7. the interest on a particular savings account is compounded continuously. the account initially had $3500 deposited in it. the worth of the account after t-years can be calculated using the formula: a(t)- 3500041 (a) by what percent will the worth of the account increase per year? round to the nearest hundredth of a percent. (b) to the nearest tenth of a year, how long will it take for the worth of the account to triple?​

7/3 t^(3/2) + C This equation represents the volume of water in the tank as a function of time t.

The equation r(t) = 7t √ represents the rate at which water is flowing into the tank, measured in cubic feet per hour, at time t after 9:00am. The expression 7t √ means that the rate of flow increases over time, starting at 0 cubic feet per hour at t = 0 and increasing as t increases.

To find the volume of water in the tank at a specific time t after 9:00am, we can integrate the rate of flow over the time interval from 9:00am to t. The volume of water in the tank at time t can be expressed as:

V(t) = ∫ r(t) dt from 9:00am to t

= ∫ 7t √ dt from 0 to t

= 7/3 t^(3/2) + C

where C is an arbitrary constant of integration. This equation represents the volume of water in the tank as a function of time t.

Therefore, 7/3 t^(3/2) + C This equation represents the volume of water in the tank as a function of time t.

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Answer:

1.) a. revenue divided by number of posts

b. revenue divided by total number of words

2.) c. no.

Step-by-step explanation:

Answer:

1.

a) Revenue divided by number of posts

b) Revenue divided by total number of words

2.

c) No. The definitions have opposite results.

The polynomials span P₂ implies any polynomial of degree 2 written as linear combination of these polynomials.

To determine whether the given polynomials span P₂,

Check whether any polynomial of degree 2 can be written as a linear combination of these polynomials.

Let us consider a general polynomial of degree 2.

p(x) = ax² + bx + c

We need to find coefficients k₁, k₂, k₃, and k₄ such that.

p(x) = k₁(1-x+2x²) + k₂(3+x) + k₃(5-x+4x²) + k₄(-2-2x+2x²)

Expanding the right side and collecting like terms, we get,

p(x) = (2k₁+4k₃+2k₄)x² + (-k₁-k₂+k₃-2k₄)x + (k₁+3k₂+5k₃-2k₄+1)

This equation must hold for any value of x.

Equate the coefficients of the powers of x on both sides,

2k₁ + 4k₃ + 2k₄ = a

-k₁ - k₂ + k₃ - 2k₄ = b

k₁ + 3k₂ + 5k₃ - 2k₄ + 1 = c

Solve this system of linear equations for k₁, k₂, k₃, and k₄.

Write this in matrix form as,

\(\left[\begin{array}{cccc}2&0&4&2\\-1&-1&1&-2\\1&3&5&-2\end{array}\right]\)\(\left[\begin{array}{ccc}k_{1} \\k_{2}\\k_{3}\end{array}\right]\)  \(= \left[\begin{array}{ccc}a \\b\\c-1\end{array}\right]\)

Solve this system using Gaussian elimination or other methods.

However, a simpler way to check whether the polynomials span P₂ is to check whether the matrix of coefficients is invertible.

If the matrix is invertible, then there is a unique solution for any value of a, b, and c.

If the matrix is not invertible,

Then there are some values of a, b, and c for which there is no solution.

And the polynomials do not span P₂.

To check whether the matrix is invertible, compute its determinant,

\(\left|\begin{array}{cccc}2&0&4&2\\-1&-1&1&-2\\1&3&5&-2\end{array}\right|\)

= 12

Since the determinant is non-zero,

The matrix is invertible, and the polynomials span P₂.

Therefore, matrix is invertible implies polynomials span P₂, any polynomial of degree 2 written as linear combination of these polynomials.

