There are 1260 eight-digit numbers that have 2 once, 3 twice, and 4 thrice.
There are 10 digits in the number system from 0 to 9.
Let the 8-digit number be represented by
_ _ _ _ _ _ _ _
Here the numbers will have a single 2, a doublet of 3, and a triplet of 4 hence we get
2 3 3 4 4 4 _ _
Now for the last 2 numbers, we have 0, 1, 5, 6, 7, 8, 9. Therefore the last 2 digits can be chosen in ⁷C₂ ways.
= 7!/(2 X 5!)
= 21 ways
There are 6 fixed numbers which can e arranged in 6! ways. Since there are numbers repeated twice and thrice, we can arrange them in
6!/(2! X 3!)
= 6 X 5 X 2
= 60 ways.
Therefore we get
60 X 21 numbers
= 1260 numbers.
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a man has 23 coins in his pocket, all of which are dimes and quarters. if the total value of his change is 380 cents, how many dimes and how many quarters does he have? your answer is
We found that after simplifying , He have 13 dimes and 10 quarters.
Given,
A man has 23 coins in his pocket.
The total value of his change is 380 cents.
Now,
23 = x + y
23 - x = y
As we know that
A dime=10 cents
So the cost of x dime is 10x.
A quarter=25 cents
so the cost of y quarters is 25y.
380 = 10x + 25y
Substitute the first equation, so
389 = 10x + 25 (23 - x)
380 = 10x + 575 - 25x
15x = 195
x = 13 dimes
Therefore,
y = 23 - 13 = 10 quarters
y = 10 quarters
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suppose the interval [-4,4]is divided into n=4 equal subintervals. what are the right endpoints, left endpoints, and midpoints of these intervals?
For the subintervals -
right endpoints: [2,4]left endpoints: [-4,-2]midpoints: [-2,0] and [0,2]Explain the term subintervals?Either of numerous smaller intervals through which a larger interval is divided. A division of an interval into subintervals is called a partition; the subintervals are the subintervals that make up the partition, in a sense. The width of a widest subinterval, not the partition's sidest subinterval, serves as the partition's norm.For the stated intervals;
interval [-4,4]
Total interval length;
= 4 - (-4)
= 4 + 4
= 8
Divide the interval in n=4 equal subintervals.
8/ 4 =2
First subinterval; [-4,-2]
Second subinterval; [-2,0]
Third subinterval; [0,2]
Fourth subinterval; [2,4]
Thus,
right endpoints: [2,4]
left endpoints: [-4,-2]
midpoints: [-2,0] and [0,2]
Thus, the subintervals of the given interval [-4,4] is obtained.
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x/-1.2-18=12
help me pleaseeeeeeee
From the parking lot at the red hill shopping center, the angle to the top of the hill is about 25°. From the base of the hill angle of elevation to the top of the hill is 55°. The horizontal distance between these two sight points is 740 feet. How high is red hill??
(1 point) in the 6/51 lottery game, a player picks six numbers from 1 to 51. how many different choices does the player have if repetition is not allowed? note that the order of the numbers is not important. your answer is :
There are 18 million different choices for a player to pick six numbers from 1 to 51. By using the combinations formula, the required value is obtained.
What is the formula for finding the number of combinations?The combinations formula is as follows:
ⁿCₓ = n!/(n - x)!x!
Where n is the total number of things and x is the required number of things.
Calculation:It is given that,
In a 6/51 lottery game, a player picks six numbers from 1 to 51.
So, the number of different choices the player has if repetition is not allowed is
ⁿCₓ = n!/(n - x)!x!
Here, n = 51 and x = 6
On substituting the values, we get
⁵¹C₆ = 51!/(51 - 6)!6!
⇒ ⁵¹C₆ = 51!/45!6!
⇒ ⁵¹C₆ = (51 × 50 × 49 × 48 × 47 × 46 × 45!)/45! × 6!
⇒ ⁵¹C₆ = (51 × 50 × 49 × 48 × 47 × 46)/6 × 5 × 4 × 3 × 2 × 1
⇒ ⁵¹C₆ = 17 × 10 × 49 × 47 × 46 = 170 × 105938 = 18,009,460
Therefore, there are 18 million choices for the player to pick six numbers from a set of 51 numbers.
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What is the image point of ( -1, -5) after a translation left 1 unit and up 4 units?
- 3/8 - 1/4 evaluate
The final solution of the given question is -0.625.
What are the denominator and numerator?
