Solve for b.

8b−1=24b+4

ANSWER: -7

i just took the test

The statements which are true are that the radius of the circle is 3 units, the center of the circle lies on the x-axis and the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

What is a circle?

A circle is formed by all points in a plane that are at a particular distance from the center. To put it another way, it is the curve that a moving point in a plane draws to maintain a constant distance from another point.

We are given a circle whose equation is [tex]x^{2}[/tex] + [tex]y^{2}[/tex] - 2x - 8 = 0.

We know that the general form of a circle is  [tex]x^{2}[/tex] + [tex]y^{2}[/tex] + 2gx + 2fy + C = 0, where (-g, -f) is the center and √[tex]g^{2}[/tex] + [tex]f^{2}[/tex] - C is the radius.

So, in the equation, g is -1 and f is 0.

So, the center is (1, 0) which represents that the center lies on the x - axis.

Now,

⇒ Radius = √[tex]g^{2}[/tex] + [tex]f^{2}[/tex] - C

⇒ Radius = √1 + 0 - (-8)

⇒ Radius = √1 + 8

⇒ Radius = √9

⇒ Radius = 3 units

So, the radius of the circle is 3 units.

Now, radius of circle x² + y² = 9 is

[tex]r^{2}[/tex] = 9

r = 3

So, the  radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

Hence, the required solution has been obtained.

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The complete question has been attached below.

The length of line EF is proved to be parallel to the length of line EF.

To prove that EF is parallel to BD, we need to show that the opposite interior angles are equal.

Let's denote the center of the circle as O, and the intersection point of BD and AE as X. Since ABCD is a square, we have:

From the above information, we can deduce that:

∠ABD = 45°, and

∠OBD = 90°.

Since line_AF = line_AE, we can also deduce that:

∠FAE = ∠FEA.

Now, let's consider the triangle AFE. We have:

∠AFE + ∠FAE + ∠FEA = 180° (sum of angles in a triangle)

∠AFE + 2∠FAE = 180° (substituting ∠FEA with ∠FAE)

∠AFE = 180° - 2∠FAE

Also, in triangle AXε, we have:

∠AXε + ∠AEX + ∠XAE = 180° (sum of angles in a triangle)

∠AXε + ∠AEX + ∠FAE = 180° (substituting ∠XAE with ∠FAE)

∠AXε + ∠FAE + ∠FAE = 180° (rearranging terms)

∠AXε + 2∠FAE = 180°

Now, let's consider the quadrilateral ABXE. We have:

∠ABX + ∠AXε + ∠AEB = 360° (sum of angles in a quadrilateral)

∠ABX + ∠AEX + ∠AEB = 360° (rearranging terms)

∠ABX + ∠FAE + ∠AEB = 360° (substituting ∠AEX with ∠FAE)

∠ABX + 2∠FAE = 360° (substituting ∠AEB with ∠FAE)

∠ABX = 360° - 2∠FAE

Finally, let's consider the triangle BDE. We have:

∠BDE + ∠BED + ∠EBD = 180° (sum of angles in a triangle)

∠BDE + ∠AEB + ∠EBD = 180° (substituting ∠BED with ∠AEB)

∠BDE + ∠FAE + ∠EBD = 180° (substituting ∠AEB with ∠FAE)

∠BDE + 2∠FAE = 180° (since ∠FAE = ∠FEA)

∠BDE = 180° - 2∠FAE

From the above equations, we can see that:

∠ABX = ∠BDE (since both are equal to 360° - 2∠FAE)

∠ABD = ∠EBD (since both are equal to 45°)

Therefore, by the angle-angle (AA) criterion for similarity, we have:

triangle ABD is similar to triangle EXD.

This implies that:

BD/AD = XD/ED (by the property of similar triangles)

Since AD = BD (since ABCD is a square), we have:

BD/BD = XD/ED

1 = XD/ED

XD = ED

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So the solutions for x and y are: (x, y) = (0, 1/5), (5, -39/5), (10, -79/5), (15, -119/5), ...

What are parallel lines?

Parallel lines are two lines in a plane that never intersect. This means that they maintain the same distance between each other at all points.

Subtracting the first equation from the second, we get:

-8x - 5y = -45 - (-1)

-8x - 5y = -44

Now we can see that the two equations are equivalent, which means that there are infinitely many solutions for x and y that satisfy both equations. Geometrically, the two equations represent two parallel lines in the x-y plane that never intersect, so there is no unique solution.

