The equation, 687.5 = 550(1 + 0.05t), represents the amount of money earned on a simple interest savings account. What does the value 550 represent?

The value 550 represents the initial balance in the account, which means the account started with $550.
The value 550 represents the final balance in the account, which means the account balance ended with $550.
The value 550 represents the final balance in the account, which means the account balance started with $550.
The value 550 represents the amount of interest earned, which means $550 was added to the initial balance.

Answer:

Standard divation of 12 , 24 , 24 , 28 , 32 , 36 , 40 , 44 , 48

10.666666666667

Step-by-step explanation:

Answer:

$1.75 per pound of apples, 10 apples can be purchased for $17.50 because you divide 17.50 by 1.75 since that is your unit rate per pound.

Step-by-step explanation:

Answer:

the answer is 17.50

Step-by-step explanation:

one pound is 1.75 so you multiply that by 10 and you get 17.50

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The circumference of the circle in terms of π whose radius is given would be = 63π. That is option D.

To calculate the circumference of a circle, the formula that should be used would be given below.

That is;

circumference of circle= 2πr

The radius = 31½

circumference = 2×π × 31½

= 2×π× 63/2

= 63π

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There are 15 different books and 3 each can be arranged on a shelf i.e., there are 15/3 i.e., 5 shelves to arrange the book in the the display case.

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The condition imposed such that a₁X₁ + a₂X₂ +.....+ aₙXₙ is an unbiased estimator of μ must be that ∑a = 1

We are given that X₁, X₂, ... Xₙ constitute a random sample from the population with the mean μ.

This implies, E(X) = μ

Now we have another set of data here, a₁X₁ + a₂X₂ +.....+ aₙXₙ

For a₁X₁ + a₂X₂ +.....+ aₙXₙ to be an unbiased estimator of μ, we should have

E(∑aX) = μ

or, ∑a E(X) = μ

Now we already know that

E(X) = μ

Hence we get

∑a = 1

Hence condition imposed must be that ∑a = 1

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Correct Question

If X₁, X₂, ... Xₙ constitute a random sample from the population with the mean μ, what condition must be imposed on the constants a₁, a₂, ... aₙ so that a₁X₁ + a₂X₂ +.....+ aₙXₙ is an unbiased estimator of μ?

The formula for the surface area of the box, in terms of the length of one side of the square base (s), is A = s^2 + 4s^2 = 5s^2.

The derivative of the surface area function with respect to s, denoted as dA/ds, gives us the rate of change of the surface area with respect to the length of one side of the base.

1. The surface area of the box consists of the area of the square base and the four equal sides. The area of the square base is s^2, and each side has a length of s. Therefore, the total surface area is given by A = s^2 + 4s^2 = 5s^2.

2. To find the derivative of the surface area function, we differentiate 5s^2 with respect to s using the power rule of differentiation. The power rule states that if we have a function f(x) = cx^n, then the derivative is f'(x) = cnx^(n-1).

  Applying the power rule, we have dA/ds = d(5s^2)/ds = 10s.

3. The derivative, dA/ds = 10s, represents the rate of change of the surface area with respect to the length of one side of the square base. This means that for every unit increase in s, the surface area increases by 10s units.

  The derivative does not provide information about minimizing the amount of material used. To find the dimensions of the box that minimize the amount of material used, we need to set up an optimization problem and solve for the critical points. This involves setting the derivative equal to zero and finding the values of s that satisfy this equation. However, since the problem statement does not provide a specific volume constraint or objective function, we cannot proceed with the optimization process.

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There are 2520 ways to seat 8 people around a circular table where two seatings are considered the same when everyone has the same two neighbors without regard to whether they are right or left neighbors.

There are a total of seven different ways for eight individuals to sit around a circular table: (8-1)!=7!. We are using the concept of circular permutation.

By using circular permutation we have,

7!=5040

All of the seating is included in these 5040 ways. Given that everyone has the same two neighbors, regardless of whether they are left or right neighbors, two seating are said to be equal. To achieve the desired outcomes, we must divide the total number of methods by 2.

5040/2

=2520 ways

Therefore, there are 2520 ways to seat 8 people around circular table where two seating are considered the same.

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The function  f(x)=2/x²+3x-10 is negative for all x < -5 option second "is negative for all x < -5" is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function:

\(\rm f\left(x\right)=\dfrac{2}{x^2}+3x-10\)

f(x) is positive for all x < -5

Plug x = -4

f(-4) = -21.875

The above statement is not true

f(x) is negative for all x < -5

Plug x = -4

f(-4) = -21.875

The above statement is true

f(x) is positive for all x < 2

Plug x = 1

f(1) = -5

The above statement is not true

f(x) is negative for all x > 2

Plug x = 3

f(3) = -0.777

The above statement is not true

Thus, the function  f(x)=2/x²+3x-10 is negative for all x < -5 option second "is negative for all x < -5" is correct.

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Answer:

\(\left \{ {{y=10} \atop {x=5}} \right.\)  \(\left \{ {{y=11} \atop {x=4}} \right.\) \(\left \{ {{y=12} \atop {x=3} \right.\) \(\left \{ {{y=14} \atop {x=1}} \right.\)

x-restaurant gift cards ;

y-movie theater gift cards

Step-by-step explanation:

x+y=15

50x+20y≤450

\(\left \{ {{x\leq 5} \atop {y\geq 10}} \right.\)

so,\(\left \{ {{y=10} \atop {x=5}} \right.\)  \(\left \{ {{y=11} \atop {x=4}} \right.\) \(\left \{ {{y=12} \atop {x=3} \right.\) \(\left \{ {{y=14} \atop {x=1}} \right.\)

Mr. Thomsen can by 5 restaurant cards and 10 movie theater gift cards

System of equations

When there are multiple unknowns and providing necessary information to set up solutions in those unknowns, systems of equations are being used to solve applications.

How to determine the each type of gift card Mr. Thomsen buy?

Consider \(x\) as the number of restaurant gift cards.

Let's take \(y\) as the numbers of movie theaters gift card.

The cost of each restaurant gift cards is 50$

The cost of each movie theater gift cards is 20$

He has 450$ to spend on 15 gift cards.

Therefore, the system of equation to find the each type of gift card will be:

\(50x+20y=450\)

How to find the value of \(x\) :

Here, we know that : \(x+y=15\)

So, the value of \(x\) will be:

\(x=15-y\)

\(50(15-y)+20y=450\)    

Expand the equation

\(750-50y+20y=450\)

Add similar elements

\(-50y+20y=-30y\)

Therefore, the equation will be:

\(750-30y=450\)

Then subtract 750 from both sides as follow:

\(750-30y =450-750\)

\(-30y=-300\)

Simplify the equation:

\(-30y=-300\)

Divide the both sides by \(-30\)

\(\frac{-30y}{-30} =\frac{-300}{-30}\)

Simplify:

\(y=10\)

Therefore the value of \(x\) will be:

\(x=15-10\)

\(x=5\)

Therefore, Mr. Thomsen can by 5 restaurant cards and 10 movie theater gift cards.

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Step-by-step explanation:

see photo for detailed analysis

Answer:Kids grow at their own pace. Big, small, tall, short — there is a wide range of healthy shapes and sizes among children. Genetics, gender, nutrition, physical activity, health problems, environment, and hormones all play a role in a child's height and weight. And many of these things can vary widely from family to family.

Step-by-step explanation:

Answer:

12−3x

Step-by-step explanation:

12+3.4x−5.4x−x

Combine 3.4x and −5.4x to get −2x.

12−2x−x

Combine −2x and −x to get −3x.

12−3x

After simplification of given expression. We get, the value of x is 4.

To simplify this 12 + 3.4x - 5.4x - x,

12 + 3.4x - 5.4x - x = 0

3.4x - 5.4x = - 2x

12  - 2x - x

-2x - x = -3x

-3x + 12 = 0

-3x = -12,

x = 4

Therefore, the value of x is 4.

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Answer:

0.016

Step-by-step explanation:

u divide 0.048 by 30 and the result is the answer

Answer:

37,500 meters long

Step-by-step explanation:

The tape plays at 0.048 meters per second. First, let's find the number of seconds in 30 minutes.

The tape plays at 0.048 meters per second for 1800 seconds

The equation is:

The tape is \(\boxed{\text{37,500 meters long}}\)

-Chetan K

Prolific will bike 2 miles to get to the mechanic at the 6th gas station if the pattern continues.

Assuming the rate remains constant, we can use the equation d = rt, where d is the distance, r is the rate, and t is the time. In this case, we want to find the equation to determine the distance of the Nth gas station.

Let's analyze the given information:

The first gas station is 1.5 miles away.

From the second gas station onwards, each gas station is located at a distance 0.1 miles greater than the previous one.

Based on this pattern, we can write the equation for the distance of the Nth gas station as follows:

d = 1.5 + 0.1(N - 1)

B. To find the distance Prolific will bike to get to the 6th gas station, we can substitute N = 6 into the equation from part A:

d = 1.5 + 0.1(6 - 1)

= 1.5 + 0.1(5)

= 1.5 + 0.5

= 2 miles

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Answer:

A) The slope is negative.  It is -30

B)The slope is positive.  It is 2.5

Step-by-step explanation:

Graph A:

I selected two points on the graph.

(1, 220) and (7, 40)

The slope is the change in y over the change in x.  The y values are 40 and 220.  The x values are 7 and 1.  You find the change by subtracting.

\(\frac{40 - 220}{7-1}\) = \(\frac{-180}{6}\) = -30

Graph B:

This graph is proportional because it is a straight line and it goes through the original.  This means that the slope can be found with any ordered pair in the form \(\frac{y}{x}\).  I am going to use the point (2, 5).  \(\frac{5}{2}\) = 2.5

Helping in the name of Jesus.

Answer:50%

Step-by-step explanation:

50% brainliest pwease

Answer:

2/21.

Step-by-step explanation:

\(\frac{2}{7}\) ÷ 3 = (2 / 7) * (1 / 3) = (2 * 1) / (7 * 3) = 2 / 21 = 0.0952380952.

Hope this helps!

Write 3 as 3/1

Now you have 2/7 / 3/1.

When you divide by a fraction change the divide to multiply and flip the second fraction over

Now you have 2/7 x 1/3 now multiply top by top and bottom by bottom to get

2/21

Answer: 7k^2+2k+10

Step-by-step explanation: To simplify this, you need to combine like terms, which are just the numbers that have the same variables and exponents. Combine 2k^2 and 5k^5 and it is 7k^2 (Just add the coefficient). Then do 3k -k, which is 2k. k just represents 1, so basically, 3-1. Finally, 7 + 3, which is 10. Then, combine the results to form an expression, which is 7k^2+2k+10.

According to the question the value of X is approximately 1.01 (rounded to two decimal places).

To find the value of X in the logistic growth model, we can use the given explicit solution for the population:

P(t) = 75 / (1 + X * e^(-0.05t))

We know that the initial population is P_0 = 74. Substituting this into the equation, we have:

74 = 75 / (1 + X * e^(0))

Since e^0 = 1, we can simplify the equation to:

74 = 75 / (1 + X)

To solve for X, we can rearrange the equation:

1 + X = 75 / 74

X = 75 / 74 - 1

Calculating this expression:

X = 1.0135135

Therefore, the value of X is approximately 1.01 (rounded to two decimal places).

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So, there are (n!)^2 ways to arrange n men and n women in a row if they alternate genders.

We need to use the principle of multiplication. We first choose the position of the first person in the row, which can be any of the n men or n women. Without loss of generality, let's say we choose a man. Then, for the next position, we need to choose a woman since we are alternating genders. There are n women to choose from. For the third position, we need to choose another man, and there are n-1 men left to choose from (since we already used one). For the fourth position, we need to choose another woman, and there are n-1 women left to choose from. We continue this pattern until all n men and n women are placed in the row.

Using the principle of multiplication, we can find the total number of ways to arrange the people by multiplying the number of choices at each step. Therefore, the total number of ways to arrange the people in a row if the men and women alternate is:

n * n-1 * n * n-1 * ... * 2 * 1

This can be simplified to:

(n!)^2

So, there are (n!)^2 ways to arrange n men and n women in a row if they alternate genders.

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Answer: = 9/2 i did this in khan academy

Step-by-step explanation:

Answer:

x = ⁻⁹⁄₂ Or -4.5

Explanation:

-2x - 5 = 4

-2x - 5 + 5 = 4 + 5

-2x = 9

-2x / -2 = 9 / -2

x = ⁻⁹⁄₂ Or -4.5

- PNW

we have the inequality

y > -1.25

the solution is the interval (-1.25, infinite)

Note that the number -1.25 is not included in the solution

so

Verify each statement

2) -1.75 is a solution ------> false

3) all the solutions are negative -------> false

Let's begin by identifying key information given to us:

Answer:

2x+7+y=0 -7

2x+y=-7 -2x

y=-2x-7

Step-by-step explanation:

not sure

Answer:

2x+7+y=0

y=-2x-7

in the form of y=MX+c where M is slope

Answer:

23 + 11 = 34

Bobby descended 34 meters

Answer:

23 is an integer

another 11 is an integer

23+11 = 34

total depth descended is 34.

Step-by-step explanation:

the general equation of a parabola is

y = a(x – h)² + k.

(h, k) is the vertex of the parabola.

comparing it to

y = 3(x + 4)² - 2

we see that (h, k) = (-4, -2).

the student made a sign mistake. it is "- h" in the squared factor. so, "+4" indicates "-4" as "h".

but the student simply used "+4".

Answer:

NO it isnt.

Step-by-step explanation:

Go right of the decimal and throught the different place values. Since the number just right of the decimal is the highest place value, whichever number is greater, holds the greater value.