After sitting out of a refrigerator for a while, a turkey at room temperature (70°F) is
placed into an oven. The oven temperature is 325°F. Newton's Law of Heating
explains that the temperature of the turkey will increase proportionally to the
difference between the temperature of the turkey and the temperature of the oven, as
given by the formula below:
T=Ta +(To-Ta)e-kt
Ta = the temperature surrounding the object
To the initial temperature of the object
=
t the time in hours
T= the temperature of the object after t hours
k = decay constant
The turkey reaches the temperature of 116°F after 2.5 hours. Using this
information, find the value of k, to the nearest thousandth. Use the resulting
equation to determine the Fahrenheit temperature of the turkey, to the nearest
degree, after 5.5 hours.

Answer:

(-∞, -12), (2, ∞)

or

(-∞, -12) U (2, ∞)

Step-by-step explanation:

|3x + 15| > 21, |3x + 15| < -21

3x + 15 > 21,  3x + 15 < - 21

     -15    -15         -15     -15

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

3x > 6               3x < - 36

÷3  ÷3               ÷3     ÷3

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

x > 2                  x < -12

(-∞, -12), (2, ∞)

or

(-∞, -12) U (2, ∞)

I hope this helps!

Firstly, we want to start by drawing the triangles

We have this as follow;

For triangle HOT, we have;

We want to get the values of x and y firstly

Since both triangles are congruent, the order of the sides match

Hence, we have angle O and H equal

Thus, we have that;

Now, to find Y, we need the measure of angle N

Angle N is same as W which we already have as 5y+ 26

Substitute N for Y

Since all the angles of a triangle sum up to 180, we have it that;

Now, we want the measure of each of the angles;

1. W = N = 5y+ 26 = 5(13) + 26 = 91

2. H = O = 5x-1 = 5(9) - 1 = 44

3. Y = T = 4x + 9 = 4(9) + 9 = 45

Answer:

The construction is a parallel line to a given line  from a point not on the line.

Step-by-step explanation:

For a given figure,

To construct a parallel line

Step 1 : Draw transversal line through any point not on line which is given.

Step 2: Using construction copy an angle, construct same angle formed by transversal line and given line.

Step 3: This is the last step in which when the copy of an angle completed draw a line parallel to the line

Step-by-step explanation:

The image of the transformation are (2, -9), (-9, -7), (-7, -4)

The coordinates of the triangle are given as

(-2, -9), (9, -7), (7, -4)

The transformation is given as

Reflection across the y-axis

This is represented as

(x, y) ⇒ (-x, y)

This means that the transformation is (-x, y)

When this rule is applied on the coordinates, we have

(2, -9), (-9, -7), (-7, -4)

Next, we plot the image of the transformation on a coordinate plane

See attachment for the image of the transformation

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q + r = p is the equation formed by using the details in the question

In an algebraic equation of the form y=mx+b, where m denotes the slope and b the y-intercept, a linear equation is a first-order (linear) term and a constant. Sometimes the phrase "linear equation with two variables" is used to describe the previous equation, which contains the variables y and x.

Ax+By=C is the standard form for two-variable linear equations. Standard form is used, for instance, in the linear equation 2x+3y=5. This method makes it simple to find an equation's two intercepts (x and y).

p the stove is hot

q the soup is cold

r the food is done

equation to be created was

the food is done and the soup is cold ,  then the stove is hot.

and means +

therefore equation formed by plugging in the values will be ,

q + r = p

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Answer:

(-12, 21)

Explanation:

3 times a number decreased by 5 means 3x -5.

This number is between -41 and 58; therefore,

Now we solve for the unknown number x.

Adding 5 to the three sides gives

finally, dividing the inequality by 3 gives

the parenthesis indicates that the -12 and 21 are not included in the solution interval =.

The correct equation to be written for 500 will be 5*100 = 500. This same can also be written as 50*10 = 500 in the equational form to represent 500.

A mathematical equation can be stated as a formula that uses the equals sign in order to represent the equality of two expressions. In other words, it's a statement that shows that the values of two mathematical expressions are equal.

The equality between the equations here is shown by the equals (=) sign

As an example, 3x + 5 = 14 can be stated as an equation, in which 3x + 5 and 14 are two expressions that are connected by an ‘equal’ sign, thus providing an equation form.

If you set on typing the actual types of equations, then you will just find many to categorize from.

But mainly the types of equations can be classified as:

1) Algebraic Equations (includes linear, quadratic, cubic, polynomial equations)

2) Radical Equations

3) Exponential Equations

4) Rational Equations

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The mean number of unoccupied seats per flight during the past year will lie between 11.15 and 12.05.

What is mean in mathematics?

There are many mean types in maths, particularly in statistics. Each mean serves to condense a specific set of data, frequently so that the general magnitude and sign of the data set can be better understood.

The arithmetic mean, also referred to as "arithmetic average," is a calculation that divides the total number of values in a data collection by their sum to get the central tendency of that set of numbers.

a) Calculations:

Degrees of freedom = n - 1 = 225 - 1 = 224

For 224 degrees of freedom and 90% confidence interval,

Critical t value = 1.652

Hence,

90% confidence interval will be:

[tex]11.6 \pm 1.652*4.1/\sqrt{225}[/tex]

[tex]11.6 \pm 0.45[/tex]

(11.15, 12.05)

b) Interpretation:

We are 90% confident that the population mean number of unoccupied seats will lie between 11.15 and 12.05

c) Caution with interpretation:

In this scenario, individual confidence interval should be calculated rather than mean number of unoccupied seats since we can't generalize this interpretation for individual flights.

d) To narrow a confidence interval, we can either increase the sample size or can decrease the confidence level.

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Complete question

Unoccupied seats on flights cause airlines to lose revenue. Suppose a large airline wants to estimate its average number of unoccupied seats per flight over the past year. To accomplish this, the records of 225 flights are randomly selected, and the number of unoccupied seats is noted for each of the sampled flights (from text, p. 306, example 6.3; use NOSHOW excel file). Given the mean number of unoccupied seats for the 225 random flights is 11.6 and the standard deviation is 4.1, estimate μ, the mean number of unoccupied seats per flight during the past year, using a 90% confidence interval.

a. Calculations

b.Interpretation

c.Caution with interpretation

d.How to narrow a confidence interval

Answer: x = -1 y=3

Step-by-step explanation:

yeah just do AP algebra.2 then you'll know the answers

Answer:

A) Reflexive Property of Equality

Step-by-step explanation:

If you look at your reflection in a mirror, you see yourself! Likewise, by the Reflexive Property, any number is its own mirror image. Any number (such as a real number) is equal to itself!

What this means is that any number is the answer as no number is given. It could be 3m = 3n, 10m = 10n, or 85m - 85n as long as the number of "m" is the same to the number of "n."

The measure of the angle having the question mark, found using the law of sines is ? ≈ 140°

The law of sines states that the sine of an interior angle of a triangle is proportional to the the length of the side opposite to the angle.

The given parameters are;

The radius of circle A = 6.4

The radius of circle B = 4.0

The radius of circle C = 3.0

The measure of angle at C = 24°

The length of the segment AB = 6.4 + 4 = 10.4

According to the law of sines, we have;

[tex]\dfrac{sin(A)}{a} = \dfrac{sin(B)}{b} = \dfrac{sin(C)}{c}[/tex]

Where;

a = The length of the side opposite angle ∠A

b = The length of the side opposite angle ∠B

c = the length of the side opposite angle ∠C

From the diagram, the side opposite angle ∠C, is AB, which by comparison indicates that when side c = AB = 10.4

c = 10.4

Similarly, the side opposite angle ∠A = a = BC = 4 + 3 = 7

a = 7

The known information are therefore; ∠C = 24°, a = 7, c = 10.4

[tex]\dfrac{sin(A)}{a} = \dfrac{sin(C)}{c}[/tex]

[tex]\dfrac{sin(A)}{7} = \dfrac{sin(24^{\circ})}{10.4}[/tex]

[tex]sin(A) = \dfrac{sin(24^{\circ})}{10.4}\times 7[/tex]

[tex]\angle A = arcsine \left( \dfrac{sin(24^{\circ})}{10.4}\times 7\right)[/tex]

∠A + ∠B + ∠C = 180° (angle sum property of a triangle)

∠B = 180° - (∠A + ∠C)

Which gives;

[tex]\angle B = 180^{\circ} -\left(24^{\circ} + arcsine \left( \dfrac{sin(24^{\circ})}{10.4}\times 7\right)\right) \approx 140^{\circ}[/tex]

The measure of the angle is ∠B ≈ 140°

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Answer:Explanation:

C. 75

n cthe oomparison of variables, a negative correlation means that as the value of one of the variables increases, the value of the other variable decreases.

Given the variables k and l.

• L=150 when k = 7

• L=? when k=14

The variable k has increased.

Thus, to satisfy the condition for a negative correlation, the variable, l must decrease.

Thus, the only likely possible value of l is 75.

Option C is correct.

Answer:

The polygon has 14 sides.

Explanation:

Given that the sum of the interior angles of the polygon is 2,160.

Recall that the sum of interior angles of a polygon can be calculated using the formula;

Substituting the value of T, to solve for n;

Therefore, the polygon has 14 sides.

when a number is power to a number a, and it is also power to another number b we can apply the property

apply this to the expression above

continue by applying the property of a product between the same number as a base but with a different exponent

apply this to the expression above

the value of p is equal to 43.

Answer:

Step-by-step explanation:

You want the factors of 5y² +13y +6, and the solutions to 5y² +13y +6 = 0.

The quadratic ax²+bx+c with a leading coefficient a≠1 can be factored by considering the factors of the product 'ac' that have a sum of 'b'.

  5·6 = 30 = (1)(30) = (2)(15) = (3)(10) = (5)(6)

The sums of these factor pairs are, respectively, 31, 17, 13, 11. The factor pair with a sum of 13 is (3)(10).

There are a couple of methods that can be used to apply this knowledge to the factorization of the quadratic. Perhaps the most straightforward is to write the quadratic as 4 terms, using the found values to rewrite the linear term as their sum:

  5y² +13y +6 = 5y² +3y +10y +6 . . . . . . . . . 13 ⇒ 3 +10

Now, pairs of terms can be factored:

  = y(5y +3) +2(5y +3)

  = (y +2)(5y +3) . . . . . . . fully factored expression

The solutions that makes the product of factors be zero will be the values of x that make the factors be zero. A product is only zero if one of the factors is.

  y +2 = 0   ⇒   y = -2

  5y +3 = 0   ⇒   y = -3/5

The solutions to the quadratic equation are y = {-2, -3/5}.

__

Additional comment

Another way to find the factors is this. For factors p, q that have a product of 'ac' and a sum of 'b', the factorization can be ...

  (ay +p)(ay +q)/a

For the values in this problem, this would be ...

  (5y +3)(5y +10)/5

The latter of these factors can be divided by 5, so this can be simplified to ...

  (5y +3)(y +2) . . . . as above

Since a sample is a subset of the population the sample mean varies around the mean of the population.

An average of a group of data is called a sample mean. A data set's central tendency, standard deviation, and variance can all be determined using the sample mean. A population average can be determined using the sample mean, among other things.

The statistic known as the sample mean is created by arithmetically averaging the values of a variable in a sample. The sample mean is an estimator of the expected value if the sample is taken from probability distributions with a common expected value.

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The result of the approximation of -16 + square root of 40 is -3.35.

An approximation refers to anything which is similar to but not identical to something else.

Rounding can be used to approximate a number. Before performing the operations, an estimate can be approximated by rounding this same values within it.

For the given number;  

-16 + square root of 40 can be written as.

= -16 + √40

Find the factors of 40 by prime factorization;

40 = 2×2×2×5

Put the value in expression.

= -16 + √2×2×2×5

Take out square root of 2.

= -16 + 2√2×5

= -16 + 2√10

Fine the approximate value of √10 as this is near to √9.

Thus, √10 = 3.12

Put the value in expression.

= -16 + 2×3.12

= -16 + 12.649

= -3.35

Thus, the approximation of -16 + square root of 40 is -3.35.

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The vertical and horizontal asymptotes for the graphed function are given as follows:

a) The vertical asymptotes are given at  x = -1 and x = 2.

b) The horizontal asymptote is given at y = -1.

In the context of this problem, we have that the asymptotes can be extracted from the graph as follows:

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Answer:

I think its 64 please let me know if its wrong

The value of x is (t - ab)/ad while taking the subject x.

So, t = a(b + dx):

Now, solve taking the subject 'x' as follows:

Therefore, the value of x is  (t - ab)/ad while taking the subject x.

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The intersection point of the circle and the line is at-(2.68, 7.36).

For the given question;

The equation of the line is; y = 2x + 2   ......eq 1

The centre of the circle (h,k) = (0,2)

The radius of the circle = 6 units.

This is the equation's standard form.

(x - h)² + (y - k)² = r²

Put the values in the formula;

(x - 0)² + (y - 2)² = r²

(x)² + (y - 2)² = r²

Put the value of y from eq 1.

(x)² + (2x + 2 - 2)² = 6²

(x)² + (2x)² = 36

Simplifying;

x = ±6/√5

But the intersection must be in first quadrant.

x = 6/√5 = 2.68

Put the value of x in eq 1.

y = 2x + 2

y = 2×2.68 + 2

y = 7.36

Thus, the coordinates of the intersection of the line and the circle are (2.68, 7.36).

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After simplified the equation we get
a=54
b= 540
c=1800
d=2000

What is simplified expression?

Solving a math problem is the same thing as simplifying an expression. You basically try to write an expression as simply as you can when you simplify it. At the conclusion, there shouldn't be any more multiplying, dividing, adding, or removing to do. Take this formula, for instance: 4 + 6 + 5. To simplify an expression, create an equivalent expression without any terms that are similar. The expression will then be rewritten using the fewest terms possible. When confronted with the phrase 4x+5(3x12),

Sol-

2(3x+10)^3

=2(Bx)^3+3.(3x)^2.10+3.3x.10^2+10^3

=2(27x^3+270x^2+900x+1000)

=54x^3+540x^2+1800x+2000

So,

a=54

b=540

c=1800

d=2000

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Answer:

47.900

Step-by-step explanation

45.50 plus 2.275 is 47.825 rounded is 47.9

Step-by-step explanation:

y = mX + c

3y = -3x - 1

divide by 3

y = -x -1/3

slope = -1 of this line and parallel lines

Answer:

-1 is the slope beause lines with the same slope are parallel.

The solution of the system of equation is the point where the 2 lines cross each other.

By looking at the graph, we can see that they cross each other at (-3,-8)

Correct option: 2

Analia proposed the following two measures to determine which school had a better academic record:

B. Graduation rate and student budget

D. Average SAT score / Per-student budget

To specify a number that represents academic accomplishment;

We compare the budget per pupil for each school to a corresponding metric or parameter that measures the academic performance of the students in each school.

The following variables could be used to gauge academic achievement:

the success rate of every school.

The SAT score of each institution.

Consequently, the amount to assess academic success in relation to each student's budget may be represented as;

Graduation rate and student budget

Average SAT score / Per-student budget

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We are asked to simplify the following expression

Recall the quotient rule of radicands given by

Applying the above rule to the given expression

Notice that the square root of 324 is equal to 18

Also, notice that we can break 405 into factors as

So, the expression becomes

Therefore, the simplified expression is

a = √5

b = 2