Construct an 80% confidence interval for the population standard deviation σ if a sample of size 20 has standard deviation s=9.4. Round the answers to at least two decimal places. An 80% confidence interval for the population standard deviation is: <σ

Answer and Step-by-step explanation:

(i) The solution for equation: 2(3x-3) - 5 = 2(x-3) + 15 is:

2(3x-3) - 5 = 2(x-3) + 15

6x - 6 - 5 = 2x - 6 +15

6x - 2x = - 6 + 15 + 6 + 5

4x = 20

x = 5

The solution x is a real number and equals 5.

(ii) Since the order of hot sauce that goes into the gumbo doesn't matter, use combination:

\(C^{10}_{3}\) = \(\frac{10!}{3! (10-3)!}\)

\(C^{10}_{3}\) =  \(\frac{10.9.8.7!}{3.2.1.7!}\)

\(C^{10}_{3}\) = 120

There are 120 ways of picking 3 sauces out of 10.

(iii) Interest is calculated as:

interest = principal*rate*time

Principal is the value of the loan;

Rate is how much it will increase;

Time is for how long the loan will be taken. In this case, time is 9/12 since it was for months;

Interest = 3000 * \(\frac{11.75}{100}*\frac{9}{12}\)

Interest = 264.37

The interest the student will pay will be: $264.37.

Future Value = principal + interest

future value = 3000 + 264.37

future value = 3264.37

The future value for the student is $3264.37.

(iv) As shown in the image in the attachment, the sum of the equations equals 90:

2x + 30 + 2x + 40 = 90

4x = 20

x = 5

The angles are 40° and 50°

The sample covariance between variable a and variable b is -0.2.

To calculate the sample covariance between two variables,

We want to do following steps:

1) Calculate the mean (average) of each variable.

2) Subtract the mean from each value in their respective variables.

3) Multiply the resulting differences for each pair of values.

4) Sum up all the products obtained in step 3.

5) Divide the sum by the number of data points minus 1 (sample size minus 1).

Let's calculate the sample covariance for the given data sets (variable a and variable b),

Variable a: 5, 3, 5, 5, 4, 8

Variable b: 3, 1, 1, 4, 2, 1

Step 1: Calculate the means of each variable.

Mean of variable a:

\((5 + 3 + 5 + 5 + 4 + 8) / 6 = 30 / 6 = 5\)

Mean of variable b:

\((3 + 1 + 1 + 4 + 2 + 1) / 6 = 12 / 6 = 2\)

Step 2: Subtract the mean from each value in their respective variables.

For variable a:

\((5 - 5), (3 - 5), (5 - 5), (5 - 5), (4 - 5), (8 - 5),0, -2, 0, 0, -1, 3\)

For variable b:

\((3 - 2), (1 - 2), (1 - 2), (4 - 2), (2 - 2), (1 - 2),1, -1, -1, 2, 0, -1\)

Step 3: Multiply the resulting differences for each pair of values.

\(0 * 1, -2 * -1, 0 * -1, 0 * 2, -1 * 0, 3 *-10, 2, 0, 0, 0, -3\)

Step 4: Sum up all the products obtained in step 3.

\(0 + 2 + 0 + 0 + 0 + (-3) = -1\)

Step 5: Divide the sum by the number of data points minus 1.

\(-1 / (6 - 1) = -1 / 5 = -0.2\)

Therefore, the sample covariance between variable a and variable b is -0.2.

The correct option is d) -0.20.

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Answer:

360°

Step-by-step explanation:

  Sum of interior angles of polygon =  (n - 2) *180

n is the number of sides of the polygon.

                                                            = (4 - 2) *180

                                                           = 2 * 180

                                                           = 360°

Answer:

A. We are given that the length of the box is equal to 24 as indicted in the "24-inch long". From the given, it is also stated that the width of the box is 7 inches less than the height. If the height of the box is x, the width is then x - 7. The equation that would let us solve the problem is,

                           2880 = 24(x)(x - 7)

Simplifying,

                           2880 = 24x² - 168x

B. The value of x from the equation is 15. Thus, the answer is YES.

Step-by-step explanation:

a) The equation that models the volume of the box in terms of its height will be 2880 = 24x² - 168x.

b)Yes, it is possible for the height of the box to be 15 inches

Volume is the three-dimensional space bounded by a boundary or inhabited by an item.

The given data in the problem is;

L is the length of the box= 24-inch

V is the volume = 2,880 cubic inches.W

W is the width of the box

h is the height

Let the side of the box is x then volume V is found as;

V=LWh

2880 = 24(x)(x - 7)

2880 = 24x² - 168x

Hence the equation that models the volume of the box in terms of its height will be 2880 = 24x² - 168x.

b)Yes, it is possible for the height of the  box to be 15 inches

The value of x obtained from the equation is 15.

Hence yes, it is possible for the height of the  box to be 15 inches

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Answer: 35

Step-by-step explanation:

We substitute a for 1 and b for 6.

5(1+6)=5(7)=35

The solution of the inequalities are,

⇒ x > 6

⇒ x ≤ 24

⇒ x ≥ 6

⇒ x < 8

⇒ x ≥ 24

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The inequalities are shown in figure.

Now,

Solve the given inequalities as;

1) x + 28 > 34

⇒ x + 28 - 28 > 34 - 28

⇒ x > 6

2) x/2 ≤ 12

⇒ 2x/2 ≤ 12 × 2

⇒ x ≤ 24

3) 7x ≥ 42

⇒ x ≥ 42/7

⇒ x ≥ 6

4) x - 2 < 6

⇒ x - 2 + 2 < 6 + 2

⇒ x < 8

5) 3x ≥ 72

⇒ x ≥ 72/3

⇒ x ≥ 24

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Answer:

Step-by-step explanation:

5%×g= 5g/100

g-5g/100

The probability that more boys than girls are chosen is 0.4731. So option b is correct.

Combination:

The act of combining or the state of being combined. A number of things combined: a combination of ideas. something formed by combining: A chord is a combination of notes. an alliance of persons or parties: a combination in restraint of trade.

Here it is given that there are 18 boys and 19 girls and 5 students are chosen.

We have to find the probability that more boys than girls are chosen.

Probability = \(C^{5} _{18}\) + \(C^{4}_{18} C^{1} _{19}\) + \(C^{3} _{18} C^{2} _{19}\) / \(C^{5}x_{37}\)

                  = 8568 + 58140 + 139536 / 435897

                  ≈ 0.4731

Therefore the probability is 0.4731.

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The measures of the side are: (c) PQ = 26 cm, PR = 28 cm

What is Circumscribed Circle?

Given that a triangle PQR is drawn to circumscribe a circle of radius 8 cm and the segments QT and TR are of length 14 cm and 16 cm respectively.

Let O be the center of the circle.

Let S and U be the points on PQ and PR.

Here, QS = QT = 14 cm and UR = TR = 16 cm.

Then, PS = PU = x cm

It is given that,

Area of ΔPOQ + Area of ΔQOR + Area of ΔPOR = 336 cm²  

\(\implies \frac{1}{2} \times PQ \times 8 + \frac{1}{2} \times QR \times 8 + \frac{1}{2} \times PR \times 8 =336\\\)     -----(1)

Here, height, h = 8 cm.

Also, PQ = 14 + x; PR = 16 + x and QR = 14 + 16 = 20 cm

Now, substituting the values in (1), we get

\(\implies \frac{1}{2} \times (14 + x) \times 8 + \frac{1}{2} \times 20 \times 8 + \frac{1}{2} \times (16 + x) \times 8 =336\\\implies 14+x+30+16+x=84\)

Solving further, we get

\(2x=24\\\implies x=12\)

So, PQ = 14 + 12 = 26 cm; and PR = 16 + 12 =28 cm

Therefore, the measures of the sides are: (c) PQ = 26 cm, PR = 28 cm

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Complete Question: A triangle PQR is drawn to circumscribe a circle of radius 8 cm such that the segments QT and TR, into which QR is divided by the point of contact T, are of length 14 cm and 16 cm respectively. If the area of the given triangle is 336 cm², find the measures of the sides PQ and PR.

(a) The exact probability that a person spends between 0 to 5 minutes waiting in line, and then 0 to 5 minutes waiting to check out is approximately 0.0424.

(b) The exact probability that a person spends at most 10 minutes total both waiting in line and checking out at this grocery store is approximately 0.406.

(c) The exact probability that a person spends at least 10 minutes total both waiting in line and checking out, but not more than 20 minutes, is approximately 0.290.

(a) To find the probability that a person spends between 0 to 5 minutes waiting in line and then 0 to 5 minutes waiting to check out, we need to integrate the joint probability density function f(x,y) over the region where 0 <= x <= 5 and 0 <= y <= 5

P(0 <= x <= 5, 0 <= y <= 5) = ∫∫ f(x,y) dy dx = ∫0^5 ∫0^5 (1/8)e^(- x/4 - y/2) dy dx

= 0.0424

(b) To find the probability that a person spends at most 10 minutes total both waiting in line and checking out, we need to integrate the joint probability density function f(x,y) over the region where x + y <= 10

P(x + y <= 10) = ∫∫ f(x,y) dy dx = ∫0^10 ∫0^(10-x) (1/8)e^(- x/4 - y/2) dy dx

= 0.406

(c) To find the probability that a person spends at least 10 minutes total both waiting in line and checking out, but not more than 20 minutes, we need to integrate the joint probability density function f(x,y) over the region where 10 <= x + y <= 20

P(10 <= x + y <= 20) = ∫∫ f(x,y) dy dx = ∫10^20 ∫(x-10)^2/4^(20-x)/2 (1/8)e^(- x/4 - y/2) dy dx

= 0.290

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The given question is incomplete, the complete question is:

Let x denote the time (in minutes) that a person spends waiting in a checkout line at a grocery store and y the time (in minutes) that it takes to check out. Suppose the joint probability density for x and y is  

f(x,y) = (1/8)e^(- x/4 - y/2)

(a) What is the exact probability that a person spends between 0 to 5 minutes waiting in line, and then 0 to 5 minutes waiting to check out? (b) Set up, but do not evaluate, an iterated integral whose value determines the exact prob- ability that a person spends at most 10 minutes total both waiting in line and checking out at this grocery store. (c) Set up, but do not evaluate, an iterated integral expression whose value determines the exact probability that a person spends at least 10 minutes total both waiting in line and checking out, but not more than 20 minutes.

Using the normal distribution, it is found that there is a 0.905 = 90.5% probability that the proportion of Grammy award winners will differ from the singers proportion by less than 3%.

The z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The proportion and the sample size are given, respectively, by:

p = 0.4, n = 743

Hence the mean and the standard error are given, respectively, by:

The probability that the proportion of Grammy award winners will differ from the singers proportion by less than 3% is the p-value of Z when X = 0.43 subtracted by the p-value of Z when X = 0.37, hence:

X = 0.43:

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem:

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{0.43 - 0.4}{0.018}\)

Z = 1.67

Z = 1.67 has a p-value of 0.9525.

X = 0.37:

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{0.37 - 0.4}{0.018}\)

Z = -1.67

Z = -1.67 has a p-value of 0.0475.

0.9525 - 0.0475 = 0.905.

0.905 = 90.5% probability that the proportion of Grammy award winners will differ from the singers proportion by less than 3%.

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Answer:Para preparar la tabla de frecuencia para un histograma, es necesario primero establecer el número de intervalos que se desea tener.

Luego, se debe determinar el ancho común de los intervalos (interval width). Para esto, se calcula la diferencia del dato mayor y el dato menor, y se divide entre el número de intervalos deseados. Este resultado se redondea al entero mayor más cercano.

Por ejemplo, si se desea tener 10 intervalos y encontramos que el dato mayor es 35 y el menor es 12,

Step-by-step explanation:

The sum of 488 in scientific notations is 4.88 × 10^1.

We are given that;

The number = 488

Now,

488 in scientific notation

Step 1: Move the decimal point so that there is only one non-zero digit to the left of it.

488.0

The decimal point is moved one place to the left.

4.88

Step 2: Write the number as a product of the decimal and a power of 10.

The decimal point was moved one place to the left, so the exponent is 1.

4.88 × 10^1

Therefore, by the algebra the answer will be 4.88 × 10^1.

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Answer:

0.772

Step-by-step explanation:

Original equation:

\(18 * 2^{5t}=261\)

Divide both sides by 18

\(2^{5t} = 14.5\)

Rewrite in logarithmic form (\(b^x=c \implies log_bc=x\))

\(log_214.5 = 5t\)

Divide both sides by 5

\(\frac{log_214.5}{5}=t\)

Rewrite the equation so that base is 10 using change of base formula: \(log_ba = \frac{log_na}{log_nb}\)

\(\frac{(\frac{log14.5}{log2})}{5}=y\)

Keep, change, flip

\(\frac{log14.5}{log2}*\frac{1}{5} = \frac{log14.5}{5 * log2}\)

Use a calculator to approximate log14.5 and log2

\(\frac{1.161368}{5 * 0.301029996} = t\)

Multiply in denominator

\(\frac{1.161368}{1.505149978} = t\)

Divide two values

\(t\approx 0.771596\)

Round to nearest thousandth

\(t\approx 0.772\)

Answer:

ok im telling people to help u because i dont know that xd

Step-by-step explanation:

Answer: y = 3.75x + 2.50

Step-by-step explanation:

The equation that can be used to find y, the total cost of renting a bike, if x represents the number of hours Violet rents the bike is:

y = 3.75x + 2.50

Explanation:

Violet pays an initial fee of $2.50, which is a fixed cost that does not depend on the number of hours she rents the bike. Additionally, she pays $3.75 per hour she rents the bike, which is a variable cost that depends on the number of hours. Therefore, the total cost of renting a bike (y) can be expressed as the sum of the fixed cost ($2.50) and the variable cost ($3.75x), which gives the equation:

Angle A of triangle ABC is decreasing at the rate of 4. degrees per second, while sides AB and AC are increasing at the rates of 4 and 5 meters per second respectively. If at certain instant A-45 degrees, AB 10m, AC 7m,fast is the area of the triangle changingGiven:A is decreasing at the rate of 4.

degrees per secondAB is increasing at the rate of 4 m/sAC is increasing at the rate of 5 m/sTo find:How fast is the area of the triangle changing?Let us first use the sine rule to find the length of BC.cos A = (b² + c² - a²) / 2bcWe have:AB = 10 mAC = 7 mA = 45°cos 45° = (10² + 7² - a²) / (2 × 10 × 7)⇒ a = 11 mArea of the triangle is given by:Area = (1 / 2) bc sin AWe have:BC = a = 11 mAt an instant when A = 45°,

we have sin 45° = √2 / 2Now, Area = (1 / 2) (10) (7) (√2 / 2)Area = 35√2 / 2Differentiating Area with respect to time t:∂Area/∂t = (1 / 2) [(b × ∂c/∂t) + (c × ∂b/∂t)] sin A + (1 / 2) bc cos A (∂A/∂t)We have:b = AB = 10 m∂b/∂t = 4 m/sc = AC = 7 m∂c/∂t = 5 m/s∂A/∂t = -4°/sAt the instant when A = 45°, we have:cos 45° = 1 / √2Now,∂Area/∂t = (1 / 2) [(10 × 5) + (7 × 4)] (1 / √2) + (1 / 2) (10) (7) (1 / √2) (1 / √2) (-4°/s)∂Area/∂t = 112.5 - 35 (-4/2)∂Area/∂t = 142.5 m²/s5) Water is leaking out of a conical tank at the rate of 0.5 m³/min

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The angle of reflection for the ray leaving mirror 2 will be 41 degrees, as this is equal to the angle of incidence for the ray striking mirror 2.

The angle of incidence is the angle between the incoming ray and the surface of the mirror, and the angle of reflection is the angle between the reflected ray and the surface of the mirror.

In the given scenario, a ray of light strikes mirror 1 with an angle of incidence of 41 degrees.

The angle of reflection can be calculated using the law of reflection, which states that the angle of incidence is equal to the angle of reflection.

Therefore, the angle of reflection of the ray when it leaves mirror 1 will be 41 degrees.

However, the ray of light continues its journey and strikes mirror 2.

When this happens, the angle of incidence is the angle between the reflected ray from mirror 1 and the surface of mirror 2.

The angle of reflection for the ray leaving mirror 2 can be calculated using the same law of reflection.

The angle of reflection will be equal to the angle of incidence, which is 41 degrees.

The angle of reflection is a crucial concept in understanding the reflection of light and is used in various applications such as mirrors, prisms, and lenses.

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Answer:

22

Step-by-step explanation:

Given

From Juan's calculation,

Difference of two positive integers = 2

From Maria's calculation,

Product of same integers = 120

Required

Find the sum of the two numbers

Let the two integers be represented by a and b

a - b = 2 ------- (1)

a * b = 120 ------- (2)

Make a the subject of formula in (1)

a = 2 + b

Substitute 2 + b for a in (2)

(2 + b) * b = 120

Open bracket

2 * b + b * b = 120

2b + b² = 120

Rearrange

b² + 2b = 120

Subtract 120 from both sides

b² + 2b - 120 = 120 - 120

b² + 2b - 120 = 0

At this point, we have a quadratic equation.

We start by expanding the expression

b² + 12b - 10b - 120 = 0

Factorize

b(b + 12) - 10(b + 12) = 0

(b - 10)(b + 12) = 0

This implies that

b - 10 = 0 or b + 12 = 0

Make b the subject of formula in both cases

b = 10 or b = -12

From the question, we understand that both numbers are positive.

This means that

b = -12 will be discarded.

Hence, b = 10

Recall that a = 2 + b

Substitute 10 for b

a = 2 + 10

a = 12

This implies that the two numbers are 12 and 10.

Their sum = 12 + 10

Sum = 22

The correct answer is 22

Answer:

Step-by-step explanation:

\(\frac{9}{11}=0 .818181....\)

     __  

= 0.81

The z-score for a raw score of 6 is 0.5.A z-score indicates how many standard deviations a raw score is away from the mean.

To calculate the z-score for a raw score of 6 given a mean of 4 and a standard deviation of 4, we can use the formula:

z = (raw score - mean) / standard deviation

Substituting the values into the formula, we get:

z = (6 - 4) / 4

z = 0.5

Therefore, the z-score for a raw score of 6 is 0.5.

In this case, a z-score of 0.5 indicates that the raw score of 6 is half a standard deviation above the mean of 4.

Z-scores are useful because they allow us to compare scores from different distributions. For example, if we have two sets of data with different means and standard deviations, we can convert them into z-scores to compare them directly. A positive z-score means that the raw score is above the mean, while a negative z-score means that the raw score is below the mean. The magnitude of the z-score indicates how far the raw score is from the mean in terms of standard deviations.

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Position of 1083 is 19 in the sequence that is the first one with a value greater than 1000.

What is Sequence?

A list of numbers or objects in a special order is called sequence.

Given that;

The nth term of a sequence = 3n²

Now,

Let \(a_{n}\) be the nth term.

Then, \(a_{n} = 3n^{2}\)

Let m be the term which is the first term with a value greater than 1000.

Then, \(a_{m} > 1000\)

Substituted the value of \(a_{m}\) we get;

3m² > 1000

Divide by 3 we get;

m² > 1000/3

m² > 333.333

Take square root both side;

m > √333.33

m > 18.25

Thus, m = 19

So, 19th term is the first one with a value greater than 1000.

Hence, \(a_{19} = 3(19)^2 = 3 * 361 = 1083\)

Thus, Position of 1083 is 19 in the sequence that is the first one with a value greater than 1000.

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The area covered by the label is 188.4cm² and total surface area is 244.92cm².

A cylinder's total surface area is equal to the sum of all of its faces' surface areas. The cylinder's total surface area—the sum of its curved and circular areas—has a radius of "r" and a height of "h."

Here, we have

Given: A can of soup in the shape of a cylinder is 10 centimeters tall and has a diameter of 6 centimeters.

We have to find the total surface area of the can including the top and bottom.

The area covered by the label = πd×height

= π(6)×10

= 3.14×6×10

= 188.4

Total surface area =  πr² +  πr³ + 188.4

= 3.14(3)² +  3.14(3)³ + 188.4

= 244.92

Hence, the area covered by the label is 188.4cm²

and total surface area is 244.92cm².

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The ratio that compares the men to the women who work at the warehouse is 4 : 1.

A ratio is a value that shows the proportional relationship between two quantities.

A ratio indicates how many times one number is contained in another.

For example, in the above task, there is 4x the number of men when compared with the number of women who work at the warehouse.

Men working at the warehouse = 1,200

Women working at the warehouse = 300

Ratio of men to women = 4 : 1 (1,200 : 300)

Thus, the ratio that compares the men to the women who work at the warehouse is 4 : 1.

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Answer: 4:1

i just took a test

Step-by-step explanation:

Answer:

I know this aint no clever bro cmon that stuff is easy

Step-by-step explanation:

Answer:

a) the midpoint is (1.5, 2.5)

b) the line is y = -(7/3)*x + 6.

Step-by-step explanation:

a)

Suppose we have two values, A and B, the mid-value between A and B is:

(A + B)/2

Now, if we have a segment with endpoints (a, b) and (c, d), the midpoint will be in the mid-value of the x-components and the mid-value of the y-components, this means that the midpoint is:

( (c + a)/2, (b + d)/2)

a) Then if the endpoints of the segment are (-2, 1) and (5, 4), the midpoint of this segment will be:

( (-2 + 5)/2, (1 + 4)/2) = (3/2, 5/2) = (1.5, 2,5)

The midpoint of the segment is (1.5, 2.5)

b)

Now we want to find the equation of a perpendicular line to our segment, that passes through the point (1.5, 2.5).

First, if we have a line:

y = a*x + b

A perpendicular line to this one will have a slope equal to -(1/a)

So the first thing we need to do is find the slope of the graphed segment.

We know that for a line that passes through the points (a, b) and (c, d) the slope is:

slope = (c - a)/(d - b)

Then the slope of the segment is:

slope = (4 - 1)/(5 - (-2)) = 3/7

Then the slope of the perpendicular line will be:

s = -(7/3)

Then the perpendicular line will be something like:

y = -(7/3)*x + d

Now we want this line to pass through the point (1.5, 2.5), then we can replace the values of this point in the above equation, and solve for d.

2.5 = -(7/3)*1.5 + d

2.5 + (7/3)*1.5 = d = 6

Then the line is:

y = -(7/3)*x + 6

Answer:

63 ÷ 84 = 0.75 // 75% // 3/4

Step-by-step explanation:

63 divided by 84 equals 0.75, 75%, or 3/4. meaning the probability of Mike making his next free throw 75%

The values of y when x = -2, 2, 3 are -1, -1, 4

Algebra is the branch of mathematics that studies the rules of operations and relations, as well as the constructions and concepts that arise from them, such as terms, polynomials, equations, and algebraic structures.

Given data

x -2 -1  0  1  2  3  4

y ---- -4 -5 -4 ---- --- 11

Given expression y = x2 -5

We have to find the y values when x =-2 ,2, 3 in the given table

If x = -2 then

Y = (-2)2 -5

Y= 4 – 5

Y= -1

If x = 2 then

Y = (2)2 -5

Y= 4 – 5

Y= -1

If x = 3 then

Y = (3)2 -5

Y= 9 – 5

Y= 4

Therefore the values of y when x = -2, 2, 3 are -1, -1, 4

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Answer:

you would role 2 about 67 times

Step-by-step explanation:

Answer:

67 times

Step-by-step explanation:

The probability of rolling a 2 is:

P(2) = number of 2's on a die / total sides on a die.

P(2) = 1/6

Multiply this probability by the number of rolls.

P(2) * 400

1/6 * 400

66 2/3

Rounding up.

67 times