Answer:
22098
Step-by-step explanation:
You want the difference between the largest and smallest 5-digit numbers whose digits are from the set {1, 2, 3} and include each of these at least once. The numbers cannot be divisible by 2 or 3.
DigitsThe number will be divisible by 3 when its sum of digits is a multiple of 3. Since 1, 2, and 3 are prescribed digits, the remaining two digits must not have a total of 3 or 6. The largest possible remaining digits are {2, 3}, and the smallest remaining digits are {1, 1}. (Using {3, 3} for the largest digits would give a number divisible by 3.)
The number will be divisible by 2 if the least significant digit is 2. The largest and smallest digits are not 2, so that will not be an issue.
LargestThe largest number will place the largest available digit in the place with the highest place value: 33221.
SmallestThe smallest number will place the smallest available digit in the place with the highest place value: 11123.
DifferenceThe desired difference is the difference of these numbers:
33221 -11123 = 22098 . . . . difference of largest and smallest
The difference between the two numbers will be 1998.
What is a number system?A numeral system is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set in a consistent manner using digits or other symbols. In different numeral systems, the same sequence of symbols can represent different numbers.
Given that Consider five-digit integers that have the following properties. Each of the digits is 1, 2 or 3, and each of 1, 2, 3 occurs at least once as a digit; also, the number is not divisible by 2 nor divisible by 3.
The largest number will be 3211.
The smallest number will be 1213.
The difference between the largest and the smallest number will be calculated as,
D = 3211 - 1213
D = 1998
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How do you find the factor of a root?
Answer:
Step-by-step explanation:
you can use the zero-product property to find the roots of a factored equation. After you factor a polynomial into its different pieces, you can set each piece equal to zero to solve for the roots with the zero-product property.
What is the mean of the following data set 4 8 11 12 13?
Answer:
9.6
Step-by-step explanation:
What is the mean of the following data set 4 8 11 12 13?
Mean: is the average of values so:
(4 + 8 + 11 + 12 + 13) / 5 = 9.6
How can I calculate my height at 2?
By combining the mother's as well as father's heights in inches, you may determine the midparental height. For boys, measure 5 inches longer; for girls, measure 5 inches shorter. multiply by two.
How can you accurately anticipate a children's adult height?A person's height can be predicted by other factors besides genes. A child may occasionally be significantly taller above their relatives and parents.There is no reliable method for estimating a children's adult height.However, a number of calculations can offer a reliable approximation of a child's growth. Here is a common illustration:
In inches or millimeters, multiply the father's height by the mother's height.For boys, add 5 inches (13 centimeters), and for girls, take 5 inches (13 centimeters) away.Multiply by 2.Double with a boy's height around age 2 or even a girl's height from age 18 months to get an idea of a child's adult height.To know more about the children's adult height, here
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You are planning on installing a security system at your home. For Safety First Security, you can get monitoring for $2 a day with a one-time set-up fee of $150. For Home Safety Security, you can get
monitoring for $1.50 a day with a one-time set-up fee of $200. Using substitution, find the number of days for which both companies would cost the same.
Step-by-step explanation:
a one-time set-up fee of $200. so that's one day a one-time set-up fee of $150. and that's day 2Is base times height divided by 2?
The base is the length of one of the triangle's sides, and the height is the distance from that side to the triangle's opposite corner.
What is triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane. Triangles are three-sided polygons with three vertices. The angles of the triangle are formed by connecting the three sides end to end at a point. The total of the triangle's three angles equals 180 degrees.
Here,
The base of the triangle is the length of one of its sides, and the height is the distance from that side to the triangle's opposite corner.
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A guy wire runs from the top of a cell tower to a metal stake in the ground. Sophia places a 11-foot tall pole to support the guy wire. After placing the pole, sophia measures the distance from the stake to the pole to be 4 ft. She then measures the distance from the pole to the tower to be 32 ft. Find the length of the guy wire, to the nearest foot.
The length of the guy wire, to the nearest foot, is 201 ft.
