What is thee 5th and 23rd term of the pattern 2x+1, 8x-2, and -6.2x+4.5?

If the lateral height of a cone is 4 inches and the area of the base of the cone is 49 in². The time it take to paint this cone if it can be painted at the same rate is 3.5 minutes.

The radius of the cone can be found using the formula for the area of a circle, A = πr^2

where:

r= radius

Rearrange this to solve for the radius:

r = √(A/π).

The original cone has a base area of 49 in², so:

r = √(49/π)

r ≈ 3 in.

The doubled cone has a base area of 2 * 49 in² = 98 in², so:

r = √(98/π)

r ≈ 4.5 in.

Hence,

Time  = 2.5 * (4.5/3)^(3/2)

Time ≈ 3.5 minutes

Therefore the time it take to paint this cone if it can be painted at the same rate is 3.5 minutes.

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The speed of the airplane in still air is 21.5 mph.

An airplane flying with the wind takes 2 hours with a 25-mph tailwind to reach its destination. the return trip takes 4 hours flying against the wind.

We must calculate the wind speed from the ground speed and airspeed as we cannot measure the wind speed directly from the aeroplane.

Flying at 35 mph requires four hours. Consequently, the distance is

25 * 2 = 50 miles.

For the same route, a return trip takes 5 hours.

Hence V-Vs= 50/4 = 12.5.

Therefore, V+Vs= 25 (1).

V-Vs = 12.5-----(2).

We obtain V=21.5 mph Vs=2.5 mph by solving for (1) and (2).

Thus, V = 21.5 mph is the airplane's windless speed.

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The value of the points in the graph is a (2,80).

According to the statement

We have to find that the points on the graph.

So, For this purpose, we know that the

A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.

From the given information:

f(x)=[tex]x^{3}[/tex]+6[tex]x^{2}[/tex]+17x+14​; slope of the tangent line=5

Then

f(x)=[tex]x^{3}[/tex]+6[tex]x^{2}[/tex]+17x+14

Now find the drivative then

f'(x)=3x^2+12x+17

Then slope of the tangent line=5

Now,

3[tex]x^{2}[/tex]+12x+17 = 5

3[tex]x^{2}[/tex]+12x+12 = 0

[tex]x^{2}[/tex]+4x+4 = 0

Now solve the equation then

[tex]1x^{2}[/tex]+2x+2x+4 = 0

x(x+2) +2(x+2) = 0

(x+2) (x+2) = 0

Here the values of the x become -2,-2.

Then

When x = 2

f(x)=[tex]2x^{3}[/tex]+[tex]6^{2}[/tex]+17(2)+14

f(x)=8+24+34+14

f(x) = 80.

So, The value of the points in the graph is a (2,80).

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The potential causes for extreme emotion are Chemical imbalance, drug use, mild stress

When someone starts displaying extreme emotions, we frequently discover that they lack emotional control, are brave, and occasionally even are annoying. This person reacts in an exaggerated way to any situation or circumstance, no matter how unimportant it may seem.

However, biological factors and other factors that interfere with a person's psyche can cause these emotions to be triggered, leading to the externalization of exaggerated emotions. Chemical imbalance, drug use, and mild stress are a few of these factors.

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Answer: The volume of a sphere can be calculated using the formula:

V = (4/3)πr^3

Where V is the volume and r is the radius of the sphere.

Given that the volume is 36 cubic inches, we can substitute into the formula:

36 = (4/3)πr^3

Dividing both sides by (4/3)π:

36 / (4/3)π = r^3

Taking the cube root of both sides:

r = ∛(36 / (4/3)π)

The radius of the sphere is approximately 2.74 inches.

Step-by-step explanation:

The total distance the tourist has to pay the taxi driver is the sum of the distance the tourist walked and the distance the taxi drove, or 8 miles + 100 miles = 108 miles.

The distance the tourist has to pay the taxi driver can be calculated using the formula for distance = rate x time.

First, let's find out how far the tourist walked. We know that he walked at a rate of 4 mph for 2 hours, so the distance he walked is 4 mph x 2 hours = 8 miles.

