what is 6 and 2/5 times 1/6

Area of sector GHJ ≈ 2.04 square units

Since we are given the central angle GHJ in degrees and the radius GH of circle H, we can find the area of sector GHJ using the formula:

Area of sector GHJ = (θ/360) × πr^2

where θ is the central angle in degrees and r is the radius.

Substituting the given values, we get:

Area of sector GHJ = (46/360) × π(4)^2

= (0.1278) × 16π

= 2.0448 square units

Rounding to the nearest hundredth, we get:

Area of sector GHJ ≈ 2.04 square units

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The Phillips curve describes the relationship between the unemployment rate and the rate of change of wages. Option C is the correct option.

What is  Phillips curve?

The relationship between the rate of inflation and the unemployment rate is represented by the Phillips curve. The analysis of wage inflation and unemployment in the United Kingdom from 1861 to 1957 by A. W. H. Phillips, despite having forerunners, is a significant development in the field of macroeconomics. When unemployment was high, wages rose slowly; when unemployment was low, wages rose quickly, according to Phillips' research.

According to Phillips' hypothesis, as the unemployment rate declines, the labor market becomes more competitive and firms are forced to raise wages more quickly in order to recruit qualified workers. The pressure decreased as unemployment rates rose. The average relationship between wage behavior and unemployment over the course of the business cycle was represented by Phillips' "curve."

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The number line that represents the solution to the inequality 3x-8≥7 is shown on the attached image.

The inequality: 3x - 8 ≥ 7

Add 8 to both sides

3x ≥ 7 + 8

Add 7 and 8 to get 15

3x ≥ 15

Divide both sides by 3

3x/3 ≥ 15/3

x ≥ 5

An inequality is a mathematical statement that compares two values or expressions, indicating whether they are equal or not. Unlike equations, which are true only if the two sides are equal, inequalities may be true for different values on either side of the inequality sign.

Inequalities are often represented using symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).

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Well, a diameter is double the radius. The radius is given in the image.

So, 2+2 = 4

Answer:

500 ≥ 245.50

500 - 245.50 ≥ 0

254.50 ≥ 0

Therefore, she needs to deposit at least $245.50 to avoid a fee.

Step-by-step explanation:

Let x be the least amount of money she needs to deposit to avoid a fee.

The balance in her checking account after writing the check would be (500 - 245.50) = 254.50.

To avoid a fee, the balance must be greater than or equal to 500, so we can write the inequality as:

x + 254.50 ≥ 500

Solving for x, we get:

x ≥ 500 - 254.50

x ≥ 245.50

The measure of a central angle of a regular polygon with 24 sides is 15 degrees.

A polygon is a two-dimensional geometric shape that is defined by a closed chain of line segments, also known as sides. These line segments must be joined end to end to form a closed shape, with no curves or self-intersections. The word "polygon" comes from the Greek words "poly" meaning "many" and "gon" meaning "angle".

To find the measure of a central angle of a regular polygon with 24 sides, we can use the formula:

central angle = 360 degrees / number of sides

Substituting the given value, we get:

central angle = 360 degrees / 24 = 15 degrees

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Answer:

15 boxes of eggs × 6 eggs/box =

90 total eggs

3 boxes of eggs × 6 eggs/box = 18 eggs

The ratio of the number of eggs in 3 boxes to the total number of eggs is 18/90 = 1/5.

The equation of the circle is (x - 2)²+ (y - 3)² = 169

A circle is a two-dimensional form that may be described as a collection of points that are equally spaced apart from a central fixed point. The radius of a circle is the separation between its centre and any other point on the circle. Another way to think of a circle is as the collection of all points at a certain radius from the centre.

The following is the equation for a circle with centres (a, b) and radius r:

(x - a)² + (y - b)² = r²

In this case, the center of the circle is A(2,3), and a point on the circle is B(7,15). The radius of the circle may be calculated using the distance formula:

r = √((7 - 2)² + (15 - 3)²) = √(5² + 12²) = 13

So the equation of the circle is:

(x - 2)² + (y - 3)² = 13²

(x - 2)²+ (y - 3)² = 169

Therefore, the equation of the circle is (x - 2)²+ (y - 3)² = 169

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The slope of the line tangent to the curve y³-xy²+x³=5 at the point (1,2) is option (B) 1/8.

To find the slope of the line tangent to the curve at the point (1,2), we first need to find the derivative of the curve with respect to x, and then evaluate it at x=1, y=2.

Taking the derivative of both sides of the equation y³-xy²+x³=5 with respect to x using the product rule, we get

3y²(dy/dx) - y² - 2xy(dy/dx) + 3x² = 0

Simplifying this expression and solving for dy/dx, we get:

dy/dx = (y² - 3x²)/(3y² - 2xy)

Substituting x=1 and y=2, we get:

dy/dx = (2² - 3(1)²)/(3(2)² - 2(1)(2))

dy/dx = (4 - 3)/(12 - 4)

dy/dx = 1/8

Therefore, the correct option is (B) 1/8

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The correct options that shows the the functions that can be used to get the number of copies are:

first week sold 800 copies

∴ at n=1  ⇒⇒⇒ f(1) = 800

Each week the number of copies sold decreased by 11%.

∴ at n = 2 ⇒ f(2) = 800 * (1-.11) = 800 * 0.89 = f(1) * 0.89

  at n = 3 ⇒ f(3) = 800 * 0.89 *0.89 = 800 * 0.89² = f(1) * 0.89 * f(2)

  at n = 4 ⇒⇒⇒ f(4) = 800 * 0.89³ = f(1) * 0.89 * f(3)

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The vectors that join the center of a clock to the hours :

At 1:00: (cos(π/6), sin(π/6)) = (√3/2, 1/2)

At 2:00: (cos(π/3), sin(π/3)) = (1/2, √3/2)

At 3:00: (cos(π/2), sin(π/2)) = (0, 1)

What is Vector?

A vector is a object that has both magnitude (size) and direction. In other words, a vector is a quantity that can be represented by an arrow or line segment, where the length of the arrow corresponds to the magnitude of the vector.

To find the vectors that join the center of a clock with radius 1 unit to the hours 1:00, 2:00, and 3:00, we can use basic trigonometry.

First, we can find the angle (in radians) between the 12:00 position and each of the desired hour positions. Since there are 12 hours on a clock and the circle has a circumference of 2πr = 2π(1) = 2π, the angle between each hour mark is:

2π/12 = π/6 radians

Therefore, the angles between the center of the clock and the hour marks are:

At 1:00, the angle is π/6 radians clockwise from the 12:00 position.

At 2:00, the angle is 2π/6 = π/3 radians clockwise from the 12:00 position.

At 3:00, the angle is 3π/6 = π/2 radians clockwise from the 12:00 position.

Next, we can use the cosine and sine functions to find the x and y components of each vector. The x-component of each vector is given by the radius times the cosine of the angle, and the y-component is given by the radius times the sine of the angle.

Therefore, the vectors that join the center of the clock to the hours 1:00, 2:00, and 3:00 are:

At 1:00: (cos(π/6), sin(π/6)) = (√3/2, 1/2)

At 2:00: (cos(π/3), sin(π/3)) = (1/2, √3/2)

At 3:00: (cos(π/2), sin(π/2)) = (0, 1)

Note that these vectors are unit vectors, meaning that they have a length of 1 unit.

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An argument can be invalid even if the premises are true and the conclusion is false.This statement is actually false.

Invalidity refers to the structure of the argument, not the truth value of the premises or conclusion. An invalid argument fails to establish the truth of its conclusion even if its premises are true. In contrast, a valid argument guarantees that the conclusion follows from the premises, regardless of the truth or falsity of the premises. Therefore, an argument can be valid with false premises, and an argument can be invalid with true premises.

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Conclude that there is no guarantee that the conclusion will be false when all the premises are false in an invalid

argument.

If an argument is invalid, then whenever the premises are all false, the conclusion must also be false.

An invalid argument is one where the conclusion does not necessarily follow from the premises, even if the premises

are all true.

In other words, it is possible for the premises to be true, but the conclusion to be false. However, in the scenario you

described, all the premises are false. In an invalid argument, there is no guarantee that the conclusion will also be false.

Identify the argument as invalid.

Recognize that all the premises are false.

Understand that in an invalid argument, the conclusion does not necessarily follow from the premises.

Conclude that there is no guarantee that the conclusion will be false when all the premises are false in an invalid

argument.

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The intermediate step in completing the square in the equation -3x² + 54x = 51 is (x - 9)² = 64

Completing the square is a method of solving a qudratic equation by converting it into a perfect square binomial.

To find the intermediate step in the form (x + a)² = b as a result of completing the square for the following equation?

-3x² + 54x = 51, we proceed as follows

-3x² + 54x = 51

Dividing through by -3, we have that

-3x²/-3 + 54x/-3 = 51/-3

x² - 18x = 51/-3

Next, we add half the square of the coefficient of x to both sides, that is (-18/2)² = (-9)²

x² - 18x + (-9)² = -17 + (-9)²

(x - 9)² = -17 + 81

(x - 9)² = 64

So, the intermediate step is (x - 9)² = 64

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It wants you to multiply (5) x (8) = 40/3

The equation that represent the number of pine cones Christian has is A)p=9 x 3 and D)p=3x9.

What is equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here Number of pine cone basket does Christian have = 3

Number of pine cone in One basket = 9.

Then the equation is,

Number of pine cones Christian has = 3 × 9

=> p = 3 × 9 or p = 9×3.

Hence the correct equation is A)p=9 x 3 and D)p=3x9.

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Analysis of variance can be used to determine differences in test scores of more than two groups. It is true.

What is variance?

Apart from the measurement of statistics range and interquartile range, variance is a measure of dispersion that takes into account the spread of all data points in a data set. It is the measure of dispersion which has the most often utility, along with the standard deviation, which is nothing but the square root of the variance.

An analysis of variance (ANOVA) is called an analysis tool in statistics which separates an observed aggregate  variability which is found inside a two part data set.

As ANOVA is the extension of of t-tests and z-tests so a one way ANOVA can be used for three or more groups of data  in the purpose to gain information about the relationship in between dependent and independent variable.

So ANOVA can be used to determine differences in test scores of more than two groups.

Hence, the statement is true.

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Any counting number can be written as the sum of distinct powers of 2.(proved).

What is counting number?

Counting numbers are nothing but  the natural numbers that can be used for counting. The numbers start from 1 and the series continues as 1, 2, 3, 4, 5, 6,-- and so on. Zero can not be included in counting numbers because we cannot count 0.

To prove this statement we have to consider two cases.

Let, n be any counting number or natural number. Then the power of 2 can be written as 2ⁿ.

n can be even or odd.

n=1:

If n=1 then it can be written as 2⁰

Let us assume that for n≤ k that n can be written as the sum of distinct powers of 2.

Now let us take, n= k+1.

Here one case is n is odd.

Then n≤ k+1

   so, n-1≤ k

By the induction hypothesis n-1 can be written as distinct power of 2.

n is the sum of these distinct powers of 2 as well 2⁰, which is not among them. as n-1 is even.

Now if n is even,

so n=2m (say) for m≤ k

Thus, by the induction hypothesis m can be written as distinct power of 2.

If for each power of 2 in this sum , increment the exponent by 1 then the resulting sum of distinct powers of 2 equals n= 2m

Hence, the statement is true.

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Answer: The First Graph and the Last Graph

Step-by-step explanation:

So all of these are inverses of a function. But as for how do you tell if the inverse is a function...

Well, it has to pass the test that all functions have to pass: the Vertical Line Test.

Any time you draw a vertical line down a graph, it should ONLY PASS THROUGH ONE POINT.

Your pictures are a little blurry, but as far as I can tell, Graph 1 is pretty linear, and a vertical line drawn would only intersect one point on the graph.

The second one however... well it seems pretty obvious why the vertical line test wouldn't work there. A vertical line drawn on the right half would intersect two points, which does not pass the test.

Same thing for Graph 3.

Graph 4 looks like it would pass the vertical line test. I cannot see the section on the y-axis that well, but it looks like it doesn't double back on itself.

Just check them with the Vertical Line Test! It's really useful for figuring out if something's a function or not.

Answer:

if no initial high im guessing 4.8 weeks

Step-by-step explanation:

4.8 divied by .8 = 6

Answer:

7 week 3 days and 12 hour

Step-by-step explanation:

x is the required week and to calculat it

1st for 1 week= o.8 inch

x = 6 inch

2nd u solve it after u solve it u get 7.5 but week dosen't said by decimals so u will multiply 0.5 by days of the week which is 7 .

3rd u will get 3.5 as we said before for days we can't use decimals so yo will multiply 0.5 by hour which 24 then u will get 12 . so the answer is 7 week 3 days and 12 hour .

The lengths of the base and height are, 13 miles and 52 miles respectively.

Given that;

The area of a parallelogram is, 676 square miles

And, the height is four times the length of the base,

Hence, We get;

Length of base = x

Height = 4x

Since, Area of the parallelogram = Base × Height

Hence, We get;

676 = x × 4x

x² = 676 / 4

x² = 169

x = √169

x = 13 miles

Thus, Length of base = x = 13 miles

Height = 4x = 4 x 13

                  = 52 miles

Thus,, The lengths of the base and height are, 13 miles and 52 miles respectively.

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The null hypothesis is that the true average amount left is equal to 10% of the advertised net contents. In In another case of true average amount is less than 10% of the advertised net contents.
Hence, we will utilize  one-tailed t-test with a significance level of 0.05 to test this hypothesis.

The sample mean of the five tubes is (0.51+0.63+0.42+0.5+0.37)/5 = 0.486 ounces.

The sample standard deviation is √(((0.51-0.486)² + (0.63-0.486)² + (0.42-0.486)² + (0.5-0.486)² + (0.37-0.486)²)/4) = 0.107 ounces.

The t-statistic is calculated as
(mean sample - hypothe -sized mean)/( standard deviation sample/√( size sample))
= (0.486 - 0.6)/(0.107/√(5))
= -3.06.

The p-value for this test is 0.0249 which is less than our significance level of 0.05.

Therefore, we reject the null hypothesis and conclude that there is evidence that the true average amount left in a tube of toothpaste is less than 10% of the advertised net contents.

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The correct statements  to conclude that a parallelogram is a rhombus are:  a.)  Segment AD ≅  Segment AB  e.)  Segment AB ≅  Segment DC

f.) ∠ABC ≅ ∠CDA

In two dimensions, a parallelogram is a geometric figure with parallel sides. It has two parallel sides that are  the same length, making it a four-sided polygon (sometimes called a quadrilateral). The sum of the adjacent angles of a parallelogram is 180 degrees. Parallelograms are a unique class of polygons.  

To conclude that a parallelogram is a rhombus, we must show that all four sides are congruent (of equal length). Therefore, statements that provide information about the sides of a parallelogram can help us make this conclusion.  

The correct statements  to conclude that a parallelogram is a rhombus are:

a.)  Segment AD ≅  Segment AB

e.)  Segment AB ≅  Segment DC

f.) ∠ABC ≅ ∠CDA

These statements tell us that opposite sides are congruent and opposite angles are congruent, which are properties of a rhombus. However, the expressions b, c and d do not give information about the sides, so it cannot be concluded from them that the parallelogram is a rhombus.

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On solving the provided question we can say that as a result, the system of equations' solution is: x = 12.62 and y = 4/13

A mathematical equation is a formula that links two statements and uses the equals sign (=) to indicate equality. In algebra, an equation is a statement that demonstrates the equality of two mathematical expressions.

We wish to eliminate one of the variables, either x or y, by adding or subtracting the two equations to solve this system of equations using the elimination technique. To do this, multiply one or both equations by a constant factor such that one of the variables has the same coefficient in both equations but with opposite signs.

By multiplying the first equation by 5 and adding it to the second, we can remove x. This results in:

5x - 10y = 60

5x + 3y = -44

-13y = -4

y = 4/13

We may now plug this y value into one of the original equations to find x. Let's look at the first equation:

x - 2y = 12

x - 2(4/13) = 12

13x - 8 = 156

13x = 164

x = 12.62

As a result, the system of equations' solution is:

x = 12.62 and y = 4/13

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The variability in the heights of the seventh graders is approximately 0.6 times the variability in the heights of the sixth graders.

The variability or dispersion of a set of data is measured by the mean absolute deviation (MAD). By averaging the absolute differences between each data point and the set mean, it is calculated. Because it is less impacted by high values or outliers, the MAD is a more reliable measure of variability than the standard deviation. The MAD is always a non-negative number and is stated in the same units as the data. Greater variability is indicated by a bigger MAD, whereas a smaller MAD suggests that the data points are more variable and are consequently closer to the mean. The MAD is frequently used to track process variation in descriptive statistics and quality control applications.

Given that, MAD for the sixth graders is 1.2 and the MAD for the seventh graders is 0.7.

To determine the relation of variability we take the ratio as:

0.7 / 1.2 ≈ 0.6

Hence, the variability in the heights of the seventh graders is approximately 0.6 times the variability in the heights of the sixth graders.

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The complete question is:

Floor space (Volume) of Firm 1's structure (cylinder)  is  230907.06 cubic ft

≈ 2.31 × 10⁵cubic ft.

Volume is characterised  as the three dimensional quantity that is used to guage the capacity of a solid shape. It implies the amount of three dimensional space a closed figure can fill. It is measured by its volume .  Some times volume can be interchanged as capacity. For instance,  the amount of water a cylindrical jar can occupy is measured by its volume .

The unit of volume is cubic units such as cubic meters, cubic centimeters , cubic millileters among others  .

Volume is gauged by multiplying the area of the shape with its third dimension .

A cylinder is a three dimensional space made up of two circular bases that are parallel to one another and are connected by a curved surface

Volume of the cylinder = [tex]\pi r^{2} h[/tex]

where r = radius of the cylinder

h = height of the cylinder

Here given that, diameter of the cylinder = 70 ft

∴ radius of the cylinder = 35 ft

Additionally, height of the cylinder = 60 ft

∴ Volume of the cylinder = [tex]\pi[/tex]× (35)²× 60 = [tex]\pi[/tex]× 1225 × 60

= 3.14 × 1225 × 60 = 230907.06 cubic ft ≈ 2.31 × 10⁵ cubic ft .

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If Jasmine saves $10 per week and her sister saves $7 per week, then Jasmine will have more "money-saved" than her sister in 10 weeks.

Let the number of weeks be denoted by "x",

We know that,

The Jasmine's initial-savings is = $50,

The amount which Jasmine weekly saves is = $10,

Her sister's initial savings is = $80,

The amount which her sister weekly-saves is = $7,

We have to find the value of "x" when Jasmine's savings exceed her sister's savings.

Total saving's of Jasmine after "x" weeks is calculated as,

⇒ Jasmine's total savings = Initial savings + (Weekly savings × Number of weeks),

⇒ $50 + ($10 × x),

Her sister's total savings after "x" weeks can be calculated as:

⇒ Sister's total savings = Initial savings + (Weekly savings × Number of weeks),

⇒ $80 + ($7 × x),

We write the equation to find the value of "x" when Jasmine's total savings exceed her sister's total savings,

⇒ 50 + 10x > 80 + 7x,

⇒ 50 + 10x - 80 > 7x,

⇒ 50 - 80 > 7x - 10x,

⇒ -30 > -3x,

⇒ -30/-3 < x,

⇒ 10 < x,

Therefore, Jasmine will have more money than her sister is after 10 weeks.

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Answer:

Step-by-step explanation:

Given 36 books in a box with toys such that the books : toys ratio is 4 : 5, you want the initial number of toys and the number given away if the ratio becomes 12 : 11.

The number of books remains constant at 36. We can rewrite the ratios so that each shows the correct number of books:

  ratios are books : toys

  before: 4 : 5 = 36 : 45 . . . . . . . multiply by 9

  after: 12 : 11 = 36 : 33 . . . . . . . . multiply by 3

Based on the above, we see the initial number of toys is 45.

The final number of toys is 33, so the number given away is ...

  45 -33 = 12

12 toys were given away.

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According to this research, options B and D appear to be the most slope plausible explanations for the data. However, without the real data, determining which equation is the best model is impossible.

The slope of a line indicates how steep it is. The gradient's mathematical equation is known as "gradient overflow" (the change in y divided by the change in x). The slope is defined as the ratio of the vertical change (rise) between two places to the horizontal change (run). The slope-intercept form of an equation is used to express a straight line's equation, which is written as y = mx + b. The y-intercept is found where the slope of the line is m, b is b, and (0, b). For example, consider the slope and y-intercept of the equation y = 3x - 7.The slope of the line is m. b is b at the y-intercept, and (0, b).  

It is impossible to establish which equation is the best model of the data without the actual data. However, we may analyse each possibility based only on the facts provided:

A. y= 2.2 - (1.1%): This equation appears to contain a constant term and a negative slope, making it unsuitable for predicting plant height over time.

B. y= 0.5x + 1.8: The positive slope of this equation indicates that the plant's height rises with time. The constant term of 1.8 might represent the plant's beginning height, while the coefficient of 0.5 could reflect the plant's growth rate.

C. y= 2.0 • (1.4%): This equation appears to contain a constant term and a positive slope, but the percentage term is not obvious how it links to the data.

D. y = 0.7 x + 2.1: This equation, like option B, has a positive slope and a constant term. The coefficient of 0.7 might reflect the plant's growth rate, while the constant term of 2.1 could represent the plant's original height.

According to this research, options B and D appear to be the most plausible explanations for the data. However, without the real data, determining which equation is the best model is impossible.

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Answer: Split it in half to turn it into a triangle! The hypotenuse if the triangle will give you the diagonal length of the suitcase, because it’s a rectangle. Hope this helps :D

Step-by-step explanation: