A model airplane flew the distance of 330 feet in 15 seconds. Select ALL the unit rates that are equivalent to the speed of the model airplane.

Answer:

1/24 = 0.041666666...

Step-by-step explanation:

when rolling 4 dice, we have

6 × 6 × 6 × 6 = 6⁴ = 1296

different possible outcomes (each die has 6 possible outcomes).

so, the probability of any particular pattern is then

1/1296.

we need to find how many patterns there are to represent the desired result of 2 identical odd numbers combined with 2 identical even numbers.

there are on every die 3 out of 6 options for an odd number, and the other 3 out of 6 options for an even number.

when we roll 2 dice, the patterns for 2 identical odd numbers are

1 1

3 3

5 5

so, 3 out of the possible 36.

similar for 2 identical even numbers.

2 2

4 4

6 6

3 out of the possible 36.

so, combining this together for a roll of 4 dice, we get then

3 × 3 out of the possible 36 × 36

9 out of the possible 1296 patterns.

that means the probability (desired over total possible cases) for a specific combination of 2-and-2 dice is

9/1296 = 1/144 = 0.006944444...

but there are 4! / (2! × 2!) = 6 possibilities (pick 2 out of 4, where the sequence of the picked ones does not matter) to pick 2 dice out of 4 and to show the same pattern across the 4 dice, as e.g. for the basic pattern 1 1 2 2 we can have

1 1 2 2

1 2 1 2

1 2 2 1

2 1 2 1

2 1 1 2

2 2 1 1

all of the 9 patterns have these 6 combination possibilities.

so, we need to multiply the individual pattern probability by 6 for the total probability

1/144 × 6 = 6/144 = 1/24 = 0.041666666...

Answer:

6a^5

Step-by-step explanation:

3a^2*2a^3

3×2+a^2×a^3

6a^5

Answer:

The answer is 6a⁵.

Step-by-step explanation:

You have to use Indices Law,

\( {a}^{m} \times {a}^{n} \: ⇒ \: {a}^{m + n} \)

So for this question :

\(3 {a}^{2} \times 2 {a}^{3} \)

\( = (3 \times 2) \times ( {a}^{2 + 3}) \)

\( = 6 \times {a}^{5} \)

\( = 6 {a}^{5} \)

The system has exactly one solution, which is (p, q) = (-0.2118, -8.0).

We are given the system of equations:

1.7p - 0.34q = 0

0.17(q+1) - 0.85(p-1) = 0

We can simplify the second equation by distributing the 0.17 and 0.85 terms:

0.17q + 0.17 - 0.85p + 0.85 = 0

0.17q - 0.85p = -0.72

Now we have two equations in two variables, which we can solve using substitution or elimination. We will use elimination here.

Multiplying the first equation by 5, we get:

8.5p - 1.7q = 0

Multiplying the second equation by 2, we get:

0.34q - 1.7p = -1.44

Adding these two equations, we get:

6.8p = -1.44

p = -0.2118

Substituting this value of p into either of the original equations, we get:

1.7(-0.2118) - 0.34q = 0

q = -8.0

So the system has exactly one solution, which is (p, q) = (-0.2118, -8.0).

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No, AAA doesn't mean triangles are congruent.

Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create a similar appearance. They are in alignment with one another when moved.

CPCT means “Corresponding Parts of Congruent Triangles”. After proving triangles congruent, the remaining dimension can be predicted without actually measuring the sides and angles of a triangle.

Different rules of congruency are as follows.

1-SSS (Side-Side-Side)

2-SAS (Side-Angle-Side)

3-ASA (Angle-Side-Angle)

4-AAS (Angle-Angle-Side)

5-RHS (Right angle-Hypotenuse-Side)

Thus, there AAA doesn't mean triangles are congruent.

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Answer:

7.5 miles

Step-by-step explanation:

1 mile=1.6 kilometer

12/1.6=7.5

Answer:

Step-by-step explanation:

A=90-64=26 degrees

Then just checking side lengths

sin26/5.4=sin64/AC

AC=5.4sin64/sin26=11.07

sin90/AB=sin26/5.4

AB=5.4sin90/sin26=12.31

So we can confirm that the fourth answer is correct.

Answer:

Expected number of winners with 52 contestants:52*5/13 = 20.The experiment result is almost twice less (12 vs 20).In order to change the results of experimental probability some of the letters may need swapped, (probably the letters are in alphabet order) but for this we need more data.

Step-by-step explanation:

Experimental probability is probability that is determined on the basis of the results of an experiment repeated many times. Theoretical probability is probability that is determined on the basis of reasoning. Probability is a value between (and including) zero and one.

also whats your discord

In order to determine the exact nature of the distribution, Professor X would need to analyze the data in more detail, for example, by creating a histogram or other visual representation of the grades, and conducting statistical tests to determine the nature of the distribution.

If Professor X finds that the grades on the first exam for their statistics class either did really well or really poorly, it suggests that the distribution of grades is bi-modal, meaning there are two distinct peaks in the distribution. This means that some students did very well on the exam and scored high grades, while others did very poorly and scored low grades, with very few students scoring grades in between these two groups.

A bi-modal distribution is not a common occurrence in a typical exam setting, as most exams tend to have a normal or bell-shaped distribution with a single peak, where the majority of students score around the average or mean grade. The bi-modal distribution found by Professor X could be due to a variety of factors, such as students having widely differing levels of prior knowledge, or students' varying levels of preparation for the exam.

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If F is a field then every ideal in F[x] is a principal ideal. Facts: An ideal I in a commutative ring with identity R is a subset of R such that: (i) 0∈I, (ii) I is closed under addition and (iii) if a∈I and r∈R, then ar and ra∈I, i.e. I is an “ideal” with respect to multiplication in R.

An ideal is principal if it is generated by a single element. A maximal ideal of a commutative ring with identity R is an ideal M such that there is no proper ideal properly containing M. A prime ideal P of a commutative ring with identity R is an ideal such that if ab∈P, then a∈P or b∈P. The notation Z stands for the ring of integers and F stands for a field. If F is a field then every ideal in F[x] is a principal ideal.

Proof: Consider an ideal I in F[x], the set of polynomials in x with coefficients from F. Case 1: If I = {0} (the zero ideal), then I is a principal ideal generated by 0. Thus, assume I≠{0}. Case 2: Pick a non-zero polynomial f(x)∈I with minimum degree among non-zero elements of I. We now show that I is a principal ideal generated by f(x). Let g(x) be an arbitrary element of I. We need to show that g(x)∈(f(x)). Using the division algorithm of polynomials, there exist unique polynomials q(x) and r(x) in F[x] such that

g(x) = f(x)q(x) + r(x) and either

r(x) = 0 or deg(r)< deg(f). Since I is an ideal and f(x)∈I, we have that f(x)q(x)∈I. Thus,

g(x) - f(x)q(x) = r(x)∈I. Case 2a:

If r(x) = 0, then

g(x) = f(x)q(x)∈(f(x)) and we are done. Case 2b: Otherwise, by the minimality of the degree of f(x) among non-zero elements of I,  deg(r)≥deg(f). But this contradicts the fact that deg(r)< deg(f). Therefore, we must have that

r(x) = 0. Thus,

g(x) = f(x)q(x)∈(f(x)). Therefore, every ideal in F[x] is a principal ideal.

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The validity of short forms may be reduced because they contain fewer items compared to the full-length version. Short forms of tests or questionnaires are often used in research and clinical settings due to their convenience and efficiency.

This means that the short form may not fully capture the construct being measured and may not accurately reflect the individual's true scores. Additionally, the items selected for the short form may not be representative of the full range of the construct, leading to bias and limited generalizability.

Therefore, researchers and clinicians should consider the trade-offs between convenience and validity when deciding to use short forms.

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The dimensions of the page that will maximize the printed area are 2 cm by 1 cm.

To maximize the printed area of the page, we need to find the dimensions that will leave the largest rectangular area within the given margins. Let's assume the width of the page is x and the height is y.

From the given information, we know that the total area of the page, including the margins, is 96 square cm. Therefore, we can write the equation: (x + 2)(y + 1) = 96.

Expanding this equation, we get xy + x + 2y + 2 = 96.

Rearranging the terms, we have xy + x + 2y = 94.

Now, we need to maximize the printed area, which is given by xy. To do this, we can rewrite the equation as: xy = 94 - x - 2y.

To find the maximum value, we can differentiate this equation with respect to x and y, and set the derivatives equal to zero.

Differentiating with respect to x, we get y - 1 = 0, which gives us y = 1.

Differentiating with respect to y, we get x - 2 = 0, which gives us x = 2.

Therefore, the dimensions of the page that will maximize the printed area are 2 cm by 1 cm.

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If the mean monthly electric bill for 71 residents of the local apartment is $62 , then the best point estimate is $62 .

In the question ,

it is given that ,

the number of residents in the local apartment complex is = 71

the mean electric bill for the 71 residents = $62 ;

we know that the sample mean is itself called as the best point estimate ;

So , best point estimate for mean monthly electric bill for all residents of local apartment complex will be = mean monthly bill for 71 residents of  local apartment complex which is given as $62 .

Therefore , the best point estimate is $62 .

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Answer:

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

Answer choices:

A. the change of the y-coordinates divided by the change in the x-coordinates

B. be always the location of the line in the xy coordinate system-that is, where the line hits the y-axis.

C. always be the location of the line in the xy coordinate system where the line hits the x-axis

D. the initial value of the output variable when the input variable is time. The y-intercept has an x-coordinate of zero, so if the input variable is time, the y-intercept is referred to as the starting value.

The general solution of the given system is x(t) = c₁e^(7t) + c₂te^(9t) + c₃e^t, where c₁, c₂, and c₃ are arbitrary constants.

To find the general solution of the given system, we need to solve the differential equation x' = A*x, where A is the given matrix [0 0 0; 7 0 0; 9 1 0]. The characteristic equation is det(A - λI) = 0, where I is the identity matrix. Solving this equation, we find that the eigenvalues are λ₁ = 0, λ₂ = 7, and λ₃ = 9.

For each eigenvalue, we find the corresponding eigenvector and construct the solution using the form x(t) = c₁e^(λ₁t)v₁ + c₂te^(λ₂t)v₂ + c₃e^(λ₃t)v₃, where v₁, v₂, and v₃ are the eigenvectors associated with the eigenvalues.

The constants c₁, c₂, and c₃ can be determined based on initial conditions or additional constraints.

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If the scale upon which points a, b, c, and d are shown is an ordinal scale, we can meaningfully say that the order of the points represents the order of the underlying variable being measured.

When using an ordinal scale, the order of the points (a, b, c, and d) represents the relative ranking or ordering of the underlying variable being measured. This means we can determine which point is higher or lower in the ranking. For example, if the variable being measured is satisfaction level, we can say that point "c" represents higher satisfaction than point "a" or "b." However, with an ordinal scale, we cannot make precise quantitative comparisons between the points or determine the exact magnitude of the differences between them. The scale only allows us to establish the relative order or ranking of the points.

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Answer:

\(\frac{\sqrt{2} }{6}\)

Step-by-step explanation

\(\frac{1}{\sqrt{18} } \\\frac{1}{\sqrt{18} } *\frac{\sqrt{18} }{\sqrt{18} } \\\frac{1*\sqrt{18} }{(\sqrt{18} )^2} \\\frac{1\sqrt{18} }{18} \\\frac{3\sqrt{2} }{18} \\\frac{\sqrt{2} }{6}\)

The following binary number has the value of 157 in decimal form.

Step 1: Compose the binary number in writing. 10011101

Multiplying each binary digit by the corresponding power of two in step two:

1x27 + 0x26 + 0x25 + 1x24 + 1x23 + 1x22 + 0x21 + 1x20

Solve the powers in Step 3:

1x128+0x64+0x32+1x16+8+4+0x2+1x1=128+0 + 0 + 0 + 16+8+4+0 + 0 + 1

Step 4: Add the figures listed above:

128 + 0 + 0 + 16 + 8 + 4 + 0 + 1 = 157.

A binary number is a number that is expressed in the binary system or base 2 numeral system, according to digital technology and mathematics. It talks about numerical values.by the two distinct digits 1 (one) and 0 (zero). The base-2 system is the positional notation that uses 2 as the radix.

A number that has been divided into a whole and a fraction is called a decimal. To express the numerical value of entirely and partially entire quantities between integers, decimal numbers are used.

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Answer:

318+954

Step-by-step explanation:

divide 1272 by 2 to get what they would cost if they were the same amount then divide that by 2 to get 318 times that by 3 to get 954 and add 318 to get 1272

The required cost of the couch and coffee table is $848 and $424 respectively.

Given that,
A couch and coffee table cost a total of $1272. The cost of the couch is two times the cost of the coffee table.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
let the cost of the coffee table be x,
Now the cost of the couch  = 2x
According to the question,
2x + x = 1272
x = 424
now,
Cost of the couch = 424 [2] = 848

Thus, the required cost of the couch and coffee table is $848 and $424 respectively.

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The width of each class interval from the given grouped frequency distribution table is 9.

In a frequency distribution, the numerical width of a class is referred to as the class interval. Data is organised into classes in a grouped frequency distribution. The class interval is determined by the difference between the upper and lower class limits.

The give class intervals are 20-29, 30-39, 40-49 and 50-59.

The size, or width, of a class interval is the difference between the lower and upper class boundaries and is also referred to as the class width, class size, or class length.

So, class width = Upper class - Lower class

29-20=9

39-30=9

Therefore, the width of each class interval is 9.

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An estimate for the total volume of food and water you've ingested in the last day is 3000-5000 milliliters. On average, the heart pumps about 5 liters of blood per minute. 10-20% or more error I'm expecting. Calculating heart blood volume compared to food and drink consumption is crucial for understanding circulation and liver function.

D.1 Estimating the amount of food and water consumed in a day can be difficult without specific measurements, but a rough estimate can be made based on typical intake amounts. On average, a person may consume 2-3 liters of water and 1000-2000 calories per day, resulting in an estimated total volume of 3000-5000 milliliters.

D.2 The amount of blood pumped by the heart varies from person to person and depends on factors such as heart rate and overall health. On average, the heart pumps about 5 liters of blood per minute, which is much larger than the estimated volume of food and water intake.

D.3 Estimating food and water intake and blood flow is prone to error due to variability and uncertainties in personal measurements. Individuals' habits, health, and physical activity levels can affect these estimates, potentially resulting in a significant error of 10-20% or more.

D.4 The calculation of the heart's blood volume compared to food and drink consumption is crucial for understanding the circulation system and liver role.

The liver processes nutrients, detoxifies, and produces blood components, while the heart is responsible for circulating blood throughout the body. The vast difference in volume between the two is emphasized, emphasizing the heart's crucial role in maintaining circulation.

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Using the answers possible, you could pick x=0 and see if 0 work.  

-3 + | 0-2 | > 5

 -3 + | -2 | > 5

      -3 + 2 > 5

             -1 > 5

this is false, so any answer that includes 0 is not correct

this eliminates "-6 < x < 10" and "x > -6 or x < 10" since they both include 0.

that leaves only "x < -6 or x > 10".  

And the graph that matches this answer is the very bottom graph with two open circles at -6 and 10 and arrows pointing outward.  

Now if you want to solve the inequality, that'd look like this:

-3 + | x - 2 | > 5

      | x - 2 | > 8    by adding 3 to both sides

this will split into "x - 2 > 8 or x - 2 < -8"

Solving each of those, you'd have "x > 10 or x < -6" which is the answer we previously determined.

Answer: 72.97 Minutes

Step-by-step explanation: We have two cars, A and B, traveling along a straight road. Car A is moving at a constant speed of 77.0 km/h, while car B is moving at a constant speed of 114 km/h. At the starting point (t=0), car B is 45.0 km behind car A.

To figure out how long it takes for car B to catch up and overtake car A, we need to consider their relative speeds. The relative speed is the difference between the speed of car B and the speed of car A.

Relative speed = Speed of car B - Speed of car A

Relative speed = 114 km/h - 77.0 km/h

Relative speed = 37.0 km/h

So, car B is moving 37.0 km/h faster than car A. Now, we need to determine the time it takes for car B to cover the initial distance between them, which is 45.0 km.

To calculate time, we use the formula: Time = Distance / Speed. In this case, the distance is 45.0 km, and the speed is the relative speed of 37.0 km/h.

Time = 45.0 km / 37.0 km/h ≈ 1.2162 hours

Now, let's convert the time to minutes by multiplying it by 60 (since there are 60 minutes in an hour).

Time = 1.2162 hours * 60 minutes/hour ≈ 72.97 minutes

Therefore, it takes approximately 1.2162 hours or 72.97 minutes for car B to catch up and overtake car A.

Hope this helps!

Answer:

\(a \: = \frac{4}{3} \\ b = - \frac{10}{3} \\ c = 4\)

-0.5

Step-by-step explanation:

um bc it is the answer

Answer:

Bc = √63 ft

Step-by-step explanation:

Here, we want to get the length of BC

As we can see, there is a right angled triangle ABC, with 12ft being the hypotenuse and 9 ft the other side

So we want to get the third leg which is BC

we can use the Pythagoras’ theorem here

And that states that the square of the hypotenuse equals the sum of the squares of the two other sides

let the missing length be x

12^2 = x^2 + 9^2

144 = x^2 + 81

x^2 = 144-81

x^2 = 63

x = √63 ft