An open box i to be contructed from a quare piece of heet metal by removing a quare of ide 3 feet from each corner and turning up the edge. If the box i to hold 300 cubic​ feet, what hould be the dimenion of the heet​ metal?

The measure of the longer leg of the triangle is given as follows:

6.93 cm.

The three trigonometric ratios are defined as follows:

The longer leg is opposite to the angle of 60º, hence the sine relation is used to find the length, as follows:

sin(60º) = x/8

x = 8 x sine of 60 degrees

x = 6.93 cm.

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The y-intercept of the line 11x + 10y = 2 is equal to 1/5.

In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:

y = mx + c

Where:

Based on the information provided about the line, it is represented by this equation;

11x + 10y = 2

By making "y" the subject of formula in the above equation, we have the following:

10y = -11x + 2

By dividing both sides of the equation by 10, we have the following:

y = -11x/10 + 2/10

y = -11x/10 + 1/5.

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The solution is Option B.

The rotation of the line JK around the point P by 180° will be J'K'

The measure of the amount a figure is rotated about the center of rotation is called the angle of rotation. The angle of rotation is usually measured in degrees. We specify the degree measure and direction of a rotation.

90° clockwise rotation: (x,y) becomes (y,-x)

90° counterclockwise rotation: (x,y) becomes (-y,x)

180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)

270° clockwise rotation: (x,y) becomes (-y,x)

270° counterclockwise rotation: (x,y) becomes (y,-x)

Given data ,

Let the rotation angle be represented as A

Now , the value of A is 180°

Let the points be represented as J and K

Let the rotated point be represented as J'K'

And , when a point is rotated by and angle 180° , the x and y coordinates of the point will become their additive inverse

For a 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)

And , the figure which represents the coordinates of the point J' and K' is when K' is below and J' is above

Hence , the solution is Option B.

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Since the value of y can be known from equation 1, we can use the substitution method to solve the system of equations. By entering the value of y in equation 2, we can quickly get the value of x. So the option B is correct.

The system of equation are:

y = 1/2x...................(1)

2x + 3y = 28...................(2)

To solve the system of equation we use substitution method because the value of y is know from the equation 1. We can find easily the value of x by putting the value of y in equation 2.

Now putting the value of y in equation 2.

2x + 3(1/2x) = 28

2x + 3/2 x = 28

7/2 x = 28

Multiply by 2 on both side, we get

7x = 56

Divide by 7 on both side, we get

x = 8

Now putting the value of x in equation 1

y = 8/2 = 4

The solution of the system of equation is (8, 4).

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Answer: 33.93 in

Step-by-step explanation:

we can see it is a right angle there. h is oppsite line of the right triangle and 70in is Hypotenuse. So, we can use the formula sin29 = h/70. Then sin29*70=h. h=33.93 in.

The rational exponent form is 5^3/5x. Option D

We know that a rational function would be the function that does not have the radical sign in it. We can see that we have the expression that have been written for us here as; 5√125x^5.

When we open up the radical we would have;

125^1/5 * 5^5/5

But we know that;

125 = 5^3

We now have;

5^3/5 * x

This becomes;

5^3/5x

Thus we are going to end up in the rational exponent form of the expression as 5^3/5x.

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The given statement about the stake holders of DMAIC is false.

The term DMAIC stands for Define, Measure, Analyze, Improve, and Control and it represents the five phases that make the process,

Here we have given that generally, all stakeholders agree that there is a problem and on what the problem is before beginning the DMAIC process.

And we need to check whether the statement is true or not.

Here we know that in DMAIC process we have to follow the following steps they are listed as,

=> Define the problem

=> Improve activity

=> To determine opportunities for improvement

=> Identify the project goals

=> To analyze project goals and customer requirements.

Hence through this we have identified that the main purpose of DMAIC is to improve the effectiveness and efficiency of an organization's existing processes.

And here we have also know that DMAIC is a core data-driven improvement methodology of Six Sigma.

So, here the given statement is false.

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A' = (-1, 3)

B' = (-4, 0)

C' = (1, 6)

=======================================================

Reason:

The notation [tex]T_{ < -3, 5 > }[/tex] means "translate 3 units left, 5 units up".

Another way to write out this rule is [tex](\text{x},\text{y}) \to (\text{x}-3,\text{y}+5)[/tex]

-------------------

Let's apply that rule to the coordinates of point A.

[tex](\text{x},\text{y}) \to (\text{x}-3,\text{y}+5)\\\\(2,-2) \to (2-3,-2+5)\\\\(2,-2) \to (-1,3)\\\\[/tex]

Point A' is located at (-1, 3)

-------------------

Repeat for the coordinates of point B.

[tex](\text{x},\text{y})\to(\text{x}-3,\text{y}+5)\\\\(-1,-5)\to(-1-3,-5+5)\\\\(-1,-5)\to(-4,0)\\\\[/tex]

Point B' is located at (-4, 0)

-------------------

Lastly do the same for point C.

[tex](\text{x},\text{y})\to(\text{x}-3,\text{y}+5)\\\\(4,1)\to(4-3,1+5)\\\\(4,1)\to(1,6)\\\\[/tex]

Point C' is located at (1, 6)

Quantitative variables provide numerical measures of individuals. The measurements yield useful results and can be added to or removed from.

A quantitative variable is one for which the data display amounts (e.g. height, weight, or age). A categorical variable is one where the data indicate categories. As was discussed in the chapter's section on variables, quantitative variables are those that are measured on a numeric scale.

Height, weight, reaction speed, subjective pain rating, temperature, and exam score are a few examples of quantitative variables.

A quantitative study works with numbers and data, whereas a qualitative study concentrates on words and meanings. Variables can be quantified, and hypotheses can be tested quantitatively. You can go more deeply into concepts and experiences by using qualitative research methods.

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The shape of the histogram is expected to be symmetric.

A histogram is a graphical representation of the distribution of a dataset. It is an estimate of the probability distribution of a continuous variable. The histogram is plotted with bin ranges on the x-axis and the frequency (count) of data points that fall within each bin on the y-axis.

The shape of the histogram can give you a sense of the underlying distribution of the data, such as whether it is symmetric or skewed.

Standardized test scores, like the SAT, are typically designed to have a normal distribution, meaning that the majority of scores fall in the middle range, with fewer scores at the extremely high or low ends.

Additionally, because the data is being collected from a large and diverse population of students from one state, it is unlikely that there would be a significant skew in one direction or another.

However, some factors such as socioeconomic status, family background, school district, and student ethnicity may affect the distribution.

Therefore, The shape of the histogram is expected to be symmetric.

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Answer:

(8,6×10^-3) (8×10^-1)

=(0,0086). ( 0.8)

The scale factor of a model is, 30 feet in a inch.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

A model of Seattle, Washington space Needle is 20 inches tall The actual Space Needle is approximately 600 feet tall.

Hence, The scale factor of a model is,

⇒ 600 feet / 20 inches

⇒ 30 feet per inches

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The required measure of the smallest angle in the triangle is 37°.

A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The sum of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.

We know that one angle in right angled triangle is 90 degree and sum of other two angle is 90 degree.

So, acute angles are (2x -3) and (3x-7).

Then

(2x -3) +  (3x-7) = 90

5x - 10 = 90

5x = 100

x = 20

Smallest angle = 2x - 3

= 2(20) - 3

= 40 - 3

= 37°

Thus, required Smallest angle is 37°

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Answer:

[tex]\frac{9}{20}[/tex]

Step-by-step explanation:

45% = [tex]\frac{45}{100}[/tex]

[tex]\frac{45}{100}[/tex] ÷ [tex]\frac{5}{5}[/tex] = [tex]\frac{9}{20}[/tex]

Answer:45%=9/20 I hope this helps

Step-by-step explanation:

45%
By definition p%=p/100 which something like this

45/100

then you Cancel out the common factor 5

45/100 cancel these numbers out by 5

Then you will get your answer which is something like this

9/20

So 45%=9/20 as a fraction

Answer: C 150-99

Step-by-step explanation:

The probability of an even number is twice as likely to occur as an odd number is 2/9 and 1/9 respectively.

Probability in math term is defined as  a number that reflects the chance or likelihood that a particular event will occur.

Here we have given that an unfair/biased die is considered as an even number is twice as likely to occur as an odd number.

And here we need to find the probability of the event.

Here let us consider that probability of getting an even number = x and let probability of getting odd number = y

Then it can be written as

=> 3x+3y=1

Here we write it as because probability of getting even number or odd number = 1 since those two are the only possibilities.

Then we have to apply the value of x=2y (given)

Now, we have to solve these two, then we get,

=> x=2/9 and y=1/9

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The maximum number of philodendron plants that will occupy the whole area is 256.

The term area in math is defined as the region bounded by the shape of an object

Here we have given that your mother is very fond of collecting rare philodendron and here we have know that If she has a garden which measures 100 m² and each philodendron will occupy an estimated area of 0. 6 x 0. 6 m of the garden.

Here we have to 10 meters divided by 0.6 of a meter gives 16 philodendrons in one direction and the same number in the other direction.

Then the maximum number of plants is calculated as,

=> 16 x 16 = 256

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The missing angles are as calculated below. Fill them accordingly.

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

Check the attached image for labeling

a = 125° (vertically opposite angles are equal)

a + b = 180 (sum of angles on a line)

b = 180 - 125 = 55°

b + c = 90  (sum of angles in a triangle)

c = 90 - 55 = 35°

d = b   (alternate angle)

d = 55°

e =   125° (alternate angle)

Fill in the missing angles accordingly

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The step that can be used to draw an Inscribed Circle of A ABC is to draw the perpendicular bisectors of AB, BC, and AC that pass through point D

Inscribed Circle is a circle that touches each of the three sides of the triangle at exactly one point. Inscribed Circle is the largest circle that can be made in a triangle. The center of the Inscribed Circle is also the center of the triangle, that is, the point where the angle bisectors of the triangle meet.

Steps to draw an Inscribed Circle:

a. construct an angle bisector of each vertex (<ABC, <BAC, <ACB) of the triangle to determine the center of the triangle.

b. draw a line perpendicular to one side of the triangle that passes through its center.

c. draw an Inscribed Circle that passes through the point where the sides of the triangle intersect and the perpendicular from above.

As in the question, it was stated that the center of the Inscribed Circle is point D, so the step that can be used to draw an Inscribed Circle of A ABC is to draw the perpendicular bisectors of AB, BC, and AC that pass through point D

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The proportion taken by John 3:4 = 5:12 is correct.

The term called proportion in math is defined as the values of the proportion that are close to each other when written in ratio form using a colon.

Here we know that the  a 3-4-5 right triangle and a 5-12-13 right triangle are set by John.

And the taken proportion is written as,

=> 3:4 = 5:12

Here we have to use the Pythagoras theorem to verify this one, then we get,

=> 3² + 4² = 5²

=> 9 + 16 = 25

=> 25 = 25

Now, we have to take the other values and verify that one also,

=> 5² + 12² = 13²

=> 25 + 144 = 169

=> 169 = 169

Therefore the proportion is correct.

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Answer: We can start by solving for one variable in one of the equations and then substituting that value into the other equation.

Solve for y in the first equation: y = 1 - 3x

Substitute this value of y into the second equation: 4(1 - 3x) + 4x = -20

Solve for x: -4x = -24

x = 6

Substitute this value of x into the first equation to find the value of y: y = 1 - 3(6) = -17

So the solution is x = 6 and y = -17.

Step-by-step explanation:

The length of Sarah's drawing is given by the following equation:

0.1g = 0.8.

The scale of the drawing is obtained applying the proportions in the context of this problem.

The scale is defined as the division of the drawn length by the actual length.

Sarah's drawing has a scale factor of 1 inch to 0.1 inch, meaning that each inch she draws has an actual length of 0.1 inch.

The rule of three is defined as follows:

1 inch - 0.1 inches

g inches - 0.8 inches

Hence the equation is:

0.1g = 0.8.

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Answer:

$560

Step-by-step explanation:

if 25% is the discount than the total of the item after the discount is .75x. So to find the original total we need the equation 420=.75x

first we need to isolate x so we divide both sides by .75, doing this will give us 560= x

to check our answer you need to multiply 560 by .75 (which I got by subtracting the discount, .25, from 1) which gives us our discounted total of $420

the average rate of change of the function over the interval 1 ≤ x ≤ 9​ is 3.75.

It is a measure of how much the function changed per unit, on average, over that interval. It is derived from the slope of the straight line connecting the interval's endpoints on the function's graph.

Given the function g(x)=-x²+5x+14, within the interval 1 ≤ x ≤ 9

At the lower interval x = 1

g(x) = -1 +5 + 14

g(x) = 18

At the lower interval x = 9

g(x) = -9²+5*9+14

g(x) = -22

The average change of the function will be expressed as:

Δy/Δx = (-22 - 8)/ (9-1)

Δy/Δx = -30/8

Δy/Δx = 3.75

therefore, the average rate of change of the function over the interval 1 ≤ x ≤ 9​ is 3.75.

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Answer: $6

Step-by-step explanation:

60% of 3.75

3.75 * 0.60 = 2.25

2.25 + 3.75 = 6

Step-by-step explanation:

The answer is 2.25 because 60% of 3.75 is equal to 2.25

The amount of gravel needed to cover the floor of the cube shaped tank to a depth of 1 inch is 0.38 ft^3.

The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere. Various forms have various volumes.

Given that the fish tank is a cube that holds 10 ft^3 of water.

The volume of the cube is given by:

V = a³

Substituting the value of 10 in V we have:

a³ = 10

a = 2.15

Now, to gravel at the bottom of the tank will have the following dimensions as height will be 1 inch.

1 inch = 0.083

V = (a)(a)(a)

V = (2.15) (2.15) (0.083)

V = 0.38 ft^3

Hence, the amount of gravel needed to cover the floor of the tank to a depth of 1 inch is 0.38 ft^3.

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Using the laws of exponential used to simplify the expression, we have; 1/x^2.

When a given expression has an exponent, this implies that the degree of one of its variable is more than 1. So that the laws of exponent which is also law of indices can be used to determine the required simplification of the expression if required.

From the given question, we have;

x^3/ x^5

So that from the law of indices,

x^3/ x^5 = x^3 x^-5

              = x^(3 - 5)

              = x^-2

From the inverse law of exponent,

x^-2 = 1/ x^2

Using the law of exponents, the simplified form of the expression is 1/ x^2.

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Answer: $840

If it's 20% off, it's 80% of it's original price.

80% = 0.8

$1,050 x 0.8 = $840

Answer: y = x - 2

Step-by-step explanation:

The equation representing the relationship between the ages of Debra and Pam is y = x + 2. This is determined by analyzing the table provided, which shows the ages of Pam (x) and Debra (y) in years. From the table, we can see that for every 1 year increase in Pam's age, Debra's age also increases by 1 year. This is represented in the equation y = x + 2, where y (Debra's age) is equal to x (Pam's age) plus 2 years. This equation is supported by the data in the table, as all of the ordered pairs (x, y) in the table satisfy the equation y = x + 2.