Mrs. Morgan made six dozen cupcakes for a party. If her guests ate 2/3 of the cupcakes, how many cupcakes remain?

Density = Mass / Volume, so you could use that information to solve for each value in the graph.

2. Mass = Density * Volume = 8.07 * 1.04 = 8.59 g

3. Volume = Mass / Density = 8.26 / 8.10 = 1.02 mL

4. Density = Mass / Volume = 7.91 / 0.99 = 7.99 g/mL

5. Mass = Density * Volume = 8.05 * 0.98 = 7.89 g

6. Volume = Mass / Density = 8.53 / 8.05 = 1.06 mL

To evaluate an integral analytically, you need to use the Fundamental Theorem of Calculus, which states that the antiderivative of a function is equal to the integral of that function.

This means that if you can find the antiderivative of a function, you can calculate the integral of that function. There are several methods for finding the antiderivative, such as using integration by parts, integration by substitution, and partial fraction decomposition. Once you have found the antiderivative, you can then use the Integral Evaluation Theorem to evaluate the integral. One of the methods for evaluating an integral analytically is integration by parts. This involves selecting two functions, u and dv, and then writing the integral as the product of these two functions. The integral is then evaluated by taking the antiderivative of each function and then subtracting the two antiderivatives. The integral of udv is equal to the product of the antiderivative of u and the antiderivative of dv minus the integral of the product of the derivatives of u and v. This method is useful for integrals with complicated functions that may be difficult to integrate directly.

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When Joe is thirty-five years old, his investment in the 403b account will be worth approximately $9,847.20.

To calculate the future value of Joe's investment when he is thirty-five, we can use the compound interest formula. The formula for compound interest is:

A = P(1 + r/n)^(nt)

Where:

A = the future value of the investment

P = the principal amount (initial deposit)

r = annual interest rate (in decimal form)

n = number of times the interest is compounded per year

t = number of years

In this case, Joe deposited $5,000 at an interest rate of 6.8% compounded monthly. We need to convert the annual interest rate to a monthly interest rate and the number of years to the number of months.

First, let's calculate the monthly interest rate. The annual interest rate of 6.8% can be written as 0.068 (decimal form). To convert it to a monthly interest rate, we divide it by 12 (number of months in a year):

Monthly interest rate = 0.068 / 12 = 0.00567

Next, we need to determine the number of months Joe will be investing for. He is currently 25 years old and wants to know the value of his investment when he is 35, which means he will be investing for 10 years. Multiply this by 12 to get the number of months:

Number of months = 10 years * 12 months/year = 120 months

Now we have all the values we need to calculate the future value (A) of Joe's investment:

A = 5000(1 + 0.00567)^(120)

Using a calculator, we can solve this equation to find the future value of Joe's investment when he is thirty-five:

A ≈ 5000(1.00567)^120

A ≈ 5000 * 1.96944

A ≈ $9,847.20

Therefore, it is important to note that this calculation assumes Joe does not make any additional deposits or withdrawals during the ten-year period and that the interest rate remains constant.

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The correct answer is it would take approximately 0.000012 seconds (or 12 microseconds) for the laptop to receive a packet of MTU size (1500 bytes) with a network speed of 1 Gbps.

To determine the time it will take for a laptop to receive a packet of MTU size (1500 bytes), we need to consider the data transfer rate or network speed.

Let's assume the network speed is given in bits per second (bps). We'll need to convert the packet size from bytes to bits and then divide it by the network speed to calculate the time.

First, let's convert the packet size from bytes to bits:

Packet size = 1500 bytes

1 byte = 8 bits

1500 bytes * 8 bits/byte = 12000 bits

Now, we need to divide the packet size by the network speed to calculate the time:

Time = Packet size / Network speed

For example, if the network speed is 1 Gbps (1 gigabit per second), the calculation would be:

Time = 12000 bits / (1 Gbps) = 12000 / (10^9) seconds = 0.000012 seconds

Therefore, it would take approximately 0.000012 seconds (or 12 microseconds) for the laptop to receive a packet of MTU size (1500 bytes) with a network speed of 1 Gbps.

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Answer: 2

Step-by-step explanation:

Answer and Explanation: The only even number that is not a composite number is 2. All even numbers are defined as numbers that are divisible by, or have a divisor of, 2.

Answer:

The answer to your question is, 2

Step-by-step explanation:

The reason why that is our answer is because, 2 can either be multiplied and divided but 2 NUMBERS.

Such as the following:

2 / 1 = 2.

1 x 2 = 2.

What is a composite number?

A composite number are numbers that have more than two factors like the number 2:

2 / 1 = 2.

1 x 2 = 2.

Thus the answer to your problem is, 2

When two angles that are located between two co-planar lines on the same side of the transversal are called Alternate external angles.

Alternate External Angles

The pairs of angles outside the two lines and on either side of a transversal that cuts two lines are referred to as the alternate external angles.

In the given diagram below, the alternate exterior angles are:

∠2 and ∠8

∠1 and ∠7

Hence, when two angles that are located between two co-planar lines on the same side of the transversal are called Alternate external angles.

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Answer:

112 seconds

Step-by-step explanation:

According to my calculations girl here to tell you how.

40*14=560

560/5=112

if 14 is hours and 40 is minutes, multiplying and dividing by five gives you

*DRAMATIC MUSIC*

112 seconds

Answer:

176 minutes

Step-by-step explanation:

14 hours equals 840minutes + 40 minutes = 880 minutes

880/5=176

There are 24 possible 3 digit numbers that can be formed using numerals 3,2,7 and 9 without repetition.

Since repetition is not allowed, the first digit can only be 3, 2, 7 or 9. Each of the four digits can be chosen in 4 ways.

For the second digit, the choices are now reduced to 3, 2 or 7 (since 9 has already been used). There can be 3 ways to pick the second digit.

For the third digit, the choices are now reduced to 2 or 7 (since 3 and 9 have already been used). There can be 2 ways to pick the third digit.

Therefore, there are 4 x 3 x 2 = 24 possible 3 digit numbers that can be formed using numerals 3,2,7 and 9 without repetition.

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Answer:

$-83.75

Step-by-step explanation:

She won't have any more money to spend

Multiply $36.75 by 5

That would be $183.75

Subtract 183.75 from 100

-83.75

So Helen wouldn't have anything left to spend.

She would actually be in debt because she used more than $100

The required values are A = 1, B = 0, and C = 8 because the equation for the thrown ball's path will be x = 8.

Let the vertical line be the y-axis and the horizontal line be the x-axis, the ball is thrown from a place that is parallel to the y-axis (8,0).

Because the house is the starting point and the ball is thrown from a position 8 feet to the right of the house,

As a result, the equation for the thrown ball's path will be x = 8.

Therefore, A = 1, B = 0 and C = 8.

Hence, the required values are A = 1, B = 0, and C = 8 because the equation for the thrown ball's path will be x = 8.

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Answer:

degree is 2

standard form is

-x^2+2x-8

classification is trinomial

leading coeff is -1

hope i helped

Step-by-step explanation:

Answer:

3z^2

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

The expression equivalent to the given expression  -2(3x + 5y) is

given that

-2(3x + 5y)

expanding the parenthesis

-6x - 10y = 0

10y = 6x

y = 6x/10

y = 3x / 5

we can conclude that y = 3x/5 is equivalent to  -2(3x + 5y)

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Answer:the answer is 4.55

Step-by-step explanation:

Answer:

432,106

Step-by-step explanation:

True, parabola consists of all the set of points that are equidistant from the fixed point and the fixed line.

As given in the question,

Given statement is: Parabola consist of set of all the points which are equidistant from fixed point and fixed line.

Therefore, parabola consists of all the set of points that are equidistant from the fixed point and the fixed line is a true statement.

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Answer:

Step-by-step explanation:

Hope this helps u!!

Combine both results:g'(x) = 6x cos(x) - 3x² sin(x) - 2 cos(2x)

To differentiate g(x) = 3x² cos(x) - sin(2x) with respect to x, we will apply the product and chain rules.

Differentiate 3x² cos(x):
- First, differentiate 3x²: d(3x²)/dx = 6x
- Second, differentiate cos(x): d(cos(x))/dx = -sin(x)
- Now, apply the product rule: (6x)(cos(x)) + (3x²)(-sin(x)) = 6x cos(x) - 3x² sin(x)

Differentiate sin(2x):
- First, differentiate 2x: d(2x)/dx = 2
- Second, differentiate sin(u) (where u = 2x): d(sin(u))/du = cos(u)
- Now, apply the chain rule: 2(cos(2x)) = 2 cos(2x)

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Answer:

Step-by-step explanation

B<-35

Answer:

B=39.78

Step-by-step explanation:

Answer:b

hope this help:)

The average velocity from t = 2s to t = 4s would be - 48 ft/s.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that an object is thrown upward with initial velocity of 48 feet per second from a high of 120 feet. The height of the object t seconds after it is thrown is given by h(t) = - 16t² + 48t + 120.

Average rate of change of velocity with time is called average velocity. Mathematically -

v{avg.} = Δx/Δt                                                         .... Eq { 1 }

Δx = x(4) - x(2)

Δx = - 16(4)² + 48(4) + 120 - {- 16(2)² + 48(2) + 120}

Δx = - 96

Δt = 4 - 2 = 2

So -

v{avg.} = Δx/Δt = -96/2 = - 48 ft/s

Therefore, the average velocity from t = 2s to t = 4s would be - 48 ft/s.

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Answer: The measures of the angles in triangle ABC are BAC = 68°, BCA = 50.6°, and ABC = 61.4°. The lengths of the sides are AB = 12, AC = 14, and BC = 13.68.

Step-by-step explanation:

To find the angles and sides of a triangle, you need to know at least three pieces of information about the triangle. In this case, you are given the lengths of sides AB and AC, and the measure of angle BAC.

You can use the Law of Sines to find the measure of the third angle and the length of the third side. The Law of Sines states that for any triangle, the ratio of the length of a side to the sine of the angle opposite that side is the same for all sides and angles in the triangle. In other words, if we let a, b, and c represent the lengths of the sides of the triangle and A, B, and C represent the measures of the angles opposite those sides, then the following equation holds:

a/sin A = b/sin B = c/sin C

In triangle ABC, we are given the lengths of sides AB and AC and the measure of angle BAC. We can use the Law of Sines to find the measure of angle BCA and the length of side BC.

First, we can find the measure of angle BCA using the equation:

a/sin A = b/sin B = c/sin C

Substituting the known values, we get:

14/sin BAC = 12/sin BCA

Solving for sin BCA, we get:

sin BCA = 14/12 * sin BAC

Plugging in the given value for sin BAC, we get:

sin BCA = 14/12 * sin 68°

Using a calculator, we find that sin 68° = 0.906308

So sin BCA = 0.763696

To find the measure of angle BCA, we can use the inverse sine function on our calculator. The inverse sine of 0.763696 is about 50.6°.

Now that we know the measures of angles BAC and BCA, we can use the fact that the angles in a triangle sum to 180° to find the measure of angle ABC:

BAC + BCA + ABC = 180°

Substituting the known values, we get:

68° + 50.6° + ABC = 180°

Solving for ABC, we get:

ABC = 180° - 68° - 50.6°

This simplifies to:

ABC = 61.4°

Now that we have found the measures of all three angles, we can use the Law of Sines again to find the length of side BC.

We can use the equation:

a/sin A = b/sin B = c/sin C

Substituting the known values, we get:

14/sin BAC = 12/sin BCA = BC/sin ABC

Solving for BC, we get:

BC = 14/sin BAC * sin ABC

Plugging in the values we found earlier, we get:

BC = 14/0.906308 * sin 61.4°

Using a calculator, we find that sin 61.4° = 0.875

So BC = 14/0.906308 * 0.875 = 13.68

The measures of the angles in triangle ABC are BAC = 68°, BCA = 50.6°, and ABC = 61.4°. The lengths of the sides are AB = 12, AC = 14, and BC = 13.68.

Answer:

<5 is the remote interior angle to <1

They are on the same line, or, they are supplementary, and will add up to 180 degrees

The remote interior angles of ∠1 are ∠2 and ∠3.

Hence, Option (b) and (c) are correct.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that:

A triangle with marked angles.

We have to find the remote interior angles of angle 1.

Now, We know that;

Remote interior angles are the two angle that are inside the triangle and are opposite from the exterior angle.

Also, Remote interior angles don't share a vertex or corner of a triangle with the exterior angle.  

Thus, for the remote interior angles of angle 1 are angle 2 and angle 3  as they do not share a vertex or corner of a triangle with the exterior angle.  

Thus, Option (b) and (c) are correct.

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The probability of drawing a white marble if we draw marbles out 25 times with replacement is 1/5.

We know that there are 5 marbles in the bag which are:

White, yellow, pink, blue, and red.

We also know that there is an equal probability of getting a marble.

Probability formula: P(E) = Favourable events/Total events

So, the probability of drawing white marble:

P(E) = Favourable events/Total events

P(E) = 5/25

P(E) = 1/5

Therefore, the probability of drawing a white marble if we draw marbles out 25 times with replacement is 1/5.

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Answer:

17, -120, 36, -0.5, -2

Step-by-step explanation:

hope this helps

Answer:

392

Step-by-step explanation:

sequence is generalized as

\(a_n=6n-4\)

to find 66th term substitute n=66

\(a_n=6*66-4\\\)

Answer:

6 over  9

Step-by-step explanation:

y2-y1 over x2-x1

The given statement "the phrase the fear of the lord appears 25 times in the book of proverbs" is true.

Given :

The phrase the fear of the Lord first appears in the Book of Proverbs

The phrase the fear of the Lord first appears in the book of Job.

The fear of the Lord produces the greatest possible life that any person can ever live. There is no better life on earth than a life lived in the will of the Lord! To put it very simply, walking in the fear of the Lord is your individual decision. 0:36. If you fear Him, then you will want to honor Him in everything.

Hence , the given statement "the phrase the fear of the lord appears 25 times in the book of proverbs" is true.

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The ordered pair of C'' after the sequence of transformation is (-14, -5)

Here we have know that  ABC can be plotted at A (-14, 14), B (-8, 11) & C (-14, 5).

Here we all know that the y-axis reflection rule is written as,

=> (x, y) → (-x, y)

And the value of x coordinate flips in sign from positive to negative, or vice versa. Then the value of y coordinate stays the same.

Then the point is look like C(-14,5) will then reflect based on the following rule,

=> (x, y) → (x, y)

The transformed coordinates are look like,

=> (-14,5) ((-14),5)

=> (-14,5)→ (14,5)

Therefore, here we have point C' located at (14,5) after applying the y-axis reflection rule on point C.

Now, the next operation to do is is the 180 degree rotation.

And this can be clockwise or counterclockwise.

Then the rotation rule is written as

=> (x, y) → (-x,y)

Now, for this time both coordinates flip in sign.

Here we have know that this rule only works if the center of rotation is the origin.

Now, let us apply that rotation rule to C' to find where C" is located.

Then the rule can be written as,  (x, y) → (-x,y)

=> (14,5)→ (-14, -5)

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