Elliot takes a roast out of the oven when the internal temperature of the roast is 165°F. After 12 minutes, the temperature of the roast
drops to 140°F.
The temperature of the room is 70°F.
How long does it take for the temperature of the roast to drop to 125°F?
Use the Newton's Law of Cooling equation, T(t)=TA+ (To-TA) e-kt
Enter your answer in the box. Round your answer to the nearest minute.
minutes

If If the measure of an angle is not 180, then it is not a straight angle" relate to the conditional statement "If an angle is a straight angle, then its measure is 180." This is a A. counterexample.

Contraposition in logic and mathematics refers to the inference of going from a conditional statement to its logically equivalent contrapositive, as well as the associated proof method known as proof by contraposition. A statement's contrapositive has its antecedent and consequent inverted and flipped.

Any exception to a generalization is a counterexample. A counterexample disproves the generalization in logic, and it does so rigorously in mathematics and philosophy.

Find a case where P is true but Q is false to provide a counterexample to a conditional statement P Q. Here is the equivalent rule for negating a conditional: (P Q) (P Q) Once again, the "if-part" P must be true and the "then-part" Q must be false (that is, Q must be true).

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Joe has $120 after all the trades, which is the entire amount.

Given that,

With $80, Joe opened a bank account. Then he took out $35, put in $115, and took out another $40.

To know how much balance left in his account after all the transactions in dollars;

Assume that,

Amount when account opened (x) = $80

Amount withdrawn (y) = $35

Amount deposited again (z) = $115

Amount withdrawn again (p) = $40

The total amount left after all the above transactions is;

A = x - y + z - p

  = 80 - 35 + 115 - 40

  = 195 - 75

A = $120

Therefore, the total amount left with Joe after all the transactions is $120.

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The solution by Elimination Method of the given equations -x+9y=35 and 2x+2y=10 is given by, x=1,y=4.

Given the equations are,

-x+9y = 35 .............(i)

2x+2y = 10 ...........(ii)

From the equation (ii) we get,

2x+2y = 10

x+y = 5 ...............(iii)

Adding (i) and (iii) we get,

-x+9y+x+y = 35+5

10y = 40

y = 40/10

y = 4

Substituting the value of y in (i) we get,

-x+9*4 = 35

-x+36 = 35

-x = 35-36

-x = -1

x = 1

Hence the solution of the equations is, x=1,y=4.

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Test of significance is  the observed effect due to chance. Option (c) is correct .

What is a significance test?

What makes significance significant?

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Answer:

Step-by-step explanation:75mph

The number of fidget spinners that had not sold yet is; 9,455.

The quantities given in the problem are the total number of fidget spinners shipped each weeks and the number of them sold.

It follows from the task content that the total number of fidget spinners that had not sold yet be determined from the information given.

According to the task content;

1st week;

12,875 fidget spinners were shipped and 9,843 of them were sold.

The number of fidget spinners that had not sold yet is therefore; = 12875 - 9843 = 3,032.

2nd week;

19,175 fidget spinners were shipped and 12,752 of them were sold.

The number of fidget spinners that had not sold yet is therefore; = 19,175 - 12,752 = 6,423.

Ultimately, the total number of fidget spinners that had not sold yet is; 3,032 + 6,423 = 9,455.

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AnThe volume of prism is equal to volume of pyramid.

What is volume of prism?

The volume of a prism is defined as the total space occupied by the three-dimensional object.

The volume of a Rectangular Prism = lbh cubic units.

Where

l = Base width of a rectangular prism

b = Base length of a rectangular prism

h = height of a rectangular prism

What is volume of pyramid?

A triangular pyramid has a base in triangle shape. As we know, the area of a triangle;

A = 1/2 b x h

where b is the base of the triangle and h is the altitude.

But we have rectangular pyramid,

volume of rectangular pyramid = 1/3lbh

Given,

The length of prism= 3a

breadth = 2b

height = c

Therefore, volume of prism = 3a(2b)(c)

= 6abc

Similarly, length of pyramid = a

breath = b

height = 18c

volume of pyramid = 1/3(a)(b)(18)c

=6abc, which is equal to volume of prism.

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The sidelength of the square is 6 units, with that we can find that the perimeter is 24 units.

For a square of side length S, the perimeter is give by the formula:

P = 4*S

In this case, the vertices of the square are given, and I and J are consecutive vertices, where:

I = (8, - 10)

J = (2, - 10)

Notice that the y-component is the same, then the side length of the square is:

S = 8 - 2= 6

Using the formula for the perimeter we get:

P = 4*S = 4*6 = 24

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After solving the value of r = (-1 - t / 5).

Given equation:

6r + t = r - 1

6r - r + t = -1

5r + t = -1

5r = -1 - t

divide by 5 on both sides

5r/5 = -1 - t / 5

r = (-1 - t / 5)

Therefore r = (-1 - t / 5)

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The slope of the line is B.

In mathematics, the slope of a line is the change in y-coordinate with respect to the change in x-coordinate.

The net change in the y coordinate is denoted by Δy and the net change in the x coordinate is denoted by Δx.

So the change in the y coordinate for a change in the x coordinate is:

The slope of a straight line can also be expressed as:

In general, the slope of a line is a measure of its steepness and direction. The slope of the line between two points (x1,y1) and (x2,y2) can be easily determined by finding the difference in the coordinates of the points.

If the x-coordinate of each point on a line is 5 more than half the y-coordinate, then x= y2+5.

To find the slope of the line, solve for y and put the equation in slope-intercept form (y = mx + b, where m is the slope).

To do so, first subtract 5 from both sides, then multiply the entire equation by 2 to get y = 2x − 10.

The slope is 2.

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The kilograms equivalent of the given pound measurement as required in the task content is; 0.8505 kg.

It follows from the task content that the equivalent measure of 15/8 y pounds is to be determined according to the given conversion factor.

Since it is given that; 50 lbs = 22.68 kg.

It follows by proportion that; 15/8 pounds is equivalent to; ( (15/8) × 22.68 ) / 50

= 0.8505 kilograms.

Therefore, the required equivalent kilogram measure is; 0.8505 kilograms.

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Answer:

8 1/3

Step-by-step explanation:

We want to find a number, x, that when divided by 10/3 equals 2.5.  We can write that as:

  x/(10/3) = 2.5

x = (2.5)*(10/3)    [MULTIPLY BOTH SIDES BY (10/3)

x = 25/3

x = 8 1/3             [

the probability of the event that  a sample of 5 cans will have a meaningful amount of at least 12.13 oz is 0.0078

We are provided with the information that cans of coke are filled in the account of having normal distribution, with the provided means which is  12.00 oz and the standard deviation of 0.12 oz and the sample size is

n= 5.

let X be the sample mean, so the probability will be :

P(X[tex]\geq[/tex] 12.13) = 1- P(X<12.13)

               =1-  P(X-(μ/(σ/[tex]\sqrt{n}[/tex])) < (12.13 -12.00)/(0.12/[tex]\sqrt{5}[/tex]))

            = 1- P(z<2.42)

            = 1-0.9922

           =0.0078

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Cans of regular Coke are labeled as containing 12 oz. Statistics students weighted the content of 5 randomly chosen cans, and found the mean weight to be 12.13. Assume that cans of Coke are filled so that the actual amounts are normally distributed with a mean of 12.00 oz and a standard deviation of 0.12 oz. Find the probability that a sample of 5 cans will have a mean amount of at least 12.13 oz.

The line r has a slope 1/3 and y-intercept (0,5)

What is the Dilation?

Math definition of dilation Resizing an object is accomplished through a change called dilation. The objects can be enlarged or shrunk via dilation. A shape identical to the source image is created by this transformation. The size of the form does, however, differ.

Given

The slope of the line and its intercept (0,2)

The slope of the line r will not change.

And intercept is the addition of their ordinate will be.

Intercept = 2+3

Intercept = 5

So, the line r has slope 1/3 and y-intercept (0,5).

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The null we are interested in testing here is that the coefficients on age and age^2 are jointly zero. So, we would need to run a restricted version of the regression above where these two variables are omitted and calculate.

Given:

what other regression do you need to run to test the null hypothesis that, holding other factors fixed, age has no effect on sleeping.

The null we are interested in testing here is that the coefficients on age and age^2 are jointly zero.

[tex]F = R^2_{ur}-R^2_r / q / 1-R^2_{ur} (n-k-1)[/tex]

Therefore the null we are interested in testing here is that the coefficients on age and age^2 are jointly zero. So, we would need to run a restricted version of the regression above where these two variables are omitted and calculate.

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The given phrase written as an algebraic expression is  c / 25 .

The given phrase is : a number c divided by 25

So if we consider any number 'c' , then the number when divided by c can be written as c ÷ 25

The required expression to represent this is given by c / 25.

Expressions are phrases used to describe statements in mathematics that contain variables, numbers, sometimes both, and at least two terms joined by an operator. Mathematical operations include addition, multiplication, and division.

The two types of expressions used in mathematics are numerical expressions, which only contain numbers, and algebraic expressions, which also contain variables.

A symbol with an unknown value is referred to as a variable. A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided. A number that has been further multiplied by a variable is referred to as a coefficient in an equation.

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A situation in which the person can afford 9 t-shirts and one 1-sweatshirts, but not 3 T-shirts and 8 sweatshirts are when the value of the gift card is $100 and the price of each t-shirt is $10.

The relation between two unequal expressions is defined as inequality.

Given that, the person can afford 9 T-shirts and 1 sweatshirt but not 3 t-shirts and 8 sweatshirts.

Let the value of the gift card be y.

Let the cost of one shirt and one sweatshirt be t and s respectively.

Then, the inequality for the condition that "the person can afford 9 T-shirts and 1 sweatshirt" is:
9t + s ≤ y

The inequality for the condition that " the person cannot afford 3 t-shirts and 8 sweatshirts" is:

3t + 8s > y

Now, let the person buys 1 sweatshirt in any situation, then from inequalities (1) and (2):

9t + 1 ≤ y

3t + 8 > y

Hence, the system of inequalities is:

9t + 1 ≤ y

3t + 8 > y

The graph of the inequalities is shown.

Let the value of the gift card be $100 and the price of each t-shirt is

t =$10, then

9(10) + 1 ≤ 100

91≤100, true

And,

3(10) + 8 > 100

38 > 100, false

Hence, a situation in which the person can afford 9 t-shirts and one 1-sweatshirts, but not 3 T-shirts and 8 sweatshirts are when the value of the gift card is $100 and the price of each t-shirt is $10.

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Answer:

24

Step-by-step explanation:

LCM 8 ,6 ,12 =24

by PRIME factorization

8  =   2 x 2 x 2

6  =   2              x 3

12 = 2  x 2       x 3

       2 x 2 x 2 x  3  =24

The total amount in his savings account after 5 years will be $10,075 if the annual simple interest rate is 0.15%.

According to the question,

We have the following information:

Dave opens a savings account that has an annual simple interest rate of 0.15%. He initially deposits $10,000 and the time given is 5 years.

We know that following formula is used to find simple interest:

Principal*rate*time/100

(10000*0.15*5)/100

100*0.15*5

$75

Now, the total amount will be the sum of interest and the principal amount:

10000+75

$10,075

Hence, the total amount in his savings account after 5 years will be $10,075 if the annual simple interest rate is 0.15%.

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50 boxes are needed to pack 600 granola bar when 12 granola bar in a single bar.

Given, a nack company that sells snacks may fit 12 granola bars in a box.

We must determine the number of boxes required to hold 600 granola bars.

By using the unitary technique, we can calculate both the value of multiple units from the value of a single unit and the value of single unit from the value of multiple units. We typically utilize this technique for math calculations. This approach will be helpful to you while tackling problems involving ratio and proportion, algebra, geometry, etc.

Now, the number of boxes= 600/12

=50

Therefore, to pack 600 granola bars they need 50 boxes.

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The slope of the line y = -3x is  -3.

The slope of a line is the measure of the steepness and the direction of the line. It is defined as the change in y coordinate with respect to the change in x coordinate of that line.

The net change in y coordinate is Δy, while the net change in the x coordinate is Δx. Then the slope

m = Δy/Δx = dy/dx

Here the line is y = -3x

Differentiating the equation of line with respect to x, we get

   dy /dx = -3

⇒ dy /dx = m = -3.

Therefore, the slope of the line y = -3x was found to be -3.

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Answer:

7 1/4

Step-by-step explanation:

convert to improper fraction 3 5/8 = 3x8/8 + 5/8 = 24+5/8 =29/8

divide 29/8 divided by 1/2 = 58/8

simplify  7 1/4

Hope this helps! <3

Answer:

In order to complete the equation we need to use this method :      

(Exponential Decay btw if you didnt know is when a population or group of something is declining, and the amount that decreases is proportional to the size of the population)

Now that we know that Time for Some Exponential Decay fun :D *sarcasm* :p

The farmer purchased a tractor for 50,000 so you start with that:

Remaining Amount = 50,000(1-r)^t

Decay rate would be 0.10 because you have to CONVERT 10% to decimal form.

Remaining Amount = 50,000(1-0.10)^t

Now time period would be 7 of course:

Remaining Amount = 50,000(1-0.10)^7

TIME TO SOLVE:

Answer 23914.845 BUT you have to round to nearest cent so then the answer would be:

Step-by-step explanation:

I learned this in my math class. ~Good------Night

Answer:

$23,914.85 (nearest cent).

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]

The given scenario can be modelled as an exponential equation.

The initial value (a) is the purchase cost of the tractor.

As the tractor depreciates by 10% each year, the value of the tractor is 90% of the previous year's value. Therefore, the base (b) is 0.9.

Therefore, the equation is:

[tex]\boxed{y=50000(0.9)^x}[/tex]

where:

To find the value of the tractor in 7 years, substitute x = 7 into the equation:

[tex]\implies y=50000(0.9)^7[/tex]

[tex]\implies y=50000 \times 0.4782969[/tex]

[tex]\implies y=23914.845[/tex]

Therefore, the value of the tractor in 7 years is $23,914.85 (nearest cent).

Randomly selecting a white golf ball first and then a white golf ball second are independent events.

What do you mean by dependent events?

Events that are dependent upon prior events are called dependent events. The results of earlier events have an impact on these current ones. For example, two or more events that are interdependent are referred to as dependent events.

It is given that in the beginning we have 3 white balss and 2 yellow balls

Total number of balls = 3 + 2 = 5

Probability of first selecting a white ball = 3/5

Now remaining white balls = 3 - 2 = 1

Remaining total balls = 5 - 1 = 4

Probability of selecting second white ball = 2/4

Probability of selecting a white golf ball first and then a white golf ball second = 3/5 × 2/4 = 3/10

Both the events are dependent as if we select first white ball, then it will change the number of white balls for selecting second time.

Therefore,  randomly selecting a white golf ball first and then a white golf ball second are independent events.

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Answer:

2x

Step-by-step explanation:

The size of the union according to the given data is 37.

The study of sets, which are collections of objects, is a topic covered by the mathematical field known as set theory. A set is a clearly defined group of unique items, sometimes referred to as its elements or members, in set theory.

Let's use the inclusion-exclusion principle to compute the number of elements in the union of four sets:

First, we add up the sizes of the individual sets:

4 x 15 = 60

Next, we subtract the sizes of the pair-wise intersections:

6 x 5 = 30

We have to multiply by 6 because there are 6 pairs of sets.

Now we need to add back the sizes of the three-way intersections:

4 x 2 = 8

We have to multiply by 4 because there are 4 triples of sets.

Finally, we need to subtract the size of the intersection of all four sets:

-1

Putting it all together, we have:

60 - 30 + 8 - 1 = 37

Therefore, the size of the union is 37.

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Answer:  [tex]h = \frac{3}{4}y[/tex] is the cone's height.

==================================================

Work Shown:

Let's set up each volume equation.

[tex]\text{VL} = \text{volume of cylinder}\\\\\text{VL} = \pi*r^2*h\\\\\text{VL} = \pi*x^2*y\\\\[/tex]

[tex]\text{VC} = \text{volume of cone}\\\\\text{VC} = \frac{1}{3}*\pi*r^2*h\\\\\text{VC} = \frac{1}{3}*\pi*(2x)^2*h\\\\\text{VC} = \frac{4}{3}\pi x^2*h\\\\[/tex]

Then we're told that VL and VC are the same value. Let's equate the right hand sides and solve for h.

[tex]\text{VL} = \text{VC}\\\\\pi x^2y = \frac{4}{3}\pi x^2 h\\\\x^2y = \frac{4}{3}x^2 h\\\\3x^2y = 4x^2 h\\\\h = \frac{3x^2y}{4x^2}\\\\h = \frac{3y}{4}\\\\h = \frac{3}{4}y\\\\[/tex]

Answer:

3y

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Volume of a cylinder}\\\\$V=\pi r^2 h$\\\\where:\\ \phantom{ww}$\bullet$ $(r)$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]   [tex]\boxed{\begin{minipage}{4 cm}\underline{Volume of a cone}\\\\$V=\dfrac{1}{3} \pi r^2 h$\\\\where:\\ \phantom{ww}$\bullet$ $(r)$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]

Given dimensions of the cylinder:

Therefore, the equation for the volume of the cylinder is:

[tex]\implies V_{\sf cylinder}=\pi x^2y[/tex]

Given dimensions of the cone:

Therefore, the equation for the volume of the cone is:

[tex]\implies V_{\sf cone}=\dfrac{1}{3} \pi x^2 h[/tex]

As the cylinder and the cone have the same volume, substitute the equation for the volume of the cylinder into the equation for the volume of the cone an solve for h:

[tex]\begin{aligned}V_{\sf cylinder}&=V_{\sf cone}\\\implies \pi x^2 y&=\dfrac{1}{3} \pi x^2 h\\y&=\dfrac{1}{3} h\\3y&=h\\h&=3y\end{aligned}[/tex]

Therefore, the height of the cone is 3y.

113 crates are needed for the company to mail an order of 8927 watermelon, if one crate can hold 79 watermelon.

A single or unique unit is referred to by the word unitary. Therefore, the goal of this strategy is to establish values in reference to a single unit. The unitary method, for instance, can be used to calculate how many kilometers a car will go on one litre of gas if it travels 44 km on two litres of fuel.

Given,

There are 8927 watermelon and each watermelon can hold 79. We have to divided the number  of watermelon by the number of watermelon each crate can hold, to get the how many crate is needed to mail the order.

8927/79

=113

Therefore, 113 crates will be needed by the company.

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Answer: I believe the answer is -8.32

Answer:

Step-by-step explanation:−8.32

Answer:$22.35

Step-by-step explanation: