bob buys 100 candy bars at the store bob eats 47 of the candy bars
what does bob have left now

Answer:

θ ≈ 71.6°

Step-by-step explanation:

The angle between two lines with slopes m₁ and m₂ is:

tan θ = | (m₂ − m₁) / (1 + m₁m₂) |

Here, m₁ = -2 and m₂ = 1.

tan θ = | (1 − (-2)) / (1 + (-2)(1)) |

tan θ = | 3 / -1 |

tan θ = 3

θ ≈ 71.6°

Answer:

see the explanation

Step-by-step explanation:

we know that

To determine the rate per pretzel or unit rate, divide the total paid by the number of pretzel

so

[tex]\frac{126}{42}=\$3\ per\ pretzel[/tex]

Jaimie's error

He subtracted 42 from $126 when he should have divided $126 by 42

Answer:

x³ − x² + 9x − 9 = 0

Step-by-step explanation:

Imaginary roots come in conjugate pairs.  So if 3i is a root, then -3i is also a root.

(x − 1) (x − 3i) (x − (-3i)) = 0

(x − 1) (x − 3i) (x + 3i) = 0

(x − 1) (x² − 9i²) = 0

(x − 1) (x² + 9) = 0

x (x² + 9) − (x² + 9) = 0

x³ + 9x − x² − 9 = 0

x³ − x² + 9x − 9 = 0

To find a third-degree polynomial equation with rational coefficients that has the given roots, we consider the conjugate of the complex root. The equation can be written as (x - 1)(x - 3i)(x + 3i) and simplified to x^3 - x^2 + 9x - 9.

To find a third-degree polynomial equation with rational coefficients that has the given roots of 1 and 3i, we need to consider the conjugate of 3i, which is -3i. Therefore, the roots of the equation are 1, 3i, and -3i.

To find the polynomial equation, we start by noting that the polynomials with rational coefficients will have complex conjugate pairs of roots. Thus, we can write the equation as (x - 1)(x - 3i)(x + 3i). Simplifying, we get (x - 1)(x^2 + 9). Expanding further, the equation is x^3 - x^2 + 9x - 9.

Therefore, the desired third-degree polynomial equation with rational coefficients is x^3 - x^2 + 9x - 9.

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Answer:

The answer is 38.7 kg·m/s

Step-by-step explanation:

Considering the definition of average velocity,

The average speed of an object is defined as the distance traveled divided by the time elapsed.

Therefore, If in the frame of 320, the blue dot appears to be at 0 cm  and 24 frames later (at 344), the blue dot appears to be at 11 cm.  24 frames is 1/10 of a second, so

V = 11cm / 0.10s = 110 cm/s = 1.10 m/s

give or take.

Bonus:  initial system (cart only) momentum

p = mv = 23.8kg * 1.80m/s = 42.8 kg·m/s  

final system (cart+disk) momentum

p = (23.8+11.4)kg * 1.10m/s = 38.7 kg·m/s

Answer:

x = 6.

Step-by-step explanation:

Because the the 2 angles are equal

4 / (x + 2) = 3 / (9-3)

4/(x+2) = 3/6

4 / (x + 2) = 1/2

x + 2 = 4*2 = 8

x = 8 - 2 = 6.

Answer:

State A has 27 screens and state B has 21 screens.

Step-by-step explanation:

Let the number of screens in state B be 'x'.

Given:

Number of screens in state A is 6 more than state B

Total number of screens = 48.

Now, as per question:

Number of screens in state A = 6 more than state B.

Framing in equation form, we get:

Number of screens in state A = [tex]6+x[/tex]

Now, total number of screens is the sum of the screens in state A and number of screens in state B. Therefore,

Total number of screens = 48

Number of screens in state A + Number of screens in state B = 48

Substituting the given values, we get:

[tex]6+x+x=48\\\\6+2x=48\\\\2x=48-6\\\\2x=42\\\\x=\frac{42}{2}=21[/tex]

So, state B has 21 screens.

State A has = 6 + 21 = 27 screens.

Therefore, state A has 27 screens and state B has 21 screens.

Answer:

Step-by-step explanation:

Using the formula of derivative, it can be easily shown that, [tex]\frac{d f(x)}{dx} = 2[/tex] where [tex]f(x) = x^{2}[/tex].

Here we need to show that as per the instructions in the given table.

Δy = f(x + Δx) - f(x) = f(1 + 0.01) - f(1) = [tex](1 + 0.01)^{2} - 1^{2} = 0.0201[/tex].

In the above equation, we have put x = 1 because we need to find the slope of the line tangent at x = 1.

Hence, dividing Δy by Δx, we get, [tex]\frac{0.0201}{0.01} = 2.01[/tex].

Let's examine this taking a smaller value.

If we take Δx = 0.001, then Δy = [tex]1.001^{2} - 1^{2} = 0.002001[/tex].

Thus, [tex]\frac{0.002001}{0.001} = 2.001[/tex].

The more smaller value of Δx is taken, the slope of the tangent will be approach towards the value of 2.

We can see here that the slope of the line tangent to the function at x = 1 is 2.001 ≅ 2.

We can use the formula of derivative: [tex]\frac{df(x)}{dx} = 2[/tex]

Looking at the instructions in the given table, we have:

Δy = f(x + Δx) - f(x) = f(1 + 0.01) - f(1) = (1 + 0.01)² - 1² = 0.0201

In the above written equation, x = 1 because we need to find the slope of the line tangent at x = 1.

Thus, Δy divided by Δx, we get, 0.0201/0.01 = 2.01

If we take Δx = 0.001, then Δy = 1.001² - 1² = 0.002001

So, we have: 0.002001/0.001 = 2.001

We can see here that the more smaller value of Δx is taken, the slope of the tangent will be approach towards the value of 2.

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Answer:

Step-by-step explanation:

The car's value was $61,412.50  in the year 2006.

x = no. of years since 2000.

Acc. to ques,

100,000 × (0.85)ˣ = 61,412.50

(0.85)ˣ = 0.614125.

ln((0.85)ˣ) = ln(0.614125).

x × ln(0.85) = ln(0.614125).

x = ln(0.614125) / ln(0.85).

x = 5.832 ≈ 6

Answer:

168 members are on the marching band but not part of the percussion.

Step-by-step explanation:

Given:

The high school marching band has 196 members,and 28 of them are a part of the percussion.

Now, to find the members on the marching band but not part of the percussion.

Total members of marching band = 196.

Members of them who part of percussion = 28.

So, to get the members of the marching band who are not the part of the percussion we subtract members of them who part of percussion from total members of marching band:

[tex]196-28[/tex]

[tex]=168.[/tex]

Therefore, 168 members are on the marching band but not part of the percussion.

ANSWER= 0.9772

STEP-BY-STEP EXPLANATION:

We are assuming that there is an underlying distribution of package weights,even though we don´t speciify the shape of that distribution.

Letting [tex]x_{i}[/tex] denote the ith package weight and S=[tex]x_{1} +....x_{100}[/tex] we are trying to find P(S ≤ 1700)

We know that the distribution of S is approximately normal with mean nцХ and variance по²Х

S≈N( 100 * 15, 100 * 10² ) = N (1500.10000) (note that they gave us the standar deviation aove; variances add, so we need to square this). Finally,

P(S ≤ 1700) = P ([tex]\frac{S-1500}{\sqrt{10000} }[/tex] ≤ [tex]\frac{1700 - 1500}{\sqrt{10000} }[/tex])

≈P (Z≤2) = 0.9772

Answer:

  about 5.52%

Step-by-step explanation:

If Lucius wants an account value of $2000 after 3 years, she can find the interest rate by solving the polynomial ...

  550x³ +600x² +650x -2000 = 0

This equation has one positive real root. It is irrational, so must be found using the rather complicated cubic solution formula or, more simply, a graphing calculator. The latter shows the root to be near 1.05516.

Lucius needs an interest rate of ...

