What is the following simplified product? Assume x 20.
(√6x² +4√8x³)(√9x-x√5x^5)
O 3x√√6x+x²√30x+24x²2x+8x³10x
O 3x√6x+x√30x+24x²√2+8x5/10
O 3x√√6x-x+√30x+24x² √2-8x² 10
O3x6x-x30x+24x²2x-8x510x

Personal car would be the best option to manage both tasks efficiently. While the train is a reliable mode of transportation, it may have fixed schedules that might not align perfectly with Patrick's needs.

On the other hand, using his personal car provides more flexibility and allows him to tailor the departure time according to his daughter's coding class schedule.

If Patrick decides to take the train, he would need to check the train schedule to see if there are convenient departure and arrival times for both the soccer game and the coding class. This option would require planning and coordination to ensure he arrives at the game on time and can pick up his daughter afterward.

Using his personal car gives Patrick the freedom to leave at a time that accommodates both the soccer game and the coding class. He can drop off his daughter at her coding class, attend the soccer game, and then pick her up afterward without being restricted by train schedules.

Considering the circumstances, Patrick might find it more convenient to use his personal car to manage both tasks effectively and ensure he can attend his son's soccer game while also ensuring his daughter arrives at her coding class on time.

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If the given point is p(x, y) and change the sign of its x coordinates and y coordinates, then the new location will be on third quadrant

The coordinates of the point p = (x, y)

In the graph, there are four quadrants.

In first quadrant the x axis value and y  axis value will be positive. In second quadrant the value of x will be negative and y will be positive. In the third quadrant the value of and y will be negative. In fourth quadrant the value of x will be positive and y will be negative

Here at first both x and y are positive and it will be on first quadrant. The the sign of the x coordinates and y coordinates will change sign. So both of them will be negative.

Therefore, the location of will be on third quadrant

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The current of the river is 3 miles per hour and the speed you would row at in still water is 15 miles per hour.

To find the current of the river and the speed you would row at in still water, we can use the formula:

Speed downstream = Speed in still water + Current of the river
Speed upstream = Speed in still water - Current of the river

Let's start by solving for the current of the river.

Given:
Distance between the two cities = 12 miles
Time downstream = 2/3 hour
Time upstream = 3/2 hour

To find the current of the river, we need to compare the time it takes to row downstream to the time it takes to row upstream.

1. Finding the speed downstream:
Distance = Speed downstream × Time downstream
12 miles = Speed in still water + Current of the river × 2/3 hour

2. Finding the speed upstream:
Distance = Speed upstream × Time upstream
12 miles = Speed in still water - Current of the river × 3/2 hour

Now we have a system of two equations:

Equation 1: 12 miles = (Speed in still water + Current of the river) × 2/3 hour
Equation 2: 12 miles = (Speed in still water - Current of the river) × 3/2 hour

We can solve this system of equations to find the values of the current of the river and the speed in still water.

Multiplying Equation 1 by 3 and Equation 2 by 2, we get:

Equation 3: 36 miles = (Speed in still water + Current of the river) × 2 hour
Equation 4: 24 miles = (Speed in still water - Current of the river) × 3 hour

Adding Equation 3 and Equation 4, we eliminate the Current of the river:

36 miles + 24 miles = (Speed in still water + Current of the river) × 2 hour + (Speed in still water - Current of the river) × 3 hour

60 miles = (2 × Speed in still water × 2 hour)

Dividing both sides by 4 hours:

15 miles/hour = Speed in still water

Now, to find the current of the river, substitute the value of Speed in still water into either Equation 3 or Equation 4.

Let's use Equation 3:

36 miles = (15 miles/hour + Current of the river) × 2 hour

Dividing both sides by 2:

18 miles = 15 miles/hour + Current of the river

Subtracting 15 miles/hour from both sides:

3 miles/hour = Current of the river

So, the current of the river is 3 miles per hour and the speed you would row at in still water is 15 miles per hour.

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Answer:

12, Brian rides 12 miles in all in 3 days.

Step-by-step explanation:

We know that each day Brian rides his bike for 4 miles, we need to figure out how many miles he rides in 3 days.