Next, let's find out how far the taxi drove. The taxi reached the destination 2 hours after the tourist started walking, so the time it took for the taxi to reach the destination is 2 hours. The taxi was traveling at a constant speed of 50 mph, so the distance it drove is 50 mph x 2 hours = 100 miles.

Finally, the total distance the tourist has to pay the taxi driver is the sum of the distance the tourist walked and the distance the taxi drove, or 8 miles + 100 miles = 108 miles.

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Complete question:

A tour begins walking along a 31-mile road to a mountain summit. He travels at a rate of 4 mph. After a while, he gets tired and calls a taxi. The taxi, traveling at a constant ped of 50 mph reached his destination 2 hours after he started walking, what distance doe he have to pay the taxi driver

By examining the expected value of a binomial distribution with n trials, (1) we may determine the typical number of successes.

The binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and each with its own Boolean-valued outcome: success (with probability p) or failure (with probability q=1-p).

This distribution is used in probability theory and statistics.

A Bernoulli trial, or experiment, is another name for a single success-or-failure experiment, and a Bernoulli process is another name for a series of results.

For a single trial, or n = 1, the binomial distribution is a Bernoulli distribution.

The popular binomial test of statistical significance is based on the binomial distribution.

We may find out the average number of successes by looking at the expected value of a binomial distribution with n trials.

Therefore, by examining the expected value of a binomial distribution with n trials, (1) we may determine the typical number of successes.

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The total distance traveled was 19 miles and the total time was 3/10 of an hour

The formula for calculating the average rate is distance divided by time, or D/T. In this problem, Jamel traveled 19 miles in a total time of 1/2 + 1/5 = 3/10 of an hour. Using the formula, the average rate can be calculated as 19/3/10 = 19/3 x 10/3 = 190/3 = 63.3 mph. Therefore, Jamel's average rate for the trip was 63.3 mph.

To explain further, when solving a problem involving average rate, it is important to remember the formula D/T. This means that the total distance traveled is divided by the total time. In this problem, the total distance traveled was 19 miles and the total time was 3/10 of an hour. To calculate the average rate, the total distance (19 miles) was divided by the total time (3/10 of an hour). This yielded a result of 190/3, which was further simplified to 63.3 mph. This was the average rate for Jamel's trip.

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Answer:

37° and 63°

Step-by-step explanation:

the measure of a secant- secant angle and a tangent- tangent angle is half the measure of the intercepted arcs.

5

∠ 1 = [tex]\frac{1}{2}[/tex] (108 - 34)° = [tex]\frac{1}{2}[/tex] × 74° = 37°

6

the sum of the arcs in a circle is 360° , then

minor arc = 360° - 243° = 117°

∠ 1 = [tex]\frac{1}{2}[/tex] (243 - 117)° = [tex]\frac{1}{2}[/tex] × 126° = 63°

Answer:

Step-by-step explanation:

-9/14=3*3/2*7

so, there are no common factors. -9/14 is the simplest form.

One millilitre is equal to 0.2028 teaspoons in the conversion from ml to tsp.

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The number line of y < 1/2 is repesented below

From the question, we have the following parameters that can be used in our computation:

y < 1/2

A number line represents all real numbers on a line and is usually represented as a horizontal line with numbers increasing from left to right.

The symbol "<" in the equation y < 1/2 means "less than."

So, all values of y that are less than 1/2 would be graphed to the left of 1/2 on the number line.

The number line would look like this:

   -1.0         -0.5           0.0         0.5         1.0

   ____________|______________|____________|____________

    y < 1/2                                 1/2

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Answer:

23

Step-by-step explanation:

you must divide tru turtle head

Answer:

575 ÷ 25 = 23!

Step-by-step explanation:

¡Espero eso ayude!

(a) The null and alternative hypothesis using proper notation is

H(0) :p ≤ 0.5

H(1) : p > 0.5

(b) The estimate of the true proportion of all orders that are delivered early is 0.6.

A delivery company samples 500 orders.

Out of 500 records, 300 of them were delivered early.

