Use the equation below to answer the question. 6x + 3 = 3(2x + 3) Which statement correctly explains whether the equation is true or not?

The system of equation to represents the relation between cakes and pie is given by 6x + 15y = 99 , x + y = 9.

The number of cakes sold is equal to 4.

Let x be the number of cakes sold

And y be the number of pies sold.

A cake costs $6

A pie costs $15,

Total revenue from selling x cakes and y pies is given by,

6x + 15y = total revenue

In one day the store sold 9 baked goods for a total of $99,

x + y = 9

System of equations in two variables,

6x + 15y = total revenue

x + y = 9

To solve for x, we can use substitution.

Solving the second equation for y, we get,

y = 9 - x

Substituting  into first equation, we get,

⇒6x + 15(9 - x) = 99

Simplifying and solving for x, we get,

⇒6x + 135 - 15x = 99

⇒-9x = -36

⇒x = 4

The store sold 4 cakes.

Number of pies sold,

x + y = 9

Substituting x = 4,

⇒4 + y = 9

⇒y = 5

store sold 5 pies

Therefore, from the system of equations 6x + 15y = 99, x + y = 9 the store sold 4cakes and5 pies.

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The standard form expression that represents the amount of border material Jessica will need is 2L + 2W - 2x - 2y = -2B

To create this expression, we need to consider a few things. Firstly, we need to know the length and width of the solar panels. Let's say the length of the solar panel is L and the width is W. We also need to know the width of the border that Jessica wants to add. Let's call this value B.

The total amount of material needed for the border will be the sum of the material needed for the four sides of the solar panel. Each side will need a length of B, so the total length of the material needed will be 2B + 2L + 2W.

However, we can simplify this expression by putting it into standard form. Standard form expressions are written in a specific way that makes them easier to read and work with. In standard form, the expression is written as Ax + By = C, where A, B, and C are constants and x and y are variables.

To put the expression 2B + 2L + 2W into standard form, we need to group the variables together and move the constants to the other side of the equation. This gives us the expression 2L + 2W - Ax - By = -2B, where A and B are both equal to -2, and C is equal to -2B.

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Answer:

8c^2 + 24c - 6

Step-by-step explanation:

I got it right on edmentum

Therefore, the statement "The sample mean absolute deviation is likely to be higher for the samples with lower satisfaction rates" would be the BEST description of the MAD for this data set.

To calculate the mean absolute deviation (MAD), we first need to find the mean of each sample.

Sample 1:[tex]17/25 = 0.68[/tex]

Sample 2: [tex]12/25 = 0.48[/tex]

Sample 3: [tex]14/25 = 0.56[/tex]

Sample 4: [tex]9/25 = 0.36[/tex]

Next, we calculate the deviation of each observation from its respective sample mean:

Sample 1: |0.68 - x1|, |0.68 - x2|, ..., |0.68 - x25|

Sample 2: |0.48 - x1|, |0.48 - x2|, ..., |0.48 - x25|

Sample 3: |0.56 - x1|, |0.56 - x2|, ..., |0.56 - x25|

Sample 4: |0.36 - x1|, |0.36 - x2|, ..., |0.36 - x25|

where xi is the satisfaction rating (0 or 1) of the Ith customer in the sample.

The MAD is the average of these deviations:

MAD = (|0.68 - x1| + |0.68 - x2| + ... + |0.36 - x25|)/100

Since we don't know the actual ratings of the customers, we cannot calculate the MAD exactly. However, we can say that the MAD is likely to be higher for samples 2 and 4, which have lower satisfaction rates, compared to samples 1 and 3, which have higher satisfaction rates. Therefore, the statement "The sample mean absolute deviation is likely to be higher for the samples with lower satisfaction rates" would be the BEST description of the MAD for this data set.

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The probability that exactly 5 of Pete's friends will pass the CPA exam is approximately 0.275

This problem can be solved using the binomial distribution. We know that the probability of passing the CPA exam for a graduate of Pete's College of Business is p = 0.71.

We also know that there are eight friends taking the exam, so the number of trials (n) is 8. We want to find the probability that exactly 5 of them will pass.

The formula for the probability mass function of the binomial distribution is

P(X = k) = (n choose k) × p^k × (1-p)^(n-k)

where X is the random variable representing the number of successes (i.e., the number of Pete's friends who pass), k is the number of successes we want to find (i.e., 5), (n choose k) is the binomial coefficient, which represents the number of ways to choose k successes out of n trials, and p is the probability of success (i.e., 0.71).

Plugging in the numbers, we get

P(X = 5) = (8 choose 5) × 0.71⁵ × (1-0.71)³

= 56 × 0.71 × 0.29³

≈ 0.275

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ok so for the first one I'm im taking a guess I think it's the first one.

the second one plot the point on the line between 14 and 15

I think those should be correct I think

Handling Exponents:

Generally when handling exponents it is necessary to follow the different Law of Exponents

1. Product rule

2.  Quotient rule

3. Power to Power rule

4. Negative exponent rule

5. Zero power rule

In this context we are finding what is equivalent to 6^8 x 6^(-4)

[tex]6^(8-4)=6^4[/tex] - this is equivalent

[tex](6^8)^-4=6^-^3^2[/tex] - not equivalent

[tex]6^2[/tex] -  not equivalent

[tex]6^-^2=\frac{1}{6^2}[/tex] - not equivalent

[tex]6^-^3^2=\frac{1}{6^3^2}[/tex] - not equivalent

[tex]\frac{6^8}{6^4}= 6^(^8^-^4^)=6^4[/tex] -  this is equivalent

The first and last options are equivalent to 6^8 x 6^(-4)

This is possible if the first twin was born just before midnight and the second twin was born just after midnight, on different calendar days.

For the most part, twins and multiples share the same birthday. However, depending on the time of day the babies are born and how long the timespan is between each baby's birth, twins can be born on different days.

Twins are defined as two offspring born together, but that doesn't necessarily mean they are born on the same date. Multiples are generally born only a few minutes apart. If delivered by cesarian section, the interval between births is usually only a minute, maybe two.

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Answer:

5 more adults than students have phones.

Step-by-step explanation:

55% of 80 students have phones. This is:

.55 × 80, which is 44 students.

For adults, 98% of 50 is .98 × 50, which is 49.

49 adults have phones. 44 students have phones.

49 - 44 is 5

5 more adults have phones than students.

After completing the following steps, you will have the quadratic regression equation that models the data with values rounded to the nearest whole number. Keep in mind that you'll need specific data points to provide an actual equation.

To find the values that complete the quadratic regression equation for a given set of data, you'll need to follow these steps:

1. Organize the data points into a table with x-values and y-values.
2. Determine the sums of x, y, x², x³, x⁴, and xy.
3. Create a system of linear equations using the sums found in step 2.
4. Solve the system of linear equations to find the coefficients a, b, and c.
5. Write the quadratic regression equation in the form y = ax² + bx + c, rounding the coefficients to the nearest whole number.

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Answer:

[tex]\large\boxed{\tt x \approx 95.6}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to solve for x by using \underline{Trigonometric Identities}.}[/tex]

[tex]\large\underline{\textsf{What are Trigonometric Identities?}}[/tex]

[tex]\boxed{\begin{minipage}{20 em} \\ \underline{\textsf{\large Trigonometric Identities;}} \\ \\ \textsf{Trigonometric Identities are trigonometric ratios determined with what's given in order to find a missing value. For a Right Triangle, the Trigonometric Identities are Sine, Cosine, and Tangent. These are used to find missing sides.} \\ \\ \tt Sine = \tt $ \tt \frac{Opposite}{Hypotenuse} \\ \\ Cosine = \frac{Adjacent}{Hypotenuse} \\ \\ Tangent = \frac{Opposite}{Adjacent} \end{minipage}}[/tex]

[tex]\textsf{We should determine whether Sine, Cosine, or Tangent will actually help us}[/tex]

