which expression has the same value as 1 2/3 + (-8 1/2)

The probability that we did not see all three colors is [tex]$\frac{13}{16}[/tex]

Consider the event,

A: Did not see all 3 colors

Complement of the event A is A’ where

A' : All colors were seen

Since 3 balls are drawn and all colors should be seen, it implies that there is 1 ball of each color

It is required to find P(A) = P(did not see all colors)

By the probability rule for complement:

P(A)  =1-P(A')

P(A') & =P(all colors were seen )

=P(1 White AND 1 Green AND 1 Red )

Total number of balls = 4

Number of combinations of 3 balls possible = 64

Since drawing a ball is with replacement, we have the following number of combinations with each color represented where R1 and R2 are the two red balls.

The table attached at end of the solution

Total number of combinations with each color represented = 12

Thus the probability of A’ is:

[tex]$P\left(A^{\prime}\right) & =\frac{12}{64} \\[/tex]

[tex]$P(A) & =1-\frac{12}{64} \\[/tex]

[tex]$=\frac{52}{64} \\[/tex]

[tex]$=\frac{13}{16}[/tex]

Hence, the required probability P(did not see all 3 colors) is [tex]$\frac{13}{16}$[/tex]

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The number of centimeters in the length of a side of this hexagon is 14√3/3 centimeters.

The lengths of the perpendiculars drawn to the sides of a regular hexagon from an interior point are 4, 5, 6, 8, 9 and 10 centimeters.

Finding the side of this hexagon using the Pythagorean Theorem

Let the side of the hexagon is s.

So according to theorem

s^2 = (s/2)^2 + 7^2

Now solving

s^2 = s^2/4 + 49

Subtract 49 on both side, we get

s^2 - 49 = s^2/4

Multiply by 4 on both side, we get

4s^2 - 196 = s^2

Subtract s^2 + 196 on both side, we get

3s^2 = 196

Divide by 3 on both side, we get

s^2 = 196/3

Taking square root on both side, we get

s = 14/√3

Multiply and divide by √3

s = 14√3/3

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Answer:

8.5m

Step-by-step explanation:

K-means clustering is an iterative algorithm that partitions a data set into k clusters, where k is predefined.

It works by first randomly selecting k points as cluster centers, also known as centroids. All points are then assigned to the nearest cluster center based on a distance metric, such as Euclidean distance. This process is repeated until the centroids no longer move, which is when the clusters have stabilized. The formula for calculating the distance between two points is d = sqrt((x1-x2)^2 + (y1-y2)^2).

Hierarchical clustering is a type of clustering algorithm that builds a hierarchy of clusters. It starts by assigning each point to its own cluster, then combines the two closest clusters and repeats the process. The calculation used to determine the distance between two clusters is the distance between their two closest points, also known as the single linkage method. The formula for calculating the distance between two clusters is d = min(d1, d2, ..., dn), where d1, d2, ..., dn are the distances between the two closest points in the two clusters.

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Answer:

see below

Step-by-step explanation:

z+66+z+69+43z=180

so 45z=180-66-69 = 45

so z=1

so angle U= 43 its opposite side length ST is the smallest

same logic for the other 2.

66+1=67

69+1=70

so ST<US <TU

Answer:

C

Step-by-step explanation:

For the second graph

the equation should be:

y = 1/2 x^2

Which makes the graph true.

You can try plug numbers into x to check your answer.

They should use 6 cup of Noah's measuring cup

They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

To solve this problem we must perform the following algebraic operations with the given information

Information about the problem:

Calculating the number of cup the should use:

Number of cup = Recipe call / Noah's cup

Number of cup = (3/4) / (1/8)

Number of cup = 3*8 / 4*1

Number of cup = 24/4

Number of cup = 6

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Correctly written question:

Melanie and Noah are baking a birthday cake for Francesca. The recipe call for 3/4 measuring cup and Noah has a 1/8 measuring cup. Which cup should they use?

Answer:

You run at a faster rate.  The rate is 19 feet per second or about 5.7912 meters per second.

Step-by-step explanation:

The expression representing the friend says the friend is running at a speed of 14 feet per second with a head start of 50 feet.  The table show that you run at a speed of 38 feet per 2 seconds otherwise said as 19 feet per second.

19 > 14, so you run faster.

The sum of the infinite series ∑n=1[infinity] 5x²(xy)ⁿ⁻¹ is 5/1-xy

The sum of an infinite series is the value that the series approaches as the number of terms in the series increases indefinitely.

In this particular problem, we are asked to find the sum of the infinite series

=>∑n=1[infinity] 5x²(xy)ⁿ⁻¹

A geometric series is a series where each term is a constant multiple of the previous term. In this case, the common ratio is xy.

The sum of an infinite geometric series can be calculated using the formula:

=> S = a / (1 - r)

where a is the first term in the series and r is the common ratio.

In this problem, the first term, a, is 5x² and the common ratio, r, is xy.

We know that |xy| < 1, which means that the absolute value of xy is less than 1.

This is important because it guarantees that the series will converge (approach a finite value) as the number of terms increases.

Using the formula for the sum of an infinite geometric series, we get:

S = 5x² / (1 - xy) = (A) 5/1-xy.

Therefore, the correct option is (a).

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Answer: i think its A

Answer: Its c

Step-by-step explanation: -2 - 6 is -8

Answer:

What additional information do you need to prove ∆ ABC ≅ ∆ def by the SSS postulate description? So, △ABC ≅ △DEF. If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent. If — AB ≅ — DE, — BC ≅ — EF, and — AC ≅ — DF, then △ABC ≅ △DEF.

The equation of a quadratic function P with rational coefficients that has a zero of (3 + i) is p(x) = x² - 6x + 10.

What is a quadratic function?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.

The complex number value is given as (3 + i)

Since, x = (3 + i) is a complex zero of p(x), then -

It is known that , the complex zeros occur in pair.

So, x=(3 - i) is also a complex zero of the quadratic function of p(x).

So, {x − (3 + i)} and {x − (3 - i)} are the factors of p(x).

Substitute the values to form a quadratic function -

p(x) = {x − (3 + i)}{x − (3 - i)}

Open the brackets and evaluate -

p(x) = (x - 3 + i)(x - 3 - i)

Use the arithmetic operation of multiplication -

p(x) = x(x - 3 - i) - 3(x - 3 - i) + i(x - 3 - i)

p(x) = x² - 3x - ix - 3x + 9 + 3i + ix - 3i - i²

Collect all the like terms -

p(x) = x² - 3x - 3x - ix + ix + 9 + 3i - 3i - i²

p(x) = x² - 6x + 9 - i²

Substitute the value of  i² = -1 into the equation -

p(x) = x² - 6x + 9 - (-1)

p(x) = x² - 6x + 9 + 1

p(x) = x² - 6x + 10

Therefore, the quadratic function is x² - 6x + 10.

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A linear relationship is depicted by a trend line. Y = mx + b, where x is the independent variable, y is the dependent variable, m is the slope of the line, and b is the y-intercept, is the equation for a linear relationship.

The change in y that results from a 1 unit increase in x is the slope of a line. In our example, the trend line would indicate that someone would be approximately 5.76 cm taller if they were one year older (x increases by 1). (y increases by 5.76).

Beer's law's equation is a simple, linear line with the general form of y = mx +b. where the slope, m, is equal to εl. 

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The solution to the squared expression using the concept of squared numbers is; A: 144

When we say a number is squared, what it simply means is that the number is multiplied by itself. Thus, for example;

z² = z × z

y² = y × y

b² = b × b

We have the expression as;

(8² × 6²)/4²

Using the concept of squared numbers gives;

(8 × 8 × 6 × 6)/(4 × 4)

= (2 × 2 × 6 × 6)

= 144

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The variance of head circumferences of adult males is 1.

Variance is a measure of how data points differ from the mean. According to Layman, a variance is a measure of how far a set of data are spread out from their mean value.

Variance means to find the expected difference of deviation from actual value. Therefore, variance depends on the standard deviation of the given data set.

The more the value of variance, the data is more scattered from its mean and if the value of variance is low or minimum, then it is less scattered from mean. Therefore, it is called a measure of spread of data from mean.

Let x be the head circumferences of some males.

[tex]X \sim N\left(57,1^2\right)[/tex]

[tex]$\mu[/tex]=57 centimeters (mean)

[tex]$\sigma[/tex]=1 centimeters (standard deviation)

The variance of head circumferences of adult males [tex]$=\sigma^2=1^2=1$$$[/tex]

Variance =[tex]\sigma^2[/tex]=1

Therefore, the variance of head circumferences of adult males is 1.

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Answer:

3) m = -3/2

4) m = 3/2

5) m = 5/3

6) m =  7/3

7) m = -3

8) m = 7/3

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

3/ ( -4, 0) ( -2, -3)

The y decrease by 3, and the x increase by 2, so the slope is

m = -3/2

4/ (2,0) (0, -3)

The y decrease by 3, and the x decrease by 2, so the slope is

m = -3/-2 = 3/2

5/ (-1,2) (-4, -3)

The y decrease by 5, and the x decrease by 3, so the slope is

m = -5/-3 = 5/3

6/ (4,3) (1, -4)

The y decrease by 7, and the x decrease by 3, so the slope is

m = -7/-3 = 7/3

7/ (1,2) (3, -4)

The y decrease by 6, and the x increase by 2, so the slope is

m = -6/2 = -3

8/ (0,3) (-3, -4)

The y decrease by 7, and the x decrease by 3, so the slope is

m = -7/-3 = 7/3

The true statements are Function B has greater slope, Function A has greater y intercept and Function B has greater x intercept.

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

We have to first find the linear equations of the functions.

Given for function A,

Let x be the number of hours.

Function A can be represented as f(x) = 4/5 + 2x

Equation in slope intercept form is y = mx + c, where m is the slope and c is the intercept along Y axis.

Y intercept is the point of the line where it touches the Y axis. x coordinate will be zero here.

x intercept is the point of the line where it touches the X axis. y coordinate will be zero here.

y = 2x + (4/5), in slope intercept form.

Here 2 is the slope and 4/5 is the y intercept.

When y = 0, 2x + (4/5) = 0, then x = -2/5

x intercept = -2/5

For function B,

we have when x = 0, f(x) = y = 2/3

y intercept = 2/3

Slope = [(2/3) - (-25/3)] / [0 - -3]

          = [27/3] / 3

          = 9 / 3

          = 3

Equation in slope intercept form of function B is,

y = 3x + 2/3

When y = 0, 3x + 2/3 = 0, then x = -2/9

x intercept = -2/9

So function B has greater slope as slope is 3 for B and 2 for A.

Function A has greater y intercept as y intercept for A is 4/5 and for B is 2/3.

Function B has greater x intercept as x intercept is -2/9 for B and -2/5 for A.

Hence the correct options are function B has greater slope, Function A has greater y intercept and Function B has greater x intercept.

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1,156,530 members were in attendance in 2016. You can round it to $1,160,000.

Functions that take the form f(x) = axe are referred to as exponential functions. where an is a constant and x is a variable.

500,000 people are registered members of the website as of 2010.

Y members grew by 15% annually.

Members and year have an exponential relationship that is

y = 500,000(1.15)^t

Then in 2016 the number of members present are given by,

y = 500,000(1.15)^6 = 1,156,530.

Hence, 1,156,530 members present in 2016. It can rounded to 1,160,000.

The complete question is:

A website 500,000 members in 2010. The number y of members increases by 15% each year. Write an exponential growth function that represents the website membership t years after 2010. How many members will there be in 2016? Round your answer to the nearest ten thousands

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Answer:

there was 6 associates assigned to the case and 2 partners

Step-by-step explanation:

what i did was did 1400 times 2 and 500 times 6. then i did 6 divided by 3 which gave me 2. So there are 3 times more associates.

Hope this helped

Looking at the logarithmic form [tex]log_a3[/tex].

3 corresponds to x.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 8 is an equation.

We have,

[tex]log_a3[/tex]

This means,

y = [tex]log_a3[/tex]

Where x = 3

So,

3 correspond to x

Thus,

3 correspond to x.

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The total surface area painted is 644.16 square inches.

Let the radius of the cylindrical rod be r. The circumference of the base is given as 12π, which can be converted to the diameter as:

diameter = circumference / π = 12π / π = 12 inches.

So, the radius of the cylindrical rod is half of that. That is 6 inches.

The area of one base of the cylindrical rod can be calculated as π [tex]r^2[/tex], which is:

π * [tex]6^2[/tex] = 3.14 * 36 = 113.04 square inches.

The surface area of one-half of the cylindrical rod can be calculated by:

2 * π * r * l + 2 * π * [tex]r^2[/tex], where l is the length of the rod.

Since the length of the rod is 4 inches, the surface area of one-half of the cylindrical rod can be calculated by:

2 * π * 6 * 4 + 2 * 113.04 = 96 + 226.08 = 322.08 square inches.

Given that two equally sized pieces are cut, the total surface area painted would be 2 * 322.08 = 644.16 square inches.

Therefore, the total surface area painted is 644.16 square inches.

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The linear equations for the two companies are:

Company 1: y = 1.5*x + 5.5

Company 2: y = 0.5*x + 6

So the rate of company 1 is trice the rate of company 2.

When we have constant rates, then we have linear relations that can be written as:

y = m*x + b

Where m is the constant rate and b is the y-intercept.

And if we have two points (x₁, y₁) and (x₂, y₂), then the constant rate is:

m = (y₂ - y₁)/(x₂ - x₁)

So for the first table we can use the pairs:

(2.5, 9.25)

(6, 14.5)

So the rate is:

m = (14.5 - 9.25)/(6 - 2.5) = 1.5

Then the line is:

y = 1.5*x + b

To find the value of b, we can replace the values of one of the points, like (2.5, 9.25), we will get:

9.25 = 1.5*2.5 + b

9.25 - 1.5*2.5 = b

5.5 = b

And for company 2 we can try to identify two points on the graph, these can be (0, 6) and (1, 6.50), so the rate is:

m' = (6.50 - 6)/(1 - 0) = 0.50

So the rate of company 1 is 3 times the one of company 2,  And the y-intercept is y = 6.

So the equations are:

Company 1: y = 1.5*x + 5.5

Company 2: y = 0.5*x + 6

So the rate of company 1 is trice the rate of company 2.

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The conversion factor along with the symmetry of the circle to complete the degree or radian measure of the missing trigonometric angles = 90° = 90° × (π/180°) = π/2.

A degree, which is referred to as the degree of arc or arc degree, is the unit of measuring a plane angle. It is denoted by the symbol (°). 360° is the angle measure for a complete rotation. A complete rotation is denoted by the angle measuring 360° and the instrument used to measure an angle in degrees is known as the protractor.

Radian is another unit of measuring an angle in geometry. One radian is the angle that is formed at the center of a circle by an arc whose length is equal to the radius 'r' of the circle. One complete counterclockwise rotation is equal to 2π in radians. The below-given image shows the measure of one radian as 57.296°. Also, a right angle is expressed as π/2 radians, and a straight angle is expressed as π radians.

We can compare the measure of angles for a complete rotation in radian and degrees as,

360 Degrees = 2π Radians

180 Degrees = π Radians

In order to convert degrees to radians manually, we use the formula: Radians = Degrees × (π/180°). We can follow the steps given below to calculate the measure of an angle given in degrees to radians.

We know, 1°= (π)/180 radians. So, to convert the angle given in degrees to radians we multiply it with π/180°.

Angle in Radians = Angle in Degrees × π/180°.

Simplify the values and express the answer in radians.

Example: Convert 90 degrees to radians.

Solution: 90° = 90° × (π/180°) = π/2.

Therefore,

The conversion factor along with the symmetry of the circle to complete the degree or radian measure of the missing trigonometric angles = 90° = 90° × (π/180°) = π/2.

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Possible values of ∠L, to the nearest degree  is ∠L = 158° or ∠L = 74°

We can use the Law of Cosines to solve for ∠L.

The Law of Cosines states that for a triangle with side lengths a, b, and c and opposite angles A, B, and C, c² = a² + b² - 2ab cos(C).

Therefore, we can substitute in the given information to solve for ∠L.

c² = l² = 84² = 7056

a² = k² = 40² = 1600

b² = m² = unknown

2ab cos(C) = 2(40)(m) cos(22°)

Solving for m, we get

m² = 7056 - 1600 + 80cos(22°) = 5496 + 80cos(22°)

Taking the square root of both sides, we get

m = √(5496 + 80cos(22°))

Now, we can use the Law of Cosines again to solve for ∠L.

m² = l² + k² - 2lk cos(L)

Substituting in the values and solving for cos(L), we get

cos(L) = (l² + k² - m²)/(2lk)

cos(L) = (84² + 40² - (√(5496 + 80cos(22°)))²)/(2(84)(40))

cos(L) = 0.7860

Finally, we can use the inverse cosine to find the angle ∠L, to the nearest degree.

cos⁻¹(0.7860) = 74° or 158°

Therefore, ∠L = 74° or 158°.

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the dangers of utilizing only a subset of the performance equation as a performance metric

SUBSET ARE

Clock rate of P1 = 4 GHz

Clock rate of P2 = 3 GHz

Average CPI of P1 = 0.9

Number of Instructions = 5.0E9 =  5 × 10^9

Clock rate of P2 = 3 GHz

Average CPI of P2 = 0.75

Number of Instructions = 1.0E9 = 10^9

To find: If the computer with largest clock rate has the largest performance?

As given in the question, clock rate of P1 = 4 GHz which is greater than clock rate of P2 = 3 GHz

According to the performance equation:

CPU Time = instruction count * average cycles per instruction/ clock rate

CPU Time = I * CPI / clock rate

Where instruction count refers to the number of instructions.

It is not true that computer with the largest clock rate as having the largest performance.

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The value of x is 39.

Alternate interior angles are the angles formed by the intersection of a transversal line with two parallel lines on the plane.

Alternate interior angles are formed on the inner side of the two parallel lines but are on the opposite side of the transversal line.

From the given figure, we have two parallel lines and two transversal lines and thus we can find alternate interior angles.

Alternate interior angles are always equal.

Angles formed by 2x° + 56° and the angle 134° are alternate interior angles and are thus equal.

2x° + 56° = 134°

2x = 134 - 56

2x = 78

x = 39

Hence the value of x is 39.

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As per the combination method, the number of ways can the bike be filled is 10

The term called combination method is defined as a way of adding equations together in such a way that the variables are set aside, one by one.

Here we have know that the motorbike can carry 3 people: the driver, one passenger behind the driver and one in the sidecar.

Here we have also know that among 5 people only two can drive.

Which defines that the value of n is 5 and the value of r is 2.

Then as per the ncr formula it can be calculated as,

=> ⁵n₂ = 5! / 2! (5 - 2)!

When we simplify this one then we get,

=>  ⁵n₂ = 5!/ 2! x 3!

=>  ⁵n₂ = 10

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The person will read 800 words in 5 minutes if he does so at the same speed.

The current average speed of the person will be given by the formula -

Average speed = number of words read ÷ total time taken

Keep the values in formula

Average speed of the person = 640/4

Performing division on Right Hand Side of the equation

Average speed of the person = 160

Now, using the same formula to find the time.

Total time required = 800/160

Performing division on Right Hand Side of the equation

Total time required = 5

Thus, it will take him 5 minutes to read.

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