between 1976 and 2016, the usa olympic team has participated in 10 olympic games (the team usa has missed the moscow 1980 games due to the cold war). the total number of gold medals won in each of the 10 games ranged between 33 and 83. the number of gold medals won in each of the games is listed below: 33 34 83 36 37 44 37 36 46 47 calculate the value, in number of gold medals, at the 69.5th percentile (show work). (2 points)'

Answer:

3800 invested at 7%; 3200 invested 12%

Step-by-step explanation:

We will need a system of equations to solve for the interest invested at both interest rates.

We can allow x to represent the amount invested at 7% and y to represent the amount invested at 12%.

We know that the amount invested at 7% + the amount invested at 12% = total investment

Thus, our first equation is x + y = 7000

We further know that the interest earned at 7% + the interest earned at 12% = total interest earned

Since we calculate interest by multiplying the investment and the interest rate, our other equation is 0.07x + 0.12y = 650 (we had to convert the percentages to decimals for the sake of the problem)

We can solve first for y by isolating x in the first equation and plugging it in for y in the second equation:

[tex]x+y=7000\\x=-y+7000\\\\0.07(-y+7000)+0.12y=650\\-0.07y+490+0.12y=650\\0.05y+490=650\\0.05y=160\\y=3200[/tex]

Now that we've found y, we can solve for x using any of the two equations, although the equation with no coefficients is much simpler:

[tex]x+3200=7000\\x=3800[/tex]

Now, we can check by plugging in 3800 for x and 3200 for y in both equations:

First equation

3800 + 3200 = 7000

7000 = 7000

Second equation

0.07(3800) + 0.12(3200) = 650

266 + 384 = 650

650 = 650

Answer:

The fourth vertex needed to create a rectangle with vertices located at (−17, 15), (−17, −7), and (−5, −7) is (-5, 15).

Step-by-step explanation:

Rectangle is a two dimensional figure which has four sides and four angles and all the angles are right angles.

Given three vertices, let it be A, B and C.

A(-17, 15), B(-17, -7) and C(-5, -7).

Let D be the point required.

By looking at other points, we can see that the sides of a rectangle will be parallel to the axes.

So, we know that the fourth point must have the same y coordinate as that of A and has same x coordinate as that of C.

So the forth vertex D is (-5, 15).

Hence the forth vertex is (-5, 15).

Parabolic Cylinder, The given vector equation is: r(s, t) = (s sin(3t), s^2, s cos(3t))

To identify the surface, let's break down the components:
1. x(s, t) = s sin(3t)
2. y(s, t) = s^2
3. z(s, t) = s cos(3t)

Now, let's eliminate the parametric s by solving for s in either the x or z component and substituting it into the y component. Since y(s, t) = s^2,

we'll solve for s in the z component:
s = z / cos(3t)
Now, substitute this expression for s into the y component equation:
y = (z / cos(3t))^2
y = z^2 / cos^2(3t)

Now we have an equation relating y and z with t as a parameter. This equation represents a parabolic cylinder, as it is quadratic in one variable (y) and linear in the other (z). The parameter t allows the parabolic shape to be rotated about the z-axis.

So, the identified surface for the given vector equation r(s, t) = (s sin(3t), s^2, s cos(3t)) is a parabolic cylinder.

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i) The variation of parameters method can be used to find the second solution. Let y = u(x)cos(2x), then y' = u'(x)cos(2x) - 2u(x)sin(2x), and y'' = u''(x)cos(2x) - 4u'(x)sin(2x) - 4u(x)cos(2x).

Substituting these into the differential equation, we get:

u''(x)cos(2x) - 4u'(x)sin(2x) - 4u(x)cos(2x) + 4u(x)cos(2x) = 0

Simplifying, we get:

u''(x)cos(2x) - 4u'(x)sin(2x) = 0

Dividing by cos(2x), we get:

u''(x) - 4tan(2x)u'(x) = 0

This is a first-order linear differential equation, which can be solved using an integrating factor. The integrating factor is e^(-2ln|cos(2x)|) = cos^(-2)(2x). Multiplying both sides by this, we get:

cos^(-2)(2x)u''(x) - 4cot(2x)cos^(-2)(2x)u'(x) = 0

The left-hand side is the derivative of cos^(-2)(2x)u'(x) with respect to x, so we can integrate both sides to get:

cos^(-2)(2x)u'(x) = C1

where C1 is a constant of integration. Integrating again, we get:

u(x) = C1int(cos^(-2)(2x)dx) + C2

This integral can be evaluated using the substitution u = sin(2x), du/dx = 2cos(2x), to get:

u(x) = C1arcsin(tan(2x)) + C2

Therefore, the second linearly independent solution is y = u(x)cos(2x) = (C1arcsin(tan(2x)) + C2)cos(2x).

ii) The general solution is y = c1cos(2x) + c2[(arcsin(tan(2x)))cos(2x)], where c1 and c2 are constants.

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The value  of the trigonometric tan of tan 26 degrees to the nearest ten thousandth is

The tangent (tan) of an angle in a right triangle is known as the measure of the ratio of the length of the side opposite the angle, against that of the side adjacent to it.

Assuming a right-angled triangle with an acute angle of 26 degrees, the tangent of this angle is calculated by comparing the measurements of the opposite and the adjacent.

A scientific calculator or trigonometric table can be employed to determine the approximate value of Tan 26, which is approximately 0.4877326.

Nearest ten thousandth is four decimal place which is written as 0.4877

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If the company uses direct materials costs as its activity base to apply overhead, the predetermined overhead rate it should use during the year is $1.42 per direct materials cost.

The predetermined overhead rate is the allocation rate used to apply the estimated cost of manufacturing overhead to cost objects.

The predetermined overhead rate is the quotient of the estimated manufacturing overhead cost and the activity base.

Estimated total direct materials costs = $1,920,000

Estimated total overhead costs = $2,726,400

Predetermined overhead rate = $1.42 ($2,726,400 ÷ $1,920,000)

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The domain is [-1, ∞)

The range is [2, ∞)

Here we have the function:

m(x) = √(x + 1) + 2

Remember that we can't evaluate something smaller than zero in a square root, then if:

x + 1 = 0

x = -1

The domain is the set [-1, ∞)

Now the square root is increasing, and its minimum is at zero when x = -1, then the minimum of the range is the costant term y = 2.

The range is [2, ∞)

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Answer:

0.36

Step-by-step explanation:

first number is who put no and safety which is 192 then the total of selected no which is 534

at least that what i got sorry if wrong

Answer:

below

Step-by-step explanation:

3. 2x² - 2x + 9 = y

a) The equation of the axis of symmetry is x = 0.5 (since it's the x-coordinate of the vertex)

b) To find the vertex, we need to complete the square:

2x² - 2x + 9 = y

2(x² - x) + 9 = y

2(x² - x + 1/4) + 9 - 2(1/4) = y

2(x - 1/2)² + 8.5 = y

So the vertex is at (0.5, 8.5).

c) The parabola opens up since the coefficient of x² is positive.

d) The vertex is the minimum point.

4. -x² + 10x = y

a) The equation of the axis of symmetry is x = 5 (since it's the x-coordinate of the vertex).

b) To find the vertex, we need to complete the square:

-x² + 10x = y

-(x² - 10x) = y

-(x² - 10x + 25 - 25) = y

-(x - 5)² + 25 = y

So the vertex is at (5, 25).

c) The parabola opens down since the coefficient of x² is negative.

d) The vertex is the maximum point.

answer:

1.78 = 1 + 0.7 + 0.08

step-by-step explanation:

1.78 = (1 • 100) + (7 • 1/101) + (8 • 1/102)

1.78 = (1 • 1) + (7 • 1/10) + (8 • 1/100)

1.78 = 1 + 7/10 + 8/100

1.78 = 1 + 0.7 + 0.08

Answer:

x = 45

Step-by-step explanation:

y is the score on the test. To find the amount of time to study he needs to get a score of 90 on his next test, we need to find x ("y=1/5x+81 models his score after studying for x minutes.")

