alice, bob and carol each think of an expression that is a fraction with 1 as the numerator and a constant integer times some power of x as the denominator. the simplest common denominator of alice's and bob's expressions is 4x2. the simplest common denominator of bob's and carol's expressions is 12x3. the simplest common denominator of alice and carol's expressions is 6x3. find all possible expressions that could be carol's

1. If the οriginal ratiο is 2:3, we can fοrm different ratiοs by:

Multiplying bοth the numeratοr and denοminatοr by the same number, such as 2:3 x 2 = 4:6 οr 2:3 x 3 = 6:9

Dividing bοth the numeratοr and denοminatοr by the same number, such as 2:3 ÷ 2 = 1:1.5 οr 2:3 ÷ 3 = 0.67:1

Any ratiο that is equivalent tο the οriginal ratiο can be fοrmed in this way

2. Tο cοmpare twο numbers using a tape diagram, yοu can use a vertical οr hοrizοntal bar tο represent the tοtal quantity being cοmpared, and then divide the bar intο segments that represent each οf the twο numbers. The length οf each segment will indicate the relative size οf each number.

3. If yοu have a pie with 8 slices and 3 οf them are apple and 5 are cherry, yοu can express the cοmparisοn οf the twο parts using a part-tο-whοle ratiο. The whοle is 8 slices, sο the fractiοn fοr the apple slices is 3/8 and the fractiοn fοr the cherry slices is 5/8. Tο write the part-tο-whοle ratiο, yοu put the fractiοn fοr the apple slices first, fοllοwed by a cοlοn, and then the fractiοn fοr the cherry slices, like this: 3:5. This tells yοu that there are 3 apple slices fοr every 5 cherry slices in the pie.

4. Suppοse a basketball team scοres 80 pοints in a game, and οne player scοres 20 pοints. Tο cοmpare the value οf the player's pοints tο the value οf the team's tοtal pοints using assοciated ratiοs, yοu first express the player's pοints as a fractiοn οf the team's tοtal pοints: 20/80, which simplifies tο 1/4. Then, yοu create the assοciated ratiο by taking the reciprοcal οf the fractiοn: 4:1. This tells yοu that the player's pοints represent οne fοurth (οr 25%) οf the team's tοtal pοints.

5. A drawing that lοοks like a sectiοn οf tape and demοnstrates a relatiοnship between quantities is called a tape diagram. Tape diagrams are useful fοr visualizing part-tο-part ratiοs, as they allοw yοu tο see the relative sizes οf the twο parts and the ratiο between them. In a tape diagram, each part is represented by a sectiοn οf the tape, and the ratiο is shοwn by dividing the tape intο equal segments cοrrespοnding tο the ratiο οf the twο parts.

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The equation of the least squares line is:y = mx + by = 3.6x - 72.1818181818182Thus, the least squares line is y = 3.6x - 72.182.

(10 points) Consider the following data from a sample of n=7 . x: 168 178 176 174 178 174 172 y: 50 57 55 55 58 54 53The y-intercept of the least squares line is given as -72.1818181818182. We have to calculate the slope of the least squares line and input the equation of the least squares line. The given data is shown below:X: 168 178 176 174 178 174 172Y: 50 57 55 55 58 54 53We know that y-intercept of the least squares line is given by b = ybar - m * xbarwhere xbar = (1/n) * ∑x and ybar = (1/n) * ∑y. Now, to calculate the slope of the least squares line, we need to calculate the value of the numerator of the following equation:Slope, m = [(n∑xy) - (∑x∑y)] / [(n∑x^2) - (∑x)^2]Here, ∑x and ∑y are the summations of x and y values, respectively. ∑xy is the sum of the products of each x and y value, and ∑x^2 is the sum of each x value squared. So, let's calculate all of these values for the given data.We have, n = 7∑x = 1202∑y = 382∑x^2 = 213468∑xy = 71848Now, substituting these values in the formula of slope, we have:Slope, m = [(7 * 71848) - (1202 * 382)] / [(7 * 213468) - (1202)^2] = 3.6000630680907Therefore, the slope of the least squares line is 3.600. Now, we can use the slope and the y-intercept to find the equation of the least squares line. Therefore, the equation of the least squares line is:y = mx + by = 3.6x - 72.1818181818182Thus, the least squares line is y = 3.6x - 72.182.

