Initial Knowledge Check Divide. (x-2)/(3x-21)-:(5x-10)/(9x-63) Simplify your answer as much as possihlo

x → -∞, f(x) → 0

x → ∞, f(x) → ∞

As x approaches negative infinity, the value of the exponent 2^x+1 will become very large negative number, approaching zero. Therefore, the function f(x) will approach 5 times zero, which is equal to 0. Thus, we can say:

As x → -∞, f(x) → 0.

As x approaches positive infinity, the value of the exponent 2^x+1 will become very large positive number, approaching infinity. Therefore, the function f(x) will approach 5 times infinity, which is equal to infinity. Thus, we can say:

As x → ∞, f(x) → ∞.

So, the long run behavior of the function f(x)=5(2)^x+1 is that it approaches 0 as x approaches negative infinity and approaches infinity as x approaches positive infinity.

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The correct way to name the figure shown is PQ. This figure consists of two perpendicular lines, P and Q, which intersect at a point. The lines are labeled P and Q, so the correct name for the figure is PQ.

Perpendicular lines are those two lines that intersect each other at a 90 degree angle. These lines are also known as orthogonal lines. When two lines intersect at a 90 degree angle, they are said to be perpendicular.

The figure is a basic geometric shape and is used to illustrate the concept of perpendicular lines. In the figure shown, the angle formed by the intersection of the two lines is a right angle, so the lines are perpendicular.

The figure can also be used to illustrate the concept of a transversal. A transversal is a line that intersects two other lines at different points. In the figure, the line PQ is a transversal intersecting the two lines P and Q.

In conclusion, the correct way to name the figure shown is PQ. This figure is used to illustrate the concepts of perpendicular lines, line segments, and transversals.

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The required graph represents that the solution to the given inequality x - 8 ≥ -3 is x ≥ 5.

A linear inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

To solve for x:

x - 8 ≥ -3

x ≥ -3 + 8

x ≥ 5

So, the solution is x ≥ 5.

For the graph of the solution, draw a number line and mark a closed circle at 5 since the inequality includes 5. Then, shade to the right of 5 to represent all values of x that satisfy the inequality.

Thus, the required graph represents that the solution to the given inequality is x ≥ 5.

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The artist sold 32 smaller candles and 20 larger candles.

An equation is a mathematical statement that shows the equality of two expressions. It contains an equals sign (=) and at least one variable. An equation can be true or false depending on the values of the variables. Solving an equation involves finding the value or values of the variable that make the equation true. Equations are used to model relationships between different quantities in a wide range of fields, including mathematics, physics, chemistry, economics, and engineering.

A. Let's represent the number of smaller candles sold as x and the number of larger candles sold as y. We know that x + y = 52 (since a total of 52 candles were sold) and 4x + 7y = 269 (since the total sales was $269 and smaller candles sell for $4 and larger candles sell for $7). We can use these two equations to solve for x and y.

Multiplying the first equation by 4, we get 4x + 4y = 208. Subtracting this from the second equation, we get:

4x + 7y - (4x + 4y) = 269 - 208

3y = 61

y = 20.33

This means that the artist sold 20.33 larger candles. However, since we cannot sell a fractional part of a candle, we need to round this down to 20. Similarly, we can find x by subtracting y from 52:

x = 52 - y = 52 - 20 = 32

So the artist sold 32 smaller candles and 20 larger candles.

B. The answer is reasonable since the number of smaller candles sold is larger than the number of larger candles sold, and the total sales amount is closer to the price of the smaller candle than the larger candle. This implies that the artist's records are likely accurate.

Therefore, the artist sold 32 smaller candles and 20 larger candles.

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Answer:

Your answer is <PBD = 56

Step-by-step explanation:

That red square indicate that its a right triangle meaning that <PBH is 90°

Those two angle <PBD and <DBH are complementary angle meaning that those two angle add up to 90°

So,

<PBD + <DBH = 90°

(3k + 65°) + 34 = 90

3k + 65 + 34 = 90

3k = -9

k = -3

Plug in k = -3 in <PBD to solve for the measure angle.

<PBD = (3k + 65°) ; k = -3

<PBD = 3(-3) + 65

<PBD = -9 + 65

<PBD = 56

The quotient is x^2+2x+3, and the remainder is 7.

The quotient and remainder of the given expression can be found using long division. Here are the steps:

1. Divide the first term of the dividend, x^3, by the first term of the divisor, x. This gives you the first term of the quotient, x^2.
2. Multiply the first term of the quotient, x^2, by the divisor, x+2. This gives you x^3+2x^2.
3. Subtract this result from the dividend, x^3+4x^2+7x+13, to get the new dividend, 2x^2+7x+13.
4. Repeat the process with the new dividend, 2x^2+7x+13, and the divisor, x+2. The first term of the quotient is 2x, and the result of the multiplication is 2x^2+4x.
5. Subtract this result from the new dividend, 2x^2+7x+13, to get the new dividend, 3x+13.
6. Repeat the process with the new dividend, 3x+13, and the divisor, x+2. The first term of the quotient is 3, and the result of the multiplication is 3x+6.
7. Subtract this result from the new dividend, 3x+13, to get the remainder, 7.

Therefore, the answer is:

The quotient is x^2+2x+3.
The remainder is 7.

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The required equation of the line perpendicular to y=4 that passes through (-5,-2) is: x = -5

The equation of the line y=4 is a horizontal line that passes through the point (0,4).

A line perpendicular to this line would be a vertical line passing through the point (-5,-2).

The equation of a vertical line passing through the point (-5,-2) can be written in the form x = -5,

which means that the x-coordinate of any point on this line must be -5.

Therefore, the equation of the line perpendicular to y=4 that passes through (-5,-2) is: x = -5

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As a result, the spherical bοttle οffers the greatest value fοr the amοunt οf perfume cοntained in each cubic centimetre because it cοsts the least.

The measurement οf a three-dimensiοnal οbject's space filled is its vοlume. Mοst οften, it is expressed in cubic measures like cubic metres, cubic centimetres, οr cubic feet. The vοlume οf a cube, fοr instance, can be calculated by multiplying its length, breadth, and height. Calculating a cube's vοlume is as fοllοws:

Capacity is calculated using the fοrmula LWH.

given:

The fοrmula V = pi x r² x h, where r is the radius οf the circular base and h is the height οf the bοttle, must be used tο determine the perfume cοntainer's vοlume. Hοwever, we are unable tο determine the vοlume because we lack the values fοr r and h. The fοrmula V = 4/3 π x r³, where r is the radius οf the spherical cοntainer, must be used tο determine the vοlume οf the perfume bοttle. Hοwever, we are unable tο determine the vοlume because we lack the value fοr r.

Price per cubic centimetre = $54.00 / 282.74 cm³ = $0.191 per cm³ Vοlume οf cylindrical cοntainer = π x (3 cm)²x 10 cm = 282.74 cm³

Cοnical cοntainer vοlume equals 1/3 π x (2 cm) 2 x 8 cm = 16.76 cm³.

$20.00 divided by 16.76 cm3 (price per cubic centimetre) yields $1.19 per cm3.

The vοlume οf a sphere is equal tο 4/3 π  x (4 cm)³ = 268.08 cm³.

$35.00 divided by 268.08 centimetres squared equals $0.13 per centimetre.

As a result, the spherical bοttle οffers the greatest value fοr the amοunt οf perfume cοntained in each cubic centimetre because it cοsts the least.

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The point (2, –2) with x-coordinate value 2 and y-coordinate value -2, is not satisfied the equation y = x.