4 miles times 3 days = Total number of miles that Brian rides

Brian rides 12 miles in 3 days

Answer:

2/3 kilometers

Step-by-step explanation:

Add the two distances together

4/9 + 2/9 = 6/9

Simplify the fraction by dividing the top and bottom by 3

2/3

Answer:

Step-by-step explanation:

(4/9) + (2/9) = 6/9 = 2/3

The perimeter of the rectangle, when the area is maximized, is approximately 24.63 units. Therefore, correct option is a.

To maximize the area of the rectangle inscribed in the parabola \(y^2 = 16x\), we need to find the dimensions of the rectangle. Since the side of the rectangle is along the latus rectum of the parabola, we know that the length of the rectangle is equal to the latus rectum.

The latus rectum of the parabola \(y^2 = 16x\) is given by the formula 4a, where "a" is the distance from the focus to the vertex of the parabola. In this case, the focus is located at (4a, 0).

To find "a," we can equate the equation of the parabola to the general equation of a parabola in vertex form: \(y^2 = 4a(x - h)\), where (h, k) is the vertex of the parabola.

Comparing the two equations, we get:

4a = 16

a = 4

Therefore, the latus rectum of the parabola is 4a = 4 * 4 = 16 units.

Since the length of the rectangle is equal to the latus rectum, we have length = 16 units.

Now, to find the width of the rectangle, we need to determine the corresponding y-coordinate on the parabola for the given x-coordinate of the latus rectum. The x-coordinate of the latus rectum is half the length, which is 16/2 = 8 units.

Substituting x = 8 into the equation of the parabola, we get:

\(y^2 = 16(8)\\y^2 = 128\\y = \sqrt{128} = 11.31\)

Therefore, the width of the rectangle is approximately 11.31 units.

The perimeter of the rectangle is given by the formula:

Perimeter = 2(length + width)

Plugging in the values, we have:

Perimeter = 2(16 + 11.31)

Perimeter ≈ 2(27.31)

Perimeter ≈ 54.62

Rounding the perimeter to two decimal places, we get approximately 54.62 units, which is equivalent to 24.63 units.

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Step-by-step explanation:

a(a²-x)=b(b²-x)

=a³-ax=b³-bx

\({ \purple{ \sf{a( {a}^{2} - x) = b( {b}^{2} - x)}}}\)

Multiply a with the terms in bracket and b with the terms in the bracket you will get

\({ \red{ \boxed{ \bold{ {a}^{3} - ax = {b}^{3} - bx}}}}\)

Answer:

1. m = 1 , b = 3

2. m = -4/5 , b = 4

3. m = 3 , b = 1

4. m = 1/2 , b = 1

Step-by-step explanation:

1. slope m = 1  

y-intercept b = 3

2. slope m = -4/5

y-intercept b = 4

3. slope m = 3

y-intercept b = 1

4. slope m = 1/2

y-intercept b = 1

By the 46th day, there are 400 water lilies in the pond. the estimate you made: a). close to 46 (or exactly right) because it was estimated well.

We know that the regression equation is: y = 3.915(1.106)ˣ and that the pond can hold 400 water lilies.

y = 3.915(1.106)ˣ

Here, y is equal to the number of water lilies the pond can hold.

So, y = 400

And,  x is the required time taken.

So,

400 = 3.915(1.106)ˣ

⇒ (1.106)ˣ = 400/3.915    

⇒ (1.106)ˣ = 102.17

Taking logarithm on both sides, we get

log (1.106)ˣ = log (102.17)

⇒ x log (1.106) = log (102.17) .............. [log aˣ = x loga]

⇒ x = [log (102.17)/log (1.106)]    

⇒ x = 45.92

x ≅ 46

So, the pond will take 46 days to become full.

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Complete question:

Regression equation: y = 3.915(1.106)ˣ . The pond can hold 400 water lilies. by what day will the pond be full? write and solve an equation. the pond will be full by the end of day.

Answer:

b

Step-by-step explanation:

just did it

The approximate probability that fewer than 71 seeds germinate is 0.0082, or 0.82%.

The probability that a seed germinates is 87%, which means the probability that a seed does not germinate is 13%.

