Use the counting principle to determine the number of elements in the sample space. The possible ways to complete a true-false examination consisting of 26 questions.

The expanded form of log(39/68) is log(39) - log(68).

To expand the logarithm log(39/68) completely, we can use the logarithmic properties.

The logarithm of a quotient can be expressed as the difference of logarithms:

log(39/68) = log(39) - log(68)

Therefore, the expanded form of log(39/68) is log(39) - log(68).

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Answer:

D. 60.3

Step-by-step explanation:

Finding the mean,

M = (sum of values of data)/(number of data)

now, number of data = 9,

calculating the mean,

M = (54 + 68 + 68 + 54 + 59 + 58 + 68 + 57 + 57)/9

M = 543/9

M = 60.333

M = 60.3

A view which Felix can use to construct the same figure include the following: A. a bottom row of 6 cubes, second row of 3 cubes, and top row of 1 cube.

In Mathematics and Geometry, an isometric sketch is sometimes referred to as an isometric drawing and it can be defined as a graphical (pictorial) representation of a physical object or geometric shape in technical and engineering drawings, especially by drawing all its three dimensions (3D) at full scale;

In this context, we can reasonably infer and logically deduce that the front view is a view which Felix can use to construct the same three-dimensional figure because its orientation influences the other views.

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The required angles are,

∠BAC = 73 degree

∠BCA = 17 degree

∠DCF = 17 degree

∠CDF = 80 degree

∠CFD = 95 degree

Since we can see that,

In triangle ABC

The angle B is right angled

Since we know that,

Sum of interior angles of triangle = 180 degree

Therefore, in triangle ABC

⇒ (9x -8 ) + (2x-1) + 90 = 180

⇒ 11x  = 99

⇒    x  = 9

Thus,

Angle BAC =  9x - 8

                   = 9x9 - 8

                   = 73 degree

Angle BCA = 2x - 1

                   = 2x9 - 1

                    =  17 degree

Now in triangle, CDF,

Angle C is alternate angle for both the triangles,

Therefore,

Interior angle C of triangle CDF = angle DCF = 17 degree

Angle CDF = 9y  - 1

                   = 9x9 - 1

                   = 80 degree

Angle CFD = 11y + 4

                   = 11x9 - 4

                   = 95 degree

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Answer:

FH = 35.64

Step-by-step explanation:

(∠A = 360 so the other angle is 40)

By law of cosines,

FH² = AH² + FA² - 2(AH)(FA) * cos(A)

= 30² + 25² - 2(30)(25) * cos(80)

= 900 + 625 - 1500 * 0.17

= 1525 - 255

FH²  = 1270

FH = √1270

FH = 35.64

Answer:  5

Step-by-step explanation:

Answer:

2(1/2)

Step-by-step explanation:

1(2/3) = 5/3

5/3 divided into 2/3

is the same as

5/3 multiplied by 3/2

        5/3 x 3/2 = 15/6  

15/6 = 5/2

5/2 = 2(1/2)

Q) [35 - (8 + 2) × 3] = ?

→ 35 - {(8 + 2) × 3}

→ 35 - {10 × 3}

→ 35 - 30

→ 5 is the correct answer.

Answer:

y = 2x  + 2

Step-by-step explanation:

slope (m) = 2  ; (3 , 8)

Equation: y - y1 = m (x - x1)

                y - 8 = 2(x - 3)

                y - 8 = 2x - 2*3

                y - 8 = 2x - 6

                      y = 2x - 6 + 8

                      y = 2x  + 2

The total cost for the electric bill is given by the equation A = $ 241

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total cost for the electric bill be A

Now , the equation will be

The amount of electricity used by Ettienne = 1,895 kWh

And , the standard plan is

8.5 cents/kWh for the first 400 kWh

12 cents/kWh for the next 400 kWh

14.5 cents/kWh for anything over 800 kWh

So , for the first 400 kWh , the cost is = 400 x 8.5 = 3,400 cents

And , for the next 400kWh , the cost is = 400 x 12 = 4,800 cents

And , the remaining units of electricity is = 1,895 - 800 = 1,095 kWh

So , for the next 1,095kWh, the cost is = 1,095 x 14.5 = 15,877.5 cents

Therefore , the total cost for 1,895kWh = 3,400 cents + 4,800 cents + 15,877.5 cents

On simplifying the equation , we get

The total cost for 1,895kWh A = 24,077.5 cents

The total cost for 1,895kWh A = $ 240.77

The total cost for 1,895kWh A = $ 241

Hence , the equation is A = $ 241

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Answer: it should be +6

Step-by-step explanation:

Answer: 4000

Step-by-step explanation:

The biconditional statement for the given conditional statement would be:

2x = 18 if and only if x = 9.

The given conditional statement "If 2x = 18, then x = 9" can be represented symbolically as p → q, where p represents the statement "2x = 18" and q represents the statement "x = 9".

To form the biconditional statement, we need to determine if the converse of the conditional statement is also true. The converse of the original statement is "If x = 9, then 2x = 18". Let's evaluate the converse statement.

If x = 9, then substituting this value into the equation 2x = 18 gives us 2(9) = 18, which is indeed true. Therefore, the converse of the original statement is true.

Based on this, we can write the biconditional statement:

2x = 18 if and only if x = 9.

The biconditional statement implies that if 2x is equal to 18, then x must be equal to 9, and conversely, if x is equal to 9, then 2x is equal to 18. The biconditional statement asserts the equivalence between the two statements, indicating that they always hold true together.

In summary, the biconditional statement is a concise way of expressing that 2x = 18 if and only if x = 9, capturing the mutual implication between the two statements.

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Diego is making the mistake of not following the correct steps while solving a quadratic equation, which has led him to divide each side of the equation by 2 instead of square root(100). This mistake has occurred because he is trying to find a value instead of the actual answer to the problem.A)

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Answer:

Step-by-step explanation:

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Answer:

-6

Step-by-step explanation:

We can use the slope formula

m = ( y2-y1)/(x2-x1)

   = ( 8-2)/(3-4)

    = 6/-1

    = -6

Answer:

\( - 6\)

Step-by-step explanation:

\(slope \: = \frac{y1 - y2}{x1 - x2} \\ = \frac{2 - 8}{4 - 3} \\ = \frac{ - 6}{1} \\ = - 6\)

Answer:

Step-by-step explanation:

To write y as a function of x using the given functions, we can substitute the value of "a" in the first equation with the expression "-5x + 1" from the second equation.

Given:

y = -3a + 3

a = -5x + 1

Substituting the value of "a" in the first equation:

y = -3(-5x + 1) + 3

Now, let's simplify this expression:

y = 15x - 3 + 3

y = 15x

Therefore, y can be expressed as a function of x as:

y = 15x

The percentage population increase from 2001 to 2011 is 50%.

To calculate the percentage population increase from 2001 to 2011, you need the population figures for both years. Let's assume the population in 2001 was 100,000 and in 2011 it was 150,000.

The formula to calculate the percentage increase is:

Percentage Increase = ((New Value - Old Value) / Old Value) * 100

Plugging in the values:

Percentage Increase = ((150,000 - 100,000) / 100,000) * 100 = (50,000 / 100,000) * 100 = 0.5 * 100 = 50%

Therefore, the percentage population increase from 2001 to 2011 is 50%.

Please note that the actual population figures for the respective years need to be used in the calculation to obtain an accurate result. The example above is for illustrative purposes.

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His tuition was increased by 10.34%

A quantity or ratio stated as a fraction of 100 is known as a % in mathematics (from the Latin per centum, "by a hundred").

The Latin word per centum, which means "hundred" or "by the hundred," is the source of the word "percent." The Italian phrase per cento, which means "for a hundred," gradually shrank to become the symbol for "percent," which is now used globally. It finally vanished totally. The word "per" was frequently shortened to "p." Two circles and a horizontal line made up the "cento," which is how the contemporary "%" symbol is now represented.

Given, Larry's tuition for last semester was $5510

% increase= (6080-5510)/5510

=0.10344

=0.10344*100

=10.34%

His tuition was increased by 10.34%

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The degree for 7pi/4 is : 315°

The coordinates of the vertices after a dilation of the scale factor would be:

To perform a dilation with a scale factor of 1/2 centered at the origin, we multiply the coordinates of each vertex by the scale factor.

Given the vertices:

W = (5, 10)

V = (0, -10)

U = (5, -10)

After applying the dilation with a scale factor of 1/2, the new coordinates of the vertices would be:

W' = (5 * 1/2, 10 x 1/2) = (2.5, 5)

V' = (0 * 1/2, -10 x 1/2) = (0, -5)

U' = (5 * 1/2, -10 x 1/2) = (2.5, -5)

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The simplified form of the given algebraic expression is 3x²√5x. The correct option is с. 3x²√5x

From the question, we are to simplify the given algebraic expression.

The given expression is

√45x^5

First, we will write the given expression properly

The expression written properly is

√45x⁵

Simplifying

√45 × √x⁵

√9×5 × √x⁴×x

√9 × √5 × √x⁴ × √x

3 × √5 × x² × √x

3 × x² × √5 × √x

3x² × √5×x

3x² × √5x

3x²√5x

Hence, the simplified expression is 3x²√5x

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Based on Pythagorean's theorem, the lengths of the sides of △OPR are:

x = 35 units.

y = 55 units.

z = 30 units.

In Mathematics and Geometry, a perpendicular bisector is a line that bisects or divides a line segment exactly into two (2) equal halves and forms an angle that has a magnitude of 90 degrees at the point of intersection.

Since line segment OS bisects line segment PQ, we have the following:

x = QR = 35 units.

y = z + 25

By applying Pythagorean's theorem, we have the following:

x² + z² = y²

(z + 25)² = 35² + z²

z² + 50z + 625 = 1,225 + z²

50z = 1,225 - 625

50z = 600

z = 600/50

z = 30 units.

y = z + 25

y = 30 + 25

y = 55 units.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Complete Question:

O is the centre of the circle. x, y, and z indicate the lengths of the sides of △OPR. Find with reasons the values of the following:

1.1.1   x

1.1.2  z

1.1.3  y

Answer:

2

Step-by-step explanation:3

Answer:

remainder = 8

answer is: 2a^(2) + 2a + 5 remainder 8

Step-by-step explanation:

Answer:

75 square units

Step-by-step explanation:

(x+10)x=3x^2

x^2+10x=3x^2

10x=2x^2

5x=x^2

x=5

Plugging in 5 into either of the initial equations yields the answer.

The fraction of the class that is sophomores is \(35/43\).

The fraction of the class that is sophomores, divide the number of sophomores by the total number of students in the class.

Number of sophomores = 35

Total number of students = 43

Fraction of sophomores = (Number of sophomores)/(Total number of students Fraction of sophomores)

Fraction of sophomores  \(= 35 / 43\)

Therefore, the fraction of the class that are sophomores is = \(35/43\).

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Answer:

1/30

Step-by-step explanation:

When you multiply fractions, you just muliply across,

1*3= 3

9*10= 90

you now have 3/90 but you have to simplify, we know 3 goes into 3 and it also goes into 90 equally

3/3= 1

90/3= 30

So your answer is 1/30!!

I hope this helps!!!!!!!!!!!

The surface area of the rectangular prism in this problem is given as follows:

A. 426 m².

The surface area of a rectangular prism of height h, width w and length l is given by:

S = 2(hw + lw + lh).

This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas. -> net method.

The dimensions for this problem are given as follows:

5 m, 12 m and 9 m.

Hence the surface area of the prism is given as follows:

S = 2(5 x 12 + 5 x 9 + 12 x 9)

S = 426 m².

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