A state’s license plates consist of 3 letters followed by 3 numbers. What is the probability of randomly generating a license plate that reads AHW 304?
Answer: [tex]\frac{1}{17576000}[/tex]
Step-by-step explanation:
Given: A state’s license plates consist of 3 letters followed by 3 numbers.
Since, there are 26 letters in English alphabet and 10 digits in set of numbers(0,1,....,9).
Then , the total number of license plates can be generated (if repetition is allowed)=
[tex]26\times26\times26\times10\times10\times10=17576000[/tex]
In AHW304, each alphabet and number occurs only once, the number of license plate with this = 1
Now, the probability of randomly generating a license plate that reads AHW 304=[tex]\frac{1}{17576000}[/tex]
Answer:
1/17,576,000
Step-by-step explanation:
Sarah decides to take her six-year-old son to the circus the price for the child ticket is $4.75 dollars Less in the price for the adult ticket if you represent their price for the child ticket using the variable X how would you write the algebraic expression for an adult ticket price?
Use the drop-down menus to complete each statement to show why √65 is between 12 and 18.
Answer:
12 < 6√5 < 18
Step-by-step explanation:
It has been given in the question 4 < 5 < 9 and we have to show 6√5 is between 12 and 18.
For box number 1.
4 < 5 < 9 ⇒ √4 < √5 < √9
For the box number 2.
√4 < √5 < √9 ⇒ 2 < √5 < 3
For the box number 3.
we multiply the inequality by 6.
6×(2 < √5 < 3) ⇒ 6×2 < 6×√5 < 6×3
Therefore final answer is 6×2 < 6×√5 < 6×3 ⇒ 12 < 6√5 < 18
The square root of 65 (√65) falls between 8 and 9, as these are the square roots of the closest perfect square numbers (64 and 81 respectively). The range of 12 to 18 provided in the question seems incorrect.
Explanation:The student's question is referring to the mathematical concept of square roots of numbers. The square root of a number is a value which, when multiplied by itself, yields the original number. In the case of √65, we need to locate it between two perfect square numbers, which are 64 (8^2) and 81(9^2). As a result, √65 should fall between 8 and 9.
However, the interval of 12 and 18 as stated in the question seems to be a mistake, as they are not the correct boundaries for the value of √65. Please verify the numbers in your question.
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Solve 3x2 + 2x + 7 = 0. Round solutions to the nearest hundredth. (5 points)
x ≈ −1.90 and x ≈ 1.23
x ≈ −1.23 and x ≈ 1.90
x ≈ −0.44 and x ≈ −3.56
No real solutions
Answer:
The answer is No Solutions Look Below
Step-by-step explanation:
In a group of students 25% are enrolled in physics, 23% in sociology, 17% in chemistry, 14% in political science, 12% in anthropology, and 9% in math. you are going to select an individual from the group of students. the probability of event a is equivalent to the probability that you select someone who studies social science (sociology, political science and anthropology) or physics. what is the probability of the event a’s complement?
The probability of event A's complement, which signifies selecting a student not studying social science or physics, is 26%.
The probability of selecting someone who studies social science (sociology, political science, and anthropology) or physics is the sum of the individual probabilities for those subjects: 23% (sociology) + 14% (political science) + 12% (anthropology) + 25% (physics) = 74%. To find the probability of the event A's complement, which is selecting a student not studying any of these subjects, we subtract the probability of event A from 100%: 100% - 74% = 26%. Therefore, the probability of selecting a student not enrolled in any of the mentioned social science subjects or physics is 26%.
What is the discriminant of the polynomial below? 4x2 - 20x + 25
The discriminant of the given polynomial is 0, indicating one real root.
Explanation:The discriminant of a quadratic equation is a value that can be used to determine the nature of the solutions (roots) of the equation. It is calculated using the formula b^2 - 4ac, where a, b, and c are the coefficients of the equation.
In the given polynomial, the coefficients are a = 4, b = -20, and c = 25. Plugging these values into the formula, we get: (-20)^2 - 4(4)(25) = 400 - 400 = 0.
Since the discriminant is equal to zero, the polynomial has one real root.
