Plot the numbers -1 1/6 and 7/3 on the number line below.

[tex]f(x)=\displaystyle\sum_{n=1}^{\infty}c_n\cdot x^n \\\\[-0.35em] ~\dotfill\\\\ \displaystyle\sum_{n=1}^{\infty}c_n\cdot n\cdot x^n\implies n\sum_{n=1}^{\infty}c_n\cdot x^n\implies n\cdot f(x)\quad \textit{assuming "n" is an constant}[/tex]

Answer:

1 over 3 would juts be 1/3

If the boat travel north at 30 km per hour .  the equivalent speed in still water required to achieve an actual speed of 30 km/h is 30.1 km/h.

Finding the boat's true speed using Pythagoras' theorem using this  formula

Speed = √((30 km/h)^2 + (4/√(2) km/h)^2)

Let plug in the formula

Speed = √(900 + 8) km/h

Speed = √(908) km/h

Speed = 30.1 km/h

Speed = 30 km/h ( Approximately)

Therefore  the speed is 30km/h.

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He completed volunteering in 39 hours 40 minutes in 4 weeks

How to determine this

If Ken volunteers 1 hr 25 mins each day

i.e 1 hr 25 mins = 1 days

By converting 1 hr 25 mins to mins

When 60 mins = 1 hr

1 hr 25 mins = 60 + 25 = 85 mins

How many hours of volunteering is completed in 4 weeks

Let x represent the numbers of hours

i.e x = 4 weeks

By converting 4 weeks to days

When 7 days = 1 week

4 weeks = 4 * 7 days

= 28 days

So, when 85 mins = 1 day

x mins = 28 days

x = 28 days * 85 mins/1 day

x = 2380 mins

By converting it back to hour

When 60 mins = 1 hour

2380 mins = x

x = 2380/60 hour

x = 39 hours 40 mins

Therefore, the hours that can be completed in 4 weeks is 39 hours 40 minutes

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Applying PEMDAS the correct expression showing where to insert brackets to make it correct are:

i. 3 × (5 + 2) + 2 = 23;      ii. (12 ÷ 4) + 2 = 5

i. 3 × (5 + 2) + 2 = 23

In this expression, we need to prioritize addition over multiplication, as per the order of operations (PEMDAS or BODMAS).

Therefore, we should add 5 and 2 first and then multiply the result by 3. Adding the brackets around 5 + 2 forces the addition to be done before multiplication, resulting in the correct answer.

ii. (12 ÷ 4) + 2 = 5

In this expression, we need to prioritize division over addition. Therefore, we should divide 12 by 4 first and then add the result to 2. Adding brackets around 12 ÷ 4 forces the division to be done before addition, resulting in the correct answer.

To understand where to insert brackets, you need to follow the order of operations, which is a set of rules that dictates the order in which arithmetic operations should be performed. The acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction)

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The kite is approximately 18.57 yards high above the edge of the pond.

The Pythagorean theorem would be used to solve the prob;lem that we have here

The theorye tell us that the squatre of the hypotenuse is the same as the sum of the square of the other two sides

The formula is written as

c^2 = a^2 + b^2

In this case:

c = 37 yards (length of the string)

a = 32 yards (distance from where the kite is tied to the ground to the edge of the pond)

b = height of the kite above the edge of the pond (which we need to find)

Now, plug the values into the Pythagorean theorem:

37^2 = 32^2 + b^2

1369 = 1024 + b^2

Subtract 1024 from both sides:

b^2 = 345

Now, take the square root of both sides to solve for b:

b = √345

= 18.57 yards

The kite is approximately 18.57 yards high above the edge of the pond.

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Okay, let's solve this step-by-step:

3.25x×400=2.50x+600

1300x = 1500

x = 500

So when x = 500, the costs are equal.

Answer:

x = (y-z)/3

Step-by-step explanation:

z = 3x + y

3x = z - y

x = (z - y)/3

To find the angle of depression, we can use the tangent function in trigonometry. In this situation, we have a right triangle where the height (opposite side) is 400 feet, and the distance (adjacent side) is 18,410 feet.

tan(angle) = opposite / adjacent

tan(angle) = 400 / 18,410

Now, we'll use the arctangent (inverse tangent) function to find the angle:

angle = arctan(400 / 18,410)

angle ≈ 1.25 degrees

The angle of depression from the top of the lighthouse to the waterline of the ship is approximately 1.25 degrees, rounded to the nearest hundredth of a degree.

Based on the information provided in the question, we can conclude that the histogram represents 20 math team members.

[tex]\huge{\colorbox{black}{\textcolor{lime}{\textsf{\textbf{I\:hope\:this\:helps\:!}}}}}[/tex]

[tex]\begin{align}\colorbox{black}{\textcolor{white}{\underline{\underline{\sf{Please\: mark\: as\: brillinest !}}}}}\end{align}[/tex]

[tex]\textcolor{blue}{\small\texttt{If you have any further questions,}}[/tex] [tex]\textcolor{blue}{\small{\texttt{feel free to ask!}}}[/tex]

♥️ [tex]{\underline{\underline{\texttt{\large{\color{hotpink}{Sumit\:\:Roy\:\:(:\:\:}}}}}}\\[/tex]

Answer:

average rate of change = 12

Step-by-step explanation:

the average rate of change of f(x) in the interval a ≤ x ≤ b is

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

here the interval is 2 ≤ x ≤ 4 , then

f(b) = f(4) = 2(4)² - 2 = 2(16) - 2 = 32 - 2 = 30

f(a) = 2(2)² - 2 = 2(4) - 2 = 8 - 2 = 6

then

average rate of change = [tex]\frac{30-6}{4-2}[/tex] = [tex]\frac{24}{2}[/tex] = 12

The rectangle's height is 2 in, and the rectangle's base is 5 x 2+ 3 = 30 in, whose area is given as 68in².

It has two pairs of equal-length sides that are at right angles to each other. It is the most common type of quadrilateral, and it can be found in everyday objects like windows, doors, and tabletops.

To solve this problem, we need to use the formula for the area of a rectangle (A = l x w), where A is the area, l is the length, and w is the width. We also know that the base is 3 inches shorter than 5 times the height. Therefore, we can set up the equation to solve for the height and the base of the rectangle as follows:

A = l x w

A = (h + 3) x (5h)

A = 5h² + 3h

5h²  + 3h = 68

h= -2 (as height can not be in negative)

h= 2

By using the quadratic formula, we can solve for the height, h, which is equal to 2.

Therefore, the rectangle's height is 2 in, and the rectangle's base is 5 x 2+ 3 = 30 in.

This problem was solved by using the quadratic equation to solve for the height of the rectangle, which was then used to solve for the base.

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The algebraic expression can be simplified to 4p√2q³r

An algebraic expression is an expression that is made up of variables and constants, along with algebraic operations like addition, subtraction, square root, etc.

The expression can be simplified as follow:

2√(8p²q³r) = 2 * √8 * √p² √(q³r)

                  = 2 * √(4 * 2) * p √(q³r)

                  = 2 * √4 * √2 * p √(q³r)

                  = 2 * 2 * √2 * p √(q³r)

                  = 4p√2q³r

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Question in English

Could you help me solve this? I have the answer what I need is the procedure. Thank you so much

2√8p²q³r

Answer:160/30000 simplified would be 2/375

Step-by-step explanation:

Exact Form:

[tex]\frac{2}{375}[/tex]

Decimal Form:

0.0053

Answer:the upper right one( the dash line that hit -2

Step-by-step explanation:

The number that could represent point Q is to be considered as the option c.  2 1/2.

Calculation of the number:

Since

p = -4

q could be 6.5 units to the right or to the left of point p.

So, to the right, it should be like

=p + q

= -4 +  6.5

= 2.5

Hence, The number that could represent point Q is to be considered as option c.  2 1/2.

In mathematics, a tool known as a number line offers a graphical representation of numerical values arranged in sequential order from left to right with zero located in the center. This instrument is frequently applied throughout mathematical fields when interpreting negative and positive numbers along with fractions and decimals.

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The y-intercept of the function F(x) = 2(x - 7)(x - 3) is 42, which means that the graph of the function intersects the y-axis at the point (0, 42).

The y-intercept is the point where a function or a curve intersects the y-axis. It is the value of the dependent variable (y) when the independent variable (x) is equal to zero.

The y-intercept of a function is the point where the graph of the function intersects the y-axis. To find the y-intercept of the function F(x) = 2(x - 7)(x - 3), we need to substitute 0 for x in the equation:

F(x) = 2(x - 7)(x - 3)

So, we have:

F(0) = 2(0 - 7)(0 - 3)

Simplifying this expression, we get:

F(0) = 2(-7)(-3)

F(0) = 42

Therefore, the y-intercept of the function F(x) = 2(x - 7)(x - 3) is 42, which means that the graph of the function intersects the y-axis at the point (0, 42).

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The zeros of f according to their multiplicity are:

Zero of multiplicity 1: x = -8, x = -3, x = 0, x = 9

Zero of multiplicity 2: None

Zero of multiplicity 3: None

Here,

We have,

The zeros of a polynomial function are the values of x that make the function equal to zero. The multiplicity of a zero is the number of times it appears as a factor in the polynomial.

In the given function f(x), the zeros are the values of x that make the function equal to zero.

We can find these values by setting the function equal to zero and solving for x.

f(x) = 7x(x-9)(x+8)^2(x+3) = 0

Therefore, the zeros of f(x) are x = -8, x = -3, x = 0, and x = 9.

To determine the multiplicity of each zero, we can look at the degree to which the corresponding factor appears in the polynomial.

For example, x = -8 is a zero of multiplicity 2 because it appears as a factor twice in the function, as (x+8)^2.

Similarly, x = -3, x = 0, and x = 9 are zeros of multiplicity 1 because they each appear as a factor once in the function.

There are no zeros of multiplicity 3 or higher in this function, so we can list "None" for those categories.

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Answer:

3) The graph that has three x-intercepts

9) Plot the points on the graphing calculator, and then generate a linear regression equation. That equation is:

y = 2.857x - 1.4286

The closest equation is y = 3x - 2. That equation best represents the regression line for this data.

Answer:

A tangent is a line that touches the curve or a circle at a point..

The two buses meet at the same time they left their respective cities, so they meet at 11 AM in NY.

Since the two buses are traveling towards each other at constant speeds, we can use the formula for finding the time two objects meet when traveling at constant speeds in opposite directions:

t = (d2 - d1)/(v1 + v2)

Where t is the time they meet, d1 is the distance the first bus travels, d2 is the distance the second bus travels, v1 is the speed of the first bus, and v2 is the speed of the second bus.

In this case, d1 is the distance between NY and Boston (approx. 200 miles), d2 is the distance between Boston and NY (also approx. 200 miles), v1 is the speed of the first bus (200 miles in 5 hours, or 40 miles/hour), and v2 is the speed of the second bus (200 miles in 5 hours, or 40 miles/hour).

Plugging these values into the formula, we get:

t = (200 - 200)/(40 + 40)

t = 0/80

t = 0

Hence, the two buses meet at the same time they left their respective cities, so they meet at 11 AM in NY.

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Answer:

[tex]x = \frac{9}{ \sqrt{2} } = \frac{9 \sqrt{2} }{2} [/tex]

Answer:

1.75 inches (pls give brainliest lol!)

Step-by-step explanation:

Let's use a proportion to solve the problem:

On the first map, 2.8 inches represents 25 miles:

2.8 / 1 = 25 / x

Simplifying the equation, we get:

x = 25(2.8)/1 = 70

Therefore, the distance between the two cities in the first map is 70 miles.

Now, let's find the distance between the same two cities on the second map, which has a scale of 1 inch to 40 miles:

We want to find how many inches on the second map represent 70 miles. Let's call this value y.

1 / 40 = y / 70

Solving for y, we get:

y = 70/40 = 1.75

Therefore, the two cities would be 1.75 inches apart on the second map with the 1 inch to 40 miles scale.

The break even sales for the current year using the contribution per unit  is 5.27.

The formula to find the break even sales is,

Break even sales = Fixed costs / Contribution per unit

Now,

Contribution per unit = Sales price per unit - Variable cost per unit.

Sales price = $6,512

Variable cost = (75% × cost of goods sold) + (50% × marketing, general and administration expenses)

                      = (75% × $1,628) + (50% × $592)

                      = $1517

Contribution margin = $6,512 - $1517 = $4995

Contribution per unit = $4995 / 37 = $135 per million

Fixed costs = (25% × cost of goods sold) + (50% × marketing, general and administration expenses)

                   = $703

Break even sales = 703 / 135 = 5.21

Hence the break even sales is 5.27.

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Answer: x = 9 units

Step-by-step explanation:

Answer: 130

Step-by-step explanation:

The problem is asking for an expression that is equivalent to the addition of 91 and 39. An expression is a combination of numbers, variables, and mathematical operations that does not have an equal sign. In this case, the expression we are looking for should evaluate to the same value as the sum of 91 and 39, which is 130.

To obtain this expression, we simply add 91 and 39, since the sum of these two numbers is equivalent to the expression we are looking for. Adding 91 and 39, we get:

91 + 39 = 130

Therefore, the expression that is equivalent to 91 plus 39 is simply 130.

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The surface area of the hexagonal pyramid is  740 metres².

The pyramid above is an hexagonal pyramid. The surface area of the pyramid can be found as follows:

Therefore,

surface area of the hexagonal pyramid = A + 1 / 2 ps

where

Therefore,

A = base area = 1 / 2 p a

where

Hence,

p = 10(6) = 60 metres

a = 5√3 metres

A = base area = 1 / 2 × 60 × 5√3 = 150√3 metres

Therefore,

surface area of the hexagonal pyramid = 150√3 + 1 / 2 × 60 × 16

surface area of the hexagonal pyramid = 150√3 + 480

surface area of the hexagonal pyramid = 739.807621135

surface area of the hexagonal pyramid = 740 metres²

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The surface area of the hexagonal pyramid is  740 metres².

The pyramid above is an hexagonal pyramid. The surface area of the pyramid can be found as follows:

Therefore,

surface area of the hexagonal pyramid = A + 1 / 2 ps

where

Therefore,

A = base area = 1 / 2 p a

where

Hence,

p = 10(6) = 60 metres

a = 5√3 metres

A = base area = 1 / 2 × 60 × 5√3 = 150√3 metres

Therefore,

surface area of the hexagonal pyramid = 150√3 + 1 / 2 × 60 × 16

surface area of the hexagonal pyramid = 150√3 + 480

surface area of the hexagonal pyramid = 739.807621135

surface area of the hexagonal pyramid = 740 metres²

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The coefficient of determination is: 88%

The following table shows the calculations:

X Y X^2 Y^2 XY

22 3 484 9 66

17 4 289 16 68

41 21 1681 441 861

5 1 25 1 5

36 16 1296 256 576

19 7 361 49 133

24 14 576 196 336

6 4 36 16 24

8 2 64 4 16

52 32 2704 1024 1664

35 23 1225 529 805

Total 265 127 8741 2541 4554

Sample size: n=11

Now,

(a)

The coefficient of correlation is :

r=[tex]\frac{S_{xy}}{\sqrt{S_{xx}S_{yy}}}=0.94[/tex]

(b)

The slope of the regression equation is 0.63

S.

and intercept of the equation will be

[tex]b_{0}=\frac{1}{n}(\sum y - b_{1} \sum x)=-3.729965\approx -3.73[/tex]

So the regression equation will be

y'=-3.73+0.63*x

(c)

The coefficient of determination is: 88%

Regression is a statistical analytical method that investigates correlations between two or more variables. Its widespread usage stems from its ability to forecast or assess the value of one contingent variable using one or many independently varying variables.

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That this is just an estimate of the true proportion of all voters who would vote for Brown, based on the sample of 350 voters surveyed. The true proportion could be different, due to sampling variability.

What is Statistic?

A statistic is a numerical measure that summarizes some aspect of a dataset. It is a way to describe a sample of data in a concise and meaningful way. Common examples of statistics include measures of central tendency such as the mean, median, and mode, as well as measures of variability such as the range, standard deviation, and variance.

The sample statistic for the proportion of voters surveyed who said they'd vote for Brown is the sample proportion, which is the number of voters who said they'd vote for Brown divided by the total number of voters surveyed:

Number of votes who said they'd vote for brown

    total number of surveyed

= 109/350

=0.31

Therefore, based on the sample of 350 voters surveyed.

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