What is approximate volume of a cone with a height of 9 feet and radius of 3 feet?

To model the scenario, we can use the exponential function A = A0 · (1/2)^(t/h), where A is the amount remaining, A0 is the initial amount, t is the time, and h is the half-life. In this case, the initial amount is 100 grams and the half-life is 6 hours. After substituting t = 12 into the function, we find that 25 grams of the isotope remain after 12 hours.

To model the scenario, we can write an exponential function using the formula:

A = A0 · (1/2)t/h

Where:

For this scenario, the initial amount is 100 grams and the half-life is 6 hours. So, the exponential function would be:

A = 100 · (1/2)t/6

To find out how much of the isotope remains after 12 hours, we can substitute t = 12 into the function and solve for A:

A = 100 · (1/2)12/6 = 100 · (1/2)2 = 100 · (1/4) = 25

Therefore, after 12 hours, 25 grams of the isotope would remain.

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Answer:

A= 20959.52 cm

Step-by-step explanation:

Formula: A= π x r^2

A=  π x 81.68^2

A= 20959.52

Answer:

Therefore out of Mr. Pringles 110 students we can expect the number that would prefer pepperoni pizza topping would be 66 students.

Step-by-step explanation:

If 3 out of every 5 students in Mr.Pringles math class prefers pepperoni pizza topping then the probability of a randomly selected student in Mr. Pringles prefers pepperoni pizza is [tex]\frac{3}{5} = 0.6[/tex].

Therefore out of Mr. Pringles 110 students we can expect the number that would prefer pepperoni pizza topping would be = 0.6 [tex]\times[/tex] 110 = 66 students.

Answer:

Option B: [tex]$ \textbf{y} \hspace{1mm} \textbf{=} \hspace{1mm} \frac{\textbf{-1}}{\textbf{2}} \textbf{x}^{\textbf{2}} \hspace{1mm} \textbf{-} \hspace{1mm} \frac{\textbf{5}}{\textbf{2}} $[/tex]

Step-by-step explanation:

When the focus (h, k) of a parabola and the equation of the directrix y = c are given, the equation of the parabola is given by:

                     [tex]$ \textbf{(x - h)}^{\textbf{2}} \hspace{1mm} \textbf{+} \hspace{1mm} \textbf{k}^{\textbf{2}} \hspace{1mm} \textbf{-} \hspace{1mm} \textbf{c}^{\textbf{2}} \hspace{1mm} \textbf{=} \hspace{1mm} \textbf{2(k - c)y}} $[/tex]

Here, we are given the focus: (h, k) = (0, -2)

Directrix: y = c = -3.

We substitute in the formula to get the equation of the parabola.

[tex]$ (x - 0)^2 + (-2)^2 - (-3)^2 = 2(-2 - (-3))y $[/tex]

[tex]$ \implies x^2 + 4 - 9 = 2(- 2 + 3)y $[/tex]

[tex]$ \implies x^2 - 5 = 2(1) y$[/tex]

[tex]$ \implies 2y = x^2 - 5 $[/tex]

Dividing by 2, throughout we get:

[tex]$ \textbf{y} \hspace{1mm} \textbf{=} \hspace{1mm} \frac{\textbf{-1}}{\textbf{2}} \textbf{x}^{\textbf{2}} \hspace{1mm} \textbf{-} \hspace{1mm} \frac{\textbf{5}}{\textbf{2}} $[/tex] which is the required answer.

Answer:

Dimension is the square root of 4w-10

Step-by-step explanation:

The length=Breadth=√4w-10

Final answer:

The expression for the area of the rectangle, 4w - 10, can be factored as 2(2w - 5). This implies that one of the rectangle's dimensions could be 2 units and the other could be a linear expression of 2w - 5 units.

Explanation:

To factor the expression 4w - 10 square units, we can find the greatest common factor (GCF) of the two terms. The GCF of 4w and 10 is 2, so we can factor out 2 from the expression:

4w - 10 = 2(2w - 5)

Given the factored form, we can conclude something about the dimensions of the rectangle. The factored expression, 2(2w - 5), suggests that one dimension of the rectangle could be 2 units, and the other is a linear expression of width, specifically 2w - 5 units. This aligns with the area formula for rectangles, A = length × width, where one dimension is considered the length and the other the width for calculation purposes.

Answer:

t = 40

Step-by-step explanation:

Start by breaking the equation down to a simpler form.  To do this you would need to divide 28 by 7.

28 / 7 = x

x = 4

Now we can create a new equation.

4x = t

T would represent the total number of students in the band.  X would be the any number from 1 to 10.  This is because 10 is the highest faction to make the fraction a whole.  Since we a looking for the total we would put ten in place for x.

4 x 10 = t

t = 40

There you go.

Hope this helped.

Answer:

"B"

Step-by-step explanation:

"the median wind speed for country B is greater than the median wind speed for county A"

got it right on the quiz, and good luck ;)

The median wind speed for country B is greater than the median wind speed for county A.

The answer is option B.

A median is a number in the middle of a list of numbers that are sorted, ascended, or descended and can define a set of data. The median is sometimes used in contrast to the definition where there are outsiders in a sequence that may distort the value ratio.

The importance of median value is that it provides an idea about the distribution of data. If the definition and median of the data set are the same, then the data is evenly distributed from the smallest to the highest values.

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Yo sup??

since the two angles are vertically opposite angles therefore they must be equal

7x-17=4x+40

3x=57

x=19

Angle2=4x+40

=116

Hope this helps.

The square root of 97 is 8.48857802, but you can round to 8.49 or 8.5 if you so desire.

Answer:

[tex]\large \boxed{\text{B) 374 mi/day}}[/tex]  

Step-by-step explanation:

The average rate of change from one point to another is the slope of the straight line joining the two points.

[tex]\text{slope} = \dfrac{ y_{2} - y_{1}}{ x_{2} - x_{1}}[/tex]

From Day 1 to Day 3, your points are (1, 383) and (3, 1132).  

[tex]\text{Slope} = \dfrac{1132 - 383 }{3 - 1} = \dfrac{749 }{2} = \textbf{374 mi/day}\\\\\text{The average rate of change from Day 1 to Day 3 was $\large \boxed{\textbf{374 mi/day}}$}[/tex]

The graph below shows the rate of change from Day 1 to Day 3 as a black line. It appears from the graph that Adam and his dad kept the same rate of change for the whole trip.

Answer:

x = 24

Step-by-step explanation:

8x + 4(4x - 3) = 4(6x + 4) - 4

8x + 16x - 12 = 24x + 16 - 4

24x - 12 = 24x + 12

24x = 24x + 12 + 12

24x = 24x + 24

24x/24x = 24

x = 24

Answer:

-5/3

Step-by-step explanation:

Answer:

it's 408,471

Step-by-step explanation:

[tex]400000 \\ + 8000 \\ \: + 400 \\ \: \: + 70 \\ \: \: \: + 1 \\ = 408471[/tex]

Answer:

a = 2 , r = 5

Step-by-step explanation:

The n th term of a geometric progression is

[tex]a_{n}[/tex] = a[tex]r^{n-1}[/tex]

where a is the first term and r the common ratio

Given the 4 th term is 250, then

ar³ = 250 → (1)

Given the 7 th term is 31250, then

a[tex]r^{6}[/tex] = 31250 → (2)

Dividing the 2 equations gives

[tex]\frac{ar^6}{ar^3}[/tex] = [tex]\frac{31250}{250}[/tex], that is

r³ = 125 ← take the cube root of both sides

r = [tex]\sqrt[3]{125}[/tex] = 5

Substitute r = 5 into (1)

a × 5³ = 250, that is

125a = 250 ( divide both sides by 125 )

a = 2

Answer: a = 2, and r = 5

Step-by-step explanation: What we have been given here is a geometric progression. Every term in the sequence of numbers is derived by multiplying the previous term by a particular number called the common ratio, otherwise known as r. Hence if the first term is 1 for instance, the second term would be derived as 1 x r (which equals 1r), the third term would be derived as 1r x r (which equals 1r squared) and so on.

Having this in mind , we can calculate the Nth term of a geometric progression as

Nth term = a x r{to the power of n - 1}

So if we want to calculate the 4th term for instance, that would be

4th = a x r{to the power of 4 - 1} OR

4th = a x r{to the power of 3}

Similarly to calculate the 7th term would be

7th = a x r{to the power of 7 - 1}

7th = a x r{to the power of 6}

Now that we have been given the 4th (250) and 7th (31250) terms, what we now have is

a x r{to the power of 3} = 250 AND

a x r{to the power of 6} = 31250

a x r{to the power of 6}/a x r{to the power of 3} = 31250/250

After reducing both sides to their simplest form, what we now have is

r{to the power of 3} = 125

If we add the cube root sign to both sides of the equation we would have

r = 5

Having computed r as 5, we can now go back to calculate a as follows;

If a x r{to the power of 3} = 250, then

a x 125 = 250

Divide both sides of the equation by 125

a = 2

Therefore, a = 2 and r = 5

The given dilation is an isometry dilation.

Step-by-step explanation:

Step 1; First, we need to compare the dimensions of the two figures. We check to see if the side lengths are the same. If the parameters are the same, the dilation could be an enlargement or a reduction. Whereas if the parameters are the same, it could be an isometric dilation or just a reflection.

Step 2; The first shape has a side length of approximately 2.5 units. We compare this to the same side length as the second shape. The second shape has the same side length.

The first shapes side length of the  / same side length of the second shape = 2.5 / 2.5 = 1,

So the scale factor is 1. As the parameters do not change, it could either be a reflection or an isometric dilation.

Step 3; The base side in shape 1 is BC whereas the same base side in shape 2 is [tex]A^{1}[/tex][tex]B^{1}[/tex]. So shape ABCDE has rotated to form the shape  the dilation is isometric and not a reflection with a scale factor of 1.

Answer:

1: Isometry

Step-by-step explanation:

As both the shapes are having equal area hence the scale factor remains 1.

As scale factor remains 1this is neither enlargement or reduction.

It is the isometry that the distance between two pints remains the same.

Answer:

Try the suggested solution, shown on the picture attached

Step-by-step explanation:

Note, 'm(MNO)' means m(∠MNO), and for issues 2, 4 ,5 - the described angles are angles inside the declared triangle.

Answer:

67º

Step-by-step explanation:

Answer:7 bags

Step-by-step explanation:

Divide 60 by 8 because she has a total of $60 and each bag costs $8. The answer would actually be 7.5 bags but since you can’t buy half a bag your answer would be 7 bags.

Answer:

4 hours

Step-by-step explanation:

I am not sure, what I did was, if Calvin and Alvin both waxed half the car, their original time would split in half, then I added those values together, which is also the average.

y=mx+b is a pretty safe form to follow

C=3

A=5

if you are doing variables

I tried my best.

Option C 40-2 x

150 square feet

Step-by-step explanation:

Step 1 :

Given that the 3 sides, a,b, and x will be made of 40 feet of fencing,

we have a + b + x = 40

Since this is a rectangular garden , b= x

substituting b= x, we have a + x  + x = 40

=> a+2 x = 40

=> a= 40-2 x

Step 2 :

To find the area in square feet,

when x = 15, a = 40 -  2 * 15 = 40-30 = 10 feet

The length and breadth of the rectangular garden are therefore 5 and 10 feet respectively

Hence, the area of the garden = length  * breadth = 15 * 10 = 150 square feet

Answer:

90°.

Step-by-step explanation:

When two straight lines intersects obliquely then there will be two angle of intersection, one angle is acute and the other one is obtuse.

But, here the two straight lines AB and xy intersects perpendicularly and AB bisects xy.

Therefore, the two angle of intersection are 90° each.

Hence, the angle of intersection in our case will be equal to 90°. (Answer)

Answer:90 degrees

Step-by-step explanation:

Answer:

There will be a total 40 jumps.

Step-by-step explanation:

Every jump a game piece makes measures [tex]\frac{8}{9} = 0.889[/tex].

Now, the piece starts at point A = 7 and jumps to the right.

So, the piece will jump over B = 24  after [tex]\frac{24 - 7}{0.889} = 19.122[/tex] ≈ 20 complete jumps.

Then it switches direction to the left and the piece then stops at point A.

So, there will be a total (20 + 20) = 40 jumps. (Answer)

The game piece took a total of 153/8 jumps.

To determine how many jumps the game piece took, we need to find the total distance it traveled. The piece starts at point A = 7 and jumps to the right, so it covers a distance of 8/9. As soon as it jumps over B = 24, it switches direction and jumps to the left, covering a distance of -8/9. The piece continues this pattern until it reaches point A again.

To find the number of jumps, we can divide the total distance traveled by the distance covered in each jump. The total distance is 24 - 7 = 17. Dividing 17 by 8/9 gives us:

17 / (8/9) = 17 * (9/8) = 153/8

So, the game piece took a total of 153/8 jumps.

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Answer:

The value of x is 120°

Step-by-step explanation:

To solve for x, you need to introduce a third line that is parallel to the two parallel lines.

This line should divide the angle at x into two as shown in the attachment.

By the alternate interior angle property, m=70°

and

n=50°

This implies that, x=50+70=120°

Answer:

Step-by-step explanation:

Answer:

C) 9 × (20 + 5) = 225

Step-by-step explanation:

The answer is c

9 x (20 + 5 )

9x20 + 9x5

180 + 45 = 225

Answer:

The measure of  XY is 79.8 cm.

Step-by-step explanation:

An image of the question is attached here.

Given:

Measure of XT = 39.9

VW is the bisector.

So T is the midpoint of XY .

Note: Bisector divides the line in two equal parts.

According to the question:

⇒ [tex]XT = TY[/tex]           ...as T is the midpoint.

⇒ [tex]XY=XT +TY[/tex] ...Segment addition Postulate

⇒ [tex]XY=XT+XT[/tex]

⇒ [tex]XY=2(XT)[/tex]

⇒ [tex]XY=2(39.9)[/tex]

⇒ [tex]XY=79.8[/tex] cm

The measure of XY in the skateboard design is 79.8 centimeter.

Answer: Since 3−5+2=0, then 2

is the additive inverse of 3−5 is 2

 Since 5−3−2=0, then −2is the additive inverse of 5−3. is -2

Step-by-step explanation: additive inverse

The additive inverse of any number

x

is the number that gives zero when added to

x

. Example: the additive inverse of

5 is −5.

Answer:

  see below

Step-by-step explanation:

The graph of the first inequality is the half-plane above and including the x-axs.

The graph of the second inequality will be the half-plane below the dashed line y = x.

The graph of the third inequality will be the half-plane below the dashed line y = 6 -x.

So, the solution space will be a triangle above the x-axis and below the two (dashed) lines that cross at (x, y) = (3, 3).

Answer:

I think, from what sqdancefan explained, the graph is this one..

Answer:

85

Step-by-step explanation:

hello :

if : g(x)= x+7; h(x)= (x-3)²   so : (4g+h)(x)=4g(x)+h(x)  = 4(x+7)+(x-3)²  

(4g+h)(8)=  4(8+7)+(8-3)²  = 60+25=85