In a newspaper,it was reported that the number of yearly robberies in springfield in 2011 was 240, and then went up by 5% in 2012.How many robberies were there in springfield in 2012?

After 31.6 minutes have passed, approximately 40.3 mg of lead-214 remains in the sample. This can be determined using the decay equation lnA = lnA₀ - kt, where A represents the amount of the substance remaining after time t, A₀ is the original amount of the substance, k is a constant characteristic of the substance, and t is the elapsed time.

The given equation, lnA = lnA₀ - kt, represents the decay of the radioactive isotope lead-214. In this equation, A represents the amount of the substance remaining after time t, A₀ is the original amount of the substance, k is a constant characteristic of the substance, and t is the elapsed time.

To find the amount of lead-214 remaining after 31.6 minutes, we can plug in the given values into the equation. We are given that A₀, the original amount of lead-214 in the sample, is 51.3 mg. The value of k for lead-214 is 2.59×\(10^(^-^2^)\)\(minutes^(^-^1^)\), as mentioned in the question. Finally, t is 31.6 minutes.

Substituting these values into the equation, we have:

lnA = ln(51.3) - (2.59×\(10^(^-^2^)\) × 31.6)

Evaluating the right side of the equation, we get:

lnA ≈ 3.937 - (2.59×\(10^(^-^2^)\) × 31.6)

    ≈ 3.937 - 0.8164

    ≈ 3.1206

To find A, we need to exponentiate both sides of the equation using the natural logarithm base, e:

\(e^(^l^n^A^)\) = \(e^(^3^.^1^2^0^6^)\)

A ≈ 22.63 mg

Therefore, after 31.6 minutes have passed, approximately 22.63 mg of lead-214 remains in the sample.

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To find the length of the curve r(t) = sqrt(2)ti, we need to use the arc length formula:L = ∫[a,b] ||r'(t)|| dt,where ||r'(t)|| is the magnitude of the derivative of the curve.

First, we need to find r'(t):

r'(t) = (d/dt) [sqrt(2)ti] = sqrt(2)i

The magnitude of r'(t) is ||r'(t)|| = sqrt(2).

So, the length of the curve is:

L = ∫[0,1] sqrt(2) dt = sqrt(2) * [t] [0,1] = sqrt(2)

Therefore, the length of the curve r(t) = sqrt(2)ti is sqrt(2).

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Answer:

a = 5, b = -3 and c =1

Step-by-step explanation:

The standard form of a quadratic equation is expressed as;

f(x) = ax² + bx + c

Given the expression

f(x) = 5x² = 3x - 1

f(x) =  5x² - 3x + 1

Comparing with the general formula;

ax² = 5x²

a = 5

bx = -3x

b = -3

c = 1

Hence a = 5, b = -3 and c =1

The coefficient of correlation in this situation is 0.65.

The coefficient of determination (R-squared) is the square of the coefficient of correlation (r). Therefore, to find the coefficient of correlation in this situation, we need to take the square root of the coefficient of determination.

In this case, the coefficient of determination is 0.4225. Taking the square root of 0.4225 gives us the coefficient of correlation:

Coefficient of correlation (r) = √0.4225

The coefficient of correlation in this situation is 0.65.

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Answer:

-3r+13

Step-by-step explanation:

11r-14r-3+16

=11r-14r+13

= -3r+13

Answer:

-3r + 13

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

Step 1: Define expression

11r - 14r - 3 + 16

Step 2: Simplify

And we have our final answer!

The probability that I will run out of money is 3.55e−11 using Asymmetric ruin probability

Given that, for each head, I win $2 and for each tail, I lose $1.

Here we have to use the Asymmetric ruin probability concept.

This means here we have rewards and losses.

Suppose we have x dollars, then we have a probability of running out of money is like p(x+2)- p(x) = p(x) - p(x-1).

p(x+2) +p(x-1) -2p(x) = 0.

It only has a solution in the form x^n, where x is a root of the characteristic polynomial.

x^3 - 2*x^2 + 1 = 0.

Now we have to solve x^3 - 2*x^2 + 1 = 0.

by solving this equation we can get p(n) = \(((\sqrt{5} - 1)/2)^n\)

if we put n = 50 so we can get p(50) = \(((\sqrt{5} - 1)/2)^(50)\)

p(50) is about  3.55e−11.

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y = 4x -21  (again cool name btw) :)

y=4x-3 has slope = to the coefficient of the x term = 4

all parallel lines have the same slope.

y=4x + b, where b can be any real number, so just plug in the point (4,-5) into the general equation

y=4x+b = -5 = 4(4) + b

-5 = 16 + b

-21 = b

b = -21 = the y intercept, so the equation is

y=4x -21

Vertex is slang for a corner or a place where two lines converge.The four corners of a square, for instance, are each referred to as a vertex.

The graph of g is a vertical stretch by a factor of 2 followed by a translation of 3 units down of the graph of f(x) = (x-1)²then the function g(x) = 2(x+4)²

f(x) =x²-2x+1 The graph of g be a vertical stretch by a factor of 3 and a reflection in the y-axis, followed by a translation 2 units left of the graph of  .f(x) =x²-2x+1

Rewrite the given function f(x).

f(x) =  (x-1)²

Now, the graph is stretched vertically by a factor of 2.

= 2(-x-1)²

reflect the graph about the y-axis.

2(x+1)²

move to the left by 3 units.

= 2(x+3+1)²

=2(x+4)²

The function g(x) =2(x+4)²

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Hello~

The answer is C. (3,0)

Hope this helps!

Ary~

Answer: b

Step-by-step explanation: b

Answer:

Option B

Step-by-step explanation:

Set 1:

med: 76, Range: 50-65= 15IQR: 77-73= 4

find the median, range, and IQRfor each data set.

Set 2:

med: 60, Range: 68-55= 13,IQR: 63-59= 4

76- 60 =16

find the difference of the medians 16 is 4 times 4

so the difference of the medians is 4 times the IQR

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

hope it helps...

have a great day!!

This expression can't be simplified.

Work/Explanation:

The given expression, \(\bf{8-3x}\), cannot be simplified further because 8 and -3x are not like terms. 8 is a constant and -3x is a term that contains a variable. We cannot add constants and variables. Moreover, the given expression can't be factored because 8 - 3x have no common factors except 1.

The proof of trigonometric identity (sin(x) + tan(x))/sin(x) = 1 +secx is given below.

The given trigonometric identity is,

(sin(x) + tan(x))/sin(x).

We know that tan(x) = sin(x)/cos(x), so we can substitute that in:

sin(x)/ sin(x) + sin(x)/cos(x) / sin(x)

We can simplify the fraction in the numerator:

sin(x)/ sin(x) + sin(x)/sin(x)cos(x)

We know that sin(x)/sin(x) = 1, so we can simplify further:

1+ 1/cos(x)

We know that 1/cos(x) = sec(x), so we can substitute that in:

1 + sec(x).

Now we have the same expression as the right-hand side of the identity, so we have proven that:

sin(x) + tan(x)/sin(x) = 1 + sec(x)

Therefore, (sin(x) + tan(x))/sin(x) = 1 +secx.

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Answer:

a) 35,  b) 25,  c) 60

Step-by-step explanation:

The number of girls is 10 more than the number of boys, so it's a good thing to choose a variable to represent the number of boys.

Number of boys:  b

Number of girls:  b + 10

Ratio of girls:boys is 7:5, so

\(\frac{b+10}{b}=\frac{7}{5}\)

"Cross multiply" to get

\(7b=5(b+10)\\7b=5b+50\\2b=50\\b=25\)

There are 25 boys.  There are 10 more girls, so the number of girls is 35, and the total number of students is 60.

That's a packed classroom!

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Answer:

(3, -2)

Step-by-step explanation:

2+4 = 6

3-7 = -4

6/2 = 3

-4/2 = -2

The function to represent the value of car is h(x) = 20000 × (0.85)ˣ which represents a dilation of factor 20000 from f(x) = 0.85ˣ and the difference in values after 5 years is $3549.64.

A function y = f(x) is a one to one relationship between two sets X and Y where the set X is called the domain and Y the range of function f(x) ans x ∈ X and y ∈ Y.

The graph represents depreciation of $12000 car as g(x) = 12000 × (0.85)ˣ.

Its parent function is f(x) = 0.85ˣ.

(a) As per the question, the equation for a $20000 car can be written as,

h(x) = 20000 × (0.85)ˣ.

(b) The function h(x) can be described as a dilation of f(x).

Its, scale factor is 20000.

(c) After 5 years the difference in values of car is as below,

20000 × (0.85)ˣ - 12000 × (0.85)ˣ

Plug x = 5 to get,

⇒ 8000 × (0.85)⁵ = $3549.64

Hence, the difference in the values of car after 5 years represented by functions g(x) = 12000 × (0.85)ˣ and 20000 × (0.85)ˣ is  $3549.64.

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Answer: 169/49

that is your awnser

12 terms are in an arithmetic sequence.

What comprises an arithmetic series?

A group of integers that are arranged in a particular order and share a difference between each term is known as an arithmetic sequence.

            For instance, the common difference between the numbers 3, 9, 15, 21, and 27 in mathematics is 6. The term "arithmetic progression" can refer to an arithmetic sequence.

a = 6,

d = -3,

last term, l = -45

a + (n - 1)*d

45 = a + (n - 1)d

45 = 6 + (n -1)-3

45 - 6 = -3(n - 1)

39 = -3(n - 1)

-3(n - 1) = 39

n - 1 = -39/3

n - 1 = -13

n = -13 + 1

n = - 12

There are 12 terms.

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To set up this confidence interval, first identify the population parameter of interest, next select the appropriate estimator, then check the conditions for constructing the confidence interval that are: Randomization, Sample size and Distribution shape.

State:
Zachary wants to estimate the mean number of daily texts he sent over the past four years using a 90% confidence interval. He has an SRS of 50 days, with a daily average of 22.5 messages. The data is strongly skewed to the right with many outliers.

Plan:
1. Identify the population parameter of interest: The mean number of daily texts sent by Zachary over the past four years (µ).
2. Select the appropriate estimator: In this case, it's the sample mean = 22.5 messages.
3. Check the conditions for constructing the confidence interval:
  a. Randomization: Zachary used a simple random sample (SRS) of 50 days, which satisfies the randomization condition.
  b. Sample size: The sample size is n = 50, which is typically considered large enough for constructing a confidence interval.
  c. Distribution shape: Since the data is strongly skewed to the right with many outliers, the normality condition might not be satisfied. In this case, the Central Limit Theorem (CLT) may not apply, and the confidence interval might not be accurate.

Given the potential issue with the distribution shape, Zachary should consider either transforming the data to approximate normality or using a nonparametric method.

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Answer:

32ft

Step-by-step explanation:

The initial speed of a ball thrown horizontally from the roof of a building at a height of 54 m and hitting the ground at a height of 32 m from the bottom is equal to 9.64 m/sec.

A ball throws horizontally from the roof of a building. This is where we have to take horizontal movement into account.

Height of building = 54 m

Height of ground from base = 32 m Calculates the initial speed of the ball.

Since the ball is thrown horizontally, its initial velocity has no vertical component. When released, the ball is subject to gravity and accelerates downward until it hits the bottom. To determine how long the ball stayed in the air before hitting the ground, use the following formula,

d = 1/2×g×t²

where g --> acceleration due to gravity

t --> time

d --> the distance covered by ball before hitting the ground, g= 9.81 m/s².

So, 54 m = (1/2) × 9,81 m/s² × t²

=> t² = 54/4.90

=> t² = 540/49

=> t² = 11.02 sec²

=> t = 3.31963 ~ 3.32 sec

So the ball will stay in the air for about 3.32 seconds. Let v₀ₓ be the horizontal component of the initial velocity. According to the information of the problem, the ball landed 32 m from the bottom of the building. Let's make the initial position x₀ = 0. Then, the final horizontal displacement of a ball will be equals to 32 metres. Using the distance velocity relation, x = x₀ + v₀ₓt and substituting all known values in it,

=> 32 m = 0 + v₀ₓ × 3.32 sec

=> v₀ₓ = 32/3.32

=> v₀ₓ = 9.6385 ≈ 9.64 m/sec

Hence, required value is 9.64 m/sec.

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Complete question:

A ball is thrown horizontally from the roof of a building 54 m high and hits the ground 32 m from the base. What was the initial speed of the ball?

The expression which is equivalent to 12 is 12 ÷ 1.

The correct answer choice is option B

check all that applies:

4 ÷ 12 = 0.34

12 ÷ 1 = 12

124 ÷ 4 = 31

12 ÷ 12 = 1

In conclusion, 12 ÷ 1 is the equivalent expression to 12

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Answer: C

Step-by-step explanation:

6+3=9

9+3=2

Answer: A

Step-by-step explanation:

6+3=9

9+3=12

Answer:

3, 4

Step-by-step explanation:

6 < 3n < 15

Divide the three "sides" by 3.

2 < n < 5

n must be between 2 and 5,a nd it must be a whole number.

n can be 3 or 4

Answer:

n= 3, and n=4

Step-by-step explanation:

whole numbers are : 0,1,2,3,4,5,....

6 < 3n < 15  

(3n has to be greater than 6 and less than 15 not including 6 and 15)

for n=3 we have 3n =9

for n=4 we have 3n= 12

Answer: 4x -8+ 125x -4x +5

The line of reflection that produces z²(10, 7) is the x-axis.

To determine the line of reflection that produces the image of point Y at the point (9,-3), we need to find the midpoint of the line segment YY', where Y' is the reflection of Y.

Using the midpoint formula, we get the midpoint N as (-4,0). Since this point lies on the horizontal line passing through the origin (0,0), the line of reflection is the x-axis.

To determine the line of reflection that produces the image of the line segment XY at the line segment X'Y', we need to find the perpendicular bisector of XY, which is the reflection line. Using the midpoint formula, we get the midpoint P as (-5.5,3.5).

The slope of XY is (3-4)/(-9+2)=-1/7, so the slope of the perpendicular bisector is 7. Therefore, the equation of the perpendicular bisector is y-3.5=7(x+5.5). Solving for y, we get y=7x+49.5. Since this line passes through the origin (0,0), the line of reflection is y=x.

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Answer:

The volume of a cylinder can be calculated using the formula:

V = πr^2h

Where r is the radius and h is the height. In this case, the volume is 500 ml, or 0.5 liters. To convert liters to cm, we can use the conversion factor 1 liter = 10 cm^3. Therefore, the height of the jug can be calculated as follows:

0.5 liters = 0.5 x 10 cm^3 = 500 cm^3

V = πr^2h

500 = π x (3 cm)^2 x h

h = 500 / (π x (3 cm)^2)

Approximating π as 3.14, we get:

h = 500 / (3.14 x (3 cm)^2)

h = 500 / (3.14 x 9 cm^2)

h = 500 / 28.26 cm^2

h = 17.67 cm

So the height of the cylindrical measuring jug is approximately 17.67 cm. Therefore, the distance between each marking, which represents 100 ml of volume, is 17.67 cm / 5 = 3.534 cm.

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

To determine the distance between each of the markings, we need to determine the height of the jug for each 100 ml increment.

The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height. We know the volume of the jug is 500 ml, or 0.5 liters, and the radius is 3 cm, so we can solve for the height:

0.5 liters = π * (3 cm)^2 * h

h = 0.5 liters / π * (3 cm)^2

h = 0.5 liters / 9π cm^2

Now that we have the height of the jug per 100 ml, we can divide it by 5 to determine the height between each marking:

Marking height = h / 5

= 0.5 liters / 9π cm^2 / 5

= 0.1 liters / 9π cm^2

So the distance between each of the markings is the height of the jug for each 100 ml increment divided by 5.