Question 3 (1 point)
A sixth-grade class collected data on the number of siblings in the class. Here is the dot plot of the data they collected.

How many students had zero brothers or sisters?

Joseph must score at least 32 on exam B to do equivalently well as he did on exam A.

To determine how well Joseph must score on exam B in order to do equivalently well as he did on exam A, we need to find the equivalent z-score for his exam A score and then use it to find the corresponding score on exam B.

First, we find the z-score for Joseph's exam A score:

z = (x - mu) / sigma

z = (516 - 600) / 40

z = -2.1

The z-score of -2.1 indicates that Joseph's exam A score is 2.1 standard deviations below the mean.

To find the equivalent score on exam B, we use the formula:

z = (x - mu) / sigma

Solving for x, we get:

x = z * sigma + mu

x = -2.1 * 20 + 76

x = 32

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The reason is 2) Vertical Angles Theorem.

Given is figure in which two triangles are joined,

We need to complete the proof of ΔBCA ≅ ΔDCE,

So,

BC = DC, AC = EC [given]

∠BCA = ∠DCE [Vertical Angles Theorem]

ΔBCA ≅ ΔDCE by SAS rule,

Hence, the reason is 2) Vertical Angles Theorem.

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The answer of this question is equation [-6x+4y=16].

An equation is a mathematical statement that shows the equality between two expressions, typically separated by an equal sign. It can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The goal of solving an equation is to find the value of the variable that makes the equation true.

In mathematics, a system refers to a collection of mathematical objects or entities that are related or interconnected in some way.

System A

5x-y=-11

3x-2y=-8

System B

5x-y=-11

-2(3x-2y)=-8×(-2)

5x-y=-11

-6x+4y=16

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The highest point of a normal curve, also known as a Gaussian distribution or bell curve, always occurs at the mean. This is because the normal curve is symmetrical around the mean, with the same number of values on either side of the mean. Therefore, the peak of the curve must be directly above the mean.

The standard deviation is a measure of how spread out the values in a distribution are. For a normal distribution, approximately 68% of the values fall within one standard deviation of the mean, 95% fall within two standard deviations of the mean, and 99.7% fall within three standard deviations of the mean. Therefore, while the highest point of the normal curve occurs at the mean, the curve does extend out to both sides of the mean, with the height of the curve gradually decreasing as the distance from the mean increases.

Specifically, the point at which the curve begins to flatten out on either side of the peak is approximately one standard deviation away from the mean. At two standard deviations away from the mean, the curve has flattened out significantly, and at three standard deviations away from the mean, the curve is almost entirely flat. This is known as the empirical rule, or the 68-95-99.7 rule.

Understanding the normal curve and its characteristics is important in statistics and data analysis, as many real-world phenomena can be approximated using a normal distribution. By knowing the mean and standard deviation of a distribution, we can make predictions about the likelihood of various outcomes occurring.

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3/4

If she ate part of the large cookie and was left with 1/4 of the cookie, that means only 3/4 of the cookie is left.

x - 4/3 ≤ 0 is equivalent to x ≥ 4/3, and they both represent the same set of values for x. My friend is correct.

The relationship between two values that are not equal is defined by inequalities.

When we subtract 4/3 from both sides; x ≤ 4/3 can be rewritten as:

x - 4/3 ≤ 0

-6x ≤ -8 can be simplified by dividing both sides by -6 and reversing the inequality which gives:

x ≥ 4/3.

Full question "Your friend says that the inequalities x ≤ 4/3 and -6x ≤ -8 is your friend correct? Explain the reason"

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The width of the parking lot in the drawing is 16 centimeters

Gabby made a scale drawing of the town library. She used the scale 1 centimeter : 5 meters. The actual width of the parking lot is 80 meters.

If the scale is 1 centimeter : 5 meters, then 1 centimeter on the drawing represents 5 meters in real life.

To find the width of the parking lot in the drawing, we need to set up a proportion

1 cm : 5 m = x cm : 80 m

Where x is the width of the parking lot in the drawing.

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

1 cm * 80 m = 5 m * x cm

80 cm = 5x

x = 16 cm

Therefore, the width of the parking lot in the drawing is 16 centimeters.

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If Y is directly proportional to the cube root of x, the percentage increase in y when x is increased by 700% is 100%.

If y is directly proportional to the cube root of x, we can write this relationship as y = [tex]kx^{(1/3)[/tex], where k is the constant of proportionality.

To find the percentage increase in y when x is increased by 700%, we first need to determine the new value of x. An increase of 700% means that x is multiplied by (1 + 700%) = 8. Therefore, the new value of x is 8 times the original value.

Substituting the new value of x into the equation for y, we get:

y = [tex]k(8x)^{(1/3)[/tex]

Simplifying this expression, we can write:

y = [tex]k(2^{3x)^{(1/3)[/tex]

y = k2x

So, we can see that when x is increased by 700%, y is increased by a factor of 2. This corresponds to a percentage increase of 100%.

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a) The exact solutions on [0, 2π) are t = π/3, π, and 5π/3. b) The exact solution on the interval [0, π) is t = 2π/3. c) The solutions are θ = π/3 and θ = 5π/3. d) The exact solutions on the interval [0, 2π) are: t = arcsin[(-1 +  [tex]\sqrt{41}[/tex])/4] and t = 2π - arcsin[(-1 +  [tex]\sqrt{41}[/tex])/4] using trigonometric identities.

a) We can rewrite the equation as:

2[tex]cos^{2}t[/tex] + cos(t) - 1 = 0

Using the quadratic formula, we get:

cos(t) = [-1 ± [tex]\sqrt{1-4(2)(-1)}[/tex] ] / (4)

cos(t) = [-1 ± [tex]\sqrt{9}[/tex]]/4

cos(t) = [-1 ± 3]/4

Thus, we have two solutions:

cos(t) = 1/2, which gives us t = π/3 and t = 5π/3

cos(t) = -1, which gives us t = π

Therefore, the exact solutions on [0, 2π) are t = π/3, π, and 5π/3.

b) We can use the identity [tex]tan^{2}t[/tex] + 1 = [tex]sec^{2}t[/tex] to rewrite the equation as:

[tex]tan^{2}t[/tex] = - [tex](3/2)^{2}[/tex]

Taking the square root of both sides and remembering that tan(t) is negative in the third quadrant, we get:

tan(t) = -3/2

Using the identity tan(t) = sin(t)/cos(t), we can rewrite this as:

sin(t)/cos(t) = -3/2

Multiplying both sides by cos(t) and rearranging, we get:

sin(t) = -3cos(t)/2

Squaring both sides and using the identity [tex]sin^{2}t[/tex] + [tex]cos^{2}t[/tex] = 1, we get:

9[tex]cos^{2}t[/tex]/4 + [tex]cos^{2}t[/tex] = 1

Expanding and simplifying, we get:

13 [tex]cos^{2}t[/tex] /4 = 1

[tex]cos^{2}t[/tex]  = 4/13

Taking the square root of both sides and remembering that cos(t) is negative in the third quadrant, we get:

cos(t) = -2[tex]\sqrt{13}[/tex] /13

Using the identity  [tex]sin^{2}t[/tex] +  [tex]cos^{2}t[/tex]  = 1, we can solve for sin(t) as:

sin(t) = -3/2 cos(t) = 3[tex]\sqrt{13}[/tex] /13

Therefore, the exact solution on the interval [0, π) is t = 2π/3.

c) We can use the identity sin(2θ) = 2sin(θ)cos(θ) to rewrite the equation as:

sin(θ) = 2sin(θ)cos(θ)

Dividing both sides by sin(θ) (assuming sin(θ) is non-zero), we get:

1 = 2cos(θ)

cos(θ) = 1/2

Therefore, the solutions are θ = π/3 and θ = 5π/3.

d) We can use the identity cos(2t) = 1 - 2 [tex]sin^{2}t[/tex]  and rearrange the equation as:

2 [tex]sin^{2}t[/tex]  + sin(t) - 5 = 0

Solving this quadratic equation using the quadratic formula, we get:

sin(t) = [-1 ± [tex]\sqrt{41}[/tex]]/4

Since the sine function has a range of [-1, 1], only the positive solution is possible, so we have:

sin(t) = (-1 + [tex]\sqrt{41}[/tex])/4

Using the identity [tex]cos^{2}t[/tex] = 1 -  [tex]sin^{2}t[/tex] , we can solve for cos(t) as:

cos(t) =[tex]\sqrt{1-sin^{2}t}[/tex] = [tex]\sqrt{17-\sqrt{41} }/4[/tex]

Therefore, the exact solutions on the interval [0, 2π) are:

t = arcsin[(-1 +  [tex]\sqrt{41}[/tex])/4] and t = 2π - arcsin[(-1 +  [tex]\sqrt{41}[/tex])/4]

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The cylinder's volume is 245 cubic units as a result.

It is possible to determine how much material a cylinder can carry by using its volume, which is known as its capacity in geometry. Cubic measurements for a cylinder's volume include cm³, m³, in³, etc.

The formula V = r²h is used to determine the volume of a cylinder, where r is the radius of its circular base and h is the height between the bases' perpendicular centers.

As a result, if r = 7 units and x = 5 units, we can use the formulas below to get the cylinder's volume:

V = πr²h

V = π(7)²(5)

= 245 cubic units per volt

Consequently, the size of the cylinder 245 cubic units as a result.

Complete question given below:

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If r = 7 units and x = 5 units, then what is the volume of the cylinder(height=x)?

The volume of the cylinder is 245π cubic units.

The cylinder is a three-dimensional shape having a circular base. A cylinder can be seen as a set of circular disks that are stacked on one another.

The formula for the volume of a cylinder is:

V = πr²h

where r is the radius of the base, h is the height, and π is the mathematical constant pi (approximately equal to 3.14).

Substituting r = 7 units and h = 5 units into the formula, we get:

V = π(7)²(5)

V = π(49)(5)

V = 245π

Therefore, the volume of the cylinder is 245π cubic units. Note that the volume is an exact value in terms of π, and cannot be simplified further without a numerical approximation of π.

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Answer:

1,760m

Step-by-step explanation:

The side of the smaller triangle is multiplied by 4, which got 44 in the bigger triangle. So you would multiply the base of the smaller by 4 as well, resulting in 80. Now you need to multiply the base and the side of the triangle, and divide that answer by half.

FORMULA FOR A TRIANGLE:

A= 1/2( L x W )

A= 1/2 (44 x 80)

A= 1/2 (3520)

A= 1760

Therefore, the area of the shaded triangle is 1,760m.

SORRY IF THIS DID NOT MAKE SENSE!

Answer:

A 48 pound catfish would be approximately 45 inches long

Step-by-step explanation:

First find the slope of the line, m, using 2 points on the line, (20, 3) and (25, 12)

m = (12-3) / (25-20) = 9/5

Use the point (30, 21) and slope to find the equation (in point-slope form) of the line:

(y - 21) = 9/5(x - 30) = 9/5x - 270/5 = 9/5x - 54

y = 9/5x - 54 + 21 = 9/5x - 33

y = 9/5x - 33      now you have the equation of the line in y = mx + b form

Find x (catfish length) when y = 48 (catfish weight)

48 = 9/5x - 33

9/5x = 48 + 33 = 81

x = 81 · 5/9 = 45

x = 45 inches

Answer: If there are 60 questions and the student has to answer 75% of questions then the number of questions the student must answer is 45

Step-by-step explanation:

No of questions= 60,

Answers to be given= 75%

then no of questions to pass the exam= No of questions*Answers to be given in percentage

=60*75/100\

=45

The x² value lie between 1.42 and 2.37

The formula to calculate the x² value is:

χ² = Σ (Observed frequency - Expected frequency)² / Expected frequency

Here, Σ represents the sum of all the values in the calculation. The observed frequency is the actual frequency of a category in the sample, while the expected frequency is the theoretical frequency based on the null hypothesis.

The x² value is compared to a chi-squared distribution table to determine its significance level. The table shows the probability of obtaining a certain x² value under the null hypothesis for different degrees of freedom. Degrees of freedom (df) are calculated as the number of categories minus 1.

If the calculated x² value is greater than the critical value from the table for a given significance level, the null hypothesis is rejected, and the alternative hypothesis is accepted. This means that there is a significant relationship between the variables. If the calculated x² value is less than the critical value, the null hypothesis is accepted, and no significant relationship is found.

In the context of the problem given, the x² value is used to test the hypothesis that the genes are unlinked. The significance level used is 0.05, which means that there is a 5% chance of rejecting the null hypothesis when it is actually true. If the probability corresponding to the x² value is less than or equal to 0.05, the hypothesis should be rejected. If it is greater than 0.05, the results are not statistically significant, and the hypothesis is accepted.

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Complete Question:

The x² value means nothing on its own- it is used to find the probability that, assuming the hypothesis is true, the observed data set could have resulted from random fluctuations. A low probability suggests that the observed data are consistent with the hypothesis, and thus the hypothesis should be rejected, A standard cutoff point used by biologists is a probability of 0.05(5%). If the probability corresponding to the x² value is 0.05or considered statistically significant, the hypothesis (that the genes are unlinked) should be rejected. If the probability is above 0.05, the results are not statistically significant: the observed data are consistent with the hypothesis.

Determines which values on the df =3 line of the table your calculated x² value lies between.

Answer:

x=4

Step-by-step explanation:

If the equation is:

[tex]x^{2} =16[/tex]

then the answer is 4, because to solve this, you would have to take the square root of both sides to cancel out the square on the left side of the equation:

[tex]\sqrt{x^{2} } =\sqrt{16}\\ x=4[/tex]

Hope this helps :)

The solution to this system of equations can be found by equating f(x) and g(x) and solving for x:

3x = x + 2

2x = 2

x = 1

Based on the given table data, we can see that the number of imports (f(x)) and the number of exports (g(x)) follow a linear relationship with respect to the month (x). The data shows that as the month progresses, both the number of imports and exports increase.

The system of equations can be represented as follows:

f(x) = 3x

g(x) = x + 2

The first equation f(x) = 3x represents the number of imports, where the coefficient of x is 3, indicating that the number of imports increases by 3 units for every increase of 1 unit in the month.

The second equation g(x) = x + 2 represents the number of exports, where the coefficient of x is 1, indicating that the number of exports increases by 1 unit for every increase of 1 unit in the month. Additionally, there is a constant term of 2, which represents the initial number of exports in the month of January.

The solution to this system of equations can be found by equating f(x) and g(x) and solving for x:

3x = x + 2

2x = 2

x = 1

The solution x = 1 represents the month of January, where both the number of imports and exports are equal to 3. This implies that in the month of January, there were 3 units of imports and 3 units of exports.

In all, the solution to the system of equations indicates that in the month of January (x = 1), the number of imports (f(x)) and the number of exports (g(x)) were both 3 units, as per the given data in the table.

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Answer:10g-3

Step-by-step explanation:

Answer:

g=0.5

Step-by-step explanation:

2(5—1)=3

10g—2=3

10g—2+2=3+2

10g=5

10g/10=5/10

g=0.5

The probability that exactly one of the computers will be defective is 0.141

To calculate the probability of exactly one defective computer being selected out of four computers, we can use the binomial distribution formula

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

where P(X = k) is the probability of exactly k successes (in this case, one defective computer), n is the total number of trials (in this case, four computers being selected), p is the probability of success (in this case, the probability of selecting a defective computer), and (n choose k) is the binomial coefficient, which represents the number of ways to choose k items out of n.

The probability of selecting a defective computer is 4/15, since there are 4 defective computers out of 15 in total. Therefore, the probability of selecting exactly one defective computer out of four is:

P(X = 1) = (4 choose 1) × (4/15)^1 × (11/15)^3

= 4 × 4/15 × 1331/3375

= 0.141

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The given question is incomplete, the complete question is:

A computer retail store has 15 personal computers in stock. A buyer wants to purchase 4 of them. Unknown to either the retail store or the buyer, 4 of the computers in stock have defective hard drives. Assume that the computers are selected at random. What is the probability that exactly one of the computers will be defective?

Answer:

sugger

Step-by-step explanation:

because she bought 34.15 super and 34.144 pepper

In 2010, Haiti was hit by a devastating earthquake, which registered at 7.0 on the Richter scale. The largest recorded earthquake since 1900 occurred in 1960 in Valdivia, Chile, and registered at 9.5 on the Richter scale. About 316 times greater was the intensity of the Chilean earthquake.

Hence, the correct option is D.

The Richter scale is a logarithmic scale that measures the magnitude of an earthquake. Each increase of one on the Richter scale represents a tenfold increase in the amplitude of the seismic waves.

To find out how many times greater the intensity of the Chilean earthquake was compared to the Haitian earthquake, we will have to find the difference in magnitude between the two earthquakes.

9.5 - 7.0 = 2.5

Since each increase of one on the Richter scale represents a tenfold increase in the amplitude of the seismic waves, a 2.5 increase represents

10^(2.5) = 316.2

Hence, the intensity of the Chilean earthquake was about 316 times greater than the intensity of the Haitian earthquake.

Hence, the correct option is D.

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Answer:d

Step-by-step explanation:

its d

The polar form of the rectangular coordinates (-3√3, 0) is r = 3√3 and θ = 0

To convert the rectangular coordinates (-3√3, 0) into polar form, we can use the following equations:

r = √(x² + y²)

θ = tan⁻¹(y/x)

In this case, x = -3√3 and y = 0, so we have:

r = √((-3√3)² + 0²) = 3√3

θ = tan⁻¹(0/(-3√3)) = tan⁻¹(0) = 0

Since the angle is given in radians over the interval 0 ≤ θ < 2π (which is equivalent to 0 ≤ θ < 6.28318), we need to add 2π to θ if it is negative, to ensure that θ is in the specified interval.

However, in this case, θ is already equal to 0, which is within the specified interval.

Therefore, the polar form of the rectangular coordinates (-3√3, 0) is:

r = 3√3

θ = 0 (in radians, over the interval 0 ≤ θ < 2π)

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Using percentages we know that Terrel has the best free throw statistics which is 70.83%.

In mathematics, a quantity or ratio known as A% stands for a percentage of 100.

There are several different ways to depict a dimensionless connection between two numbers, including ratios, fractions, and decimals.

To represent percentages, the symbol "%" is typically written after the number.

In mathematics, a percentage is a number or ratio that is expressed as a fraction of 100.

So, in the given situation where we need to get whose statistics are the best.

We need to calculate the percentages in all cases as follows:

Jack: 18/39*100 = 46.15%

Henry: 54%

Terrel: 17/24*100 = 70.83%

Riley: 9/23*100 = 39.13%

Since Terrel has the highest %, so he has the best free throw statistics.

Therefore, using percentages we know that Terrel has the best free throw statistics which is 70.83%.

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An argument can be invalid even if the premises are true and the conclusion is false.This statement is actually false.

Invalidity refers to the structure of the argument, not the truth value of the premises or conclusion. An invalid argument fails to establish the truth of its conclusion even if its premises are true. In contrast, a valid argument guarantees that the conclusion follows from the premises, regardless of the truth or falsity of the premises. Therefore, an argument can be valid with false premises, and an argument can be invalid with true premises.

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Conclude that there is no guarantee that the conclusion will be false when all the premises are false in an invalid

argument.

If an argument is invalid, then whenever the premises are all false, the conclusion must also be false.

An invalid argument is one where the conclusion does not necessarily follow from the premises, even if the premises

are all true.

In other words, it is possible for the premises to be true, but the conclusion to be false. However, in the scenario you

described, all the premises are false. In an invalid argument, there is no guarantee that the conclusion will also be false.

Identify the argument as invalid.

Recognize that all the premises are false.

Understand that in an invalid argument, the conclusion does not necessarily follow from the premises.

Conclude that there is no guarantee that the conclusion will be false when all the premises are false in an invalid

argument.

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The expression that represents the relationship between the step number n and the total number of small squares in the pattern is this: (n-1)^2.

From the given information, we can see that the pattern starts with 0 squares at step 1, and each subsequent step adds a square to the pattern. However, the lower right square is always missing. Therefore, the total number of small squares in the pattern at step n can be represented by the expression: (n-1)^2

The reason we subtract 1 from n is that we started counting from step 1, whereas the expression (n-1)^2 assumes that we start counting from 0. Then we square (n-1) to account for the number of squares in the pattern, excluding the missing square in the lower right corner.

Complete Question:

Which expression represents the relationship between the step number n and the total number of small squares in the pattern?

A pattern of small squares. Step 1 has 0 squares. Step 3 has 3 squares: 2 by 2 but missing the lower right square. Step 3 has 8 squares: 3 by 3 but missing the lower right square.

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After Derek drinks 1/4 ounce of water, he is left with 95/3 ounces of water in his glass.

Derek initially had 10 2/3 ounces of water in his glass. To find out how much water is left after he drinks 1/4 ounce of water, we need to subtract 1/4 from 10 2/3. To do that, we need to convert the mixed number (10 2/3) into an improper fraction.

To convert a mixed number into an improper fraction, we multiply the whole number by the denominator of the fraction and then add the numerator. In this case, we have:

10 x 3 + 2 = 32/3

Therefore, Derek initially had 32/3 ounces of water in his glass.

To subtract 1/4 from 32/3, we need to make sure the denominators are the same. We can convert 1/4 into twelfths by multiplying both the numerator and denominator by 3. This gives us:

1/4 x 3/3 = 3/12

Now that we have a common denominator of 12, we can subtract:

32/3 - 3/12 = 383/12 - 3/12 = 380/12

To simplify, we can divide both the numerator and denominator by 4:

380/12 ÷ 4/4 = 95/3

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Complete question is:

Derek had 10 2/3 ounce of water in a glass He drank 1/4 of an ounce of the water from his glass how much water is left in Derek's glass?

We can say with 82% confidence that the true difference in mean times for left-handed and right-handed people is between -0.978 s and -0.222 s and t-distribution is used.

To calculate the certainty interim for the contrast between left-handed and right-handed individuals, we are able to utilize the taking-after equation:

CI = (x1 - x2) ± t*SE 

where:

x1 = the meantime for left-handed people

x2 = the meantime for right-handed people

t = the critical value for the t-distribution with n1+n2-2 degrees of freedom and the desired confidence level (in this case, 82%)

SE = the standard error of the difference in means, which is calculated as:

[tex]SE = sqrt((s1^2/n1) + (s2^2/n2))[/tex]

where:

s1 = the standard deviation for left-handed people

s2 = the standard deviation for right-handed people

n1 = the sample size for left-handed people

n2 = the sample size for right-handed people

Plugging in the given values, we get:

x1 - x2 = 1.1 - 1.7 = -0.6

s1 = 0.4

s2 = 1.4

n1 = 47

n2 = 42

[tex]SE = sqrt((0.4^2/47) + (1.4^2/42)) = 0.261[/tex]

To find the critical value for the t-distribution, we can use a t-table or a calculator. With n1+n2-2 = 87 degrees of freedom and an 82% confidence level, the critical value is approximately 1.360.

Thus, the 82% confidence interval for the difference in left-handed or right-handed people is:

CI = (-0.6) ± (1.360*0.261) = (-0.978, -0.222)

hence, we can say with 82% confidence that the true difference in mean times for left-handed and right-handed people is between -0.978 s and -0.222 s.

Note that we used the t-distribution because the sample sizes for both groups are relatively small (n1 = 47, n2 = 42).

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The option (3) is correct the quotient is −5x³ + x + 3.

To solve quadratic equations by factoring, we first express the quadratic polynomial into a product of factors by using middle term splitting or different identities and then set each factor equal to 0. The equation a x 2 + b x + c = 0 ( a ≠ 0 ) can be written as.

According to given question

To divide[tex]15x^5[/tex] − 3x³ − 9x² by −3x² using the factorization method, we can factor out −3x² from the expression and simplify to get:

[tex]15x^5[/tex]− 3x³ − 9x²= −3x²(−5x³ + x + 3)

Therefore, the quotient is −5x³ + x + 3.

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