Which expression has the greatest−−−−−−−
value?


93/2


82/3


45/2

The general formula for all solutions of t, by adding multiples of some positive integer n, is:

t = 1 + 6k - 6n

What is the Trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships and properties of angles and triangles.

To find the values of t for which the ball is 1 inch above its rest position, we can set the value of d in the equation d = 2cos(π/3t) to 1, and then solve for t.

2cos(π/3t) = 1

Divide both sides by 2 to isolate the cosine term:

cos(π/3t) = 1/2

To find the general formula for all solutions by adding multiples of some positive integer n, we can use the periodicity of the cosine function. The cosine function has a period of 2π, which means that its values repeat every 2π units.

Therefore, we can add multiples of 2π to the angle π/3t and still obtain the same value for cosine.

cos(π/3t + 2πn) = 1/2

where n is any positive integer.

Now we can solve for t by taking the inverse cosine of both sides:

π/3t + 2πn = arccos(1/2)

π/3t + 2πn = π/3 + 2πk (using the fact that arccos(1/2) = π/3 and k is any integer)

π/3t = π/3 + 2πk - 2πn

t = 1 + 6k - 6n

Hence, the general formula for all solutions of t, by adding multiples of some positive integer n, is:

t = 1 + 6k - 6n

where k and n are any integers.

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tan = 1/√3= perpendicular/ base

1/√3 = AB / AC

AB / 6 = 1/√3

AB = 6/√3

The function that models the relationship between the number of students enrolled, f(x) and the number of years after 2015, x,  is D. f(x) = 3000(0.98)*.

Mathematically, a function defines a mathematical relationship or an algebraic expression involving one variable (the independent variable) and another variable (the dependent variable).

There are four main types of mathematical functions, including:

The number of students enrolled in 2015 = 3,000

The annual decrease in students enrollment = 2%

Let f(x) the model modeling the relationship between the number of students enrolled and the number of years after 2015.

Let the number of years after 2015 = x.

Thus, the correction function is D. f(x) = 3000(0.98)*.

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Assuming the time begins after the car is fully accelerated to 64 mph, 4 hours 45 minutes

IG:whis.sama_ent

Simplifying this fraction gives us 1/4. The answer is (D) 1/4.

What is arithmetic sequence?

An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term.

Let's start by finding the fraction of Michelle's patients who are under 12 or over 65. We know that one-third of her patients are under 12, so two-thirds must be 12 or older. Similarly, five-twelfths of her patients are over 65, so seven-twelfths must be 65 or younger.

Now, we want to find the fraction of Michelle's patients who are between 12 and 65. To do this, we need to subtract the fraction of patients who are under 12 or over 65 from 1 (since these are the only two age groups we're considering).

Fraction of patients under 12: 1/3

Fraction of patients over 65: 5/12

Fraction of patients 12 to 65: 1 - 1/3 - 5/12

We can simplify this expression by finding a common denominator:

Fraction of patients 12 to 65: 12/12 - 4/12 - 5/12

Fraction of patients 12 to 65: 3/12

Simplifying this fraction gives us 1/4. Therefore, the answer is (D) 1/4.

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Answer:

Step-by-step explanation:

just add the two numbers up 576x1 1/2= 864

The height is 3 units.

We have,

l = 4 and b= 3

Using Pythagoras theorem

d² = l² + b²

d² = 4² + 3²

d² = 16 + 9

d² = 25

d= 5 unit

let h be the height.

Again, using Pythagoras theorem

34 = 25 + h²

h² = 9

h= 3 unit

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The logarithmic form of the given exponential equation in the question,     4³ = (5x + 4) is Log₄ (5x + 4) = 3.

The exponential-to-logarithmic format is useful because it makes it easy to compute large numeric expressions. Expressions involving exponential multiplication and division can be converted to addition and subtraction by applying logarithms. Logarithmic exponential form is a common means of converting mathematical expressions in one form to another form.

The exponential form aˣ = N is transformed and written logarithmically as LogₐN = x.

The exponential form of a for the exponent of x equal to N is converted to the logarithm of the number N in base a, equal to x.

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1.) The probability of rolling two even numbers would be = 1/4

2.) The probability of rolling one even and one odd number = 1/2

3.) The probability of flipping tails on a coin and by rolling a factor of 6 on a six sided die would be = 1/3

To calculate the probability the formula that should be used is given as follows;

probability = possible outcome/sample space

For question 1.):

Sample space when two dice are thrown = 36

possible outcome = (2,2),(2,4),(2,6),(4,2),(4,4),(4,6),(6,2),(6,4),(6,6)= 9

Probability = 9/36 = 1/4

For question 2.)

Sample space when two dice are thrown = 36

possible outcome = 18

probability = 18/36 = 1/2

for question 3.)

Sample space when two dice are thrown = 12

possible outcome = 4

probability = 4/12 = 1/3

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Question A) A 99% confidence interval estimate of his population mean finishing time of 100 meters race is (12.8081,15.5919)

Question B) Option II) narrower is the correct Option.

Let X be the time required to finish 100 meters race competition with Tom ( in seconds.)

A) A 99% confidence interval estimate of his population mean finishing time of 100 meters race is (12.8081,15.5919)

x = 14.2

s^2= 0.9867

s= 0.9933

t \aplha/2, n-1 = 3.7074

Margin of error= 1.3919

lower bound= 12.8081

upper bound= 15.5919

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The correct answer is: A. Y intercept will be less and X will be less.

A linear function's slope is a gauge of how steep the line is. Between any two points on the line, it is the ratio of the change in the y-coordinate to the change in the x-coordinate. The formula is used to compute it:

slope equals (y2 - y1)/. (x2 - x1)

where any two points on the line (x1, y1) and (x2, y2) are.

The company's expenses will rise once it begins paying a driver at a rate of 0.25 cents per mile, which means its profit will decline. The profit curve on the y-axis will go vertically downward as a result of this. But, because the cost of paying the driver is fixed per mile and has no impact on the profit per mile, the slope of the line—which reflects the profit per mile—will stay the same.

Hence, A. Y intercept will be less and X will be less is correct.

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Basically M will be equal to T if the value of M is assigned to T or vice-versa.

The equality of numbers refers to a mathematical concept that indicates that two numbers are the same. When two numbers are equal, they represent the same quantity, and we can use the symbol "=" to indicate this relationship. For example, "2 + 3 = 5" indicates that the sum of 2 and 3 is equal to 5. Similarly, "7 = 7" indicates that the number 7 is equal to itself.

The concept of equality is a fundamental concept in mathematics and is used extensively in various mathematical operations and equations. We can use the concept of equality to compare two or more numbers, variables, expressions, and equations.

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1) probability that Ed will answer all 6 questions correctly is approximately 0.00024.

2) probability that Ed will answer exactly 2 questions correctly is approximately 0.29663.

3) probability that Ed will answer at least 2 questions correctly is approximately 0.46606.

What is Probability?

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

1) Probability of answering 6 questions correctly:

Since there are 4 choices for each question, the probability of guessing the correct answer for a single question is 1/4.

P(6 correct) = [tex](1/4)^{6}[/tex] = 0.00024414 ≈ 0.00024

So the probability that Ed will answer all 6 questions correctly is approximately 0.00024.

2) Probability of answering exactly 2 questions correctly:

The probability of guessing exactly 2 questions correctly can be calculated using the binomial probability formula:

P(exactly 2 correct) = (6 choose 2) * (1/4)² * [tex](3/4)^{4}[/tex]

P(exactly 2 correct) ≈ 0.29663

So the probability that Ed will answer exactly 2 questions correctly is approximately 0.29663.

3) Probability of answering at least 2 questions correctly:

P(at least 2 correct) = P(2 correct) + P(3 correct) + P(4 correct) + P(5 correct) + P(6 correct)

P(k correct) = (6 choose k) * [tex](1/4)^{k}[/tex] * [tex](3/4)^{(6-k)}[/tex]

where k can be 3, 4, or 5.

P(at least 2 correct) ≈ 0.46606

So the probability that Ed will answer at least 2 questions correctly is approximately 0.46606.

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The weight of the diamonds in each lot is 4.9 pounds.

Here, the fractional idea can be used. A fraction represents a portion of a total. A fraction is a numerical figure that designates a portion of a whole. A fraction is a component or section taken from a whole, which can be any number, a certain value, or an object.

A cargo of half a pound's worth of diamonds was received by a diamond trader. He separated the stones into 4 equal lots and sold them to jewelers so they could be used to make necklaces and rings.

Total shipment = 7/10 pound

number of equal lots = 7

then,   7 x weight = 7/10

weight = 4.9

Therefore, the weight of each lot is 4.9 pounds.

