For 1-4, write "yes" or "no" to describe whether or not the line is a good trend line. Explain.

The length of f = 66 centimeters

It is a law that express a relationship between side length of triangle and their opposite angles.

If ABC is triangle, then sine rule can be expressed as

BC/ sin A = AB /sin C = AC /sin B

Given, a triangle fgh where angle ∠ f = 131° and ∠g = 47°

also, side length, g = 64 cm

the remaining angle ∠ h = 180° - (131°+47°)

∠h = 2°

this is because angle sum of three angle for a triangle is 180 degrees.

what is the length of f?

we know that Δf g h has three side f g, g h and f h.

we denote the side f g = h, side g h = f and side f h = g

according to the sine rule for a triangle

h/ sin h = f /sin f = g /sin g

f/ sin f = g/ sin g

f / sin 131° = 64 / sin 47°

f = (64 × sin 131°) / sin 47°

f = 66 cm

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2a³b⁻⁴/3a⁵b⁻² =  2/3(ab)²

The exponent of a number shows how many times the number is multiplied by itself.

Example: 2×2×2×2 can be written as 24, as 2 is multiplied by itself 4 times. Here, 2 is called the "base" and 4 is called the "exponent" or "power."

In general, xⁿ means that x is multiplied by itself for n times.

Properties of exponents:

Law of Product: a ^m × a ^n = a ^(m + n)

Law of Quotient: a ^m/a ^n = a ^(m - n)

Law of Negative Exponent: a^-m = 1/a ^m

Law of Power of a Product: (ab)^m = a ^m . b ^m

Law of Power of a Quotient: (a/b) ^m = a ^m/b ^m

Given expression

2a³b⁻⁴/3a⁵b⁻²

= 2/3 . a³/a⁵ . b⁻⁴/b⁻²

Law of Negative Exponent: [tex]a^{-m} = 1/a^{m}[/tex]

= 2/3 . a³/a⁵ . b²/b⁴

Law of Quotient: [tex]a^{m} /a^{n} = a^{m-n}[/tex]

= 2/3 . a³⁻⁵ . b²⁻⁴

= 2/3 . a⁻² .b⁻²

Law of Power of a Product: [tex]a^{m} .b^{m}= (ab)^{m}[/tex]

= 2/3 . (ab)⁻²

Law of Negative Exponent: [tex]a^{-m} = 1/a^{m}[/tex]

= 2/3 . 1/(ab)²

= 2/3(ab)²

Hence the simplified expression of 2a³b⁻⁴/3a⁵b⁻² is  2/3(ab)².

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A random selection of one of the families is made, and a computer is discovered there. P(computer AND TV) = 5/6.

We surveyed 400 households. 60% of people had computers, while 90% of them had TVs.

These were something that every family owned at least one of.

A random selection of one of the families is made, and a computer is discovered there.

Check to see if there is a TV there as well.

union: # with computer, # with TV, - # with both, # with both

400 = 360 + 240 - # with both # with both = 200 / 400 = 0.9 * 400 + 0.6 * 400

P(computer AND TV) = 200/400 = 1/2 ——-

P(TV | computer) + P(TV and computer) / P(computer) = 0.5/0.6 = 5/6

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Answer:

£15158.00

Step-by-step explanation:

The profit on the sale of 1 computer is the difference between the selling price and the buying price.

Profit on 1 computer:

£2081.00 - £915.00 = £1166.00

The profit on 13 computers is 13 times the profit on 1 computer.

13 × £1166.00 = £15158.00

Answer: £15158.00

(a) If an orchestra has a sound intensity of [tex]6.4 \times 10^-^3\ Wm^{-2[/tex], then

the intensity level of sound, L, is 98.062 dB.

(b) If a rock concert has an intensity level of 112 dB, then the sound intensity, S, is [tex]10^{-0.8}\ Wm^{-2[/tex].

Sound intensity, also known as acoustic intensity, is defined as the dominion ferried by sound waves per unit area in a direction perpendicular to that area.

Given that the intensity level of sound, L, measured in decibels (dB), is a function of the sound intensity, S, watts per square meter ([tex]Wm^{-2[/tex]) as

[tex]L = 10log_{10}(S\times10^1^2), S\geq 0[/tex]

(a) If an orchestra has a sound intensity of [tex]6.4 \times 10^-^3\ Wm^{-2[/tex], then

the intensity level of sound,

[tex]L = 10log_{10}(6.4\times10^{-3}\times10^1^2)[/tex]

   [tex]= 10log_{10}(6.4\times10^9)\\= 10(log_{10}6.4\ +\ log_{10}10^9 )\\= 10(0.8062\ +\ 9)\\=10 \times 9.8062\\= 98.062\ dB[/tex]

(b) If a rock concert has an intensity level of 112 dB, then

[tex]112 = 10log_{10}(S\times10^1^2)\\log_{10}(S\times10^1^2) = \frac{112}{10}\\log_{10}(S\times10^1^2)= 11.2\\S\times10^1^2 = 10^{11.2}\\S = \dfrac{10^{11.2}}{10^1^2} \\S = 10^{-0.8}\ Wm^{-2[/tex]

The sound intensity is [tex]10^{-0.8} Wm^{-2[/tex].

Hence, (a) L = 98.062 dB and (b) S [tex]= 10^{-0.8}\ Wm^{-2[/tex].

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The Boolean dual are created by replacing AND operator with OR operator and the complement is defined as the negation of the statement .

What is Boolean Expression ?

The Boolean Expression is defined as a logical statement that is either TRUE or FALSE . It compares data of any type as long as both the parts of  expression have same basic data type.

The Dual of Boolean Expression are calculated by simply replacing AND operator with OR and OR operator with AND .

The Compliment of Boolean Expression  is defined as negation of  variables with replacement .

For Example : if the statement is [tex]A+B[/tex] ,

then the dual will be [tex]AB[/tex] and the compliment will be [tex]A'B'[/tex] .

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The number of phones sold is 26 and the number of accessories sold is 30.

An equation is said to be linear if the maximum power of the variable is usually 1.  A linear equation with one variable has the standard form Ax + B = 0. In this case, x is the variable and A is the coefficient of x, and B is a constant.

In mathematical problems, 'x' stands for unknown value or quantity. Here we use the Linear equation concept to solve the problem.

Given that

Cameron earns an $11 commission for every phone he sells and a $2. 50 commission for every accessory he sells.

On a given day Cameron made a total of $361 in commission from selling a total of 56 phones and accessories sold. ​

Let x and y be the number of phones and accessories

Given that

Cameron made a total of $361 in commission

=> 11x + 2.5y = 361  ----- (1)

Total number of phones and accessories sold

=> x + y = 56

Multiply by 11

=> 11x + 11y = 616 ----- (2)

Do (2) - (1)

=> 11x + 11y - ( 11x + 2.5y) = 616 - 361

=> 11x + 11y - 11x - 2.5y = 255

=> 8.5y = 255

=> y = 255/8.5

=> y = 30  

Substitute y = 30 in x + y = 56  

=> x + 30 = 56

=> x = 26

Therefore,

The number of phones sold is 26 and the number of accessories sold is 30.

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Reducing the object's size by dilation is a change. The items are enlarged or shrunk through dilation.

Resizing an object is accomplished through a change called dilation. The objects can be enlarged or shrunk via dilation.

A diminution in the image occurs when the scale factor is between 0 and 1. An enlarged version of the image is shown if the scale factor is larger than 1.

An enlargement (imagine stretching) is a dilation that makes a larger image, whereas a reduction (think shrinking) is a dilation that creates a smaller image. A diminution in the image occurs when the scale factor is between 0 and 1. An enlarged version of the image is shown if the scale factor is larger than 1.

A transformation called a dilation (similarity transformation) alters the size of a figure. A center point and a scaling factor, k, are necessary. Which kind of dilation it is—an enlargement or a reduction—depends on the value of k. An enlargement results from a dilatation if |k|>1.

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Answer:

x = 8

Step-by-step explanation:

x + 4 = 12

Subtract 4 from both sides

x = 8

Let's check

8 + 4 = 12

12 = 12

So, x = 8 is correct!

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Therefore the rounded numbers are 23.54 and 0.9160.

An integer containing one or more "0"s at the end in a certain base is said to be round. In this way, 590 is more rounded than 592 but less rounded than 600. A round number is frequently understood to stand for a value or values close to the nominal value given in both formal and informal language.

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The set of integers is frequently represented in mathematical notation by the boldface Z or blackboard bold mathbb Z.

a. To round 23.54 to five decimal places, we look at the sixth decimal place, which is 4. Since 4 is less than 5, we leave the fifth decimal place as is, and the number rounded to five decimal places is 23.54.

b. To round 0.916 to five decimal places, we look at the sixth decimal place, which is 1. Since 1 is greater than or equal to 5, we increase the fifth decimal place by one, and the number rounded to five decimal places is 0.9160.

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As per the zeros of the function, the value of the function 3x + 1 is  x = -1/3.

Zeros of the function in math is defined as the values of the variable of the function such that the function equals 0.

Here we have given the function 3x + 1.

Now, we have to equate the function with zero, in order to solve it, then we get,

=> 3x + 1 = 0

Now, we have to subtract 1 on both sider to individualize the x value then we get the rewritten expression as,

=> 3x = -1

Now, we have to divide each side by 3, then we get the value of x as,

=> x = -1/3

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In the equation y = mx + c if we substitute the value of x as zero we will get a point on the y axis given by y =(m × 0) + c ⇒ y = c. Therefore the point of the line on the y axis is (0, c) and so c is also called the y -intercept  of the line.

Now, According to the question:

i) from the general equation of line we know that any line can be represented in the form y = mx + c , where m is a constant and is called the slope of the line and c is also a constant and is the y-intercept.

ii) In the equation y = mx + c if we substitute the value of x as zero we will get a point on the y axis given by y =(m × 0) + c ⇒ y = c. Therefore the point of the line on the y axis is (0, c) and so c is also called the y intercept  of the line.

iii) If for example we have the line 3y = 6x + 12 then we first get this equation of the line to match the general form of the equation of the line, that is y = mx + c. Therefore dividing both the left and the right sides of the given equation of the line by 3 we get y = 2x + 4 which matches with the general form of the equation for line and we see that the slope of the given line is m = 2 and the y intercept is given by c = 4.

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The function y = -2x + 9 have ordered pairs (-4, 17), (-2, 13), (0, 9), (2, 5) and (4, 1)

An equation shows how two or more numbers and variables are related to each other.

The standard linear equation is:

y = mx + b

Where m is the rate of change and b is the y intercept

Given that:

y = -2x + 9

When x = -2; y = -2(-2) + 9 = 13

When x = 0; y = -2(0) + 9 = 9

When x = 2; y = -2(2) + 9 = 5

When x = 4; y = -2(4) + 9 = 1

The function y = -2x + 9 is a linear equation

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The equation of the line will be y = -2/3x + 5.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given that the line passes through points (9, -1) and (6, 1).

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = ( 1 - (-1) / ( 6 - 9 )

Sloe = - 2 / 3

The y-intercept will be calculated as,

y = mx + c

-1 = (-2/3) x 9 + c

c = 5

The equation of the line,

y = mx + c

y = -2/3x + 5

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The required value of z is "i√6" to the given expression√(6/2 - 9) = z.

A complex number is a combination of real values and imaginary values. It is denoted by z = a + ib, where a, and b are real numbers and i is an imaginary number.

The expression is given in the question, as follows:

√(6/2 - 9) = z

We have to determine the value of z to the given expression.

As per the question, we have

⇒ √(6/2 - 9) = z

⇒ √(3 - 9) = z

⇒ √(- 6) = z

⇒ √(6 × -1 ) = z

⇒ (√6 × √-1 ) = z    [∵ imaginary number i = √-1 ]

⇒ (√6 × i ) = z

⇒ z = i√6

Therefore, the required value of z is "i√6" to the given expression.

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The amount of square inches of the cake that are covered with icing is 201.06, calculated by using the formula (π * radius2), with π equal to 3.14 and the radius equal to 8 inches.

1. Use the formula (π * radius2), with π equal to 3.14

2. The radius is half of the diameter, divide the diameter (16 inches) by 2

3. Radius = 16 inches / 2 = 8 inches

4. Calculate π * radius2: 3.14 * (8 inches)2 = 201.06 square inches

π * (8 inches)2

= 3.14 * (64 inches2)

= 201.06 square inches

Dominique is decorating a round cake with fruits and has frosted just the top of the cake. To determine the area of the cake that is covered with icing, we can use the formula (π * radius2). Since the cake is round, we can determine the radius of the cake by dividing the diameter of the cake (16 inches) by 2, resulting in the radius being 8 inches. We can then calculate the area of the cake covered with icing by multiplying π by the radius squared. Using the number 3.14 for π, the calculation is 3.14 * (8 inches)2, which equals 201.06 square inches. Therefore, 201.06 square inches of the cake are covered with icing.

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The graph best represents a function with a domain of all real numbers greater than or equal to 1 and less than or equal to 2 are area between equation x + y [tex]\geq[/tex] 1 and x + y [tex]\leq[/tex] 2 .

The collection of all potential inputs for a function is known as its domain. For instance, the domain of f(x)=x2 is all real numbers, and the domain of g(x)=1/x is all real numbers other than x=0.

The real numbers are all the numbers that make up the real number line, per definition. Thus, all real numbers can be graphed by simply drawing a number line. The number line is a graph of all real numbers since it contains all of the rational numbers.

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We can solve this equation by using quadratic formula. So we have two solution of given equation.

Write the quadratic equation in standard form a + bx + c = 0. Identify the values of a, b, c. Then write the Quadratic Formula. Then substitute in the values of a, b, c. Then solve and check the solution.

Quadratic formula that gives the solutions of the general quadratic equation a + bx + c = 0 and that is usually written in the form quadratic formula x = [-b ± √(b² - 4ac)] / (2a). So to solve a quadratic equation using quadratic formula just get the equation into standard form a + bx + c = 0 and apply the quadratic formula.

Here we have equation 5-7x+4

where a=5  b= -7   c=4

putting values in the formula

x= -(-7) +[tex]\sqrt{(-7)^2-4(5)(4)/2(5)}[/tex]

x= 7 + [tex]\sqrt{49+80/10}[/tex]

x= 7+[tex]\sqrt{129/10}[/tex]

Hence given values given two solutions.

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Complete question is: How to solve the given  quadratic equation?

Answer:

10

Step-by-step explanation:

35% of x = 3.5  To change a percent to a decimal, divide by 100%

.35x = 3.5  Divide both sides by 3.5

[tex]\frac{.35x}{.35}[/tex] = [tex]\frac{3.5}{.35}[/tex]

x = 10

Check:

.35 x 10 = 3.3.5 = 3.5

Answer:

10

Step-by-step explanation:

Let the unknown number be x.

35% of x = 3.50

35/100 * x = 3.50

35x = 3.50 * 100

35x = 350

x = 350/35

x = 10

Hence, the unknown number is 10.

a) The domain and the range of the function are given as follows:

b) The zero of the function is given as follows: (3,0).

c) The behaviors are given by these following intervals:

d) The extremas are given as follows:

e) The function is neither even nor odd.

The domain of a function is the set that contains all the input values for the function, hence in the graph it is given by the values of x.

The range of a function is the set that contains all the output values for the function, hence in the graph it is given by the values of y.

The zeros are the points of the function at which it either crosses or touches the x-axis.

The function is increasing when the graph is moving up, and decreasing it the graph is moving down.

The extremas are given as follows:

The function is classified as even, odd or neither as follows:

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Answer: The graph is NOT [tex]\text{y} > 3\text{x}-4[/tex]

Explanation:

The inequality of [tex]\text{y} > 3\text{x}-4[/tex]  has the boundary equation [tex]\text{y} = 3\text{x}-4[/tex]

That equation is in the format [tex]\text{y} = m\text{x}+b[/tex] which is slope-intercept form.

m = 3 = slope

b = -4 = y intercept

The positive slope indicates the boundary line goes uphill when moving to the right. However, the graph shows the complete opposite with the line going downhill. This means that the graph cannot possibly be [tex]\text{y} > 3\text{x}-4[/tex]

Answer:

Step-by-step explanation:

The perimeter of a regular pentagon is equal to the sum of the lengths of its sides. The length of each side of a regular pentagon inscribed in a circle with radius 1 meter can be found using the formula: side length = 2 * radius * sin(180/number of sides).

For a regular pentagon, the number of sides is 5. Plugging this into the formula gives us:

side length = 2 * 1 * sin(180/5) = 2 * 1 * sin(36) = 2 * 0.587785 = 1.175570

So the perimeter of the regular pentagon is equal to 5 * 1.175570 = 5.877849 meters.

Answer:

Option 2

Step-by-step explanation:

Hello!

We can solve the equation for n by isolating the variable.

The answer would be the second option: "n = the quantity 3 times c minus 9 all over negative p."

The total hours did Brendan work that week is 669.86.

A finite collection of symbols that are properly created in line with context-dependent criteria is referred to as an expression, sometimes known as a mathematical expression. Operations include addition, subtraction, multiplication, and division.

The collection of mathematical symbols that emerges from the right arrangement of numbers is known as a mathematical expression and variables using operations like addition, subtraction, multiplication, division, exponentiation, and other as-yet-unlearned operations and functions.

The three different types of algebraic expressions are monomial, binomial, and polynomial.

The total hours did Brendan work that week is 669.86.

The complete question is: Brendan is an hourly worker and earns $15.25/hour. During a week's pay period, he worked the following hours and minutes:

Day Hours Minutes

Monday 8 45

Tuesday 7 52

Wednesday 8 0

Thursday 9 36

Friday 8 24

Using the hundredth-hour method, what is Brendan's gross pay for the week? The employer pays overtime for all time worked in excess of 40 hours per week.

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A transformation that alters the size of a figure is called a dilation (similarity transformation). It needs a scale factor of k and a central point. Depending on the value of k, the dilatation is either an enlargement or a decrease. The dilation is an enlargement if |k|>1.

If two figures have the same shape but different sizes, they are said to be comparable. A stiff motion combined with a rescaling constitutes a similarity transformation. In other words, a similarity transformation can change shape without changing location or size.

A dilation is a transformation that yields a different-sized picture with the same general shape as the original. Enlargements are dilations that result in a bigger picture. Reduction is the name for a dilatation that shrinks the picture. The initial figure is stretched or contracted by a dilatation.

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Answer:

Step-by-step explanation:

18. m∠1 = 104°

19. m∠2 = 79°

20. m∠3 = 65°

21. m∠5 = 73°

The constant term in the expression 2x + 3 is 3.

The term expression in math is called as the algebraic expression consists of unknown variables, numbers and arithmetic operators.

Here we have the expression 2x + 3.

Now, we have to find the constant term in the expression.

As per the definition of expression, we know that the expression has two part one is variable part and the remaining second part is the constant parts.

As the name suggest, the variable part contains the unknown value like x, y etc. that changes value of the expression depending upon the given value.

Another term is constant, where its value can't be changed.

While we looking into the given expression here we have identified that

=> 2x is the variable term because the value of the term is changed based on the value of x.

Therefore, the constant term is 3.

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There is no sufficient evidence that we can use in order to substantiate the claim of the publisher,

The null hypothesis H0: p = 0.47

The alternative hypothesis is H1: p > 0.47

The question requires us to test the fact that more than 47 percent of the readers have their own personal computer. This is therefore the claim that is to be tested here.

There is no sufficient evidence to substantiate the claim because of the lack of certain details that would have been used to carry out the hypothesis test.

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Answer:

7/15

Step-by-step explanation:

number of favorable outcomes (red jelly beans) = 7

number of total outcomes (total jelly beans) = 7 + 2 + 6 = 15

probability of red = number of favorable outcomes/number of total outcomes = 7/15

The probability of getting a red jelly bean is 7/15

Total number of jelly beans in the jar (sum of all the jelly beans): 7+6+2= 15

Total number of red jelly beans: 7

Therefore, the probability of getting a red jelly bean= number of red jelly beans/ total number of jelly beans

=7/15

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The horizontal distance required for the ramp is 143.5 inches

Consider the following figure.

In right triangle ACB, CB is the horizontal distance,

hypotenuse AB = 144 in.

and the vertical distance AC = 12 in.

We need to find the measure of side CB

Let m be the measure of the horizontal distance CB

Using Pythagoras theorem for right triangle ACB,

(AB)² = (AC)² + (CB)²

Substitute given values in above equation.

(144)² = (12)² + (m)²

20736 = 144 + m^2

20736 - 144 = 144 + m^2 - 144

20592 = m^2

m^2 = 20592

m = 143.5 in.

Therefore,  the horizontal distance is 143.5 in.

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