There are 35 different 3-digit numbers that can be formed using the digits 0, 1, 2, 3, 4, 5, 6, if the repetition of digits is not allowed.
What is probability?Probability is a branch of mathematics that deals with the study of randomness and uncertainty in events. It is the measure of the likelihood or chance that an event will occur. Probability is expressed as a number between 0 and 1, where 0 indicates that the event will not occur and 1 indicates that the event will occur with certainty.
According to the given information :To form a 3-digit number using the given set of 7 digits (0, 1, 2, 3, 4, 5, 6) without repetition, we need to choose 3 different digits from the set.
We can count the number of ways to select 3 distinct digits from the set of 7 using the combination formula, which is:
C(n, k) = n! / (k! * (n-k)!)
Where n is the total number of items in the set, and k is the number of items we want to choose.
In this case, n = 7 (because we have 7 digits to choose from), and k = 3 (because we want to choose 3 digits to form a 3-digit number).
Therefore, the number of ways to select 3 distinct digits from the set of 7 is:
C(7, 3) = 7! / (3! * 4!)
= (7 * 6 * 5 * 4 * 3 * 2 * 1) / ((3 * 2 * 1) * (4 * 3 * 2 * 1))
= (7 * 6 * 5) / (3 * 2 * 1)
= 35
Therefore, there are 35 different 3-digit numbers that can be formed using the digits 0, 1, 2, 3, 4, 5, 6, if the repetition of digits is not allowed.
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A. 1/2 + 1/4
B. 5/6 + 5/12
C. 13/14 + 5/7
D. 3/4 + 5/24
Please
Odero sold a suit for 960 making a loss of 20% for how much would he have sold it to make a profit of 20%
From the given information provided, Odero would have had to sell the suit for 1224 to make a profit of 20%.
If Odero sold a suit for 960 and made a loss of 20%, it means his selling price was only 80% of the cost price. We can use this information to find his cost price:
Cost price = Selling price / (1 - Loss%)
Cost price = 960 / (1 - 0.20)
Cost price = 960 / 0.80
Cost price = 1200
Therefore, Odero's cost price for the suit was 1200.
Now, we need to find the selling price that would give him a profit of 20%. Let's call this selling price S:
Profit% = (Selling price - Cost price) / Cost price × 100
20% = (S - 1200) / 1200 × 100
2 = (S - 1200) / 12
S - 1200 = 24
S = 1224
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please I really need help by tmr!!
How many intersections are there between the graphs of f(x) = 0.8x and g(x) = \lfloor x \rfloor?
The answer is one intersection.
What is a function?
A function is a relationship or expression involving one or more variables. It has a set of input and outputs.
The graph of the function f(x) = 0.8x is a straight line with slope 0.8 passing through the origin (0, 0). The graph of the function g(x) = ⌊x⌋ is the collection of all points (x, y) where y is the greatest integer less than or equal to x. This function is not continuous and has a discontinuity at each integer.
To find the intersections between the two graphs, we need to determine where the values of f(x) and g(x) are equal.
we need to find the integer values of x where 0.8x and x are equal.
0.8x = x
0.2x = 0
x = 0
Thus, the two graphs intersect at the point (0, 0). There are no other intersections between the two graphs, since they have different slopes and one is continuous while the other is not. Therefore, the answer is one intersection.
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Please help I’ll give brainliest
The solutions to the equation [tex]15z^2 +6z -8 =4z[/tex] are z = 2/3 or z = -4/5.
To solve the quadratic equation [tex]15z^2 +6z -8 =4z[/tex], we first need to rearrange it into standard form:
[tex]15z^2 + 2z - 8 = 0[/tex]
Now we can apply the quadratic formula:
z = (-b ± √(b² - 4ac)) / 2a
where a = 15, b = 2, and c = -8.
