Given r(x) = 11/(x-4) ^2 , which represents a domain restriction on r(x) and the corresponding inverse function?

QUESTION:- EVALUATE THE EXPRESSION

EXPRESSION:-

\({( \sqrt[6]{27 {a}^{3} {b}^{4} } )}^{2} \)

\({( \sqrt[6]{27 {a}^{3} {b}^{4} } )}^{2} \\ {( {27 {a}^{3} {b}^{4} } )}^{ \frac{2}{6} } \\ {({27 {a}^{3} {b}^{4} } )}^{ \frac{ \cancel{2}}{ \cancel6 {}^{ \: 3} } } \\ {(27)}^{ \frac{1}{3} } {a}^{ \frac{3}{3} } {b}^{ \frac{4}{3} } \\{(3)}^{ \frac{ \cancel3}{ \cancel3} } {a}^{ \frac{ \cancel3}{ \cancel3} } {b}^{\frac{3 + 1}{3} } \\3a {b}^{ \frac{ \cancel3}{ \cancel3} } {b}^{ \frac{1}{3} } \) \( \\ ANSWER->3ab \sqrt[3]{b} \: \: \: \: \: or \: \: 3a {b}^{ \frac{4}{3} } \)

The probability of completing the final examination in one hour or less, given a normal distribution with a mean of 79 minutes and a standard deviation of 8 minutes, is approximately 0.8413.

To find the probability of completing the exam in one hour or less, we need to convert one hour (60 minutes) into z-scores. The formula for calculating the z-score is (x - μ) / σ, where x is the value we want to convert, μ is the mean, and σ is the standard deviation.

In this case, we want to find the z-score for 60 minutes. Substituting the values into the formula, we have (60 - 79) / 8 = -2.375.

Next, we need to find the probability associated with this z-score. We can look up the corresponding probability from a standard normal distribution table or use a calculator. The probability corresponding to a z-score of -2.375 is approximately 0.0087.

However, we are interested in the probability of completing the exam in one hour or less, which includes all values less than or equal to 60 minutes. Since we are dealing with a continuous distribution, we need to consider the area under the curve up to the z-score of -2.375. This area represents the probability of completing the exam in one hour or less.

Looking up the z-score of -2.375 in the standard normal distribution table, we find that the corresponding probability is approximately 0.0087. Therefore, the probability of completing the exam in one hour or less is approximately 0.0087 or 0.8413 (rounded to four decimal places).

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Answer: No, the correct answer is 125/100

Step-by-step explanation:

When adding fractions together the denominator must always be the same and stay the same when added together.

The question is : The maximum load that a truck can carry is 3500 kg. If it is known that each trip carries at least 2800 kg, how many packages weighing 70 kg can it transport on each trip?

The truck can transport 10 packages weighing 70 kg each on each trip.

To determine the number of packages of 70 kg that can be transported on each trip, we need to find the difference between the maximum load capacity of the truck and the minimum weight already being transported.

Maximum load capacity: 3500 kg

Minimum weight already being transported: 2800 kg

Therefore, the remaining weight capacity for additional packages is:

3500 kg - 2800 kg = 700 kg

Since each package weighs 70 kg, we can divide the remaining weight capacity by the weight of each package to determine the number of packages that can be transported:

700 kg ÷ 70 kg = 10 packages

Therefore, the truck can transport 10 packages weighing 70 kg each on each trip.

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The function's one sided limit is \(+\infty\).

Given function,

\(\lim_{x \to 2^-} \frac{x-3}{x-2}\\\\= \frac{2-3}{2-2}\\\\=\frac{-1}{0}\\\\=\infty\)

Thus, it reaches infinity then the limit does not exist.

From the given function, it is observed  x belongs to \(2^-\) it means it's graph will start from left.

To determine it's one sided limit, substitute a smaller number which is very close to 2 i.e.1.9999

It's one sided limit will be

\(\lim_{x \to 2^-} \frac{x-3}{x-2}\\\\=lim_{x \to 2^-}(x-3)*lim_{x \to 2^-}(\frac{1}{x-2})\\\\=(1.9999-3)*(\frac{1}{1.99999-2})\\\\=-1.0001*(\frac{1}{-0.0001})\\\\\)

When denominator is a very small number in a fraction then the fraction equals to infinity.

\(=-1.0001*-\infty\\=+\infty\)

Hence, the function's one sided limit reaches to positive infinity.

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Answer:

x=0.38

Step-by-step explanation:

3x+0.15=1.29    1. -0.15 on both sides

3x=1.14  2. /3 on both sides

x=0.38

Answer:

it's like this the answer

Step-by-step explanation:

x⁴-8x²y²+16y²-256

(x²-8xy)²+(4y-16)²

Answer:

x⁴-8x²y²+16y²-256

(x²-8xy)²+(4y-16)²

Step-by-step explanation:

Answer:

The average speed was about 6,000 kilometers (or 3,200-3,700 miles)

Step-by-step explanation:

hope this helps!

Answer:

137 degrees

Step-by-step explanation:

Fuel used = 392 km * 7.9 liters/100 km = 31.068 liters, average speed = 74.4 km/h.

It is defined as the distance traveled by an object in a certain amount of time. The unit of speed is usually meters per second (m/s) or kilometers per hour (km/h). Speed is a fundamental concept in physics, as it is a measure of the motion of objects. It is also an important concept in engineering, transportation, and many other fields. The speed of an object can be determined by dividing the distance traveled by the time taken to travel that distance.  The magnitude of speed represents the rate of change of position, and the direction indicates the direction of the change.

To find the amount of fuel used to get to the gate, we need to multiply the distance traveled by the fuel consumption per kilometer.

1. Fuel used = 392 km * 7.9 liters/100 km = 31.068 liters. Rounding to the nearest whole number, the answer is 31 liters.

2. To find the average speed, we need to divide the distance traveled by the time taken.

Average speed = 392 km / (5 hours + 14 minutes/60) = 74.4 km/h.

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The root of the equation sinx = 2x-3 is 0.8401 (approx).

Given equation is sinx = 2x-3

We need to solve this equation using false position method.

False position method is also known as the regula falsi method.

It is an iterative method used to solve nonlinear equations.

The method is based on the intermediate value theorem.

False position method is a modified version of the bisection method.

The following steps are followed to solve the given equation using the false position method:

1. We will take the end points of the interval a and b in such a way that f(a) and f(b) have opposite signs.

Here, f(x) = sinx - 2x + 3.

2. Calculate the value of c using the following formula: c = [(a*f(b)) - (b*f(a))] / (f(b) - f(a))

3. Evaluate the function at point c and find the sign of f(c).

4. If f(c) is positive, then the root lies between a and c. So, we replace b with c. If f(c) is negative, then the root lies between c and b. So, we replace a with c.

5. Repeat the steps 2 to 4 until we obtain the required accuracy.

Let's solve the given equation using the false position method.

We will take a = 0 and b = 1 because f(0) = 3 and f(1) = -0.1585 have opposite signs.

So, the root lies between 0 and 1.

The calculation is shown in the attached image below.

Therefore, the root of the equation sinx = 2x-3 is 0.8401 (approx).

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Answer:

\(\frac{4}{5}\)

Step-by-step explanation:

Given

\(\frac{12x-4}{15x-5}\) ← factorise numerator and denominator

= \(\frac{4(3x-1)}{5(3x-1)}\) ← cancel (3x - 1) on numerator and denominator

= \(\frac{4}{5}\)

Answer:

58 for the opposite angle and 180 for the regular angle

Answer:

They will need $13.97 worth of ground beef for their recipes.

Step-by-step explanation:

First, we know that 1 pound equals 3.49, so for Brenda we can put 1 pound aside.

