Find the midpoint of segment AB if A(3, 2) and B(-1,4) Select one: O b (2, 1) O b. (1,3) O c. (2,6) O d. (2,3)​

the lower bound of the 95% confidence interval is approximately -63.20
To calculate the lower bound of a 95% confidence interval for a normal population, we need to use the formula:

Lower bound = x - (Z * (s / √n))

Given that the sample size is 30, the sample mean x is -61, and the sample standard deviation (s) is 4, we can plug in these values.

The critical value for a 95% confidence interval is approximately 1.96 (obtained from the standard normal distribution table).

Substituting the values into the formula:

Lower bound = -61 - (1.96 * (4 / √30))

CalculatingCalculating this expression:

Lower bound ≈ -61 - (1.96 * (4 / √30)) ≈ -63.20 (rounded off to two decimal places)

Therefore, the lower bound of the 95% confidence interval is approximately -63.20

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To solve the given third-order linear homogeneous differential equation, we can use the method of finding the characteristic equation and its roots. Let's denote y(x) as the solution to the equation.  Answer :  1,7,-31

The characteristic equation is obtained by substituting y(x) = e^(rx) into the differential equation, where r is an unknown constant. Plugging this into the equation, we get:

r^3 - 3r^2 - r + 3 = 0

To solve this equation, we can use various methods, such as factoring, synthetic division, or numerical methods. By applying these methods, we find that the roots of the characteristic equation are r = -1, r = 1, and r = 3.

Since we have distinct real roots, the general solution for y(x) can be expressed as a linear combination of exponential functions:

y(x) = C1e^(-x) + C2e^x + C3e^(3x)

To find the specific solution for the given initial conditions, we can substitute the values of x = 0, y(0) = 1, y'(0) = 7, and y''(0) = -31 into the equation and solve for the unknown coefficients C1, C2, and C3.

Using the initial condition y(0) = 1, we get:

C1 + C2 + C3 = 1

Using the initial condition y'(0) = 7, we get:

-C1 + C2 + 3C3 = 7

Using the initial condition y''(0) = -31, we get:

C1 + C2 + 9C3 = -31

Solving this system of linear equations, we can find the values of C1, C2, and C3. Substituting these values back into the general solution, we obtain the specific solution for y(x).

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Answer:

\(k = 7 \times \frac{3}{1} \)

Step-by-step explanation:

\(k = 7 \times \frac{3}{1} \)

Answer:

B

Step-by-step explanation:

Given :

\(k = 7 \div \frac{1}{3}\)

============================================================

Multiply both sides with 1/3 :

⇒ \(\frac{1}{3} \times k = 7 \div \frac{1}{3} \times \frac{1}{3}\)

⇒ \(\frac{1}{3} \times k = 7\)

⇒ Equation B

Answer: 58 = h-9

Step-by-step explanation:

Answer:

The answer is 32

Step-by-step explanation:

First (6-2)= 4

Second 4+4= 8

Third 2+12+16= 30

and lastly 38-6= 32

HOPE THIS HELPED!

\(\huge\text{Hey there!}\)

\(\large\text{Do PEMDAS}\)

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\(\large\text{Exponents}\)

\(\large\text{Multiplication}\)

\(\large\text{Division}\)

\(\large\text{Addition}\)

\(\large\text{Subtraction}\)

\(\large\text{6 - 2 + 4}\times\large\text{2}\)

\(\large\text{6 - 2 = 4}\)

\(\large\text{4 + 4}\times\large\text{2}\)

\(\large\text{4}\times\large\text{2 = 8}\)

\(\large\text{4 + 8 = 12}\)

\(\boxed{\boxed{\large\text{Answer: \huge \bf 12}}}\huge\checkmark\)

\(\text{Good luck on your assignment and enjoy your day!}\)

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(a) After integrating and simplification, the ∫(3x² - 4)² x³ dx is 9(x⁸/8) - 24(x⁵/5) + 16(x⁴/4) + C, and also

(b) The integral ∫(x + 3)/x⁷ dx is = (-1/5x⁵) - (1/2x⁶) + C.

