A checkout clerk at a department store is expected to complete 16 transactions every hour.
In the past 20 minutes, he completed 6 transactions.
Choose True or False for each statement.

Statements:

If the clerk continues at the same rate, he will meet his goal of 16 transactions in 1 hour.

At his current rate, the clerk will complete 12 transactions in 1 hour.

At his current rate, the clerk will complete 9 transactions every half hour.

If the clerk continues at this rate for a 6-hour shift, he will complete 96 transactions.

Answer:

266.6 ft

Step-by-step explanation:

If a person stands at a point and looks up at an object, the angle between their horizontal line of sight and the object is called the angle of elevation.

To find how far away from the building you are standing, we need to find the distance labelled "x" on the attached diagram. We can do this by modelling the given scenario as a right triangle and solving for x by using the tangent trigonometric ratio.

[tex]\boxed{\tan \theta=\sf \dfrac{O}{A}}[/tex]

where:

Given information:

As your eyes are 5 ft above the ground, we have to model the line of sight as 5 ft above ground level.  Therefore, the side of the right triangle opposite the angle of elevation is the height of the building less 5 ft:

[tex]\implies \sf 1000 \; ft - 5\; ft=995 \; ft[/tex]

Let "x" be the horizontal distance between you and the building.

Therefore, the values to substitute into the tangent ratio are:

Substitute these values into the ratio and solve for x:

[tex]\tan 75^{\circ}=\dfrac{995}{x}[/tex]

[tex]x=\dfrac{995}{\tan 75^{\circ}}[/tex]

[tex]x=266.609446...[/tex]

[tex]x=266.6\; \sf ft\; (nearest\;tenth)[/tex]

Therefore, you are standing 266.6 ft from the building.

Thus, the statement  -3 to the -3 power written without using exponents is -1/27.

A number's power or exponent, in other words, tells how many times it must be multiplied by itself. Any integer, fraction, or decimal can serve as the basis in this situation. Moreover, the exponent might have either a positive or negative value.

Given that-

-3 to the -3 power

This can written as:

= (-3)⁻³

Now using the property of exponents,taking reciprocal of the number will remove the negative number.

= (1 /-3)³

= (1)³ / (-3)³

= 1/(-27)

= - 1/ 27

Thus, the statement  -3 to the -3 power written without using exponents is -1/27.

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The monthly payment and total price paid by Antony at interest rate of 6.8% for vehicle is $362.59 and $21204.4 respectively.

Cost price of the car Antony decided to purchase = $19,000

Down payment =  20% of purchase value

Interest rate of amount to be finance = 6.8%

Time period of finance amount = 4 years

Down payment = 0.2 × $19,000

                         = $3,800

Amount that Anthony needs to finance,

Amount to finance = $19,000 - $3,800

                               = $15,200

The monthly payment , use the formula for the monthly payment on a loan,

M = P × r × (1 + r)ⁿ / ((1 + r)ⁿ - 1)

where M is the monthly payment,

P is the principal the amount to finance

r is the monthly interest rate

n is the total number of payments which is the number of years multiplied by 12

The monthly interest rate is 6.8% / 12 = 0.00567,

and the total number of payments is 4 × 12 = 48.

Substituting these values into the formula, we get,

⇒M = $15,200 × 0.00567 × (1 + 0.00567)⁴⁸ / ((1 + 0.00567)⁴⁸ - 1)

⇒M = $15,200 × 0.00567 × 1.3118 / (1.3118 -1)

⇒M = $15,200 × 0.00567 × 1.3118 / 0.3118

⇒M = 113.056 / 0.3118

⇒M ≈ $362.59

Anthony's monthly payment will be about $362.59

Total price that Anthony paid for his vehicle,

add up the down payment and the total amount of payments over the 4-year period.

Total price = $3,800 + ( $362.59 × 48)

                  = $21204.4

Therefore, the monthly payment and the total price at interest rate of 6.8% that Anthony paid for vehicle is $362.59 and $21204.4 respectively.

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We can see here that from the available information it is clear that imports of Benin were:

While the exports are:

A locally produced commodity or service that is sold to another nation is referred to as an export. To put it another way, it's a good or service that is sold or sent to another nation to be utilized or consumed there.

Exports may help a nation's economy expand by bringing in money and creating jobs.

Imports are actually known to be goods and services that are brought into a country/nation.

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Answer: It is 1.24x smaller.

Step-by-step explanation:

1.2(106)= 127.2

1.47(107)= 157.3

157.3/127.2 = 1.24x smaller

The effective annual yield of the investment is 0.1501

To find the effective annual yield, we need to use the formula:

(1 + r/n)^n - 1

where r is the annual interest rate and n is the number of times the interest is compounded per year.

In this case, r = 0.14 (14% expressed as a decimal), and n = 52 (since interest is compounded weekly).

Plugging these values into the formula, we get:

(1 + 0.14/52)^52 - 1 = 0.1501

Therefore, the effective annual yield is 0.1501, which is equivalent to 15.01% (rounded to two decimal places).

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Answer:

66 because 10 percent of 60 is 6 so add 60 and 6

the third term of the expansion of (11x+3y)⁶ is 798,720x³y³.we can use the binomial theorem to solve this .

what is  binomial theorem ?

The binomial theorem is a theorem in algebra that describes the algebraic expansion of powers of a binomial. A binomial is a polynomial with two terms, such as (a + b) or (x - y).

In the given question,

To find the third term of the expansion of (11x+3y)⁶, we can use the binomial theorem, which states that:

(a + b)ⁿ = C(n,0)aⁿb⁰ + C(n,1)*aⁿ⁻¹*b¹+ C(n,2)*aⁿ⁻¹*b² + ... + C(n,n)a⁰bⁿ

where C(n,k) denotes the binomial coefficient, which is the number of ways to choose k items from a set of n items.

In this case, we have a = 11x and b = 3y, and n = 6. We want to find the third term, which corresponds to k = 3 in the expansion. Therefore, we need to compute the binomial coefficient C(6,3), as well as the powers of 11x and 3y that appear in the third term.

The binomial coefficient C(6,3) can be computed as follows:

C(6,3) = 6! / (3! * (6-3)!) = 20

To find the powers of 11x and 3y that appear in the third term, we need to look at the general pattern in the expansion. Each term in the expansion consists of a product of powers of a and b, with the powers of a decreasing by 1 from n to 0, and the powers of b increasing by 1 from 0 to n. Therefore, the kth term in the expansion will have powers of a and b given by aⁿ⁻ᵇand bᵃ, respectively.

In the third term, we have k = 3, so we need to find the coefficient of a³ = a³ = (11x)³ and b³ = (3y)³. The third term is given by:

C(6,3)(11x)³(3y)³

Plugging in the values for C(6,3), (11x)³, and (3y)³, we get:

20*(11x)³*(3y)³ = 2011³x³3³y³ = 798,720x³y³

Therefore, the third term of the expansion of (11x+3y)⁶ is 798,720x³y³.

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The firm expects replacing around 734 batteries out of the 32,200 produced.

using the normal distribution formula z = (x - )

When z denotes the z-score,

x denotes the battery life of interest, is the mean battery life, and is the standard deviation.

For x = 100, use the z-score: z = (100 - 120) / 10 z = -2

Calculate the area under the normal curve to the left of z = -2.

0.0228 is the approximate value.

The number of batteries expected to be replaced by the manufacturer is equal to the proportion of batteries with a battery life of less than 100 hours multiplied by the total number of batteries produced:

Number of batteries to be replaced = 0.0228 x 32,200

734.16 batteries are expected to be replaced.

As a result, the firm anticipates replacing around 734 batteries out of the 32,200 produced.

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Answer:

13

Step-by-step explanation:

First of all riley saved 200.73$ she needs 1,290.78$ so,

1290.78$-200.73$=1090.95$

she earns 83.85$ a week

then, 1090.95÷83.85= 13

13 weeks

A)By applying permutation and combination we can select committee in  1782 ways.

B) The probability cannot be determined with the given information, as the calculated probability is greater than 1, which is not possible.

Permutation and combination are two concepts in mathematics that deal with counting the number of possible outcomes or arrangements in a given situation. Permutation refers to the arrangement of objects in a specific order, while combination refers to the selection of objects without regard to the order in which they are chosen.

Probability is a measure of the likelihood or chance that an event will occur. It is a number between 0 and 1.

According to the given information:

A) To find the number of ways to select a committee of 5 members, where exactly one of Mr Lan and Mrs Lan must be on the committee, we can use the principle of inclusion-exclusion i.e. Permutation and combination:

First, we find the total number of ways to select a committee of 5 members from 14 members (6 men and 8 women), which is given by:

C(14,5) = 2002

Next, we find the number of ways to select a committee of 5 members that includes both Mr Lan and Mrs Lan, which is given by:

C(12,3) = 220

Note that we choose 3 members from the remaining 12 members after Mr and Mrs Lan have been chosen.

Finally, we subtract the number of committees that include both Mr Lan and Mrs Lan from the total number of committees, since we only want committees that include exactly one of them:

2002 - 220 = 1782

Therefore, there are 1782 different ways to select a committee of 5 members where exactly one of Mr Lan and Mrs Lan must be on the committee.

B) To find the probability that there are more women than men on the committee, given that Mrs Lan was selected, we need to consider the number of committees that satisfy this condition and divide by the total number of committees that include Mrs Lan.

If Mrs Lan is selected, there are two cases to consider:

Case 1: The committee has more women than men.

In this case, we need to select 4 members from the 8 women and 1 member from the 5 men, which can be done in C(8,4) x C(5,1) = 560 ways.

Case 2: The committee has an equal number or more men than women.

In this case, we need to select 3 members from the 8 women and 2 members from the 5 men, which can be done in C(8,3) x C(5,2) = 560 ways.

Therefore, the total number of committees that include Mrs Lan and have more women than men or an equal number of women and men is 560 + 560 = 1120.

The total number of committees that include Mrs Lan is C(13,4) = 715, since we choose 4 members from the remaining 13 members after Mrs Lan has been chosen.

Therefore, the probability of selecting a committee with more women than men or an equal number of women and men, given that Mrs Lan was selected, is:

1120/715 = 1.5664

Note that this probability is greater than 1, which is not possible. Therefore, there is an error in the calculation, and the correct probability cannot be determined with the given information.

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The only possible solution is x = 2. Therefore, the three consecutive integers that form the sides of the right triangle are 2, 3, and 4.

Since they are consecutive integers, let's assume that the hypotenuse, which is the longest side of the right triangle, is x+2, as it is three units longer than the shortest side.

In a right triangle, the hypotenuse's square is equal to the sum of the squares of the other two sides, according to the Pythagorean theorem. We can thus write:

[tex](x+2)^2 = x^2 + (x+1)^2[/tex]

Expanding the squares, we get:

[tex]x^2 + 4x + 4 = x^2 + x^2 + 2x + 1[/tex]

Simplifying and rearranging terms, we get:

[tex]2x^2 - 2x - 3 = 0[/tex]

We can solve this quadratic equation by using the quadratic formula:

x = (-b ± [tex]\sqrt{b^2 - 4ac}[/tex]) / 2a

where a = 2, b = -2, and c = -3.

Plugging in these values, we get:

x = (-(-2) ± [tex]\sqrt{((-2)^2 - 4(2)(-3)))[/tex] / 2(2)

x = (2 ± [tex]\sqrt{(4 + 24))[/tex] / 4

x = (2 ± [tex]\sqrt28}[/tex] / 4

x = (2 ± [tex]2\sqrt{7}[/tex]) / 4

x = 1/2 ± [tex]\sqrt{7}[/tex]/2

The only option is x = 2, since x must be an integer. As a result, the numbers 2, 3, and 4 are the three consecutive integers that make up the sides of the right triangle.

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Hence ,the sum of ∠1 and ∠2  is 90 degrees this is a relationship between ∠1 and ∠2.

In Euclidean geometry, an  angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles  formed by two rays lie in the plane that  contains the rays. Angles are also formed by the  intersection of two planes. These are called dihedral angles.

complementary angles are two angles that add up to 90 degrees, supplementary angles are two angles that add up to 180 degrees,

vertical angles are opposite angles at an intersection of two straight lines, and adjacent angles are two angles that are next to each other.

According to figure , the sum of ∠1 and ∠2  is 90 degrees and If the sum of the two angles is equal to the measurement of a right angle .

So, the pair of angles ∠1 and ∠2  is said to be complementary angles.

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Answer:

  D.  9 clubs

Step-by-step explanation:

Given a stem-and-leaf plot of the number of members in clubs, you want to know the number of clubs with 30 or more members.

The plot shows the club membership to be ...

  {10, 13, 15, 24, 26, 30, 36, 39, 50, 55, 59, 61, 66, 78}

The 9 clubs whose member numbers are in bold have at least 30 members.

The number of clubs with at least 30 members is ...

  D.  9 clubs

<95141404393>

The difference between 6 5/6 and 5 1/2 is 4/3 .

To subtract these mixed numbers, we need to first convert them into improper fractions:

6 5/6 = (6 x 6 + 5)/6 = 41/6

5 1/2 = (5 x 2 + 1)/2 = 11/2

Now we can subtract:

41/6 - 11/2

To deduct divisions with various denominators, we really want to track down a shared factor. 6 is the smallest common multiple of 6 and 2 in this instance. Therefore, we can use denominator 6 to convert 11/2 into an equivalent fraction:

11/2 = (11 x 3)/(2 x 3) = 33/6

Now we can subtract the fractions with the same denominator:

41/6 - 33/6 = 8/6

Working on the portion by partitioning both the numerator and denominator by their most prominent normal component, we get:

8/6 = 4/3

As a result, in mixed numbers, the difference between 6 5/6 and 5 1/2 is 4/3, or 1 1/3..

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The complete question is:

What is the rule for the sequence

5/6, 1 1/2, 2 1/6, 2 5/6.....

Answer:

n + 8

M - x

z - 12

c + d

2f + 20 or 20 + 2f

(x + y)^2 or (x + y) × (x + y)

2mn or 2 × m × n

2b - 6 or 6 - 2b

u^2 + v^2 or v^2 + u^2

(xy)/2 or xy/2

The final amount with interest earned at a rate of 3.4% compounded semi-annually would be approximately $7,758.

Let's calculate the values based on the given information.

Given:

Initial deposit (P) = $7,500

Interest rate (r) = 3.4% or 0.034 (decimal)

Compounding frequency (n) = 2 (semi-annually)

We can use the compound interest formula to calculate the values:

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

Where:

A = the final amount (including interest)

P = the principal amount (initial deposit)

r = the interest rate (in decimal)

n = the number of times interest is compounded per time period

t = the number of time periods

Let's calculate the final amount (A) after one year (2 semi-annual periods):

A =[tex]$7,500(1 + 0.034/2)^(2*1)[/tex]

A =[tex]$7,500(1.017)^2[/tex]

A = $7,500(1.034344) [rounded to 6 decimal places]

A ≈ $7,758 [rounded to the nearest dollar]

So, after one year, the final amount with interest earned at a rate of 3.4% compounded semi-annually would be approximately $7,758.

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The function y = √x+2 is undefined for any value of x that makes the expression inside the square root negative, which in this case is x ≤ -2.

What is an inequality equation?

An inequality equation is a mathematical statement that compares two expressions using an inequality symbol such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).

The function that is undefined for x = 0 is y = √x+2.

When x = 0, we have:

y = √0+2

y = √2

Since there is no real number whose square is negative, the square root of a negative number is undefined in real numbers.

Therefore, the function y = √x+2 is undefined for any value of x that makes the expression inside the square root negative, which in this case is x ≤ -2.

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On solving the provided question we can say that As a result, set D denotes a linear function.

The slope of a line indicates how steep it is. The gradient's mathematical equation is known as "gradient overflow" (the change in y divided by the change in x). The slope is defined as the ratio of the vertical change (rise) between two places to the horizontal change (run). The slope-intercept form of an equation is used to express a straight line's equation, which is written as y = mx + b. The y-intercept is found where the slope of the line is m, b is b, and (0, b). For example, consider the slope and y-intercept of the equation y = 3x - 7.The slope of the line is m. b is b at the y-intercept, and (0, b).

The set of ordered pairs expressing a linear function must meet the requirement that any two locations in the set have a constant rate of change (slope).

We can determine the rate of change between the two supplied positions using set D:

slope = (y2 - y1) / (x2 - x1)

slope = (1 - 2) / (2 - (-1))

slope = -1/3

We may use the slope-intercept form of a linear equation to see if the remaining points in set D fulfil the same rate of change: y = mx + b, where m is the slope and b is the y-intercept.

We can solve for b using the first point in D, (-1,2):

2 = (-1/3)(-1) + b

b = 7/3

So the linear equation for set D is: y = (-1/3)x + 7/3

Now we can check if the remaining points in set D satisfy this equation:

(2, 1): 1 = (-1/3)(2) + 7/3 (satisfies the equation)

As a result, set D denotes a linear function.

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The equilibrium tuition price p and the consumers' and producers' surpluses at this tuition level is 11400

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

q = 20,000 − 2p

q = 8,500 + 0.5p

The equilibrium tuition price p and the consumers' and producers' surpluses at this tuition level is when q = q

So, we have

20,000 − 2p = 8,500 + 0.5p

Evaluate the like terms

2.5p = 28500

Divide by 2.5

p = 28500/2.5

Evaluate

p = 11400

Hence, the equilibrium tuition price p is 11400

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Answer:

Therefore, Frank's monthly credit card payment will be $454.31.

Step-by-step explanation:

Monthly payment = (PV * r) / (1 - (1 + r)^-n)

PV = $2,500 + $1,000 + $3,000 + $1,500

= $8,000

r = 0.18 / 12

= 0.015

Monthly payment = ($8,000 * 0.015) / (1 - (1 + 0.015)^-24)

= $454.31

The appropriate domain for the function h(t) = −3t^2 + 9t + 12 is [0, 3.08].

The domain of a function is the set of all possible input values for which the function is defined. In this case, the function h(t) gives the height of the ball above the ground as a function of time t.

The ball is thrown from the tree house at some initial time, and it continues to travel until it hits the ground. The height of the ball is defined for all values of t between the time it is thrown and the time it hits the ground.

To find the domain of h(t), we need to determine the range of values of t for which the function is defined. The ball cannot have a negative height, so the function is undefined for values of t that would make h(t) negative.

To find the time at which the ball hits the ground, we need to set h(t) equal to zero and solve for t:

h(t) = -3t^2 + 9t + 12 = 0

Using the quadratic formula, we get:

t = (-9 ± √(9^2 - 4(-3)(12)))/(2(-3))

t = (-9 ± √(105))/(-6)

t ≈ -0.41 or t ≈ 3.08

Since the ball cannot have a negative height, the domain of the function is the interval [0, 3.08]. Therefore, the appropriate domain for the function h(t) = −3t^2 + 9t + 12 is [0, 3.08].

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This shows that the two circles intersect at a point P, and that the distance between their centers, OP1OP2, is less than the sum of their radii, r1 + r2. Thus, the two circles touch each other internally at point P.

You must calculate each circle's radius and centre in order to accomplish this. The circles will externally touch if the total of the radii and the space between the centres are identical. The circles will internally touch if the variations in radii and the separation between their centres are equal.

Let C1 and C2 stand for the two circles, with O1 and O2 serving as their respective centres. Let r1 and r2 represent the radius of C1 and C2, respectively.

Let's say that point P is where the two circles converge. The Pythagorean Theorem thus gives us:

OP1² = r1²

OP2² = r2²

OP1² + OP2² = (r1 + r2)²

Simplifying the third equation, we get:

OP1² + OP2² = r1² + 2r1r2 + r2²

The left half of this equation can be rewritten as (OP1 + OP2)2 - 2OP1OP2. When we simplify the equation above and substitute this, we get:

(OP1 + OP2)² = (r1 + r2)² + 2OP1OP2

Since OP1 and OP2 are both positive, we have:

(OP1 + OP2)²> (r1 + r2)²

Therefore, we must have:

OP1OP2 < r1 + r2

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The volume of the block of wood is 104.7634 cm³ and the total surface area is 186.4502 cm².

Volume is the measure of the amount of space occupied by a three-dimensional object. It is typically measured in cubic units such as cubic meters (m³), cubic centimeters (cm³), or cubic inches (in³).

The volume of the block of wood will be;

V = l x w x h = 4.55 cm x 9.1 cm x 2.54 cm

= 104.7634 cm³

Therefore, the volume of the block of wood is 104.7634 cm³.

The total surface area of the block of wood will be;

SA = 2lh + 2wh + 2lw

= 2(4.55 cm x 2.54 cm) + 2(9.1 cm x 2.54 cm) + 2(4.55 cm x 9.1 cm)

= 58.0094 cm² + 46.4314 cm² + 82.0094 cm²

= 186.4502 cm²

Therefore, the total surface area is 186.4502 cm².

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By sample distribution, (0.431,0.487) is Complete parts​ (a) through​ (d) below.

What does a statistical sample distribution mean?

An accurate probability distribution of a statistic is known as a sampling distribution, and it is created by repeatedly sampling a certain population. It depicts a spectrum of potential results for a statistic, such as the mean or mode of a variable, for a population.

Given

Favourable cases (X)=?

Sample size(n)=510

Sample proportion (p_hat)=X/n=0.459

X=np_hat=510*0.459=234.09=234

Confidence level(1-α)=99%=0.99

α=0.0

The critical value for  α=0.01 is Zc=2.576

The margin of error is E=Zc* √((p_hat(1-p_hat)/n))

E=2.576* √((0.459(1-0.459)/510))=0.0568

The 99% confidence interval for p

CI=(p_hat-E,p_hat+E)

CI=(0.459-0.0568,0.458+0.0568)

CI=(0.402,0.516)

Confidence level(1-α)=80%=0.80

α=0.20

The critical value for  α=0.2 is Zc=1.282

The margin of error is E=Zc* √((p_hat(1-p_hat)/n))

E=1.282* √((0.459(1-0.459)/510))=0.0283

The 80 % confidence interval for p

CI=(p_hat-E,p_hat+E)

CI=(0.459-0.0283,0.458+0.0283)

CI=(0.431,0.487)

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The ratio of the areas is given as follows:

1:5.8.

The ratio of the areas is obtained applying the proportions in the context of the problem.

When a prism is dilated by a scale factor of k, we have that:

Hence the ratio of the areas is the cubic root of the ratio of the volumes squared, thus, as the ratio of the volumes is of 1:14, we have that:

(14²)^(1/3) = 5.8.

Hence:

1:5.8.

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The only option given that has a variable raised to the third power is D. -2x³, so the correct answer is D.

In algebra, a monomial is an expression that consists of a single term, which is a product of a constant coefficient and one or more variables raised to non-negative integer powers. In each of these expressions, there is only one term, and each term is a product of a constant coefficient and one or more variables raised to non-negative integer powers. Monomials are important in algebra because they can be combined using various operations such as addition, subtraction, multiplication, and division, to form more complex expressions.

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the guests arrived for dinner at 6:39 P.M.which is solved by according to given question.

How to solve the question?

To solve this problem, we need to first convert the fraction of an hour that Miss Johnson's guests were late into minutes. We know that 1 hour is equal to 60 minutes, so we can find the number of minutes the guests were late by multiplying 2/5 by 60:

2/5 hour * 60 minutes/hour = 24 minutes

So the guests were 24 minutes late. To find out what time they arrived, we need to add 24 minutes to the original arrival time of 6:15 P.M.:

6:15 P.M. + 24 minutes = 6:39 P.M.

Therefore, the guests arrived for dinner at 6:39 P.M.

It's important to note that fractions can often be confusing when dealing with time calculations. In this case, we converted the fraction of an hour to minutes to make the calculation easier. Additionally, it's always a good idea to double-check your work to ensure that your answer makes sense in the context of the problem.

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The required value of z such that 0.6318 of the area lies between −z and z is 0.89.

If 0.6318 of the area lies between −z and z, then the area outside of this range is (1-0.6318) = 0.3682.

Since the normal distribution is symmetric, the area to the left of −z is equal to the area to the right of z. So, the area to the right of z is (0.3682 / 2) = 0.1841.

Using a standard normal distribution table, we can find the z-score corresponding to an area of 0.1841 to the right of z:

z = invNorm(0.1841) ≈ 0.89

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