Initial equation
[tex]y = \frac{1}{5}x + 81[/tex]

Replace y with 90
[tex]90 = \frac{1}{5}x + 81[/tex]

Find for x
[tex]90 - 81 = \frac{1}{5}x[/tex]
[tex]9 = \frac{1}{5}x[/tex]
[tex]5 * 9 = 5 * \frac{1}{5}x[/tex]
[tex]45 = x[/tex]

Therefore, Jonas needs 45 minutes to get 90 on his next test.

The solution to the line diagram are:

1) AB

2) Point B

3) A, B and C are the three collinear points

4) ABD

1) A line can be defined by two points that are connected by the given line.

We can see that the line r connects the points A and B, then we can call this line as:

AB (the notation usually uses a double arrow in top of the letters)

2) In the image we can see that lines r and s intersect at the point B, then another name for that intersection is: B.

3) 3 collinear points are 3 points that are connected by a single line, an example of this can be the points A, B and C.

4) A plane can be defined by a line and a point outside the line.

For example, we can choose the line AB and the point D, that does not belong to the line.

Then we can call the plane as ABD.

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Answer:

2 olives

Step-by-step explanation:

To find the answer, just divide 22 by 4, and the remainder will be your answer.

The remainder is 2.

~~~Harsha~~~

Answer:

f(0)=-9 and f(3)=-3

Step-by-step explanation:

f(-3)=15 - so to solve this we have to replace x with -3, which would equal:

2(-3)-9=-15.  -15 doesn't equal 15, so this is incorrect.

f(-1)=-11 Substitute x for -1: 2(-1)-9=-12.  -12 doesn't equal -11, so this is also incorrect.

f(0)=-9 Substitute x for 0.  2(0)-9= -9.  -9 does equal -9, so this is correct.

f(2)=5 Substitute x for 2.  2(2)-9=-5. This isn't correct.

f(3)=-3 Substitute x for 3.  2(3)-9=-3.  This is also correct because -3 does equal -3.

Hope this helps!  :)

The cylinders that have the same volume as the one given are: option C and option F.

The volume of a cylinder = V = πr²h

Note: r is the radius and h is the height of the cylinder.

The cylinder given has:

h = 32 m

r = 20/2 = 10 m

V = π* 10² * 32 ≈ 10053.1 m³

Option A:

h = 16 m

r = 40/2 = 20 m

V = π*20²*16 ≈ 20106.2 m³

Option B:

h = 64 m

r = 5/2 = 2.5 m

V = π * 2.5² * 64 ≈ 1256.6 m³

Option C:

h = 8 m

r = 40/2 = 20 m

V = π * 20² * 84 ≈ 10053.1 m³

Option D:

h = 64 m

r = 10/2 = 5 m

V = π * 5² * 64 ≈ 5026.55

Option E:

h = 20 m

r = 32/2 = 16 m

Volume = π * 16² * 20 ≈ 16084.95 m³

Option F:

h = 128 m

r = 10/2 = 5 m

Volume = π * 5² * 128 ≈ 10053.1 m³

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We can say with 99% confidence that the true population mean commute time to work falls within the range of 29.95 to 37.25 minutes. The margin of error of 1.83 indicates that the sample mean of 33.6 minutes may differ from the true population mean by up to 1.83 minutes in either direction.

To construct a 99% confidence interval for the population mean commute time to work, we need to use the T distribution since the sample size is less than 30. From the given information, the sample mean commute time to work is 33.6 minutes and the standard deviation is 7.1 minutes.

The formula for the confidence interval is:

(sample mean) +/- (t-value)(standard error)

The t-value is found using a T distribution table with a degree of freedom of n-1 (29-1=28) and a confidence level of 99%. This gives us a t-value of 2.763.

The standard error is calculated as the standard deviation divided by the square root of the sample size. So,

standard error = 7.1/sqrt(29) = 1.32

Plugging in the values, we get:

33.6 +/- 2.763(1.32)

This simplifies to:

33.6 +/- 3.65

Therefore, the 99% confidence interval for the population mean commute time to work is (29.95, 37.25).

The margin of error of the mean is the difference between the upper and lower bounds of the confidence interval divided by 2. In this case, the margin of error is (37.25-29.95)/2 = 3.65/2 = 1.83.

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An expression equivalent to (5x2 + 3x + 4)-(2x2 + 1)-(7x + 3) using the fewest number of possible terms is calculated to be 3x² - 4x.

We can simplify the given expression by combining like terms. By doing so, we can obtain an equivalent expression with the fewest number of possible terms. In this case, we combine the terms with the same variable and exponent and simplify the constant terms to get the simplified expression of 3x² - 4x.

(5x² + 3x + 4) - (2x² + 1) - (7x + 3)

= 5x² + 3x + 4 - 2x² - 1 - 7x - 3 (distributing the negative sign)

= (5x² - 2x²) + (3x - 7x) + (4 - 1 - 3)

= 3x² - 4x

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A community health association is interested in estimating the average number of maternity days women stay in the local hospital. A random sample is taken of 36 women who had babies in the hospital during the past year. Considering all the given values, the higher value of the interval is 3.870.

To construct a 98% confidence interval to estimate the average maternity stay in the hospital for all women who have babies in this hospital, we can use the following formula:
Confidence interval = sample mean +/- (t-value * population standard deviation / [tex]\sqrt{(sample size)}[/tex])
where the t-value is obtained from a t-distribution table for a 98% confidence level and 35 degrees of freedom (since we have a sample size of 36).
First, we need to calculate the sample mean:
Sample mean = (1+3+4+3+2+5+3+1+4+3+4+2+3+5+3+2+4+3+2+2+1+6+3+4+3+3+5+2+3+4+3+5+4+3+5+1) / 36 = 3.306
Next, we can find the t-value for a 98% confidence level and 35 degrees of freedom, which is approximately 2.429.
Plugging in the values, we get:
Confidence interval = 3.306 +/- (2.429 * 1.15 / [tex]\sqrt{(36)}[/tex]) = (3.306 +/- 0.564) = (2.742, 3.870)
Therefore, the higher value of the interval is 3.870.

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The domain of the given function is the one in option A,

Domain = 4 ≤x ≤13

To identify this, just look at the horizontal axis (which is the axis of the inputs, and we know that the domain is the set of the inputs of the function), here we can see that the graph (which is the bell-shaped curve) starts at 4 and ends at 13.

Then the domain is the set of all values between these two, we can write this as:

Domain = 4 ≤x ≤13

Thus the correct option is A.

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Answer:60

Step-by-step explanation:

We can start by splitting the figure into 3 rectangals. one with side lengths 4,6 another with 5,4 and another with 4,4. Then we get 24+20+16=60

Our test statistic t (-1.86) is greater than the critical value of t (-2.602), we fail to reject the null hypothesis. This means that we do not have sufficient evidence to conclude that state employees earn on average less than federal employees at the 0.01 level of significance.

To determine if state employees earn on average less than federal employees, we can perform a hypothesis test using the given information. Let's denote the population mean salary of federal government employees by μ and the population mean salary of state employees by μ1. We want to test the null hypothesis that the average salary of state employees is equal to or greater than the average salary of federal employees, against the alternative hypothesis that the average salary of state employees is less than the average salary of federal employees. This can be expressed as:

H0: μ1 >= μ

Ha: μ1 < μ

We will use a one-tailed t-test with a 0.01 level of significance, since we are testing for a difference in one direction (state employees earning less than federal employees) and the sample size is small (n=32).

First, we need to calculate the test statistic t, which can be calculated using the formula:

t = X - μ) / (s / sqrt(n))

where X is the sample mean, s is the sample standard deviation, n is the sample size, and μ is the hypothesized population mean. In this case, X= $59,000, s = $1500, n = 32, and μ = $59,593.

Plugging in these values, we get:

t = (59,000 - 59,593) / (1500 / sqrt(32)) = -1.86

Next, we need to find the critical value of t from the t-distribution table with 31 degrees of freedom (since n-1=31 for a sample size of 32) and a one-tailed significance level of 0.01. The critical value is -2.602.

Since our test statistic t (-1.86) is greater than the critical value of t (-2.602), we fail to reject the null hypothesis. This means that we do not have sufficient evidence to conclude that state employees earn on average less than federal employees at the 0.01 level of significance

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True. In 2016, the percentage of the ageing population (55 years or older) in state prisons surpassed the percentage of people aged 18-24 for the first time.

This trend reflects the overall growth of the ageing population within the United States and is a result of various factors such as longer life expectancy, harsher sentencing laws, and an increase in older individuals being convicted of crimes.
As the ageing population in state prisons continues to grow, it poses several challenges for the correctional system. These challenges include providing appropriate healthcare and accommodations for older inmates and addressing the specific needs of this population, such as mobility assistance and specialized medical care.
In conclusion, the shift in the age demographics of state prisons has significant implications for the management and administration of correctional facilities. It is crucial to address the unique needs of the ageing population within these institutions and adapt policies and practices accordingly to ensure the well-being and fair treatment of all inmates, regardless of their age.

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The ratio of the volumes of two spheres is proportional to the cube of their radii (or diameters), hence it is 125:1.

Since planet A has a diameter that is approximately 10 times that of planet B, its radius is 5 times that of planet B.

Therefore, the ratio of the volumes of planet A to planet B can be calculated as follows:

(Volume of A) / (Volume of B) = (4/3)πrA³ / (4/3)πrB³

where rA is the radius of planet A and rB is the radius of planet B.

Since rA = 5rB, we can substitute this into the equation above:

(Volume of A) / (Volume of B) = (4/3)π(5rB)³ / (4/3)πrB³

Simplifying the equation by canceling out the common terms, we get:

(Volume of A) / (Volume of B) = 5³

Therefore, the ratio of the volumes of planet A to planet B is 125:1. In other words, planet A has a volume that is 125 times greater than that of planet B.

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For a 95% lower confidence bound, we only need the lower limit. The 95% lower confidence bound on the mean life of a 75-watt light bulb is approximately 1003.045 hours.

To construct a 95% two-sided confidence interval on the mean life, we can use the formula:

CI = x ± tα/2 * (σ/√n)

where x is the sample mean (1014 hours), σ is the population standard deviation (25 hours), n is the sample size (20), and tα/2 is the critical value from the t-distribution with (n-1) degrees of freedom at a significance level of α/2 = 0.025 (since we want a 95% confidence interval).

Using a t-table or calculator, we can find that t0.025,19 = 2.093. Substituting these values into the formula, we get:

CI = 1014 ± 2.093 * (25/√20) = (970.5, 1057.5)

Therefore, we are 95% confident that the true mean life of the 75-watt light bulb is between 970.5 hours and 1057.5 hours.

To construct a 95% lower confidence bound on the mean life, we can use the formula:

LB = x - tα * (σ/√n)

where LB is the lower bound, x is the sample mean, σ is the population standard deviation, n is the sample size, and tα is the critical value from the t-distribution with (n-1) degrees of freedom at a significance level of α = 0.05 (since we want a one-sided confidence bound).

Using the same values as before, we can find that t0.05,19 = 1.734. Substituting these values into the formula, we get:

LB = 1014 - 1.734 * (25/√20) = 991.2

Therefore, we are 95% confident that the true mean life of the 75-watt light bulb is at least 991.2 hours.

Step 1: Identify the given information
- Sample mean (x) = 1014 hours
- Sample size (n) = 20 bulbs
- Population standard deviation (σ) = 25 hours
- Confidence level = 95%

Step 2: Calculate the standard error (SE)
SE = σ / √n = 25 / √20 = 5.590

Step 3: Find the critical value (z) for the 95% confidence level (two-sided)
For a 95% confidence interval, the z-value is 1.96.

Step 4: Calculate the margin of error (ME)
ME = z * SE = 1.96 * 5.590 = 10.955

Step 5: Construct the 95% confidence interval
Lower limit = x - ME = 1014 - 10.955 = 1003.045
Upper limit = x + ME = 1014 + 10.955 = 1024.955

The 95% two-sided confidence interval on the mean life of a 75-watt light bulb is approximately (1003.045 hours, 1024.955 hours).

Step 6: Construct the 95% lower confidence bound
For a 95% lower confidence bound, we only need the lower limit.
The 95% lower confidence bound on the mean life of a 75-watt light bulb is approximately 1003.045 hours.

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The number 1.1 in this scenario is the population standard deviation, which represents the variability of the entire population.

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

The sample standard deviation of 0.92 is an estimate of the population standard deviation based on the sample data. The sample mean of 5 is also an estimate of the population mean based on the sample data. By using the sample statistics, we can make inferences about the population parameters with a certain level of confidence.

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The A matrix for this transformation has 2 rows and 5 columns.

The A matrix has M rows and N columns, where M is the number of rows in A and N is the number of columns in A. Since the transformation goes from R5 to R2, the codomain is R2, which means that the A matrix has 2 rows in the codomain. However, we do have number of columns for 2 columns and 2 rows.

A transformation that goes from R5 to R2 has a matrix A with the following dimensions:

- The number of columns in A corresponds to the dimension of the domain, which is R5. So, A has 5 columns.
- The number of rows in A corresponds to the dimension of the codomain, which is R2. So, A has 2 rows.

Therefore, the A matrix for this transformation has 2 rows and 5 columns.

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Answer:

23/77

Step-by-step explanation:

To simplify this expression, we need to find a common denominator for all the fractions. The smallest common multiple of 7 and 11 is 77. So, we'll convert each fraction to an equivalent fraction with a denominator of 77.

5/7 = (5 * 11)/ (7 * 11) = 55/77

2/11 = (2 * 7)/ (11 * 7) = 14/77

-8/7 = (-8 * 11)/ (7 * 11) = -88/77

6/11 = (6 * 7)/ (11 * 7) = 42/77

Now we can add the fractions:(55/77) + (14/77) + (-88/77) + (42/77) = 23/77So the simplified answer is 23/77.

In this case, the exponential term (4^n) grows much faster than the quadratic term (n^2). Therefore, the numerator will grow at a much faster rate than the denominator as n approaches infinity. Consequently, the limit does not exist, and the sequence is divergent.

The given sequence is: f_n = 9/(4^n) + 13.

To determine whether this sequence is convergent or divergent, we can take the limit of f_n as n approaches infinity:

lim (n → ∞) f_n = lim (n → ∞) (9/(4^n) + 13)

As n approaches infinity, (4^n) goes to infinity much faster than 9, so the entire first term of the sequence goes to 0. Therefore:

lim (n → ∞) f_n = lim (n → ∞) (0 + 13) = 13

Since the limit exists and is finite, the sequence converges. Its limit is 13.
To determine whether the given sequence is convergent or divergent, we first need to identify the sequence. Based on your question, it appears the sequence is:

f(n) = (9(4^n) + 13) / (n^2)

Now, let's evaluate the limit as n approaches infinity:

lim (n → ∞) (9(4^n) + 13) / (n^2)

In this case, the exponential term (4^n) grows much faster than the quadratic term (n^2). Therefore, the numerator will grow at a much faster rate than the denominator as n approaches infinity. Consequently, the limit does not exist, and the sequence is divergent.

Your answer: The sequence is divergent.

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The temperature of the turkey after 4.5 hours in the oven is 192°F, to the nearest degree.

We have,

We can use the given formula to solve for the value of k:

T = Ta + (To – Ta)e^{-kt}

Ta = 350°F (oven temperature),

To = 69°F (room temperature),

T = 110°F (temperature after 2 hours).

Plugging these values in and solving for k, we get:

110 = 350 + (69 - 350)e^{-2k}

-240 = -281e^{-2k}

0.855 = e^{-2k}

ln(0.855) = -2k

k = 0.211

Now that we know k, we can use the same formula to find the temperature of the turkey after 4.5 hours:

T = Ta + (To – Ta)e^{-kt}

Ta = 350°F,

To = 69°F

k = 0.211.

Plugging these values in and solving for T.

T = 350 + (69 - 350)e^{-0.211(4.5)}

T = 192

Thus,

The temperature of the turkey after 4.5 hours in the oven is approximately 192°F, to the nearest degree.

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