what is the value of the underlined digit in the number 27,416,385. 4 is the underlined number.

The length of the rectangle is 300 cm and its width is 150 cm, given that the perimeter is 900 cm and the length is twice the width.

Let's assume that the width of the rectangle is w, then the length of the rectangle is twice the width, 2w.

The perimeter of a rectangle is given by the following formula:

Perimeter = 2 * (Length + Width)

Substituting the values given, we get:

900 = 2 * (2w + w)

Simplifying this equation, we get:

900 = 6w

Dividing by 6 on both sides, we get:

w = 150

Now that we know the width of the rectangle is 150cm, we can find its length as follows:

Length = 2 * Width = 2 * 150 = 300

Therefore, the length of the rectangle is 300 cm and its width is 150 cm.

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The height at a time of 1.6 seconds is 185 feet.

Here, we have,

Since we want to find a quadratic regression equation, we'll use the quadratic model: y = ax^2 + bx + c.

Using the data in the table, we can set up the following system of equations:

a(0)^2 + b(0) + c = 0

a(1)^2 + b(1) + c = 85

a(2)^2 + b(2) + c = 140

Simplifying, we get:

c = 0

a + b + c = 85

4a + 2b + c = 140

Substituting c = 0 into the second equation, we get:

a + b = 85

Subtracting twice the first equation from the third equation, we get:

2a + 2b = 140

Subtracting the first equation from the second equation, we get:

a = 85 - b

Substituting this into the previous equation, we get:

170 - 2b = 140

Solving for b, we get:

b = 15

Substituting this value of b into the equation a + b = 85, we get:

a = 70

Therefore, the quadratic regression equation is:

y = 70x^2 + 15x

To find the height at a time of 1.6 seconds, we plug in x = 1.6:

y = 70(1.6)^2 + 15(1.6) = 184.8

Rounding to the nearest foot, the height at a time of 1.6 seconds is 185 feet.

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Answer:6. Calculate the appropriate measure of Skewness for the data below. Class 0-10 10-20 20-30 30-40 40-50 50-60 12 25 35 40 50 No. of workers 10 Ans: -0.49

Step-by-step explanation:

The given data for both History and Geography tests are discrete data.

The given data for both History and Geography tests can be categorized as discrete data because the values are distinct and separate.

To identify the minimum value for the Geography test, we look for the smallest value among the given percentages.

From the given data, the minimum value for the Geography test is 35.

The range for the History test is calculated by finding the difference between the maximum and minimum values.

Since the maximum value for the History test is given as 60 and the minimum value is 30 so the range is 30 not 60.

To arrange the Geography test in ascending order, we sort the given percentages from lowest to highest.

The ascending order for the Geography test is as follows:

35, 45, 50, 53, 58, 60, 60, 64, 75

To find the mode for the History test, we look for the value that appears most frequently.

From the given data, the mode for the History test is 60 as there are 3 times repeated values of 60.

Hence the given data for both History and Geography tests are discrete data.

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Based on the information provided, it seems like there is a dataset that contains three values: 30, 39, and 45. The prompt states that each value appears a certain number of times in the dataset.

For example, the value 30 appears "time(s)" in the dataset, although we don't know exactly how many times it appears. Similarly, the value 39 appears a certain number of times, as does the value 45.

Without more information about the dataset, it is difficult to draw any conclusions about the significance or pattern of these values. It is possible that they are part of a larger dataset and represent only a small portion of the data.

Alternatively, they could be outliers or represent a significant trend in the data. Further analysis would be necessary to determine their meaning and significance.

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The length of side KL is approximately 4.8 cm.

To solve this problem, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is equal for all sides of the triangle. In other words:

a/sin(A) = b/sin(B) = c/sin(C)

Where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the measures of the angles opposite those sides.

Using the Law of Sines, we can set up the following proportion:

l/sin(L) = m/sin(M)

Where l is the length of side KL, L is the measure of angle KLM (which is 72 degrees), m is the length of side LM, and M is the measure of angle KML (which we can find by subtracting L from 180 degrees).

M = 180 - L

= 180 - 72

= 108 degrees

Now we can substitute the given values into the proportion and solve for l:

l/sin(72) = 5.9/sin(108)

l = sin(72) * (5.9/sin(108))

≈ 4.8 cm (rounded to the nearest 10th of a centimeter)

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Rina will earn approximately $28.13 in interest in one quarter on her 12-month CD.

To calculate the amount of interest Rina will earn in one quarter on her 12-month CD, we can use the formula for compound interest:

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

Where:

A is the final amount (including both principal and interest)

P is the principal amount (initial deposit)

r is the annual interest rate (in decimal form)

n is the number of times the interest is compounded per year

t is the time in years

In this case, Rina deposited $3,000 into a 12-month CD, so:

P = $3,000

r = 3.75% = 0.0375 (as a decimal)

n = 4 (compounded quarterly)

t = 1/4 (one quarter, or 1/4 of a year)

Substituting these values into the formula, we have:

A = 3000(1 + 0.0375/4)^(4 * 1/4)

= 3000(1 + 0.009375)^1

= 3000(1.009375)^1

= 3000(1.009375)

= 3028.13

The final amount (including both principal and interest) after one quarter is approximately $3,028.13.

To calculate the amount of interest earned in one quarter, we subtract the principal amount from the final amount:

Interest earned in one quarter = $3,028.13 - $3,000

= $28.13

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By algebra properties, the simplified form of the expression is equal to [2 · e⁽ᵃ⁻¹⁾ˣ · (a · x - 1) - 2 · (eᵃˣ · a · x + e⁻ˣ)] / (2 · e⁻ˣ - 2)².

In this question we find the representation of a rational-like expression involving exponential functions that must be simplified by means of algebra properties. Now we proceed to show the complete procedure for simplification:

[(eᵃˣ · a · x) · (2 · e⁻ˣ - 2) - (eᵃˣ - 1) · 2 · (- e⁻ˣ)] / (2 · e⁻ˣ - 2)²

[2 · e⁻ˣ · (eᵃˣ · a · x) - 2 · (eᵃˣ · a · x) - 2 · (- e⁻ˣ) · eᵃˣ + 2 · (- e⁻ˣ)] / (2 · e⁻ˣ - 2)²

(2 · e⁽ᵃ⁻¹⁾ˣ · a · x - 2 · eᵃˣ · a · x + 2 · e⁽ᵃ⁻¹⁾ˣ - 2 · e⁻ˣ) / (2 · e⁻ˣ - 2)²

[2 · e⁽ᵃ⁻¹⁾ˣ · (a · x - 1) - 2 · (eᵃˣ · a · x + e⁻ˣ)] / (2 · e⁻ˣ - 2)²

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The equation of the parabola from the given graph is y=-3x². Therefore, option A is the correct answer.

From the given graph vertex is (0, 0) and the point on x-axis (-3, 0).

The general equation of a parabola is: y = a(x-h)² + k or x = a(y-k)² +h, where (h, k) denotes the vertex. The standard equation of a regular parabola is y² = 4ax.

Substitute (h, k)=(0, 0) and a=-3 in y = a(x-h)² + k, we get

y=-3(x-0)² + 0

y=-3x²

Therefore, option A is the correct answer.

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$105 is higher than $100, the minimum Payment due on Josiah's credit card is $105.

The minimum payment due on Josiah's credit card 3% of his outstanding balance and compare it to the minimum payment of $100. The higher amount between the two will be the minimum payment.

1. Calculate 3% of $3,500:

3% * $3,500 = 0.03 * $3,500 = $105

2. Compare the calculated amount with the minimum payment of $100:

Minimum payment = max($105, $100)

Since $105 is higher than $100, the minimum payment due on Josiah's credit card is $105.

The credit card company sets a minimum payment to ensure that the cardholder makes regular payments towards their outstanding balance. The minimum payment is usually a percentage of the balance or a fixed amount, whichever is higher. In this case, the minimum payment is calculated as 3% of the outstanding balance or $100, whichever amount is greater.

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The total amount for the new vehicle, considering the given costs, is $16,692.

To calculate the total amount of a new vehicle, you need to consider the standard vehicle price, options cost, and destination charge. In this case, the standard vehicle price is $14,530, the options cost is $1,717, and the destination charge is $445.

To find the total amount, simply add these three amounts together:

$14,530 (standard vehicle price) + $1,717 (options cost) + $445 (destination charge) = $16,692

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The pulse rate of 133.9 beats per minute is significantly high.

We have to use the range rule of thumb. The range rule of thumb states that values within two standard deviations of the mean are considered typical, while values outside this range may be considered significantly low or significantly high.

The range in this case would be calculated as follows:

= 2 * standard deviation

= 2 * 11.3

= 22.6 beats per minute.

Lower Limit = Mean - Range

Lower Limit = 71.3 - 22.6

Lower Limit = 48.7 beats per minute.

Upper Limit = Mean + Range

Upper Limit = 71.3 + 22.6

Upper Limit = 93.9 beats per minute.

Since the pulse rate of 133.9 beats per minute is higher than the upper limit of 93.9 beats per minute, it is considered significantly high.

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Answer:

[tex]\mathrm{\frac{n(n-1)}{2}}[/tex]

Step-by-step explanation:

[tex]\mathrm{The\ formula\ for\ the\ number\ of\ handshakes\ possible\ among\ n\ participants\ is:}\\ \mathrm{ \frac{n(n-1)}{2}}\\\mathrm{It's\ because\ each\ of\ the\ n\ participants\ may\ shake\ hands\ with\ n-1\ people}\mathrm{(they}\\\mathrm{cannot\ shake\ their\ own\ hands)\ and\ the\ handshake\ between\ two\ people\ is\ not}\\ \mathrm{counted\ twice.}[/tex]

hello

the answer to the question is:

[tex]surface \: area = 2bs + {b}^{2} \\ = 2 \times 2 \times 6 + {2}^{2} = 28[/tex]

The type of experimental design where the assignment of Experimental units to treatment and control groups is random is called a randomized controlled trial (RCT).

The type of experimental design where the assignment of experimental units to treatment and control groups is random is called a randomized controlled trial (RCT).

Randomized controlled trials are widely used in various fields of research, including medicine, psychology, and social sciences. They are considered the gold standard for evaluating the effectiveness of interventions or treatments. The key feature of an RCT is the random assignment of participants or experimental units to either the treatment group or the control group.

Randomization helps to ensure that the treatment and control groups are similar in terms of both observed and unobserved characteristics, reducing the potential for bias and confounding variables. By randomly assigning participants, researchers can make causal inferences about the effects of the treatment, as any observed differences between the groups can be attributed to the intervention.

In an RCT, experimental units can be individuals, groups, organizations, or any other defined units depending on the research context. The random assignment process involves using a randomization procedure, such as coin flipping, random number tables, or computer-generated randomization, to assign participants to the treatment and control groups.

By comparing the outcomes or responses of the treatment and control groups, researchers can determine the effectiveness or impact of the intervention being studied. Statistical techniques, such as hypothesis testing and analysis of variance, are commonly used to analyze the data collected from the RCT and draw conclusions.

a randomized controlled trial is the type of experimental design where the assignment of experimental units to treatment and control groups is random. It is a rigorous approach to evaluating the effects of interventions and minimizing biases, providing robust evidence for decision-making and policy development.

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Signing a note payable allows the buyer to defer payment and provides a formal agreement outlining the terms and conditions of the debt.

A piece of equipment was acquired at a total cost of $40,000. Initially, a cash payment of $10,000 was made, leaving a remaining balance to be settled. To cover this outstanding amount, a note payable was issued to the seller.

The transaction reflects a combination of cash and credit financing. The cash payment of $10,000 represents the immediate cash outflow associated with the equipment purchase. The remaining balance of $30,000 is represented by the note payable, which indicates a promise to pay the seller in the future.

Signing a note payable allows the buyer to defer payment and provides a formal agreement outlining the terms and conditions of the debt. The specific terms, such as the interest rate and repayment schedule, would be detailed in the note payable agreement.

This method of financing enables the purchaser to acquire the equipment while spreading out the financial obligation over time, aligning with their cash flow capabilities and financial strategy.

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Answer:

Step-by-step explanation:

Answer $1260

The figure has line symmetry since one half of the figure is a mirror image of the other half.

A point symmetry, also known as reflection symmetry or symmetry with respect to a point, is a type of symmetry where an object remains unchanged when it is rotated by 180 degrees around a fixed point.

So in point symmetry  if you have a line and you can find a point such that if you fold the line along that point, the two halves coincide perfectly, then the line possesses point symmetry.

This is not the case for this diagram as both halves does not have equal height.

For line symmetry, if you can draw a line (known as the line of symmetry) through a figure in such a way that one half of the figure is a mirror image of the other half, then the figure exhibits line symmetry.

The given figure passes line symmetry test.

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The probability of drawing a number more than 5​ is 0.167

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

A number cube of 6 faces

Where we have

Total outcomes = 6

Outcome greater than 5 = 1 i.e. face e

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

P(Number greater than 5) = 1/6

Evaluate

P(Number greater than 5) = 0.167

Hence, the the probability of drawing a number more than 5​ is 0.167

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Complete question

A number cube with faces labeled from 1 to 6 is rolled once.

Find the probability of drawing a number more than 5​

The integer representation of a debt of R16,00 would be -1600.

In integer representation, debts are typically represented as negative numbers.

In this case, since the debt is R16,00, we would represent it as -1600.

The negative sign indicates that it is a debt or a negative value, and the number 1600 represents the magnitude or amount of the debt.

By using a negative integer, we can accurately represent the concept of a debt in mathematical calculations and representations.

Hence, the integer representation of a debt of R16,00 would be -1600.

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The expected value is X/1000.

To find the expected value for this game, we need to calculate the average value of the winnings over the long run. In this case, the player has a 1 in 1000 chance of winning $X and a 999 in 1000 chance of winning $0. Let's assume that X is the amount won when the selected number is chosen.

The expected value (EV) can be calculated using the following formula:

EV = (Probability of winning $X) * (Amount won) + (Probability of winning $0) * (Amount won)

In this game, the probability of winning $X is 1/1000, and the probability of winning $0 is 999/1000. The amount won is $X when the selected number is chosen. Therefore, the expected value can be calculated as follows:

EV = (1/1000) * X + (999/1000) * 0

= X/1000 + 0

= X/1000

The expected value is X/1000. This means that on average, for every game played, the player can expect to win X/1000 dollars. It represents the long-term average winnings per game.

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Answer:

To convert feet to yards, we can use the conversion factor:

1 yard = 3 feet

To find out how many yards long Joey's truck is, we divide the length of the truck in feet by 3:

Length in yards = Length in feet / 3

Length in yards = 18 feet / 3

Length in yards = 6 yards

Therefore, Joey's truck is 6 yards long.

Answer:

a

Step-by-step explanation:

Note that m and n are 2 digit numbers. Let m be even and n be odd. The product of these numbers is 180.

Notice that:

[tex]180=12\times 15[/tex]

So, [tex]m=12[/tex] and [tex]n=15[/tex]. Then, the lowest common multiple of [tex]m=12[/tex] and [tex]n=15[/tex] is 60.

The smallest common multiple of m and n is 60.

The correct option is (a) 60.

We are given two conditions about two numbers m and n:

We are also given that the product of m and n is 180.

We need to find the smallest common multiple of m and n.

Let's first find the factors of 180.

Out of these factor pairs, we need to find the pair that satisfies the given conditions.

Since one number is odd and the other number is even, we can eliminate the factor pairs (2, 90), (4, 45), (6, 30), and (10, 18).

Now, we are left with the factor pairs (1, 180), (3, 60), and (9, 20).

Since both numbers are 2-digit numbers, we can eliminate the factor pair (1, 180).

Out of the remaining factor pairs, (3, 60) and (9, 20), we need to find the smallest common multiple.

The smallest common multiple of two numbers is the product of the two numbers divided by their greatest common divisor (GCD).

The GCD of 3 and 60 is 3, and the GCD of 9 and 20 is 1.

Therefore, the smallest common multiple of m and n is:

For the pair (3, 60): (3 x 60) / 3 = 60

For the pair (9, 20): (9 x 20) / 1 = 180

Thus, the smallest common multiple of m and n is 60.

Answer:

x = 4 and y = 8

Step-by-step explanation:

It is a simultaneous equation

y = 2x --- (1)

6x - 2y = 8 ---(2)

Using substitution method:

Substitute equ1 into equ2:

6x - 2(2x) = 8

6x - 4x = 8

2x = 8

x = 8/2

x = 4

From equ1: y = 2x, substituting back the value of x, we have:

y = 2(4)

y = 8

The value of price of the bond is , £36.37.

Now, For the price of the bond with a face value of £100, an annual coupon rate of 3%, 28 years to maturity and an annual yield of 14%,

Hence,  we can use formula for the present value as;

PV = (C / i) x [1 - (1 / (1 + i)^n)] + FV / (1 + i)^n

Where:

PV is the present value

C is the annual coupon payment

i is the yield to maturity

n is the number of years to maturity

FV is the face value of the bond

Hence, Plugging in the values, we get:

PV = (3 / 0.14) x [1 - (1 / (1 + 0.14))] + 100 / (1 + 0.14)

PV = (21.43) x [1 - (1 / 6.646)] + 1.34

PV = £36.37

Therefore, The value of price of the bond is , £36.37.

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(a) The probability of selecting exactly two white balls and two red balls is 5/11.

(b)The probability of selecting at least two white balls is 208/33, or about 0.63

To solve this problem, we can use the formula for probability:

P(event) = number of favorable outcomes / total number of outcomes

There are several approaches to this problem, but one popular option is to employ combinations. The combination formula gives the number of possibilities to pick k things from a set of n objects:

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

where n! represents n factorial (the sum of all positive integers up to and including n).

a) To calculate the chance of picking exactly two white balls and two red balls, we must count the number of possibilities to select two white balls and two red balls from a set of six white balls and five red balls. We may then divide this number by the total number of ways to select any four balls from the 11 available.

Number of favorable outcomes:

C(6, 2) x C(5, 2) = 15 x 10 = 150

Total number of outcomes:

C(11, 4) = 330

Probability of selecting exactly two white balls and two red balls:

P(2 white and 2 red) = 150/330 = 5/11

Therefore, the probability of selecting exactly two white balls and two red balls is 5/11.

b)To calculate the probability of picking at least two white balls, count the number of ways to select 2, 3, or 4 white balls and then sum the probabilities. We may also remove the probability  of picking 0 or 1 white balls from 1 (the overall probability).

Number of favorable outcomes:

C(6, 2) x C(5, 2) + C(6, 3) x C(5, 1) + C(6, 4) x C(5, 0)

= 150 + 120 + 15

= 285

Total number of outcomes:

C(11, 4) = 330

Probability of selecting at least two white balls:

P(at least 2 white) = 1 - P(0 white) - P(1 white)

To calculate P(0 white), we count the number of ways to select four red balls from a possible five and divide by the total number of outcomes:

C(5, 4) / C(11, 4) = 5/33

To find P(1 white), we count the number of ways to choose 1 white ball and 3 red balls, and multiply by the number of ways to arrange these balls (4!):

C(6, 1) x C(5, 3)x 4! / C(11, 4) = 120/33

Therefore, we have:

P(at least 2 white) = 1 - 5/33 - 120/33 = 208/33

The chance of picking at least two white balls is thus 208/33, or approximately 0.63 (rounded to two decimal places).

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11 athletes can finish first or second the track meet in 110 ways

Permutation is an arrangement of a set of objects without repetition where a different order of the same set of objects counts as a different.

How to determine this

When there are 11 athletes at a track meet

In how many ways can they finish first or second

When first choice = 11 possible ways

Second choice will be = 10 possible ways

So, to finish first or second = 11 * 10

= 110 ways

Therefore, there are 110 ways to finish first or second.

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The probability of picking an ace of hearts from a standard deck of playing cards is 1/52.

Consider a standard deck of cards.

We know that a standard deck of cards contains 52 cards.

So, total number of cards in the standard deck of cards = 52 cards

Now, we have to assume that there are no jokers in the set of cards.

We have to find the probability of picking an ace of hearts from a standard deck of playing cards.

For that we need to first find the number of cards which are ace of hearts.

Number of cards which are ace of hearts = 1

Probability of picking an ace of hearts from a standard deck of playing cards is,

P = Number of ace of hearts / Total number of cards

  = 1/52

Hence the probability is 1/52.

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The points with black dots on the number line represent the fractions.

In elementary mathematics -

A number line is a picture of a graduated straight line that serves as visual representation of the real numbers.

Every point of a number line is assumed to correspond to a real number, and every real number to a point.

Given are the fractions -

5/6 and 2 2/3

We can write

2 2/3 = 8/3 = 16 / 6

And, 5/6 = 5/6

Refer to the number line attached.

The points with black dots represent the numbers.

Therefore, the points with black dots on the number line represent the fractions.

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