Question 1-10 A golf ball has a circumference of 13.408 cm , and 336 dimples on its surface. Approximately how many dimples per squarecentimeter are on the surface of a golf ball 0.170, 1.468,4.638,5.872

The solution set of the given homogeneous system in parametric vector form is x = (0, 0, t), where t is a real number

Vectors are an important mathematical tool for representing complex data and equations. In this problem, we are given a homogeneous system of equations and asked to write the solution set in parametric vector form.

The homogeneous system consists of three equations: 3x₁ + 3x₂ + 6x₃ = 0, -6x₁ - 6x₂ - 12x₃ = 0, and -4x₂ + 4x₃ = 0. To solve this system, we need to use linear algebra techniques, such as Gaussian elimination, to find the solution set.

By using Gaussian elimination, we can reduce the system to a simpler system, which has the form x₁ = 0, x₂ = 0, and x₃ = t, where t is a real number. This can be written as a parametric vector form as x = (0, 0, t).

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The slope and y - intercept of the line of best fit are 1.22 and -0.09 respectively.

a.

To fill the table of the residuals, we can approach it as;

residual = food waste - number of people.

3.2 - 2 = 1.4

2.5 - 3 = -0.5

8.9 - 4 = 49

4.7 - 4 = 0.7

3.5 - 4 = -0.5

4 - 4 = 0

5.3 - 5 = 0.3

4.6 - 5 = -0.4

7.8 - 5 = 2.8

3.2 - 6 = -2.8

12 - 8 = 4

b.

The equation is given as;

y = 1.22x - 0.09

The slope of the line of best fit is 1.22

c.

The y - intercept is given as -0.99

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In this problem, the lower limit of integral is -3 and the upper limit of integration is 3.

We can use the formula for the surface area of a solid of revolution generated by a curve revolving around a given axis. The formula is S = 2π ∫ a b y dx, where a and b are the lower and upper limits of integration, and y is the height of the curve at x. In this problem, the lower limit of integration is -3 and the upper limit of integration is 3. Substituting y = 1/16(e^8x + e^-8x) into the equation gives S = 2π ∫ -3 3 (1/16(e^8x+e^-8x)) dx. Integral this expression gives S = 10512π.

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The sale price of the green beans represents a decrease of 16.67% compared to the original price of the beans.

To find the percent increase or decrease in the price of a can of green beans during the sale, we need to compare the sale price with the original price.

During the sale, the green beans were sold at a rate of 3 cans for $1.25, or approximately 41.67 cents per can:

Sale price per can = $1.25 / 3 = $0.4167 ≈ 41.67 cents

The original price of a can of green beans was 50 cents.

To find the percent increase or decrease in the price, we can use the following formula:

Percent increase or decrease = ((New value - Old value) / Old value) x 100%

Substituting the values, we get:

Percent increase or decrease = ((0.4167 - 0.5) / 0.5) x 100%

Percent increase or decrease = (-0.0833 / 0.5) x 100%

Percent increase or decrease = -16.67%

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We converted the measurement of 6 ft x 6 ft to inches using a conversion factor of 12 inches per foot, resulting in a total area of 5,184 square inches.

Measurement is an important aspect of our daily lives, and it involves quantifying the size, length, or dimensions of an object or space. Different units of measurement are used to express the size or length of an object, depending on the context or purpose.

The measurement of 6 ft x 6 ft is the size or area of a square-shaped object, where each side is 6 ft long. To convert this measurement to inches, we need to use a conversion factor that relates feet to inches. One foot is equal to 12 inches, so we can multiply each side of the square by 12 to get the corresponding measurement in inches.

6 ft x 12 inches/ft = 72 inches

Therefore, the measurement of 6 ft x 6 ft in inches is 72 inches x 72 inches, which equals 5,184 square inches. This means that if we had a square-shaped object with sides measuring 6 feet, the total area of the object would be 5,184 square inches.

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The mean value of the scores is 19.83, based on their sum and quantity of numbers.

The mean or average is calculated using the formula -

Mean = sum of all the numbers ÷ quantity of numbers.

We see that there are six numbers and hence the quantity of numbers will be 6.

Sum of all the numbers = 12 + 25 + 15 + 27 + 32 + 8

Performing addition on Right Hand Side of the equation

Sum of all the numbers = 119

Now calculating the mean of the scores by keeping the values in formula -

Mean = 119/6

Performing division on Right Hand Side of the equation

Mean of scores = 19.83

Hence, the average of scores is 19.83.

