Tamara and Clyde got different answers when dividing 24 + 7x- 18x2 + 11x-2 by 2x2 – 3x + 1. Analyze their individual

work

The least cοmmοn denοminatοr οf the fractiοn is 24.

Part οf a whοle is a fractiοn. The quantity is written as a quοtient in mathematics, where the numeratοr and denοminatοr are divided. Each is an integer in a simple fractiοn. Whether it is in the numeratοr οr denοminatοr, a cοmplex fractiοn cοntains a fractiοn. The numeratοr and denοminatοr οf a cοrrect fractiοn are οppοsite each οther.

Here the given fractiοn is \($\frac{11}{8}\ \text{and}\ \frac{7}{12}\).

We knοw that Least cοmmοn denοminatiοn οf the fractiοn is lοwest cοmmοn multiple. Then, factοrs οf the denοminatοr

8 = 2*2*2

12=2*2*3

Nοw LCD = 2*2*2*3 = 24.

Hence the least cοmmοn denοminatοr οf the fractiοn is 24.4.

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Answer:

87.96

Step-by-step explanation:

87.9645943

Round to either 0 or the next tenth.

87.9645943

87.964594(0)

87.96459(0)

87.9646(0)

87.965(0)

87.96(0)

87.9645943 rounded to the nearest hundredth is​ 87.96

Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.

Rounding to some place keeps it accurate on the left side of that place but rounded or sort of trimmed from the right in terms of exact digits.

87.9645943

We have to Round to either 0 or the next tenth.

87.9645943

87.964594(0)

87.96459(0)

87.9646(0)

87.965(0)

87.96(0)

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Answer:

Los corredores deben dar 5 vueltas al circuito.

Step-by-step explanation:

En este caso, para saber cuantas vueltas deben dar los corredores al circuito, debes dividir los kilómetros totales de la carrera entre la longitud del circuito:

180/36=5

De acuerdo a esto, la respuesta es que los corredores deben dar 5 vueltas al circuito.

The total number of proper subsets of a set consisting of n elements is 2^n - 1.

A proper subset of a set is a subset that contains fewer elements than the original set. The total number of proper subsets of a set consisting of n elements is given by 2^n - 1.

This is because each element in the set can either be included or excluded in a subset, leading to 2^n possible combinations. However, the empty set (i.e., the subset with no elements) is not considered a proper subset, hence the total number of proper subsets is 2^n - 1.

For example, if n = 3, then the set has 8 possible subsets: {}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, and {1, 2, 3}. Out of these, only 7 are proper subsets. Hence,

the total number of proper subsets of a set consisting of 3 elements is 2^3 - 1 = 7.

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The closest value among the given options to ln(17/3) is 1.466. The value of f(2) is approximately 1.466.

To find the value of f(2), we need to first solve for the particular solution y=f(x) using the given differential equation and initial condition.

We can rewrite the differential equation as dy/dx = x^2 + e^(-y). Separating variables and integrating both sides, we get:

∫e^y dy = ∫x^2 dx + C
e^y = (1/3)x^3 + C
y = ln[(1/3)x^3 + C]

Using the initial condition f(1) = 0, we can solve for the constant C:

0 = ln[(1/3)(1)^3 + C]
C = -1/3

Thus, the particular solution is:

y = ln[(1/3)x^3 - 1/3]

To find f(2), we plug in x=2 into the equation above:

f(2) = ln[(1/3)(2)^3 - 1/3] = ln[8/3 - 1/3] = ln(7/3) ≈ 1.253

Therefore, the value of f(2) is approximately 1.253.
To find the value of f(2) for the given differential equation dy/dx = x^2 + 1/e^y with the initial condition f(1) = 0, first, we need to solve the equation. Since it is a first-order, nonlinear, separable differential equation, we can rewrite it as:

e^y dy = (x^2 + 1) dx

Now, integrate both sides:

∫e^y dy = ∫(x^2 + 1) dx

e^y = (1/3)x^3 + x + C

Apply the initial condition f(1) = 0:

e^0 = (1/3)(1)^3 + 1 + C
1 = 4/3 + C
C = -1/3

So, the particular solution is:

e^y = (1/3)x^3 + x - 1/3

To find f(2), solve for y when x = 2:

e^y = (1/3)(2)^3 + 2 - 1/3
e^y = 8/3 + 2 - 1/3
e^y = 17/3

Now, find the natural logarithm of both sides:

y = ln(17/3)

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Answer:

7^5 (the arrow means it is an exponent)

The approximate distance from the playground to the road along the other path is 1.3 miles.

The angle of the top vertex is 50 degrees. The length of the hypotenuse is 2 miles and the swing stands on the downside of the triangle.

Using trigonometric ratios, let's find the approximate distance from the playground to the road along the other path as follows:

cos 50 = adjacent / hypotenuse

cos 50° = x / 2

cross multiply

x = 2 cos 50°

x = 2 × 0.64278760968

x = 1.28557521937

x = 1.3 miles

Therefore,

distance from the playground to the road along the other path = 1.3 miles

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The slope of the line is m = -3

The y-intercept is (0,5)

The equation of the line in the slope-intercept form is y = 5-3x

Answer:

a)628 b)20

Step-by-step explanation:

a)

V=πr^2h

=3.14*5^2*8

b)V=πr^2h

=3.14*(4.1/2(2.05))*3.1

=3.14*2.05*3.1

=20 (nearest whole number)

Answer:

a) 628

b) 20

Step-by-step explanation:

1. Find circumference

2. Multiply by width

Answer:

129

Step-by-step explanation:

the sum of the interior angles of a quadrilateral is 360, so you add 71+112+48 and subtract it from 360 to get x

The taxi driver charges an initial fare of $3.00 plus $0.40 for each 1/5 of a mile driven. If the total charge for a ride is $27.00, the distance traveled, in miles is 9.

  The data given in the question is, The taxi driver charges an initial fare of $3.00 plus $0.40 for each 1/5 of a mile driven. The total charge for a ride is $27.00.

   Let's calculate the distance traveled:

                  Let d be the distance traveled. The given data in the problem is in dollars and cents. Therefore, let's first change it to the same units (cents). We know that 1 dollar is equal to 100 cents. Thus $27.00 is equal to 27 * 100 cents.

    Therefore, $27.00 is equal to 2700 cents.

     Now, we know that the driver charges $3.00 as an initial fare.

                    So, he charged 300 cents. Therefore, the remaining amount of money he charged for the distance is (2700 - 300) cents.

      Hence, he charged 2400 cents for the distance traveled. The driver charges $0.40 for each 1/5 of a mile. That is 40 cents for each 1.2 km.

     Therefore, he charges 200 cents for each 1.2 km of distance traveled.

      Hence, he charges (2400/200) * 1.2 km of distance traveled.

       Therefore, the distance traveled is 14.4 km or 9 miles. Accordingly, the distance traveled, in miles, is 9.

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The FT of 1 meter is 3.28084 feet.

A meter is a unit of length in the metric system. It is defined as the length of the path traveled by light in vacuum during a time interval of 1/299,792,458 of a second.

In contrast, a foot is a unit of length commonly used in the imperial system. One foot is equal to 12 inches.

To convert meters to feet, we use the conversion factor of 1 meter = 3.28084 feet. This means that one meter is equal to 3.28084 feet.

So, to find the number of feet in one meter, we multiply 1 meter by the conversion factor of 3.28084 feet per meter:

1 meter * 3.28084 feet/meter = 3.28084 feet.

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The probability density function of the given random variable X is as follows,√f(x) = π/2 cos(πx) for 0 < x < 0.25,0 otherwise.

We are to determine the expected value of X.We know that the expected value of X is given by

E(X) = ∫xf(x)dx.

Now, we can use the given probability density function to evaluate E(X).E(X) = ∫xπ/2 cos(πx)dx,

for 0 < x < 0.25and E(X) = 0, otherwise.

= [π/2 sin(πx) / π²] * x - [cos(πx) / π²] / 0 to 0.25

= [π/2 sin(π/4) / π²] * 0.25 - [cos(π/4) / π²]

= 0.25[π/2 √2 / π²] - [√2 / π²]

= [π/4√2] - [√2/π²]

Hence, the expected value of X is given by [π/4√2] - [√2/π²].

