A circle has a circumference of 20 m.
Work out the radius of the circle.
Give your answer correct to 1 decimal place.

Hence, we get the curve, [tex]$$\mathrm{y}(\mathrm{x})=\left[-\frac{3}{4 \mathrm{x}^4}+7 \ln (\mathrm{x})-\mathrm{x}\right]+\frac{23}{4}$$[/tex].

What is  slope of function ?

Algebra. Finding the rate at which the value of y (the dependent variable) changes in relation to x is what this process entails. The slope itself identifies the line's slope and direction.

Given the slope of function is,

[tex]$$\begin{aligned}\frac{\mathrm{dy}}{\mathrm{dx}} & =\frac{3}{\mathrm{x}^5}+\frac{7}{\mathrm{x}}-1 \\\Rightarrow \mathrm{dy} & =\left(\frac{3}{\mathrm{x}^5}+\frac{7}{\mathrm{x}}-1\right) \mathrm{dx}\end{aligned}$$[/tex]

Taking integration both side, we get

[tex]$$\begin{aligned}\int \mathrm{dy} & =\int\left(\frac{3}{\mathrm{x}^5}+\frac{7}{\mathrm{x}}-1\right) \mathrm{dx} \\\Rightarrow \mathrm{y} & =3 \int \mathrm{x}^{-5} \mathrm{dx}+7 \int \frac{1}{\mathrm{x}} \mathrm{dx}-\int \mathrm{dx} \\& =\left[3 \cdot \frac{\mathrm{x}^{-5+1}}{-5+1}+7 \ln (\mathrm{x})-\mathrm{x}\right]+\mathrm{c} \\& =\left[-\frac{3}{4 \mathrm{x}^4}+7 \ln (\mathrm{x})-\mathrm{x}\right]+\mathrm{c}\end{aligned}$$[/tex]

( where, [tex]$\mathrm{c}=$[/tex] constant)

Now. given that the curve is passing through point (1,4). So, putting $x=1$ and, y=4 into the curve,

[tex]$$\begin{aligned}\mathrm{y} & =\left[-\frac{3}{4 \mathrm{x}^4}+7 \ln (\mathrm{x})-\mathrm{x}\right]+\mathrm{c} \\\Rightarrow 4 & =\left[-\frac{3}{4}+7 \ln 1-1\right]+\mathrm{c} \\\Rightarrow 4 & =-\frac{7}{4}+\mathrm{c} \\\Rightarrow \mathrm{c} & =\frac{23}{4}\end{aligned}$$[/tex]

Therefore,

[tex]$$\mathrm{y}(\mathrm{x})=\left[-\frac{3}{4 \mathrm{x}^4}+7 \ln (\mathrm{x})-\mathrm{x}\right]+\frac{23}{4}$$[/tex]

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The given statement can be written in terms of inequality as b + 10.7 ≤ 3.2. The correct option is (d).

Linear inequality refers to the relation between a linear algebraic expression to some known value that contains inequality sign.

Unlike a linear equation it can have a range of values inside an interval.

The given statement can be written in terms of inequality as follows,

The statement is, "the sum of a number and 10.7 is at most −3.2".

Suppose the number be b.

The following expression can be written,

b + 10.7 ≤ 3.2

Hence, the required inequality expression for the given problem is b + 10.7 ≤ 3.2.

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Answer:

[tex]2\sqrt{281}[/tex] inches

Step-by-step explanation:

Using the 3D Pythagorean theorem, the diagonal has length [tex]\sqrt{32^2+6^2+8^2}=2\sqrt{281}[/tex] inches.

Answer:

y = 5x - 2

Step-by-step explanation:

y-8 = 5(x-2)

y-8 = 5x - 10

y = 5x - 10 + 8

y = 5x -2

Answer: Based on the information you provided, it seems that the correct answer is "left 6 units, down 1 unit." This translation will map the graph of the function f(x) = x² onto the graph of the function g(x) = x² - 6x + 6.

To understand why this is the case, it helps to understand what the different parts of the function g(x) represent. The term x² represents the original function f(x) = x², the term -6x represents a horizontal translation of the graph of f(x) by 6 units to the left, and the constant term 6 represents a vertical translation of the graph of f(x) by 1 unit downward. Together, these transformations map the graph of f(x) onto the graph of g(x).

Note that if we were to apply the other translations you listed, they would not produce the correct graph. For example, if we were to apply a translation of "right 3 units, down 3 units," this would produce a graph that is shifted 3 units to the right and 3 units down, which is not the same as the graph of g(x). Similarly, if we were to apply a translation of "right 6 units, down 1 unit," this would produce a graph that is shifted 6 units to the right and 1 unit down, which is also not the same as the graph of g(x).

Therefore, the equation that best fits these facts as the answer to this problem is y=661-0.1x.

The term "scatter plot" refers to a particular sort of graph in which the x- and y-axes are used to represent the values of two variables, with the dots that arise indicating any association between the data.

Given the correlation between the data at this moment and the graph provided in the question, y=661-0.1x is an equation that best captures the scatterplot's line of best fit.

y=661-0.1x is the equation whose solution best fits this data.

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Using the Pythagorean Theorem for the right angled triangles and observing the given figure, The value of x can't be solved because the hypotenuse must be the longest side of the right angled triangle which is violated in this question.

A triangle is a three-sided polygon with three vertices. The triangle's internal angle, which is 180 degrees, is constructed. It implies that the internal angles of a triangle add up to 180 degrees.

The required formula is:

[tex]h^{2}=p^{2}+b^{2}[/tex]

In the triangle, Hypotenuse is not the biggest side. So, We can't solve for the value of x.

[tex]10^{2} = 15^{2}+x^{2}[/tex]

[tex]x=\sqrt{10^{2}-15^{2}}[/tex]

which yields a negative number inside square root which is not possible to solve.

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(p-124) / 9 min many liters of water are in the tank after 109 seconds.

for 4 min =  65 + (6.5x4) = 91 lit

for  109 sec = 65 + (9x 109/60) = 81.35 lit

for m min = 65 + (9m) lit

how long time

for 151 lit = (151 - 124)/9 = 3 min

for 191.5 lit = (191.5-124) /9 = 67.5/9 = 7.5 min means 7 min 30 sec

for 270.25 lit = (270.25 - 124)/9 = 146.25/9 = 16.25 means 16 min 15 sec

for p lit = (p-124) / 9 min

What is liters ?

The water must be measured and expressed in the same unit for all of the containers. The litre is the name of that common unit for measuring liquid. Liquids are measured in litres, millilitres, centilitres, kiloliters, etc., including water, milk, gasoline, and oil.

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Answer:

256 feet.

Step-by-step explanation:

The equation for the surface area of a rectangular prism is lw x lh x hw. That means it would be 12x4, 12x5, and 4x5. In total that is 256.

Answer:

explain m ore

Step-by-step explanation:

Answer:

The ball reaches 14 ft in 0.75 seconds

Step-by-step explanation:

[tex]h(t) = -16t^2+24t+5\\h'(t) = -32t+24\\[/tex]

The highest point occurs when the derivative is equal to 0, because the tangent line is horizontal at that point

[tex]-32t + 24 = 0\\24 = 32t\\t = \frac{24}{32}=\frac{3}{4}=0.75s\\[/tex]

plug t back into h(t) to get height

[tex]h(0.75) = -16(0.75)^2+24(0.75)+5\\=(-16)(9/16)+23\\=-9 + 23\\= 14 ft[/tex]

Note: If you are not familiar with the concept of derivatives yet, you can find the time of the highest point using the equation [tex]t =-\frac{b}{2a}[/tex] where [tex]h(t) = at^2 + bt + c[/tex]

The total years taken to double the money according to Compounding will be  12.5 years.

What is compound interest?

Compound interest is that the interest on savings calculated on each the initial principal and therefore the accumulated interest from previous periods.

Main body:

Given :

rate = 6%

amount = $2500

Total amount = $5000

Compounded semi -anually,so formula becomes,

Total amount = amount (1+r/200)^2t

T = A[tex](1+r/200)^{2t[/tex]

5000 = 2500 (1+3/100)^2t

2 =(1+ 0.03)^2t

2 =(1.003)^2t

taking log on both sides

log 2 = 2t *log 1.03

0.3/0.012 = 2t

t = 12.5 years

Hence the time taken to double the money is 12.5 years.

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y = -1.893x + 31.901

Detailed explanation:

We are given the following values in a table:

x  y

2  30

5  19

7  20

12  9

16  2

It is now abundantly evident from the set of values that when x increases, the y-value decreases, indicating a negative connection.

Therefore, the line of best fit will have a negative slope.

Consequently, a scatter plot is used to display the data values.

As can be seen, the line of best fit equation

y = -1.893x + 31.901T

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The equations will be 20x and 500w.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this case, when offered a job in sales where you can choose to either make a salary $500 (constant) every week or commission of $20 per sale. This will be:

Let the sales be x

The equation will be:

= 20 × x

= 20x.

The second equation will be:

= 500 × w

where w = number of weeks.

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the anwser is 14 degrees for angle 1

The expression for the given variable is -276

What is variable?

A variable is anything that can take on any one of a number of values. A variable is a symbol. A variable is something that can change in an experiment.An amount that can fluctuate depending on the mathematical issue is referred to as a variable. The generic letters x, y, and z are often employed in mathematical expressions and equations. A variable, then, is a symbol denoting a number whose value is unknown. In this case, x + 5 Equals 10. "X" in this case is a variable.

[tex]\sqrt[3]{6 \times 288}-288[/tex]

[tex]\sqrt[3]{6 \times 288}=12[/tex]

[tex]=12-288[/tex]

[tex]Subtract the numbers: $12-288=-276$$$=-276$$[/tex]

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The expression that is an equivalent expression of 12x+10+4y is D 2(6x + 5 + 2y).

In Mathematics, expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.

In this case, the expression that is an equivalent expression of 12x+10+4y is 2(6x + 5 + 2y). The correct option is D.

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Which expression is an equivalent expression of 12x + 10 + 4y?

A.) 2(6x + 2y + 6)

B.) 3(4x + y + 10)

C.) 2(6x + 4y + 8)

D.) 2(6x + 5 + 2y)

The number of days it will take the bacteria to multiply to 10,000,000 colonies will be 39,493.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

The exponent is given as

y = a(b)ˣ

There were 700 provinces of microbes on day 1 of refined. With a development pace of 2.3. Then the equation is given as,

[tex]\rm A = 700 \times (2.3)^{t - 1}[/tex]

Then the number of days it will take the bacteria to multiply to 10,000,000 colonies will be given as,

[tex]\rm 10,000,000 = 700 \times (2.3)^{t - 1}\\[/tex]

Take log on both sides, then we have

(t - 1) × log 2.3 = 14,285.71

t - 1 = 39,492.99

t ≈ 39,493 days

The number of days it will take the bacteria to multiply to 10,000,000 colonies will be 39,493.

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The markup from cost to sale price is $135.

What is the cost price?

Cost price, for instance, equals selling price plus profit ( when selling price and profit are given ) Cost is equal to Selling price plus Loss ( when selling price and loss is given ).

Cost price = 100 Selling Price + 100 + Profit (where the Selling Price and Profit Percentage are supplied)

Given the selling price of the item = $650

The cost = $450

Therefore,

10% × $650 = $585

$585-$450=$135

Hence,  the markup from cost to sale price is $135.

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Complete question:

The selling price of an item is ​$650 It is marked down by 10%, but this sale price is still marked up from the cost of ​$450.Find the markup from cost to sale price.

The coordinates of the intersection with the x-axis are (-2,0), and (4, 0) and the maximum point is (1,9).

What are the coordinates of the axis?

A Cartesian coordinate system in a plane is a system of coordinates that uniquely identifies each point by a pair of numerical coordinates. These numerical coordinates are the signed distances from two fixed perpendicular oriented lines to the point, measured in the same unit of length.

We have,

The graph shows the sketch of y=f(x).

The graph passes through the points (-2,0), (0,8), (4, 0), and (1,9).

The coordinates of the intersection with the x-axis are

(-2,0), and (4, 0).

The maximum point is (1,9).

Hence, the coordinates of the intersection with the x-axis are

(-2,0), and (4, 0) and the maximum point is (1,9).

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A) The probability that the tyre wears out before 60000 miles is 0.4221

B) The probability that the tyre lasts more than 83000 miles is 0.49534

The distance the tyres can run until wear-out is a normally distributed, the formula for normal distribution is expressed as

z = (x - u)/s

Where

x = the distance the tyres can run until wear-out

u = mean distance

s = standard deviation

From the information given,

u = 70000 miles

s = 7000 miles

A) We want to find the Probability that the tyre wears out before 60000 miles. It is expressed as

P(x lesser than 60000)

For x = 60000,

z = (60000 - 70000)/7000 = - 1.42

Looking at the normal distribution table, the corresponding z score is 0.4221

B)We want to find the probability that the tyre lasts more than 83000 miles. It is expressed as

P(x greater than 83000) = 1 - P(x lesser than or equal to 83000)

For x = 83000,

z = (83000 - 70000)/5000 = 2.6

Looking at the normal distribution table, the corresponding z score is 0.49534

P(x greater than 83000)

= 1 - 0.49534  = 0.50466

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Answer:

(-8, -10)

Step-by-step explanation:

(-4 + x)/2 = -6

-4 + x = -12

x = -8

(4 + y)/2 = -3

4 + y = -6

y = -10

Answer: (-8, -10)

Answer:

60

Step-by-step explanation:

Answer:

Line t:  y = 1/9x + 8

Step-by-step explanation:

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

The formula for finding the slope the line perpendicular to line s is:

[tex]m_{2}=-\frac{1}{m_{1} }[/tex], where m2 is the slope of the line we don't know (in this case, line t) and m1 is the slope of the line we're given (in this case, line s).

Currently line s is in point-slope form or

[tex](y-y_{1})=m(x-x_{1})[/tex].  Since m is the slope, we know that the slope of line s is -9.

By plugging in -9 for m1 in our equation, we have:

[tex]m_{2}=-\frac{1}{-9}\\ m_{2}=-\frac{1}{9}[/tex]

Since we know -1/9 is the slope of line t, we can plug this in for m and (9,9) for x and y in the slope-intercept equation to find b:

[tex]9=1/9(9)+b\\9=1+b\\8=b[/tex]

Thus, the equation of line t in slope intercept form is y = 1/9x + 8

The ball may rise up to a height of 20 feet. and it will strike the ground in 1 second.

Height is the vertical measurement from an object's top to its base. On sometimes, it has the designation "altitude."

The vertex at point (h,k) of a parabola, y = ax2 + bx + c, is first determined using the equation h = -b / 2a, and then that point is entered into the equation to determine k.

Let's now solve for h in this issue. We know that a = -16, b = 32, and c = 4 in the equation y = -16t2 + 32t + 4.

h = -b/2a

h = -(32) / 2(-16) (-16)

1 second is equal to h = -32/-32.

This means the the ball will reach it's maximum height after 1 seconds. But the problem is asking is for what that height is. So for our final step, let's plug in t=1 to our equation:

y = -16t^2 + 32t + 4

y = -16*(1)^2 + 32*(1)+ 4

y = -16 + 36

y = 20 feet

which means that the final answer is that the maximum height of the ball is 20  feet. and it will take 1sec to hit the ground.

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The area of the given figure is 48 [tex]ft^{2}[/tex].

Area is a measurement of the space inside a two-dimensional shape. It is determined by multiplying the length and width of the shape together. Area is most commonly measured in square units, such as square feet, square meters, or square kilometers. When measuring curved shapes, the area is determined by measuring the space inside the shape and applying a mathematical formula to calculate the total area. Area is an important concept in mathematics and is used to measure surface area, volume, length, and other measurements. It can also be used to compare the sizes of different shapes.

Firstly, to calculate the area assume the figure as two separate rectangles. Think that you a drawing an imaginary line in the gap between the two 4-ft segments to make a line of 12ft in length.

To solve, multiply to find individual areas then add together to get the total area.

Given: The first rectangle is 5ft by 4ft.

We know, the area of a rectangle = Base × Height

[tex]4ft[/tex] × [tex]3ft[/tex] = [tex]12ft^{2}[/tex] .....(1)

The next rectangle is 12 by 3ft, as you have to add the missing length in the middle to accurately calculate the length of the line.

[tex]12ft[/tex] × [tex]3ft[/tex] = [tex]36ft^{2}[/tex] .....(2)

Adding (1) and (2) we get,

[tex]12ft^{2} +36ft^{2}[/tex] = [tex]48ft^{2}[/tex]

Hence, the area is [tex]48ft^{2}[/tex].

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