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Answer: -20

Step-by-step explanation:

2(-1 x 3 - 7)

2(-3-7)

2(-10)

-20

Answer:

[tex]\huge\boxed{\sf -20}[/tex]

Step-by-step explanation:

= 2(xy - 7)

Put x = -1, y = 3

= 2[(-1)(3) - 7]

= 2(-3 - 7)

= 2(-10)

[tex]\rule[225]{225}{2}[/tex]

For sum of all angles of polygon=900°, no. of sides will be 7.

What exactly is a polygon?

Polygons are two-dimensional geometric objects that have the same number of sides on all sides. The sides of a polygon are made up of straight line segments linked end to end. As a result, the line segments of a polygon are referred to as sides or edges. The place where two line segments meet is known as the vertex or corners, and an angle is generated as a result. A triangle of a polygon. A circle is a planar figure, however it is not regarded a polygon since it is curved and lacks sides and angles. As a result, we may argue that all polygons are 2d forms, but not all two-dimensional figures are polygons.

For a polygon with n no. of sides

sum of all interior angles=(n-2)*180°

Now,

As given the sum of all angles=900°

then number of sides of a polygon will be

(n-2)*180=900

n-2=5

n=7

Hence,

          For sum of all angles of polygon=900°, no. of sides will be 7.

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Answer:

x+y=17

y can be 1,3,5,7 or 9

Let's start at 9

x+9=17

x=8

So the burner is 89

7, 5, 3 and 1 don't work

For example In order x+7=17, x should be 10, which is a contradiction; x is the one-digit number. If 7 doesn't work, lower numbers shouldn't work as well.

Step-by-step explanation:

The upper quartile of the data set is, 56.

The process for combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Given that;

The values of 42, 44, 50, 54, and 56 are all marked by the box plot.

Hence, The value of upper quartile is,

⇒ Upper quartile = 3/4 (n + 1)

Where, n is number of terms.

Hence, We get;

⇒ Upper quartile = 3/4 (5 + 1)

                           = 3/4 × 6

                           = 4.5

                           ≈ 5th term

Thus, The value of Upper quartile = 56

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Answer:

To find your answer, you will divide 252  by 123, and then multiply it by 10:

252 / 12 = 21

21 * 10 = 210

210 soft drinks are required.

Step-by-step explanation:

Hope it helps! =D

the initial value problem dy/dt = 5y, y(0) = y0, the solution has a vertical asymptote at t = 4 only when y0 = 0, and the time interval of existence is the entire real line, (-∞, ∞).

The initial value problem given is: dy/dt = 5y, y(0) = y0

The solution to this differential equation is: y(t) = y0 × e⁽⁵t⁾

To find the value(s) of y0 for which the solution has a vertical asymptote at t = 4, we need to set t = 4 and solve for y0 such that the solution becomes infinite.

y(4) = y0 × e⁽⁵ˣ⁴⁾ = y0 × e²⁰

For the solution to have a vertical asymptote at t = 4, y0 × e²⁰ must be infinite. This means that y0 must be equal to 0.

Next, we need to determine the time interval of existence C<4 for the solution. The solution is continuous and differentiable for all values of t, so the time interval of existence is the entire real line, (-∞, ∞). Therefore, for the initial value problem dy/dt = 5y, y(0) = y0, the solution has a vertical asymptote at t = 4 only when y0 = 0, and the time interval of existence is the entire real line, (-∞, ∞).

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To find the equation of the tangent line to a curve at a given point, we will need the equation of the curve and the place where you want to locate the tangent line in order.

Calculate the derivative by differentiating the curve's equation. This will reveal the tangent line's slope at any point along the curve.

Put the derivative you discovered in step 1's derivative into the x-coordinate of the place where you wish to find the tangent line. This will reveal the tangent line's slope at that particular position.

To determine the equation of the tangent line, use the point-slope form of the equation of a line. A line's point-slope formula is written as y - y1 = m(x - x1), where (x1, y1) is the line's point and m is its slope. Both the slope of the line and the location on the line where you wish to find the tangent line are known to you from step 2.

Put the tangent line's equation in a simpler, more conventional form,        as y = mx + b.

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Answer: 16

Step-by-step explanation: Basic multiplication

4+4=8

4+4=8

8+8=16    [16!]

