The mass of a radioactive substance is given by the function M(t) = 12(0.5)^(t/138), where t is the initial mass of polonium, in milligrams, and M (t) is the mass, in milligrams, after t days. At what rate is the polonium decaying when a sample has decayed to 25% of its initial mass? Round to 3 decimals.

The margin of error if we want a 90% confidence interval for the true population mean age is calculated to be 1.62 years, therefore option (a) is correct.

We can use the formula for the margin of error:

Margin of error = z × (σ / √(n))

where z is the z-score for the desired level of confidence, σ is the population standard deviation, and n is the sample size.

For a 90% confidence interval, the z-score is 1.645. Substituting the given values, we get:

Margin of error = 1.645 × (9.84 / √(100)) = 1.62

Therefore, the margin of error is 1.62 years, which is option (a).

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Answer:

4 and 1/8

Step-by-step explanation:

1 and 3/8 is equivalent to 11/8 which is one lap. If she ran 3 laps, you would multiply 11/8 by 3 which would get you 33/8- which is equivalent to 4 and 1/8.

Answer:

The answer is not -1/2

Step-by-step explanation:

I got the answer from the person above and the answer is not -1/2 so do not believe them.

Answer:

$758 per week

Step-by-step explanation:

15.16 x 50 = 758

Answer:$758 per week

Step-by-step explanation:Answer:15.16 x 50 = 758

The statement that shows equivalent measurements is "52 meters = 520 decimeters." Option C.

To determine the equivalent measurements, we need to understand the relationship between different metric units.

In the metric system, each unit is related to others by factors of 10, where prefixes indicate the magnitude. For example, "deci-" represents one-tenth (1/10), "centi-" represents one-hundredth (1/100), and "kilo-" represents one thousand (1,000).

Let's analyze each statement:

5.2 meters = 0.52 centimeters: This statement is incorrect. One meter is equal to 100 centimeters, so 5.2 meters would be equal to 520 centimeters, not 0.52 centimeters.

5.2 meters = 52 decameters: This statement is incorrect. "Deca-" represents ten, so 52 decameters would be equal to 520 meters, not 5.2 meters.

52 meters = 520 decimeters: This statement is correct. "Deci-" represents one-tenth, so 520 decimeters is equal to 52 meters.

5.2 meters = 5,200 kilometers: This statement is incorrect. "Kilo-" represents one thousand, so 5.2 kilometers would be equal to 5,200 meters, not 5.2 meters.

Based on the analysis, the statement "52 meters = 520 decimeters" shows equivalent measurements. So Option C is correct.

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Note the correct and the complete question is

Select the statement that shows equivalent measurements.

A.) 5.2 meters = 0.52 centimeters

B.) 5.2 meters = 52 decameters

C.) 52 meters = 520 decimeters

D.) 5.2 meters = 5,200 kilometers

False. The margin of error only accounts for sampling variability (the fact that my sample will be different that many other people's and therefore provide different statistics.

Statistics is a technique for interpreting, analyzing, and summarizing data in mathematics. In light of these characteristics, the various statistical types are divided into: Statistics that are descriptive and inferential. We analyze and understand data based on how it is presented, such as through graphs, bar graphs, or tables.

Inferential statistics, which draws conclusions from information using statistical tests like the student's t-test, is one of the two main statistical methods used in data analysis. Descriptive statistics presents data using indices like mean and median.

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Statement which is correctly identifies the local minimum of the graphed function is given by over the interval \([-1,0.5],\) the local minimum is \(1\).

" Graph is defined as the pictorial representation of the relation between the given variables on the coordinate plane along x-axis and y-axis."

According to the question,

Form the given graph of the function local minimum is given by

a. Over the interval \([-3, -2]\), the local minimum is \(0\):

From the graph value of y coordinate at \(x= -3\) is closest to \(-6\). As per given statement local minimum is zero . \(-6 < 0\)

At \(-2\) closest to \(1\) , \(1 > 0\)

Therefore , local minimum \(=0\)  is not a correct option.

b.  Over the interval\([-2, -1]\), the local minimum is \(2.2.\)

From the graph at \(-2\) closest to \(1\) , \(1 \neq 2.2\).

Moving from \(-2\) to \(-1\) graph is increasing . At \(-1\) y - coordinate is equals to \(2\).

Again \(2\neq 2.2\)

Therefore, it is not a correct option.

c.  Over the interval\([-1, 0.5]\), the local minimum is \(1\)

From the graph at \(-1\) closest to \(2\) ,and keep on decreasing till \(x=0\) .

From \(0\) to \(0.5\) graph keep on increasing.

At \(x= 0\) value of y-coordinate is equals to \(1\) , which represents the local minimum at \(x= 0\) which is in the interval \([ -1, 0.5]\)

At \(x= -1\) y- coordinate is equals to \(2\)

At  \(x= 0.5\) y- coordinate is equals to \(2\)

Local minimum \(= 1\) at \(x=0\)

Therefore, it is a correct option.

d. Over the interval \([0.5, 2],\) the local minimum is \(4.\)

In the given interval graph keeps on increasing \(1\) to \(4\) and so on.

It is not a correct option.

Hence, statement which is correctly identifies the local minimum of the graphed function is given by over the interval \([-1,0.5],\) the local minimum is \(1\).

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To solve this problem, we can use the binomial probability formula:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

Where:
- P(X=k) is the probability of getting k nonconforming washing machines in the sample
- n is the sample size, which is 10 in this case
- p is the probability of getting a nonconforming washing machine, which is 0.08
- (n choose k) is the binomial coefficient, which is the number of ways to choose k items from n without replacement, and is calculated as n! / (k! * (n-k)!)

So, to find the probability of getting 1 nonconforming washing machine in the sample, we plug in k=1:

P(X=1) = (10 choose 1) * 0.08^1 * (1-0.08)^(10-1)
P(X=1) = 10 * 0.08 * 0.9227
P(X=1) = 0.0738

Therefore, the probability of getting 1 nonconforming washing machine in the sample is approximately 0.0738, or 7.38%.

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Answer:

24 miles

Step-by-step explanation:

3x is the miles from downstream

4 (x - 1) is the return trip

Solution:

3x = 4 (x - 1)

3x =4x - 4

-x = -4

x = 4

The outward journey 3x = 12 miles

Return journey is same length

Therefore the distance travel is 24 miles

The equation that Amy can use to find how many games of Balloon Bouncer, g, she played is; g = (35 - 2a)/3

We are told that Amy used her first 2 tokens at Glimmer Arcade to play a game of Roll-and-Score.

Balloon Bouncer costs 3 tokens per game, and Amy started with a bucket of 35 game tokens.

Thus, the expression for the number of balloon bouncer games played at the arcade is :

2a + 3g = 35

Let :

Glimmer arcade, a = $2 per game

Balloon bouncer, g = $3 per game

Total game tokens = 35

Her spending could be represented using the expression :

2a + 3g = 35  

g = number of balloon bouncer games played

Thus, making g the subject of the formula we have;

g = (35 - 2a)/3

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Answer:

3g + 2 = 35 is the answer.

She played 11 games.

Step-by-step explanation:

Answer:

There are 48 pages in the whole book.

Step-by-step explanation:

We know that 36 is 3/4 of the book. To find the total number of pages, we have to divide 36 by 3. We know that is 12. Then, we have to multiply 12 by 4 to get the answer, 48.

Answer:

69

Step-by-step explanation:

92 * 3/4 is equal to 69.

The house was in the shape of an octagon, with eight separate bedrooms on each side.

The house described in the statement has an octagonal shape. An octagon is a polygon with eight sides, characterized by its eight equal angles. In this case, each side of the house corresponds to one of these angles, resulting in eight separate bedrooms on each side of the octagonal structure.

The choice of an octagon as the shape of the house can have various implications. Octagonal buildings are often admired for their unique architectural design and aesthetic appeal. The shape provides symmetry and balance, allowing for an interesting and visually pleasing structure. Additionally, an octagonal layout can offer practical advantages in terms of space utilization and room distribution. In the case of the house described, each side of the octagon accommodates a separate bedroom, providing privacy and ample living space for its occupants. The symmetrical arrangement of the bedrooms around the central area of the house could create a harmonious and well-organized living environment. Overall, the octagonal shape of the house with eight separate bedrooms on each side offers both architectural and functional benefits.

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Thus, the value of y for the given direct variation is found as y = 34.96 (Rounded up to two decimal places).

When two quantities, including such time and distance or hours and compensation, change directly, they do so at a predictable rate.

The constant of variation is another name for the constant rate of increase or decline. We will examine three different methods of showing direct variation in this lesson: an equation, a table, and just a graph.

For the given question:

y varies directly as the square root of x.

y ∝ √x

y = k√x  

Here, k is the constant of proportionality

Now,

y=43 when x=289 .

43 = k√289

k = 43/√289

k = 2.53

Now, y when  x=191.

y = k√x  

y = 2.53√191

y = 34.96

Thus, the value of y for the given direct variation is found as y = 34.96 (Rounded up to two decimal places).

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The length of the garden is 99 m.

The formula for the area of a rectangle is:

Area = Length x Width

We are given that the area of the rectangle is 8811 \(m^{2}\) and the width is 89 m. Substituting these values into the formula, we get:

8811 \(m^{2}\) = Length x 89 m

To solve for the length, we can divide both sides of the equation by 89 m:

Length = 8811 \(m^{2}\) / 89 m

Simplifying, we get:

Length = 99 m

Therefore, the length of the garden is 99 m.

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to G H I would be 2x2x3.

Answer: 7/8

Step-by-step explanation: First you have to multiple 3/4 by 2 so it would be 6/8 and then add it to the 1/8 and it'll be 7/8 correct me if I'm wrong.

Answer:

The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set.

a. One possible curve C1 is a line segment from (0,0) to (π/2,0), given by r(t) = <t, 0>, 0 ≤ t ≤ π/2. One possible curve C2 is the line segment from (0,0) to (0,-14π), given by r(t) = <0, -14πt>, 0 ≤ t ≤ 1.

a) We have F = ∇f = <∂f/∂x, ∂f/∂y>.

So, F(x, y) = <cos(x-7y), -7cos(x-7y)>.

To find a curve C1 such that F · dr = 0, we need to solve the line integral:

∫C1 F · dr = 0

Using Green's Theorem, we have:

∫C1 F · dr = ∬R (∂Q/∂x - ∂P/∂y) dA

where P = cos(x-7y) and Q = -7cos(x-7y).

Taking partial derivatives:

∂Q/∂x = -7sin(x-7y) and ∂P/∂y = 7sin(x-7y)

So,

∫C1 F · dr = ∬R (-7sin(x-7y) - 7sin(x-7y)) dA = 0

This means that the curve C1 can be any curve that starts and ends at the same point, since the integral of F · dr over a closed curve is always zero.

One possible curve C1 is a line segment from (0,0) to (π/2,0), given by:

r(t) = <t, 0>, 0 ≤ t ≤ π/2.

b) To find a curve C2 such that F · dr = 1, we need to solve the line integral:

∫C2 F · dr = 1

Using Green's Theorem as before, we have:

∫C2 F · dr = ∬R (-7sin(x-7y) - 7sin(x-7y)) dA = -14π

So,

∫C2 F · dr = -14π

This means that the curve C2 must have a line integral of -14π. One possible curve C2 is the line segment from (0,0) to (0,-14π), given by:

r(t) = <0, -14πt>, 0 ≤ t ≤ 1.

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The total number of seeds that Josiah would plant would be = nR×S

To determine the total number of seeds that Josiah will plant will be to add the seeds in the total number of rooms he planted.

Let each row be represented as = nR

Where n represents the number of rows planted by him.

Let the seed be represented as = S

The total number of seeds he planted = nR×S

Therefore, the total number of seeds that was planted Josiah would be = nR×S.

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a). The power efficiency is 99.7%.b). The modulation index is 10. c. The average message power is 50 W. d. The power efficiency is 99.7%.

The given AM signal is bobo

PAM(t) = (3 + 2 cos( 21fmt)] cos(21fct)

a. Modulating signal

The message signal is the term inside the cosine. Thus, the modulating signal ism(t) = 3 + 2 cos( 21fmt)

b. Modulation index

The modulation index is the ratio of the amplitude of the modulating signal to the amplitude of the carrier wave. Thus, the modulation index ism = (amplitude of m(t))/(amplitude of c(t))

Let's calculate the amplitude of the modulating signal. The maximum amplitude of cos (21 fmt) is 1.

Therefore, the maximum amplitude of m(t) is 3 + 2 = 5 V.

Let's calculate the amplitude of the carrier wave. The amplitude of cos(21 fct) is 1/2.

Therefore, the amplitude of the carrier wave is

Ac = (1/2) V.

Substituting the above values in the formula for modulation index, we get

m = 5/(1/2) = 10

Therefore, the modulation index is 10.

c. Average message power

The average message power is given by

Pm = (A^2m)/2

Where Am is the amplitude of the modulating signal.

We have already calculated Am in the previous step. Thus, substituting the above value of Am, we get

Pm = (10^2)/2 = 50 W.d.

Power efficiency

The total power of the AM signal is the sum of the carrier power and the message power.

Thus

,Pt = Pc + Pm

We need to calculate the power efficiency, which is the ratio of the message power to the total power of the signal. Thus, we need to calculate Pt.

Substituting the values in the expression for the AM signal,

we get bobo PAM(t) = (3 + 2 cos( 21fmt)] cos(21fct)

We can rewrite the above expression as bobo

PAM(t) = 3 cos(21fct) + cos(21fct) 2 cos( 21fmt)

Let's assume that the frequency of the carrier wave is fc = 100 kHz.

Therefore, the frequency of the modulating signal is fm = 4.76 kHz.

We can find the bandwidth of the signal as

B = 2 fm = 2 x 4.76 = 9.52 kHz.

The value of fe is much greater than the bandwidth of the signal. Therefore, we can assume that the envelope of the signal will be identical to the carrier wave envelope.

Therefore, the total power of the signal is the carrier power.

We know that the amplitude of cos (21 fct) is 1/2. Therefore, the amplitude of the carrier wave isAc = (1/2) V.

The carrier power isPc = (A^2c)/2

Where Ac is the amplitude of the carrier wave.

Substituting the above values, we get

Pc = (1/2)^2/2 = 0.125 W

Thus, the total power of the signal is

Pt = Pc + Pm = 0.125 + 50 = 50.125 W

Therefore, the power efficiency is

Pm/Pt = 50/50.125 = 0.997 or 99.7%.

Therefore, the power efficiency is 99.7%.

The modulation index is 10.c. The average message power is 50 W.d. The power efficiency is 99.7%.

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The  examples that would constitute a discrete random variable are;

I. Total number of points scored in a football game

III. Number of near collisions of aircraft in a year

A discrete random variable has only a countable number of different values that it can assume. Usually, but not always, discrete random variables are counts. A random variable is discrete if it can only take a finite number of different values. A variable whose value is determined by counting is referred to as a discrete variable.

A continuous variable is one whose value may be determined through measurement. A random variable is a variable whose value is the resultant number of an unpredictable event.

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Answer:

6/21

Step-by-step explanation:

Brainliest?

Answer:

2/7=6/21

Step-by-step explanation:

well uh, if you multiply the denominator which is 7 by 3 you get 21 so doing the same thing to the numerator (2*3) will result in the correct answer

Answer:

n = 23

Step-by-step explanation:

Let Sara's number be n.  Then -3(n - 11) = -36

Solve for n - 11 by dividing both sides by -3:  n - 11 = 12.

Adding 11 to both sides yields n = 23

Answer:

i believe that the correct answer is -1

The approximate air pressure at the center of a hurricane is 910 millibars.

Given,

The mean sustained wind velocity equation, v = 6.3 × √(1013 - p)

p is the air pressure in millibars

The mean sustained wind velocity - 64 meters per second.

We have to find the approximate air pressure.

Here,

The equation for wind velocity ;

v = 6.3 × √(1013 - p)

v is given 64

Then substitute;

64 = 6.3 × √1013 - p

64/6.3 = √1013 - p

10.16 = √1013 - p

Square both sides

(10.16)² = (√1013 - p)²

We get,

103.23 = 1013 - p

p = 1013 - 103.33 = 909.67 ≈ 910 millibars

That is,

The approximate air pressure at the center of a hurricane is 910 millibars.

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The rate of flow outward through the slant surface of the tetrahedron is 18e z + 9.

The rate of flow outward through the slant surface of the tetrahedron can be found using the divergence theorem. The divergence theorem states that the outward flux of a vector field through a closed surface is equal to the volume integral of the divergence of the vector field over the volume enclosed by the surface. In this case, we can use the divergence theorem to find the rate of flow without evaluating any integrals.
To begin, let's calculate the divergence of the given vector field ⟨ x e z , − y e z , z ⟩. The divergence of a vector field in three dimensions is defined as the sum of the partial derivatives of each component with respect to its corresponding variable. In this case, the divergence of the vector field is:
div(⟨ x e z , − y e z , z ⟩) = ∂/∂x (x e z) + ∂/∂y (-y e z) + ∂/∂z (z)
= e z + e z + 1
= 2e z + 1
Now, since the tetrahedron has only one face that is not parallel to any of the coordinate planes, we can consider this face as our closed surface. The outward flux through this surface is equal to the volume integral of the divergence of the vector field over the volume enclosed by the surface.
Since the vertices of the tetrahedron are at the origin and (3,0,0), (0,3,0), and (0,0,3), we can see that the tetrahedron is a regular tetrahedron with side length 3.
Therefore, the volume of the tetrahedron is (1/3) * (base area) * (height) = (1/3) * (3 * 3) * 3 = 9.
Now, the rate of flow outward through the slant surface can be calculated as the volume integral of the divergence of the vector field over the volume enclosed by the surface:
Rate of flow = (2e z + 1) * (volume of tetrahedron)
= (2e z + 1) * 9
= 18e z + 9
So, the rate of flow outward through the slant surface of the tetrahedron is 18e z + 9.

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Answer:

Step-by-step explanation:

There is one value 9 which is a lot less than the rest of the values.

I would the median is the best.

Answer:

Step-by-step explanation:

x^2 + 3x + 2 = (x+1)(x+2)

x^2 + 4x + 3 = (x+1)(x+3)

LCM = (x+1)(x+2)(x+3) = (x^2 + 3x + 2) (x+3) = x^3 + 6x^2 + 11x + 6

Step-by-step explanation:

1st expression

x2 + 3x + 2

x²+2x+x+2

x(x+2)+1(x+2)

(x+2)(x+1)

2nd expression

x2 + 4x + 3

x²+3x+x+3

x(x+3)+1(x+3)

(x+3)(x+1)

L.C.M=(x+1)(x+2)(x+3)

(a) P(Ac) = 6/10

(b) P(A∪B) = 7/10

(c) P(A|B) = 2/5

(d) P(B|A) = 2/4

(e) P(B|Ac) = 3/6

(f) A and B are not independent since P(A∩B) ≠ P(A) * P(B).

(g) A and B are not mutually exclusive since P(A∩B) ≠ 0.

(a) To find the complement of event A, we subtract the probability of A from 1: P(Ac) = 1 - P(A) = 1 - 4/10 = 6/10.

(b) To find the union of events A and B, we sum their probabilities and subtract the probability of their intersection: P(A∪B) = P(A) + P(B) - P(AB) = 4/10 + 5/10 - 2/10 = 7/10.

(c) To find the conditional probability of A given B, we use the formula P(A|B) = P(A∩B) / P(B) = (2/10) / (5/10) = 2/5.

(d) To find the conditional probability of B given A, we use the formula P(B|A) = P(A∩B) / P(A) = (2/10) / (4/10) = 2/4 = 1/2.

(e) To find the conditional probability of B given Ac (complement of A), we use the formula P(B|Ac) = P(Ac∩B) / P(Ac). Since A and B are mutually exclusive, P(Ac∩B) = 0. Therefore, P(B|Ac) = 0 / (6/10) = 0.

(f) A and B are not independent because P(A∩B) = 2/10 ≠ (4/10) * (5/10) = 2/25.

(g) A and B are not mutually exclusive because P(A∩B) = 2/10 ≠ 0. Mutually exclusive events cannot occur together, but in this case, there is a non-zero probability of their intersection.

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