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Answer:

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

After 3 half-lives the remaining amount becomes:

Convert 1/8 to percent:

two whose product is a trinomial is (x + 2)(x + 3) = x^2 + 5x + 6.

We are given two binomials: (x + 2) and (x + 3). To find their product, we need to multiply each term in the first binomial by each term in the second binomial. Let's go step by step:

Step 1: Multiply the first terms:

(x + 2) * (x + 3)

= x * x

= x^2

Step 2: Multiply the outer terms:

(x + 2) * (x + 3)

= x * 3

= 3x

Step 3: Multiply the inner terms:

(x + 2) * (x + 3)

= 2 * x

= 2x

Step 4: Multiply the last terms:

(x + 2) * (x + 3)

= 2 * 3

= 6

Step 5: Combine the like terms:

The terms 3x and 2x are like terms since they both have the variable x. To combine them, we add their coefficients:

3x + 2x

= 5x

Step 6: Write the resulting terms together:

Now, we put all the resulting terms together to form the trinomial:

x^2 + 5x + 6

Therefore, the product of (x + 2)(x + 3) is the trinomial x^2 + 5x + 6.

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The interval containing the middle 95% of the simulation data is approximately 0.3426 to 0.5374.

To create an interval containing the middle 95% of the data based on the simulation results, we can use the concept of confidence intervals. Since the simulation was repeated 100 times, we can calculate the proportion of tails in each set of 100 flips and then find the range that contains the middle 95% of these proportions.

Let's calculate the interval:

Calculate the proportion of tails in each set of 100 flips:

Proportion of tails = 44/100 = 0.44

Calculate the standard deviation of the proportions:

Standard deviation = sqrt[(0.44 * (1 - 0.44)) / 100] ≈ 0.0497

Calculate the margin of error:

Margin of error = 1.96 * standard deviation ≈ 1.96 * 0.0497 ≈ 0.0974

Calculate the lower and upper bounds of the interval:

Lower bound = proportion of tails - margin of error ≈ 0.44 - 0.0974 ≈ 0.3426

Upper bound = proportion of tails + margin of error ≈ 0.44 + 0.0974 ≈ 0.5374

Therefore, the interval containing the middle 95% of the simulation data is approximately 0.3426 to 0.5374.

Now, we can compare the observed proportion of 44 tails in 100 flips with the simulation results. If the observed proportion falls within the margin of error or within the calculated interval, then it can be considered consistent with the simulation results. If the observed proportion falls outside the interval, it suggests a deviation from the expected result.

Since the observed proportion of 44 tails in 100 flips is 0.44, and the proportion falls within the interval of 0.3426 to 0.5374, we can conclude that the observed proportion is within the margin of error of the simulation results. This means that the result of 44 tails in 100 flips is reasonably likely to occur with a fair coin based on the simulation.

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The average length of time for each missed appointment was 22 minutes, calculated by dividing the total of 25.3 hours of missed appointments by the 115 missed appointments.

25.3 hours / 115

= 0.21945652173913043

hours per missed appointment. 0.21945652173913043 hours per missed appointment x 60 minutes per hour

= 13.167

minutes per missed appointment. 13.167 minutes per missed appointment rounded up to the nearest minute is 22 minutes per missed appointment.The total of 25.3 hours of missed appointments from last month was divided by the 115 missed appointments to calculate the average length of time for each missed appointment. This calculation came to 0.21945652173913043 hours per missed appointment. To convert this figure to minutes, it was multiplied by 60 minutes per hour. This gave the result of 13.167 minutes per missed appointment. As 13.167 minutes was not a whole number, it was rounded up to the nearest minute, giving a total of 22 minutes per missed appointment.

1. 25.3 hours / 115 missed appointments

= 0.21945652173913043 hours per missed appointment

2. 0.21945652173913043 hours per missed appointment x 60 minutes per hour

= 13.167 minutes per missed appointment

3. 13.167 minutes per missed appointment rounded up to the nearest minute is 22 minutes per missed appointment

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Answer:

47 students in each bus

Step-by-step explanation:

243-8= 235

235/5=47

Answer:

Answer:

x = 30

Step-by-step explanation:

The problem is \(\frac{x}{5}\) = 6.  We need to end up with "x equals some number."  This is called solving for x.  In order to do this we need to have x by itself.  We look at the problem and ask, "what is preventing x from being by itself?"  In this case x has a "divided by 5" with it.  How can we get rid of that?  Well we can do the opposite of "divided by 5,"  and that is to multiply the left side by 5.  That leaves x by itself which is exactly what we need.  But if do something to one side of an equation, we need to do it to the other side for the equation to still be true.  So in this case we also have to multiply the right side by 5 also, which gives us 30 on the right side.  So in our original problem:

 \(\frac{x}{5}\)= 6

Multiply both sides by 5 and we have the answer:

x = 30

Answer:

1). 10  2). 8/5  3). 8

Step-by-step explanation:

I. f(2) = 3(2) + 4

= 6 + 4

= 10

II. f(4) = 3(4) - 4/5

= 12 - 4/5

= 8/5

III). 3y - 6 = y + 10

2y - 6 = 10

2y = 16

y = 8

For spinning the spinner one time A could be {1, 2, 3} or, A = {1, 2, 3, 4} is possible.

The set is mathematical model for a collectionof different things;a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables or even other sets.

The given spinner is divided into 8 equal sized sections, so the possible set can be written as-

S = {1, 2, 3, 4, 5, 6, 7, 8}

Now the possible subsets can be-

Even numbers = {1,3,5,7}

Odd numbers = {2,4,6,8}

Any number or group from 1 to 8, inclusive

Hence for spinner the spinner for one time, suppose A be the possible set. Then,

    A could be {1, 2, 3}.

or, A = {1, 2, 3, 4}.

where A is the subset of S.

Hence, For spinning the spinner one time A could be {1, 2, 3} or, A = {1, 2, 3, 4} is possible.

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Answer:

696 39/100 meters

Step-by-step explanation:

Ben needs to replace two sides of his fence. One side is 367 9/100 meters long, and the other is 329 3/10 meters long. How much fence does Ben need to buy?

Side A = 367 9/100 meters

Side B = 329 3/10 meters

How much fence does Ben need to buy?

Total fence Ben needs to buy = Side A + side B

= 367 9/100 + 329 3/10

= 36709/100 + 3293/10

= (36709+32930) / 100

= 69639/100

= 696 39/100 meters

Ben needs to buy 696 39/100 meters

Answer:

(4, –47)

Step-by-step explanations

I think this is the right answer but sorry if im wrong.

Answer:

Aubree can use 4.6 gigabytes of data while staying within her budget.

If the answer choices only use whole numbers, use 4 gigabytes, because it is the number of full gigabytes she can use.

Step-by-step explanation:

x= gigabyte

58.50 + 3x = 72.30

3x = 72.30-58.50

3x= 13.8

x= 4.6

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the formula for the rate of change

STEP 2: Write the given intervals

STEP 3: Find the average rate of change of f(x)

We substitute the coordinates into the rate of change formula:

STEP 4: Find the rate of change of g(x)

STEP 5: Find the rate of change of h(x)

STEP 6: Write the average rates of change for the functions

The average rates of change in ascending order will be -8,-3,-1

Hence, the arrangement of the functions according to their ascending order of average rates of changes are:

Answer:

11 boxes of candles

Step-by-step explanation:

first, set it up as an equation. let x stand for the amount of boxes she needs.

100=8x+15

next, subtract 15 from both sides of the equation.

100-15=8x+15-15

85=8x

then, you need to get x by itself. to do this, divide 8 from both sides of the equation.

85/8=8x/8

x=10.62, but you can't buy half a box, so you have to round up.

so, she needs to buy 11 boxes of candles.

Answer:

The value of X is 10 As the two triangles are similar X= 10

The value of ( g o f ) (x) is x^2 + 2

A function is a rule or an expression that shows relationship between a variable known as the independent variable and another variable known as the dependent variable.

From the information given, we have;

( g o f ) (x) can be determined by substituting the value for x in g(x) as the function f(x) = x + 1

( g o f ) (x) = (x+ 1) ^ 2 + 1

( g o f ) (x) = x^2 + 1^ 2 + 1

Find the square

( g o f ) (x) = x^2 + 1 + 1

( g o f ) (x) = x^2 + 2

The value of ( g o f ) (x) is x^2 + 2

Thus, the value of ( g o f ) (x) is x^2 + 2

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Sara, as a social worker at an inner-city public school, has worked with 200 high school students to improve their study skills.

You'll assist people in finding answers to their difficulties as a social worker.

This could involve supporting people to live independently or shielding vulnerable persons from injury or abuse.

You will interact with clients, their families, people in the immediate vicinity, and a variety of clientele, including the elderly.

Sara, as a social worker at an inner-city public school, has worked with 200 high school students to improve their study skills.

Now, she wants to determine if their grades have increased. To do this, she should analyze the grade point averages (GPAs) of the students.

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The common sum is 18 as "the numbers from 1 to 8 are placed at the vertices of a cube in such a manner that the sum of the four numbers on each face is the same".

A summation, also known as a sum, is the outcome of adding two or more numbers or quantities. There are always an even number of terms in a summation. There could be only two terms, or there could be one hundred, thousand, or a million. The outcome or conclusion we arrive at when we add two or more numbers is known as the SUM. Addends are the numbers that are added.

Here,

The sum of the numbers on one face of the cube is equal to the sum of the numbers on the opposite face of the cube; these 8 numbers represent all of the vertices of the cube.

=(1+2+3+4+5+6+7+8)/2

=18

Since "the numbers from 1 to 8 are placed at the vertices of a cube in such a manner that the sum of the four numbers on each face is the same," the common sum is 18.

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Answer:

40

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

The equivalent expression in the form of statement will be -

"negative 5 over 8 times g plus negative 19".

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is the following statement - "3 over 4 times g minus 6 minus 7 over 8 times g minus the expression one over 2 times g plus 13"

We can write the statement in the form of a equation as -

(3g/4 - 6) - (7g/8) - (g/2 + 13)

3g/4 - 6 - 7g/8 - g/2 - 13

(3g/4 - 7g/8 - g/2) - (6 + 13)

On solving, we get -

- 5g/8 - 19

Therefore, the equivalent expression in the form of statement will be -

"negative 5 over 8 times g plus negative 19".

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Answer:

Please find attached the required graph and

Step-by-step explanation:

The values for the information given can be written down as follows;

Time, seconds             Volume mL

0,                                    500

12,                                   450

24,                                  400

36,                                  350

48,                                  300

60,                                  250

72 250

84 250

96 250

108 250

120 250

132 250

144 250

156 250

168 250

180 250

192 250

204 250

216 250

228 250

240 250

252 250

264 250

276 250

288 250

300 250

312 225

324,                                        200

336,                                         175

348,                                         150

360,                                         125

372,                                         100

384,                                         75

396,                                        50

408,                                        25

420,                                        0

We can estimate that B × T is roughly 0.57, or equivalently, T is roughly 0.57 / B.

Assuming that the rumor spreads according to the logistic law, we can use the following formula to estimate the number of people who will hear the rumor by 5 pm:

\(P(t) = K / (1 + A \times e^{(-B\times t)})\)

where:

P(t) is the number of people who have heard the rumor by time t,

K is the maximum possible number of people who can hear the rumor (in this case, the total population of the town, which is 10,000),

A and B are constants that determine the shape of the logistic curve, and

e is the mathematical constant approximately equal to 2.71828.

To solve for A and B, we need to use the information given in the problem. We know that at noon, 4,000 people have heard the rumor. Let's assume that "noon" corresponds to t=0 (i.e., we start counting time from noon). Then we have:

\(P(0) = 4,000 = K / (1 + A \times e^{(-B\times 0)})\)

4,000 = K / (1 + A)

1 + A = K / 4,000

We also know that the logistic law predicts that the number of people who hear the rumor will eventually level off and approach the maximum value K. Let's assume that the leveling off occurs after a long time T (which we don't know). Then we have:

P(T) = K

We can use these two equations to solve for A and B:

A = (K / 4,000) - 1

B = ln((K / 4,000) / (1 - K / 4,000)) / T

where ln denotes the natural logarithm.

Unfortunately, we don't know the value of T, so we can't calculate B directly. However, we can make an educated guess based on the shape of the logistic curve. Typically, the curve starts out steeply and then levels off gradually. Therefore, we can assume that the time it takes for the curve to reach 90% of its maximum value is roughly equal to T. In other words, we want to solve for T such that:

\(P(T) = 0.9 \times K\)

Substituting the expression for P(t) into this equation, we get:

\(0.9 \times K = K / (1 + A \times e^{(-BT)})\\0.9 = 1 / (1 + A \times e^{(-BT)})\\1 + A \times e^{(-BT)} = 1 / 0.9\\A \times e^{(-BT)} = 1 / 0.9 - 1\\e^{(-B\times T)} = (1 / 0.9 - 1) / A\\B \times T = -ln((1 / 0.9 - 1) / A)\)

Plugging in the values for K and A, we get:

A = (10,000 / 4,000) - 1 = 1.5

\(B \times T = -ln((1 / 0.9 - 1) / 1.5) = 0.57\)

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Answer:

Stratified Sampling

Step-by-step explanation:

Stratified sampling involves dividing the population into subpopulations that may differ in important ways. It allows you draw more precise conclusions by ensuring that every subgroup is properly represented in the sample.

To use this sampling method, you divide the population into subgroups (called strata) based on the relevant characteristic (e.g. gender, age range, income bracket, job role).

Based on the overall proportions of the population, you calculate how many people should be sampled from each subgroup. Then you use random or systematic sampling to select a sample from each subgroup.

I hope this helped!

Answer:

49pi m^2

Step-by-step explanation:

Area of circle=pi r^2

D=2r=14

r=7

Area of circle =7^2pi=49pim^2

Answer:

Step-by-step explanation:

The diameter = 14m

r = d/2

r = 14/2

r = 7

Area = pi * r * r

Area = 7 * 7 * pi

Area = 49 pi

Answer: x+6

Step-by-step explanation:

The probability of getting exactly 16 heads is 0.0877.

This is a binomial distribution with n = 18, p = 0.70, and we want to find the probability of getting exactly 16 heads. The probability mass function for a binomial distribution is given by P(X = k) = (n choose k) p^k (1-p)^(n-k), where (n choose k) = n! / (k! (n-k)!). Plugging in the values, we get:

P(X = 16) = (18 choose 16) (0.70)^16 (0.30)^2

= 0.0877

So the probability of getting exactly 16 heads is 0.0877.

The probability of at least 10 out of 15 patients surviving the disease is 0.0086.

This is also a binomial distribution with n = 15, p = 0.30 (since the mortality rate is 70%, the survival rate is 30%), and we want to find the probability of at least 10 successes (i.e., surviving patients). We can use the complement rule and find the probability of getting fewer than 10 successes, then subtract that from 1 to get the probability of at least 10 successes:

P(X >= 10) = 1 - P(X < 10)

= 1 - (P(X = 0) + P(X = 1) + ... + P(X = 9))

Using the binomial probability mass function, we can calculate each of these probabilities and add them up:

P(X >= 10) = 1 - (P(X = 0) + P(X = 1) + ... + P(X = 9))

= 1 - ((15 choose 0) (0.30)^0 (0.70)^15 + (15 choose 1) (0.30)^1 (0.70)^14 + ... + (15 choose 9) (0.30)^9 (0.70)^6)

= 0.0086

So the probability of at least 10 out of 15 patients surviving the disease is 0.0086.

The probability of getting exactly 12 P events is 0.19.

This is a binomial distribution with n = 15, p = 0.50, and we want to find the probability of getting exactly 12 P events. Using the binomial probability mass function, we get:

P(X = 12) = (15 choose 12) (0.50)^12 (0.50)^3

= 0.1964

So the probability of getting exactly 12 P events is 0.19.

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\(3y + 37 + 4y = 9 \\ 3y + 4y = 9 - 37 \\ 7y =- 28 \\ \frac{7y}{7} = \frac{-28}{7} \\ y = -4\)

ATTACHED IS THE SOLUTION

The end behavior of a polynomial function is as x tends to infinity, f(x) tends to negative infinity.

In this question,

The power function is f(x) =-2x^3

The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.

The degree and the leading coefficient of a polynomial function determine the end behavior of the graph.

The graph below shows the behavior of the function f(x).

The above equation has the degree of 3, which is odd and the leading coefficient has the negative coefficient.

Then the end behavior is

As x -> ∞,

\(\lim_{x \to \infty} f(x)\)

⇒ \(\lim_{x \to \infty} -2x^{3}\)

⇒ \(-2(\infty)^3\)

⇒ - ∞

Hence we can conclude that the end behavior of a polynomial function is as x tends to infinity, f(x) tends to negative infinity.

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Plane B was farther away from the airport when it was 5 miles from the ground. To determine which plane was farther away from the airport when it was 5 miles from the ground, we can use trigonometry.

We can consider the situation as a right triangle, with the distance from the airport as the hypotenuse and the altitude as one of the legs. For Plane A, the angle of departure is 41°. Using trigonometry, we can calculate the distance from the airport as follows:

Distance_A = altitude / sin(angle) = 5 / sin(41°) ≈ 7.62 miles.

For Plane B, the angle of departure is 43°. Similarly, we can calculate the distance from the airport as:

Distance_B = altitude / sin(angle) = 5 / sin(43°) ≈ 6.84 miles.

Comparing the distances, we find that Plane B was farther away from the airport when it was 5 miles from the ground, with a distance of approximately 6.84 miles, while Plane A was approximately 7.62 miles away. Therefore, the correct answer is "Plane B because it was 6.84 miles away."

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