The cork in a wine bottle should not exceed 8.77KPa of normal stress. If the shear stress induced by the friction of its perimeter with the bottle is 4.98KPa, which is the maximum allowed ratio between the cork length H and the cork radius R?

Answer:

[tex]r=\left(\dfrac{y}{P}\right)^{\frac{1}{x}}-1[/tex]

Step-by-step explanation:

Given exponential function:

[tex]f(x)=P(1+r)^x[/tex]

Replace f(x) with y:

[tex]y=P(1+r)^x[/tex]

Divide both sides by P:

[tex]\dfrac{y}{P}=(1+r)^x[/tex]

Take natural logs of both sides:

[tex]\ln \left(\dfrac{y}{P}\right)=\ln (1+r)^x[/tex]

[tex]\textsf{Apply the power law}: \quad \ln x^n=n \ln x[/tex]

[tex]\ln \left(\dfrac{y}{P}\right)=x \ln (1+r)[/tex]

Divide both sides by x:

[tex]\dfrac{1}{x}\ln \left(\dfrac{y}{P}\right)=\ln (1+r)[/tex]

[tex]\textsf{Apply the power law}: \quad n \ln x=\ln x^n[/tex]

[tex]\ln \left(\dfrac{y}{P}\right)^{\frac{1}{x}}=\ln (1+r)[/tex]

Raise both sides to power of e:

[tex]\large\text{$e^{\ln \left(\frac{y}{P}\right)^{\frac{1}{x}}}=e^{\ln (1+r)}$}[/tex]

[tex]\textsf{Apply the power law}: \quad e^{\ln x}=x[/tex]

[tex]\left(\dfrac{y}{P}\right)^{\frac{1}{x}}=1+r[/tex]

Subtract 1 from both sides:

[tex]\left(\dfrac{y}{P}\right)^{\frac{1}{x}}-1=r[/tex]

Therefore, the equation to find r is:

[tex]r=\left(\dfrac{y}{P}\right)^{\frac{1}{x}}-1[/tex]

An exponential decay function to model the situation is f(x) = 49(0.7)^x.

The average rate of change over 1 ≤ x ≤ 4 is -7.5.

The average rate of change over 5 ≤ x ≤ 7 is -1.4.

The rate of change decreases as x increases.

In Mathematics, an exponential function can be modeled by using this mathematical expression:

f(x) = ab^x

Where:

Since the initial value is 49 and the decay factor is 0.7, an exponential function that models the situation is given by:

f(x) = ab^x

f(x) = 49(0.7)^x

When x = 1, the value of f(x) is:

f(1) = 49(0.7)^1

f(1) = 34.3.

When x = 4, the value of f(x) is:

f(4) = 49(0.7)^4

f(4) = 11.7649.

For the average rate of change over 1 ≤ x ≤ 4, we have:

Average rate of change = [f(b) - f(a)]/(b - a)

Average rate of change = [11.7649 - 34.3]/(4 - 1)

Average rate of change = -22.5351/3

Average rate of change = -7.5

For the average rate of change over 5 ≤ x ≤ 7, we have:

Average rate of change = [f(b) - f(a)]/(b - a)

Average rate of change = [49(0.7)^7 - 49(0.7)^5]/(7 - 5)

Average rate of change = [4.0354 - 8.2354]/2

Average rate of change = -4.2/3

Average rate of change = -1.4.

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Therefore , the solution of the given problem of circle comes out to be

the diameter is 62 cm.

A circle is created in the plane by each point that is a specific distance from another point (center). Thus, it is a curve made up of points that are separated from one another by a defined distance in the plane. Additionally, it is rotationally symmetrical about the center at every angle. Every pair of endpoints in a circle's closed, two-dimensional plane are evenly spaced apart from the "center." A circular symmetry line is made by drawing a line through the circle. Additionally, it is rotationally equal about the center at every angle.

Here,

Given : Sue covered 2.4 km distance and

bike wheel rotated 1225 times.

Thus,

To find the value of diameter of the wheel

=>2400=2πr*1225

=> 2400/2 = πr*1225

=> 1200 = πr*1225

=>r=31

Diameter = 2*31 = 62cm

Therefore , the solution of the given problem of circle comes out to be

the diameter is 62 cm.

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The value of x, given the angle measures in Triangle ABC, can be found to be 22.

Triangle ABC is a right angled triangle which means that ACB has the angle measure of 90 degrees. This means that the angle measures left will add up to :

= Sum of interior angles in triangle - Angle ACB

= 180 - 90

= 90 degrees

If the sum of 2 x and ( 3 x - 20 ) adds up to 90 degrees, the value of x would then be:

90 = 2 x + ( 3 x - 20 )

2 x + 3 x - 20 = 90

2 x + 3 x = 90 + 20

5 x = 110

x = 110 / 5

x = 22

In conclusion, the value of x is 22.

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The question is:

What is the value of x?

The salesman needs to sell $25937.5 to reach his needed monthly income needs.

Commission, also known as sales commission, is a payment given to employees based on the sales they make.

Given that, A local salesman receives a base salary of $925 monthly. He also receives a commission of 8% on all sales over $1250.

Monthly salary = fixed part + commission part

The fixed salary is $925.

The commission part is 8% on all sales over $1250

Let x = amount of sales, and x must be greater than $1250.

Then, the amount of sales over $1250 is x - 1250.

He earns 8% on that amount, so the commission part is 8%(x - 1250),

or 0.08(x - 1250).

Monthly salary = fixed part + commission part

Monthly salary = 925 + 0.08(x - 1250)

925 + 0.08(x - 1250) = 2900

0.08x = 2075

x = 25937.5

Therefore, he needs to sell $25937.5.

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Answer:Angle

Step-by-step explanation:

Answer:

96:144

Step-by-step explanation:

240/5=48

48*2=96

48*3=144

So your answer is 96:144

Answer:

-9

Step-by-step explanation:

The constant doesn't have a letter attached to it

The measure of side FG for the triangle FGH is equal to 18 using a scale factor of 1/3 to dilate it.

Scale factor is the ratio between the scale of a given original object and a new object, which is its representation but of a different size either bigger or smaller.

The dilation if the triangle FGH implies it is expanded to the bigger triangle F'G'H' with a scale factor 1/3

side F'G' = 6

side FG = 6 ÷ 1/3

side FG = 6 × 3/1 {change division to multiplication}

side FG = 18.

Therefore, the triangle FGH have the measure of its side FG equal to 18 using a scale factor 1/3.

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Answer:

A represents f(x) and B represents g(x)

Step-by-step explanation:

choose a value for x, substitute , say x = 1 into both f(x) and g(x) , then check the values obtained on the graph.

f(x) = 100 × [tex](\frac{3}{5}) ^{1}[/tex] = 100 × [tex]\frac{3}{5}[/tex] = 20 × 3 = 60

thus (1, 60 ) is a point on the graph of f(x)

the point (1, 60 ) is on graph A

g(x) = 100 × [tex](\frac{2}{5}) ^{1}[/tex] = 100 × [tex]\frac{2}{5}[/tex] = 20 × 2 = 40

thus (1, 40 ) is a point on the graph of g(x)

the point (1, 40 ) is on graph B

Answer: 103

Step-by-step explanation: 309/3 = 103

The required correct product is (x + 4)/(x - 4)(x  + 1) for the rational expressions.

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

Anderson multiplies two rational expressions with the given results.

His error is the inequivalent can't be canceled out.

The two rational expressions are given in the question, as follows:

(x² - 16)/(x² - 8x + 16) × (x + 1)/(x² + 2x + 1)

(x² - 4²)/(x² - 2 × 4 × x + 4² ) × (x + 1)/(x² + 2 × 1 × x + 1²)

(x + 4)(x - 4)/(x - 4)² × (x + 1)/(x + 1)²

(x + 4)/(x - 4)(x  + 1)

Thus, the required correct product is (x + 4)/(x - 4)(x  + 1).

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The required factors of the polynomial by grouping are  (x-3)(x^2 + 2).