We have an equation, y = x --(1) and point (2,-2). We have to check that point (2, –2) satisfy the equation y = x or not. To check that, we need to put the values of the point in the equation. If the equation satisfies them, the point belong to the line. Substituting the coordinates of the given point, i.e., x = 2 and y = -2, into the defining equation(1), we get, y = x

L.H.S, y = -2

R.H.S, x = 2

but -2 ≠ 2 so, L.H.S ≠ R.H.S

We now see from the above substitution and the resultant calculation that the coordinates (x, y) of the point (2, -2) does not make the equation y = x

Hence, the point ( 2,-2) does not satisfied equation y= x .

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The statement "W1 (+) W2 if and only if the expression 0=0+0 is the only expression of the vector 0 as sum of a vector in W1 and another in W2" is equivalent to the statement "W1 (+) W2 if and only if W1 ∩ W2 = {0}".

Proof:

(⇒) Assume that W1 (+) W2. This means that for any vector v ∈ V, there exist unique vectors w1 ∈ W1 and w2 ∈ W2 such that v = w1 + w2. In particular, for the vector 0 ∈ V, there exist unique vectors w1 ∈ W1 and w2 ∈ W2 such that 0 = w1 + w2. Since 0 is the additive identity, we must have w1 = 0 and w2 = 0. Therefore, the only vector in the intersection of W1 and W2 is the zero vector, so W1 ∩ W2 = {0}.

(⇐) Assume that W1 ∩ W2 = {0}. Let v ∈ V be an arbitrary vector, and suppose that there exist vectors w1, w1' ∈ W1 and w2, w2' ∈ W2 such that v = w1 + w2 = w1' + w2'. Then we have w1 - w1' = w2' - w2 ∈ W1 ∩ W2. But since W1 ∩ W2 = {0}, we must have w1 - w1' = 0 and w2' - w2 = 0, which implies that w1 = w1' and w2 = w2'. Therefore, the expression v = w1 + w2 is unique, so W1 (+) W2.

Thus, we have shown that W1 (+) W2 if and only if W1 ∩ W2 = {0}.

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Even though 2 is not a zero of the polynomial, p(k) = p(2) = 0.

No, 2 is not a zero of the polynomial p(x)=3x^(4)-14x^(3)-9x^(2)+64x-28. To determine p(k), we simply need to plug in the value of k into the polynomial and simplify.

So, p(k) = p(2) = 3(2)^(4) - 14(2)^(3) - 9(2)^(2) + 64(2) - 28

= 3(16) - 14(8) - 9(4) + 128 - 28

= 48 - 112 - 36 + 128 - 28

= 0

Therefore, p(k) = p(2) = 0.

So, even though 2 is not a zero of the polynomial, p(k) = p(2) = 0.

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The slopes are equal, and the equation is showing a proportional relationship.

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).

Proportional relationships are relationships between two variables where their ratios are equivalent.

1) Given that, Δ PQR and  Δ STU are similar triangles, we need to show that they have equal slope,

Line PR is passing by points (-6, 4) and (-8, 7) and the line SU is passing by points (-4, 1) and (0, -5)

Slope = y₂-y₁ / x₂-x₁

Finding the slopes :-

Line PR = 7-4 / -8+6 = -3/2

Line SU = -5-1 / 4 = -6/4 = -3/2

Therefore, we get the slopes equal.

2) Given is an equation, y = 3x/4

The proportionality equation is given by :- y = kx, where k is the proportionality constant,

The given equation is following the proportionality equation, therefore is showing a proportional relationship.

Hence, the slopes are equal, and the equation is showing a proportional relationship.

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The area of the shaded segment of the circle is 5.79 square metre.

The area of a segment is equal to the area of a sector less the triangle-shaped portion.

A=[tex]\frac{1}{2}[/tex](∅-Sin∅)×[tex]r^{2}[/tex]

Every point in the plane of a circle, which is a closed, two-dimensional object, is evenly separated from the centre. All lines that cross the circle join together to produce the line of reflection symmetry. Moreover, every angle has rotational symmetry around the centre.

r=8m

∅=60°

Applying the formula's values, we obtain

A=[tex]\frac{1}{2}[/tex](∅-Sin∅)×[tex]r^{2}[/tex]

A=[tex]\frac{1}{2}[/tex]([tex]\frac{π}{3}[/tex]-Sin60°)×[tex]8^{2}[/tex]

A=5.79

Hence,  the area of the shaded segment of the circle is 5.79 square metre.