(a) To determine if the true proportion of orders that were delivered early occurs most of the time or not, i.e., whether the true proportion of orders that were delivered early is more than 0.5, we will perform a one proportion z-test.

Let p stand for the actual ratio. Our theory is stated as follows:

H(0) :p ≤ 0.5

H(1) : p > 0.5

We specifically want to determine whether the true proportion is greater than 0.5, hence this is a right-tailed test.

(b) The sample proportion's estimated value is provided as

P = Number of people who wake up early/Total Number of people

P = 300/500

P = 0.6

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Cellphone carriers charge a monthly fee and a per-minute rate. Every minute costs $0.06, so Option C is correct. Part 2, the carrier charges $60 monthly.

To obtain the constant rate of 0.06, we can use the two equations from January and February to solve for x, the constant rate:

Let x be the constant rate and y be the fixed monthly fee.

We can use these two equations to find the constant rate. Solving for x in the first equation, we get:

Next, we substitute this expression for x into the second equation:

Finally, we solve for x:

So, the constant rate is 0.06 dollars per minute.

To find the fixed monthly fee, we can use the constant rate of 0.06 and one of the equations from January or February.

For January: y + 150x = $69

Substituting the constant rate x = 0.06, we have:

So, the fixed monthly fee is $60.

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The value of the variable x is 23

Supplementary angles are simply described as pair of angles which sum up to 180 degrees.

Some properties of supplementary angles are;

From the information given, we have that;

x + 1 and 7x - 5 area supplementary

Then, we have the representation as;'

x + 1 + 7x - 5 = 180

collect like terms

8x = 180 + 4

8x = 184

make 'x' the subject of formula

x = 23

Hence, the value is 23

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Answer: 4 ways of solving one-step equations are the following: Adding, Substracting, Multiplication and Division. If we add the same number to both sides of an equation, both sides will remain equal.

Step-by-step explanation:

Adding, Substracting, multiplication and division

We have four methods for solving one-step equations: adding, subtracting, multiplying, and dividing. Both sides of an equation will stay equal if we add the same integer to both sides. Both sides of an equation will stay equal if we deduct the same integer from both sides. To solve systems of equations, three approaches are used: graphing, substitution, and elimination.

Fong, Alissa. A system of equations is made up of two or more equations with the same variables. A solution to an equation system is the point at which the lines intersect. Graphing, substitution, elimination, and matrices are the four methods for solving systems of equations.

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Answer:

33

Step-by-step explanation:

44

Answer:

C. 12,000(1.05)^n < 20,000

Step-by-step explanation:

A = P(1 + r)^t

P = $12,000

r = $5 dollar per year

t = n years

$12,000(1 + 5/100)^n

$12,000(1 + 0.05)^n

$12,000(1.05)^n

The question states, "The tuition is less than 20,000", therefore:

[$12,000(1.05)^n < 20,000]

The 8-Point Radix-2 Decimation-in-Frequency FFT is a fast Fourier transform algorithm used to decompose a signal into its individual frequency components.

The process begins by splitting the input sequence into even and odd samples using a butterfly operation. The even samples are then further split using a second butterfly operation, followed by a third butterfly operation on the odd samples. The outputs of the butterfly operations are then combined using a summation operation.

To draw the signal flow graph, we must first compute the intermediate values. The first step is to split the input sequence of 8 samples into two sequences of 4 samples each, with the even samples in the first sequence and the odd samples in the second. The second step is to further split the even samples into two sequences of 2 samples each. The third step is to apply a butterfly operation to the odd samples, resulting in two new sequences of 2 samples each. The fourth and final step is to combine the outputs from the butterfly operations using a summation operation.

The signal flow graph for the 8-Point Radix-2 Decimation-in-Frequency FFT is shown below:

                                          +---------------------+

                                          |  Input Sequence     |

                                          |  (8 samples)        |

                                          +----------+----------+

                                                     |

                                           +-----------+----------+

                                           |  Butterfly Operation |

                                           |  (Split Even/Odd)   |

                                           +-----------+----------+

                                              |  |  |  |

                                           +--+--+--+--+

                                           |  Butterfly Op.  |

                                           |  (Split Even)   |

                                           +--+--+--+--+

                                              |  |  |

                                           +--+--+--+

                                           |  Butterfly Op.  |

                                           |  (Split Odd)    |

                                           +--+--+--+

                                              |  |

                                           +--+--+

                                           |  Summation Op.  |

                                           |  (Combine Even/Odd)   |

                                           +--+--+

                                              |

                                          +----------+----------+

                                          |  Output Sequence    |

                                          |  (8 samples)        |

                                          +---------------------+

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N(t) approaches 550.

The equation N(t) = 550 / (1 + 49e^(-0.7t)) models the number of people in a town who have heard a rumor after t days. The equation describes the growth of the number of people who have heard the rumor over time. The e^(-0.7t) term in the denominator represents the rate of decay or the slowing down of the spread of the rumor as t increases. As t increases without bound, the exponential term approaches 0, so the fraction approaches 550 / (1 + 49 * 0) = 550 / 1 = 550.

This means that as time goes on, the number of people who have heard the rumor will approach 550, the limit or maximum value of N(t). This value is not limited by any of the factors mentioned in the options (b) to (e).

The number of people who started the rumor is not given in the equation and cannot be determined from the information provided.

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Answer:

Step-by-step explanation:

To find the largest angle in the kitchen triangle, we can use the Law of Cosines. The Law of Cosines states that in any triangle with sides a, b, and c and opposite angles A, B, and C, the following relationship holds:

c^2 = a^2 + b^2 - 2ab * cos C

In the kitchen triangle, we have the sides a = 6, b = 7, and c = 8. We can use the Law of Cosines to find the cosine of each angle and then use the inverse cosine function to find the angles themselves:

cos A = (b^2 + c^2 - a^2) / (2bc) = (7^2 + 8^2 - 6^2) / (2 * 7 * 8) = 0.41

A = cos^-1(0.41) = 61.8°

cos B = (a^2 + c^2 - b^2) / (2ac) = (6^2 + 8^2 - 7^2) / (2 * 6 * 8) = 0.95

B = cos^-1(0.95) = 18.4°

cos C = (a^2 + b^2 - c^2) / (2ab) = (6^2 + 7^2 - 8^2) / (2 * 6 * 7) = -0.15

C = cos^-1(-0.15) = 120.0°

The largest angle in the kitchen triangle is C, which measures 120.0°.

The maximum compression of the spring will depend on the spring's elasticity, or its ability to return to its original length after being stretched or compressed which is 2cm

If the same puck hits the spring at a speed of 2v, the spring will compress twice as much as it did when the puck was traveling at v. Thus, the spring's maximum compression will be 2 cm or twice its original compression of 1 cm.

It is important to note that the spring's elasticity will affect the maximum compression. If the spring is relatively stiff and has a low elasticity, it will not compress as far as a spring with a higher elasticity.

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The complete question should be: A hockey puck sliding along frictionless ice with speed v to the right collides with a horizontal spring and compresses it by 1.0 cm before coming to a momentary stop. What will be the spring's maximum compression if the same puck hits it at a speed of 2v?

The amount of same profit is $19.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

It costs $20 to rent a hot dog roller and it costs $10 to rent a nacho chip warmer.

The cost of additional supplies for the hotdog is $0.02 per tray.

The additional cost for the nachos is $0.06 per container.

Team A will sell the hot dogs for $1.50 each.

Team B will sell the nachos for $1.00 each.

let x be the same amount of profit both earn.

1.48x - 20 = 0.94x - 10

1.48x - 0.94x = 10

0.54x= 10

x = 18.51

hence, the profit is $19.

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Answer:

Always true

Step-by-step explanation:

A rhombus is a parallelogram with equal sides, and a square is a rectangle with equal sides. As a rectangle can also be a parallelogram, you can prove that a square is always a rhombus.

Answer:

This is always true.

Step-by-step explanation:

They both have 4 congruent sides

The volume of a right rectangular prism can be calculated by multiplying the length, width, and height together. Therefore, the volume of the jewelry box will depend on the specific measurements of the box.

To calculate the volume of the wooden jewelry box, we need to know its length, width, and height. Once we have those measurements, we can multiply them together to determine the volume of the box.

For example, if the length of the box is 5 inches, the width is 3 inches, and the height is 2 inches, then the volume of the box would be 5 x 3 x 2 = 30 cubic inches.

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The x-intercept of the function is 0.

The x-intercept of a function is the point where the graph of the function intersects the x-axis.

In other words, it is the point at which the y-value is equal to zero. For the function y = x, the x-intercept occurs when y = 0, and we can find the x-coordinate of this point by solving the equation x = 0.

Here we need to find the x-intercept, we set y equal to zero and solve for x. In this case, we have:

=> y = x

=> 0 = x

So the x-intercept of the function y = x is x = 0. This means that the graph of the function intersects the x-axis at the point (0,0).

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Answer:

A. 1/3

Step-by-Step Explanation

When a six-sided die is rolled, sample space = {1, 2, 3, 4, 5, 6}.

A is the event of getting an even number = {2, 4, 6}.

P(A) = 3/6 = 1/2

B is the event of getting a number less than or equal to 3 = {1, 2, 3}.

P(B) = 3/6 = 1/2

A∩B = {2}

P(A∩B) = 1/6

Using the P(A/B) formula:

P(A/B) = P(A∩B) / P(B) = 1/6/1/2 = 1/3

So P(A/B) = 1/3

Hope it helps.

If you have any query, feel free to ask.

Answer:

d

Step-by-step explanation:

D. 24 humans and 50 horses.

We can use a system of equations to solve for the number of horses (x) and number of humans (y):

x + y = 74 (the total number of heads)

y = 196 - 4x (the total number of legs, with each horse having 4 legs)

Substituting the second equation into the first:

x + (196 - 4x) = 74

5x = 122

x = 24.5 (number of horses rounded down to the nearest whole number)

y = 74 - x = 50 (number of humans)

Answer:

Answer should be

Step-by-step explanation:

Limit and say that the computation is justified by the limit laws x7limg(x)h(x)f(x) = -31.

A limit in mathematics is a value that a function approaches when the input gets closer to a certain value. Limits are used to find a function's derivative and integral as well as to characterize how a function behaves around particular places.

The following is the official definition of a limit: Let c be a real value and f(x) be a function. The symbol for the limit of f(x) as x gets closer to c is L.

lim x -> c f(x) = L

if for every ε > 0, there exists a δ > 0 such that for all x, 0 < |x - c| < δ implies |f(x) - L| < ε. In other words, as x gets arbitrarily close to c, the values of f(x) get arbitrarily close to L.

The limit can be computed as follows:

x→7limg(x)−h(x)f(x) = limx→7g(x)−h(x)limx→7f(x) = 5−3limx→7f(x) = 5−3(12) = 5−36 = -31

So, x→7limg(x)−h(x)f(x) = -31.

The limit of two functions that differ from one another is equal to the difference between their limits.

Both laws were used to simplify the expression in the limit.

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Limit and state that the computation is justified by the limit laws x→7limg(x)−h(x)f(x) = -31.

A limit in mathematics is a value that a function approaches when the input gets closer to a certain value. Limits are used to find a function's derivative and integral as well as to characterize how a function behaves around particular places.

The following is the official definition of a limit: Let c be a real value and f(x) be a function. The symbol for the limit of f(x) as x gets closer to c is L.

lim x -> c f(x) = L

if for every ε > 0, there exists a δ > 0 such that for all x, 0 < |x - c| < δ implies |f(x) - L| < ε. In other words, as x gets arbitrarily close to c, the values of f(x) get arbitrarily close to L.

The limit can be computed as follows:

x→7limg(x)−h(x)f(x) = limx→7g(x)−h(x)limx→7f(x) = 5−3limx→7f(x) = 5−3(12) = 5−36 = -31

So, x→7limg(x)−h(x)f(x) = -31.

The limit of two functions that differ from one another is equal to the difference between their limits.

Both laws were used to simplify the expression in the limit.

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