[tex]\textsf{determine x. We are given a Right Triangle that has 1 15}^{\circ} \ \textsf{angle, and a side with}[/tex]

[tex]\textsf{a length of 99. Because this side is opposite of the right angle, this side is called}[/tex]

[tex]\textsf{the \underline{Hypotenuse}.}[/tex]

[tex]\textsf{The side labeled x is \underline{Adjacent}, which means that it's touching the given angle.}[/tex]

[tex]\textsf{Using what was given to us, we should use Cosine since we are asked for the}[/tex]

[tex]\textsf{Adjacent Angle when given the Hypotenuse.}[/tex]

[tex]\large\underline{\textsf{Solving;}}[/tex]

[tex]\textsf{Remember that;}[/tex]

[tex]\tt \cos(15^{\circ}) =\frac{Adjacent}{Hypotenuse}[/tex]

[tex]\textsf{We're given;}[/tex]

[tex]\tt \cos(15^{\circ}) =\frac{x}{99}[/tex]

[tex]\textsf{To find the value of x, we first should remove the fraction using cancellation.}[/tex]

[tex]\textsf{We are able to use the \underline{Multiplication Property of Equality} to prove that the}[/tex]

[tex]\textsf{equation remains equal.}[/tex]

[tex]\underline{\textsf{Multiply both expressions by 99;}}[/tex]

[tex]\tt 99 \cos(15^{\circ}) =\not{99} \frac{x}{\not{99}}[/tex]

[tex]\tt 99 \cos(15^{\circ}) =x[/tex]

[tex]\underline{\textsf{Evaluate;}}[/tex]

[tex]\tt 99 \cos(15^{\circ}) \approx \boxed{\tt 95.6}[/tex]

[tex]\large\boxed{\tt x \approx 95.6}[/tex]

Step-by-step explanation:

.600  is   600 thousandths =    600/1000    (this can be reduced to 3/5)

Answer: so it will be 6 6/10

Step-by-step explanation:600l100 = 6 6/10

We can use the formula for inverse variation, which states that the product of the time and the speed is constant:

time × speed = constant

Let's use t to represent the time needed to travel the distance at 54 miles per hour. We know that the time is 10 hours when the speed is 24 miles per hour. So we can set up the equation:

10 × 24 = t × 54

Simplifying, we get:

240 = 54t

Dividing both sides by 54, we get:

t = 240/54

Simplifying this fraction, we get:

t = 40/9

So it will take approximately 4.44 hours, or 4 hours and 26 minutes, to travel the same distance at 54 miles per hour.

The aircraft carrier's average speed was 120 mph.

7.071 is the length, in inches, of each side of the square.

What is meant by "square"?

The term "square" refers to a regular quadrilateral having four equal-length sides and angles. Angles in the square are at right angles or are separated by 90 degrees. The diagonals of the square are also equal and meet at a 90-degree angle.

                             Having equal length sides and right angles on all four, a square is a quadrilateral. Due to the fact that a square's sides are all the same length, it may be distinguished from other types of rectangles. Every square consequently becomes a rectangle since it is a quadrilateral with right angles at all four of its angles.

If the side od=f a square is s, the diagonal is  s√2

  This comes from Pythagoras as diagonal is

   √s² + s²  = √2s² = s√2

 as such s√2 = 10

           s = 10/√2

        = 10 * √2/√2  * √2

         = 5√2

    5 * 1.4142  = 7.071

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The volume of the given prism is 3.118 cubic centimeters.

What is a prism?

A prism is a polyhedron in geometry that has n parallelogram faces that connect the n-sided polygon basis, the second base, which is a translated duplicate of the first base, and the n faces.

We know that volume of prism is given by:

Volume = length * width * height

We are given the following:

Length (l) = 1.67 cm

Width (w) = 0.83 am

Height (h) = 2.25

So, from this we get

⇒ Volume = 1.67 * 0.83 * 2.25

⇒ Volume = 3.118 cubic centimeters

Hence, the volume of the given prism is 3.118 cubic centimeters.

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The inequality relating the figures are

25 XZ > AC

26. DF < FD

27.  38 > x > 11

28. 37/3 > x > 7/3

In the figure, the angles are related from the concept that one angle in a triangle must be greater than zero and less than 180.

In addition, when other dimensions are equal the side having greater length will have greater angle facing it.

27. since side 18 > side 12 we have that

5x - 10 > 45

5x > 45 + 10

5x > 55

x > 11

each angle must be less than 180

Also, 5x - 10 < 180

5x < 180 + 10

5x < 190

x < 38

The range of values of x is 38 > x > 11

28. since side 9 > side 6

30 > 3x - 7

30 + 7 > 3x

37 > x

x < 37/3

each angle must be greater than 0

3x - 7 < 0

3x > 7

x > 7/3

The range of values of x is 37/3 > x > 7/3

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The exponential function of the form y=ab^x that has the given points is y = (25/7)(7/5)^x

We can use the given points to set up a system of equations and solve for the values of a and b in the exponential function y = ab^x.

Using the point (1,5), we get:

5 = ab^1

Using the point (2,7), we get:

7 = ab^2

Now, we can solve for a and b by dividing the second equation by the first:

7/5 = (ab^2)/(ab^1

Simplifying this expression, we get:

7/5 = b

Substituting this value of b back into one of the original equations, we can solve for a:

5 = a(b^1) = a(b) = a(7/5)

Simplifying this expression, we get:

a = 25/7

So, the exponential function that passes through the points (1,5) and (2,7) is:

y = (25/7)(7/5)^x

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Answer: We can use the trigonometric ratios of a 30-60-90-degree triangle to find the length of side x. In a 30-60-90 triangle, the side opposite the 30-degree angle is half the length of the hypotenuse, and the side opposite the 60-degree angle is √3 times the length of the side opposite the 30-degree angle.

Let's call the length of the hypotenuse h. Then, the length of the side opposite the 30-degree angle is h/2, and the length of the side opposite the 60-degree angle is (h/2)√3.

Using this information, we can set up the following equation:

(h/2)√3 = 9

Solving for h, we get:

h = 18/√3

To find the length of side x, we need to use the trigonometric ratio for the sine of the 60-degree angle:

sin(60°) = opposite/hypotenuse

sin(60°) = x/(h/2)

Substituting h = 18/√3, we get:

sin(60°) = x/((18/√3)/2)

Simplifying, we get:

sin(60°) = x/(9/√3)

√3/2 = x/(9/√3)

Multiplying both sides by 9/√3, we get:

x = (9/√3) * (√3/2)

Simplifying, we get:

x = (9/2)√3

Therefore, the length of side x is (9/2)√3 with a rational denominator.

Step-by-step explanation:

A. The number of 7-card stud poker hands is 133,784,560 and the number of 7-card stud poker hands is 674,274,182,400.

B. The number of hands of 7-draw poker that contain the ace of hearts is 18,009,460.

C. The probability that a 7-card draw hand contains the ace of hearts is 0.135.

a) The number of 7-card draw poker hands can be calculated using the combination formula, which is:

[tex]^{n} C_{r}[/tex] = n! / (r! * (n - r)!)

where n is the total number of cards in the deck (52) and r is the number of cards in each hand (7).

So, the number of 7-card draw poker hands is:

[tex]^{52} C_{7}[/tex] = 52! / (7! * (52 - 7)!)

= 133,784,560.

The number of 7-card stud poker hands can be calculated using the permutation formula, which is:

[tex]^{n} P_{r}[/tex] = n! / (n - r)!

where n is the total number of cards in the deck (52) and r is the number of cards in each hand (7).

So, the number of 7-card stud poker hands is:

[tex]^{52} P_{7}[/tex] = 52! / (52 - 7)!

= 674,274,182,400.

b) To count the number of hands of 7-draw poker that contain the ace of hearts, we can treat the ace of hearts as a special card that must be included in each hand. Then, we need to choose the remaining 6 cards from the 51 cards that are not the ace of hearts.

So, the number of hands of 7-draw poker that contain the ace of hearts is:

[tex]^{51} C_{6}[/tex] = 51! / (6! * (51 - 6)!)

= 18,009,460.

c) To calculate the probability that a 7-card draw hand contains the ace of hearts, we can use the formula:

P(event) = number of favourable outcomes / total number of possible outcomes

The total number of possible 7-card draw hands is 133,784,560, which we calculated in part (a).

The number of favourable outcomes is the number of hands of 7-draw poker that contain the ace of hearts, which we calculated in part (b).

So, the probability that a 7-card draw hand contains the ace of hearts is:

P(ace of hearts) = 18,009,460 / 133,784,560 ≈ 0.135

The required probability is 0.135.

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The variance of the area of the circle is [tex]\pi^2\theta^{4/45}[/tex].

The mean area of the circle is [tex]\pi\theta^{2/3}.[/tex]

Let X be the radius of the circle, uniformly distributed on [0, θ].

The probability density function of X is given by:

[tex]f(x) = 1/\theta, for 0 \leq x \leq θ[/tex]

= 0, otherwise

Let Y be the area of the circle. Then[tex]Y = \pi X^2.[/tex] We want to find the mean and variance of Y.

Mean of Y:

By the law of the unconscious statistician, the mean of Y is given by:

[tex]E(Y) = E(\pi X^2) = \pi E(X^2)[/tex]

[tex]E(X^2)[/tex] using the formula for the variance of X:

[tex]Var(X) = E(X^2) - [E(X)]^2[/tex]

Since X is uniformly distributed on [0, θ], we have:

[tex]E(X) = (0 + \theta)/2 = \theta/2[/tex]

[tex]Var(X) = [(\theta - 0)^2]/12 = \theta^{2/12}[/tex]

Solving for [tex]E(X^2)[/tex], we get:

[tex]E(X^2) = Var(X) + [E(X)]^2 = \theta^2/12 + (\theta/2)^2 = \theta^{2/3}[/tex]

Substituting this into the expression for E(Y), we get:

[tex]E(Y) = \pi E(X^2) = \pi (\theta ^{2/3}) = \pi \theta^{2/3}[/tex]

Variance of Y:

To find the variance of Y, we can use the formula for the variance of a function of a random variable:

[tex]Var(Y) = E(Y^2) - [E(Y)]^2[/tex]

We can find[tex]E(Y^2)[/tex] using the law of the unconscious statistician:

[tex]E(Y^2) = E[(\pi X^2)^2] = \pi^2E(X^4)[/tex]

To find [tex]E(X^4)[/tex], we can use the formula for the fourth moment of a uniform distribution:

[tex]E(X^4) = (\theta^4 + 2\theta^2)/5[/tex]

Substituting this into the expression for[tex]E(Y^2)[/tex], we get:

[tex]E(Y^2) = \pi^2E(X^4) = \pi^2[(\theta^4 + 2\theta^2)/5] = \pi^2\theta^{4/5} + 2\pi^2\theta^{2/5}[/tex]

Substituting this and the expression for E(Y) into the formula for the variance of Y, we get:

[tex]Var(Y) = E(Y^2) - [E(Y)]^2[/tex]

[tex]= \pi^2\theta^{4/5} + 2\pi^2\theta^{2/5} - (\pi\theta^2/3)^2[/tex]

[tex]= \pi^2\theta^4/45[/tex]

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Answer:

x = 16

Step-by-step explanation:

The inference engine in an expert system will use both forward and backward chaining as needed to manipulate the rules and make decisions based on the available data and the desired outcome.

To address your question concisely:
The component of an expert system that uses forward and backward chaining to manipulate a series of rules is called the Inference Engine.
An expert system is composed of three primary components: the Knowledge Base, the Inference Engine, and the User Interface.

The Knowledge Base contains the domain-specific facts and rules that the system relies on to solve problems.

The User Interface facilitates communication between the user and the system.
The Inference Engine is responsible for reasoning and drawing conclusions based on the knowledge stored in the Knowledge Base.

It applies logical techniques such as forward and backward chaining to manipulate and evaluate rules.
In forward chaining, the Inference Engine begins with the available data and applies rules to deduce new information or conclusions.

This approach is data-driven, as it starts with facts and moves towards conclusions.
In backward chaining, the Inference Engine starts with a goal or hypothesis and works backward to find supporting evidence or facts.

This approach is goal-driven, as it begins with a desired conclusion and looks for rules that can lead to it.
By employing both forward and backward chaining, the Inference Engine is able to effectively analyze and manipulate rules to provide accurate and reliable solutions to problems within the domain of the expert system.

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By using both forward and backward chaining, the inference engine can efficiently evaluate complex sets of rules and make accurate decisions based on the available data.

The inference engine component of an expert system uses forward and backward chaining to manipulate a series of rules. Forward chaining involves starting with initial data and applying rules to draw a conclusion, while backward chaining involves starting with a goal and working backward to find the necessary data and rules to reach that goal.

By using both forward and backward chaining, the inference engine can efficiently evaluate complex sets of rules and make accurate decisions based on the available data.

The component of an expert system that uses forward and backward chaining to manipulate a series of rules is called the "inference engine". The inference engine applies logical reasoning to deduce new information based on the provided facts and rules in the knowledge base, ultimately assisting in problem-solving and decision-making processes.

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a. The bagel needs to be dilated by a scale factor of 5 to serve 25 people.
b. 25 times more cream cheese will be required for the dilated bagel compared to the original bagel.

a. To find the scale factor for the large bagel that serves 25 people, we need to find the square root of the ratio of the number of people the large bagel serves to the number of people the small bagel serves.
Scale factor = [tex]\sqrt{(large_bagel_serving / small_bagel_serving)}[/tex]
Scale factor = [tex]\sqrt{(25 / 1)}[/tex]
Scale factor =[tex]\sqrt{ 25}[/tex]
Scale factor = 5
So, the bagel needs to be dilated by a scale factor of 5 to serve 25 people.
b. Since the bagels are in the same shape, the area of the large bagel will be the square of the scale factor times the area of the small bagel.

The cream cheese is spread over the area, so the ratio of the cream cheese needed for the large bagel to the small bagel will be the same as the ratio of their areas.
Ratio of cream cheese = [tex](scale factor)^2[/tex]
Ratio of cream cheese = [tex](5)^2[/tex]
Ratio of cream cheese = 25
So, 25 times more cream cheese will be required for the dilated bagel compared to the original bagel.

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The dilated bagel requires 25 times more cream cheese than the original single serving bagel. Round your answer to the nearest tenth: 25.0 times more cream cheese.

a) To determine the scale factor for the dilated bagel, first, we need to find the ratio between the area of the large bagel and the area of a single serving bagel. Since the large bagel serves 25 people, the area ratio will be 25:1.

Area ratio = (scale factor)^2
25:1 = (scale factor)^2

To find the scale factor, take the square root of the area ratio:
scale factor = √25 = √(25/1) = 5

Therefore, the bagel will need to be dilated by a scale factor of 5 to serve 25 people.

b) Since the thickness of the cream cheese remains the same on both bagels, we only need to consider the difference in area between the two bagels. As calculated before, the area ratio is 25:1.

Thus, the dilated bagel requires 25 times more cream cheese than the original single serving bagel. Round your answer to the nearest tenth: 25.0 times more cream cheese.

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The annual incidence rate of cryptosporidiosis in your county is approximately 11.57 cases per 100,000 people.

To calculate the annual incidence rate of cryptosporidiosis in the county, we need to divide the number of reported cases (89) by the total population of the county (769,000) and multiply by 100,000 to get the rate per 100,000 people.

Annual incidence rate = (number of cases / total population) x 100,000
Annual incidence rate = (89 / 769,000) x 100,000
Annual incidence rate = 11.57 per 100,000 people
In this case, the number of cases is 89, and the total population is 769,000.

Plugging these numbers into the formula, we get:

Annual incidence rate = (89 / 769,000) x 100,000 ≈ 11.57

Therefore, the annual incidence rate of cryptosporidiosis in the county was 11.57 per 100,000 people.

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the length of each Segment WY = 7.2 .

What is line Segment?

A portion of a straight line or curve between two points. A portion of a plane or solid figure truncated by intersecting lines, planes, or planes, especially between chords and arcs of a circle.

                                      In geometry, a line segment is bounded by two different points on the line. Or we can say that the line segment is part of the line connecting his two points. Lines have no endpoints and extend infinitely in either direction, while lines have two fixed or definite endpoints. 

In both triangles

        VW/WX = YW/WU

         7/8.75 =  YW/9

           9 * 7/8.75  = YW

               7.2 = WY

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The prompt on measurement of rooms and surface area is given below. Note that the total surface area of the room is 752 ft².

Therefore, the total surface area of the room is 96 + 96 + 160 + 160 + 120 + 120 = 752 square feet.

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a) 160 cans are needed to make 5 pounds of aluminum

b) There are 32 cans per pound of aluminum.

To determine how many cans are needed to make 5 pounds of aluminum, we need to use the given information that 8 empty cans make 1/4 pound of aluminum. We can set up a proportion to solve for the number of cans needed:

8 cans : 1/4 lb = x cans : 5 lbs

To solve for x, we can cross-multiply and simplify

8 cans × 5 lbs = 40 cans

1/4 lb × x cans = 5 lbs

x cans = 5 lbs / (1/4 lb) = 20 lbs

Therefore, 20 × 8 = 160 cans are needed to make 5 pounds of aluminum.

To find out how many cans are there per pound of aluminum, we can use the inverse of the given information:

8 cans : 1/4 lb = 32 cans : 1 lb

So, there are 32 cans per pound of aluminum.

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Answer: 5.966 feet

Step-by-step explanation: To find the depth of the river in 1848, we can start by calculating the depth of the river in 1847 after the 16% drop.

16% of 6.7 feet is 0.16 x 6.7 = 1.072 feet.

So the depth of the river in 1847 was 6.7 - 1.072 = 5.628 feet.

Next, we can calculate the depth of the river in 1848 after the 6% rise.

6% of 5.628 feet is 0.06 x 5.628 = 0.338 feet.

So the depth of the river in 1848 was 5.628 + 0.338 = 5.966 feet.

Therefore, the depth of the river in 1848 was approximately 5.966 feet.

If Cara's calculation of the sum of the squared differences i.e. 1370 from the mean is incorrect, that would be the first error she made in computing the variance.

As the steps for finding the variance are not provided, it is difficult to determine the first error Cara made.

However, the formula for calculating the variance is:

Variance = (sum of the squared differences from the mean) / (number of observations)

The first error Cara may have made is in calculating the sum of the squared differences from the mean.

The correct steps to find the variance are:

Find the mean:

Mean = (87 + 46 + 90 + 78 + 89) / 5 = 78

Calculate the differences from the mean for each observation:

87 - 78 = 9

46 - 78 = -32

90 - 78 = 12

78 - 78 = 0

89 - 78 = 11

Square each difference:

[tex]9^2 = 81[/tex]

[tex](-32)^2 = 1024[/tex]

[tex]12^2 = 144[/tex]

[tex]0^2 = 0[/tex]

[tex]11^2 = 121[/tex]

Find the sum of the squared differences:

81 + 1024 + 144 + 0 + 121 = 1370

Divide the sum of squared differences by the number of observations:

Variance = 1370 / 5 = 274.

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The probability of someone randomly selecting a computer that does not have a virus is 0.8.

Total number of computers = 20

Virus affected = 4

Perfect computers = 20 - 4 = 16

The probability of choosing a computer that does not have a virus is equivalent to the number of computers without a virus and divided by the total number of computers in the lab.

The probability of selecting a computer without a virus is:

P(C) = 16/20

Simplifying this fraction, we get:

P(20 - 4 = 16) = 4/5

P(20 - 4 = 16) = 0.8

Therefore we can conclude that the probability of someone randomly selecting a computer that does not have a virus is 0.8.

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