The list below shows the ages of 10 visitors at a museum one morning.


17 30 17 26 48 39 18 45 17 32



The median age of the 10 visitors was 28. The median age of the visitors remained the same after the ages of two more visitors were added to the list. What are the possible ages of these 2 visitors?



a
17 and 18
b
18 and 26
c
26 and 32
d
39 and 48

No, the events A and B are not independent because the two events are dependent as drawing of the draw by first person affects probability of drawing the straw by the second person.

In the given question, eight friends are drawing straws. The one who picks the short straw must cook dinner for the others.

We have to determine whether the events A and B are independent.

Events classified as independent do not depend on other events for their occurrence. For instance, if we toss a coin in the air and it lands on head, we can toss it again and this time it will land on tail. Both instances include independent occurrences of the two events.

The two events are dependent as drawing of the draw by first person affects probability of drawing the straw by the second person.

Hence, the events A and B are not independent.

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a.) The value of pulses exported by US in billion would be=30 billion.

b.) The ratio of wheat export of UK to maize export of IND would be= 6:5

For question a.)

To calculate the pulses, the following steps should be taken as follows:

From the bar chart, the value of pulses in billions = 30 billions.

For question b.)

The ratio of wheat export at UK and maize export at IND would be calculated as follows:

The quantity of wheat export at UK = 24

The quantity of maize export at IND = 20

Therefore, the ratio of wheat to maize = 24:20= 6:5

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The slοpes οf the οppοsite sides are negative reciprοcals and alsο, the rectangle is a square because the οppοsing angles are cοngruent.

A unique kind οf rectangle called a square is οne with fοur cοngruent sides and fοur cοngruent angles (90 degrees). A square alsο has the same characteristics as a rectangle (οppοsite sides are parallel and cοngruent, and οppοsing angles are cοngruent) plus the fοllοwing characteristics:

Cοngruence exists οn all fοur sides. Cοngruent angles exist fοr all fοur (90 degrees).

Right angles separate the diagοnals frοm οne anοther and they are cοngruent. The square is divided alοng the diagοnals intο fοur identical right triangles.

Tο determine if ABCD is a square, we need tο check if all fοur sides are cοngruent and if the οppοsite angles are cοngruent.

Using the distance fοrmula, we can find the lengths οf each side:

AB = √[(9-(-1))² + (4-9)²] = \(\sqrt{170}\)

BC = √[(4-9)² + (-6-4)²] = \(\sqrt{170}\)

CD = √[(-6-4)² + (-1-(-6))²] = \(\sqrt{170}\)

DA = √[(-1-(-6))² + (9-(-1))²] = \(\sqrt[]{170}\)

All fοur sides have the same length, thus the rectangle is a rhοmbus.

Tο determine if it is alsο a square, we need tο check the angles.

Using the slοpe fοrmula:

slοpe AB = (4-9)/(9-(-1)) = -5/10 = -1/2

slοpe BC = (-6-4)/(4-9) = -10/-5 = 2

slοpe CD = (-1-(-6))/(-6-4) = 5/10 = 1/2

slοpe DA = (9-(-1))/(-1-(-6)) = -10/-5 = 2

The slοpes οf the οppοsite sides are negative reciprοcals οf each οther, indicating that they are perpendicular tο οne anοther. The rectangle is a square because the οppοsing angles are cοngruent.

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Step-by-step explanation:

$1 = 200 Hungarian Forints

$ 150 = 150×200

= 30,000 Hungarian Forints is the answer.

Answer:

30,000 Hungarian Forints in $150

Answer:

Step-by-step explanation:

Its A

Answer:A

Step-by-step explanation:A cylinder with 8 units.

Answer:

Step-by-step explanation:

December 15, 1791

Answer:

December 15, 1791

Step-by-step explanation:

The daughter's age is 7 years old.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, a parent is 20 years older than twice his daughter's age, and he was half of his present age 17 years back.

Let the age of the parent be x,

He/she was half of the age 17 years back, then,

x/2 = x-17

x = 34

Therefore, parent's present age is 34 years.

He is  20 years older than twice his daughter's age,

Let his daughter's age be y,

2y+20 = 34

2y = 14

y = 7

Hence, his daughter's age is 7 years old.

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The expected value  that  this broker assign to this stock's end-of-the-year price is $58.50.

Using this formula

Expected value=Stock worth at $50+ Stock worth at $60+ Stock worth at $70

Where:

Stock worth at $50=40% chance

Stock worth at $60=35% chance

Stock worth at $70=25% chance

Let plug in the formula

Expected value=(40%×$50)+($35%×$60)+($25%×$70)

Expected value=$20+$21+$17.5

Expected value=$58.50

Inconclusion the expected value  that  this broker assign to this stock's end-of-the-year price is $58.50.

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The given equation is,

-2x-1=0

The line equation is given by,

y=mx+c

So equating both the equations, we get, for y=0

The Slope m=-2

The y intercept, c=-1

So for, x=1,

y= -2-1 = -3.

Answer:

17/5

It is already simplified to lowest terms.

This number, as a mixed fraction, would look like this:

3 2/5.

Answer:

If I am not mistake I am pretty sure its graph B.

Step-by-step explanation:

Answer: bottom right

============================================================

Explanation:

We'll need to compute the difference quotient. In this case, we need to find what \(\frac{g(h+t)-g(t)}{h}\) is equal to. It's called a difference quotient because there's a subtraction in the numerator (aka "difference") and we're dividing to form the quotient.

The idea is that as h approaches 0, then that expression I wrote will approach the derivative we're after. Keep in mind that h will technically never get to 0 itself. It only gets closer and closer.

Anyways, let's compute \(g(h+t)\) first

\(g(t) = 5t^2+5t\\\\g(h+t) = 5(h+t)^2+5(h+t)\\\\g(h+t) = 5(h^2+2ht+t^2)+5(h+t)\\\\g(h+t) = 5h^2+10ht+5t^2+5h+5t\\\\\)

Then we'll subtract off g(t)

\(g(h+t)-g(t) = (5h^2+10ht+5t^2+5h+5t) - (5t^2+5t)\\\\g(h+t)-g(t) = 5h^2+10ht+5t^2+5h+5t - 5t^2-5t\\\\g(h+t)-g(t) = 5h^2+10ht+5h\\\\\)

A very important thing to notice: the terms that don't have any 'h's in them have been canceled out (eg: 5t^2 combined with -5t^2 added to 0). Why is this important? It's because we need to factor 'h' out and we'll have a pair of 'h's cancel like so

\(\frac{g(h+t)-g(t)}{h} = \frac{5h^2+10ht+5h}{h}\\\\\frac{g(h+t)-g(t)}{h} = \frac{h(5h+10t+5)}{h}\\\\\frac{g(h+t)-g(t)}{h} = 5h+10t+5\\\\\)

The left hand side cannot have h = 0, or else we have a division by zero error. But if we approached 0 (not actually getting there), then the expression 5h+10t+5 will approach 5(0)+10t+5 = 10t+5

---------------------

In short: The derivative of \(5t^2+5t\) is \(10t+5\)

In terms of symbols, \(g ' (t) = 10t+5\)

Later on in calculus, you'll learn a shortcut so you won't have to compute the difference quotient every time you need a derivative. Refer to the power rule for more information.

After we find the derivative, it's as straight forward as plugging in t = 6 to compute g ' (6)

\(g ' (t) = 10t+5\\\\g ' (6) = 10(6)+5\\\\g ' (6) = 60+5\\\\g ' (6) = 65\\\\\)

Side note: This tells us that the slope of the tangent line is m = 65 when t = 6. In other words, this line is tangent to g(t) when t = 6, and this particular tangent line has slope m = 65.

The answer is (D) (7, 3), (9, 7) and (8, 3) when A triangle with vertices (2, 3), (4, 7), and (3, 3) is translated a distance of 5 units to the right.

To translate a two-dimensional figure such as a triangle, we move all its points a certain distance in a certain direction. In this case, we need to move the triangle 5 units to the right. This means we need to add 5 to the x-coordinate of each vertex, while leaving the y-coordinate unchanged.

In this case, we need to add 5 units to the x-coordinates of each vertex of the triangle.

The new coordinates of the triangle's vertices would be:

(2+5, 3) = (7, 3)

(4+5, 7) = (9, 7)

(3+5, 3) = (8, 3)

Therefore, the answer is (D) (7, 3), (9, 7) and (8, 3).

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The complete question is :

A triangle with vertices (2, 3), (4, 7), and (3, 3) is translated a distance of 5 units to the right. What are the new coordinates?

A.(-3, 3), (-1, 7), (-2, 3)

B.(2, -2), (4, 2), (3, -2)

C.(2, 8), (4, 12), (3, 8)

D.(7, 3), (9, 7) and (8, 3)

Answer:

you see

Step-by-step explanation:

Answer0.7

Step-by-step explanation:In math of mostly means to multiply ,so 2/10x3 1/2=0.7

Based on the cross-price elasticity of Demand, we can conclude that good X and good Y are substitutes.

Let's calculate the cross-price elasticity of demand using the given information:

a. Find the percentage change in quantity demanded of good Y:

Percentage Change in Quantity Demanded of Good Y = (New Quantity Demanded - Initial Quantity Demanded) / Initial Quantity Demanded * 100

Percentage Change in Quantity Demanded of Good Y = (6250 - 5000) / 5000 * 100 = 25%

b. Find the percentage change in the price of good X:

Percentage Change in Price of Good X = (New Price - Initial Price) / Initial Price * 100

Percentage Change in Price of Good X = (5 - 4) / 4 * 100 = 25%

Now, we can calculate the cross-price elasticity of demand:

Cross-Price Elasticity of Demand = Percentage Change in Quantity Demanded of Good Y / Percentage Change in Price of Good X

Cross-Price Elasticity of Demand = 25% / 25% = 1

b. Based on the calculated cross-price elasticity of demand, we can determine the types of goods:

If the cross-price elasticity of demand is positive (as in this case, where it is 1), it indicates that the two goods are substitutes. This means that when the price of good X increases, the quantity demanded of good Y also increases, suggesting that consumers view these goods as alternatives to each other.

Therefore, based on the cross-price elasticity of demand, we can conclude that good X and good Y are substitutes.

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Answer:

Step-by-step explanation:

The correct answer is Part 1: The 99% confidence interval for the population proportion is approximately (0.4716, 0.5416).Part 2: With 99% confidence, the population proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval.

Part 1:

To construct a 99% confidence interval for the population proportion, we can use the formula:

Confidence Interval = Sample Proportion ± Margin of Error

where the margin of error is determined by the level of confidence and the standard error.

First, let's calculate the sample proportion:

Sample Proportion = (Number of adults who say they have started paying bills online) / (Total number of adults surveyed)

Sample Proportion = 1436 / 2837 ≈ 0.5066 (rounded to four decimal places)

Next, we need to calculate the standard statistics error, which is the measure of the variability in the sample proportion:

Standard Error = sqrt((Sample Proportion * (1 - Sample Proportion)) / Sample Size)

Standard Error = sqrt((0.5066 * (1 - 0.5066)) / 2837) ≈ 0.0136 (rounded to four decimal places)

Now, we can calculate the margin of error:

Margin of Error = Critical Value * Standard Error

The critical value is based on the desired confidence level. For a 99% confidence level, the critical value is approximately 2.576 (obtained from a standard normal distribution table).

Margin of Error = 2.576 * 0.0136 ≈ 0.0350 (rounded to four decimal places)

Finally, we can construct the confidence interval:

Confidence Interval = Sample Proportion ± Margin of Error

Confidence Interval = 0.5066 ± 0.0350

Confidence Interval ≈ (0.4716, 0.5416) (rounded to four decimal places)

Part 2:

The correct interpretation is:

C. With 99% confidence, it can be said that the population proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval.

This means that we are 99% confident that the true proportion of adults who have started paying bills online falls within the range of 0.4716 to 0.5416. The survey results suggest that approximately 47.16% to 54.16% of the population of adults have started paying bills online in the last year.

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Answer: Answer below

Step-by-step explanation: So you would simply have to divide 8 into 72 which would be 9.

we can verify our answer by doing 9x8 which equals 72.

Answer: 9

Step-by-step explanation:

bears divided by shelves = number of bears per shelf

72 bears divided by 8 shelves= 9 bears per shelf

Answer:

40

Step-by-step explanation:

P=2(l+w)

2·(10+10)

          =40

Answer:

one way to convert from inches to centimeters is to multiply the number of inches by 2.54. how many centimeters are there in 1/4 inch? (i need this in long division)

Greetings from Brasil...

We have to remember 2 details:

→ When X = 0, the function intersects the Y axis

→ When Y = 0, the function intersects the X axis

So

1: X = 0

Y = X + 5

Y = 0 + 5

Y = 5

X = 0 and Y = 5 ⇔ (0; 5)

2: Y = 0

Y = X + 5

0 = X + 5

X = - 5

Y = 0 and X = - 5 ⇔ (- 5; 0)

Then the point at which the graph intersects the X and Y axis will be

(0; 5) and (- 5; 0)

Answer: 1/3

Step-by-step explanation:

In a multiple-choice examination with 3 choices for each question, the probability of guessing the correct answer is 1/3. Since you are trying to guess exactly 6 of 10 answers correctly, this means that you will be guessing incorrectly on 4 of the 10 questions. The probability of guessing incorrectly on a single question is 2/3.

To find the probability of guessing exactly 6 of 10 answers correctly, we can use the binomial probability formula, which is given by the following expression:

P(x) = (n!/(x!(n-x)!) * p^x * (1-p)^(n-x)

In this formula, n is the total number of trials, x is the number of successes, p is the probability of success on a single trial, and 1-p is the probability of failure on a single trial.

Plugging in the values for this problem, we get:

P(6) = (10!/(6!(10-6)!) * (1/3)^6 * (2/3)^4

= 210 * (1/3)^6 * (2/3)^4

= 210 * (1/3^6) * (2/3^4)

= 210 * (1/3^6) * (1/3^2)

= 210 * (1/3^8)

= 210 * (1/6561)

= 0.0322

So the probability of guessing exactly 6 of 10 answers correctly in a multiple-choice examination with 3 choices for each question is approximately 0.0322, or about 3.22%.

The conditional probability for this problem is given as follows:

C. P(A|B) = 2/5 = 0.4 = 40%.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

For this problem, we have that 5 students play soccer, and of those, 2 play basketball, hence the conditional probability is given as follows:

C. P(A|B) = 2/5 = 0.4 = 40%.

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Bob can deduct a total of $2,210 on his Schedule C related to these expenses.

To determine the total amount Bob can deduct on his Schedule C related to these expenses, consider the specific categories that can be deducted. Based on the information provided, categorize the expenses as follows:

Course fees for continuing legal education: $1,400

Airfare and hotel room: $500

Meals provided by the hotel's restaurant: $300

Snacks from the newsstand: $10

To calculate the total amount that Bob can deduct, add up these expenses:

$1,400 + $500 + $300 + $10 = $2,210

Therefore, Bob can deduct a total of $2,210 on his Schedule C related to these expenses.

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Answer:

Mean = 59.1, Median = 61

(there might have been a mistake in calculation (a lot of numbers!))

Step-by-step explanation:

The sample size is 40,

Now, the formula for the mean is,

Mean = (sum of the sample values)/(sample size)

so we get,

\(Mean = (49+63+78+22+41+39+75+61+63+65+58+37+45+52+81+75+78+72+68+59+72+85+63+61+75+39+41+48+59+55+61+25+61+52+58+71+75+82+49+51)/40\\Mean = 2364/40\\Mean = 59.1\)

To find the median, we have to sort the list in ascending (or descending)order,

we get the list,

22,25,37,39,39,41,41,45,48,49,

49,51,52, 52,55,58, 58, 59, 59, 61,

61, 61, 61, 63, 63, 63, 65, 68, 71, 72,

72, 75, 75, 75, 75, 78, 78, 81, 82, 85

Now, we have to find the median,

since there are 40 values, we divide by 2 to get, 40/2 = 20

now, to find the median, we takethe average of the values above and below this value,

\(Median = ((n/2+1)th \ value + (n/2)th \ value )/2\\where, \ the\ (n/2)th \ value \ is,\\n/2 = (total \ number \ of \ samples) /2\\n/2=40/2\\(n/2)th = 20\\Hence\ the (n/2)th \ value \ is \ the \ 20th \ value\)

And the (n+1)th value is the 21st value

Now,

The ((n/2)+1)th value is 61 and the nth value is 61, so the median is,

Median = (61+61)/2

Median = 61

In this case, we are to determine the probability of selecting two even numbers. This can be solved as follows:There are six even numbers: {2, 4, 6, 8, 10, 12}.We can use the concept of conditional probability since the first event affects the probability of the second event. This can be expressed as follows:

In this case, P(A) represents the probability of selecting an even number, and P(B|A) represents the probability of selecting an even number given that the first card selected was even. P(A) = 6/12 = 1/2 (there are six even numbers and twelve cards in total)P(B|A) = 5/11 (there are five even numbers left in the box after the first even number is selected, and eleven cards are left in total).

The probability of selecting two even numbers can be found by multiplying these probabilities: P(A) x P(B|A) = (1/2) x (5/11) = 5/22Therefore, the probability of selecting two even numbers is 5/22.Answer: 5/22

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The equation with a solution of x = -3 is7x-(x - 9) = 2x - 3

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

7x-(x - 9) = 2x -

Rewrite as

7x-(x - 9) = 2x - [ ]

Replace the blank with y

So, we have

7x-(x - 9) = 2x - y

The solution is x = -3

So, we have

7(-3) - (-3 - 9) = 2(-3) - y

Evaluate the expression

-9 = -6 - y

Make y the subject

y = 9 - 6

Evaluate

y = 3

Hence, the equation is 7x-(x - 9) = 2x - 3

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