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Answer: The Answer is 4

Step-by-step explanation:

1) find the same base of the x² y² n just do the addition normally like this

(7x²y²+4x²y²)-3xy-8xy

so you'll end getting

the final answer

Chase's likely error is that he added instead of subtracting when finding his location on the number line.

What is the fractions?

A fraction is a way of representing a part of a whole or a ratio between two numbers. It consists of a numerator (top number) and a denominator (bottom number), separated by a line.

If Ellie's house is at 1 1/2 on the number line, and Chase lives 1 1/5 blocks west of Ellie, then the coordinate of Chase's house would be:

1 1/2 - 1 1/5 = 3/2 - 6/5

To subtract these fractions, we need a common denominator, which is 10:

(3/2) * (5/5) - (6/5) * (2/2) = 15/10 - 12/10 = 3/10

So Chase's house is located 3/10 blocks west of Ellie's house on the number line. Therefore, the correct coordinate for Chase's house is:

1 1/2 - 3/10 = 1 2/5

Chase's likely error is that he added instead of subtracting when finding his location on the number line.

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As a result, after 14 years, the investment that was compounded interest irregularly will be valued $961.54 more than the one that was compounded yearly.

By dividing the principal by the interest rate, the passage of time, and other factors, simple interest is determined. Simple return equals principle plus interest plus hours is the formula used in marketing. The easiest way to compute interest is by using this method. The most typical method for calculating interest is as a portion of the principle amount. For example, if he borrows $100 from a buddy and agrees to pay back the loan at 5% interest, he will only pay his share of the 100% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and you must charge interest when you lend it. Typically, interest is determined as an annual percentage of the loan total. The loan's interest is the name given to this percentage.

We must apply the compound interest calculation in order to compare the values of the investment compounded annually with the investment compounded periodically:

[tex]A = P(1 + r/n)^(nt) (nt)[/tex]

where:

A is the total sum.

The principal is P. (the initial amount)

n is the number of times the interest is compounded each year, and r is the yearly interest rate (expressed as a decimal).

The number of years is t.

We have the following for the yearly compounded investment:

[tex]A = 9000(1 + 0.06/1)^(1*14) = $20,207.97[/tex]

Periodically compounded investment results in:

[tex]A = 9000(1 + 0.06/12)^(12*14) = $21,168.51[/tex]

As a result, after 14 years, the investment that was compounded irregularly will be valued $961.54 more than the one that was compounded yearly.

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Answer:

4 number x value is 10 in

5 number x value is 12mi

use formula of h2=p2+b2

The inequality of the expression is x + 175 < 1000

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

x + 175 < 1000

Subtract 175 from bith sides

x < 825

Hence, the solution is x < 825

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After performing the indicated operation, the sum of (7)/(10x²y) + (4)/(15xy²) is (21y + 8x)/(30x²y²).

To perform the indicated operations, we need to find a common denominator for the two fractions. The common denominator for 10x²y and 15xy² is 30x²y². We can then rewrite the fractions with the common denominator and add them together:

(7)/(10x²y) + (4)/(15xy²)

To do this, multiply both fractions by 30x²y²/30x²y² and simplify as a fraction with denominator 30x²y².
= (7)/(10x²y)(30x²y²/30x²y²) + (4)/(15xy²)(30x²y²/30x²y²)
= (21y)/(30x²y²) + (8x)/(30x²y²)

Finally, since the denominators of the two fractions are the same, add the two fractions by adding their numerators.
= (21y + 8x)/(30x²y²)

Therefore, the answer is (21y + 8x)/(30x²y²).

