A rectangular prism has a base area of 54 m (to the 2nd power) and a volume of 702 m (to the 3rd power). What is its height?

The formula for the general term of an arithmetic sequence is:

an = 14 - 3(n-1)

Arithmetic progression (AP) is a sequence of numbers in which each term after the first is obtained by adding a fixed constant value, called the common difference, to the preceding term. For example, 2, 4, 6, 8, 10, 12, 14... is an arithmetic progression with a common difference of 2. The formula for the nth term of an arithmetic progression is given by:

an = a1 + (n-1)d

The given sequence 14, 11, 8, 5, 2 is an arithmetic sequence with a common difference of -3.

The formula for the general term of an arithmetic sequence is:

an = a1 + (n-1)d

where:

an = the nth term of the sequence

a1 = the first term of the sequence

d = the common difference between consecutive terms

n = the position of the term we want to find

Using the values given in the sequence, we have:

a1 = 14

d = -3

To find the general term, we need to determine the value of n. Let's assume that the first term of the sequence corresponds to n = 1.

For the first term (n = 1):

a1 = 14

For the second term (n = 2):

a2 = a1 + d = 14 - 3 = 11

For the third term (n = 3):

a3 = a1 + 2d = 14 - 6 = 8

For the fourth term (n = 4):

a4 = a1 + 3d = 14 - 9 = 5

For the fifth term (n = 5):

a5 = a1 + 4d = 14 - 12 = 2

Therefore, the general term for the given sequence is:

an = 14 - 3(n-1)

or

an = 17 - 3n (Alternative form)

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Answer: Option B

Step-by-step explanation:

A. The range of the ages are greater. This statement is false because in the box plot movies A, the range is 26 (subtract highest value from lowest value) which is not greater. Thus, this statement is false.

B. A smaller range normally means that there is a more consistent range. TRUE

C: The IQR, looking at the box plot, is much greater.

D: In Movie 2, the median ages of attendees are greater. False

The property used between step 3  is the D)addition property of inequality and step 4 is the B) division property of inequality.

In mathematics, an inequality is a mathematical statement that indicates that twο expressiοns are nοt equal. It is a statement that cοmpares twο values, usually using οne οf the fοllοwing symbοls: "<" (less than), ">" (greater than), "≤" (less than οr equal tο), οr "≥" (greater than οr equal tο).

The property used between step 3  is the addition property of inequality and step 4 is the division property of inequality. answer is D addition property of inequality.

In step 3, -6x - 8 < -2 is οbtained by adding 8 tο bοth sides οf the inequality -6x - 8 + 8 < -2 + 8.

Then, in step 4, -6x < 6 is οbtained by dividing bοth sides οf the inequality -6x - 8 < -2 by -6, which requires the use οf the division property of inequality.

Therefore, the property used between step 3 and step 4 is the addition property of inequality.

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Step-by-step explanation:

you have to subtract them which would be -1.05

Answer:

92 hours

Step-by-step explanation:

7 * 12 + 8 = 92

If a tank is shaped like an upside down square-pyramid, then the rate at which the height of water is increasing when the water is 2 m deep is 51.75 m/sec.

The tank is upside down square-pyramid, with sides as 4 meter,

Let the height of water at any time "t" be = "h",

The height of the tank is = 12 meter,

Let, the side of the base of pyramid shaped water at any time "t" be = "b",

So, b = (1/3)h   ...because height of pyramid is 12 and each side is of 4, the ratio is 1/3,

The volume of water at nay time "t" is (V) = (1/3)b²h,

⇒ V = (1/3)(1/3h)²h,

⇒ V = h³/27,

Now, dv/dt = (d/dt)(h³/27),

On simplifying further,

we get,

⇒ dv/dt = (h²/9)(dh/dt),

⇒ dh/dt = (9/h²)(dv/dt),

We know that, when the water is 2 meter deep, and if water is pumped out at rate of 23 m³/sec, it means that h = 2, and dv/dt = 23,

So, dh/dt = (9/2²)(23) = 51.75 m/sec.

Therefore, the rate of change of height is 51.75 m/sec.

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There are [tex]18[/tex] square units in the area of the shaded rectangle.

The Latin words "rect" (which means "right") and "angulus" (which means "angle") are the roots of the English word "rectangle." These two words together form the term "rectangle." A rectangle has 90° straight angles at each of its four corners. A rectangular also has two equal-length diagonals that meet in the centre.

In addition to rectangles, we also refer to them as geometric figures, quadrilaterals, and polygons. This is so that it is clear that a rectangle fulfils the specifications of all of these other forms.

width [tex]= 7[/tex] units

length [tex]= 10[/tex] units

We remove the frame, each measure will lose[tex]2*2[/tex] units, or [tex]4[/tex] units

[tex]width = 7 units - 4 units = 3 units[/tex]

[tex]length = 10 units - 4 units = 6 units.[/tex]

[tex]A = (3 units)*(6 units) = 18[/tex] square units.

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The completed question is:

One rectangle is "framed" within another. Find the area of the shaded region if the

"frame" is 1 unit wide.

10

5

Rounding to the nearest tenth, the measure of UV is 7.1.

An angle is a measure of space between two lines or planes. It is measured in degrees, using a protractor, and can range from 0 to 360. Angles can be either acute, obtuse, right, straight, reflex, or full. Acute angles are angles that measure less than 90 degrees, obtuse angles measure more than 90 degrees, right angles measure exactly 90 degrees, straight angles measure 180 degrees, reflex angles measure more than 180 degrees, and full angles measure 360 degrees.

To find the measure of UV in ∆ UVW, we will use the law of cosines. The law of cosines states that [tex]c^{2} =a^{2} +b^{2} -2ab cos C[/tex], where c is the length of the side opposite angle C, a and b are the lengths of the other two sides, and C is the angle opposite side c. In this case, side c is UV, a is UW, b is VW, and C is ∠ W.

Plugging in the given values, we get:

[tex]U^{2}V^{2}[/tex] = [tex]9^{2} + 12^{2} - 2 *9* 12 cos *35[/tex]

[tex]U^{2} V^{2}[/tex] = 81 + 83.44 – 162.08 cos 35°

[tex]U^{2} V^{2}[/tex] = 164.44 – 114.45

[tex]U^{2} V^{2}[/tex] = 49.99

Taking the square root of both sides, we get:

UV = 7.086

Rounding to the nearest tenth, the measure of UV is 7.1.

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Answer:

(2, 3)

Step-by-step explanation:

     9x - 7y = -3                

+   -9x + 15y = 27

             8y = 24           (Divide by 8 on both sides)

             8   =  8

y = 3

Substitute y = 3 in any of the two equations.

9x - 7(3) = -3

9x - 21 = -3

     +21 = +21         (Add 21 on both sides)

 9x     =  18               (Divide by 9 on both sides)

  9      =   9

x = 2

Answer: D.) 2x + 22 = 50

Step-by-step explanation:

P=2(l+w)

2x+22=50 is correct because

2 times x is 2 times the unknown length

11 times 2 is 22 so, you add that to the 2x

50 is the perimeter

Answer: C. The median of 20 is the most accurate to use, since the data is skewed.

The most accurate measure of center to use in this case is the median of 20. This is because the data is skewed, with a few high-value donations (such as the two donations of 55 dollars) that pull the mean up. However, most of the donations are clustered around 10 to 20 dollars. As a result, the median, which is the middle value when the data is sorted in order, is a better representation of the "typical" donation amount.

In this case, the median is 20, which means that half of the donations were less than 20 dollars and half were more. This is a more accurate representation of the central tendency of the data than the mean of 22.7, which is influenced by the high-value donations. Therefore, the charity should use the median of 20 to accurately represent the typical donations received.

Step-by-step explanation:

The value of the expression 5x - 3y, is -29 obtained by elimination method by eliminating the two equations.

The equations are :

3x - 4y= -24     -----------   A

3x +2y= -6       -----------   B

On multiplying minus sign in B equation, to eliminate the x- component in the equation.

3x +2y= -6 becomes (-3x - 2y = 6)

Then, the equation becomes,

3x - 4y= -24

-3x - 2y = 6          (+ 3x - 3x are equal and opposite becomes zero.)

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

    -6y = -18

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

6y = 18          (both minus sign gets cancelled)

y = 18/6

 = 3

The value of y=3.

Substitute the value of y=3 in A equation.

Equation A is,  3x - 4y= -24

3x - 4(3) = -24

3x = -24 + 12

3x = -12

x = -12 / 3

 = -4

The value of x= -4.

Thus, the value of x= -4 and y = 3. By using this x and y values, the equation  5x - 3y, can be solved as,

= 5x - 3y

= 5(-4) - 3 (3)

= -20 -9

= -29

The value of the expressions 5x - 3y = -29.

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The straight lines that pass through the points Θ = π, Θ = 2π, Θ = 3π, and so on are known as the f-intercepts. At the multiples of, these lines cross the x-axis (or -axis).

The points where a line intersects an axis are known as the x-intercept and the y-intercept, respectively.

A periodic function, f(Θ) = tan(Θ), oscillates between positive and negative infinity at certain points that correlate to the function's zeros. These zeros are referred to as the function's x-intercepts or roots.

The x-intercepts are not clearly specified, though, because the function has a periodic nature with a period of. Or, to put it another way, the function has an unlimited number of x-intercepts at each integer multiple of π (i.e., π, 2π, 3π, -π, -2π, -3π, and so on).

The values are represented by the x-axis in the setting of the function's graph. As a result, the values of for which the function equals zero correlate to the x-intercepts or roots of the function.

We can see that the function equals zero when sin() = 0, which happens when is an integer multiple of, by using the equation tan() = sin() / cos().

As a result, the vertical lines going through Θ = π, Θ = 2π, Θ = 3π, and so on are the -intercepts of the graph of f. These lines cross the x-axis (also known as the -axis) at multiples of.

In conclusion, the straight lines at  = n, where n is an integer, are the -intercepts of the graph of f(Θ) = tan(Θ).

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The equation of the parabola in factored form is: y = 16(z - 1/2)(z - 8)

What is parabola?

A parabola is a symmetrical plane curve that is shaped like an arch. It is a quadratic function and is defined by the equation y = ax² + bx + c, where a, b, and c are constants.

Ryan's reasoning is justified because the z-intercepts of a parabola are the points where the parabola intersects the z-axis, which are the points where x = 0. Therefore, if the parabola can be expressed in the form y = a(x + 1)(x - 4), then its z-intercepts are at x = -1 and x = 4. This is because when x = -1, (x + 1) = 0 and when x = 4, (x - 4) = 0, which makes y = 0, indicating that the parabola intersects the z-axis at these two points.

To find the value of a, we need to use the given information that the y-intercept of the parabola is at (0, 2). Substituting x = 0 and y = 2 into the equation y = a(x + 1)(x - 4), we get:

2 = a(0 + 1)(0 - 4)

2 = -4a

Therefore, a = -1/2. So the equation of the parabola is y = (-1/2)(x + 1)(x - 4), in factored form.

To find the equation of the parabola in factored form y = a(z-p)(z-g), we can use the given information about its intercepts and symmetry axis. Since the symmetry axis is parallel to the y-axis, the parabola is of the form y = a(z - h)² + k, where (h, k) is the vertex. We know that the a-intercepts are -2 and 3, which means that the points (-2, 0) and (3, 0) lie on the parabola. Substituting these points into the equation, we get:

0 = a(-2 - h)² + k

0 = a(3 - h)² + k

Solving for h and k, we get:

h = 1/2

k = 4

Therefore, the vertex is at (1/2, 4), and the equation of the parabola is:

y = a(z - 1/2)² + 4

We can find the value of a by using the fact that the y-intercept is 4. Substituting z = 0 and y = 4, we get:

4 = a(0 - 1/2)² + 4

4 = a(1/4)

a = 16

Therefore, the equation of the parabola in factored form is:

y = 16(z - 1/2)(z - 8), which is sometimes referred to as intercept form because it explicitly shows the intercepts of the parabola on the z-axis.

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After answering the presented question, we can conclude that As a result, the line connecting the points A(-7, -1) and B(8, 2) is divided by the line x + y = 2 in the ratio about 65.63:56.63.

In mathematics, ratios demonstrate how frequently one number is contained in another. For example, if there are 8 oranges and 6 lemons in a fruit dish, the ratio of oranges to lemons is 8 to 6. In a similar vein, the orange-to-whole-fruit ratio is 8, whereas the lemon-to-orange ratio is 6:8. A ratio is an ordered pair of numbers a and b represented as a / b, where b is not zero. A ratio is an equation that equates two ratios. For example, if there is one male and three girls (for every boy she has three daughters), 3/4 are girls and 1/4 are boys.

[tex]m = (y2 - y1)/(x2 - x1) = (2 - (-1))/(8 - (-7)) = 3/15 = 1/5\\y - y1 = m(x - x1)\\y - (-1) = (1/5)(x - (-7))\\y + 1 = (1/5)(x + 7)\\y = (1/5)x + 6/5 - 1\\y = (1/5)x + 1/5\\x + (1/5)x + 1/5 = 2\\(6/5)x = 9/5\\x = 3\\[/tex]

[tex]y = (1/5)(3) + 1/5\\y = 4/5\\AP = \sqrt[(3 - (-7))^2 + (4/5 - (-1))^2] = \sqrt[10^2 + 9/5^2] = \sqrt[100 + 81/25] = \Sqrt[4301]/5\\PB = \Sqrt[(8 - 3)^2 + (2 - 4/5)^2] = \sqrt[25 + 81/25] = \sqrt[3206]/5\\[/tex]

The ratio in which AB is divided by x + y = 2 is:

[tex]AP:PB = \sqrt[4301]:\sqrt[3206] = 65.63:56.63 \\[/tex]

As a result, the line connecting the points A(-7, -1) and B(8, 2) is divided by the line x + y = 2 in the ratio about 65.63:56.63.

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Step-by-step explanation:

To find Sara's semi-monthly salary, we need to divide her annual salary by the number of semi-monthly periods in a year.

Since there are 24 semi-monthly periods in a year (twice a month), we can divide her annual salary by 24 to get her semi-monthly salary:

$37,560 ÷ 24 = $1,565.00

Therefore, Sara's semi-monthly salary to the nearest cent is option C) $1,565.00.

The solution set can be written in parametric vector form as: [tex]X = x3 [-1 0 1]^T + x2 [-2 1 0]^T[/tex]

We can rewrite the system of equations in matrix form as AX = 0, where [tex]A =[2 2 4]\\[-4 -4 -8]\\[0 -3 -9][/tex]

[tex]X = [x1 x2 x3]^T[/tex]

To solve for the solution set, we can row reduce the augmented matrix [tex][A|0].\\[2 2 4|0]\\[-4 -4 -8|0]\\[0 -3 -9|0][/tex]

[tex][2 2 4|0]\\[0 0 0|0]\\[0 -3 -9|0][/tex]

[tex][2 2 4|0]\\[0 0 0|0]\\[0 1 3|0][/tex]

[tex][2 2 4|0]\\[0 0 0|0]\\[0 1 3|0][/tex]

[tex][1 1 2|0]\\[0 0 0|0]\\[0 1 3|0][/tex]

Therefore, the system has two free variables, x2 and x3, while x1 is a pivot variable. where x2 and x3 are arbitrary constants.

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We have the following system of equations:

x₁ + 0.5x₂ + 0.1x₃ = 100

0.25x₁ + x₂ + 0.2x₃ = 75

0.3x₁ + 0.4x₂ + x₃ = 200

Statement gives the equality of different mathematical expressions is called as an equation.

Let x₁, x₂, and x₃ be the outputs of I₁, I₂, and I₃, respectively. Then the total production must satisfy the following system of equations:

For I₁:

For I₂:

For I3:

Therefore, the system equations are:

x₁ + 0.5x₂ + 0.1x₃ = 100

0.25x₁ + x₂ + 0.2x₃ = 75

0.3x₁ + 0.4x₂ + x₃ = 200

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Answer:

evaluate: −0.68171817=18.7

Step-by-step explanation:

Using the given clues, we can fill out the table as follows:

Section     Number      Color

A                    3             Green

B                    5              Purple

C                    9              Brown

D                    8              Orange

E                    1               Yellow

F                    6                Blue

G                   4                 Pink

Using this information, we can deduce the values of each section:

The number 8 is in all shapes

So, D = 8

Number C is the largest

For the blue section, we have

F = Blue

For the triangle, we have

DEF = 48

D + E + F = 15

So, we have

EF = 6

E + F = 7

This means that

(E, F) = (1, 6) or (6, 1)

Number 1 is yellow

So, we have

Since F is not yellow, then

A = Green

A and G add up to 7, and A's number is smaller than G's.

So A and G must be (1, 6), (3, 4) because 2 and 7 are not used

Because of the values of E and F, we have

A = 3 and G = 4

Green and pink are in the rectangle only

So:

G = Pink

Purple and Orange are in the circle

So:

(B, D) = (Orange, Purple), (Purple, Orange)

The purple section is 5 and D = 8

So:

(B, D) = (Purple, Orange) = (5, 8)

The table has been completely filled

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The length AC of the triangle is 4.47 units.

The diagram on the graph is a triangle. The question wants us to find the length AC of the triangle.

To find the length AC in the triangle, we have to use distance formula as follows:

Therefore,

A = (1, 1)

C = (3, 5)

AC = √(y₂ - y₁)² + (x₂ - x₁)²

AC = √(5 - 1)² + (3 - 1)²

AC = √4² + 2²

AC = √16 + 4

AC = √20

Hence,

AC = 4.472135955

AC = 4.47 units

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Greg's backyard is 14 yards and 1 foot wide. To summarize, we can say that 42 feet is equivalent to 14 yards and 1 foot.

To convert 42 feet to yards and feet, we need to know that there are 3 feet in 1 yard. We can divide the total number of feet (42) by 3 to get the number of yards, and then take the remainder to get the remaining feet.

So, 42 feet divided by 3 feet/yard equals 14 yards. This means that Greg's backyard is 14 yards wide.

To find the remaining feet, we can multiply the decimal part of the result by 3. So, 0.333 x 3 = 0.999. Since we cannot have a fraction of a foot, we round up to the nearest whole foot, which gives us 1 foot.

Therefore, Greg's backyard is 14 yards and 1 foot wide. To summarize, we can say that 42 feet is equivalent to 14 yards and 1 foot.

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The parametric equation of the line is given by;  x(t)=-2 + 5ty(t)=2 - 3tz(t)=5 - 3t

To find the vector and parametric equations for the line through the point P(-2, 2, 5) and orthogonal to the plane 5x - 3y - 3z = -3, the following  

Write the equation of the plane.5x - 3y - 3z = -3  is the given equation

Find a vector that is orthogonal to the planeThis can be done by finding the normal vector of the plane. Using the coefficients of x, y, and z in the equation of the plane.  A normal vector of the plane is obtained and simplified:<5,-3,-3>.

Find the vector equation of the line.

Let L be the line through P(-2, 2, 5) and orthogonal to the plane. A direction vector of the line,  v is the normal vector of the plane (which is <5,-3,-3>), a point P(-2, 2, 5) on the line can be used to obtain the vector equation of the line:

Parametric form (parameter t, and passing through P when t = 0):x(t)=-2 + 5ty(t)=2 - 3tz(t)=5 - 3t

The vector form:<-2, 2, 5> + t<5,-3,-3> The parametric equation of the line is given by;  x(t)=-2 + 5ty(t)=2 - 3tz(t)=5 - 3t

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If it rained on Monday, Tuesday, Thursday and Friday Last week then probability of rain would be 4/7 as there are 7 days in a week.

Total days in week = total outcome = 7days
Possible outcome = 4
P(rain) = 4/7

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will learn the potential outcomes for a random experiment using this fundamental theorem of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

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The percent increase in her pay is by 26.06% if she takes the new job.

A quantity's percentage increase is a way to represent how much it has grown in comparison to its starting point. The formula is as follows: take the new value, remove the original value, divide the outcome by the original value, and then multiply by 100%. When comparing two quantities, such as incomes, prices, or test scores, it is common to use the percentage increase to gauge how much has changed. A value rise is indicated by a positive percent increase, whilst a value loss is shown by a negative percent increase.

Given that, the pat increases from $8.25 an hour to $8.25 an hour.

percent increase = [(new value - old value) / old value] x 100%

Substituting the values we have:

percent increase = [(10.40 - 8.25) / 8.25] x 100%

percent increase = 26.06%

Therefore, Lily's pay would increase by 26.06% if she takes the new job.

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Answer:

8

Step-by-step explanation:

To find the length of the third side, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side (the hypotenuse).

So, in this case, we have:

x^2 + 6^2 = 10^2

Simplifying this equation, we get:

x^2 + 36 = 100

Subtracting 36 from both sides, we get:

x^2 = 64

Taking the square root of both sides, we get:

x = 8 or x = -8

Since the length of a side of a triangle can't be negative, the length of the third side is x = 8 cm.

According to the evidence from graph a and graph b, graph a indicates that the model for the data was a good fit because it is a random.

Hence, the correct option is B.

Based on graph a, the residual plot shows a random scattering of points around the horizontal line at y=0. This indicates that the residuals (the differences between the observed and predicted values) are distributed randomly and do not show any clear pattern. This suggests that the data points are evenly distributed around the regression line, indicating a good fit for a linear regression model.

On the other hand, graph b shows a residual plot with a clear pattern or trend. The residuals are not randomly scattered, but instead show a curved pattern or a fan-like shape. This indicates that the model used to fit the data may not be appropriate, as it is not capturing the underlying relationship between the variables accurately.

Hence, the correct option is B.

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-- The given question is incomplete, the complete question is

"The residual plots from two different sets of bivariate data are graphed below. Explain, using evidence from graph a and graph b which graph indicates that the model for the data was a good fit and what is the reason?

A. Graph A because it is symmetrical

B. Graph A because it is random

C. Graph B because there is a pattern

D. Graph B because it is symmetrical" --