PLEASE HELP!! Quadrilaterals and other polygons

6.665 grams of the 13 grams remain after 8 hours.

The decay equation for the 13 grams of iron-52 is:

\(N(t) = 13g*e^{(-ln(2)/8.3h)*t}}\)

Where N is the amount of iron-52, and t is the time in years.

Where we used the fact that the half-life is exactly 8.3 hours.

Now, the amount that is left is given by N(8h), so we just need to replace the variable t by by 8 hours, so we get:

\(N(8h) = 13g*e^{(-ln(2)/8.3h)*8h}} = 6.665g\)

So 6.665 grams of the 13 grams remain after 8 hours.

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Answer:

15\(\pi\)

Step-by-step explanation:

with diameter

A=\(\pi\)d

A=\(\pi\)(15)

A=15\(\pi\)

Answer:

The measure of CD is 46

Step-by-step explanation:

From the midpoint theorem, we have,

FG = (1/2)CD

so,

\(13+5x=(1/2)(-3x+52)\\So,\\2(13+5x)=-3x+52\\26+10x=-3x+52\\13x=52-26\\13x=26\\x=26/13\\x=2\)

Now,

\(CD = -3x+52\\since \ x=2\\we \ get\\CD=-3(2) +52\\CD=-6+52\\CD=46\)

Answer:

7x26

Step-by-step explanation:

x = y² - 7 is the simplified inverse equation of the equation y = x² - 7.

Inverse function is a function which reverse one function to another.

If a function f takes the variable x to y, then the inverse of a function must takes y to x.

To get the inverse of the function, we have to interchange the variables.

Given equation is y = x² - 7

Now interchange the variable x to y and y to x,

we get  x = y² - 7

Hence, the required equation is x = y² - 7

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Dos veces más que cuatro es igual a seis. La respuesta está implicita en la misma pregunta y se puede representar de la siguiente manera:

The angle measure of x is 115°.

A parallelogram is a four-sided shape with two sets of parallel sides, which means that opposite sides are both parallel and have equal length. Parallelograms also have opposite angles with the same measure, and their diagonals intersect at the midpoint and bisect each other. This results in the parallelogram being divided into two triangles that are congruent. Examples of parallelograms include rectangles, squares, and rhombuses, and they are commonly used in both geometry and everyday life, particularly in the design of buildings and other structures.

We can call this figure ACDEF. Let us join CB.

Now we can see that BDEF is a parallelogram. Opposite angles of a parallelogram are equal, hence ∠DBF = ∠DEF = x°

And also consider the triangle ABC,

∠BAC = 50°

∠ABC = 180 - ∠DBF = 180° - x° (linear pair)

∠ACB = 180 - ∠ACD = 180° - x° (linear pair)

We know that all the angles of a triangle adds up to 180°.

Using this we can find x°:

∠BAC + ∠ABC + ∠ACB = 180°

50° + 180° - x° + 180° - x° = 180°

-2x° + 410 = 180°

-2x° = 180° - 410° = -230°

x° = -230/ -2

x ° = 115°

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Answer:

15%

Step-by-step explanation:

Change = (3-2.55) = 0.45 milliliters

Percentage decrease = (o.45/3)*100

= 15%

The most reasonable explanation for why Medera received zero calls between 3pm and 5pm is that she turned the phone off while playing in a soccer game.

Number is an abstract concept used to count or measure something. It is present in many aspects of our lives, from counting the number of people in a room to measuring a distance between two points. Numbers are also used to represent information and to quantify facts. We use numbers in mathematics, science, engineering, business, and many other fields. Numbers are also used in everyday life, such as for telling time, counting items, and measuring distances.

The most reasonable explanation for why Medera received zero calls between the hours of 3pm and 5pm is that Medera turned the phone off while playing in a soccer game. This can be seen by looking at the histogram, which shows that there were zero calls received around this time, while Medera was likely playing in the game. The graph also shows that Medera usually receives a cluster of calls at certain times. This is also evidence that she turned her phone off while playing in the game, as it would be unlikely that she would receive no calls if her phone was still on. Additionally, it is unlikely that Medera's phone can only receive 22 calls a day, as this would be an unusually low limit. Furthermore, it is unlikely that Medera lost her phone for two hours, as this would not explain why there were zero calls received. Therefore, the most reasonable explanation for why Medera received zero calls between 3pm and 5pm is that she turned the phone off while playing in a soccer game.

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The hours when no calls were received were most likely when Madera turned off the phone while practising soccer.

According to the question,

Madera, a middle school student, got phone calls from 10 a.m. to 10 p.m. on one Saturday.

From the scenarios presented, the one that would suggest this would be when Medera turned off his phone while playing soccer. This is because, her phone was turned off, it was not receiving any phone signal, which meant that no inbound calls were received during that time. Medara lost her phone for two hours, but even though she didn't have it with her, the phone was still on and connected to a network, indicating that calls were still streaming.

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The area under the standard normal distribution curve between z=-2 and z=-3 is 97.73%.

If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z score.

If we have

\(X \sim N(\mu, \sigma)\)

Here X is following normal distribution with mean\(\mu\)and standard deviation \(\sigma\)

Then it can be converted to standard normal distribution as

\(Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)\)

Given that

\(z=-3\text{ and }z=3p(-3)\)

Therfore, 97.73% of the area is between z=-3 and z=3.

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9514 1404 393

Answer:

  (b)  y = -5x

Step-by-step explanation:

When "y varies directly as x" the equation for that is ...

  y = kx . . . . . . . for some constant k

The value of k can be found by solving for it:

  k = y/x . . . . . . divide by x

So, the given point (x, y) = (2, -10) tells you the value of k is ...

  k = -10/2 = -5

and the direct variation equation is ...

  y = -5x

_____

Additional comments

There are a couple of other useful facts about direct variation. When you compare the equation to the slope-intercept form equation for a line, ...

  y = mx + b

you see that b=0 and the slope, or rate of change, (m) is the same as k.

The y-intercept of 0 means that the graph of any direct-variation equation must go through the origin. (If it does not, then the variation is not direct.)

ANSWER 92°

REMEMBER! angles in a triangle add up to 180°

this means that:

(x) + (3x + 13) + (x - 8) = 180

5x + 5 = 180

5x = 175

therefore x = 35

now that we know x, we can apply this to work out the angle mentioned, the angle a:

A = 3(35) - 13

   = 92°

1)

The axis of symmetry is x = -6.

2)

Vertex is (-6, 26).

3)

f(x) has a maximum value.

4)

f(x) is concave down.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 7 is an equation.

We have,

f(x) = -x² - 12x - 10

This is in the form of ax² + bx + c.

a = -1, b = -12, c = -10

The axis of symmetry is x = -b/2a

x = 12/(-2)

x = -6

Now,

f(x) = -x² - 12x - 10

f(x) = -(x² + 12x + 10)

f(x) = - { (x² + 12x + 36) - 36 + 10}

f(x) = -(x + 6)² + 26

This is in the form of f(x) = a (x - h)² + k

a = -1, h = -6, k = 26

Vertex = (h, k) = (-6, 26)

Now,

f(x) = -x² - 12x - 10

f'(x) = -2x - 12

f''(x) = -2

It is a negative value.

This means f(x) has a maximum value.

Now,

From the graph, we see that f(x) is concave down.

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Answer:

x is greater or equal to 5.5

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

Sin(∅) = Opposite angle ÷ hypotenuse.

Sin (45) = 7\(\sqrt{2}\) ÷ hypotenuse

hypotenuse = 7\(\sqrt{2}\) ÷ sin(45)

*********************

Keep in mind

sin(45) = √2÷2

*********************

so we have:  Hypotenuse = 7√2 ÷ (√2÷2)

Hypotenuse= 14.

The Least common multiple (LCM)  The time at which both bells will ring together is 10:45 am, and the Subsequent times will be 11:30 am, 12:15 pm, 1:00 pm, and so on, with an interval of 45 minutes between each occurrence.

The time at which both bells will ring together, we need to find the least common multiple (LCM) of the intervals at which each bell rings.

The first bell rings every 45 minutes, and the second bell rings every minute. We want to find the point at which both intervals align, meaning they both divide evenly into the same amount of time.

To find the LCM, we can list the multiples of each interval until we find a common multiple.

Multiples of 45 minutes: 45, 90, 135, 180, 225, 270, 315, 360, 405, ...

Multiples of 1 minute: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...

From the lists above, we can observe that the least common multiple occurs when both intervals coincide at the same time, which is 45 minutes.

Thus, the two bells will ring together every 45 minutes.

If we consider the initial adjustment time of 10:00 am, the first time both bells will ring together is at 10:45 am. After that, they will continue to ring together every 45 minutes throughout the day.

Therefore, the time at which both bells will ring together is 10:45 am, and the subsequent times will be 11:30 am, 12:15 pm, 1:00 pm, and so on, with an interval of 45 minutes between each occurrence.

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We need to represent the product of two exponents as one single exponent. To do that we need to calculate their product, when the bases are equal we can conserve the base and add the exponents. We will do this below:

Answer:

\(n=4\sqrt{3}\)

Step-by-step explanation:

Let the only unmarked side of the triangle in the given figure be x. By the Pythagorean Theorem, \(12^2+n^2=x^2.\) Mark this as equation 1.

By the Pythagorean Theorem also, \(x^2+m^2=(12+4)^2\) or \(x^2+m^2=16^2.\) Mark this as equation 2.

Substituting equation 1 to equation 2 results to

\((12^2+n^2)+m^2=16^2\\n^2+m^2=16^2-12^2\\n^2+m^2=112.\)

Mark \(n^2+m^2=112\) as equation 3.

Looking at the smallest triangle and using the Pythagorean Theorem, then

\(n^2+4^2=m^2\\n^2-m^2=-4^2\\n^2-m^2=-16.\)

Mark \(n^2-m^2=-16\) as equation 4.

Adding equation 3 and equation 4 results in

\(n^2+m^2+(n^2-m^2)=112+(-16)\\2n^2=96\\n^2=48\\n=\sqrt{48}\\n=\sqrt{16\cdot3}\\n=4\sqrt{3}.\)

Hence, the value of n is \(n=4\sqrt{3}.\)

The assemble for maximum profit  is mathematically given as

For maximum profit, 100 tire and 0 strings must be assembled.

Generally, the equation for the max number  is mathematically given as

Mx=50x+20y

Therefore

2x+3y \leq 250

x1+x\leq=100

Therefore

with cordinates of

(0,0)

(100,0)

(50,50)

(0,250/3)

In conclusion, The mx of 50x+20y is (100,0)

Hence, for maximum profit 100 tire and 0 strings must be assembled.

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The  number of 50¢ coins is 200, number of  25¢ coins is 360

and number of  10¢ coins is 160.

The quantitative relation between two or more amounts showing the number of times one value is contains or contained within other.

Now the given ratio is 5 : 9 : 4.

and total amount of the coins is $206.

There are three types of coins in the bag, 50¢, 25¢ and 10¢.

Suppose x be the the ratio of coins in the bag.

Hence, number of  50¢ coins = 5x

number of  25¢ coins = 9x

number of  10¢ coins = 4x

Now, given total amount = $206

and since $1 = 100¢

⇒ ($0.5)(5x) + ($0.25)(9x) + ($0.1)(4x) ¢ = $206

Solving them,

⇒ 2.5x + 2.25x + 0.4x = 206

⇒ 5.15x = 206

⇒ x = 40

Therefore,

number of  50¢ coins = 5*40 = 200

number of  25¢ coins = 9*40 =  360

number of  10¢ coins = 4*40 =  160

Hence, number of 50¢ coins is 200, number of  25¢ coins is 360

and number of  10¢ coins is 160.

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Answer:

The value of y is 216

(and the value of x is 12)

Step-by-step explanation:

The general formula for a geometric sequence is,

\(a_n = a_1(r)^{n-1}\)

Where n represents the nth term, a_1 is the first term and r is the common ratio,

we see that,

r = 6,

the first term is,

a_1 = (x-6)

the 2nd term is,

a_2 = 3x,

the 3rd term is,

a_3 = y, finding y,

first we find x, using the above given formula we have,

\(a_2 = a_1(6)^{2-1}\\3x = (x-6)(6^1)\\3x = 6x -36\\36 = 6x - 3x\\36 = 3x\\x=36/3\\x=12\)

x = 12,

Now, for y we can use the relation between a_3 and a_2,

\(a_3 = a_1(6)^{3-1}\\y = (x-6)(6)^2\\y = (12-6)(6^2)\\y = 6(6^2)\\y = 6^3\\y = 216\)

y = 216

(∀x)P(x) can be written as p ∧ q, (Ǝx)P(x) can be written as ¬p ∨ ¬q, and the universal and existential negation rules of predicate logic correspond to the DeMorgan's law of propositional logic, which states that ¬(p ∨ q) = ¬p ∧ ¬q.

a) The statement (∀x)P(x) states that P(x) is true for all x in the domain, which consists of just 0 and 1. So, if P(0) is true, represented by p, and P(1) is true, represented by q, then (∀x)P(x) is true. Therefore, (∀x)P(x) can be written as p ∧ q.

b) The statement (Ǝx)P(x) states that P(x) is true for at least one x in the domain, which consists of just 0 and 1. So, if either P(0) is true, represented by p, or P(1) is true, represented by q, then (Ǝx)P(x) is true. Therefore, (Ǝx)P(x) can be written as p ∨ q.

c) The negation of (∀x)P(x), represented as ¬(∀x)P(x), is equivalent to the negation of (∀x)P(x) in predicate logic, represented as (Ǝx)¬P(x). This corresponds to DeMorgan's law of propositional logic, which states that ¬(p ∧ q) = ¬p ∨ ¬q.

Similarly, the negation of (Ǝx)P(x), represented as ¬(Ǝx)P(x), is equivalent to the negation of (Ǝx)P(x) in predicate logic, represented as (∀x)¬P(x). This corresponds to DeMorgan's law of propositional logic, which states that ¬(p ∨ q) = ¬p ∧ ¬q.

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Proof: If mn is even, then either m = 2k/n or n = 2k/m for an integer k, meaning either m or n must be even.

The following is a direct proof:

The proof shows that if m and n are integers and mn is even, then either m must be even or n must be even. The proof starts by assuming that m and n are integers and that mn is even. It then proceeds to show that one of the factors, either m or n, must also be even.

The proof uses the definition of an even number, which is a number that is divisible by 2, to conclude that if mn is even, then there must be an integer k such that mn = 2k. From this equation, the proof derives the expressions m = 2k/n or n = 2k/m. Since k is an integer, it follows that either m or n must be even, since the result of dividing an integer by another integer is also an integer.

The proof concludes by stating that if mn is even, then either m must be even or n must be even, based on the logical reasoning provided in the proof.

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The area of ΔQRS is 26.10 square units.

What is triangle?

A triangle is a closed, two-dimensional geometric shape with three straight sides and three angles.

To find the area of \($\triangle QRS$\), we can use the formula:

\($Area = \frac{1}{2} \times base \times height$\)

where the base and height are the length of two sides of the triangle that are perpendicular to each other. We can find these sides using trigonometry.

First, we need to find the length of side \($QR$\). We can use the Law of Cosines:

\($QR^2 = QS^2 + RS^2 - 2(QS)(RS)\cos(R)$\)

where \($R$\) is the angle at vertex \($R$\). Substituting the given values, we get:

\($QR^2 = 9^2 + 5^2 - 2(9)(5)\cos(57^\circ)$\)

\($QR \approx 8.02$\)

Next, we need to find the height of the triangle, which is the perpendicular distance from vertex \($R$\) to side \($QS$\). We can use the sine function:

\($\sin(R) = \frac{opposite}{hypotenuse}$\)

\($\sin(57^\circ) = \frac{height}{8.02}$\)

\($height \approx 6.51$\)

Now we can find the area of the triangle:

\($Area = \frac{1}{2} \times QR \times height$\)

\($Area = \frac{1}{2} \times 8.02 \times 6.51$\)

\($Area \approx 26.10$\) square units

Therefore, the area of \($\triangle QRS$\) is approximately \($26.10$\) square units.

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The number of square inches of cardboard that are needed to make one

the container is 18.

We have,

The volume of the triangular prism.

= Area of the triangle x height

Now,

Height = 6 in

And,

To find the area of a triangle, we can use Heron's formula.

A = √(s(s-a)(s-b)(s-c))

where s is the semi-perimeter of the triangle, calculated as:

s = (a + b + c) / 2

In this case, the side lengths of the triangle are 3.2 in, 3.2 in, and 2 in.

Let's calculate the area using Heron's formula:

s = (3.2 + 3.2 + 2) / 2 = 4.2

A = √(4.2(4.2 - 3.2)(4.2 - 3.2)(4.2 - 2))

A = √(4.2 x 1 x 1 x 2.2)

A = √(9.24)

A ≈ 3.04 square inches

Now,

The volume of the triangular prism.

= Area of the triangle x height

= 3.04 x 6

= 18.24 in²

Now,

Area of one cardboard.

= 1² in²

= 1 in²

Now,

The number of square inches of cardboard that are needed to make one

container.

= The volume of the triangular prism / Area of one cardboard

= 18.24 in² / 1 in²

= 18.24

= 18

Therefore,

The number of square inches of cardboard that are needed to make one

the container is 18.

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Answer: 118

Step-by-step explanation:

Angle ABC and Angle BCD add up to 180 degrees, because Line AB and line CD are parallel. Because of this, Angle BCD can be moved up the the angle above 3n-47. Because the two angles fall on to a straight line, we can say that (3n-47)+(n+7)=180. Solving, n=55, so angle ABC equals 118 degrees.

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Answer:

7 quarts = 28 cups 10 cups = 2.5 quarts

Answer:

28 cups

Step-by-step explanation: