Consider a population of 200 with a mean of 55 and a standard deviation equal to 25. What is the probability of obtaining a sample mean of 58 or less from a sample of 50? Click here to view page 1 of the Cumulative Standardized Normal Table. Click here to view page 2 of the Cumulative Standardized Normal Table. C. What is the probability of obtaining a sample mean of 58 or less from a sample of 50? Pis58) = 0 (Round to four decimal places as needed.)

Therefore, the estimated fox population in the year 2008 is 40689 using function.

Part (a) is answered correctly. The function P(t) represents the fox population in years after 2000, where t is the number of years. The formula for the function is obtained using the exponential growth model, where the initial population in 2000 is multiplied by the growth factor (1 + 0.04)^t.

(a) The function that models the fox population in years after 2000 is given by:

P(t) = 29700 * (1 + 0.04)^t, where t is the number of years after 2000.

For part (b), we substitute t = 8 into the function P(t) to estimate the fox population in the year 2008. We get P(8) = 29700 * (1 + 0.04)^8, which simplifies to P(8) = 40688.76. Since the answer should be an integer, we round the result to the nearest whole number and get 40689 as the estimated fox population in the year 2008.

(b) To estimate the fox population in the year 2008, we need to find P(8):

P(8) = 29700 * (1 + 0.04)^8 = 29700 * 1.369 = 40689 (rounded to the nearest integer)

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Answer:

3+1/6a

Step-by-step explanation:

3/2-1/2a+2/3a+3/2

3/2+3/2-1/2a+2/3a

6/2-1/2a+2/3a

3-1/2a+2/3a

3-3/6a+4/6a

3+1/6a

the simplified value of the given expression is 3 + 1/6a.

One strategy to promote uniformity in work efforts, costs, and time is to simplify procedures. It lessens diversity and variation that is damaging, unnecessary, or meaningless. PEMDAS stands for parenthesis, exponents, multiplication, division, addition, and subtraction. Given two or more operations in a single statement, the order of the letters in PEMDAS tells you what to compute first, second, third, and so on, until the computation is complete.

Given, an algebraic expression 3/2-1/2a+2/3a+3/2

Simplification of the expression:

=>  3/2-1/2a+2/3a+3/2

compare the values with the same variables

=> 3/2 +3/2 +2/3a -1/2a

=> 3 + a(2/3 -1/2)

=> 3 + a1/6

therefore, the simplified value of the given expression is 3 + 1/6a.

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The region enclosed by the curves y = x, y = 3x, and y = -x + 4 needs to be sketched, and its area should be found.

To sketch the region enclosed by the curves, we need to plot the three given curves on a coordinate plane. The first curve is y = x, which represents a straight line passing through the origin (0,0) with a slope of 1. The second curve is y = 3x, which is also a straight line passing through the origin but with a steeper slope of 3. The third curve is y = -x + 4, which represents a line with a y-intercept of 4 and a negative slope of -1. By plotting these three lines on the same coordinate plane, we can see that they intersect at three points: (0,0), (1,3), and (3,1). The region enclosed by these curves is a triangular region with vertices at these three points. To find the area of this triangular region, we can use the formula for the area of a triangle: A = (1/2) * base * height. Let's draw the graph:

     |

   4 |         .  (2, 2)

     |      .

     |   .

     | .

   0 |_____________________

     0     1     2     3     4     5     6

In this graph, the first equation (y = x) is depicted by a diagonal line passing through the origin (0,0). The second equation (y = 3x) is a steeper line, while the third equation (y = -x + 4) is a downward-sloping line with a y-intercept of 4. In this case, the base of the triangle is the distance between the points (0,0) and (3,1), which is 3 units. The height of the triangle is the distance between the point (1,3) and the line y = -x + 4, which is also 3 units. Substituting these values into the area formula, we get A = (1/2) * 3 * 3 = 4.5 square units.

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Answer:

Hope this helps

The numbers represent the translation group

The dark blue is the final result

Step-by-step explanation:

Answer:

Step-by-step explanation:

(3 + x)/2 = 6

3 + x = 12

x = 9

(2 + y)/2 = -2

2 + y = -4

y = -6

(9, -6) the other endpoint C

Answer:

(8a)⁻¹⁸

1 / (8a)¹⁸

Step-by-step explanation:

(((8a)^6a)^4/4a))^-3

((8a)^6a*4/4a)^-3

((8a)^6)^-3

(8a)^6*(-3)

(8a)⁻¹⁸

1 / (8a)¹⁸

Step-by-step explanation:

Answer:

y = -3x + 7.

Step-by-step explanation:

First find the slope of the given line by converting to intercept form:

3x + y + 2 = 0

y = -3x - 2

So the slope is -3.

Then the line we want has a slope of -3 also (as it is parallel).

y - y1 = m(x - x1)   where m is the slope and (x1, y1) is a point on the line:

m = -3,  x1 = 1 and y1 = 4, so we have:

y - 4 = -3(x - 1)

y = -3x + 3 + 4

y = -3x + 7.

The process capability index gauges how much variance a process encounters in comparison to its specification parameters.

We might compare various procedures in terms of the ideal circumstance or whether they live up to our expectations. In the event that the process is not centered, the capability ratio formula is employed.

Process capability uses capability indices to compare an in-control process output to the specification's upper and lower bounds.

Calculated for steady, non-automated processes is the process capability index. The operator is then instructed to check samples at random and center the process.

The processing capability declined.

One would expect to find that the process capability has gotten worse.

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The two scales used in a classroom demonstration to suspend a \(10N\) weight can register a weight of \(10N\) due to the principle of equilibrium of forces.Each scale can register a weight of \(10N\) because the total weight is supported by two scales at the same time and at the same height.

When a weight of \(10N\) is suspended using the two scales, the weight pulls down on both of them by the same force. Since each scale supports half of the weight, the force exerted on each scale is \(5N\).In order to understand how the scales can register a weight of \(10N\) each, we need to take a look at the forces acting on the weight.

The weight is suspended from two scales, so it is acted upon by two forces: the force of gravity pulling it down and the upward force exerted by the scales.The two scales have a spring inside that is compressed when the weight is suspended from them.

The compression of the spring inside each scale generates an upward force that balances out the weight of the object. This results in an equilibrium of forces, with the upward force exerted by the scales balancing out the force of gravity pulling the object down. Therefore, each scale can register a weight of \(10N\) because the force exerted by each scale is equal to half the weight of the object (\(5N\)), and the two scales together can support the entire weight of the object (\(10N\)).

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Given:

The objective is to find the line of reflection at which the triangle carries onto itself.

Explanation:

To obtain the reflection of the rectangle on itself, it must reflect over the midpoint of each parallel side of the rectangle.

The line passing through the midpoint of the rectangle in the x-axis is x= 2.

Similarly, the line passing through the midpoint of the rectangle in the y-axis is y = 1/2.

Thus, the reflecting lines are x = 2 and y = 1/2.

Hence, option (A) is the correct answer.

Answer:

Step-by-step explanation:

Answer:

Cubed

Explanation:

Given the function:

The highest power of the function = 3

Therefore, it is a cubic/cubed function.

Note:

• If the highest power is 1, it is a linear function.

• If the highest power is 2, it is a square/quadratic function.

X is equal to 5500.

To determine the value of X, we can set up an equation based on the given information.

Let's assume that X represents the unknown value we're trying to find. According to the problem, 10% more than X is equal to 550.

Mathematically, we can express this as:

X + 10% of X = 550

To find 10% of X, we multiply X by 0.10:

0.10X = 550

Next, we solve for X by dividing both sides of the equation by 0.10:

X = 550 / 0.10

Simplifying this expression, we have:

X = 5500

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Answer:

A

Step-by-step explanation:

For A, y=1,300x

Answer:

106142400

Step-by-step explanation:

2*5*5*6*8*9*13*14*15*18=1061424000

1061424000/10=106142400

Step-by-Tarea:

Tengo una cantidad de caramelos. Si los agrupo de a tres me sobran dos, si los agrupo de a cuatro me sobra uno y si los agrupo de a cinco no me sobra ninguno. ¿Cuántos caramelos puede ser que tenga?

- Solución:

✤ Si agrupa los caramelos de a cinco no sobra ninguno. Entonces la cantidad de caramelos es un múltiplo de cinco. Recuerda que un múltiplo es un número que contiene una cantidad exacta de veces a otro número.

Para hallar los múltiplos de cinco debemos multiplicar a cinco por cualquier otro número. Algunos ejemplos de múltiplos de cinco son 5, 10, 15 y 20. Estos números son múltiplos de cinco porque lo contienen una cantidad de veces exactas:

5 . 1 = 5

5 . 2 = 10

5 . 3 = 15

5 . 4 = 20

Por ejemplo el número 20 es múltiplo de cinco porque lo contiene cuatro veces exactas.

Si los agrupa de a tres sobran dos caramelos y si los agrupa de a cuatro sobra un caramelo. Entonces el menor número de caramelos que puede tener es cinco.

Si los agrupa de a cinco no sobra ninguno (el resto o residuo es cero):

5 l__5__

0     1

Si los agrupa de a tres, sobran dos (el resto es dos):

5 l__3__

2      1

/

Si los agrupa de a cuatro, sobra uno (el resto es uno):

5 l__4__

1      1

/

Otros ejemplos de cantidades de caramelos que puede tener son 65, 845, entre otras.step explanation:

Answer:

Pick two points from the graph. X1 y1 and x2 y2. Example points from your graph:

(4,1) and (-4,3)

x1=4

y1=1

x2=-4

y2=3

Step-by-step explanation:

To find slope take the points you got from graph and put it into the equation y2-y1/x2-x1

3-1/-4-4=-2/8=-1/4

Then take that slope u got and plug into this equation to find equation of the line

y-y1=m(x-x1)

y-1=-1/4(x-4)=y-1=1/4x+(1/4)(4)

y-1=-1/4x+1

+1 +1

——————

y=-1/4x+2 ANSWER CHECK

m=slope! Which is -1/4

y=-1/4x+2 is your answer!!

The mass of salt in the tank at time t.

dS/dt = 10 - S/400

S(0) = 100 grams

The solution is S(t) = 4000 - 3900\(e^{\frac{-t}{400}}\)

A tank holds water V(0) = 4000 liters in which salt S(0) = 100 grams.

So dS/dt = S(in) - S(out)

S(in) = 1 × 10 = 10 gram/liters

S(out) = S/V × 10 = 10S/V gram/liters

V = V(0) + q(in) - q(out)

V = 4000 + 10t - 10t

V = 4000 liters

dS/dt = 10 - 10S/V

dS/dt = 10 - 10S/4000

dS/dt = 10 - S/400

Now given; S(0) = 100.

Here, p(t) = 1/400, q(t) = 10

\(\int p(t)dt = \int\frac{1}{400}dt\)\(\int p(t)dt = \frac{1}{400}t\)

\(\mu=e^{\int p(t)dt}\)

\(\mu=e^{\frac{t}{400}}\)

So, S(t) = \(\frac{\int\mu q(t)dt+C}{\mu}\)

S(t) = \(\frac{\int e^{\frac{t}{400}} \cdot10dt+C}{e^{\frac{t}{400}}}\)

S(t) = \(e^{\frac{-t}{400}} \left({\int e^{\frac{t}{400}} \cdot10dt+C}\right)\)

S(t) = \(e^{\frac{-t}{400}} \left({10\times\frac{e^{\frac{t}{400}}}{1/400} +C}\right)\)

S(t) = \(e^{\frac{-t}{400}} \left({4000\times{e^{\frac{t}{400}} +C}\right)\)

Now solving the bracket

S(t) = 4000 + \(e^{\frac{-t}{400}}\)C.....(1)

At S(0) = 100

100 = 4000 + \(e^{\frac{-0}{400}}\) C

100 = 4000 + \(e^{0}\) C

100 = 4000 + C

Subtract 4000 on both side, we get

C = -3900

Now S(t) = 4000 - 3900\(e^{\frac{-t}{400}}\)

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The complete question is:

A tank holds 4000 liters of water in which 100 grams of salt have been dissolved. Saltwater with a concentration of 1 grams/liter is pumped in at 10 liters/minute and the well mixed saltwater solution is pumped out at the same rate. Write initial the value problem for:

The mass of salt in the tank at time t.

dS/dt =

S(0) =

The solution is S(t) =

Answer:

i don get it

Step-by-step explanation:

i stil don get it

Answer: 92

Step-by-step explanation:

Observe that the probability is symmetric around \(45^{\circ}\).

If \(0^{\circ} < x < 45^{\circ}\), then \(\cos^2 x > \cos x > \sin x\). By the triangle inequality, it follows that \(\cos^2 x > \sin^2 x+\sin x \cos x\).

We can now rearrange as follows:

\(\cos^2 x > \sin^2 x+\sin x \cos x\\\\\cos^2 x -\sin^2 x > \sin x \cos x\\\\\cos 2x > \frac{1}{2}\sin 2x\)

Since \(\cos 2x\) and \(\sin 2x\) are both positive for the chosen interval,

\(2 > \tan x \implies x < \frac{1}{2}\arctan 2\).

Therefore, the probability is \(\frac{\frac{1}{2} \arctan 2}{45}=\frac{\arctan 2}{90}\).

This means, \(m=2, n=90 \implies m+n=92\).

The p-value for the hypothesis test is approximately 0.65.

To find the p-value for the hypothesis test, we need to determine the test statistic and the corresponding probability.

First, we need to state the null and alternative hypotheses:

Null Hypothesis: The mean number of alcoholic drinks for college students at the liberal arts college is equal to the mean number of alcoholic drinks for U.S. college students in general, which is 4.73.

Alternative Hypothesis: The mean number of alcoholic drinks for college students at the liberal arts college is not equal to the mean number of alcoholic drinks for U.S. college students in general.

Next, we need to determine the test statistic, which is calculated as follows:

t = (sample mean - hypothesized mean) / (standard deviation / sqrt(sample size))

t = (4.45 - 4.73) / (3.92 / sqrt(70))
t = -0.28 / 0.47
t = -0.596

Using a t-distribution table with 69 degrees of freedom (70 - 1), we find the corresponding two-tailed probability to be 0.553.

Therefore, the p-value for the hypothesis test is 0.553. This means that if we assume the null hypothesis is true, there is a 55.3% chance of observing a sample mean of 4.45 drinks per week or more extreme. Since this p-value is greater than the commonly used significance level of 0.05, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the mean number of alcoholic drinks for college students at the liberal arts college differs from the mean number of alcoholic drinks for U.S. college students in general.
To find the p-value for the hypothesis test, we first need to set up the null and alternative hypotheses:

Null hypothesis (H₀): The mean number of alcoholic drinks for college students at this liberal arts college is equal to the national mean (µ = 4.73).
Alternative hypothesis (H₁): The mean number of alcoholic drinks for college students at this liberal arts college is different from the national mean (µ ≠ 4.73).

Next, we'll perform a t-test, since we have a sample mean, standard deviation, and sample size, but not the population standard deviation.

First, calculate the t-statistic:
t = (sample mean - population mean) / (sample standard deviation / √sample size)
t = (4.45 - 4.73) / (3.92 / √70)
t ≈ -0.46

Now, we need to find the degrees of freedom (df) for the t-distribution:
df = sample size - 1
df = 70 - 1 = 69

Using a t-table or t-distribution calculator, we can find the p-value for a two-tailed test (since we're testing for a difference, not specifically greater or lesser) with t ≈ -0.46 and df = 69. The p-value is approximately 0.65.

Your answer: The p-value for the hypothesis test is approximately 0.65.

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Answer:

D. $870; $31,320 from deposits and $3,680 from interest

Explanation:

In order to calculate the monthly payment, we use the formula below:

Given:

• The Financial Goal, A= $35,000

• Rate = 7.5% = 0.075

• Number of compounding period = 12 (Monthly)

• Time, t = 3 years

Substitute into the given formula:

The monthly payment is $870.

Option D is correct.

Answer:

divide them by what?

or fivide it with eachother?

Question options:

A. Yes, Walter is correct.

B. No 3.612 is less than 13.

C. No, both 3.612 and 3.622 are greater than

D. No, both 3.612 and 3.622 are less than 13

Answer:

C. No, both 3.612 and 3.622 are greater than the square root of 13

Explanation:

13 is a prime number and must have a decimal number as its square root and so the square root should be between √9 and √16

Using the Newton Raphson method to estimate the square root of 13 with the formula: ai +1= ai²+n/2ai

We get square root of 13 = 3.6055512

This is the same result we get using a calculator to calculate square root of 13= 3.6055512

So yes Walter is not correct

The determinant of the given matrix is \(2a^4bc+2c^4ab+6a^3b^2c+6a^3bc^2+6c^3ab^2+6a^2b^3c+12a^2b^2c^2+6a^2c^3b+6c^2ab^3+2acb^4\)

Determinant of the matrix:

Determinant of the matrix is defined as a scalar value which is associated with the square matrix.

Given,

Here we have the matrix show in the question.

Now, we need to find the determinant of the matrix.

To find the determinant of the matrix we have to do the following steps:

1) First we have to pick any row or column in the matrix. It does not matter which row or which column you use, the answer will be the same for any row or column.

2) After the selection you have to multiply every element in that row or column by its cofactor and add. The result is the determinant.

This process can be elaborated in the following steps:

\(=(b+c)^2 \times ((a+c)^2 \times (a+b)^2 - b^2 \times c^2) -a^2 \times (b^2 \times (a+b)^2 - b^2 \times c^2) +a^2 \times (b^2 \times c^2 - (a+c)^2 \times c^2)\)

When we expand the equation then we get,

\(=(b+c)^2 \times (a^4+2a^3b+2a^3c+a^2b^2+4a^2cb+c^2a^2+2c^2ab+c^2b^2+2acb^2 -b^2c^2) -a^2 \times(b^4+2b^3a+b^2a^2 -b^2c^2) +a^2 \times(b^2c^2 -c^4-2c^3a-c^2a^2)\)

Group the similar terms and arrange them in order,

\(=(b+c)^2 \times (a^4+2a^3b+2a^3c+a^2b^2+4a^2cb+c^2a^2+2c^2ab+2acb^2) -a^2 \times (b^4+2b^3a+b^2a^2-b^2c^2) +a^2 \times (-c^4-2c^3a+b^2c^2-c^2a^2)\)

Again we have to expand it and then we get,

\(= a^4b^2+2a^4bc+a^4c^2+c^4a^2+2c^4ab+2a^3b^3+6a^3b^2c+6a^3bc^2+2a^3c^3+6c^3ab^2+a^2b^4+6a^2b^3c+10a^2b^2c^2+6a^2c^3b+6c^2ab^3+2acb^4 -b^4a^2-2b^3a^3-b^2a^4+b^2c^2a^2 -c^4a^2-2c^3a^3+b^2c^2a^2-c^2a^4\)

After the simplification, the resulting determinant is

\(=2a^4bc+2c^4ab+6a^3b^2c+6a^3bc^2+6c^3ab^2+6a^2b^3c+12a^2b^2c^2+6a^2c^3b+6c^2ab^3+2acb^4\)

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Let θ be equal to 855∘. Sketch θ in standard position. θ = 855∘ is in the fourth quadrant of the coordinate plane θ = 855∘

Hence, we sketch θ in the standard position with its initial side along the positive x-axis.

Find an angle between 0∘ and 360∘ that is coterminal with θ.

The angle between 0∘ and 360∘ that is coterminal with θ is given by:

θ1 = θ - n × 360∘θ1 = 855∘ - 2 × 360∘θ1 = 855∘ - 720∘θ1 = 135∘

Find an angle between −360∘ and 0∘ that is coterminal with θ.

The angle between −360∘ and 0∘ that is coterminal with θ is given by:

θ2 = θ + n × 360∘θ2 = 855∘ + 2 × 360∘θ2 = 855∘ + 720∘θ2 = 1575∘

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Answer:

167

Step-by-step explanation:

2500÷15=166.666667

Round it up to 167

*I used 2500 and 15 because that's a point (15,2500) that you can see very clearly on the graph*

Answer:

reflection across the y- axis

Step-by-step explanation:

Under a reflection in the y- axis

a point (x, y ) → (- x, y )

Thus

The given transformation rule (x, y ) → ( - x, y )

Represents a reflection in the y - axis

Answer:

The options with the closed circles are correct

Step-by-step explanation: