Iron has a density of 7.9 g/cm³. Gold has a density of 19.3 g/cm³.
I have a piece of metal that has a volume of 200 cm³ and a mass of 3.86 kg. Is it gold or iron?

A) The single biconditional statement of the given statement is;

A quadrilateral is a rectangle if and only if it has all perpendicular sides

B) The statement made by your friend about only true conditional statements having a true contrapositive is; True

A biconditional statement is one that combines 2 conditional statements that are related to one another. An example of a biconditional statement is;

The polygon has only four sides if and only if the polygon is a quadrilateral.

That biconditional statement has combined two individual conditional statements.

Now, to our question, we are given two statements;

Statement 1; A rectangle is a quadrilateral that has all perpendicular sides.

Statement 2; If all sides of a quadrilateral are perpendicular, then it is a rectangle.

Combining both statements means that the biconditional statement will be; A quadrilateral is a rectangle if and only if it has all perpendicular sides

B) A contrapositive is when we switch and negate the hypothesis and the conclusion of a conditional statement. For example, the contrapositive of "If it is raining then the grass is wet" is "If the grass is not wet then it is not raining."

Thus, if the conditional statement is true, then we will have a true contrapositive.

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Answer:

Length of the base = 15 cm

Volume = 1125√2 cm³ = 1590.99 cm³ (2 d.p.)

Step-by-step explanation:

\(\boxed{\begin{minipage}{6.6cm}\underline{Lateral Surface Area of a square pyramid}\\\\$LSA=a \sqrt{a^2+4h^2}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the base edge \\\phantom{ww}$\bullet$ $h$ is the height\\\end{minipage}}\)

\(\boxed{\begin{minipage}{6.6cm}\underline{Base Area of a square pyramid}\\\\$BA=a^2$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the base edge \\\end{minipage}}\)

If the lateral surface area (LSA) of the pyramid is three times the base area (BA):

\(\implies a \sqrt{a^2+4h^2}=3a^2\)

Rearrange the equation to isolate h²:

\(\implies \sqrt{a^2+4h^2}=3a\)

\(\implies (\sqrt{a^2+4h^2})^2=(3a)^2\)

\(\implies a^2+4h^2=9a^2\)

\(\implies 4h^2=8a^2\)

\(\implies h^2=2a^2\)

\(\boxed{\begin{minipage}{6.6cm}\underline{Total Surface Area of a square pyramid}\\\\$SA=a^2+a \sqrt{a^2+4h^2}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the base edge \\\phantom{ww}$\bullet$ $h$ is the height\\\end{minipage}}\)

Given:

Substitute these values into the formula for the total surface area and solve for a:

\(\implies a^2+a\sqrt{a^2+4(2a^2)}=900\)

\(\implies a^2+a\sqrt{a^2+8a^2}=900\)

\(\implies a^2+a\sqrt{9a^2}=900\)

\(\implies a^2+a(3a)=900\)

\(\implies a^2+3a^2=900\)

\(\implies 4a^2=900\)

\(\implies a^2=225\)

\(\implies a=15\)

Therefore, the length of the base of the square based pyramid is:

To find the height (h), substitute the found value of a into the formula for h² and solve for h:

\(\implies h^2=2(15)^2\)

\(\implies \sqrt{h^2}=\sqrt{2(15)^2}\)

\(\implies h=\sqrt{2}\sqrt{(15)^2}\)

\(\implies h=15\sqrt{2}\)

Therefore, the height of the square based pyramid is:

\(\boxed{\begin{minipage}{5cm}\underline{Volume of a square pyramid}\\\\$V=\dfrac{1}{3}a^2h$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the base edge \\\phantom{ww}$\bullet$ $h$ is the height\\\end{minipage}}\)

Given:

Substitute the values into the formula and solve for volume:

\(\implies V=\dfrac{1}{3}(15)^2 \cdot 15\sqrt{2}\)

\(\implies V=\dfrac{225}{3} \cdot 15\sqrt{2}\)