Then, she needs 0.5 more pounds. To figure this out, set up this equation:

0.5 x 3.49 = 1.75.

3.49 + 1.75 = $5.24 for Brenda.

Now, for Mary, we have 2 pounds:

2 x 3.49 = 6.98

Take the 0.25, and multiply it:

0.25 x 6.98 = 1.75

6.98 + 1.75 = $8.73 for Mary.

Take their totals and add them together:

$5.24 + $8.73 = $13.97

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The bus 2 will pass bus 1 at 12.30 pm, when both are at 360 miles.

The bus 1 starts half hour earlier than bus 2. But since bus 2 is faster, it will overtake at some point. At 8 am, bus 1 will start. By the time 8.30, it will cover a distance of 40 miles.

Bus 2 starts at 8.30, So it will be at 0 miles.

By 10, the bus 1 will be at 160 miles, bus 2 at 135 miles

By 10.30, the bus 1 will be at 200 miles, bus 2 at 180 miles.

By 11.30, bus 1 will be at 280 miles, bus 2 will be at 270 miles

By 12.30, bus 1 will be at 360 miles, bus 2 will be at 360 miles.

So at the 360 the, the both the buses passes each other.

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a) The relevant population is the heavy soft-drink users in the given case, and the appropriate sampling design that should be used is  stratified random sampling. The list of all heavy soft-drink users is the sampling frame.

b) Cluster sampling refers to a sampling design where population is divided into naturally occurring groups and a random sample of clusters is chosen.

The advantages are efficient, easy to perform, and used when the population is widely dispersed. The disadvantages are sampling errors, have lower level of precision, and have the standard error of the estimate.

a) The relevant population for the public relations research department to investigate the initial reactions of heavy soft-drink users to a new all-natural soft drink is heavy soft-drink users. The appropriate sampling design that can be used to investigate the issues is stratified random sampling.

Stratified random sampling is a technique of sampling in which the entire population is divided into subgroups (or strata) based on a particular characteristic that the population shares. Then, simple random sampling is done from each stratum. Stratified random sampling is appropriate because it ensures that every member of the population has an equal chance of being selected.

Moreover, it ensures that every subgroup of the population is adequately represented, and reliable estimates can be made concerning the entire population. The list of all heavy soft-drink users can be the sampling frame.

b) Cluster sampling is a type of sampling design in which the population is divided into naturally occurring groups or clusters, and a random sample of clusters is chosen. The elements within each chosen cluster are then sampled.

The advantages of cluster sampling are:

The disadvantages of cluster sampling are:

A situation where cluster sampling would be appropriate is in investigating the effects of a new medication on various groups of people. In this case, the population can be divided into different clinics, and a random sample of clinics can be selected. Then, all patients who meet the inclusion criteria from the selected clinics can be recruited for the study. This way, the study will be less expensive, and it will ensure that the sample is representative of the entire population.

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The height at time t (in seconds) of a mass, oscillating at the end of a spring, is s(t) = 300 + 16 sin t cm. We have to find the velocity and acceleration at t = π/3 s.

Let's first find the velocity of the mass. The velocity of the mass is given by the derivative of the position of the mass with respect to time.t = π/3 s
s(t) = 300 + 16 sin t cm
Differentiating both sides of the above equation with respect to time
v(t) = s'(t) = 16 cos t cm/s

Now, let's substitute t = π/3 in the above equation,
v(π/3) = 16 cos (π/3) cm/s
v(π/3) = -8√3 cm/s

Now, let's find the acceleration of the mass. The acceleration of the mass is given by the derivative of the velocity of the mass with respect to time.t = π/3 s
v(t) = 16 cos t cm/s
Differentiating both sides of the above equation with respect to time
a(t) = v'(t) = -16 sin t cm/s²
Now, let's substitute t = π/3 in the above equation,
a(π/3) = -16 sin (π/3) cm/s²
a(π/3) = -8 cm/s²
Given, s(t) = 300 + 16 sin t cm, the height of the mass oscillating at the end of a spring. We need to find the velocity and acceleration of the mass at t = π/3 s.
Using the above concept, we can find the velocity and acceleration of the mass. Therefore, the velocity of the mass at t = π/3 s is v(π/3) = -8√3 cm/s, and the acceleration of the mass at t = π/3 s is a(π/3) = -8 cm/s².
At time t = π/3 s, the velocity of the mass is -8√3 cm/s, and the acceleration of the mass is -8 cm/s².

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The equation of the circle can be given by: (x - 8)² + (y - 5)² = 9.

The equation for a circle in standard form is (x - x1)² + (y - y1)² = r², where (x, y) denotes arbitrary coordinates on the circle's perimeter, r denotes the circle's radius, and (x1, y1) denotes the coordinates of the circle's center.

Now,

=> (x - 8)² + (y - 5)² = 9

Hence, the equation that describe the circle of radius 3 centered at (8, 5, 6) that is parallel to the xy-plane is given by: (x - 8)² + (y - 5)² = 9

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A. 2x+30=90

Step-by-step explanation:

To find x they must add to 90 degrees

Answer:

The products of -3(1) and -3(-1) are the same because both expressions result in the multiplication of -3 and a number, where one of the numbers is positive and the other is negative. The product of these two numbers is always negative.

Step-by-step explanation:

-3(1) means multiplying -3 by 1, which gives -3 as the product.

-3(-1) means multiplying -3 by -1, which gives 3 as the product.

Even though the two expressions are different, we can see that both involve multiplying -3 with a number, where one of the numbers is positive and the other is negative.

When we multiply a negative number and a positive number, the product is always negative. Similarly, when we multiply a negative number and a negative number, the product is always positive.

So, in both -3(1) and -3(-1), we are multiplying a negative number (-3) with a positive number (1 in the first expression and -1 in the second expression). Therefore, the products of both expressions are negative (-3 in the first expression and 3 with a negative sign in the second expression).

Hence, we can conclude that the products of -3(1) and -3(-1) are the same and equal to -3.

Answer: Jerod took at least $18.50 to the mall to ensure that he had at least $10.00 left after buying a snack.

Step-by-step explanation:

Let's use "x" to represent the amount of money Jerod took to the mall.

After he spends $8.50 on a snack, he will have x - 8.50 dollars left.

Since he wants to keep a minimum of $10.00 in his pocket at all times, we can set up an inequality:

\(\sf:\implies x - 8.50 \geqslant 10.00\)

To solve for x, we can add 8.50 to both sides of the inequality:

\(\sf:\implies x \geqslant 18.50\)

Therefore, Jerod took at least $18.50 to the mall to ensure that he had at least $10.00 left after buying a snack.

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The probability of a person being randomly choosing having waiting time greater than 4.25 is 0.2917 or 29.17%.

To answer this question we need to know about-

Probability is the measure of the likelihood of an event to happen. The probability value ranges between 0 and 1.

When the probability value is 0, it means that the event is impossible to happen.

When the probability value is 1, it means that the event is certain to happen.

Uniform distribution is when the values of a probability distribution are spread uniformly across the interval, it is called a Uniform distribution

The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 6 minutes.

The probability that a randomly selected passenger has a waiting time greater than 4.25 minutes is found as follows:

Let X = Waiting time of a randomly selected passenger P(X > 4.25) = ?

Now we have to use the uniform distribution formula to find the probability:

P(C< X >D)=C-D/B-A

where C = lower value of the selected interval

           D= upper value of the selected interval

           B= highest value of the selected interval

           A= lowest value of the selected interval

putting above values in the formula -

P(X > 4.25) = 6 - 4.25/6-0= 0.2917

Hence the probability that a randomly selected passenger has a waiting time greater than 4.25 minutes is 0.2917.

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Answer:

18.18%

Step-by-step explanation:

Selling price of one coker = Rs.2574

If she loose 10% on one;

%loss = Cost price - Selliing price/cost price * 100

10 =Cp-2574/Cp * 100

10/100 = Cp-2574/Cp

0.1Cp = Cp-2574

0.1Cp - Cp = -2574

-0.9Cp =  -2574

Cp = 2574/0.9

Cp = Rs. 2860

Amount lost = 2860-2574 = Rs. 286

If she gains 10% on the second

%loss =Sp-Cp/Cp * 100

10 = 2574-Cp /Cp * 100

10/100 = 2574-Cp /Cp

0.1Cp = 2574-Cp

1.1Cp = 2574

Cp = 2574/1.1

Cp = Rs. 2340

Amount gained = 2340-2574 = Rs. 234

Total Loss = Amount lost - Amount gained

Total loss = 286 - 234

Total loss = Rs. 52

Total loss % = 52/286 * 100

Total loss % = 5200/286

Total loss % = 18.18%

Answer:

-12 percent

Step-by-step explanation:

Where: 75 is the old value and 66 is the new value. In this case we have a negative change (decrease) of -12 percent because the new value is smaller than the old value.

Answer:

C option: 6 feet

Step-by-step explanation:

Since Yolanda wants to keep the pool in proportion to the model, the ratio of diameter to depth of model and the pool will be same.

Let the depth of pool is x feet.

Ratio of Diameter to Depth of Model = Ratio of Diameter to Depth of pool

This means the depth of pool should be 6 feet if Yolanda wants to keep the pool in proportion to the model.

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Answer:

its c

Step-by-step explanation:

i got it right

If MSwithin is smaller than MSbetween, then increasing MSwithin and/or decreasing MSbetween will lead to an increase in the F statistic.

The F statistic is calculated by dividing the variance between groups (MSbetween) by the variance within groups (MSwithin). Therefore, to increase the value of the F statistic, either the numerator (MSbetween) needs to increase, or the denominator (MSwithin) needs to decrease.

So, the answer is:

a. MSwithin > MSbetween

If the variance within groups (MSwithin) is reduced or the variance between groups (MSbetween) is increased, the F statistic will increase. Therefore, if MSwithin is smaller than MSbetween, then increasing MSwithin and/or decreasing MSbetween will lead to an increase in the F statistic.

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Using the central limit theorem, the conditions are:

The population should be symmetrical. If the population is skewed sample size should be sufficiently large at least 30.

Samples should be drawn strictly at random.

The sample observations should be independent.

The central limit theorem states that, under certain circumstances, the sampling distribution of the sample mean is roughly normal.

The circumstances are

I) The population ought to be balanced. If the population is skewed, the sample size should be at least 30.

ii) Samples must be chosen completely at random.

iii) Independent observations for the sample should be used.

The sample size must be large (e.g., at least 30) as the necessary condition.

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Answer:

Plato answer.

Answer:

(−3, −2) (−2, −1) (−1, −2) (−1, −4)

Angle of Rotation (CCW)    

90°   (2, −3) (1, −2) (2, −1) (4, −1)

180°  (3, 2) (2, 1)  (1, 2)         (1, 4)

270° (−2, 3) (−1, 2) (−2, 1) (−4, 1)

360° (−3, −2) (−2, −1) (−1, −2) (−1, −4)

Answer:

The circumference of circle with radius x+3 is: \(2\pi x+6\pi\)

Step-by-step explanation:

Given that

Radius = r =x+3

The circumference of a circle is the distance around boundary of the circle.

The circumference of circle is given by the formula.

\(C = 2\pi r\)

Putting the value of r, we get

\(C = 2\pi (x+3)\\C = 2\pi x+6\pi\)

Hence,

The circumference of circle with radius x+3 is: \(2\pi x+6\pi\)

Answer:

64 robberies

Step-by-step explanation:

45.8 is 10%

4.58 is 1%

4.58 times 4 is 18.32

45.8 plus 18.32 is 64.18 or just 64