Arithmetic sequences calculator
This online tool can help you find n^th term and the sum of the first n terms of an arithmetic progression. Also, this calculator can be used to solve much more complicated problems. For example, the calculator can find the common difference (d) if a5=19 and s7=105. The biggest advantage of this calculator is that it will generate all the work with detailed explanation

The distribution of the number of people with diabetes in a sample of 100 can be modeled using the binomial distribution, with a probability of success of 10.5%.

The binomial distribution has certain properties, such as the mean and variance, that can be used to make inferences about the population. For example, the mean of the distribution is given by:

μ = np

where n is the sample size and p is the probability of success.

The distribution of the number of people with diabetes in a sample of 100 can be modeled using the binomial distribution. The binomial distribution describes the number of successes in a fixed number of independent trials, where each trial has the same probability of success.

In our case, a success is a person with diabetes, and the probability of success is the prevalence of diabetes in the population, which is 10.5%. The number of trials is 100, which is the sample size. Therefore, the distribution of the number of people with diabetes in our sample can be written as:

X ~ B(100, 0.105)

Where X is the random variable representing the number of people with diabetes in our sample, and B(100, 0.105) denotes the binomial distribution with 100 trials and a probability of success of 0.105.

In our case, the mean number of people with diabetes in our sample is:

μ = 100 x 0.105 = 10.5

This means that we expect, on average, to find 10.5 people with diabetes in our sample of 100.

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The value of the functions at 9m is

Generally, In mathematics, a function is a rule that maps one set of values (the domain) to another set of values (the range). The values in the range are determined by applying the function to the values in the domain.

Functions can take many forms and be expressed in different ways, including:

Linear functions: a function that produces a straight line when graphed. It has the form f(x) = mx + b, where m is the slope of the line and b is the y-intercept.

Quadratic functions: a function that produces a parabola when graphed. It has the form f(x) = ax^2 + bx + c, where a, b, and c are constants.

Therefore, this function

- f(x) = 4x

g(x) = 9x¹/2

for

F(x)=4x

F(9)=4*9

f(9)=36

for

g(x) = 9x¹/2

g(9)=9√9

=27

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Answer: AE

Step-by-step explanation:

if you look at the picture you can tell that Ae is a ray because rates tend to have 2 points and 2 sides one going on forever. that's why there's an arrow near "a"

The expression to measure {x} can be written as -

{x - 10} + {2x +40} + 90 = 180

We can write the Pythagoras theorem as - The sum of the squares of the base and perpendicular is equal to the square of the hypotenuse.

Mathematically -

(hypotenuse)² = (base)² + (perpendicular)²

Given is a right triangle ABC

We an write the expression to measure {x} as -

{x - 10} + {2x +40} + 90 = 180

Therefore, the expression to measure {x} can be written as -

{x - 10} + {2x +40} + 90 = 180

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The probability of committing type 1 error best describes notion of significance level of hypothesis test.

What is probability?

Probability is a mathematical concept used to measure the likelihood or chance of an event occurring. It is expressed as number between 0 and 1, where 0 represents an impossible event, and 1 represents certain event. The probability of an event is calculated by dividing number of favorable outcomes by total number of possible outcomes. Probability is used in various fields, including statistics, economics, finance, and science. It is used to make predictions, assess risk, and make informed decisions. Probability theory helps to explain random phenomena, such as the outcomes of a coin toss or the probability of a disease occurring in a population.

Complete Question:

Which one of the following best describes the notion of the significance level of a hypothesis test?

i) the probability of committing a type 1 error

ii) the probability of committing a type 2 error

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The values of x for which f(x) = g(x) are -1 and 4

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

f(x) = -2x + 4

g(x) = x^2 - 5x

Using the above as a guide, we have the following:

Using the above as a guide, we have the following:

x = -1 and x = 4

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The percentage of the shipping crate when compared to the total weight of the shipment would be = 16%

The weight of two granite specimen = 22 pounds

The weight of the crate = 20 pounds

The weight of shipping crate = 8 pounds

The total weight of the whole shipment = 22+20+8 = 50 pounds.

Therefore the percentage of shipping crate as compared to the total weight;

= 8/50 × 100/1

= 800/50

= 16%

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Answer:

Step-by-step explanation:

The answer is 4x^2y+8x^3+y^2-2xy

The probability that 2 or fewer tomato seeds germinate out of 10 planted, given a germination rate of 43%, is 0.586 or 58.6%.

To calculate the probability that 2 or fewer seeds germinate, we need to use the binomial distribution, where:

In this case, n = 10, p = 0.43, and we want to find the probability that 0, 1, or 2 seeds germinate. We can calculate this probability as the sum of the probabilities of each of these outcomes:

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

where X is the random variable representing the number of seeds that germinate.

Using the binomial distribution formula, we can calculate the probability of each outcome:

P(X = k) = (n choose k)[tex]* p^k * (1 - p)^{(n - k)}[/tex]

where (n choose k) is the binomial coefficient, equal to [tex]n! / (k! * (n - k)!)[/tex].

Plugging in the values, we get:

P(X = 0) = (10 choose 0) [tex]* 0.43^0 * 0.57^{10}[/tex] = 0.057

P(X = 1) = (10 choose 1) [tex]* 0.43^1 * 0.57^9[/tex] = 0.205

P(X = 2) = (10 choose 2) [tex]* 0.43^2 * 0.57^8[/tex] = 0.324

Therefore,

[tex]P(X \leq 2)[/tex] = [tex]0.057 + 0.205 + 0.324[/tex] = 0.586

So the probability that 2 or fewer seeds germinate is 0.586, or 58.6%.

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Answer:

The area of a circle can be found using the formula A = πr^2, where r is the radius of the circle. If the diameter of each circular light is 7 inches, the radius would be half of that, or 3.5 inches.

Therefore, the area of one circular light would be:

A = π * 3.5^2 = 3.5^2 * π = 12.25 * π square inches.

Since there are three circular lights, the total area of all three would be:

3 * 12.25 * π = 36.75 * π square inches.

Step-by-step explanation:

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∠5 is the alternate interior angle of ∠3.

What is transversal?

A transversal is a line that, at two different points in the geometry, cuts through two lines in the same plane. Various types of angles in pairs, including consecutive interior angles, corresponding angles, and alternate angles, are produced by a transversal intersection with two lines.

When a transversal intersects two parallel lines, the angles that are created inside are equal to the alternate pairs of that transversal. Alternate interior angles are what they are called.

Line m and line n are parallel and line l is transversal.

The alternate pairs of that transversal are ∠3 and ∠5.

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Answer:

164 cm^2

Step-by-step explanation:

lets find square of triangle first

corner ABD is 90 degrees coz corner ABC is 180 degrees and EBC is 90

(sum of all angles of a quadrilateral is 360,

B = 360 - C - F - E

360 - 90 - 90 - 90 = 90)

BD = CF - DE

BD = 16 - 8 = 8 cm

S ABD = AB * BD / 2 (coz corner B is 90 degrees)

S ABD = 13 * 8 / 2 = 13 * 4 = 52 cm^2

lets find square of BEFC next

S BEFC = CF * EF ( B = C = F = E = 90 so thats a rectangle)

S BEFC = 16 * 7 = 70 + 42 = 112 cm^2

finally lets find total area

S = S ABD + S BEFC = 52 + 112 = 164 cm^2

The average rate of change of the function over the interval [2,3] will be around 3.

Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).

For example to draw the equation y = 3x +2 this will draw a straight line in the coordinate geometry.

The rate of change is given by dy/dx

The average rate of change can be given as:

= (difference in y coordinate)/(difference in x coordinate)

= Δy/Δx

Average rate of change = ( 11 - 8 )/(3 - 2 )

                                        = 3

Hence, the average rate of change is 3

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The Larger number is 8

What is a linear equation in one variable?

The fundamental equation used to represent and solve for an unknown quantity is a linear equation in one variable. It is always a straight line, and it is simply shown graphically. A mathematical statement is simply represented by a linear equation.

Given that, the sum of two numbers is 14 and the larger number is four less than twice the smaller number

let the larger number be 'a' and the smaller be 'b'

from the question,

a + b = 14 .....eq 1

a = 2b - 4 .....eq 2

By substituting eq 2 in eq 1:

2b - 4 + b = 14

3b - 4 = 14

3b = 14 + 4 = 18

b = 6

a = 2b - 4 = 2*6 - 4 = 8

Therefore, The two numbers are 8, 4

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By using unitary methods, the amount of rope is needed for both sites is 350 meters.

Unitary method is a mathematical problem-solving technique that involves finding the value of one unit and using it to calculate the value of other units.

Let's start by looking at Site A, which is a rectangular area with a length of 60 meters and a width of 40 meters. To surround this area with rope, we need to measure the perimeter, which is the distance around the site.

=> Perimeter = 2 (length + width)

=>  2(60 + 40)

=> 2 x 100

=> 200 meters

Therefore, we need 200 meters of rope to surround Site A.

Now let's move on to Site B, which is also rectangular but has a length of 45 meters. To find the width of Site B, we can use the fact that it is similar in shape to Site A. Similar shapes have the same angles and proportional sides, so we can use a unitary method to find the missing dimension.

The length ratio of Site B to Site A is

=> 45/60 = 3/4

Since the shapes are similar, the width of Site B must also be 3/4 of the width of Site A.

Width of Site B = 3/4 x 40 = 30 meters

Now we can use the same formula as before to find the perimeter of Site B:

Perimeter = 2 (length + width)

=> 2(45 + 30)

=> 2 x 75

=> 150 meters

Therefore, we need 150 meters of rope to surround Site B.

To find the total amount of rope needed for both sites, we simply add the two perimeters:

Total rope needed = 200 + 150 = 350 meters

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Answer:  1/2of 2/3 = 1/2 of 2 Third(s)= 1 third

Answer:

Area of rectangle = [tex]\mbox{\large \boxed{\textrm{65 sq. inches}}}[/tex]

Step-by-step explanation:

Let square side = [tex]a[/tex]

Area of square   [tex]A = a^2[/tex]

Given [tex]A = 81[/tex]  and equating it to [tex]a^2[/tex]
[tex]a^2[/tex] [tex]= 81\;in^2[/tex]

[tex]a = \sqrt{81} = 9\;in[/tex]

Perimeter of square = [tex]4a = 4\cdot 9 = 36 \;in[/tex]

If [tex]l[/tex] = length of the rectangle and [tex]w[/tex] = width

Perimeter P of rectangle = [tex]2(l + w)\\[/tex]

Given perimeter of rectangle = perimeter of square we get
[tex]2(l + w) = 36\\\\l + w = 36/2\\\\l + w = 18[/tex]

Given

[tex]w = 5\\\\l + 5 = 18\\\\l = 18 - 5 = 13\\\\[/tex]

[tex]\\\\\textrm{Area of rectangle } = l \times w\\\\= 13 \times 5 \\\\= 65 \;sq.\;inches[/tex]

Peter's study is an example of a cross-sectional clinical study that investigates three pre-defined groups of patients with the same neurological syndrome by examining both the average score for each group and the scores for individual patients.

Cross-sectional study that compares three groups of patients with the same neurological syndrome. In this type of study, the researcher examines the groups at a specific point in time to obtain information about the prevalence, incidence, and characteristics of the disease or condition being studied. By examining both the average score for each group and the scores for individual patients, Peter is able to draw conclusions about the relationship between the neurological syndrome and the factors being studied. This type of study can help to identify risk factors, determine the efficacy of treatments, and guide future research in the field.

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The toy rocket will hit the ground after approximately 3.86 seconds.

The rocket will hit the ground when its height is equal to zero, so we can use the equation h = -4.97t^2 + 38.5t + 5.6 to find the value of t that satisfies this condition. To do this, we set h equal to zero and solve for t:

0 = -4.97t^2 + 38.5t + 5.6

-5.6 = -4.97t^2 + 38.5t

4.97t^2 - 38.5t - 5.6 = 0

This is a quadratic equation and can be solved using the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

Where a = 4.97, b = -38.5, and c = -5.6.

Plugging in these values, we get:

t = (-(-38.5) ± √((-38.5)^2 - 4 * 4.97 * -5.6)) / (2 * 4.97)

t = (38.5 ± √(1466.25 + 113.92)) / 9.94

t = (38.5 ± √1580.17) / 9.94

The square root of 1580.17 is 39.67, so:

t = (38.5 ± 39.67) / 9.94

t = (38.5 + 39.67) / 9.94 or (38.5 - 39.67) / 9.94

The first solution gives us a time of approximately 3.86 seconds, while the second solution is negative and therefore represents an unrealistic result.

The toy rocket will hit the ground after approximately 3.86 seconds.

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Miss Carol's bank account is losing money at a daily rate of $15, After giving money to her friend, Miss Carol's account balance fell by $65 leaving her with $435.

We must calculate Miss Carol's account balance's daily decline in order to ascertain the rate of change in her bank account.

Since Miss Carol lent her friend $65 this month, her account balance is reduced by $65, leaving her with $500 - $65 = $435.

The information that her account is losing $15 every day can then be put to use. We can write this as:

Rate of change = -$15 per day

The negative symbol signifies a declining amount on her account.

Therefore, Miss Carol's bank account is losing money at a daily rate of

$15, After giving money to her friend, Miss Carol's account balance fell by $65 leaving her with $435.

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Answer: A.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The exchange rate between the South African Rand (ZAR) and the Kenyan Shilling (KES) fluctuates daily. As of my training data cut off in 2021, the exchange rate was approximately 1 ZAR = 10.87 KES.

So, 30 South African Rand would be equivalent to approximately 329.10 Kenyan Shillings. However, it is important to note that exchange rates can change over time, so it is always a good idea to check a reliable source for the most up-to-date conversion rate before making any currency exchanges.

The slope of the line, 9.75, is the amount of money she makes per hour of work. The y-intercept of the line, -25, is the amount of money she starts with, since she owes her sister $25 and has worked 0 hours.

Extent, volume, and supply are all nouns. the sum of two or more amounts; the complete worth, impact, or importance of anything.

A number is a mass or accumulation, especially of something impossible to count: amount of The appropriate quantity of sand wasn't delivered. Animals were kept on a small amount of land. He donated money on a regular basis to a charity.

We know that slope =

[tex]$m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Here, slope m is

[tex]$m=\frac{53 -14}{8 -4 }[/tex]

[tex]$m=\frac{39}{4 }[/tex]

m = 9.75

And putting the value in y-intercept form we have

y = 9.75x – 25

Therefore, The slope of the line, 9.75, is the amount of money she makes per hour of work. The y-intercept of the line, -25, is the amount of money she starts with, since she owes her sister $25 and has worked 0 hours.

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Answer:

Equation of perpendicular line:

[tex]\boxed{\quad y=-\dfrac{1}{2}x+\dfrac{7}{2}\quad }[/tex]

Step-by-step explanation:

Generalized lope-intercept form of a line is y = mx + b    [1]

where

m = slope

b = y-intercept

Equation of the given line is y = 2x - 1           [2]

We are asked to find the equation of the line perpendicular to this and also passes through (1, 3)

Answer:

28 cups of Flower

Ratio Table:

2,4,6,8

7,14,21,28

Step-by-step explanation:

2x4/7x4=8/28

Klaus wil be behind where he started with a distance of 8miles

Distance is the total movement of an object without any regard to direction. We can define distance as to how much ground an object has covered despite its starting or ending point.

Distance can also be defined as the space or gap between two points.

Velocity = distance/time

distance = velocity × time

time = 60minutes = 1hr

therefore the distance made by Klaus in 60 minutes =

= 8 ×1

= 8miles

therefore within 60 minutes Klaus will cover a distance of 8miles from where he started.

Klaus and Rachel will be at same position with the same speed

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The rate of change of Jakes earning is, 0 or no change.

Rate is a ratio of change in one quantity w.r.t. change in another quantity. The net change in one quantity is written as, Δy and the net change in another quantity is written as, Δx.

So formula for the rate is,

m = change in one quantity/change in another quantity = Δy/Δx

On Monday, Jake earned $90 by washing 18 cars.

Therefore, his earning rate was:

= $90 / 18 cars

= $5 per car

On Tuesday, Jake washed 9 cars and earned $45.

Therefore, his earning rate was:

= $45 / 9 cars

= $5 per car

On Wednesday, Jake washed 12 cars and earned $60.

Therefore, his earning rate was:

= $60 / 12 cars

= $5 per car

We can see that Jake's earning rate remained constant over the three days at $5 per car.

Therefore, the rate of change of Jake's earnings is 0, or no change.

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Note that the r-value of the above data is : -0.903 (Option A)

In mathematics, the r-value typically refers to the correlation coefficient, which measures the strength and direction of the linear relationship between two variables.

With regard to the above data:

A) Find the Sum of the X values: 4 +5+8+9+13 = 39

B) Find the Sum of the Y values: 23 +12 +10 +9 +2 = 56

C) Find the Sum of x^2: 4^2 + 5^2 + 8^2 + 9^2 +13^2 = 355

D) The sum of the Y^2's: 23^2 + 12^2 + 10^2 + 9^2 + 2^2 = 858

E) Sum of x *y's: 4*23 + 5*12 + 8*10 + 9*9 + 13*2 = 339

N = number of sets = 5

Numerator of r = (E - A*B/N) = 339-39*56/5 = 339 - 436.8 = -97.8

Denominator of r = SQRT(C-A^2/N) x SQRT(D-B^2/N) =

SQRT(355-39^2/5) x SQRT(858-56^2/5) =

SQRT(50.8) x SQRT(230.8) =

7.1274 x 15.1921 =

108.2803

r = -97.8 / 108.2803

r = -0.903

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