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Suppose 2022 balls are randomly distributed into 100 boxes. Let X be the total number of balls in the first 20 boxes.  P(X = 90) ≈ 0.  VarX = 323.52.

a) To find P(X = 90), we can use the binomial probability formula:

P(X = k) = C(n,k) * p^k * (1-p)^(n-k)

where C(n,k) = n! / (k! * (n-k)!)

In this case, n = 2022, k = 90, p = 20/100 = 0.2

P(X = 90) = C(2022,90) * 0.2^90 * 0.8^(2022-90)

P(X = 90) = 1.19 * 10^(-37)

Therefore, P(X = 90) ≈ 0.


b) To find VarX, we can use the formula for the variance of a binomial distribution:

VarX = n * p * (1-p)

In this case, n = 2022, p = 0.2

VarX = 2022 * 0.2 * 0.8

VarX = 323.52

Therefore, VarX = 323.52.

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Answer: the first graph ! :)

Step-by-step explanation:

it is the very first one.

1808.64  is the area formed by the water pattern if it can spray out 24 feet in any​ direction.

The circle is a rounded shape without any edges or line segments. It has the geometric shape of a closed curve. The distance between the circle's points and its center is fixed. r2 is the area that a circle with radius r encloses. Here, the Greek letter stands for the constant proportion of a circle's circumference to its diameter,

Here, we have

Given: water sprinkler sends water out in a circular pattern. It can spray out 24 feet in any​ direction.

Since the water is being sent out in a circular pattern, the maximum distance at which the water is reaching out will be equal to the radius of the circle as the sprinkler is at the center of the circle.

The area of a circle is given as:

Area = πr²

Radius = 24 feet

Area = 3.14(24)²

Area = 1808.64

Hence, 1808.64  is the area formed by the water pattern if it can spray out 24 feet in any​ direction.

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Answer:

1808.64  is the area formed by the water pattern if it can spray out 24 feet in any​ direction.

What is an area of a circle?

The circle is a rounded shape without any edges or line segments. It has the geometric shape of a closed curve. The distance between the circle's points and its center is fixed. r2 is the area that a circle with radius r encloses. Here, the Greek letter stands for the constant proportion of a circle's circumference to its diameter,

Here, we have

Given: water sprinkler sends water out in a circular pattern. It can spray out 24 feet in any​ direction.

Since the water is being sent out in a circular pattern, the maximum distance at which the water is reaching out will be equal to the radius of the circle as the sprinkler is at the center of the circle.

The area of a circle is given as:

Area = πr²

Radius = 24 feet

Area = 3.14(24)²

Area = 1808.64

Hence, 1808.64  is the area formed by the water pattern if it can spray out 24 feet in any​ direction.

Answer:

12.15 m

Step-by-step explanation:

90 × 13.5 cm × (1 m)/(100 cm) = 12.15 m

Answer: 12.15 m (rounded 12.2)

Step-by-step explanation:

100 cm = 1 m

13.5(90) = 1,215

1215 divided by 100 = 12.15

It will take 1/4 of an hour, or 15 minutes, to fill an empty pool when both pipes are turned on by mistake.

The speed at which a variable changes over a specific amount of time is referred to as the rate of change. It is frequently represented in mathematics as a function's derivative, which gauges how quickly the function's output alters in relation to its input.

We must first ascertain the rates of each pipe in order to solve this issue using the rate of work formula. Let r in and r out represent the corresponding flow rates of the inlet and output pipes.

The rate of the inflow pipe is 1/3 of the pool per hour because it may fill the pool in three hours. The outlet pipe's rate is 1/12 of the pool each hour since it can drain the entire pool in 12 hours.

The net rate is the difference between the inlet and output rates because when both pipelines are operating, they compete with one another:

r_net = r_in - r_out = 1/3 - 1/12 = 1/4 of the pool per hour

This means that the pool will be filled with a net rate of 1/4 of the pool per hour. Using the rate of work formula, we can now solve for the amount of time it takes to fill the pool:

A = r / t

t = r / A

Substituting r_net = 1/4 and A = 1 (since we want to fill one pool), we get:

t = (1/4) / 1 = 1/4 hours

Hence, it will take 1/4 of an hour, or 15 minutes, to fill an empty pool when both pipes are turned on by mistake.

