Suppose you have a cache of radium, which has a half-life of approximately 1590 years. how long would you have to wait for 1/5 of it to disappear?

Answers

Answer 1

You would have to wait approximately 3691.86 years for 1/5 of the radium to disappear, considering its half-life of 1590 years.

The decay of a substance with a half-life can be modeled using the formula [tex]\(N(t) = N_0 \left(\frac{1}{2}\right)^{\frac{t}{T_{\text{half}}}}\)[/tex], where:

- [tex]\(N(t)\)[/tex] is the remaining quantity after time \(t\),

- [tex]\(N_0\)[/tex] is the initial quantity,

- [tex]\(T_{\text{half}}\)[/tex] is the half-life.

In this case, [tex]\(N(t) = \frac{1}{5}N_0\)[/tex] and [tex]\(T_{\text{half}} = 1590\)[/tex] years.

Substituting these values into the formula and solving for \(t\):

[tex]\[ \frac{1}{5}N_0 = N_0 \left(\frac{1}{2}\right)^{\frac{t}{1590}} \][/tex]

Solving this equation yields[tex]\(t \approx 3691.86\)[/tex] years.

Therefore, you would have to wait approximately 3691.86 years for 1/5 of the radium to disappear, considering its half-life of 1590 years.


Related Questions

Thomas collects dimes and quarters in his change jar. if he has 8 more dimes than quarters, and the total amount of money in the jar is $26.70, find the number of each type of coin in the jar.

Answers

Final answer:

Using algebraic expressions, we figured out that Thomas has 74 quarters and 82 dimes in his change jar, based on the total value of $26.70 and the fact that he has 8 more dimes than quarters.

Explanation:

To solve the problem involving the collection of dimes and quarters in Thomas's change jar, we need to use algebra. Let's define the variables first: let q be the number of quarters and q + 8 be the number of dimes since Thomas has 8 more dimes than quarters.

Since each quarter is worth $0.25 and each dime is worth $0.10, we can set up the following equation to represent the total amount of money ($26.70):

0.25q + 0.10(q + 8) = 26.70

Now, we simply solve for q:

Multiply each term within the parenthesis by 0.10:0.25q + 0.10q + 0.80 = 26.70Combine like terms:0.35q + 0.80 = 26.70Subtract 0.80 from both sides to isolate the variable term:0.35q = 25.90Divide both sides by 0.35 to find q:q = 25.90 / 0.35q = 74

Therefore, Thomas has 74 quarters. To find the number of dimes:

q + 8 = 74 + 8 = 82

Thus, Thomas has 82 dimes.

Thomas's change jar has a total of 74 quarters and 82 dimes.

Suppose an isosceles triangle ABC has A = 45° and b = c = 4. What is the length of a^2?

A.22.63
B.54.63
C.9.37
D.3.10

Answers

Since b = c, the angles B and C are congruent.
180 - 45 = 135
135/2 = =67.5

A = 45
B = 67.5
C = 67.5
a = ?
b = 4
c = 4

Since we know two sides and all three angles, we can use the law of sines to find a.

b/sin B = a/sin A

4/(sin 67.5) = a/(sin 45)

a = 4(sin 45)/(sin 67.5)

a^2 = (4(sin 45)/(sin 67.5))^2

a^2 = 9.37

Please help! 3 questions, 1. Determine if the ordered pair is a solution of the equation. Is (-1,-30) a solution of y =10x?: a) True b) False
2.The point (5, -1) is a solution of the equation: y = 2x − 11 options: a) True b) False 3.Which ordered pairs are a solution to the equation? y = 8x options: a) (-1,-7) b) (2,16) c) (1,8) d) (-2,-6)

Answers

this is just a matter of subbing and solving to see if the equations are true

(-1,-30)...x = -1 and y = -30
y = 10x...so we sub
-30 = 10(-1)
-30 = -10 (incorrect)...so this is not a solution
================
(5,-1)...x = 5 and y = -1
y = 2x - 11
sub
-1 = 2(5) - 11
-1 = 10 - 11
-1 = -1 (correct)....so this is a solution
==============
y = 8x
sub in (2,16)...x = 2 and y = 16
16 = 8(2)
16 = 16 (correct)...so (2,16) is a solution

y = 8x
subbing in (1,8)...x = 1 and y = 8
8 = 8(1)
8 = 8 (correct)...so (1,8) is also a solution

thats all...just those 2 are the solutions

Two lines intersect to form a linear pair with equal measures. One angle had the measure 2x and the other angle had the measure (2y-10) find the value of x and y

Answers

Final answer:

To find the values of x and y, set up an equation by equating the two angles and solve for x and y using the given measures.

Explanation:

To find the values of x and y, we need to equate the two angles and solve for x and y.

According to the given information, the measure of one angle is 2x, while the measure of the other angle is 2y - 10.

Since the two angles are equal, we can set up the equation: 2x = 2y - 10.

Now, we can solve for x and y.

2x = 2y - 10
x = y - 5

So, the value of x is y - 5.

Final answer:

The values for x and y are found by solving the system of equations that arise from setting up the condition that two angles forming a linear pair add up to 180 degrees and are equal. The solution is x = 45 and y = 50.

Explanation:

The student's question involves finding the values of x and y when two lines intersect to form a linear pair with equal measures. Since the angles form a linear pair, they add up to 180 degrees. Therefore, we must set up an equation 2x + (2y - 10) = 180 to find the values of x and y. Because the question tells us the angles are equal, we also know that 2x = 2y - 10. Solving this system of equations will provide the values for x and y.

To solve for x, we can use the second equation directly, 2x = 2y - 10. Since the angles are equal, we substitute the first angle's measure for the second, meaning x = y - 5. Then, we can substitute x into the first equation: 2(y - 5) + 2y - 10 = 180, simplifying it to 2y - 10 + 2y - 10 = 180, which further simplifies to 4y - 20 = 180. Finally, adding 20 to both sides and then dividing by 4 gives us y = 50. With the value of y, we can then find x: x = y - 5, so x = 50 - 5, meaning x = 45.

If 2(m-10) +2=24, then m= ?

Answers

2(m-10) + 2 = 24

2m - 20 + 2 = 24

2m - 18 = 24

2m - 18 (+18) = 24 (+18)

2m = 42

2m/2 = 42/2

m = 21

hope this helps
So first you subtract 2 from both sides and you get
2(m-10)=22

Then divide both sides by 2:
m-10=11

And finally, add 10 to both sides
m=21

@ sitora @jyoung HELPPPPP PLEASE WILL GIVE BRAINLEST AND THANKS

1. first question : The graph shows a predicted population as a function of time.

Choose the one statement below that is true about this graph.


The initial population was more than 500.


The graph shows the population decreasing without bound.


The graph has an x-intercept and a y-intercept.


The graph shows quadrant III because only negative values make sense for this situation.


Based on the graph, it is predicted that it will take more than 3 years for the population to be greater than 500.


2. question

Let f(x)=3x

.

Let g(x) = 3x−2+5

.

Which two statements describe the graph of g(x) with respect to the graph of f(x)?



g(x) is translated 2 units right from f(x).


g(x) is translated 2 units left from f(x).


g(x) is translated 5 units down from f(x).


g(x) is translated 5 units up from f(x).




3. What is the equation of the function shown in the graph, given the equation of the parent function is f(x)=1.5x

?



g(x)=1.5x−2



g(x)=1.5x−2



g(x)=−2(1.5)x



g(x)=−3(1.5)x+1


4. The exponential function in the graph shows the population of Greeville in the years since 2010.

What real-world information is given by the point (6, 2707)?
Question 7 options:


The population in 2006


The population in 2010


The population in 2016


The year in which the population is twice the population in 2010

5. What is the average rate of change of the function below on the interval from x = 0 to x = 2?

f(x)=250(0.5)x

Question 8 options:


-93.75


62.5


0


-0.25

6. On the same day, Maysa and Ethan each bought one baseball card from a baseball card store.

The equation f(x)=2x+5

represents the value of Maysa's baseball card, in dollars, x years later.

The graph above shows the value of Ethan's baseball card, in dollars, x years later.

Select the one correct statement below.
Question 10 options:


When they bought their baseball cards, Maysa's card was worth $4 more than Ethan's card.


When they bought their baseball cards, Maysa's card was worth $5 more than Ethan's card.


When they bought their baseball cards, Ethan's card was worth $4 more than Maysa's card.


When they bought their baseball cards, Ethan's card was worth $5 more than Maysa's card.

Answers

Hi Gigi! 

I know it's 5 days late, and I know I'm not one of the people you asked, but I do have a few answers that I hope can still help you and other people that still need these answers. 

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


1.   Answer: Based on the graph, it is predicted that it will take more than 3 years for the population to be greater than 500.


2. I'm not sure, sorry :(


3.   Answer: g(x)=-2(1.5)^x


4.   Answer: The population in 2016.


5.   Answer: -93.75


6. Answer:   When they bought their baseball cards, Maysa's card was worth $4 more than Ethan's card.

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


I hope this helps you, baii <3





A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 108.7-cm and a standard deviation of 0.6-cm. For shipment, 22 steel rods are bundled together.

Find the probability that the average length of rods in a randomly selected bundle of steel rods is less than 109.1-cm.


Round to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 2 decimal places are accepted.

Answers

Let x be the lengths of the steel rods and X ~ N (108.7, 0.6)

To get the probability of less than 109.1 cm, the solution is computed by:


z (109.1) = (X-mean)/standard dev

= 109.1 – 108/ 0.6

= 1.1/0.6

=1.83333, look this up in the z table.


P(x < 109.1) = P(z < 1.8333) = 0.97 or 97%

How can 52 over 9 be expressed as a decimal?
1. 4.3 with bar over 3
2. 4.7 with bar over 7
3. 5.3 with bar over 3
4. 5.7 with bar over 7

Answers

Answer:

so divide 52 divided by 9 and your awnser would be 5.7 with bar over 7 and the awnser would be the fourth one hope it helped.

Step-by-step explanation:

Answer:

D. 4. 5.7 with bar over 7

you sasy bacass

Step-by-step explanation:

you sasy bacass     you sasy bacass     you sasy bacass    you sasy bacass

If two angles are complementary to the same angle, then they are

Answers

If two angles are complementary to the same angle, then they are congruent.
Them angles are congoont my dood

if the x intercept of a line is positive and the y intercept is negative, does the line slant upwards or downwards from left to right?

Answers

From left to right, the line slants upwards like in this image:
Final answer:

If the x-intercept of a line is positive and the y-intercept is negative, the line will slant downwards from left to right.

Explanation:

The line will slant downwards from left to right. The x-intercept being positive means that the line crosses the x-axis at a point to the right of the origin. The y-intercept being negative means that the line crosses the y-axis at a point below the origin. Since the slope of a line represents the direction and steepness of the line, a positive slope combined with a negative y-intercept indicates a line that slants downwards.

Learn more about Line graph here:

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Miko’s restaurant bill was $16. She used the expression 1.18(16) to find the total cost, including an 18% tip.

Which expression is equivalent to the amount Miko paid?

A. (1+0.18)16

B. 16+0.18(16)

C. 16 + 1.18

D. 1+0.18(16)


Please explain your answer

Answers

I say the answer is: D) 16 + 0.18(16) But i don't remember how to explain it. Sorry! This probably didn't help.

Ms. Weasley

Answer:

D) 16 + 0.18(16)

Step-by-step explanation:

What is the volume of the composite figure?

Answers

volume of a sphere is 4/3 * PI * r^3

r = 6

r^3 = 6^3 = 216

4/3 * 216 = 288

 Volume = 288 PI in^3

Rachel budgeted 76.50 for school clothes. this is only 0.45 of her total budget. how much does she have in her total budget

Answers

To find the total amount, divide the amount that you have by the fraction it is, so 76.5/0.45=170, so her total is 170.  Please mark Brainliest!!!
You mean 0.45 percent?

The set of complex numbers is the set of all numbers of the form a + bi, where a and b are real numbers and i=

Answers

√-1.  the i represents an imaginary number where you take the square root of -1.

Answer:

i = [tex]\sqrt{-1}[/tex]

Step-by-step explanation:

A complex number is that one having two parts:

One called real part, represented by a.And another called imaginary part, represented by bi, where b is also a real number plus i, as it was describe in the answer [tex]i = \sqrt{-1}[/tex].

Although  [tex]i =\sqrt{-1}[/tex], it is also [tex]i^{2} = -1[/tex], which has some interesting properties like [tex]i^{3}[/tex] = [tex]i * i^{2}= i * -1 = -i [/tex] , and so on.

These numbers came along when it was necessary to take the squared root of negative numbers:

[tex]\sqrt{-4} = \sqrt{-1} * \sqrt{4} = 2i ; -2i[/tex] .

I have another Brainliest ☺

Answers

Hello!

Question 7

x + 8 = -2
x + 8 - 8 = -2 - 8 (subtract 8 from both sides to remove +8 from x)
x = - 10

Choice A.


Question 8

x - 7 = -3
x - 7 + 7 = -3 + 7 (add 7 to both sides to remove -7 from x)
x = 4

Choice A.


Question 9

36½ - 24½ = 12

Choice B.


Question 10

29 - x = 17 ¼
The reason the value of the number reduces is because a number, x, is subtracted from the original value.
So when subtracting by a number, let's say variable x, the result is naturally a smaller number. (unless the variable is negative)

Choice B.

Please help and show all work.

Answers

1. 73
2.40
3.78
werent too hard

A point on a coordinate plane is located 3 units to the right of the origin and 7 units above the origin. What are the coordinates of this point? Use the drop-down menus to enter the coordinates below.

The coordinates of the point are
(
( ,
)
)

Answers

(3,0)(0,7) is the correct answer

This question is based on the coordinates of a plane. Therefore,  ( 3, 0) and ( 0, 7) are coordinates of this points.

Given:

A point on a coordinate plane is located 3 units to the right of the origin and 7 units above the origin.

We need to determined the coordinates of the points.

According to the question,

It is given that, 3 units to the right of the origin means that, 3 units on positive x - axis.

As we know that,

On x -axis, y is equal to zero.

Therefore, the co-ordinate of this point is located on ( 3, 0).

Now, 7 units to the above the origin means that, 7 units on positive y - axis.

As we know that,

On y -axis, x is equal to zero.

Therefore, the co-ordinate of this point is located on ( 0, 7).

Hence,  ( 3, 0) and ( 0, 7) are coordinates of this points.

For more details, prefer this link:

https://brainly.com/question/17499193

which inequality best represents the situation of you must be at least 52 inches tall to ride the water ride

Answers

C ; x must be greater than or equal to 52 because you have to be 52 inches or greater to ride this ride.

Answer:

Option C is the correct choice.

Step-by-step explanation:

We have been given a graph and we are asked to find the correct option which represents the inequality for the situation of one must be at least 52 inches tall to ride the water ride.

At least 52 inches means one should not be less than 52 inches. This means the length of one should be 52 inches or any number greater than 52 inches.

Let us see our given inequalities one by one.

A) Our first inequality represents height less than or equal to 52, which means that one should be at-most 52 inches, therefore, 1st inequality is not true for our given situation.

B) Our 2nd inequality represents height less than 52, therefore, 2nd inequality is not true for our given situation.

C) We can see from our inequality represented in option C that height is greater than or equal to 52 inches. It is including 52 (at least) and greater heights than 52, therefore, option C is the correct choice.

D) Option D shows an inequality that represents heights greater than 52 as it is not including 52, therefore, option D in not a correct choice.    

$10,000 is compounded semiannually at 12% interest for t years. what expression represents the amount of money after t years?

Answers

The expression would be
0.12t=10,000(2)

The expression that represents the amount of money after t years when $10,000 is compounded semiannually at 12% interest is [tex]10000(1.06)^{(2t)}[/tex].

The amount of money after t years can be represented by the following expression:

[tex]A = P(1 + \frac{r}{n})^{(n*t)}[/tex]

Where:

A is the amount of money after t years

P is the principal amount (initial investment), which is $10,000 in this case

r is the interest rate, which is 12% expressed as a decimal (0.12)

n is the number of times interest is compounded per year, which is semiannually (2 times per year)

Substituting the values into the expression, we have:

[tex]A = 10,000(1 + \frac{0.12}{2})^{(2*t)}[/tex]

Simplifying further, we get:

[tex]A = 10000(1.06)^{(2t)}[/tex]

Therefore, the expression that represents the amount of money after t years when $10,000 is compounded semiannually at 12% interest is [tex]10000(1.06)^{(2t)}[/tex].

To learn more about compound interest click here:

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shana wants to make a birthday cake for her mother. her old fashioned recipe calls for 3/12 Of a teaspoon of salt but she only has measuring spoons that use fourths. How many fourths of a teaspoon should she use ?


I get 2/4 because I did 1/4 of 3/12

Answers

it will be 1\4 what it measuring spoons

The answer is 1/4ths because if you do the equation correctly you get 1/4.

Your welcome

Evaluate the functions for the domain values indicated. a. p(x) = 3x + 14 for x = −5, 0, 4 b. h(t) = t2 = 5t for t = −2, 0, 5, 7 9. Consider the sequence −7, −3, 1, 5, 9, …. a. What is f(2)? b. What is f(5)?

Answers

A is 20 and B is 29 I believe if you're using 2 and 5 for x

Solve the following inequality. Then place the correct answer in the box provided. Answer in terms of a mixed number. 12z - 3 ≥ 2z - 15

Answers

12z - 3 ≥ 2z - 15
When you have to solve an equality like that, you need to put the variables apart (the numbers with letters) and the numbers apart.
So first, we need to reunite the variables, by subtracting "2z" from both sides of the equation:
12z - 3 ≥ 2z -15
12z - 2z - 3 ≥ 2z - 2z - 15
12z - 2z - 3 ≥ -15
10z - 3 ≥ 15

Then we add 3 to both sides:
10z - 3 + 3 ≥ -15 + 3
10z ≥ -12

Now divide both sides by 10
(10z)/10 ≥ -12/10
z ≥ -6/5

Now we need to write the answer as a mixed number.
-6/5 = -1.2
0.2 = 1/5
9
So -6/5 = -1 1/5.

So 12z - 3 ≥ 2z - 15 for Z ≥ -1 1/5

Hope this helps! :)

Assume RST MNO. If MN = 6, NO = 7, and MO = 11, what is the length of RS?

Answers

the answer is 6 hope this answers your question

Answer with explanation:

It is given that,

 R ST  ≅ M NO.

Also, MN=6 unit

NO=7 Unit

MO=11 unit.

When two triangles are congruent , their corresponding Sides and Angles are Congruent, that is equal.

So,Corresponding Side to MN is RS .

So, MN=RS

MN=6 unit

RS=6 unit

50 points! Write a compound inequality to represent all of the numbers between -4 and 6.

Answers

you want  x >-4 and x<6

 s0 the equation would be: -4<x<6

Which statement is true about this argument?

Premises:
If two lines are parallel, then the lines do not intersect.
Lines m and n do not intersect.

Conclusion:
Lines m and n are parallel.

Which statement is true about the argument?

The argument is not valid because the premises are not true.

The argument is not valid because the conclusion does not follow from the premises.

The argument is valid by the law of detachment.

The argument is valid by the law of syllogism.

Answers

B) The argument is not valid because the conclusion does not follow from the premises.

Although parallel lines cannot intersect, that does not mean that two lines are parallel just because they do not intersect. Two lines can be not parallel and still not intersect.

A group of 120 people were asked whether their income level is above or below $25,000 and whether they subscribe to a movie channel. The data from the survey is shown in the Venn diagram. Use the Venn diagram to find the missing values in the frequency table.

Which shows the correct values for the variables in the table?

A. a = 18, b = 34, c = 65
B. a = 34, b = 18, c = 68
C. a = 34, b = 68, c = 47
D. a = 47, b = 18, c = 68

Answers

Answer:

The answer is B on edge 2020.

Step-by-step explanation:

If you flip the graph of the quadratic parent function, f(x) = x2, over the x-axis, what is the equation of the new function?

A. g(x) = –x2
B. g(x) = x–2
C. g(x) = (–x)2
D. g(x) =

Answers

i think the answer might be A.

Answer:

A. [tex]g(x)=-x^2[/tex]

Step-by-step explanation:

In flipping across x-axis a function gives its mirror image through the x-axis,

That is, when a function f(x) is flipped over x-axis,

Then the new function would be -f(x).

Here, the given function,

[tex]f(x)=x^2[/tex]

After flipping the function over x-axis,

[tex]g(x)=-f(x)[/tex]

[tex]\implies g(x)=-x^2[/tex]

Hence, option 'A' is correct.

write two equations for a horizontal line and a vertical line.

Answers

Two equations for a horizontal line could be y = 1 & y = 5
Two equations for a vertical line could be x = 2 & x = 6

Horizontal lines are created when y is always equal to one number, while vertical lines are created when x is always equal to one number.

Hope this helps!

Sonia graphs the equations y = –x2 + 4x and y = x – 4 to solve the equation –x2 + 4x = x – 4. Her graph is shown below.

What are the solutions of –x2 + 4x = x – 4?

A. –5 and 0
B. –5 and –1
C. –1 and 4
D. 0 and 4

Answers

The line and parabola intersect at x=-1 and x=4, so your solution is C. –1 and 4

c.-1 and 4 because thats where it intercepts

How would the distance formula be used in real life?

Answers

one example I can think of is to measure the direct distance between two locations. suppose A lives on the intersection of 30th avenue and 50th street, B lives on 70th avenue and 80th avenue, the distance between them would be the square root of [(70-30)^2 +(80-50)^2)], which is 50, so the straight-line distance between the two places are 50 blocks. 
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Selena, Ben, and Raj all won leads in the musical, and they has practiced every afternoon during study hall for the past two weeks. Which is the best replacement for the underlined words? A - have practice B - will practice C - will be practicing D - have practiced In 300 words or less, identify a conflict from The Most Dangerous Game, identify what type it is, and explain why it is important to the storys overall themes. What are the basic building blocks of DNA and RNA? Describe the Archetype between Albert Einstein and Leonardo da Vinci. I will pick the Brainliest! Consider the photosynthetic conversion of co2 and h2o to form glucose, c6h12o6, and o2.a. write the balanced reaction.b. is the number of each type of atom on either side of the arrow the same?c. is the number of molecules on either side of the equation the same HELP PLEASE ASAP!!!!Which of the following terms describes how mountains form?A: GraduallyB: RapidlyC: ExplosivelyD: Destructively someone please help!The various melodies heard in Antonin Dvok's "String Quartet in F Major" have a/an _______ quality. Which element can help you identify the theme of a story ? A. The amount of dialogue B. An important idea or refrain C. The success of the story D. A mistake in grammar The state achieved when energy from food equals energy expended, maintaining body weight is known as Which equation shows how the properties of numbers extend to negative whole numbers by the Commutative Property of Addition?A) 2 + 4 = 4 + (2) B) 2(4) = 4(2) C) (2 + 4) + 3 = 2 + (4 + 3) D) 2(4 + 3) = (2 x 4) + (2 x 3) What causes high and low tides? A. The ocean's conveyor belt and refraction B. Earthquakes and volcanoes C. Cold and warm currents D. The moon's gravity and Earth's rotation Would Peyton Farquhar do anything for the Confederacy? Provide evidence from the story that supports your answer. 11 relaxing after work. the 2010 general social survey asked the question: "after an average work day, about how many hours do you have to relax or pursue activities that you enjoy?" to a random sample of 1,155 americans.41 a 95% confidence interval for the mean number of hours spent relaxing or pursuing activities they enjoy was (1.38, 1.92). (a) interpret this interval in context of the d If there are two species of butterfly that are able to mate but produce sterile offspring, are the offspring considered a new species? which value for the number makes the statement true?the quotient of a number and five is eighta.4b.8c.40d.80 The Griffins and the Corbins live in the same city and pay the same sales tax rate, and both families made $12,000 in taxable purchases last year. If the Griffins made $73,000 and the Corbins made $29,000 last year, is the sales tax in their city an example of a regressive tax?A.Yes, because the Corbins paid a higher percentage of their income in sales tax than the Griffins did. B.No, because the Corbins paid a higher percentage of their income in sales tax than the Griffins did. C.No, because the Griffins and the Corbins both paid the same sales tax rate. D.Yes, because the Griffins and the Corbins both paid the same sales tax rate. "which method of data collection is most appropriate for a nurse researcher to use in a survey study?" Domain is a newer portion of the classification system that includes Eukarya and Prokarya. What information most likely dictated that this new level be created? New data about the geographic location of organisms New data about evolutionary relationship between organisms New data about the behavior and interactions of organisms in the wild New data about the physical appearance of organisms Can someone please clearly explain and workout Q5? Much appreciated Describe three ways Ida B. Wells fought lynching and other forms of discrimination Steam Workshop Downloader