1. Four letters, T, H, M, A, are placed in a hat. If one is randomly pulled out of the hat at at time, what is the
probability of the order spelling MATH?
How many different ways can the 4 letters be selected when order matters?
P(MATH) = ___
(Enter your answer as a reduced fraction using / for the fraction bar)
Answers
The probability of of the order spelling MATH is 1/24.
What is probability?Probability is the chance of happening something or the occurrence of something . We can also define the probability as the chance of occurring or the chance of selecting something from the total set of value. It is always ranges from 0 to 1 where 0 is minimum value and 1 is maximum value of probability.
Formula for probability is :
\(prabability(event) = \frac{Favourable \ outcomes}{Total \ outcomes}\)
where, the total outcomes is the sample space of our given data or we can say the total number of values in the sample space.
In the question given,
The sample space is the different ways of arranging the letter which is equals to 4 factorial.
=> Sample space = 4! = 24
and the Favorable outcome is the word "MATH".
Thus, The probability is 1/24, because out of 24 of them only one can spell math.
To know more about probability, visit:
brainly.com/question/11234923
#SPJ1
Related Questions
10 items cost $15. how much does 1 item cost? how much would 5 items cost?
Answers
Answer:
1 Item cost $0.66, 5 Items would cost $7.5
Step-by-step explanation:
Use the long division method to find the
result when 2x³ + 13x² − 4x − 14 is
divided by 2x + 1. If there is a remainder,
express the result in the form q(x) +
r(x)
b(x)*
Answers
Answer:
Step-by-step explanation:
The long division method is a method of finding the result of dividing a polynomial by a linear polynomial.
To use the long division method, we divide the polynomial by the linear term in the divisor (in this case, 2x + 1). We then multiply the divisor by the result and subtract it from the polynomial, and repeat the process until we are left with a remainder.
For 2x³ + 13x² − 4x − 14 divided by 2x + 1, the process is as follows:
2x³ | 2x + 1
2x² + 2x
-------------
13x² + 4x
-------------
13x² + 12x + 14
-------------
14
-------------
So the result is 2x² + 2x + 7, with a remainder of 14.
Therefore, the answer is q(x) = 2x² + 2x + 7 and r(x) = 14, in the form q(x) + r(x).
28) The number of hours per week that high school students spend on computers is normally distributed, with a mean
of 5 hours and a standard deviation of 2 hours. 70 students are chosen at random. Let y represent the mean number
of hours spent on the computer for this group. Find the probability that y is between 5.1 and 5.7.
Answers
The probability that y is between 5.1 and 5.7 is approximately 0.4292.
What is probability?Probability is a way to gauge how likely or unlikely something is to happen. It is a number between 0 and 1, where 0 denotes an improbable event and 1 denotes an inevitable one.
According to question:Since the sample size is large (n = 70), we can use the Central Limit Theorem to approximate the sampling distribution of the sample mean as normal with mean μ = 5 and standard deviation σ/sqrt(n) = 2/sqrt(70) ≈ 0.24.
Now we want to find the probability that y, the sample mean, is between 5.1 and 5.7. We can use the standard normal distribution to do this by standardizing y:
z = (y - μ) / (σ / sqrt(n)) = (y - 5) / 0.24
The probability that y is between 5.1 and 5.7 is equivalent to the probability that z is between:
z1 = (5.1 - 5) / 0.24 ≈ 0.42
and
z2 = (5.7 - 5) / 0.24 ≈ 2.92
Using a standard normal distribution table or calculator, we can find that the probability of z being between z1 and z2 is approximately 0.4292.
Therefore, the probability that y is between 5.1 and 5.7 is approximately 0.4292.
To know more about probability visit:
https://brainly.com/question/30034780
#SPJ1
PLEASE HELPPP!!!!SOMEONEEEE
Answers
Answer:
(i) x ≤ 1
(ii) ℝ except 0, -1
(iii) x > -1
(iv) ℝ except π/2 + nπ, n ∈ ℤ
Step-by-step explanation:
(i) The number inside a square root must be positive or zero to give the expression a real value. Therefore, to solve for the domain of the function, we can set the value inside the square root greater or equal to 0, then solve for x:
\(1-x \ge 0\)
\(1 \ge x\)
\(\boxed{x \le 1}\)
(ii) The denominator of a fraction cannot be zero, or else the fraction is undefined. Therefore, we can solve for the values of x that are NOT in the domain of the function by setting the expression in the denominator to 0, then solving for x.
\(0 = x^2+x\)
\(0 = x(x + 1)\)
\(x = 0\) OR \(x = -1\)
So, the domain of the function is:
\(R \text{ except } 0, -1\)
(ℝ stands for "all real numbers")
(iii) We know that the value inside a logarithmic function must be positive, or else the expression is undefined. So, we can set the value inside the log greater than 0 and solve for x:
\(x+ 1 > 0\)
\(\boxed{x > -1}\)
(iv) The domain of the trigonometric function tangent is all real numbers, except multiples of π/2, when the denominator of the value it outputs is zero.
\(\boxed{R \text{ except } \frac{\pi}2 + n\pi} \ \text{where} \ \text{n} \in Z\)
(ℤ stands for "all integers")
Answer:
(i) x ≤ 1
(ii) All real numbers except x = 0 and x = -1.
(iii) x > -1
(iv) All real numbers except x = π/2 + πn, where n is an integer.
Step-by-step explanation:
What is the domain?The domain of a function is the set of all possible input values (x-values).
\(\hrulefill\)
\(\textsf{(i)} \quad f(x)=\sqrt{1-x}\)
For a square root function, the expression inside the square root must be non-negative. Therefore, for function f(x), 1 - x ≥ 0.
Solve the inequality:
\(\begin{aligned}1 - x &\geq 0\\\\1 - x -1 &\geq 0-1\\\\-x &\geq -1\\\\\dfrac{-x}{-1} &\geq \dfrac{-1}{-1}\\\\x &\leq 1\end{aligned}\)
(Note that when we divide or multiply both sides of an inequality by a negative number, we must reverse the inequality sign).
Hence, the domain of f(x) is all real numbers less than or equal to -1.
\(\boxed{\begin{aligned} \textsf{Inequality notation:} \quad &x \leq 1\\\textsf{Interval notation:} \quad &(-\infty, 1]\\\textsf{Set-builder notation:} \quad &\left\{x \in \mathbb{R}\left|\: x \leq 1 \right\} \end{aligned}}\)
\(\hrulefill\)
\(\textsf{(ii)} \quad g(x) = \dfrac{1}{x^2 + x}\)
To find the domain of g(x), we need to identify any values of x that would make the denominator equal to zero, since division by zero is undefined.
Set the denominator to zero and solve for x:
\(\begin{aligned}x^2 + x &= 0\\x(x + 1) &= 0\\\\\implies x &= 0\\\implies x &= -1\end{aligned}\)
Therefore, the domain of g(x) is all real numbers except x = 0 and x = -1.
\(\boxed{\begin{aligned} \textsf{Inequality notation:} \quad &x < -1 \;\;\textsf{or}\;\; -1 < x < 0 \;\;\textsf{or}\;\; x > 0\\\textsf{Interval notation:} \quad &(-\infty, -1) \cup (-1, 0) \cup (0, \infty)\\\textsf{Set-builder notation:} \quad &\left\{x \in \mathbb{R}\left|\: x \neq 0,x \neq -1 \right\} \end{aligned}}\)
\(\hrulefill\)
\(\textsf{(iii)}\quad h(x) = \log_7(x + 1)\)
For a logarithmic function, the argument (the expression inside the logarithm), must be greater than zero.
Therefore, for function h(x), x + 1 > 0.
Solve the inequality:
\(\begin{aligned}x + 1 & > 0\\x+1-1& > 0-1\\x & > -1\end{aligned}\)
Therefore, the domain of h(x) is all real numbers greater than -1.
\(\boxed{\begin{aligned} \textsf{Inequality notation:} \quad &x > -1\\\textsf{Interval notation:} \quad &(-1, \infty)\\\textsf{Set-builder notation:} \quad &\left\{x \in \mathbb{R}\left|\: x > -1\right\} \end{aligned}}\)
\(\hrulefill\)
\(\textsf{(iv)} \quad k(x) = \tan x\)
The tangent function can also be expressed as the ratio of the sine and cosine functions:
\(\tan x = \dfrac{\sin x}{\cos x}\)
Therefore, the tangent function is defined for all real numbers except the values where the cosine of the function is zero, since division by zero is undefined.
From inspection of the unit circle, cos(x) = 0 when x = π/2 and x = 3π/2.
The tangent function is periodic with a period of π. This means that the graph of the tangent function repeats itself at intervals of π units along the x-axis.
Therefore, if we combine the period and the undefined points, the domain of k(x) is all real numbers except x = π/2 + πn, where n is an integer.
\(\boxed{\begin{aligned} \textsf{Inequality notation:} \quad &\pi n\le \:x < \dfrac{\pi }{2}+\pi n\quad \textsf{or}\quad \dfrac{\pi }{2}+\pi n < x < \pi +\pi n\\\textsf{Interval notation:} \quad &\left[\pi n ,\dfrac{\pi }{2}+\pi n\right) \cup \left(\dfrac{\pi }{2}+\pi n,\pi +\pi n\right)\\\textsf{Set-builder notation:} \quad &\left\{x \in \mathbb{R}\left|\: x \neq \dfrac{\pi}{2}+\pi n\;\; (n \in\mathbb{Z}) \right\}\\\textsf{(where $n$ is an integer)}\end{aligned}}\)
give five equivalent fractions for 4/7
Answers
Answer:
8/14, 12/21, 16/28, 20/35, 40/70
Step-by-step explanation:
Nicks lunch cost $14.75 tax was 1.03 and he left a tip of 2.50 how much did he pay for his lunch
Answers
Answer:
$18.28
Step-by-step explanation:
To complete this problem is a straightforward answer:
First, you add 14.75 + 1.03 which equals $15.78 then, you'll want to add 2.50 to 15.78 and there you have your answer!!
A jar contains 6 red marbles numbered 1 to 6 and 8 blue marbles numbered 1 to 8 . A marble is drawn at random from the jar. Round your answer to four decimal places. Find the probability that the a. marble is red: b. marble is odd-numbered: c. marble is red or blue
Answers
The probability that a marble drawn is red is 0.4286, marble is odd-numbered is 0.5, and marble drawn is red or blue is 1.
There are 6 red marbles and 8 blue marbles, for a total of 14 marbles. The probability of drawing a red marble is the number of red marbles divided by the total number of marbles
P(Red) = 6/14 = 0.4286 (rounded to four decimal places)
There are 6 red marbles and 8 blue marbles, and 7 of them are odd-numbered (1, 3, 5, 7). The probability of drawing an odd-numbered marble is the number of odd-numbered marbles divided by the total number of marbles:
P(Odd) = 7/14 = 0.5 (rounded to four decimal places)
The probability of drawing a red or blue marble is the sum of the probabilities of drawing a red marble and a blue marble:
P(Red or Blue) = P(Red) + P(Blue)
To find P(Blue), we note that there are 8 blue marbles and 14 total marbles. Therefore,
P(Blue) = 8/14 = 0.5714 (rounded to four decimal places)
Now we can find P(Red or Blue)
P(Red or Blue) = P(Red) + P(Blue) = 6/14 + 8/14 = 14/14 = 1
To know more about Probability here
https://brainly.com/question/16946329
#SPJ4
What value in place of the question mark makes the polynomial below a perfect square trinomial?
x^2 + 24x + ?
A. 24
B. 48
C. 144
D. 12
Answers
Answer:
144
Step-by-step explanation:
\(x^2+24x +144\\\\=x^2 + 2\cdot 12x +12^2\\\\=(x+12)^2\)
Benny had 79 dollars to spent on 9 Books after buying then he had 17 dollars. How much did each book cost
Answers
Find x and y.
Give reasons to justify your solution
Answers
Answer:
X=32, Y=148
Step-by-step explanation:
X is 32 degrees because it is parallel to that 32 between f and b.
Y is 148 degrees because x and y together make a straight line and a straight line is 180 degrees therefore, 180-32 = 148.
What are the important variables in the problem below?
A test is worth 80 points. Multiple-choice questions are worth 2 points, and
short-answer questions are worth 4 points. If the test has 25 questions, how
many multiple-choice questions are there?
OA. p for points, m for multiple choice
OB. s for short answer, t for test
OC. m for multiple choice, s for short answer
OD. t for test, q for questions
Answers
The important variables are the two types of test questions which can be represented as :
m for multiple choice, s for short answerVariables are used to represent unknown values which could be worked out in a mathematical expression or problem.
The variables or unknown in this case are the type of test questions. which are : m for multiple choice, s for short answer
Therefore, the correct option is C. m for multiple choice, s for short answer
Learn more on word problems:https://brainly.com/question/25693822
#SPJ1
if the standard deviation of the data values in a sample is 14, what is the variance of the data values? A. 225 B. 144 C. 256 D. 196
Answers
Answer:
196
Step-by-step explanation:
since the standard deviation is 14
variance=the square of the standard deviation i.e
14*14=196
A company has recently been hiring new employees. Today the company has 32% more employees than it did a year ago. If there are currently 69,300 employees, how many employees did the company have a year ago?
Answers
Answer:
52500
Step-by-step explanation:
Let there be x employees in the previous year
Now, the company has 32% more employees whis is 69300
i.e.
\(x + \frac{32}{100} x = 69300\\\\ \implies\frac{132x}{100} = 69300 \\\\\implies 132x = 6930000\\\\\implies x = \frac{6930000}{132}\\\)
⇒ x = 52500
There were 52500 employees in the previous year
Triangle A′B′C′ is a dilation of triangle ABC .
What is the scale factor?
Enter your answer in the box.
Answers
Answer:
1/2
Step-by-step explanation:
The scale factor is 1/2 because each side length of \(\triangle{A'B'C'}\) is 1/2 of the length of the side lengths of \(\triangle{ABC}\).
Hope this helps :)
Answer:
1/2
Step-by-step explanation:
took the test
Is this a function?
Answers
Answer:
no
Step-by-step explanation:
Answer:
Step-by-step explanation:
In my opinion I would say No but I could be wrong
Please answer, will give 5 star.
Answers
Answer:
The first one
Step-by-step explanation:
She cant buy anything over $15, but she can buy something thats $15 :))
find the area of the shaded region below. Give your answer as a completely simplified exact value in terms of π (no approximations).
Answers
The area of the shaded regions is 4π - 8
How to determine the area of the shaded regionsFrom the question, we have the following parameters that can be used in our computation:
Shape = circleShaded region = chordsWe start by calculating the area of the triangle using
Area of triangle = 1/2absin(C)
Substitute the known values in the above equation, so, we have the following representation
Area of triangle = 1/2 * 4 * 4 * sin(90 degrees)
Evaluate
Area of triangle = 8
Next, we calculate the area of the semicircle using
Area = 0.125πd²
Where
d² = (4² + 4²) = 32
So, we have
Area semicircle = 0.125π * 32 = 4π
The area of the circle is
Area circle = 0.25πd²
This gives
Area circle = 0.25π * 32 = 8π
The area of the shaded regions is
Shaded region = circle - semicircle - triangle
Substitute the known values in the above equation, so, we have the following representation
Shaded region = 8π - 4π - 8
Evaluate
Shaded region = 4π - 8
Hence, the shaded region is 4π - 8
Read more about area at
https://brainly.com/question/22972014
#SPJ1
find the inequality represented by the graph please helpp
Answers
Answer:
y=3/4x
Step-by-step explanation:
what is the X intercept of the graph of the equation Y=-2x +6 in the xy-plane
Answers
Answer:
( 3 , 0 )
Step-by-step explanation:
→ When does the x - intercept occur
when y is 0
→ Substitute y = 0
0 = -2x + 6
→ Subtract 6 from both sides
-6 = -2x
→ Divide both sides by -2
3 = x
There were 8500 patients in total last month in the trust. 25% of these are smokers. How many patients smoke? *
Answers
Answer:
To find out how many patients smoke, you can multiply the total number of patients by the percentage of smokers:
8500 x 25% = 2125
Therefore, there were 2125 patients who smoke last month in the trust.
Step-by-step explanation:
2125 of the patients are smoker.
What is percentage?Percentages are fractions with 100 as the denominator. It is the relation between part and whole where the value of whole is always taken as 100.
Given that, there were 8500 patients in total last month in the trust. 25% of these are smokers.
We need to find the number of the patients who smoke.
So,
25% of 8500
= 0.25 × 8500
= 25 × 85
= 2125
Hence, 2125 of the patients are smoker.
Learn more about percentage, click;
https://brainly.com/question/29306119
#SPJ2
Examine the system of equations.
6x + y = −30,
36x + 6y = 24
Which statement is true about the system of equations?
A) After solving this system, you get a true statement.
B) This system has one solution.
C) If this system were graphed, the lines would be parallel.
D) The equations in this system have the same y-intercept.
Answers
Answer:
answer is c
Step-by-step explanation:
An algebraic equation that is in the form of y= mx + b having only a constantand a first-order term is called a linear or system equation. Where m is the slope and b is the y-intercept.Given equations are and .Let reframe these equations into the standard form. and and The above system equation shows that the slop of both the lines will be the same. Hence both the lines will be parallel to each other.Hence we can conclude that statement C will be true about the given system equations.
Answer:
C is a true statement
*View the attached graph*
Step-by-step explanation:
6x + y = −30 and 36x + 6y = 24
6x + y = −30
-6x -6x
y = -6x - 30
36x + 6y = 24
-36x -36x
6y = -36x + 24
\(\frac{6y}{6} =\frac{-36x+24}{6}\)
y = -6x + 4
If this system were graphed, the lines would be parallel.
Hope this helps!
A dice is rolled twice.
What is the probability of getting a 2 AND a 5?
Answers
Raoul has 72 wristbands and 96 movie passes to put in gift bags. The greatest common factor for the number of wristbands and the number of movie passes is qual to the number of gift bags. Raoul needs to make. Then find how many wristbands and how many movie passes raoul can put in each gift bag if he evenly distributes the items.
Please help I am stuck I am doing work nonstop on all weekends if I don’t get this right and done please help and will give brainlesst for the correct answer
Answers
Answer:
Step-by-step explanation:
I do know give me brainliest first
Answer:
24 gift bags
Step-by-step explanation:
Well first the question says to find the GCF and you find that by finding prime factors in each number. Then you would want to subtract 96-72 and get the answer of 24 so you would be able to make 24 gift bags. Hope this helps!!
May I have heart, 5 star, and brainliest please?
factorise x³-4x²+x+6
Answers
The binomial factors of x³- 4x²+x+6 are (x+2), (x+3), and (x-1).
Using the splitting and grouping the terms:
x³ + 4x² + x - 6
= x³ + 2x² + 2x² + x - 6 [Splitting 4x² = 2x² + 2x²]
= (x³ + 2x²) + (2x² + x - 6)
= x² (x + 2) + (2x² + 4x - 3x - 6)
= x² (x + 2) + [ 2x (x + 2) - 3 (x + 2)]
= x² (x + 2) + (x + 2) (2x - 3)
= (x + 2) ( x² + 2x - 3)
= (x + 2) ( x² + 3x - x - 3)
= (x + 2) [x (x + 3) - 1 (x + 3)]
= (x + 2) (x + 3) (x - 1)
Hence, the binomial factors are (x + 2), (x + 3) and (x - 1)
To learn more about factorise here,
https://brainly.com/question/10718512
https://brainly.com/question/24734894
A bag is filled with an equal number of red, yellow, green, blue, and purple marbles. The theoretical probability of Jonah drawing 2 red marbles from the bag with replacement is one fifth. If the experiment is repeated 100 times, what is a reasonable prediction of the number of times he will select 2 red marbles?
one fifth
5
20
25
Answers
Answer:
20
Step-by-step explanation:
The theoretical probability of drawing 2 red marbles from the bag with replacement is one-fifth, which means that the probability of drawing 2 red marbles in any one trial is 1/5 or 0.2.
The number of times Jonah is expected to select 2 red marbles in 100 trials can be predicted using the expected value formula:
Expected value = (Number of trials) x (Probability of success in one trial)
Expected value = 100 x 0.2
Expected value = 20
Therefore, a reasonable prediction of the number of times Jonah will select 2 red marbles in 100 trials is 20. Therefore, the answer is 20.
Answer: 20 i took the test
Step-by-step explanation:
I’m really confused what does j=, L=, M=
Answers
Answer: J = 83, L = 97, M = 97
Step-by-step explanation:
Since it is a isosceles trapezoid, J = K and M = L. Also, a trapezoid is cyclic, so K and L are supplementary.
A pair of jeans originally cost $85 but you are on sale for 45% off what is the sale price
Answers
Answer:
The sale price is $46.75
Step-by-step explanation:
The price of a pair of jeans that has on sale for 45% off with the original price of $85 is $46.75.
What is the percentage?The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.
A pair of jeans originally cost $85 but you are on sale for 45% off. Then the price of a pair of jeans will be
→ 0.55 × $85
→ $46.75
More about the percentage link is given below.
https://brainly.com/question/8011401
#SPJ2
what is the value of the expression shown below
2 3/5 - 1 3/5
^ ^
TWO THREE-FIFTHS MINUS ONE THREE-FIFTHS
THE NUMBERS ARE MIXED FRACTIONS
Answers
Answer:
1
Step-by-step explanation:
1. One way to do this is converting both into improper fractions. To do this, multiply the whole number by the denominator and add that to the numerator.
2 3/5 --> 2*5 is 10 --> 10+3 is 13. --> 13/5
2. This leaves us with 13/5 - 8/5
3. Subtract the numerators
13/5 - 8/5 = 5/5
4. Simplify. If the numerator is the same number as the denominator, it's a whole number.
5/5 = 1
8 19. Marcus claims that fractions with denominators 1 through 10 follow a pattern
when they are converted to decimal form. If any one fraction can be converted
to a terminating decimal, then all of the fractions with that same denominator
will also convert to terminating decimals. On the other hand, if one fraction
converts to a repeating decimal, then all fractions with that same denominator
will convert to a repeating decimal. Is Marcus correct? Explain.
Answers
Answer:
No
Step-by-step explanation:
Marcus is not correct because 1/12 converts to the repeating decimal 0.8333... but 3/12 converts to 0.25 which is not a repeating decimal.
FICA Taxes
Tax source
Social Security
Medicaid
Tax rate
6.2%
1.45%
How much does
an employee who
earns $64,000
gross salary pay
total for FICA
Taxes?
Answers
The total gross salary for FICA taxes is $4896 with the tax rates 6.2% and 1.45%.
What is meant by gross salary?The amount you earn each month before taxes and other deductions is referred to as your monthly gross income. In other words, it's your annual salary divided by 12. It's only a simple metric to aid in budgeting and other routine financial computations.
Annual Salary Amount / Number of Pay Periods = Gross Pay.
Gross pay equals the number of hours worked in a pay period multiplied by the hourly rate (+ overtime hours multiplied by the hourly overtime rate).
Given,
Tax rate=6.2%
=64000(6.2/100)
=3968
And also given another tax rate is 1.45%
=64000(1.45/100)
=92.8
Total=3968+928
=$4896
Therefore, the total gross salary for FICA taxes is $4896.
The total gross salary for FICA taxes is $4896 with the tax rates 6.2% and 1.45%.
To know more about gross salary, visit:
https://brainly.com/question/13582411
#SPJ9