To factor polynomial equations, a specialized approach is called grouping. It can be applied to polynomials with four terms as well as quadratic equations. Although they differ significantly, the two approaches are comparable.The first two terms and the final two terms are combined: p(x)=(x3 - 4x2) + (3x - 12), and we then identify the shared

factors as follows: p(x) = x2(x - 4) + 3(x - 4). (x - 4).

x^3 - 3x^2 + 2x -6

(x-3)(x^2 + 2)

Thus, required factors are (x-3)(x^2 + 2).

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The sequence of 100, 25, 6.25, 1.5625 is geometric.

The Geometric Mean (GM) in mathematics is the average value or mean that, by calculating the product of the values of the set of numbers, denotes the central tendency of the numbers.

In essence, we multiply the numbers together and calculate their n[tex]th[/tex]root, where n is the total number of data values.

A succession of shapes are used to create geometric patterns.

Because the pattern is governed by a rule, patterns created from shapes are comparable to patterns created from numbers.

The dimensions, perimeter, area, surface area, volume, etc. of geometric shapes are determined using geometry formulas.

Mathematics' branch of geometry examines the connections between points, lines, angles, surfaces, solids' measurements, and qualities.

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the  parallelogram JKLM is a square.

What is square?

Having four equal sides, a square is a quadrilateral. There are numerous square-shaped objects in our immediate environment. Each square form may be recognized by its equal sides and 90° inner angles. A square is a closed form with four equal sides and interior angles that are both 90 degrees. Numerous different qualities can be found in a square.

We are given that rajiv wishes to make a cube without lid with cardboard.

JM = -5² = 25

KL =  -5² = 25

JK = -4²=16

LM =-4²=16

So, the parallelogram JKLM is a square.

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12 is the denominator because it represents the total number of times Nicanor selects a diving ring from the bag

Explaination:

Nicanor randomly selects a ring from the bag a total of 12 times. 3 times he selects a red ring, 4 times a yellow one, and 5 times a blue one.

When he selects a red ring, he selects it 3 times out of the 12 times total, which is represented as the fraction 3/12.

When he selects a yellow ring, he selects it 4 times out of the 12 times total, which is represented as the fraction 4/12.

When he selects a blue ring, he selects it 5 times out of the 12 times total, which is represented as the fraction 5/12.

Hope this helps you!

The percentage of the people surveyed that had a cell phone will be 38.9%.

A percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.

The percentage of the people surveyed that had a cell phone will be;

= 236 / (317 + 236 + 263) × 100

= 236 / 816

= 28.9%

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A 140-pound person will typically burn 4 calories per mile of walking at a rate of 3 miles per hour.

Walking at a pace of 3 miles per hour results in an average calorie burn of 4 for a 140-pound person. This person would therefore burn around 112 calories in a period of 30 minutes. On the other hand, a 200-pound person burns roughly 5 calories per minute, or 159 calories every 30 minutes.

An average walking speed of 3 miles per hour (or 120 steps per minute) is recommended for health reasons. That is a mile that takes 20 minutes. You must increase your pace to 4 miles per hour (135 steps per minute), or a 15-minute mile, to walk for weight loss.

Walking and running have about equal calorie burn rates per minute. Walking at 3.5 mph for 40 minutes for a 160-pound person would take 40 minutes.

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The total number of gallons of oil consumed during the first 14 days of the month is (b) 13.739

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

F (t) = 0.3 + 0.1t — 0.85 cos(2pi/15 (t+ 5))

The question is asking for the total number of gallons of oil consumed by the furnace during the first 14 days of the month,

This can be found by integrating the function F(t) with respect to t from 0 to 14

Using a graphing calculator, we have the integrated function to be

f(t) =  0.3t + 0.05t^2 - 0.85(2/15)sin(2π/15(t+5))

Also, we have

f(14) - f(0) = 13.739

Hence, the solution is 13.739

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Answer: The diagonal AC of a square bisects the square and the midpoint of the diagonal is the center of the square. Since the center of the square is the midpoint of the diagonal, we can find the midpoint of AC by averaging the x-coordinates and y-coordinates of A and C.

The coordinates of the center of the square is ( (2+(-2))/2 , (4+1)/2) = (0, 2.5)

Since a square is a special case of rectangle, which means all sides are equal, the length of the side of the square is the distance between A and C.

Using the distance formula, we can find the length of the side of the square:

d = sqrt( (2-(-2))^2 + (4-1)^2 ) = sqrt(4^2 + 3^2) = sqrt(16+9) = sqrt(25) = 5

The coordinates of the vertex D can be found by subtracting half of the side length from x and y coordinates of the center point.

D(0-5/2, 2.5 - 5/2) = (-2.5, 0.5)

The coordinates of the vertex B can be found by adding half of the side length from x and y coordinates of the center point.

B(0+5/2, 2.5 + 5/2) = (2.5, 5.5)

So the remaining vertices are (2.5, 5.5) and (-2.5, 0.5)

Step-by-step explanation:

Answer:

95 6/7

Step-by-step explanation:

The perimeter can be found by adding the length and width together and then multiplying the sum by 2.

Perimeter = 2(L + W)

Where L is the length and W is the width.

So, using the given measurements:

Perimeter = 2(33 5/7+ 14 3/14) = 94 26/14

94 26/14 -> 95 12/14 -> 95 6/7

Answer:

The perimeter is [tex]95\frac{6}{7}[/tex] inches.

Step-by-step explanation:

The formula for the perimeter of a rectangle is

[tex]P=2L+2W[/tex]

We are given the length and the width. Lets evaluate the perimeter.

First lets convert the length and width to an improper fraction.

Length: [tex]33\frac{5}{7}[/tex]

To write 33 as a fraction with a common denominator, multiply by [tex]\frac{7}{7}[/tex]. Then simplify.

[tex]\frac{33*7}{7} +\frac{5}{7}[/tex]

[tex]\frac{231}{7} +\frac{5}{7}[/tex]

[tex]\frac{231+5}{7}[/tex]

[tex]\frac{236}{7}[/tex]

Width:

To write 14 as a fraction with a common denominator, multiply by [tex]\frac{14}{14}[/tex]. Then simplify.

[tex]\frac{14*14}{14} +\frac{3}{14}[/tex]

[tex]\frac{196}{14} +\frac{3}{14}[/tex]

[tex]\frac{196+3}{14}[/tex]

[tex]\frac{199}{14}[/tex]

Lets enter the 2 fractions into the perimeter equation.

[tex]P=(2*\frac{236}{7} )+(2*\frac{199}{14} )[/tex]

Simplify each term.

[tex]P=\frac{2*236}{7} +2*\frac{199}{14}[/tex]

[tex]P=\frac{472}{7} +2*\frac{199}{14}[/tex]

Factor 2 out of 14.

[tex]P=\frac{472}{7} +2*\frac{199}{2(7)}[/tex]

Cancel the common factor of 2.

[tex]P=\frac{472}{7} +\frac{199}{7}[/tex]

Combine the numerators over the common denominator.

[tex]P=\frac{472+199}{7}[/tex]

[tex]P=\frac{671}{7}[/tex]

[tex]P=95\frac{6}{7}[/tex]

Answer:

Step-by-step explanation:

the answer is:

5y^10

_____

7x^4

If this isnt the simplified version, you want im sorry

Answer:

[tex]\frac{5y^{10} }{7x^{4} }[/tex]

Step-by-step explanation:

[tex]\frac{30x^{3}y^{2} }{42x^{7} y^{-8} }[/tex]  to make [tex]y^{-8}[/tex] positive we need to put it in the numerator (top)

[tex]\frac{30x^{3}y^{2}y^{8} }{42x^{7} }[/tex]  Now I am going to write it in expanded form

[tex]\frac{2x3x5xxxyyyyyyyyyyyy}{2x3x7xxxxxxx}[/tex]  If we cross out what we have on the bottom and the top, we will be left with our answer simplified.

