A group of students was surveyed in a middle school class. They were asked how many hours they work on math homework each week. The results from the survey were recorded.


Number of Hours | Total Number of Students
0 | 1
1 | 8
2 | 2
3 | 5
4 | 9
5 | 7
6 | 3


Determine the probability that a student studied for exactly 1 hour. Round to the nearest hundredth.
0.03
0.23
0.30
0.77

The Maclaurin series is xln(2x + 1) - x^2 + (2x^3)/3 - (2x^4)/4 + ... and the arc is (-1/2, 1/2).

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

f(x) = x ln(2x+1)

The Maclaurin series of f(x) = x ln(2x + 1) can be found by using the power series expansion of the logarithm function and the definition of a derivative.

Starting with the power series expansion of ln(1 + x):

ln(1 + x) = x - (x^2)/2 + (x^3)/3 - (x^4)/4 + ...

We can then substitute x = 2x + 1 - 1 to obtain the power series expansion of ln(2x + 1):

ln(2x + 1) = (2x + 1 - 1) - (2x + 1 - 1)^2/2 + (2x + 1 - 1)^3/3 - (2x + 1 - 1)^4/4 + ...

= 2x - x^2 + (2x^3)/3 - (2x^4)/4 + ...

Next, we use the definition of a derivative to find the Maclaurin series of f(x) = x ln(2x + 1):

f'(x) = d/dx (x ln(2x + 1)) = ln(2x + 1) + x * d/dx ln(2x + 1)

= ln(2x + 1) + x * (2 - 2x + 2x^2 - 2x^3 + ...)

= ln(2x + 1) + 2x - 2x^2 + 2x^3 - 2x^4 + ...

Therefore, the Maclaurin series of f(x) = x ln(2x + 1) is:

f(x) = ∫ f'(x) dx = ∫ (ln(2x + 1) + 2x - 2x^2 + 2x^3 - 2x^4 + ...) dx

= xln(2x + 1) - x^2 + (2x^3)/3 - (2x^4)/4 + ...

The arc of a Maclaurin series refers to the range of values for x for which the series converges to the actual value of the function.

For the Maclaurin series above, the range of convergence depends on the function ln(2x + 1) which has a singularity at x = -1/2.

This implies that the Maclaurin series converges for all x such that |x| < 1/2.

Rewrite as

(-1/2, 1/2)

So, the arc of the series is (-1/2, 1/2).

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Answer:

Below

Step-by-step explanation:

Squares have equal side lengths

area = side X side

      = 2.4 m  X  2.4 M = 5.76 m^2

Answer:

If 55% of the fish in the pond are goldfish, that would be 55/100 of the total number of fish. To express this as a fraction in its simplest form, we would divide the numerator and denominator by the greatest common divisor, 5. So, 55/100 simplifies to 11/20.

10/3 of the fish in the pond are perch, which in its simplest form is already in the form of 10/3.

The rest of the fish are sticklebacks, meaning the total number of goldfish, perch, and sticklebacks must add up to 100%. Therefore, to find the ratio of sticklebacks to goldfish and perch, we can subtract the percentage of goldfish and perch from 100%.

100 - 55 - (10/3) = 100 - 55 - 10/3 = 100 - 55 - (10/3) = 100 - 55 - (10*3/3) = 100 - 55 - 10 = 35.

So the ratio of goldfish to perch to sticklebacks in this pond is 11/20: 10/3: 35/100 in its simplest form.

Step-by-step explanation:

The diameter of the circle whose circumference is 62.8 feet is 20 ft, thus the correct option is C.

Remember that for a circle of diameter D, the circumference is given by the formula:

C = pi*D

Where pi = 3.14

Here we know that the circumference is 62.8 feet, then we can rewrite:

62.8 feet = 3.14*D

Now we can solve that equation for D, then we will get:

D = 62.8ft/3.14 = 20ft

The diameter is 20 ft, thus, the correct option is C.

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The unknown values in the triangle is calculated to be

PL = 14.3 cm

CY = 7.74

NY = 9.9 mm

LJ = 8.3

The unknown values in the triangle is worked using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

1. using Sin = opposite / hypotenuse - SOH

sin x = PL / PX

sin 54.25 = PL / 17.62

PL = sin 54.25 * 17.62

PL = 14.3 cm

2. using Tan = opposite / adjacent - TOA

tan 52.67 = CY / 5.9

tan 52.67 * 5.9 = CY

CY = 7.74

3. using Sin = opposite / hypotenuse - SOH

sin 33.06 = YC / NY

NY = 5.4 /  sin 33.06

NY = 9.9 mm

4. using Tan = opposite / adjacent - TOA

tan 55.05 = LJ / VJ

tan 55.05 * 5.8 = LJ

LJ = 8.3

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To purchase the Apple iPad Pro, based on an equation, Sandra contributed $257 while her parents contributed $643.

An equation is a mathematical statement that states that two or more mathematical expressions are equal or equivalent.

Mathematical expressions are depicted as equations using variables, constants, numbers, and values and the equation symbol (=).

The total cost of the Apple iPad Pro = $900

The contribution of Sandra's parents per $2 = $5

The contribution of Sandra = $2

Let x = the variable contributed by each party

2x + 5x = 900

7x = 900

x = 128.57

Sandra's contribution = $257 (2 x 128.57)

Parents contribution = $643 (5 x 128.57)

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The value of k in the cuboid is 7 cm when the volume is 196cm³.

The space taken up by any three-dimensional solid constitutes a volume, to put it simply. They can be a cube, cuboid, cone, cylinder, or sphere.

The volumes of various shapes vary. In three-dimensional geometry, we have examined a variety of solids and shapes that are defined in three dimensions, including cubes, cuboids, cylinders, cones, etc. We are going to learn to calculate the volume for each of these shapes.

The volume of cuboid = l × b × h

Here,

4 × k × k = 196cm³

k² =  196/4

k² = 49

k = √49

k = 7

Thus, The value of k in the cuboid is 7 cm when the volume is 196cm³.

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The expression \root(4)(10mn) and (10mn)^((1)/(4)) are equivalent

Index forms are described as that number written in the form of an exponential expression.

It is also described as a single number raised to another number.

The exponent of an exponential expression explains how many times to multiply the base by itself to simply the expression.

Standard forms and scientific notation are other names for index forms.

It is important to note that the fourth root of a number or variable is  the biquadratic root.

From the information given, we have that;

[tex]\sqrt[4]{10mn}[/tex]

[tex](10mn)^1^/^4[/tex]

Note the following;

√2 = 2^1/2

∛2 = 2^1/3

Hence, the expressions are equivalent

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The cosine of the angle opposite the side of length 5.64 meters is 0.4536.

In a triangle, the cosine of the angle opposite a side is given by the formula:

cos(angle) = (a^2 + b^2 - c^2)/(2ab) where a, b, and c are the lengths of the sides of the triangle and angle is the angle opposite the side of length c. Given the side lengths of the triangle as 3.18 meters, 7.82 meters and 5.64 meters, the side opposite angle we want to find is 5.64 meters.

so we can use the above formula and substitute the values,

cos(angle) = (3.18^2 + 7.82^2 - 5.64^2)/(23.187.82) = 0.4536

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The volume of the pyramid is, 72 cm³.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

Height of pyramid = 12 cm

Base of pyramid = 12 cm

Weight of pyramid = 14 cm

Now, We know that;

⇒ Volume of pyramid = 1/2 × Base × Height

Substitute all the values, we get;

⇒ Volume of pyramid = 1/2 × 12 × 12

⇒ Volume of pyramid = 6 × 12

⇒ Volume of pyramid = 72 cm³

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The overall probability that Harry will take Mathematics A during the two years is (0.5 * 0.5) + (0.5 * 1) = 0.75

The probability that Harry will take Mathematics A and B during the two years is (0.5 * 0.5) = 0.25

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain.

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The type of sampling used in this example is a. random sampling

One of the most straightforward methods for gathering information from the entire population is random sampling. Every member of the subset has an equal chance of being chosen as part of the sampling process when using random sampling. For instance, if an organization employs 300 people overall, a sample group of 30 workers will be chosen to participate in the survey. In this instance, the population is the entire workforce of the organization, and the sample is 30 employees. Since all of the employees who were picked to participate in the survey were chosen at random, every worker has an equal chance of getting chosen.

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Each person buys a number of cakes

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given, Andy buys x cakes, Betty buys 4 times as many cakes as andy, and colin buys 3 more cakes than andy

So,

Andy has = x Cakes

Betty have = 4x Cakes

Clin has = x +3 Cakes

Since each cake costs 65p and the total cost of the cakes is £52.65

thus,

0.65( x + 4x + x +3) = 52.62

x + 4x + x +3 = 81

6x = 78

x = 13

Therefore,

Andy has = 13 cakes

Betty has = 4x = 4*13 = 52 cakes

Colin has = x + 3 = 16 cakes

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The expression equivalent to the expression 2(3t + 4) is 6t + 8

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

2(3t + 4)

To start with, we need to open the bracket of the expression

so, we have the following representation

2 * 3t + 2* 4

Evaluate the products

6t + 8

hence, the equivalent expression is 6t + 8

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Step-by-Step Explanation:

n = 45

Therefore, 2 + 4(n - 1)

Putting n = 45, we have

2 + 4(45 - 1)

= 2 + 4 × 44

= 2 + 176

= 178

Answer:

B) 178

Hope it helps.

If you have any query, feel free to ask.

Answer: x=-13, y=-23

Step-by-step explanation:

y in terms of x

-2x+y=3

y=3+2x

Substitute in other equation:

5x-4(3+2x)=27

5x-12-8x=27

-3x=39

x=39/-3

x=-13

Solve for y, substitute for x:

-2(-13)+y=3

26+y=3

y=-23

The right answer is that a 90% confidence interval containing the actual mean amount of money kids spend on lunch would be produced by 90% of all random samples of 50 students collected at this high school.

It is given that the 90% confidence interval for the mean amount of money students spend on lunch time at a high school is ($3.45,$4.15)

A 90% confidence interval interprets that, 90% of the random samples will result in a 90% confidence interval that contain the true value of the population parameter.

In other words, 90% of the random samples of 50 students obtained at this high school would result in a 90% confidence interval that contains the true mean amount of money students spend on lunch.

Thus, the correct answer is option (D) or The right answer is that a 90% confidence interval containing the actual mean amount of money kids spend on lunch would be produced by 90% of all random samples of 50 students collected at this high school.

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a. Equation for Bert to figure out Ernie's original number is x = 5(2x - 6) + (-6).

b. Ernie's original number/integer was 4.

c. On checking and verifying the original integer is obtained as 4.

What is integers?

The Latin term "Integer," which implies entire or intact, is where the word "integer" first appeared. Zero, positive numbers, and negative numbers make up the particular set of numbers known as integers.

Ernie picks an integer from 1 to 10.

Let the value of the integer be x.

First the number is doubled, so the value of integer becomes = 2x.

Then 6 is subtracted from the number, so the value of integer becomes = 2x - 6.

Then the entire difference is multiplied by 5, so the value of integer becomes = 5(2x - 6).

Lastly -6 is added to the product, so the value of integer becomes = 5(2x - 6) + (-6).

So, the equation to find the integer is -

x = 5(2x - 6) + (-6)

Now, simplify this expression to obtain the number.

x = 5(2x - 6) + (-6)

x = 10x - 30 - 6

x - 10x = -36

-9x = -36

x = -36/-9

x = 4

Check if 4 is the correct number -

First the number is doubled = 4 × 2 = 8

Subtract 6 from the number = 8 - 6 = 2

Then multiply the difference by 5 = 5 × 2 = 10

Then subtract -6 from the number = 10 - 6 = 4

Therefore, the original number was 4.

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Answer:

Exact volume: 500π/3 cm³

Approximate volume:  523.6 cm³

Step-by-step explanation:

For a cone,

V = (1/3)πr²h

V = (1/3)π(5 cm)²(20 cm)

V = 500π/3 cm³ ≈ 523.6 cm³

The true statements are the study does not involve a voluntary response, the first stage creates a stratified random sample and the whole study creates a multistage random sample.

In the given question, the study done ideally creates a multistage random sample. There are two parts to the sampling process for the study in the given question. Initially, a combined sample of thousand of individuals was assembled by combining a randomly selected sample of fifty individuals, that were from each of the 20 regions of each nation. The next step was to choose a random sample of fifty individuals from every one of the five income groups represented among those 1,000 individuals.

Additionally, because the study doesn't entirely rely on a discretionary answer, individuals were picked by a random sample approach rather than explicitly or through self-selection. A stratified random sample is also created during the initial step. This shows that a random sample was drawn from each subgroup after the dataset was separated into groups. 

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In a synthetic polynomial , the real solution of 2 is found; the year is 1996, and $20,300,000,000 was sold.

a. 20,300,000,000 = -10t^3 + 140t^2 - 20t + 18,150

b. Suggestions for the problem: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

b. To solve, use synthetic division; the solution is 2; the year is 1996.

In order to discover the year in which the specified quantity of sporting equipment was sold, we must create a polynomial equation. E(t) = -10t3 + 140t2 - 20t + 18,150, where t is the number of years since 1994, is the equation given in the problem. We must rewrite the equation so that the right side equals 20,300,000,000 in order to determine the year in which $20,300,000,000 worth of sporting equipment was sold. After that, the equation is 20,300,000,000 = -10t3 + 140t2 - 20t + 18,150, which needs to be solved. The equation can have whole-number solutions that are less than 10, including 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. We may use synthetic division to identify which of these answers is the true solution. this method, the coefficients of the equation are divided by the coefficient of the equation with the highest degree, and the quotient is then multiplied by the solution. Until the last portion is identified, this process is repeated. The answer is the quantity that equals the remainder.

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The value of the sigma notation is 55924050

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

sigma1^12 10×4^n-1

Express properly

So, we have the following representation

[tex]\sum^{12}_{1} 10*4^{n-1[/tex]

The sum of the geometric series can be calculated using the formula:

S = a(1 - r^n)/(1 - r)

From the sigma notation, we have the following parameters

a = 10,

r = 4

n = 12.

Substituting these values, we get:

S = 10 * (1 - (4)^12) / (1 - 4)

Evaluate the expression

S = 55924050

Hence, the sum is 55924050

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Answer:

see below

Step-by-step explanation:

1. study hard and go to a good college and then find a good job.

2. be intelligent on spending and save money to invest in the financial markets

3. buy a few life insurance policies with living benefits.

4. find a niche on social media and create contents to attract followers, and then invest the earnings in stock market or bond market.

5. invest in real estate

6. start a small business and then grow into franchise.

Answer:

11.6 ft

Step-by-step explanation:

    |\

    |   \

    |      \

    |         \

h   |            \    12 ft

    |               \

    |                  \

    |                     \

    |                        \

    ------------------------

              3 ft

Use the Pythagorean theorem: a² + b² = c²

(3 ft)² + h² = (12 ft)²

9 ft² + h² = 144 ft²

h² = 135 ft²

h = √(135 ft²)

h = 11.6 ft

The slope of the line is -20

The slope of a line is a measure of how steep the line is. It is defined as the ratio of the change in the y-coordinate (rise) to the change in the x-coordinate (run) between two points on the line. The formula for the slope of a line is:

m = (y2 - y1) / (x2 - x1)

Where (x1, y1) and (x2, y2) are the coordinates of two distinct points on the line.

From the graph, you can pick any two points. That is:

x1 = 0, y1 = 120 and x2 = 4, y2 = 40

m = (y2 - y1) / (x2 - x1)

m = (40- 120) / (4 - 0)

m = -80/4

m = -20

Thus, the slope is -20

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The unit rate of Lena's bicycle trip if she travelled 212 miles in 5 days is 42.4 miles per day

Unit rate refers to the rate of traveling in miles per day.

Number of miles Lena has ridden= 212 miles

Number of days = 5 days

Lena’s rate as a unit rate = Number of miles Lena has ridden / Number of days

= 212 miles / 5 days

= 42.4 miles per day

Hence, Lena is traveling at a unit rate of 42.4 miles per day.

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Using the Triangle Inequality Theorem, the range of heights his ladder should have would be greater than or = 23 feet.

The Triangle Inequality Theorem states that the sum of any two sides of a triangle is greater than or equal to the third side.

That is c >/= a + b

a = 5 feet

b = 18 feet

C >/ = 5+18 = 23 feet

Therefore, the range of heights his ladder should have would be greater than or = 23 feet.

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The explicit formula that represents the nth term of the sequence will be aₙ = 18 - 7n.

A series of integers called an arithmetic succession or arithmetic chain of events has a fixed difference between the terms.

Let a₁ be the first term and d be a common difference.

Then the nth term of the arithmetic sequence is given as,

aₙ = a₁ + (n - 1)d

The arithmetic sequence is given below.

11, 4, -3, .....

The first term is 11. And the common difference is given as,

d = 4 - 11

d = - 7

The explicit formula that represents the nth term of the sequence is given as,

aₙ = a₁ + (n - 1)d

aₙ = 11 + (n - 1)(-7)

aₙ = 11 - 7n + 7

aₙ = 18 - 7n

The explicit formula that represents the nth term of the sequence will be aₙ = 18 - 7n.

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