What is the measure of angle k?
102
118
134
156

Step-by-step explanation:

To solve a two-step equation with fractions, we can use the same steps as we would for a two-step equation without fractions  

Here are the steps:

1.

Simplify both sides of the equation by multiplying both sides by the least common multiple (LCM) of all the denominators in the equation.

2.

Solve the resulting two-step equation using inverse operations.

For example, let's say we have the equation 3/4x - 1/2 = 5/8  

Step 1: Multiply both sides by the LCM of 4, 2, and 8 which is 8. This gives us:

3x - 4 = 5

Step 2: Add 4 to both sides to get:

3x = 9

Step 3: Divide both sides by 3 to get:

x = 3

Therefore, x = 3 is the solution to the equation  

Each of Carl's friends will be getting 1/9 of his original collection.

Carl is giving away 1/3 of his collection. Let's assume that the original collection is x. Carl is giving away 1/3 of x.

1/3x divided by 3 = 1/3x x 1/3

                            = 1/9x

In other words, if Carl has a total of 9 baseballs, he wants to give away 1/3 of them which is 3 baseballs. He’s dividing these 3 baseballs among 3 friends, so each friend will get 1/3 of the 3 baseballs which is 1/9 of the original collection.

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In a percentage change income statement over the period of 2009 to 2011, the change in net income is 27.6%. Therefore, correct answer is D).

Here, we have,

The change in net income from 2009 to 2011 can be calculated using the formula:

[(Net income in 2011 - Net income in 2009) / Net income in 2009] x 100

Using the given information from the income statement, we can plug in the values and calculate the change in net income:

[(13,400 - 10,500) / 10,500] x 100

= [2,900 / 10,500] x 100

= 0.276 x 100

= 27.6%

Therefore, the change in net income from 2009 to 2011 is 27.6%.

(Option D)

In a percentage change income statement over the period of 2009 to 2011, the change in net income is 27.6%. Therefore, correct answer is D).

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complete question:

The question is incomplete. The complete question probably is: Ramos Company Ramos Company Included the following information in its annual report:

                                           2011  2010   2009

Sales                $178,400 $162,500  $155,500

Cost of goods sold      115,000 102,500    100,000

Operating expense      50,000  50,000     45,000

Net income               13,400  10,000     10,500

In a percentage change income statement over the period of 2009 to 2011, what is the change in net income? A) 100%  B) 21.6% C) 72.4% D) 27.6%

The surface area of the cylindrical pottery vase is 177.55 in².

Given that a cylindrical pottery vase has a diameter of 4.3 inches and a height of 11 inches, we need to find the surface area of the vase,

SA of a cylinder = 2π×radius(h+r)

= 2×3.14×2.15(2.15+11)

= 177.55 in²

Hence, the surface area of the cylindrical pottery vase is 177.55 in².

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To understand this problem:

a. My first thought is to try to maximize the numerator while minimizing the denominator.

To do this, I can try to use the largest digits (9, 8, 7) in the numerator and the smallest digits (1, 2, 3) in the denominator.

b. To find the largest possible ratio for the sine of an angle, I will start by trying to use the digits 9, 8, and 7 in the numerator and digits 1, 2, and 3 in the denominator.

I will try different combinations until I find the largest possible ratio.

First, I will try 987/321. Using a calculator, I find that sin(987/321) ≈ 0.9984.

Next, I will try swapping the digits in the numerator to see if I can get a larger ratio. I will try 987/231. Using a calculator, I find that sin(987/231) ≈ 0.9999, which is larger than the previous ratio.

Finally, I will try using the digit 6 in the denominator instead of 3, since 6 is closer in value to 7 and 8 than 3. I will try 987/216. Using a calculator, I find that sin(987/216) ≈ 0.9999999955, which is even larger than the previous ratio.

Therefore, I believe that the largest possible ratio for the sine of an angle using the digits 1 through 9, each used once, is approximately 0.9999999955, and it can be obtained with the ratio 987/216.

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The expression is equivalent to the expression (12 + 3) ÷ 5 is (3 + 12) ÷ 5

From the question, we have the following parameters that can be used in our computation:

(12 + 3) ÷ 5

The above expression is a quotient expression

However, we can apply some algebraic properties

Take for instance;

12 + 3 can be expressed as 3 + 12

So, we have

(12 + 3) ÷ 5 = (3 + 12) ÷ 5

Hence, the expression is equivalent to the expression is (3 + 12) ÷ 5

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Answer:

We can start with the left side of the identity and try to manipulate it algebraically to transform it into the right side:

Left side: tan X + cot X

We know that cot X is equal to 1/tan X, so we can substitute this expression in for cot X:

Left side: tan X + 1/tan X

Next, we can use the identity that (a + 1/a) = (a^2 + 1)/a to rewrite the expression as a single fraction:

Left side: (tan^2 X + 1)/tan X

We can then use the trigonometric identity that 1 + tan^2 X = sec^2 X to substitute in for the numerator:

Left side: sec^2 X / tan X

Finally, we can use the identity that csc X = 1/sin X to substitute in for tan X:

Left side: sec^2 X / (sin X / cos X)

We can simplify this expression by multiplying the numerator and denominator by cos X:

Left side: (sec^2 X * cos X) / sin X

We know that sec X is equal to 1/cos X, so we can substitute this expression in for sec X:

Left side: (cos X / cos X * sin X) = cos X * csc X

Therefore, we have shown that the left side (tan X + cot X) is equal to the right side (sec X csc X), and the identity is proven:

tan X + cot X = sec X csc X

The relative frequency probability of rain in April is 0.4.This means that it rained on 40% of the days in April in the suburban Maryland neighborhood, which is higher than the average probability of 31%.

The relative frequency probability of rain in April is the proportion of days on which it rained in April out of the total number of days in April.

The total number of days in April is 30, and rain was recorded on 12 of those days.

Therefore, the relative frequency probability of rain in April is:

12/30 = 0.4

This means that it rained on 40% of the days in April in the suburban Maryland neighborhood, which is higher than the average probability of 31%

The relative frequency probability gives us an idea of how often an event is likely to occur based on past occurrences. In this case, it tells us that it rained on 40% of the days in April in the suburban Maryland neighborhood.

Comparing this probability to the average probability of rain in April in the area, which is 31%, we can see that the observed probability is higher. This suggests that this particular April was rainier than usual.

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The present value needed to get $110 after 1 1/4 years at 4% compounded continuously is about $102.79.

We will use the continuous compound interest formula:

[tex]A = Pe^{(rt)[/tex]

Wherein

Substituting the given values, we've got:

[tex]110 = Pe^{(0.04*1.25)[/tex]

Simplifying, we get:

[tex]110 = Pe^{0.05[/tex]

Dividing each sides by using [tex]e^{0.05[/tex], we've got:

[tex]P = 110/e^{0.05[/tex]

Using a calculator, we get:

[tex]P \approx $102.79[/tex]

consequently, the present value needed to get $110 after 1 1/4 years at 4% compounded continuously is about $102.79.

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Answer:

1/9

Step-by-step explanation: 1/3/3

The amount of water in the pond after 14 minutes will be 1006 L.

Given that the pound already having 600 L of water is being filled at rate of 29 L per minutes, we need to establish an equation that represent the relation between number of minute and amount of water in the pond.

So,

The relation can be defined as;

W = 600+29T

When T = 14

W = 600+29(14)

W = 1006

Hence, the amount of water in the pond after 14 minutes will be 1006 L.

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a) Equating the expressions, the time that will pass before the planes are at the same altitude is 59.27 seconds.

b) The altitude when the two planes are at the same altitude is 5,870.8 feet.

An expression is a mathematical statement that combines variables with constants, numbers, or values without the equal symbol (=).

An equation is two or more mathematical expressions using the equal symbol (=).

Starting altitude of Plane A = 3,500 feet

Starting altitude of Plane B = 2,285 feet

Plane A's speed = 40 feet per second

Plane B's speed = 60.5 feet per second

Let the number of seconds for the planes to be at the same altitudes = x

3,500 + 40x

2,285 + 60.5x

For the two planes to be at the same altitudes, 3,500 + 40x = 2,285 + 60.5x

1,215 = 20.5x

x = 59.27 seconds

Check:

Plane A's attitude = 3,500 + 40(59.27) = 5,870.8 feet

Plane B's attitude = 2,285 + 60.5(59.27) = 5,870.8 feet

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The graph of inequality x<-2 is given in the attachment.

The inequality x < -2 represents a portion of the number line to the left of -2, but it does not specify a graph in the traditional sense.

If you want to graph the inequality, you can represent the shaded region of the number line to the left of -2, and you can use an open circle to indicate that -2 itself is not included in the solution set

The open circle at -2 indicates that -2 is not included in the solution set, and the shaded region to the left of -2 represents all the numbers that satisfy the inequality x < -2.

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1/13 will be the fraction to represent the tosses are tails.

If the ratio of heads to total tosses is 24:26, then we can express the ratio of tails to total tosses as:

Tails : Total Tosses = 2 : 26

Simplifying this ratio by dividing both terms by 2, we get:

Tails : Total Tosses = 1 : 13

Therefore, the fraction of tosses that tail is 1/13.

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The required equation is:

(x-(-1))²/3² — (y − 3)²/6² = 1

From the figure above, it is clear that it is a horizontal hyperbola

Step 2: The center is at (-1, 5) and the vertices are at (-4, 5) and (2, 5).

Step 3

The co-vertices are (3, 3) and (3, 7).

Step 4

Comparing the center from general equation of a hyperbola gives:

(h, k) = (3,5)

Step 5

(h, k) = (3,5)

So it can be written that:

h = 3 and k = 5

Step 6

Comparing the vertices from general equation of a hyperbola gives:

(h - a, k) = (-4,5), (h+a, k) = (2,5)

Step 7

(h-a, k) = (-4,5)

So it can be written that:

h-a = -4 and k = 5

Step 8

h-a = -4

Now substitute in the equation h = -1 to get:

-1 - a = -4

Step 9

Find value of a:

-1- a = -4

Step 10

Comparing the co-vertices from general equation of a hyperbola gives:

(h, k - b) = (3, 3) , (h, k + b) = (3, 7)

Step 11

(h, k - b) = (3, 3)

So it can be written that:

h = 3 and k - b = 3

Step 12

k - b = 3

Now substitute in the equation k = 5

5 - b = - 1

Step 13

Find the value of b:

5 - b = -1

Step 14

(x− h)²/a² - (y – k)²/b² = 1

Now substitute h = -1, k = 5, a = 3 and b = 6 in the equation to get:

(x-(-1))²/3² — (y − 3)²/6² = 1

Step 15

Therefore, the required equation is:

(x-(-1))²/6² — (y − 3)²/4² = 1

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The linear correlation coefficient is 0.99.

Yes, there is a linear relationship between x and y.

In this scenario, the hours worked (x) would be plotted on the x-axis of the scatter plot while the final grade (y) would be plotted on the x-axis of the scatter plot.

By critically observing the scatter plot (see attachment) which models the relationship between the hours worked (x) and final grade (y), an equation for the linear regression is given by:

y = 96.49860724 - 2.682451253x

Correlation coefficient, r = -0.9922898032 ≈ 0.99.

In conclusion, there is a strong correlation between the data because the correlation coefficient (r) approximately equals to 1;

0.7＜|r| ≤ 1   (strong correlation)

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(1000-(-800))/(900-300) = 3 (slope)

y=mx+b

1000=3(900)+b

b = -1700
y=3x-1700

The sale price of the item when displayed on sales costs $8.75 based on the stated original price and percentage discount offered.

The formula to calculate sale price of the item according to discount and original price will be -

Sale price = 25% × original price

Keep the value of original price in the formula to find the sale price

Sale price = 25% × 35

Performing multiplication and division by solving the percentage on Right Hand Side of the equation to find the value of sale price of the item

Sale price = 8.75

Hence, the item on sale costs $8.75.

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Answer: You cannot add (or subtract) fractions with different denominators, so therefore the answer would not be 3/8.

The complex value fraction is simplified and A = ( x² - 9 ) / ( 3x² ) ( 15x - 3x² )( x - 12 ) / ( 2/15x ) ( 15x - 3x² )( x - 12 ) - 3x ( ( 3x⁴ - 15x )

Given data ,

Let the fraction be represented as A

Now , the value of A is

The last denominator of the fraction is

x² / 15x - 1/3x²

On simplifying , we get

( 3x⁴ - 15x ) / ( 15x - 3x² ) , and this fraction is multiplied by the fraction above which is x/( x/3-4 )

So , the above fraction is 3x ( ( 3x⁴ - 15x ) / ( 15x - 3x² ) ) / ( x - 12 )

Now , taking the LCM of the denominator of the fraction , we get

( 2/15x ) - 3x ( ( 3x⁴ - 15x ) / ( 15x - 3x² )( x - 12 ) , we get

( 2/15x ) ( 15x - 3x² )( x - 12 ) - 3x ( ( 3x⁴ - 15x ) / ( 15x - 3x² )( x - 12 )

And , the numerator of the fraction is ( 1/3 ) - ( 3/x² )

On taking the LCM on the numerator , we get

( x² - 9 ) / ( 3x² ) / ( 2/15x ) ( 15x - 3x² )( x - 12 ) - 3x ( ( 3x⁴ - 15x ) / ( 15x - 3x² )( x - 12 )

The denominator will get multiplied by the reciprocal of the fraction and ,

A = ( x² - 9 ) / ( 3x² ) ( 15x - 3x² )( x - 12 ) / ( 2/15x ) ( 15x - 3x² )( x - 12 ) - 3x ( ( 3x⁴ - 15x )

Hence , the fraction is A = ( x² - 9 ) / ( 3x² ) ( 15x - 3x² )( x - 12 ) / ( 2/15x ) ( 15x - 3x² )( x - 12 ) - 3x ( ( 3x⁴ - 15x )

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Based on the given data, it is MOST LIKELY TRUE that Mrs. Newton is likely moving to a higher grade level. This can be inferred because the median number of upper-level vocabulary words in her new library (9) is higher than the median in her old library (5), and the range of the number of upper-level vocabulary words is also greater in her new library (18) compared to her old library (10). These findings suggest that the books in her new library have a higher level of vocabulary and may be more appropriate for older or more advanced readers.

Answer:

Step-by-step explanation: multiply the coins by 7

An equation of the line in point-slope form is y - 7 = 6(x - 4).

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

4 7 3 1

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (1 - 7)/(3 - 4)

Slope (m) = -6/-1

Slope (m) = 6

At point (4, 7) and a slope of 6, an equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 7 = 6(x - 4)

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To find the smallest possible integer of the terms of the series that need to be added to find the sum to the indicated accuracy, we use the formula for the remainder of the geometric series.

The formula for the remainder of the geometric series is R = a (1 - rn) / (1 - r)Where R is the remaining term of the geometric series, a is the first term of the geometric series, r is the common ratio of the geometric series, n is the number of terms of the geometric series up to the given partial sum.

The formula for the sum of a finite geometric series is: S = a (1 - rn) / (1 - r)

By using the formula for the remainder of the geometric series, the smallest possible integer of the terms of the series that need to be added to find the sum to the indicated accuracy is given by:

S - Sn = R

Where, S is the sum of the geometric series, Sn is the sum of the first n terms of the geometric series.

From the given question, the number of terms of the geometric series required to find the sum to the indicated accuracy is not given.

Hence, we cannot find the smallest possible integer of the terms of the series that need to be added to find the sum to the indicated accuracy.

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Correct question:

How many terms of the series do we need to add in order to find the sum to the indicated accuracy?

We can see here that the incorrect statement is #1: The image is located in Quadrant IV.

Transformation in mathematics is a function or a set of rules that converts a collection of points or geometric figures in one coordinate system into a different set of points or geometric figures in a second coordinate system while maintaining some characteristics of the original set.

We can see here that the statement that is incorrect is actually #1: The image is located in Quadrant IV. This is true because the image is in Quadrant I while the transformation is in Quadrant IV.

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The solution is, the value of the digit 3 in the number 63,297 compare to the value of the digit of 3 in the number 60,325 is 2700.

Here,  we have,

given that,

the value of the digit 3 in the number 63,297 compare to the value of the digit of 3 in the number 60,325.

we have,

The value of the digit 3 in the number 63,297 is 3,000 while the value of the digit 3 in the number 60,325 is 300.

we know,

the value of the digit 3 in the number 63,297 = 3000

the value of the digit 3 in the number 60,325 = 300

so, we get,

The difference between value of the digit 3 in the number 63,297 and the value of the digit 3 in the number 60,325 will be:

= 3000 - 300

= 2700

Hence, the value of the digit 3 in the number 63,297 compare to the value of the digit of 3 in the number 60,325 is 2700.

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The maximum quantity of snowfall logged in any one city came out to be an astounding 42 inches.

Most of the data is densely concentrated within the second quarter, spanning between 6 and 14 inches in terms of depth. This surplus can be evidenced by scrutinizing the box plot that has a comparatively slim interquartile range (IQR) within the second quarter with the outline stretching from the bottom quartile (Q1) at 6 inches up to the top quartile (Q3) at 14 inches - denoting that the majority of the numbers lie within this scope, making it the most heavily populated.

In contrast, the data is generally dispersed by the fourth quarter comprising the interval spanning from 30 to 50 inches of snowfall.

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The baseball game ended at 2:23 p.m

How to determine this

When 60 minutes makes 1 hour

If the game started at 10:50 a.m

And it was 3 hours and 33 minutes long

To calculate when the game ended,

By adding the hours together and the minutes together separately

10 hours + 3 hours

= 13 hours

50 minutes + 33 minutes

= 83 minutes

83 minutes is more than 60 minutes

And 60 minutes make 1 hour

So, by subtracting 60 minutes from 83 minutes

= 83 - 60

= 23 minutes

So, the 1 hour when added to 13 hours = 14 hours

14 hours when converted to p.m

= 14 hours - 12 hours

= 2 pm

So, when added to the minutes

= 2:23 p.m.

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