500 g of a radioactive element is decaying exponentially. After 8 days 358 g of the element is left.
a. Write a function in the form y = yo ekt giving the number of grams of the element after t days.
358 f(t)
b. Write the function from part a in the form y=Yo
500
c. Use the answer from part a to find the half-life of the element.
a. The exponential equation in the form y=yoekt is
(Round to three decimal places as needed.)

When 3,422 is divided by 12, the decimal that remains when converted to fraction form is 1 / 6

First, divide 3,422 by 12 to find the result.

Dividing 3,422 by 12 gives:

= 3,422 / 12

= 285.16667

You need to convert 0.16667 to a fraction. When done, this is:

= 16,667 / 100,000

= 2 / 12

= 1 / 6

In conclusion, the decimal when turned to a fraction is 1/6.

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Answer:

See attached table and graph!

Step-by-step explanation:

Brainly says there was "inappropriate language" in my explanation ( I assure you, there isn't!) So I attached it as an an image below! Hope this helps!

Answer: should be C

Step-by-step explanation:

The scale of the map is 1:4000000

From the question, we are to determine the scale of the map

From the given information,

3cm on the map correspond to 120 km

First, we will convert 120 km to cm

120 km = 120000 m

120000 m = 12000000 cm

Thus,

3cm on the map correspond to 12000000 cm

Then,

The scale of the map is

3:12000000

Reducing to the lowest term

1:4000000

Hence, the scale of the map is 1:4000000

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Answer:

20.7 acres

Step-by-step explanation:

A=wl=340·294=99960

convert 99960 yards to acres

Formula

divide the area value by 4840

= 20.7 acres

[tex] \bf \implies \:(x,y) = (2,0)[/tex]

There are four quadrants in graph:

Note that : x axis is also known as abscissa and y axis is also known as ordinate

Answer:

(5x-2)(x+1)

means that x = -1 or x =[tex] \frac{2 }{5} [/tex]

Step-by-step explanation:

the quadratic formula is

[tex] \frac{ -b ± \sqrt{(b)^{2} - 4ac } }{2a} [/tex]

where a = 5

b = 3

c = -2

substitute with the equation above this gives you the answer

hope this helps

Answer:

Step-by-step explanation:

Francis bought 5 holiday gifts that were between $42 and $87. What is a reasonable amount that he paid for the items?

we find the average between 42 and 87 and multiply by 5

[(42 + 87) : 2] * 5 =

(129 : 2 ) * 5 =

64.5 * 5 = 322.5$

Domain: (-infinity, 5)

Range: [-3, infinity)

The area of the circle is 254. 502 square units

The formula for area of a circle is expressed as;

Area = πr²

Where;

r is the radius of a circle

Note that the radius of a circle with an inscribed triangle is expressed as;

Radius = ABC/4A

Where;

A, B and C are the sides of the inscribed triangle

Radius = 6 × 6 × 6 / 4(6)

Radius = 216/ 24

Radius = 9 units

Now, substitute the value of the radius into the formula

Area = 3. 142 × (9)²

Area = 3. 142 × 81

Area = 254. 502 square units

Thus, the area of the circle is 254. 502 square units

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The area of the portion of the windshield cleaned by the 10-in wiper blade is 106.85in² .

We have been provided that the Length of blade is 15 inches and the Angle of rotation = 98°

We are required to calculate the area of the portion of the windshield cleaned by the 10-in wiper blade.

We have to solve this by using area of a sector.

Area of a sector = ½r²θ

where θ is in radians.

So, angle of rotation (98°) must first be converted to radians

Converting 98º to radians, we get

98×π/180 = 49π/90

The area of the region swept out by the wiper blade

= (area of the sector where r = 15 and θ = 49π/90) - (area of the sector where r = (15-10) and θ = 49π/90).

So, Area = ½×15²×49π/0 - ½×5²×49π/90

= ½×49π/90(15²-10²)

= 49π/180× (225 - 100)

= 49π/180 × 125

= 1225π/36

Area = 106.8472in²

=106.85 in²

Hence, the area of the portion of the windshield cleaned by the 10-in wiper blade is 106.85in²

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The number of 46-ounce cans of tomato juice to be ordered for the reception is 42.

A chef plans the menu for a particular reception for 322 guests.

The appetizer is a 6-ounce serving of tomato juice for each guest.

He has 322 guest to cater for.

Each of his guest will get an appetizer of 6 -ounce serving of tomatoes juice.

Therefore,

1 guest = 6 ounce of tomato serving

322 guest = ?

cross multiply

amount of tomato serving required = 322 × 6

amount of tomato serving required = 1932 ounces

Therefore,

the number of 46-ounce cans tomatoes juice ordered = 1932 / 46

the number of 46-ounce cans tomatoes juice ordered = 42

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Answer:

1/4 ft

Step-by-step explanation:

A = l x w

5/24 = 10/12 x w

Solve for w

5/24 divided by 10/12 = w

Take inverse of 10/12 and multiply

5/24 times 12/10

1/4

Hence , the shading of the linear inequalities 9y - 2 < 13 and 3y - > -29 is given below.

The graph of the equation 9y - 2 < 13  equation (1) is represented by green colour and graph of the equation  3y - > -29  equation (2) is represented by yellow colour .

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The complete question is given below :

Shade the graph of 9y - 2 < 13 and 3y - > -29 .

Answer:

(2,4)

Step-by-step explanation:

The range is the second number of each set. Take all of those and you get 2,4,2,4. You only need one of each number so you end up with (2,4).

Answer:

Step-by-step explanation:

x -> +1  ->×2

The volume of the shed is 1033.2 cubic feet.

Space occupied by an object in three-dimensional space is called as volume of an object. In simple words, space is taken by object.

Given:

Lorie ordered a shed to hold her gardening supplies.

The shed had a length of 10.25 ft, a width of 14 ft, and a height of seven and one fifth ft.

l = 10.25 feet,

w = 14 feet

h = [tex]7\frac{1}{5}[/tex] = 7.2 feet

And we have the formula to calculate volume,

V = lwh

Substituting all the values,

V = 10.25 x 14 x 7.2

V = 1033.2 cubic feet.

Therefore, the volume is 1033.2 cubic feet.

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Answer:

4.

∠ABC + ∠BCA + ∠CAB = 180

therefore, ∠ABC = 180 - ∠BCA - ∠CAB

using this formula to solve 4a, 4b and 4c:

4a. ∠ABC = 180 - ∠BCA - ∠CAB = 180 - 49 -57 = 26

∠ABC = 26

4b. ∠ABC = 180 - ∠BCA - ∠CAB = 180 - 28 -90 = 62

∠ABC = 62

4c. ∠ABC = 180 - ∠BCA - ∠CAB = 180 - 38 - 25 = 117

∠ABC = 117

5a. In the Triangle ABC, ∠BCA + ∠CAB + ∠ABC = 180

∠BCA = 180 - ∠CAB - ∠ABC = 180 - 55 - 60 = 65

∠BCA = 65

∠BCD + ∠BCA = 180

therefore substituting for ∠BCA in, ∠BCD = 180 - ∠BCA = 180 - 65 = 115

∠BCD =115

5b. In the Triangle ABC, ∠BCA + ∠CAB + ∠ABC = 180

∠BCA = 180 - ∠CAB - ∠ABC = 180 - 125 - 30 = 25

∠BCA = 25

∠BCD + ∠BCA = 180

therefore substituting for ∠BCA in, ∠BCD = 180 - ∠BCA = 180 - 25 = 155

∠BCD = 155

5c. ∠ABD + ∠CBD = 180

therefore ∠CBD = 180 - ∠ABD = 180 - 132 = 48

∠CBD = 48

In the Triangle BCD, ∠CBD + ∠BDC + ∠BCD = 180

therefore ∠BCD = 180 - ∠CBD - ∠BDC = 180 - 48 - 71 = 61

∠BCD =61

6. 4 angles of a quadrilateral = 360

∠a+110+60+80=360

∠a=360-110-60-80=110

∠a = 110

7. four angles of a quadrilateral = 360

using his formula to solve for ∠a, ∠b and ∠c.

for angle a: ∠a+110+95+63=360

∠a=360-110-95-63=92

∠a = 92

for angle b: ∠b+40+62+35=360

∠b=360-40-62-35=223

∠b=223

for angle c: ∠c+100+172+35=360

∠c=360-100-172-35=53

∠c=53

Answer:

46

Step-by-step explanation:

75 degrees is the entire angle and you need to find out what h is, you need to subtract 29 from 75 and you will get h.

H=46.

Answer:

3 feet below the surface

Step-by-step explanation:

2 - 5 = -3

it is called business company

Answer:

b: 56

Step-by-step explanation:

x + y = 88

x is 4 more than half the other number.

half of y is 1/2y

4 more than that is 1/2y + 4

substitute

1/2y + 4 + y = 88

solve for y

3/2y = 84

y = 168 / 3 = 56

solve for x

x = 88 - 56 = 32

not sure where you would answer 32 from what's given :)

Answer:

The answer would be: A = 5 1/4

The value of x is 6

A line segment can be defined as the partition formed by end points of a line.

From the information given, we have that line JL is the line with segments JK, KL and JL and K and the midpoint between J and L

This can be represented as;

JK + KL = JL

Where;

Substitute the values into the formula, we have;

5x -8 + 7x - 12 = 52

Now, collect like terms

12x = 52 + 20

Add like terms

12x = 72

Make 'x' the subject of formula

x = 72/12

x = 6

Thus, the value of x is 6

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The properties of algebra used here are

For first point the algebraic properties used is  Distributive Properties of Addition Over Multiplication.

For Second point the algebraic properties used is  Associative Property of Addition

For third point the algebraic properties used is Associative Property of Multiplication.

For fourth point the algebraic properties used is  Commutative Property of Multiplication

For fifth point the algebraic properties used is  Distributive Properties of Addition Over Multiplication.

For sixth point the algebraic properties used is Associative Property of Addition

The correct question is Write the property that justifies each mathematical statement. Look carefully!!

1. a(c-d) = ac - ad

2. 2x + y = y + 2x

3. — 3(4c) = (- 3 * 4)c

4. 3(4ab) = (4ab)3

5. - 9(3 + 2x) = -9(3) - 9(2x)

6. 3+ (2 + n) = (3 + 2) + n

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The total surface are of the cylinder is approximately 180.64 square inches.

One of the most fundamental curvilinear geometric shapes, a cylinder is a three-dimensional solid. It has been regarded geometrically as a prism whose base is a circle.

The properties of a cylinder with radius r and height h are:

Given dimension of the cylinder are:

Diameter=5 inches and height=9inches

We know that radius=diameter/2

Therefore radius of the cylinder is 5/2=2.5 inches

Now the total surface are of the cylinder

=2πr(r+h)

=2π×2.5×(2.5+9)

=2π×28.75

=57.5π square inches

=180.6415...

≈180.64 square inches

The total surface area of the cylinder is approximately 180.64 square inches.

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The area, in square meters, of the trapezoid is 56.16 m²

A trapezoid with height 5.2m and parallel base is 14.6m and 7m.

We have to find the area of area of this trapezoid.

Area of trapezoid =  1/2(sum of parallel sides)(height)

                             = 1/2(14.6+7)(5.2)

                             = 1/2(21.6)(5.2)

                             = 1/2(112.32)

                             = 56.16 m²

A quadrilateral with as a minimum one pair of parallel aspects is known as, in American and Canadian English, a trapezoid (/ˈtræpəzɔɪd/). In British and other forms of English, a (North American) trapezoid is known as a trapezium (/trəˈpiːziəm/). The transposition of these two terms become a result of an blunders in Charles Hutton's mathematical dictionary.

A trapezoid is always a convex quadrilateral in Euclidean geometry. The parallel aspects are known as the bases of the trapezoid. the opposite  facets are known as the legs (or the lateral aspects) if they're no longer parallel; otherwise, the trapezoid is a parallelogram, and there are  pairs of bases)

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Larry is carrying 4 pounds of dirt. Moe receives 2 3/5 pounds of dirt, and Curly receives 1 1/3 pounds. Larry has 0.07 pounds of dirt.

Given that,

Larry is carrying 4 pounds of dirt. Moe receives 2 3/5 pounds of dirt, and Curly receives 1 1/3 pounds.

We have to find how much dirt does Larry have

Larry =4 pounds of dirt

Larry=4 pound of dirt-Moe receives 2 3/5 pounds of dirt- curly receives 1 1/3 pounds of dirt.

Larry=4-2 3/5-1 1/3

Larry=4-13/5-4/3

Larry=4-2.6-1.33

Larry=4-3.93

Larry=0.07

Therefore, Larry has 0.07 pounds of dirt.

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Function for MX the cost for X megabytes of data used in a month is -

m(x) = {0.149.8,ifr>2

          {10,ifr≤2

A function in mathematics from a set X to a set Y allocates precisely one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

• Data exceeding 2 MB is charged at a rate of $0.10 per MB; one-time fee is $10;

The cost per month for x MB of data is:

1. Up to 2 Mb of data utilized; $10

2. Data use of over 2 MB

• m(x) = 10+ 0.1(x-2)= 10+ 0.1x 0.2 0.1x + 9.8 m(x) = 0.1x + 9.8

Thus, the function is:

m(x) =  = {0.1x+9.8, if r>2

              { 10,ifr≤2

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