Plugging in these values, we get:
z = (-2 ± √(2² - 4(15)(-8))) / (2(15))
z = (-2 ± √(4 + 480)) / 30
z = (-2 ± √484) / 30
z = (-2 ± 22) / 30
So z equals either (-2 + 22)/30 = 2/3 or (-2 - 22)/30 = -4/5.
Therefore, the solutions to the equation 15z² +6z -8 =4z are z = 2/3 or z = -4/5.
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jordan wants to create an equiangular octagon whose side lengths are exactly the first 8 positive integers, so that each side has a differetn length. how many such octagons can jordan create
There is only one equiangular octagon that Jordan can create with side lengths as the first 8 positive integers.
To create an equiangular octagon with side lengths as the first 8 positive integers, each side must have a different length. The sum of the interior angles of an octagon is 1080 degrees, so each angle in the octagon must measure 135 degrees.
If we arrange the 8 integers in decreasing order, we can label the longest side as a and the remaining sides as b1, b2, b3, b4, b5, b6, in descending order. Then, we must have:
a + b1 + b2 = a + b2 + b3 = a + b3 + b4 = a + b4 + b5 = a + b5 + b6 = a + b6 + b1 = 135 degrees
Simplify each equation, we get:
b1 - b3 = b2 - b4 = b3 - b5 = b4 - b6 = b5 - b1 = b6 - a
Since all the side lengths are different, we can use these equations to find all possible combinations of side lengths. By inspection, we can see that there is only one set of side lengths that satisfies these conditions, namely:
a = 8
b1 = 7
b2 = 6
b3 = 5
b4 = 4
b5 = 3
b6 = 2
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Which number is a perfect square
Responses
2
8
16
20
Answer:
16
Step-by-step explanation:
because it is a square number. The other numbers, if you square root them you won't get a whole number.
What is the volume of the cone expressed in terms of pi?
Select the correct answer. Simon used these steps to solve an equation: Step 1: -6(x + 7) = 2(x − 11) Step 2: -6x − 42 = 2x − 22 Step 3: -8x − 42 = -22 Step 4: -8x = 20 Which property did he use to get from step 3 to step 4? A. addition property of equality B. distributive property C. subtraction property of equality D. transitive property
Answer: A - addition property of equality
Explanation: because -8x - 42 = -22
+42 +42
____________
-8x = 20
__ __
-8 -8
x = -2.5
If you are solving the area of a trapezoid or a triangle, you multiply the base and the height. BUTTTT, I don't know if you divide the "area" by 2 to find the answer because the area solves two next to each other ALWAYS, or you do it depending on how many trapezoids are in the problem.
Answer:
When calculating the area of a triangle, you multiply the base by the height and then divide the result by 2. This is because a triangle is half of a parallelogram or a rectangle, and these shapes have an area equal to base times height. By dividing by 2, you are finding half of the area of the parallelogram or rectangle.
For a trapezoid, you can find the area by taking the average of the bases and multiplying it by the height. So the formula for the area of a trapezoid is A = (b1 + b2)h/2, where b1 and b2 are the lengths of the two parallel bases and h is the height. There is no need to divide the result by 2 because the formula already takes the average of the bases into account.
pre-event tickets for a local theater fundraiser cost $35 and $40 for at-the-door tickets. organizers sell a total of 250 tickets and generate a total revenue of $9,375. how many pre-event and at-the-door tickets were sold?
This can be calculated by multiplying the number of tickets sold by their respective prices: 200 x $35 = $7,000 and 50 x $40 = $2,375.
The local theater fundraiser sold 200 pre-event tickets at $35 each and 50 at-the-door tickets at $40 each to generate a total revenue of $9,375. This can be calculated by multiplying the number of tickets sold by their respective prices: 200 x $35 = $7,000 and 50 x $40 = $2,375.
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help pls
1. Renae has been playing Tower of Hanoi and has noticed that the minimum number of moves it takes to defeat the game is related to the number of disks she must move. She has recorded her observations below. Write an equation that describes this pattern.
