Solve the recurrence relation an = 4an−1 + 4an−2 with initial terms a0 =1 and a1 =2.

Answer:

X=4

Step-by-step explanation:

(2x-5)+(4x-1)=7x-10

2x-5+4x-1=7x-10

6x-6=7x-10

6x=7x-4

x=4

Answer:

slope 1 over 2

y incept is where the graph starts it is usually represented by a dor

equation y equals mx plus b

Step-by-step explanation:

tip mx is your slope

The long run behavior of the function f(x)=5(2)x+1 is that it approaches 1 as x approaches negative infinity and it approaches infinity as x approaches positive infinity.

The long-term behavior of the function f(x)=5(2)x+1 can be discovered by examining how the function behaves as x gets closer to negative and positive infinity.

As x→−[infinity], f(x) = 5(2)^ -∞+1 = 5(0)+1 = 1

As x approaches negative infinity, the value of the function approaches 1.

As x→[infinity], f(x) = 5(2)^ ∞+1 = 5(∞)+1 = ∞

As x approaches positive infinity, the value of the function approaches infinity.

As a result, the function f(x)=5(2)x+1 behaves in the long run in such a way that it approaches 1 as x approaches negative infinity and infinity as x approaches positive infinity.

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Answer:

El precio original era $62.50

Step-by-step explanation:

espero haber ayudado :)

Step-by-step explanation:

l = length

w = width

l = 3w

perimeter p = 2l + 2w = 56

using the identity of the first equation

p = 2(3w) + 2w = 56

6w + 2w = 56

8w = 56

w = 7 cm

l = 3w = 3×7 = 21 cm

so, the area is

l×w = 21×7 = 147 cm²

Substitute -6 for x.

(-6+3)/(-6-1).

-3/-7.

--=+

Answer: 3/7.

Answer:

0.125

Step-by-step explanation:

Answer:

.125 bc I use a calendar

Step-by-step explanation:

that assignment

The quadratic equation does not have solutions where both x and y are integers.

Here we have the following quadratic equation:

2x^2 + 5y^2 = 14

We want to check that we can't solve this equation with x and y integers, to see that, we can start by isolating one of the variables:

2x^2 + 5y^2 = 14

5y^2 = 14 - 2x^2

y^2 = (14 - 2x^2)/5

y = ±√((14 - 2x^2)/5)

Now, trivially:

(14 - 2x^2)/5

Is not an integer for any integer value of x, and this happens because 5 is not a factor of 14, thus, for any integer value of x the value of y that we get is non integer, then there aren't two integers that solve the quadratic equation.

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Answer:

4 meters

Step-by-step explanation:

Given a quadratic equation in which the coefficient of \(x^2\) is negative, the parabola opens up and has a maximum point. This maximum point occurs at the line of symmetry.

Since the divers height, y is modeled by the equation

\(y= -x^2 + 2x + 3\)

Step 1: Determine the equation of symmetry

In the equation above, a=-1, b=2, c=3

Equation of symmetry, \(x=-\dfrac{b}{2a}\)

\(x=-\dfrac{2}{2*-1}\\x=1\)

Step 2: Find the value of y at the point of symmetry

That is, we substitute x obtained above into the y and solve.

\(y(1)= -1^2 + 2(1) + 3=-1+2+3=4m\)

The maximum height of the diver is therefore 4 meters.

The scale drawing of the mural would be 594.36 cm wide and 1097.28 cm tall.

A scale drawing is a drawing that shows an object or area at a scale that differs from the real size of the object or area. A scale, which is a ratio comparing the size of the drawing to the size of the actual item or location, is used to make scale drawings. A scale of 1:50, for instance, indicates that one unit on the design corresponds to fifty in real life.

In several disciplines, including architecture, engineering, and design, scale drawings are employed in real-world situations. Scale drawings are used by architects to construct building floor plans, elevations, and sections. Scale drawings are used by engineers to develop mechanical systems and machinery.

Given that the dimensions of the mural is 13 feet by 24 feet.

Converting into cm we have:

width = 13 feet * 30.48 cm/foot = 396.24 cm

height = 24 feet * 30.48 cm/foot = 731.52 cm

Now using the scale we have:

3cm : 2ft = x cm : 396.24 cm

Using cross multiplication we have:

2ft * x cm = 3cm * 396.24 cm

x = (3cm * 396.24 cm) / 2ft = 594.36 cm

For the height, we have:

3cm : 2ft = y cm : 731.52 cm

2ft * y cm = 3cm * 731.52 cm

y = (3cm * 731.52 cm) / 2ft = 1097.28 cm

Hence, the scale drawing of the mural would be 594.36 cm wide and 1097.28 cm tall.

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Answer:

1:3

Step-by-step explanation:

4:(3+4+5)

4:12

1:3

The reason for the required step using property of equality are as follow:

1.  Subtraction property of equality.

2. Subtraction property of equality.

3.  Addition property of equality.

As given in the question,

The reason for the required step using property of equality are as follow:

1. 3x + 3 = 5 + x

3x - x + 3 = 5

2x + 3 = 5

Here

Subtraction property of equality is applied.

If x, y, and z are real numbers and x = y

then

x - z = y - z

2. 2x + 3 = 5

2x = 5-3

2x = 2

Here Subtraction property of equality is applied.

If a, b, and c are real numbers and a = b, then

a - c = b - c

3. -x - 1 = 3

-x = 3 + 1

-x = 4

Here Addition property of equality is applied.

If x, y and z are real numbers and x = y, then

x + z = y + z

Therefore, the reason for the required step using property of equality are as follow:

1.  Subtraction property of equality.

2. Subtraction property of equality.

3.  Addition property of equality.

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Step-by-step explanation:

F = ka, where k is a real constant.

When a = 9, F = 36.

=> (36) = k(9), k = 4.

Therefore when a = 4,

F = (4)(4) = 16.

The value of F is 16 when a is 4.

Answer:

container A

Step-by-step explanation:

In Container A, we can plot the points (0,60) adn (2, 35)

The slope is :

\(m_A = \frac{y_2-y_1}{x_2-x_1} \\\\= \frac{35-60}{2-0} \\\\= \frac{-25}{2}\\ \\m_A = -12.5\\\)

For container B, the slope is:

\(m_B = \frac{y_2-y_1}{x_2-x_1} \\\\= \frac{32-54}{3-1} \\\\= \frac{-22}{2}\\ \\m_B = -11\\\)

The negative sign of the slope indicates the direction of the slope

\(|m_A| = 12.5\\\\|m_B| = 11\)

12.5 > 11

The slope of container A is steeper than container B

Therefore, the water is draining out of container A at a faster rate than container B

The first three non-zero terms in the power series are

\(x^2 - x4/3! + x6/5!.\)

Given f(x) = ex and g(x) = sinx,

we need to find the first three non-zero terms in the power series expansion for the product f(x)g(x).

Using the formula for the product of two series, we have:

\((ex)(sinx)\) = \((x - x3/3! + x5/5! - x7/7! + ...) (x - x3/3! + x5/5! - x7/7! + ...)\)

Expanding the above expression using the distributive property, we get:

\(x2 - x4/3! + x6/5! + ...\)

Taking the first three non-zero terms, we have:

\(x2 - x4/3! + x6/5!\)

Therefore, the answer is

\(x^2 - x4/3! + x6/5!.\)

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The probability that the weight of a randomly selected steer is less than 1700lbs is 0.9772.

To solve this problem, we need to use the standard normal distribution with a mean of 0 and a standard deviation of 1. We can convert the given data into a standard normal distribution by using the formula:

z = (x - μ) / σ

where z is the z-score, x is the given value, μ is the mean, and σ is the standard deviation.

In this case, we want to find the probability that a randomly selected steer weighs less than 1700lbs. So we need to find the z-score for 1700lbs:

z = (1700 - 1400) / 200

z = 1.5

We can then use a standard normal distribution table or calculator to find the probability that a z-score is less than 1.5. This probability is 0.9332.

