ADAM!!!!!!!!!!!!!!!!!!!

\(\\ \sf\Rrightarrow 12\dfrac{5}{6}-5\dfrac{1}{6}\)

\(\\ \sf\Rrightarrow \dfrac{77}{6}-\dfrac{31}{6}\)

\(\\ \sf\Rrightarrow \dfrac{77-31}{6}\)

\(\\ \sf\Rrightarrow \dfrac{46}{6}\)

\(\\ \sf\Rrightarrow \dfrac{23}{3}\)

\(\\ \sf\Rrightarrow 7\dfrac{2}{3}\)

Given info:- Subtract and simplify. 12(5/6) - 5(1/6) The given options are (a) 6(1/3) (b) 5(2/3) (c) 7(1/3) (d) 7(2/3)

Solution: 12(5/6) - 5(1/6)

= (72+5)/6 - (30+1)/6

= 77/6 - 31/6

Take the LCM of 6 and 6 is 6.

so,

= (77*1 - 31*1)/6

= (77-31)/6

= 46/6

= (46÷2)/(6÷2)

= 23/3

= 7(2/3) Ans.

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Jerome solved the equation 1 3 x + 5 6 = 1 as shown. 1. Subtraction property of equality: 1 3 x + 5 6 − 5 6 = 1 1 − 5 6 2. LCD: 1 3 x = 1 6 − 5 6 3. Multiply by...

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6(x-2) > 15

6x - 12 > 15

6x > 27

x > 27/6

Hope it helps!

Answer:

x>4.5

Step-by-step explanation:

6(x-2)>15

We do this is as if it were an equation:

6(x-2)>15

Expand the brackets:

6x-12>15

Add 12 to both sides:

6x-12+12>15+12

Simplify:

6x>37

Now we divide both sides by 6:

6x÷6>37÷6

x > 4.5

If we put 5 into the original equation as it is more than 4.5, we get:

6(5-2)>15

We can simplify the brackets or expand first:

Simplifying the brackets first:

6(3)>15

18>15 ✅

Expanding first:

6(5-2)>15

30-12>15

18>15 ✅

Q3. Integrate by using partial fraction, \( \int \frac{2 x^{2}+9 x-35}{(x+1)(x-2)(x+3)} d x \).The given integral can be solved using partial fraction as follows:\[\frac{2x^2+9x-35}{(x+1)(x-2)(x+3)}=\frac{A}{x+1}+\frac{B}{x-2}+\frac{C}{x+3}\]Multiplying both sides by the product of the denominators we get:\[2x^2+9x-35=A(x-2)(x+3)+B(x+1)(x+3)+C(x+1)(x-2)\]Substituting values of x and solving for A, B and C we get,\[A=3\] \[B=-2\] \[C=2\]Thus, the integral can be written as:\[\begin{aligned}\int \frac{2 x^{2}+9 x-35}{(x+1)(x-2)(x+3)} d x&=\int \frac{3}{x+1} d x-\int \frac{2}{x-2} d x+\int \frac{2}{x+3} d x\\&=3 \ln|x+1|-2 \ln|x-2|+2 \ln|x+3|+C\end{aligned}\]where C is the constant of integration.Q4. Find the area of the region bounded by the curves \( y=x^{2}+4 \) lines \( y=x, x=0 \) and \( x=3 \)We are required to find the area of the region bounded by the curves \( y=x^{2}+4 \) lines \( y=x, x=0 \) and \( x=3 \)The given curves can be plotted as shown below:Since the function \( y=x^{2}+4 \) lies above the line y = x in the interval [0, 3] the area can be computed as:\[\begin{aligned}Area&=\int_{0}^{3}(x^{2}+4-x)dx\\&=\left[\frac{x^{3}}{3}+4x-\frac{x^{2}}{2}\right]_{0}^{3}\\&=\frac{9}{2}+6-\frac{9}{2}-0\\&=6\end{aligned}\]Hence, the area of the region bounded by the curves \( y=x^{2}+4 \) lines \( y=x, x=0 \) and \( x=3 \) is 6 square units.

Q.3

To integrate the given function using partial fractions, we need to decompose the rational function into simpler fractions. Let's proceed step by step:

1. Factorize the denominator:

(x+1)(x-2)(x+3)

2. Write the partial fraction decomposition:

\(\frac{2x^{2}+9x-35}{(x+1)(x-2)(x+3)} = \frac{A}{x+1} + \frac{B}{x-2} + \frac{C}{x+3}\)

3. Multiply both sides by the denominator to clear the fractions:

2x^2 + 9x - 35 = A(x-2)(x+3) + B(x+1)(x+3) + C(x+1)(x-2)

4. Expand and simplify the right-hand side:

2x^2 + 9x - 35 = A(x^2 + x - 6) + B(x^2 + 4x + 3) + C(x^2 - x - 2)

Expanding further:

2x^2 + 9x - 35 = (A + B + C)x^2 + (A + 4B - C)x + (-6A + 3B - 2C)

5. Equate the coefficients of corresponding powers of x:

For x^2: A + B + C = 2

For x: A + 4B - C = 9

For constant term: -6A + 3B - 2C = -35

Solving these equations simultaneously will give us the values of A, B, and C.

6. Solve the system of equations:

From the first equation, we can express C in terms of A and B:

C = 2 - A - B

Substituting this into the second equation:

A + 4B - (2 - A - B) = 9

2A + 3B = 11

From the third equation, we can express B in terms of A:

B = (35 + 6A - 2C)/3

B = (35 + 6A - 2(2 - A - B))/3

B = (35 + 6A - 4 + 2A + 2B)/3

3B - 2B = 6A + 35 - 4 - 2A

B = 4A + 31

Substituting B = 4A + 31 into the equation 2A + 3B = 11:

2A + 3(4A + 31) = 11

2A + 12A + 93 = 11

14A = -82

A = -82/14

A = -41/7

Substituting A = -41/7 into B = 4A + 31:

B = 4(-41/7) + 31

B = -164/7 + 217/7

B = 53/7

Now, substituting the values of A, B, and C into the partial fraction decomposition, we get:

\(\frac{2x^{2}+9x-35}{(x+1)(x-2)(x+3)} = \frac{-41/7}{x+1} + \frac{53/7}{x-2} + \frac{2-(-41/7)-(53/7)}{x+3}\)

7. Integrate each term separately:

∫\(\frac{2x^{2}+9x-35}{(x+

1)(x-2)(x+3)} dx = \frac{-41}{7} \int \frac{1}{x+1} dx + \frac{53}{7} \int \frac{1}{x-2} dx + \frac{64}{7} \int \frac{1}{x+3} dx\)

Simplifying the integrals:

∫\(\frac{-41}{7} \frac{1}{x+1} dx + \frac{53}{7} \frac{1}{x-2} dx + \frac{64}{7} \frac{1}{x+3} dx = -\frac{41}{7} \ln|x+1| + \frac{53}{7} \ln|x-2| + \frac{64}{7} \ln|x+3| + C\)

Therefore, the integral of the given function is:

∫\(\frac{2x^{2}+9x-35}{(x+1)(x-2)(x+3)} dx = -\frac{41}{7} \ln|x+1| + \frac{53}{7} \ln|x-2| + \frac{64}{7} \ln|x+3| + C\)

Now, let's move on to the next question.

Q4.

To find the area, we need to calculate the definite integral of the difference between the curves \(y = x^{2} + 4\) and \(y = x\) over the given interval [0, 3]:

Area = ∫[0, 3] (x^2 + 4 - x) dx

Simplifying:

Area = ∫[0, 3] (x^2 - x + 4) dx

Integrating each term separately:

Area = ∫[0, 3] x^2 dx - ∫[0, 3] x dx + ∫[0, 3] 4 dx

Calculating the integrals:

Area = [(1/3)x^3] [0, 3] - [(1/2)x^2] [0, 3] + [4x] [0, 3]

Substituting the limits:

Area = [(1/3)(3)^3 - (1/3)(0)^3] - [(1/2)(3)^2 - (1/2)(0)^2] + [4(3) - 4(0)]

Simplifying:

Area = [(1/3)(27 - 0)] - [(1/2)(9 - 0)] + [12 - 0]

Area = 9 - 4.5 + 12

Area = 16.5

Therefore, the area of the region bounded by the curves \(y = x^{2} + 4\), \(y = x\), \(x = 0\), and \(x = 3\) is 16.5 square units.

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The conductance of a conductor is inversely related to the cross-sectional area of the conductor.

Conductance is directly related to the ease offered by any material to the passage of electric current. Conductance is the opposite of resistance. The higher the conductance, the lower the resistance, and vice versa, the greater the resistance, the less conductance, so both are inversely proportional

Which of the following describes the relationship of conductance to a conductor?

The conductance of a conductor is directly proportional to the length of the conductor.

The conductance of a conductor is directly proportional to the cross-sectional area of the conductor.

The conductance of a conductor is inversely proportional to the square of the length of the conductor.

The conductance of a conductor is inversely proportional to the cross-sectional area of the conductor.

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Answer:

The Answer would be The first ab

Step-by-step explanation:

The prefix "kilo-" in the metric system means one thousand. Therefore, one kilometer equals 1000 meters.

The metric system is a decimal-based system that uses prefixes to denote multiples and submultiples of units. In this system, the prefix "kilo-" represents a factor of one thousand, which is equivalent to 10^3. For instance, one kilogram is equal to one thousand grams, and one kilometer is equal to one thousand meters. Similarly, other prefixes like "centi-" (one hundredth), "milli-" (one thousandth), and "mega-" (one million) are used in the metric system to denote different multiples and submultiples of units.

In conclusion, the prefix "kilo-" in the metric system represents a factor of one thousand. Therefore, when we use this prefix with the unit of length "meter," we get "kilometer," which is equal to 1000 meters.

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The eigenvalues of A are λ = 0 and λ = 2, and the corresponding eigenvectors are [1, 0, -1], [0, 1, -1], and [1, -1, 1].

The matrix

\(A=\left[\begin{array}{ccc}2&2&2\\2&2&2\\2&2&2\end{array}\right]\)

is a 3 x 3 matrix with all entries equal to 2.

First, we can calculate the determinant of A - λI, where I is the identity matrix and λ is an unknown eigenvalue:

\(A - λI =\left[\begin{array}{ccc} [2-λ& 2&2&2& 2-λ& 2& 2&2& 2-λ\end{array}\right]\)

\((A - λI) = (2-λ)[(2-λ)(2-λ)-4] - 2[2(2-λ)-4] + 2[2-4]\)

\(6 + \hat I\)

From this equation, we can see that the eigenvalues are λ = 0 and λ = 2

To find the eigenvectors, we can substitute each eigenvalue into the equation (A - λI)x = 0 and solve for x.

For λ = 0, we have:

\(A = \left[\begin{array}{ccc}2&2&2\\2&2&2\\2&2&2\end{array}\right]\)

(A - 0I)x = 0x = [0 0 0]

This implies that any vector of the form [a, b, -a-b] is an eigenvector for λ = 0. For

example, we can choose [1, 0, -1] and [0, 1, -1] as linearly independent eigenvectors corresponding to λ = 0.

For λ = 2, we have:

\(A - 2I =\left[\begin{array}{ccc} 0 &2 &2&2 &0 &2& 2& 2 &0\end{array}\right]\)

(A - 2I)x = 0

⇒ 2x₂ + 2x₃ = 0

⇒ 2x₁ + 2x₃ = 0

⇒ 2x₁ + 2x₂ = 0

This implies that any vector of the form [1, -1, 1] is an eigenvector for λ = 2. Therefore, we can choose [1, -1, 1] as another linearly independent eigenvector corresponding to λ = 2.

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When an upper outlier is added to the dataset, the mean and median will increase. This means that the analyst's decision to add the upper outlier will have a positive effect on the dataset.

The mean will increase and the median will increase.

The mean and median are the two measures of central tendency, and they are calculated to represent the dataset as a whole.

Mean and median are determined by removing or adding the outliers, which are numbers that are either too high or too low. median was 26, the effects are likely to be positive.

However, when the analyst decides to include the upper outlier in the calculations, it will lead to an increase in the mean and median.The effect of outliers on the mean and median is different.

The mean is greatly influenced by outliers. The median is not affected as much by outliers as the mean because it is calculated by arranging the dataset from lowest to highest and selecting the middle value of the dataset.

When an upper outlier is added to the dataset, the mean and median will increase. This means that the analyst's decision to add the upper outlier will have a positive effect on the dataset.

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Therefore, the coefficient of x² in the Maclaurin series for f(x) = exp(x²) is 1/4.

The coefficient of x² in the Maclaurin series for f(x) = exp(x²) is given by: C. 1/4.

In order to determine the coefficient of x² in the Maclaurin series for f(x) = exp(x²), we need to use the formula for the Maclaurin series expansion, which is given as:

\($$f(x)=\sum_{n=0}^{\infty}\frac{f^{(n)}(0)}{n!}x^n$$\)

Therefore, we can find the coefficient of x² by calculating the second derivative of f(x) and evaluating it at x = 0, and then dividing it by 2!.

So, first we take the derivative of f(x) with respect to x:

\($$f'(x) = 2xe^{x^2}$$\)

Then we take the derivative again:

\($$f''(x) = (2x)^2 e^{x^2} + 2e^{x^2}$$\)

Now, we evaluate this expression at x = 0:

\($$f''(0) = 2 \cdot 0^2 e^{0^2} + 2e^{0^2} = 2$$\)

Finally, we divide by 2! to get the coefficient of x²:

\($$\frac{f''(0)}{2!} = \frac{2}{2!} = \boxed{\frac{1}{4}}$$\)

Therefore, the coefficient of x² in the Maclaurin series for f(x) = exp(x²) is 1/4.

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The graph is misleading because the x-axis scale shows that the given data is more clustered than it actually is.

What is a misleading graph?

A misleading graph, sometimes referred to as a distorted graph, misrepresents data, amounts to statistical abuse, and may lead to the drawing of an inaccurate conclusion.

What is a data set?

A data set is a grouping of connected, discrete pieces of connected data that can be viewed separately, together, or handled as a single unit. A data structure of some kind is used to arrange a data set.

Here, we have

2 events with a cost of 1,000-1,499;

4 events with a cost of 1,500 to 1,999;

3 events with a cost of 2,000 to 2,499;

1 event with a cost of 3,000 to 3,499

We concluded from the given dataset that the cost of the event is plotted on the x-axis.

In a given dataset, the entry from 2500 to 2599 is missing.

The graph generates a point cluster that isn't actually displayed on the data components because of the missing item.

Hence, the graph is misleading because the x-axis scale shows that the given data is more clustered than it actually is.

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Answer:

m= -5

Step-by-step explanation:

This is very simple.

Basically, the formula for a slope intersect form is this:

y= mx+b

Where y is the y value, x is the x value, b is the y intercept, and m is the slope.

Because m is -5 in this equation, that means the slope is -5.

A = [1 0 0; 0 1 0; 0 0 0] and B = [1 1 0; 0 0 0; 0 0 0] are two integer matrices that are not multiples of each other such that Nul(A) = Nul(B) and Col(A) = Col(B).

To find integer matrices A and B that are not multiples of each other such that Nul(A) = Nul(B) and Col(A) = Col(B), we can start with the following matrices:

A = [1 0 0; 0 1 0; 0 0 0]

B = [1 1 0; 0 0 0; 0 0 0]

The null space of A consists of all vectors of the form [x; y; 0], where x and y are integers. Similarly, the null space of B also consists of all vectors of the form [x; y; 0]. Therefore, Nul(A) = Nul(B).

The column space of A consists of all vectors of the form [x; y; 0], where x and y are integers. Similarly, the column space of B also consists of all vectors of the form [x; y; 0]. Therefore, Col(A) = Col(B).

We can verify that A and B are not multiples of each other by computing their determinants. The determinant of A is 0, while the determinant of B is 0 as well. However, A and B are not multiples of each other because the first column of A is [1; 0; 0], while the first column of B is [1; 0; 0] + [0; 1; 0], which is a linear combination of the columns of A.

Therefore, A = [1 0 0; 0 1 0; 0 0 0] and B = [1 1 0; 0 0 0; 0 0 0] are two integer matrices that are not multiples of each other such that Nul(A) = Nul(B) and Col(A) = Col(B).

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Find integer matrices A, B not multiples of each other such that Nul(A)=Nul(B)andCol(A)=Col(B)?

Answer:

25%

Step-by-step explanation:

If you raised it by 50.

\(\frac{200}{50} =\frac{100}{y}\)

200 × y = 50 × 100

200y = 5000

200y ÷ 200 = 5000 ÷ 200

y = 25

Answer: y=3x-12

Step-by-step explanation:

49.2 calories are in  would that contribute per serving .

What does a calorie mean ?

Carbohydrates provide 4 calories per gram.

              1 gm Carbohydrates = 4 calories

 then 12.3 gm Carbohydrates  = 12.3 * 4

                                             = 49.2 calories

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Answer:

123 people

Step-by-step explanation:

60 + 36x ≤ 4500  x is  the number of people

36x ≤ 4440  Subtract 60 from both sides of the equation

x ≤ 123.333...  Divide both sides  by 36.

We cannot have a portion of a person, so we would round down to the next person which would be 123.

Answer:

the answer is x < 5

Step-by-step explanation:

-5x/-5 < -25/-5

Cancel terms that are in both the numerator and denominator

Divide the numbers
x < 5

This indicates that there is an about 0.1587 chance that a particular student will like Eminem tracks between 5.5 and 8.5.

The quantity of possible outcomes is known as probability. all events that could possibly occur. For instance, there is a 1 in 2 chance of receiving a head when flipping a coin, and there are 2 possible outcomes overall (a head or tail). P(heads) = 12 is the formula.

There are four primary categories of probability: axiomatic, axiomatic, classical, and empirical. Probability is the area of mathematics that deals with the possibility of a random event.

How likely something is to occur is known as its probability. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out. Statistics describes the examination of events subject to probability.

To find:

P(X < 5.5)

Z = -1.0

However;

P(X< 5.5) = P(Z < -1.0)

P(X< 5.5) = 0.1587

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Answer:

B. a6b8c3

Step-by-step explanation:

Answer:

22.5 feet

Step-by-step explanation:

volume of a retangular shape: l*w*h

4.5*2.5*2=22.5

The decimal equivalent of the hex number 0x3F is 63.

To convert the hex number 0x3F to its decimal equivalent, we need to multiply each digit by the corresponding power of 16 and sum them up.

Starting from the rightmost digit, we have:

Now, we multiply each digit by the corresponding power of 16:

Finally, we sum up the results:

(15 * 1) + (3 * 16) = 15 + 48 = 63

Therefore, the decimal equivalent of the hex number 0x3F is 63.

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A line of best fit is a line drawn at average distance to a series of scattered points. Thus, the correct option is:

Option B. The data point is 4. 5 units below the line of best fit.

A graph is said to be formed by plotted points on a Cartesian coordinate plane. When the plotted points are scattered, a line of best fit is required to shoe the relationship among the plotted points.

A residual value is a form of error that is determined from the line of best fit. A line of best fit is a line drawn at average point to a series of plotted scattered points.

Therefore, a residual value of 4.5 with respect to a line of best fit implies that: The data point is 4. 5 units below the line of best fit.

Thus the correct option is B.

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Answer:

What does a residual value of –4.5 mean in reference to the line of best fit?

❌ O A) The data point is 4.5 units above the line of best fit.

❌ O C) The line of best fit is not appropriate to the data.

❌ O D) The line of best fit has a slope of –4.5.

i Guest it So Your Answer is B . Have a Nice Day.

The horse's average speed for the race in units of kilometers per hour will be 178.06.

The winning horse in a recent race covered the 5.50-furlong distance in 22.37 seconds.

The distance covered by the particle or the body in an hour is called the average speed. It is a scalar quantity. It is the ratio of the total distance to the total time.

We know that the average speed formula is given as,

Average speed = Total distance / Total time

The conversion is given as,

1 furlong = 0.201168 km

5.50-furlong = 0.201168 x 5.5 km

5.50-furlong = 1.10642 km

1 second = 1/3600 hour

22.37 seconds = 22.37/3600 hour

22.37 seconds = 0.0062 hour

The average speed is calculated as,

Average speed = 1.10642 / 0.0062

Average speed = 178.06 km per hour

The horse's average speed for the race in units of kilometers per hour will be 178.06.

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The expression provided is 7(42³ + 42² - 7z + 3) - (4x² + 2x - 2). The task is to simplify the expression and enter the correct number in each box. However, the specific numbers in the boxes are not provided in the question.

Therefore, it is not possible to determine the correct values to enter in the boxes or provide a specific answer. To simplify the given expression, we can apply the distributive property and combine like terms. Starting with the expression: 7(42³ + 42² - 7z + 3) - (4x² + 2x - 2)

Expanding the multiplication within the first set of parentheses:

7(74088 + 1764 - 7z + 3) - (4x² + 2x - 2)

Simplifying the terms inside the first set of parentheses:

7(75855 - 7z) - (4x² + 2x - 2)

Applying the distributive property:

529985 - 49z - (4x² + 2x - 2)

Removing the parentheses:

529985 - 49z - 4x² - 2x + 2

Combining like terms:

4x² - 2x - 49z + 529987

The simplified expression is 4x² - 2x - 49z + 529987. However, without the specific numbers provided in the boxes, it is not possible to determine the correct values to enter in the boxes or provide a specific answer. In conclusion, the given expression has been simplified to 4x² - 2x - 49z + 529987, but the specific values to enter in the boxes are not provided, making it impossible to complete the question accurately.

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With Alpha set to .05, increasing the sample size would not directly reduce the probability of a Type I error. The probability of a Type I error is determined by the significance level (Alpha) and remains constant regardless of the sample size.

However, increasing the sample size can indirectly affect the probability of a Type I error by increasing the statistical power of the test. With a larger sample size, it becomes easier to detect a statistically significant difference between groups, reducing the likelihood of falsely rejecting the null hypothesis (Type I error).

Increasing the sample size generally decreases the probability of a Type II error, which is failing to reject a false null hypothesis. With a larger sample size, the test becomes more sensitive and has a higher likelihood of detecting a true effect if one exists, reducing the likelihood of a Type II error. However, it's important to note that other factors such as the effect size, variability, and statistical power also play a role in determining the probability of a Type II error.

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1. The source of documents for:

2. Predetermined overhead rate = Manufacturing overhead cost/ Direct labor cost * 100

= 550/440* 100 = 125%

Therefore, the predetermined manufacturing overhead rate is 125% of the direct labor cost.

3. Total cost = Direct material + Direct labor + Manufacturing overhead

= 700 + 900 + 440 + 550 + 380 + 475 + 1600 +1500 + 540 + 675 = $7760

Unit cost =  Total cost/ Total Quantity = $7760/ 2500= $3.104

4. Finished goods inventory $7760

To Work in progress $7760

(To record the completion of job)

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The answer of the question based on the volume of  prism is given below, the volume of the prism is 48 cubic units.

The Pythagorean Theorem is fundamental theorem in mathematics that relates to three sides of  right-angled triangle. It states that in any right-angled triangle,  square of length of the hypotenuse (the longest side) is equal to sum of  squares of  lengths of other two sides.

we know that the area of the base is given by:

Area of base = (1/2) * base * height

where base = 4 and height = 3 (using the Pythagorean Theorem).

Therefore, Area of base = (1/2) * 4 * 3 = 6 square units.

The height of the prism is given as 8 units.

Hence, the volume of the prism is given by:

Volume = Area of base * height

= 6 * 8

= 48 cubic units.

Therefore, the volume of the prism is 48 cubic units.

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Answer: The least common denominator is 3x(x+10)

The equation will have 2 valid solutions

Step-by-step explanation: sorry if wrong

We have in this scatter plot a high correlation between the variables. This correlation is positive.

For question a, we can see that as the number of hours worked by these 25 students increases, the amount of money also increases. Therefore, we can say that the amount of money spent tends to increase.

In this case, we have that the correlation between these variables is positive: as the values of one variable increases the other increases too. Therefore: For these 25 students, there is a positive correlation.

To predict that a student working 12 hours would spend a certain number of dollars, we need to use the line in the graph, We need to find, x = 12, and, then, we need to find the corresponding y-coordinate for x. In this case, we have that, for x = 12, we have that the value is near $30. From the choices, we have that the nearest value is $28.

In summary:

a ---> increase

b ---> a positive

c ---> $28

The formula is incorrect, as it should be $A = P(1+r/n)^(nt)$ instead of $A = P + (1+r/n)^(nt)$, which the student has incorrectly used. Explanation: A = the balance after the specified time P = principal r = interest rate n = the number of times per year the interest is compounded t = time in year.

We have the following information given to us in the question: A corporation issues a bond costing $600 and paying interest compounded quarterly. After 5 years, the bond is worth $800. What is the annual interest rate as a percent rounded to 1 decimal place? A = 800, P = 600, n = 4 (compounded quarterly), and t = 5 years The formula that should be used is A = P(1+r/n)^(nt).

The student has incorrectly used A = P + (1+r/n)^(nt). Step 1: Incorrectly using formula: A = P + (1+r/n)^(nt). The student has used the incorrect formula. The correct formula to use is A = P(1+r/n)^(nt).Step 2: 600=8001+r420. This is correct as it uses the correct formula A = P(1+r/n)^(nt). Step 3: 600=800+200r20. This is correct as it uses the correct formula A = P(1+r/n)^(nt).Step 4: 600-800=200r20. This is correct as it uses the correct formula A = P(1+r/n)^(nt).Step 5: -200=200r20. This is incorrect, the student has solved for r incorrectly.

They have divided 200 by 20 instead of multiplying. It should be -200/400 = -0.5. The student should have written -200 = 200r(20) instead of -200=200r20. This step gets 4 points out of 7.Step 6: 400=r20. This is incorrect as the student has written the value of r first instead of solving for it. It should be r = 20. The student should have written 200r = 400 instead of 400=r20. This step gets 3 points out of 7.Step 7: r=20.

This is correct. The annual interest rate is 20.0%.This error analysis of the problem is correct, and all the steps have been explained correctly.

To know more about interest refer here:

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