work out the binomial expansion including and up to x^2 of 1/(4+4x+x^2)

Answer:

(2,4)

Step-by-step explanation:

x=2

y=4

Answer: 4% of ___days is 56 days Answer If 0.04x = 56 days 0.01x = 14 days x = 14*100 = 1400 days To see more answers head over to College Study Guides

Step-by-step explanation:

The partial sum of the geometric series is:

125 + 25 + 5 + 1

Option First is true.

What is Geometric series?

Geometric series is the sum of an infinite number of terms that have a constant ratio between successive terms. The formula for calculating the sum of a finite geometric sequence, the sum of an infinite geometric series, and the nth term of a geometric sequence is known as the geometric series formula. The series has the following notation: a, ar, ar2, ar3,... where r is the "common ratio" and an is the first  term

Given that;

The geometric series.

∑ 125 (1/5)ⁿ⁻¹ ; where, n = 1 to 4.

Now, Calculate the partial sum of the geometric series as;

The geometric series = ∑ 125 (1/5)ⁿ⁻¹

Substitute n = 1, 2, 3, 4, we get;

= 125 (1/5)¹⁻¹ + 125 (1/5)²⁻¹ + 125 (1/5)³⁻¹ + 125 (1/5)⁴⁻¹

= 125 (1/5)⁰ + 125 (1/5)¹ + 125 (1/5)² + 125 (1/5)³

= 125 + 25 + 125/25 + 125/125

= 125 + 25 + 5 + 1

Thus, The partial sum of the geometric series 125+ 25 + 5 + 1

Option A is true.

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The surface area of a cylinder can be calculated using the following formula: Surface Area = 2πr2 + 2πrh, where r is the radius and h is the height of the cylinder.

In this case, Jenny is looking to store her soup in a cylindrical container and completely cover it in aluminium foil. This means the surface area of the container will be equal to the surface area of the cylinder plus the surface area of the foil. So, if the radius of the cylinder is r and the height is h, the surface area of the container is:

Surface Area = 2πr² + 2πrh  
Surface Area of Foil = 2πr² + 2πrh + 2r²π

Substituting in the given value for pi, we get Surface Area = 6.28r² + 6.28rh + 2r²π.

Therefore, the surface area of the container is equal to 6.28r² + 6.28rh + 2r²π, where r is the radius and h is the height of the cylinder.

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Answer:

18-15

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Plug in: d = 9, e = 5

(9)2 - 3(5)

9 x 2 = 18

-3 x 5 = -15

18 - 15 = 3

Time taken to reach the population size to reach 37,500 is 195 minutes.

Given that, a bacterial culture initially starts with 2,500 bacteria.

The population size of the bacterial culture doubles every 15 minutes, so in x minutes, the population size should double x/15 times. We can write this as an equation:

2,500 × 2^(x/15) = 37,500

\(2500\times2^\frac{x}{15} =37500\)

Now, we can take the logarithm of both sides to solve for x:

\(log_22500\times2^\frac{x}{15} =log_237500\)

x/15 = 13

So x = 195 minutes.

Therefore, time taken to reach the population size to reach 37,500 is 195 minutes.

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The correlation coefficient is strongly positive.

A correlation coefficient is a number between -1 and 1 that tells you the strength and direction of a relationship between variables.

Given:

r= 0.92

As, When r (the correlation coefficient) is near 1 or −1, the linear relationship is strong;

when it is near 0, the linear relationship is weak.

As, we have correlation coefficient, r= +0.92 which is very close to 1.

So, we have strong positive relation.

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The question attached is incomplete

The complete question is:

Number of steps taken per day and number of kilometers walked per day.  r=.92  

The coefficients and constant in the quadratic function f(x) = x² - 5x + 6 are coefficients: 1, -5 and constant: 6.

A quadratic function is an algebraic function with one or more variables where the largest exponent of the variable is two. The equation for a quadratic function is of the form f(x) = ax² + bx + c, where 'a' is a non-zero integer and a, b, and c are real numbers. A quadratic function is a polynomial of degree 2, and its definition is as follows.

The "a", "b", and "c" from "ax2 + bx + c" are used in the quadratic formula; they are known as the "numerical coefficients" of the quadratic equation. Therefore,

f(x) = x²– 5x + 6

a = 1

b = -5

c = 6

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Question:

Identifying the Coefficients and Constanta

Consider the quadratic function f(x) = x2 – 5x + 6.

What are the values of the coefficients and constant in the function?

Answer: 28282

Step-by-step explanation:

I think

Answer:

24 blocks

Step-by-step explanation:

The problem with Rodell's method for collecting data is that it may result in a biased sample.

Rodell is only polling the students on his football and basketball teams, which means the sample he collects is not representative of the entire student population at his school.

The favorite gaming app among the students on his teams may not be the same as the favorite gaming app among the broader student population.

To obtain a more accurate representation of the students' preferences, Rodell should aim for a random sample that includes students from various groups within the school, such as different grade levels or extracurricular activities.

This would help to minimize bias and ensure that the results reflect the overall preferences of the student body.

By solely relying on the football and basketball teams, Rodell's method limits the diversity of the sample, potentially leading to skewed results and an inaccurate conclusion about the favorite gaming app among all students at the school.

Therefore, Rodell's data collection method is flawed because it could lead to a biased sample, as it only includes students from his football and basketball teams.

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The possible outcomes for rolling a 30-sided die are numbers 1 through 30. Therefore, the probability of rolling a single digit number is zero.First, let's break down the problem into two parts: rolling a single-digit number on the 30-sided die, and flipping heads on the coin.

1. Rolling a single-digit number on a 30-sided die:
There are 9 single-digit numbers (1 to 9) on the die, and there are a total of 30 sides. So, the probability of rolling a single-digit number is 9/30, which can be simplified to 3/10.

2. Flipping heads on the coin:
A coin has 2 sides (heads and tails), and we are looking for the probability of getting heads, which is 1 side out of 2. So, the probability of flipping heads is 1/2.

Now, to find the probability of both events happening together (rolling a single-digit number and flipping heads), we need to multiply the probabilities:

(3/10) * (1/2) = 3/20

So, the probability of rolling a single-digit number and flipping heads is 3/20 or 0.15 (15%).

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On evaluating the given expression 7.5 + (4² − 2³) ÷ 4, we get 9.5 as the result.

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. For example -

5x + 7 = 6

7r + π = 4

Given is the following expression -

7.5 + (4² − 2³) ÷ 4

The given expression is -

7.5 + (4² − 2³) ÷ 4

Using the BODMAS rule, we can solve -

7.5 + (16 - 8) ÷ 4

7.5 + 8 ÷ 4

7.5 + 2

9.5

Therefore, on evaluating the given expression 7.5 + (4² − 2³) ÷ 4, we get 9.5 as the result.

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Answer:

I think 3 is the median.....

Answer:

approx. 3 hours

Step-by-step explanation:

14 newspapers in 20 minutes means he can deliver 42 newspapers an hour.

60/42 = 1.4285 newspapers per minute

131 x 1.4285 = 187.1335 minutes = 3.1188 hours

Answer:

1.-2x+4y=17

if you want me to solve for x : x=-17/2 +2y

If you want me to solve for y: y=17/4+x/2

2. If you want me to solve for x: x=-1+10y/3

If you want me to solve for y: y=3/10+3x/10

3. If you want me to do it all together it would be:

x=-79/4, y=-45/8

Step-by-step explanation:

A real-world example of how piecewise functions can be used is in:

Piecewise functions are tools that are often used for representing ways where the connection between variables alters under varying intervals or conditions.

To demonstrate the application of piecewise functions, consider the following example such as  calculating taxes on income. where a different nations implement an income tax system that make use of a segmented function to determine tax rates based on various income brackets.

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A loan fee is an amount a consumer pays for a loan. This includes taking out a car loan, credit card, or mortgage. Common loan fees include interest rates, origination fees, service fees, late fees, etc. Gross Loan Fees are typically associated with your credit card and consist of any outstanding balance plus any other fees incurred if you carry overdue amounts to your credit card.

If you know three numbers related to your credit card account: credit card (or loan) balance, APR, and billing cycle length, you can calculate your loan fees.

Current Balanced Owned =$785

APR = 24.42%

Let’s suppose the billing cycle is 30 days, then

Finance charge = $15.76

The new balance you owe = $800.76.

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To find the transition matrix, express the basis vectors of one basis in terms of other basis then construct using coefficients, convert it between two bases and express \(p(x)=a+bx+cx^{2}\) as a linear combination.

(a) To find the transition matrix from basis C to basis B, we express the basis vectors of C in terms of B and construct the matrix. The basis vectors of C can be written as \([ 1, (4-1),(x-1)^{2} ]\) in terms of B. Therefore, the transition matrix from C to B would be:

\(\left[\begin{array}{ccc}1&0&0\\0&3&0\\0&0&1\end{array}\right]\)

(b) To find the transition matrix from basis B to basis C, we express the basis vectors of B in terms of C and construct the matrix. The basis vectors of B can be written as [1, 2, 2x] in terms of C. Therefore, the transition matrix from B to C would be:

\(\left[\begin{array}{ccc}1&0&0\\0&\frac{1}{3} &0\\0&0&\frac{1}{(x-1)^{2} } \end{array}\right]\)

(c) Given the polynomial \(p(x)=a+bx+cx^{2}\), we can express it as a linear combination of the basis vectors of B or C. For example, in terms of basis B, p(x) would be:

p(x) = a(1) + b(2) + c(2x)

Similarly, we can express p(x) in terms of basis C:

\(p(x)=a(1)+\) \(b(4-1)\) \(+\) \(c(x-1)^{2}\)

By substituting the values for a, b, and c, we can evaluate p(x) using the corresponding basis.

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Answer:

Its A. Just had this question

Step-by-step explanation:

Answer:

3/4

Step-by-step explanation:

The exact surface area of the cylinder is 17.5π cm².

The surface area of a cylinder is the sum of the areas of all of its surfaces. A cylinder is a three-dimensional shape that consists of a circular base and a curved surface that connects the edges of the base.

The formula for the surface area of a cylinder is given by:

Surface Area = 2πr² + 2πrh

where r is the radius of the cylinder and h is the height of the cylinder.

Using the given values, we have:

r = 1 and three fourths centimeters = 1.75 cm

h = 3 and one fourth centimeters = 3.25 cm

Substituting these values into the formula, we get:

Surface Area = 2π(1.75)² + 2π(1.75)(3.25)

Surface Area = 2π(3.0625) + 2π(5.6875)

Surface Area = 6.125π + 11.375π

Surface Area = 17.5π

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Answer:

7.81 units

Step-by-step explanation:

To find the distance between two points, we can use the distance formula:

d = √((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

Using the coordinates given in the problem, we can plug in the values into the formula:

d = √((4 - (-2))^2 + (1 - (-4))^2)

Simplifying this expression, we get:

d = √((6)^2 + (5)^2)

d = √(36 + 25)

d = √61

Therefore, the distance between the two points (-2,-4) and (4,1) is √61 (square root of 61), which is approximately 7.81 units.

Answer:

Surface area 12cm, and volume is 60

Step-by-step explanation:

Correct me if im wrong plz

9514 1404 393

Answer:

  D) 45 and 1.2

Step-by-step explanation:

The "varies inversely" relationship is described by the equation ...

  y = k/x . . . . . . y varies inversely with x (and vice versa)

The value of k can be found from known values of x and y:

  xy = k . . . . . . multiply the above equation by x

  (10)(6) = k = 60 . . . . using the given values

__

To check if a given pair of numbers satisfies ...

  y = 60/x

you can multiply them together to see if the product is 60.

  (A) 12×5 = 60

  (B) 15×4 = 60

  (C) 25×2.4 = 60

  (D) 45×1.2 = 54 . . . . . not a possible pair of corresponding values.

45 and 1.2 are not a possible solution for x and y.

the correct answer is option C: The company rejects H0, making a Type II error. In this hypothesis test, the null hypothesis H0 is that the machine produces no more than 98% high-quality candy, and the alternative hypothesis Ha is that the machine produces more than 98% high-quality candy. The significance level is α = 0.05.

The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed test statistic, assuming that the null hypothesis is true. A p-value of 0.15 is greater than the significance level of 0.05, which means that the result is not statistically significant.

However, the company is unaware that the machine is actually producing 99% high-quality candy. This means that the null hypothesis is actually false, and the alternative hypothesis is true. In other words, the machine is producing more than 98% high-quality candy.

Based on these observations, the company failing to reject the null hypothesis (option B) would be a Type II error, as it would mean that the company is not detecting a significant difference in the candy quality when, in fact, the machine is producing candy of higher quality than the null hypothesis assumes.

Therefore, the correct answer is option C: The company rejects H0, making a Type II error.

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the base of the triangular window is 24 feet and the height is 10 feet.

Let's denote the height of the triangular window as h feet. According to the given information, the area of the window is 120 square feet.

The formula to calculate the area of a triangle is:

Area = (1/2) × base × height

In this case, we can write the equation as:

120 = (1/2) × base × h

Now, we are also given that the base of the window is 4 feet more than twice the height. So we can express the base as:

base = 2h + 4

Substituting this expression for the base into the area equation, we have:

120 = (1/2) × (2h + 4) × h

Now we can solve this equation for the height.

Multiplying both sides of the equation by 2 to remove the fraction:

240 = (2h + 4) × h

Expanding the right-hand side:

240 = 2h² + 4h

Rearranging the equation and setting it equal to zero:

2h² + 4h - 240 = 0

Now we can solve this quadratic equation. Factoring out a 2:

2(h² + 2h - 120) = 0

Factoring the quadratic expression inside the parentheses:

2(h + 12)(h - 10) = 0

Setting each factor equal to zero:

h + 12 = 0   or   h - 10 = 0

Solving these equations, we get:

h = -12   or   h = 10

Since height cannot be negative in this context, we discard the negative value. Therefore, the height of the triangular window is h = 10 feet.

Substituting the height value back into the expression for the base:

base = 2h + 4

    = 2(10) + 4

    = 20 + 4

    = 24

Therefore, the base of the triangular window is 24 feet and the height is 10 feet.

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Answer:

8 inches

Step-by-step explanation:

The volume of a hemisphere is half the volume of a sphere.

Therefore, the sum of the volumes of the two hemisphere-shaped scoops of ice cream (with diameters of 4 inches), is equal to the volume of a sphere with diameter of 4 inches.

If the melted ice cream fills the cone exactly to the top without overflowing, the volume of the cone with diameter of 4 inches must be equal to the volume of a sphere with diameter of 4 inches.

As the diameter of a circle is twice its radius, then the radius of the sphere and cone is r = 2 inches.

The formulas for the volume of a cone and the volume of a sphere are:

\(\boxed{\begin{minipage}{4 cm}\underline{Volume of a cone}\\\\$V=\dfrac{1}{3} \pi r^2 h$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}\)   \(\boxed{\begin{minipage}{4 cm}\underline{Volume of a sphere}\\\\$V=\dfrac{4}{3} \pi r^3$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius.\\\\\end{minipage}}\)

The depth of the cone is its height.

Therefore, to calculate how deep the cone must be so that the melted ice cream will fill the cone exactly to the top without overflowing, set the two equations equal to each other, substitute r = 2, and solve for h (the depth of the cone).

\(\begin{aligned}\textsf{Volume of a cone}&=\textsf{Volume of a sphere}\\\\\dfrac{1}{3} \pi (2)^2 h & = \dfrac{4}{3} \pi (2)^3\\\\\dfrac{1}{3} \pi \cdot 4 h & = \dfrac{4}{3} \pi \cdot 8\\\\\dfrac{4}{3} \pi h& = \dfrac{32}{3} \pi \\\\\dfrac{4}{3} h& = \dfrac{32}{3} \\\\4 h& = 32 \\\\h&=\dfrac{32}{4}\\\\h&=8\; \sf inches\end{aligned}\)

Therefore, the depth of the cone must be 8 inches.

The cone must be at least 8 inches deep in order for the melted ice cream to fill the cone exactly to the top without overflowing.

1. The opening of the ice cream cone has a diameter of 4 inches. This means that the radius of the cone's opening is 4/2 = 2 inches.

2. The two hemisphere-shaped scoops of ice cream have diameters of 4 inches each. This means that the radius of each scoop is 4/2 = 2 inches.

3. When the ice cream melts, it will take up the space between the scoops and fill the cone. In order for the melted ice cream to fill the cone exactly to the top without overflowing, the depth of the cone must be equal to the combined height of the two ice cream scoops.

4. The height of each hemisphere-shaped scoop can be calculated using the formula for the volume of a sphere, which is (4/3)πr³, where r is the radius.

  - For each scoop, the radius is 2 inches, so the height of each scoop is (4/3)π(2)³ = (4/3)π(8) = (32/3)π.

5. Since there are two scoops, the combined height of the two scoops is 2 * (32/3)π = (64/3)π.

6. Therefore, the cone must be at least (64/3)π inches deep in order for the melted ice cream to fill the cone exactly to the top without overflowing. This is approximately equal to 67.03 inches.

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