To approximate the probability that fewer than 71 seeds germinate, we can use the normal approximation to the binomial distribution since the sample size is large (90 seeds) and the probability of success is not too close to 0 or 1 (0.87).

First, we calculate mean and standard deviation of this binomial distribution:

Mean = n * p = 90 * 0.87 = 78.3
Standard deviation =\(\sqrt{(n * p * (1 - p))}  = \sqrt{(90 * 0.87 * 0.13)}\) = 3.25

Now, we can standardize the random variable X (number of seeds that germinate) using the formula:

Z = (X - mean) / sd

For X = 70.5 (the midpoint of the interval "fewer than 71 seeds germinate"), we get:

Z = (70.5 - 78.3) / 3.25 = -2.40

Using a standard normal table or calculator, we find probability that Z value is less than -2.40, which equals to nearly 0.0082.

Therefore, the approximate probability that fewer than 71 seeds germinate is 0.0082, or 0.82%.

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Answer:

The answer to your question is: 6 units

Step-by-step explanation:

Data

A (-4, 0)

B (-3,1)

C (0,-2)

D (-1,-3)

Formula

d = √((x2 - x1)² + (y2 - y1)²)

Process

dAB = √((x2 - x1)² + (y2 - y1)²)                 dAC = √((0 + 4)² + (-2 + 0)²)

      = √((-3 + 4)² + (1 - 0)²)                      dAC = √((4)² + (-2)²)

      = √((1)² + (1)²)                                    dAC = √(16 + 4)

      = √1 + 1                                             dAC = √20

dAB = √2  = dCD

dAD = √((-1 + 4)² + (-3 - 0)²)                    

dAD = √((3)² + (-3)²)

dAD = √9 + 9

dAD = √18 = dBC

reactangle's area = base x height = √18 x √2 = √18 x 2 = √36

                                                       = 6 units

Answer: Probability is 35%

Step-by-step explanation:

12 goes in yellow boy. 40 goes in yellow girl. 22 goes in green girl. 26 goes  in green boy. Total for boys is 38. Total for girls is 62. Yellow total is 62. Green total is 48. Over all total is 100. The probability is 35% that a girl will choose Green Smarties over Yellow

p(0)=2

p(1)=2+1+2-1=4

p(2)=2+2+8-8=4

Answer:

b. 29°

Step-by-step explanation:

In the given diagram, the smallest angle in the diagram is ∠FLG = 29°.

When to lines are meeting at a point, then the geometrical figure is formed called an angle.

Given, four lines extend from point L.

They are lines LF, LG, LH, and LI.

∠FLI = 106°, ∠FLG = (2x - 1)°, ∠GLH = (x + 17)°, ∠HLI = (4x - 15)°

Here, ∠FLI = ∠FLG + ∠GLH + ∠HLI

106°  = (2x - 1)° + (x + 17)° + (4x - 15)°

⇒ (2x - 1)° + (x + 17)° + (4x - 15)° = 106°

⇒ (7x + 1)° = 106°

⇒ 7x = 105

⇒ x = 15

Now, ∠FLG = (2x - 1)° = (2 × 15 - 1)° = 29°

GLH = (x + 17)° = (15 + 17)° = 32°

∠HLI = (4x - 15)° = (4 × 15 - 15)° = 45°

Therefore, the smallest angle in the diagram is ∠FLG = 29°.

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Answer:

The answer is 1.35 answer (1). You can graph both equations to give you the answer.

Step-by-step explanation:

Graph the equations and see where they intersect.

The positive x coordinate is given as √13/2 - 1.

The equation for a circle having the centre located at a point (a, b) and the radius r can be written as (x - a)² + (y - b)² = r².

Given that,

The equation for the line is y = x + 2

And, the equation of the circle is x² + y² = 13.

In order to find the point of intersection substitute the equation of line into that of circle as below,

x² + y² = 13

=> x² + (x + 2)² = 13

=> x² + x² + 4x + 4 = 13

=> 2x² + 4x - 9 = 0

Use quadratic formula to solve the above equation as,

x = (-4 ± √(4² - 4 × 1 × -9))/(2 × 2)

  = -1 ± √13/2

Thus, the positive x coordinate is given as √13/2 - 1.