The given random variable X has a probability density function that is defined differently for different regions of the real line. Since the probability density function is non-negative over the entire real line, we can evaluate the expected value of X by integrating the product of X and the probability density function over the entire real line. However, since the probability density function is zero outside the interval (0, 0.25),

the expected value of X can be computed as the integral of the product of X and the probability density function over the interval (0, 0.25).

We can use the given probability density function to evaluate the integral. We first evaluate the integral over the interval (0, 0.25).

We obtain E(X) = [π/4√2] - [√2/π²]. T

his is the expected value of X when the probability density function is defined as √ f(x) = π/2 cos(πx) for 0 < x < 0.25 and f(x) = 0

otherwise.We conclude that the expected value of X is [π/4√2] - [√2/π²].

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Answer:

170.67 cm^3

Step-by-step explanation:

The volume is given by ...

 V = 1/3s²h

We are given that 4s=32, so s=8. We are also given that h=8. (All linear dimensions are in centimeters.) Then the volume is ...

 V = (1/3)(8²)(8) = 512/3 = 170.67 . . . . cm³

Answer:

170.67 cm^3

Step-by-step explanation:

took the test

Answer:

Variable income is amount of money a person receives that changes over an amount of time, or changes according to the situation. The Commissions and interest on investments or savings might be examples of variable income.

Step-by-step explanation:

Answer:

"Variable income means earned or unearned income that is not always received in the same amount each month."

Step-by-step explanation:

Answer:

y-1=-4(x-7) is the correct answer

Answer:

-10.5n + 14

Step-by-step explanation:

Answer:

g12. 85 + b4. 79

Step-by-step explanation:

g and b is just the amount she buys

Answer:

Step-by-step explanation:

Cost = 12.85g + 4.79b

That's all you can do to set up the total cost. There is no further reduction or combination that can take place. B and G are different.

we get the coordinates of Q' as (2,3) after rotation of the triangle.

What is rotation of axis?

Rotation of axes is a transformation in which the coordinate axes are rotated by a certain angle with respect to the original axes. This transformation can be used to simplify the equations of curves and to make it easier to solve problems involving them. The rotation is usually done by finding the angle of rotation, which is the angle between the original x-axis and the new x-axis. The formulae for converting coordinates from the old system to the new system can then be applied.

In the given problem, we are given that triangle PQR is located in the xy-plane with coordinates of Q being (2,-3). The task is to find the coordinates of Q' when triangle PQR is rotated 180 degrees clockwise about the origin and then reflected across the y-axis to produce triangle P'Q'R'.

To start, we apply the 180 degree clockwise rotation about the origin transformation rule to the coordinates of Q (2,-3) which gives us (-2,3).

Next, we reflect the point (-2,3) across the y-axis. Reflecting across the y-axis involves changing the sign of the x-coordinate while leaving the y-coordinate unchanged. Applying this rule,

Hence, we get the coordinates of Q' as (2,3) after rotation of the triangle.

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When comparing the 95% confidence and prediction intervals for a given regression analysis, it's important to understand their purposes and interpretations.

The 95% confidence interval provides a range within which we can be 95% confident that the true mean of the dependent variable lies, given a specific value of the independent variable. It helps us estimate the population mean based on our sample data. For example, if the confidence interval for the average test score of students in a certain class is [80, 90], we can be 95% confident that the true average test score of all students in the class falls between 80 and 90.

On the other hand, the 95% prediction interval provides a range within which we can be 95% confident that an individual observation will fall, given a specific value of the independent variable. It takes into account both the variability in the data and the variability in future individual observations. For instance, if the prediction interval for the test score of a specific student is [75, 95], we can be 95% confident that the student's actual test score will be between 75 and 95.

In summary, the confidence interval estimates the mean of the population, while the prediction interval estimates the range of individual observations. Both intervals are useful in regression analysis, but they serve different purposes. It's important to understand their distinctions and choose the appropriate interval based on the specific context and question at hand.
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To determine the limit, we can simplify the expression inside the limit notation and analyze the behavior as x approaches infinity.

The given expression is:

lim(x->∞) (24x³ + 4x² - 2x) / (28x + x + 5x + 5)

Simplifying the expression:

lim(x->∞) (24x³ + 4x² - 2x) / (34x + 5)

As x approaches infinity, the highest power term dominates the expression. In this case, the highest power term is 24x³ in the numerator and 34x in the denominator. Thus, we can neglect the lower order terms.

The simplified expression becomes:

lim(x->∞) (24x³) / (34x)

Now we can cancel out the common factor of x:

lim(x->∞) (24x²) / 34

Simplifying further:

lim(x->∞) (12x²) / 17

As x approaches infinity, the limit evaluates to infinity:

lim(x->∞) (12x²) / 17 = ∞

Therefore, the correct choice is:

B. The limit as x approaches infinity does not exist and is neither infinity nor negative infinity.

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The height of the steeple is 12.66 feet.

To find the height of the steeple, we will use the concept of angle of elevation. Angle of elevation is the angle between the horizontal line and the line of sight when we look up at an object.

Let's denote the height of the church as h1 and the height of the steeple as h2. Then, the total height of the church and the steeple is h1 + h2.

Using the concept of angle of elevation, we can write the following equations:

tan(35°) = h1/50 tan(47°40') = (h1 + h2)/50

Solving the first equation for h1, we get:

h1 = 50 * tan(35°) = 35.08 feet

Substituting the value of h1 into the second equation and solving for h2, we get:

50 * tan(47°40') = 35.08 + h2

h2 = 50 * tan(47°40') - 35.08

= 47.74 - 35.08 = 12.66 feet

Therefore, the height of the steeple is 12.66 feet.

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ANSWER

EXPLANATION

For the first cylinder;

Recall, the formula for calculating the surface area of a cylinder is;

Now, substitute the values for the first cylinder;

The volume of the first cylinder is calculated using the formula;

Substitute the values of r and h for the first cylinder;

To get the surface area of the second cylinder, we need to calculate the height (h).

To get the height, we use the volume of the first cylinder to get the height of the second (since they have the same volume).

Hence;

Substitute the height to calculate the surface area is calculated thus;

The value of the given integral {xⁿ·mxInxdx} is x²mxdx/(mx(x²Inx + 3x)).

Given, x>0

Now we have to evaluate the given integral by differentiating.

{xⁿ·mxInxdx}

First, we take the derivative of the given integral.

Applying the product rule, we get;

d/dx[xⁿ·mxInxdx]

=d/dx[xⁿ]·mxInx + xⁿ·d/dx[mxInx]

Differentiating both sides of the given equation;

x²mxInxdx + x³mxd(Inx/dx)dx + x²mxdx = 0

mx[x²Inx + 2x] + x³mx(1/x) - x²mxdx = 0

mx[x²Inx + 2x + x] = x²mxdx

Therefore, the value of the given integral {xⁿ·mxInxdx} is x²mxdx/(mx(x²Inx + 3x)) as shown above.

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If an observation yields a Z-score of -3, this indicates that the observed value is 3 standard deviations below the mean.

The Z-score measures the number of standard deviations an observation is away from the mean of a distribution. A Z-score of -3 means that the observed value is 3 standard deviations below the mean. In a standard normal distribution (with a mean of 0 and a standard deviation of 1), a Z-score of -3 indicates that the observed value is 3 standard deviations below the mean. This means the observed value is relatively far from the mean in the negative direction. For example, if the mean of a dataset is 50 and the standard deviation is 10, an observation with a Z-score of -3 would have a value of:

Value = Mean + (Z-score * Standard Deviation)

Value = 50 + (-3 * 10)

Value = 50 - 30

Value = 20

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Answer:

56

Step-by-step explanation:

because of the type of triangle (isosceles) the 2 angles on the bottom near the equal sides will have equal angle sizes so...

62+62+x=180

124+x=180

x=180-124

x=56

Answer:

Step-by-step explanation:

Conversion ratio = 8/5 = 1.6

So,

     25.9 miles = 25.9 x 1.6

                       = 41.44 km

Answer:

22) 3 in<x<11 in

23) 8 cm<x<26 cm

24) 0 ft<x<10 ft

25) 9 m<x<31 m

26) 2 km<x<14 km

27) 13 in<x<61 in

Step-by-step explanation:

It has to be greater than the difference and smaller than the sum.

22) 7-4=3, 4+7=11, so the answer is 3<x<11

23) 8<x<26

24) 0<x<10

25) 9<x<31

26) 2<x<14

27) 13<x<61