\(\implies V=75\cdot 15\sqrt{2}\)

\(\implies V=1125\sqrt{2}\)

\(\implies V=1590.99\)

Therefore, the volume of the square based pyramid is:

Linear equations are equation that has a degree of 1. The solution to the given linear equation is 4/5

Linear equations are equation that has a degree of 1

Given the linear equation expressed as
4b + 6 = 2 - b

Collect the like terms

4b +b = 2- 6

5b = -4

Divide both sides by 5

b = 4/5

Hence the solution to the given linear equation is 4/5

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Answer:

b= 0 (option B)

Answer:

1) 1(1/32)

2) 1.8

Step-by-step explanation:

2(3/4)=11/4

2(2/3)= 8/3

(11/4)/(8/3)=33/32

33/32= 1(1/32)

1(4/5)=9/5

9/5=1.8

The minimum dividend that the REIT must pay per share to maintain its tax-exempt status is $3.15 per share.

To determine the minimum dividend per share, we need to consider the requirements for a Real Estate Investment Trust (REIT) to maintain its tax-exempt status. According to the tax laws governing REITs, they are required to distribute at least 90% of their taxable income to shareholders in the form of dividends.

In this case, the net income of the REIT is $300,000. To calculate the taxable income, we need to add back the deduction for depreciation and amortization, as these are non-cash expenses. Therefore, the taxable income is $3,500,000 ($300,000 + $4,600,000).

To maintain the tax-exempt status, the REIT must distribute at least 90% of the taxable income to shareholders. Thus, the minimum dividend per share can be calculated as follows:

Minimum Dividend per Share = (Taxable Income / Number of Shares) * 90%

= ($3,500,000 / 1,000,000) * 90%

= $3.15 per share

In order for the REIT to maintain its tax-exempt status, it must pay a minimum dividend of $3.15 per share. By distributing at least 90% of the taxable income to shareholders, the REIT fulfills the requirements set by tax laws governing REITs.

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The graph of f(x)=√x+3+2 is shifted 3 units up and 2 units to the right from the parent graph of f(x)=√x.

We have,

Graph is a type of data structure that consists of a set of nodes (also called vertices) and edges. Each node is connected to other nodes by edges. Graphs are used to represent networks of communication, data organization, computational devices, the flow of computation, etc. They are also very useful for visualizing relationships between data points in a variety of fields.

The translation of the parent graph of f(x)=√x+3+2 is a vertical shift upward 3 units, followed by a horizontal shift to the right 2 units. This is represented by the bold line in the graph. In terms of the equation, the translation is represented by the addition of the 3 and the 2 to the function. The 3 causes the graph to shift vertically upward and the 2 causes the graph to shift horizontally to the right. As a result, the graph of f(x)=√x+3+2 is shifted 3 units up and 2 units to the right from the parent graph of f(x)=√x.

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complete question:

Below, the graph of f(x) = √x +3 + 2 is sketched in bold. Its parent function f(x)=√x is represented

by the thin curve.

1) Describe the

translation of the parent

graph.

2) How does the translation relate to the equation?

The probability that there are an equal number of heads and tails and the first three flips are heads, given six total flips, is 1/64.

To calculate the probability that there are an equal number of heads and tails and the first three flips are heads, we need to consider the number of possible outcomes and the number of favorable outcomes.

In this case, we have a sequence of coin flips, and we want an equal number of heads and tails. For an equal number of heads and tails, we need an even total number of flips.

Let's consider the possible number of total flips:

If we have 2 flips, the sequence can be "HH" or "TT," but we need the first three flips to be heads. Therefore, 2 flips is not a favorable outcome.

If we have 4 flips, the possible sequences are "HHHH" or "HHTT" or "TTHH" or "TTTT." Out of these sequences, only "HHHH" satisfies the condition of having the first three flips as heads. Therefore, 4 flips is a favorable outcome.

If we have 6 flips, the possequences sible are "HHHHHH," "HHHHTT," "HHTTHH," "HHTTTT," "TTTTTT," "TTTTHH," "TTTTHH," and "TTTTTT." Among these sequences, only "HHHHHH" satisfies the condition of having the first three flips as heads. Therefore, 6 flips is a favorable outcome.

From this pattern, we can see that for an even number of total flips, there will always be one favorable outcome where the first three flips are heads.

Now let's consider the total number of possible outcomes:

For each flip, there are two possible outcomes, either a head or a tail. Therefore, for N flips, the total number of possible outcomes is 2^N.

So, for an even number of total flips, the probability of having an equal number of heads and tails and the first three flips being heads is:

Probability = (Number of favorable outcomes) / (Total number of possible outcomes)

= 1 / 2^N

In this case, since we have 6 flips (N = 6), the probability is:

Probability = 1 / 2^6

= 1 / 64

Therefore, the probability is 1/64.

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Answer:

In a nutshell, you have to graph the parabola. Where the parabola intersects the x-axis is the solutions to the quadratic equation.

The polynomial expansion evaluates to n for x = 1, we can conclude that the sum of the reciprocals of all these products is also equal to n.

The sum of the reciprocals of all products of k distinct positive integers (a1, a2,..., ak) is denoted by the expression "a1,...,ak," where each ai is selected from the set "1,2,...,n."

To show that this aggregate equivalents n, we can consider the polynomial extension of (1 + x)(1 + x^2)(1 + x^3)...(1 + x^n). Each term in this extension addresses a result of unmistakable powers of x, going from 0 to n.

Presently, assuming we assess this polynomial at x = 1, each term becomes 1, and we acquire the amount of all results of k unmistakable positive numbers, where every whole number is browsed the set {1,2,...,n}.

Since the polynomial development assesses to n for x = 1, we can infer that the amount of the reciprocals of this multitude of items is likewise equivalent to n.

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We have proved both implications, we can conclude that 4 divides (m^2 * n^2) if and only if m and n are both even.

To prove that 4 divides (m^2 * n^2) if and only if m and n are even, we need to prove two implications:

If 4 divides (m^2 * n^2), then m and n are even.

If m and n are even, then 4 divides (m^2 * n^2).

Let's start with the first implication:

If 4 divides (m^2 * n^2), then m and n are even.

We can prove this by contrapositive. Assume that m and n are not both even, which means that at least one of them is odd. Without loss of generality, let's assume that m is odd. Then m can be written as m = 2k + 1, where k is an integer. Substituting this into the expression for m^2 * n^2, we get:

m^2 * n^2 = (2k + 1)^2 * n^2

= 4k^2 * n^2 + 4kn^2 + n^2

Note that the first two terms in this expression are both divisible by 4, but the last term (n^2) is not necessarily divisible by 4, since n could be odd. Therefore, m^2 * n^2 is not divisible by 4 if m and n are not both even. This proves the contrapositive, and hence the first implication.

Now, let's move on to the second implication:

If m and n are even, then 4 divides (m^2 * n^2).

We can prove this directly. Since m and n are even, we can write them as m = 2k and n = 2j, where k and j are integers. Substituting these into the expression for m^2 * n^2, we get:

m^2 * n^2 = (2k)^2 * (2j)^2

= 4k^2 * 4j^2

= 16(k^2 * j^2)

Since k and j are integers, k^2 * j^2 is also an integer, and hence 16(k^2 * j^2) is divisible by 4. Therefore, m^2 * n^2 is divisible by 4 if m and n are both even. This proves the second implication.

Since we have proved both implications, we can conclude that 4 divides (m^2 * n^2) if and only if m and n are both even.

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One possible value of ∠U is 80° (to the nearest degree).

A triangle is a three-sided polygon with three vertices. The triangle's internal angle, which is 180 degrees, is constructed.

To find the possible values of ∠U, we can use the Law of Cosines:

c² = a² + b² - 2ab cos(C)

Where c is the side opposite the angle we want to find (∠U), a and b are the other two sides, and C is the angle opposite side c.

In this case, we want to find ∠U, so we'll use side u as c and sides t and s (which we don't know yet) as a and b, respectively:

u² = t² + s² - 2ts cos(U)

Substituting the given values, we get:

340² = 620² + s² - 2(620)(s)cos(U)

Simplifying:

115600 = 384400 + s² - 1240s cos(U)

Subtracting 384400 and rearranging:

s² - 1240s cos(U) + 268800 = 0

Now we can use the quadratic formula to solve for s:

s = [1240 cos(U) ± √(1240² cos²(U) - 4(1)(268800))]/(2)

Simplifying under the square root:

s = [1240 cos(U) ± √(1537600 cos²(U) - 1075200)]/(2)

s = [1240 cos(U) ± √(409600 cos²(U) + 1742400)]/(2)

s = [620 cos(U) ± √(102400 cos²(U) + 435600)]

Since s must be positive, we can discard the negative solution, and we have:

s = 620 cos(U) + √(102400 cos²(U) + 435600)

Now we can use the fact that the sum of angles in a triangle is 180° to find ∠U:

∠U = 180° - ∠T - ∠S

Since we know ∠T = 110°, we just need to find ∠S. We can use the Law of Sines to do this:

sin(S)/s = sin(T)/t

sin(S) = (s/t)sin(T)

Substituting the values we know:

sin(S) = (620 cos(U) + √(102400 cos²(U) + 435600))/620 * sin(110°)

sin(S) ≈ (1.481 cos(U) + 2.225)/6.959

Now we can use a calculator to find the arcsin of both sides to get ∠S:

∠S ≈ arcsin((1.481 cos(U) + 2.225)/6.959)

Finally, we can substitute the values we found for ∠S and ∠T into the equation we found earlier for ∠U:

∠U = 180° - 110° - arcsin((1.481 cos(U) + 2.225)/6.959)

Simplifying:

∠U = 70° - arcsin((1.481 cos(U) + 2.225)/6.959)

Now we can use trial and error or a graphing calculator to find the values of ∠U that satisfy this equation. One possible solution is:

∠U ≈ 80°

Therefore, one possible value of ∠U is 80° (to the nearest degree).

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The effect on the correlation coefficient if the additional data point was added would be a decrease.

The correlation coefficient is a measure of the linear relationship between two variables. A value of 0.93 indicates a strong positive linear relationship. The additional data point (7,30) is an outlier, meaning that it is far away from the rest of the data points.

Outliers can have a significant impact on the correlation coefficient, especially if there are few data points. In this case, the outlier would pull the correlation coefficient down. The new correlation coefficient is approximately 0.85.

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You can use the formula for finding the roots of a quadratic equation here.

The solution of given equation is: x = -1

The standard form is \(ax^2 + bx + c = 0\)

The solutions are:

\(x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)

To find the solutions, firstly we've to simplify it.

\(\sqrt{1-3x} = x + 3\\ \text{Taking square on both sides}\\ (\sqrt{1-3x})^2 = (x+3)^2\\ 1-3x = x^2 + 9 + 6x\\ x^2 + 9x + 8 = 0\)

Know that we took square.

Also know that \((\sqrt{1-3x})^2 = (-\sqrt{1-3x})^2 = 1-3x\\ \) This is the reason that both roots we will obtain won't belong to our quadratic equation we obtained. Thus, we will have to check which root is correct solution of the obtained quadratic equation.

Thus, we have a = 1, b = 9, c= 8, and thus,

\(x = \dfrac{-9 \pm \sqrt{81 - 32}}{2}\\\\ x = \dfrac{-9 \pm \sqrt{49}}{2}\\\\ x = \dfrac{-9 \pm 7}{2}\\\\ x = \dfrac{-9-7}{2} , \: x = \dfrac{-9+7}{2}\\\\ x = -8, \: x = -1\)

Putting x = -8 doesn't satisfy the equation. But x = -1 does.

Thus, the solution to the given equation is  x = -1

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Answer:

c

Step-by-step explanation:

edg

In the book "Sarah, Plain and Tall" by Patricia MacLachlan, Anna, one of the main characters, describes what she thinks the prairie looks like after the hail storm.

After the hail storm, the prairie is likely to have undergone some visible changes. Hail storms can cause damage to crops, vegetation, and the overall landscape. It's possible that Anna perceives the prairie as altered or damaged due to the hail storm.

Given Anna's deep connection to the prairie and her love for the natural world, it is likely that she feels concerned and saddened by the effects of the storm. The prairie holds great significance to Anna and her family, representing their home and way of life. Therefore, she may have mixed emotions of worry and sadness, hoping for the prairie to recover and return to its previous beauty.

Anna's observations and thoughts about the prairie after the hail storm may also reflect her resilient and optimistic nature. Despite the temporary changes caused by the storm, Anna may find solace in the knowledge that the prairie has the ability to heal and rejuvenate over time. She may view it as a natural cycle, understanding that the prairie will eventually flourish once again.

In summary, while the exact thoughts of Anna about the prairie after the hail storm are not explicitly stated in the book, we can infer that she experiences a mixture of concern, sadness, and hope for the prairie's recovery. The book portrays Anna as a character deeply connected to the land, making her emotional response to the storm's impact on the prairie significant and meaningful.

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The vendor sold 172 sodas and 58 hotdogs at the hockey game.

An equation of degree one is known as a linear equation.

A linear equation of two variables can be represented by ax + by = c.

let, the number of soda cans be 'x' and the number of hot dogs be 'y'.

So, From the given information x = 3y and the vendor sold a total of 232.

Therefore, x + y = 232.

3y + y = 232.

4y = 232.

y = 232/4.

y = 58.

So, He sold 58 hot dogs and 3×58 = 172 soda cans.

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Answer:

Solve through trigonmetry:

Im writing the 3 root as 3 because my computer doesnt have the root...though i'll add it in the calculator

For b

Tan-theta= P/B

tan45= 3/b

btan45=3

b=3/tan45

b= 1.73

For a

Sin-theta= P/H

sin45= 3/a

asin45=3

a= 3/sin45

a= 2.45

Answer:

Are there any options?  If so then, I say C

Step-by-step explanation:

I really hope this helped! °ω°

Answer: <3, <6, <8

Step-by-step explanation:

Trust me

There is only 1 power of 7 contained in 10.

Students use powers of numbers to solve this problem and learn what is occurring to the numbers as a result.

Students also learn how to divide a seemingly vast and challenging equation into smaller, more accessible components. The pupils should understand that raising 7 to a power only produces a finite number of unit digits. Furthermore, as the power of 7 rises, these particular numbers "circle round." 7, 9, 3, and 1 make up this cycle.

The digit in the tens place is the same.

The total number of times we multiply a number is known as its exponent or power. For instance, 2 to the power 3 denotes a 3x3 multiplication of 2.

The largest power of 7 that is less than 10 is 7^1 = 7, therefore there is only 1 power of 7 contained in 10.

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There is only 1 power of 7 contained in 10.

Students use powers of numbers to solve this problem and learn what is occurring to the numbers as a result.

Students also learn how to divide a seemingly vast and challenging equation into smaller, more accessible components. The pupils should understand that raising 7 to a power only produces a finite number of unit digits. Furthermore, as the power of 7 rises, these particular numbers "circle round." 7, 9, 3, and 1 make up this cycle.

The digit in the tens place is the same.

The total number of times we multiply a number is known as its exponent or power. For instance, 2 to the power 3 denotes a 3x3 multiplication of 2.

The largest power of 7 that is less than 10 is 7^1 = 7, therefore there is only 1 power of 7 contained in 10.

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Answer:

there are 0 significant digits

Step-by-step explanation:

0.0005 has 1 significant digit which is 5

25.725 has 5 significant digits

If S = Z2, it consists of two elements: {0, 1}. The units of S are the elements that have multiplicative inverses. In this case, 1 is the only element in S that has a multiplicative inverse, which is also 1. Therefore, the set of units of S, denoted as R, is {1}.

To show that R is a field, we need to demonstrate that it satisfies the properties of a field. In this case, R = {1} is a field because it is a commutative ring with unity (1), and every nonzero element (1) has a multiplicative inverse (1). It also satisfies all the properties of a field, including closure under addition and multiplication, associativity, distributivity, and the existence of additive and multiplicative inverses.

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Answer:

$360

Step-by-step explanation:

Calculation for what would be the total cost of next month's order

First step is to calculate how much they paid per the two cases of printer papers

Two cases of printer paper=$48 /2

Two cases of printer paper=$24 per case

Second step is to calculate the cost of each package of printer paper

Cost of each package of printer paper=$24/12 packages of paper

Cost of each package of printer paper=$2

Last step is to calculate the total cost of next month's order

Total cost=180 packages*$2

Total cost=$360

Therefore what would be the total cost of next month's order is $360

Answer:

91

Step-by-step explanation:

the common diference is : d = ( 13)-(7)=(7)-(1)=(1)-(-5)=6

the first term is A1 = -5

the n-ieme term is : An = A1 +(n-1)d

An = -5+6(n-1)

An = 6n-11

the 17th term in the arithmetic sequence  is : A17 = 6(17)-11 =91

Answer:

c

Step-by-step explanation:

-5,1,7,13,19,25,31,37,43,49,55,61,67,73,79,85,91

Answer:

≈ 14 feet

Step-by-step explanation:

this situation creates a right triangle with the ladder being the hypotenuse and legs distance from base of ladder and height of ladder (h) up the wall

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other two sides, that is

h² + 5² = 15²

h² + 25 = 225 ( subtract 25 from both sides )

h² = 200 ( take square root of both sides )

h = \(\sqrt{200}\) ≈ 14 feet ( to the nearest foot )

Answer:

\(BC \approx 1.82\)

Step-by-step explanation:

Utilize the trigonometric ratio tangent.

\(\tan(70 \textdegree ) = \dfrac{5}{?}\)

\(\tan(70 \textdegree ) \div 5 = \dfrac{1}{?}\)

\(? = \dfrac{5}{\tan(70 \textdegree )}\)

\(? \approx 1.82\)

\(BC \approx 1.82\)

Answer:

True

Right angles measure 90° . So each vertical angle = 90° and hence they are equal

Step-by-step explanation:

Answer:

t=144x3+432x2y+432xy2+144y3−x2

2xy2

Step-by-step explanation:

Answer:

110 ft  

Step-by-step explanation:

The length of fencing is four times the perimeter of one garden.

The formula for the perimeter of a rectangle is  

P = 2l + 2w

The total perimeter for all four rectangles is

P = 4× (2l + 2w) = 8l + 8w

Data:

 l = 9¼ ft

w = 4½ ft

Calculation:

P = 8l + 8w = 8×9¼ + 8×4½ = 72⁸/₄ + 32⁸/₂ =(72 + 2) + (32 + 4) = 74 + 36 = 110 ft

The total length of fencing is 110 ft.

The given function have 3 complex roots.

The "solutions" or numerical values that are equal to the given equation's variable are known as the roots of the equation.

The zeros are frequently referred to as the function's roots, solutions, or x-intercepts. These are all used in mathematics and have the same meaning as the zero definition. The zeros of a function are hence function values where y=0 or f(x)=0 or f (x) = 0 is specified when a function y= or f(x)= is given.

Given:

f(x) = (x+3) (2x − 1)²

Now solving,

f(x) = (x+ 3) ( 4x² + 1 -4x)

f(x) = 4x³ + x - 4x² + 12x² + 3 -12 x

f(x) = 4x³ - 8x² -11x + 3

As, the above polynomial of degree 3.

Hence, there are 3 complex roots.

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