Let a be the first, b be second and c be the third whole number.
Since the sum of these three numbers is 100.
So, [tex]a+b+c=100[/tex] (equation 1)
Since, The first number is a multiple of 15
Therefore, [tex]a = 15n[/tex]
And, the second number is ten times the third number.
[tex]b = 10c[/tex]
Substituting the values of 'a' and 'b' in equation 1
So, [tex]15n+10c+c=100[/tex]
[tex]15n+11c=100[/tex]
[tex]11c=100-15n[/tex]
[tex]c=\dfrac{100-15n}{11}[/tex]
Therefore, [tex]100-15n[/tex] should be exactly divisible by 11.
So, by taking [tex]n= 1[/tex] and 2, [tex]100-15n[/tex] is not divisible by 11
Let [tex]n =3[/tex]
[tex]c=\dfrac{100-15\times3}{11}[/tex]
[tex]c= 5[/tex]
Now, second number (b) [tex]= 10c = 10\times5=50[/tex]
As, [tex]a+b+c=100[/tex]
[tex]a+50+5=100[/tex]
[tex]a+55=100[/tex]
[tex]a=45[/tex]
Therefore, the three whole numbers are 45, 50, 5.
PLEASEE HELP FASTT!!!
To build a large sand castle, Sam takes an old traffic cone and fills it with sand. The cone is 18 in. tall and has a diameter of 7 in
To the nearest cubic inch, how much sand does Sam use?
A) 26 in³
B) 103 in³
C) 231 in³
D) 308 in³
PLS HELP AND GIVE THE CORRECT ANSWER WITH EXPLANATION WILL GIVE BRAINIEST!!!
Answer:
Even
Step-by-step explanation:
Its even because a parabola as the equation of x^2, that is an even graph!
:)
Answer:
even
(sorry if it's wrong but I'm pretty sure it's even.)
9,857 + 310 ÷ 2 - 10 = ?
Answer:
10002
Step-by-step explanation: I think this is correct
Answer:
10002
Step-by-step explanation:
9,857 + 310 ÷ 2 - 10 = 10002
please solve question with explanation *TEST REVISION*
Answer:
Step-by-step explanation:
Geometry 1. Which of the following may not be true? Select all that apply. A. If a point and a plane intersect, the intersection is a line. B. If two lines intersect, both lines are in one plane. C. If two lines intersect but do not coincide, the intersection is a point. D. If two planes intersect but do not coincide, the intersection is a line. E. If two points lie in a plane, then the line that contains the points is in that plane. F. There is exactly one line through any two points.
Answer:
There are two statements that may not be true:
B. If two lines intersect, both lines are in one plane.
F. There is exactly one line through any two points.
Statement B is not true because if two lines intersect at an angle, they are not in the same plane. This is known as skew lines.
Statement F is not true in non-Euclidean geometries, such as spherical or hyperbolic geometry. In these geometries, there can be multiple lines that pass through two points. However, in Euclidean geometry (which is what is typically taught in high school), there is exactly one line that passes through any two points.
Step-by-step explanation:
Answer: B. If two lines intersect, both lines are in one plane.
F. There is exactly one line through any two points
Step-by-step explanation:
The rest are true because I remember learning those in Geometry but B and F aren’t true because they just don’t make sense and aren’t true in general.
witch shapes have atleats one right angle ?? please anwser fluently
Answer:
top left and top right
Step-by-step explanation:
a right angle is 90⁰
Can u guys factorize this equations please
Answer: Answer is below <3
Step-by-step explanation:
1. —1x²(3x²—7x—5)
2. 14x ² (y²—2x+4x²)
3. 8100m²y4
4. (a5— 7b6) (a5 — 7b6)
5. (m+1) (m+11)
6. (a+1) (a+6)
7. —3x+6
8. (—6a+1) (—6a+1) / 4
9. (x+5)²
10. X² — 7xy—88x
Hope this helps!
What is the value of x?
Answer:
c
Step-by-step explanation:
Each rectangle is 16% longer than the original. Complete the table with the length of each new rectangle.
It seems that the table has not been provided in the question. However, I can provide a general method to complete the table based on the given information.
If each rectangle is 16% longer than the original, we can calculate the length of each new rectangle by adding 16% of the original length to the original length.
Let L be the original length of the rectangle. Then, the length of the new rectangle would be L + 0.16L = 1.16L.
