Which of these denominations in no longer made in the United States?

A. $1000
B. $50
C. $2
D. $100

The slope of a line perpendicular to the line with equation y = 4x + 5 will be, [tex]-\frac{1}{4}[/tex].

A straight line is a combination of endless points joined on both sides of the point.

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

The slope 'm' of any straight line is given by:

The given equation in the problem is;

y = 4x + 5

The slope of the given equation is found from the standard equation of the straight line as;

y=mx+c

On comparing, we get, m = 4.

The perpendicular line slopes are reciprocals with the negative sign of each other.

Hence, the slope of a line perpendicular to the line with equation y = 4x + 5 will be, [tex]-\frac{1}{4}[/tex]

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The range of the function f(x) = |x - 1| - 2 is all real numbers greater than or equal to -2.

The function f(x) = |x - 1| - 2 represents the absolute value of x minus 1, subtracted by 2.

The range of the function can be determined by finding the minimum and maximum values it can take.

Since the absolute value of a number is always greater than or equal to zero, the lowest value that f(x) can take is when |x - 1| = 0, which happens when x = 1.

Therefore, the minimum value of f(x) is -2.

As x increases or decreases from 1, the value of f(x) increases.

So, there is no upper bound for the range of f(x).

Therefore, the range of the function is all real numbers greater than or equal to -2.

Answer with explanation:

Mean is sum of all the observation divided by total number of observation, where as median is middlemost observation of the data set, while mode is most occurring variate or data value in the data set.

1. Variate or Data set which is represented in Histogram is

 3,8,4,8,3

Arranging it in ascending order, we get

3,3,4,8,8

Data is skewed right.So, Mean >Median>Mode

Mean =5.2

Number of observation is 5. So,Median will be Middle term,that is third term equal to 4.

Mode =3 or ,8 which will be equal to 3,as data is skewed right.

→Mean gives better representation of data set,because, 5.2-3=2.2 and, 8-5.2=2.8

2. Variate or Data set which is represented through dots is

 2, 2, 3,5,5

Arranging it in ascending order, we get

2,2,3,5,5

Data is skewed right.So, Mean >Median>Mode

Mean=3.4

Number of observation is 5. So,Median will be Middle term,that is third term equal to 3.

Mode =2 or 5 which will be equal to 2,as data is skewed right.

→Mean gives better representation of data set,because, 3.4-2=1.4 and, 5-3.4=1.6

3. Variate or Data set which is represented in Histogram is

 6,2,6,2,6

Arranging it in ascending order, we get

2,2,6,6,6

Data is skewed left.So, Mean <Median<Mode

Mean=4.4

Number of observation is 5. So,Median will be Middle term,that is third term equal to 6.

Mode =6

→Mode gives better representation of data set.

4.Variate or Data set which is represented through dots is

 1,3,4,3,1

Arranging it in ascending order, we get

1,1,3,3,4

Data is skewed left.So, Mean <Median<Mode

Mean=2.4

Number of observation is 5. So,Median will be Middle term,that is third term equal to 3.

Mode =1 or 3,data is skewed left,so mode =3

Here, in this data set, both mode and median are better measure of center than Mean,as there are two modes in the data set, so choosing median as measure of center,because data is skewed left,

For ,Option 4: Median is the better measure of center.

The expression is 26x36 to the 7th power if the number of 8-character passwords.

A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.

It is given that:

The number of 8-character passwords that can be formed using letters and digits if the password must begin with a letter.

From the condition given:

= 26 x (36)⁶

Thus, the expression is 26x36 to the 7th power if the number of 8-character passwords.

a. 21x36 to the 7th power

b.26x36 to the 7th power

c.26 to the 5th power x 10 to the 3rd

d.36 to the 8th power

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we have

[tex]\frac{2-\sqrt{8}}{4+\sqrt{12}}[/tex]

Multiply the numerator and denominator by the conjugate of the denominator

so

[tex]\frac{2-\sqrt{8}}{4+\sqrt{12}}*\frac{4-\sqrt{12}}{4-\sqrt{12}}=\frac{(2-\sqrt{8})(4-\sqrt{12)}}{4^{2}-(\sqrt{12})^{2}}\\ \\= \frac{2*4-2*\sqrt{12}-4*\sqrt{8}+\sqrt{12}*\sqrt{8}}{16-12}\\ \\=\frac{8-4\sqrt{3}-8\sqrt{2}+4\sqrt{6}}{4} \\ \\=2-\sqrt{3}-2\sqrt{2}+\sqrt{6}[/tex]

therefore

the answer is

[tex]2-\sqrt{3}-2\sqrt{2}+\sqrt{6}[/tex]

To convert log4 14 to a logarithm of base 3, you can use the change of base formula. The required conversion would be log3 14 divided by log3 4.

To write log4 14 as a logarithm of base 3, we would use the change of base formula. The change of base formula is logba = logca / logcb, where logba is the logarithm we want to convert, c is the new base, a is the number, and b is the original base. So, in this case, we want to write log4 14 as a logarithm of base 3, so using the formula, it would be (log3 14) / (log3 4).

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There will be, 590490 possible combinations.

The number of different groups which can be formed from the available things can be calculated using combinations.

Given that, A small combination lock on a suitcase has 6 wheels, each labelled with the 10 digits 0 to 9.

We have 10 for the first wheel, but second wheel only has 9 options because 2nd number can't be the same as first. The third and fourth wheels also has 9 options for the same reason.

10x9x9x9x9x9 = 590490 combinations

Hence, There will be, 590490 possible combinations.

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Answer:  The correct option is (B) 81°.

Step-by-step explanation:  We are given to find the measure of the missing angle of the quadrilateral shown in the figure.

The measures of three angles of the quadrilateral are 65°, 78° and 136°.

To find the value of x, the measure of the fourth angle.

We know that

the sum of the measures of four angles of a quadrilateral is 360°. so, we must have

[tex]65^\circ+78^\circ+136^\circ+x=360^\circ\\\\\Rightarrow 279^\circ+x=360^\circ\\\\\Rightarrow x=360^\circ-279^\circ\\\\\Rightarrow x=81^\circ.[/tex]

Thus, the measure of the missing angle is 81°.

Option (B) is CORRECT.

The measurements given can form a triangle, and to solve it, we would use the Law of Sines. After confirming the possibility of a triangle, we solve for the unknown angle C using the known values and compute the remaining angle and side.

To determine if a triangle is formed by the given measurements and solve it using the Law of Sines, we need to check if the given angle and sides satisfy the triangle inequality. The measurements given are angle B = 137°, side c = 6, and side b = 11. A triangle is possible if the sum of the two smallest sides is greater than the length of the longest side. Here the angle is very large, suggesting that the opposite side (b) must be the longest; however, since side b is indeed longer than side c, this condition is satisfied, so a triangle can be formed.

To solve the triangle using the Law of Sines, we set up the following ratio:

    b/sin(B) = c/sin(C)

After substituting the known values into the equation, we get:

    11/sin(137°) = 6/sin(C)

Now, we solve for sin(C) to find the angle C, and subsequently use the sum of angles in a triangle (180°) to find the remaining angle A. Once angle A is known, we can use the Law of Sines again to find the remaining side a. If at any point we find that the calculation results in an invalid sine value (greater than 1 or less than -1), we must then state that no real solution exists.

It is important to note that if we find angle C to be obtuse (greater than 90°), the triangle will not have a unique solution because it would contradict our initial assumption that angle B, being the largest given angle, is opposite the longest side.