After heating up in a teapot, a cup of hot water is poured at a temperature of
20
3
∘
203
∘
F. The cup sits to cool in a room at a temperature of
6
9
∘
69
∘
F. Newton's Law of Cooling explains that the temperature of the cup of water will decrease proportionally to the difference between the temperature of the water and the temperature of the room, as given by the formula below:
�
=
�
�
+
(
�
0
−
�
�
)
�
−
�
�
T=T
a
​
+(T
0
​
−T
a
​
)e
−kt

�
�
=
T
a
​
= the temperature surrounding the object
�
0
=
T
0
​
= the initial temperature of the object
�
=
t= the time in minutes
�
=
T= the temperature of the object after
�
t minutes
�
=
k= decay constant

The cup of water reaches the temperature of
18
5
∘
185
∘
F after 1.5 minutes. Using this information, find the value of
�
k, to the nearest thousandth. Use the resulting equation to determine the Fahrenheit temperature of the cup of water, to the nearest degree, after 4.5 minutes.

Enter only the final temperature into the input box.

Answer:

(C) 297

Step-by-step explanation:

Write a proportion. 45 miles is to 5 gallons as x miles is to 33 gallons.

45 / 5 = x / 33

9 = x / 33

x = 297

[tex]D:2x > 0\wedge x+2 > 0\\D:x > 0 \wedge x > -2\\D: x > 0[/tex]

[tex]\log_42x+\log_4(x+2)=2\\\log_4(2x(x+2))=2\\2x^2+4x=4^2\\2x^2+4x-16=0\\x^2+2x-8=0\\x^2+2x+1-9=0\\(x+1)^2=9\\x+1=3 \vee x+1=-3\\x=2 \vee x=-4[/tex]

[tex]-4\not\in D[/tex]

Therefore [tex]x=2[/tex].

Answer: THE TOTAL AMOUNT TAKEN BY KEVIN IN MIXING, BAKING, AND COOLING THE MUFFINS IS 30 MINUTES.

Step-by-step explanation:

1. AMOUNT TAKEN BY KEVIN FOR MIXING=8MIN.

2. AMOUNT TAKEN BY KEVIN FOR BAKING=17 MIN.

3. AMOUNT TAKEN BY KEVIN FOR COOLING=5MIN.

IN TOTAL, (8+17+5)MIN. = 30 MIN.

Answer:

30 minutes

Step-by-step explanation:

8+7  =15 +5=20+ another 10 = 30

The length of the line is given as follows:

B. 12 units.

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The theorem is expressed as follows:

c² = a² + b².

In which:

The parameters for this problem are given as follows:

Hence the length of the line is given as follows:

l² = 10² + 6²

[tex]l = \sqrt{10^2 + 6^2}[/tex]

l = 12 units. (rounded up).

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Answer:

The history class started at 2:35 pm

Step-by-step explanation:

To find the before time or starting time, we need to subtract 55 min from 3:30.

We cannot subtract 55 min from 30 min.

1 hour = 60 minutes. 3 : 30 can be written as 2: 90 minutes

Now subtract,

               2 : 90

          -      : 55

               2 : 35

The history class started at 2:35 pm

The equivalent expressions are 32, 27, 64, 36, 1/16, 1/9 respectively.

Given are the numbers we need to simplify them,

2⁵ = 2·2·2·2·2 = 32

3³ = 3·3·3 = 27

4³ = 4·4·4 = 64

6² = 6·6 = 36

(1/2)⁴ = 1/2·1/2·1/2·1/2 = 1/16

(1/3)² = 1/3·1/3 = 1/9

Hence the equivalent expressions are 32, 27, 64, 36, 1/16, 1/9 respectively.

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The probability that a student who passed the test did not complete the homework is 1 / 6.

This is a conditional probability problem and we are looking for the probability that a student who passed the test did not complete the homework.

Assuming event A is the event that a student passed the test and B is  event that a student completed the assignment.

We have :

P ( B' | A ) = P ( A ∩ B ' ) / P (A)

P ( B' | A ) = ( 3 / 27 ) / ( 18 / 27 )

P ( B' | A ) = 3 / 18

P (B' | A ) = 1 / 6

In conclusion, the probability that a student who passed the test did not complete the assignment is 1/6.

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For the sample of n sludge specimens is selected and the conclusion and the pH of each one is determined.

