Which are the ordered pairs?

To solve for x, we just need to compute the inverse of A (if it exists) and multiply it by b. If A is invertible, then this method will give us the unique solution to the linear system Ax=b.

To solve a linear system of the form Ax=b using inverse matrices, we can first find the inverse of matrix A (if it exists) and then multiply both sides of the equation by \(A^-1\), giving us:

\(A^-1Ax = A^-1b\)

Since\(A^-1A\) is the identity matrix I, we can simplify the left-hand side to just x:

\(x = A^-1b\)

However, it's worth noting that computing the inverse of a matrix can be computationally expensive, particularly for large matrices.

So, while using inverse matrices can be a useful technique for solving small systems, it may not be the most efficient approach for larger systems. In those cases, other techniques such as Gaussian elimination or LU decomposition may be more appropriate.

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Answer:

The red marbles.

Step-by-step explanation:

It is because Red has the least amount of marbles, therefore it is most likely for you to not pull out a red marble.

The probability that more than one-third of the students in this sample wear contacts is roughly 0.234, according to the Normal model.

Probability is the concept that describes the likelihood of an event occurring.

In real life, we frequently have to make predictions about how things will turn out.

We may be aware of the result of an occurrence or not.

When this occurs, we state that there is a possibility that the event will occur.

In general, probability has many excellent applications in games, commerce, and this newly growing area of artificial intelligence

The chance of an event can be calculated using the probability formula by only dividing the favourable number of possibilities by the total number of potential outcomes.

Hence, The probability that more than one-third of the students in this sample wear contacts is roughly 0.234, according to the Normal model.

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The estimated probability of finding at most 50 acceptable circuits in a batch of 60 is approximately 0.6591.

To estimate the probability of finding at most 50 acceptable circuits in a batch of 60 from a certain factory, where the probability of passing the quality test is (p = 0.8) and the outcomes of the tests are mutually independent, we can use the Central Limit Theorem (CLT).

The CLT states that for a large enough sample size, the distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution.

Let's denote (X) as the number of acceptable circuits in a batch of 60. Since each circuit passes the test with a probability of 0.8, we can model (X) as a binomial random variable with parameters (n = 60) and (p = 0.8).

To estimate the probability of finding at most 50 acceptable circuits, we can calculate the cumulative probability using the normal approximation to the binomial distribution.

Since the sample size is large \((\(n = 60\))\), we can approximate the distribution of (X) as a normal distribution with mean \(\(\mu = np = 60 \times 0.8 = 48\)\) and standard deviation \(\(\sigma = \sqrt{np(1-p)}\) = \(\sqrt{60 \times 0.8 \times 0.2} \approx 4.90\).\)

Now, we want to find the probability of\(\(P(X \leq 50)\)\). We can standardize the value using the z-score:

\(\[P(X \leq 50) = P\left(\frac{X - \mu}{\sigma} \leq \frac{50 - 48}{4.90}\right) = P(Z \leq 0.41)\]\)

Using the standard normal distribution table or calculator, we can find that \(\(P(Z \leq 0.41) \approx 0.6591\).\)

Therefore, the estimated probability of finding at most 50 acceptable circuits in a batch of 60 is approximately 0.6591.

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Answer: Try 3x+6

Step-by-step explanation:

Given:

The objective is to find the number.

Explanation:

Consider the unknown number as x,

First, four times the number can be written as 4x.

Twenty more than 4 time the number will be,

Then, twice the number can be represented as 2x.

And the difference between 2 and twice the number will be,

Now, equate both the equations (1) and (2).

Hence, the unknown number is -3.

After 12 weeks, Darnell′s savings account will have a total of $750.

When the difference between the consecutive terms of a sequence is constant, the succession is classified as an arithmetic sequence.

For solving questions about this subject, you can use the formula below.

an=a1+d*(n-1), where:

an= n th term of the sequence

a1= first term of the sequence

d= common difference

n=total numbers of the sequence

Therefore,

f(n)= a1 + d*(n-1), with a1=310, d=350-310=40

f(n)= 310+ 40*(n-1)

For f(12), you should replace n for 12, then:

f(12)= 310+ 40*(12-1)

f(12)= 310+ 40*(11)

f(12)=310+440

f(12)=750

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Answer:

y = 2x - 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = A(4, 7) and (x₂, y₂ ) = B(2, 3)

m =  =  = 2, thus

y = 2x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation.

Using B(2, 3), then

3 = 4 + c ⇒ c = 3 - 4 = - 1

y = 2x - 1 ← equation of line

Answer:

3 / 19

Step-by-step explanation:

Given the following :

ratio of college graduates with a graduate degree to non-college graduates = 1:8

ratio of college graduates without a graduate degree to non-college graduates is 2:3

If college graduate with a degree = A

College graduate without a degree = B

Non-college graduate = C

College graduate to non college graduate = A:C

College graduate without degree to non college graduate = B:C

A:C = 1:8 - - - (1) ; B:C = 2:3 - - - (2)

Combining the two ratios :

To do so : the proportion of non college graduate should be the same in both ratios

To do this, multiply (1) by 3 and (2) by 8

A:C = 3 : 24

B:C = 16 : 24

combining both, we have :

A:B:C = 3:16:24

If one random college graduate is picked, what is the probability that they hold a graduate degree?

Total proportion of college graduate : (college graduates with degree + college graduates without degree)

A + B = (3 + 16) = 19

Proportion who hold a graduate degree = A = 3

Probability = require outcome / Total possible outcomes

Thus :

P = A / (A +B)

= 3/19

Answer:

Step-by-step explanation:

The first step in solving the equation is to cube both sides:

  (∛x)³ = (-4)³ . . . . . = (-4)(-4)(-4) = 16(-4) = -64

  x = -64 . . . . . simplified

__

We're not sure what "checking" is supposed to involve here. Usually, one would check the answer by seeing if a true statement is made when the answer is put into the original equation.

  ∛(-64) = -4 . . . true

Many calculators will not compute √(-64) because they compute roots using logarithms. The log of a negative number is not defined.

So, the way one would check this is to cube both sides, which is how we got the answer in the first place. We expect the same result from doing the same operation again, so it isn't really a check.

(a) The probability that both John and Jane watch the show is 0.07.

(b) The probability that Jane watches the show, given that John does, is 0.11

(c) No. John and Jane do not watch the show independently of each other.

(a) The probability that both John and Jane watch the show is given by the product of their individual probabilities:

P(John and Jane watch) = P(John watches) x P(Jane watches)

     = 0.7 x 0.1

     = 0.07.

(b) The probability that Jane watches the show, given that John does, is given by Bayes' theorem:

P(Jane watches | John watches) = P(John watches | Jane watches) x P(Jane watches) / P(John watches)

From the information given, we know that:

To find P(John watches), we can use the law of total probability:

P(John watches) = P(John watches | Jane watches) * P(Jane watches) + P(John watches | not Jane watches) * P(not Jane watches)

           = (0.8 x 0.1) + (0.7 x 0.9)

           = 0.71

Therefore,

P(Jane watches | John watches) = 0.8 x 0.1 / 0.71 = 0.1127

(c) John and Jane do not watch the show independently of each other, since the probability that John watches the show changes depending on whether or not Jane watches it. In other words, the events "John watches the show" and "Jane watches the show" are dependent events.

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Answer:

x is greater than or equal to 8.75 or 8 3/4

Step-by-step explanation:

So we first write the inequality 3 + 1.2c "is greater than or equal to sign" 13.5. Then we subtract 3, then divide both sides by 1.2 to isolate c. We get x "is greater than or equal to" 8.75.

Let x be the length of the pen and y be the width of the pen.

The total cost of the pen is given by:

Cost = 3x + 5y = 300

3x + 5y = 300

3x = 300 - 5y

x = (300 - 5y)/3

The area of the pen is given by:

Area = xy = (300 - 5y)/3 * y

Answer: u=1

Step-by-step explanation: add 36 to both sides to get -6u=-6 then divide both sides by -6 to get u=1

Answer:

2.25x+2.50=9.25

3 games

Step-by-step explanation:

Answer:

The first one is 2.50+2.25x=9.25

The second one is 3 games

Answer:

(x, y) = (1, 4)

Step-by-step explanation:

Given:  x+y=5 and 2x-y=-2

Solve for y and x

x+y=5; solve for y

y = 5 - x; substitute into other equation

2x-y= -2

2x - (5 - x) = -2

2x - 5 + x = -2; combine x's

3x - 5 = -2; add 5 to both sides

3x =3; divide by 3

x = 1; use this to solve for y

x+y=5

1 + y = 5; subtract 1 from both sides

y = 4

(x, y) = (1, 4)

Answer:

11x+4

Step-by-step explanation:

To do this, we can substitute 3x+10x for f(x) and 2x-4 for g(x), and we get 13x-(2x-4). By distributing the negative to 2x-4, we just swap the signs, and get 13x-2x+4, which equals 11x+4

Also, is there supposed to be an exponent on the first f(x)? I'm not sure because I haven't seen the real problem.

(Otherwise it would just be f=13x.) Maybe try being a little more clear when asking a question :)

Please let me know if you need more help or explanation on another problem!

The derivative operator distributes over sums, so

\((a f(x) + b g(x))' = a f'(x) + b g'(x)\)

Then

\(h(x) = 5f(x) - 4g(x) \implies h'(x) = 5 f'(x) - 4 g'(x) \\\\ \implies h'(2) = 5(-2) - 4(7) = \boxed{-38}\)

Use the product rule,

\((f(x)g(x))' = f'(x) g(x) + f(x) g'(x)\)

Then

\(h(x) = f(x) g(x) \implies h'(x) = f'(x) g(x) + f(x) g'(x) \\\\ \implies h'(2) = (-2) (4) + (-3) (7) = \boxed{-29}\)

Use the quotient rule,

\(\left(\dfrac{f(x)}{g(x)}\right)' = \dfrac{f'(x) g(x) - f(x) g'(x)}{g(x)^2}\)

Then

\(h(x) = \dfrac{f(x)}{g(x)} \implies h'(x) = \dfrac{f'(x) g(x) - f(x) g'(x)}{g(x)^2} \\\\ \implies h'(2) = \dfrac{(-2)(4) - (-3)(7)}{4^2} = \boxed{\dfrac{13}{16}}\)

Use the quotient rule again.

\(h(x) = \dfrac{g(x)}{1 + f(x)} \implies h'(x) = \dfrac{g'(x) (1+f(x)) - g(x) f'(x)}{(1+f(x))^2} \\\\ \implies h'(2) = \dfrac{7(1 - 3) - 4 (-2)}{(1 - 3)^2} = -\dfrac64 = \boxed{-\dfrac32}\)

To find the probabilities for different response times, we can use the properties of the normal distribution. Given that the police response time follows a normal distribution with a mean of 11.2 minutes and a standard deviation of 2.1 minutes, we can calculate the probabilities as follows:

(a) The probability that the response time is between 7 and 13 minutes:

We need to calculate the area under the normal curve between 7 and 13 minutes. We can do this by finding the z-scores corresponding to these values and then using a standard normal distribution table or a calculator.

The z-score for 7 minutes is calculated as:

z1 = (7 - 11.2) / 2.1 ≈ -1.9524

The z-score for 13 minutes is calculated as:

z2 = (13 - 11.2) / 2.1 ≈ 0.8571

Using a standard normal distribution table or calculator, we can find the cumulative probabilities for these z-scores.

P(7 < response time < 13) = P(z1 < z < z2)

P(7 < response time < 13) ≈ P(-1.9524 < z < 0.8571)

Looking up the corresponding cumulative probabilities for the z-scores, we find:

P(7 < response time < 13) ≈ 0.7937

Therefore, the probability that the response time is between 7 and 13 minutes is approximately 0.7937.

(b) The probability that the response time is less than 7 minutes:

To calculate this probability, we need to find the cumulative probability for a z-score corresponding to 7 minutes.

z = (7 - 11.2) / 2.1 ≈ -1.9524

P(response time < 7) ≈ P(z < -1.9524)

Looking up the corresponding cumulative probability for the z-score, we find:

P(response time < 7) ≈ 0.0250

Therefore, the probability that the response time is less than 7 minutes is approximately 0.0250.

(c) The probability that the response time is more than 13 minutes:

To calculate this probability, we need to find the cumulative probability for a z-score corresponding to 13 minutes.

z = (13 - 11.2) / 2.1 ≈ 0.8571

P(response time > 13) ≈ P(z > 0.8571)

Looking up the corresponding cumulative probability for the z-score, we find:

P(response time > 13) ≈ 0.1957

Therefore, the probability that the response time is more than 13 minutes is approximately 0.1957.

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Answer:b would be 19 points

Step-by-step explanation:

The water level is rising at a rate of 32 ft/min when the water is 6 inches deep.

How to solve rise of water level?

Let's first draw a diagram to better understand the problem:

            /|\

           / | \

          /  |  \

         /   |h \

        /    |   \

       /     |    \

      /      |     \

     /       |      \

    /        |       \

   /         |        \

  /_________|

       b

where h is the height of the water, b is the width of the trough at water level, and 10 is the length of the trough.

Since the trough is being filled at a rate of 12 ft³/min, the volume of water in the trough is increasing at a rate of 12 ft³/min. Let's use this to find the rate at which the water level is rising.

The volume of water in the trough is given by the formula:

V = (1/2)bh²

where b is the width of the trough at water level, h is the height of the water, and 1/2 is the area of the triangular cross-section of the trough. We want to find the rate at which h is changing when h = 6 inches = 0.5 ft.

Differentiating both sides of the formula with respect to time t, we get:

dV/dt = (1/2)(db/dt)(h^2) + (1/2)(b)(2h)(dh/dt)

where db/dt is the rate at which the width of the trough at water level is changing, and dh/dt is the rate at which the water level is changing (i.e., the rate we want to find).

We know that dV/dt = 12 ft³/min and h = 0.5 ft. We also know that the width of the trough at the water level is 3 ft. To find db/dt, we need to use similar triangles. The triangle formed by the water and the sides of the trough is similar to the isosceles triangle at the end of the trough. Therefore, the ratio of the width of the trough at the water level to the height of the water is constant:

b/h = 3/1

Solving for b, we get:

b = 3h

on diffrentiating

db/dt = 3(dh/dt)

Substituting the values we know into the formula for dV/dt, we get:

12 = (1/2)(3h)(h²) + (1/2)(3h)(2h)(dh/dt)

12 = (3/2)h³+ 3h²(dh/dt)

4 = h²(dh/dt)

Solving for dh/dt, we get:

Therefore, the water level is rising at a rate of 32 ft/min when the water is 6 inches deep.

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Answer:

44 i think :|

The approximate size of the cover that Maria will need to buy is 45. 84 square feet

The formula for calculating the circumference of a circle is expressed as;

Circumference = πr²

Where 'r' is the radius of the circle

Now, let's substitute the value of the circumference

24 = 2 × 3. 14 × r

r = 24/6. 28

r = 3. 82 feet

Formula for area = πr²

Substitute value of r

Area = 3. 14 × (3. 82)²

Area = 3. 14 × 14. 59

Area = 45. 84 square feet

Hence, the value is  45. 84 square feet

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Answer:

A

Step-by-step explanation:

Answer:

\( \sqrt{3} \)

Step-by-step explanation:

- since it's an isosceles triangle, the other two angle is the same, so 180-90÷2=45

- i use SOH, CAH, TOA rule and in this case, i use SOH.

Answer:

x = √3

Step-by-step explanation:

Let us use the Pythagoras theorem to find the value of x.

Accordingly,

x² + x² = (√6)²

2x² = 6

Divide both sides by 2.

x² = 3

Put square roots on both sides.

x = √3

11.9 km/l of gasoline  correspond to 0.24 Miles/gallon in miles per gallon while driving the car.

One mile is generally considered to be equal to around 1.4 miles.

When we talk about volume or capacity, one liter can be taken to be approximately equal to 0.264 gallon.

Now, while driving the rental car in Europe during vacation, we get, 11.9 km/l.

Now, converting the values,

11.9 liters = 11.9 x 0.264 gallons.

11.9 liters = 2.92 gallon.

Also,

one km = 1/1.4 miles.

Putting values,

Mileage = 1/1.4 x 1/2.92

Mileage = 0.24 Miles/Gallon

So, 11.9 km/l of gasoline is corresponding to 0.24 Miles/Gallon.

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The probability that the sample mean will be between 295 to 305 is  0.99921

Since we are given that the mean is 300  and the standard deviation of  18 and we were given a total of 144 observations.A z-score gives you a thought of how distant from the mean a data point is. A z-score can be put on a normal distribution curve. Z In arrange to utilize a z-score, you wish to know the mean μ additionally the population standard deviation σ.

The formula  we are referring to for calculating the  Zscore is :

Zscore = (x - mean) ÷ σ/√n

At first, let x be = 295, so  the

Zscore = (295 - 300) / (18/12) = - 3.33

The probability for zscore for z<-3.33  is,

=>P(Z< - 3.33) = 0.00039

Similarly for the  second part x  305, Sp

The Zscore will be  (305 - 300) / (18/12) = 3.33

so the probability of z<3.33

=>P(Z< 3.33) = 0.9996

so the probability of mean between the range 295 to 305

P(Z < 3.33) - P(Z < - 3.33)

=0.9996-0.00039

= 0.99921

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Answer:

27

Step-by-step explanation:

basic pemdas essentially

6^2-4^2+7

36-4^2+7

36-16+7

20+7

27

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Answer:

27

Step-by-step explanation:

6² - ( 8 - 4)² + 7

= 36 - ( 8 - 4)² + 7

= 36 - (4)² + 7

= 36 - 16 + 7

= 20 + 7

= 27

The statement "Quadrilaterals A and B are both squares" does not provide enough information to determine whether A and B are scale copies of one another.

To determine if two quadrilaterals are scale copies of each other, we need to compare their corresponding sides and angles. If the corresponding sides of two quadrilaterals are proportional and their corresponding angles are congruent, then they are scale copies of each other.

In this case, since both A and B are squares, we know that all of their angles are right angles (90 degrees). However, we do not have any information about the lengths of their sides. Without knowing the lengths of the sides of A and B, we cannot determine if they are scale copies of each other.

Therefore, the statement cannot be determined as true or false based on the given information.

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