Hence, the positive x-coordinate of the point of intersection of the circle and line is given as √13/2 - 1.

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False. To obtain a representative sample, it is not necessary to sample a large fraction of the population.

The representativeness of a sample depends on its ability to accurately reflect the characteristics and variability of the population it is drawn from. The size of the sample required for representativeness is determined by the level of precision desired and the inherent variability within the population.

Sampling a large fraction of the population, also known as a census, is one way to achieve representativeness, but it is often impractical, time-consuming, and costly. Instead, researchers often use statistical techniques to select a smaller subset of the population that can still provide accurate estimates.

The key factor in obtaining a representative sample is the use of random sampling techniques, such as simple random sampling or stratified sampling, which ensure that every individual in the population has an equal chance of being included in the sample. By using appropriate sampling methods and considering the variability within the population, it is possible to obtain a representative sample without sampling a large fraction of the population.

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Answer:

\(m = \frac{2.90 - 2.50}{20 - 0} = \frac{.40}{20} = .02\)

\(f(x) = .02x + 2.50\)

\(f(30) = .02(30) + 2.50 \)

\(f(30) = 3.10\)

In 2030, the price of oil would be $3.10.

Answer:

x=\(\sqrt{169} \)

x=13

Step-by-step explanation:

12*12+5*5=x*x

x*x=169

x=\(\sqrt{169} \)

x=13

Answer:

7x+4.81=49.82x

x=6.43

We know that 68.26% of data is between 580 and 620 using a normal distribution table.

A data set must (when graphed) follow a bell-shaped, symmetrical curve that is centered around the mean in order to be regarded as having a normal distribution.

Additionally, it must follow the empirical rule that shows the proportion of the data set that lies within (plus or minus) 1, 2, and 3 standard deviations of the mean.

So, we know that:

μ = 600

σ = 20

Use the equation:
z - score = x-μ/σ

580 in the data's Z-score:

= 580-600/20

= -20/20

= -1

While the data's z-score in 620:

= 620-600/20

= 20/20

= 1

Using a table of the normal distribution:

P(580 < z) = 0.1587

Also, P(620 > z) = 0.8413

As a result, the percent of the data that falls between 580 and 620 is given by: P(620 > z) - P(580 z).

= 0.8413  - 0.1587

= 0.6826

= 68.26 %

Therefore, we know that 68.26% of the data is between 580 and 620 using a normal distribution table.

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Answer:

10x + 4y < 40

Step-by-step explanation:

The creation of an inequality is as follows"

The cost of the 10 wings box = $10

The cost of nachos = $4 per tray

And, the amount that can be incurred less is $40

Based on the information,

The equation would be

10x + 4y < 40

Hence, the inequality equation is 10x + 4y<40

Answer: 7/18

Step-by-step explanation:

Number of customers at Eva's boutique = 90

Number of customers who wore a size extra-large = 35

The probability that a randomly selected customer wore a size extra-large will be:

= Number of customers who wore a size extra-large / Number of customers at Eva's boutique

= 35 / 90

= 7/18

Therefore, the probability that a randomly selected customer wore a size extra large is 7/18.

Answer: Check below

Step-by-step explanation:

Okay so the Pythagorean Theorem was made by some old guy and the formula is a^2+b^2=c^2. You ALWAYS have to subtract the leg of the triangle when your finding a leg. You squareroot the square of the two legs if your finding the hypotnuse. The Theorem can be used to find any side of the triangle ONLY IF its a right triangle. An adult might use it in real life like when your an architect trying to find how much material you should use to make something thats in the shape of a right triangle.

Ps. Sorry if there's a bunch of grammar mistakes since this is kinda rushed

Answer:

The probability that a randomly selected call is for a car that won't start because of dead battery or because of no gas is 0.96

Step-by-step explanation:

The percentage of calls for emergency due to dead battery = 90%

The percentage of calls for emergency due to no gas = 10%

The percentage of calls for emergency due to dead battery and no gas  = 4%

Therefore;

The probability that a call for a car that won't start because of dead battery, P(B) = \(\left | B \right |\) = 0.9

The probability that a call for a car that won't start because of no gas, P(N) = \(\left | N \right |\) = 0.1

The probability that a call for a car that won't start because of dead battery and no gas, P(B∩N) = \(\left | B \cap N \right |\) = 0.04

Therefore, the probability that a randomly selected call is for a car that won't start because of dead battery or because of no gas is given as follows;

\(\left | B \cup N \right | = \left | B \right | + \left | N \right | - \left | B\cap N \right |\)

Where;

Therefore, we have;

\(\left | B \cup N \right |\) = The probability that a randomly selected call is for a car that won't start because of dead battery or because of no gas

Substituting gives;

\(\left | B \cup N \right |\) = 0.9 + 0.1 - 0.04 = 0.96

∴ The probability that a randomly selected call is for a car that won't start because of dead battery or because of no gas = 0.96.

By using a maclaurin series to obtain the maclaurin series for the given function is  F(x) = x cos(5x) = \(1 - 25x^2/2! + 625x^4/4! - 15625x^6/6! + ...\)

To obtain the Maclaurin series for the function f(x) = x cos(5x), we need to write the Maclaurin series for cos(5x). The Maclaurin series for cos(x) is: \(cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! + ...\)

Using this formula, we can substitute 5x for x and obtain the Maclaurin series for cos(5x): cos(5x) =\(1 - (5x)^2/2! + (5x)^4/4! - (5x)^6/6! + ...\)

\(= 1 - 25x^2/2! + 625x^4/4! - 15625x^6/6! + ...\)

We can substitute this series into the original function f(x) = x cos(5x) and obtain its Maclaurin series: f(x) = x cos(5x)

\(= x[1 - 25x^2/2! + 625x^4/4! - 15625x^6/6! + ...]\)

\(= x - 25x^3/2! + 625x^5/4! - 15625x^7/6! + ...\)

This is the Maclaurin series for the function f(x) = x cos(5x). It is obtained by substituting the Maclaurin series for cos(5x) into the original function and simplifying the resulting series. Maclaurin series are useful for approximating functions using polynomials. By truncating the series after a certain number of terms, we can obtain a polynomial that approximates the original function to a certain degree of accuracy. The accuracy of the approximation depends on the number of terms in the series that are used. The more terms we include, the more accurate the approximation will be.

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The bacteria that cause foodborne illness multiply most abundantly between 40 and 140 degrees Fahrenheit.

Bacteria that cause foodborne illnesses grow and reproduce rapidly at temperatures between 40°F (4.4°C) and 140°F (60°C), which is known as the "Danger Zone." These temperatures allow bacteria to multiply rapidly and increase the risk of foodborne illness.

Therefore, it is important to keep food out of this temperature range as much as possible. Food should be kept below 40°F (4.4°C) or above 140°F (60°C) to reduce the risk of bacterial growth.

Proper cooking, refrigeration, and heating of food can help prevent the growth and spread of harmful bacteria.

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Answer: The percentage change is 20%.

Step-by-step explanation: It was from $0 to $10 which means you would 10/50 and you would get 0.2 which is 20%. I hope I explained it and saved your day:) Have a good day!

Step-by-step explanation:

Change in money = $50- $10=$40

%change = change/total money × 100%

= 40/50 ×100%

The percentage change is 80%.

This means He spent 80% of his $50 on a lunch.

Answer:

16

Step-by-step explanation:

just use a mean absolute deviation calculator next time

Answer:

$180=4c+6a

Step-by-step explanation:

Yes, If a null hypothesis is rejected at the 0.02 level of significance, it means that the probability of observing such a result by chance is less than 2%. Option A is the correct answer.

The level of significance, also known as alpha, is the probability of making a Type I error, which is the rejection of a null hypothesis when it is actually true. Commonly used levels of significance are 0.05 and 0.01, but they can also be set to any value depending on the context and the researcher's preference.

If a null hypothesis is rejected at the 0.02 level of significance, it means that there is strong evidence against the null hypothesis and the result is statistically significant.

This also implies that the probability of observing such a result by chance is less than 2%. Therefore, if the null hypothesis can be rejected at a lower level of significance, it automatically implies that it can also be rejected at a higher level of significance.

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