The null hypothesis will be rejected in favour of the alternative hypothesis only if sample evidence suggests that H0 is false. If the sample does not strongly contradict H0, we will continue to believe in the plausibility of the null hypothesis. The two possible conclusions from a hypothesis-testing analysis are then reject H0 or fail to reject H0.

A) Reject the null hypothesis. There is sufficient evidence that the true average pH is less than 7.0.

B) Reject the null hypothesis. There is sufficient evidence that the true average pH is less than 7.0.

C) Reject the null hypothesis. There is sufficient evidence that the true average pH is less than 7.0.

D) Reject the null hypothesis. There is sufficient evidence that the true average pH is less than 7.0.

E) Reject the null hypothesis. There is sufficient evidence that the true average pH is less than 7.0.

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We can use the distance formula to find the distances between the fire hydrants and determine whether they form a right triangle. The value of y is 4.

The distance between (0,0) and (2,5) is:

√((2-0)² + (5-0)²) = √29

The distance between (0,0) and (7,y) is:

√((7-0)² + (y-0)²) = √(49 + y²)

The distance between (2,5) and (7,y) is:

√((7-2)² + (y-5)²) = √(25 + (y-5)²)

If these distances form a right triangle, then the Pythagorean theorem must be satisfied:

(√29)² + (√(49 + y²))² = (√(25 + (y-5)²))²

Simplifying this expression, we get:

29 + 49 + y² = 25 + (y-5)²

Expanding the square on the right-hand side, we get:

29 + 49 + y² = 25 + y² - 10y + 25

Simplifying this expression, we get:

y = 4

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Answer:

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

Let the dimensions be x and y.

The area is:

When sides have changed we get:

The new area is:

The difference in areas is:

It represents 17% increase.

The angles in the triangle are as follows:

m∠S = m∠Q = 58°

m∠T = 64°

The unknown angles in the triangle can be found as follows:

In the triangle STQ, ST = TQ and SD is perpendicular to TQ.

Therefore, let's find the unknown angles as follows:

Hence, base on ST = TQ, STQ is an isosceles triangle. Therefore,

m∠S = m∠Q

Therefore,

m∠Q = 180 - 90 - 32

m∠Q = 58 degrees

m∠S = m∠Q = 58 degrees

Finally,

m∠T = 180 - 58 - 58

m∠T = 64 degrees

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The specific form of the function G(t) and the limits of integration would depend on the available data or assumptions about gas consumption during the specified months.

To express the average monthly U.S. gas consumption during the part of the year between the beginning of April and the end of September, we can set up an integral to calculate the average value of a function over a specific interval.

Let's denote the gas consumption as a function of time, G(t), where t represents the months from April to September. We'll integrate this function over the interval [April, September] to find the average gas consumption.

The integral that represents the average monthly U.S. gas consumption is:

(1 / (September - April)) ∫[April, September] G(t) dt

In this integral, G(t) represents the gas consumption in a given month, and the integration is taken over the interval from April to September. The average gas consumption is obtained by dividing the integral by the length of the interval (September - April).

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1. The value of x in the expression is 3

2. The value of y in the expression is -9/16

3. The value of d in the expression is -16 / 25

4. The value of x in the expression is 1

The value of x in the expression can be obtained as follow:

x + 5 = 3x - 1

Collect like terms

5 + 1 = 3x - x

6 = 2x

Divide both sides by 2

x = 6 / 2

Value of x = 3

The value of y in the expression can be obtained as follow:

5y/6 + 1 = -1y/2 + 1/4

Collect like terms

5y/6 + y/2 = 1/4 - 1

(5y + 3y)/6 = (1 - 4)/4

8y/6 = -3/4

Cross multiply

8y × 4 = 6 × -3

32y = -18

Divide both sides by 32

y = -18 / 32

Value of y = -9/16

The value of d in the expression can be obtained as follow:

20 + 3d = 36 + 28d

Collect like terms

20 - 36 = 28d - 3d

-16 = 25d

Divide both sides by 25

d = -16 / 25

Value of d = -16 / 25

The value of x in the expression can be obtained as follow:

4(x + 8) - 4 = 34 - 2x

Clear bracket

4x + 32 - 4 = 34 - 2x

4x + 28 = 34 - 2x

Collect like terms

4x + 2x = 34 - 28

6x = 6

Divide both sides by 6

x = 6 / 6

Value of x = 1

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Answer:58

Step-by-step explanation:

The range of a set of numbers is the difference between the largest and smallest numbers in the set.

To find the range of the following set of numbers: 68, 56, 40, 10, 51, 15

First, we need to find the largest and smallest numbers in the set.

The largest number is 68 and the smallest number is 10.

So, the range is:

68 - 10 = 58

Therefore, the range of the set of numbers is 58.

Answer:

6 books

6 packages of mints

It would cost $240.00 is carpet was purchased.

Step-by-step explanation:

If 2 books cost 16.40, then one book costs 16.40/2 = 8.20 each.

50/8.20 = 6.1 rounded. You cannot buy part of a book, so 6 books may be purchases.

If 2 packages of mints cost .69, then I package costs .69/2 = .345

2.25/ .345 = 6.5 rounded.  You cannot buy .5 of a package, so you can purchases 6 packages.

192/16 = 12

There are 12 square meters of flooring

12 x 20 = 240

Helping in the name of Jesus.

Population proportion (claim): p = 0.85

Sample proportion: [tex]\hat p[/tex]= 19/25

What is proportion?

In statistics, proportion typically refers to the proportion or percentage of individuals or items in a population that have a specific characteristic or belong to a certain category.

In this scenario, the population proportion refers to the proportion of all Prime members' packages that arrive within two business days. The claim made by Amazon is that this population proportion is 85%.

Let's denote the population proportion as p.

a. The population proportion:

p = 0.85

The sample proportion, on the other hand, refers to the proportion of packages that arrived within two business days among the 25 students in the random sample. We can calculate the sample proportion using the number of students who claimed their packages arrived within two business days.

Let's denote the sample proportion as [tex]\hat p[/tex] (pronounced "p-hat").

Given:

Number of students in the sample (n) = 25

Number of students who claimed their packages arrived within two business days (x) = 19

b. The sample proportion:

[tex]\hat p[/tex] = x / n

[tex]\hat p[/tex] = 19 / 25

Therefore, the sample proportion is 19/25.

To summarize:

Population proportion (claim): p = 0.85

Sample proportion: [tex]\hat p[/tex] = 19/25

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Using the given information, the measure of each exterior angle in the polygon is 20°

From the question, we are to determine the measure of each exterior angle in the polygon

Let the number of sides in the polygon be n.

Sum of exterior angles in a polygon = 360°

Thus,

Measure of one exterior angle = 360°/n

From the given information,

The measure of each exterior angle is 12.5% of the measure of each interior angle

The measure of each interior angle = (n - 2)180° / n

Thus,

360°/n = 12.5% of (n - 2)180° / n

360° = 12.5% of (n - 2)180°

Solve for n

360° = 0.125 × (n - 2)180°

360° =  (n - 2)22.5°

360° = 22.5n° - 45°

22.5n° = 360° + 45°

22.5n° = 405°

n = 405°/22.5°

n = 18

Then,

Measure of each exterior angle = 360° / 18

Measure of each exterior angle = 20°

Hence, the measure of each exterior angle is 20°

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The type of correlation that occurs when two variables are statistically correlated due to the influence of a third variable is called a spurious correlation.

A spurious correlation is a type of correlation that occurs when two variables are statistically related to each other, but the relationship is not causal. Instead, the relationship is driven by the influence of a third variable that is related to both variables. This type of correlation can be misleading and can lead to incorrect conclusions if not properly understood.

For example, consider the relationship between ice cream sales and violent crime. Studies have found a positive correlation between these two variables, meaning that as ice cream sales increase, so do violent crimes. However, it is unlikely that there is a causal relationship between these two variables. Instead, the real cause of the correlation is likely the temperature. As the temperature increases, people are more likely to buy ice cream and to be out and about, which increases the opportunity for violent crime to occur. Thus, the temperature is the third variable that is driving the spurious correlation between ice cream sales and violent crime.

It is a type of correlation where there is no causal relationship between the two variables that are correlated. Instead, the correlation is driven by the influence of a third variable that is related to both variables. In the example given, the correlation between ice cream sales and violent crimes is spurious, as the real cause of the correlation is the temperature, which influences both variables.

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The factor that -8 - 7i should be multiplied by to find the quotient is 1 + 2i and the quotient is (-22 - 23i) / 5.

When dividing complex numbers of the form a + bi by another complex number of the form c + di, we use the following method:

Multiplying both the numerator and denominator by the conjugate of the denominator, c - di, we get:

(a + bi)(c - di)/(c + di)(c - di) = [(ac + bd) + (bc - ad)i]/(c² + d²)

where a, b, c, and d are real numbers and i is the imaginary unit with the property i² = -1.

In the given question, the denominator is 1 - 2i, so its complex conjugate would be 1 + 2i. Therefore, we need to multiply -8 - 7i by 1 + 2i in both numerator and denominator to get the quotient: (-8 - 7i)(1 + 2i) / (1 - 2i)(1 + 2i) = (-8 - 23i - 14) / (1 + 4) = (-22 - 23i) / 5

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To determine Cody's total revenue if he charges $20 for each mailbox, we need to know the number of mailboxes he sells. Let's denote the number of mailboxes as 'n'.

Cody's total revenue can be calculated by multiplying the price per mailbox ($20) by the number of mailboxes sold (n):

Total revenue = Price per mailbox × Number of mailboxes sold

Total revenue = $20 × n

Therefore, Cody's total revenue will be $20n, where 'n' represents the number of mailboxes he sells.

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10 liters of water was drained out of the tank in one minute and it would take 80 minutes to completely drain the water

This is the slope of the graph

From the graph, we have

(x, y) = (0, 800) and (40, 400)

So, we have

Slope = (400 - 800)/(40 - 0)

Evaluate

Slope = -10

This means that 10 liters of water was drained out of the tank in one minute

From (a), the equation of the line would be

y = -10x + 800

When the water is completely out, we have

-10x + 800 = 0

So, we have

x = 80

This means that it would take 80 minutes

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[tex]|\Omega|=6+4+2=12\\|A|=4\\\\P(A)=\dfrac{4}{12}=\dfrac{1}{3}\approx33.3\%[/tex]

Answer:

Step-by-step explanation: 6 + 4 + 2 = 12 (denominator)

Put 4 (blue beads) in numerator

4/12 reduces to 1/3

Final answer is 1/3

Answer:

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

The first step involves addition of 7 to both sides and the second step involves division of both sides by 9.

They indicate the addition and division property of equality respectively.

Therefore correct choice is A.

V = 1000

Put the sides together: 4/6

Cube the sides (for volume you cube): 64/216

Then put the volume across from the side that has that volume: 64 x

----- = -----

216 3375

Cross multiply.

It should then equal this: 216x=216000

Divide by 216 and then you find x, which in other words the volume

x = 1000

Answer:

6/55

Step-by-step explanation:

4 red + 7 blue = 11 marbles in total

P(first red) = 4/11.

we now have 10 marbles left. 3 of them are red.

P(second red) = 3/10

P(both red) = 4/11 X 3/10 = 12/110 = 6/55

The volume of composite solid is 418.67 cm³.

We have to find the volume of Cone and cylinder.

First, Volume of Cone

=  (1/3)πr²h

Given that the radius (r) of the cone is 5 cm and the height (h) is 4 cm, we can substitute these values into the formula:

= (1/3) (3.14) (5)² (4)

= 104.67 cm³

Second, Volume of cylinder

= πr²h

Given that the radius (r) of the cylinder is 5 cm and the height (h) is 4 cm, we can substitute these values into the formula:

= π (5)² (4)

= 3.14 x 100

= 314 cm³

Thus, the volume of composite solid

= 314 + 104.67

= 418.67 cm³

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P(A AND B) is approximately 0.101 (rounded to three decimal places).

Conditional probability is defined as the likelihood of an event or outcome occurring, based on the occurrence of a previous event or outcome. Conditional probability is calculated by multiplying the probability of the preceding event by the updated probability of the succeeding, or conditional, event.

To find P(A AND B), we can use the conditional probability formula:

P(A AND B) = P(A|B) * P(B)

Given:

P(A|B) = 0.22

P(B) = 0.46

Plugging in the values:

P(A AND B) = 0.22 * 0.46

Calculating the result:

P(A AND B) = 0.1012

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because their sides were corresponding.

answers:

1. aas (g).

2. sas (h).

3. sss (n).

4. asa (s).

5. hl (c).

6. none - aaa (t).

7. asa (0).

8. none - ssa (d).

9. aas (i).

10. sas (w).

11. sss (p).

12. hl (r).

13. asa (e).