A spherical scoop of ice cream with a diameter of 8 cm rests on top of a sugar cone that is 12 cm deep and has a diameter of 8 cm. What percent of the ice cream must be eaten to insure it does not overflow the cone when it melts?

Answer:

Length 19.11 and width 5.89.

Step-by-step explanation:

Let the length be x and width be y metres.

Then,  using the  Pythagoras theorem:-

x^2 + y^2 =  20^2 = 400....................(1)

The perimeter = 50 so:-

2x + 2y = 50

Dividing through by 2:-

x + y = 25 .............................(2)

So  y = 25 - x

Substitute for y in  equation (1):-

x^2 + (25 - x)^2 = 400

x^2 + 625 - 50x + x^2 = 400

2x^2 - 50x + 225 = 0

x = 19.11 , 5.89,     x = 19.11 as its the length

and y = 25 - 19.11 = 5.89  ( from equation (2).

"Parameter" = Perimeter.

Look at the picture.

We have the perimeter = 50 m.

The perimeter is 2l + 2w (l - length, w - width). Therefore

2l + 2w = 50      divide both sides by 2

l + w = 25     subtract w from both sides

l = 25 - w.

Use the Pythagorean theorem:

[tex]l^2+w^2=20^2\to(25-w)^2+w^2=20^2[/tex]

Use (a - b)² = a² - 2ab + b²

[tex]25^2-2(25)(w)+w^2+w^2=400\\\\625-50w+2w^2=400\qquad\text{subtract 400 from both sides}\\\\225-50w+2w^2=0\\\\2w^2-50w+225=0[/tex]

Use quadratic formula:

[tex]ax^2+bx+c=0\\\\\Delta=b^2-4ac\\\\x_1=\dfrac{-b-\sqrt\Delta}{2a};\ x_2=\dfrac{-b+\sqrt\Delta}{2a}[/tex]

We have:

[tex]a=2,\ b=-50,\ c=225[/tex]

Substitute:

[tex]\Delta=(-50)^2-4(2)(225)=2500-1000=1500\\\\\sqrt\Delta=\sqrt{1500}=\sqrt{100\cdot15}=\sqrt{100}\cdot\sqrt{15}=10\sqrt{15}\\\\w_1=\dfrac{-(-50)-10\sqrt{15}}{2(2)}=\dfrac{50-10\sqrt{15}}{4}=\dfrac{25-5\sqrt{15}}{2}\\\\w_2=\dfrac{-(-50)+10\sqrt{15}}{2(2)}=\dfrac{50+10\sqrt{15}}{4}=\dfrac{25+5\sqrt{15}}{2}[/tex]

[tex]l_1=25-w_1\\\\l_1=25-\dfrac{25-5\sqrt{15}}{2}=\dfrac{50}{2}-\dfrac{25-5\sqrt{15}}{2}=\dfrac{50-25+5\sqrt{15}}{2}=\dfrac{25+5\sqrt{15}}{2}\\\\l_2=25-w_2\\\\l_2=25-\dfrac{25+5\sqrt{15}}{2}=\dfrac{50}{2}-\dfrac{25+5\sqrt{15}}{2}=\dfrac{50-25-5\sqrt{15}}{2}=\dfrac{25-5\sqrt{15}}{2}[/tex]

[tex]Answer:\ \boxed{\dfrac{25+5\sqrt{15}}{2}\ m\times\dfrac{25-5\sqrt{15}}{2}\ m}[/tex]

The sum converges to 1000.

The [tex]n[/tex]-th partial sum of the series is

[tex]S_n=\displaystyle\sum_{i=1}^n100\left(\dfrac9{10}\right)^{i-1}=100\left(1+\dfrac9{10}+\left(\dfrac9{10}\right)^2+\cdots+\left(\dfrac9{10}\right)^{n-1}\right)[/tex]

Then

[tex]\dfrac9{10}S_n=100\left(\dfrac9{10}+\left(\dfrac9{10}\right)^2+\left(\dfrac9{10}\right)^3+\cdots+\left(\dfrac9{10}\right)^n\right)[/tex]

so that

[tex]S_n-\dfrac9{10}S_n=\dfrac1{10}S_n=100\left(1-\left(\dfrac9{10}\right)^n\right)[/tex]

[tex]\implies S_n=1000\left(1-\left(\dfrac9{10}\right)^n\right)[/tex]

As [tex]n\to\infty[/tex], [tex]\left(\dfrac9{10}\right)^n\to0[/tex], so we're left with

[tex]\displaystyle\sum_{i=1}^\infty100\left(\dfrac9{10}\right)^{i-1}=\lim_{n\to\infty}S_n=1000[/tex]

The given infinite series is a converging geometric series with an initial term of 100 and a common ratio of 9/10. Using the formula for the sum of an infinite geometric series, we find that the sum is 1000.

To evaluate an infinite sum, or a series, we need to recognize the series structure. The given series ∑^{∞}_{i=1} 100(9/10)^{i-1} is a geometric series where the initial term (a) is 100 and the common ratio (r) is 9/10.

A geometric series converges only when the absolute value of r is less than 1, which is true in this scenario. When it converges, the sum (S) of the infinite geometric series can be calculated using the formula S = a / (1 – r).

By plugging into this formula, we get: S = 100 / (1 - 9/10) = 100 / (1/10) = 1000.

Therefore, the sum of the infinite series ∑^{∞}_{i=1} 100(9/10)^{i-1} is 1000.

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Answer:At a company fish fry, 1/2 in attendance are employees.

Employees’ spouses are 1/3 of the attendance. What is

the percentage of the people in attendance who are not

employees or employee's spouses?

One half of X are employees.

One third of X are employee's spouses.

Step-by-step explanation:1/2 + 1/3 = 3/6 + 2/6 = 5/6

Then we subtract that fraction from one whole, or 1,

to see what fraction is left.  That is, we say

1 minus 5/6

which is

1 - 5/6

Now write 1 as 6/6

6/6 - 5/6

We get 1/6

So 1/6 is left.  Now we need to make that into

a percent by multiplying it by 100 and tacking on a "%"

1/6 × 100

1/6 × 100/1

100/6

50/3

16 2/3 %

So 16 2/3 % of the people in

attendance are neither employees

nor employee's spouses.

Now let's check:

1/2 are employees.  That's 50%

1/3 are wmployee's spouses. That's 33 1/3%

15 2/3 % are neither employees nor employee's spouses.

Add them up

50     %

33 1/3 %

16 2/3 %

--------

99 3/3 %

And 99 3/3% = 100%

16.67% of the people in attendance are neither employees nor their spouses.

To calculate the percentage of people who are neither employees nor their spouses, we need to consider the total attendance as 100%. Since half of the attendance, i.e., 50%, are employees and one third, i.e., about 33.33%, are spouses, we add these figures to find the combined percentage of employees and spouses. We then subtract this combined percentage from 100% to find the percentage of people who are neither.

Combined percentage of employees and spouses: 50% (employees) + 33.33% (spouses) = 83.33%

Now, to find the percentage who are neither employees nor spouses, we subtract the combined percentage from 100%:

Percentage of neither: 100% - 83.33% = 16.67%

Therefore, 16.67% of the people in attendance are neither employees nor their spouses.

Answer:

A = B

Step-by-step explanation:

This is because they are alternate exterior angles and they equal the same thing.

Answer:2/9

Step-by-step explanation:

If you count the lines form zero like 0/9 1/9 2/9 3/9 4/9 5/9 6/9 7/9 8/9 then 1 is the whole so that would be 9/9

Answer:

2/9 is the answer

Answer:

y=10 is the value of y

Step-by-step explanation:

The given equation is

3y - 7 =23                               ..............................(i)

We have to find out the value of y from the equation (i)

Now the equation is

3y - 7 = 23

adding 7 on both sides of the equation

3y - 7 + 7 = 23 + 7

3y = 30

as we need the value of y so

Dividing both sides of the equation by 3

[tex]\frac{3y}{3}=\frac{30}{3}[/tex]

which will lead us to

y = 10

so this is the value of y

Answer:

y=10

Step-by-step explanation:

3y-7 =23

3y = 23+7  -move 7 over

3y=30 -add remaing

3y/3 =30/3 -divide 3

y=10 -answer

check work 3x10-7=23

The perimeter of any polygon is equal to the sum of the length of all sides of this polygon.

Therefore:

Answer:

So, we know that sides are 29, 15 and 4xy long. The perimeter would be

[tex]P=29+15+4xy[/tex]

Now, we sum like terms

[tex]P=44+4xy[/tex]

[tex]P=44+4xy[/tex]

Answer: the number of students participating this year is 57.

Step-by-step explanation:

5% of 60 is 3.

60-3=57

I believe this is correct :)

Answer: Number of students participated this year = 57

Step-by-step explanation: Number of student participated  last year = 60

                                          Decreased by 5%

                                          Decreased in number = 5% of 60 = 0.05x 60 =3

    Number of Students this year = Number of student last year - decreased

                                                        =               60    -   3

                                                        =  57

E = 360/n

is the formula to use when computing the exterior angle E for any regular polygon with n sides. For an octagon, we have 8 sides meaning n = 8 leads to

E = 360/n = 360/8 = 45

The exterior angle of a regular octagon is 45 degrees

Repeat for n = 6 (hexagon) to get E = 360/n = 360/6 = 60. A regular hexagon has exterior angles of 60 degrees each.

We see that the regular octagon's exterior angles (45) are smaller than the regular hexagon's exterior angles (60)

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

Answer: less than (choice B)

Final answer:

The measure of each exterior angle of a regular octagon is less than the measure of each exterior angle of a regular hexagon since the sum of the exterior angles is always 360 degrees and there are more sides on an octagon to divide this sum. The correct option is: B- Less than

Explanation:

To determine whether the measure of each exterior angle of a regular octagon is greater than, less than, or equal to the measure of each exterior angle of a regular hexagon, we must first understand how to calculate the measure of an exterior angle in a regular polygon. The sum of the exterior angles of any polygon is always 360 degrees, regardless of the number of sides. Therefore, to find the measure of a single exterior angle, you would divide 360 degrees by the number of sides the polygon has.

For a regular hexagon, which has six sides, the exterior angle is calculated as 360 ÷ 6, which equals 60 degrees. For a regular octagon, which has eight sides, the exterior angle is calculated as 360 ÷ 8, which equals 45 degrees.

Comparing the two measurements, we can clearly see that the measure of each exterior angle of a regular octagon is less than the measure of each exterior angle of a regular hexagon.

Look at the picture.

[tex\alpha+\beta=180^o[/tex] - supplementary angles

Therefore we hve the equation:

[tex](14x-6)+(15+5x)=180\\\\(14x+5x)+(-6+15)=180\\\\19x+9=180\qquad\text{subtract 9 from both sides}\\\\19x=171\qquad\text{divide both sides by 19}\\\\\boxed{x=9}[/tex]

Answer: 5 hours

Step-by-step explanation:

$35 per hour is the rate

$25 is the flat fee

$200 is the maximum you can spend

⇒ 35x + 25 ≤ 200

            -25     -25

    35x          ≤ 175

  ÷35              ÷35

         x         ≤   5

Answer:

Step-by-step explanation:

At a sales rate of 56 boxes of gummy bears per week, the movie theater will sell

= 56 × 6

= 336 boxes

This is on the assumption that the rate is sustained.

At that rate (of 56 boxes per week), the company (movie theater) would have sold 336 boxes.

Answer:

The first one is correct the rest are not

Step-by-step explanation:

I don't know if you need an explanation or not.

Answer:

it 1,2,and 4 just took it

Step-by-step explanation:

Tienes que usar la fórmula cuadrática:

(-b +/- √(b^2-4ac))/2a

Primero identificas los valores de a,b y c en kx^2-3x+2=0

K=a, b=-3, c=2

Luego sustituis en la fórmula y te queda:

(3+/-√(9-8k))/2k

Para que las raíces Sena reales se tienen que cumplir que 9-8k>=0

Answer:

Step-by-step explanation:

Therefore discriminant = b^2-4ac =0

b=-k, a=3,c=2

b^2-4ac= (-k)^2-4*3*2=0

k^2-24=0

k^2=24

k= +/- 2sqrt(6)

Answer:

22.5

Step-by-step explanation:

If you expand the series, you can see the first few terms of the series:

We can see the series is 0, 0.5, 1, 1.5, ....

This is an arithmetic series with common difference (the difference in 2 terms) 0.5 and first term 0.

We know formula for sum of arithmetic series:

[tex]s_{n}=\frac{n}{2}(2a+(n-1)d)[/tex]

Where,

Substituting these into the formula, we get the 10th partial sum to be:

[tex]s_{10}=\frac{10}{2}(2(0)+(10-1)(0.5))\\s_{10}=5(0+(9)(0.5))\\s_{10}=5(0+4.5)\\s_{10}=5(4.5)\\s_{10}=22.5[/tex]

So the sum of the first 10 terms is 22.5. Third answer choice is right.

Answer is 22.5  so c :)

The equation tells you that Henry swims 1.6·1 = 1.6 laps when x = 1 minute.

The table tells you Larry swims 4.5 laps in 2.5 minutes. Dividing these numbers by 2.5 tells you Larry swims 4.5/2.5 = 1.8 laps in 2.5/2.5 = 1 minute.

Henry's rate is 1.6 laps per minute; Larry's rate is 1.8 laps per minute.

___

1.8 is larger than 1.6, so Larry swims faster than Henry. That is, Larry swims farther in the same amount of time, or takes less time to swim the same distance.

by the transitive property of equality

Answer:

the transitive property of equality

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

Mr Jone's home distance is 60 miles away from his appointment place .

Distance = Speed x Time

Distance planned & distance covered is same.

Time covered is 20 minutes more than time planned ; Actual Speed is 15mph lower than planned speed (60 mph) , ie = 45 mph.

Let the planned time be = t , Actual time = t + 20 mints = t + 20 / 60 = t + 1/3 =  4 t / 3

As distance is same : 60 t = 45 ( 4t / 3)

60t = 60t

t = 1 hour

Distance = Speed x Time :

60 x 1 = 45 ( 4/3) = 60 miles

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Answer:

1000*(1,025)=1025 $ the 1st year

After 4 years, the account will be 4* 1025=4100

Answer:

Amount after 4 years = 1000+100=$1100

Step-by-step explanation:

To solve this, we will simply use the simple interest formula;

S.I = PRT/100

where p=principal

R=rate   and   T= time

S.I = simple interest

From the question

Principal=$1000

Rate = 2.5    and time=4

We can now proceed to inert the values into the equation

S.I = 1000×2.5×4   /100

Two zeros at the numerator will cancel-out the two zeros at the denominator, Hence;

S.I = 10×2.5×4

S.I =$100

Amount after 4 years = 1000+100=$1100

Answer: No solutions

The two lines are parallel. They never intersect. You need a point of intersection to have a solution. Note how the lines have the same slope (2) but different y intercepts (3 and -4). This fact backs up the idea the lines are parallel.

The system has no solution, so we consider this system to be inconsistent. If we were to convert each equation into standard form, then we would have 2x-y = -3 and 2x-y = 4. If we made z = 2x-y, then z = -3 and z = 4 at the same time; but z is only one number at a time. This is one way to see the inconsistency.

Answer:

Density of material would be 4.09 [tex]g/cm^3[/tex]

units is [tex]g/cm^3[/tex]

Step-by-step explanation:

Given: The mass of a material is 45 grams and the volume of the material is 11 cubic centimeter

Density is defined as mass per unit volume.

It is given by:

[tex]p= \frac{m}{V}[/tex] where p is the density , m is the mass and V is the volume of the material respectively.

Here, Density is expressed in grams per centimeter cubed (g/cubic cm)

Here, m = 45 g , V = 11 cubic cm

We get;

[tex]p= \frac{45}{11}[/tex] = 4.09 [tex]g/cm^3[/tex]

therefore, density of a material would be, [tex]4.09 g/cm^3[/tex]

and its units is [tex]g/cm^3[/tex]

Answer:

Equation in point-slope form=  [tex]{y+3}=\frac{-1}{2}(x+3)[/tex]

Step-by-step explanation:

The given end points are B(−1,1) and C(−5,−7)

Mid point M of BC= [tex]\frac{-5-1}{2}[/tex] , [tex]\frac{-7+1}{2}[/tex]

Mid point M of BC = -3 , -3

Slope of BC =  [tex]\frac{-7-1}{-5+1}[/tex] = 2

Slope of bisector= m= [tex]\frac{-1}{2}[/tex]

Equation of perpendicular bisector : [tex]\frac{y+3}{x+3}=\frac{-1}{2}[/tex]

                                                           ⇒   [tex]{y+3}=\frac{-1}{2}(x+3)[/tex]

                                                          ⇒   2(y+3)= -(x+3)

                                                          ⇒  [tex]2y+x=-9[/tex]

Answer:

197

Step-by-step explanation:

Initial population of rabbit is 139

after 2 years , rabbit population is 556

For exponential growth use y=ab^x

where a is the initial population

x is the time period

b is the growth rate, y is the final population

a= 139 is already given

when x=2, the value of y = 557

plug in all the values  in the formula and find out 'b'  

[tex]y=ab^x[/tex]

[tex]557=139(b)^2[/tex]

Divide both sides by 139

[tex]\frac{557}{139} =b^2[/tex]

take square root on both sides

b=2.00180 and b=-2.00180

growth factor cannot be negative

So b= 2.0018

The equation y=ab^x  becomes

[tex]y=139(2.0018)^x[/tex]

To find population after 6 months

1 year = 12 months

so 6 months = 0.5 years

we plug in 0.5 for x

[tex]y=139(2.0018)^{0.5}[/tex]

y= 196.66

so population after 6 months = 197

Answer:

Add [tex]-x^2+2xy[/tex]

Step-by-step explanation:

The polynomial [tex]x^2+y^2-2xy+1[/tex] can be added to eliminate the x terms by adding the additive inverse. We add [tex]-x^2+2xy[/tex] which has the inverse sign value of the polynomial terms.

[tex](x^2+y^2-2xy+1)+(-x^2+2xy)[/tex]

[tex]x^2-x^2+y^2-2xy+2xy+1[/tex]

When we simplify, this leaves [tex]y^2+1[/tex] without an x term.

Answer:

-x^2+2xy

Step-by-step explanation:

x^2 + y^2 -2xy + 1 +something  = y^2 +1

This will get rid of the x and x^2 terms

Subtract y^2 from each  side

x^2 + y^2 -y^2 -2xy + 1 +something  = y^2-y^2 +1

x^2 -2xy+1 +something  = 1

Subtract 1 from each side

x^2 -2xy+1 -1+something  = 1-1

x^2 -2xy+something  = 0

Subtract x^2 from each side

x^2 -x^2 -2xy+something  = 0-x^2

-2xy+something  = -x^2

Add 2xy to each side

2xy -2xy+something  = -x^2+2xy

something = -x^2+2xy

We need to add  -x^2+2xy

Remember a binomial is 2 terms

Answer:

A. Definition of Segment Bisector

Step-by-step explanation:

One have to understand that according to data given in the question, we only know that AD and BC are bisected at the intersection point E. Now two triangles are formed which are ΔABE and ΔCDE.

Now by definition of segment bisector, we know that

AE = DE

BE = CE

Now, what is to understand that this information is based on the clue which is given in the question that AD and BC bisects each other. All the remaining options like SAS postulate, SSS postulate and definition of congruent triangle are not useful here if we don't know that these two lines bisect each other. Because, the fact that  

AE = DE

BE = CE

is only derived by the information that AD and BC bisect each other. Now we can derive SSS and SAS postulate both because we know by the theorems of trigonometry that if two sides of two different triangles are equal in length,  then their third sides must be equal, or when two lines bisect or intersect each other, vertical angles are always equal. So the answer is A.

Answer:

Step-by-step explanation:

Alright, lets get started.

The original photo size is 4 inches wide and 6 inches tall.

So, the ratio of width and height will be = [tex]\frac{4}{6}=\frac{2}{3}[/tex]

The new enlarged photo will be of the same ratio means 2:3

The width of enlarged photo is given as 12 inches.

Suppose new height of enlarged photo is H, so

[tex]\frac{12}{H}=\frac{2}{3}[/tex]

Cross multiplying

[tex]2H=36[/tex]

Dividing 2 in both sides

[tex]H=18[/tex] inches

So the height of new enlagred photo will be 18 inches.  :   Answer

Hope it will help :)

Answer:

(3,1)

Step-by-step explanation

All you have to do is change the y-coordinate to its opposite. Ex- (-2,3) coordinates of reflection. (-2,-3)

Answer:

D. [tex]x=3[/tex]

Step-by-step explanation:

We have been graph of two functions on coordinate plane. We are asked to find the input value that produces the same output value for the two functions.

To find the input value that produces the same output value for the two functions, we need to find x-value for which both functions has same y-value.

Upon looking at our given graph, we can see that at [tex]x=3[/tex], the value of both functions is [tex]-1[/tex].

Therefore, our required input value is [tex]x=3[/tex] and option D is the correct choice.