Part(a) : We have to integrate : ∫(3x² - 4)² x³ dx,

We simplify using the algebraic-identity,

= ∫(9x² - 24x + 16) x³ dx,

= ∫9x⁷ - 24x⁴ + 16x³ dx,

On integrating,

We get,

= 9(x⁸/8) - 24(x⁵/5) + 16(x⁴/4) + C,

Part (b) : We have to integrate : ∫(x + 3)/x⁷ dx,

On simplification,

We get,

= ∫(x/x⁷ + 3/x⁷)dx,

= ∫(1/x⁶ + 3/x⁷)dx,

= ∫(x⁻⁶ + 3x⁻⁷)dx,

On integrating,

We get,

= (-1/5x⁵) - (3/6x⁶) + C,

= (-1/5x⁵) - (1/2x⁶) + C,

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The given question is incomplete, the complete question is

(a) Use algebra to rewrite the integrand; then integrate and simplify. (Use C for the constant of integration.)

∫(3x² - 4)² x³ dx,

(b) Use algebra to rewrite the integrand; then integrate and simplify. (Use C for the constant of integration.)

∫(x + 3)/x⁷ dx.

Answer:

So its C! Heart it if its explained well, thanks!

Step-by-step explanation:

There is a pattern. The ordered pairs look like this...(1,10), (2,20), (3,30), (8,80) etc. So if we keep going (12,120)

Answer:

C

Step-by-step explanation:

Answer:18

Step-by-step explanation:

Answer:

C. 16

Explanation:

\(\rightarrow \sf \dfrac{9}{4} = \dfrac{x+2}{8}\)

cross multiply

\(\rightarrow \sf \dfrac{9(8)}{4} = x + 2\)

simplify integers

\(\rightarrow \sf 18 = x + 2\)

exchange sides

\(\rightarrow \sf x =18-2\)

subtract integers

\(\rightarrow \sf x =16\)

If a 20. 0 kg double coconut oscillates on a spring 42. 7 times each minute, then the spring constant of the spring is 689 N/m.

The spring constant, also known as the force constant or stiffness, is a measure of the elasticity of a spring or any other elastic object. It is defined as the force required to stretch or compress a spring by a unit distance.

The period of oscillation of the coconut can be calculated as:

\(T = \frac{60}{42.7} = 1.405\) seconds

The mass of the coconut is 20.0 kg, so we can use the formula for the period of oscillation of a mass on a spring:

\(T=2\pi \sqrt{\frac{m}{k}}\)

where m is the mass of the coconut and k is the spring constant.

Rearranging this formula gives:

\(k = (2\pi)^2 *(\frac{m}{T})^2\)

Substituting the values we have:

\(k = (2\pi)^2 *(\frac{20.0}{1.405})^2\)

k = 689 N/m (to three significant figures)

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The number of seasoning batches required by the teacher is 4.

Given, there are 26 students in a class.

The teacher is adding 1 batch of hawaiian popcorn seasoning to 13 cups of popcorn.

Each student gets 2 cups of popcorn.

If 26 students are getting 2 cups of popcorn, then the total cups required by the students will be :

26×2

= 52 cups.

Now, one batch of seasoning is consumed by 13 cups.

how many batches of seasoning will be required for 52 cups = ?

⇒ 13 cups + 13 cups + 13 cups + 13 cups = 52 cups

Hence 4 batches of seasoning is required for 26 students to get two cups each popcorn with seasoning.

Therefore 4 batches of seasoning the teacher used.

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To find the weight of the helium in the balloon, you need to multiply the volume of the helium in cubic meters by its density in kilograms per cubic meter. The volume of the helium is 2,200 cubic meters and the density is 0.1785 kilograms per cubic meter, so the weight of the helium is: 2,200 cubic meters * 0.1785 kilograms/cubic meter = 393.7 kilograms

Rounded to the nearest tenth of a kilogram, the weight of the helium is 393.7 kilograms or 393.7 kilograms.

A conversion factor is a number used to change one set of units to another, by multiplying or dividing. When a conversion is necessary, the appropriate conversion factor to an equal value must be used. For example, to convert inches to feet, the appropriate conversion value is 12 inches equal 1 foot.

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Writing as an equation :

X = 0.475 + 0.56

Add:

X = 1.035

Answer:

1.035 is 0.475 more than 0.56

p(x) must be equal to (x-a)(x-b) where b is another number.

If p(a) = 0, then this implies that (x-a) is a factor of p(x). Therefore, p(x) can be factored into (x-a)q(x), where q(x) is a polynomial of degree one less than the degree of p. This means that p(x) must be equal to (x-a)(x-b) for some other number b. It does not mean that p(x) must be equal to the zero polynomial or (x-a)².

The product of two factors, (x-a) and (x-b), is a polynomial of degree two, p(x). This can be expressed in expanded form as p(x) = x² - (a + b)x + ab, where a and b are any two numbers

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The Taylor series for a function f about x=1 is an infinite sum that represents the function using its derivatives at x=1. It starts with the value of the function at x=1 and includes terms involving higher derivatives multiplied by powers of (x-1) divided by factorials. It allows us to approximate the function near x=1 using a polynomial.

1. The first term, f(1), represents the value of the function at x=1.
2. The subsequent terms involve the derivatives of the function at x=1. The second term, f'(1)(x-1), is the first derivative of f at x=1 multiplied by (x-1).
3. Each subsequent term involves higher derivatives of f at x=1, with each derivative being multiplied by (x-1) raised to a power and divided by the corresponding factorial.

The Taylor series is a way to represent a function as an infinite sum of terms derived from its derivatives at a specific point. In this case, the Taylor series for function f about x=1 is given by f(x) = f(1) + f'(1)(x-1) + f''(1)(x-1)^2/2! + f'''(1)(x-1)^3/3! + ...

Each term involves a derivative of f evaluated at x=1, multiplied by (x-1) raised to a power and divided by the corresponding factorial. By including more terms in the series, we can approximate the function better near x=1 using a polynomial.

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Answer:

(-3/7, 0)

Step-by-step explanation:

7x=2y-3

To find the x intercept, set y = 0 and solve for x

7x = 0-3

7x = -3

Divide each side by 7

7x/7 = -3/7

x = -3/7

The x intercept is

(-3/7, 0)

Answer: A

Step-by-step explanation:

For the x-intercept, we know y=0. We can eliminate B and D.

We know either A or C is the correct answer. This line is linear so there should be only one x-intercept. We can solve this equation to see which is correct. Let's plug in A and C into the equation to see which is right.

A. Correct

\(7(-\frac{3}{7} )=2(0)-3\)

\(-3=-3\)

C. Incorrect

\(7(\frac{3}{2} )=2(0)-3\)

\(\frac{21}{2}\neq -3\)

Given equation of the line is

Dividing both sides of the above equation by -18, we get

The line cuts the x axis at (-9,0) and the y axis at (0,-3).

Therefore, the x intercept is -9 and the y intercept is -3.

The graph of the line is shown below.

Answer:

Y= -2x+4

Step-by-step explanation:

Answer: You have to add friends

Step-by-step explanation:

Let's break down the expression for Tony's combined total earnings step by step.

First, we consider Tony's earnings as a tutor. He earns $11 per hour as a tutor, so the amount he earns from tutoring is given by the product of his hourly rate ($11) and the number of hours he worked as a tutor (t). This can be represented as $11t.

Next, we consider Tony's earnings as a waiter. He earns $13 per hour as a waiter, so the amount he earns from waiting tables is given by the product of his hourly rate ($13) and the number of hours he worked as a waiter. Since Tony worked a total of 106 hours this month and spent t hours as a tutor, he must have worked (106 - t) hours as a waiter. This can be represented as $13(106 - t).

To calculate Tony's combined total earnings for the month, we add the amount he earned as a tutor ($11t) to the amount he earned as a waiter ($13(106 - t)). This yields the expression:

Earnings = $11t + $13(106 - t)

This expression represents the total dollar amount Tony earned this month, considering the number of hours he worked as a tutor (t) and waiter (106 - t).

A linear regression equation that represents this set of data is y = 31x + 799.8.

The calendar year in which the number of new cases would reach 1141 is 2022.

In this scenario, the Year since 2011 (x) would be plotted on the x-axis of the scatterplot while the New cases (y) would be plotted on the x-axis of the scatterplot.

On the Excel sheet, you should right click on any data point on the scatterplot, select format trend line and then tick the box to display an equation for the linear regression (line of best fit) on the graph.

By critically observing the scatterplot (see attachment) which models the relationship given in the table for the Year since 2011 (x) and the New cases (y), an equation for the linear regression is given by:

y = 31x + 799.8

Now, we can estimate the calendar year in which the number of new cases would reach 1141:

1141 = 31x + 799.8

31x = 1141 - 799.8

31x = 341.2

x = 341.2/31

x = 11.0

Calendar year = 2011 + 11

Calendar year = 2022.

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Answer:

1⁷/15

Step-by-step explanation:

2¾(3⅜-1½)

using the rule of BODMAS

change the fractions in the bracket into improper fraction

2¾(27/8-3/2)

find LCM of the fractions in the bracket

2¾(27-12)/8

2¾(15/8)

convert the other mixed fraction to an improper fraction

11/8(15/8)= 5.15625~ 5.2

Answer: \(x= \frac{3}{4}\)

Step-by-step explanation:

Solve for x by simplifying both sides of the equation, then isolating the variable.

The total surface area of the cylindrical dowels that must be covered with glue  8020 mm2 this is less than the 52,000 mm2 of glue that Eduardo calculated so the correct answer is Francisca.

To find out who is correct, we need to calculate the total surface area of the 20 dowels that Eduardo will use. Each dowel has a diameter of 8 mm and a length of 40 mm, so its surface area can be approximated as the sum of the area of two circles (one for each end) and the area of a cylinder (the lateral surface). Using an approximation of π ≈ 3.14, the surface area of one dowel can be calculated as:

2 × (π × (8/2)2) + π × 8 × 40 ≈ 401 mm2

The total surface area of the 20 dowels is therefore:

20 × 401 ≈ 8020 mm2

This is less than the 52,000 mm2 of glue that Eduardo calculated he would need, so it seems that Francisca is correct and Eduardo will not have enough glue to cover all the dowels. Therefore, the answer is:

Francisca.

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_____The given question is incorrect, the correct question is given below:

"In carpentry class, the teacher explains that cylindrical wooden dowels are used to join the pieces of a desk. The measurements of the dowels are shown in the following image:

To assemble a desk, Eduardo will have to use 20 dowels, which he must completely cover with a layer of glue. He calculates that he must have enough glue to cover 52,000 mm2 of the surface of the dowels used. However, his classmate Francisca tells him that that amount of glue will not be enough to cover all the dowels.

Who is correct? Mark your answer.

Eduardo

Francisca

Justify your answer by calculating the total surface area of the dowels that must be covered with glue. Use an appropriate approximation."

Answer:

9

Step-by-step explanation

First you multiply 3 five times, then you multiply 3 seven times and you divide the results of each multiplication

Answer:

0.111111111111111

Step-by-step explanation:

=> 3⁵÷3⁷

Note 3⁵ means multiplying 3 five times

And 3⁷ means multiplying 3 7 times

=> 3×3×3×3×3÷3×3×3×3×3×3×3

multiply the values and then divide

=> 243÷2,187

divide 243 by 2187

=> 0.111111111111111

We want to find an equation that gives the cost of renting a car for x days from Rent-AIL. We are given the table with the total cost for 3, 4, 5 or 6 days.

We will assume that the values are in a linear relationship, and thus we will use two of the data given as points of the cartesian plane for finding the the equation. We have that for 3 days the cost is $49.50, and the corresponding point will be:

And for 4 days the cost is $66, the point will be:

We will find the slope of the line that passes through those two points, with the formula:

And the slope will be 16.5. Now we will find the y-intercept,

This means that the y-intercept is 0, and thus, the equation that gives the cost of renting a car for x days from Rent-AIL is:

Hope you get the right answer

Step-by-step explanation: