Determine the level of measurement of the variable. capacity of a backpack a.interval b.ordinal c.nominal d.ratio

2 can be used as the base for 8 and 16 to write in exponent form.

A number system is defined as a system of writing to express numbers.

We have to rewrite both 8 and 16 with same base as using exponents.

8 can be written 2×2×2

8 as 2³

16 can be written as 2×2×2×2

16 as 2⁴

Hence, 2 can be used as the base for 8 and 16 to write in exponent form.

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Answer:

y = (9/2)x + 26.5

Step-by-step explanation:

Lets rewrote the equation in standard format of y = mx + b, where m is the slope and b is the y-intercept.

-2x-9y = 1

-9y = 2x + 1

y = -(2/9)x - (1/9)

The slope of this line is -(2/9)

A line that is perpendicular to this line will have a slope that is the negative inverse of -(2/9).  That would be (9/2).  So a perpendicular line will have the form of y = (9/2)x + b.  Any value of b can be chosen and the lines will still be perpendicular to each other.  However, we want to find a value of b that will force the line through point (-7,-5).  This is done by using the point in the above equation and solving for b:

y = (9/2)x + b

-5 = (9/2)(-7) + b  for point (-7,-5)

-5 = -(63/2) + b

b = -5 + (63/2)

b = -5 + 31.5

b = 26.5

The equation is y = (9/2)x + 26.5

See the attached graph.

a) The equation in slope-intercept form is y = 112.5x - 11,875, where x is the age of the tree in years and y is the number of board feet that can be created from the tree.

b) The independent variable represents the age of the tree in years.

c) The dependent variable represents the number of board feet that can be created from the tree.

d) For a tree that is 100 years old, the number of board feet that can be used is 11,875.

e) To find how old the tree is, we need to solve the equation for x.

First, subtract 6,825 from both sides of the equation to get y = 112.5x - 11,875 - 6,825.

Next, add 11,875 to both sides of the equation to get y + 11,875 = 112.5x.

Finally, divide both sides of the equation by 112.5 to get x = (y + 11,875) / 112.5.

Thus, the age of the tree is x = (6,825 + 11,875) / 112.5 = 100 years old.

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Answer:

No solutions

Step-by-step explanation:

Sorry to say, there are no solutions to this system of linear equations.  A quick look at the attached graph will illustrate this conclusion.  The two lines that go through the given points are parallel.  They both have a slope of (1/3), with y-intercepts of 4 and -2.

Calculate the slopes of both lines:

Line A:    

Point 1    (0,3)

Point 2   (3,4)

Rise = 4-3 = 1

Run = 3-0 = 3

Slope = Rise/Run = (1/3)

Line B:    

Point 1   (0,-2)

Point 2   (3,-1)

Rise = -1-(-2) = 1

Run = 3-0 = 3

Slope = Rise/Run = (1/3)

Since the lines have the same slope, no more work is needed.  They are parallel and will not intersect.  Therefore, there are no solutions.

=====

If interested:

The y-intercept for each line can be found by using one of the points for each line in the equation y = mx + b, where m is the slope of (1/3) and b is the y-intercept.

Line 1:  y = (1/3)x + b

3 = (1/3)*(0) + b  for (0,3)

b = 3

Both lines have a slope of (1/3).  They are parallel and will never meet, even though they have a lot in common.  

Line 2:  y = (1/3)x + b

-2 = (1/3)*(0) + b for (0,-2)

b = -2

Answer:

No solutions

Step-by-step explanation:

I got it right on the test

The number of successful 3-point shots must be 51.

If the away team scored a total of 93 points and made 42 successful field goals, then the remaining points must have come from successful 3-point shots.

Since there were no successful free throw shots, the number of successful 3-point shots must be 93 - 42 = 51.

The information provided is about a basketball game where the away team lost and scored a total of 93 points. The team made 42 successful field goals, but there were no successful free throw shots. Based on this information, the remaining points were determined to have come from successful 3-point shots, which numbered 51.

The information is specific to this basketball game and the scoring system used in this game. Different basketball games may have different scoring systems and rules, so the information may not be applicable to other basketball games.

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The confidence interval has a lower bound of 6.04 and an upper bound of 9.96.

A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. A confidence interval is calculated at a specified confidence level; the 95% confidence level is most commonly used, but other levels, such as 90% or 99%, are occasionally employed. The confidence interval is the range of values within which you expect your estimate to fall a given proportion of the time if you repeat your experiment or re-sample the population in the same manner. A 95% confidence interval is a range of values above and below the point estimate where the real value in the population is 95% likely to reside.

Here,

For a two-tailed 95% confidence interval, the alpha value is 0.025, and the corresponding critical value is 1.96. This means that to calculate the upper and lower bounds of the confidence interval, we can take the mean ±1.96 standard deviations from the mean.

sample mean=8

upper and lower bounds of the confidence interval,

=mean ±1.96

=[8-1.96,8+1.96]

=[6.04,9.96]

The lower bound of the confidence interval is 6.04 and the upper bound is 9.96.

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Answer:

3¼% of $500 is $16.25.

Step-by-step explanation:

The length of AL, BK and CH are 12, 9 and 6 respectively.

Similar triangles are those triangles which has the same shape but different size.

The length of sides are proportional in similar triangles.

Given a figure of a big triangle.

We can clearly see that angles made by each of the triangles ALE, BKE, CHE and DGE are equal and thus they are similar triangles.

The sides of similar triangles are proportional.

DG / GE = CH / HE = BK / KE = AL / LE

We have DG = 3, GE = 5,HG = 5, KH = 5, LK = 5

HE = 5 + 5 = 10

KE = 5 + 5 + 5 = 15

LE = 5 + 5 + 5 + 5 = 20

Substituting,

Consider DG / GE = CH / HE

3 / 5 = CH / 10

CH = (3/5) × 10 = 6

Consider DG / GE = BK / KE

3 / 5 = BK / 15

BK = (3/5) × 15 = 9

Consider DG / GE = AL / LE

3 / 5 = AL / 20

AL = (3/5) × 20 =  12

Hence the length of AL is 12, length of BK is 9 and length of CH is 6.

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The cost of a 32-ounce container is 2.92 and the cost of 6 8-ounce containers is $4.18.

Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.

Let's call the unit price of 8-ounce yogurt x.

32-ounce unit price = x + 0.002

32-ounce container cost = 32 * (x + 0.002) =0.064 + 32x

6 * 8-ounce container cost = 6 * 8 * x = 48x

Given, 32-ounce container cost = 6 * 8-ounce container cost - $1.33

Substituting the costs,

0.064 + 32x = 48x - 1.33

Solving for x,

48x - 32x = 0.064 + 1.33

16x = 1.394

x = $0.087125

So, the unit price of 8-ounce container is $0.087125

Cost of 32-ounce container = $0.064 + 32 * (0.087125 + 0.002) = $2.92

Cost of 6 8-ounce containers = 6 * 8 * 0.087125 = $4.18.

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The cosine functions are used to find the angle if the length of the hypotenuse and the length of the adjacent side is known.

The ratio of the adjacent side of a right triangle to the hypotenuse is called the cosine and is given the symbol cos.

The cosine function in a triangle is the ratio of the adjacent side to that of the hypotenuse.

The general formula for cosine is:

cos α = Adjacent Side/Hypotenuse

Cosine has a few properties, which are periodic and even.

It is the ratio of the length of the side that is ADJACENT the angle to the length of the longest side, or HYPOTENUSE, of the triangle.

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The scatter plot shows [negative linear] association.

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

The image of the scatter plot

On the scatter plot, we can see that

The points appear to be on a straight line

Also, we can see that

As the x values increases the y values decreases

This represents a negative linear] association.

Hence, the association is a negative linear] association.

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Answer:

12. m = 1/3

14. m = 5/6

16. m = -5/2

Step-by-step explanation:

m = y2-y1/x2-x1

Cost of goods manufactured= $905,000 Overhead cost applied to Work in Process and hence option c is correct

To calculate the cost of goods manufactured, we need to use the following formula:

cost of goods manufactured= beginning WIP + direct materials + direct labor + allocated manufacturing overhead - Ending WIP

Schedule cost of goods manufactured:

Beginning WIP= 40,000

Direct materials used= 20,000 + 400,000 - 30,000= 390,000

Direct labor= 60,000

Allocated manufacturing overhead= 485,000

Ending WIP= (70,000)

Cost of goods manufactured= $905,000

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Check the picture below.

The segment drawn from the apex to the edge of the circular base is 24.2 units.

A right triangle's hypotenuse, or side opposite the right angle, has a square length that, according to the Pythagorean theorem, is equal to the sum of the squares of the lengths of the other two sides.

The Pythagorean Theorem can be used to determine the slant height of a right cone. The circular base's radius is equal to its diameter times half, or 6/2 = 3 units.

The volume of the cone can be found using the formula:

V = (π/3)r²h

Where r is the radius, and h is the height of the cone. Plugging in the given values, we have:

72π = (π/3)r²h

72π = (π/3)3²h

72π = (π/3)9h

72π = 3πh

24 = h

Using the Pythagorean Theorem, we can find the slant height as follows:

c² = a² + b²

Where a and b are the height and radius of the cone, and c is the slant height. Plugging in the values we have:

c² = 24² + 3²

c² = 576 + 9

c² = 585

c = 24.2

Hence, the segment drawn from the apex to the edge of the circular base is 24.2 units.

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The polynomials is divided using synthetic division and the remainder theorem to 3x³ -6x² - 20x - 77/x + 4

Synthetic division is described as one of the methods that is used to manually perform the Euclidean division of polynomials.

The steps taken in a synthetic division include;

Given the polynomial;

f(x) = 3x³ + 6x² + 4x +3 by x + 4

We have;

        3          6        4         3

-4     _____-12__24___80__

        3          -6       -20      -77

Then, we have;

3x³ -6x² - 20x - 77/x + 4

Hence, the expression is 3x³ -6x² - 20x - 77/x + 4

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Answer:

[tex]\frac{92}{100\\}[/tex], 77%, 58%,  [tex]\frac{36}{100}[/tex], [tex]\frac{11}{100}[/tex], 3%

Step-by-step explanation:

I changed them all to percents

3 %

[tex]\frac{11}{100}[/tex]  Percent means what out of 100? 11%

77%

92/100  = 92%

36/100 = 36%

58%

Answer:

Step-by-step explanation:

q x q + r² and 2q + (r + r)

q × q + r² = q² + r²

----------

2q + (r + r) = 2q + 2r

An ordered pair that is a solution to the equation represented by the graph include the following: A. (-4, 0).

In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph.

In order to determine the ordered pairs that represent points on the graph of any given function, we would read all the ordered pairs that lie on its line, with respect to the x-coordinate (abscissa) and the y-coordinate (ordinate).

By critically observing the graph of the given function, the required solutions are include following;

Ordered pair = (-4, 0).

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0.947 g/ml is the cube density the volume was 9.01.

The term "density" refers to the ratio between the volume (the amount of space taken up by an item or substance) and the amount of matter contained inside (its mass). The quantity of mass per unit of volume is another method to define density.

We are know that items float in liquids when their density is less than that of the liquid.

Objects floating in a liquid are those whose density is equal to that of the liquid.

So, in this case, the cube is solely suspended in the first liquid combination. Therefore, the first liquid mixture's density is the same as a cube. The other mixes have densities that are higher than that of the cube.

Density of methanol = 0.7913 g/ml

Density of water = 1 g/ml

Density of the 6th liquid mixture:

= {(2 × 0.7913 ) + (1 × 6)}/8 g/ml

= 0.947 g/ml

Therefore density of cube = 0.947 g/ml

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The complete question is as follows:

What Is The Cube Density The Volume Was 9.01? The Cube Floated Up To 8.1 Ml

The Surface area are shown below.

The total area of an object's external facing surfaces is its surface area. The base, top, and lateral surfaces (sides) of the object's surface are added together to get the object's overall surface area.

1. The measure of sides are

A = 3

B = 15

C= 17

D= 8

So, the Lateral Surface Area

= ( 15+17+8) x 3

= 117 mm²

and, the total surface Area

= Area of two triangles + Area of rectangle

= 2 x 1/2 x 8 x 15 + 117

= 120 + 117

= 237 mm²

2. The measure of sides are

A = 5

B = 2

C= 9

D= 2

So, the Lateral Surface Area

= 2 x (5 x 9) + 2 (2 x 5)

= 110 m²

and, the total surface Area

= 110 + 2 (2 x 9)

= 146 m²

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(a) The tree diagram by filling in the missing path probabilities by subtracting the given value by 1 is given below.

(b) The probability that the car is repaired under budget, on time, and with company D is 0.00652.

(c) The probability that the cost of the repair exceeds the estimate is 0.3909.

(d) The probability that the car is repaired under budget, given that it is ready on time is 0.5804.

D = driver takes his car to shop D.

L = driver takes his car to shop L.

T= the work is complete on time.

B= the cost is less than or equal to the estimate (under budget).

(a) We have to complete the tree diagram by filling in the missing path probabilities.

The complete tree diagram is given below:

We used to complete the tree

1 - 0.634 = 0.366

1 - 0.226 = 0.774

1 - 0.844 = 0.156

(b) We have to determine the probability that the car is repaired under budget, on time, and with company D.

P(DTB) = 0.634 × 0.226 × 0.455

P(DTB) = 0.00652

(c) We have to determine the probability that the cost of the repair exceeds the estimate.

P(B') = P(DTB') + P(DT'B') + P(LTB') + P(LT'B')

P(B') = 0.634 × 0.226 × 0.545 + 0.634 × 0.774 × 0.622 + 0.366 × 0.156 × 0.105 + 0.366 × 0.844 × 0.005

P(B') = 0.390855

P(B') = 0.3909

(d) We have to determine the probability that the car is repaired under budget, given that it is ready on time.

P(B|T) = P(BT)/P(T)

P(B|T) = (0.634 × 0.226 × 0.455 + 0.366 × 0.156 × 0.895)/(0.634 × 0.226 + 0.366 × 0.156)

P(B|T) = 0.580373

P(B|T) = 0.5804

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The postulate theorem used to prove the congruence of triangles MNQ and PXN is given as follows:

B. SAS.

The Side-Angle-Side congruence theorem states that if any of the two sides on a triangle are the same, along with the angle between them, then the two triangles are congruent.

The congruent sides are given as follows:

The angle between these two sides is a vertical angle, having the same measure in each of the triangles, hence the SAS theorem can be applied and the correct option is given by option B.

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Answer:

The percent error of Jack's measurement was 3.6%, to the nearest tenth of a percent. This is calculated by subtracting the actual length (16.6 inches) from the measured length (17.2 inches) and dividing by the actual length, then multiplying by 100.

Step-by-step explanation:

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The equation is z = (-2/3)*xy with of x , y and z are jointly varied.

Joint variation describes a situation in which, while the other variables are held constant, the value of one variable relies on the values of two or more additional variables.

Joint variation is used to describe when more than two variables are directly correlated or when one variable changes as a result of the change product of more than two variables. X can be symbolically expressed as X YZ if it is in joint variation with Y and Z. If Y is also constant, then X and Z directly depend on one another.

Joint variation is a type of variation where a quantity changes when two or more other numbers are multiplied together. For instance, when a rectangle's length or breadth changes, so does its area. Where A is the area, l is the length, and w is the width, we say that A = lw.

Joint Variation of x,y and z

z = kxy

k is the cofficient

for x = 7, y = 3 and z = -14

-14 = k*3*7

⇒k = -2/3

for x= 3 and z = -8

-8 = (-2/3)*3*y

y = 4

The equation is z = (-2/3)*xy with of x , y and z are jointly varied.

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The standard form of the equation of the circle with the given characteristics is  (x - 6)² + (y - 1)² = 65.

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

Given, center:  (6, 1) and solution Point: (5,9)

By solution point, it means that the circle passes through that point. Hence, the radius of the circle is the distance between  (6, 1) and  (5,9)

Distance formula is given by

D = √[(x2 - x1)² + (y2 - y1)²]

D=  √[(5 - 6)² + (9 - 1)²] = 8.062

r= 8.062  or r²=65

We have, equation of the circle centered ant (h, k) and radius ‘r’ as

(x - h)² + (y - k)² = r².

=>  (x - 6)² + (y - 1)² = 65.

The standard form of the equation of the circle with the given characteristics is  (x - 6)² + (y - 1)² = 65.

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The equation of the plane that passes through (1, 3, 6) and is parallel to x = 11 is x = 1.

An algebraic expression is a mathematical phrase that can contain numbers, variables, and operations (such as addition, subtraction, multiplication, and division). It represents a value that can be determined if the values of the variables are known. An algebraic expression does not contain an equal sign and cannot be solved like an equation, but it can be simplified or manipulated using algebraic rules. For example, the expression 2x + 3y is an algebraic expression, where x and y are variables.

A plane can be represented by a normal vector (a,b,c) and a point (x⁰,y⁰,z⁰) that lies on the plane. If a plane is parallel to the plane x = 11, the normal vector must be in the direction of the x-axis, meaning (a,b,c) = (1,0,0).

The equation of the plane can then be found using the point-normal form, which is given by:

ax + by + cz = d, where d = ax⁰ + by⁰ + cz⁰

Plugging in the values for (1,3,6) and (a,b,c) = (1,0,0), we get:

a(1) + b(3) + c(6) = d

1 + 0 + 0 = d

d = 1

So the equation of the plane that passes through (1,3,6) and is parallel to x = 11 is: x = 1

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Haruka hiked about 14 kilometres in total.

According to the question

We don't know precisely how many kilometres Haruka travelled in the morning, but she hiked several kilometres in the morning and six kilometres in the afternoon. We may utilise the information provided—that her afternoon hike was 25% shorter than her morning trip—to solve the problem.

The unknown quantity (the number of kilometres hiked in the morning) may be represented as X in algebra. We may express the equation as follows if Haruka travelled 6 kilometres in the afternoon, which was 25% less than her morning hike:

6 = X - 0.25X

This equation can be simplified to:

6 = 0.75X

And finally, by solving for X, we get:

X = 8

In the morning, Haruka walked 8 kilometres. The distance travelled in the morning and afternoon are simply added together to provide the total number of kilometres hiked:

8 + 6 = 14 kilometers

Thus, during the course of the two excursions, Haruka covered a distance of 14 kilometres.

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Haruka hiked about 14 kilometres in total.

According to the question

We don't know precisely how many kilometres Haruka travelled in the morning, but she hiked several kilometres in the morning and six kilometres in the afternoon. We may utilise the information provided—that her afternoon hike was 25% shorter than her morning trip—to solve the problem.

The unknown quantity (the number of kilometres hiked in the morning) may be represented as X in algebra. We may express the equation as follows if Haruka travelled 6 kilometres in the afternoon, which was 25% less than her morning hike:

6 = X - 0.25X

This equation can be simplified to:

6 = 0.75X

And finally, by solving for X, we get:

X = 8

In the morning, Haruka walked 8 kilometres. The distance travelled in the morning and afternoon are simply added together to provide the total number of kilometres hiked:

8 + 6 = 14 kilometers

Thus, during the course of the two excursions, Haruka covered a distance of 14 kilometres.

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Answer:

3 Degrees each hour

Step-by-step explanation:

27 divided by 9 = 3

The system is dependent and has infinitely many solutions.

What is the system of equations?

A system of linear equations is a set of two or more equations that includes common variables. To solve a system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.

The system of equations below can be written as:

9x + 6y = -2

-18x - 12y = -4

To find the number of solutions, we need to determine if the system has a unique solution, no solution, or infinitely many solutions.

To do this, we can use the concept of compatibility. If the system is compatible, meaning that there exists a set of values for x and y that satisfy both equations, then the system has at least one solution.

If the system is inconsistent, meaning that there is no set of values for x and y that satisfies both equations, then the system has no solution.

If the system is dependent, meaning that the two equations represent the same line in the plane, then the system has infinitely many solutions.

In this case, we can see that both equations represent the same line in the plane.

Therefore, the system is dependent and has infinitely many solutions.

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