4 + 10

y = 6

Eq. 3

2x - 6y + 0z = 5

2x - 6(6) = 5

2x - 12 = 5

2x = 12 + 5

2x = 17

x = 17/2

Eq. 4

w - 4x + 4y + 0z = -2

w - 4(17/2) + 4(6) = -2

w - 34 + 24 = -2

w - 10 = -2

w = -2 + 10

w = 8

Answer:

C

Step-by-step explanation:

undefined slope means tat the denominator=0 in the equation

m=y2-y1/x2-x1

A: m=-1-1/1+1=-2

B;2-2/2+2=0

C: 3+3/-3+3 = 6/0 undefined

D: 4+4/4+4=1

Two ratios that are equal to 7:6 are 14:12 and 21:18, as they are the same, but 7 and 6 are multiplied by the same number (2 in the first, and 3 in the second.)

Answer:

The upper confidence bound for the true average difference between 1-minute modulus and 4-week modulus is 2933.82.

Step-by-step explanation:

Compute the mean difference and standard deviation of the difference as follows:

[tex]\bar d=\frac{1}{n}\sum d_{i}=\frac{1}{15}\times [1380+3370+2580+...+3520]=2642.67\\\\S_{d}=\sqrt{\frac{1}{n-1}\sum (d_{i}-\bar d)^{2}}\\=\sqrt{\frac{1}{15-1}[(1380-2642.67)^{2}+(3370-2642.67)^{2}+...}=525.69[/tex]

The degrees of freedom is:

df = n - 1

   = 15 - 1

   = 14

Th critical value of t is:

[tex]t_{\alpha/2, (n-1)}=t_{0.05/2, 14}=2.145[/tex]

*Use a t-table.

Compute the upper confidence bound for the true average difference between 1-minute modulus and 4-week modulus as follows:

[tex]\text{Upper Confidence Bound}=\bar d+t_{\alpha/2, (n-1)}\cdot \frac{S_{d}}{\sqrt{n}}[/tex]

                                        [tex]=2642.67+2.145\cdot \frac{525.69}{\sqrt{15}}\\\\=2642.67+291.15\\\\=2933.82[/tex]

Thus, the upper confidence bound for the true average difference between 1-minute modulus and 4-week modulus is 2933.82.

Answer:

x - y = -7

Step-by-step explanation:

Standard Form: Ax + By = C

Step 1: Move the x over

-x + y = 7

Step 2: Factor out a -1

-1(x - y) = 7

Step 3: Divide both sides by -1

x - y = -7

Answer:

x-y = -7

Step-by-step explanation:

Ax + By = C  is the standard form for a line where A is a positive number

y = x + 7

Subtract x from each side

-x+y = x+7-x

-x+y = 7

Multiply each side by -1

x-y = -7

Answer:

Step-by-step explanation:

Answer:

1 woman Teacher

Step-by-step explanation:

We proceed as follows;

Let W and M represent the set of women and men respectively , and T represent teachers

from the information given in the question we have

n(W)=29

n(M)=23

n(T)=4

n(M U T)=24

Mathematically;

n(MUT)=n(M)+n(T)-n(MnT)

24=23+4-n(Mn T)

n(MnT)=3

that is number of men teachers is 3,

so out of 4 teachers there are 3 men ,

and remaining 1 is the women teacher .

so the number of women teachers attending the lecture is 1

Answer:

D

Step-by-step explanation:

We calculate the z-score for each

Mathematically;

z-score = (x-mean)/SD

z1 = (1.9-2.1)/0.2 = -1

z2 = (2.3-2.1)/0.2 = 1

So the proportion we want to calculate is;

P(-1<x<1)

We use the standard score table for this ;

P(-1<x<1) = P(x<1) -P(x<-1) = 0.68269 which is approximately 68%

Answer:

68

Step-by-step explanation:

Recall the definition of the cross product:

i x i = j x j = k x k = 0

i x j = k

j x k = i

k x i = j

The cross product is antisymmetric, or anticommutative, meaning that for any  vectors u and v, we have u x v = - (v x u).

It's also distributive, so for any vectors u, v, and w, we have (u + v) x w = (u x w) + (v x w).

Taking all of these properties together, we get

b x a = (6i - j + 2k) x (2i + 2j - 5k)

b x a = 12 (i x i) - 2 (j x i) + 4 (k x i)

............. + 12 (i x j) - 2 (j x j) + 4 (k x j)

............. - 30 (i x k) + 5 (j x k) - 10 (k x k)

b x a = 1 (j x k) + 34 (k x i) + 14 (i x j)

b x a = i + 34j + 14k

Answer:

Short answer, it is D)  i+34j + 14k

Step-by-step explanation:

Edge 2021.

Answer:

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

H0: µ = 7.2

For the alternative hypothesis,

H1: µ ≠ 7.2

This is a two tailed test.

Since the population standard deviation is given, the test statistic would be the z score determined from the normal distribution table. The formula is

z = (x - µ)/(σ/√n)

Where

x = sample mean

µ = population mean

σ = population standard deviation

n = number of samples

From the information given,

µ = 7.2

x = 7.3

σ = 0.8

n = 250

z = (7.3 - 7.2)/(0.8/√250) = 1.976

Test statistic is 1.976

Answer:

It's written as

[tex]2.6 \times {10}^{ - 3} [/tex]

Hope this helps you

Answer:

2.6 × 10⁻³

Step-by-step explanation:

To write a number in scientific notation, move the decimal to the right or left until you reach a number that is 1 or higher.

In the decimal 0.0026, the first number that is 1 or higher is 2.

0.0026 ⇒ 2.6

When trying to figure out the exponent, here are some things to keep in mind:

- when you move the decimal to the right, the exponent is negative

- when you move the decimal to the left, the exponent is positive

You moved the decimal to the right three places. So the exponent will be -3.

The result is 2.6 × 10⁻³.

Hope this helps. :)

Answer:

[tex]-\theta cos\thsta+sin\theta = \frac{y^{2} }{2} + ln y + \pi - \frac{1}{2}[/tex]

Step-by-step explanation:

Given the initial value problem [tex]\frac{1}{\theta}(\frac{dy}{d\theta} ) =\frac{ ysin\theta}{y^{2}+1 } \\[/tex] subject to y(π) = 1. To solve this we will use the variable separable method.

Step 1: Separate the variables;

[tex]\frac{1}{\theta}(\frac{dy}{d\theta} ) =\frac{ ysin\theta}{y^{2}+1 } \\\frac{1}{\theta}(\frac{dy}{sin\theta d\theta} ) =\frac{ y}{y^{2}+1 } \\\frac{1}{\theta}(\frac{1}{sin\theta d\theta} ) = \frac{ y}{dy(y^{2}+1 )} \\\\\theta sin\theta d\theta = \frac{ (y^{2}+1)dy}{y} \\integrating\ both \ sides\\\int\limits \theta sin\theta d\theta =\int\limits \frac{ (y^{2}+1)dy}{y} \\-\theta cos\theta - \int\limits (-cos\theta)d\theta = \int\limits ydy + \int\limits \frac{dy}{y}[/tex]

[tex]-\theta cos\thsta+sin\theta = \frac{y^{2} }{2} + ln y +C\\Given \ the\ condition\ y(\pi ) = 1\\-\pi cos\pi +sin\pi = \frac{1^{2} }{2} + ln 1 +C\\\\\pi + 0 = \frac{1}{2}+ C \\C = \pi - \frac{1}{2}[/tex]

The solution to the initial value problem will be;

[tex]-\theta cos\thsta+sin\theta = \frac{y^{2} }{2} + ln y + \pi - \frac{1}{2}[/tex]

