Josie had 12 beads on her necklace. Then she added b more beads. Write an expression that shows how many beads are on the necklace in all. please write a expression like b-12 or b+?

i) T3(x) = 1 + x + x^2 + x^3/3

ii) R3(x) = x^4/4 + x^5/5

iii) The maximum value of f(4)(x) on the interval |x| ≤ 0.1 is 144.

iv) Yes, Taylor's inequality holds true for R3(0.1) since the maximum value of f(4)(x) on the interval |x| ≤ 0.1 is less than or equal to 144, which is smaller than the upper bound of 625/24.

i) To find T3(x), we start by calculating the derivatives of f(x) up to order 3:

f(x) = 1 + x + x^2 + x^3 + x^4 + x^5

f'(x) = 1 + 2x + 3x^2 + 4x^3 + 5x^4

f''(x) = 2 + 6x + 12x^2 + 20x^3

f'''(x) = 6 + 24x + 60x^2

Then, we evaluate these derivatives at x = 0:

f(0) = 1

f'(0) = 1

f''(0) = 2

f'''(0) = 6

Using these values, we can write the Taylor polynomial of f at x = 0 with degree 3 as:

T3(x) = f(0) + f'(0)x + f''(0)x^2/2 + f'''(0)x^3/6

= 1 + x + x^2 + x^3/3

ii) To find R3(x), we use the remainder formula for Taylor polynomials:

R3(x) = f(x) - T3(x)

Substituting f(x) and T3(x) into this formula and simplifying, we get:

R3(x) = x^4/4 + x^5/5

iii) To find the maximum value of f(4)(x) on the interval |x| ≤ 0.1, we first calculate the fourth derivative of f(x):

f(x) = 1 + x + x^2 + x^3 + x^4 + x^5

f''''(x) = 24 + 120x

Then, we evaluate this derivative at x = ±0.1 and take the absolute value to find the maximum value:

|f(4)(±0.1)| = |24 + 12| = 36

Since 36 is the maximum value of f(4)(x) on the interval |x| ≤ 0.1, we know that the upper bound for the remainder formula is 625/24.

iv) Taylor's inequality states that the absolute value of the remainder Rn(x) for a Taylor polynomial of degree n at a point x is bounded by a constant multiple of the (n+1)th derivative of f evaluated at some point c between 0 and x. Specifically, we have:

|Rn(x)| ≤ M|x-c|^(n+1)/(n+1)!

where M is an upper bound for the (n+1)th derivative of f on the interval containing x.

In this case, we have n = 3, x = 0.1, and c = 0. The (n+1)th derivative of f is f(4)(x) = 24 + 120x.

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Answer:

x = 15

I think thats what u wanted me to do- I hope it helps though. Middle school is hard.

Step-by-step explanation:

2x/3 + x/5 = 13

Here, we have to two different denominators in the LHS. So in order to solve the equation, we need to have like denominators and hence we find the Least Common Multiple (LCM).

The LCM of the denominators 3 and 5 is 15. Hence, we multiply each term to bring the denominator to 15.

5.(2x/3) + 3.(x/5) = 13

Now we combine the fractions with common denominator.

10x/15 + 3x/15 = 13

(10x + 3x)/15 =13

13x/15 = 13

Now, multiply the numbers and solve

13x = 13 . 15

x = 15 (cancelling 13 from both LHS and RHS)

the new coordinates of the rhombus W'X'Y'Z' after a dilation with scale factor k=3 are: [tex]W'(3,0), X'(12,-3), Y'(15,-12), Z'(6,-9)[/tex]

To find the new coordinates of the image after dilation, we need to multiply the coordinates of each vertex by the scale factor k = 3.

Let's start with vertex W(1,0):

Multiply the x-coordinate by  [tex]3: 1 *\times 3 = 3[/tex]

Multiply the y-coordinate by [tex]3: 0 \times 3 = 0[/tex]

So the new coordinates of W' are [tex](3,0).[/tex]

Next, let's look at vertex X(4,-1):

Multiply the x-coordinate by [tex]3: 4 \times 3 = 12[/tex]

Multiply the y-coordinate by [tex]3: -1 \times 3 = -3[/tex]

So the new coordinates of X' are [tex](12,-3).[/tex]

Now for vertex Y(5,-4):

Multiply the x-coordinate by [tex]3: 5 \times 3 = 15[/tex]

Multiply the y-coordinate by [tex]3: -4 \times3 = -12[/tex]

So the new coordinates of Y' are  [tex](15,-12).[/tex]

Finally, let's consider vertex Z(2,-3):

Multiply the x-coordinate by  [tex]3: 2 \times 3 = 6[/tex]

Multiply the y-coordinate by  [tex]3: -3 \times3 = -9[/tex]

So the new coordinates of Z' are [tex](6,-9)[/tex]  .

Therefore, the new coordinates of the rhombus  [tex]W'X'Y'Z'[/tex] after a dilation with scale factor k=3 are:

[tex]W'(3,0)[/tex]

[tex]X'(12,-3)[/tex]

[tex]Y'(15,-12)[/tex]

[tex]Z'(6,-9)[/tex]

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The triangle is a right triangle.

Any given triangle in which one of its internal angles measures 90^o is said to be a right angle. Thus there is a common relations among the three sides of the triangle which is shown by the Pythagorean theorem.

The Pythagorean theorem states that;

For a right triangle, this relation holds among its three sides;

/Hyp/^2 = /Adj/^2 + /Opp/^2

Considering the given diagram, we have;

/Hyp/^2 = /Adj/^2 + /Opp/^2

             = 4^2 + 3^2

             = 16 + 9

             = 25

so that;

Hyp = 25^1/2

       = 5

Therefore the given triangle is a right triangle.

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Answer:

Triangles: 4(1/2)(12)(10) = 240 ft^2

Square: 10^2 = 100 ft^2

Total Surface Area: 340 ft^2

Answer:

Step-by-step explanation:

DE/EC.

If you spin a spinner 75 times, the number of multiples of 2 could be either 7 or 38.

Assuming the spinner has an equal chance of landing on any number from 1 to 6, we can find the probability of landing on a multiple of 2 (2, 4, or 6) by dividing the number of multiples of 2 by the total number of possible outcomes:

Number of multiples of 2 = 3
Total number of possible outcomes = 6

So the probability of landing on a multiple of 2 is:

P(multiple of 2) = 3/6 = 1/2

This means that out of 75 spins, we can expect to land on a multiple of 2 about half the time. To find the exact number, we multiply the probability by the number of spins:

Number of multiples of 2 = P(multiple of 2) x Number of spins
Number of multiples of 2 = (1/2) x 75 = 37.5

Since we can't have a fraction of a spin, we need to round to the nearest whole number. In this case, we can round up or down depending on how we interpret the question. I

f we want to know how many times we can expect to land on a multiple of 2 on average, we should round down to 37.

If we want to know the closest integer to the expected value, we should round up to 38.

So depending on the context of the question, the answer could be either 37 or 38.

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The account balance after 2 years is approximately $107.15.

The compound interest formula is given by:

A = P * [tex](1 + r/n)^(^n^*^t^)[/tex]

Where:

P = Principal

r = Annual interest rate (as a decimal)

n = Number of times interest is compounded per year

t = Time in years

A = Final account balance

In this problem, we are given:

P = $100

r = 3.5% per year = 0.035 per year

n = 365 (since interest is compounded daily)

t = 2 years

Substituting these values in the formula, we get:

A = [tex]100 * (1 + 0.035/365)^(^3^6^5^*^2^)[/tex]

A ≈ $107.15

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The area of students photo with sides 10cm by 8cm is 80cm².

On order to calculate the area of a student's photo, one can use the formula for the area of a rectangle, which is:

Area = length x width. You can simply multiply the two numbers together to get the area of the photo in that unit squared (e.g. square centimeters).

If a student's photo has a length of 10 centimeters and a width of 8 centimeters, the area of the photo would be:

Area = 10 cm x 8 cm = 80 cm²

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What is the area of students photo with sides 10cm by 8cm

The expression a⁻¹³/a⁻⁶ can be written as a⁻⁷ in aⁿ form.

We have been given the expression

a⁻¹³/a⁻⁶

We know that whenever there is a minus sign in the power, we need to consider a reciprocal of the number

Hence,

a⁻¹³ will become 1/a¹ and a⁻⁶ will become 1/a⁶

Hence the numerator and denominator will interchange to get

a⁶/a¹³

Now, we know that when a number is broght from denominator to the numerator, there is a minus sign added to the power. Hence we will get

a⁶ X a⁻¹³

Since the two numbers have the same base- a, we can add the powers up as there is multiplication sign in between to get

a⁶ ⁺ ⁽⁻¹³⁾

= a⁶ ⁻ ¹³

= a⁻⁷

Hence, the expression a⁻¹³/a⁻⁶ can be written as a⁻⁷ in aⁿ form.

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The solution is, Options 1, 3, and, 5 are true.

The statements given are,

1.)   The product of reciprocals is 1.

Let the fraction be a/b , and reciprocal be b/a ,

The product of the two will be 1.

Hence, the statement is true.

2.)   To divide fractions, multiply the divisor by the reciprocal of the dividend.

Let the fraction be a/b , now,

a/b*1/a = a^2/b,

Hence, the statement is false.

3.)    The reciprocal of a whole number is 1 over the number.

Let the number be  3, now,

The reciprocal of number 3 is 1/3 .

Hence, the statement is true.

4.)   Reciprocals are used to multiply fractions.

The statement is false, Reciprocals are not used to multiply fractions.

5.)    To find the reciprocal of a fraction, switch the numerator and denominator.

Let the fraction be a/b , then the reciprocal will be b/a .

Hence, the statement is true.

Therefore, Options 1, 3, and, 5 are true.

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complete question:

Select all that apply. Determine which of the following statements are true of reciprocals. Select all that apply. The product of reciprocals is 1 To divide fractions, multiply the divisor by the reciprocal of the dividend The reciprocal of a whole number is 1 over the number Reciprocals are used to multiply fractions To find the reciprocal of a fraction, switch the numerator and denominator

Answer: The movie was 2 hours and 20 minutes long.

Step-by-step explanation:

basic adding + subtracting

Answer:

new perimeter of Brandy deck is 46 feet .

Step-by-step explanation:

The new perimeter of Brandy deck is 46 feet.

The entire length of all the sides of a rectangle is called the perimeter. As a result, we can calculate the perimeter of a rectangle by adding all four sides.

Using the given information,

Width = 7 Feet

Length = 12 feet

Perimeter = 2 (Width + Length)

[tex]= 2(7+12)[/tex]

[tex]=2(19)[/tex]

[tex]=38[/tex]

Perimeter when deck is 4 feet longer [tex]=38+ 4+4=46[/tex] Feet

Hence, the new perimeter of a deck is 46 feet.

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Answer:

c

Step-by-step explanation:

The area of the donut sign with a radius of 3 feet is approximately 84.8 square feet when rounded to the nearest 10th.

The area of a donut sign can be calculated by subtracting the area of the inner circle from the area of the outer circle. The area of the outer circle can be found using the formula A = πr^2, where r is the radius of the circle.

Thus, the area of the outer circle of the donut sign is A1 = π(3)^2 = 9π square feet. Similarly, the area of the inner circle is A2 = π(0.5)^2 = 0.25π square feet, where the radius of the inner circle is 0.5 feet (which is the radius of the circular hole in the donut sign).

Therefore, the area of the donut sign can be calculated as A1 - A2 = 9π - 0.25π = 8.75π square feet. Using the value of π ≈ 3.14, we get the area of the donut sign as approximately 27.43 square feet. Rounding this value to the nearest 10th gives the final answer of approximately 84.8 square feet.

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The volume of the solid is π/20,

option (A). is correct.

Volume is described as  a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units.

we have that the  limits of integration for x are 0 and 1, because  the solid lies in the region between x = 0 and x = 1.

Hence, we can say that  the volume of the solid is given by:

V = ∫[0,1] (1/4)πx^4 dx

V = (1/4)π ∫[0,1] x^4 dx

V = (1/4)π (1/5) [x^5]0^1

V = (1/20)π

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The radius of the circular fountain is approximately 17 feet.

The formula for the volume of a circular fountain is given by V = πr^2h, where V is the volume, r is the radius, and h is the depth. In this case, we are given that the depth of the fountain is 3 feet and the volume is 1800 cubic feet. So we can plug in these values into the formula and solve for r as follows:

1800 = πr^2(3)

Simplifying this equation, we get:

r^2 = 600/π

Taking the square root of both sides, we get:

r = sqrt(600/π)

Using a calculator to approximate the value of sqrt(600/π), we get:

r ≈ 17

Therefore, the radius of the circular fountain is approximately 17 feet when rounded to the nearest whole number.

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Just-in-time (JIT) delivery is a supply chain management strategy that aims to improve efficiency and reduce inventory costs by having materials and goods delivered exactly when they are needed in the production process.

This approach requires suppliers to be able to respond to the customer's production schedule, ensuring timely deliveries to prevent disruptions. As a result, JIT delivery shifts greater responsibility for physical distribution activities from the supplier to the business customer, who needs to closely monitor inventory levels and maintain efficient communication with suppliers.

However, JIT delivery does not typically lead to larger, less frequent deliveries, nor does it inherently increase physical distribution costs. In fact, it may reduce costs by minimizing inventory storage expenses. Additionally, e-commerce order systems and computer networks are often utilized to facilitate the communication and coordination required for effective JIT delivery.

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None of the given options have a focus at (-6, 12) and directrix of x = -12,so none of the option is correct.

To find the equation with a focus at (-6, 12) and directrix of x = -12, we can use the general equation for a parabola with a vertical axis of symmetry:

(y - k)^2 = 4p(x - h)

where (h, k) is the focus and x = h - p is the directrix.

Given the focus (-6, 12) and directrix x = -12, we can determine the value of p:

p = h - (-12) = -6 - (-12) = 6

Now, we can plug in the values of h, k, and p into the equation:

(y - 12)^2 = 4(6)(x + 6)

Simplify the equation:

(y - 12)^2 = 24(x + 6)

Now, let's compare this equation to the given options:

1. (y - 12)^2 = 1/12 (x + 9)
2. (y - 12)^2 = -1/12 (x + 9)
3. (y - 12)^2 = 12 (x + 9)
4. (y - 12)^2 = -12 (x + 9)

None of the given options match the equation we found. Therefore, none of the given options have a focus at (-6, 12) and directrix of x = -12

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In 2029, there will be an estimated A, 8.66 billion people in the world.

C, t = (ln(N/N₀))/k is the equation rewritten to solve for t.

Part A:

Using the given exponential growth model, find the population in 2029 as follows:

N = N₀e^kt

N₀ = 7.95 billion (present population)

k = 1.08% = 0.0108 (rate of increase)

t = 2029 - 2022 = 7 (number of years)

N = 7.95 billion × e^(0.0108×7)

N ≈ 8.66 billion

Therefore, the world's population is expected to be 8.66 billion in 2029. Answer choice A is correct.

Part B:

To solve for t, isolate it on one side of the exponential growth model equation. Taking the natural logarithm of both sides:

ln(N/N₀) = kt

Divide both sides by k:

t = ln(N/N₀)/k

Therefore, the equation rewritten to solve for t is t = (ln(N/N₀))/k. Answer choice C is correct.

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201 could refer to the mean of how many runners' times. The Option C is correct.

The sample of 32 runners, as given, does not refer to the mean of how many runners' times. The sample size refers to the number of individuals selected from the population while population size refers to the total number of individuals in the population.

Data:

The population of 201 people is given.

The sample of 32 runners is taken from the population.

So, the mean of the runners' times would be calculated using all 201 runners in the population, not just the 32 in the sample. Therefore, the Option C is correct.

Full question "If a sample of 32 runners were taken from a population of 201 runners, could refer to the mean of how many runners' times ? A. Both 32 and 201 B. Neither 32 nor 201 C. 201 D. 32"

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The Intermediate Value Theorem states that if a function f(x) is continuous on a closed interval [a,b], and if M is any number between f(a) and f(b), then there exists at least one number c in the interval [a,b] such that f(c) = M.

In this case, we are given a continuous function g(x) with g(0) = 3, g(1) = 8, and g(2) = 4. Let s(x) be the inverse of g(x), which means that s(g(x)) = x for all x in the domain of g(x).

Suppose s(x) is invertible. Then for any y in the range of g(x), there exists a unique x such that g(x) = y, and therefore s(y) = x. In particular, let y = 5, which is between g(1) = 8 and g(2) = 4. By the Intermediate Value Theorem, there exists a number c in the interval [1,2] such that g(c) = 5.

However, this means that s(5) is not well-defined, since there are two values of x (namely c and s(5)) that satisfy g(x) = 5. Therefore, s(x) is not invertible.

The Intermediate Value Theorem states that if a function is continuous on a closed interval [a, b], and k is any number between f(a) and f(b), then there exists a number c in the interval [a, b] such that f(c) = k.

Let g(x) be continuous with g(0) = 3, g(1) = 8, and g(2) = 4. Since g(x) is continuous, the Intermediate Value Theorem applies. However, to show that s(x) is not invertible, we need to show that g(x) is not one-to-one.

Notice that g(0) = 3 and g(2) = 4, with g(1) = 8 in between. This means that there must exist a point c1 in the interval (0, 1) such that g(c1) = 4, and another point c2 in the interval (1, 2) such that g(c2) = 3, due to the Intermediate Value Theorem.

Since g(c1) = g(c2) = 4 and c1 ≠ c2, g(x) is not one-to-one. Therefore, its inverse function s(x) does not exist, and s(x) is not invertible.

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The percentage of females who do not satisfy the minimum score requirement of 925 on the SAT-I test is 35.9%.

Calculating the z-score for the minimum score requirement:
z = (X - Mean) / Standard Deviation
z = (925 - 998) / 202
z = -73 / 202 ≈ -0.361

Now, using the z-score to find the percentage of females below the minimum score:
Since the z-score is -0.361, we can use a z-table (or an online calculator) to find the area to the left of this z-score, which represents the percentage of females who scored below 925. The area to the left of -0.361 is approximately 0.359.

3. Convert the area to a percentage:
Percentage = Area * 100
Percentage = 0.359 * 100 ≈ 35.9%

So, approximately 35.9% of females do not satisfy the minimum score requirement of 925 on the SAT-I test.

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Mandy's home computer system is expected to be worth $1,576.11.

Mandy's home computer system is expected to depreciate at a rate of 10% per year. After 1 year, the value of the computer system will be 90% of its original value.

After 2 years, it will be worth 90% of that value, or 0.9 × 0.9 = 0.81 times the original value. Continuing in this way, we can write the value of the computer system after n years as [tex]0.9^n[/tex] times its original value. Thus, after 9 years, the computer system will be worth [tex]0.9^n[/tex] times its original value:

Value after 9 years = 4995 × [tex]0.9^n[/tex]

Using a calculator, we find that the value is approximately $1,576.11 when rounded to the nearest hundredth. Therefore, after 9 years, Mandy's home computer system is expected to be worth $1,576.11.

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ABC4 base 16 is equal to 43972 in base ten (decimal).

In order to represent any given number, numerals might be numbers, symbols, figures, or sets of figures.

To convert the number ABC4 base 16 to a numeral in base ten (decimal), we can use the positional notation system. Each digit in the number represents a power of 16, starting from the rightmost digit.

The rightmost digit is 4, which represents 4 x 16⁰ = 4 x 1 = 4.

The next digit is C, which represents 12 (since C is equivalent to the decimal number 12), and it is in the second position from the right. So the value of the second digit is 12 x 16¹ = 12 x 16 = 192.

The next digit is B, which represents 11, and it is in the third position from the right. So the value of the third digit is 11 x 16² = 11 x 256 = 2816.

The leftmost digit is A, which represents 10, and it is in the fourth position from the right. So the value of the fourth digit is 10 x 16³ = 10 x 4096 = 40960.

Now we can add up the values of each digit to get the decimal equivalent of the number:

4 + 192 + 2816 + 40960 = 43972

Therefore, ABC4 base 16 is equal to 43972 in base ten (decimal).

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Answer:

when it's maintain supplimentary , it means that the sum of the angles given is 180° , In this case let one of the angle be x and the other is given as 125° .

therefore

125° + x = 180°

x = 180° - 125° = 55°

the compliment of x is the angle which when added to x givens 90° , Let the angle be y.

therefore

x + y = 90°

y = 90° - x = 90° - 55° = 35°

35° is the answer

71.38 in word form is Seventy-one and thirty-eight hundredths.

What is the decimal number?

The accepted method for representing both integer and non-integer numbers is the decimal numeral system. Decimal notation is the term used to describe the method of representing numbers in the decimal system.

A number is a numerical unit of measurement and labeling in mathematics. The natural numbers 1, 2, 3, 4, and so on are the first examples. Number words are a linguistic way to express numbers.

To write decimals in word form, you can read the whole number part, write "and," and then read the decimal part according to place value.

For example: 0.25 can be written as "zero and twenty-five hundredths"

Hence, the correct answer is 'D. Seventy-one and thirty-eight hundredths'.

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Answer:

62.29

Step-by-step explanation:

100 - 3(4.25) - 13 - 4(2.99)

= 100 - 12.75 - 13 - 11.96

= 62.29

explanation in the picture

the answer is

62,29

Answer:

1,400

Step-by-step explanation:

its the same thing as 7 times 200

For question 2, the zoologists can conduct an analysis of variance (ANOVA) test to investigate whether the four different diets impact the weight gains of the 6-month baby elephants. The ANOVA test will compare the mean weight of each diet group to determine if there is a statistically significant difference between them. If the test shows that there is a significant difference, then the zoologists can conclude that the diets are impacting the weight gains of the baby elephants.

For question 3, the researchers can also conduct an ANOVA test to investigate whether the nursery locations affect the growth of oak trees. The test will compare the mean circumference growth of the oak trees at each nursery location to determine if there is a statistically significant difference between them. If the test shows that there is a significant difference, then the researchers can conclude that the nursery locations are impacting the growth of the oak trees.

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