  (1.05516 -1)×100% = 5.516%

The interest rate needed for a balance of $2000 after 3 years is about 5.52%.

Answer:

The answer to your question is below

Step-by-step explanation:

f(x) = 2x + 5

To solve letter a, just multiply each term of f(x) by 3 and subtract 2.

a) 3f(x) - 2 = 3(2x + 5) - 2

                 = 6x + 15 - 2

               = 6x + 13

To f(x) subtract twice g(x)

b) f(x) - 2g(x) = 2x + 5 - 2(x² - 3x + 2)

                    = 2x + 5 - 2x² + 6x - 4

                    = -2x² + 8x + 1

Multiply 5 by each term of f(x) and divide it by g(x)

c)      [tex]\frac{5f(x)}{g(x)} = \frac{5(2x + 5)}{x^{2} - 3x + 2}[/tex]  

                = [tex]\frac{10x + 25}{x^{2}-3x + 2}[/tex]

Answer:

Step-by-step explanation:

You swim at 3 km/hr with your body perpendicular to a stream with a current of 5 km/hr.

If your actual velocity is the vector sum of the stream's velocity and your swimming velocity, it means that your actual velocity is the resultant velocity. Let R represent the resultant velocity. It means that

R² = 3² + 5² = 9 + 25

R² = 34

Taking square root of the left hand side and the right hand side of the equation, it becomes

R = √34 = 5.83 km/hr.

Final answer:

To find the swimmer's actual velocity in a stream where the swimmer's velocity is 3 km/hr and the stream's velocity is 5 km/hr, we use the Pythagorean theorem, resulting in an actual velocity of approximately 5.83 km/hr.

Explanation:

The question involves calculating the actual velocity of a swimmer moving in a stream. The swimmer swims at a rate of 3 km/hr perpendicular to the stream, while the stream itself has a current of 5 km/hr.

To find the swimmer's actual velocity when these two vectors are combined, we use the Pythagorean theorem, as the velocities are perpendicular to each other.

Let the swimmer's velocity be represented by Vswimmer = 3 km/hr and the stream's velocity by Vstream = 5 km/hr.

The actual velocity (Vactual) is the vector sum of these two velocities. Since they are at right angles to each other, Vactual can be calculated as [tex]\sqrt{((Vswimmer)^2 + (Vstream)^2)[/tex] .

Substituting the values gives Vactual =[tex]\sqrt{(3^2 + 5^2)} = \sqrt{(9 + 25)} = \sqrt{(34),[/tex] which approximately equals 5.83 km/hr.

Therefore, the actual velocity of the swimmer, taking into account the stream's current, is approximately 5.83 km/hr.

Answer:

Mrs. Fowler will get [tex]9[/tex] free pizza. And she needs two more coupon for the next pizza.

Step-by-step explanation:

Given that pizza stand gives a free pizza for every [tex]8[/tex] coupons.

And Mrs. Fowler has [tex]78[/tex] coupons.

Part (a)

How many free pizzas can Mrs. Fowler get if she has [tex]78[/tex]coupons?

We will divide total number of coupons [tex]78[/tex] by [tex]8[/tex] coupons.

[tex]\frac{78}{8}=9\frac{6}{8}[/tex]

When we divide we get quotient as [tex]9[/tex], with a remainder of [tex]6[/tex]. So, Mrs. Fowler will get [tex]9[/tex] free pizza.

Now, part (b)

If  Mrs. Fowler adds two more coupons that will turn remainder [tex]6[/tex] into [tex]6+2=8[/tex].

So, she can have next pizza.

Answer:

31.67

Step-by-step explanation:

12 2/3 X 2 1/2

we begin by converting this into improper fractions,

= 38/3 * 5/2

= 95/3

= 31.67

Answer:

[tex]\dfrac{5}{10}\ miles\ and\ \dfrac{6}{10}\ miles[/tex]

Step-by-step explanation:

Given:

The fractions are given as:

[tex]\dfrac{1}{2}\ and\ \dfrac{3}{5}[/tex]

The denominators of the first fraction is 2 and that of the second fraction is 5.

In order to find the common denominator for 2 and 5, we have to find the least common multiple of each of the numbers.

Multiples of 2 = 2, 4, 6, 8, 10, 12,....

Multiples of 5 = 5, 10, 15, 20, 25, 30,....

Therefore, the least common multiple of 2 and 5 is 10. So, the common denominator is 10.

Now, multiply the numerator and denominator of each fraction by the same suitable number such that the denominator becomes 10.

So, for the first fraction, 2 is in the denominator.

So, 2 when multiplied by 5 gives 10.

So, we multiply the numerator and denominator of first fraction by 5. This gives,

[tex]\dfrac{1}{2}=\dfrac{1\times 5}{2\times 5}=\dfrac{5}{10}[/tex]

Now, for the second fraction, 5 is in the denominator.

So, 5 when multiplied by 2 gives 10.

So, we multiply the numerator and denominator of first fraction by 2. This gives,

[tex]\dfrac{3}{5}=\dfrac{3\times 2}{5\times 2}=\dfrac{6}{10}[/tex]

Therefore, the new fractions after making the denominators same are:

[tex]\dfrac{5}{10}\ and\ \dfrac{6}{10}[/tex]

So, the miles covered in fraction with same denominators are:

[tex]\dfrac{5}{10}\ miles\ and\ \dfrac{6}{10}\ miles[/tex]

Final answer:

To calculate the total number of cherries that the bakery started with, multiply the number of pies by cherries per pie and then add the ones thrown away, resulting in 3026 cherries.

Explanation:

The question asks how many cherries the bakery started with before making the cherry pies. To find the answer, we multiply the number of cherry pies by the cherries used per pie and then add the number of cherries thrown away.

Multiply the number of pies (26) by the number of cherries used for each pie (115).

The result from step 1 gives the number of cherries used to make the pies.

Add the number of cherries thrown away (36) to the result from step 2.

The sum from step 3 is the total number of cherries the bakery started with.

Let's do the calculations:
26 pies × 115 cherries per pie = 2990 cherries
2990 cherries + 36 bad cherries = 3026 cherries

Therefore, the bakery started with 3026 cherries.

Answer: c. sampling error

Step-by-step explanation:

Since, the sample is a subset of population , so there are chances for unavoidable variation in sample mean from the population mean that varies from sample to sample .

This variation is known as sampling error.

∴ The difference between the value of the sample statistic and the value of the corresponding population parameter is called the sampling error .

Hence,the correct answer is c. sampling error .

The difference between the sample statistic and the population parameter is known as the sampling error. This error occurs due to the sample selected being unrepresentative of the entire population.

The difference between the value of the sample statistic and the value of the corresponding population parameter is referred to as the sampling error. This definition directly fits the option c. Listed among the given options. A sampling error is a discrepancy that occurs due to an unrepresentative selection of observations from the whole population. The nature of statistical sampling means there will always be some level of uncertainty or error because we are making estimates based on a sample from a larger population, rather than the entire population itself.

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Final answer:

To find the length of each piece of ribbon, divide the total length of 2.65 feet by 5, resulting in 0.53 feet per piece, or approximately 6 inches after converting to a more convenient measurement.

Explanation:

The student's question involves the division of a length of ribbon into equal pieces. Miss Alvarez has a piece of ribbon that is 2.65 feet long and she cuts it into 5 equal pieces. To estimate the length of each piece, we would divide the total length of the ribbon by the number of pieces.

The calculation would be: 2.65 feet ÷ 5 pieces = 0.53 feet per piece. If we want a more convenient measure, we could convert feet to inches since there are 12 inches in a foot, resulting in approximately 6.36 inches per piece (0.53 feet × 12 inches/foot).

As an estimate and for ease of measurement, we might round this to the nearest whole number, suggesting that each piece of ribbon is approximately 6 inches in length.

Answer: The probability of drawing 5 cards in either ascending or descending order out of the deck of 52 standard playing cards is 0.84%.

Step-by-step explanation: We have the following cards in a deck: 1(ace), 2, 3, 4, 5, 6, 7, 8, 9, 10, 12(Jack), 13(Queen), 14(King) (thirteen different in total). There are 4 copies of each of them yielding 52 cards in total. First to draw all of the cards in the ascending order all of the drawn cards need to be different. Imagine you have 13 piles of 4 identical cards. Let us calculate the number of ways you can select 5 different ones (the order matters). First you select 5 different piles (this secures that each card is different) and this is possible to do in [tex]\frac{13!}{(13-5)!}[/tex] (we use the formula for variations since the order matters). Now, each card in the pile can be selected in [tex]4[/tex] different ways so the total number of sequences with [tex]5[/tex] different cards is [tex]4^5\frac{13!}{(13-5)!}[/tex]. Now we select out of these sequences the clases of those that contain exactly the same cards but in different order. Only 4 of the sequences within the same class will be in ascending order out of 4*5! which is the total number of the sequences within the class! This means that we have to multiply our total number of sequences of 5 different cards by [tex]\frac{4}{4\cdot 5!}=\frac{1}{5!}[/tex] and this yields the final answer of total number of ascending sequences to be

[tex]4^5\frac{13!}{(13-5)!5!}.[/tex]  

The total number of possible ways to draw 5 out of 52 cards is just

[tex]\frac{52!}{(52-5)!}.[/tex]

This yields for the probability

[tex]\frac{4^5\frac{13!}{(13-5)!5!}}{\frac{52!}{(52-5)!}}=0.42\%[/tex]

Exactly the same calculation applies for the descending order. So the probabilty of the cards being in either ascending or descending order is just the sum of these two (the events are mutually exclusive, you cannot have both the ascending and descending order at the same time) yielding the final probability of [tex]0.84\%[/tex].

Answer:

this is a left tailed test

   Null hypothesis,  [tex]H_{0} :[/tex] σ = 40 seconds

   Alternate hypothesis, [tex]H_{a} :[/tex] σ < 40 seconds.

Step-by-step explanation:

i) the standard deviation of duration times in seconds of the old faithful geyser is less than 40 sec. identify the null hypothesis and alternative hypothesis in symbolic form

ii) this is a left tailed test

   Null hypothesis,  [tex]H_{0} :[/tex] σ = 40 seconds

   Alternate hypothesis, [tex]H_{a} :[/tex] σ < 40 seconds.

Answer:

Bb

Step-by-step explanation:

Final answer:

After applying a 20% discount and a 10% service fee to a pair of shoes originally priced at $75, Martinez ends up saving 12% from the original price.

Explanation:

Martinez is looking to calculate the final price of a pair of shoes after applying a 20% discount and a 10% service fee. She wants to know the overall percentage saved from the original price. First, let's calculate the discount: $75.00 × 0.20 = $15.00. Thus, the discounted price is $75.00 - $15.00 = $60.00. Next, we add the service fee on the discounted price: $60.00 × 0.10 = $6.00. Therefore, the total cost after the discount and service fee is $60.00 + $6.00 = $66.00.

To find the percent decrease from the original price, we can use the formula 'Percent Decrease = ((Original Price - Final Price) / Original Price) × 100%'. Substituting the respective values, we get: ((75 - 66) / 75) × 100% = 12%. Martinez saved 12% off the original price of the shoes after all the adjustments.

Answer:

Leo is 1 year old.

Step-by-step explanation:

Given:

Lily's age = 5

Leo's age = [tex]3x-14[/tex]

we need to find the Leo's age.

Solution:

Leo's age = [tex]3x-14[/tex]

where x ⇒ Lilly age

But Lilly's age = 5 years (given)

So we will substitute the value of x as 2 in Leo's age expression.

On Substituting we get;

Leo's age = [tex]3x-14 = 3\times5-14 = 15-14 = 1\ year[/tex]

Hence Leo is 1 year old.

Answer:

x = 6.54 cm

h = 3.27 cm

Step-by-step explanation:

Volume of open top box

V = 140 cm³

Dimensions of the box

It is a base square box then area of the base of side x is

A(b) = x²

And we will call h the height of the box then

V = 140   ⇒    140 = x²*h     ⇒   h = 140/ x²

We have to calculate the area of the 4 sides

Area of one side is  As = x*h        ⇒ total area of 4 sides = 4 x* 140/x²  

Ats  =  560/x

Then Total area of the box is

A(t)  =  Area of the base  +  Total area of sides

A(x)  =   x²  +   560/x

Taking derivatives on both sides of the equation we get:

A´(x)  =  2x   -  560/x²

A´(x)  =  0     ⇒    2x   -  560/x² = 0   ⇒   2x³  -  560  = 0

x³  =  280     ⇒    x  = 6.54 cm

And h      h  =  140/ (6.54)²    ⇒ h =  140/ 42.77    h  = 3.27 cm

Answer:

The weight of the seventh linebacker is = 214 lb.

Step-by-step explanation:

Given:

Mean of 7 linebackers = 236 lb

The weights of first 6 linebackers are:

215 lb, 305 lb, 265 lb, 196 lb, 221 lb and 236 lb

To find the weight of seventh linebacker.

Solution:

Let the weight of the seventh linebacker be = [tex]x[/tex]

The mean of 7 line backers will be given as:

⇒ [tex]\frac{215+305+265+196+221+236+x}{7}[/tex]

The mean of the 7 linebackers is given = 236 lb

Thus, the equation to find [tex]x[/tex] will be :

[tex]\frac{215+305+265+196+221+236+x}{7}=236[/tex]

Simplifying.

[tex]\frac{1438+x}{7}=236[/tex]

Multiplying both sides by 7.

[tex]7.\frac{1438+x}{7}=236(7)[/tex]

[tex]1438+x=1652[/tex]

Subtracting both sides by 1438.

[tex]1438-1438+x=1652-1438[/tex]

∴ [tex]x=214[/tex]

Thus, the weight of the seventh linebacker is = 214 lb.

Answer:

  d.  300%

Step-by-step explanation:

The given relation is ...

  60%·A = 20%·B

Dividing by 20%, we see that ...

  3·A = B

Of course, 3 = 3×100% = 300%, so B is 300% of A.

First, let's write the given condition in the form of an equation. If 60% of A is 20% of B, it can be written as:

60/100 * A = 20/100 * B

In order to proceed, we begin simplifying the equation by eliminating the fractions. This can be achieved by multiplying both sides of the equation by 100, turning our equation into:

60A = 20B

Following this, we can further simplify by solving for B. This involves dividing the equation through by 20A which yields:

B = 60A / 20

This simplification results in the following expression:

B = 3A

This means that B equals three times the value of A. However, we have been asked to express B in terms of what percent it is of A. Knowing that 'percent' may be understood as 'per hundred', this corresponds to converting the ratio to a percentage.

We can safely say therefore that B is 300% of A which corresponds to choice (d) among our original options.

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Answer:

A frequency distribution lists the number of occurrences of each category of​ data, while a relative frequency distribution lists the proportion of occurrences of each category of data.

Explanation:

A "frequency distribution" is one of the ways in organizing a data, either by listing the information, putting them in a table or showing them in a graph. The items in the list (distinct values) are then counted when it comes to the number of times they've occurred.

Thus, this explains the first answer, "number."

On the other hand, a "relative frequency distribution" refers to the proportion of the overall number of observations in a particular category.  You can get this by dividing each frequency with the total number of data in a sample.

Thus, this explains the second answer, "proportion."

A frequency distribution lists the number of occurrences for each category of data, whereas a relative frequency distribution provides the proportion of occurrences for each category in relation to the total number of data points. Histograms are a common tool to visualize these distributions, with the heights of bars representing either frequency or relative frequency.

The frequency distribution primarily deals with the number of occurrences of each category of data. For instance, in a class of 20 students, if the question is how many students scored in a particular range, the frequency distribution helps identify this - telling us how many students achieved each possible score.

In contrast, a relative frequency distribution showcases the proportion of the total number of data points that each category represents. So, instead of just telling you how many students achieved each score, it would express these amounts as a ratio or percent of the 20 total students, giving you a relative perspective of the categories.

An example of these principles might be visualized in a histogram: a type of graph that can express either frequency or relative frequency. The horizontal axis represents the categories of data (such as score ranges), while the vertical axis reflects frequency or relative frequency, displaying these values through the heights of bars along the graph.

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Answer:

[tex] r =\frac{2437points}{25 years} =97.45 \frac{points}{year}[/tex]

So then we have that Morten Andersen scored on average 97.45 points per year in his career.

Step-by-step explanation:

Assuming the following table on the figure attached.

We see that the career points for Morten Andersen was 2437. That include all the points over alll the years the he played in the NFL.

Since the total years played by Morten Andersen was 25 we can write the following equation:

[tex] 25 r =2437[/tex]

Where [tex] r[/tex] represent the rate of points average per year.

If we solve for r from the last equation we can divide both sides of the equation and we got:

[tex] r =\frac{2437points}{25 years} =97.45 \frac{points}{year}[/tex]

So then we have that Morten Andersen scored on average 97.45 points per year in his career.

Answer: The area of triangle ΔXYZ is 12 square inches.

Step-by-step explanation:

Since we have given that

RS = 3 inches

XY = 2 inches

Area of ΔRST = 27 in²

Since ΔRST is similar to ΔXYZ.

So, using the "Area similarity theorem":

[tex]\dfrac{\Delta RST}{\Delta XYZ}=\dfrac{RS^2}{XY^2}\\\\\dfrac{27}{\Delta XYZ}=\dfrac{3^2}{2^2}\\\\\dfrac{27}{\Delta XYZ}=\dfrac{9}{4}\\\\\Delta XYZ=3\times 4=12\ in^2[/tex]

Hence, the area of triangle ΔXYZ is 12 square inches.

The area of triangle XYZ is found by squaring the ratio of the corresponding sides of the similar triangles and multiplying it by the area of the larger triangle RST. With the side length ratio of 2:3, the area ratio is (2/3)², resulting in an area of 12  in² for triangle XYZ.

The student's question involves determining the area of a smaller similar triangle (XYZ) given the area of the larger similar triangle (RST) and the lengths of corresponding sides. To solve, we utilize the property that similar triangles' areas are proportional to the square of the ratio of their corresponding sides.

Given:
Length of RS in triangle RST = 3 inches
Length of XY in triangle XYZ = 2 inches
Area of triangle RST (A1) = 27  in²

We establish the ratio of their sides as 2 inches (XY) / 3 inches (RS), which simplifies to 2/3. The ratio of their areas would then be (2/3)² because the area of similar triangles scales with the square of the ratio of their corresponding linear dimensions. Hence, the Area of triangle XYZ (A2) will be A1 × (2/3)².

A2 = 27 in² × (2/3)2 = 27 × 4/9 = 12 in².

The area of triangle XYZ is 12 in².

-8bits is equivalent yo 1 byte

-bit is(0 or 1)

So each pixel requires 3 bytes

Primary colors are RGB(red,green and blue),so each color represent one byte.

The frame size is:

1280×1024=1310720 pixels

So that the frame contained 1310720 pixels

The size of the frame buffer is equal to the product of RGB and frame pixels:

=3 × 1310720

=3932160 bytes

The minimum size of the frame buffer to store a frame of 1280 x 1024 pixels, with 8 bits used for each of the three primary colors (red, green, blue) per pixel, is 3932160 bytes.

When calculating the size of a frame buffer, you want to take into account the number of pixels in the frame, the number of bits used to represent each primary color per pixel, and the number of primary colors. In this case, the frame is 1280 x 1024 pixels, and 8 bits are used for each of the three primary colors (red, green, blue) per pixel.

Therefore, the calculation will be as follows:

So, the minimum size of the frame buffer to store a frame in this context would be 3932160 bytes.

Learn more about Frame Buffer Size here:

https://brainly.com/question/32733356

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