Find the value of cos θ for the angle shown. A line is drawn from the origin through the point four comma negative square root of thirty-three. The angle theta is given as the measurement from the positive x axis counterclockwise to the line.
cos θ = seven-fourthsAnswer
Cos θ = 4/7
Explanation
The angle θ is in the 3rd quadrant. So, it is positive.
cos θ = adjacent / hypotenuse
hypotenuse = √(4² + (√33)²)
= √(16 + 33)
= √47
= 7
Cos θ = 4/7
Answer:
Step-by-step explanation:
cos 0= 4/7
reason: i took the test
if a circle is inscribed in a triangle, the center of the circle is called the _____ of the triangle.
A. radius
B. incenter
C. circumcenter
Answer:
The correct answer to the following question will be Option B (Incenter).
Step-by-step explanation:
The middle of the circle which is carved in a triangle is the triangle incenter, the point where the triangle angle bisectors cross.
There are following steps to construct an inscribed circle in a triangle are as follows:
Step 1: Create the incenter.
Step 2: Construct a line that passes through incenter, perpendicular to one side of the triangle. The segment which connects the incenter with the triangle intersection point and the perpendicular line is the circle radius.
Step 3: Build a centered circle at the incenter with radius spotted in step 2.
A right triangle has a side with length 12 in and a hypotenuse with length 20 in. find the length of the second leg (in inches). (round to the nearest hundredth if needed)
You are taking a multiple-choice test that has 10 questions. each of the questions has four answer choices, with one correct answer per question. if you select one of these four choices for each question and leave nothing blank, in how many ways can you answer the questions?
Charmaine pays $848 for landscaping rocks for a project. The cost per pound is 32 cents. How many pounds did she purchase?
Answer:
D
Step-by-step explanation:
How many different 1010-letter permutations can be formed from 88 identical h's and two identical t's?
which situation involving raul's Bank account would be modeled by a positive number?
A.Raul deposited his paycheck.
B.Raul wrote a check to his grandmother
C.Raul withdrew cash from an ATM
D.Raul paid for groceries with his debit card.
positive means add
so it would be a deposit into the account
so A is the correct answer
The gold leaf on your necklace is 0.000045 of an inch thick. How do you write 0.000045 in scientific notation?
A brick oven has an opening as shown. What is the area of the entire opening?
Answer:
[tex]13.93ft^{2}[/tex]
Step-by-step explanation:
The area of the opening will be the sum of the area of the two shapes shown which are rectangle and half ellipse:
[tex]Area =Area_{rectangle}+\frac{1}{2} Area_{Ellipse}[/tex]
The area of the rectangle is:
[tex]Area_{Rectangle}=a*b[/tex]
where:
[tex]a=4ft\\b=2\frac{1}{2}ft[/tex]
we replace values(we convert the mixed fraction to improper fraction by multiplying the whole number part by the fraction's denominator, then add that to the numerator then write the result on top of the denominator.):
[tex]Area_{Rectangle}=4*2\frac{1}{2} =4*\frac{5}{2}=10[/tex]
The area of the ellipse is:
[tex]Area_{Ellipse}=a*b*\pi[/tex]
where:
[tex]a=Radius1=1\frac{1}{4}ft\\b=Radius2=2ft\\[/tex]
Radius2 will be half the side of the rectangle
[tex]Radius2=\frac{4}{2}=2[/tex]
we replace the values:
[tex]Area_{Ellipse}=1\frac{1}{4} *2*\pi=\frac{5}{4}*2*\pi=\frac{5}{2}\pi =7.85[/tex]
we calculate now the total area:
[tex]Area =Area_{rectangle}+\frac{1}{2} Area_{Ellipse}\\Area=10+\frac{1}{2}(7.85)=10+3.93=13.93ft^{2}[/tex]
You need to have a password with 55 letters followed by 33 odd digits between 00 and 99, inclusive. if the characters and digits cannot be used more than once, how many choices do you have for your password?
If one honey bee makes 1/2 teaspoon of honey during its lifetime, how many honey bees are needed to make 1/2 teaspoon of honey
Graph the following piecewise function and then find the range.
Answer:
The correct option is 3.
Step-by-step explanation:
The given piecewise function is
[tex]f(x)=\begin{cases}3x^2+1 & \text{ if } -4<x<6 \\ 6 & \text{ if } 6\leq x<9 \end{cases}[/tex]
Range is the set of output or y values.
The given function for 6 ≤ x < 9 is
[tex]f(x)=6[/tex]
It is a constant function, the value of function is 6 for all values of x.
Range = 6
The given function for -4 < x < 6 is
[tex]f(x)=3x^2+1[/tex] .... (1)
It is a quadratic function.
The vertex form of a quadratic function is
[tex]f(x)=a(x-h)^2+k[/tex] ....(2)
Where (h,k) is vertex and a is constant.
From (1) and (2), we get a=3,h=0,k=1.
The vertex of this function is (0,1), it means the range of this function is greater than or equal to 1. But this function is only defined for -4 < x < 6.
[tex]f(-4)=3(-4)^2+1=49[/tex]
[tex]f(6)=3(6)^2+1=109[/tex]
The maximum value of the maximum value of the function is 109 at x=6. Since 6 is not included in the interval -4 < x < 6, therefore 109 is not included in the range.
Range = [1,109)
When we combined the range of both functions we get
Range = [1,109)
Therefore the correct option is 3.
given that (6 3) is on the graph of f(x) find the corresponding point for the function f(-1/2x)
Answer:
this answer is wrong on plato, trust me
Step-by-step explanation:
We need to find the corresponding y-coordinate for x = -3. Unfortunately, since we don't have additional information about the function f(x), we cannot determine the value of f(-3) and provide the corresponding point.
To find the corresponding point for the function f(-1/2x) when (6, 3) is on the graph of f(x), we need to substitute the x-coordinate of (6, 3) into the function -1/2x and determine the resulting y-coordinate.
Given that (6, 3) is on the graph of f(x), it means that f(6) = 3.
Now let's substitute -1/2x into the function:
f(-1/2x) = f(-1/2 * 6) = f(-3)
Therefore, we need to find the corresponding y-coordinate for x = -3. Unfortunately, since we don't have additional information about the function f(x), we cannot determine the value of f(-3) and provide the corresponding point.
In summary, without more information about the function f(x), we cannot find the corresponding point for the function f(-1/2x) when (6, 3) is on the graph of f(x).
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equations that look different but have the same solution are said to be
a. equivalent
b. expressions
c. equals
d. similar
e. radical
a hot air balloon holds 3,249 cubic meters kf helium. the density of the helium is 0.1785 kilograms per cubic meter. how many kilograms of helium does the balloon contain, round to the nearest tenth of a kilogram?
How can I do this with the function (x+2)/x-3
Create a rational function with a linear binomial in both the numerator and denominator.
Part 1. Graph your function using technology. Include the horizontal and vertical asymptotes and the x- and y-intercepts on your graph. Label the asymptotes and intercepts.
Part 2. Show all work to identify the vertical asymptote, the x-intercepts, and the y-intercept.
A license plate comprised of 3 letters followed by 3 numbers is to be chosen (repetition is allowed). If the first letter cannot be a "Z", how many different ways can this occur? In your answer, include the set up and calculations for the license plate.
The diagonal of the rectangle is 13 inches, and the side lengths of the triangles are Pythagorean triples. To the nearest tenth, what is the area of the shaded part of the figure?
Please help me round 34,699 to the nearest ten thousand
In a plane, line N is parallel to line O, Line O is parallel to P, and line L is perpendicular to line N. Which must be true?
A) N||L
B) N||P
C) L||O
D) P||L
Answer:
The correct answer is option B) N || P
Step-by-step explanation:
N || P.
As it is given, in a plane, line N is parallel to line O, Line O is parallel to P, and line L is perpendicular to line N.
Since, N is parallel to O, and O is parallel to P, then N must be parallel to P.
So, option B is correct.
Let f(x) = 2x − 6. Solve f−1(x) when x = 2. (1 point) explanation please! algebra 2 makes no sense to me!
The sum of three numbers is 91 . the third number is 2 times the first. the first number is 9 more than the second. what are the numbers?
What is the fifth term in the expansion of (3x - 3y)7?
__ x3y4
Answer:
76545
Step-by-step explanation:
got it write on edge :)
Select all of the coefficients in the expression.
12xy3 + 2x5y + 4x5y2 + 7x5y.
2
3
4
5
7
12
2,4,7,12 for edgynuity. the way you can tell is because you look at the front. 12xy3 + 2x5y + 4x5y2 + 7x5y. the 12 1 4 7 are the coefficients.
Final answer:
The coefficients in the algebraic expression are 12, 2, 4, and 7, which are the numerical multipliers of the variable terms.
Explanation:
The coefficients in the expression 12xy^3 + 2x^5y + 4x^5y^2 + 7x^5y are the numerical factors that multiply the variables x and y in each term of the polynomial expression. The coefficients in this expression are 12, 2, 4, and 7. These are the numbers in front of the variable terms and not the exponents or the variables themselves.