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The above question is incomplete, the complete question is:

Determine whether the following polynomials span P₂ (polynomial of degree 2):

p₁=1−x+2x²,

p₂=3+x,

p₃=5−x+4x²,

p₄=−2−2x+2x²

Answer:-8 1/10

Step-by-step explanation:

-2 3/5 - 5 1/2

-13/5 -11/2

-81/10

-8 1/10

The simplified expression of the statement is -81/10

From the question, we have the following statement that can be used in our computation:

negative 2 and three fifths minus 5 and one half.

Express as numbers

So, we have

-2 3/5 - 5 1/2

Convert the fractions to improper fractions

So, we have

-13/5 - 11/2

Take the LCM of the above fractions

(-13 * 2 - 11 * 5)/10

Evaluate the difference

So, we have

-81/10

Hence, the value of the expression is -81/10

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The correct interpretation of the 95% confidence interval is:

"We estimate with 95% confidence that the true population mean height of orangutans is between 52 and 58 inches."

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data. It involves the use of methods and techniques to gather, summarize, and draw conclusions from data.

The confidence interval provides a range of values within which the true population mean height is likely to fall with a 95% level of confidence. It does not provide information about individual orangutans' heights or the sample mean's precise location within the interval.

Therefore, The correct interpretation of the 95% confidence interval is:

"We estimate with 95% confidence that the true population mean height of orangutans is between 52 and 58 inches."

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Step-by-step explanation:

1. Simplify |-15|∣−15∣ to 1515.

15+|13|

15+∣13∣

2 Simplify.

28

28

Done

2.Simplify |-12|∣−12∣ to 1212.

Simplify |-12|∣−12∣ to 1212.12-|-8|

Simplify |-12|∣−12∣ to 1212.12-|-8|12−∣−8∣

Simplify |-12|∣−12∣ to 1212.12-|-8|12−∣−8∣2 Simplify |-8|∣−8∣ to 88.

Simplify |-12|∣−12∣ to 1212.12-|-8|12−∣−8∣2 Simplify |-8|∣−8∣ to 88.12-8

Simplify |-12|∣−12∣ to 1212.12-|-8|12−∣−8∣2 Simplify |-8|∣−8∣ to 88.12-812−8

Simplify |-12|∣−12∣ to 1212.12-|-8|12−∣−8∣2 Simplify |-8|∣−8∣ to 88.12-812−83 Simplify.

Simplify |-12|∣−12∣ to 1212.12-|-8|12−∣−8∣2 Simplify |-8|∣−8∣ to 88.12-812−83 Simplify.4

Simplify |-12|∣−12∣ to 1212.12-|-8|12−∣−8∣2 Simplify |-8|∣−8∣ to 88.12-812−83 Simplify.44

3. Simplify.

\frac{3}{7.1\times 2}

7.1×2

3

2 Simplify 7.1\times 27.1×2 to 14.214.2.

\frac{3}{14.2}

14.2

3

3 Simplify.

0.211268

0.211268

Answer:

200+(50x) x = months

Step-by-step explanation:

the start up is 200, every month x han has to pay 50

total cost = 200+(50x)

Answer:

3.99

Step-by-step explanation:

The total sum of central angle of circle is 360 which mean the area of the circle = (12.36 x 360)/89

A=πr^2

=> (12.36 x 360)/89 = 3.14(r^2)

r^2 = 15.92

r = 3.99

Answer: 15.64

Step-by-step explanation:

kahn

Answer:

$18000

Step-by-step explanation:

To find the do $30000/5 ( do divide the price into 5 parts)

30000/5

6000

5/5 minus 2/5

3/5

6000 times 3

18000

Answer:

-0.1, -0.02, \(\frac{5}{6}\), \(|\frac{9}{8}|\), 10

Step-by-step explanation:

A type I error occurs when a researcher mistakenly rejects a true null hypothesis. In other words, it is a false positive result. Let's break down what happens in a type I error:

1. The researcher starts with a null hypothesis, which assumes that there is no significant relationship or effect between the variables being studied.

2. To test the null hypothesis, the researcher collects data and performs statistical analysis.

3. In a type I error, the researcher incorrectly concludes that there is a significant relationship or effect when, in fact, there is none.

