A radioactive compound with mass 470 grams decays at a rate of 3% per hour. Which
equation represents how many grams of the compound will remain after 6 hours?
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O C = 470(0.03)
O C = 470(0.7)
O C = 470(1 + 0.03)
C = 470(1 – 0.03)

78 is the answer

Step-by-step explanation:

The two angles are complementary so m<A + m<B = 90

we are given m<A = 3x + 9 and m<B = x - 11

substituting we get 3x + 9 + x - 11 = 90

4x - 2 = 90

4x = 92

x = 23

m<A = 3x + 9 = 3(23) + 9 = 78

Step-by-step explanation:

when 2 objects are similar, that means that all the angles of one object are the same as the angles in the other object. and - the scaling factor of one pair of correlating sides is the same for all pairs of correlating sides.

therefore,

x/2.7 = 4.8/3.6 = 4/3

x = 4×2.7/3 = 4×0.9 = 3.6 m

Answer:

2x + 2x + x =180
x = 36 degree

Step-by-step explanation:

Step-by-step explanation:

out of the total possibilities of 20 student council members, 8 are in Nina's math class, and 6 are in Nina's science class.

as I understand the given information, out of these 14 council members, 4 are in her math and in her science class. but this is then irrelevant for the question (and do not add more possibilities), as these 4 are already covered by the 8 and 6 in her individual classes.

remember, a probability is always

desired cases / possible cases

so, let's pick the first random choice :

the probabilty to pick one that is either in her math or her science class is

14/20 = 7/10

because there are 20 total possibilities to pick from, and 14 of these 20 are in at least one of her classes.

now let's pick the second one.

I assume the first pick has not been returned to the pool and cannot be picked a second time.

so, this time we have therefore only 19 total choices, and 13 of them are in at least one of Nina's classes.

so, the probability for the second pick is

13/19

so, the probability that both picks are in at least one of her classes is then the combination of both probabilities (they have to happen together) :

7/10 × 13/19 = 91/190 = 0.478947368...

Answer:

The mode of a data set is ALWAYS equal to the mean.

Step-by-step explanation:

The square of the altitude is equal to the product of the base of the triangles

The square of the altitude is equal to the product of the base of the triangles. The length of line segment GJ is 8units

According to the theorem;

GJ² = HJ*JF

Determine the value of x using the pythagorean theorem

[tex]x^2+x^2=16\\2x^2=16\\x^2=8\\x=\sqrt{8}\\x=2\sqrt{2}[/tex]

According to the theorem;

GJ² = HJ*JF

HJ + JF = 16

Since HJ = JF, hence

HJ = JF = 8

Substitute

GJ² = HJ*JF

GJ² = 8 * 8
GJ² = 64

GJ = 8units

Hence the length of line segment GJ is 8units

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Answer:

8

Step-by-step explanation:

The factor of the quadratic equation will be (x − 1) and (x − 5). Then the correct option is A.

It's a polynomial with a value of zero. There exist polynomials of variable power 2, 1, and 0 terms. A quadratic equation is an equation with one statement in which the degree of the parameter is a maximum of 2.

The graph of a quadratic function with a maximum value at the point (3,4) and zeros at 1 and 5.

Then the factor of the quadratic equation will be (x − 1) and (x − 5).

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Answer:

A.

Step-by-step explanation:

The equation of a circle with radius of 6 units and center on the x axis could be (x - 6)² + y² = 36

An equation is an expression that shows the relationship between two or more variables and numbers.

The circle has a diameter of 12 units. Hence, radius = 12/2 = 6 units.

The center of the circle is at x axis (*, 0), the equation could be:

(x - 6)² + (y - 0)² = 6²

(x - 6)² + y² = 36

The equation of a circle with radius of 6 units and center on the x axis could be (x - 6)² + y² = 36

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convert both heights to inches:

Jack = 12 x 6 = 72 + 3 = 75 inches tall

Hill = 12 x 5 = 60 + 8 = 68 inches tall

now subtract:

75-68 = 7 inches

Jack is 7 inches taller

Step-by-step explanation:

here is your answer, step by step

Problem 7 (a)

Pick any two values you want for the radius and height (r and h). Repeats are allowed.

I'll go with r = 1 and h = 1

Compute the surface area of the cylinder with these parameters.

SA = 2pi*r^2 + 2*pi*r*h

SA = 2pi*1^2 + 2pi*1*1

SA = 2pi + 2pi

SA = 4pi

Now double the radius. We go from r = 1 to r = 2. Keep the height the same and compute the new surface area.

SA = 2pi*r^2 + 2*pi*r*h

SA = 2pi*2^2 + 2*pi*2*1

SA = 8pi + 4pi

SA = 12pi

The jump from 4pi to 12pi is "times 3".

========================================================

Problem 7 (b)

Let's go back to r = 1 and h = 1 again.

LSA = lateral surface area of the cylinder

LSA = 2*pi*r*h

LSA = 2*pi*1*1

LSA = 2pi

Now double r, but keep h the same

LSA = 2*pi*r*h

LSA = 2*pi*2*1

LSA = 4pi

Going from 2pi to 4pi is a jump of "times 2"

========================================================

Problem 7 (c)

We'll go back to r = 1 and h = 1.

Compute the volume of this cylinder.

V = pi*r^2*h

V = pi*1^2*1

V = pi

Then compute the volume with double the radius, but the same height

V = pi*r^2*h

V = pi*2^2*1

V = 4pi

The volume has quadrupled since we have gone from pi to 4pi.

========================================================

Problem 8

The volume of the block, before the half cylinders are removed, is 10*3*8 = 240 cubic inches.

The two half cylinders removed can be rearranged to combine to a full cylinder. This empty space cylinder has a radius of 8/2 = 4 inches and height 3 inches. This means we'll be kicking out the volume of pi*r^2*h = pi*4^2*3 = 48pi cubic inches of empty space.

The resulting volume of this weird looking solid is 240-48pi cubic inches.

--------------

The front panel is a 3 in by 10 in rectangle. It has area of 3*10 = 30 square inches. The same goes for the back wall.

The top or ceiling panel is going to involve us first finding the area of the 8 by 10 rectangle (if you didn't remove those circular portions). So we have 8*10 = 80 square inches to start with. Then we kick out the circle of radius 4. So the top and bottom panels have area of 80 - 16pi square inches each.

The left and right curved walls are the lateral sides of a full cylinder of radius 4 inches and height 3 inches. This is when we combine the two curved sides to form one cylinder.

LSA = 2*pi*r*h = 2*pi*4*3 = 24pi

This means each curved wall is 24pi/2 = 12pi square inches in surface area

Now add up the 6 sides mentioned

(front)+(back)+(top)+(bottom)+(left)+(right)

(30)+(30)+(80 - 16pi)+(80 - 16pi)+(12pi)+(12pi)

220-8pi

--------------

Answer:

The value of 5 is 500,000

Step-by-step explanation:

becuse their is 5 numbers behind it making it equivilant to 500,000

Hey there!

EXPANDED FORM:

500,000
+ 60,000

+ 4,000

+ 200

+ 40

+ 02

WORD FORM:

Five hundred 6

Sixty four thousand, two hundred forty two

PLACE VALUE FORM

5: 500,000 (hundred thousand)

6: 60,000 (ten thousand)

4: 4,000 (thousand)

,

2: 200 (hundreds)

4: 40 (tens)

2: 02 (ones)

To sum it is all up {5} is in the: [hundred thousands] place

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

the opposite sides in a rectangle are equal

Answer:

312 ft²

Step-by-step explanation:

Area of the garden = Length x Width

Area of the garden = 30 x 40 = 1200ft²

Length of the garden and path = Length of the garden + 3 ft on both sides

Length of the garden and path = 30 + 3 + 3 = 36 ft

Width of the garden and path = Width of the garden + 2 ft on both side

Width of the garden and path = 40 + 3 + 3 = 46 ft

Area of the garden and path = Length x Width

Area of the garden and path = 36 x 46 = 1512 ft²

Area of the path = Area of the garden and path - Area of the garden

Area of the path = 1512 - 1200 = 312 ft²

Answer: 312 ft²

Answer:

The slope of this line is 1/5

Step-by-step explanation:

You can find the answer easily by graphing the problem. In doing so, you will find the slope (rise over run) to be one over five. This is because you rise one unit, and run five.

Answer:

30

Step-by-step explanation:

There are 30 possible types of sandwiches .

5 meats x 3 different types of bread x 2 types of cheese=  30

Answer: 4.52 miles

Step-by-step explanation:

The single transformation that maps shape a onto shape b is [tex]\left[\begin{array}{c}-5&-5\end{array}\right][/tex]

From the figure, we have the following highlights

The above highlights mean that the triangle A must be translated 5 units left and 5 units down to get triangle B.

This is represented as:

(x,y) -> (x - 5, y - 5)

By vector representation, we have:

[tex]\left[\begin{array}{c}-5&-5\end{array}\right][/tex]

Hence, the single transformation that maps shape a onto shape b is [tex]\left[\begin{array}{c}-5&-5\end{array}\right][/tex]

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Answer:

Step-by-step explanation:

a) Reflection over the x axis then a translation directly to the right

b) All the figures are conrguent since only rigid motions were used.

The eccentricity of the conic section that is graphed is C. One.

It should be noted that the eccentricity of the clinic section simply means the distance from the point to its focus.

In this case, the eccentricity of the conic section that is graphed is one. The eccentricity value is usually constant for any conics.

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Answer:

The answer is B. Between 0 and 1

Step-by-step explanation:

Answer:

First choice top-down

Step-by-step explanation:

The Similarity Theorem Side-Angle-Side it can be checked here to see what triangles are similar.

All 3 triangles have 2 congruent sides so the triangles are all isosceles.

The base angles of isosceles triangles are congruent so knowing this and that the sum of angles in a triangle is 180° we can calculate the measure of all angles.

180-20 = 160; 160/2 = 80°

180-30 = 150;  150/2 = 75°

Now we can conclude that  Δ JLK is not similar with Δ MNO ≈ ΔPRQ

Answer:

a. mode

b. median

c. median

Step-by-step explanation:

the mode is the most common number

the median is when you order the numbers in order and use the middle number

Answer:

7.4 in

Step-by-step explanation:

Surface area of a cube = 6s²

(where s is the side length)

Given:

Substituting the given value into the formula and solving for s:

⇒ 328.56 = 6s²

⇒ 328.56 ÷ 6 = 6s² ÷ 6

⇒ 54.76 = s²

⇒ s = √54.76

⇒ s = 7.4 in

TSA of a cube=328.56

Side be x

The slope of the equation will be 12 and the y-intercept of the equation will be 200.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

You're learning yoga in a fitness center that charges a $200 registration fee plus $12 per lesson.

If an equation is made to calculate the total charge you need to pay.

Let y be the total amount and x be the number of the lesson. Then we have

y = 12x + 200

Then the slope of the equation will be 12 and the y-intercept of the equation will be 200.

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Answer:

area is length x width multiply one side by the other

Step-by-step explanation:

The factorization of the given expression is:

p(x) = (x - 2.66)*(x - 0.25)

We have the quadratic equation:

12x^2 + 29x - 8

To get the factors we need to find the roots, then we use Bhaskara's formula:

[tex]x = \frac{-29 \pm \sqrt{29^2 - 4*(-8)*12} }{2*12} \\\\x = \frac{-29 \pm 35}{24}[/tex]

Then the solutions are:

x = (-29 + 35)/24 = 0.25

x = (-29 - 35)/24 = -2.66

Then the factors of the expression are:

(x - 2.66) and (x - 0.25)

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Answer:

y = -x + 4

Step-by-step explanation:

y = mx + b

m - since the line is going downwards. the slope is negative

slope = rise / run = 1 / 1 = 1 but negatuve siunce diwnawards

b - this the y - intercept (when x = 0), the point of intersect is (0, 4)

Answer:

8 miles

Step-by-step explanation:

because 83-75=8 miles