John’s age in 5 years time will be the same as Jack’s age is now. In two years, Jack will be twice as old as John. How old are they now?

Answer:

Thus, the surface area equals S(r)=πr2+2πrl+πr54r=πr2(1+54)+2πr(14r2−r4)=94πr2+28πr−π2r2=74πr2+28πr.Jul 15, 2016

Step-by-step explanation:

Answer:

r = -3

16th term: -516560652

Step-by-step explanation:

Let's use the formula for a geometric sequence:

[tex]a_n=a_1r^{n-1}[/tex], where [tex]a_n[/tex] is the nth term, [tex]a_1[/tex] is the first term, and r is the common ratio

Here, we know the first term is 4. To find r, let's plug in 8 for n and -8748 for [tex]a_n[/tex]:

[tex]a_n=a_1r^{n-1}[/tex]

-8748 = 4 * [tex]r^{8-1}[/tex]

-8748 = 4 * [tex]r^7[/tex]

[tex]r^7[/tex] = -2187

r = -3

So we know that the common ratio is -3. Now, we want to find the 16th term, so n = 16:

[tex]a_n=a_1r^{n-1}[/tex]

[tex]a_{16}=a_1*(-3)^{16-1}=4*(-3)^{17}=-516560652[/tex]

Answer:

r = -3

16th term: -516560652

Step-by-step explanation:

Let's use the formula for a geometric sequence:

, where is the nth term, is the first term, and r is the common ratio

Here, we know the first term is 4. To find r, let's plug in 8 for n and -8748 for :

-8748 = 4 *

-8748 = 4 *

= -2187

r = -3

There are 154,440 different ways for the names of the top 5 participants to be listed on the leaderboard.

To determine the number of ways the names can be listed for the top 5 participants on the leader board, you can use the concept of permutations. The formula for permutations is:

[tex]\[ P(n, r) = \frac{n!}{(n - r)!} \][/tex]

where [tex]\( n \)[/tex] is the total number of items and [tex]\( r \)[/tex] is the number of items to be selected.

In this case, you have 13 participants, and you want to select and order the top 5 participants. So, the formula becomes:

[tex]\[ P(13, 5) = \frac{13!}{(13 - 5)!} \][/tex]

Now, calculate the permutations:

[tex]\[ P(13, 5) = \frac{13!}{8!} \][/tex]

[tex]\[ P(13, 5) = \frac{13 \times 12 \times 11 \times 10 \times 9 \times 8!}{8!} \][/tex]

[tex]\[ P(13, 5) = 13 \times 12 \times 11 \times 10 \times 9 \][/tex]

Now, calculate the result:

[tex]\[ P(13, 5) = 154,440 \][/tex]

So, there are 154,440 different ways for the names of the top 5 participants to be listed on the leader board.

Answer:

с. 60

Step-by-step explanation:

This is an equilateral triangle since all the sides are the same.

That means all the angles are the same.

The sum of the angles is 180

There are 3 angles

180/3 = 60

Each angle is 60 degrees

Answer:

8

Step-by-step explanation:

Key to this question is assume that each exchange preserves the total dollar amount of Nick’s money.

If He exchanges all his $5 bills for $1 bills, it means that a $5 bill will result in 5 $1 bills as such, if he had x number of $5 bill, after the exchange, he would have 5x $1 bills.

then all his $20 bills for $5 bills, it means that for each $20 bill, he gets 4 $5 bills which means that if he had y number of $5 bills, after the exchange, he would have 4y $5 bills.

and finally all his $100 bills for $20 bills, then he must have received 5 $20 bills for each $100 such that if he had z number of $100 bills before the exchange, he would have 5z number of $20 bills after the exchange. Given that originally he had 17 bills and later 77 bills then

x + y + z  = 17

5x + 4y + 5z = 77

Multiplying the first equation by 5,

5x + 5y + 5z = 85

5x + 4y + 5z = 77

subtract 2 from 1

y = 8

So the right answer is of option A.

Look at the attached picture ⤴

Hope it will help u...

Answer:

c

Step-by-step explanation:

trust me

Answer:

it is the 3rd one

Step-by-step explanation:

I did this question

Answer:

2.25

Step-by-step explanation:

The old width of 4 inches became a new width of 9 inches.

Old: 4 in.

New 9 in.

The old length of 6 inches became a new length of 13.5 inches.

Divide the new size by the corresponding old size.

9/4 = 2.25

13.5/6 = 2.25

You see in both cases, the scale factor is 2.25

The scale factor is 2.25

Answer: 120 km/h

Step-by-step explanation:

Hi, to answer this question, first, we have to calculate Hunk's time spent on his travel.

Speed rate = distance /time

Time = distance /speed = 540/ 90 =6 hours

Now, since Tim completed the same amount of distance with 1 hour and 30 min less (1.5) we have to subtract 1.5 hours to Hunk's time to calculate Tim’s time:

6-1.5 = 4.5 hours

Tim's speed rate = distance /time

s = 540/4.5 = 120 km/h

Feel free to ask for more if needed or if you did not understand something.  

Answer:

The range of areas is 3.14ft^2- 12.56ft^2

Step-by-step explanation:

I don't know which graph the question is referencing but I found the range of areas this way

first I found out what the range of radius would be

since the circumference is pi*diameter

So to find the diameter I did the individual areas divided by pi

6.28/3.14=2

12.56/3.14=4

So the range of diameters is 2 to 4 this means the range of radius's are 1 to 2

Since area of a circle is r^2*pi

This means the range of areas is

1^2*3.14=3.14

2^2*3.14=12.56

So the range of areas is 3.14ft^2 to 12.56ft^2

Answer:

B

Step-by-step explanation:

sorry this doof was being confusing

Answer:

10.4

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

14^2 + 6^2 = H^2

196 + 36 = H^2

232 = H^2

*Square root both sides*

About 15 = H

Also: H means hypotheses

Answer:

|x - 8| = y + 6

Step-by-step explanation:

The vertex of the equation must be somewhere on the line x = 8, because it is the average of the answers.

If the slope of x is 1, then the vertex is (8, -6)

Plug that into the equation and you get  Ix - 8I = y + 6

Answer:

lx-8l=6

RSM said It was right

Step-by-step explanation:

Answer:

[tex]-3m^{12}{n^{6} }[/tex]

Step-by-step explanation:

To begin simplifying this, we can first divide the coefficients, giving us:

[tex]\frac{-3m^{5}n^{4} }{m^{-7} n^{-2} }[/tex]

We know that when dividing exponents, this means we need to subtract the exponent on the denominator from the numerator. This gives us:

[tex]\frac{-3m^{5+7} n^{4+2} }{1}[/tex]

Now, simplifying this gets:

[tex]-3m^{12}{n^{6} }[/tex]

I got the correct answers! :)

The rate at which the water level fell is 1.05 mm/year. To find the total variation in water level, multiply this rate by 2.48 years, giving a total variation of 2.604 mm.

In Mr. Whittaker's science class, Matea recorded that the water level in one part of the river fell by 1.05 millimeters per year. This number - 1.05 millimeters - represents the rate at which the water level fell each year. To find the total variation in water level over the 2.48 years, you would multiply the rate (1.05 mm/year) by the time (2.48 years). So, the solution would be: 1.05 mm/year * 2.48 years = 2.604 mm. This results in a total variation of 2.604 millimeters over the 2.48 years. This total variation can now be compared to the average annual trend which is a rise of 1.8 mm/year.

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Answer:

SR

Step-by-step explanation:

Answer:

x=9

Step-by-step explanation:

3 ^ (x-4) = 243

Rewrite 243 as a power of 3

3 ^ (x-4) =3^5

Since the bases are the same, the exponents are the same

x-4 =5

Add 5 to each side

x-4+4 = 5+4

x=9

Answer:

3625

Step-by-step explanation:

Answer:

2.8

Step-by-step explanation:

the formula of volume of cylinder is pi*r^2*h. if you plug in, you get (3.14)(r^2)(8.7). if you solve for r, you get 2.8!

Answer:

12

Step-by-step explanation:

Pythagorean theorem

a²+b²=c²

a²+35²=37²

a²+1225=1369

manipulate the equation

1225-1369=-a²

-144=-a²

√-144=12

a=12

Answer:

-1

Step-by-step explanation:

real numbers stars from zero

eg. 01234567....

Answer:

Step-by-step explanation:

The solutions of the quadratic equation 3x² + 9x + 17 = 0 are x₁ = (-9 + √(123)i) / 6 and x₂ = (-9 - √(123)i) / 6, where "i" represents the imaginary unit.

To find the solutions of the quadratic equation 3x² + 9x + 17 = 0, we'll use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a.

Here, a = 3, b = 9, and c = 17. We'll plug these values into the formula and simplify the expression step-by-step.

Step 1: Calculate the discriminant (Δ) using the formula Δ = b² - 4ac.

Δ = (9)² - 4 * 3 * 17

Δ = 81 - 204

Δ = -123

Step 2: Substitute the values of a, b, and Δ into the quadratic formula.

x = (-9 ± √(-123)) / 2 * 3

Step 3: Since the discriminant (Δ) is negative, the quadratic equation has no real solutions. Instead, it has two complex solutions.

Step 4: Simplify the expression under the square root.

x = (-9 ± √(-123)) / 6

Step 5: Now, we deal with the square root of a negative number, which is denoted by "i" in the complex number system. √(-123) = √(123)i.

Step 6: Substitute the value of √(-123) back into the equation.

x = (-9 ± √(123)i) / 6

Step 7: Divide both the real and imaginary parts by 6 to get the two complex solutions.

x₁ = (-9 + √(123)i) / 6

x₂ = (-9 - √(123)i) / 6

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Final answer:

The quadratic equation 3x^2 + 9x + 17 = 0 has no real solutions because the discriminant is negative. The solutions are complex numbers and can be expressed as x = -3/2 ± √(123)/6 × i.

Explanation:

To find the solutions of the quadratic equation 3x^2 + 9x + 17 = 0, we will use the quadratic formula, which is x = (-b ± √(b^2 - 4ac)) / (2a) for a quadratic equation of the form ax^2 + bx + c = 0. In our case, a = 3, b = 9, and c = 17. Plugging these values into the formula gives:

x = (-(9) ± √((9)^2 - 4(3)(17))) / (2(3))

x = (-9 ± √(81 - 204)) / 6

x = (-9 ± √(-123)) / 6

Since the discriminant (the part under the square root, b^2 - 4ac) is negative, the equation has no real solutions. Instead, the solutions are complex numbers:

x = (-9 ± √(-123)i) / 6

The final solutions can be expressed as:

x = -3/2 ± √(123)/6 × i

Answer:

4√3

Step-by-step explanation:

sorry that I was late I just taken it sorry

Prisms are 3-D shape with triangles and a base. The value of x from the diagram in radical form is 4√3

From the given figure, we are to find the value of "x". To do this, we will use the identity

Given the following parameters

slant height  = 8m

Opposite side = x

Determine the value of "x"

Sin 60 = x/8
x = 8 sin60
x = 8 * √3/2
x = 4√3

Hence the value of x from the diagram in radical form is 4√3

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Answer:

2. Denote two pieces: x, y

x + y = 40

x = 2y + 10

=> 2y + 10 + y = 40 => 3y = 30 => y = 10 => x = 2 x 10 + 10 = 30

=> Solution: 10 and 30

3. Denote 4 consecutive number: 2k, 2k+2, 2k+4, 2k+6

(2k + 2k + 4) x 2 + 20 = 2 x (2k + 6)

=> 8k + 28 = 4k + 12

=> 4k = -16

=> k = -4

=> Solution: -8, -6, -4, -2

4. The number of shoppers after announcement :

N = 320 x 150/100 = 480

Hope this helps!

:)

Answer:

irrational :)

Step-by-step explanation:

Answer:

1). 1 decade

2). 2 decades

Step-by-step explanation:

Number of years in decade = 10 years

1). When we are calculating the population of Florida between 1840 to 1850,

Number of years between 1850 and 1840 = 1850 - 1840

                                                                      = 10 years

So number of decades between 1840 and 1850 = [tex]\frac{10}{10}[/tex] = 1 decade

2). Number of years between 1840 and 1860 = 1860 - 1840

                                                                           = 20 years

Therefore, number of decades between this gap = [tex]\frac{20}{10}=2[/tex] decades

Answer:

2.376 b

Step-by-step explanation:

Answer:

b. 2.376 square feet

Step-by-step explanation:

In the figure attached, the prism is shown.

Area of the bottom rectangle: 40*24 = 960 square feet

Area of the two side rectangles: 2*40*15 = 1200 square feet

Area of the two triangles: 2*24*9/2 = 216 square feet

Surface area of the triangular prism = 960 + 1200 + 216 = 2376 square feet

The distance around the window is 92.52 inches.

A semicircle is a one-dimensional locus of points that forms half of a circle. It is a circular arc that measures 180°. It has only one line of symmetry.

Given that, The stained-glass window is semicircular and the bottom edge of the window is 36 in.

We get that, diameter of the window = 36 in

radius = 18 in

Circumference of semicircle = r(2+π)

= 18(2+3.14)

= 92.52 in

Hence, The distance around the window is 92.52 inches.

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