Natalie is the creator of Better Brain, a new mindfulness app for teens. The app currently has 1,262 downloads, and Natalie has set a goal of doubling the downloads every month.
Write an exponential equation in the form y=a(b)x that can model Natalie's goal for the number of downloads, y, in x months.

The best estimate for the age of the sample is; 9.4 days

We are told that;

The amount of a sample remaining after t days is given by the equation; P(t) = A(¹/₂)^(t/h)

Where;

A is the initial amount of the sample.

h is the half-life, in days, of the substance

The equation is:

P(t) = A(¹/₂)^(t/h)

If a sample contains 18% of the original amount of Radon - 222 and h = 3.8, then we have;

0.18 * A = A * (0.5)^(t/3.8)  

divide both sides of the equation by A to get;

0.18 = ( 0.5 )^(t/3.8)

(t/3.8)log 0.5 = log 0.18

(t/3.8) = log 0.18/log 0.5

t/3.8 = 2.47

t = 3.8 * 2.47 ≈ 9.4 days

This is the best estimate for the age of the sample

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The complete question is;

The amount of a sample remaining after t days is given by the equation P(t)=A(1/2)^(t/h), where A is the initial amount of the sample and h is the half-life, in days, of the substance. A sample contains 18% of its original amount of Radon-222. The half-life of Radon-222 is about 3.8 days. Which is the best estimate for the age of the sample?

Answer:

It's C

Step-by-step explanation:

Answer:

Step-by-step explanation:

The answer is that yes it is because a pentagon has three triangles inside it  and a triangle is equal to 180 degrees so you times 180 times three and you get 540 degrees so yes that is correct!

Answer: D

Step-by-step explanation:

A function in a set of ordered pairs cannot have repeating x values

A have a repeated x values of -12

B have a repeated x values of 8

C have a repeated x values of 13

D does not have a repeated x value.

D is the correct answer.

Answer:

height: 27 area: 176

Step-by-step explanation:

Answer: 1

Step-by-step explanation: -2 times x the x would just be 1 so -2 times 1 equals -2 then -2 plus 3 is 1

to properly examine the effect of a categorical independent variable in a multiple linear regression model we use an interaction term then it is a true statement

we have given that the by which method we use the different levels of a qualitative independent variable and we have to explain about it.

So, For his purpose, we know that the

A dummy variable is a variable that takes values of 0 and 1, where the values indicate the presence or absence of something.

And in the multiple regression method there are a lot of different variables which are used for a qualitative and for this a variable is used which is called the dummy variables.

By this variables we show the analysis between the given data. it gives the output in the 0 and 1 numbers.

So, For the levels of qualitative, the variable called dummy variables is used in the multiple regression method.

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Answer:

[tex]f(g(16)) = 6[/tex] and [tex]f(g(x)) = \sqrt{x} + 2[/tex]

Step-by-step explanation:

Step 1 and Step 2 appear to be asking the same thing, so I will assume you meant for g(16) to be found in Step 1 and for f(g(16)) to be found in Step 2.

Step 1: Find g(16)

[tex]g(x) = \sqrt{x}[/tex], so we must plug in 16 for x to find g(16)

[tex]g(16) = \sqrt{16} = 4[/tex]

Step 2: Find f(g(16))

In order to do this, we must plug the value we found for g(16) into the equation for f(x). Thus, we must plug in 4 (the value we found in Step 1) for x in f(x).

[tex]f(x) = x + 2[/tex], so we must plug in 4 to find f(4)

[tex]f(4) = 4 + 2 = 6[/tex]

Thus, [tex]f(g(16)) = 6[/tex]

Step 3: Find f(g(x))

We must plug in the value of g(x) into f(x) to find f(g(x)).

These are the expressions for f(x) and g(x):  [tex]g(x) = \sqrt{x}[/tex], [tex]f(x) = x + 2[/tex]

We find that [tex]f(g(x)) = \sqrt{x} + 2[/tex]

The required value of the function f(g(16)) is given as f(g(16)) = 6.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
f(x) = x + 2
g(x) = √x

In order to determine f(g(16)),
g(16) = √16
g(16) = 4

Now,

f(g(16)) = 4 + 2 = 6
f(g(16)) = 6

Thus, the required value of the function f(g(16)) is given as f(g(16)) = 6.

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Answer:

2.15

Step-by-step explanation:

I will assume that "−1/4(−8.6)" is telling us to multiply (-8.6) times -(1/4):

(-1/4)*(-8.6)

= (8.6/4)

= 2.15

Answer:

(1,0) and (-3,0)

Step-by-step explanation:

Add 5 to 2 = 2 will make 7 = 7 a true statement and adding 5 to 2 ≠ 3 to make 7 ≠ 8 will make a true statement.

A way to express or represent numbers is through the number system.

We often employ decimal numbers because they are so widely used.

The Number System includes any of the several sets of symbols and the rules for using them to represent numbers.

(1)

As per the given,

2 = 2

Add 5 on both sides of the above equation,

2 + 5 = 2 + 5

7 = 7 (True)

(2)

As per the given

2 ≠ 3

Add 5 on both sides of the above equation,

2 + 5 ≠ 3 + 5

7 ≠ 8 (True)

Hence "It is correct that if you add 5 to 2 = 2, you will get 7 = 7, and if you add 5 to 2 ≠ 3, you will get 7 ≠ 8".

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The property illustrated in the statement "If ∠A ≅ ∠B, ∠B ≅ ∠C, then ∠A ≅ ∠C" is the Transitive Property.

This property states that if two elements are related by a certain relationship, and another element is related to the second element by the same relationship, then the first and third elements are related by the same relationship.

In this statement, the relationship is that of congruency, meaning that each angle has the same measure. Therefore, the Transitive Property states that if angle A is congruent to angle B, and angle B is congruent to angle C, then angle A is congruent to angle C.

The other three properties listed do not apply to this statement. The Reflexive Property states that a given element is related to itself by a certain relationship, which does not apply to this statement.

The Symmetric Property states that if two elements are related by a certain relationship, then the two elements are related to each other in the same way, which is not applicable in this statement.

Lastly, the Addition Property states that the sum of two elements related by a certain relationship is related to the two elements by the same relationship, which is not applicable in this statement.

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Answer:

22 is the third quartile for this set

Answer: 5

Step-by-step explanation:

slope is m in the formula y=mx+b

plug in the numbers for m and that's the slope

Answer:

2398 cents

Step-by-step explanation:

Every dollar equals 100 cents

So 23 times 100 equals 2300, then we add the 98 cents left over from the dollar

Which would be 2398 cents

The total surface area of a solid quarter-cylinder is 10(13π + 32) cm².

Given:-

The radius of a solid quarter-cylinder = 10 cm.

Height of solid quarter-cylinder = 16 cm.

To calculate the surface area we have a formula:-

Total surface area of solid quarter-cylinder = (TSA of cylinder / 4) + 2(Area of rectangle)= 2πr(h + r)/4 + 2(r * h) = πr(h + r)/2 + 2rh .

Solution:-

r = 10 cm.

h = 16 cm.

So,

→ Area of rectangle so formed = r * h = 10 * 16 = 160 cm².

then,

→ Area of two rectangles so formed = 2 * 160 = 320 cm².

Therefore,

→ Total surface area of solid quarter-cylinder = πr(h + r)/2 + Area of two rectangles.

→ Total surface area of solid quarter-cylinder = π * 10 * (10 + 16) / 2 + 320

→ Total surface area of solid quarter-cylinder = 5π * 26 + 320

→ Total surface area of solid quarter-cylinder = 5(26π + 64)

→ Total surface area of solid quarter-cylinder = 5*2(13π + 32)

→ Total surface area of solid quarter-cylinder = 10(13π + 32) cm².

Hence, the Total surface area of a solid quarter-cylinder is 10(13π + 32) cm².

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Answer:

1 liter

Step-by-step explanation:

A milliliter is 1/1000 of a meter; measuring a pool by millimeters wouldn't make sense.

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{0}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~6 - 0~~)^2 + (~~1 - 9~~)^2} \implies d=\sqrt{(6 +0)^2 + (1 -9)^2} \\\\\\ d=\sqrt{( 6 )^2 + ( -8 )^2} \implies d=\sqrt{ 36 + 64 } \implies d=\sqrt{ 100 }\implies d=10[/tex]

The inequality which represents the given phrase is 1/2(3x - 2/3) + 6 ≤  x+5​ and the solution are x ≤ -4/3.

A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.

In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.

As per the given,

1/2(3x - 2/3) + 6 ≤  x+5​

3/2 x - 1/3 + 6 ≤  x+5​

3/2 x + 17/3 - x ≤ 5

x/2 ≤ -2/3

x ≤ -4/3

Hence "The inequality 1/2(3x - 2/3) + 6 ≤ x+5 represents the provided sentence, and the answer is x ≤  -4/3.".

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The expected gain after 16 tosses of the coin is $400.

Let x stand in for your entire savings.

There is a 0.5 likelihood of heads and a 0.5 possibility of tails. (equally likely events).

The value of accepting this offer is 1.5. The formula is as follows:

2 heads.

0.5 = P(Heads)

Value anticipated if the coin came out heads: 2x*0.5 = x

Plus

(1 - 0.5)x = 0.5x for tails.

0.5 = P(Tails)

Value anticipated if the coin came up tails: 0.5x*0.5 = 0.25x

Total projected value is equal to 1.25x.

For x = $20

Thus,

Amount = 1.25(20) = $25.

Thus, for the 16 tosses = $25 x 16 = $400.

Therefore, the expected gain after 16 tosses of the coin is $400.

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Shortest time taken for a is 0.666hours and for b is 0.866hours.

Take a variable x on the possible road. Evaluate an equation of time in terms of x and find the extrema of the function. To find extrema differentiate the function and equal it to zero. Then find the roots of equation to get the extreme value, which should be the minimum time path.

A is initial point

P is oasis

S is intermediate point

Let us assume he directly reaches  x km from N at S.

then AS=[tex]\sqrt{100+X^2}[/tex] and SP=20-X

Time taken:

[tex]\frac{\sqrt{100+X^2}}{30}[/tex]+[tex]\frac{20-X}{50}[/tex]

Differentiating it and putting this to zero gives extrema value

[tex]\frac{2x}{60(\sqrt{100+X^2})}[/tex]=[tex]\frac{1}{50}[/tex]

⇒[tex]\frac{50x}{30}[/tex]=[tex]\sqrt{100+X^2}[/tex]

⇒By squaring on both sides

⇒100+X^2=[tex]\frac{25x^2}{9}[/tex]

⇒x=7.5km

x is independent of PN as while differentiating PN term became 0

Now time:

a) t= [tex]\frac{\sqrt{100+7.5^2}}{30}[/tex]+[tex]\frac{20-7.5}{50}[/tex]=0.666hours

b) t=[tex]\frac{\sqrt{100+7.5^2}}{30}[/tex]+[tex]\frac{30-7.5}{50}[/tex]=0.866hours

Shortest time taken for a is 0.666hours and for b is 0.866hours.

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Answer:

Step-by-step explanation:

Answer: Ben paid the most

Step-by-step explanation: Okay, to find the prices of the 4, we need to follow what the problem says. So, we know Hannah paid 21, so we know that is how much she paid. Now, we need to find 1/3 of the total cost ($64.80) So, we do 1/3 divided by $64.80 and get $21.60. For Stephanie, we need to find 15% of $64.80, so we can write it as a proportional relationship, so 15 x $64.80 / 100 is 9.27. (as a decimal) Now, we subtract all of those numbers from the total cost ($64.80) to find Brayden's pay. After I subtracted all of the amounts, I got $12.93. I'll list all the amounts.

Hannah - 21

Ben - 21.60

Stephanie - 9.27

Brayden- 12.93

So, as we see Ben paid the most. I hoped this LONG explanation helped you!

it should be ben.

Hannah paid $21;

ben paid 1/3 of 64.80 and that's $21.6 (64.84÷3);

Stephanie paid 15% of $64.80 and that's $9.72 (15÷100×64.80);

Brayden paid $12.48 [64.80-(21+21.6+9.72)].

hope I helped (btw sorry for any mistake english isnt my forst language)

The value of  f(g(5)) is obtained as -2.

For two functions f(x) and g(x), a composite function is defined as f(g(x)) or g(f(x)). The properties of this function are as follows,

The inverse of a composite function is the same as the composition of the inverse of both functions.

The composition of two one to one functions is always one to one.

The value of f(g(5)) is equal to the value of the composite function f(g(x)) at x = 5.

The value of g(5) from the graph is 2.

Now, f(g(5)) = f(2)

The value of f(2) from the graph is -2.

Thus, f(g(5)) = -2

Hence, the value of the given composite function is f(g(5)) = -2.

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The solution to the given quadratic equation by completing the square is; x = 3 ± √2

We are given the quadratic equation;

y = x² - 6x + 7

1) Set the value of y to zero to get;

x² - 6x + 7 = 0

2)  Remove the constant term from both sides using the opposite operation to get;

x² - 6x = -7

3) Take half of the x term and square it and add to both sides of the equation to get;
x² - 6x + 9 = -7 + 9

4) Rewrite the perfect square on the left to get;

(x - 3)²  = 2

5) Take the square root of both sides to get;

x - 3 = ±√2

6) The solution will be;

x = 3 ± √2

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The domain of the red curve in the given graph is

x > 4

The domain is controlled by the input values. considering the graph the input values are in the x axis

The least number and the maximum number is what makes the domain as it shows the extents the input values can go

The maximum number is not showing so we assume infinity since the curve continued.

For the minimum this is the point before 5 which is 4

The domain starts from 4, with 4 not inclusive to infinity and the correct option is x > 4

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The probability of washing dishes by me tonight will take between 15 and 16 minutes is 14.29%.

The term "uniform distribution" refers to a type of probability distribution in which the likelihood of each potential result is equal.

Let's consider, the lower limit for this distribution as a and the upper limit for this distribution as b.

The following formula gives the likelihood that we will discover a value for X between c and d,

[tex]P(c\leq X\leq d)=\frac{d-c}{b-a}[/tex]

Given the time it takes me to wash the dishes is 11 minutes and 18 minutes. From this, a = 11 and b = 18.

Then,

[tex]P(15\leq X\leq 16)=\frac{16-15}{18-11}=0.1429=14.29\%[/tex]

The answer is 14.29%.

The complete question is -

The time it takes me to wash the dishes is uniformly distributed between 11 minutes and 18 minutes. What is the probability that washing dishes tonight will take me between 15 and 16 minutes?

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Answer:

15 dimes and 6 pennies

To carpet the rectangular floor, it will cost $1,137.6. The result if obtained by multiplying the area of the carpet by the cost per square yard.

To calculate the cost of a product, multiply the product price for one item by the quantity.

We have a rectangular floor with a dimension of 27 feet by 24 feet. The carpet cost is $15.8 per square yard. Find the total cost to carpet it!

Let's change the unit of length.

The area of the carpet is

A = 9 yard × 8 yard

A = 72 square yard

The total cost is

C = A × price/square yard

C = 72 × $15.8

C = $1,137.6

Hence, the total cost to carpet the floor is $1,137.6.

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Answer:

-2,838

Step-by-step explanation:

A good way to do this is 2,938-100 which equals 2,838. Then since you know it will be a negative number add the negative sign.