2. Use a proof by mathematical induction to show that your equation from question 1 applies to the minimum number of moves required to defeat the Tower of Hanoi game, based on the number of disks you must move. Think about the process of the game; and describe how your equation applies to it.
The minimum number of moves required to complete the Tower of Hanoi game is related to the number of disks, and can be described by the equation m = [tex]2^n - 1[/tex].
Let n be the number of disks and m be the minimum number of moves required to complete the Tower of Hanoi game. Renae's observations suggest that the equation m = [tex]2^n - 1[/tex] describes this pattern.
When n=1, the minimum number of moves required to complete the game is m=1. Plugging this value into the equation m=[tex]2^n-1[/tex]gives m=[tex]2^1-1[/tex]=1. Therefore, the equation holds true for n=1.
Assume that the equation holds true for n=k. That is, m=[tex]2^k-1[/tex] is the minimum number of moves required to complete the game with k disks.
Now, consider the case where n=k+1. This requires a minimum of m=[tex]2^k-1[/tex] moves, according to the equation. Then, the largest disk can be moved to the ending peg in one move. Finally, the k disks that were moved to the spare peg must be moved to the ending peg, which requires another minimum of m=[tex]2^k-1[/tex] moves.
Thus, the total minimum number of moves required to complete the game with k+1 disks is:
m = [tex]2(2^k-1) + 1[/tex]
m = [tex]2^(k+1) - 2 + 1[/tex]
m = [tex]2^(k+1) - 1[/tex]
This is the same as the equation we started with, but with k+1 in place of n. Therefore, the equation holds true for all positive integers n by mathematical induction.
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jamal throws a ball up in the air. The graph below shows the height of the ball h in feet after t seconds. after how many seconds does the ball hit the ground? (1,16) (2,0) area amd projectile motion
Answer:
Step-by-step explanation:
please need full answer asap
Answer:
Step-by-step explanation:
[tex](x+14)^2+x^2=22^2[/tex] (Pythagoras Theorem)
[tex](x^2+28x+196)+x^2=484[/tex]
[tex]2x^2+28x+196=484[/tex]
[tex]2x^2+28x-288=0[/tex]
[tex]x^2+14x-144=0[/tex]
Using quadratic formula,
[tex]x=\frac{-b\pm \sqrt{b^2-4ac} }{2a}[/tex]
[tex]x=\frac{-14\pm \sqrt{(14^2-4\times1\times(-144)} }{2\times1}[/tex]
[tex]=\frac{-14\pm \sqrt{(196+576} }{2}[/tex]
[tex]=\frac{-14\pm 2\sqrt{193} }{2}[/tex]
[tex]=-7\pm\sqrt{193}[/tex]
[tex]=-7\pm13.89[/tex]
[tex]=6.89 ,-20.89[/tex] (-20.89 is not useful...cannot have a negative length for
radius)
Solution: radius is 6.89
In Problem 3, determine the level of measurement of each variable. 1. Birth order among siblings in a family
2. Volume of water used by a household in a day
3. Highest degree conferred (high school, bachelor’s, and so on)
4. Ages of children: 4 years, 5 years, 6 years, 7 years, and 8 years
1) Birth order among siblings in a family: Nominal level of measurement
2) Volume of water used by a household in a day: Ratio level of measurement
3) Highest degree conferred (high school, bachelor's, and so on): Ordinal level of measurement
4) Ages of children: 4 years, 5 years, 6 years, 7 years, and 8 years: Interval level of measurement
1) Birth order among siblings in a family: This variable is measured at the nominal level of measurement, as there is no inherent order or ranking to the categories
2) Volume of water used by a household in a day: This variable is measured at the ratio level of measurement, as it has a true zero point (i.e., no water usage) and the values can be compared in terms of ratios
3) Highest degree conferred (high school, bachelor's, and so on): This variable is measured at the ordinal level of measurement, as the categories have an inherent order or ranking (e.g., a bachelor's degree is higher than a high school diploma, but it does not necessarily indicate that someone with a bachelor's degree is "twice as educated" as someone with a high school diploma).