However, since we want to find the probability that a randomly selected steer weighs less than 1700lbs (not less than or equal to), we need to add half of the probability of the z-score being exactly 1.5 to this result:

0.9332 + 0.0228 = 0.956

Therefore, the probability that a randomly selected steer weighs less than 1700lbs is 0.9772 (rounded to four decimal places).

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For this series 10, 100, 1000 the common differences are (9 × 10), (9 × 10²), (9 × 10³)

To determine the common difference

100 - 10 = 90

1000 - 100 = 900

similarly, 10000 - 1000 = 9000, 100000 - 10000 = 90000,...........

Therefore, the common differences are (9 × 10), (9 × 10²), (9 × 10³),......

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Based on the calculations, the most likely value of t is equal to 2.2.

Given the following data:

A null hypothesis (\(H_0\)) can be defined the opposite of an alternate hypothesis (\(H_a\)) and it asserts that two (2) possibilities are the same.

For the one-tail test, we would reject the null hypothesis (\(H_0\)) when the p-value is lesser than the value of \(\alpha\);

\(H_o: P(Z > |\delta|) < 0.02\)

For the two-tail test, we would fail to reject the null hypothesis (\(H_0\)) when the p-value is greater than the value of \(\alpha\);

\(H_o: 2P(Z > |z|) > 0.02\\\\H_o: P(Z > |z|) > 0.01\)

Next, we would determine the positive value of z-score that satisfies this expression;

\(0.01 < P(Z < z) < 0.02\\\\\)

From the z-table, we have:

\(P(Z > 2.326)\;and\; P(Z > 2.054)\\\\2.054 < z < 2.326\)

Therefore, t = 2.2.

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Answer:

A v=2.25   H=1

b. 5.625

Step-by-step explanation:

Answer:

V = 3.90625 cm³

Step-by-step explanation:

Given that V varies directly as h³ then the equation relating them is

V = kh³ ← k is the constant of variation

To find k use the condition

V = 6.75 when h = 3 , then

6.75 = k × 3³ = 27k ( divide both sides by 27 )

0.25 = k

V = 0.25h³ ← equation of variation

(b)

When h = 2.5 , then

V = 0.25 × 2.5³ = 3.90625 cm³

how will his speed compare?  or namely, will he be within speed limits or should we give him a big fat ticket for speeding?

well, the 25 mi/hr limit is expecting anyone on that road to only do 40,234 meters per hour, so since an hour is 60 minutes and a minute is 60 seconds, that means an hour is really (60)(60) seconds, or 3600 seconds, so the limit is expecting anyone on that road to do no more than 40,234 meters per 3600 seconds, let's see how Usain fares

\(\begin{array}{ccll} meters&seconds\\ \cline{1-2} 100 & 9.63\\ 40234& x \end{array} \implies \cfrac{100}{40234}~~=~~\cfrac{9.63}{x} \implies 100x=(40234)(9.63) \\\\\\ x=\cfrac{(40234)(9.63)}{100}\implies x\approx 3874.53\)

so Usain will covering those 40,234 meters in about 3875 seconds, that's longer than 3600 seconds, meaning Usain will need more than 3600 seconds to cover those meters so he's really going slower 40,234 meters per 3600 seconds, so he's golden,  he's within speed limits, because the limit is expecting noone to do them in less than 3600 seconds.

Answer:

x = 138

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the opposite interior angles

x = B+ C

x = 68+ 70

x =138

Answer:

138 degrees

Step-by-step explanation:

A triangle is made up of 180 degrees, it lists 2 values already, 68&70. when added that equals 138.

So 180-138 is 42 degrees, which would be the last angle within the triangle.

Since a line is also 180 degrees, its 180-42, which makes x 138 degrees

The statement is true. If we take any two distinct prime numbers, and the number "1", these numbers will always be pairwise relatively prime.

Two numbers are said to be pairwise relatively prime if their greatest common divisor (GCD) is equal to 1. In this case, since we are considering distinct prime numbers, their GCD will always be 1 since prime numbers have no common factors other than 1 and themselves. Therefore, any two distinct prime numbers will be relatively prime.

Similarly, when we consider the number "1", it is relatively prime to any other number because its only divisor is 1. Hence, when "1" is paired with any prime number, the GCD will be 1.

In summary, whether we consider two distinct prime numbers or pair them with the number "1", the resulting numbers will always be pairwise relatively prime.

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Answer:

You can use a sequence of two or more transformations to map a preimage to its image. You can map AABC onto AA"B"C" by a translation 3 units right followed by a 90° clockwise rotation about the origin.

A sequence of transformations to map a preimage to its image is reflection.

It is required to find the transformations to map a preimage to its image.

A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure. The original shape of the object is called the Pre-Image and the final shape and position of the object is the Image under the transformation.

Given:

Transformation maps the pre-image, DEFG, to the image, D'E'F'G'. The transformation is a reflection.

The line of reflection must go through the center point. Two lines of reflection go through the sides of the figure. Two lines of reflection go through the vertices of the figure. Thus, there are four possible lines that go through the center and are lines of reflections.

Therefore, a sequence of transformations to map a preimage to its image is reflection.

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The signof function is defined as follows:

def signof(num):
   if num > 0:
       return 1
   elif num == 0:
       return 0
   else:
       return -1

In the above code snippet, we have defined a function named signof which receives an integer argument named num. The if condition checks if the num is greater than 0, if yes, the function will return 1 as it is positive. Else if the num is equal to 0, then it will return 0, as per the requirement. Otherwise, it will return -1 as the number is negative. This code snippet will give the required output as per the requirement of the problem statement.

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D. The energy used is the same for both segments, the power while running is greater.

Walking and running both require energy, but the distance covered and the time taken are different. In this case, the person covers the same distance of 1 km in both segments.

Therefore, the energy used is the same for both. However, since running involves covering the same distance in less time, the power while running is greater. Power is the rate at which energy is used, and since running takes less time, the power output is higher.

D. The energy used is the same for both segments, the power while running is greater.

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Answer:

hdjhdhdhdjdvdvddiwhegwiwiwhegeeuui

Answer: it would be 15

Step-by-step explanation:

to do this add 15 five times and you will get 75

just tell the teacher that you started at ten and then when you got to 15 it worked. orrrr...  you know there is 60 minutes in an hour and you know that it can be divided by 4 to equal 15 so you added 15 one more time and got 75

The value of IQR is 90 when box plot data where Q₁ = 200, Q₂ = 250, and Q₃ = 290.

Given that,

For box plot data where Q₁ = 200, Q₂ = 250, and Q₃ = 290

We have to find the data of IQR.

We know that,

IQR is define as the variation in the distribution of your data's middle quartile is measured by the interquartile range (IQR). It is the range that corresponds to your sample's middle 50%. Measure the variability where the majority of your numbers are by using the IQR.

IQR Formula is Q₃ - Q₁

So,

Q₃ = 290

Q₁ = 200

Then ,

IQR = Q₃ - Q₁

IQR = 290 - 200

IQR = 90

Therefore, The value of IQR is 90.

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Based on the survey results, a typical parent would spend around $44 on their child's birthday gift, with a margin of error of approximately $2.9 at a 99% confidence level.

To estimate how much a typical parent would spend on their child's birthday gift, we use the sample mean and standard deviation as estimates of the population parameters. The sample mean of $44 serves as the point estimate for the population mean.

To determine the margin of error, we use the standard error, which is the standard deviation divided by the square root of the sample size. In this case, the standard error is approximately $2.5 (standard deviation of $10 divided by the square root of 20). Multiplying the standard error by the critical value corresponding to a 99% confidence level (z-value of 2.58 for a large sample size) gives us the margin of error.

Therefore, the typical amount spent on a child's birthday gift is estimated to be $44, with a margin of error of approximately $2.9. This means that we can be 99% confident that the true mean amount spent by parents falls within the range of $41.1 to $46.9.

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