Write a recursive formula for the following arithmetic sequence.

-6, -9, -12, -15, ...

First, by solving for y, convert the equation of the given line into slope-intercept form y=mx+c .You obtain the slope of the equation as m. Since the slopes of perpendicular lines are negative reciprocal, the slope of the line we're looking is the negative reciprocal of the perpendicular equation.

By entering the supplied point into the formula y = mx + b and solving for b, we arrive at the value of b. Consequently, the line's equation is formed.

A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.

Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by Δy and Δx, respectively.

m = y/x = y/x = change in y/change in x

where "m" represents a line's slope.

Additionally, the slope of the line may be shown as

tan θ = Δy/Δx

A line's slope often indicates the steepness and direction of the line.

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m = y/x = y/x = change in y/change in x

where "m" represents a line's slope.

Additionally, the slope of the line may be shown as

tan θ = Δy/Δx

Answer:

b+2.673

Step-by-step explanation:

substitute the value of the variable into the equation and simpilfy

Answer:

8.807

Step-by-step explanation:

1. 6.134 + (5.68 - 3.007)

   6.134 + 2.673

   = 8.807 or \((\frac{8807}{1000}, 8\frac{807}{1000} )\)

A normal distribution curve with mean 110 and standard deviation 10.  Percentages of students scoring below 90, higher than 115, lower than 115, and between IQ score cut offs for the top 15% and the middle 36% of students were 105.7 and 114.3. The percentage of students falling between IQ scores of 95.6 and 105 is  23.5%..

To find the percentage of students who scored below a 90, we need to find the area under the normal distribution curve to the left of 90. Using a standard normal distribution table or calculator, we find that this area is about 0.16 or 16%.

To find the percentage of students who scored higher than a 115, using a standard normal distribution table or calculator, we find that this area is about 0.16 or 16%. To find the percentage of students who scored lower than a 115, we need to find the area under the normal distribution curve to the left of 115, which is about 84%.

To find the IQ score cutoff for the top 15% of students, using a standard normal distribution table or calculator, we find that the z-score is about 1.04. We can then use the formula z = (x - μ) / σ to solve for x, the IQ score cutoff:

1.04 = (x - 110) / 10

x = 121.04

So the IQ score cutoff for the top 15% of students is about 121.04.

To find the IQ scores, using a standard normal distribution table or calculator, we find that the z-scores are about -0.43 and 0.43. We can then use the formula z = (x - μ) / σ to solve for x, the IQ score cutoffs:

-0.43 = (x - 110) / 10

x = 105.7

0.43 = (x - 110) / 10

x = 114.3

So the IQ score cutoffs for the middle 36% of students are about 105.7 and 114.3.

To find the percentage of students who fall between IQ scores of 95.6 and 105, we find that the z-scores are about -1.04 and -0.46. Using a standard normal distribution table or calculator, we find that the area between these z-scores is about 0.235 or 23.5%.

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Answer:

2) 30, 70, 80

Step-by-step explanation:

Well there has to be 3 angles that all add up to 180°.

1)

100+130+130

=360

2)

30+70+80

= 180

3)

25+3+35

=63

4)

45 + 105 + 120

=150

150+120

270

Answer: x=π/3+2πn, 5π/3+2πn, for any integer n

Answer:

Step-by-step explanation:

2cos²x-7cosx+3=0

2cos²x-6cosx-cosx+3=0

2cosx(cosx-3)-1(cosx-3) =0

cosx=3, 1/2

cosx =3 is rejected as range of cosx lies between [-1, 1]

so cosx=1/2 is the only solution of the given equatiom

Answer:

600 calories

Step-by-step explanation:

120 (# of minutes in 2 hours) divided by 40 is 3, so multiply 200 by 3 and you get 600

Answer:

600 calories burnt

Step-by-step explanation:

What I started with is 200/40=5 calories burned per min

60 plus 60=120

5x120=600

Hope this helps

Answer:

C

Step-by-step explanation:

since the dilatation is centred at the origin then multiply the coordinates of the point by scale factor of \(\frac{1}{3}\)

(- 3, 6 ) → (\(\frac{1}{3}\) (- 3), \(\frac{1}{3}\) (6) ) → (- 1, 2 )

The margin of error can be calculated using the formula:
Margin of error = (upper limit of the confidence interval - lower limit of the confidence interval) / 2

In this case, a margin of error of 9.55 suggests that the sample mean is quite precise, since it's relatively close to the true population mean (which we know to be 52.90).

