Find the distance between point k and point L

The radius of the sphere  1.5  units

The volume of the cone is   pi (3)^2 *4 / 3   units^3  =  12pi  units^3

The volume of the sphere is (4/3)pi (1.5)^3  units^3 = 4.5 units^3

So   ratio  of the volume of the sphere to the cone is :

4.5 pi  / 12 pi  =    4.5 / 12  =      (9/2) / (24/2)  =  9 / 24  =  3 / 8

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The required expression that has the coefficient 4 is 4x⁵. Option B is correct.

The expression is the relationship between variables and represented as y = ax + b is an example of a polynomial expression.

here,
Since the question seems to be incomplete,
A standard question can be given as,
Among the following option find the expression that has a coefficient of 4.
(a) 2x + 1
(b) 4x⁵
(c) ax⁶
(d) 7x²

Since the coefficient is the value present at the prefix of the variable term,
So the variable term that holds the coefficient 4 is 4x⁵.

Thus, the required expression is 4x⁵. Option B is correct.

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On solving the provided question, we can say that - The provided arithmetic sequence's 66th term is -950.

An arithmetic sequence is a set of integers that are ordered and have a common difference between each following word.An ordered group of integers with a shared difference between each word is known as an arithmetic sequence.

The given arithmetic sequence is,

25, 10, -5, .....

The sequence's initial word, a, equals 25, while the common difference, d, equals -15.

Use the formula nth term of arithmetic series = a+ (n-1)d to determine the 66th term of the sequence.

66th term =

[tex]25 + (66-1)(-15)\\ = 25 + 65× (-15)\\ = 25 - 975\\ = -950\\[/tex]

The 66th term of the arithmetic sequence is -950.

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Answer:

[tex]x=-6, 0[/tex]

Step-by-step explanation:

Using the zero-product property, we know that [tex]x=0[/tex] or [tex]x+6=0[/tex].

This means [tex]x=-6, 0[/tex].

A problem is just a function or even a mapping of inputs to outputs. An algorithm is a recipe for solving a problem with concrete and unambiguous steps.

In mathematics and computer science, an algorithm is a finite sequence of rigorous instructions used to solve a class of specific problems or perform a computation.

Algorithms are data calculation and processing specifications. More advanced algorithms can use conditionals to divert code execution through various paths (referred to as automated decision-making) & deduce valid inferences (referred to as automated reasoning), eventually achieving automation.

Alan Turing used metaphorical terms like "memory", "search," and "stimulus" to describe machines.

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Answer:

yes

Step-by-step explanation:

The word linear is used for a straight line. A linear function is a function of a straight line, which means that the degree of a linear function must be 0 or 1 . In this case, The degree of f(x)=2x−3 f ( x ) = 2 x - 3 is 1 , which makes the function a linear function.

The number of  pastries will be offered in one year could be 26 and the algebraic expression could be  x = 2 + 2y

What is Arithmetic progression ?

Arithmetic progression could be defined as the sequence of number where the difference between two consecutive number is same.

Given,

Mamas bakery just opened and is currently selling only two types of pastry.

Each month mamas bakery will add two more types of pastry to their menu.

let the number of pastries be x.

let y be the given number of pastries.

Hence the algebraic expression could be

x = 2 + 2y

Number of pastries will be offered in one year could be

x = 2 + 2 * 12

x = 26

Hence, the number of  pastries will be offered in one year could be 26 .

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So Cheng must purchase 32 cubic feet of sculpting material.

Each pyramid has a square base with edge length of 2 feet and a height of 6 feet. The area of the square base is (2 feet)^2 = 4 square feet. The volume of each pyramid is 1/3 * base area * height = 1/3 * 4 square feet * 6 feet = 8 cubic feet.

Since there are four identical pyramids in the sculpture, the total volume of material needed to create the sculpture is 4 * 8 cubic feet = 32 cubic feet. So Cheng must purchase 32 cubic feet of sculpting material.

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Answer:

D

Step-by-step explanation:

The area of the shaded region is, 201.0 cm².

What is circle?

A circle is a closed, two-dimensional figure in which all points in the plane are equally spaced apart from the center. The symmetry line of reflection is formed by each line that traverses the circle. Additionally, it is rotationally symmetric around the center for all angles.

