Round to the nearest degree

(a) 794g of the initial sample will be left in the sample after 25 years. (b) Time taken to decay to half of its original amount is 3.39 years.

Isotopes(200g) are atoms that have the same number of protons in their nucleus, but a different number of neutrons. This means that they have the same atomic number, but a different atomic mass. Because of this, isotopes have different physical and chemical properties. Isotopes can be stable, meaning that they do not undergo radioactive decay, or they can be unstable, meaning that they will undergo radioactive decay over time.

(a) Substituting 25 for t in the expression, we get:

[tex]A(25) = 200e^{0.0541 \times 25}[/tex]

         [tex]= 200e^{1.3525}[/tex]

Thus, after 25 years, there will be

[tex]200e^{1.3525} = 2003.97[/tex]

794 g of the initial sample left in the sample.

(b) We want to find t such that

[tex]A(t) = 200e^{0.0541}[/tex]                                          

       = 100.

Solving for t, we get:

[tex]= 200e^{0.0541} \times t=100[/tex]

Dividing both sides by 200 and applying the natural logarithm to both sides, we get:

0.0541 × t = ln(0.5)

Therefore,

[tex]t = \frac{ln(0.5)}{0.0541}[/tex]

  = 3.39 years.

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Answer:

Step-by-step explanation:

Therefore, C is the correct option.

Step-by-step explanation:

We have been given the equation

The GCF of the right hand side of the equation is t. Hence, factored out the GCF.

Now,  is in multiplication with 't'. So in order to isolate t, we can divide both sides by

Therefore, C is the correct option.

Applying the triangle midsegment theorem, the length of CD is: 8 units.

If the midpoints of two sides of a triangle are joined together by a line segment, that line segment is called the midsegment of the triangle. Every triangle has three of these.

According to the triangle midsegment theorem, the third side of a triangle is parallel to its midsegment, and also has a length that is twice of the length of the midsegment.

Given the image above, where points G, E, and F are the midpoints of the sides of the given triangle, thus:

EG is a midsegment that is parallel to a third side CD.

Therefore:

Length of CD = 2(EG)

Substitute

CD = 2(4)

CD = 8 units.

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On solving the question as said we get to know that the maximum possible length of the repeating section of the decimal representation of the given number is 10.

As 941 and 1549 are already in whole number lets assume that the question says to find the decimal repetition is 941 and 15  divided by 41 and 59 respectively.

9 divided by 41 is equal to 0.2195121951

15 divided by 49 is equal to 0.306122449.

Therefore, the maximum possible length for their repeating section is 10.

The preferred method for representing both integer and non-integer numbers is the decimal numeral system, often known as the base-ten positional numeral system and denary.

It is the expansion of the Hindu-Arabic numeral system to non-integer values. Decimal notation is the term used to describe the method of representing numbers using the decimal system.

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It takes 11.55 years for money to double if invested at 6% compound interest.

What is compound interest?

Calculating the answer exactly:  P⁰°⁰⁶ⁿ=A .

We don’t know the initial value of the principal but we do know that the accumulated value is double (twice) the principal.

P⁰°⁰⁶ⁿ = 2P

We divide both sides by  P

e⁰°⁰⁶ⁿ = 2

Using natural logarithm:

0.06 n = ln(2)

n = ln(2)/0.06

n = 11.55 years

Hence, It takes 11.55 years for money to double if invested at 6% compound interest.

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The required quotient is 34.2 ÷ 3.8 = 9.

A quotient is defined as the outcome of dividing an integer by any divisor that can be said to be a quotient. The dividend contains the divisor a specific number of times.

We have been given 3.8 divided by 34.2

According to the given question, we can write the quotient as:

⇒ 34.2 ÷ 3.8

⇒ 34.2 / 3.8

⇒ 342 / 38

Apply the division operation, and we get

⇒ 9

Therefore, the required quotient is 34.2 ÷ 3.8 = 9.

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Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

tan x= -3/1

So, H = √1 + 9 = √10

sin x= -3/ √10 and cos x= 1/ √10

So, sin 2x= 2 sin x cos x =2 ( -3/ √10 )(1/ √10) = -3/10

and, cos 2x= 1- 2 sin²x

                  = 1- 2( 9/10)

                  = -8/10

and, tan 2x = sin 2x/ cos 2x =  -3/10 / ( -8/10) = 3/8

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The slope of the line that passes through the points (-6,1) and (-6,-4) is Undefined.

The slope(m) of the line passing through two points is X1,Y1 and X2, Y2 is

m=[tex]\frac{y2-y1}{x2-x1}[/tex]

we have (x1,y1) and (x2,y2) is (-6,1) and (-6,-4) respectively substitute the values in m=[tex]\frac{y2-y1}{x2-x1}[/tex],

we get m=[tex]\frac{-4-1}{-6-(-6)}[/tex] = -5/0 which is Undefined.

Whenever the slope of the line is undefined then the line must be vertical. Because the slope of the vertical line cannot be defined.

The slope of the line that passes through the points (-6,1) and (-6,-4) is Undefined.

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Answer:

Yes

Step-by-step explanation:

Answer:4.05

Step-by-step explanation: Walnut divided by 2 is 0.9 and Oak is 0.9. Maple is 0.45 and Spruce. All that is added up to 4.05

The given division will give the result as (x-3) + [2/(x+3)].

Polynomial are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non negative exponentiation of variables involved.

The given division of the two of the polynomial can be carried out as shown below,

[tex]\dfrac{x^2-7}{x+3}\\\\=x+\dfrac{-3x-7}{x+3}\\\\=x-3+\dfrac{2}{x+3}\\\\=(x-3)+\dfrac{2}{x+3}[/tex]

Hence, [tex]\dfrac{x^2-7}{x+3}=(x-3)+\dfrac{2}{x+3}[/tex].

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The solutions to the quadratic linear system equations are (11, 41) and (3, 9).

The given equations are y=x²-10x+30 and y=4x-3.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Here, y=x²-10x+30 -------(I) and y=4x-3 -------(II)

Substitute equation (II) in the equation (I), we get

4x-3=x²-10x+30

⇒ x²-10x+30-4x+3=0

⇒ x²-14x+33=0

⇒ x²-11x-3x+33=0

⇒ x(x-11)-3(x-11)=0

⇒ (x-11)(x-3)=0

⇒ x=11 and x=3

So, y=4(11)-3=41 and y=4(3)-3=9

Therefore, the solutions to the quadratic linear system equations are (11, 41) and (3, 9).

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Answer:

NO

Step-by-step explanation:

Two fourths =

[tex] \frac{2}{4} = 0.5[/tex]

Two thirds =

[tex] \frac{2}{3} = 0.66667[/tex]

Therefore

0.66667 > 0.5

[tex] \frac{2}{3} > \frac{2}{4} [/tex]

or

0.5 < 0.66667

[tex] \frac{2}{4} < \frac{2}{3} [/tex]

i hope this helped

Answer: No, 2/4 is not greater than 2/3

Step-by-step explanation: To find an easy way to calculate their values we have 2 options. So, the 1st option is to turn them into a decimal. I already calculated their values which are:

2/4 = 0.5

2/3 = 0.667

Then, we compare the two decimal numbers to get the answer.

0.5 is not greater than 0.667.

The 2nd way is to find a common denominator, which would look like this:

2/4 =  6/12

2/3 =  8/12

8/12 is greater than 6/12, so that also proves that 2/4 is not greater than 2/3.

Answer: $1000 = 12x + 112

Step-by-step explanation:

let x be the amount of hours worked

Answer:

perimeter of a triangle is the total

Step-by-step explanation:

p=48cm

Length=3x

width=x

Now P= 2(L+W)

48 =2(3x+x)

48=2(4x)

48=8x

dividing both sides by 8

we have x=6

and so length=18 and width =6

Let the dimensions of the pen be L for the length and W for the width. The area of the pen is L*W.

We are given that the width of the pen is 80 meters and that the length of the pen is greater than the width. Therefore, the length of the pen must be greater than 80 meters.

Since the area of the pen is L*W, the area will be greatest when L is as large as possible and W is as large as possible. Therefore, we can set L equal to 80 and W equal to 80 to find the dimensions of the pen that give the greatest area:

L = 80

W = 80

The dimensions of the pen that give the greatest area are 80 meters by 80 meters. Therefore, the answer is 80m x 80m.

The dimensions of the pen are 20 m × 40 m and the area will be 600 m².

An object's area is how much space it takes up in two dimensions. It is the measurement of the number of unit squares that completely encompass the surface of a compact figure. The squared unit, which is frequently expressed as inches, square feet, etc., is the accepted unit of area.

As per the given data in the question,

Let the length of the rectangle is x and,

Let the width of the rectangle is y.

So, the equation will be,

2x + y = 80              (1)

y = 80 - 2x              (2)

Use the formula of the area of a rectangle,

A = x × y

Substitute y = 80 - 2x in the above formula,

A = x × (80 - 2x)

= 80x - 2(x)²

= -2x² + 80x

dA/dx = -2x² + 80x

A' = -4x + 80

-4x = -80

x = 80/4

x = 20 m

Substitute x = 20 in equation (2)

y = 80 - 2(20)

y = 40 m  

So, the area should be,

A = 20 × 40

A = 600 m².

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Answer: hope it helps

Step-by-step explanation:

2^6=64≡ -1 ( mod 13)

So 2^70=16*(2^6)^11=16*(-)^11(mod 13)

2^70 ≡-16 ( mod 13)

2^70 ≡10 ( mod 13)

Now 3^3=27≡1 ( mod 13)

So 3^70= 3*(3^3)^23≡ 3*(1)^23 ( mod 13)

≡ 3 ( mod 13)

Thus 2^70+3^70 ≡ 10+3 (mod 13)

≡ 0 ( mod 13)

An inequality that expresses the mean number of steps that Diego needs to walk during the last 3 days of this week to more than 70,000 steps is  32076+3x>70000.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Given that, Diego's goal is to walk more than 70,000 steps this week.

a) The mean number of steps that Diego walked during the first 4 days of this week is 8019.

So, the number of steps =4×8019

= 32076

Let x be the mean number of steps that Diego needs to walk during the last 3 days of this week to walk more than 70,000 steps.

Now, the inequality is 32076+3x>70000

b) The mean number of steps that Diego needs to walk during the last 3 days of this week is 12642

Substitute x=12642 in the inequality 32076+3x>70000, we get

32076+37926>70000

70002>70000

Yes, Diego will reach his goal of walking more than 70,000 steps this week.

Therefore, the inequality to represent the given situation is 32076+3x>70000.

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Answer: about 4:30

Step-by-step explanation:

he used the restroom starting at 4:15, he sat on the toilet and watched tt for exactly 14 minutes, He then whiped himself which took about 50 seconds. Flushing the toilet took 10 seconds and when he flushed it was 4:30.

The domain of the given function is z<0 or z>0

The entire range of independent variable values is the domain of a function.

According to this definition, it means:

The collection of all x-values that can cause the function to "work" and produce actual y-values is known as the domain.

Keep these things in mind when locating the domain:

A fraction's denominator (bottom) cannot be 0.

In this section, the integer following a square root symbol must be positive.

The domain of a function is a set of input of argument values for which the function is real or defined.

1) Finding the singularity point:

Taking the denominator 4×[tex]z^{2}[/tex] = 0 ⇒ z = 0

∴The following function will not be defined if z = 0

So the function domain is z>0 or z<0

The domain of the given function is z<0 or z>0

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Answer: To find out how many seconds it will take for the egg to hit the ground, we need to find the value of x when the height of the egg is 0 feet. We can do this by setting the height of the egg equal to 0 in the equation 27 - 16x^2 and solving for x.

The equation for the height of the egg in feet x seconds after being dropped is given as:

27 - 16x^2 = 0

Subtracting 27 from both sides of the equation gives us:

-16x^2 = -27

Dividing both sides of the equation by -16 gives us:

x^2 = 27/16

Taking the square root of both sides of the equation gives us:

x = sqrt(27/16)

Plugging this value into the equation for the height of the egg gives us:

27 - 16(sqrt(27/16))^2 = 0

Simplifying this equation gives us:

27 - 16(27/16) = 0

Which simplifies to:

27 - 27 = 0

This equation is true, so the value of x that we found is a solution to the equation. This means that the egg will hit the ground after sqrt(27/16) seconds.

I hope this helps! Let me know if you have any other questions.

The profit function is 250x  and the profit earned is 375000.

What is cost?

In production, research, retail, and accounting, a cost is that the value of cash that has been spent to provide one thing or deliver a service, and thence isn't obtainable to be used any longer.

Main body:

A) Profit function = R() – TC()

                        = 750 – (300+200)x

                        = 750 – 500x

                        = 250 x

b) total profit = 250 x

                     = 250 *1500

                     = 375000

c) The zero-profit condition is that the condition that happens once AN business or kind of business has a very low (near-zero) value of entry to or exit from the business. during this scenario, some companies not already within the business tend to hitch the business if they calculate that they're going to create a positive economic profit (profit in more than the price of effort investible funds). a lot of and a lot of companies can enter till the economic profit per firm has been driven all the way down to zero by competition.

hence the profit function is 250x

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Answer:

552 mph

Step-by-step explanation:

414 / 3/4 = 414 * 4/3 = 1656/3 = 552

Answer

150000 after 4 years

Step-by-step explanation:

The area of regular hexagon in simplest radical form is [tex]600\sqrt{3}[/tex] m².

There are many different types of hexagons. The most common type is a regular hexagon, which is a hexagon that has sides of equal length and angles of equal measure. The perimeter is the total length or distance around a two dimensional shape. In the figure below, the perimeter of each shape is the sum of the lengths of each side, shown in red. The perimeter of a circle or ellipse is called the circumference. For a polygon, the perimeter is the sum of its side lengths.

The given polygon is a regular hexagon with perimeter 120 m.

Thus, the length of each side,

s = 120/6 = 20 m.

The area, A, of a regular hexagon can be found given only its side length, s, with the formula:

[tex]A = \frac{3\sqrt{3} }{2} s^{2}[/tex]

Substitute s = 120 m in above formula:

[tex]A = \frac{3\sqrt{3} }{2} (20)^{2} \\A = \frac{3\sqrt{3} }{2}(400)\\A = 600 \sqrt{3}[/tex]

Thus, the area of regular hexagon in simplest radical form is [tex]600\sqrt{3}[/tex] m².

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The value of hypotenuse will be;

⇒ Hypotenuse = 132.35

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The values are,

⇒ θ = 20° opposite = 45

Now,

Since, The values are,

⇒ θ = 20° opposite = 45

We know that;

⇒ sin θ = Opposite / Hypotenuse

⇒ sin 20° = 45 / Hypotenuse

⇒ Hypotenuse = 45 / sin 20°

⇒ Hypotenuse = 45 / 0.34

⇒ Hypotenuse = 132.35

Thus, The value of hypotenuse will be;

⇒ Hypotenuse = 132.35

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If the hypotenuse and one leg of one right-angled triangle are equal to the corresponding hypotenuse and leg of another right-angled triangle, the two triangles are congruent.

Here in the figure attached below,

Given two triangles ΔABC and ΔDEF

Also given that,

ΔABC and ΔDEF are congruent to each other.

Given AC = 4cm

Since both triangles are congruent ,

Side AC is congruent to DF

Therefore DF = 4cm (based on SSS theorem).

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A horizontal asymptote of a graph is a horizontal line y = b where the graph approaches the line as the inputs approach ∞ or –∞.

6. x = 28 degrees

7.  z = 1.6 cm

6.  Notice that you can use the property that tells us that the addition of all internal angles of a triangle must give 180 degrees, then you write the following equation:

50 + 69 + (2 x +5) = 180

combine like terms:

119 + 2 x + 5 = 180

124 + 2 x = 180

subtract 124 from both sides:

2 x = 56

divide by 2 both sides:

x = 56 / 2

x = 28 degrees

Problem 7.

If the two triangles are congruent, then the side MN must equal side RS.

Since MN  measure 1,8 cm, then RS must also measure 1.8 cm

and we can write the equation:

1.8 = 3 z - 3

adding 3 to both sides:

1.8 + 3 = 3 z

4.8 = 3 z

dividing both sides by 3:

z = 4.8 / 3

z = 1.6 cm

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the answer will be "all steps are correct"