A barrel shaped like a cylinder is laid on its side and rolled up a ramp. The barrel has a circular base that is 1.1 inches in diameter. If the barrel turns 47 times in being rolled up the ramp, how long is the ramp?

Answer:

Step-by-step explanation:

You have three segments totaling 82 cm, with the first being 4/9 of the second, and the third being 16 cm more than the second.

We can describe the relationship by the equations ...

  a + b + c = 82

  a = 4/9b

  c = b +16

The equations give each segment in terms of the second one, so we can substitute those relations into the sum:

  (4/9b) +b +(b +16) = 82

  22/9b = 66

  b = 66(9/22) = 27

  a = (4/9)(27) = 12

  c = 27 +16 = 43

The first segment is 12 cm; the second is 27 cm; and the third is 43 cm.

__

Additional comment

We used an ad hoc solution based on the observation that segments 'a' and 'c' were defined in terms of 'b'. We could write the equations as a system of 3 linear equations in 3 unknowns, and solve using matrix methods:

The solution is shown in the attachment: a=12, b=27, c=43.

The sum of the first 20 terms of the sequence is - 206.25

Arithmetic Progression (AP) is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value. It is also called Arithmetic Sequence. For example, the series of natural numbers: 1, 2, 3, 4, 5, 6,… is an Arithmetic Progression, which has a common difference between two successive terms (say 1 and 2) equal to 1 (2 -1). Even in the case of odd numbers and even numbers, we can see the common difference between two successive terms will be equal to 2

a + 18d = - 5

a + 14d = -7 1/2

---------------------

4d = -5 + 15/2

8d = -10 + 15

8d = 5

d = 5/8

a + 18(5/8) = -5

8a + 90 = -40

8a = -40 - 90

8a = -130

a = -130/8

The sum of the first 20 will be;

Sum = (20/2) (2(-130/8) + (20-1)(5/8))

Sum = 10 (-260/8 + 95/8)

Sum = 10 (-165/8)

Sum = - 206.25

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Therefore . the solution of the given problem of equation comes out to be x-intercept(s): (9,0) and y-intercept(s): (0,−6).

A depiction of two equal variables, one on either side of a "equals" sign, is what constitutes an equation in mathematics. To solve common issues, one can use equations. We frequently look for help with pre algebra to overcome obstacles in real life. Basic mathematical concepts are covered in pre-algebra lessons.

Here,

the x-intercepts,

In order to determine the x-intercept(s), put in for y and calculate 4x6y=36.

Make the equation work.

x=9 point form x-intercepts.

x-intercept(s): \s(9,0) (9,0)

the y-intercepts, please.

In order to determine the y-intercept(s), replace with and solve for y=.4(0-)6y=36.

Make the equation work.

To continue, tap.

Point shape y=6 y-intercept(s).

The y-intercept is (0, 6).

Write down the junctions.

x-intercept(s): (9,0)

The y-intercept is (0, 6).

Therefore . the solution of the given problem of equation comes out to be x-intercept(s): (9,0) and y-intercept(s): (0,−6).

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To find the slope of two points on a graph, use the formula:

[tex]Slope =\frac{y2 - y1}{x2 - x1}[/tex]

Substitute the coordinates of the two points into the formula and solve for the slope.

The slope of two points on a graph is a measure of how steep the line connecting the two points is. To find the slope, you can use the slope formula: [tex]Slope =\frac{y2 - y1}{x2 - x1}[/tex]

This formula requires the coordinates of the two points, which can be found on the graph. Once you have the coordinates, you can substitute them into the formula and solve for the slope. This will give you the slope of the line connecting the two points.

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There is a 0.0001 percent chance that the average amount of cereal in these boxes is less than 9.65 ounces.

Given that,

Mean µ = 9.70

Sample size = n = 5

standard deviation = σ = 0.03

Its distribution is normal, therefore

σx = σ/

σx = 0.03

σx = 0.0134

We must now determine the z value in order to use the table.

z = (x - µ) ÷ σ

z = (9.65 - 9,70) ÷ 0.0134

z = -3.73

Now

From the probability index tables

So P (z ≤ - 3.73) = 0.0001

Hence, the correct option is e) 0.0001

The complete question is:

A company’s cereal boxes advertise that each box contains 9.65 ounces of cereal. In fact, the amount of cereal in a randomly selected box follows a Normal distribution with mean μ = 9.70 ounces and standard deviation σ = 0.03 ounce. Now take an SRS of 5 boxes. What is the probability that the mean amount of cereal in these boxes is less than 9.65 ounces?

a. 0.4525

b. 0.9522

c. 0.9999

d. 0.0478

e. 0.0001

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Lines running horizontally and vertically are parallel. So, angles A, B, and C are right angles by definition of perpendicular lines. All right angles are equal. Therefore, △ABC ~ △DEF by the SAS similarity theorem.

Given that startfraction a b over d e endfraction = startfraction b c over e f endfraction = one-half

Step 1: Multiply both sides of the equation by de:

a/b * de = bc/ef * de

Step 2: Simplify the left side of the equation:

ade = bcde

Step 3: Divide both sides of the equation by ad:

a/d = b/e

Step 4: Multiply both sides of the equation by be:

ab/d = be/e

Step 5: Simplify the left side of the equation:

ab = be

Step 6: Divide both sides of the equation by be:

a/b = 1/e

Step 7: Multiply both sides of the equation by ef:

a/b * ef = 1/e * ef

Step 8: Simplify the left side of the equation:

aef = ef

Step 9: Divide both sides of the equation by ef:

a/b = 1/e

Conclusion: startfraction a b over d e endfraction = startfraction b c over e f endfraction = one-half

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Answer:

perpendicular

b and e

congruent

The number of people who bought fewer than 30 items exists 204.

The frequency distribution of a few data points for one variable is represented graphically by a histogram. Heterogeneous "bins" or "range groups" are frequently used in histograms in order to categorize data and count the number of data points that are part of each bin.

Among graphing tools, the histogram is widely used. It is utilized to encapsulate discrete or continuous data that is measured on an interval scale. It is frequently employed as a convenient way to highlight the key characteristics of the data distribution.

As opposed to bar charts, which show categorical variables, histograms visualize quantitative or numerical data. Typically, a histogram's numerical data will be continuous (having infinite values).

Number of people who bought fewer than 30 items

= (0.14 + 0.12 + 0.24)400

= 0.51 x 400 = 204

Therefore, the correct answer is option B) 204.

The complete question is:

The histogram shows the number of items that customers bought during a trip to the grocery store one day. Four hundred customers took a trip to the grocery store that day. Which is the best estimate for the number who bought fewer than 30 items during their trip?

A) 278

B) 204

C) 148

D) 106

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The slope intercept form of the equation is

y = -1/4x -11/4

One of the most popular ways to describe a line's equation is in the slope intercept form of a straight line. When the slope of the straight line and the y-intercept are known, the slope intercept formula may be used to get the equation of a line ( the y-coordinate of the point where the line intersects the y-axis). The equation of a line is the equation that each point on the line fulfills.

The slope intercept form is a technique for figuring out a straight line's equation in the coordinate plane. Any point's coordinates on a straight line must fulfill a certain relation, which is known as the equation of a straight line.

Any location that is not on the line will not fulfill the coordinates.

This equation's solution is simple to find. A straight line's slope, or angle of inclination from the x-axis, and the intercept it makes with the y-axis are both necessary to determine the slope intercept form of the line.

The line passes through (1,-3)

slope = -1/4

The equation of the line

y = mx + c

here m is the slope and c is the intercept.

putting the point and slope in the equation

-3 = -1/4 *1 + c

⇒ c = -11/4

So the slope intercept form of the equation is

y = -1/4x -11/4

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The solution of the given function cosx - √(3 - 3cos³x) = 0 is C. 30° + 360° n, 330° + 360°n

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

We are given the function as;

cosx - √(3 - 3cos³x) = 0

cosx = √(3 - 3cos³x)

Taking square root on both sides.

cos ²x = √(3 - 3cos³x) ²

cos ²x = (3 - 3cos³x)

For solving for x in

cos ²x = (3 - 3cos³x)

cos ²x = 3 (1 - cos³x)

(1 - cos³x) = cos ²x/3

x= π/6 + 2πn

or

x=11π/6 + 2πn

where n is an integer.

30° + 360° n, 330° + 360°n

The correct answer is C.

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If the coach buys the packs of Gummi Bears at $0.60 and resales them at $1 , then the percent markup for the candy is (d) 67% .

The price for which the Coach buys Gummi Bears is = $0.60 ;

the price at which the Coach resales them is = $1 ;

So , the Markup is the difference in the price of purchase and price of resale of the candy ,

that means ; the [tex]Markup = \$1 - \$0.60[/tex] ;

= $0.4

So , the Percent Markup is = [tex]\frac{0.4}{0.6} \times 100[/tex]

= 66.66666...

≈ 67% .

Therefore , the percent Markup for the Candy is 67% .

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Step-by-step explanation:

For Pythagoras' Theorem to be valid, the triangle must be a right-angled one.

The formula is:

c^2 = a^2 + b^2

Where c is the longest side. While a,b are the side lengths.

Using the above formula and the measurements given in the question, we can find the value of x.

By Pythagoras' Theorem,

26^2 = (5x)^2 + (12x)^2

676 = 25x^2 + 144x^2

169x^2 = 676

x^2 = 676 ÷ 169

x^2 = 4

x = 2

The height of the cone is 24.6cm and the volume of the cone is 1/3 * pi * 4^2 * 24.6 = 268.08cm^3

We can start by using the formulas for the surface area of a sphere and the curved surface area of a cone. The surface area of a sphere is given by 4 * pi * r^2, where r is the radius of the sphere. The curved surface area of a cone is given by pi * r * l, where r is the radius of the base of the cone and l is the slant height of the cone.

Given that the surface area of the sphere is five times the area of the curved surface of the cone, we can write the following equation:

4 * pi * (5^2) = 5 * pi * r * l

We can then solve for the slant height l of the cone:

l = (4*5^2) / r

Given that the radius of the cone is 4 cm, we can substitute this into the equation and solve for l:

l = 100/4 = 25cm

The volume of the cone is 1/3 * pi * r^2 * h, where r is the radius of the base and h is the height of the cone.

As we know the slant height and radius of the cone, we can use the Pythagorean theorem to find the height of the cone:

h = sqrt(l^2 - r^2) = sqrt(25^2 - 4^2) = sqrt(625 - 16) = sqrt(609) = 24.6cm

Therefore, the height of the cone is 24.6cm and the volume of the cone is 1/3 * pi * 4^2 * 24.6 = 268.08cm^3

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Answer:

Step-by-step explanation:

(100xInterest)(RatexTime)

hope this helps

Step-by-step explanation:

The formula for calculating Principal amount would be P = 100I / (RT) where Interest is Interest Amount, R is Rate of Interest and T is Time Period.

Shortest distance between start and end point is 55.9 miles

According to given statement,

Terry had to travel south 50 miles and then west 25 miles.

We are taking X as a start point and Z is end point.

In triangle XYZ, we are taking angle Y to be of 90 degrees, which qualifies the Triangle XYZ to qualify Pythagorean theorem [The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right angle triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.]

XY = 50 miles

YZ= 25 miles

XZ^2 = XY^2 + YZ ^2

XZ^2 = (50) ^2 + (25) ^2 = 3125

XZ = 55.9

Shortest distance between start and end point is 55.9 miles

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Starting out with the fraction of 5/9, Jess would be thinking of the fraction 144/125 at the end of the game if the ten coin flips turn out to be {THTTHTHTTT}.

Since both outcomes are equally likely, the probability of getting heads is 0.5 and the probability of getting tails is also 0.5. Alternatively, the probability of getting H or T in a coin flip is 1.

Probability is an important method for comprehending and making judgments regarding uncertain occurrences in many disciplines, including statistics, finance, and science. It aids in quantifying and forecasting the probability of specific events, enabling us to make better educated choices and comprehend the degree of risk involved with various activities. In summary, probability is a key idea in decision-making and risk management because it is a potent instrument for comprehending and managing uncertainty.

Taking the sequence of coin flips in ten tires, i.e THTTHTHTTT , and starting from the fraction 5/9, the fraction that jess would be thinking at the end of the game can be calculated as,

5/9 * (6/5)^7 *(5/6)^3 , since there are 7 Tails and 3 Heads during the whole game. Which is equal to the fraction 144/125.

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Han is wrong , we do not agree with him. The value of the 7 in 735,208 is not the 10 times the value of the 7 in 137,342.

The value of 7 here refers to the place value of 7 , in 735,208  7 is at lakhs place whereas in 137,342 , 7 is in thousandth place .

Therefore , Han is wrong as because if we will the 7 in 137,342. when multiplied by 10 will go to the ten thousandth place and not the lakh place.

The  place value is a measure which is used to represent the position of each digit in a number . Based on their position in the number, digits are assigned place values such as ones, tens, hundreds, thousands, ten-thousands, and so on. For example, 1 in 512400 has a place value of ten thousands, i.e. 10000.

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Therefore , the solution to the given problem of linear equation comes out to be T= 64.

Any function that fulfills the algebraic equation y=mx+b is said to be linear. B is the slope, and m is the y-intercept. Since both x and y are factors, the previous sentence is commonly referred to as an equation system with two variables." Two-variable linear equations are referred to as bivariate equations. There are several applications for linear equations: x + z = 2, and 3z - y + z = 3 both have a zero solution. If an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept, it is referred to as linear. The equation is written as Y=mx+b, where m denotes the slope and b the y-intercept.

Here,

Given : 3+ T/2 = 35

thus,

=>  3+ T/2 = 35

=> T/2 = 35-3

=> T/2 = 32 *2

=> T= 64

Therefore , the solution to the given problem of linear equation comes out to be T= 64.

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The angles associated to the trigonometric equation 2 · tan² θ - 7 · sec θ + 8 = 0 are θ₁₁ ≈ 131.810°, θ₁₂ ≈ 228.190°, θ₂₁ ≈ 120° and θ₂₂ ≈ 240°.

In this question we find a trigonometric equation, that is, an equation involving trigonometric functions, that must be solved for the interval between angles of 0° and 360°. This can be done by algebra properties and trigonometric formulas.

First, write the complete expression:

2 · tan² θ - 7 · sec θ + 8 = 0

Second, use trigonometric formulas and algebra properties to reduce the number of trigonometric functions within the equation:

2 · sin² θ / cos² θ - 7 / cos θ + 8 = 0

2 · sin² θ - 7 · cos θ + 8 · cos² θ = 0

2 - 2 · cos² θ - 7 · cos θ + 8 · cos² θ = 0

6 · cos² θ - 7 · cos θ + 2 = 0

Third, use algebraic subtitution and quadratic formula to determine the roots of the quadratic-like equation:

6 · u² - 7 · u + 2 = 0

u = - 7 / (2 · 6) ± [1 / (2 · 6)] · √[(- 7)² - 4 · 6 · 2]

u = - 7 / 12 ± (1 / 12) · 1

u = - 7 / 12 ± 1 / 12

There are two possibilities:

u₁ = - 2 / 3, u₂ = - 1 / 2

Fourth, find the angles associated to roots by inverse trigonometric functions:

u₁ = - 2 / 3

θ₁₁ ≈ 131.810°, θ₁₂ ≈ 228.190°

u₂ = - 1 / 2

θ₂₁ ≈ 120°, θ₂₂ ≈ 240°

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The equation for the maximum number of yards per second that can be run is y = 5/3 s.

A direct variation measurement between distance covered and time taken can be composed as:

y=kx,

where,

This is because the athlete's distance travelled directly varies with the amount of time it takes.

Find k using the given values:

y=kx,

10 = k(6)

k = 10/6

k = 5/3

As a result, the equation for the maximum number of yards per second is y = 5/3 s.

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answer:

b+24

step-by-step explanation:

it’s just asking for the sum so add the two values. there are no other integers given other than 24 so the answer is in expression form. hope that helps!

One mole of H2 contains 6.022 x 10^23 H2 molecules. This can be used to calculate the number of H2 molecules in a given volume or mass of hydrogen gas.

A mole is a unit of measurement in chemistry that expresses the amount of a substance. It is defined as the number of entities (such as atoms, ions, or molecules) in a sample of the substance. The number of entities in one mole of a substance is known as Avogadro's number.

Avogadro's number is a fundamental constant of physics and chemistry, defined as the number of atoms, ions or molecules in one mole of substance. It is approximately 6.022 x 10^23 and is used in many calculations in chemistry and physics, such as the number of atoms in a sample of an element, the number of ions in a salt, or the number of molecules in a gas sample. The constant is named after Amedeo Avogadro, an Italian scientist who first proposed the concept in 1811.

One mole of a substance is equal to Avogadro's number, which is approximately 6.022 x 10^23.

The mole of H2 (hydrogen gas) is the number of H2 molecules in a sample of hydrogen gas. One mole of H2 contains 6.022 x 10^23 H2 molecules. This can be used to calculate the number of H2 molecules in a given volume or mass of hydrogen gas.

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The range of the amount Tyrese makes each hour if he can only work a total of 8 hours is 20 ≤ x ≤ 24.80

The range is the space between the highest and lowest numbers.

Given: Tyrese works every day and gets paid more per hour the more time he puts in. Create a function to represent a starting wage of $20 that rises by 3% each hour.

To find: Establish the range of Tyrese's hourly pay if he can only work a total of 8 hours.

The beginning wage is $20.

Suppose x hours are in a day.

A $20 salary is offered, with a 3% hourly raise.

e.g., increment = (3/100)*20*x = (3/5)x

A function's maximum possible earnings are

y = 20 + (3/5)x

He is only allowed to work a total of 8 hours, per our instructions.

Therefore, the most money she can make in 8 hours is

y = 20 + (3/5)*8

y = 20 + 4.8

y = 24*8

$20 is the first sum.

As a result, if Tyrese can only work a total of 8 hours every day, the range of his hourly wage is .

Therefore, the correct answer is option B) 20 ≤ x ≤ 24.80.

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Answer:

r < 6

Step-by-step explanation:

[tex] \implies \dfrac{1}{2}r + 3 < 6[/tex]

[tex] \implies \dfrac{r}{2} < 6 - 3[/tex]

[tex] \implies \dfrac{r}{2} < 3[/tex]

[tex] \implies r < 3 \: \cdot \: 2[/tex]

[tex] \implies \underline{ r < 6}[/tex]

4-6 = -2

x/7-6

Substitute

28/7-6

PEMDAS

28/7 = 4

4-6 = -2

(If you're looking for the expression, it's 4-6. But if straight answer, -2)

Answer:

[tex] \sf \: \frac{x}{7} - 6 = - 2[/tex]

Step-by-step explanation:

Given information,

[tex] \sf \rightarrow \: \frac{x}{7} - 6[/tex]

[tex] \sf \rightarrow \: x = 28[/tex]

Now the value of expression is,

[tex] \sf \rightarrow \: \frac{x}{7} - 6[/tex]

[tex] \sf \rightarrow \: \frac{28}{7} - 6[/tex]

[tex] \sf \rightarrow \: 4 - 6[/tex]

[tex] \sf \rightarrow \: - 2 = > final \: value[/tex]

Therefore, the answer is -2.

Line segment theorem states that if a line segment is bisected by another line, then the two parts of the line segment are equal.

This theorem is also known as the Midpoint Theorem. The formula for the Line Segment Theorem is A/B = C/D, where A and C are the two halves of the line segment, and B and D are the distances from the midpoint to the two endpoints of the line segment.

For example, consider a line segment AB with endpoints at A(-3, 2) and B(3, 2). The midpoint of the line segment is at (0,2). To calculate the length of each half of the line segment, we would use the distance formula and plug in the coordinates of the two endpoints and the midpoint.

For half A, the distance is d(A, M) = sqrt[(-3 - 0)^2 + (2 -2)^2] = 3.

For half C, the distance is d(M, B) = sqrt[(3 - 0)^2 + (2 -2)^2] = 3.

Therefore, A/B = 3/3 = 1 and C/D = 3/3 = 1. This confirms that the two halves of the line segment are equal in length.

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The X-intercept is the point where the line crosses the x-axis. This happens where the Y is equals to zero.

The point slope form of a line is an equation of the line that takes on the form y - y1 = m(x - x1). In this equation, m is the slope of the line, and (x1, y1) is a point on the line. The x-intercept of a line is the x-coordinate of the point where the line crosses the x-axis. This always happens at the point where y is equal to 0. Therefore, we find the x-intercept of a line in point-slope form by plugging y = 0 into the equation and then solving for x. The point-slope formula is composed of a specific point of coordinates and a slope indicating a type of change over a given variable, such as distance over time. It is said to be as the x-coordinate of a point where a line, curve, or surface intersects the x-axis.

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Answer: O x<12

Step-by-step explanation:

Step 1: Simplify both sides of the inequality.

5x+25<85

Step 2: Subtract 25 from both sides.

5x+25−25<85−25

5x<60

Step 3: Divide both sides by 5.

5x/5 < 60/5

x<12

Graph of given system of equations is shown in figure with intersection point (2, 4).

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The system of equation is,

⇒ 2x + y = 8

⇒ - x + 2y = 6

By solving both equation , we get;

⇒ (x, y) = (2, 4)

Thus, The graph of system of equation intersect on point (2, 4).

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