4) Ages of children: 4 years, 5 years, 6 years, 7 years, and 8 years: This variable is measured at the interval level of measurement, as the values have a meaningful order and distance between them (i.e., the difference between 4 years and 5 years is the same as the difference between 7 years and 8 years). However, there is no true zero point, as "zero years old" is not a meaningful category in this context.
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How do you decide what numbers to use as the numerator and the denominator in each equivalent fraction to the given decimal?
Answer:
To convert a decimal to an equivalent fraction, we need to first determine the place value of the decimal. For example, a decimal that ends in the tenths place (such as 0.4) has a denominator of 10. A decimal that ends in the hundredths place (such as 0.25) has a denominator of 100.
Once we have determined the denominator, we can convert the decimal to a fraction by placing the digits of the decimal in the numerator and the denominator. For example, 0.4 can be converted to the fraction 4/10. We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which in this case is 2. So 4/10 simplifies to 2/5.
In general, to convert a decimal to a fraction, we can follow these steps:
1. Determine the denominator based on the place value of the decimal.
2. Place the digits of the decimal in the numerator and the denominator.
3. Simplify the fraction by dividing both the numerator and denominator by their greatest common factor.
It's important to note that sometimes decimals can be rounded, so the resulting fraction may not be exact. In such cases, we can use approximations or continue to simplify the fraction until we reach a desired level of accuracy.
When K is small, x is also small.The "x is small" approximation only works when: the initial concentration of the reactant is relatively large and the equilibrium constant is small.The x is small approximation does not mean that x is zero. If that were the case, the reactant and product concentrations wouldn't change from their initial values. The x is small approximation just means that when x is added or subtracted to another number, it doesnt' change that number by very much.The x is small approximation must satisfy the <5% rule, whereby the x approximation divided by the number it was subtracted from is is less than 5% (or 0.05).The method of successive approximation is solving for x as if it were small, and then substituting the value obtained back into the equation (where x was initially neglected) to solve for x again. This can be repeated until the calculated value of x stops changing with each iteration, an indication that we have arrived at an acceptable value for x.
The "x is small" approximation only works when the initial concentration of the reactant is relatively large and the equilibrium constant is small.
What does the "x is small" approximation mean? The x is small approximation does not mean that x is zero. If that were the case, the reactant and product concentrations wouldn't change from their initial values. The x is small approximation just means that when x is added or subtracted to another number, it doesn't change that number by very much. When does the "x is small" approximation work? The "x is small" approximation only works when the initial concentration of the reactant is relatively large and the equilibrium constant is small. What is the <5% rule? The x is small approximation must satisfy the <5% rule, whereby the x approximation divided by the number it was subtracted from is less than 5% (or 0.05). What is the method of successive approximation? The method of successive approximation is solving for x as if it were small, and then substituting the value obtained back into the equation (where x was initially neglected) to solve for x again. This can be repeated until the calculated value of x stops changing with each iteration, an indication that we have arrived at an acceptable value for x.
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(BRAINLIEST) A baker sells cupcakes and bases her prices on the number of cupcakes purchased.
The graph shows a piecewise function with one piece increasing from the point 0 comma 0 through the point 12 comma 18 to the endpoint 24 comma 36 and another piece going from the point 24 comma 36 through the point 48 comma 60 and increasing to the right.
Based on the graph, what is the pricing the baker uses for her sales?
The first 24 cupcakes cost $1.50 each, and all cupcakes after that cost $1 each.
The first 24 cupcakes cost $1 each, and all cupcakes after that cost $1.50 each.
The first 36 cupcakes cost $1.50 each, and all cupcakes after that cost $1 each.
The first 36 cupcakes cost $1 each, and all cupcakes after that cost $1.50 each.
Answer: The first 24 cupcakes cost $1.50 each, and all cupcakes after that cost $1 each.
Step-by-step explanation:
The graph shows two pieces of the function, with one increasing from the point (0, 0) through the point (12, 18) to the endpoint (24, 36) and the other increasing from the point (24, 36) through the point (48, 60) to the right.
This means that the first 24 cupcakes cost $1.50 each and all cupcakes after that cost $1 each, as shown by the first piece of the function. The second piece of the function shows that the price per cupcake does not increase after 36 cupcakes, so option 3 and option 4 can be eliminated.
Therefore, the correct answer is: The first 24 cupcakes cost $1.50 each, and all cupcakes after that cost $1 each.
Gene expression occurs through transcription and then translation. From the provided list, select all that pertain to transcription. (Check all that apply.) Check All That Apply Creation of mRNA Linking together amino acids Using RNA polymerase Using DNA as a template Reading codons
Gene expression occurs through transcription and then translation. From the given list, select all that pertain to transcription. Transcription is the process of converting DNA into RNA. The following are the items that are included in transcription: Using DNA as a template Using RNA polymerase Creation of mRNA Reading codons The RNA polymerase enzyme is responsible for catalyzing the formation of phosphodiester bonds between nucleotides that have been added to the growing RNA chain.
The RNA polymerase enzyme binds to the promoter region of a gene before unwinding the DNA helix and beginning transcription. In transcription, the DNA template strand is read by RNA polymerase in the 3′-to-5′ direction, but RNA is synthesized in the 5′-to-3′ direction. RNA polymerase reads the DNA template strand in the 3′-to-5′ direction, synthesizes the mRNA transcript in the 5′-to-3′ direction, and produces a new RNA molecule that is complementary to the DNA template strand. Thus, transcription is responsible for creating a single-stranded RNA molecule called messenger RNA (mRNA).Therefore, the correct answer is:
Using RNA polymerase Using DNA as a template Creation of mRNA Reading codons
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what is an equivalent expression to 4x(2x-3)-5(3x-4)
Answer:4x + 3x + 2x - 4 - 3
Step-by-step explanation:Hope this helps
Which correlation coefficient reflects the strongest relationship?
a) +0.05
b) +0.25
c) +1.23
d) -0.33
The correlation coefficient that reflects the strongest relationship is +0.25, the correct option is b.
EXPLANATION:
The correlation coefficient ranges from -1 to +1.
The magnitude (absolute value) of the correlation coefficient indicates the strength of the relationship, with values closer to -1 or +1 indicating a stronger relationship.
Therefore, the correlation coefficient that reflects the strongest relationship is +1.23.
However, since this value is greater than +1, which is not possible, it seems to be an invalid value.
Among the given options,
The correlation coefficient that reflects the strongest relationship is b) +0.25.
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While birdwatching, Vicki saw 7 red birds, 9 white birds, and 19 black birds. Johnny saw 9 red birds, 12 blue birds, and 29 brown birds. Estimate how many more birds Johnny saw by rounding all numbers to the nearest ten before adding and subtracting.
Answer:
10
Step-by-step explanation:
7 rounds to 10
9 rounds to 10
19 rounds to 20
so Vicki has 40 birds
9 rounds to 10
12 rounds to 10
29 rounds to 30
so johnny has 50 birds
now subtract 50-40=10
Shaila is riding on a rollercoaster when her phone falls out of her pocket. The phone followed the equation y=−16t2+400
where y
gives the height of the phone after t
seconds. How long did it take her phone to hit the ground?
The phone hit the ground after seconds.
Answer:
5 seconds
Step-by-step explanation:
when the phone hits the ground then y = 0 , that is
- 16t² + 400 = 0 ( subtract 400 from both sides )
- 16t² = - 400 ( divide both sides by - 16 )
t² = 25 ( take square root of both sides )
t = [tex]\sqrt{25}[/tex] = 5
the phone hits the ground after 5 seconds
Answer:
5 seconds
Step-by-step explanation:
y = [tex]-16t^{2} + 400 \\[/tex]
Make t the subject:
[tex]16t^{2} = -400\\t^{2} = \frac{400}{16} = 25\\ t = \sqrt{25} = 5[/tex]
Therefore the answer is 5 seconds
Solve for x and y and how.
Answer:
The lines that go through all 3 sides of the triangle mean the angles are all equal. Since a triangle is 180 degrees, to find a single angle, we must divide by 3.
180 degrees / 3 = 60 degrees
Solve for X
60 = (2x + 10)
-10 from both sides:
50 = (2x)
x = 25
Solve for Y
60 = (3y + 3)
-3 from both sides:
57 = (3y)
y = 19
Hope that helps
Please Help! I don't understand this question!
Answer:
all you gotta do is mirror that half u and make it a full u
and since the points it intersects at is (1,-1) plot the other half on (1,1)
At a school of 550 children 80% walk to school
If at a school of 550 children 80% walk to school, the 110 children come to school by other means.
If 80% of the children walk to school, then the remaining 20% of children must arrive at school by other means (such as being driven by a parent, taking public transportation, etc.).
To find out how many children come to school by other means, we can use the following formula:
Number of children who come to school by other means = Total number of children x Percentage who don't walk to school
In this case, we have:
Number of children who come to school by other means = 550 x 20% = 110
Therefore, 110 children come to school by other means.
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The given question is incomplete, the complete question is:
At a school of 550 children 80% walk to school, how many comes in other way ?
For breakfast each day, you plan to flip a coin to decide whether to have cereal or toast. When you flip heads, you will have cereal. When you flip tails, you will have toast. Your friend predicts that you will have cereal 15 times this month. Is your friend correct? Explain your reasoning.
Answer: yes
Step-by-step explanation:
there is a 50% chance of landing on heads which means that you are statistically likely to have cereals for half a month and toast for half a month. half a month is usually 15 days so your friend is correct
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what is the constant of proportionality in the table below
Answer: 3
Step-by-step explanation:
k = y/x
maple has 4 identical loaves of bread that weigh a total of 6.6 pounds how much does 1 loaf of bread weigh
Answer:
1.65 pounds
Step-by-step explanation:
6.6 ÷ 4 = 1.65
Answer:
1.65
Step-by-step explanation:
since all together it weighs 6.6 pounds then 1 = x then you cross multiply after cross multiplying you divide 4 by 6.6. Then x = 1.65
The door is 0. 9 m wide and 2. 1 m high. Each of the four windows is 1. 5 m wide and 1. 2 m high. Work out the total area of the door and the four windows
Answer: The total area for the door is 1.89 and the total area for the windows is 7.2
Step-by-step explanation:
door+ 0.9 x2.1= 1.89 and window= 1.5 x 1.2=1.8 x 4= 7.2
what is the probability of getting all tails? express your answer as a simplified fraction or a decimal rounded to four decimal places.
The probability of getting all tails when flipping a coin three times can be calculated using the multiplication rule of probability. For each flip of the coin, there are two possible outcomes: heads or tails.
Assuming the coin is fair, both outcomes are equally likely, so the probability of getting tails on any one flip is 1/2.
To calculate the probability of getting all tails in three flips, we need to multiply the probabilities of getting tails on each individual flip. Since the flips are independent events (i.e. the outcome of one flip does not affect the outcome of another flip), we can simply multiply the probabilities together:P(all tails) = P(tails on first flip) x P(tails on second flip) x P(tails on third flip)
= (1/2) x (1/2) x (1/2)
= 1/8
Therefore, the probability of getting all tails when flipping a coin three times is 1/8 or 0.125 when expressed as a decimal rounded to four decimal places.
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