For the following exercises, set up and evaluate each optimization problem. Find two positive integers such that their sum is 10, and minimize and maximize the sum of their squares.

The volume of Miriam's container is approximately 58.22 cubic inches

A square prism is simply a three-dimensional solid shape which has six faces that are rectangles.

The volume of a square prism is expressed as;

V = l × l × h

Where l is the side length, h is height.

We know that the height of the container is 11.5 inches.

We also know that the side length of the base is 2.25 inches, which means that the length and width of the base are also 2.25 inches.

Therefore, we can plug in the values into the formula and get:

V = 2.25 × 2.25 × 11.5

V = 58.22 cubic inches

Therefore, the volume is approximately 58.22 in³.

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The correct answer is A because this represents discrete categories - ice cream toppings specifically, and not continuous numerical data

The provided data showcases the popular toppings among a random selection of customers and their respective frequency counts.

As this represents discrete categories - ice cream toppings specifically, and not continuous numerical data – it merits presentation via a bar graph which makes a suitable choice for accurate representation.

In contrast, using a histogram is inappropriate in this instance as histograms are intended to exhibit the distribution of frequency for continuous data points.

The relevant chart, Option A displays information using a precisely labeled x-axis ("Topping") along with a y-axis (“Number of Customers”) showcasing labeled bars, each accounting for exact values regarding topping popularity:

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The units of your measurements will determine the square units of your final result

Calculating the area of a shape is reliant on determining how many square units can be accommodated within the perimeter, without gaps or overlaps.

Here are instructions to help determine this for various shapes:

Rectangle or Square:

Start by gauging both the length (l) as well as width (w) measurements of the rectangle/square.

Compute the dimensions by multiplying the pre-existing values which in turn will give you the overall area; Area = l × w.

The concluding value shall be measured in square units such as e.g., square centimeters, and square inches.

Triangle:

Begin by gauging two factors -- base (b), and height (h) of the triangle. The height refers to the perpendicular measurement from one end of a baseline to its opposite vertex.

Next, obtain the magnitude of the intended dimension by computing the product of base and height measurements before dividing by 2 which leads to arriving at the final area figure: Area = (b × h) / 2

This resultant figure also measures in square units.

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The question in English is:

Deepa uses square units to find the area of ​​the figure

This is an incomplete question, so a general overview was provided above.

Rationalizing the denominator and simplifying a+√b / √b gives (a√b + b)/b

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

a+√b / √b

Rationalizing the denominator, we get

a+√b / √b * √b/√b

So, we have

(a√b + b)/b

Hence, the solution is (a√b + b)/b

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The total cost of the television after tax is $962.09.

The total cost of the television after tax is equal to the sum of the cost of the television and the tax amount.

The tax amount is calculated as,

Tax amount = 8.1% of $890

Tax amount = 0.081 x $890

Tax amount = $72.09

Total cost of the television after-tax = Cost of the television + Tax amount

Total cost of the television after tax = $890 + $72.09

The total cost of the television after-tax = $962.09

Therefore, the total cost of the television after tax is $962.09.

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The half-life is the amount of time it takes for a quantity to reduce to half its initial value.

In the equation y = A(0.5)^(t/half-life), the half-life is represented as a variable in the denominator of the exponent.

y is the final value of the quantity after a certain amount of time, t.
A is the initial value of the quantity at the beginning (t = 0).
0.5 is the factor that represents a 50% decrease, as we are considering half-life.
t is the time that has passed.
half-life is the time it takes for the quantity to reduce to half its initial value.

In this equation, the half-life is used to determine how much of the initial quantity (A) remains after a certain amount of time (t). By dividing t by the half-life in the exponent, we can calculate the remaining quantity (y) after the specified time.

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The correct necessary assumptions for a significance test for comparing two independent means are:

To conduct a significance test for comparing two independent means, you need to ensure the following necessary assumptions are met:

The reasons why the other options are incorrect:

So, the correct answer is: B, C and D.

This question should be provided as:

Identify all of the necessary assumptions for a significance test for comparing two independent means. group of answer choices:

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Answer:

8 6/11 is about 8.545, 17/2 = 8.5

From least to greatest: 17/2, 8 6/11, 8.83, 8.838

Step-by-step explanation:

8 6/11 is a mixed fraction

Converting it to improper fraction

Converting it to improper fraction11*8+6=88+6

Converting it to improper fraction11*8+6=88+6=94

Converting it to improper fraction11*8+6=88+6=9417/2 =8.5

8.838 is approximately 8.84

Having simplified all the values

The values to be arranged are 94, 8.838, 8.5 and 8.83

From smallest to biggest you have:

8.83, 8.838, 8.5, 94

I hope I helped

The solution for the inequality expression g/20 ≤ 5 is derived to be g ≤ 100, which makes option B correct.

Inequality signs are mathematical symbols used to indicate that one quantity is greater than, less than, or equal to another quantity. These inequality signs includes:

Less than: <

Greater than: >

Less than or equal to: ≤

Greater than or equal to: ≥

These symbols are used in mathematical expressions and equations to compare values and express relationships between them.

Solving for the solution of the expression g/20 ≤ 5 as follows:

multiply both side of the inequality by 20

20 × g/20 ≤ 5 × 20

g ≤ 5 × 20 {20 will cancel out at the left hand side}.

g ≤ 100.

Therefore, the solution for the inequality expression g/20 ≤ 5 is derived to be g ≤ 100.

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Step-by-step explanation:

=  6m* 4      - 7 *4

= 24 m - 28      

Answer:

y = -1/4x -17/4

Step-by-step explanation:

find answer attached...

Answer:

Since we are given a straight line on the graph that connects the two endpoints, we can assume that Wilson's scores will follow a linear relationship with the number of hours of science homework done. We can use the equation of the line to estimate Wilson's approximate science score for 6 hours of science homework.

From the graph, we can see that the slope of the line is:

slope = (50 - 14.9) / (5 - 0) = 35.1 / 5 = 7.02

This means that Wilson's science score increases by approximately 7.02 for each additional hour of science homework per week.

To estimate Wilson's score for 6 hours of science homework, we can use the equation of the line:

y = mx + b

where y is Wilson's science score, x is the number of hours of science homework per week, m is the slope of the line, and b is the y-intercept of the line.

We can use the point (0, 14.9) on the line to find the value of b:

14.9 = 7.02(0) + b

b = 14.9

Now we can use the equation of the line to estimate Wilson's score for 6 hours of science homework:

y = 7.02(6) + 14.9

y = 42.12 + 14.9

y = 57.02

Therefore, Wilson's approximate science score if he does science homework for 6 hours a week would be around 57.02.

Step-by-step explanation:

The graph of {(x, y)} : x3 } and { ( x, y ) : y-3} is shown in image.

We have to given that;

Expression is,

⇒ {(x, y)} : x3 } and { ( x, y ) : y-3}

Now, We can find that;

Point (1.672, 4.672) is a solution of the give expression.

Hence, We get;

The graph of {(x, y)} : x3 } and { ( x, y ) : y-3} is shown in image.

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The number that makes the equation 0.54 + 17/100 = x/100 + 17/100 true is 54.

To solve this equation, we want to isolate x on one side of the equation.

Starting with:

0.54 + 17/100 = x/100 + 17/100

We can first simplify the left side by finding a common denominator for 0.54 and 17/100:

0.54 = 54/100

54/100 + 17/100 = 71/100

Now, we can simplify the right side by combining like terms:

x/100 + 17/100 = (x + 17)/100

Substituting these simplifications back into the original equation, we get:

71/100 = (x + 17)/100

To isolate x, we can multiply both sides by 100:

71 = x + 17

Subtracting 17 from both sides, we get:

x = 54

Therefore, the number that makes the equation true is 54.

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The question is -

Enter the number that makes the equation true.

0.54 + 17/100 = x/100 + 17/100

The expression (2√2+1)² can be simplified to 9 + 4√2 using the identity (a+b)² = a² + 2ab + b².

We can simplify the expression (2√2+1)² using the identity (a+b)² = a² + 2ab + b².

The identity (a+b)² is a useful tool in simplifying expressions and can be used in a variety of mathematical problems.

Let a = 2√2 and b = 1, then we have:

(2√2+1)² = (2√2)² + 2(2√2)(1) + 1²

= 8 + 4√2 + 1

= 9 + 4√2

Therefore, (2√2+1)² simplifies to 9 + 4√2.

In summary, we can use the identity (a+b)² = a² + 2ab + b² to simplify expressions of the form (a+b)². In this case, we identified a = 2√2 and b = 1 and used the identity to simplify (2√2+1)² to 9 + 4√2.

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The differential of the function, dt, can be represented as: dt = (∂t/∂v) dv + (∂t/∂u) du + (∂t/∂w) dw = (6v^5 + uw) dv + (vw) du + (uv) dw, Therefore, the differential of the function t = v6 + uvw is (6v5 + uw) dv + uv dw.

To find the differential of the function t = v6 + uvw, we can use the rules of calculus.

First, we can take the derivative of each term separately. The derivative of v6 is 6v5, and the derivative of uvw with respect to v is uw.

Then, we can multiply each derivative by the differential of the corresponding variable. So the differential of v is dv, the differential of u is du, and the differential of w is dw.

Putting it all together, we get:

dt = 6v5 dv + uw dv + uv dw + uv dv

Simplifying this expression, we get:

dt = (6v5 + uw) dv + uv dw

Therefore, the differential of the function t = v6 + uvw is (6v5 + uw) dv + uv dw.

To find the differential of the function t = v^6 + uvw with respect to a variable, say x, we'll use partial derivatives.

The partial derivative with respect to v: ∂t/∂v = 6v^5 + uw
The partial derivative with respect to u: ∂t/∂u = vw
The partial derivative with respect to w: ∂t/∂w = uv

The differential of the function, dt, can be represented as:

dt = (∂t/∂v) dv + (∂t/∂u) du + (∂t/∂w) dw = (6v^5 + uw) dv + (vw) du + (uv) dw

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The formula for calculating the volume of an octagonal pyramid is

V = 1/3(Bh)

From the question, we are to determine the formula that can be used to determine the volume of octagonal pyramid.

An octagonal pyramid is a pyramid that has a bottom that's the shape of an octagon and has triangles as sides. It has a total of nine faces. The octagonal base and eight connecting triangles.

The formula for calculating the volume of an octagonal pyramid is

V = 1/3(Bh)

Where V is the volume of the octagonal pyramid

B is the area of the base

and his the perpendicular height

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In a Cartesian coordinate system for a three-dimensional space, let the sphere S be represented by the equation:

(x - a)^2 + (y - b)^2 + (z - c)^2 = r^2

where (a, b, c) are the coordinates of the center of the sphere, and r is the radius.

Let the plane P be represented by the equation:

Ax + By + Cz + D = 0

where (A, B, C) is the normal vector to the plane.

Since the line d is parallel to P and passes through the origin, it can be represented by the equation:

lx + my + nz = 0

where (l, m, n) is a vector parallel to the plane P.

To find the intersection points of the sphere S and the line d, we can substitute the equation of the line into the equation of the sphere, which gives us a quadratic equation in t:

(lt - a)^2 + (mt - b)^2 + (nt - c)^2 = r^2

Expanding this equation and collecting terms, we get:

(l^2 + m^2 + n^2) t^2 - 2(al + bm + cn) t + (a^2 + b^2 + c^2 - r^2) = 0

Since the line d passes through the origin, we have:

l(0 - a) + m(0 - b) + n(0 - c) = 0

which simplifies to:

al + bm + cn = 0

Therefore, the quadratic equation reduces to:

(l^2 + m^2 + n^2) t^2 + (a^2 + b^2 + c^2 - r^2) = 0

This equation has two solutions for t, which correspond to the two intersection points of the line d and the sphere S:

t1 = -(a^2 + b^2 + c^2 - r^2) / (l^2 + m^2 + n^2)

t2 = -t1

The coordinates of the intersection points can be obtained by substituting these values of t into the equation of the line d:

A = lt1, B = mt1, C = nt1

and

D = lt2, E = mt2, F = nt2

To find the distance between A and B, we can use the distance formula:

AB = sqrt((A - D)^2 + (B - E)^2 + (C - F)^2)

To maximize this distance, we can differentiate the distance formula with respect to t1 and set the derivative equal to zero:

d/dt1 (AB)^2 = 2(A - D)l + 2(B - E)m + 2(C - F)n = 0

This equation represents the condition that the direction vector (A - D, B - E, C - F) is orthogonal to the line d. Therefore, the vector (A - D, B - E, C - F) is parallel to the normal vector (l, m, n) of the plane P.

Using this condition, we can find the values of t1 and t2 that correspond to the maximum distance AB. Then we can substitute these values into the distance formula to find the maximum length of AB.

The value of x is given as follows:

x = 9.

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The theorem is expressed as follows:

c² = a² + b².

In which:

For this problem, we have that x is the length of the radius of the circle, hence:

Hence the value of x is obtained as follows:

12² + x² = (x + 6)²

144 + x² = x² + 12x + 36

12x = 108

x = 108/12

x = 9.

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Answer:4

Step-by-step explanation:

Since the slope of a line is equal to

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex], you can use this to find the slope.

[tex]\frac{7-\left(-5\right)}{5-2}[/tex]

[tex]\frac{7+5}{5-2}[/tex]

[tex]\frac{12}{5-2}[/tex]

[tex]\frac{12}{3}[/tex]

[tex]4[/tex]

Answer:

3.04

Step-by-step explanation:

df/7.6=4.4/11

11df=4.4×7.6

df=4.4×7.6/11

df=3.04

Answer:

Parallelogram

Step-by-step explanation:

is a polygon that has exactly four sides. (This also means that a quadrilateral has exactly four vertices, and exactly four angles.)

The approximate increase in area, rounded to two decimal places, is: ΔA ≈ 61 × 3.14 ≈ 191.54 mm². The estimated change in area can be calculated using the formula for the area of a circle, A = πr^2.

When the radius increases from 30 mm to 31 mm, the new area can be found as:

A_new = π(31 mm)^2 = 961π mm^2

Similarly, the original area can be found as:

A_old = π(30 mm)^2 = 900π mm^2

The approximate increase in area can be found by subtracting the old area from the new area:

ΔA = A_new - A_old = 961π mm^2 - 900π mm^2 = 61π mm^2

Using a calculator or approximating π to 3.14, we can calculate the approximate increase in area as:

ΔA ≈ 61(3.14) mm^2 ≈ 191.54 mm^2

Therefore, the estimated change in area is approximately 191.54 mm^2.

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The equation in point-slope form of the line that passes through the points given is expressed as: y - 6 = 3(x + 3).

The equation of a line can be expressed in the point-slope form, where (x1, y1) is a point on the line and m is the slope of the line, as:

y - y1 = m(x - x1).

Given the following points:

A (-3,6 ) and B (-2,9 )

Slope (m) = change in y / change in x = (9 - 6) / (-2 - (-3))

Slope (m) = 3 / 1

m = 3

Using one of the points and the slope, we can write the equation by substituting x1 = -3, y1 =6, and m = 3 into y - y1 = m(x - x1):

y - 6 = 3(x + 3)

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True. Pooled variance is the weighted average of the variances of two or more groups or samples, and it is used in calculating the estimated standard error of the difference in sample means.

The estimated standard error of the difference in sample means, on the other hand, is a measure of the variability of the differences between two sample means, and it takes into account the sample sizes and variances of the two groups being compared. Therefore, these two terms are related, but they represent different concepts in statistics.
The difference between pooled variance and the estimated standard error of the difference in sample means lies in their purpose and calculation. Pooled variance is a weighted average of the variances from two or more independent samples, while the estimated standard error of the difference in sample means measures the variability of the difference between the means of two samples.

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If the coefficient of determination is 0.94, we can say that ninety-four percent of the total variation of the dependent variable is explained by the independent variable. The correct answer is: ninety-four percent of the total variation of the dependent variable is explained by the independent variable.

This means that there is a strong positive relationship between the two variables. The coefficient of determination, represented as R², measures the proportion of the total variation in the dependent variable that is explained by the independent variable. In this case, an R² of 0.94 indicates that 94% of the total variation in the dependent variable can be explained by the independent variable. The coefficient of determination does not provide information about the direction or strength of the relationship. The correct answer therefore is ninety-four percent of the total variation of the dependent variable is explained by the independent variable.

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The forecast for t=11 is 90.76.

a) To construct a time series plot in Excel, you can follow these steps:

Enter the time period (t) in column A, starting from cell A2 and continuing down to A11.

Enter the corresponding values of the time series (yt) in column B, starting from cell B2 and continuing down to B11.

Select the range of cells containing the time period and the time series values (A1:B11).

Click on the "Insert" tab in the Excel ribbon.

Click on the "Line" chart type and select the first option (2-D Line).

Your time series plot should now appear on the worksheet.

Based on the plot, it appears that there is a downward linear trend in the data.

b) To develop the linear trend equation, we can use Excel's LINEST function. Follow these steps:

In cell D2, enter the formula "=LINEST(B2:B11,A2:A11)"

Press CTRL+SHIFT+ENTER to enter the formula as an array formula. The slope and intercept values should appear in cells D2 and D3, respectively.

The linear trend equation is: yt = -3.04t + 123.6

The slope is -3.04 and the intercept is 123.6.

c) To find the forecast for t=11, we can use the linear trend equation and substitute t=11.

Therefore, yt = -3.04(11) + 123.6 = 90.76.

So the forecast for t=11 is 90.76.

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The required measure of the angle ∠KJL is 40°.

From the figure,
The circle O, with tangent JPL and secant JIKY,
The sum of the arcs is 360°,

KP + IP + IK = 360°
IP + IP + 120 = 360
IP = 80°

Now,
KP = 2 × 80 = 160°

Here,
Following the expression to determine the ∠KJL,
= KP - IP / 2
= 160 - 80 / 2
= 40°

Thus, the required measure of the angle ∠KJL is 40°.

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Answer:

d = [tex]\sqrt{13}[/tex]

Step-by-step explanation:

The formula for distance, d, between two points is

[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex], where (x1, y1) are one point and (x2, y2) are another point.  

We can allow (-6, 5) to be our (x1, y1) point and (-3, 7) to be our (x2, y2) point and plug the points into the formula:

[tex]d=\sqrt{(-6-(-3))^2+(5-7)^2}\\ d=\sqrt{(-6+3)^2+(-2)^2}\\ d=\sqrt{(-3)^2+4}\\ d=\sqrt{9+4}\\ d=\sqrt{13}[/tex]

√13 is already in simplest radical form because there are no perfect squares which can be factored out from 13