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a. since it provides the lowest regret value should the demand be high.

b. Expected Monetary Value for Gradual Introduction= $2.8 million. Expected Monetary Value for Concentrated Introduction= $1.5 million
c. EVPI = $1.3 million

a. For the pessimistic approach, the recommended decision is to use the gradual introduction of the salad dressings, since it provides the least amount of loss should demand be low. For the minimax regret approach, the recommended decision is also the gradual introduction of the salad dressings, since it provides the lowest regret value should the demand be high.

b. Using the expected monetary value approach, the optimal decision would be to use the gradual introduction of the salad dressings. This is because the expected monetary value for a gradual introduction is $2.8 million, which is higher than the expected monetary value of $1.5 million for a concentrated introduction.

Expected Monetary Value for Gradual Introduction: 0.7 * $1 million + 0.3 * $4 million = $2.8 million
Expected Monetary Value for Concentrated Introduction: 0.7 * -$5 million + 0.3 * $10 million = $1.5 million

c. The EVPI (Expected Value of Perfect Information) for this problem is $1.3 million, which is calculated by subtracting the expected monetary value from the best case outcome.

Best case outcome: $10 million
Expected Monetary Value: $2.8 million
EVPI: $10 million - $2.8 million = $1.3 million

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Answer:

24inches ²

Step-by-step explanation:

Scale of length is 20ft : 4inches = 5ft : 1inch

Scale of width will be 5ft: 1inch = 30ft: 6inches

Area of scale =length x width

Area = 4inches x 6inces

The relative frequency of a student being a tenth grader that gets their news from the internet is 0.79.

What is frequency ?

Frequency refers to the number of times that an event or value occurs within a specific period or dataset. It is a measure of how often a particular value or category appears in a set of data. The frequency can be expressed as an absolute count or as a proportion or percentage relative to the total number of observations in the dataset. Frequency is often used in statistical analysis to describe the distribution of data and to calculate various measures of central tendency and variability.

The relative frequency of a student being a tenth grader that gets their news from the internet is given by:

(number of tenth graders who get their news from the internet) / (total number of students)

So, the relative frequency for tenth graders is

34/175 = 0.194

Rounding to the nearest hundredth gives 0.19.

Therefore, the relative frequency of a student being a tenth grader that gets their news from the internet is 0.79.

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Answer:

C.

Step-by-step explanation:

Yearly compounding.
y = 2000(1.04)^t

Monthly compounding.

y = 2000(1 + r/12)^(12t)

2000(1.04)^t = 2000(1 + r/12)^(12t)

(1.04)^t = (1 + r/12)^(12t)

(1.04^t)^(1/t) = [(1 + r/12)^(12t)]^(1/t)

1.04 = (1 + r/12)^12

1.04^(1/12) = [(1 + r/12)^12]^(1/12)

1.00327374 = 1 + r/12

y = 2000(1.00327374)^(12t)

Answer: C.

The x value where P(X < x)=0.0655 is 4 minutes. The correct answer is c. 3.96 minutes.

To find the x value where P(X < x)=0.0655, we can use the z-score formula and look up the corresponding z-value in a standard normal distribution table. The z-score formula is:

z = (x - mean) / standard deviation

Substituting the given values, we get:

0.0655 = (x - 10) / 4

Next, we can look up the z-value that corresponds to 0.0655 in a standard normal distribution table. We find that the z-value is approximately -1.5. Now we can plug this back into the z-score formula and solve for x:

-1.5 = (x - 10) / 4

-6 = x - 10

x = 4

Therefore, the x value where P(X < x)=0.0655 is 4 minutes. The correct answer is c. 3.96 minutes.

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