4. This error can happen due to various reasons, such as sample size, random chance, or flaws in the experimental design.

To avoid type I errors, researchers typically set a predetermined significance level (often denoted as α) before conducting the study. The significance level represents the probability of making a type I error. By setting a lower significance level, such as α = 0.05, researchers aim to reduce the chances of mistakenly rejecting the null hypothesis.

In the context of the given question, if the researcher is trying to reduce error and avoid a type I error, it means they want to minimize the risk of incorrectly inferring findings to another practice setting. This would increase the confidence that nurses have in applying the research findings to their own work.

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If a Pearson correlation coefficient has a final value of +10, interpretation of this result is that it is an impossible value of r. Therefore, the correct option is A.

It is given that the Pearson correlation coefficient you calculated has a value of +10. This is actually an impossible value of r. Pearson correlation coefficient (r) ranges between -1 and +1. A value of +1 indicates a perfect positive correlation, while a value of -1 indicates a perfect negative correlation. A value of 0 suggests no correlation between the variables.

A value of +10 would fall outside of this range, making it an impossible value of r. Therefore, this result cannot be interpreted in terms of positive or negative correlation, nor can it be considered a significant correlation. It is important to ensure that the range of possible values is considered when interpreting statistical results. Hence, the correct answer is option A.

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The expressions for the lengths of the segments obtained using vectors notation are;

a. i. \(\overrightarrow{LA}\) = q - (1/2)·p  ii. \(\overrightarrow{AN}\) = (2/7)·(p - q)

b. The expressions for \(\overrightarrow{MN}\), \(\overrightarrow{LA}\), and \(\overrightarrow{AN}\) indicates;

\(\overrightarrow{MN}\) = (1/84)·(46·q - 11·p)

A vector is a quantity that has magnitude and direction and are expressed using a letter aving an arrow in the form, \(\vec{v}\)

a. i. \(\overrightarrow{LA}\) = \(\overrightarrow{BA}\) - \(\overrightarrow{LB}\) =  \(\overrightarrow{BA}\) - (1/2) × \(\overrightarrow{CB}\)

\(\overrightarrow{BA}\) - (1/2) × \(\overrightarrow{CB}\) = q - (1/2)·p

\(\overrightarrow{LA}\) = q - (1/2)·p

ii. \(\overrightarrow{AC}\) = \(\overrightarrow{BC}\) - \(\overrightarrow{BA}\)

\(\overrightarrow{AN}\) = (2/7) × \(\overrightarrow{AC}\)

\(\overrightarrow{AN}\) = (2/7) × \(\overrightarrow{BC}\) - \(\overrightarrow{BA}\)

\(\overrightarrow{AN}\) = (2/7) × (p - q)

b. \(\overrightarrow{MN}\) = \(\overrightarrow{MA}\) + \(\overrightarrow{AN}\)

\(\overrightarrow{MA}\) = (5/6) × \(\overrightarrow{LA}\)

\(\overrightarrow{LA}\) = q - (1/2)·p

\(\overrightarrow{AN}\) = (2/7) × (p - q)

Therefore;

\(\overrightarrow{MN}\) = (5/6) × ( q - (1/2)·p) + (2/7) × (p - q)

\(\overrightarrow{MN}\) = (1/84) × ( 70·q - 35·p + 24·p - 24·q) = (1/84)(46·q - 11·p)

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Answer:

13

Step-by-step explanation:

you have to use Pythagorean Theorem which is

(a^2) + (b^2) = (c^2)

where a and be are the legs 45° from each other and c is the hypotenuse.

so just plug in the numbers

5^2 + 12^2 = c^2

25 + 144 = c^2

169 = c^2

now square root both sides to get rid of the square on c

root(169) = root(c^2)

13 = c

It took both Sandy and Tom 54 seconds to cover the same distance.

We can set up an equation based on their relative speed

Take the supposition that Tom needs "t" seconds to travel the distance. Sandy started jogging 12 seconds before Tom, so it will take her "t + 12" seconds longer to complete the same distance.

To determine the distance traveled by Sandy, multiply her speed (7 meters per second) by her time (t + 12) seconds. Tom's distance traveled may be determined by dividing his speed (9 meters per second) by his time (t) seconds.

Equating the distances covered by Sandy and Tom:

7(t + 12) = 9t

Expanding the equation:

7t + 84 = 9t

Subtracting 7t from both sides:

84 = 2t

Dividing both sides by 2:

t = 42

Tom traveled the distance in 42 seconds as a result. We add the 12-second lead Sandy had to determine the time it took for both Sandy and Tom to travel the same distance:

t + 12 = 42 + 12 = 54

So, it took both Sandy and Tom 54 seconds to cover the same distance.

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The  answer is:Karen would have $1000000 in the second account when she is 23 years old.

In order to calculate at what age Karen would have $1000000 in the second account, we need to calculate the future value of her investment in the first account, and then use that as the present value for the second account.Let us complete the tables given:

First Account PV: $0 FV: $0 Periods: 144 Rate: 5.75% Payment: $500 PMT/yr: 12 CMP/yr: 4Second Account PV: $163474.72 FV: $1000000 Periods: 23 Rate: 7% Payment: $0 PMT/yr: 1 CMP/yr: 1.

In the first account, Karen invested $500 a month for 12 years.

The total number of periods would be 12*4 = 48 (since it is compounded quarterly). The rate of interest per quarter would be (5.75/4)% = 1.4375%.

The PMT/yr is 12 (since she is investing $500 every month). Using these values, we can calculate the future value of her investment in the first account.FV of first account = (500*12)*(((1+(0.014375))^48 - 1)/(0.014375)) = $162975.15

Rounding off to the nearest cent, the future value of her investment in the first account is $162975.15.

This value is then used as the present value for the second account, and we need to find out at what age Karen would have $1000000 in this account. The rate of interest is 7% compounded annually.

The payment is 0 since she does not make any further investments in this account. The number of periods can be found by trial and error using the formula for future value, or by using the NPER function in Excel or a financial calculator.

Plugging in the values into the formula for future value, we get:FV of second account = 162975.15*(1.07^N) = $1000000Solving for N, we get N = 22.93. Rounding off to the nearest year, Karen would have $1000000 in the second account when she is 23 years old.

Therefore, the main answer is:Karen would have $1000000 in the second account when she is 23 years old.

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Answer:

P(X ≥ 1) = 0.50

Step-by-step explanation:

Given that:

The word "supercalifragilisticexpialidocious" has 34 letters in which 'i' appears 7 times in the word.

Then; the probability of success = 7/34 = 0.20588

Using Binomial distribution to determine the probability; we have:

\(P(X = x) = ^nC_x \ \beta^x \ (1 - \beta)^{n-x}\)

where;

x = 0,1,2,...n    and    0  <  β   <   1

and x represents the  number of successes.

However; since the letter is drawn thrice; the probability that the letter "i" is drawn at least once can be computed as:

P(X ≥ 1) = 1 - P(X< 1)

P(X ≥ 1) = 1 - P(X =0)

\(P(X \ge 1) = 1 - \bigg [ {^3C__0} (0.21)^0 (1-0.21)^{3-0} \bigg]\)

\(P(X \ge 1) = 1 - \bigg [ 1 \times 1 (0.79)^{3} \bigg]\)

P(X ≥ 1) = 1 - 0.50

P(X ≥ 1) = 0.50

Answer:

161.68°F to 182.32°F

Step-by-step explanation:

6%=6/100= 0.06

0.06×172=10.32°F

thus temperature ️ range is

(172 + or - 10.32)°F

Answer:

75 is the prime number if I am correct

Answer:

big bodie built

Step-by-step explanation:

i used to be dusty

Based on the calculations, the value of the given prefix expression is equal to 2205.

The preorder traversal of a tree (T) are typically used in discrete mathematics to determine the value of a prefix expression on a specific expression tree.

For the preorder traversal of this tree (T), we would start from the right most expression:

Prefix expression = * + 3 + 3 ↑ 3 + 3 3 3

Prefix expression = * + 3 + 3 ↑ 3 6 3

Prefix expression = * + 3 + 3  3⁶  3

Prefix expression = * + 3 3 729 3

Prefix expression = * + 3 732 3

Prefix expression = * 735 3   ⇒ 735 × 3

Value = 2205.

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Complete Question:

Given the following prefix expression:

* + 3 + 3 ↑ 3 + 3 3 3

What is the value of the prefix expression?

The MATLAB code to solve the Cauchy problem and plot the graph of the solution for the given differential equation is provided.

To solve the given Cauchy problem in MATLAB and plot the graph of the solution, you can follow these steps:

%Define the symbolic variables and the differential equation:

syms t x(t)

eqn = diff(x, t, 2) - 3*diff(x, t) + 2*x == 12*exp(5*t);

%Define the initial conditions:

x0 = 1;

v0 = 4;

%Convert the differential equation into a system of first-order differential

equations:

x1(t) = diff(x);

ode = [diff(x1, t) == 3*x1 - 2*x + 12*exp(5*t), diff(x, t) == x1];

%Solve the differential equation system using the dsolve function:

sol = dsolve(ode, x(0) == x0, x1(0) == v0);

%Convert the symbolic solution to a MATLAB function:

X = matlabFunction(sol);

%Generate a vector of time values and evaluate the solution function:

t = linspace(0, 1, 100); % adjust the time interval as needed

x_vals = X(t);

%Plot the graph of the solution:

plot(t, x_vals);

xlabel('t');

ylabel('x(t)');

title('Solution of the Cauchy problem');

By following these steps and executing the MATLAB code, you will solve the given Cauchy problem and obtain a graph of the solution, which represents the behavior of the function x(t) over the specified time interval.

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closed circles are at negative 2 and positive 8. everything between the points is shaded.

We have the equation:

|h - 3| \(\leq\) 5

Remember that the equation:

|f(x)| = A

with A > 0

means that:

f(x) = A

or

f(x) = -A

Then for our case, we can rewrite:

|h - 3| \(\leq\) 5

as:

(h - 3) \(\leq\) 5

or

-(h - 3) \(\leq\) 5

Now we can solve these two equations to find the two possible values of p.

From the first one, we get:

h \(\leq\) 8

Now from the other equation, we can get the other solution:

h \(\geq\) -2

Then the correct option is:

closed circles are at negative 2 and positive 8. everything between the points is shaded.

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The solutions to the quadratic equation \(x^2 - 23 = 0\) are \(x = \sqrt{23\) and \(x = - \sqrt{23\).

The square root is a mathematical operation that gives the value which, when multiplied by itself, results in a given number. It is denoted by the symbol "\(\sqrt{}\)".

For example, the square root of 9 is \(\sqrt9\) = 3, because 3 multiplied by itself equals 9.

The square root can also be expressed using fractional exponents. The square root of the number "a" can be written as \(a^{1/2}\).

For example, the square root of 16 can be written as \(16^{1/2}\) = 4, because 4 raised to the power of 2 equals 16.

Similarly in the given case to solve the equation \(x^2 - 23 = 0\), we can isolate the variable x by adding 23 to both sides of the equation:

\(x^2 - 23 + 23 = 0 + 23\\x^2 = 23\)

Next, we take the square root of both sides of the equation to solve for x:

\(\sqrt{x^2} = \sqrt{23}\\x = \pm \sqrt{23{\)

Therefore, the solutions to the equation \(x^2 - 23 = 0\) are \(x = \sqrt{23\) and \(x = - \sqrt{23\).

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Answer:

aa is the repuestos yes ok

Answer:

A

Step-by-step explanation:

Answer:

462 ways

Step-by-step explanation:

The formula to use in solving this problem is given as the Combination formula

The Combination formula is given as

C(n , r) = nCr = n!/r! (n - r)!

We are told that a food bakery has 12 pies unsold at the end of the day which they intend to share to 6 food banks

n = 12, r = 6

In order to ensure that at least 1 food bank gets 1 pie, we have:

n - 1 = 12 - 1 = 11

r - 1 = 6 - 1 = 5

Hence,

C(11, 5) = 11C5

= 11!/ 5! ×(11 - 5)!

= 11!/5! × 6!

= (11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1)/ (5 × 4 × 3 × 2 × 1) ×( 6 × 5 × 4 × 3 × 2 × 1)

= 462 ways

Yes, 12 refrigerators and 11 pianos overload the truck, because 12 refrigerators and 11 pianos weighs more than 7100 lb.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Given that, a truck that can carry no more than 7100 lb is being used to transport refrigerators and upright pianos

Let the number of refrigerators be x and the number of pianos be y.

Each refrigerator weighs 250 lb and each piano weighs 425 lb.

Here, 250x+425y≤7100

Will 12 refrigerators and 11 pianos overload the truck

Now, put x=12 and y=11 in the inequality 250x+425y≤7100, we get

250×12+425×11≤7100

7675≤7100 not true

Therefore, the inequality represent the given scenario is 250x+425y≤7100.

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You can buy car A, because the acceptable rate is 14% and here car A has a rate of 20%

Given,

There are three different cars that you could buy. They differ in initial cost, annual operating costs, and life. Your minimum acceptable rate of return is 14%. Use the ROR method to select the best alternative.

Alternative            A             B                 C

Initial Cost          10,000     8,000       5,000

Annual Cost       1,000       1,500        1,500

Life                     8 years    8 years     5 years

Here,

Rate of Return of car A = (10,000 - 1000 x 8) / 100 = 2000/100 = 20%

Rate of Return of car B = (8,000 - 1500 x 8) / 100 = -4000/100 = -40%

Rate of Return of car B = (5,000 - 1500 x 5) / 100 = -2500/100 = -25%

That is,

You can buy car A, because the acceptable rate is 14% and here car A has a rate of 20%

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Answer:

Step-by-step explanation:

B

(a) The interval on which f is increasing: (0, ∞)

The interval on which f is decreasing: (0, 1)

(b) Local minimum: At x = 1, f(x) has a local minimum value of -1.

There is no local maximum value.

(c) Inflection point: At x ≈ 0.293, f(x) has an inflection point.

The function f(x) = x^2 - x - ln(x) is a quadratic function combined with a logarithmic function.

To find the interval on which f is increasing, we need to determine where the derivative of f(x) is positive. Taking the derivative of f(x), we get f'(x) = 2x - 1 - 1/x. Setting f'(x) > 0, we solve the inequality 2x - 1 - 1/x > 0. Simplifying it further, we obtain x > 1. Therefore, the interval on which f is increasing is (0, ∞).

To find the interval on which f is decreasing, we need to determine where the derivative of f(x) is negative. Solving the inequality 2x - 1 - 1/x < 0, we get 0 < x < 1. Thus, the interval on which f is decreasing is (0, 1).

The local minimum is found by locating the critical point where f'(x) changes from negative to positive. In this case, it occurs at x = 1. Evaluating f(1), we find that the local minimum value is -1.

There is no local maximum in this function since the derivative does not change from positive to negative.

The inflection point is the point where the concavity of the function changes. To find it, we need to determine where the second derivative of f(x) changes sign. Taking the second derivative, we get f''(x) = 2 + 1/x^2. Setting f''(x) = 0, we find x = 0. Taking the sign of f''(x) for values less than and greater than x = 0, we observe that the concavity changes at x ≈ 0.293. Therefore, this is the inflection point of the function.

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