AP Stats work, really confused please help asap!! Thank you

In case whereby the the Roman Empire began in 31 B.C. and fell to the Goths in A.D. 476,the Roman civilization lasted for 445 years.

The Roman Empire  can be described as the post-Republican period that can be associated with the ancient Rome , it can be described as the empire that came into the lime light around the 8th century BC , and actually came to an end around  5th century AD and the period it laste can be calculated below as :

In this case as regards to the question, we can calculate how long the Roman civilization lasted as [476+(-31)]

=445 years.

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The rate at which the grocery store clerk can scan products is 2 products per second.

Rate is the speed at which an activity can be carried out. Rate can be determined by dividing the total products that are bagged by the time it takes to bag the product.

Division is used to determine the product of two or more numbers. The sign that represent division is ÷. Division is a mathematical operations. Other mathematical operations include addition, subtraction and multiplication. Division entails grouping a number into equal groups using another number.

Rate = number of products ÷ time

1 ÷ 1/2

1 x 2 = 2 products per second

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[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{ 2}(x-\stackrel{x_1}{(-2)}) \implies y -6= 2 (x +2) \\\\\\ y-6=2x+4\implies {\Large \begin{array}{llll} y=2x+10 \end{array}}[/tex]

Based on the population density of the area in 1980 and the area, the population in 1980 was 807,750 people

The population density of an area is based on the population of the area and the area. The formula is:

Population density = Population of area / Surface area

Given that the surface area is 750 square miles and the population density in 1980 was 750 square miles, the population of the area can be found by the formula:

Population in 1980 = Population density in 1980 x surface area

Population in 1980 = 1,077 x 750

= 807,750 people

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first function: y = ([tex]\frac{3}{4}[/tex])x

Second function: y=[tex]\frac{12}{x}[/tex]

Third function y = 30 + 2x.

A) In the first function, y directly depends on x.

first formula: y = ([tex]\frac{3}{4}[/tex])x

2) Graph: It has a slope of ([tex]\frac{3}{4}[/tex]) and is a straight line that goes through the origin. According to the slope, the function changes at a rate of 3 units for every 4 units of x-value growth, or 0.75 units for every additional unit of x-value growth.

3) Use a real-world example

According to a cake recipe, 3 cups of sugar should be combined with every 4 cups of flour. Therefore, if you have 12 cups of sugar, how much flour do you need?

Y = ([tex]\frac{3}{4}[/tex])x, so if x = 3, y =([tex]\frac{3}{4}[/tex])×12= 9.

Given that : the variation is direct, you must multiply the number of cups of sugar by the constant rate, which is ([tex]\frac{3}{4}[/tex])x, to determine how many cups of flour correspond to the specified amount of sugar.

B) The second equation has an inverse relationship between y and x.

Inverse variation causes either y = constant / x or y*x = constant.

In other words, if x increases, y will decrease by the same amount as x increases.

1) formula: y=[tex]\frac{12}{x}[/tex]

2) Graph: The hyperbola, a diminishing line extending from left to right, is the shape of this graph. Both the x-axis and the y-axis asymptote to zero. This implies that neither x nor y can be zero.

As the x-value gets closer to 0, the y-value gets closer to positive or negative infinity; conversely, as the y-value gets closer to 0, the x-value gets closer to positive or negative infinity.

The graph is a declining curve in the first quadrant if you pick the positive numbers (x and y are positive).

The graph has a declining slope in the third quadrant if you pick the negative values (x and y are negative)

3) An actual world instance.

a uniform motion's relationship between time and velocity.

If an object runs a constant distance, time slows down proportionately as velocity rises.

Give the distance between cities A and B as 100 kilometers.

How long will it take to get from point A to point B traveling at 50 km/h or 25 km/h?

100 kilometers = speed * time

at 50 km/h: t = [100 km] / [50 km/h] = 2 hours 100 km = 50 km/h * t

at 25 km/h: t = [100 km] / [25 km/h] = 4 hours; 100 kg = 25 km/h * t.

C) In the third scenario, x and y should not have an inverse variation or a direct variation.