Refer to the diagram attached below for the given information
We have two similar right triangles, ΔABE and ΔCDE.
CD = 11 ft
DE = 4 ft
BD = 32 ft
Length of the guy wire (AE)
Since ΔABE ~ ΔCDE, therefore,
AB/CD = BE/DE (proportional sides)
Plug in the values:
AB/11 = (32 + 4)/2
AB/11 = 36/2
Cross multiply:
AB = (36 × 11)/2
AB = 198 ft
Apply Pythagorean Theorem to find AE:
AE = √(AB² + BE²)
AE = √(198² + 36²)
AE = 201 ft (nearest foot)
Therefore, the length of the guy wire, to the nearest foot is 201 ft.
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We have two similar right triangles, ΔABE and ΔCDE.
CD = 11 ft
DE = 4 ft
BD = 32 ft
Length of the guy wire (AE)
Since ΔABE ~ ΔCDE, therefore,
AB/CD = BE/DE (proportional sides)
AB/11 = (32 + 4)/2
AB/11 = 36/2
AB = (36 × 11)/2
AB = 198 ft
AE = √(AB² + BE²)
AE = √(198² + 36²)
AE = 201 ft (nearest foot)
Solve the system of linear equations by substitution.
x=17-4y
y=x-2
Answer:
Step-by-step explanation
In the first equation
x=17-4y
In the second equation
We clear "x"
y=x-2
x=y+2
We ecuate "x"
x=17-4y=y+2
17-4y=y+2
15=5y
y=3
we substitute to find "x"
x=17-4y=17-4(3)=5
Is AAA a triangle congruence theorem?
A triangle AAA does not satisfy congruence theorem. Triangle denoted by AAA refers a triangle having three equal side lengths and three equal angles.
what is congruence theorem?Congruence theorem is developed based on two triangles which have equal corresponding side lengths and equal corresponding angles.
what are the criteria for satisfying congruence theorem?there are four criteria in where one or more criteria needed to satisfy. if two triangles have all three equal side lengths and equal corresponding angles then they satisfy congruence theorem. if two triangles have 2 equal side lengths and angle between sides are equal, they satisfy congruence theorem. If two triangles have equal two angles along
with equal similar side length, they satisfy congruence theorem.
hence, the triangle mentioned in the question is not congruent.
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Answer:
FALSE
Step-by-step explanation:
The angles can be the same, but the lengths of the sides can differ.
How many integers are there between 100 and 999?
898 integers in that range excluding 100 and 999
There are 900 integers between 100 and 999, inclusive.
Numbers between 999 and 100 inclusive: 999 - 99 = 900
If you want to know the number of integers between 100 and 999, but not including either 100 or 999, then there are 898 integers in that range.
What is an integers number:
An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion. Integers include things like -5, 0, 1, 5, 8, 97, and 3,043. Z is a set of integers that consists of the following:
Positive Numbers: If a number is greater than zero, it is considered positive. For instance, 1, 2, 3, etc.
Negative numbers are those that are less than zero. For instance: 1, 2, 3, etc.
Zero is described as being neither a positive nor a negative number. A whole number, that is.
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How do you find the median step by step?
The median is the exact middle number in a sequence or set of numbers.
Steps to find the median is given below:
Finding the Median in an Odd Set of Numbers:
Step 1: Sort your set of numbers from least to greatest. If they're scrambled, line them up, starting with the lowest number and ending with the highest number.
Step 2: Find the number that is exactly in the middle. This means that the median number has the same amount of numbers in front of it as it does behind it.
Finding the Median in an Even Set of Numbers
Step 1: Sort out your set of numbers from least to greatest. An even set of numbers is going to have two numbers exactly in the middle.
Step 2: Find the average of the two numbers in the middle. If 2 and 3 are both in the middle, so you need to add 2 and 3, then divide the sum by 2. The formula for finding the average of two numbers is (the sum of the two middle numbers) ÷ 2.
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How do you draw a SSS triangle?
We need to draw all sides of the triangle equal in order to make a SSS triangle because we know that the SSS triangle has all 3 sides equal.
What is the SSS triangle condition?Two triangles are said to be congruent if all three corresponding sides and all three corresponding angles have the same size.
We u can move, flip, twist, and turn these triangles to produce the same effect.
When relocated, they are parallel to one another.
Two triangles are deemed similar by the SSS test for triangle resemblance if their third sides are proportionate to one another.
Therefore, we need to draw all sides of the triangle equal in order to make a SSS triangle because we know that the SSS triangle has all 3 sides equal.
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Suppoe a merry-go-round i pinning once every 3 econd. If a point on the outide edge ha a peed of 12. 56 feet per econd, what i the radiu of the merry-go-round? (Ue 3. 14 for
The value of radius of the merry-go-round will be 6 feet.
What is a circle?A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.
In our daily life, we always see circular objects for example our bike wheel.
The longest line which can be drawn inside the circle will be the diameter.
The perimeter of the circle = 2πr where r is the radius of the circle.
The Merry cover on the round in 3 seconds thus, to cover the 2πr path it takes 3 seconds.
2πr/3 = 12.56
2πr = 37.68
r = 5.996 ≈ 6 feet.
Hence "The value of the radius of the merry-go-round will be 6 feet".
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Is the equation 3x² 11x 10 0 a quadratic equation?
Yes , the equation 3x² + 11x + 10 = 0 is a quadratic equation and the roots are x = -5/3 and x = -2
What is Quadratic Equation?
A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c = 0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the equation be represented as A
Now , the value of A is
3x² + 11x + 10 = 0 be equation (1)
Now , the equation is of the form ax² + bx + c = 0 , where the value of a = 3 , b = 11 and c = 10
So , the coefficient a is has the variable x² and equation 3x² + 11x + 10 = 0 is a quadratic equation
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
Substituting the values in the equation , we get
x = [ -11 ± √ ( ( 11 )² - 4 ( 3 ) ( 10 ) ) ] / 2 ( 3 )
On simplifying the equation , we get
x = [ -11 ± √ ( 121 - 120 ) ] / 6
x = ( -11 ± 1 ) / 6
So , the two roots of the equations are
x = ( -11 - 1 ) / 6 and
x = ( -11 + 1 ) / 6
x = -2 and
x = -5/3
Therefore , the values of x are -5/3 and -2
Hence , the roots of the quadratic equations are -5/3 and -2
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a tennis player computes her win ratio by dividing the number of matches she has won by the total number of matches she has played. at the start of a weekend, her win ratio is exactly $0.500$. during the weekend, she plays four matches, winning three and losing one. at the end of the weekend, her win ratio is greater than $0.503$. what's the largest number of matches she could've won before the weekend began?
Using the ratio we know that before the weekend started, she could have won as many as 164 games.
What is the ratio?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0.
A proportion is an equation that sets two ratios at the same value.
For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.
So, let n be the number of victories so that:
n/2n = 1/2 and n+3/2n+4 > 503/1000
Now, cross multiply as follows:
1000n + 3000 > 1006n + 2012
n < 988/6 = 164 4/6 = 164 2/3
Therefore, using the ratio we know that before the weekend started, she could have won as many as 164 games.
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What is the standard deviation of the data given below 10 28 13 18 29 30 22 23 25 and 32?
Hence, the standard deviation of the given data is 7 .
10 28 13 18 29 30 22 23 25 32
Here is the total number of observations n are 10
total= 10 +28+ 13+ 18+ 29+ 30+ 22+ 23+ 25+ 32 = 230
mean (μ) = total/n
= 230/10
= 23
Xi Xi-μ (Xi-μ)²
10 10-23=-13 169
28 28-23=5 25
13 13-23=-10 100
18 18-23=-5 25
29 29-23=6 36
30 30-23=7 49
22 22-23=-1 1
23 23-23=0 0
25 25-23=2 4
32 32-23=9 81
Use the formula to calculate the standard deviation.
√1/n*∑ (Xi-μ)² =√1/10*490
= √49
=7
Hence, the standard deviation of the given data is 7 .
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Is 5 a high standard deviation?
Yes, 5 is the high standard deviation which is considered very good.
What is a standard deviation evaluation?A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed. In contrast, a low or a high standard deviation indicates that the data points are, respectively, above or below the mean. A standard deviation that is close to zero implies that the data points seem to be close to the mean.85 persons responded to my survey about their capacity to carry out specific duties.
The responses are rated on a Likert scale of 1 to 5:
2 = Poor, 1 = Very Poor, 2 = Poor, 4 = Good, 3 = Average, 5 = Very GoodIts standard deviation is 0.54 and the mean score is 2.8.To know more about the standard deviation, here
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17. एउटा वस्तुको अङ्कित मूल्यमा 20% छुट दिएपछि 13% भ्याट जोडेर रु. 18080 मा बिक्री गरियो भने उक्त वस्तुको अङ्कित मूल्य पत्ता लगाउनुहोस् । (Allowing 20% discount on the marked price of an article, the value of the article will be Rs. 18080 when a VAT of 13% is added, find its marked Ans: Rs. 20,000 price.)
Answer:
11111111111111111111
The matrix below is named E. Create a matrix that is 5E. Now what is the element
at e12?
4 -6 -7
12 3 4
five plus eight times nine
How do the base and height of the rectangle compare to the base and height of the parallelogram?
In Parallelogram: Area = base x height(perpendicular distance).
In rectangle: Area = base x height.
Explain some properties of the parallelogram?Parallelogram:
A parallelogram is a particular sort of polygon. It's a quadrilateral in which the opposite side pairs are parallel to one another.
Congruent sides are those when AB = DC.Congruent opposite angels are D = B.(A + D = 180°) Consecutive angles are supplementary.All angles are correct if just one of them is.A parallelogram's diagonals cut each other in half.A parallelogram can be divided into two congruent pieces along each diagonal.Area = base x height(perpendicular distance)
Rectangle:
A quadrilateral having four equal internal angles is a rectangle.A rectangle's opposing sides are equal as well as parallel to one another.Each vertex of a rectangle has a 90° internal angle.The total of a rectangle's internal angles is 360°.The diagonals cut each other in half.The diagonals are all the same length.Area = base(length) x height(width).
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In the parallelogram below,
x = [? ]
3x+7
75x-17
Answer:
x=12
Step-by-step explanation:
3x+7 = 5x-17
-2x=-24
x=12
Hope this helps you can thank me if this helps and 5 star if you dont mind :)
Answer:
x=12
Step-by-step explanation:
The two sides must be equal in length
3x+7 = 5x-17
Subtract 3x from each side
3x-3x+7 = 5x-3x-17
7 = 2x-17
Add 17 to each side
7+17 = 2x-17+17
24 = 2x
Divide each side by 2
24/2 = 2x/2
12 =x
6. From the menu, select the correct
approximation.
If the expression
√24 × √10
represents the area of a rectangle, then
the approximate area of the rectangle is
60 square units
15 square units
8 square units
120 square units
The approximate area of the rectangle as per the options will be equal to 15 square units. Hence, option B is correct.
What is area?An object's area is how much space it takes up in two dimensions. It is the measurement of the amount of unit squares which completely encompass the surface of a compact figure.
The squared unit, which is frequently expressed as inches, square feet, etc., is the accepted unit of area.
As per the given information in the question,
Let the length is given as, l = √24 and,
The width is given as, w = √10
Use the formula of area of rectangle,
A = lw
A = √24 × √10
A = 4.89 × 3.16
A = 15.45 ≈ 15 square units.
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cm 2 What is the area of the rectangle? Enter the answer in the box. 9 cm 4 cm
Answer:
Let,
length of rectangle ( L) =9cm
breadth of rectangle (b) =4cm
Area of rectangle=L×b
=9×4
=36cm^2
One of the solutions to the quadratic equation x - 12x – 45 = 0 is x = -3 Which statement is true? Select all that apply. (Check Screenshot)
Answer:
1st and 3rd 4th
graph of f(x) = x² - 12x-45 has an x-intercept at x = -3
-3 is a zero of the function f(x) = x²-12x- 45
x + 3 is a factor of x² - 12x-45
Steps:
other solution is (x - 15) or x = 15
x² - 12x-45
2 numbers that when multiplied give -45 & when added give -12 are -15 & 3
(x-15) (x+3)
"zero" is a fancy way for asking for the answer or root
imaginary number is i which is √-1 so
if you have √-9 = √9 * √-1 = 3i
if you have √-20 = √4 * √-1 * √5 = 2i√5
.
A car travels 210 miles in 3 hours and 45 minutes. How many miles does it travel per hour?
Answer: 56 miles per hour
Step-by-step explanation:
45 minutes = 0.75 hour
3 hours and 45 minutes = 3.75 hours
Takes 210 divided by 3.75 = 56 miles per hour
Which would cost more: 15 trips to Boston or 11 trips to New York? Explain
Answer:
I think 11 trips to New York because it's a popular tourist attraction.
What is the x and y intercept of y=3x-15 and is (2,-9) a solution
The x and y intercept of y=3x-15 is X intercept is 5, Y interceptis -15
How to find X intercept and Y intercept?To find X intercept substitute y=0
y=0
0=3x-15
3x=15
x=15/3
x=5
X intercept is 5 line cuts at (5,0)
To find Y intercept substitute x=0
y=3(0)-15
y=-15
Y interceptis -15 line cuts at (0,-15)
The distance on the axis from the origin where a line or a curve intersects the coordinate axis of the graph is known as the X and Y-intercept. The distance from the origin of a line or curve that cuts the x-axis at a point is known as the x-intercept, and the distance from the origin of a line or curve that cuts the y-axis at a point is known as the y-intercept.-c/m for the x-interceptc = y-interceptA line's equation has the general form axe + by + c = 0. Here, we change y to equal 0 and solve for x to obtain the x-intercept of the line. We then change x to equal 0 and solve for y in the same equation.To learn more about intercepts refer to:
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Hi can someone answer this
Answer:
first one and second one
Step-by-step explanation:
x + y is lesser or equal to 20
20 being the max amount of hours he can work in one week and x and y being hours he works
second one because they can earn at least 300 dollars, not less than, but x+Y must still be less than 20 though
Are isosceles triangles equal to 180?
Yes, the isosceles triangles are equal to 180 degrees.
We know that isosceles triangles are triangles which have two equal sides. Since the sides are equal, they subtend equal angles as well.
However, the two equal angles subtended by the equal sides and one more angle which is subtended by the third side of the isosceles triangle all add up to a total of 180 degree as we know that the sum of all the angles of a triangle is always equal to 180 degrees.
Hence we can conclude that the isosceles triangles are also equal to 180 degrees like every other triangle.
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How do you prove SSS and SAS?
The triangles are congruent if all three sets of comparable sides are present. The side-side-side shortcut is a congruence technique (SSS).
Triangles are considered congruent by SAS if their two sides match up with their corresponding two sides on the other triangle, and if their included angles match up in both triangles.
We can prove two triangles, either by SSS or SAS by simply taking two triangles and checking whether the sides and the angles of the corresponding triangles are congruent or not.
By simply comparing it on the basis of their sides and angles we can easily prove the corresponding triangles by SSS or SAS.
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What are the 3 methods to find the mean?
The three methods to find the mean are arithmetic, geometric and harmonic .
The arithmetic mean method: This method involves adding up all the values in the set and dividing by the total number of values. This gives the average value of the set.The geometric mean method: This method involves finding the product of all the values in the set and taking the square root of that product. This gives the average value of the set when the values represent quantities that are multiplied together (such as interest rates or growth rates).The harmonic mean method: This method involves taking the reciprocal of each value in the set (1/value), adding those reciprocals up, and taking the reciprocal of that sum. This gives the average value of the set when the values represent quantities that are inversely related (such as speeds or rates).To learn more about mean, visit:
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