Using separation of variables, it is found that the solution of the initial value problem is:

The differential equation is given by:

[tex]\frac{1}{\theta}\left(\frac{dy}{d\theta}\right) = \frac{y\sin{\theta}}{y^2 + 1}[/tex]

Applying separation of variables, we have that:

[tex]\frac{y^2 + 1}{y}dy = \theta\sin{\theta}d\theta[/tex]

[tex]\int \frac{y^2 + 1}{y}dy = \int \theta\sin{\theta}d\theta[/tex]

The first integral is solved applying the properties, as follows:

[tex]\int \frac{y^2 + 1}{y}dy = \int y dy + \int \frac{1}{y} dy = \frac{y^2}{2} + \ln{y} + K[/tex]

The second integral is solved using integration by parts, as follows:

[tex]u = \theta, du = d\theta[/tex]

[tex]v = \int \sin{\theta}d\theta = -\cos{\theta}[/tex]

Then:

[tex]\int \theta\sin{\theta}d\theta = uv - \int v du[/tex]

[tex]\int \theta\sin{\theta}d\theta = -\theta\cos{\theta} + \int \cos{\theta}d\theta[/tex]

[tex]\int \theta\sin{\theta}d\theta = -\theta\cos{\theta} + \sin{\theta}[/tex]

Then:

[tex]\frac{y^2}{2} + \ln{y} + K = -\theta\cos{\theta} + \sin{\theta}[/tex]

[tex]y(\pi) = 1[/tex] means that when [tex]\theta = \pi, y = 1[/tex], which is used to find K.

[tex]\frac{1}{2} + \ln{1} + K = -\pi\cos{\pi} + \sin{\pi}[/tex]

[tex]\frac{1}{2} + K = \pi[/tex]

[tex]K = \pi - \frac{1}{2}[/tex]

Then, the solution is:

[tex]\frac{y^2}{2} + \ln{y} + \pi - \frac{1}{2} = -\theta\cos{\theta} + \sin{\theta}[/tex]

[tex]\frac{y^2}{2} + \ln{y} + \pi - \frac{1}{2} + \theta\cos{\theta} - \sin{\theta} = 0[/tex]

To learn more about separation of variables, you can take a look at https://brainly.com/question/14318343

Answer:

B

Step-by-step explanation:

Given

x² + 14x = 51

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(7)x + 49 = 51 + 49 , that is

(x + 7)² = 100 ( take the square root of both sides )

x + 7 = ± [tex]\sqrt{100}[/tex] = ± 10 ( subtract 7 from both sides )

x = - 7 ± 10

Thus

x = - 7 - 10 = - 17

x = - 7 + 10 = 3

Answer:-4-5

Step-by-step explanation:

Answer:

f(–3) = –5

Step-by-step explanation:

Answer:

Amount after 12 years is $205.42

Step-by-step explanation:

Fibal amount a is not given and to be found

Principal amount p = $100

Rate r = 6% ° 0.06

Years t = 20

Number if times computed n = 20*12

n = 240

a(t)=p(1+r/n)^nt

a = 100(1+0.06/240)^(240*12)

a = 100(1+0.00025)^(2880)

a= 100(1.00025)^2880

a= 100(2.054248)

a= 205.4248

To the nearest cent

a =$ 205.42

Amount after 12 years is $205.42

Answer:

C.

Step-by-step explanation:

Restrictions that limit the settings of the decision variables. Therefore, option C is the correct answer.

Linear programming, mathematical modeling technique in which a linear function is maximized or minimized when subjected to various constraints.

Constraints are conditions or restrictions imposed on a system in order to ensure that it functions properly. In linear programming, constraints are used to limit the settings of the decision variables in order to ensure that the model's objective is met. For example, a constraint might be that the sum of two decision variables must equal a certain value. The constraints help to ensure that the solution obtained from the model is feasible and meets the objectives of the problem.

Therefore, option C is the correct answer.

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