In this case, the lower limit of the confidence interval is 43.85 and the upper limit is 61.95.
Margin of error = (61.95 - 43.85) / 2
Margin of error = 9.55
Therefore, the margin of error is 9.55. This means that if the sample size were to be repeated, we would expect the sample mean to be within 9.55 units of the true population mean 95% of the time.
It's worth noting that the confidence interval provides a range of values within which we can be reasonably certain that the true population mean lies. The margin of error, on the other hand, gives us an indication of the precision of our estimate. However, if the margin of error were larger, this would indicate that our estimate is less precise and that we need a larger sample size to obtain a more accurate estimate of the population mean.

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Step-by-step explanation:

Let (x, y) be the coordinates of point B.

(4, 6) => (-2, 4) => (x, y)

We have 2(-2) = 4 + x and 2(4) = 6 + y.

Solving these, we get x = -8 and y = 2.

Hence the coordinates of point B is (-8, 2).

Point Q is the midpoint of AB. Q has coordinates of (-2, 4) and A has coordinates of (4,6). Hence the coordinates of point B will be (-8, 2).

Suppose we've two endpoints of a line segment as:

A (p,q), and B (m,n)

Then let the midpoint be M(x,y) on that line segment.

Then, its coordinates are:

\(x = \dfrac{p+m}{2}\)

and

\(y = \dfrac{q+n}{2}\)

Let (x, y) be the coordinates of point B.

Q has coordinates of (-2, 4).

A has coordinates of (4,6).

A (p,q) = (4, 6)

M(x,y)=  (-2, 4)

B = (x, y)

We have

2(-2) = 4 + x

2(4) = 6 + y.

Solving these, we get

x = -8 and y = 2.

Hence the coordinates of point B will be (-8, 2).

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The answer is H, B and C; And Z, K and R

Step-by-step explanation:

H, B and C; And Z, K and R form a straight line

The value of f(5)(0) for the given Maclaurin series is -1/750.

The Maclaurin series for a function f(x) is given by the formula:

f(x) = Σn=0 to infinity [f^(n)(0) / n!] x^n

where f^(n)(0) is the nth derivative of f evaluated at x=0.

In this case, we are given the Maclaurin series for the function f(x) as:

f(x) = x * Σn=1 to infinity (-1)^n (1 / (x^n * 3n^2 * (n+5)))

To find the 5th derivative of f(x) evaluated at x=0, we need to differentiate the series 5 times and then evaluate it at x=0.

f(1)(x) = Σn=1 to infinity (-1)^n (1 / (x^(n-1) * 3n^2 * (n+5)))

f(2)(x) = Σn=1 to infinity (-1)^n * (n-1) / (x^n * 3n^2 * (n+5))

f(3)(x) = Σn=1 to infinity (-1)^n * (n-1) * (n+2) / (x^(n+1) * 3n^2 * (n+5))

f(4)(x) = Σn=1 to infinity (-1)^n * (n-1) * (n+2) * (n+7) / (x^(n+2) * 3n^2 * (n+5))

f(5)(x) = Σn=1 to infinity (-1)^n * (n-1) * (n+2) * (n+7) * (n+12) / (x^(n+3) * 3n^2 * (n+5))

Substituting x=0, we get:

f(5)(0) = Σn=1 to infinity (-1)^n * (n-1) * (n+2) * (n+7) * (n+12) / (0^(n+3) * 3n^2 * (n+5))

Simplifying the denominator, we get:

f(5)(0) = Σn=1 to infinity (-1)^n * (n-1) * (n+2) * (n+7) * (n+12) / (3n^2 * (n+5))

To evaluate this series, we can use partial fraction decomposition and then use the formula for the sum of the series 1/n^2.

After simplifying, we get:

f(5)(0) = -1/750

Therefore, the value of f(5)(0) is -1/750, which is option (C).

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Answer:

1:27pm

Step-by-step explanation:

52 + 8 = 1 hour

29 - 8 = 21

1 hour and 21 minutes

2:48 - 1:21

1:27pm

Answer:

well i dont know what you meant by the misplaced equal sign, but i removed it, this is the equation i solved

8(2x-2)=7(3w+2)

Step-by-step explanation:

the answer is in the file below

If this answer helped you out, please consider leaving a thanks,  thank you.

the radius of convergence is 1 and the interval of convergence is (1, 3) in terms of x-values.

To determine the radius of convergence, we can use the ratio test. The ratio test states that if the limit of the absolute value of the ratio of consecutive terms is less than 1 as n approaches infinity, then the series converges. Applying the ratio test to the given series, we have:

lim(n->∞) |((x - 2)^(n+1)/(n+1)) / ((x - 2)^n/n)| < 1

Simplifying the expression, we get:

lim(n->∞) |(x - 2)n+1 / (n+1)(x - 2)^n| < 1

Taking the absolute value and rearranging, we have:

lim(n->∞) |x - 2| < 1

This implies that the series converges when |x - 2| < 1, which gives us the interval of convergence. The radius of convergence is the distance between the center of the series (x = 2) and the nearest point where the series diverges, which in this case is 1.

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Answer:

x=30

Step-by-step explanation:

Answer:

C. $147,926.83

Step-by-step explanation:

Answer:

424000

Step-by-step

Answer: $0.53 Per Pound.

Work: I did 2 tons divided by $2120. But, before I did the division, I made sure that the 2 tons were in pounds. 1 ton is 2000 pounds, so it's of course 4000 pounds. So, 2120/4000. After the division, I got 0.53 per pound

Check: 0.53 x 4000 = 2120. (Check)

Answer:

628.31853

Step-by-step explanation:

V=πr2h

3=π·102·6

3≈628.31853

Answer:

200π

Step-by-step explanation:

h/3πr²

6/3· 10² · π

2 · 100 · π

= 200 π

The number of grams of salt in the tank at time t is given by the differential equation \(A(t)=200-170e^{-\frac{1}{50}t}\).

The rate is basically a measurement of something's number, amount, or degree in relation to another item. Its the ratio of some quantity to some other quantity.

An equation with a function and one or more of its derivatives is referred to as a differential equation:

At the start, the tank contains A(0) = 30 g of salt.

Salt flows in at a rate of

(1 g/L) * (4 L/min) = 4 g/min

and flows out at a rate of

(A(t)/200 g/L) * (6 L/min) = 3A(t)/100 g/min

so that the amount of salt in the tank at time t changes according to

A'(t) = 4 - A(t)/50

So,

\(A'(t) = 4 - \frac{A(t)}{50}\)

The solution of linear differential equation y' + ay = g(x) is in the form,

\(e^{ax}y=\int {e^{ax}g(x)} \, dx +c\)

Now, putting the values,

\(a=\frac{1}{50} \\g(x)=4\)

\(e^{\frac{1}{50}t}A(t)=\int {e^{\frac{1}{50}t}4} \, dt +c\\=4\int {e^{\frac{1}{50}t}} \, dt +c\\=4\times50e^{\frac{1}{50}t}+c\\=200e^{\frac{1}{50}t}+c\\\)

Now,

\(A(t)=200+Ce^{-\frac{1}{50}t}\\\)

Putting the initial value,

\(30=200+Ce^{-\frac{1}{50}(0)}\\\\200+C=30\\C=-170\)

So, the function will be \(A(t)=200-170e^{-\frac{1}{50}t}\).

Therefore, the number of grams of salt in tank at time t is given by differential equation \(A(t)=200-170e^{-\frac{1}{50}t}\).

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The length of the pendulum is approximately 24.99 cm.

The formula for the period of a pendulum is:

T = 2π√(L/g)

where T is the period in seconds, L is the length of the pendulum in meters, and g is the acceleration due to gravity (approximately 9.81 \(m/s^2\)).

To find the length L of the pendulum in centimeters, we can rearrange the formula as follows:

L = (T/2π\()^2\) * g

Substituting T = 0.537 s and g = 9.81 m/s^2 (which is equivalent to 981 cm/s^2), we get:

L = (0.537/(2π)\()^2\) * 981

L ≈ 24.99 cm

Therefore, the length of the pendulum is approximately 24.99 cm.

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Answer:

x - 6y = 14

Step-by-step explanation:

Add the like terms (x's and y's and constants):

 -2x+4y= 17

+ (3x-10y= -3​)

   x - 6y = 14

Answer:

Step-by-step explanation:

Area of triangle = 1/2 × Base × Height

Mr.Eastman drew triangle JKL,with a height of 12 inches and a base of 12 inches

Area of JKL = 1/2 × 12 inches × 12 inches

= 72 Square inches

triangle XLZ, with a height of 8 inches and a base of 16 inches. Which triangle has the greater area?

Answer:

a.) For the Junior Varsity Team, mean would be the appropriate measure of center since the data is symmetric or well-proportioned while we should use standard deviation for getting the measure of spread since it also measures the center and how far the values are from the mean.

b.) For the Varsity Team, the median would be the appropriate measure of the center since the data is skewed left and not evenly distributed so median could be used since it does not account for outliers while we use IQR or interquartile range in measuring the spread of data since IQR does not account for the data that is skewed.

For the Junior Varsity Team, the mean would be the appropriate measure of the center since the data is symmetric or well-proportioned .

Median represents the middle value of the given data when arranged in a particular order.

Since the data for the Junior Varsity Team is symmetric or well-proportioned, the mean would be the best way to determine the center, and standard deviation, which also measures the center and how far the values deviate from the mean, should be used to determine the spread.

The median could be utilized for the Varsity Team since the data is not evenly distributed and skewed to the left, and it does not take into account outliers.

We can use the interquartile range (IQR) to quantify the spread of the data because IQR does not take into account the skewed data.

Therefore, the varsity squad competes in intercollegiate or international competitions on behalf of the high school or institution while we should use standard deviation for getting the measure of spread since it also measures the center and how far the values are from the mean.

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The generating function for the sequence {an} is given by a(x) = (1 + 2x) / (1 - x - 6x^2). It captures the terms of the sequence {an} as coefficients of the powers of x.

To find the generating function of the sequence {an}, we can use the properties of generating functions and solve the given recurrence relation.

The given recurrence relation is: an = an-1 + 6an-2

We are also given the initial conditions: a0 = 1 and a1 = 3.

To find the generating function, we define the generating function A(x) as:

a(x) = a0 + a1x + a2x² + a3x³ + ...

Multiplying the recurrence relation by x^n and summing over all values of n, we get:

∑(an × xⁿ) = ∑(an-1 × xⁿ) + 6∑(an-2 × xⁿ)

Now, let's express each summation in terms of the generating function a(x):

a(x) - a0 - a1x = x(A(x) - a0) + 6x²ᵃ⁽ˣ⁾

Simplifying and rearranging the terms, we have:

a(x)(1 - x - 6x²) = a0 + (a1 - a0)x

Using the given initial conditions, we have:

a(x)(1 - x - 6x²) = 1 + 2x

Now, we can solve for A(x) by dividing both sides by (1 - x - 6x^2²):

a(x) = (1 + 2x) / (1 - x - 6x²)

Therefore, the generating function for the given sequence is a(x) = (1 + 2x) / (1 - x - 6x²).

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Answer:

bx8

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Hope thats the correct answer.

The expression (1.4 × 10¹)(8 × 10⁴) in scientific notation is 1.12 × 10⁵ and for expression (1.1 × 10⁻⁵)(3 × 10²) the  scientific notation is 3.3 × 10⁻³

The given expressions are (1.4 × 10¹)(8 × 10⁴) can be calculated as:

Firstly we will multiply the decimal numbers and whole numbers

1.4 × 8

One point four times eight is equal to eleven point two

= 11.2

Now we multiply the base with ten

10¹ × 10⁴

We know that when the bases are same then the powers will be added in multiplication

= 10⁵

Combining these results, we have 11.2 × 10⁵

Therefore, the result in scientific notation is 1.12 × 10⁵

Similarly, for (1.1 × 10⁻⁵)(3 × 10²)

We will multiply the decimal numbers and whole numbers

1.1 × 3 = 3.3

Now the base with ten will be multiplied

10⁻⁵ × 10²

The bases are same the powers will be added

= 10⁻³

Combining these results, we have 3.3 × 10⁻³

Therefore, the result in scientific notation is 3.3 × 10⁻³

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i cant see the question good enough

Answer:

1. y = 2x

2. y = 1/5x

Step-by-step explanation:

To write the equation of the line we need to find the slope and the y-intercept.

1. slope = y/x

4/2 = 2

y = 2x or y = 2x + 0

2.

1/5

y = 1/5x

To calculate the volume left unoccupied in the cylinder, we need to subtract the volume of the ball from the volume of the cylinder.

The volume of the cylinder can be calculated using the formula:

V_cylinder = π * r^2 * h

where π is the mathematical constant (approximated as 3.14), r is the radius of the cylinder, and h is the height of the cylinder.

Given that the cylinder has a height of 8 inches and a radius of 3 inches, we can calculate its volume:

V_cylinder = 3.14 * 3^2 * 8

V_cylinder = 3.14 * 9 * 8

V_cylinder = 226.08 cubic inches

Next, let's calculate the volume of the ball. The formula for the volume of a sphere is:

V_sphere = (4/3) * π * r^3

where r is the radius of the sphere.

Given that the ball has a diameter of 5 inches (radius = 2.5 inches), we can calculate its volume:

V_sphere = (4/3) * 3.14 * 2.5^3

V_sphere = (4/3) * 3.14 * 15.625

V_sphere = 65.45 cubic inches (rounded to two decimal places)

Volume left unoccupied = V_cylinder - V_sphere

Volume left unoccupied = 226.08 - 65.45

Volume left unoccupied = 160.63 cubic inches (rounded to two decimal places)

Therefore, approximately 160.63 cubic inches of volume is left unoccupied in the cylinder.

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