A fraction's top digit is always referred to as the numerator. It displays the number of our parts. A fraction's numerator—the lowest digit—is referred to as the denominator. It displays the overall number of pieces that something can be broken down into.
We have,
- 3/8 - 1/4
so, calculating the given values,
((-3) ÷ (8)) - (1 ÷ 4)
make the denominator the same by multiplying 1/4 by 2, we get,
((-3) ÷ (8)) - (2 ÷ 8)
add the numerator and one common denominator,
-3 - 2 ÷ 8
-5 ÷ 8
= -0.625
Hence, the final solution to the given question is -0.625.
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What is the measure of angle B in this triangle?
Enter your answer in the box.
m∠B=
By using the fact that the sum of all internal angles must be equal to 180°, we will see that the measure of angle B is 70°.
How to find the measure of angle B?Remember that the sum of the internal angles of a triangle is always equal to 180°, then we can write the linear equation:
40° + (2x - 30°) + (x + 20°) = 180°
(2x - 30°) + (x + 20°) = 180° - 40°
2x + x - 30° + 20° = 140°
3x = 140° + 30° - 20°
3x = 150°
x = 150°/3
x = 50°
Then the measure of angle B is (2x - 30°) = (2*50° - 30°) = 70°.
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The correct answer is 70
describe all numbers x that are at a distance 2 from the number 6
Answer:
x = 4 or x = 8
Step-by-step explanation:
6-2=4
6+2=8
All the numbers 'x' that are at a distance of 2 from the number 6 will be 4 and 8.
What is a number line?A number line refers to a straight line in mathematics that has numbers arranged at regular intervals or portions along its width. A number line is often shown horizontally and can be postponed in any direction.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
All the numbers 'x' that are at a distance 2 from the number 6 are given as,
⇒ 6 ± 2
For a negative sign, then the number is given as,
⇒ 6 - 2
⇒ 4
For a positive sign, then the number is given as,
⇒ 6 + 2
⇒ 8
All the numbers 'x' that are at a distance of 2 from the number 6 will be 4 and 8.
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For the binomial distribution, which formula finds the standard deviation? Choose the correct answer below: np npq npnpq
The formula for finding the standard deviation for a binomial distribution is σ2=npq. f.
What means binomial distribution?
When each trial has the same probability of achieving a given value, the number of trials or observations is summarized using the binomial distribution.
what is binomial Distribution Formula?For each random variable X, the binomial distribution formula is given by;
P(x:n,p) = nCx px (q)n-x
Where,
n = the number of experiments
x = 0, 1, 2, 3, 4, …
p = Probability of Success in a single experiment
q = Probability of Failure in a single experiment = 1 – p
formula for finding standard deviation of a binomial distribution is npq. f.
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Fifteen less than twice a number is the same as the number plus two. What is the number?
The number is 17.
The first part is "Fifteen less than twice a number".
Let us say that n represents the unknown number.
Twice a number is the same as two times the number or 2n, and fifteen less than 2n is 2n−15.
The next part "is the same as the" part of the word problem indicating that the two parts are equal. So we use an equal sign to represent it⇒2n−15 =
The third part of the problem is "the number plus two". This is the same as n+2
The final equation is 2n-15=n+2
To solve for n, we would add 15 to both sides: 2n=n+17
Then subtract 1n from both sides: n=17
The number is 17.
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Pls helppp it’s timed
The range of the graph shown is
range { y | y < 0 }
What is translation?When a figure is transported from one place to another without changing its size, shape, or orientation, a translation takes place.
How to find the rangeAll of a function's x-values, or inputs, make up the domain, and all of a function's y-values, or outputs, make up the range.
The graph's entire range, from lower to upper numbers vertically, represents the range.
The translation downwards, means that the graph moved down and considering the image of the attached graph, the effect of the translation means that the range to be numbers less than zero
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Pls I need help for Mid terms
Answer:
3x at the power of 2 -2x+21
ask for explanation if needed
undergraduate students at a college belong to one of four groups depending on the year in which they are expected to graduate. each student must choose one of 21 differ- ent majors. how many students are needed to assure that there are two students expected to graduate in the same year who have the same major?
Maximum number of distinct majors/groups: 84 therefore, the 85th student must be the same as one of the 84 students.
What would a typical graduation date be?Date of anticipated graduation: May 15, 2020, or Spring 2020 for graduation (expected). Instead of expected or anticipated, you can use the word pending if you're presently working to finish your final semester.
Do I need to mention my anticipated graduation date on my resume?Employers may be able to see that you are actively pursuing your degree even though you haven't graduated by seeing your anticipated graduation date on your resume.
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2. There are 108 feet in 36 yards. What is the
constant of proportionality that relates y, the
number of yards to x, the number of feet?
Answer:
x=36
Step-by-step explanation:
Based on the given conditions, formulate: x = 108 / 3
Cross out the common factor: x = 36
get the result: x = 36
Answer: x = 36
Answer: 36
Step-by-step explanation:
Maria was given this absolute value graph and needs to come up with the equation, domain, range and intercepts.
function is y = |x|..and from her knowledge with translations she knows that it has translated horizontally to the right 4 units.
So she says the new equation must be y = |x+4|. The domain is all values of x. The range is all values of y greater u
to zero. The y-intercept is (0,4). There isn't an x intercept, because it just sits at (4,0). can you find any errors in her solution?
Maria wrote incorrectly the function, it is:
y = |x - 4|
And:
Domain: all real numbers.Range: all real numbers equal to or larger than zero.y-intercept: (0, 4)x-intercept: (4, 0).There are errors in her solution?She started with the parent absolute value function:
y = |x|
And wrote a translation to the right as:
y = |x + 4|
That is her mistake, a translation to the right of N units is written as:
g(x)= f(x - N)
So for a translation to the right of 4 units, we need to subtract 4 to the input, the actual function that we can see on the graph is written as:
y = |x - 4|
Now, the y-intercept is what we get when we evaluate in x = 0:
y = |0 - 4| = 4
So the y-intercept is (0, 4).
The x-intercept is the value of x such that y = 0, so we need to solve:
|x - 4| = 0
x - 4 = 0
x = 4
The x-intercept is (4, 0).
Finally, the domain (like in all absolute value functions) is the set of all real numbers, and the range is the set of all real numbers equal to or larger than zero.
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Fill in the blank random variable has either a finite or a countable number of values A discrete random variable has either a finite or a countable number of values. probability continuous discrete required
A discrete random variable has either a finite or a countable number of values.
Discrete random variables are defined as variables that can only take on a finite number of values. If any random variable takes a countable number of all the possible values, it is referred to be a discrete random variable. For instance, while flipping a coin, the random variable X will take the values 0, 1, and 2 depending on the number of heads.
If the value of any variable, such as X, is uncertain, that variable is said to be a random variable. It may also be defined as a function that is crucial in giving values to the results of any random experiment. Depending on the sort of numeric values they include, random variables can be either discrete or continuous.
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how to construct a confidence interval of the population proportion given at the level of confidence
Answer:
Step-by-step explanation:
what i do not undersante
Amir bought 10 bags of Takis and 2 small waters for $32. Jaishawn bought 4 bags of Takis and 6 small waters for $18. What was the cost of one bag of Takis and the small water?
t = price of bag of takis
w = water price
10t + 2w = 32
4t + 6w = 18
get both equations in terms of w
2w = 32 - 10t
6w = 18 - 4t
multiply first equation by -3
-6w = -96 + 30t
6w = 18 - 4t
add
0 = -78 + 26t
78 = 26t
t = 3
price of taki bag is 3 dollars
plug into any of the formulas and solve for w
6w = 18 - 4(3)
6w = 18 - 12
6w = 6
w = 1
price of water is 1 dollar
make sure this is correct by plugging into one of the formulas and verifying if true
4t + 6w = 18
4(3) + 6(1) = 18
18 = 18
answers are correct
takis are 3 dollars
waters are 1 dollars
hope this helps :)
- jeron
comment if you have questions
look up "solving linear equations" for more information
if a sample of items is taken and the mean of the sample is outside the control limits, the process is:
If a sample of items is taken and the mean of the sample is out of control and the cause should be established producing high quality products.
The correct option is option (A).
When Statistical Process Control (SPC) samples an item and the mean of the sample is outside the control limits, the process is as follows. You don't have to worry within certain control limits using only natural sources of variation to produce under control within certain control limits. The process is said to be out of control and the cause should be investigated. That is, many sample points are outside the control limits, a sample of the item is taken, and the average of the samples is outside the control limits.
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Complete question:
In Statistical Process Control (SPC), if a sample of items is taken and the mean of the sample is outside the control limits, the process is:
a) out of control and the cause should be established producing high quality products b)in control and capable of producing within the established control limits in control,
c)there is no need for concern
d)within the established control limits with only natural causes of variation
At a particular restaurant, each mini hotdog has 60 calories and each mozzarella stick has 70 calories. A combination meal with mini hotdogs and mozzarella sticks is shown to have 1080 total calories and 5 more mini hotdogs than mozzarella sticks. Write a system of equations that could be used to determine the number of mini hotdogs in the combination meal and the number of mozzarella sticks in the combination meal. Define the variables that you use to write the system.
Answer:
the combination meal contains 18 mini hotdogs and 13 mozzarella sticks.
Step-by-step explanation:
To determine the number of mini hotdogs and mozzarella sticks in the combination meal, we can use the following system of equations:
Let x be the number of mini hotdogs in the combination meal.
Let y be the number of mozzarella sticks in the combination meal.
The first equation represents the total number of calories in the combination meal: 60x + 70y = 1080
The second equation represents the difference between the number of mini hotdogs and mozzarella sticks: x - y = 5
Thus, the system of equations is:
60x + 70y = 1080
x - y = 5
To solve this system, we can use a variety of methods, such as substitution or elimination. For example, we can eliminate x by adding the equations together, which yields:
60x + 70y = 1080
x - y = 5
60x - x + 70y - y = 1080 - 5
59x + 69y = 1075
Dividing both sides by 59, we find that x = 18.
Substituting this value into the second equation, we find that y = 18 - 5 = 13.
Therefore, the combination meal contains 18 mini hotdogs and 13 mozzarella sticks.
Answer:
There are 9 pizza rolls and 12 mini hotdogs in the combination meal.
Step-by-step explanation:
We are given the following in the question.
Let x be the number of pizza rolls sold and y be the number of mini hotdogs in the combination meal.
Total number of items in combination meal = 21
Thus, we can write the equation
Calorie in a pizza roll = 60
Calorie in a mini hotdog = 70
Total calories = 1380
Thus, we can write the equation
Solving the two equations, we get,
Thus, there are 9 pizza rolls and 12 mini hotdogs in the meal.
The Girl Scouts sponsor a Movie Night each year. In the first year, there were 26 participants. In the fourth year, there were 89 participants. Write an equation in slope-intercept form modeling this situation where y, number of participants, is a function of x, number of years. How many participants are predicted for the 6th year?
The required Slope-intercept form is y = 21x + 5 and the number of participants in the 6th year is 131.
Slope-intercept form:The slope-intercept form is One of the most common ways to describe a line's equation. The general form of a slope-intercept form is given by
y = mx + cWhere m is the slope and c is the y-intercept
And the formula for Slope is given by
Slope (m) = (y₂ - y₁)/ (x₂ - x₁)Here we have
Number of participants in 1st year = 26
Number of participants in 4th year = 89
Take number of years as x - coordinate
Number of participants as y - coordinate
As we know for 1 year, number of participants is 26
=> The pair of coordinates = (1, 26)
For 4th year, number of participants is 89
=> The pair of coordinates = (4, 89)
Now we will find the slope-intercept form for the situation
using the coordinates (1, 26) (4, 89)
As we know slope m = (y₂ - y₁)/(x₂- x₁)
Slope m = (89 - 26)/(4 - 1) = 63/3 = 21
As we know slope intercept form, y = mx + c
=> y = 21x + c --- (1)
As per the situation, Line (1) will pass through (1, 26)
=> 26 = 21(1) + c
=> c = 26 - 21
=> c = 5
=> y = 21x + 5
Therefore,
The required Slope-intercept form is y = 21x + 5
To find the number of participants in the 6th year, take x = 6
=> y = 21(6) + 5
=> y = 126 + 5
=> y = 131
Therefore,
The required Slope-intercept form is y = 21x + 5 and the number of participants in the 6th year is 131.
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5. Marcus, Alaina, and Tory recorded the number of text messages
they sent on a certain day. Marcus sent 24 text messages, Alaina
sent 8 fewer messages than Marcus, and Tory sent twice as many
messages as Alaina. What is the ratio of the number of texts that Tory
sent to the total number of texts sent by all three friends?