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Answer:

54

Step-by-step explanation:

if you look at the ratios between the values of A and B. you will see that the successive values of A increase by 10 while B increase by 12

Therefore for A

35 + 10 = 45

for B

42 + 12 = 54

The investor's stock balance has decreased by a total of [tex]24.36[/tex]%.

You aren't a property owner; you are a lending investor. You have invested in ownership if you purchase stock in a corporation. Your proportionate part of the company's profits will be deducted from the return you get. The original investment sum will continue to be correlated to the overall worth of the business.

The investors is someone or something that makes investments in other persons or groups with the intention of profiting to them in the future. On principle, everyone who invests money for something qualifies as an investor.

The decrease in stock A,

[tex]= 1300 * 22[/tex]%

[tex]= 286[/tex]

Decrease in stock B,

[tex]= 4820 * 25[/tex]%

[tex]= 1205[/tex]

Total decrease [tex]= 286+1205[/tex]

[tex]= 1491[/tex]

Total percentage decrease,

[tex]= (1491 / (1300 + 4820) ) * 100[/tex]%

[tex]= 1491 / 6120 * 100[/tex]%

[tex]= 24.36[/tex]%

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After answering the prοvided questiοn, we can cοnclude that Therefοre, equatiοn there are 26 twο-pοint questiοns and 16 three-pοint questiοns οn the test.

In mathematics, an equatiοn is a statement that implies the unity οf twο traits. An equatiοn cοnsists οf twο sides separated because οf an analytical sοlutiοn (=). Fοr instance, the debate "2x + 3 = 9" asserts that the remark "2x + 3" equals the valuatiοn "9". The gοal οf sοlving equatiοns is tο determine the amοunt οr values οf the variable in the mοdel) that wοuld allοw the equatiοn tο really be true.

Fοrmulae can be simple οr cοmplex, regular οr nοnlinear, and cοntain οne οr mοre variables. Fοr example, in the equatiοn "x² + 2x - 3 = 0," the variable x is elevated tο the secοnd pοwer. Lines are used extensively in mathematics, including algebra, equatiοns, and geοmetry.

Let the number οf twο-pοint questiοns οn the test be "x" and the number οf three-pοint questiοns be "y".

[tex]x+y=42[/tex]

[tex]2x+3y=100[/tex]

[tex]x+y=42[/tex]

[tex]x=42-y[/tex]

[tex]2(42-y)+3y=100[/tex]

[tex]84-2y+3y=100[/tex]

[tex]Y=16[/tex]

[tex]x+y=42[/tex]

[tex]x+16=42[/tex]

[tex]x=26[/tex]

Therefore, there are 26 two-point questions and 16 three-point questions on the test.

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The linearization of the function √????(x,y)=18−2x2−3y2 at the point (1, -2) is (x,y)≈6.4−4(x−1)−6(y+2). Using this linear approximation, we can estimate the value of (0.9,−1.9) to be approximately 6.1.

To explain further, linear approximation is a method used to approximate a function with a linear equation near a given point. We use linear approximation to estimate the value of a function at a certain point without actually having to evaluate it.

First, we find the linearization of the function √????(x,y)=18−2x2−3y2 at the point (1, -2). We do this by finding the derivative of ????(x,y) with respect to x and y and substituting the coordinates of the given point.

Taking the partial derivative of ????(x,y) with respect to x, we get ????x(x,y)=4x−4 and substituting x = 1 and y = -2, we get ????x(1,−2)=−4.

Similarly, taking the partial derivative of ????(x,y) with respect to y, we get ????y(x,y)=−6y−6 and substituting x = 1 and y = -2, we get ????y(1,−2)=18.

Therefore, the linearization of the function √????(x,y)=18−2x2−3y2 at the point (1, -2) is ????(x,y)≈6.4−4(x−1)−6(y+2).

Using this linear approximation, we can estimate the value of ????(0.9,−1.9) to be approximately 6.1. We do this by substituting x = 0.9 and y = -1.9 in the linear approximation, which gives us ????(0.9,−1.9)≈6.1.

Hence, the value of ????(0.9,−1.9) is estimated to be approximately 6.1 using the linear approximation of the function ????(x,y)=18−2x2−3y2 at the point (1, -2).

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Answer:

Step-by-step explanation:

A credit score is a number that helps lenders assess how well you manage your financial obligations in the past.

I hope this helps.

The proof that line segment PR is greater than the line segment PF is shown below

Given that

The above statements mean that we have a right triangle PFR such that

In a right triangle, the longest side is the hypotenuse

This means that

PR is greater than PF

This proves that if R is any point on line l that is different from F, then PR > PF.

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well, we know that a year has 12 months, so 6 months is really just 6/12 of a year.

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 2588\\ P=\textit{original amount deposited}\dotfill & \$2500\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\to \frac{6}{12}\dotfill &\frac{1}{2} \end{cases}[/tex]

[tex]2588 = 2500[1+(\frac{r}{100})(\frac{1}{2})] \implies \cfrac{2588}{2500}=1+\cfrac{r}{200}\implies \cfrac{647}{625}=\cfrac{200+r}{200} \\\\\\ \cfrac{(200)(647)}{625}=200+r\implies \cfrac{(200)(647)}{625}-200=r\implies \boxed{7.04=r}[/tex]

(u - 5 + (7))(u - 5 - (7)) = 0 is the equation we created in u that simplifies to 2u2 - 20u + 36 = 0.

The two forms of equations are identity equations and conditional equations. The variables all have the same identity for all conceivable values.

Creating an equation in u that can be solved for 2u² - 20u + 36 = 0

It indicates that the following are the solutions for x for a quadratic equation of the form ax² + bx + c = 0:

x = (-b±√(b²-4ac))/2a

By dividing both sides by 2, we can rewrite the equation 2u2 - 20u + 36 = 0 as follows:

u² - 10u + 18 = 0

u = (-(-10) ± √((-10)² - 4(1)(18))) / 2(1)

Simplifying this expression, we get:

u = (10 ± √(100 - 72)) / 2

u = (10 ± √(28)) / 2

u = (10 ± 2√(7)) / 2

u = 5 ± √(7)

A quadratic equation with roots r1 and r2 can be expressed as: This allows us to merge the two solutions into a single equation.

(x - r1)(x - r2) = 0

By substituting in the two answers we discovered for u, we obtain:

(u - 5 + √(7))(u - 5 - √(7)) = 0

Extending this phrase results in:

u² - 10u + 18 = 0

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Answer:  960 eggs are not sold.

Step-by-step explanation:

Let t be the number of total eggs.

36%(t) = 540

0.36(t) = 540

         t = 1500

1500 - 540 = 960

The specific values of [tex]$\underline{-33.78}$[/tex] and [tex]$\overline{-33.78}$[/tex] depend on the level of precision required.

The upper and lower bounds for -33.78 depend on the level of precision required. For example, if we only need to round to the nearest whole number, the lower bound is -34 and the upper bound is $-33$. If we need to round to the nearest tenth, the lower bound is -33.8 and the upper bound is -33.7.

In general, we can use the following notation to indicate the upper and lower bounds of a number x:

[tex]$$\underline{x} \leq x \leq \overline{x}$$[/tex]

Using this notation, we can write the upper and lower bounds for -33.78 as:

[tex]$$\underline{-33.78} \leq -33.78 \leq \overline{-33.78}$$[/tex]

Again, the specific values of [tex]$\underline{-33.78}$[/tex] and [tex]$\overline{-33.78}$[/tex] depend on the level of precision required.

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(a) Yes, the player makes the shot; (b) A quadratic function in standard form that models the path of the shot is: [tex]f(x) = -\frac{3}{50} (x-13)(x-3)[/tex]

(a) We need to find the x-int to see if he makes the shot at (3,0).

    so, first we factor!

[tex]y=-\frac{1}{20} (x-6)(x-3)[/tex]

0 = (x - 6) = (6, 0)

0 = (x - 3) = (3, 0)

This shows that the player makes the shot.

(b) x- int = (13, 0) and (3, 0)

    random point = (10, 1.4)

    f(x) = a(x - 13) (x - 3)

    1.4 = a(10 - 13) (10 - 3)

    1.4 = a(-3) (7)

   [tex]\frac{1.4}{-21} = \frac{-21a}{-21}[/tex]

       a = 0.06 ≈ [tex]\frac{-3}{50}[/tex]

the Quadratic function is [tex]f(x) = -\frac{3}{50} (x-13)(x-3)[/tex]

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Full Question:

A professional basketball player's shot is modeled by the function shown, where x and y are measured in feet.

a. Does the player make the shot?

b. The basketball player releases another shot from the point (13,0) and makes the shot. The shot also passes through the point (10, 1.4). Write a quadratic function in standard form that models the path of the shot.

Answer:

Step-by-step explanation:

<ATC+90+60=180

<ATC=30

we know that,

if 30-------x

60--------[tex]x\sqrt{3}[/tex]

90---------2x

so,  x\sqrt{3}=10

x=10/sqrt{3}

Answer:

Step-by-step explanation:

LCM: 1750

GCD: 50

We meet the SAS requirement for congruence because the two triangles share two congruent sides as well as the included angle.

To prove that △BEC≅△DEA, we can use the Side-Angle-Side (SAS) congruence theorem.

First, we can see that BE=ED, as both are radii of the same circle.

Secondly, angle BEC and angle DEA are both 90 degrees, as they are inscribed angles that subtend the same arc BD.

Lastly, we can see that EC=EA, as they are both radii of the same circle.

Therefore, we have the two triangles sharing two congruent sides and the included angle, satisfying the SAS criterion for congruence. Hence, we can conclude that △BEC≅△DEA.

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Jorge needs to sell at least $88.89 worth of products for the week in order to be able to purchase the new tire and cover his commission.

A commission is a payment made to a salesman or agent in exchange for the sale of a good or service. Salespeople are frequently motivated to close more deals by commissions, which are normally set as a percentage of the entire transaction price. For instance, a salesman may receive a 5% commission on each product they sell, which translates to $5 for every $100 in sales. Several businesses, including retail, real estate, and banking, use commission-based pay.

Let us suppose the amount he needs to sell = x.

Thus, for 5% commission on his sales to purchase a $80 tire we have the equation:

x * 0.95 - 0.05x >= 80

0.9x >= 80

x >= 80/0.9

x >= 88.89

Therefore, Jorge needs to sell at least $88.89 worth of products for the week in order to be able to purchase the new tire and cover his commission.

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In the wοrd prοblem, the number οf seeds Val is gοing tο plant is 6d+d.

Wοrd prοblems are οften described verbally as instances where a prοblem exists and οne οr mοre questiοns are pοsed, the sοlutiοns tο which can be fοund by applying mathematical οperatiοns tο the numerical infοrmatiοn prοvided in the prοblem statement.

Determining whether twο prοvided statements are equal with respect tο a cοllectiοn οf rewritings is knοwn as a wοrd prοblem in cοmputatiοnal mathematics.

Here accοrding tο the given,

Number οf seeds planted in οne garden = d

Number οf seed planted in anοther garden = 5d+6

Then , Tοtal number οf seed Val is gοing tο plant is,

=> Number οf seeds in οne garden+ Number οf seed in anοther garden

=> d+5d+6

=> 6d+6

Hence the total number of seed Val is going to plant is 6d+6.

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According to the information, it can be inferred that if he has a total of $8,080 a that week, he has sold 40 suits.

To calculate how many suits he sold during that week we must find the total value that he would give with each of the answer options as shown below:

Based on the above, the closest value is $8,000, so we can conclude that he sold 40 suits. Now to find the missing money we must find 10% of 40 and identify the value that these t-shirts would have:

So the total value of all the products would be $8,080.

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Answer:

b

d

.  ._-_-_-__---_--_--_----___-_--------_--------------------------__-_______--_-__-________---_-_--___-----__--

According to the slope, the angle 3 also has a measure of 143 degrees.

To find the measure of angle 3, we first need to understand how angles 2 and 3 are related.

In other words, angles 2 and 3 are congruent (have the same measure). Therefore, if we can find the measure of angle 2, we can determine the measure of angle 3.

We know that angle 2 has a measure of 143 degrees. We also know that angles 2 and 3 are alternate interior angles, which means they are congruent.

Now, let's justify why this is true using the concept of slopes. Since the power lines are parallel, they have the same slope. This means that the angle between each power line and the horizontal is the same.

Since angle 2 is the angle between one of the power lines and the horizontal, we know that angle 3 must also have the same measure because it is the angle between the other power line and the horizontal.

Therefore, we can confidently say that the measure of angle 3 is also 143 degrees.

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Complete Question:

A pair of parallel power lines in Mohamed Bin Zayed City is installed on a slope. Find m∠3 if m∠2= 143 degrees . Justify your answer

The solution to the equation is x = 22.5.

To solve the equation x-9 = (3/5)x, we can first simplify the right-hand side by multiplying both sides by 5 to get rid of the fraction:

5(x-9) = 3x

An equation is a mathematical statement that indicates the equality of two expressions. Equations typically contain variables, which are represented by letters, and mathematical operations such as addition, subtraction, multiplication, and division. The expressions on either side of the equals sign are called the left-hand side and right-hand side of the equation.

Expanding the left-hand side, we get

5x - 45 = 3x

Next, we can simplify by subtracting 3x from both sides:

2x - 45 = 0

Adding 45 to both sides, we get:

2x = 45

Finally, dividing both sides by 2, we get:

x = 22.5

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Answer:

0.8

Step-by-step explanation:

8 divided by 0.8= 10

10 times 0.8= 8

:)

Therefore, it is not possible to determine if the value that occurred the most often would change without knowing the frequency and values of the new data  points.

Adding two more data points that are each 2 1/2 hours to a line plot would not necessarily change the value that occurred the most often. The value that occurred the most often would depend on the frequency of the new data points in relation to the existing data points. If the new data points have the same value as one of the existing data points, then the mode would not change. However, if the new data points have a different value than the existing data points, and they occur more frequently, then the mode would change.

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The words from a written text that a person can remember after five minutes with the text are known as short-term memory.

Short-term memory refers to the storage of information for a brief period of time, usually a few seconds to a few minutes. It is a type of memory that is involved in the conscious processing of information and is responsible for holding information in mind for immediate use.

The capacity of short-term memory is limited and varies from person to person. Generally, it can hold about 7 pieces of information or less, and can only hold it for a short period of time. This is why it is important to transfer important information from short-term memory to long-term memory through a process called encoding.

To improve short-term memory, one can use techniques such as repetition, chunking, visualization, and association. By doing this, it is possible to hold more information in short-term memory for a longer period of time.

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Answer:

Starting with the given equation:

P = N / (1 + 5 / (t - 1))

First, we can simplify the expression in the denominator:

P = N / (1 + 5 / (t - 1))

P = N / (1 + 5 / t - 5)

P = N / (-4 + 5 / t)

Then, we can take the reciprocal of both sides to get rid of the fraction:

1 / P = (-4 + 5 / t) / N

Next, we can cross-multiply:

N / P = -4 + 5 / t

And then isolate t:

N / P + 4 = 5 / t

t = 5 / (N / P + 4)

Therefore, t = 5 / (N/P + 4) is the solution for t.

According to the figure the value of a b and c is

a = 39

b = 141

c = 39

The angles are solved using the concept of sum of angles in a triangle is equal to 180 degrees

Solving for a

a + 106 + 35 = 180

a + 106 + 35 = 180

a + 141 = 180

Next, we can isolate a by subtracting 141 from both sides:

a + 141 - 141 = 180 - 141

a = 39

a = c = 39 corresponding angles

b + c = 180 degrees (linear pair theorem)

b + 39 = 180

b + 39 - 39 = 180 - 39

b = 141

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Answer: Voluntary Response

Step-by-step explanation:

The question was, "Mrs. Finn had a terrible experience at a hotel last weekend. The water was cold, the bathroom wasn't cleaned, and it smelled really bad. She decided to write a horrible review on travel.com about the experience."

And we're asked to evaluate whether this is

A) Statistic

B) Random Sampling

C) Voluntary Response

A statistic is "any quantity computed from values in a sample which is considered for a statistical purpose."

Random sampling is "a method of data collection and analysis designed to select a representative sample of respondents out of a larger population."

Finally, we have voluntary response which is "a deliberately chosen reaction to a stimulus that may require a complex coordination of excitatory and inhibitory impulses with feedback from visual, motor, and other systems."

Out of all of the following definitions, voluntary response is what fits this scenario best. Voluntary response usually includes the response of people with very strong opinions, and recalling how Mrs. Finn reacted to her hotel, I'd say it fits.

The number of jars of raspberry jam filled is required.

The number of jars of raspberry jam is 1/24

Fraction:

A fraction represents a part of a whole, or more generally, any number of equal parts. In common English, a fraction describes the number of parts of a certain size, such as half, eight-fifths, three-quarters. A common, vulgar, or simple fraction consists of a numerator that appears above (or before a slash, such as 1⁄2) a line, and a non-zero denominator that appears. Multipliers and denominators are also used in less common fractions, including complex, complex, and mixed fractions.

According to the Question:

The number of jars of strawberry jam is 1/8 jars.

The number of jars of raspberry jam is half of the number of jars of strawberry jam.

So,

1/8 × 1/3

= 1/24

The number of jars of raspberry jam is 1/24.

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Answer:

429

Step-by-step explanation: