Use the Laws of Logarithms to combine the expression. log4(8) + 2 log4(5)

On solving the provided question, we can say that - there are 67 numbers less than 100 are divisible by 3, by divisibility test.

The divisibility rule is a concise and practical approach to check, often by looking at the integer's digits, whether a given integer is divisible by a given set divisor without actually executing division. Without actually doing the division procedure, you may quickly discover if a given number can be divided by a defined divisor using the divisibility test. When dividing two numbers exactly, the quotient must be an integer and the remainder must be zero.

= n(A ∪ B)

= n(A) + n(B) - n(A ∩ B)

= 33 + 50 - 16

= 67

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On solving the provided question, we can say that by trigonometry, t = [tex]4\pi /3[/tex]; x = cos([tex]4\pi /3)[/tex] = [tex]-\sqrt{2}/4[/tex] and y = sin([tex]4\pi /3)[/tex] = [tex]-3\sqrt{2}/11[/tex]

The area of mathematics known as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, around the third century BC. from the use of geometry in astronomical study. The area of mathematics known as exact methods deals with specific trigonometric functions and how they might be used in calculations. There are six popular trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics of triangles, particularly right triangles, is called trigonometry. The study of geometry, however, is the characteristics of all geometric figures.

here,

by trigonometry,

t = [tex]4\pi /3[/tex]

x = cos([tex]4\pi /3)[/tex] = [tex]-\sqrt{2}/4[/tex]

y = sin([tex]4\pi /3)[/tex] = [tex]-3\sqrt{2}/11[/tex]

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The area of an 8 cm by 5 cm triangle is 20 cm^2.

The area of a triangle is calculated using the formula A = 1/2 * b * h, where b is the length of the base and h is the height. In this case, the base is 8 cm and the height is 5 cm, so the area of the triangle can be calculated as follows:

A = 1/2 * 8 * 5

A = 20 cm^2

Therefore, the area of an 8 cm by 5 cm triangle is 20 cm^2.

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Answer:$30

Step-by-step explanation:

$75 jacket is 60% off

Step 1: Plug in numbers

Use is/of=%/100 method

is/75=60/100=45

Step 2: Find the Price of Discounted Jacket

75-45=$30

Answer:

-----------------------------------

Initial cost is $75 and the discount is 60%.

Subtract 60% to find the discounted amount:

Answer: x = 3; y = -2

Step-by-step explanation:

Simultaneous Equations:
3^(2x) x 3^(3y) = 3^0
2x + 3y = 0

2^(2x) x 2^(-0.5y) = 2^7
2x - 0.5y = 7

2x = -3y

-3y - 0.5 y = 7

y = -2

x = 3

Answer:

x=3 y=-2

Step-by-step explanation:

its at the bottom of the page ‍♂️‍♂️

Answer:

see drawing

Step-by-step explanation:

Answer:

Step-by-step explanation:

The layaway fee for this purchase should be considered as the $60 when the purchase should be done.

Marty is making a layaway purchase of a $1,500 couch at Frank’s Furniture Store. He will be paying $156 every 2 weeks for 20 weeks

So, it can be like

= $1,560 - $1500

= $60

The layaway fee for this purchase should be considered as the $60 when the purchase should be done.

Answer:

Step-by-step explanation:

Slope intercept for y=mx+b

point it passes (-14, 6) wherein b (0, b) is b=6

slope m = -5/8  

substitute: y = mx+b

                 y= (-5/8)x+6

Answer:

this is it

Step-by-step explanation:

The points on the coordinate plane which represent the ratio values given in the table are given attached, where Distance is on the Y-Axis and Time is on the X-Axis.

Ratio data is a type of numerical (quantitative) data. It computes the distance between neighboring numbers on a continuous scale.

While it shares these characteristics with interval data (another form of quantitative data), ratio data is distinguished by the presence of a 'real zero.' In other words, a ratio scale measure of zero is absolute: ratio data can never be negative.

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The secant segment theorem states that If two secant segments intersect outside a circle, then the product of the secant segment with its external portion equals the product of the other secant segment with its external portion.

A secant is a line on the circle that connects exactly two distinct points on the curve. Secant is not a chord but a chord is part of a secant. Two different secants can intersect each other internally or externally.

Further, the secant segment theorem defines two more theorems or properties and they are:-

Arcs are line segment that is part of the circumference of a circle. It is like a smooth curve that joins two points. If an arc is of exactly the half-length of circumference then it is called a semicircular arc.

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The equivalent to 3/4 equal 6/ is 8

Equivalent fractions are the fractions that have different numerators and denominators but are equal to the same value. For example, 2/4 and 3/6 are equivalent

from the question,

3/4 equal 6/?

Let x represent the unknown value

= 3/4=6/x

We can simplify this by cross multiplying

3x=24

Divide both sides of the equation by 3

3x/3 = 24/3

x=8

Hence the equivalent to  3/4 equal 6/? is 8

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There are many different types of inequality, but generally, they can be grouped into two main categories economic inequality and social inequality.

Economic inequality: This refers to the unequal distribution of wealth, income, and resources among individuals or groups within a society. Economic inequality can manifest in various forms, such as income inequality, wealth inequality, and poverty.

Social inequality: This refers to the unequal distribution of social status, power, and privilege among individuals or groups within a society. Social inequality can manifest in various forms, such as discrimination, prejudice, and bias, which can limit opportunities and access to resources for certain groups.

It's important to note that these two types of inequality are often interconnected and can have a significant impact on individuals and groups, leading to reduced opportunities, access to resources, and lower quality of life.

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Answer:

1 /5

Step-by-step explanation:

formulae -

possible outcomes / total chances

2/10

1/5

The image point of P(x,y) = ( 6 , 5 ) after applying a horizontal reflection is P'(x,y) = (1, 5).

In geometry, a rigid transformation is a transformation applied onto a geometric object such that Euclidean distance in every point of it is conserved. Translations are examples of rigid transformations and are defined by this formula:

P'(x,y) = P(x,y) + T(x,y)                    (1)

Where:

P(x,y) - Original point

T(x,y) - Translation vector

P'(x,y) - Image point

If we know that P(x,y) = (6, 5) and T(x,y) = (5, 0), then the image point is:

P'(x,y) = (6, 5) + (5, 0)

P'(x,y) = (1, -6)

The image point of P(x,y) = (6, 5) after applying a horizontal reflection is P'(x,y) = (1, 5).

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Correct form of the question

What is the image point of (x, y) = (6, 5) after the transformation of translating horizontally the point 5 units to the y-axis?

The expression that the quotient of the number 9 and the letter 'c' will be 9 / c.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The quotient of the number 9 and the letter 'c' is written as,

⇒ 9 / c

The expression that the quotient of the number 9 and the letter 'c' will be 9 / c.

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The gymnast trains 5 hours per day making a total of 120 hours in a 4 week period

An equation is a expression that shows the relationship between numbers and variables.

Let x represent the number of hours practiced per day. A gymnast practices 6 days each week, hence:

Number of hours practiced per week = 6x

If she practices a total of 120 hours in a 4- week period. Therefore:

6x hours per week * 4 weeks = 120 hour

24x = 120

x = 5

The gymnast trains 5 hours per day.

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After responding to the question, we can therefore say that the numbers in the four-way tables are 4,8,12,16,20,24,28,32,36, and 40.

A mathematical table is a collection of numbers that shows the outcome of a calculation using multiple inputs. data with numbers and descriptions that is arranged in rows and columns. The table and 10 pattern are easy to remember. The following is the order of the numbers:2,4,6,8,10,12,14,16,18,20. Value maps are used to show how different data pieces are related to one another. You can incorporate the values table into your science lecture. Scientists and researchers use tables of values to store data and seek for patterns in that data. Then, this pattern is used in forecasting.

Here,

Thus,

table of four are as follows:

4,8,12,16,20,24,28,32,36 and 40.

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Answer: 4.17

Step-by-step explanation:

.

So, on solving the provided question we can say that in this quadrilateral we know that sum of all angles is 360, so other will be 90 each too.

A quadrilateral is a four-sided polygon in geometry that has four edges and four corners. The word is a derivative of the Latin words quadri and latus (meaning "side"). Having four sides, four vertices, and four corners, a rectangle is a two-dimensional form. Concave and convex come in primarily two varieties. Additionally, there are several subclasses of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up a rectangle, which is a two-dimensional form. There are several different types of quadrilaterals, including parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.

here in this quadrilateral

we know that sum of all angles is 360

two of the are 90 each

so other will be 90 each too.

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Answer:

6

Step-by-step explanation:

36/6

equals 6

Answer:

6 days.

Step-by-step explanation:

36 total pages

6 page a day

Then:

36/6 = 6

To determine if three points are in a straight line in 3D, you can calculate the vector between the first two points and then check if the third point is in the same direction as the vector.

Straight line is a line that extends infinitely in two opposite directions and has no curves or bends. It is the shortest distance between two points and is the basic form of geometry. A straight line is composed of two end points and all the points in between that make up the line. Straight lines are used to create shapes and constructions in mathematics, science and engineering.

If the dot product of the vector and the point is 0, then the three points are in a straight line. Alternatively, you can calculate the area of the triangle formed by the three points and if it is 0, then the points are in a straight line. Another option is to calculate the determinant of the matrix formed by the three points and if it is 0, then the points are in a straight line. Finally, you can calculate the angle between the two vectors formed by the three points and if it is 0, then the points are in a straight line.

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Answer:

B) 2 5/8 - 1 4/8

Step-by-step explanation:

I'm bad at explaining but I hope this helps!! ₍^ >ヮ<^₎

Answer:

Step-by-step explanation:do 1/8 *2/5*=

Answer:

180 m , ≈ 6.9 seconds

Step-by-step explanation:

let vertical distance be represented by d and time t

given d is directly proportional to t² , then the equation relating them is

d = kt² ← k is the constant of proportion

to find k use the condition , the ball falls 80 m in 4 seconds , then

80 = k × 4² = 16k  ( divide both sides by 16 )

5 = k

d = 5t² ← equation of proportion

(a)

when t = 6

d = 5 × 6² = 5 × 36 = 180 m

(b)

when d = 240

240 = 5t² ( divide both sides by 5 )

48 = t² ( take square root of both sides )

[tex]\sqrt{48}[/tex] = t , that is

t ≈ 6.9 seconds ( to the nearest tenth )

According to the table for a $150,000 mortgage, Lastri's credit score needs to improve by 62 points for her to take a mortgage for $150,000.

The credit score refers to an individual's or entity's creditworthiness rating.

The credit score predicts a person's credit behavior and ability to repay credit.

Financial institutions and lenders use the credit score to determine the amount of credit to offer a borrower, the attached credit risks, and the accompanying interest rate, including monthly payments.

Annual mortgage payments Lastri can afford = $13,900

Monthly payment = $1,158 ($13,900 ÷ 12)

Current credit score = 498

Minimum credit score for a monthly payment of $1,158 = 560

Additional credit score improvement = 62 (560 -498)

Thus, for Lastri to qualify for a $150,000 mortgage, her FICO credit score must improve by 62 points.

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Table

FICO              Interest    Monthly

Score               Rate      Payment

720 - 850       5.59%       $860

700 - 719        5.71%        $872

675 - 699       6.25%      $924

620 - 674       7.40%    $1,039

560 - 619       8.53%     $1,157

500 - 559      9.29%    $1,238

The reasonable estimate of the probability that it is sunny tomorrow is 25%.

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

The value of probability will be always in the range from 0 to 1.

Probability of an event is calculated by dividing the number of desirable outcomes by the total number of events possible.

From the graph, we have,

Number of days weather is sunny = 3

Total number of days = Days weather is sunny + Days weather is cloudy + Days weather is rainy + Days weather is snowy

Total number of days = 3 + 5 + 2 + 2 = 12

Probability that weather is sunny = 3 / 12 = 1/4 = 0.25 = 25%

Hence there is a 25% probability that weather is sunny.

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The complete question is as follows :

The following bar graph summarizes the weather conditions in Crayonton for each day this month so far. Based on this data, what is a reasonable estimate of the probability that it is sunny tomorrow? Choose the best answer.

The following are the 5 steps in solving a rational inequality: simplifying the inequality, factoring the numerator and denominator of the inequality, set the numerator and denominator equal to zero.

Solving a rational inequality involves isolating the variable and determining the range of values that make the inequality true.

Simplify the inequality by clearing any fractions: This can be done by multiplying both sides of the inequality by the least common multiple (LCM) of the denominators of the fractions.

Factor the numerator and denominator of the inequality: This can be done to cancel out any common factors between the numerator and denominator.

Set the numerator and denominator equal to zero and solve for the zeros: This can be done to find the values of the variable that make the numerator and denominator equal to zero.

Test the zeros and any critical values: This can be done by substituting the zeros and critical values back into the inequality and determining if they make the inequality true or false.

Plot the solution on the number line: This can be done by plotting the zeros and critical values on a number line and shading the region that makes the inequality true.

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These ratios are different because they express the number of laps for two different numbers of hours.

To better understand how these ratios compare, let's simplify the second ratio:

192 laps/ 8 hours = 24, which means the ratio would be 24 laps per hour

This means that the ratios express the same number of laps per hour.

Basically, the two ratios tell us the number of laps but using different hours. In this way, the first ratio expresses the number of laps in only one hour, while the second ratio amplifies this ratio to eight hours.

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Answer: x = 2, y = -3

Step-by-step explanation: From the question,

-3x -3y = 3 ---------- this becomes the first equation

Make y the subject

-3y = 3 + 3x

y = (3 + 3x)/ -3  ----------this becomes our second equation

Substitute the value of y into the first equation

-3x -3(3 + 3x) = 3

-3x -9 + 9x = 3

Collect like terms

-3x + 9x = 3 + 9

6x = 12

Divide both sides by 6

6x/ 6 = 12/ 6

x = 2

Substitute x = 2 into the second equation to find y

y = (3 + 3(2) )/ -3

y = ( 3 + 6) / -3

y = 9/ -3

y = -3