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Answer:

it would be C

Step-by-step explanation:

The expression 8×2 can be used to find the total number of head wraps on the shelf when there are 8 head wraps per shelf and 2 shelves in total, resulting in a total of 16 head wraps.

Expression in mathematics is a combination of symbols and numbers, often using an operation, such as addition, subtraction, multiplication, or division. It can represent a number, a variable, a function, or a mathematical statement. It can also represent a combination of these things. Expressions are used to describe relationships between numbers, variables, and mathematical concepts.

The expression 8×2 can be used to find the total number of head wraps on the shelf when there are 8 head wraps per shelf and there are 2 shelves in total. This expression can be used to calculate the total number of head wraps on the shelves by multiplying 8 (the number of head wraps per shelf) by 2 (the number of shelves). As such, the expression 8×2 can be used to find the total number of head wraps on the shelf when there are 8 head wraps per shelf and 2 shelves in total, resulting in a total of 16 head wraps.

In conclusion, the expression 8x2 can be used to calculate the total number of head wraps on the shelf when there are 8 head wraps per shelf and 2 shelves in total. By multiplying 8 (the number of head wraps per shelf) by 2 (the number of shelves), the total number of head wraps on the shelf can be found, resulting in a total of 16 head wraps.

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Complete questions as follows-
In which situation can the Expression
on 8×2 be used to find the total number of head wraps on the shelf?

Therefore, **x < 7** is the inequality that may be utilized to find x

A mathematical statement known as an inequality compares two expressions using an inequality sign, such as (less than), > (greater than), or (less than or equal to).

For instance, the inequality x + 2 5 signifies that "x + 2 is less than 5".

Let x represent how many days the client paid for pet sitting.

$15 per day plus a $20 fixed service fee equals the total cost of pet sitting.

We are aware that the customer's purchase was under $125. Consequently, we can write:

20 + 15x < 125

Putting this disparity simply:

15x < 105

x < 7

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To find the specified scalar, we need to first find the dot product of U and V, and then the dot product of U and W, and add these two dot products together:

U·V + U·W

where U·V denotes the dot product of U and V, and U·W denotes the dot product of U and W.

The dot product of two vectors a = (a1, a2) and b = (b1, b2) is given by:

a · b = a1b1 + a2b2

Using this formula, we can find the dot product of U and V:

U · V = (4i - j) · (5i + j) = 4i · 5i + 4i · j - j · 5i - j · j = 20i^2 + (4i · j - 5i · j) - j^2 = 20 + (-i · j) - 1 = 19 - i · j

Next, we can find the dot product of U and W:

U · W = (4i - j) · (i + 6j) = 4i · i + 4i · 6j - j · i - j · 6j = 4i^2 + (4i · 6j - j · i) - 6j^2 = 4 + (24i · j) - 6 = -2 + 24i · j

Now we can substitute these values into the original expression:

U·V + U·W = (19 - i·j) + (-2 + 24i·j) = 17 + 23i·j

Therefore, the specified scalar is 17 + 23i·j.

Step-by-step explanation:

You are given the formula for surface area of the cone

  r = 7 cm     l = 13 cm

Sooooo  ...just plug the numbers into the formula :

SA = pi (7^2)  + pi (13)(7)     =

      =  22/7 * 49  + 22/7 * 13 * 7 = 440 cm^2

The probability of choosing 5 CDs in alphabetical order out of a collection of 23 CDs is approximately 0.00003 or 0.003%.

What is combination?

In mathematics, a combination is a way of selecting objects from a larger group of objects, where the order of selection is not important. A combination is a subset of objects that are chosen from a larger set without regard to the order in which they are selected.

The formula  is given by:

C(n, r) = [tex]\frac{n!}{r!* (n - r)!}[/tex]

The total number of ways to choose 5 CDs from a collection of 23 CDs is given by the combination formula:

C(23, 5) = [tex]\frac{23!}{5!* (23 - 5)!}[/tex]

             = 33649

This means there are 33649 different ways to arrange 5 CDs out of the 23 CDs.

Out of these 33649 ways, only one arrangement is alphabetical. For this to happen, the first CD chosen must be the first one alphabetically, the second CD chosen must be the second one alphabetically, and so on.

The first CD can be any of the 23 CDs. However, once the first CD is chosen, there is only one CD that can be the second one alphabetically, two CDs that can be the third one alphabetically, and so on. Therefore, the probability of choosing 5 CDs in alphabetical order is:

P = 1 / C(23, 5)

P = 1 / 33649

P ≈ 0.00003

So the probability of choosing 5 CDs in alphabetical order out of a collection of 23 CDs is approximately 0.00003 or 0.003%.

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Answer:

Step-by-step explanation:

(a) The estimate for the difference in population means is 6.000.

(b) The standard error for the difference in population means is 3.208.

Conclusion:

Based on the given data, the 95% confidence interval for the difference in population means between this year's sales and last year's sales is between -0.608 and 12.608. This suggests that the population mean for this year's sales is likely to be higher than the population mean for last year's sales. This is supported by the fact that the estimate for the difference in population means is 6.000, which is greater than 0.

Answer:

Step-by-step explanation: $130-$70 lift = $60/$20 per hour= 3 hours ski time

Thus, the value of measurement in the unit of feet converted from inch are - Measurement: 26 ft. x 32.5 ft.

The ratio of equivalent sides on two comparable figures is known as the scale factor. Scale factor in mathematics is used to quantify how much larger or smaller one object or figure is in comparison to another. On a map, scales are frequently present. The scale factor in geography typically refers to how accurately the scale depicted on the map reflects actual distance.

Given:

Measurement: 3 1/4 in. x 4 1/16 in.

Scale: 1/8 in. = 1 ft

Convert the mixed fraction of measurement into proper fraction:

Measurement: (3*4 + 1)/4 in. x (4*16 + 1)/16 in.

Measurement: 13/4 in. x 65/16 in.

Now,

Scale: 1/8 in. = 1 ft

1 in. = 1*8 ft

1 in. = 8 ft

Thus, multiply each measurement by 8 to get the values in ft.

Measurement: 13*8/4 ft. x 65*8/16 ft.

Measurement: 13*2 ft. x 65/2 ft.

Measurement: 26 ft. x 32.5 ft.

Thus, the value of measurement in the unit of feet converted from inch are - Measurement: 26 ft. x 32.5 ft.

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Step-by-step explanation:

x = 6 x = -5

x - 6 = 0 x + 5 = 0

f(x) = 2(x-6)(x+5)

f(x) = 2(x² +5x - 6x - 30)

f(x) = 2(x² - x - 30)

f(x) = 2x² - 2x - 60

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Therefore, the graph of the given set is: closed circles on 1 and 4 with a line segment between.

A common form for an algebraic expression is one of the following: addition, subtraction, multiplication, or division. Simplify the values to determine the result.

The expression (x I x ≤ 1) U (x I x ≥ 24) represents the set of all values of x that are less than or equal to 1 or greater than or equal to 24.

the graph of this set will have a closed circle at x=1 and a closed circle at x=24

The arrows pointing outward indicate that the set continues indefinitely in both directions.

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Yes, the player earned 67 points from Level 2 to Level 4 and 69 points from Level 3 to Level 5.

Given that: A student claims that the graph shows the player earned more points from Level 2 to Level 3 than from Level 4 to Level 5.

Let's examine the line graph:

At level 2 the point is 45 and at level 4 the point is 112. Thus, the points earned moving from Level 2 to Level 4 will be:

= 112 - 45

= 67

At level 3 the point is 112 and at level 5 the point is 156. Thus, the points earned moving from Level 4 to Level 5 will be:

= 156 - 87

= 69

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The direction and angle of rotation include the following: B. 90° counterclockwise rotation.

In Mathematics and Geometry, a transformation is the movement of a point from its initial position to a new location. This ultimately implies that, when a geometric figure or object is transformed, all of its points would also be transformed;

In Mathematics, a rotation refers to a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

By critically observing the geometric figures, we can reasonably infer and logically deduce that the pre-image was rotated counterclockwise to produce the image.

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The value of

m∠GHJ = (3(20°)+50)° = 110°.

m∠GkJ = (4(20°)-10)° = 70°

m∠HJK = (4(20°))° = 80°

What is an angle?

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

Here, we have

Given: Circle B is shown, with GHJK inscribed in the circle. The m∠GHJ = (3x+50)°, and m∠HJK = (4x)° and mLGK] = (4x-10)°.

we have to find the value of HJK and JHG.

We know that

m∠GHJ + m∠GkJ = 180°

(3x+50)° + (4x-10)° = 180°

7x + 40 = 180°

7x = 140°

x = 20°

Hence, the value of

m∠GHJ = (3(20°)+50)° = 110°.

m∠GkJ = (4(20°)-10)° = 70°

m∠HJK = (4(20°))° = 80°

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