[tex]\frac{5y^{10} }{7x^{4} }[/tex]

y = 1/2x + 1 is the line's equation in slope-intercept form.

The equation of a line in slope intercept form is expressed as y = mx + b where:

m is the slope

b is the y-intercept

Given the following coordinate points (4, 3) and (0, 1), the slope is calculated as:

Slope = 1-3/0-4
Slope = -2/-4
Slope = 1/2

For the y-intercept, it is the point where the x-coordinate is zero, hence the y-intercept if (0, 1)

Determine the required equation
y = mx + b

y = 1/2x + 1

Hence the equation of the line in slope-intercept form is y = 1/2x +1

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Answer:24.353333333

Step-by-step explanation:

Answer:  48 square inches

Step-by-step explanation:

To find the area of an irregular shape, we first break the shape into common shapes. Then we find the area of each shape and add them. For example, if an irregular polygon is made up of a square and a triangle, then: Area of irregular polygon = Area of Square + Area of Triangle.

area of triangle L x W = 6x4=24

area of rectangle LxW =6x4=24

24+24=48

Answer:

amazon

Step-by-step explanation:

let's find the price per pack to solve

best buy:

7 packs = 28 dollars

divide both sides by 7 to get 1 pack = something

1 pack = 4 dollars

amazon:

12 packs = 38 dollars

divide both sides by 12 to get 1 pack = something

1 pack = 38/12 dollars = 3.16666666667 dollars which is less than 4 dollars, so amazon is cheaper in terms of price per pack

The area under the standard normal curve to the right of Z (3.15) = 0.0008

The total area under the standard normal curve happens to be 1 which is divided between two parts having an area under the curve = 0.5 on each side.

I.e. from 0 to the right side, the area under the curve = 0.5

Similarly, from 0 to the left side, the area under the curve = 0.5

Now, from the standard normal table,                                  

                                                          {the table is given in the attachment}

The area under the curve for the value of Z (3.15) = 0.4992

                                                                         {This value is the area under the curve from 0 to Z (=3.15)}

Hence, the Area under the curve to the right of Z (3.15) = 0.5 – 0.4992

                                                                                            = 0.0008

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For z = 3.15, the area under the standard normal curve is 0.99918365.

Normal distributions are symmetrical, bell-shaped distributions that are useful in describing real-world data.

The standard normal distribution, represented by the letter Z, is the normal distribution having a mean of 0 and a standard deviation of 1.

If {X} is a random variable from a normal distribution with mean {μ} and standard deviation {σ}, its Z-score may be calculated from X by subtracting μ and dividing by the standard deviation :

[tex]${\displaystyle Z={\frac {X-\mu }{\sigma }}}[/tex]

If {X} is the mean of a sample of size {n} from some population in which the mean is {μ} and the standard deviation is {σ}, the standard error is σ/√n :

[tex]${\displaystyle Z={\frac {{\overline {X}}-\mu }{\sigma /{\sqrt {n}}}}}[/tex]

If [tex]{\textstyle \sum X}[/tex] is the total of a sample of size {n} from some population in which the mean is {μ} and the standard deviation is {σ}, the expected total is nμ and the standard error is σ √n :

[tex]${\displaystyle Z={\frac {\sum {X}-n\mu }{\sigma {\sqrt {n}}}}}[/tex]

Given is the value of z = 3.15.

For z = 3.15, the area under the standard normal curve is 0.99918365.

Therefore, for z = 3.15, the area under the standard normal curve is 0.99918365.

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Answer:

1,2,3,4,6,12,18

Step-by-step explanation:

uh

Answer:

Step-by-step explanation:

put the 2x and make it 2

Here, two sides of the triangle are equal.

Therefore, perimeter of the triangle

= p - 5 + p - 5 + 2p + 8

= 4p - 2

= 2(2p - 1)

Answer:

2(2p - 1)

Hope it helps.

Answer: 4p - 2

Step-by-step explanation:

Sum of all sides is the perimeter.

According to the figure, the two sides are equal.

therefore, perimeter = p - 5 + p - 5 + 2p + 8

= 4p - 2