18. In a two-digit number, digit in unit's place is twice the digit in ten's place. If
27 is added to it, digits are reversed. Find the number.

Answers

Answer 1

Answer:

the given number is (3×10)+6=36.

Step-by-step explanation:

Let x denote the digit in the tenth  place and y denote the digit in unit place..  So, the number may be written as x y 10 + in the expanded form. (just like 35= 10(3) +5)  

When the digits are reversed, x becomes the digit in unit place and y becomes the digit in the tenth place. The changed number, in the expanded form is 10y+x.

According to the first condition, we have y=2x which is written as  

2x−y=0      (1)

Also, by second condition, we have

(10+x)−(10x+y)=27

That is,   −9x+9y=27→−x+y=3            (2)

Adding equations (1) and (2),  we get  x= 3.  

Substituting x 3 = in the equation (2), we get y = 6.  

Thus,  the give

n number is (3×10)+6=36.

Hope this helps!

Answer 2

Answer: 36

Step-by-step explanation:

\(\displaystyle \overline {xy} - two \ digit \ number \\\\ Where :\\\\ 1) y=2x \\\\ 2) \ \overline{xy} +27= \overline{yx} \\\\ 10x+y+27=10y+x \\\\ 10x+2x+27=2x\cdot 10+x\\\\ 11x+27=20x \\\\ 9x=27 \\\\ x=3 \ ; \ y=2x=6 \\\\ Then:\\\\ \large \boxed{\mathfrak{Answer}: \overline {xy}=36}\)


Related Questions

Question Which is closest to the surface area of the figure below? 1463.8 m squared 578.1 m squared 923.2 m squared 3692.6 m2

Question Which is closest to the surface area of the figure below? 1463.8 m squared 578.1 m squared 923.2

Answers

The closest option to the cone area is 923.2 m². 

What is a cone?

A cone is a shape formed from a series of line segments or lines that connect a common point, called a vertex or vertex, to all points on the base of a circle that do not contain vertices. The distance from the apex of the cone to the base is called the height of the cone.

To solve this problem, we need to find the surface of the cone. Formula for the surface area of cone:

A = \(\pi\)r² + \(\pi\)rℓ

where r is the radius of the base, ℓ is the height of the depression, and π is a constant of approximately 3.14159.

First, we find the radius of the base. Since the bottom line of the cone is listed as 18 feet and we know the radius is 14 feet, we can use the Pythagorean theorem to find the height of the cone.

h² = ℓ² - r²

h² = 19.3² - 14²

h ≈ 11.48 feet

Now we can compute the surface.

A = \(\pi\)(14)² + \(\pi\)(14)(19.3)

A ≈ 923.2 square feet

So the closest option to the cone area is 923.2 m². 

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What is the round trip distance in miles from city 1 to city 3?
15
30
50
70

Answers

The round trip distance in miles from city 1 to city 3 is given as follows:

30 miles.

How to obtain the round trip distance?

The matrix corresponding to the distances between each of the cities is given by the image presented at the end of the answer.

Looking at row 1, column 3, we have that the distance from city 1 to city 3 is of 15 miles.

For the round trip distance, we have to go back from city 3 to city 1, more 15 miles, hence the distance is given as follows:

2 x 15 = 30 miles.

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What is the round trip distance in miles from city 1 to city 3?15305070

large pies cost $5 and small pots cost $2. If $45 pies were sold for $120 how many small pies were sold​

Answers

Answer:

I'm assuming that's supposed to just be 45, not $45

Step-by-step explanation:

35 small pies were sold

10 large pies = $50

35 small pies = $70

50 + 70 = 120

Consider the line 5x+2y=−4. What is the equation of the line parallel to the given line that passes through the point (−2, 6) in slope-intercept form? Enter your answer by filling in the boxes to complete the equation.

Answers

Answer:

  y = -5/2x +1

Step-by-step explanation:

You want the slope-intercept form equation for the line through the point (-2, 6) that is parallel to 5x +2y = -4.

Parallel line

The equation of a parallel line can be the same as the given equation, except for the constant. The new constant can be found by substituting the given point coordinates:

  5(-2) +2(6) = c

  -10 +12 = c

  2 = c

Now we know the equation of the parallel line can be written as ...

  5x +2y = 2

Slope-intercept form

Solving for y puts this in slope-intercept form:

  2y = -5x +2 . . . . . . . . subtract 5x

  y = -5/2x +1 . . . . . . . . divide by 2

We don't know what your boxes look like, but we can separate the numbers to make it look like this:

  \(\boxed{y=\dfrac{-5}{2}x+1}\)

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Consider the line 5x+2y=4. What is the equation of the line parallel to the given line that passes through

Your friend was bored one day and started making patterns using Cheerios from a new box he had opened. He laid the Cheerios on the table as such:
Based on the two images above and the information about the box, answer the following questions.
A) Identify and label the variable
B) Make a table for up to 8-figure patterns
C) Write an equation to represent the nth term of the sequence.
D) If the pattern continues, what figure number will have 20 whole Cheerios in it?
E) Is it reasonable to think this pattern would continue forever? If not, explain.
F) Based on the information provided, what is the largest figure number we can have using a full box of Cheerios?

PLS ANSWER ALL OF THE QUESTIONSSS I REALLY NEED THE ANSWERS ASAPPPPPPP PLEASE AND THANK YOU

Your friend was bored one day and started making patterns using Cheerios from a new box he had opened.
Your friend was bored one day and started making patterns using Cheerios from a new box he had opened.
Your friend was bored one day and started making patterns using Cheerios from a new box he had opened.

Answers

A) The variable is n, which represents the number of the figure in the pattern.

B) Here is a table for up to 8-figure patterns:

Figure Number of Cheerios

1                      1

2                      3

3                      6

4                     10

5                     15

6                     21

7                    28

8                    36

C) The equation to represent the nth term of the sequence is n(n+1)/2.

D) If the pattern continues, the figure number that will have 20 whole Cheerios in it is 12.

E) It is not reasonable to think this pattern would continue forever. The number of Cheerios in each figure is increasing by 2 each time. This means that the number of Cheerios in the figure will eventually exceed the number of Cheerios in a box.

F) Based on the information provided, the largest figure number we can have using a full box of Cheerios is 107. This is because there are 108 Cheerios in a box, and the number of Cheerios in each figure is increasing by 2 each time.

Here is a more detailed explanation of how to answer each question:

A) Identify and label the variable

The variable is n, which represents the number of the figure in the pattern. For example, the first figure is figure 1, the second figure is figure 2, and so on.

B) Make a table for up to 8-figure patterns

Here is a table for up to 8-figure patterns:

Figure Number of Cheerios

1                        1

2                        3

3                        6

4                        10

5                        15

6                        21

7                        28

8                        36

C) Write an equation to represent the nth term of the sequence

The equation to represent the nth term of the sequence is n(n+1)/2. This equation can be derived by looking at the table of values. For example, the number of Cheerios in the first figure is 1, which is equal to 1(1+1)/2. The number of Cheerios in the second figure is 3, which is equal to 2(2+1)/2. And so on.

D) If the pattern continues, what figure number will have 20 whole Cheerios in it?

If the pattern continues, the figure number that will have 20 whole Cheerios in it is 12. This can be found by solving the equation n(n+1)/2 = 20. The solution is n = 12.

E) Is it reasonable to think this pattern would continue forever? If not, explain.

It is not reasonable to think this pattern would continue forever. The number of Cheerios in each figure is increasing by 2 each time. This means that the number of Cheerios in the figure will eventually exceed the number of Cheerios in a box.

F) Based on the information provided, what is the largest figure number we can have using a full box of Cheerios?

Based on the information provided, the largest figure number we can have using a full box of Cheerios is 107. This is because there are 108 Cheerios in a box, and the number of Cheerios in each figure is increasing by 2 each time.

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Find the value of x

Find the value of x

Answers

Answer: The value of x is 49.

Step-by-step explanation:

To find the value of x, you will first need to cross multiply the fractional variables together.

5x - 80 = 3x + 18

Then, move the numerical term 80 to the right side of this equation and add it to 18.

5x - 80 = 3x + 98

Move 3x to the left side of the equation and subtract it this time to the variable 5x.

2x = 98

Finally, you divide both of the equation's sides by 2 and you will get 49.

x = 49

When you actually add x to this problem, you would get 33/55.

49 - 16/49 +6 = 33/55

You can then simplify 33/55 and get the same answer 3/5.

3/5

Therefore, the value of x for this variable equation with the fractions would be equal to x = 49. Hope this helps!

-From 5th Grader Honors Student

so the answer of the equation would be x=49!

XPO Corporation has a minimum tax credit of $51,000 from 2017. XPO’s 2018 tax liability before any MTC carryover is $30,500. What is XPO’s minimum tax credit carryover to 2019, if any?

Answers

XPO's minimum tax credit carryover to 2019 is $20,500.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants. An algebraic expression is a mathematical phrase that can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

XPO's minimum tax credit from 2017 is $51,000. This means that they are allowed to reduce their 2018 tax liability by up to $51,000 using this credit.

Since their 2018 tax liability before any MTC carryover is $30,500, they have not used the entire minimum tax credit for 2017. Therefore, they can carry over the remaining credit to 2019.

To calculate the minimum tax credit carryover to 2019, we need to subtract the amount of the minimum tax credit that XPO used in 2018 from the total minimum tax credit of $51,000:

Minimum tax credit carryover = $51,000 - $30,500 = $20,500

Therefore, XPO's minimum tax credit carryover to 2019 is $20,500.

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1. Find the ratio of oranges to apples if there are 2 pineapples, 4 apples,
6 bananas, and 3 oranges in a fruit bowl.
a. 1 to 2
b. 2 to 4
c. 3 to 4
d. 3 to 2

Answers

Answer: the answer is C because there are 3 oranges and 4 apples

the answer is C. 3 to 4

For her party can Nina fill fewer than 10 bags with treats between 10 and 20 bags between 20 and 30 bags or more than 30 bags explain

Answers

The correct option regarding the number of bags filled by Nina, using proportions, is given as follows:

Between 20 and 30 bags.

What is a proportion?

A proportion is a fraction of an amount, and this fraction is combined with the unit rates of the problem and basic arithmetic operations, especially multiplication and division, to find the desired amounts in the context of the problem.

In this problem, a proportion is applied to find the number of bags filled by Nina, which is given by the division presented as follows:

Number of bags = Number of treats / Treats per bag.

The values of these parameters are given as follows:

Number of treats: 78.Number of treats per bag: 3.

Hence the numeric value of the expression is:

Number of bags = 78/3 = 26.

Which is a number between 20 and 30.

Missing Information

The problem states that Nina had 78 treats, and each bag has 3 treats, then it asks the correct option regarding the number of bags.

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How many 11-card hands are possible with a 20-card deck?

Answers

There is only 1 possible 11-card hand that can be formed from a 20-card deck.

To determine the number of 11-card hands possible with a 20-card deck, we can use the concept of combinations.

The number of combinations, denoted as "nCk," represents the number of ways to choose k items from a set of n items without regard to the order. In this case, we want to find the number of 11-card hands from a 20-card deck.

The formula for combinations is:

nCk = n! / (k!(n-k)!)

Where "!" denotes the factorial of a number.

Substituting the values into the formula:

20C11 = 20! / (11!(20-11)!)

Simplifying further:

20C11 = 20! / (11! * 9!)

Now, let's calculate the factorial values:

20! = 20 * 19 * 18 * ... * 2 * 1

11! = 11 * 10 * 9 * ... * 2 * 1

9! = 9 * 8 * 7 * ... * 2 * 1

By canceling out common terms in the numerator and denominator, we get:

20C11 = (20 * 19 * 18 * ... * 12) / (11 * 10 * 9 * ... * 2 * 1)

Performing the multiplication:

20C11 = 39,916,800 / 39,916,800

Finally, the result simplifies to:

20C11 = 1

Consequently, with a 20-card deck, there is only one potential 11-card hand.

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Plz help I’m really confused

Plz help Im really confused

Answers

Answer: i think its 134

Step-by-step explanation:

6 minutes 20 seconds into seconds.​

Answers

Answer:

380 seconds

Step-by-step explanation:

Convert 6 minutes to seconds by multiplying 6 times 60, because there are 60 seconds per minute.
6 x 60 = 360

Now add the 20 seconds.
360 + 20 = 380

6 minutes and 20 seconds are equal to 380 seconds.

HELP!!

Calculate the residuals for your scatterplot in step 2d.

HELP!!Calculate the residuals for your scatterplot in step 2d.

Answers

In statistics, a residual is defined as the difference between the predicted value of an outcome variable and the observed value of that variable. Residuals are used to evaluate how well a regression model fits the data.In order to calculate the residuals for a scatterplot, follow these steps:

Step 1: Plot the data on a scatterplot.