Using this formula, we can calculate the length of the new rectangle for any given original length. For example, if the original length is 10 cm, then the length of the new rectangle would be:
1.16 x 10 cm = 11.6 cm
Similarly, we can calculate the length of the new rectangle for any other original length and complete the table accordingly.
Anya has a number of square bricks with a side length of 1 foot that 164) she wants to use to create a rectangular patio in her backyard. At first, she arranges them so the rectangle is 12 bricks long by 3 bricks wide, but then she decides she does not like that arrangement. How can Anya arrange the bricks if she would rather have a square-shaped patio?
Answer: 6 bricks long by 6 bricks wide
Step-by-step explanation:
Since her first arrangement is a 12 x 3 brick patio, we can assume she has 36 bricks. A square has equal lengths of all sides, with this info, she can arrange the 36 bricks into a 6 by 6 patio
SOMEONE PLEASE HELP ME WITH QUESTION 22
Answer:
Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
Determine the values of x where the function f(x) is not continuous. Label each discontinuity as removable, jump or infinite. f(x)={1/2x+5. x<=2 { x+3. x>2 Enter your answers as integers in increasing order. If there are no discontinuities, enter NA in both response areas and select continuous in both drop-down menus. If there is only one discontinuity, enter NA in the second response area and select continuous in the second drop-down menu.
The values of x where the function f(x) is not continuous are x = 2, and the discontinuity at x = 2 is a jump discontinuity.
The function f(x) is defined as:
f(x) = {1/2x+5, x<=2
{x+3, x>2
To find the values of x where f(x) is not continuous, we need to check for three types of discontinuities: removable, jump, and infinite.
Removable discontinuity: This occurs when a function has a hole at a certain point, but can be made continuous by defining or redefining the value of the function at that point. In order for a discontinuity to be removable, the limit of the function as x approaches that point must exist.
To check for removable discontinuity, we need to check if the limit of the function as x approaches a certain point exists, but the function value is different from the limit. In this case, we only need to check the function at x = 2.
lim x->2- f(x) = lim x->2- 1/2x+5 = 6
lim x->2+ f(x) = lim x->2+ x+3 = 5
Since the limits from both sides are not equal, there is a removable discontinuity at x = 2. We can redefine the value of f(x) at x = 2 as 6 to remove the discontinuity.
Jump discontinuity: This occurs when the function has two distinct finite limits from both sides of a point, but the limits are not equal.
To check for jump discontinuity, we need to check if the limit of the function as x approaches a certain point exists from both sides, but they are not equal. In this case, we only need to check the function at x = 2.
lim x->2- f(x) = lim x->2- 1/2x+5 = 6
lim x->2+ f(x) = lim x->2+ x+3 = 5
Since the limits from both sides are not equal, there is a jump discontinuity at x = 2.
Infinite discontinuity: This occurs when the function approaches infinity or negative infinity as x approaches a certain point.
To check for infinite discontinuity, we need to check if the limit of the function as x approaches a certain point approaches infinity or negative infinity. In this case, there is no such point where f(x) approaches infinity or negative infinity.
Therefore, the values of x where the function f(x) is not continuous are x = 2, and the discontinuity at x = 2 is a jump discontinuity.
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11. If the null space of an 8 x 5 matrix A is 2-dimensional, what is the dimension of the row space of A? 12. If the null space of a 5 x 6 matrix A is 4-dimensional, what is the dimension of the row space of A? 13. If A is a 7 x 5 matrix, what is the largest possible rank of A? If A is a 5 x 7 matrix, what is the largest possible rank of A? Explain your answers. 14. If A is a 4 x 3 matrix, what is the largest possible dimension of the row space of A? If A is a 3 x 4 matrix, what is the largest possible dimension of the row space of A? Explain. 15. If A is a 6 x 8 matrix, what is the smallest possible dimension of Nul A?
11. Dimension of Row Space = 3.
12. Dimension of Row Space = 1.
13. largest possible rank is 5.
14. largest possible dimension is 3.
15. Dimension of Nul A = 2.
Let's discuss it further below.
11. The dimension of the row space of an 8x5 matrix A can be found using the Rank-Nullity theorem, which states that the rank of a matrix (dimension of the row space) plus the dimension of the null space equals the number of columns in the matrix. So, if the null space is 2-dimensional, then the dimension of the row space is:
Dimension of Row Space = 5 (number of columns) - 2 (dimension of null space) = 3.
12. For a 5x6 matrix A, the Rank-Nullity theorem can also be applied. If the null space is 4-dimensional, then the dimension of the row space is:
Dimension of Row Space = 5 (number of rows) - 4 (dimension of null space) = 1.
13. The largest possible rank of a 7x5 matrix A is equal to the minimum of the number of rows and columns, which in this case is 5. For a 5x7 matrix A, the largest possible rank is also the minimum of the number of rows and columns, which is 5.
14. The largest possible dimension of the row space of a 4x3 matrix A is the minimum of the number of rows and columns, which is 3. For a 3x4 matrix A, the largest possible dimension of the row space is also the minimum of the number of rows and columns, which is 3.
15. The smallest possible dimension of Nul A for a 6x8 matrix can be found using the Rank-Nullity theorem. The largest possible rank of a 6x8 matrix A is the minimum of the number of rows and columns, which is 6. Thus, the smallest possible dimension of Nul A is:
Dimension of Nul A = 8 (number of columns) - 6 (largest possible rank) = 2.
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the first table shows the number of meals or females who ordered a small or large sandwich for lunch. complete the second table with the joint relative frequencies
Then we can fill out the table of joint relative frequency as follows:
Small Large
Male 5/50 18/50
Female 21/50 6/50
What is joint relative frequency?Joint relative frequency is a statistical term that refers to the proportion of individuals in a population that share two or more specific characteristics. In other words, it measures the frequency or occurrence of a specific combination of two or more variables within a larger population.
Here,
To find the joint relative frequencies, we need to divide each cell by the total number of people (males + females).
Here, we added up the number of males and females to get the total number of people (50). Then, we divided the number of males who ordered a small sandwich (5) by 50 to get the relative frequency of males who ordered a small sandwich (5/50), and so on for each cell in the table.
To calculate the joint relative frequencies, we need to divide each cell in the second table by the total number of observations, which is the sum of all cells in the first table.
The total number of observations is:
5 + 18 + 21 + 6 = 50
To calculate the joint relative frequency for the first cell (small sandwich, male), we divide the number of observations in that cell by the total number of observations:
joint relative frequency = 5/50 = 0.1
Note that the sum of the relative frequencies in each column should add up to 1, since we are dividing by the total number of people.
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The weekly wages of a man and a boy engaged for the same kind of work is Rs. 80 and Rs. 35 respectively. If the wages of both are increased by the same amount then the men's wage is 8/5 of the boy's wage. What is the increase?
The increase in weekly wages for both the man and the boy is Rs. 40.
Let's assume that the increase in wages for both the man and the boy is x.
After the increase, the man's weekly wage will be Rs. 80 + x and the boy's weekly wage will be Rs. 35 + x.
We know that the man's wage after the increase is 8/5 of the boy's wage after the increase. Mathematically,
80 + x = (8/5)(35 + x)
Simplifying this equation, we get:
80 + x = 56 + (8/5)x
Multiplying both sides by 5, we get:
400 + 5x = 280 + 8x
Subtracting 5x from both sides, we get:
400 = 280 + 3x
Subtracting 280 from both sides, we get:
120 = 3x
Dividing both sides by 3, we get:
x = 40
Therefore, the increase in wages is Rs. 40.
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for every 1,000 babies born in india in 2011, an estimated 50 of them will have died before reaching their first birthday. the rate of 50 deaths per 1,000 births is known as the
The rate of 50 deaths per 1,000 births is known as the infant mortality rate.
What is infant mortality rate?
Infant mortality rate (IMR) is the total number of deaths per 1,000 live births of infants under one year of age. Infant mortality rate is an essential demographic statistic for assessing population health status and identifying health disparities among different groups of the population.
IMR reflects the underlying mortality rate of infants in a society, which can be influenced by several factors, including maternal health, access to healthcare, nutrition, and socio-economic factors.Infant mortality rate (IMR) is the total number of deaths per 1,000 live births of infants under one year of age.
The rate of 50 deaths per 1,000 births is known as the infant mortality rate. The infant mortality rate is considered one of the most critical indicators of a country's health status and is often used to compare the health status of different populations.
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The number a is 110% greater than the number b.
The number b is 90% less than 47. What is the
value of a ?
If the number b is 90% less than 47 and the number a is 110% greater than b, then the value of a is 9.87.
If the number b is 90% less than 47, that means b is equal to 10% of 47, which can be calculated as:
b = 0.1 x 47
b = 4.7
If the number a is 110% greater than b, that means a is equal to 100% (or 1) plus 110% (or 1.1) of b, which can be calculated as:
a = (1 + 1.1) x b
a = 2.1 x 4.7
a = 9.87
Therefore, the value of a is 9.87.
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p+13+q+27 prove that 6=p and q=20
hi i need help checking 12x + 9 = - 15
i know the answer ( x = 2) i just need help checking!!
well actually, your answer is -2
not positive 2
you have to take the 9, and subtract it from the other side (the -15), giving you -24
then you divide -24 by 12, giving you x=-2
this is true because when you plug it back in, you get 12 x -2 = -24
-24 + 9 = -15
gabriel bought 16 pens 12 of the pens are blue what is
the percentage of the blue pens
Answer: 75%
Step-by-step explanation: 12 of 16 is expressed as 12/16. 12/16 is equal to .75 and a percent requires you to move the decimal place 2 to the right.
Name the marked angle in 2 different ways.
J, K, I
Answer: Where is the image?
Step-by-step explanation:
I NEED HELP ASAP!!! IT'S DUE TONIGHT!!
Answer:
5
Step-by-step explanation:
0+5+0= idc
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar.
Complete the table of inputs and outputs for the given function.
g(x) = -4x - 1
To complete the table of inputs and outputs for the function g(x) = -4x - 1:
x | g(x)
-------------------
-3 | 11
-2/3 | 1/3
0 | -1
1/2 | -3
2 | -9
Part A: The line of best fit for this data is y = 5. 3x + 23. Use this equation to make a conjecture about the temperature of the water in the beaker if heated for 6 minutes. Explain your thinking
The line of best fit suggests that the temperature of the water in the beaker after 6 minutes will be approximately 91.8°C. This is because when x = 6, the equation gives us y = 91.8.
The line of best fit for this data is y = 5.3x + 23. This equation can be used to make a conjecture about the temperature of the water in the beaker if heated for 6 minutes. To calculate this, substitute x = 6 into the equation: y = 5.3(6) + 23. Simplifying this equation, we get y = 31.8 + 23, which gives us y = 54.8. This is the temperature of the water in the beaker if heated for 6 minutes, which is approximately 91.8°C. hence, The line of best fit suggests that the temperature of the water in the beaker after 6 minutes will be approximately 91.8°C. This is because when x = 6, the equation gives us y = 91.8.
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alan's camping troop is raising money for a camping trip. the camping troop is selling boxes of popcorn, b, for $3.75 each. each camper starts with a credit of $25. to make the first deposit on the camping trip, alan total sales, f(b), needs to be at least $1100. write an inequality to represent the problem:
Answer:
$3.75b + $25 >= $1100
Step-by-step explanation:
List down three (3) equations that can be seen in the graph for each type of function and identify their
domain and range. Please helpp
constant funtion
Function,Domain,Range=
linear function
function,domain,range=
quadratic function
function,domain,range=
Equatiοns such as f(x) = x² - 4x + 3, f(x) = -2x² + 4x - 1, and f(x) = 0.5x² + 2x - 1 are examples.
what is functiοns ?A mathematical entity knοwn as a functiοn cοnverts an input frοm οne set (knοwn as the dοmain) tο a singular οutput frοm anοther set (called the range). A functiοn, then, is a rule that designates precisely οne οutput fοr each input in the dοmain. The nοtatiοn f(x), where f is the functiοn's name and x is the input value, is frequently used tο denοte a functiοn. Fοr instance, the functiοn f(x) = 2x + 1 takes any input x, dοubles it, adds 1, and returns the οutcοme.
Cοntinuοus Functiοn
Functiοn: If c is a cοnstant, f(x) = c
All real numbers dοmain
Range: {c}
Examples οf equatiοns are f(x) = 2, f(x) = -5, and f(x) = 0.
Linear Prοcess:
m is the slοpe and b is the y-intercept in the equatiοn f(x) = mx + b.
All real numbers dοmain
the entire real number range
Examples οf equatiοns include: f(x) = 2x + 1, f(x) = -3x + 5, and f(x) = 0.5x - 2.
Functiοn: where a, b, and c are cοnstants and a 0; f(x) = ax² + bx + c
All real numbers dοmain
Range: If a > 0 οr if a 0, then y | y h, where h is the vertex's y-cοοrdinate
Equatiοns such as f(x) = x² - 4x + 3, f(x) = -2x²+ 4x - 1, and f(x) = 0.5x² + 2x - 1 are examples.
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what number is 15.5% less than 144
Answer:
121,68
Step-by-step explanation:
First we need to find how smaller the new number will be:
[tex] \frac{144 \times 15.5\%}{100\%} = 22.32[/tex]
Then we subtract this number from 144:
144 - 22,32 = 121,68
And there we have the answer
khloe walks from school 20 miles due west, 8 miles due north, and 3 miles due east how far is khloe from school?
The approximate distance between Khloe and school is given by 18.78 miles.
Representing Khloe's movements on a coordinate plane.
Let us assume that Khloe's starting point (her school) is at the origin (0,0).
She walks 20 miles due west,
which means she moves 20 units to the left on the x-axis. Her new position is (-20,0).
She then walks 8 miles due north,
which means she moves 8 units up on the y-axis.
Her new position is (-20,8).
Finally, she walks 3 miles due east,
which means she moves 3 units to the right on the x-axis.
Her new position is (-17,8).
Distance between Khloe's final position and her starting point (the school),
Use the Pythagorean theorem,
Distance = √((change in x)^2 + (change in y)^2)
⇒Distance = √((-17-0)^2 + (8-0)^2)
⇒Distance = √(289 + 64)
⇒Distance = √353
⇒Distance ≈ 18.78 miles
Therefore, Khloe is approximately 18.78 miles away from her school.
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mathematical analysis DPM
Answer:
The Distributed Pattern Matching (DPM) problem have provided mathematical analysis and simulation results for establishing the effectiveness of the proposed architecture. DPMS achieves many desirable properties of both the unstructured and structured P2P systems. Like unstructured systems DPMS supports partial keyword matching, utilizes the heterogeneity in peer capabilities, and does not place any hard restriction on index/document placement. Like structured systems, on the other hand, DPMS attains logarithmic bound on search complexity and offers guarantee on search completeness and discovery of rare items. Advertisement traffic in DPMS is comparable to that of DHT-based structured P2P systems. To our knowledge Distributed Pattern Matching (DPM) problem has never been addressed by any research activity in P2P context. 1 The index distribution architecture of DPMS is unique and has been designed specifically to solve the DPM problem. The novel aggregation scheme, proposed in this paper, can effectively reduce storage overhead at the indexing peers without incurring a significant decrease in query routing performance. However, the use of bloom filter for representing indices is not new. Many network applications use bloom filters. A comprehensive list of such applications can be found in [6]. The rest of this paper is organized as follows. Section II highlights and compares the approaches related to DPMS. The architecture and operation of DPMS are presented in section III. Mathematical analysis of search complexity in DPMS is provided in section IV.
in a recent year, about 22% of americans 14 years and older are single. what is the probability that in a random sample of 190 americans 14 or older, more than 27 are single? round the final answer to at least 4 decimal places and intermediate z-value calculations to 2 decimal places.
The probability that in a random sample of 190 Americans aged 14 or older, more than 27 are single is approximately 0.9975
To solve this problem, we can use the normal approximation to the binomial distribution.
First, we need to calculate the mean and standard deviation of the number of singles in a sample of 190 Americans aged 14 or older.
Mean
μ = n × p = 190 × 0.22 = 41.8
Standard deviation
σ = sqrt(n ×p × (1 - p)) = sqrt(190 × 0.22 × (1 - 0.22)) = 5.27
Now, we can use the standard normal distribution to calculate the probability that more than 27 people in the sample are single. We convert the binomial distribution to a normal distribution by using the following formula
z = (x - μ) / σ
where x is the number of singles in the sample.
z = (27 - 41.8) / 5.27 = -2.80
Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score of -2.80 or lower is approximately 0.0025.
However, we want to find the probability of getting more than 27 singles, so we need to find the area to the right of z = -2.80. This is equivalent to subtracting the probability of getting a z-score of -2.80 or lower from 1:
P(Z > -2.80) = 1 - 0.0025 = 0.9975
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