Step-by-step explanation:
Marcus 24
Alaina 24 - 8 = 16
Tory 16×2 = 32
in total they sent
24 + 16 + 32 = 72
the ratio of Tory's texts to the total of all 3 friends is
32/72 = 4/9
write 2 differnt expressions that involve only oots and powers of 2 which are equivalent 4 2/3 / 8 1/4
2 different expressions that involve only outs and powers of 2 which are equivalent 4 2/3 / 8 1/4
1) (4^2 * 2^-1 * 3^1) / (8^1 * 2^-2 * 4^-1)
2) (2^5 * 3^1) / (2^6 * 4^-1)
1) (4^2 * 2^-1 * 3^1) / (8^1 * 2^-2 * 4^-1)
This expression is equivalent to 4 2/3 / 8 1/4 because it is written in terms of powers of two. 4^2 is equal to 16, which is the numerator in 4 2/3. 2^-1 is the same as 1/2, which is the second fraction in 4 2/3. 3^1 is equal to 3, which is the numerator in 8 1/4. 8^1 is equal to 8, which is the denominator in 8 1/4. 2^-2 is the same as 1/4, which is the second fraction in 8 1/4. 4^-1 is equal to 1/4, which is the first fraction in 8 1/4. When all the terms are multiplied and divided, it is the same as 4 2/3 / 8 1/4.
2) (2^5 * 3^1) / (2^6 * 4^-1)
This expression is also equivalent to 4 2/3 / 8 1/4 because it is written similar to above equation.
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jenny buys 222222 sports drinks for her soccer team. they are on sale for \$0.35$0.35dollar sign, 0, point, 35 off per drink. jenny paid \$18.70$18.70dollar sign, 18, point, 70 for the 222222 sports drinks. what question does the equation 22(x-0.35)
The original cost of each sports drink that Jenny bought for her soccer team was $1.20.
Number of sports drink that Jenny bought for her soccer team
= 22
The amount of discount that Jenny got on each drink as they were on sale
= $0.35
Amount that Jenny paid for 22 sports drinks
= $18.70
Let the original cost of each sports drink be $x
Amount that Jenny paid for each drink
= $(x-0.35)
Therefore, amount that Jenny paid for 22 sports drink
= 22× (x-35) = 18.70
(x-0.35) = 18.70/22
x = 0.85 + 0.35
x = $1.20
The question is incomplete, the complete question is:
Jenny buys 22 sports drinks for her soccer team, they are on sale for $0.35 off per drink. Jenny paid $18.70 for 22 sports drink. How much does each drink cost originally?
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(-12, 14) and (6,-1) in linear equation
Answer:
y = -5/6 x + 4
Step-by-step explanation:
y = mx + b
m = slope = (-1 - 14)/(6 - (-12)) = -15/18 = -5/6
y = -5/6 x + b
14 = -5/6 × (-12) + b
14 = 10 + b
b = 4
y = -5/6 x + 4
(9x-6)ln(3)=(12x-8)ln(4)
solve for x with steps
Answer:
x = 2/3
Step-by-step explanation:
ln3^(9x-6) = ln4^(12x-8)
9x - 6 = 12x - 8
12x - 9x = -6 + 8
3x = 2
3/3 x = 2/3
x = 2/3
Evaluate the integral. ∫ x sec x tan x dx
The integral is ∫ x sec x tan x dx. We can solve it using integration by parts xln|sec(x) + tan(x)| - x + C
We have u = x, dv = sec(x)tan(x)dx, du = dx, and v = ln|sec(x) + tan(x)|.
The integral is then
Integrating the second part we get:
xln|sec(x) + tan(x)| - x + C
The integral is ∫ x sec x tan x dx. We can solve it using integration by parts. We let u = x and dv = sec(x)tan(x)dx. Then, du = dx and v = ln|sec(x) + tan(x)|. So, the integral becomes xln|sec(x) + tan(x)| - ∫ ln|sec(x) + tan(x)| dx. We can integrate the second part to get xln|sec(x) + tan(x)| - x + C.
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Find The Slope
The answer has to be in fraction form
Please help I need the answer asap
Thanks
Answer:
7/5
Step-by-step explanation:
Go up from the lower left point along the orange line 7 units.
7 units up = a rise of 7
Now go right on the orange line 5 units.
5 units right = a run of 5
slope = rise/run = 7/5
Answer: 7/5
fine the product of 1/100
The product of 1/100 is 0.01.
What is decimal?Decimals are numbers that have two components, a whole number component and a fractional component, which are separated by a decimal point.
Given that the expression 1/100.
To find the product of 1/100,
means the decimal value of 1/100
And the decimal value of 1/100 is part of 1 in hundredth
= 1/100
= 0.01
Hence, product of 1/100 is 0.01.
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