By using the concept of combinations, we have determined that there are 210 three-digit numbers that can be formed using the digits 0-6 without repeating any of them. Among them, there are 90 odd numbers and 120 numbers greater than 330.
Combinations are a fundamental concept in mathematics, particularly in the field of combinatorics, which deals with counting and arranging objects.
To solve this problem, we can use the concept of combinations, which is a way of counting the number of ways we can choose k items from a set of n items. In this case, we want to find the number of three-digit numbers we can form from the set {0, 1, 2, 3, 4, 5, 6}, without repeating any of the digits.
First, we can determine the number of ways we can choose the first digit. Since there are seven digits to choose from, we have 7 options for the first digit.
Next, we can determine the number of ways we can choose the second digit. Since we have already used one of the digits, we only have 6 options left for the second digit.
Finally, we can determine the number of ways we can choose the third digit. Since we have used two of the digits, we only have 5 options left for the third digit.
Therefore, the total number of three-digit numbers we can form is given by the product of the number of choices for each digit:
7 x 6 x 5 = 210
So there are 210 different three-digit numbers that can be formed using the digits 0, 1, 2, 3, 4, 5, and 6, without repeating any of the digits.
To find the number of odd numbers, we need to consider that the last digit must be either 1, 3, or 5, since these are the only odd digits in the set. We can choose the first two digits in the same way as before, and then choose one of the three odd digits for the last digit. Therefore, the number of odd three-digit numbers is:
6 x 5 x 3 = 90
To find the number of three-digit numbers greater than 330, we need to consider that the first digit must be either 3, 4, 5, or 6. We can choose the first digit in 4 ways, and then choose the remaining two digits as before. Therefore, the number of three-digit numbers greater than 330 is:
4 x 6 x 5 = 120
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HELP QUICKLY
what is x
2.5/x = 10/12
PLS HELP ASAP
Answer:
x = 3
Step-by-step explanation:
2.5/x = 10/12
Multiply both sides by x
2.5 = 10/12x
Divide both sides by 10/12
3 = x
A chemist has 20% and 50% solutions of acid available. How many liters of each solution should be mixed to obtain 180 liters of 22% acid solution?
Answer:
22% = 163.63636364 litres.
50% = 409.090909 litres
Step-by-step explanation:
when 22% acid solutions = 180 litres
then 20% acid solutions = ?
therefore =
[tex] = \frac{20}{22} \times 180 \\ = \frac{3600}{22} \\ = 163.63636364.litres[/tex]
Also when 22% acid solutions = 180 litres
then 50% acid solutions = ?
therefore
[tex] = \frac{50}{22} \times 180 \\ = \frac{9000}{22} \\ = 409.090909.litres[/tex]
therefore 22% = 163.63636364 litres.
50% = 409.090909 litres.
A bus leaves the station every 12 minutes
A train leaves the station every 18 minutes
At 8am a bus and a train leave their stations at the same time.
a) when is the next time that a bus and a train leave at the same time?
b) Between 8am and 11am, on how many occasions does a bus and a train leave at the same time?
thank you so much for the help
Answer:
a) 8:32 am
b) 5 occasions
Which equations are true for the values of x, y, and z? Select three options.
2 lines intersect to form 4 angles. Clockwise, from top, the angles are: 65 degrees, x, y, z.
Answer:
Step-by-step explanation:
Based on the information provided, the following three equations are true for the values of x, y, and z:
x + y + z = 360 degrees (Since the sum of the angles in a quadrilateral must equal 360 degrees)
x = 65 degrees (As given, the first angle is 65 degrees)
y + z = 295 degrees (From equation 1, 360 - 65 = 295)
So, the values of x, y, and z can be calculated as 65 degrees, 115 degrees, and 180 degrees respectively.
Jan has a cookie jar that contains five peanut butter cookies, eight chocolate chip cookies, and twelve oatmeal raisin cookies. Jan reaches in and grabs a cookie, what is the probability that she will get a chocolate chip cookie?
Answer:
8/25
Step-by-step explanation:
5+8+12=25
8/25
Answer: 8/25
Step-by-step explanation:
Find probability with item/total.
total is 25
there are 8 chocolate chip cookies
8/25 is your answer
HOPE THIS HELPS _ MM
Select all the equations that are equivalent. 52 = 8n + 4 4(2n + 1) = 52 4 = 52 – 8n 4n = 48 n = 6
Answer:
all of these equations except 4n = 48
Step-by-step explanation:
your equations are
52 = 8n+4
4(2n+1) = 52
4 = 52-8n
4n = 48
n = 6
let's solve these equations!
52 = 8n + 4
48 = 8n
n = 6
4(2n+1) = 52
8n + 4 = 52
8n = 48
n = 6
4 = 52-8n
-48 = -8n
n=6
4n = 48
n = 12
all of these equations simplify to n = 6 except for 4n = 48, so they're all equivalent
Factor 26r³s
O 13(2r³s + 475-37²54)
037²s(27+ 47³-38³)
O 13r²(2rs + 4r3 – 384)
O 13r²(26r³s + 527-5-39²4)
+5275-39724. What is the resulting expression?
The factor of the algebraic expression is 13r²(2rs + 4r³ - 3s⁴).
option C is the correct answer
What is the factor of the algebraic expression?
The factor of the algebraic expression given as
26r³s + 52r^(5) - 39r²s⁴
can be determined by finding the highest common factor and factorize it out.
The highest common factor of the letters is r²
Factors of 26 = 1, 2, 13, 26
Factors of 39 = 1, 3, 13, 39
Factors of 52 = 1, 2, 4, 13, 26, 52
The highest common factor for the 3 numbers is 13.
Thus, in total, the highest common factor for the algebraic expression is 13r².
Finally, we have;
13r²(2rs + 4r³ - 3s⁴)
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The complete question is below:
Factor 26r³s + 52r^(5) - 39r²s⁴
A. 13(2r³s + 475-37²s⁴)
B. 37²s(27+ 47³-38³)
C. 13r²(2rs + 4r³ – 3s⁴)
D. 13r²(26r³s + 527-5-39²4)
question 4
help me asap
The unknown angle in the cyclic quadrilateral is as follows:
m∠B = 121 degrees.
How to find angles in a cyclic quadrilateral?In a cyclic quadrilateral, the sum of a pair of opposite angles is 180° (supplementary). The sum of angles in a cyclic quadrilateral is 360 degrees.
Therefore, let's find the angle m∠B in the cyclic quadrilateral.
m∠D = 59 degrees
m∠A = 33 degrees
Therefore,
m∠B = 180 - m∠D
This is because the angle m∠B is opposite to the angle m∠D.
Hence,
m∠B = 180 - 59
m∠B = 121 degrees.
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in a sample of 20 men, the mean height was 178 cm. in a sample of 30 women, the mean height was 164 cm. what was the mean height for b oth groups put together?
In a sample of 20 men, the mean height was 178 cm and a sample of 30 women, the mean height was 164 cm, then the mean height for both groups combined is approximately 172.4 cm.
To find the mean height for both groups combined, we need to calculate the weighted average of the means of each group, where the weight of each group is proportional to its sample size.
We can begin by finding the total height of all the individuals in both groups combined. The total height for the men's group would be 20 multiplied by the mean height of 178 cm, which is 3560 cm.
Similarly, the total height for the women's group would be 30 multiplied by the mean height of 164 cm, which is 4920 cm. Adding these two values gives a total height of 8480 cm for both groups combined.
Next, we need to find the total sample size, which is the sum of the sample sizes of the two groups. The total sample size is 20 + 30 = 50.
Finally, we can calculate the weighted average of the means of each group using the formula:
Weighted average = (weight of group 1 * mean of group 1 + weight of group 2 * mean of group 2) / (weight of group 1 + weight of group 2)
In this case, the weights of each group are proportional to their sample sizes. Therefore, the weighted average can be calculated as:
Weighted average = (20/50 * 178 cm) + (30/50 * 164 cm) = 172.4 cm
In summary, to find the mean height for both groups combined, we need to calculate the weighted average of the means of each group, where the weight of each group is proportional to its sample size. This is done by multiplying the sample size of each group by its mean height, adding the values, and then dividing by the total sample size.
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2. Matt measures the angle of elevation of the peak of a mountain as 35º. Susie, who is 1200
feet closer on a straight level path, measures the angle of elevation as 42º. How high is the
mountain?
The height of the mountain using the angle of elevation is 3858.85 units.
What are trigonometric functions?The three basic categories of trigonometric functions are sine, cosine, and tangent. And from the basic functions, one can deduce the three cotangent, secant, and cosecant functions. In contrast to the fundamental trigonometric functions, the other three functions are essentially employed more frequently.
Let the distance between the mountain and Matt = x.
Then the distance of Susie will be:
S = x - 1200
Matt measure the angle of elevation as 35 degrees.
Using the trigonometric function we have:
tan (35) = h / x
x = h/ 0.7.......(1)
For Susie:
tan(42) = h / x - 1200
0.9(x - 1200) = h
0.9x - 1080.48 = h .........(2)
Substitute the value of x in equation 2:
0.9 ( h/ 0.7) - 1080.48 = h
1.28h - 1080.48 = h
1.28h - h = 1080.48
0.28h = 1080.48
h = 3858.85
Hence, the height of the mountain using the angle of elevation is 3858.85 units.
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Solve the following system of inequalities graphically on set of axes below. State the coordinates of a point in the solution set.
Answer:
see below for a graph
(-8, 4) is in the solution set
Step-by-step explanation:
You want the graph and a solution point for the inequalities y ≤ -6/5x -4 and y ≥ 2/5x +4.
GraphThe solid boundary line of the first inequality will cross the y-axis at -4, and will have a "rise" of -6 units for each "run" of 5 units. Shading is below this boundary line.
The solid boundary line of the second inequality will cross the y-axis at +4 and will have a "rise" of 2 units for each "run" of 5 units. Shading is above this boundary line.
Solution setThe boundary lines make an X shape on the graph, crossing at the point (-5, 2). The solution set is in the left quadrant.
Point (-5, 2) is in the solution set, as are points in the doubly-shaded space to its left. (-8, 4) is one of those.
__
Additional comment
The boundary lines are solid because the "or equal to" case is included in each.
The ≤ symbol tells you y-values that satisfy the first inequality will be less than (or equal to) those on the boundary line.
The ≥ symbol tells you y-values that satisfy the second inequality will be greater than (or equal to) those on the boundary line.
What are the answers for this
Please help me with this it will mean a lot I need help with 17
The equivalent expressions are 7(2)^3x = 7(8)^x, 7(1/2)^x = 7(2)^-x, 7(4)^(3x + 1) = 7(2)^(6x + 2), 14(2)^x = 7(2)^(x + 1) and 14(2)^x = 14(4)^(x/2)
How to match the equivalent expressionFrom the question, we have the following parameters that can be used in our computation:
The expressions on the left and those on the right
To do this, we solve the expressions on the left and look for a match
Using the above as a guide, we have the following:
(a) 7(2)^3x
Evaluate the exponent
7(2)^3x = 7(8)^x
(b) 7(1/2)^x
Apply the law of indices
7(1/2)^x = 7(2^-1)^x
So, we have
7(1/2)^x = 7(2)^-x
(c) 7(4)^(3x + 1)
Apply the law of indices
7(4)^(3x + 1) = 7(2^2)^(3x + 1)
So, we have
7(4)^(3x + 1) = 7(2)^(6x + 2)
(d) 14(2)^x and (e) 14(2)^x
Without solving them, we have
14(2)^x = 7(2)^(x + 1)
14(2)^x = 14(4)^(x/2)
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The stock price of Company A decreased by $1.27 every day for 4
days. The fifth day, the stock price increased by $3.47. What was
the total change in the stock's price over 5 days?
Answer:
Step-by-step explanation:
The stock price of Company A decreased by $1.27 for 4 days, so the total decrease in the stock's price would be $1.27 * 4 = $5.08.
On the fifth day, the stock price increased by $3.47, so the total change in the stock's price over 5 days would be $3.47 - $5.08 = -$1.61.
So the total change in the stock's price over 5 days was a decrease of $1.61.
What information does the source supply?
The information provided by a source in a graph is C. Who put the data together.
How does a source contribute to a graph ?The information provided by a source in a graph can include various aspects such as the data being displayed, the method used to collect the data, and who put the data together (also known as the data source).
The data source is important because it provides context and credibility to the data being presented. It helps to understand the reliability and accuracy of the data, as well as any potential biases that may be present. In this case, the source is the Human Resources Department.
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18y-5= -17x in slope intercept form
Answer:
y = -17/18x + 5/18
Step-by-step explanation:
isolate the y so add five to the other side
18y = 5 + -17x
divide everything by 18
18y/18 -17x/18 5/18
y= -17/18x + 5/18
Bonus: (up to 5 points) The answer to the clues on the left goes on the first line. When you rearrange the
letters of this answer, you will reveal the word that is the answer to the clue on the right
What we do at night for 7-8 hours
Piece of lumber
Where you buy pastrami, etc/sandwiches (plural)delic slide
Christmas decoration
A direction
north
Sleep
OFFIC
thern
Part of bananas
Wide
A piece of playground equipment
Part of a rose
Answer:
sleep-peels:board-broad:delis-slide:tinsel-silent:north-thorn
Step-by-step explanation:
Those are the corresponding words
If 6% of a number is 48, find 1% of that number.
Answer:
8
Step-by-step explanation:
0.06/48=800 0.01x800=8
Jamarie and DJ go bowling. Jamarie knocks a total of 26 pins. DJ knocks down three times as
many. How many did they knock down together?
Show your work
In total they knocked down 104 pins.
I got this by multiplying 26 by 3, which equals 78, then adding 26 to 78 to get the final answer, 104.
Hope this helps!
If the length of the rectangle is (7x − 6) and the width is (5x + 6). Find the area of the rectangle
The area of a rectangle is 35x^2 + 12x - 36
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
To determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given that the length of the rectangle is (7x − 6) and the width is (5x + 6).
Thus the width be (5x + 6).
So, the length = (7x − 6)
So,
Area of rectangle = (7x − 6) (5x + 6).
= 35x^2 + 42x -30x - 36
= 35x^2 + 12x - 36
So, The area is 35x^2 + 12x - 36
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Compare the slope and length of segment EF with the slope and length of segment AB. What do you notice? What are you wondering?
The slope of segment EF and AB is same but the length of segment EF is half of the length of segment AB.
What is Line segment ?
An unmoving portion of a line is called a line segment. Two points serve as its ends. By the termination points, it is identified.
Let's assume the length of EF to be "x"
from the figure, we can clearly see that AB is made up of two segments which are of same length as EF.
So, we can say that AB = 2 times of the length of EF
i.e. AB = 2 x
Hence, By comparing, we conclude that AB's length is double of EF.
Now, if we look at slope,
Slope of EF = CE/CF
and, Slope of AB = BC/AC
But, we know that AC = 2 CF and BC = 2 CE
So, Slope of EF = CE/CF
and, Slope of AB = 2 CE / 2 CF
= CE/CF.
Hence, Both segments have same slope direction.
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Use the drop-down menus to complete the statements
to match the information shown
by the graph.
The correct drop down menus from the graph are:
First box: faster than, slower than, at the same rate as.Second box: greatest x-value, line, y-intercept, slope.Third box: greater than, less than, equal to.Fourth box: greatest x-value, x-intercept, y-intercept, slope, origin.Fifth box: minutes per gallon, gallons per minute.What is our observation on the graph?Pool A is filling up slower than Pool B because the slope of the graph of Pool A is less than that of the graph for Pool B.
The slope of the graph tells you the unit rate in gallons per minute. Its means the ratio of the vertical change between two points, the rise, to the horizontal change between the same two points, the run.
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ABCD is a kite with AB = BC and AD = DC = AC, the size of
The size of angle BCA is 45 degrees
How to determine the size of angle BCAFrom the question, we have the following parameters that can be used in our computation:
AB = BC and AD = DC = AC
Also, we have
ABC = 90 degrees
Considering the triangle ABC, we have
A + B + C = 180
This is so because the sum of angles in a triangle is 180 degrees
Using the above as a guide, we have the following:
A + 90 + C = 180
So, we have
A + C = 90
Given that
AB = BC
We have
2C = 90
C = 45
Hence, the angle is 45 degrees
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Complete question
ABCD is a kite with AB = BC and AD = DC = AC, What is the size of angle BCA
Tanya is renting a bounce house for a birthday party. The graph shows the time in hours (x)
compared to the total cost in dollars (y). Determine rate and initial value to write a linear equation.
=mx+b): _____
Find the rate (M). Find the initial value (B).
Equation (y=mx+b).
the equation of the straight line will be y = 10x+10.
What is equation straight line?
Y = mx + c is the general equation for a straight line, where m denotes the line's slope and c the y-intercept. It is the version of the equation for a straight line that is used most frequently in geometry. There are numerous ways to express the equation of a straight line, including point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a geometric object with two dimensions and infinite lengths at both ends. The formulas for the equation of a straight line that are most frequently employed are y = mx + c and axe + by = c. Other versions include point-slope, slope-intercept, standard, general, and others.
The initial value 10
slope m = 30-20/2-1
m = 10/1=10
So the equation of the straight line will be y = 10x+10.
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Which graph represents the scenario of a woman who climbs a hill at a steady pace and then starts to run down the side?
Graph II
Graph III
Graph I
Graph IV
which of the following are true statements? select all that apply: 1. a 95% confidence interval is a random interval that contains the true parameter 95% of the time 2. the true parameter is a random value that has 95% chance of falling in the 95% confidence interval 3. i perform a linear regression and get a 95% confidence interval from 0.4 to 0.5. there is a 95% probability that the true parameter is between 0.4 and 0.5. 4. the true parameter (unknown to me) is 0.5. if i sample data and construct a 95% confidence interval, the interval will contain 0.5 95% of the time. answer :
Among the following statements, The true statements are:
Option (1) a 95% confidence interval is a random interval that contains the true parameter 95% of the time, (2)the true parameter is a random value that has 95% chance of falling in the 95% confidence interval, (3) i perform a linear regression and get a 95% confidence interval from 0.4 to 0.5. there is a 95% probability that the true parameter is between 0.4 and 0.5, (4) the true parameter (unknown to me) is 0.
A 95% confidence interval is a random interval that contains the true parameter 95% of the time.
The true parameter is NOT a random value, and it is not correct to say that it has a 95% chance of falling in the 95% confidence interval.
If you perform a linear regression and get a 95% confidence interval from 0.4 to 0.5,
it means that if you repeated the same experiment many times, 95% of the resulting confidence intervals would contain the true parameter.
It is not correct to say that there is a 95% probability that the true parameter is between 0.4 and 0.5 because the true parameter is either in the interval or not.
If the true parameter is 0.5 and you sample data and construct a 95% confidence interval, the interval may or may not contain 0.5.
The 95% confidence interval is a statement about the probability of the interval containing the true parameter, not about the probability of the true parameter being any specific value.
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1004.8 into 3 significant figures
Rounding off the 1004.8 into 3 significant figures will give 1000.
Significant Figures:Since significant figures are established as digits, they are also known as significant digits. By counting all of the values beginning with the first non-zero digit on the left, it is possible to determine the number of significant digits.
For example, the number of significant figures in 567 is 3.
The number of significant figures in 2.671 is 4.
Here we have a number
1004.8 need to be rounded off for 3 significant figures
Since 4 is less than 5 then the resultant number = 1000
[ 4 and 8 neglected since 4 < 5]
Therefore,
Rounding off the 1004.8 into 3 significant figures will give 1000.
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2[73-(4x5)]
I think the answer is 106 but can someone double check? Thanks
Answer:
yes its 106
Step-by-step explanation:
brainly removed my answer
Please help with triangles
The value of x is given as follows:
x = 131º.
How to obtain the value of x?An interior angle is supplementary with it's exterior angle, meaning that the sum of their measures is of 180º.
Considering the above text, the measure of the top angle of the bottom triangle is given as follows:
a = 180 - 98
a = 82.
The base angles of the bottom triangle have the same measure, as the triangle is isosceles, hence:
2b + 82 = 180
2b = 98
b = 49.
(the sum of the measures of the internal angles of a triangle is of 180º).
Considering the vertical angles, the base angles of the top triangle are given as follows:
b = 49.
Hence the value of x is given as follows:
x = 180 - 49
x = 131º.
(as the top triangle is also isosceles, and the angle measure x is the exterior angle of an interior angle with measure of 49º).
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The total change in the daily high temperature from Monday to Saturday in one week in Columbus was -15° F.
Complete the table to show the possible temperature change for Monday.
Monday
Tuesday: +7
Wednesday: 12
Thursday: +2
Friday: -6
The temperature change for Monday is -30 degrees Fahrenheit,
The completed table is: Monday: -30, Tuesday: +7, Wednesday: +12, Thursday: +2, Friday: -6, to make the total change from Monday to Saturday equal to -15 degrees Fahrenheit.
To complete the table, we need to find the temperature change for Monday that makes the total change from Monday to Saturday equal to -15 degrees Fahrenheit.
Let x be the temperature change for Monday. Then, we can set up the equation:
x + 7 + 12 + 2 - 6 = -15
Simplifying and solving for x, we get:
x = -30
Therefore,
The temperature change for Monday is -30 degrees Fahrenheit, and the completed table is:
Monday: -30
Tuesday: +7
Wednesday: +12
Thursday: +2
Friday: -6
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