The missing sides of each pair of similar triangles are listed below:

Case 15: w = 5, x = 25 / 12, y = 65 / 12, z = 169 / 12

Case 16: x = 12, y = 6√3, z = 3√5

Case 17: x = 40 / 3, y = 32 / 3

Case 18: x = 5, y = 20, z = 10√3

In this problem we find four cases of pairs of similar triangles, whose missing sides can be found by means of proportion formulas and Pythagorean theorem. Now we proceed to determine the missing lengths for each length:

Case 15

w = √(13² - 12²)

w = 5

12 / w = w / x

w² = 12 · x

x = w² / 12

x = 5² / 12

x = 25 / 12

y = √[(25 / 12)² + 5²]

y = 65 / 12

z = 12 + x

z = 169 / 12

Case 16

6 / 3 = x / 6

x = 36 / 3

x = 12

y = √(x² - 6²)

y = √(12² - 6²)

y = 6√3

z = √(3² + 6²)

z = 3√5

Case 17

y / 8 = 8 / 6

y = 8² / 6

y = 64 / 6

y = 32 / 3

x = √(8² + y²)

x = √[8² + (32 / 3)²]

x = 40 / 3

Case 18

x = √[10² - (5√3)²]

x = 5

y = x + 15

y = 20

z = √[15² + (5√3)²]

z = 10√3

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From the given information provided, the first three common denominators of 7/9 and 2/3 are 9, 18, and 27.

To find the common denominators of 7/9 and 2/3, we need to find the least common multiple (LCM) of their denominators.

The prime factorization of 9 is 3 x 3, and the prime factorization of 3 is 3.

The prime factorization of 2 is 2, and the prime factorization of 3 is 3.

The common factors are 3, so the LCM of 9 and 3 is 9.

Therefore, the common denominator of 7/9 and 2/3 is 9.

To find the next two common denominators, we can continue to find the LCM of the denominators with the added factor of 9.

The prime factorization of 18 (2 x 3 x 3) includes the prime factors of 9, so it is a common denominator.

The prime factorization of 27 (3 x 3 x 3) also includes the prime factors of 9, so it is another common denominator.

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The total price for paint with an 8.5% sales tax is $69.02928.

The space enclosed by the boundary of a plane figure is called its area. The area of a figure is the number of unit squares that cover the surface of a closed figure.

Given:

Length = 14 feet

width = 17 feet

Height = 9 foot

So, the area of Four walls

= 2(14 x 9) + 2( 17 x 9)

= 2 x 126 + 2 x 153

= 252 + 306

= 558

Now, Area of ceiling

= lw

= 14 x 17

= 238

So, the total Area = 558 + 238 = 796

Now, the cost of painting room

= 796/350 x 28

= 63.68

and, After sales tax

= 63.68 + 0.085 x 63.68

= $69.02928

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Exponential functions are mathematical functions that involve an exponent or power. There are two types of exponential functions: growth and decay.

1. Exponential Growth Functions: These functions have the form y = a*b^x, where a > 0 and b > 1. They model exponential growth, where the value of y increases rapidly as x increases. For example, the function y = 2^x is an exponential growth function, as the value of y doubles for each increase in x.

2. Exponential Decay Functions: These functions have the form y = a*b^x, where a > 0 and 0 < b < 1. They model exponential decay, where the value of y decreases rapidly as x increases. For example, the function y = (1/2)^x is an exponential decay function, as the value of y is halved for each increase in x.

Both types of exponential functions are important in many fields, including finance, biology, and physics. They are used to model phenomena such as compound interest, population growth, and radioactive decay.

The given function[tex]Y=20(1+0.025)^x[/tex]  is an exponential gr.

What is an exponential function?

An exponential function is a mathematical function of the form [tex]f(x) = a^x[/tex], where "a" is a constant and "x" is the input variable. These functions are commonly used to model situations that involve continuous growth or decay.

In the given example you provided[tex]Y=20(1+0.025)^x[/tex] represents growth because the base of the exponential term, 1+0.025, is greater than 1. As x increases, the exponential term gets larger and the value of y increases, which indicates growth.

Hence, the given function,[tex]Y=20(1+0.025)^x[/tex]  is exponential growth.

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The probability that a continuous random variable equals any of its values is called Continuous probability distribution.

Continuous probability distribution:

A probability distribution in which the random variable X can take on any value (which is continuous). Since there are infinitely many possible values ​​for X, the probability that X takes on any particular value is zero. So we often talk about a range of values ​​[p(X >0] = 0.50).

An absolutely continuous probability distribution is a probability distribution of real numbers with an uncountable set of possible values, such as the full interval of a solid line, where the probability of any event can be expressed as an integral. More precisely, there exists a function f: R − [0, so that for each interval[ 0,∞] ⊂ R, the probability that X belongs to [a, b] is given by the integral of f over I.

[tex]P(a\leq X\leq b) = \int\limits^a_b {f(x)} \, dx[/tex]

Since this is the definition of a probability density function, an absolutely continuous probability distribution is exactly equivalent to a probability density function. In particular, the probability that X takes any single value a (i.e. a≤X≤b) is zero because integrals with the same upper and lower bounds are always zero. If the interval [a, b] is replaced by the measurable set A, then the equivalence remains valid.

P(X ∈ A) = [tex]\int\limits^a_b {f(x)} \, dx[/tex]

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The mean and variance of the number x of unusable fasteners in a randomly selected box are about 150 and 150 respectively.

Poisson distribution is a distribution function useful for characterizing events with very low probabilities of occurrence within some definite time or space. It is used when the number of trials is very large and the probability of success is comparatively small.

In Poisson distribution, the mean is defined as:

λ = np

where n = number of items and p = probability of success

Given: n = 5000 and p = 3/100 = 0.03

Thus,  λ = np = 5000 * 0.03 = 150

Since the mean and variance are equal in Poisson distribution. Thus, the variance (σ²) =  150

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The inequalities representing the two lines are y ≤ 3x + 8 and y < - 2x - 8.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

The two lines can be obtained by identifying the points.

(0, - 8) and (1, - 10) are the points of the non-dotted line.

So, m = (- 10 + 8)/(1 - 0).

m = - 2.

Now, - 8 = 0(-2) + b.

b = - 8.

y = - 2x - 8.

The points for the dotted line are, (0, 8) and (1, 11).

m = (11 - 8)/(1 - 0).

m = 3

8 = 3(0) + b.

b = 8.

y = 3x + 8.

The dotted line is y ≤ 3x + 8 and the non-dotted line is y < - 2x - 8.

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93 centimeter is approximately equal to 36.6142 inches ( rounded to four decimal places )

To convert 93 cm to inches, we can use the following formula:

1 cm = 0.393701 inches

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

Therefore,

The length in inches = conversion factor × The length in centimeter

Substitute the values in the equation

93 cm = 93 x 0.393701

Multiply the numbers

= 36.6142 inches ( rounded to four decimal places )

Therefore, 93 centimeter is 36.6142 inches

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The sequence of transformations performed by Isabella is Rotate 90° clockwise about the origin; translate 10 units down.

A transformation is a process that manipulates a polygon or other two-dimensional object on a plane or coordinate system.

Given that, Luther drew on his graph paper. After performing a series of transformations, Isabella drew. we need to find the transformations performed by Isabella,

We see, that, the sequence performed by Isabella is a rotation of 90°, from the origin, also the image is 10 units down to the original figure.

Hence, the sequence of transformations performed by Isabella is Rotate 90° clockwise about the origin; translate 10 units down.

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The complete question :-

The scalars c1 = 2/5, c2 = -3/5, and c3 = -8/5 satisfy the equation:

c1M1 + c2M2 + c3M3 = [ 2 3 ][ 1 2 ]

We want to find the scalars c1, c2, and c3 such that:

c1M1 + c2M2 + c3M3 = M

Substituting the given matrices:

c1[ 2 2 ] c2[ -1 1 ] c3[ 1 2 ] [ 2 3 ]

[ 1 1 ] [ 2 1 ] [ 3 1 ] [ 1 2 ]

Multiplying each scalar by its corresponding matrix:

[ 2c1 - c2 + c3 2c1 + 2c2 + 3c3 ]

[ c1 + 2c2 + 3c3 c1 + c2 + 2c3 ]

Setting the result equal to M:

[ 2c1 - c2 + c3 2c1 + 2c2 + 3c3 ] = [ 2 3 ]

[ c1 + 2c2 + 3c3 c1 + c2 + 2c3 ] [ 1 2 ]

This gives us two equations:

2c1 - c2 + c3 = 2

2c1 + 2c2 + 3c3 = 3

c1 + 2c2 + 3c3 = 1

c1 + c2 + 2c3 = 2

We can solve this system of equations using any method we prefer, such as elimination or substitution. Here, we will use elimination.

Subtracting the first equation from the second, we get:

3c2 + 4c3 = 1

Subtracting the third equation from fourth, we get:

c2 - c3 = 1

Multiplying second equation by 2, we get:

4c1 + 4c2 + 6c3 = 6

Subtracting first equation from this, we get:

5c2 + 5c3 = 4

Now we have three equations for c2 and c3:

3c2 + 4c3 = 1

c2 - c3 = 1

5c2 + 5c3 = 4

Solving for c2 and c3 using elimination, we get:

c2 = -3/5

c3 = -8/5

Substituting these values into the third equation, we get:

c1 = 2/5

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All five answers are (1) 285.7 ft2 (2) 1056 cm2 (3) 105 mm3 (4) 108 cm3 (5) 628 mm3 in accordance with the provided assertion.

In mathematics, volume refers to the amount of space present within a specific 3D object. As an example, the dimensions of a fish aquarium are three feet long, one foot broad, and two feet height.

By increasing the length, width, and height, or 3x1x2, which also equals six, the volume is determined. Consequently, the fish tank has a 6 cubic foot size.

(1) The lateral area of a cone can be calculated using the formula L = πrℓ, where r is the radius and ℓ is the slant height. Using the given values, we have:

L = π(7)(13) ≈ 285.7 ft²

Rounding to the nearest tenth, the answer is 285.7 ft².

(2) A = B + (1/2)Pl, where B is the base area, P is the base circumference, l is the slope height, and A is the surface area, can be used to determine the surface area of a square pyramid. Since the pyramid's foundation is square, we have:

B = (24)² = 576 cm²

The perimeter of the base is 4 times the base length, so we have:

P = 4(24) = 96 cm

Now we can use the formula to find the surface area:

A = 576 + (1/2)(96)(16) = 1056 cm²

Therefore, the surface area of the square pyramid is 1056 cm².

(3) The volume of a rectangular prism can be calculated using the formula V = lwh,

where

l is the length

w is the base

h is the height

V is the volume.

Substituting the given values, we have:

V = (5)(7)(3) = 105 mm³

Therefore, the volume of the rectangular prism is 105 mm³.

(4) The formula V = (1/3)Bh, where B is the base area, h is the height, and V is the volume, can be used to determine the volume of a square pyramid. Since the pyramid's foundation is square, we have:

B = (9)² = 81 cm²

Now we can use the formula to find the volume:

V = (1/3)(81)(4) = 108 cm³

Therefore, the volume of the square pyramid is 108 cm³.

(5) The volume of a cone can be calculated using the formula V = (1/3)πr2h, where r is the radius, h is the height, and V is the volume. Substituting the given values, we have:

V = (1/3)π(10)²(6) ≈ 628.3 mm³

Rounding to the nearest whole number, the answer is 628 mm³.

Therefore, the volume of the cone is 628 mm³.

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3x=108

and y= 54

by linear pair angle

Answer:

[tex] \sf \: a) \: 2x + 7y - 2 [/tex]

[tex] \sf \: c) \: 7y - 2 + 2x [/tex]

Step-by-step explanation:

Now we have to,

→ Simplify the given expression.

The expression is,

→ -2x + 3 + 7y + 4x - 5

Let's simplify the expression,

→ -2x + 3 + 7y + 4x - 5

→ -2x + 4x + 7y + 3 - 5

→ (-2x + 4x) + (7y) + (3 - 5)

→ (2x) + 7y + (-2)

→ 2x + 7y - 2

→ 7y - 2 + 2x

Hence, option (a) & (c) is correct.

Step-by-step explanation:

-2x + 3 + 7y + 4x - 5 = 2x + 7y - 2

as addition is commutative (= can be done in any sequence of terms), the right answers are variations in the sequence of these 3 terms :

A and C are correct.

B and D disqualify themselves right away by including mixed terms of xy. you can never ever create such a mixed term just out of addition or subtraction of single x and y terms. you need multiplication to do that. but there is none.

Answer:

We can use the following logarithmic identities to simplify the expression:

log a + log b = log (ab)

log a - log b = log (a/b)

n log a = log (a^n)

Using these identities, we can simplify the expression as follows:

1/2(log₂x + log₂y) - 5 log₂(x+6)

= 1/2 log₂(xy) - log₂(x+6)^5 (using the first two identities)

= log₂[(xy)^(1/2)/(x+6)^5] (using the third identity to combine the logarithms)

Therefore, the simplified expression is:

log₂[(xy)^(1/2)/(x+6)^5]

Step-by-step explanation: