An unknown radioactive element decays into non-radioactive substances. In 180 days the radioactivity of a sample decreases by 73 percent.
(a) What is the half-life of the element? (in days)
(b) How long will it take for a sample of 100 mg to decay to 60 mg? (in days)

Answer:

x must be 5

Step-by-step explanation:

Recall that the area formula for a trapezoid is

A = (average of base lengths)(width)

Here we have

                                                                   17 cm + x

      (average of base lengths) = 11 cm = ----------------

                                                                           2

So 2(11 cm) = 17 cm + x, or

      22 cm = 17 cm + x

Then x must be 5.

To find the length of the other base of the trapezoid with a midsegment of 11 cm and one base of 17 cm, use the average property of the midsegment. The calculation reveals the other base is 5 cm in length.

The question is about finding the length of the other base of a trapezoid when the length of the midsegment and one of the bases is known. The midsegment of a trapezoid is parallel and equal to the average of the two bases. Therefore, if the midsegment is 11 cm and one base is 17 cm, the other base can be found by setting up the equation:

Midsegment = (Base1 + Base2) / 2

Substitute the known values:

11 = (17 + Base2) / 2

Multiplying both sides by 2 gives:

22 = 17 + Base2

Subtracting 17 from both sides gives:

Base2 = 22 - 17

Base2 = 5

Thus, the length of the other base of the trapezoid is 5 cm.

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Answer:

(-5 +/- sqrt(65))/2

Step-by-step explanation:

To solve this, we can use the quadratic formula!

So,

x = (-b +/- sqrt(b^2-4ac))/2a

x = (-5 +/- sqrt(25+40))/2

x = (-5 +/- sqrt(65))/2

So (-5 +/- sqrt(65))/2  is our answer.

Check the picture below.

so, the triangular prism is really 2 triangles and 3 rectangles stacked up to each other at the edges.  Let's simply get the area of each shape and sum them up, and that's the area of the prism.

[tex]\bf \stackrel{\textit{two triangles}}{2\left[ \cfrac{1}{2}(\stackrel{base}{6})(\stackrel{height}{5.2}) \right]}+\stackrel{\textit{right-side rectangle}}{(8\cdot 6)}+\stackrel{\textit{left-side rectangle}}{(8\cdot 6)}+\stackrel{\textit{base rectangle}}{(8\cdot 6)} \\\\\\ 31.2+48+48+48\implies 175.2[/tex]

Answer:

The surface area = 175.2 mm²

Step-by-step explanation:

Formula:-

Area of rectangle = lb

Area of triangle = bh/2

It is given a triangular prism.

To find the surface area

Surface area = 3 Rectangle area + 2 triangle area

Rectangle area = 3 * lb

 = 3 * 8 * 6

 = 144  mm²

Triangle area  = 2 * bh/2 = bh

  = 6 * 5.2 = 31.2²

Total area = 144 + 31.2 = 175.2 mm²

Answer:

  62 Sunday papers were sold

Step-by-step explanation:

Let x represent the number of Sunday papers sold. Then half that many, or x/2, is the number of Friday papers sold. The total revenue from the sales is the sum of products of quantity and price:

  1.50 · x + 0.75 · (x/2) = 116.25

Multiplying by 2, this becomes ...

  3.00x +0.75x = 232.50

  3.75x = 232.50

Dividing by the coefficient of x gives ...

  232.50/3.75 = x = 62

The number of Sunday newspapers sold is 62.

39.4 degrees Celsius

Hope this helps :)

Answer:

39.4°C

Step-by-step explanation:

The equation for fahrenheit to celsius is

(°F − 32) × 5/9 = °C

With our variable of 103 plugged in it is

(103°F − 32) × 5/9 = 39.444°C

Therefore, her fever is 39.4°c

Answer:

28

Step-by-step explanation:

7*4

Answer:

28

Step-by-step explanation:

7*4

Answer:

e = 8x + 0.1y

Step-by-step explanation:

If Gustavo makes no sales at all, he still gets $8 per hour worked (x).  We can model this part with this equation:

e = 8x

But then, if he sells something, he makes extra money.. He makes 10% (0.1) of every sale (y).  So the equation becomes:

e = 8x + 0.1y

or you can express it this way:

e = 8x + y/10

which is the same thing just written differently.

Answer: 5 Vertices

Step-by-step explanation: I believe if it had 4 faces and 8 edges it would have 5 vertices.

Hm, it seems like his answer is off. The image is what I got.

Answers:

X+3

Step-by-step explanation:

I got it right

Answer:

60

Step-by-step explanation:

(This is not how teachers usually teach you)

First i divided 36 by 2 to get 30% = 18 then i multiplied 30% by 3.3333etc. to get 100% and i multiplied 18 by the same number (18*3.3333 = 60) and i got 60.

Answer:

Step-by-step explanation:

Givens

To find the regular price for tickets, we can use the rule of three.

If $36 represents 60%, how much would represents 100%?

[tex]x=100\% \frac{\$36}{60\%} = \$60[/tex]

Therefore, the cost of a regular price ticket is $60.

Answer:

15 g

Step-by-step explanation:

30% · 50 g = 30/100 · 50 g = 1500/100 g = 15 g

Answer:

15g

Step-by-step explanation:

Answer:

Option D. [tex]x=10[/tex]

Step-by-step explanation:

step 1

Find the midpoint of the given line segment

we know that

The formula to calculate the midpoint between two points is equal to

[tex]M=(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]

we have

[tex]A(5,10),B(15,10)[/tex]

substitute the values

[tex]M=(\frac{5+15}{2},\frac{10+10}{2})[/tex]

[tex]M=(10,10)[/tex]

step 2

Find the equation of the perpendicular bisector

we know that

The equation of a perpendicular bisector is equal to the x-coordinate of the midpoint, because is a vertical line (parallel to the y-axis)

therefore

the equation is equal to

[tex]x=10[/tex]

Answer:

10

Step-by-step explanation:

It takes 5 meters per second.

If you divide 250 by 50 you would get his average speed

The average speed of Ahmed is 5 meters per second.

Important information:

We need to find the average speed of Ahmed.

Formula for average speed is:

[tex]\text{Average Speed}=\dfrac{\text{Distance}}{\text{Time}}[/tex]

Using this formula, the average speed of Ahmed is:

[tex]\text{Average Speed}=\dfrac{250}{50}[/tex]

[tex]\text{Average Speed}=5[/tex]

Thus, the average speed of Ahmed is 5 meters per second.

Find out more about 'Average speed' here:

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Answer:

It would be 139$

Step-by-step explanation:

In order to find a percent of a value you first move the decimal place over 2 to the left or divide by 100(percentage is no longer there). In this case it would be .20. You multiply that with the total number(695) and the product is your answer.

Answer:

[tex]y=\sqrt{x} -5[/tex]

Answer:

The function [tex]f(x)=\sqrt{x-5}[/tex]

Step-by-step explanation:

The Range of any function is complete set of all possible resulting values of the dependent variable , after substituting the domain.

so, the function [tex]f(x)=\sqrt{x-5}[/tex] has range [tex]f(x)$\geq$ -5[/tex]

This includes - 4 .

Hence, the function is [tex]f(x)=\sqrt{x-5}[/tex] .

Explanation:

1. In order for the idea of "perpendicular distance" to make any sense in this context, the number of sides of the polygon must be even. Then the "diameter" is the diameter of the inscribed circle. As the number of sides increases, the polygon differs less and less from a circle, so the relationship of perimeter and "diameter" becomes closer to the relationship in a circle.

"As the number of sides in a regular polygon increases, the ratio of perimeter to diameter for that polygon approaches pi."

__

2. We know from the first question that ...

circumference/diameter = π

And we know that ...

diameter = 2·radius

Then the following are true:

A. circumference = π · diameter

B. circumference = (2·radius) · π

__

3. The expressions in order evaluate to approximately ...

4.0, 3.45, 3.31, 3.24

Of these, the last is closest to pi (3.14....). The appropriate choice is ...

D. (10·5)/15.4

__

4. Pi cannot be expressed as a rational number, because pi is irrational. A number of lengthy proofs have been offered to demonstrate this fact. One of them makes use of the fact that the tangent of any rational number is irrational, and the tangent of π/4 is 1. Since 1 is a rational number, π/4 cannot be, so π cannot be expressed as a rational number.

Answer:

x= 0 and x=-3/4

Step-by-step explanation:

[tex]4x^2 + 3x =0[/tex]

We need to solve this equation using quadratic formula.

The quadratic formula is:

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

for the type of equation

[tex]ax^2 +bx+c=0[/tex]

So, for our given equation:

a= 4

b= 3

c=0

putting values in the formula

[tex]x=\frac{-3\pm\sqrt{9-0}}{8}\\x=\frac{-3\pm3}{8}\\x=\frac{-3+3}{8}\,and\, x=\frac{-3-3}{8}\\x=\frac{0}{8}\,and\, x=\frac{-6}{8}\\x=0\,and\, x=\frac{-3}{4}[/tex][/tex]

so, x= 0 and x=-3/4.

Answer:

the point r would be located at (4,3)

Step-by-step explanation:

granted that the quadralaterel is a square that would mean that all side lengths are equal and the distance between points x and q is 3 meaning that the same would have to be said about the distance between s and r

Answer:

"the addition of a negative constant"

Step-by-step explanation:

Please note the following points of functions regarding transformations:

1. If there is a change in amplitude, the function will be compressed/stretched vertically, keeping other variables constant

2. If there is a phase shift, the function would be horizontally transformed

3. If there is a period change, the function would be horizontally compressed/stretched

4. If there is addition of positive/negative constant, the function would shift vertically upward/downwards, respectively.

We can clearly see from the graph that the new function is a vertical downward shift from the original. Hence, looking at the above points, point #4, addition of a negative constant, is correct.

Answer:

[tex]\boxed{\text{b. \$1845 a month}}[/tex]

Step-by-step explanation:

   Amount if retired at 66 = $2460/mo

Less 25 % = 0.25 × 2460 =    -615

   Amount if retired at 62 = $1845/mo

John would receive [tex]\boxed{\text{\$1845/mo}}[/tex] if he retired at 62.

Answer:

31.4cm

Step-by-step explanation:

C = 2*pi*r

2r = d

2r=10

r=5

C = 2*5*pi

C = 10*3.14

C = 31.4cm

Answer: Option a.

Domain: (-∞, ∞)

Range: (-∞, ∞)

Step-by-step explanation:

We have the function [tex]f(x) = 2x + cosx[/tex]

Note that f(x) is the sum of two continuous functions [tex]h(x) = 2x[/tex] and [tex]g(x) = cosx[/tex]

The domain and range of h(x) are all real numbers

The domain of g(x) is all real numbers. The range of g(x) is [-1, 1]

Then the domain of [tex]f(x) = h(x) + g(x)[/tex] will be the intersection of the domains of the function [tex]h(x) = 2x[/tex] and the function [tex]g(x) = cosx[/tex].

Therefore the domain of f(x) are all real numbers.  x ∈ (-∞, ∞)

The range of f(x) will be equal to the union of the range of g(x) and h(x)

Therefore the range will be all real numbers f(x) ∈ (-∞, ∞)

Answer:

4046.56 cm3

Step-by-step explanation:

The base is made by 5 isosceles triangles, with one side of 14 cm, and the opposite angle of [tex] \frac{360} 5 = 72° [/tex]. Each of the other angle is [tex]\frac{180-72} {2} =54°[/tex]. From there, you can calculate the height of each base triangle as in [tex]\frac {h} 7 = tan54[/tex] or 9.634...cm.

Your volume will be [tex]5 * \frac  {(14 * 9.634)} 2 * 12 = 4046.56 cm^3[/tex]

Answer:

Option 1.

[tex]P(A) = \frac{1}{8},\ P(A|B) = \frac{1}{3}[/tex]     Dependent

Option 2

[tex]P(A) = \frac{1}{4},\ P(A|B) = \frac{1}{4}[/tex]    Independent

Option 3

[tex]P(B) = \frac{1}{8},\ P(B|A) = \frac{1}{4}[/tex]    Dependent

Option 4

[tex]P(B) = \frac{1}{4},\ P(B|A) = \frac{1}{4}[/tex]     Independent

Step-by-step explanation:

Two events A and B are independent if the occurrence of A does not affect the probability of B.

On the other hand The probability of A given B is defined as:

[tex]P (A | B) = \frac{P (A\ and\ B)}{P (B)}[/tex]

When two events are independent then:

[tex]P (A\ and\ B) = P (A) * P (B)[/tex]

So if the two events A and B are independent this means that:

[tex]P (A | B) = \frac{P (A) * P (B)}{P (B)}[/tex]

[tex]P (A | B) = P (A)[/tex]

Which makes sense because if the events are independent then the probability of A not being affected by B.

So to solve this problem identify in what cases

[tex]P (A | B) = P (A)[/tex] or [tex]P (B | A) = P (B)[/tex]

When this happens those events are independent

Option 1.

[tex]P(A) = \frac{1}{8},\ P(A|B) = \frac{1}{3}[/tex]     Dependent

Option 2

[tex]P(A) = \frac{1}{4},\ P(A|B) = \frac{1}{4}[/tex]    Independent

Option 3

[tex]P(B) = \frac{1}{8},\ P(B|A) = \frac{1}{4}[/tex]    Dependent

Option 4

[tex]P(B) = \frac{1}{4},\ P(B|A) = \frac{1}{4}[/tex]     Independent

Answer:

Quadrant II

Step-by-step explanation:

I attached an image of the quadrants system.

You'll see that the scenario where we have a point with a negative X value and a positive Y value, it belongs to Quadrant II.

Quadrant I

Degrees: 0-90

X values: positive (+)

Y values: positive (+)

Quadrant II

Degrees: 90-180

X values: negative (-)

Y values: positive (+)

Quadrant III

Degrees: 180-270

X values: negative (-)

Y values: negative (-)

Quadrant IV

Degrees: 270-360

X values: positive (+)

Y values: negative (-)

Answer:

Step-by-step explanation:

A=BH/2

A=9x12/2

A=54

Answer: 54

Step-by-step explanation:

A = base * height ÷ 2

A = 12 * 9 ÷ 2

A = 108 ÷ 2

A = 54

Answer: 118.3 m^2

Step-by-step explanation:

Use Heron's formula: √s(s-a)(s-b)(s-c)

s= a+b+c/2

13+18.2+22.3/2 = 26.75

√26.75(26.75-13)(26.75-18.2)(26.75-22.3)

√26.75(13.75)(8.55)(4.45)

√13994.34609

118.297701 = 118.3 m^2

Answer:

A = 21.65 cm squared

Step-by-step explanation:

The basic area formula for a triangle is

[tex]A= \frac{1}{2}bh[/tex]

We have our base as 5, so we can find the height using right triangle trig.  Side BC is opposite the given angle, which is the height, and we are given side CD as 5 which is the base.  Using the tangent ratio to find side BC:

[tex]tan(60) = \frac{x}{5}[/tex] which simplifies to

5 tan(60) = x so

x = 8.66

Filling in for the area:

[tex]A= \frac{1}{2}(5)(8.66)[/tex] so

A = 21.65 cm squared

Answer:

Use the square root function on your calculator

Step-by-step explanation:

Look at the third line down, where is says that 936 = AD^2.  If you hit the 2nd button on your calculator then the x^2 button, you will get the square root function.  After you hit those buttons in that order, you'll get the opportunity to find the square root of 936 by entering it in and hitting "enter" on your calculator.  The square root of 936 is 30.59417

ANSWER

B. 13cm

EXPLANATION

The radius of the circle becomes the hypotenuse of the right triangle formed.

We can use the Pythagoras Theorem to obtain,

AC²+CY²=r²

This implies that,

r²=5²+12²

r²=25+144

r²=169

Take positive square root to get;

r=√169

r=13

AB and AC are two equal chord of a circle, therefore the centre of the circle lies on the bisector of ∠BAC.

OA is the bisector of ∠BAC.

Again, the internal bisector of an angle divides the opposite sides in the ratio of the sides containing the angle.

P divides BC in the ratio 6:6=1:1.

P is mid-point of BC.

OP ⊥ BC.

In △ ABP, by pythagoras theorem,

AB2=AP2+BP2

BP2=36−AP2         ....(1)

In △ OBP, we have

OB2=OP2+BP2

52=(5−AP)2+BP2

BP2=25−(5−AP)2      .....(2)

From 1 & 2, we get,

36−AP2=25−(5−AP)2

36=10AP

AP=3.6cm

Substitute in equation 1,

BP2=36−(3.6)2=23.04

BP=4.8cm

BC=2×4.8=9.6cm