Step 2: Perform a regression analysis on the data to find the equation of the regression line. This equation should take the form y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept.

Step 3: Using the equation of the regression line, calculate the predicted value of y for each data point in the scatterplot.

Step 4: Subtract each predicted value of y from the actual value of y for each data point in the scatterplot. This difference is the residual for that data point.

Step 5: Plot the residuals on a new scatterplot. The x-axis of this scatterplot should be the independent variable, and the y-axis should be the residual values.

Step6: This scatterplot is called a residual plot.Residuals are useful for identifying patterns in data that the regression model fails to capture. If the residuals are randomly scattered around the horizontal axis, then the regression model is a good fit for the data. If there are clear patterns in the residual plot, then the regression model may not be a good fit for the data and further analysis is required.

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William leaves his home at 15:03 and walks for 12 minutes to Euston station.
He spends 4 minutes buying a ticket and then catches the next train to Bletchley.
What time will he arrive at Bletchley?
Train timetable
Euston
14:49 15:18 15:29
14:52
15:32 15:35
Harrow
Watford 15:01
15:30
15:41 15:44 16:11
Hemel
15:39 15:50
15:53
16:20
Tring
15:31
16:00
Q
16:14 16:41
Bletchley 15:47
16:16
16:30
Bedford 15:54 16:23 16:34 16:37 17:04
15:32 15:59

Answers

William catches the train from Euston station to Bletchley. According to the timetable, the next train from Euston to Bletchley departs at 15:32. William spends 4 minutes buying a ticket, so he will board the train at 15:36.

To find out what time he will arrive at Bletchley, we need to look at the arrival time for the train that departs Euston at 15:32. According to the timetable, this train arrives at Bletchley at 16:16.

William spends 12 minutes walking to Euston station and 4 minutes buying a ticket, so his total journey time is 12 + 4 + 44 = 60 minutes (since there are 60 minutes in an hour). Therefore, he will arrive at Bletchley at 16:16 + 60 minutes = 17:16.

So, William will arrive at Bletchley at 17:16.

*Answer*

15:47

Step-by-step explanation:

He left; 15:03

Walk for; 12mins

Spends extra;4min

So by my side,

I'll sum up those values we're having to find the total time that was spent

12+4= 16mins

So, at that time when he reached at the station it was 15:19 when we add those extra mins

And so I think it'll 15:47

My thought told me so though

Which point is located at (0.25,-0.5) point A O point O point R​

Which point is located at (0.25,-0.5) point A O point O point R

Answers

Answer:

• point C

Step-by-step explanation:

______________

The correct answer is the second choice Point C

A function is graphed on the coordinate grid.

The output for the function when the input is -1 is ___?

A. -4.2
B. -3
C. 3
D. 1.2

A function is graphed on the coordinate grid.The output for the function when the input is -1 is ___?A.

Answers

Answer:

C) 3

Step-by-step explanation:

Assuming the standard of x = input and y = output.

What is the range of the function graphed below?

Answers

Answer:

n mathematics, the range of a function may refer to either of two closely related concepts: The codomain of the function The image of the function Given two sets X and Y, a binary relation f between X and Y is a function if for every x in X there is exactly one y in Y such that f relates x to y

Step-by-step explanation:

You are offered a job that pays $34,000 during the first year, with an annual increase of 5% per year beginning in the second year. That is, beginning in year 2, your salary will be 1.05 times what it was in the previous year. What can you expect to earn in your fourth year on the job?

In your fourth year on the job, you can expect to earn $______
(Round to the nearest dollar)

Answers

In your fourth year on the job, you can expect to earn $41,327.

What is simple interest?

Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time period.

Simple Interest = (Principal × Rate × Time) / 100

Compound interest is a method of calculating the interest charge. In other words, it is the addition of interest on interest.

Compound Interest =P(1+r/n)^rt

We are given that;

In this case, P = 34,000, r = 0.05, and n = 4.

Plugging these values into the formula, we get:

A = 34,000(1 + 0.05)^4

A = 34,000(1.05)^4

A = 34,000(1.2155)

A = 41,327

Therefore, by the simple interest the answer will be $41,327.

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A car travels 55 miles per hour for two hours. Complete the table.

Answers

Answer:

if you are looking for how many miles the car will travel for 2 hours then it would be 110

Step-by-step explanation:

55×2=110

AB and AD are tangent to circle C. Find the length of AB, if AB = 8x and AD = x + 9. Round your answer to 2 decimal places.​

Answers

To find the length of AB, we need to use the properties of a tangent to a circle.

When a line is tangent to a circle, it forms a right angle with the radius drawn to the point of tangency. This means that triangle ABD is a right triangle with AB as the hypotenuse.

We can use the Pythagorean theorem to find the length of AB:

AB^2 = AD^2 + BD^2

Since AD = x + 9 and BD = 8x - (x + 9) = 8x - x - 9 = 7x - 9, we can substitute these values into the equation:

(8x)^2 = (x + 9)^2 + (7x - 9)^2

64x^2 = x^2 + 18x + 81 + 49x^2 - 126x + 81

64x^2 = 50x^2 - 108x + 162

14x^2 + 108x - 162 = 0

Dividing the equation by 2, we get:

7x^2 + 54x - 81 = 0

Using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

a = 7, b = 54, c = -81

x = (-54 ± √(54^2 - 4 * 7 * -81)) / (2 * 7)

x = (-54 ± √(2916 + 2268)) / 14

x = (-54 ± √5184) / 14

x = (-54 ± 72) / 14

Now we solve for x:

Case 1: x = (-54 + 72) / 14 = 18 / 14 = 9 / 7

Case 2: x = (-54 - 72) / 14 = -126 / 14 = -9

Since the length of a segment cannot be negative, we discard the second case and focus on the positive solution.

Therefore, x = 9/7.

Substituting this value back into AB = 8x:

AB = 8 * (9/7) = 72/7 ≈ 10.29

Rounding to 2 decimal places, the length of AB is approximately 10.29 units.

Answer:

To find the length of AB, we can use the property that two tangents to a circle from the same external point are equal. This means that AB = AD. Substituting the given values, we get:

8x = x + 9

Solving for x, we get:

x = 1.5

Therefore, AB = 8x = 8(1.5) = 12.

To check our answer, we can use the Pythagorean theorem on triangle ABD, since AB is perpendicular to BD at the point of tangency. We have:

AB^2 + BD^2 = AD^2

Substituting the values, we get:

12^2 + BD^2 = (1.5 + 9)^2

Simplifying, we get:

BD^2 = 56.25

Taking the square root of both sides, we get:

BD = 7.5

Hence, the length of AB is 12 and the length of BD is 7.5.

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Based on the picture above, what is the solution to the system of equations?
Type a response

Based on the picture above, what is the solution to the system of equations?Type a response

Answers

Step-by-step explanation:

The 'solution ' is the point where the two lines intersect :    ( 0,-1)

Reduce the fraction, then change to a mixed number. 20/3

Answers

Given:

\( \frac{20}{3} \)

To find:

\( \frac {20}{3} \) as a mixed number.

Solution:

First, divide the numerator by the denominator.

\(20 \div 3 \)

\( = 6 \: R2\)

Then, write the whole number value and use the remainder as the numerator over the denominator. As we all know the denominator won't change.

\(\large\boxed{\sf{= 6 \frac{2}{3}}}\)

5h-6-8+7h what’s the answer ?

Answers

Simplified ? 12h -(-2)

HELP ME PLS ;-;

Plot -3 1/2, 1 1/4 on the coordinate plane

HELP ME PLS ;-; Plot -3 1/2, 1 1/4 on the coordinate plane

Answers

Answer:

black fart matters

Step-by-step explanation:

Answer:

iwkwkwkwkkwrlrkkdkdkdkelrlfkfkrkrk

Find the circumference and the area of a circle with radius 9m .
Use the value 3.14 for , and do not round your answers. Be sure to include the correct units in your answers.

Answers

The circumference of the circle will be 56.52 m.

And, The area of a circle will be 254.34 m².

What is Circle?

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

The radius of circle = 9 m

Now,

Since, The area of circle = πr²

Hence, The area of circle = 3.14 × 9²

                                        = 3.14 × 81

                                        = 254.34 m²

And, The circumference of the circle = 2πr

                                                         = 2 × 3.14 × 9

                                                         = 56.52 m

Thus, The circumference of the circle will be 56.52 m.

And, The area of a circle will be 254.34 m².

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The midpoint of JK is point L at (–1, 8). One endpoint is J(4, –15). Which equations can be solved to determine the coordinates of the other endpoint, K? Select two options. = –1 = 4 –15 + y1 =16 = y1

Answers

The other endpoint of a line segment JK is K(- 6, 31).

What is the midpoint formula of a straight line?

The formula for midpoint \(x_m\) = (x₁ + x₂)/2 and \(y_m\) = (y₁ + y₂)/2.

Where x₁, y₁, and x₂, y₂ are the endpoint of the line.

Given, The midpoint of JK is point L at (-1, 8) and One endpoint is J(4, - 15).

Assuming the other endpoint(K) to be (x₂, y₂).

∴ - 1 = (4 + x₂)/2.

- 2 = 4 + x₂.

x₂ = - 6.

And,

8 = (- 15 +  y₂)/2.

16 = - 15 +  y₂.

y₂ = 31.

So, K(- 6, 31).

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In circle R, What is the name of line segment BE and AD?

In circle R, What is the name of line segment BE and AD?

Answers

a diameter is a line that starts from the circumference to the other part of the circumference

Select the correct answer from the drop-down menu.

Three segments AB, AC, and AE share a common endpoint A. Point D lies on segment AB. Arc BC and arc DE is drawn. The length of arc between segments AB and AC is 1.18 radians. The length of arc between segments AE and AC is 2.36 radians.

If AD=2/3 AB , the ratio of the length of BC to the length of DE is [1/6, 1/4, 3/2, 3/4].

Answers

The ratio of the length of BC to the length of DE is 1/2.

What is Arc Length?

Arc length is defined as the distance between any two points on a section of a circle or curve.

The figure in the question is given below.

The formula to find the length of an arc is given as,

Arc length, l = rθ, where r is the radius and θ is the central angle in radians.

Given that,

Central angle for arc BC, θ = 1.18 radians.

Radius for arc BC, r = AC = AB

Arc length of BC = rθ

                            = 1.18 (AB)

Central angle for arc DE, θ = 1.18 + 2.36 = 3.54 radians

Radius for arc DE, r = AE = AD = 2/3 AB

Arc length of DE = rθ

                            = 3.54 × (2/3) AB

                            = 2.36 (AB)

Arc length of BC / Arc length of DE = 1.18 (AB) / 2.36 (AB) = 1/2

Hence the ratio of BC to DE is 1/2.

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Select the correct answer from the drop-down menu. Three segments AB, AC, and AE share a common endpoint

Answer:

DE: 3/4

Step-by-step explanation:

PlatoGang

Wei Jing has between 70 and 150 baseball
cards in his collection. When he arranges them
in groups of 10, he has 3 left over. When he
arranges them in groups of 9, he has 5 left
over. If he arranges them in groups of 8, how
many will he have left over?

Answers

Answer:

117$.

Step-by-step explanation:

Let $x$ represent the number of cards in Wei Jing's collection. We are given that $70 \leq x \leq 150$. We are also given that $x \equiv 3 \pmod{10}$ and $x \equiv 5 \pmod{9}$. Since $x \equiv 3 \pmod{10}$, $x - 3$ is divisible by 10. Since $x \equiv 5 \pmod{9}$, $x - 5$ is divisible by 9. The least common multiple of 10 and 9 is $90$, so $(x - 3) - 90$ is divisible by 90 and $(x - 5) - 90$ is divisible by 90. Adding these equations gives us $2x - 98$ is divisible by 90. Dividing both sides by 2 gives us $x - 49$ is divisible by 45. Since $70 \leq x \leq 150$, the only solution for $x$ is $x = 117$.

Find the critical value ta/2 needed to construct a confidence interval of the given level with the given sample size. Round the answers to three decimal places.
(a) For level 90% and sample size 8.
(b) For level 99% and sample size 11.
(c) For level 95% and sample size 25.
(d) For level 99.5% and sample size 10.

Answers

Answer:

1.894

3.169

2.064

3.690

Step-by-step explanation:

A.) 90% ; sample size = 8

Degree of freedom, df = n - 1

t(1 - α/2, 7) = t0.05, 7 = 1.894

B.) 99% ; sample size = 11

Degree of freedom, df = n - 1

t(1 - α/2, 10) = t0.005, 10 = 3.169

C.) 95% ; sample size = 25

Degree of freedom, df = n - 1

t(1 - α/2, 24) = t0.025,24 = 2.064

(D.) 99.5% and sample size 10.

Degree of freedom, df = n - 1

t(1 - α/2, 9) = t0.0025,9 = 3.690

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