What the values of angles B and C?

The expression's fully factored form is:[tex]72x^{3} + 72x^{2} + 18x = 18x(4x^{2} + 1)(x + 1)[/tex]

Factored Value, also known as "trended value," is the base annual value plus a yearly inflation factor based on a variation in the cost if live that is not to exceed 2% and is set by the State Agency of Equalization.

Rewriting an expression as the sum of factors is referred to as factor expressions or factoring. For instance, 3x + 12y may be expressed as 3 (x + 4y), which is a straightforward equation. The computations get simpler in this method. Three or (x + 4y) were examples of factors.

We can factor out [tex]18x[/tex] from each term to simplify the expression:

[tex]72x^{3} + 72x^{2} + 18x = 18x(4x^{3} + 4x^{2} + 1)[/tex]

An expression enclosed in parentheses can now be calculated by grouping or factoring.

[tex]4x^{3} + 4x^{2} + 1 = (4x^{2} + 1)(x + 1)[/tex]

The expression's properly factored version has the following result,

[tex]72x^{3} + 72x^{2} + 18x = 18x(4x^{2} + 1)(x + 1)[/tex]

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Answer:

See below.

Step-by-step explanation:

We can solve this linear programming problem using the simplex method. We will start by converting the problem into standard form

Maximize z = 3x₁ + 5x₂ + 0s₁ + 0s₂

subject to

x₁ - 5x₂ + s₁ = 35

3x₁ - 4x₂ + s₂ = 21

x₁, x₂, s₁, s₂ ≥ 0

Next, we create the initial tableau

Basis x₁ x₂ s₁ s₂ RHS

s₁ 1 -5 1 0 35

s₂ 3 -4 0 1 21

z -3 -5 0 0 0

We can see that the initial basic variables are s₁ and s₂. We will use the simplex method to find the optimal solution.

Step 1: Choose the most negative coefficient in the bottom row as the pivot element. In this case, it is -5 in the x₂ column.

Basis x₁ x₂ s₁ s₂ RHS

s₁ 1 -5 1 0 35

s₂ 3 -4 0 1 21

z -3 -5 0 0 0

Step 2: Find the row in which the pivot element creates a positive quotient when each element in that row is divided by the pivot element. In this case, we need to find the minimum positive quotient of (35/5) and (21/4). The minimum is (21/4), so we use the second row as the pivot row.

Basis x₁ x₂ s₁ s₂ RHS

s₁ 4/5 0 1/5 1 28/5

x₂ -3/4 1 0 -1/4 -21/4

z 39/4 0 15/4 3/4 105

Step 3: Use row operations to create zeros in the x₂ column.

Basis x₁ x₂ s₁ s₂ RHS

s₁ 1 0 1/4 7/20 49/10

x₂ 0 1 3/16 -1/16 -21/16

z 0 0 39/4 21/4 525/4

The optimal solution is x₁ = 49/10, x₂ = 21/16, and z = 525/4.

Therefore, the maximum value of z is 525/4, which occurs when x₁ = 49/10 and x₂ = 21/16.

Perfect numbers between 1 and n (where n is a positive integer) are 6, 28, 496, 8128.

A positive integer that is the sum of its appropriate divisors is referred to as a perfect number. The sum of the lowest perfect number, 6, is made up of the digits 1, 2, and 3. The digits 28, 496, and 8,128 are also ideal.

Perfect numbers are whole numbers that are equal to the sum of their positive divisors, excluding the number itself. Examples of perfect numbers include 6 (1 + 2 + 3 = 6), 28 (1 + 2 + 4 + 7 + 14 = 28) and 496 (1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248 = 496).

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The complete question is:

What are all the perfect numbers between 1 and n (where n is a positive integer)?

The measure of angle BAC is 55°, which is closest to option B (50°).

The ratio of the length of the side directly opposite an acute angle to the side directly adjacent to the angle is known as the tangent in trigonometry. Only triangles with straight angles can have this.

Let's give the angles shown in the diagram the following labels:

Angle ACD = 55°

Angle ABD = 35°

Angle BCD = 90°

To determine the size of angle ABC, we can use the knowledge that a triangle's total angles equal 180°. Because the straight line formed by angles ABD and BCD, we have:

[tex]Angle ABC = 180° - Angles ABD and BCD.[/tex]

[tex]Angle ABC = 180° - 35° - 90°Angle ABC = 55°[/tex]

Given that triangle ABC has two angles, we can use the knowledge that a triangle's total of angles equals 180° to determine the size of angle BAC:

[tex]Angle BAC = 180° - Angle ABC - Angle ACBAngle BAC = 180° - 55° - 70°Angle BAC = 55°[/tex]

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It is most similar to option B (50°) when the angle BAC is 55°.

What is a tangent angle?

The tangent in trigonometry is the length of the side directly opposite an acute angle divided by the length of the side directly next to the angle.

This property can only be found in triangles with straight angles.

Let's give the angles shown in the diagram the following labels:

Angle ACD = 55°

Angle ABD = 35°

Angle BCD = 90°

We can use the fact that a triangle's total number of angles is 180° to calculate the size of angle ABC. due to the fact that the straight line created by angles ABD and BCD

Triangle ABC has two angles, so we can use the fact that a triangle's sum of angles is 180° to calculate the size of angle BAC.

Therefore, the BAC measurement is 55°, which is closest to option B's 50°.C is 55°, which is closest to option B (50°).

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The sample mean is 2.1, the sample variance is 212.5% and the standard deviation is 14.57%

a. The sample mean can be computed as the average of the quarterly percent total returns:

[tex](11.2 - 20.5 + 13.2 + 12.6 + 9.5 - 5.8 - 17.7 + 14.3) / 8 = 2.1[/tex]

So the sample mean is 2.1%, which can be interpreted as the average quarterly percent total return for the stock over the sample period.

b. The sample variance can be computed using the formula:

[tex]s^2 = sum((x - mean)^2) / (n - 1)[/tex]

where x is each quarterly percent total return, mean is the sample mean, and n is the sample size. Plugging in the values, we get:

[tex]s^2 = (11.2 - 2.1)^2 + (-20.5 - 2.1)^2 + (13.2 - 2.1)^2 + (12.6 - 2.1)^2 + (9.5 - 2.1)^2 + (-5.8 - 2.1)^2 + (-17.7 - 2.1)^2 + (14.3 - 2.1)^2 / (8 - 1) = 212.15[/tex]

So the sample variance is 212.15%. The sample standard deviation can be computed as the square root of the sample variance:

[tex]s = \sqrt(s^2) = \sqrt(212.15) = 14.57[/tex]

So the sample standard deviation is 14.57%.

c. To construct a 95% confidence interval for the population variance, we can use the chi-square distribution with degrees of freedom n - 1 = 7. The upper and lower bounds of the confidence interval can be found using the chi-square distribution table or calculator, as follows:

upper bound = (n - 1) * s^2 / chi-square(0.025, n - 1) = 306.05

lower bound = (n - 1) * s^2 / chi-square(0.975, n - 1) = 91.91

So the 95% confidence interval for the population variance is (91.91, 306.05).

d. To construct a 95% confidence interval for the standard deviation (as percent), we can use the formula:

lower bound = s * √((n - 1) / chi-square(0.975, n - 1))

upper bound = s * √((n - 1) / chi-square(0.025, n - 1))

Plugging in the values, we get:

lower bound = 6.4685%

upper bound = 20.1422%

So the 95% confidence interval for the standard deviation (as percent) is (6.4685%, 20.1422%).

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The answer is A, rhombus.

From the discriminant of the give quadratic equation, the temperature of the machine will part after 50 minutes of operation.

The given equation that models the temperature of the machine is;

T = -0.005x² + 0.45x + 125

Let check if there's a value that exists for T = 135

Putting T = 135 in the given equation,

135 = -0.005x² + 0.45x + 125

We can simplify this to;

0.005x² - 0.45x + 10 = 0

From the general form of quadratic equation which is ax² + bx + c = 0, where a = 0.005, b = -0.45, and c = 10.

The discriminant of this quadratic equation is given by:

D = b² - 4ac

= (-0.45)² - 4(0.005)(10)

= 0.2025 - 0.2

= 0.0025

The discriminant of the equation is positive which indicates we have two roots. Therefore, the temperature of the machine part will cross 135°F at some point during the operation.

We can also find the roots of the quadratic equation using the formula:

[tex]x = (-b \± \sqrt(D)) / 2a[/tex]

Substituting the values of a, b, and D, we get:

[tex]x = (0.45 \± \sqrt(0.0025)) / 2(0.005)\\= (0.45 \± 0.05) / 0.01[/tex]

Taking the positive value, we get:

x = 50

Therefore, the temperature of the machine part will cross 135°F after 50 minutes of operation.

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After answering the provided question, we can conclude that slant height  of pyramid  [tex]= \sqrt((2/2)^2 + 5^2) = \sqrt(29) = 5.39 units.[/tex]

A pyramid is a polygon formed by connecting points known as bases and polygonal vertices. For each hace and vertex, a triangle known as a face is formed. A cone with a polygonal shape. A pyramid with a floor and n pyramids has n+1 vertices, n+1 vertices, and 2n edges. Every pyramid is dual in nature. A pyramid contains three dimensions. A pyramid is made up of a flat tri face and a polygonal base that come together at a single point known as the vertex. A pyramid is formed by connecting the base and peak. The edges of the base form triangle faces known as sides, which connect to the top.

            /\

          /    \

        /         \

      /______\

         5

         |

         |

         |

         |

         |

         2

The square pyramid in the diagram above has a two-unit-long square base and four five-unit-high triangular faces. The Pythagorean theorem can be used to calculate the slant height of each triangular face:

slant height [tex]= \sqrt((2/2)^2 + 5^2) = \sqrt(29) = 5.39 units.[/tex]

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Answer:

Show your solution ( 3. ) C + 18 = 29

Step-by-step explanation:

To solve the equation C + 18 = 29, we want to isolate the variable C on one side of the equation.

We can start by subtracting 18 from both sides of the equation:

C + 18 - 18 = 29 - 18

Simplifying the left side of the equation:

C = 29 - 18

C = 11

Therefore, the solution to the equation C + 18 = 29 is C = 11.

Answer:

1 cubic meter = 1000000 cm cubed

Step-by-step explanation:

[tex]1m^3*10^6=1000000cm^3[/tex]

Answer:

1 cubic meter = 10000000 cm cube

Therefore, A, B, C, and F are the proper responses as the congruence theories or postulates based on the data.

Having three straight sides and three angles where they intersect, a triangle is a closed, two-dimensional shape. It is one of the fundamental geometric shapes and has a number of characteristics that can be used to study and resolve issues that pertain to it. The triangle inequality theory states that the sum of a triangle's interior angles is always 180 degrees, and that the longest side is always the side across from the largest angle. Triangles can be used to solve a wide range of mathematical issues in a variety of disciplines and can be categorised based on the length of their sides and the measurement of their angles.

given

We can use the following congruence theories or postulates based on the data in the diagram:

A. ASA

B. AAS

C. LL (corresponding angles hypothesis)

F. SAS

Therefore, A, B, C, and F are the proper responses as the congruence theories or postulates based on the data.

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Step-by-step explanation:

Use the 110 to find the 70 degree angle   (they form a straight line = 180°)

   then 70 + 64 + R angle = 180°    ( sum of angles of a triangle)

        then  :    R angle = 46°

then the R angle + 2x-10 = 90°    ( because the two lines are perpendicular)

(2x -10)°   + 46 °  = 90 °

x = 27

Therefore, the possible number of pens in the box is p, where p is greater than 135.

Inequality refers to a situation in which there is a difference or disparity between two or more things, usually in terms of value, opportunity, or outcome. Inequality can take many forms, including social, economic, and political inequality.

Inequalities are mathematical expressions that compare two values using the symbols < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to). To solve an inequality, you need to isolate the variable (the unknown quantity) on one side of the inequality symbol and determine the range of values for which the inequality holds true.

Here are some general steps to solve an inequality:

by the question.

Let's say there are 'p' pens in the box. Each pack has more than 15 pens, so we can write the inequality:

p/9 > 15

Multiplying both sides by 9, we get:

p > 135

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The cardinality of set A, n(A) = 29

The cardinality of a set is the total number of elements in the set

Given the Venn diagram here shows the cardinality of each set. To find the cardinality of set A, n(A), we proceed as follows.

Since the cardinality of a set is the total number of elements in the set, then cardinality of set A , n(A) = 9 + 8 + 3 + 9

= 29

So, n(A) = 29

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The inverse of the coefficient matrix is A^-1 = [-2 2]. The solution to the system of equations is x = -1 and y = 1/5.

To solve the system of equations:

2x + 2y = 1

2x - 3y = 0

We can write this system in matrix form as:

[2 2] [x] [1]

[2 -3] [y] = [0]

The coefficient matrix is:

[2 2]

[2 -3]

To find the inverse of the coefficient matrix, we can use the following formula:

A^-1 = (1/|A|) adj(A)

where |A| is the determinant of A and adj(A) is the adjugate of A.

The determinant of the coefficient matrix is:

|A| = (2)(-3) - (2)(2) = -10

The adjugate of the coefficient matrix is:

adj(A) = [-3 2]

[-2 2]

Therefore, the inverse of the coefficient matrix is:

A^-1 = (1/-10) [-3 2]

[-2 2]

Multiplying both sides of the matrix equation by A^-1, we get:

[x] 1 [-3 2] [1]

[y] = -10 [-2 2] [0]

Simplifying the right-hand side, we get:

[x] [-1]

[y] = [1/5]

Therefore, the solution to the system of equations is:

x = -1

y = 1/5

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_____The given question is incomplete, the complete question is given below:

solve the systems of equations by finding the inverse of the coefficient matrix. a. 2x+2y=1 2x-3y-0

Answer:

x = 30

Step-by-step explanation:

We know

The three angles must add up to 180°. We know one is 20°, so the other two must add up to 160°.

2x + 3x + 10 = 160

5x + 10 = 160

5x = 150

x = 30

In one of his experiments conducted with animals, Thorndike found that cats learned to escape from a puzzle box is increased gradually

To quantify the learning process, Thorndike used a mathematical formula known as the Law of Effect equation. The equation is:

B = f(log S1/S2)

where B represents the strength of the behavior, S1 represents the satisfaction of the positive consequence, and S2 represents the degree of frustration or negative consequence.

In the context of Thorndike's puzzle box experiment, the Law of Effect equation can be used to describe how the cat's behavior changed over time as it learned to escape the puzzle box more quickly and efficiently. Initially, the cat's behavior was weak because it did not know which actions would lead to a positive outcome.

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Using the power property to simplify the expression (9¹⁺⁴)⁷⁺², we have 9^7/8

Given the expression

(9¹⁺⁴)⁷⁺²

To simplify this expression using the power of a power property, we need to multiply the exponents:

(9¹⁺⁴)⁷⁺² = 9(¹⁺⁴ ˣ ⁷⁺²)

Simplifying the exponents in the parentheses:

(9¹⁺⁴)⁷⁺² = 9⁷⁺⁸ or 9^7/8

Therefore, (9¹⁺⁴)⁷⁺² simplifies to 9^(7/8).

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The equation that represents the value of the collection after 5 years is:

Value of collection after 5 years = 190 x (1 + 0.06)^5

Explanation:

To calculate the value of the collection after 5 years, we need to use the compound interest formula. This formula is represented as A = P x (1 + r)^n, where P is the principal amount (initial value of the collection), r is the rate of interest (in this case, 6%), and n is the number of years (in this case, 5).

Therefore, the equation for the value of the collection after 5 years is:

Value of collection after 5 years = 190 x (1 + 0.06)^5

This can also be written as:

Value of collection after 5 years = 190 x 1.31 (1.31 is the result of (1 + 0.06)^5)

Therefore, the value of the collection after 5 years is $246.90.

Answer: 254.26

Step-by-step explanation:

Answer:

To subtract 1/9 - 1/14, we need to find a common denominator. The smallest number that both 9 and 14 divide into is 126.

So, we will convert both fractions to have a denominator of 126:

1/9 = 14/126

1/14 = 9/126

Now we can subtract them:

1/9 - 1/14 = 14/126 - 9/126

Simplifying the right-hand side by subtracting the numerators, we get:

5/126

Therefore, 1/9 - 1/14 = 5/126 as an improper fraction.

Answer:

1/9-1/14

=14-9/9*14

=5/126

= 25 1/5

If "f" is differentiable and f(1) < f(2), then there is a number "c", in the interval  (1, 2)  such that f'(c)>  0.

Applying the  Mean Value Theorem for derivatives, if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one number c in the interval (a, b) such that:

f'(c) = (f(b) - f(a)) / (b - a)

In the scenario above, we have that f is differentiable, and that f(1) < f(2).

choosing a = 1 and b = 2.

Then applying the Mean Value Theorem, there exists at least one number c in the interval (1, 2) such that:

f'(c) = (f(2) - f(1)) / (2 - 1)

f'(c) = f(2) - f(1)

We have that f(1) < f(2), we have:

f(2) - f(1) > 0

We can conclude by saying that there exists a number c in the interval (1, 2) such that:

f'(c) = f(2) - f(1) > 0

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a) Velocity vector v(t) = i - 2tj, Speed s(t) = sqrt(1 + 4t²), Acceleration vector a(t) = -2j. b) Velocity vector v(1) = i - 2j, Acceleration vector a(1) = -2j

This problem is about finding the velocity, speed, and acceleration vectors of an object moving in the xy-plane, described by a position vector r(t). We can find the velocity vector by taking the derivative of the position vector, and the speed by taking the magnitude of the velocity vector. The acceleration vector can be found by taking the derivative of the velocity vector. We can then evaluate the velocity and acceleration vectors at a given point by plugging in the coordinates of the point. This problem requires basic vector calculus and understanding of the relationship between position, velocity, speed, and acceleration vectors.

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Complete question is attached below

Answer: 2/13

Step-by-step explanation:

There are four jacks and four tens in a standard deck of 52 cards. However, the jack of spades and the ten of spades are counted twice since they are both a jack and a ten. Therefore, there are 8 cards that are either a jack or a ten, and the probability of drawing one of these cards at random is:

P(Jack or Ten) = 8/52 = 2/13

So the answer is 2/13.

Step-by-step explanation:

a probability is airways the ratio

desired cases / totally possible cases

in each of the 4 suits there is one Jack and one 10.

that means in the whole deck of cards we have

4×2 = 8 desired cases.

the totally possible cases are the whole deck = 52.

so, the probability to draw a Jack or a Ten is

8/52 = 2/13

Answer:

x²  + 4x - 6

Step-by-step explanation:

x(x + (1 + x) + 2x) - 3(x² - x + 2) ← simplify parenthesis on left

= x(x + 1 + x + 2x)  - 3(x² - x + 2)

= x(4x + 1) - 3(x² - x + 2) ← distribute parenthesis

= 4x² + x - 3x² + 3x- 6 ← collect like terms

= x² + 4x - 6

Therefore, the length of segment AB is approximately 7.4 units.

Area is a mathematical concept that describes the size of a two-dimensional surface. It is a measure of the amount of space inside a closed shape, such as a rectangle, circle, or triangle, and is typically expressed in square units, such as square feet or square meters. The area of a shape is calculated by multiplying the length of one side or dimension by the length of another side or dimension. For example, the area of a rectangle can be found by multiplying its length by its width.

Here,

To find the radius of the circle, we can use the formula for the area of a sector:

Area of sector = (θ/360) x π x r²

where θ is the central angle of the sector in degrees, r is the radius of the circle, and π is approximately 3.14.

We're given that the area of sector COD is 50.24 square units and the central angle of the sector is 90°. So we can plug in these values and solve for r:

50.24 = (90/360) x 3.14 x r²

50.24 = 0.25 x 3.14 x r²

r² = 50.24 / (0.25 x 3.14)

r² = 201.28

r = √201.28

r ≈ 14.2

Therefore, the radius of the circle is approximately 14.2 units.

Next, we need to find the length of segment AB. Since AB is a chord of the circle, we can use the formula:

AB = 2 x r x sin(θ/2)

where θ is the central angle of the sector in degrees, r is the radius of the circle, and sin() is the sine function.

We're given that the central angle of sector COD is 30°. So we can plug in this value and the radius we found earlier to solve for AB:

AB = 2 x 14.2 x sin(30/2)

AB = 2 x 14.2 x sin(15)

AB ≈ 7.4

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Answer:

In mathematics, an inequality is a statement that compares two values, indicating that they are not equal, and specifies the relationship between them. In other words, an inequality expresses a relative difference between two values or quantities, rather than an exact equality.

There are different types of inequalities, but the most common ones involve comparisons between numerical values or algebraic expressions using inequality symbols, such as:

Greater than: x > y (read as "x is greater than y")

Less than: x < y (read as "x is less than y")

Greater than or equal to: x ≥ y (read as "x is greater than or equal to y")

Less than or equal to: x ≤ y (read as "x is less than or equal to y")

Inequalities can also involve multiple variables and can be used to describe ranges of values or conditions that must be satisfied. For example, x + y > 5 is an inequality that describes a region of the xy-plane where the sum of x and y is greater than 5.

Inequalities are used extensively in many areas of mathematics, including algebra, calculus, and optimization, and also have applications in other fields such as economics, physics, and engineering.

Step-by-step explanation:

There are 92 elements in A but not in B.

In mathematics, a set is a well-defined collection of objects or elements. Sets are denoted by uppercase symbols, and the number of elements in a finite set is denoted as the cardinality of the set enclosed in curly braces {…}.

Empty or zero quantity:

Items not included. example:

A = {} is a null set.

Finite sets:

The number is limited. example:

A = {1,2,3,4}

Infinite set:

There are myriad elements. example:

A = {x:

x is the set of all integers}

Same sentence:

Two sets with the same members. example:

A = {1,2,5} and B = {2,5,1}:

Set A = Set B

Subset:

A set 'A' is said to be a subset of B if every element of A is also an element of B. example:

If A={1,2} and B={1,2,3,4} then A ⊆ B

Universal set:

A set that consists of all the elements of other sets that exist in the Venn diagram. example:

A={1,2}, B={2,3}, where the universal set is U = {1,2,3} 

n(A ∪ B) = n(A – B) + n(A ∩ B) + n(B – A)

Hence, There are 92 elements in A but not in B.

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The ROC of a given signal's Z-transform can be determined without actually computing the Z-transform by identifying the maximum and minimum magnitude of the signal and checking for any poles of the Z-transform within the resulting annular region.

Let's take a signal as an example, suppose x[n] = {1, -2, 3, -4, 5}. In order to determine the ROC of its Z-transform, we are firstly required to first look for any regions in the complex plane where the sum of the absolute values of the Z-transform is found finite. It can be done by looking for the maximum and minimum magnitude of x[n] and denote them as R1 and R2 respectively. Then, the ROC of the Z-transform will be the annular region between R1 and R2, excluding any poles of the Z-transform that lie within this annular region.

In this case, the maximum absolute value of x[n] is 5 and the minimum is found being 1. So, the ROC of the Z-transform will be the annular region between |z| = 1 and |z| = 5. We can denote this as 1 < |z| < 5. We also need to check if there are any poles of the Z-transform within this annular region. Since we haven't actually computed the Z-transform, we cannot determine the exact location of any poles.

However, we can check for any values of z that would make the Z-transform infinite. For example, if x[n] is a causal signal (i.e., x[n] = 0 for n < 0), then the ROC cannot include any values of z for which |z| < 1, since this would make the Z-transform infinite.

So, the ROC of the Z-transform for the given signal x[n] can be written as 1 < |z| < 5, assuming that x[n] is a causal signal.

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The complete question is :

Can you explain how to determine the ROCs (regions of convergence) for the Z-transform of a given signal without actually computing the Z-transform? Please provide an example signal with random data and demonstrate how to find its ROCs using this method.

The required probability that a household in Maryland with annual income of ,

$90,000 or more is equal to 0.3377.

$50,000 or less is equal to 0.2218.

Annual household income in Maryland follows a normal distribution ,

Median =  $75,847

Standard deviation = $33,800

Probability of household in Maryland has an annual income of $90,000 or more.

Let X be the random variable representing the annual household income in Maryland.

Then,

find P(X ≥ $90,000).

Standardize the variable X using the formula,

Z = (X - μ) / σ

where μ is the mean (or median, in this case)

And σ is the standard deviation.

Substituting the given values, we get,

Z = (90,000 - 75,847) / 33,800

⇒ Z = 0.4187

Using a standard normal distribution table

greater than 0.4187  as 0.3377.

P(X ≥ $90,000)

= P(Z ≥ 0.4187)

= 0.3377

Probability that a household in Maryland has an annual income of $90,000 or more is 0.3377(rounded to four decimal places).

Probability that a household in Maryland has an annual income of $50,000 or less.

P(X ≤ $50,000).

Standardizing X, we get,

Z = (50,000 - 75,847) / 33,800

⇒ Z = -0.7674

Using a standard normal distribution table

Probability that a standard normal variable is less than -0.7674 as 0.2218. This implies,

P(X ≤ $50,000)

= P(Z ≤ -0.7674)

= 0.2218

Probability that a household in Maryland has an annual income of $50,000 or less is 0.2218.

Therefore, the probability with annual income of $90,000 or more and  $50,000 or less is equal to 0.3377 and 0.2218 respectively.

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