In 8 days the radioactivity of 1 mg of an element decreases to 4%. what is the half-life of the element in days? round your answer to the nearest hundredth.

eighteen fahrwnheit    

goodluck :)

Answer:

22 degrees celsius turns to 71.6 into fahrenheit.

The solution is Option A.

The translation of the center of circle is given by ( x , y ) ⟶ ( x - 15 , y + 1 )

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

Given data ,

Let the equation for the circle A be represented as

( x - 7 )² + ( y - 1 )² = 16

Now , the equation is of the form ( x - h )² + ( y - k )² = r²

So , the radius of the circle is 4 and the center of the circle is ( 7 , 1 )

Let the equation for the circle A be represented as

( x + 8 )² + ( y - 2 )² = 16

Now , the equation is of the form ( x - h )² + ( y - k )² = r²

So , the radius of the circle is 4 and the center of the circle is ( -8 , 2 )

So , the translation of circle A to B is given by

( 7 , 1 ) to ( -8 , 2 )

So , the x coordinate is translated by 15 units to left and the y coordinate is translated by 1 unit up

Hence , the translation is given by ( x , y ) ⟶ ( x - 15 , y + 1 )

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Answer:

10^8 pennies in a million dollars.

Step-by-step explanation:

I will work with the accepted number of pennies in a dollar:  100.

Then the number of pennies in a million dollars is

p = 100*10^6, or 1*10^8,  or just 10^8.

Answer:

D.

Step-by-step explanation:

By calculation (I used a calculator for this one):

Therefore, the answer is D.

Answer:

Point-slope is the general form y-y₁=m(x-x₁) for linear equations. It emphasizes the slope of the line and a point on the line (that is not the y-intercept).

Step-by-step explanation:

Answer: y - 2 = -6/5(x - 0)

You use the equation (y - y1) = m(x - x1)

Where y1 and x1 are coordinates of a point on the equation.

If the y intercept is 2, then the point (0, 2) is on the equation.

Answer:

11 in = 33 in.

Step-by-step explanation:

6 in. = 18 in.

the second triangle is 3 times bigger than the smaller one.

Answer:

26 inches long.

Step-by-step explanation:

5/1 is just 5 and 5 1/5 is 5.2 and you just multiply 5.2 by 5 :5.2x5=26.0

The value of tan(t−π) is 4/9.

According to the statement

we have given that  tan(t)=4/9 and we have to find the value of tan(t−π).

So,

tan(t−π)  -(1)

take negative sign common from equation (1) it then

tan(t−π) = -tan(-t+π)

and we know that the according to the mathematics formula it become

tan(-t+π) is -tan t

then

tan(t−π) = -(-tan t)

it becomes

tan(t−π) = tan t

then its value becomes

tan(t−π) = tan(t)=4/9.

because we have given that the value of tan t is tan(t)=4/9.

So, The value of tan(t−π) is 4/9.

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To solve for the Marshallian demands x1(p1, p2, m) and x2(p1, p2, m) in the consumer problem with utility function U(x1, x2) = min{x1, ax2}, we need to maximize the utility subject to the budget constraint p1x1 + p2x2 ≤ m, where p1 and p2 are the prices of goods 1 and 2 respectively, and m is the consumer's income.

To find the Marshallian demands, we need to solve the consumer's optimization problem. The objective is to maximize the utility function U(x1, x2) = min{x1, ax2} subject to the budget constraint p1x1 + p2x2 ≤ m.

The first step is to set up the Lagrangian function:

L(x1, x2, λ) = min{x1, ax2} + λ(m - p1x1 - p2x2)

Next, we take the first-order conditions by differentiating the Lagrangian with respect to x1, x2, and λ, and setting the derivatives equal to zero. This will give us the equations for the optimal values of x1, x2, and the Lagrange multiplier λ.

By solving these equations, we can find the specific values for x1(p1, p2, m) and x2(p1, p2, m) that maximize the utility function while satisfying the budget constraint. The resulting demands will depend on the prices (p1, p2) and the consumer's income (m).

Note that the specific calculations involved in solving the optimization problem can be quite involved and may require further mathematical manipulation.

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Using Algebra operation,

the total revenue from ticket sales on that day is $ 3444..

We have given the following information,

timing of museum for entry is 9:00 am to 5:55pm. i.e 8 hours 55 minutes .

price of ticket for a regular admission= $10

price of ticket for a student admission = $6

30 people's admission in every 5 minutes so,

inclusive there are 9×12=108 five-minute intervals, total of tickets were sold = 108× 30

= 3240

let x student and 3x regular tickets were sold on that day.

then, x+3x= 108× 30 –> x= 3240/4 = 810

put x= 7560 in above formula, for regular admission, 3x=3× 81 = 243

So, the total revenue from ticket sales that day was 243×$10 + 810×$6 = $2430 + $4860

= $7290

Hence, total revenue from tickect sales is $7290.

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Answer:

30.

Step-by-step explanation:

first term = a

3r term = ar^2

So here ar^2/ a  = r^2

r^2 = 5/180 = 1/36

r = 1/6

So missing term = 180 * 1/6 = 30.

A regular polygon is a polygon with all sides and angles congruent. It exhibits symmetry and uniformity in its sides and angles, creating a visually appealing shape.

A polygon with all sides and angles congruent is called a regular polygon. In a regular polygon, all sides have the same length, and all angles have the same measure. This uniformity in the lengths and angles of the polygon's sides and angles gives it a symmetrical and balanced appearance.

Regular polygons are named based on the number of sides they have. Some common examples include the equilateral triangle (3 sides), square (4 sides), pentagon (5 sides), hexagon (6 sides), and so on. The names of regular polygons are derived from Greek or Latin numerical prefixes.

In a regular polygon, each interior angle has the same measure, which can be calculated using the formula:

Interior angle measure = (n-2) * 180 / n

Where n represents the number of sides of the polygon.

The sum of the interior angles of any polygon is given by the formula:

Sum of interior angles = (n-2) * 180 degrees

Regular polygons have several interesting properties. For instance, the

exterior angles of a regular polygon sum up to 360 degrees, and the measure of each exterior angle can be calculated by dividing 360 degrees by the number of sides.

Regular polygons often possess symmetrical properties and are aesthetically pleasing. They are commonly used in design, architecture, and various mathematical applications.

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Answer:

70t = 60t + 10

10t = 10

t = 1 hour

----------

1 hour  70 mi/hr = 70 miles

Step-by-step explanation:

After 14 months after the first month would the sales reach $9000

For given question,

A Hammer Hardware has sales of $5000 in its first month.

The sales were to increase by 4% every month.

We need to find the number of months after the first month would the sales reach $9000

Let the exponential function for sales is,

f(n)= a (1 + r)^{n}

where, n is the number of months

a is the sales of the first month

r is the rate of increment

So, a = $5000, r = 0.04, f(n) = $9000

Substitute values in above equation.

⇒ 9000 = 5000 × (1 + 0.04)^{n}

Solve above equation for n.

⇒ 1.8 = (1.04)^n

⇒ n = \(log_{1.04}^{(1.8)}\)

⇒ n = 14.9

⇒ n ≈ 15

Therefore, after 14 months after the first month would the sales reach $9000

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To evaluate the line integral ∮C F · dr using Green's theorem, we need to confirm the orientation of the curve C and apply the appropriate sign. Therefore, ∮C F · dr = -8 - 8π.

Given the vector field F(x, y) = ⟨y - cos(y), x sin(y)⟩ and the curve equation \((x - 4)^2 + (y + 9)^2 = 16\), let's proceed with the evaluation.

1. Orientation of Curve C:

To determine the orientation, we can parametrize the curve equation. Let's use the parameterization:

x = 4 + 4cos(t)

y = -9 + 4sin(t)

By analyzing the parameterization, we find that the curve C is oriented counterclockwise as t varies from 0 to 2π.

2. Green's Theorem:

Green's theorem states that ∮C F · dr = ∬D (∂Q/∂x - ∂P/∂y) dA, where D is the region enclosed by the curve C, F = (P, Q) is the vector field, and dr = (dx, dy) is the differential displacement vector.

3. Apply Green's Theorem:

Let's compute the double integral of (∂Q/∂x - ∂P/∂y) over the region D.

∬D (∂Q/∂x - ∂P/∂y) dA = ∬D ((∂/∂x)(x sin(y)) - (∂/∂y)(y - cos(y))) dA

4. Evaluate the Double Integral:

Integrate (∂/∂x)(x sin(y)) and (∂/∂y)(y - cos(y)) with respect to x and y over the region D.

∬D (∂Q/∂x - ∂P/∂y) dA = ∫(0 to 2π) ∫(0 to 4) (sin(y) - 1) dx dy

Evaluate the inner integral:

= ∫(0 to 2π) [x sin(y) - x] |(0 to 4) dy

= ∫(0 to 2π) (4sin(y) - 4) dy

Evaluate the outer integral:

= [-4cos(y) - 4y] |(0 to 2π)

= [-4cos(2π) - 4(2π)] - [-4cos(0) - 4(0)]

Simplifying, we get:

= [-4 - 8π] - [-4]

= -8 - 8π

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use green’s theorem to evaluate yc f dr. (check the orientation of the curve before applying the theorem. \(F(x, y) &= \langle y - \cos(y), x \sin(y) \rangle\) C is a circle \((x - 4)^2 + (y + 9)^2 &= 16\) oriented counterclockwise.

Answer:

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

Put the data in an ascending order:

There are 7 numbers.

With odd number of data, the middle number is the median. Hence the median is 6.

The median of the given series of numbers is 6, after arranging them in ascending order.

The student wants to find the median of a series of numbers: 8 6 9 2 5 3 7. First, arrange these numbers in ascending order, this becomes: 2, 3, 5, 6, 7, 8, 9. The median is the middle number in an ordered set of numbers. In our case, since there are 7 numbers, the median is the fourth number, which here is 6. Therefore, the median of these numbers is 6.

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Answer:

The answer is 10.

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

When a number is next to another number number, that means that you have to multiply the two numbers

-5 x -2

-5 x -2 is 10

This 10 is positive because when two negatives are multiplied, the solution will be positive.  

so

-5 x -2 = 10

Hope this helps : )

Answer:

\(D.\ 7 \frac{3}{4} * \frac{\sqrt{16} }{5} = \frac{31}{4} * \frac{4}{5} = \frac{31}{5} \\\\C. \ 7 \frac{3}{4} + \frac{\sqrt{16} }{5} =\frac{31}{4} + \frac{4}{5} = \frac{171}{20}\)

Answer:

14x-21=14x +7

x cancels all out which leaves with just

28

Answer:

There is no x that satisfies the condition.

Step-by-step explanation:

7(2x - 3) = 14x + 7

14x - 21 = 14x + 7

-21 = 7

contradiction

Therefore, the inverse Laplace transform of the potential function \(\( H(s) \) is:\( h(t) = 20e^{(-200 + 3090i)t} + 20e^{(-200 - 3090i)t} \)\)

Step 1: Factorize the denominator of \(\( H(s) \):The denominator \( s^2 + 400s + 6290000 \)\) cannot be factored further, so we move to the next step.

Step 2: Express\(\( H(s) \) using partial fractions:\( H(s) = \frac{A}{s - s_1} + \frac{B}{s - s_2} \)\)

To find A and B, we need to solve for the values of s_1 and s_2, which are the roots of the denominator equation \(\( s^2 + 400s + 6290000 = 0 \)\).

Using the quadratic formula, we find that the roots are complex:\(\( s_1 = -200 + 3090i \) and \( s_2 = -200 - 3090i \).\)

Step 3: Substitute the values of s_1 and s_2 into the partial fraction decomposition:

\(\( H(s) = \frac{A}{s - (-200 + 3090i)} + \frac{B}{s - (-200 - 3090i)} \)\)

Step 4: Find the values of A and B:

We multiply both sides of the equation by the denominator to eliminate the fractions and then substitute the values of s_1 and s_2:

\(\( 40(s+200) = A(s - (-200 - 3090i)) + B(s - (-200 + 3090i)) \)\)

Simplifying the equation, we get:

\(\( 40s + 8000 = As + A(-200 + 3090i) + Bs + B(-200 - 3090i) \)\)

Matching the coefficients of like terms, we get the following system of equations:

\(\( A + B = 40 \)\( A(-200 + 3090i) + B(-200 - 3090i) = 8000 \)\)

Solving this system of equations, we find that A = 20 and B = 20.

Step 5: Write the partial fraction decomposition:

\(\( H(s) = \frac{20}{s - (-200 + 3090i)} + \frac{20}{s - (-200 - 3090i)} \)\)

Step 6: Find the inverse Laplace transform using lookup tables:

The inverse Laplace transform of each term can be looked up in the Laplace transform table. The inverse Laplace transform of \(\( \frac{20}{s - (-200 + 3090i)} \) is \( 20e^{(-200 + 3090i)t} \), and the inverse Laplace transform of \( \frac{20}{s - (-200 - 3090i)} \) is \( 20e^{(-200 - 3090i)t} \).\)

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Measures which examine the spread of different values around the measures of central tendency is measures of variability.

A central tendency in statistics is a typical or characteristic value for a probability distribution. Measures of central tendency are commonly referred to as averages in everyday speech. In the late 1920s, the phrase "central tendency" first appeared. The arithmetic mean, the median, and the mode are the three most popular ways to measure central tendency. The number used to represent the center or middle of a set of data values is known as the central tendency measure.

Given,

Measures which examine the spread of different values around the measures of central tendency:

B. Measures of variability

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The fraction that's left to read in the book is 3/8.

From the information given, it should be noted that Tim has 5/10 of a book left to read for school. Tim read 1/8 of a book on Monday.

Therefore, the fraction that will be left to read will be:

= 5/10 - (1/8)

= 20/40 - 5/40

= 15/40

= 3/8.

The fraction that is left will be 3/8.

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Answer:

200 Meters!

Step-by-step explanation:

Answer:

200 m

Step-by-step explanation:

Distance from Jason's house to school = 0.2 kilometers

Converting into metres

0.2 km = 0.2 * 1000 m = 200 m

Hope it will help :)

The observed value of z (test statistic) is greater than 1.96 (the test statistic does fall into the rejection region), so Reject H₀ .

p₁ = the proportion of the non-smoker population who reply "yes"

p₂ = the proportion of the smoker population who reply "yes," then we are interested in testing the null hypothesis

H₀:  p₁ = p₂

Alternate hypothesis:

Hₐ:  p₁≠p₂

That implies then that the test statistic for testing:

H₀ : p1 = p2

Hₐ : p1 ≠ p2.                              (Two – tailed)

n1 = 605, y1 = 351

p1 = y1 / n1

= 351/605

≈ 0.58

n2 = 195, y2 = 41.

p2 = y2/n2

= 41 / 195

≈0.21

p = y1 + y2 / n1 + n2

= 351 + 41 / 605 + 195

= 392 / 800

= 0.49

The test statistic is

\(z = \frac{p1 - p2}{\sqrt{p(1-p). (\frac{1}{n1}}+ \frac{1}{n2} ) } }\)

z = \(\frac{0.58 - 0.21}\sqrt{{0.49 . 0.51 (\frac{1}{605} + \frac{1}{195} )} }\)    

= 8.988

critical region for α = 0.01

z = 2.576

The observed value of z (test statistic) is greater than 1.96 (the test statistic does fall into the rejection region),

so Reject H₀ .

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The binomial probabilities directly from the formula for b(x; n, p) can be compute as follows:

(a) b(5; 8, 0.35) is 0.278

(b) b(6; 8, 0.6) is 0.311

(c) P(3 ? X ? 5) when n = 7 and p = 0.55 is 0.609

(d) P(1 ? X) when n = 9 and p = 0.1 is  0.613

Binomial probability distribution is used to calculate the probability of getting a certain number of successes in a fixed number of trials, where each trial has only two possible outcomes: success or failure. The formula for calculating the binomial probability is:

b(x; n, p) = (nCx) * p^x * (1-p)^(n-x)

where x is the number of successes, n is the total number of trials, p is the probability of success in each trial, and nCx is the number of combinations of n things taken x at a time.

In part (a), we are asked to find the probability of getting exactly 5 successes in 8 trials with a probability of success of 0.35. Using the formula, we get:

b(5; 8, 0.35) = (8C5) * 0.35^5 * (1-0.35)^(8-5) = 0.278

In part (b), we are asked to find the probability of getting exactly 6 successes in 8 trials with a probability of success of 0.6. Using the formula, we get:

b(6; 8, 0.6) = (8C6) * 0.6^6 * (1-0.6)^(8-6) = 0.311

In part (c), we are asked to find the probability of getting between 3 and 5 successes in 7 trials with a probability of success of 0.55. We can find this probability by summing the individual probabilities of getting 3, 4, and 5 successes. Using the formula, we get:

P(3 ≤ X ≤ 5) = b(3; 7, 0.55) + b(4; 7, 0.55) + b(5; 7, 0.55) = 0.609

In part (d), we are asked to find the probability of getting at least 1 success in 9 trials with a probability of success of 0.1. We can find this probability by subtracting the probability of getting 0 successes from 1. Using the formula, we get:

P(X ≥ 1) = 1 - b(0; 9, 0.1) = 1 - 0.387 = 0.613

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