In the given figure we have to find the area of the shaded region.

First to find the area of circle with radius 10cm.

Area of circle = [tex]= \pi r^2 = 3.14*(10)^2 = 3.14*100 = 314cm^2[/tex]

Now to find the area of circle with radius 6cm.

Area of circle = [tex]= \pi r^2 = 3.14*6^2=3.14*36 = 113.04 cm^2[/tex]

So, the area of the shaded region is,

[tex]314cm^2 - 113.04cm^2 = 200.96cm^2=201.0cm^2[/tex]

Hence, the area of the shaded region is, 201.0 cm².

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The point(s) on the surface at which the tangent plane is horizontal are (0, 0, 1).

To find the point(s) on the surface at which the tangent plane is horizontal, we need to find the points at which the partial derivatives of z with respect to x and y are both equal to 0. This means we need to solve the system of equations:

Solving this system of equations yields x = 0, y = 0, and z = 1. Therefore, the point(s) on the surface at which the tangent plane is horizontal is (0, 0, 1).

To understand why solving the system of equations yields the points for which the tangent plane is horizontal, it is important to understand what the partial derivatives represent. The partial derivative of z with respect to x is the rate of change of z with respect to x, and similarly for y.

When the partial derivatives are both equal to 0, it means that the rate of change of z with respect to x and y is 0, which implies that the tangent plane is horizontal.

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The block weighed 8 grams. The other two blocks average have weighed the same amount as the first block, so they also weighed 8 grams each.

1. Joe has three metal blocks.

2. The weight of each block is the same.

3. Joe weighed one of the blocks against 8 grams.

4. The block weighed 8 grams.

5. The other two blocks must have weighed the same amount as the first block, so they also weighed 8 grams each.

Joe had three metal blocks that all weighed the same. He weighed one of the blocks against 8 grams, and it weighed exactly 8 grams. This meant that the other two blocks must also have weighed 8 grams each, since the weight of all three was the same. Joe was able to determine the weight of all three blocks with just one measurement.

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The solution to the exponential equation 8^(x/2)/4^(x/3) = 2^(-5/2) is given as follows:

x = -6/5.

The exponential equation for this problem is defined as follows:

[tex]\frac{8^{\frac{x}{2}}}{4^{\frac{x}{3}}} = 2^{-\frac{5}{2}}[/tex]

Both 8 and 4 are powers of 2, as follows:

Applying the power of power rule (multiplying the exponents), the expression on the left side can be rewritten as follows:

[tex]\frac{2^{\frac{3x}{2}}}{2^{\frac{2x}{3}}} = 2^{-\frac{5}{2}}[/tex]

When two terms with the same base and different exponents are divided, we keep the base and subtract the exponents, hence:

[tex]\frac{2^{\frac{3x}{2}}}{2^{\frac{2x}{3}}} = 2^{\frac{3x}{2} - \frac{2x}{3}}[/tex]

The subtraction is obtained as follows:

3x/2 - 2x/3 = 9x/6 - 4x/6 = 5x/6.

(as the least common factor of 2 and 3 is of 6).

Then the simplified expression is of:

[tex]2^{\frac{5x}{6}} = 2^{-\frac{5}{2}}[/tex]

As the exponential function y = 2^x is injective, the solution is obtained as follows:

5x/6 = -5/2.

10x = -12

x = -6/5.

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Answer:

Laura has "n" amount of nickels. She receives 75 more from her grandmother.

Explanation:

(If this is not what the question meant, please let me know!)

Because the question is asking us to write a sentence for an addition problem, we need to write a sentence that involves two amounts of one thing being combined, in this case nickels.

0.27 is the experimental probability of selecting a green marble.

It is a branch of mathematics that deals with the occurrence of a random event.

Given that Michael has a bag of marbles.

The frequency of selecting each color is recorded  

Outcome Frequency

Green 4

Black 6

Orange 5

The total number of marbles are 4+6+5=15 marbles.

We need to find the experimental probability of selecting a green marble.

We need to select green marbles (4) from total marbles (15).

Probability=4/15=0.266=0.27

Hence, 0.27 is the experimental probability of selecting a green marble.

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The probabilities are given as follows:

a) No injuries: 0.4493 = 44.93%.

b) More than two injuries: 0.0474 = 4.74%.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following equation:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

The parameters are:

The mean for this problem is of:

[tex]\mu = 0.8[/tex]

The probability of no injuries is of P(X = 0), hence:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-0.8}(0.8)^{0}}{(0)!} = 0.4493[/tex]

The probability of more than two injuries is of:

P(X > 2) = 1 - P(X <= 2)

In which:

P(X <= 2) = P(X = 0) + P(X = 1) + P(X = 2)

Hence:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-0.8}(0.8)^{0}}{(0)!} = 0.4493[/tex]

[tex]P(X = 1) = \frac{e^{-0.8}(0.8)^{1}}{(1)!} = 0.3595[/tex]

[tex]P(X = 2) = \frac{e^{-0.8}(0.8)^{2}}{(2)!} = 0.1438[/tex]

Then:

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The steps for measuring the angle b is shown below, <b= 41.

If a triangle side is created, the outside angle that results is equal to the sum  of the two opposite internal angles.

If an equivalent angle is measured at each triangle vertex, the exterior angles always add up to 360 degrees.

Given:

exterior angle = 113

and, opposite interior angle =72

Using Exterior angle property we have

72 + b = 113

Subtract 72 from both side

72 + b -72 = 113 -72

b = 113- 72

b = 41

Hence, the measure of b is 41 degree.

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Answer:

6[tex]x^{2}[/tex] + 1

Step-by-step explanation:

[tex]\frac{6x^{3}+ 2x-x }{x}[/tex]   combine 2x -x = x

[tex]\frac{6x^{3} + x}{x}[/tex]

[tex]\frac{x(6x^{2} + 1) }{x}[/tex]  the x's cancel out

6[tex]x^{2}[/tex] + 1

The real and complex solutions of the polynomial equation are 2,-3i and 3i

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables

The given polynomial is x³-2x²+9x-18

Factor out x² from  x³-2x² which becomes  x²(x-2)

Factor out 9 from 9x-18 which becomes 9(x-2)

x³-2x²+9x-18

x²(x-2)+9(x-2)

Factor out common term x-2

( x²+9)(x-2)=0

x²+9=0

x=-3i and 3i

x-2=0

x=2

Hence, the real and complex solutions of the polynomial equation are 2,-3i and 3i

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The p-value of the test statistic is p-value = 0.006. The null hypothesis will be rejected at 5% level of significance.

A two-tailed test in statistics determines if a sample is more than or less than a specific range of values by using a two-sided critical area of a distribution. It is employed in testing the null hypothesis and determining statistical significance. The alternative hypothesis is accepted in place of the null hypothesis if either of the critical areas apply to the sample under test.

A two-tailed test in statistics determines if a sample is greater or less than a range of values by using a two-sided critical area of a distribution.

It is employed in testing the null hypothesis and determining statistical significance.

The alternative hypothesis is accepted in place of the null hypothesis if either of the crucial areas apply to the sample under test.

Conventionally, two-tailed tests with a 2.5% cutoff on each side of the distribution are employed to evaluate significance at the 5% level.

How to calculate the p-value?

Determine the level of relevance, sometimes referred to as the level, in step one. Assume 0.05 if it isn't specified. Step 2: Evaluate the level of significance in relation to the p-value. Make the conclusion that supports the possible change and reject the null hypothesis if the p-value is lower.

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Equivalent function has the same domain and range. Equivalent and equal terms are not the same both have different meanings in mathematics.

A function is said to be equal if its Domain and Range are identical. Complete solution, step by step: A and B should be two sets. Now, by function, we mean a rule that guarantees that f(a)=b exists for all a. As a result, set A is referred to as the Domain of File and set B as the Range Off.

Despite being comparable to 1 + 1, 2 is believed to be equal to 2. When two items or amounts are exactly the same, as when 12 is equal to 12, yet 12 is equivalent to 2/4 since they reflect the same value, we can say that they are equal.

In mathematics, an equivalent can be defined in one of two ways. This is thus because there are various definitions for the concept of equivalent in mathematical theory. Equivalent refers to the mathematical notion that distinct terms and expressions having a similar value are treated equally.

Equivalent is not the same as equal in mathematics. While equivalent indicates similar but not the same, equal means the same in all respects.

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50-50-80 is a Isosceles acute triangle.

An isosceles acute triangle is a triangle in which all three angles are less than 90°, and at least two of its angles are equal in measurement. One example of the angles of an isosceles acute triangle is 50°, 50°, and 80°.

Properties of Isosceles Acute Triangle

It is easy to point to an isosceles acute triangle if we know its properties. The properties of the isosceles acute triangle are noted below:

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Answer:

120x - 96y + 32

Step-by-step explanation:

12 (10x + 3 -8y)

We use the distributive property to solve

120x - 96y + 32

One of the most important when writing the order of an equation is always written the number with the variable first; that is why the answer is

120x - 96y + 32

34.7 is the monthly phone use will Plan A cost no more than Plan B and 2.1 is the value of m in the inequality.

a relationship between two expressions or values that are not equal to each other is called 'inequality.

In Plan A, the customer pays a monthly fee of $20 and then an additional 7 cents per minute of use

20+7m

In Plan B, the customer pays a monthly fee of $26.30 and then an additional 4 cents per minute of use

26.3+4m

We need to find the amounts of monthly phone use will Plan A cost no more than Plan B

20+7m<26.3+4m

7m-4m<26.3-20

3m<6.3

m<2.1

Hence, 34.7 is the monthly phone use will Plan A cost no more than Plan B and 2.1 is the value of m in the inequality.

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A statement which correctly describes the solution set of the given inequality include the following: C. all rational-number values of n that are at least 0.5.

In Mathematics, a rational number can be defined a type of number which comprises fractions, integers, terminating or repeating decimals such as the 12, 0.5, √16, etc.

Next, we would translate the word problem into algebraic inequality and then solve for the value of n as follows;

5n + 1.5 ≥ 4

Subtracting 1.5 from both sides of the algebraic inequality, we have:

5n + 1.5 - 1.5 ≥ 4 - 1.5

5n ≥ 2.5

Dividing both sides of the algebraic inequality y 5, we have:

n ≥ 2.5/5

n ≥ 0.5

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In simplest radical form as A = 22 = 4 cm2

The formula for the volume of a cube is V = a3, where a is the length of each of the cube's sides. In this case, we know that the volume of the cube is 8 cm3, so a3 = 8. When we take the cube root of 8, we get that a = 2 cm.

Therefore, the area of the rectangle formed by the intersection of the plane and cube is A = 2*2 = 4 cm2. This can also be expressed in simplest radical form as A = 22 = 4 cm2.

To calculate this step by step, we first use the formula V = a3 to find the length of each side of the cube. We plug in 8 cm3 for V and solve for a.

V = a3

8 cm3 = a3

Taking the cube root of both sides gives us:

a = ∛8

a = 2 cm

Next, we use the formula for the area of a rectangle, A = l*w, where l is the length and w is the width. We know that the length and width of our rectangle are both equal to 2 cm.

A = l*w

A = 2*2

A = 4 cm2

This can also be expressed in simplest radical form as A = 22 = 4 cm2.

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The way to find the horizontal asymptote of the limit is evaluate the limit of the function as it approaches infinity, and again as it approaches negative infinity.

The term asymptote in math is defined as  a line that the graph of a function approaches as either x or y go to positive or negative infinity.

Here we have to find the horizontal asymptote of a limit.

The process of finding the horizontal asymptote is the line y = 0 is called the asymptote of the graph, and it also represents the value that f(x) will never quite reach.

Here we can also say that f ( x ) = 1 x is asymptotic to the line y = 0.

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The length of each piece of wood needed to build each brace of the bookcase will be 4.24 feet.

Based on the dimensions, the shape of bookcase is square. So the diagonal of the bookcase will be calculated from the formula -

Diagonal = ✓side² + side²

Keep the values in formula to find the value of diagonal

Diagonal = ✓ 3² + 3²

Taking square on Right Hand Side of the equation

Diagonal = ✓9 + 9

Performing addition on Right Hand Side of the equation

Diagonal = ✓ 18

Finding square root on Right Hand Side of the equation

Diagonal = 4.24 feet

Thus, each diagonal will be 4.24 feet.

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Answer: x=(y+9)5−32 simplified

Step-by-step explanation: