Write each system as a matrix equation. Identify the coefficient matrix, the variable matrix, and the constant matrix. .[3a+5b=0 a+b=2]

The actual length of the living area is 134.4 feet if the length in the scale drawing is 16.8 in the scale.

To determine the actual length of the living space from a scale drawing, we need to use the scale factor, which is the ratio of the length in the drawing to the actual length. If the length in the scale drawing is 16.8 inches and the scale is given as a ratio of 1 inch in the drawing to 8 feet in actual size, we can set up a proportion:

1 inch (drawing) / 8 feet (actual)

= 16.8 inches (drawing) / x (actual)

We can cross-multiply and simplify to find x's value:

1 inch × x = 8 feet × 16.8 inches

x = (8 feet × 16.8 inches) / 1 inch

x = 134.4 feet.

Therefore, the actual length of the living space is 134.4 feet.

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Using arithmetic operations it is obtained that the patient inhales approximately 29,520 times in a 24-hour day.

What is arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

We can start by converting the patient's breathing rate from seconds to minutes, since we have the heart rate in minutes.

Use the arithmetic operation of multiplication and division -

The patient inhales once every 3 seconds, which is equivalent to -

(1 inhale / 3 seconds) x (60 seconds / 1 minute) = 20 inhales per minute

Next, we can use the patient's heart rate to find the number of breaths per heartbeat, and then multiply by the heart rate to get the total number of breaths per minute -

Breaths per heartbeat = 1 inhale / 4 heartbeats (since each heartbeat corresponds to 4 phases of the cardiac cycle, during which the patient inhales and exhales once)

Breaths per minute = (Breaths per heartbeat) x (Heart rate)

= (1/4) x 82

= 20.5

So the patient takes approximately 20.5 breaths per minute.

Multiplying this by the number of minutes in a day (24 hours x 60 minutes per hour = 1440 minutes) gives -

Breaths per day = (Breaths per minute) x (Minutes per day)

= 20.5 x 1440

= 29,520

Therefore, the number of inhales is 29,520.

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Answer:

A,   38

Step-by-step explanation:

the 180 - 114 = 66, so the vertical angle is 66, x = 38, 38 x 2 = 76 + 38 + 66 = 180

Therefore, the 90% confidence interval for the mean repair cost for the VCRs is ($82.40,$90.12).

Subject to the exclusions outlined in this clause, the repair cost is defined as the cost of the parts and labor required to fix or replace any covered component as a result of a covered mechanical breakdown. We reserve the right to substitute components of comparable sort and quality, whether they are new, OEM, swapped, rebuilt, remanufactured, or used. The suggested retail price of a part of a like type and quality, or the manufacturer's indicated retail price for Your Vehicle, whichever is higher, may not be exceeded when pricing out parts. A current, widely used flat-rate labor guide will be used to calculate labor costs. According to state-specific rules, the Repair Cost includes the necessary taxes related to the covered Mechanical Breakdown.

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The probability that the colour changes, while she is watching, is 1/7

Concept: Event probability = number of favorite results /Total number of results

It is given that the traffic light runs repeatedly in the following time cycle: green for 30 seconds, then yellow at 3  seconds, and then red for 30 seconds.

This means that the traffic light passes through 63 seconds to complete one-time cycle.

It is also given that Leah chooses a random 3 second time interval to watch the light.

We should find the probability that the color changes while Leah is looking.

The green light will change after 30 seconds and after three seconds it will change to yellow light, that is at 33 second it is yellow and after another 30 seconds it will change to red light.

Now let time t=0

The light changes at three different times: t=30,t = 33 and t = 63

This means that the light will change if Leah watches at intervals [27,30]

, [30,33] or [60,63]

Since each interval is 3 seconds and there are 3 intervals, Leah will have a chance of 9 seconds.

That makes a total of 9 seconds out of 63

⇒Probability that Leah watches the color change=Number of seconds she watches/Total seconds

=9/63=17

∴ The probability that Leah observes the color change is 1/7

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Step-by-step explanation:

1.

4×3=12 ÷4 =3

2.

\( \frac{3}{4} + \frac{3}{4} + \frac{3}{4} + \frac{3}{4} = \frac{12}{4} = 12 \div 4 = 3\)

Compound Interest

The final value of an investment of P dollars for t years at an interest rate of r is given by:

Where m is the number of compounding periods per year.

(a)

Lori buys a CD for P = $1500 that earns r = 6% = 0.06 interest compounded monthly for t = 10 years. Here m = 12 because there are 12 months in a year.

Substituting:

The CD will be worth $2729.10 in 10 years.

(b) If the interest compounds daily, then m = 360. Calculating:

The CD will be worth $2733.04 in 10 years.

(c) For t = 5 years:

The CD will be worth $2024.74 in 5 years.

In general, 62% of the values in a data set lie at or below the 62th percentile. 76% of the values in a data set lie at or above the 76th percentile. If a sample consists of 900 test scores, 504 of them would be at or below the 56th percentile. If a sample consists of 900 test scores, 540 of them would be at or above the 40th percentile.

A percentile is a comparison score among a particular score and the scores of the rest of a group. It presents the percentage of scores which a particular score surpassed. For example, if you score 85 points on a test, and are ranked in the 75th percentile, this means that the score 85 is higher than 75% of the scores. In general, percentile defines the percentage of a data set which is below or at a value which is being considered.

Thus, the percentage of the values of a data set that lies below or at the 62th percentile is 62%.

And also, the values of a data set that lies below or at the 76th percentile is 76%.

Given a sample of 900 test scores, the number of test scores that will be at or below the 56th percentile is 56% of 900 which is mathematically represented as:

n = 56% x 900

n = 56/100 x 900

n = 504 test scores

Given a sample of 900 test scores, the number of test scores that will be above the 40th percentile is (100 - 40 = 60) % of 900 which is mathematically represented as:

n = 60% x 900

n = 60/100 x 900

n = 540 test scores

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Answer:

d+6

Step-by-step explanation:

Because d is representing dogs and sum means add, and it's asking to add the number of cats which is 6 so it's d+6

The value of the SW is 12 units.

What is a chord in a circle?

The chord of a circle can be defined as the line segment joining any two points on the circumference of the circle. It should be noted that the diameter is the longest chord of a circle that passes through the center of the circle.

Since we want to find SW to get SV, we can change SW to x.

We already know the other lengths:

ST = 3

SU = 18

SW=x

SV=x-3

So, 3(18)=x(x-3).

From here, we see that when expanded, this becomes 54 = x² - 3x.

Solving the quadratic, we see that SW is 12, therefore SV is 9.

Hence, the value of the SW is 12 units.

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complete question: Let TU and VW be chords of a circle, which intersect at S, as shown. If ST = 3, TU = 15, and VW = 3, then find SW.

Given information: Mass of dolphin, m = 1800 N; Height of jump, h = 2.10 m.

The gravitational potential energy of the dolphin can be calculated as follows: Gravitational potential energy = mgh where, m is the mass of the dolphin, g is the acceleration due to gravity, and h is the height of the jump.

Given that the dolphin jumps from the water, its initial potential energy is zero. Hence, the total energy of the dolphin is equal to the potential energy at the highest point. At this point, the kinetic energy of the dolphin is also zero. Therefore, the energy conservation equation can be written as follows: mg h = (1/2)mv²where, v is the velocity of the dolphin just before it jumps out of the water.  

Solving for v, we get v = sqrt(2gh)where sqrt denotes the square root, g is the acceleration due to gravity, and h is the height of the jump. Substituting the given values, we get v = sqrt(2 x 9.8 x 2.10)v = 6.22 m/s Therefore, the dolphin must be moving at a speed of 6.22 m/s as it leaves the water in order to jump to a height of 2.10 m.

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Probability refers to the measure of the likelihood or chance of an event occurring, expressed as a value between 0 and 1, where 0 represents impossibility and 1 represents certainty.

To find the probability that the driver will find the second traffic light green, we need to make an assumption that the probability of each traffic light being green is independent of the other traffic lights. This means that the probability of finding the second traffic light green is the same as the probability of finding the first traffic light green.

Since the probability of finding the first green light is given as 0.56, the probability of finding the second green light is also 0.56.

Therefore, the probability that the driver will find the second traffic light green is 0.56.

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Answer:

The product of two rational numbers is rational, and the sum of two rational numbers is irrational.

Step-by-step explanation:

Let be \(a\) and \(b\) rational numbers whose forms are, respectively:

\(a = \frac{m}{n}\) and \(b = \frac{q}{r}\), \(m\), \(n\), \(q\), \(r\) \(\in \mathbb{Z}\)

We proceed to demonstrate if the Pythagorean sum of two rational numbers leads to a rational number.

1) \(a = \frac{m}{n}\),  \(b = \frac{q}{r}\), \(m\), \(n\), \(q\), \(r\) \(\in \mathbb{Z}\) Given.

2) \(c^{2} = a^{2}+b^{2}\) Given.

3) \(c^{2} = \left(\frac{m}{n} \right)^{2}+\left(\frac{q}{r} \right)^{2}\) 1) in 2)

4) \(c^{2} = (m\cdot n^{-1})^{2}+(q\cdot r^{-1})^{2}\) Definition of division.

5) \(c^{2} = [m^{2}\cdot (n^{-1})^{2}]+[q^{2}\cdot (r^{-1})^{2}]\)    \((a\cdot b)^{c} = a^{c}\cdot b^{c}\)

6) \(c^{2} = m^{2}\cdot n^{-2}+q^{2}\cdot r^{-2}\)   \((a^{b})^{c} = a^{b\cdot c}\)

7) \(c^{2} = [m^{2}\cdot (n^{2})^{-1}]+[q^{2}\cdot (r^{2})^{-1}]\)  \((a^{b})^{c} = a^{b\cdot c}\)

8) \(c^{2} = \frac{m^{2}}{n^{2}}+\frac{q^{2}}{r^{2}}\) Definition of division.

9) \(c^{2} = \frac{m^{2}\cdot r^{2}+q^{2}\cdot n^{2}}{n^{2}\cdot r^{2}}\)  \(\frac{x}{y} +\frac{w}{z} = \frac{x\cdot z+w\cdot y}{y\cdot z}\)

10) \(c^{2} = \frac{(m\cdot r)^{2}+(q\cdot n)^{2}}{(n\cdot r)^{n}}\)    \((a\cdot b)^{c} = a^{c}\cdot b^{c}\)/Result.

If \(c\) is a rational number, then \((m\cdot r)^{2}+(q\cdot n)^{2} = a^{2}\), so that \(a \in \mathbb{Z}\). Which means that \(c\) will be rational number if and only if the square root of \((m\cdot r)^{2}+(q\cdot n)^{2}\) is an entire number.

Which means that correct answer is B.

Answer:

The length of the blue ribbon is 10 inches.

Red ribbon length = 10 - 7 = 3 inches

b) The length of the blue ribbon is 27 inches.

Red ribbon length = 27 - 7 = 20 inches

c) The length of the blue ribbon is x inches.

Red ribbon length = (x - 7) inch

Step-by-step explanation:

When a thesis test is being performed for a population mean, the probability of a type II error isn't dependent on the sample mean. Option B is the right answer.

A type II error occurs when a null thesis isn't rejected despite it being incorrect. It's worth noting that the threat of making a type II error is affected by several factors, including the sample size, the true population mean, the position of significance, and the variability of the data.

As a result, the larger the sample size, the lower the threat of making a type IIerror.The true population mean also has an impact on the liability of a type II error. As the difference between the true mean and the hypothecated mean grows, the threat of a type II error decreases.

The position of significance is also pivotal in determining the threat of a type II error. As the significance position increases, the threat of a type II error decreases.

So, the correct answer is B

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Answer:

4.5 pie cubic inches

Answer:

B. 4.5π cubic inches

Step-by-step explanation:

The volume of a cylinder is given by the formula below, where r is the radius of the base and h is the height.

\(\boxed{\text{Volume of cylinder}=πr^2h}\)

Given: diameter= 3 in, height= 2 in.

Diameter= 2(radius)

r= 3 ÷2

r= 1.5

Substitute the value of r and h into the formula:

Volume of cylinder

= π(1.5²)(2)

= 4.5π in³

Thus, B is the correct option.

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a) The Current labor productivity is: 0.8 crates per labor- hour    

(b) Labor productivity with buyer is:  0.844 crates per labor-hour    

Labor productivity is defined as the ability of an organization to generate maximum profit for its employees' time. For example, if a chef cooks 10 meals for her in 1 hour, she earns 100 dollars for 10 meals, but he is only paid 10 dollars. Because of his labor productivity, the company makes him $90 for his time.

(a) Current labor productivity = 240 crates / (100 logs * 3 hours>log)  

=  240 / 300  

= 0.8 crates per labor- hour    

(b) Labor productivity with buyer = 260 crates  / (100 logs * 3 hours>log) + 8 hours  = 260 /  308  = 0.844 crates per labor-hour    

Using current productivity (0.80 from [a]) as a base, the increase will be 5.5%  (0.844/0.8 = 1.055, or a 5.5% increase).   0.8+5.5% = 0.844

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a) The Current labor productivity is: 0.8 crates per labor- hour    

(b) Labor productivity with buyer is:  0.844 crates per labor-hour    

How to calculate the labour productivity?

Labor productivity is defined as the ability of an organization to generate maximum profit for its employees' time. For example, if a chef cooks 10 meals for her in 1 hour, she earns 100 dollars for 10 meals, but he is only paid 10 dollars. Because of his labor productivity, the company makes him $90 for his time.

(a) Current labor productivity = 240 crates / (100 logs * 3 hours>log)  

=  240 / 300  

= 0.8 crates per labor- hour    

(b) Labor productivity with buyer = 260 crates  / (100 logs * 3 hours>log) + 8 hours  = 260 /  308  = 0.844 crates per labor-hour    

Using current productivity (0.80 from [a]) as a base, the increase will be 5.5%  (0.844/0.8 = 1.055, or a 5.5% increase).   0.8+5.5% = 0.844

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Answer:

c = 18.47

Step-by-step explanation:

This would create a triangle in which the length of the wall would be the missing side. We can use the Pythagorean Theorem to find this:

1. \(a^{2}\) + \(b^{2}\) = \(c^{2}\)

2. \(5^{2}\) + \(14^{2}\) = \(c^{2}\)

3. 25 + 196 = \(c^{2}\)

4. 221 = \(c^{2}\)

5. \(\sqrt{221}\) = c

6. 18.47 = c

Answer:

10feet

Step-by-step explanation:

Calculate the length from the base of the stair to the walls of the house.

We have the ladder extend 2 feet beyond the edge of the roof so 28-2=26feet

Let x is the length from the base of the stair to the wall of the house

(26)²=(24)²+x²

x²=(26)²-(24)²=676-576=100

x=√100=10feet

So the length from the base of the stair to the wall of the house is 10 feet.

There are -5 limbs does the mutant zombie has compared to yesterday in linear equation.

What in mathematics is a linear equation?

Now,

Based on the given conditions, we formulate;

5 - 12 + 2

Calculate the sum or difference = - 7 + 2 = -5

We get the result = -5

Therefore, There are -5 limbs does the mutant zombie has compared to yesterday.

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Answer:

19

Step-by-step explanation:

If the number of skits is x we can write:

9x + 5 = 176

9x = 171

x = 19

Answer:

\(x=11\)

Step-by-step explanation:

So we have the equation:

\(12x-39=8x+5\)

First, subtract 8x from both sides:

\(4x-39=5\)

Add 39 to both sides:

\(4x=44\)

Divide both sides by 4:

\(x=11\)

And we're done!

Step-by-step explanation:

The absolute value of a number is the positive of that number.

For example, number 22:

| n − 3 | = 5

n − 3 = -5 or n − 3 = 5

n = -2 or n = 8

For number 24, it's impossible for an absolute value to be negative, so there's no solution.

Given the function, K = x²y². To differentiate K w.r.t x, we first need to differentiate y² w.r.t x using the chain rule. Then, we differentiate x²y² w.r.t y and then multiply by the result obtained earlier, that is, d(y²)/dx.

To differentiate the given function, K = x²y² w.r.t x, we can use the product rule of differentiation. The formula for the product rule is given as below:

(f(x)g(x))' = f'(x)g(x) + f(x)g'(x)Now, we can write

K = f(x)g(x) where

f(x) = x² and

g(x) = y²Hence, the product rule can be applied as below:

(K)' = f'(x)g(x) + f(x)g'(x)Here, we need to find the value of (K)'. Thus, we need to calculate the values of f'(x) and g'(x) separately and then substitute them in the above formula to obtain the final answer. The value of f'(x) can be found as below:

Let f(x) = x²Therefore,

f'(x) = d/

dx(x²) = 2xThe value of g'(x) can be found using the chain rule of differentiation.

The chain rule states that if we have a function g(u), where u is itself a function of x, then the derivative of g with respect to x is given by:

g'(x) = g'(u) * u'(x)We can write

y² = g(u) where

u = x. Therefore, we have:

g'(x) = g'(u) *

u'(x) = d/dx(y²) * d/

dx(x) = 2y *

(d/dy(y)) = 2y *

1 = 2yNow, we can substitute the values of f'(x) and g'(x) in the formula for (K)' to get the final answer as below:

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

(x)= 2x * y² + x² *

2y= 2xy² + 2x²yHence, the answer to the differentiation of K w.r.t x is

(K)' = 2xy² + 2x²y.

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Answer:

Between the two quantities, the sales have a longer increase rate for dollars than the bicycle has for speed, and the bicycle travel had a good speed rate, but slowed down the increased again.

Step-by-step explanation:

The correlation coefficient can take values between -1 and 1, inclusive. A correlation coefficient of -1 indicates negative correlation and 1  indicates positive correlation.

A correlation coefficient of -1 indicates a perfect negative correlation, meaning that as the values of one variable increase, the values of the other variable decrease. A correlation coefficient of 1 indicates a perfect positive correlation, meaning that as the values of one variable increase, the values of the other variable also increase.

A correlation coefficient of 0 indicates no correlation, meaning that there is no relationship between the two variables. Correlation coefficients can take any value between -1 and 1, inclusive, including fractional and decimal values.

Positive values indicate positive correlation, negative values indicate negative correlation, and values close to 0 indicate little or no correlation. The magnitude of the correlation coefficient indicates the strength of the relationship between the two variables.

The closer the coefficient is to 1 or -1, the stronger the relationship between the variables.

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Answer:

Domain(-3 , 1]

Range [-4,0)

Step-by-step explanation:

Domain is the values that x can take

x > -3 since it is an open circle and x≤ 1

Using interval notation

(-3 , 1]

The range is the value that y can take

y ≥-4 for the closed circle and y <0 since it doesn't touch 0 at x=0

Using interval notation

[-4,0)

Answer:

Attached to this answer are some of the ways you could rewrite \(4*10^{-3}\)

Answer:

it changes it by putting it into quadrant 2.

Step-by-step explanation:

(x,y) → (x,-y)

KLMN is an upside down image of PQRS So it was reflected across the x axis and then scaled by 1/2

Preston is correct