What is the measure of C?

Answer:

mean is $11

median is $10

Step-by-step explanation:

We are given that Jane used 200 minutes and the cost was $75, and also she used 680 minutes and the cost was $195. To determine a function of the cost "C" as a function of the minutes "x" we will assume that the behavior of this function is that of a line. Therefore, the function must have the following form:

Where "m" is the slope and "b" the y-intercept. We will determine the slope using the following formula:

Where:

Are points in the line. The given points are:

Substituting in the formula for the slope we get:

Solving the operations we get:

Now we substitute in the formula for the line:

Now we determine the value if "b" by substituting the first point. This means that when C = 200, x = 75.

Solving the product:

Now we subtract 18.75 from both sides:

Therefore, the formula of the cost is:

Part B. We are asked to determine the cost is there is a consumption of 323 minutes. To do that we will substitute in the formula for "C" the value of x = 323.

Solving the operations we get:

Therefore, the cost is $262.

Answer:

Step-by-step explanation:

We will make use of algebra here.

First of all, we know that the monthly fee will be the same throughout all the months.
So, let's consider that cost to be the yet-to-find constant: \(a\).

A charge is accumulated for every minute on the call, so let's consider that minutely charge to be the constant: \(b\).

\(x\) is the number of minutes spent on the call.
So, the total charge after talking for \(x\) minutes would be:

\(b \times x\\=bx\)

The monthly cost is the sum of the monthly fee and the total charge.

So, if this is represented mathematically, we get:

\(C(x)= a+bx\)

A piece of information that we have is that, after calling for 200 minutes (which means \(x=200\)), the monthly cost ( \(C(x)\) ) would be $75.

Upon substituting these values in the equation we found above, we get:

\(C(x)=a+bx\\\\75=a+200b\)

Similarly, we have another piece of information, which states that calling for 680 minutes (\(x=680\)) produced a monthly cost of $195.

Upon substituting these values in the equation we found above, we get:

\(C(x)=a+bx\\\\195=a+680b\)

And, thus we have found a system of equations:

 \(a+200b=75\\a+680b=195\)

For the first equation, let's make \(a\) the subject:

\(a+200b=75\\\\a+200b-200b=75-200b\\\\a=75-200b\)

Substitute this expression for \(a\) into the second equation:

\(a+680b=195\\\\75-200b+680b=195\\\\75+480b=195\)

Find the value of \(b\) using this equation:

\(75+480b=195\\\\75+480b-75=195-75\\\\480b=120\\\\\frac{480b}{480}=\frac{120}{480}\\\\b=\frac{1}{4}\)

Insert the value for \(b\) into the expression for \(a\):

\(a=75-200b\\\\a=75-200(\frac{1}{4})\\\\a=75-50\\\\a=25\)

Since we have the values for the constants \(a\) and \(b\), we can complete the function/equation  \(C(x)\):

\(C(x)=a+bx\\\\C(x)=25+\frac{1}{4}x\)

So, the answer for (A) is:

\(C(x)=25+\frac{1}{4}x\)

For (B), we have to find the monthly bill/cost ( \(C(x)\) ) when 323 minutes have been spent on calling.

So, we just have to substitute \(x\) for 323, since \(x\) represents the number of minutes spent on calling:

\(C(x)=25+\frac{1}{4}x\\\\C(x)=25+\frac{1}{4}(323)\\\\C(x)=25+80.75\\\\C(x)=100.75\)

The answer for (B) is \(\$100.75\)

Answer:

Step-by-step explanation:

8% supporting the visiting team, so:

92% is 2576, find the total number:

Since there are 10 persons in the group who do not know one another, the real number of handshakes will be 45.

In probability theory and other branches of mathematics, the term "combination" refers to a succession of results where the order is irrelevant. A combination is a selection of all or a portion of a group of items, regardless of the sequence in which the items are chosen. Combinations and permutations may appear to be synonyms. However, they are defined differently in probability theory. Combinations: The sequence of results is irrelevant. Permutations: The sequence of events matters.

Here,

Total number of handshakes = 10C2 = (10 × 9)/2 = 45 handshakes.

When 10 people are shaking hands, each one will shake hands with 9 others.

The total number of handshakes in actual = 90/2 = 45 handshakes.

The total number of handshakes in actual will be 45 handshakes as there are 10 people in the group who do not know each other.

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To determine how many layers of 1-inch cubes Clarice packed into the box with a volume of 36 cubic inches, we need to divide the total volume of the box by the volume of one cube. Since the volume of one cube is 1 cubic inch (1 x 1 x 1), we can divide 36 cubic inches by 1 cubic inch to get the number of cubes that can fit in the box. This gives us a total of 36 cubes.

Next, we need to figure out how many layers of cubes there are. If we imagine the cubes being packed tightly together, then each layer would consist of the same number of cubes as the bottom layer. Therefore, the number of layers would be equal to the total number of cubes divided by the number of cubes in one layer.

Since we know that there are 36 cubes in total, we can find the number of cubes in one layer by taking the square root of 36 (which is 6). Therefore, Clarice packed the cubes into the box in 6 layers (36 cubes ÷ 6 cubes per layer = 6 layers).

In summary, Clarice packed 36 1-inch cubes into a box with a volume of 36 cubic inches, which resulted in 6 layers of cubes.

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The smallest value that can be written to the address of the LED array in order to turn on all 8 LEDs is 0b1111, or binary 1111.

To understand why the binary value 0b1111 is the smallest value that can turn on all 8 LEDs, we need to look at the binary representation of the LED array. Binary is a base-2 numbering system, where each digit can have one of two values: 0 or 1. In this case, each LED in the array likely corresponds to one bit in the binary representation, with 1 indicating the LED is turned on and 0 indicating it is turned off.

The binary value 0b1111 represents four bits, each set to 1. This means that all 4 bits are turned on, which would likely correspond to turning on all 8 LEDs in the array (assuming one bit per LED).

Now let's look at the other options provided:

0xf: This is a hexadecimal value, which is a base-16 numbering system. It represents the decimal value 15 in binary, which is 0b1111. So this option is equivalent to binary 0b1111, which we have already determined to be the correct answer.

256: This is a decimal value, which is a base-10 numbering system. It does not directly represent a binary value that can turn on all 8 LEDs, as it is larger than the maximum binary value that can be represented by 8 bits (which is 0b11111111 or 255 in decimal).

0xff: This is a hexadecimal value, which represents the decimal value 255 in binary (0b11111111). This is the largest binary value that can be represented by 8 bits, so it would indeed turn on all 8 LEDs. However, it is larger than the binary value 0b1111, which is the smallest value that can achieve the same result.

0xf01000ff: This is a hexadecimal value that is larger than the maximum value that can be represented by 8 bits. It is also not equivalent to the binary value 0b1111, as it contains additional bits beyond the first 4 bits set to 1. Therefore, it is not the smallest value that can turn on all 8 LEDs.

Therefore, the correct answer is 0b1111, as it represents the smallest binary value that can be written to the LED array to turn on all 8 LEDs.

therefore not the smallest value that can achieve this result.

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The graph that most resembles y=3^x is Graph B

Answer:

I think graph B

Step-by-step explanation:

It makes more sense

The missing sides of the right triangle are DE = 4.195 and DF = 6.527 and the missing angle is 50°.

In this question we find a right triangle with a known side and two known angles. The missing sides can be found by following trigonometric functions:

tan F = DE / EF

cos F = EF / DF

And the angle D is found by the following expression:

D = 90° - F

If we know that EF = 5 and F = 40°, then missing sides and angle are, respectively:

DE = EF · tan F

DE = 5 · tan 40°

DE = 4.195

DF = EF / cos F

DF = 5 / cos 40°

DF = 6.527

D = 90° - 40°

D = 50°

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The co-terminal angle to 5π/6 in the unit circle is C. 17π/6

Co-terminal angles in a unit circle are angles that share the same terminal point

Given the angle 5π/6, we desire to find the angle that shares the same terminal point in the unit circle. We proceed as follows.

We know that x = 5π/6 + 2π

Taking the L.C.M which is 6, we have that

x = (12π + 5π)/6

x = 17π/6

So, the angle is C. 17π/6

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The equation of the line is found as y = -x/2 + 9/2.

For the given question;

The equation of the perpendicular line is given as;

y = 2x - 7

Compare the equation with the standard form of slope intercept.

y = mx + c

m = slope and c is the y intercept.

m1 = 2

Now, the line is perpendicular, thus the relation between both slopes is;

m1 × m2 = -1

m2 = -1/2

The passing coordinates of the line is (1. 4).

Find the equation using formula.

y - y1 = m2(x - x1)

y - 4 = (-1/2) (x - 1)

Simplifying,

y = -x/2 + 9/2

Thus, the equation of the line is found as y = -x/2 + 9/2.

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Answer:

The expression x⁴ + 8x³ + 34x² + 72x + 81 cannot be factored further using simple integer coefficients. It does not have any rational roots or easy factorizations. Therefore, it remains as an irreducible polynomial.

To calculate the interest earned over a period of time, we can use the formula for compound interest. In this case, Natalie Engineering invested $95,000 at an interest rate of 6.5 percent, compounded annually for 5 years. The company earned $30,875.00 in interest over this period.

The formula for compound interest is given by:

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

Where:

A is the final amount (including both the principal and the interest),

P is the principal amount (initial investment),

r is the interest rate (as a decimal),

n is the number of times interest is compounded per year, and

t is the number of years.

In this case, the principal amount (P) is $95,000, the interest rate (r) is 6.5% (or 0.065), the number of times interest is compounded per year (n) is 1 (since it is compounded annually), and the number of years (t) is 5.

Substituting these values into the formula, we have

\(A = 95,000(1 + 0.065/1)^(1*5) - 95,000\)

Simplifying the expression:

A = 95,000(1.065)^5 - 95,000

Using a calculator, we find that A ≈ 125,875.00.

To calculate the interest earned, we subtract the principal amount from the final amount:

Interest = A - P = 125,875.00 - 95,000 = 30,875.00

Therefore, Natalie Engineering earned $30,875.00 in interest over the 5-year period.

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Answer:

4 1/2

33/56

Step-by-step explanation:

1/4 multiplied by 1/2

1/2 multiplied by 5/16

The area of logo 1 is  24 ft² and logo 2 is 16.28  ft².

                                = \(\frac{5}{32}\) + \(\frac{\pi }{32}\)

                                 =  0.2544 inch²

Thus, the area of logo 1 is  24 ft² and logo 2 is 16.28  ft².

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The number of families with more than 3 people is 436.

To find the probability that a given family has more than 3 people, we need to sum up the frequencies for all family sizes with more than 3 people and divide by the total number of families surveyed, which is 1000.

Looking at the frequency table provided, we can see that the family sizes with more than 3 people are 4, 5, and 6. So, we need to add up the frequencies for these family sizes:

Frequency for family size 4 = 245

Frequency for family size 5 = 125

Frequency for family size 6 = 66

Adding these frequencies together, we get:

245 + 125 + 66 = 436

Therefore, the number of families with more than 3 people is 436.

To find the probability, we divide this number by the total number of families surveyed (1000) and multiply by 100 to convert it to a percentage:

Probability = (436/1000) x 100

Simplifying this fraction, we get:

Probability = 43.6%

So, to the nearest percent, the probability that a given family has more than 3 people is 44%.

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Answer:

SA = 10,800 ft²

Step-by-step explanation:

To find the surface area of a rectangular prism, you can use the equation:

SA = 2 ( wl + hl + hw )

SA = surface area of rectangular prism

l = length

w = width

h = height

In the image, we are given the following information:

l = 40

w = 60

h = 30

Now, let's plug in the information given to us to solve for surface area:

SA = 2 ( wl + hl + hw)

SA = 2 ( 60(40) + 30(40) + 30(60) )

SA = 2 ( 2400 + 1200 + 1800 )

SA = 2 ( 5400 )

SA = 10,800 ft²

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The solution to this equation is x = -7 and x = 7.

The two numbers 7 units away from 0 on a number line are -7 and 7. This can be expressed mathematically as |x-0|=7, where x is the unknown number. Solving this equation yields two solutions, x = -7 and x = 7.

To solve this equation, first subtract 0 from both sides of the equation to get |x| = 7. Then, take the absolute value of both sides of the equation to get x = 7. Finally, note that the absolute value of any number is equal to that number's positive value. Therefore, the solution to this equation is x = -7 and x = 7.

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According to the information in the nutritional table, it can be inferred that the amount of milligrams of sodium that we should consume during the rest of the day must be less than 2,175mg,

To calculate the amount of sodium that we can consume during the rest of the day after breakfast, we must subtract the value of sodium consumed to the amount of total sodium that we want to ingest as shown below:

According to the above, it can be inferred that after consuming the cereal bar at breakfast, we should consume an amount less than or equal to 2,175mg of sodium in the other meals of the day (lunch, dinner and snacks).

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Where the derivative of a function f′ is rising, the function f is concave up (or upwards). The function f is concave up when the derivative of a function f′ is rising (or upwards).

When a function is concave, the second derivative must be obtained, set to zero, and then used to establish the range of zero values in which the function is negative. Test values on each side of these to see if the function is negative and hence dropping.

A section of the graph of f has an upward concavity if the curve "bends" upward. The entire y=x2 parabola is concave upward, for instance. A section of the graph of f is concave downhill if the curve "bends" downward.

Concave up is from (-∞ , 1]

Concave down is from [1, ∞)

y-intercept coordinates = - 8.2, 4

increasing value = x = - 8

decreasing value = x = 2.1

end behavior of the graph = downwards

factored form = y = a(x-r)(x-s)

y = a(x+2)(x-1)

-8.2 = a(-8 + 2)(-8-1)

-10 = a (-6)(-9)

a = 10/54

factored form = y = 10/54 (x+2)(x-1)

standard form = Ax + By = C

Yes, the graph has relative min/max values,

min = (-8,8.2)

max = (2.1,4)

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Answer:

My answer to your question is a "No".

We can know that a and b are the same numbers. If we multiply the same number on each side, the answer will be the same. However, x and y have different values. So, it will show differently.

Let's have an example:

It we say a = 5, x = 6, y = 7.

We know a and b are the same number so, both a and b will be 5. If we multiply a by x, it will be 5 x 6 which is 30. It will show the same answer on multiplying b because as you said a and b are the same. The equation will be 5(a) x 6(x) = 5(b) x 6(x) Let's look at multiplying y. If we multiply a by y, it will be 5 x 7 which is 35. As you said it will show the same answer on multiplying b because a and b are the same. The equation for this will be 5(a) x 7(y) = 5(b) = 7(y). Finally, let's compare the two equations.

5(a) x 6(x) = 5(b) x 6(x) -> 30 = 30

5(a) x 7(y) = 5(b) = 7(y) -> 35 = 35

You can see it more clearly when we compare those to the equations that I made.

Thank you

Yes, if a = b, then ax = bx and ay = by for any value of x.

This is because the equation a = b implies that a and b are equal in value, so any expression involving a can be replaced with an equivalent expression involving b. In other words, any operation performed on a can be performed on b and produce the same result.

For example, if a = b, then multiplying both sides of the equation by x yields ax = bx, and multiplying both sides of the equation by y yields ay = by. This means that any power, root, logarithm, or other mathematical operation performed on a can also be performed on b and produce the same result.

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The probability that the jury makes the correct decision is approximately 0.7063.

To solve this problem, we need to find the probability that the jury makes the correct decision if the defendant is guilty. Let's break down the problem into smaller steps.

We know that the probability of a single juror making the correct decision is 0.80. If the defendant is guilty, then the probability of a juror making the correct decision is still 0.80. Therefore, the probability that a single juror makes the correct decision if the defendant is guilty is 0.80.

We can use the binomial distribution formula to determine the probability of at least 10 out of 12 jurors making the correct decision. The formula is:

P(X ≥ k) = 1 - Σ(i=0 to k-1) [n!/(i!(n-i)!) x \(p^i \times (1-p)^{(n-i)}\) ]

where:

P(X ≥ k) is the probability of at least k successes

n is the total number of trials (in this case, 12 jurors)

p is the probability of success in a single trial (in this case, 0.80)

k is the number of successes we want to find the probability of (in this case, 10)

Plugging in the values, we get:

P(X ≥ 10) = 1 - Σ(i=0 to 9) [12!/(i!(12-i)!) x \(0.80^i \times (1-0.80)^{(12-i)}\)]

Using a calculator or software, we can calculate this to be approximately 0.7063.

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Answer:

Below

Step-by-step explanation:

This is your posted line:

4 3/4 = 19 / 4

2 1/3 = 7/3

19/4  * 7/3  =  (19*7) /(4*3) = 133/12  = 11  1/12

BUT the question in the picture shows

2 4/7 * 2/3 =

18/7   * 2/3 =  (18*2) / ( 7*3) = 36/21 = 1  15/21   =    1 5/7

Answer: lesser x = 3.76 & greater x = 8.24

Step-by-step explanation: just took the test

For the given quadratic equation lesser x=3.765 and greater x=8.235.

The given quadratic equation is (x-6)²-5=0.

We need to find the solutions from least to greatest.

The formula to find the solution to the quadratic equation is \(x=\frac{-b\pm\sqrt{b^{2}-4ac }}{2a}\).

Now, (x-6)²-5=0 can be written as x²-12x+31=0

Here, a=1, b=-12 and c=31

x=(12±√20)/2

⇒x=(12±4.47)/2

⇒x=3.765 or x=8.235

Therefore, lesser x=3.765 and greater x=8.235.

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The height of the flagpole is 12.9 feet to the nearest tenth.

The ratio is a numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.

Given:

The boy is 5' 3" tall and his shadow is 4 feet.

The shadow of the flagpole is 17 feet.

The boy is 5.25 feet tall.

Let the height of the flagpole is h feet.

So,

17/h = 5.25/4

h = 68/5.25

h = 12.95

h = 12.9 to one decimal place.

Therefore, h = 12.9 to one decimal place.

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After solving the given equations the answer is an Infinite solution. Hence, option A is correct

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given equation in the question,

8 + 4x = 2x + 8 + 2x

Firstly, let's write the given equation in a simplified manner,

8 + 4x = 8 + 4x  

As we can see that LHS = RHS, which means that both equations are the same then which means they will give infinite solutions.

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The correlation in error terms that arises when the error terms at successive points in time are related is termed autocorrelation

The correct answer is an option (a).

Correlation is the mutual connection between two or more variables. These variables can be dependent or independent but there should be random variables.

Autocorrelation is the degree of correlation between the values of the same variables across different data.

Instead of correlation between two different variables, the correlation is between two values of the same variable at times i and i + k.

It is used for the following two purposes:

- To detect non-randomness in data.

- To identify an appropriate time series model if the data are not random.

Therefore, The correlation in error terms that arises when the error terms at successive points in time are related is termed autocorrelation

The correct answer is an option (a).

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The equation of the quadratic graph that has moved 4 units left, 6 units up, compressed by ½ from the parent graph is \(y=2(x-4)^2+6\).

The curve-shaped graph of a quadratic function is known as a parabola. The vertex of a parabola is one of its focal points. On the graph, it is either the highest or lowest point. You can imagine it as the parabola's endpoint.

The parent function of a quadratic function is \(y=x^2\).

The transformed equation will be \(f'(x)=a(x-h)^2+k\).

Where a represents the wider  and compressed nature of the graph and (h,k) is the locator point.

It is given that the new quadratic graph is compressed by 1/2 from the parent graph which means a=2.

It is also given that the new graph is moved 4 units left, which means that h=4.

It is also given that the new graph is moved 6 units upward, which means that k=6.

Therefore by substituting all these values, the equation for the transformed graph will be \(y=2(x-4)^2+6\).

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If Ethan watches fewer than 6 movies per month, Plan A would be more expensive. If he watches more than 6 movies per month, Plan B would be more expensive.

For Plan A, the monthly cost is composed of a fixed fee of $28 plus a variable fee of $2.50 per movie watched. So, if Ethan watches x movies per month, the monthly cost for Plan A can be represented by the equation:

A = 28 + 2.5x

Here, A represents the monthly cost of Plan A, and x represents the number of movies Ethan watches per month.

For Plan B, the monthly cost is also composed of a fixed fee of $37, but the variable fee per movie watched is only $1. So, if Ethan watches x movies per month, the monthly cost for Plan B can be represented by the equation:

B = 37 + 1x

Again, B represents the monthly cost of Plan B, and x represents the number of movies Ethan watches per month.

To find the number of monthly movies watched, x, that would make the two plans have an equal monthly cost, we need to solve the equation:

A = B

So, we can substitute the equations for A and B to get:

28 + 2.5x = 37 + 1x

Now we can solve for x:

2.5x - 1x = 37 - 28

1.5x = 9

x = 6

So, if Ethan watches 6 movies per month, the monthly cost of Plan A and Plan B would be equal, at $41 per month.

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The congruent segments, \( SC \cong HR \) and \( HR \cong AB\), according to the substitution property of equality, gives; \( SC \cong AB \)

The given parameters are;

Required;

To prove;

\( SC \cong AB\)

Solution;

From the given parameters, and the definition of congruency, we have;

According to the symmetric property of equality, we have;

SC = HR

Therefore;

According to the substitution property of equality, we have;

If a = b and a = c, therefore;

b = c

Which gives;

HR = SC

HR = AB

Therefore;

SC = AB

Which gives;

\( SC \cong AB \) (Inverse of the definition of congruency)

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Answer:

56

Step-by-step explanation:

56 would be the arc. reasoning is because line CG form an arch of 56 and Angle A and C also form a angle of 34