There are infinite types of functions that are neither inverse variations nor direct variations, including trigonometric sine, exponential, logarithmic, exponential, linear (that do not pass through the origin), and exponential, quadratic, and exponential.

1) A function illustration is y = 30 + 2x.

2) Graph: The line has a slope of 2 and a y-intercept of 30.

3) A case in point

In order to create chairs, it costs 30 dollars to rent the facility plus 2 dollars for each chair, for a total cost of 30 + 2x.

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The probability of getting all 5 cards hearts 13C₅/ 52C₅.

The probability of an event occurring is defined by probability.

There are many instances in real life where we may need to make predictions about how something will turn out.

The outcome of an event may be known to us or unknown to us.

When this happens, we say that there is a chance that the event will happen or not.

Given : A five card poker card

To find : the probability of all hearts

Let E be the events of getting all 5 cards of hearts

therefore n(E)= [tex]13C[/tex]₅

As we know that probability is defined as total number of favourable outcomes divided by total number of possible outcomes.

Thus the required probability is 13C₅/ 52C₅

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The amounts of time it takes for a student to complete a statistics quiz uniformly distributed between 30 and 60 minutes. One student is selected at random. Find the probability of the following events.

a) the student requires more than 55 minutes to complete quiz

b) the student completes the quiz in a time between 30 and 40 minutes

c) the student completes the quiz in exactly 37.23 minutes

A student to complete a statistics quiz uniformly distributed between 30 and 60 minutes The probability of the events are a) 1/6, b )1/3 c) 0

Given, X similar U( a = 30, b = 60)

f(x) =1/60-30, 30 ≤ X ≤60

f(x) = 1/30, 30  ≤ X  ≤60

a) the student requires more than 55 minutes to complete quiz

P(X > 55) = ∫_55^60▒f(x)dx = ∫_55^60▒〖1/30dx〗 = 1/30[x]6055 = 1/6

b) the student completes the quiz in a time between 30 and 40 minutes P (30 < X < 40) = ∫_30^40▒f(x)dx == ∫_30^40▒〖1/30dx〗 = 1/30[x]4030 = 1/3

C) the student completes the quiz in exactly 37.23 minutes P(X = 37.23) = ∫_37.23^37.23▒f(x)dx=∫_37.23^37.23▒〖1/30dx〗 = 0

A student to complete a statistics quiz uniformly distributed between 30 and 60 minutes The probability of the events are a) 1/6, b )1/3 c) 0

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Answer:

The function whose value at any number x is the smallest integer greater than of equal to x is called the least integer function.

Step-by-step explanation:

It is denoted by ⌈x⌉ It is also known as ceiling of x. For example ⌈3.578⌉ = 4 , ⌈0.78⌉ = 1 , ⌈-4.64⌉ = - 4.

the answer is 29 hope this helps

Answer:

x=(-3-√17)/4

x=(-3+√17)/4

Step-by-step explanation:

2x^2+3x-1=0

it can rewrite as,

x^2+3x/2-1/2=0

now adding and subtracting (3/4)^2 , in R.H.S,

x^2+3x/2+9/16-9/16-1/2=0

(x+3/4)^2-17/16=0

(x+3/4)^2-((√17)/4)^2=0

(x+3/4+√17/4)(x+3/4-√17/4)=0

x=(-3-√17)/4

x=(-3+√17)/4

Answer:

t = 10b + 10c

Step-by-step explanation:

As stated in the problem, 1 bag holds 10 doughnuts so that give us 10b since we don't know how many bags were bought/sold but we do know how many comes in each. Same goes for cartons.

Were asked to write a formula for t, and since we don't know how many bags(b) or cartons(c) were sold, our t remains t.

Answer:

5u

Step-by-step explanation:

9-4=5

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{9u - 4u}\\\large\text{COMBINE the LIKE TERMS}\\\mathsf{= (9u - 4u})\\\mathsf{= 9u - 4u}\\\mathsf{= 5u}\\\huge\text{Therefore, your answer should be: \boxed{\mathsf{\mathsf{5u}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

each chicken cost 3.65

Step-by-step explanation:

divide 18.25 by 5 and you'll get 3.65

Answer:70.409

Step-by-step explanation:73.261-2.852

Answer:

Step-by-step explanation:

36=p*60

36/60=(p*60)/60

p=0.6 or 60%

60%

Pls brainliest

The answer to 32z - 48 using factoring is 3/2.

Given,

32z - 48

We have to find the answer using factoring:

Factoring:

Finding things to multiply together to produce an expression is known as factoring. It is comparable to splitting an expression into numerous smaller expressions.

Here,

32z - 48 = 0

Add 48 to both sides

32z - 48 + 48 = 0 + 48

32z = 48

Divide 32 on both sides

32z/32 = 48/32

z = 48/32

Now, we can factorize 48/32

Take 2 as common factor

(48/2) / (32/2) = 24/16

Again, take 2 as common factor

(24/2) / (16/2) = 12/8

Now, take 4 as common factor

(12/4) / (8/4) = 3/2

Here, z = 3/2

That is, the answer for 32z - 48 using factoring is 3/2.

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9:

By taking the quotient between the total debt and what they earn in a sold-out show, we conclude that they need to sell a total of 7 sold-out shows.

10:

A discount of 30%. Correct option is B.

Answering part 9:

We know that they asked for a loan of $8,000, such that an interest of the 6% is applied to this, so the total amount that they need to return is:

$8,000*(1 + 6%/100%) = $8,000*(1.06) = $8,480

Now we know that the theater has 150 seats, and each ticket costs $8.50, so for every sold-out show they earn a total of:

T = 150*$8.50 = $1,275

Then the number of sold-out shows that they need is given by the quotient:

$8,480/$1,275 = 6.65

Rounding to the next whole number we get to 7. To cover the debt, they need to sell a total of 7 sold-out shows.

10. The original price is $180 and she pays $126, then the discount k is:

$180*k = $126

k = $126/$180 = 0.7

and 1 - 0.7 = 0.3

So the discount is of the 30%.

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The solution that will be eliminated when a quarterback throws an incomplete pass is –0.2 s can be eliminated because time cannot be a negative value

This is the equation used to trace the path made by a parabola. It is another name for quadratic equation.

We can say that the football traced a parabolic path represented by the equation h(t) = –16t2 + 40t + 7.

Parabolic equation will always produce two solutions then depending on the applicability of the solution the best option will be picked.

In this case time, which cannot be a negative value  hence option A is the correct answer

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Answer:

17%

Step-by-step explanation:

Hello!

Out of the 6 options, only 1 option will be correct. This can be represented as a ratio of 1:6.

If you randomly guess, there is an equal chance of choosing any of the 6 options.

To find the percentage of guessing the correct option, simply divide 1 by 6 (1 option is correct out of 6), and multiply the outcome by 100 (for percentage).

The probability of getting an answer correct would be 17%.

The probability of getting an answer wrong would be 83%, which can be found by subtracting 17% from 100%.

The two consecutive whole numbers that √72 lies between are 8 and 9.

As per the question statement, we are supposed to find two consecutive whole numbers that √72 lies between.

We know,

8 squared is 64 and 9 squared is 81

since 72 lies in between 64 and 81, then the square root must lie between 8 and 9 which are also whole numbers and consecutive too.

Hence we accept out answer to be 8 and 9.

Hence the two consecutive whole numbers that √72 lies between are 8 and 9.

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Answer:

d(-6,-9),e(3,-9),f(3,-3),g(-6,-3

Step-by-step explanation:

first you look at the location of the point and follow in the direction of which number it is on the X line, then in the direction of which number it is on the Y line and in the parentheses of the coordinates, first write the number from the X line, then from the Y line

ps: I hope I helped you a bit :)

Answer:

Step-by-step explanation:

-5/9* -4 = 20/9

Answer=20/9

When you multiply them, there is nothing to simplify in any of them. So when you multiply, the negatives become a positive because -*- is + so the answer is 20/9.

Answer: f(1)=0

Step-by-step explanation:

f(x)=1-x

f(1)=1-1

f(1)=0

The calculation shown in the number line is -4/10 + ( -7/10) = - 1 1/10

This is a sequential arrangement of numbers in a straight line. The scale of number line is shown to suit the problem at hand.

The number line in the question here has a scale of 1. This means that every number represent a unit. However in between the numbers are 10 strokes.

The value of each stroke is gotten from division of one by ten which is

1 ÷ 10 = 1/10

So every line in the number line represent 1/10. The positive side is 1/10 while the negative side is -1/10

The calculation done here is counting from 0 in the negative direction to get -4/10. Then adding -7/10 units to arrive at the point which  is -1 1/10

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Answer:

see explanation

Step-by-step explanation:

[tex]\frac{x+2}{3}[/tex] - [tex]\frac{2x-4}{2}[/tex] = 0

multiply through by 6 ( the LCM of 3 and 2 ) to clear the fractions

2(x + 2) - 3(2x - 4) = 0 ← distribute parenthesis on left side and simplify

2x + 4 - 6x + 12 = 0

- 4x + 16 = 0 ( subtract 16 from both sides )

- 4x = - 16 ( divide both sides by - 4 )

x = 4

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

[tex]\frac{5x}{2}[/tex] + [tex]\frac{x-2}{8}[/tex] = 2 ( multiply through by 8 to clear the fractions )

4(5x) + x - 2 = 16

20x + x - 2 = 16

21x - 2 = 16 ( add 2 to both sides )

21x = 18 ( divide both sides by 21 )

x = [tex]\frac{18}{21}[/tex] = [tex]\frac{6}{7}[/tex]

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

[tex]\frac{x-5}{4}[/tex] - [tex]\frac{3x-1}{5}[/tex] = - [tex]\frac{3}{2}[/tex]

multiply through by 20 ( the LCM of 4, 5, 2 ) to clear the fractions

5(x - 5) - 4(3x - 1) = - 30 ← distribute parenthesis on left side and simplify

5x - 25 - 12x + 4 = - 30

- 7x - 21 = - 30 ( add 21 to both sides )

- 7x = - 9 ( divide both sides by - 7 )

x = [tex]\frac{9}{7}[/tex]

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

[tex]\frac{1}{x-1}[/tex] + [tex]\frac{1}{x+1}[/tex] = [tex]\frac{4x+2}{x^2-1}[/tex] ← x² - 1 is a difference of squares , then

[tex]\frac{1}{x-1}[/tex] + [tex]\frac{1}{x+1}[/tex] = [tex]\frac{4x+2}{(x-1)(x+1)}[/tex]

multiply through by (x - 1)(x + 1) to clear the fractions

x + 1 + x - 1 = 4x + 2

2x = 4x + 2 ( subtract 4x from both sides )

- 2x = 2 ( divide both sides by - 2 )

x = - 1

If we substitute this value back into the original equation, we find

[tex]\frac{1}{-1-1}[/tex] + [tex]\frac{1}{-1+1}[/tex] = [tex]\frac{4(-1)+2}{(-1)^2-1}[/tex]

[tex]\frac{1}{-2}[/tex] + [tex]\frac{1}{0}[/tex] = [tex]\frac{-2}{1-1}[/tex]

[tex]\frac{1}{-2}[/tex] + [tex]\frac{1}{0}[/tex] = [tex]\frac{-2}{0}[/tex]

division by zero is undefined

thus x = - 1 is an extraneous solution

the equation has no solution

Answer:

[tex]\textsf{1.} \quad x=4[/tex]

[tex]\textsf{2.} \quad x=\dfrac{6}{7}[/tex]

[tex]\textsf{3.} \quad x=\dfrac{9}{7}[/tex]

[tex]\textsf{4.} \quad \textsf{No solution}[/tex]

Step-by-step explanation:

Given equation:

[tex]\dfrac{x+2}{3}-\dfrac{2x-4}{2}=0[/tex]

[tex]\textsf{Add \; $\dfrac{2x-4}{2}$ \; to both sides of the equation}:[/tex]

[tex]\implies \dfrac{x+2}{3}-\dfrac{2x-4}{2}+\dfrac{2x-4}{2}=0+\dfrac{2x-4}{2}[/tex]

[tex]\implies \dfrac{x+2}{3}=\dfrac{2x-4}{2}[/tex]

Cross multiply:

[tex]\implies 2(x+2)=3(2x-4)[/tex]

[tex]\implies 2x+4=6x-12[/tex]

Subtract 2x from both sides:

[tex]\implies 2x+4-2x=6x-12-2x[/tex]

[tex]\implies 4=4x-12[/tex]

Add 12 to both sides:

[tex]\implies 4+12=4x-12+12[/tex]

[tex]\implies 16=4x[/tex]

[tex]\implies 4x=16[/tex]

Divide both sides by 4:

[tex]\implies \dfrac{4x}{4}=\dfrac{16}{4}[/tex]

[tex]\implies x=4[/tex]

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

Given equation:

[tex]\dfrac{5x}{2}+\dfrac{x-2}{8}=2[/tex]

Multiply the numerator and denominator of the first fraction by 4:

[tex]\implies \dfrac{5x \cdot 4}{2\cdot 4}+\dfrac{x-2}{8}=2[/tex]

[tex]\implies \dfrac{20x}{8}+\dfrac{x-2}{8}=2[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}+\dfrac{b}{c}=\dfrac{a+b}{c}:[/tex]

[tex]\implies \dfrac{20x+x-2}{8}=2[/tex]

[tex]\implies \dfrac{21x-2}{8}=2[/tex]

Multiply both sides by 8:

[tex]\implies \dfrac{(21x-2) \cdot 8}{8}=2 \cdot 8[/tex]

[tex]\implies 21x-2=16[/tex]

Add 2 to both sides:

[tex]\implies 21x-2+2=16+2[/tex]

[tex]\implies 21x=18[/tex]

Divide both sides by 21:

[tex]\implies \dfrac{21x}{21}=\dfrac{18}{21}[/tex]

[tex]\implies x=\dfrac{18}{21}[/tex]

Reduce the fraction by dividing the numerator and denominator by 3:

[tex]\implies x=\dfrac{18 \div 3}{21 \div 3}[/tex]

[tex]\implies x=\dfrac{6}{7}[/tex]

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

Given equation:

[tex]\dfrac{x-5}{4}-\dfrac{3x-1}{5}=-\dfrac{3}{2}[/tex]

Multiply the numerator and denominator of the first fraction by 5, and the numerator and denominator of the second fraction by 4:

[tex]\implies \dfrac{(x-5) \cdot 5}{4\cdot 5}-\dfrac{(3x-1)\cdot 4}{5\cdot 4}=-\dfrac{3}{2}[/tex]

[tex]\implies \dfrac{5x-25}{20}-\dfrac{12x-4}{20}=-\dfrac{3}{2}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}-\dfrac{b}{c}=\dfrac{a-b}{c}:[/tex]

[tex]\implies \dfrac{5x-25-(12x-4)}{20}=-\dfrac{3}{2}[/tex]

[tex]\implies \dfrac{5x-25-12x+4}{20}=-\dfrac{3}{2}[/tex]

[tex]\implies \dfrac{-7x-21}{20}=-\dfrac{3}{2}[/tex]

Cross multiply:

[tex]\implies 2(-7x-21)=-3(20)[/tex]

[tex]\implies -14x-42=-60[/tex]

Add 42 to both sides:

[tex]\implies -14x-42+42=-60+42[/tex]

[tex]\implies -14x=-18[/tex]

Divide both sides by -14:

[tex]\implies \dfrac{-14x}{-14}=\dfrac{-18}{-14}[/tex]

[tex]\implies x=\dfrac{18}{14}[/tex]

Reduce the fraction by dividing the numerator and denominator by 2:

[tex]\implies x=\dfrac{18 \div 2}{14 \div 2}[/tex]

[tex]\implies x=\dfrac{9}{7}[/tex]

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

Given equation:

[tex]\dfrac{1}{x-1}+\dfrac{1}{x+1}=\dfrac{4x+2}{x^2-1}[/tex]

Factor the denominator of the fraction on the right side of the equation:

[tex]\implies \dfrac{1}{x-1}+\dfrac{1}{x+1}=\dfrac{4x+2}{(x+1)(x-1)}[/tex]

Multiply the numerator and denominator of the first fraction by (x+1), and the numerator and denominator of the second fraction by (x-1):

[tex]\implies \dfrac{x+1}{(x+1)(x-1)}+\dfrac{x-1}{(x+1)(x-1)}=\dfrac{4x+2}{(x+1)(x-1)}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}+\dfrac{b}{c}=\dfrac{a+b}{c}:[/tex]

[tex]\implies \dfrac{x+1+x-1}{(x+1)(x-1)}=\dfrac{4x+2}{(x+1)(x-1)}[/tex]

[tex]\implies \dfrac{2x}{(x+1)(x-1)}=\dfrac{4x+2}{(x+1)(x-1)}[/tex]

Multiply both sides by (x+1)(x-1):

[tex]\implies \dfrac{2x(x+1)(x-1)}{(x+1)(x-1)}=\dfrac{(4x+2)((x+1)(x-1)}{(x+1)(x-1)}[/tex]

[tex]\implies 2x=4x+2[/tex]

Subtract 4x from both sides:

[tex]\implies 2x-4x=4x+2-4x[/tex]

[tex]\implies -2x=2[/tex]

Divide both sides by -2:

[tex]\implies \dfrac{-2x}{-2}=\dfrac{2}{-2}[/tex]

[tex]\implies x=-1[/tex]

However, if we substitute x = -1 into the original equation we get:

[tex]\implies \dfrac{1}{(-1)-1}+\dfrac{1}{(-1)+1}=\dfrac{4(-1)+2}{(-1)^2-1}[/tex]

[tex]\implies -\dfrac{1}{2}+\dfrac{1}{0}=\dfrac{-2}{0}[/tex]

A number divided by zero is undefined.  Therefore, there is no solution for this equation.

The expression of the number 0.133333 as a fraction would give us 133333/1000000.

Let us recall that the term fraction is used to show that there is a top and a bottom part in the expression. The top part of the fraction is called the numerator while the bottom part of the fraction is called the denominator.

If we want to convert the fraction as we have it back to the decimal then we just have to divide the numerator by the denominator and we are back to the decimal. The decimal is marked by the presence of a decimal point.

To convert 0.133333 to fraction, we would take the decimal point as 1 and all other digits after it as zero thus we have;

133333/1000000.

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Lines through the given points are as follow:

a. Line1 is perpendicular to line2.

b. Line1 is neither perpendicular nor parallel to line2.

c. Line1 is parallel to line2.

As given in the question,

Slopes of the lines through the given points are as follow:

Let m₁ and m₂ be the slope of line1 and line2 respectively.

a. Line1 ( 2,-3) , (-4, -6) and Line2 (-3,2) ,  (2,-8)

m₁=(-6+3)/ (-4-2)

    =1/2

m₂=(-8-2)/ (2+3)

    =-2

m₁ × m₂ = -1

Line1 and line2 are perpendicular.

b. Line1(-4, -5) , (4,1) and line2 (6,10) , (-3,-2)

m₁=(1+5)/ (4+4)

    =3/4

m₂=(-2-10)/ (-3-6)

    =4/3

m₁ × m₂=1

Line1 and line2 are neither perpendicular nor parallel .

c. Line1 (0,-4) , (-2,-8) and line2 (-1,5), (1,9)

m₁=(-8+4)/ (-2-0)

    =2

m₂=(9-5)/ (1+1)

    =2

m₁=m₂

Line1 and line2 are parallel

Therefore, lines through the given points are as follow:

a. Line1 is perpendicular to line2.

b. Line1 is neither perpendicular nor parallel to line2.

c. Line1 is parallel to line2.

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