PLEASE FOR 100 POINTS!!! PLEASE!!!

Step-by-step explanation:

To solve the problem, we'll use the information given to find the values of A and k in the equation T = 20 + Ae^(-kt), where T is the temperature in degrees Celsius at time t.

a. Finding the value of A:

We're given that the initial temperature of the tea was 70℃. Substituting this into the equation, we get:

70 = 20 + Ae^(0) (since e^0 = 1)

70 - 20 = A

A = 50

So the value of A is 50.

b. Finding the value of k:

We're told that it takes 4 minutes for the tea to decrease in temperature from 70℃ to 50℃. We can use this information to set up an equation and solve for k.

Substituting T = 70 and t = 4 into the equation, we have:

70 = 20 + 50e^(-4k)

Subtracting 20 from both sides:

50 = 50e^(-4k)

Dividing both sides by 50:

1 = e^(-4k)

Taking the natural logarithm (ln) of both sides:

ln(1) = ln(e^(-4k))

0 = -4k

Dividing both sides by -4:

0 = k

However, we need to check if this solution satisfies the condition for the tea to decrease in temperature from 70℃ to 50℃ in 4 minutes.

Substituting T = 50 and t = 4 into the equation, we have:

50 = 20 + 50e^(-4(0))

50 = 20 + 50e^0

50 = 20 + 50(1)

50 = 20 + 50

50 = 70

Since 50 is not equal to 70, the value of k = 0 does not satisfy the given condition.

Let's try another approach:

Substituting T = 50 and t = 4 into the equation, we have:

50 = 20 + 50e^(-4k)

Subtracting 20 from both sides:

30 = 50e^(-4k)

Dividing both sides by 50:

0.6 = e^(-4k)

Taking the natural logarithm (ln) of both sides:

ln(0.6) = ln(e^(-4k))

ln(0.6) = -4k ln(e)

ln(0.6) = -4k(1)

ln(0.6) = -4k

Simplifying further:

k = ln(0.6) / -4

Using a calculator or computer to evaluate ln(3/5) / -4, we get approximately:

k = ln(5/3) / 4

To recap:

a. The value of A is 50.

b. The value of k is approximately k = ln(5/3) / 4

.

Note: The calculations provided are based on the given information and assumptions. If there are any additional details or specific conditions provided, please let me know, and I'll be happy to assist you further.

Answer:

45

Step-by-step explanation:

First we write the first 10 multiples of 9 (the first denominator) :

9,18,27,36,45,54,63,72,81,90

Now we write the first 10 multiples of 5 (the second denominator) :

5,10,15,20,25,30,35,40,45,50

As we can see 45 is the lowest number that appears in both list.

Therefore 45 is the LCD of 8/9 and 4/5

Answer:

45

Step-by-step explanation:

So since we are finding the LCD, we only look at the denominators, 9 and 5.

We can count until we find the denominator:

\(9,18,27,36,45\\5,10,15,20,25,30,35,40,45\)

So the LCD would be 45.

Answer:

\(f(126) \approx 5.01333\)

Step-by-step explanation:

Given

\(\sqrt[3]{126}\)

Required

Solve using differentials

In differentiation:

\(f(x+\triangle x) \approx f(x) + \triangle x \cdot f'(x)\)

Express 126 as 125 + 1;

i.e.

\(x = 125; \triangle x = 1\)

So, we have:

\(f(125+1) \approx f(125) + 1 \cdot f'(125)\)

\(f(126) \approx f(125) + 1 \cdot f'(125)\)

To calculate f(125), we have:

\(f(x) = \sqrt[3]{x}\)

\(f(125) = \sqrt[3]{125}\)

\(f(125) = 5\)

So:

\(f(126) \approx f(125) + 1 \cdot f'(125)\)

\(f(126) \approx 5 + 1 \cdot f'(125)\)

\(f(126) \approx 5 + f'(125)\)

Also:

\(f(x) = \sqrt[3]{x}\)

Rewrite as:

\(f(x) = x^\frac{1}{3}\)

Differentiate

\(f'(x) = \frac{1}{3}x^{\frac{1}{3} - 1}\\\)

Using law of indices, we have:

\(f'(x) = \frac{x^\frac{1}{3}}{3x}\)

So:

\(f'(125) = \frac{125^\frac{1}{3}}{3*125}\)

\(f'(125) = \frac{5}{375}\)

\(f'(125) = \frac{1}{75}\)

So, we have:

\(f(126) \approx 5 + f'(125)\)

\(f(126) \approx 5 + \frac{1}{75}\)

\(f(126) \approx 5 + 0.01333\)

\(f(126) \approx 5.01333\)

Answer: 30 cents

Step-by-step explanation:

1/20 of a dollar is 5 cents

Then we multiply by the numerator (6) to get our answer....

5x6= 30

Hoped this helps! :)

Answer:

10/7

Step-by-step explanation:

6/7+4/7= 6+4/7= 10/7

Is this your question?

Answer:

1, hope this helps!

Step-by-step explanation:

I took the test

Answer:

A. Relation

B. Relation

C. Function

D. Function

E. Relation

The correct option is D.

Given that ABCD is a parallelogram, we need to prove AD ≅ CB.

So,

Properties of a parallelogram =

Opposite sides are parallel.

Opposite sides are congruent.

Opposite angles are congruent.

             Statement                                                    Reason

1. ABCD is a parallelogram                                           Given

2. AB║CD and AD║BC                                      Definition of parallelogram

3. ∠BAC ≅ ∠DCA and ∠BCA ≅ ∠DAC    Alternate interior angles theorem

4. AC ≅ AC                                                              Reflexive property

5. ΔBAC ≅ ΔDCA                                                       A.S.A Postulate

6. AD ≅ CB                                                                        CPCTC

Hence the correct option is D.

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Answer:

y = 8

Step-by-step explanation:

Since the y- coordinates of the points are equal, both 8 , then

This indicates the line is horizontal and parallel to the x- axis with equation

y = c

where c is the value of the y- coordinates the line passes through

The line passes through (- 3, 8 ) and (- 7, 8 ) with y- coordinates 8 , then

y = 8 ← equation of line

Answer:

Changes made to your input should not affect the solution:

(1): "x2" was replaced by "x^2". 1 more similar replacement(s).

STEP

1

:

Equation at the end of step 1

(12 • (x3)) - 32x2

STEP

2

:

Equation at the end of step

2

:

(22•3x3) - 32x2

STEP

3

:

STEP

4

:

Pulling out like terms

4.1 Pull out like factors :

12x3 - 9x2 = 3x2 • (4x - 3)

Final result :

3x2 • (4x - 3)

The value of side EA is,

EA = 16.9

We have to given that;

Circle E with diameter CD and radius EA.

And, AB is tangent to E at A.

Here, AB = 34 and EB = 38

Hence, By using Pythagoras theorem we get;

AB² + AE² = EB²

34² + AE² = 38²

1156 + AE² = 1444

AE² = 1444 - 1156

AE² = 288

AE = √288

AE = 16.9

Thus, The value of side EA is,

EA = 16.9

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1. The benchmark fractions that can be used to estimate how much farther Roy ran than Jack is 1/4 and 2/3.

2. By using the benchmark fractions, what is a reasonable estimate for the difference between the two distances is 5/12 mile.

3. The actual difference is 5/12 mile.

In order to determine the benchmark fractions that can be used to estimate how much farther (the amount of distance) Roy ran than Jack, we would first of all, simplify the fraction representing the amount of distance covered by Jack as follows;

Jack's distance = 2/8 mile

Dividing by 2, we have this simplified fraction;

Jack's distance = 1/4 mile

Benchmark fractions = 2/3 and 1/4.

Part b

Additionally, by subtracting the amount of distance covered by Jack from the amount of distance covered by Jack as follows;

Difference = 2/3 - 1/4

Difference = (8 - 3)/12

Difference = 5/12 mile.

Part c

Actual Difference = 2/3 - 2/8

Actual Difference = (16 - 6)/24

Actual Difference = 10/24 mile.

Actual Difference = 5/12 mile.

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Complete Question:

Jack ran 2/8 mile and Roy ran 2/3 mile.

a. What benchmark fractions can be used to estimate how much farther Roy ran than Jack?

b. Using the benchmark fractions, what is a reasonable estimate for the difference between the two distances?

c. What is the actual difference?​

Answer:

35

Step-by-step explanation:

You can easily graph this in desmos for a visual understanding.

The slope of a line is received by (y2-y1)/(x2-x1). Assuming that Days is X and the cost is Y, we get (160-90)/(4-2), and it makes 70/2, which equates out to 35. Because the prices become more and more expensive, the slope is positive 35.

Answer:

$6.42

Step-by-step explanation:

It's very simple, all you have to do is subtract 13.58 by the 20.00$, so you will get that.

The number of feet of fencing that will be needed ​is illustrated below

The feet of fencing that will be needed ​is the perimeter of the fence

To find the perimeter of a composite figure, we need to add up the lengths of all the sides of the figure.

In this case, we add the side lengths of the rectangle to the side lengths of the right triangle and subtracting the common lengths between both shapes

Take for instance, we have

So, we have

Fencing = 2 * (4 + 5) + 3 + 4 + 5 - 2 * 4

Fencing = 22 units

So, the amount of fencing for the assumed dimensions is 22 units

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Answer: 15

Step-by-step explanation:

The range is the set of all Y values, in this question -8 is the minimum and +7 is the maximum, therefore the range is (-8-7) = -15, but range is not negative so we get 15

The correct match for each linear system with one of the phase plane direction fields will be:

1:B

2:C

3:D

4:A

What is plane?

In geometry, a plane is a surface made up of all the straight lines connecting any two locations on it. It is, in other words, a level or flat surface. A plane is uniquely defined in a Euclidean space of any number of dimensions by one of the following: three non-collinear points are used. Other names for it include a two-dimensional surface. A plane has an unlimited width, an endless length, zero thickness, and no curvature. The flat surfaces of a cube or cuboid, as well as the flat surface of paper, are all true instances of geometric planes, despite the fact that it is difficult to envision a plane in real life.

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Answer:

m= -12

Step-by-step explanation:

m/2= -6

-multiply both sides by 2 to get rid of  ( /2)

m= -12

The time it will take for about a fourth of the original amount of P-32 remain is given as follows:

27 days.

An exponential function is defined as follows:

y = ab^x.

In which:

Considering that the initial amount is of 100, while after one day the amount was of 95, the parameters are given as follows:

a = 100, b = 95/100 = 0.95.

Hence the function for the amount remaining after x days is given as follows:

y = 100(0.95)^x.

One fourth of the amount will be remaining when y = 25, hence:

25 = 100(0.95)^x.

(0.95)^x = 0.25

xlog(0.95) = log(0.25)

x = log(0.25)/log(0.95)

x = 27 days.

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A) The percentage of nurses completing the task in less than 5 minutes is approximately 4.75%. b) The percentage of nurses requiring more than 10 minutes to complete the task is approximately 50%

To solve this problem, we will use the properties of the normal distribution and z-scores. Given that the average completion time for the task is 10 minutes and the standard deviation is 3 minutes, we can proceed with the following calculations:

a) To find the percentage of nurses completing the task in less than 5 minutes, we need to calculate the z-score corresponding to a time of 5 minutes and then determine the area under the normal distribution curve to the left of that z-score.

The z-score formula is given by: z = (x - μ) / σ

where x is the time in question (5 minutes), μ is the mean (10 minutes), and σ is the standard deviation (3 minutes).

z = (5 - 10) / 3 = -5/3 ≈ -1.67

Using a standard normal distribution table or a calculator, we can find that the area to the left of -1.67 is approximately 0.0475 or 4.75%. Therefore, approximately 4.75% of nurses complete the task in less than 5 minutes.

b) To find the percentage of nurses requiring more than 10 minutes to complete the task, we calculate the z-score for a time of 10 minutes and find the area to the right of that z-score.

z = (10 - 10) / 3 = 0

The area to the right of z = 0 is 0.5 or 50%. Therefore, approximately 50% of nurses require more than 10 minutes to complete the task.

c) To find the probability that a nurse will take between 8 and 12 minutes to complete the task, we need to find the area under the curve between the z-scores for 8 and 12 minutes.

z1 = (8 - 10) / 3 = -2/3 ≈ -0.67

z2 = (12 - 10) / 3 = 2/3 ≈ 0.67

Using a standard normal distribution table or a calculator, we find the area to the left of z = -0.67 as approximately 0.2514, and the area to the left of z = 0.67 as approximately 0.7514. Therefore, the probability that a nurse will take between 8 and 12 minutes to complete the task is approximately 0.7514 - 0.2514 = 0.5 or 50%.

d) To find the task times that qualify staff nurses for additional training, we need to determine the z-score corresponding to the slowest 20% of completion times and then convert it back to the original time scale.

The z-score corresponding to the slowest 20% is found by locating the z-score that has an area of 0.2 to its left. Using a standard normal distribution table or a calculator, we find this z-score to be approximately -0.84.

Now, we can convert the z-score back to the original time scale:

z = (x - μ) / σ

-0.84 = (x - 10) / 3

Solving for x, we have:

-0.84 * 3 = x - 10

-2.52 = x - 10

x = 10 - 2.52

x ≈ 7.48

Therefore, the task times that qualify staff nurses for additional training are approximately greater than 7.48 minutes.

In summary:

a) The percentage of nurses completing the task in less than 5 minutes is approximately 4.75%.

b) The percentage of nurses requiring more than 10 minutes to complete the task is approximately 50%

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Answer:

The equation that represents the perimeter of the rectangle is:

\(\text{Perimeter} = \frac{2}{3} \times [4l-27]\)

Step-by-step explanation:

The perimeter of a rectangle is given by the formula:

Perimeter = 2 × [l + w]

It is provided that the width of a rectangle is 9 less than one-third it's length.

That is:

\(w = \frac{1}{3}l-9\)

The perimeter is given as 45.

The equation that represents the perimeter of the rectangle is:

\(\text{Perimeter} = 2 \times [l + \frac{1}{3}l-9]\\\\\text{Perimeter} = 2 \times [\frac{3l+l-27}{3}]\\\\\text{Perimeter} = 2 \times [\frac{4l-27}{3}]\\\\\text{Perimeter} = \frac{2}{3} \times [4l-27]\)

Thus, the equation that represents the perimeter of the rectangle is:

\(\text{Perimeter} = \frac{2}{3} \times [4l-27]\)

8/21 of the lawn still needs to be mowed.

To compare fractions, we need a common denominator. The least common multiple of 7 and 3 is 21.

Miss Lianto's fraction: (2/7) x (3/3) = 6/21

Son's fraction: (1/3) x (7/7) = 7/21

To calculate how much of the lawn still needs to be mowed, we can subtract the combined fractions mowed from the total:

Combined fractions mowed: 6/21 + 7/21 = 13/21

So, Remaining fraction: 1 - 13/21 = 8/21

Therefore, 8/21 of the lawn still needs to be mowed.

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What item shown below?? Imao I'll edit my answer if you put it below in the comments

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "/-32" was replaced by "/(-32)".

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

f/(-32)-(-31)=0

Step by step solution :

STEP

1

:

f

Simplify ———

-32

Equation at the end of step

1

:

f

——— - -31 = 0

-32

STEP

2

:

Rewriting the whole as an Equivalent Fraction

2.1 Subtracting a whole from a fraction

Rewrite the whole as a fraction using -32 as the denominator :

-31 -31 • -32

-31 = ——— = —————————

1 -32

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2 Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

f • -1 - (-31 • 32) 992 - f

——————————————————— = ———————

32 32

Equation at the end of step

2

:

992 - f

——————— = 0

32

STEP

3

:

When a fraction equals zero

3.1 When a fraction equals zero

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

992-f

————— • 32 = 0 • 32

32

Now, on the left hand side, the 32 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

992-f = 0

Solving a Single Variable Equation:

3.2 Solve : -f+992 = 0

Subtract 992 from both sides of the equation :

-f = -992

Multiply both sides of the equation by (-1) :

f = 992

the answer is f = 992

99.4% chance that you are healthy if you receive a negative test. 67.9% chance that you are sick if you receive a positive test.

14% of population would test positive for the disease

Step 1. Give algebraic names to various events described:

Step-2: Model the given situation mathematically.

In other words, the conditional probability of the event that the diagnostic test gives a negative result (not A), given that the tested person does not have the disease (E2 = not E1) is given to be 90%

Thus P(not A/E2)=90%

Further, it is given that five percent of the population has the disease. In other words, the event that a person has the disease (E1) has the probability of 5% Thus P(E1)=5%

It is needed to find what percent of that population would test positive for the disease.

Thus, the probability that a person will have a positive result when tested, P(A) is to be determined.

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So the different number has a 4 with a value of 40.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

To solve this problem, we need to first identify the place value of the digit 4 in the given number.

The digit 4 is in the hundreds place in the number 431.67, so its value is 4 x 100 = 400.

According to the problem statement, the 4 in the different number represents a value which is one-tenth of the value of the 4 in 431.67. Therefore, the value of the 4 in the different number is:

400/10 = 40

To determine the value of the different number, we need to look at the other digits in the number. Since we don't have any information about the other digits, we cannot determine the value of the different number. The answer is that the value of the different number cannot be determined with the information given.

Therefore, So the different number has a 4 with a value of 40.

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Answer:

(-3, 7)

Step-by-step explanation:

It is like putting a mirror on the y-axis. It is asking what point is the photo negative of the point, like a mirror. You see yourself in the mirror but everything is opposite. Your right hand is your left. So which point is the photo negative of (3, 7)? (-3, 7) Because it is only across the y-axis, the y value stays the same.

The amount of Duane's first payment that goes to interest is approximately $26.47.

To determine the amount of Duane's first payment that goes to interest, we need to use the amortization formula for a loan.

The formula to calculate the interest portion of a loan payment is:

Interest = Remaining Balance * Monthly Interest Rate.

Let's calculate the interest for the first payment using the given information:

Loan Amount = $5,000.00

Monthly Payment = $118.57

First, we need to calculate the monthly interest rate:

Monthly Interest Rate = Annual Interest Rate / 12

= 6.5% / 12

= 0.00542

Next, we need to calculate the remaining balance after the first payment:

Remaining Balance = Loan Amount - Principal Paid

= $5,000.00 - $118.57

= $4,881.43

Finally, we can calculate the interest portion of the first payment:

Interest = Remaining Balance * Monthly Interest Rate

= $4,881.43 * 0.00542

= $26.47

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Answer:

-560 is the answer

Step-by-step explanation:

658 - (-560 )= 98

Answer:

Hello!!! erz here ^^

Step-by-step explanation:

658 - 560 = 98

Hope this helps!! :D