However, we can still find a solution for x and y in terms of one variable. Let's solve for y in terms of x:

-8x - 5y = -1

-5y = 8x - 1

y = (-8/5)x + 1/5

Now we can choose any value for x and plug it into this equation to get the corresponding value of y. For example, if we set x = 0, then y = 1/5. If we set x = 5, then y = -39/5.

So the solutions for x and y are:

(x, y) = (0, 1/5), (5, -39/5), (10, -79/5), (15, -119/5), ...

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Answer:

x = 7, y = 5

Step-by-step explanation:

Given the 2 equations

x = 12 - y → (1)

2x + 3y = 29 → (2)

Substitute x = 12 - y into (2)

2(12 - y) + 3y = 29 ← distribute and simplify left side

24 - 2y + 3y = 29

24 + y = 29 ( subtract 24 from both sides )

y = 5

Substitute y = 5 into (1)

x = 12 - 5 = 7

Solution is x = 7, y = 5

If the height of the triangular roof is half its base, then the height of the roof is:

h = (1/2) * 32 = 16 feet

The area of a triangle is given by the formula:

A = (1/2) * base * height

Plugging in the values we have:

A = (1/2) * 32 * 16

A = 256 square feet

Therefore, the area of the triangular roof is 256 square feet.

The required coordinate points are (3, 0) and (-4, 0)  

To find the exponential function from two points, you need to know the coordinates of two points on the graph of the function.

If you have access to the graph, you can try to estimate the coordinates of two points by using the grid lines on the axes.

Choose two points that lie on the curve and try to read their coordinates as accurately as possible from the gridlines.

Here we have an exponent graph

In the given picture,

The curve cuts the y-axis at 3 and the x-axis at - 4

Hence,

The required coordinate points are (3, 0) and (-4, 0)

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The equation is 9x + 8y = 81.

Answer:

To solve for Z in the equation X = Y + Z, we need to isolate Z on one side of the equation. We can do this by subtracting Y from both sides:

X - Y = Y + Z - Y

Simplifying the right-hand side, we get:

X - Y = Z

Therefore, the equation X = Y + Z solved for Z is:

Z = X - Y

The probability of randomly selecting a student that didn't get an A is P = 0.61

We want to find the probability that the student did not get an A.

To get this, we need to take the quotient between the number of students that didn't get an A, and the total number of students.

In the table,  can see that there is a total of 69 students and we also can see that of these 69, 27 got an A.

Then the number that did not get an A is:

69 - 27 = 42

Then the probability is:

P = 42/69 = 0.61

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x²+(9/2)x-3/2

=2x²+9x-3

After answering the presented question, we can conclude that As a quadrilateral result, the value of x is 112 degrees.

In geometry, a quadrilateral is a four-sided polygon with four edges and four corners. The term is derived from the Roman terms quadri and latus (meaning "side"). A rectangle is a two-dimensional form with four sides, four vertices, and four corners. Concave and convex surfaces are basically of two types. In addition, trapezoids, parallelograms, rectangles, rhombuses, and squares are subclasses of convex quadrilaterals. A rectangle is a two-dimensional structure with four straight sides. Quadrilaterals come in a variety of shapes, including parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.

Because PQRS is inscribed in circle O, the quadrilateral's opposite angles sum up to 180 degrees. Therefore,

QOS angle + QOR angle = 180 degrees

Angle QOS x (Angle R x Angle OQR) = 180°

Angle QOS = 180 degrees + (180 degrees - Angle P + 38 degrees)

Angle P = 180 degrees - Angle QOS + 218 degrees

Angle P - 38 degrees - 218 degrees = Angle QOS

QOS angle = Angle P - 256 degrees

Lastly, we may get Angle P by using the knowledge that the total of the angles of a triangle is 180 degrees.

QOS angle = 8 degrees, 38 degrees, and 218 degrees

QOS angle = -248 degrees

QOS angle = -248 degrees plus 360 degrees = 112 degrees

As a result, the value of x is 112 degrees.

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The SUMIF function in excel combines a condition and a sum of the values which meet the stated condition.  The SUMIF statement required on Cell A17 would be =SUMIF(C1:C50, '>=40')

How to write functions in Excel?

In Microsoft Excel, formulas are usually used to generate results or values for a cell.

Now, there are different ways that a formula can be written but then the formula must start with an equal sign. The formula to be used for the cells given has the function "SUMIF" and this is used to provide a sum of numeric values based on a condition.

The SUMIF syntax goes thus ; SUMIF(row_range, condition)

Assume the total membership count is in cells A1 to A50.

Cells, where the values are greater than or equal to 40, should be summed.

Hence, the required formula would be =SUMIF(C1:C50, '>=40')

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The angle measures in the figure are 45°, 55° and 145° respectively.

Angles are measured in degrees (°) using a protractor, which is a measuring device used to calculate or draw angles in terms of degrees

From the figure,

7x + 5 + 35 = 180      (angle on a straight line)

7x = 180-35-5

7x = 180-40

7x = 140

Making x the subject of the relation by dividing both sides by 7

7x/7 = 140/7

x = 20

Now, 7(20) +5 = 140+5 = 145°

Also, 90 -35 = 55

Therefore the angles that are measures of angles are 45°, 55°,145°

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[tex]Therefore, (gof)(x) = 0.9(x - 220).[/tex]

This function models the price of the computer after first taking a $220 discount and then taking a 10% discount on the discounted price.

Discount refers to a reduction in the price of a product or service. It is often used as a marketing strategy to attract customers and increase sales. The discount can be in the form of a percentage reduction from the original price, a fixed amount off the price, or other incentives such as free gifts or coupons. Discounts can be offered for various reasons, such as to clear out inventory, reward loyal customers, or to promote a new product or service. Businesses use discounts as a way to create a sense of urgency and encourage customers to make a purchase.

Sure, here's a step-by-step explanation:

Given:

The regular price of a computer is x dollars.

[tex]f(x) = x - 220[/tex] is a function that gives the price of the computer after a $220 discount.

[tex]g(x) = 0.9x[/tex] is a function that gives the price of the computer after a 10% discount.

To understand what these functions model in terms of the price of the computer, we can break down each function:

Function f(x):

[tex]f(x) = x - 220[/tex]

This function takes the regular price of the computer (x) and subtracts $220 from it.

Therefore, the result of this function gives us the price of the computer after a $220 discount.

Function g(x):

[tex]g(x) = 0.9x[/tex]

This function takes the regular price of the computer (x) and multiplies it by 0.9 (which is the same as taking 10% off).

Therefore, the result of this function gives us the price of the computer after a 10% discount.

In summary, function f models the price of the computer after a $220 discount, while function g models the price of the computer after a 10% discount.

To find (gof)(x), we need to first find g(f(x)):

[tex]g(f(x)) = g(x - 220)[/tex] [Substituting f(x) into g(x)]

[tex]= 0.9(x - 220)[/tex] [Substituting g(x) into the above expression]

[tex]Therefore, (gof)(x) = 0.9(x - 220).[/tex]

This function models the price of the computer after first taking a $220 discount and then taking a 10% discount on the discounted price.

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Answer:

3.1

Step-by-step explanation:

To express a percent as a mixed number, we need to divide the percent by 100 and convert it to a mixed number.

Let's do this for each option:

310% = 310/100 = 3.1

3.1 can be written as the mixed number 3 1/10.

49% = 49/100 = 0.49

0.49 cannot be expressed as a mixed number because it is less than 1.

7.4% = 7.4/100 = 0.074

0.074 cannot be expressed as a mixed number because it is less than 1.

0.001% = 0.001/100 = 0.00001

0.00001 cannot be expressed as a mixed number because it is less than 1.

Therefore, the percentage that can be expressed as a mixed number is 310%, which is equivalent to 3 1/10.

a) To graph y=2g(x)+3, we need to take the graph of y=g(x) and vertically stretch it by a factor of 2, then shift it upward by 3 units.

Start by identifying some key points on the graph of y=g(x). For example, if we take x=0, we see that y=g(0)=2, so the point (0,2) is on the graph. If we take x=1, we see that y=g(1)=4, so the point (1,4) is on the graph. If we take x=-1, we see that y=g(-1)=1, so the point (-1,1) is on the graph.

Now, to graph y=2g(x)+3, we take these key points and apply the transformation.

- Vertically stretch: Multiply the y-coordinates by 2. So (0,2) becomes (0,4), (1,4) becomes (1,8), and (-1,1) becomes (-1,2).
- Shift upward: Add 3 to each y-coordinate. So (0,4) becomes (0,7), (1,8) becomes (1,11), and (-1,2) becomes (-1,5).

These points give us enough information to sketch the graph of y=2g(x)+3. It will look like the original graph of y=g(x), but stretched vertically and shifted upward.

b) To graph y=-h(x-2), we need to take the graph of y=h(x) and reflect it across the y-axis, then shift it to the right by 2 units, and finally reflect it again across the x-axis.

Again, start by identifying some key points on the graph of y=h(x). For example, if we take x=0, we see that y=h(0)=1, so the point (0,1) is on the graph. If we take x=1, we see that y=h(1)=3, so the point (1,3) is on the graph. If we take x=-1, we see that y=h(-1)=2, so the point (-1,2) is on the graph.

Now, to graph y=-h(x-2), we take these key points and apply the transformation.

- Reflect across y-axis: Multiply the x-coordinates by -1. So (0,1) becomes (0,1), (1,3) becomes (-1,3), and (-1,2) becomes (1,2).
- Shift to the right: Add 2 to each x-coordinate. So (0,1) becomes (2,1), (-1,3) becomes (1,3), and (1,2) becomes (3,2).
- Reflect across x-axis: Multiply the y-coordinates by -1. So (2,1) becomes (2,-1), (1,3) becomes (1,-3), and (3,2) becomes (3,-2).

These points give us enough information to sketch the graph of y=-h(x-2). It will look like the original graph of y=h(x), but reflected across the y-axis, shifted to the right, and reflected across the x-axis.

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In the word problem , the length of wood Mr. DeWitt carved off is 3.6cm.

What is word problem?

Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided statements are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.

According to the given ,

Length of wood = 20.3 cm

The length of boat = 16.7 cm.

Now Length of wood he carved off is,

=> Length of wood - length of boat

=> 20.3 - 16.7

=> 3.6 cm.

Hence the length of wood Mr. DeWitt carved off is 3.6cm.

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The angles that have the given tangents, correct to 2 significant figures, are: 45°, 30° and 15°

To find the angles that have the given tangents, we can use the inverse tangent function (tan⁻¹) or the arctan function on a calculator. Remember that the arctan function gives an angle in radians, so we need to convert the result to degrees.

[tex]\tan \theta = 1.000\ \theta = \tan^{-1}(1.000)\\\\ \theta \simeq 45^{\circ}[/tex]

tan θ = 0.577

θ = tan⁻¹(0.577)

θ ≈ 30°

tan θ = 0.268

θ = tan⁻¹(0.268)

θ ≈ 15°

tan θ = 4

θ = tan⁻¹(4)

θ ≈ 75.96°

θ ≈ 76° (rounded to 3 significant figures)

tan θ = 2.747\\θ = tan⁻¹(2.747)

θ ≈ 70.53°

θ ≈ 71° (rounded to 3 significant figures)

tan θ = 3.732

θ = tan⁻¹(3.732)

θ ≈ 75.89°

θ ≈ 76° (rounded to 3 significant figures)

Therefore, the angles that have the given tangents, correct to 2 significant figures, are:

45°

30°

15°

And the angles that have the given tangents, correct to 3 significant figures, are:

76°

71°

76°

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The percentage of compaction of the tested soil is 92.1%.

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that can include numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, and division.

a) To compute the water content, we need to find the weight of water in the soil sample.

Wet unit weight of soil = (weight of wet soil)/(volume of soil)

The volume of soil can be found using the weight of sand (sand core) to fill the test hole:

Volume of soil = Volume of sand cone = (weight of sand)/(bulk density of sand)

Volume of soil = 1636 g / 15.73  = 0.104

Wet unit weight of soil = (2100 g - 1636 g) / 0.104  = 5490

The dry unit weight of soil can be found by dividing the dry weight of the soil sample by its volume:

Dry unit weight of soil = (weight of dried soil)/(volume of soil)

Dry unit weight of soil = 1827 g / 0.104 = 17558.5

b) To compute the in-place dry unit weight of tested soil, we need to know the water content of the soil.

Water content = [(weight of wet soil - weight of dry soil) / weight of dry soil] x 100%

Water content = [(2100 g - 1827 g) / 1827 g] x 100% = 14.4%

Dry unit weight of tested soil = (dry unit weight of soil) / (1 + water content)

Dry unit weight of tested soil = 17558.5 / (1 + 0.144) = 15294.3

c) To compute the percentage of compaction, we need to compare the in-place dry unit weight to the maximum dry unit weight.

Maximum dry unit weight = 18.09

Optimum moisture content = 13%

Maximum wet unit weight = maximum dry unit weight / (1 - optimum moisture content/100)

Maximum wet unit weight = 18.09  / (1 - 0.13) = 20.805

Maximum weight of soil = maximum wet unit weight x volume of soil

Maximum weight of soil = 20.805  x 0.104 = 2.161 kN

Actual weight of soil = (dry unit weight of tested soil) x (1 + water content) x volume of soil

Actual weight of soil = 15.294  x (1 + 0.144) x 0.104  = 1.990 kN

Percentage of compaction = (actual weight of soil / maximum weight of soil) x 100%

Percentage of compaction = (1.990 kN / 2.161 kN) x 100% = 92.1%

Therefore, the percentage of compaction of the tested soil is 92.1%.

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Therefore, the value of the car in the year 2003 will be approximately $8,962 when rounded to the nearest 50 dollars.

The annual rate of change is a measure that indicates the percentage increase or decrease in a value over a period of one year. It is commonly used to track changes in economic indicators such as Gross Domestic Product (GDP), inflation, and unemployment.

To calculate the annual rate of change, you need to first determine the starting value and ending value for the period in question. You then calculate the percentage change between the two values using the following formula:

[tex]Annual rate of change = ((Ending value - Starting value) / Starting value) * 100[/tex]

A) To find the annual rate of change between 1991 and 2000, we can use the formula:

[tex]r = (V1/V0)^{(1/n)} - 1[/tex]

where V0 is the initial value, V1 is the final value, and n is the number of years. Plugging in the given values, we get:

[tex]r = (12000/45000)^{(1/9)} - 1[/tex]

r ≈ -0.1049

Therefore, the annual rate of change between 1991 and 2000 is approximately -0.1049.

B) To express the rate of change as a percentage, we can multiply it by 100:

[tex]r = -0.1049 * 100[/tex]

r ≈ -10.49%

Therefore, the correct answer to part A written in percentage form is approximately -10.49%.

C) Assuming the car value continues to drop by the same percentage, we can use the formula:

[tex]V = V_0 * (1 + r)^n[/tex]

where V0 is the initial value, r is the annual rate of change, and n is the number of years. Plugging in the given values, we get:

[tex]V = 12000 *(1 - 0.1049)^3[/tex]

V ≈ $8,961.75

Therefore, the value of the car in the year 2003 will be approximately $8,962 when rounded to the nearest 50 dollars.

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Answer:

To determine the number of different ways the leader can appoint 3 members to clean up camp from a troop of 18 members, we can use the combination formula: n C r = n! / r!(n - r)! where n is the total number of members in the troop (18), and r is the number of members to be chosen (3). Plugging in the values, we get: 18 C 3 = 18! / 3!(18 - 3)! = (18 x 17 x 16) / (3 x 2 x 1) = 816 Therefore, there are 816 different ways the leader can appoint 3 members to clean up camp from a troop of 18 members.

Answer: 106 stickers

Step-by-step explanation:

38 + 75 + 18 = 131 (total amount of stickers she got)

131 - 25 = 106

Answer: In dilation, the parent function is scaled or stretched by a given value, and can be presented by the equation y = a*x^2 where "a" is the dilation factor and a ≠ 0.

When a > 1, the dilation stretches the graph vertically, making the parabola narrower and taller. When a < 1, the dilation compresses the graph vertically, making the parabola wider and shorter. When a is negative, the dilation reflects the graph across the x-axis.

Step-by-step explanation:

By metric system it can be determined that Jasοn lives οn 0.075 hectare.

The metric system is a prοcess οf measuring things. The measurements are used wοrldwide in calculatiοns and research. Sοme examples οf measurements οf things using the metric system are given belοw:

Meter is the unit οf measuring distances and lengths.

Kilοgram οr Gram is used tο measure weight.

Jasοn lives οn 750m plοt .

The given prοblem can be sοlved by metric system.

By metric system

1 hectare =10000m

10000m = 1 hectare

1m= 1/10000 hectare

750m= 750/10000 hectare

Hence,

Jasοn lives οn 0.075 hectare.

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The equation Hats 2030=230.09+23x represents a linear relationship between the number of years since 2010 (x) and the projected number of hats sold in the year 2030.

The slope of the equation, 23, indicates that for each additional year since 2010, the projected number of hats sold in 2030 increases by 23. The y-intercept of the equation, 230.09, represents the projected number of hats sold in 2030 if x is equal to zero (i.e., in the year 2010). This equation can be used to forecast future hat sales based on past trends and can help businesses and organizations plan for inventory and production needs. However, it is important to note that unforeseen events, changes in consumer behavior, and other factors can impact actual hat sales and should be considered when making business decisions.

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Step-by-step explanation:

pi ( x^2 - 36 )

pi ( x-6)(x+6)     Done.

The given cylindrical wind chime of dimensions 16 inches long will not fit inside the box in the shape of rectangular-prism having dimensions 10 inches x 8 inches x 6 inches.

1)shorter than

2) shorter than

3)will not fit.

What is a rectangular-prism?

Rectangular prism also called as cuboid, is a closed three dimensional solid having six faces. This prism has eight vertices or corners and 12 edges. The perimeter of this shape is the total length of 12 edges. The area of this shape is the sum of area of for or six surfaces depending on the given situation.

Given dimensions of cuboid/rectangular prism:

Length=10 inches, height= 6 inches & Width=8 inches

Dimensions of cylindrical wind chime: Length of cylinder = 16 inches

Case I: comparision of diagonal of base of the box & length of wind chime.

Diagonal of base can be found using pythagorean theorem:

Diagonal=[tex]\sqrt{L^{2} +W^{2} }[/tex]

              =[tex]\sqrt{(10)^{2} +(8)^{2} }[/tex]

              =[tex]\sqrt{100+64\\}[/tex]

               =[tex]\sqrt{164}[/tex]

               =12.8 inches ≠ 16 inches

Diagonal of rectangular prism base shorter than length of wind chime.

Case II:comparision of interior diagonal of the box & length of wind chime.

Interior diagonal of box=[tex]\sqrt{L^{2} +W^{2} +H^{2} }[/tex]

                                       =[tex]\sqrt{(10)^{2} + (8)^{2} +(6)^{2} }[/tex]

                                       =[tex]\sqrt{100+64+36}[/tex]

                                        =[tex]\sqrt{200}[/tex]

                                        =14.14 inches ≠ 16 inches

Interior Diagonal of rectangular prism is shorter than length of wind chime.

As the wind chime is greater than both the diagonals of cuboid, the chime will not fit into the prism.

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Refer to the complete question attached below.

The exponential function that relates the mass of the substance (y) to the number of years since 2004 (t) is: y = 450 * (0.923) ^ t

In this function, 0.923 is the decimal equivalent of 1 - 0.077, which represents the decay factor of 7.7%. The exponent t represents the number of years since 2004.

So, for example, if we want to know the mass of the substance in 2010 (6 years after 2004), we can plug t = 6 into the function:

y = 450 * (0.923) ^ 6 = 298.8 milligrams

Therefore, the mass of the substance in 2010 would be approximately 298.8 milligrams.

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Note that the exponential function that shows the relationship between the mass y of the substance and the number of years t since 2004 is:

y = 450 * 0.923^t

The general formula for exponential decay is:

y = a * (1 - r)^t

where:

y = final amount

a = initial amount

r = decay rate

t = time elapsed

In this problem, the initial amount is 450 milligrams, and the decay rate is 7.7% per year, or 0.077 as a decimal. We can use the formula above to write an exponential function for the relationship between y and t:

y = 450 * (1 - 0.077)^t

Simplifying this expression, we get:

y = 450 * 0.923^t

Therefore, the exponential function that shows the relationship between the mass y of the substance and the number of years t since 2004 is:

y = 450 * 0.923^t

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Full Question:

Although part of your question is missing, you might be referring to this full question:

In 2004, a sample of a radioactive substance had a mass of 450 milligrams. Since then, the sample has decayed by 7.7% each year. Let t be the number of years since 2004. Let y be the mass of the substance in milligrams. Write an exponential function showing the relationship between y and t.