The probability that 4 randomly selected people all have the same birthday, ignoring leap years, is 0.00000002 when rounded to eight decimal places.
Explanation:The problem is asking about the probability that 4 people, selected at random, all have the same birthday. Since we're ignoring leap years, each person can have a birthday on any of 365 days of the year. The probability that the first person has a birthday on any day of the year is 1, because there's no restriction on when their birthday can be. However, the probability that the second, third, and fourth people share this same birthday becomes much less.
Given that we've selected a specific day for the first person, the second person has a 1 in 365 chance (or approximately a 0.00274 chance) of having that same birthday. The same applies for the third and fourth person. Since each of these events is independent (meaning the outcome of the first event doesn't change the probability of the next event), we can find the total probability by multiplying the individual probabilities together: 1 (for the first person) * 0.00274 (for the second person) * 0.00274 (for the third person) * 0.00274 (for the fourth person) = 0.000000020500. To the eight decimal place, this becomes 0.00000002.
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What is the equation of the quadratic graph with a focus of (1, 1) and a directrix of y = −1?
f(x) = − one fourth (x − 1)2 + 1
f(x) = − one fourth (x − 1)2
f(x) = one fourth (x − 1)2 + 1
f(x) = one fourth (x − 1)2
HELP! Algebra!
The following two-way table shows the number of students of a school who have a cell phone and/or have a part-time job:
Based on the table, how many students have both a cell phone and a part-time job?
Answers:
A- 10
B- 40
C- 50
D- 100
The number of students have both a cell phone and a part-time job is 40.
The correct option is (B)
What is algebra?
Algebra is a branch of mathematics that deals with symbols or variables and uses arithmetic operations (+, –, ×, ÷) to find the unknown quantities represented by these variables.
Given table shows that,
The students having whether having cell phones or not and whether the students are having part time job or not.
As we can see from the Column I shows students having cellphones and the first row shows students having part time job. which is 40.
Hence, the students have both a cell phone and a part-time job is 40.
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The football team has 30 more members than the basketball teams. If each group had 10 more members, the ratio of their membership would be 3.2. How many members are in each group? Write your answer as football x basketball y
****PLEASE HELP********
Which expression can be used to determine the average rate of change in f(x) over the interval [2,9]
a) f(9-2)
b) f(9)-f(2)
c) f(9-2)/9-2
c) f(9)-f(2)/9-2
Answer:
D. f(9-2)/9-2 on Edg2020
Step-by-step explanation:
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Use the distributive property to remove the parentheses.
-5(5v-4x-1)
Joan likes to watch the birds in her yard.one morning,she notices that there are twice as many robins as blue jays.if she counted 21 blue jays and robins in all, how many blue jays did she count. Need help badly
The foodservice department has been asked to prepare a special luncheon for the grandway hospital board of directors on tuesday. there will be 25 board members at the luncheon. there are 125 portions of vegetable lasagna needed for the hospital's lunch service that day. the standardized vegetable lasagna recipe yields 125 portions and requires 21 lb of ricotta cheese. how much ricotta cheese must chef carl order to meet production needs?
Read the following statement: All prime numbers are odd. Which of the following choices is a counterexample to the statement?
1
17
2
7
The choice which is a counterexample to the statement is 2.
What are prime numbers?"It is a number that is divisible only by itself and 1 "
For given question,
We have been given a statement 'All prime numbers are odd. '
We need to select a counterexample to given statement.
Consider a number 2.
2 is divisible only by itself and 1
This means, 2 is a prime number.
We know that 2 is an even number.
Therefore, the choice which is a counterexample to the statement is 2.
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Which of the following equations has the solution x = all real numbers? Select one: a. 4(3 - x) + 6x = 3x + 12 - x b. 4(3 - x) + 6x = 3x + 10 - x c. 4(3 - x) + 6x = 3x + 12 + 2x d. 4(3 - x) + 6x = x + 12 - 3x
The equation that has the solution x = all real numbers is given by option a) (4(3 - x) + 6x = 3x + 12 - x) and this can be determined by using the arithmetic operations.
Check all the options in order to determine which of the following equations has the solution x = all real numbers.
A) 4(3 - x) + 6x = 3x + 12 - x
Simplify the above equation separately that is:
LHS = 12 - 4x + 6x
= 12 + 2x
RHS = 3x + 12 - x
= 2x + 12
LHS = RHS means there is an infinite number of solutions.
B) 4(3 - x) + 6x = 3x + 10 - x
Simplify the above equation separately that is:
LHS = 12 - 4x + 6x
= 12 + 2x
RHS = 2x + 10
LHS [tex]\neq[/tex] RHS means that there are no solutions.
C) 4(3 - x) + 6x = 3x + 12 + 2x
Simplify the above equation separately that is:
LHS = 12 - 4x + 6x
= 12 + 2x
RHS = 5x + 12
LHS [tex]\neq[/tex] RHS means that there are no solutions.
D) 4(3 - x) + 6x = x + 12 - 3x
Simplify the above equation separately that is:
LHS = 12 + 2x
RHS = 12 - 2x
LHS [tex]\neq[/tex] RHS means that there are no solutions.
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Let u = <-9,4>, v = <8, -5>. Find u - v.
To find the difference between vectors u and v, subtract corresponding components.
Given vectors u = <-9,4> and v = <8, -5>, to find the difference u - v, subtract corresponding components:
Subtract the x-components: -9 - 8 = -17
Subtract the y-components: 4 - (-5) = 9
Therefore, u - v = <-17, 9>.
Write 14/42 in simplest form
How to solve (8.76 x 109)(6.52 x 10-3)/13.27 x 105?
Which function represents g(x), a reflection of f(x) =2/5 (10)x across the x-axis? g(x) =-2/5 (10)x g(x) =-2/5(1/10)^x g(x) =2/5(1/10)^-x g(x) =2/5 (10)-x
Answer:
A. [tex]g(x)=-\frac{2}{5}(10)^x[/tex].
Step-by-step explanation:
We are given the function [tex]f(x)=\frac{2}{5}(10)^x[/tex].
Now, g(x) is obtained by reflecting the function f(x) over x-axis.
Reflection of f(x) over x-axis changes f(x) to -f(x).
So, we get,
[tex]g(x)=-f(x)[/tex]
i.e. [tex]g(x)=-\frac{2}{5}(10)^x[/tex]
Thus, the reflected function is [tex]g(x)=-\frac{2}{5}(10)^x[/tex].
So, option A is correct.
What is the following product
Evaluate 5x + (-2x 2) for x = 3.
Enter the degree of the polynomial below
7x^7+10x^4+4x^3-5x^11-10x^6-6x^7
A. 11
B. 10
C. 6
D. 7
Of the 30 girls who tried out for lacrosse team 12 were selected. Of the 40 boys that tried out 16 were selected. Are the ratios of the number of students on the team to the number of students trying out the same for both boys and girls? Explain.
Assuming that n 1 , rewrite the compound interest equation B t 900 1.185 t in the general form.
Solve and check the inequality
|8m+4|<12
The population of a town is 500,000 in 1990. The population increases at a rate of 5% every five years. What will be the approximate population of the town in 2005?
A. 578,813
B. 587,712
C. 499,354
D. 512,945
The curve y = x/(1 + x2) is called a serpentine. find an equation of the tangent line to this curve at the point (2, 0.40). (round the slope and y-intercept to two decimal places.) y =
The equation of the tangent line to the curve y = x/(1 + x2) at the point (2, 0.40) is given by y = -0.24x + 0.88, rounded to two decimal places.
Explanation:The subject of the question refers to calculus, specifically the concept of finding the equation of a tangent line to a curve. This process typically involves finding the derivative of the function (which gives the slope of the tangent), and then using the point-slope form of the line equation.
The derivative of y = x/(1 + x2) can be found using the quotient rule for differentiation and is given by y' = (1 - x2)/(1 + x2)2. Evaluating this at x = 2 gives a slope of about -0.24 (rounded to two decimal places).
The equation of the line is usually written in the slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept. Since we know that the line passes through the point (2, 0.40), we can substitute these values into the equation and solve for b. This yields a y-intercept of about 0.88 (rounded to two decimal places).
Therefore, the equation of the tangent line to the curve y = x/(1 + x2) at the point (2, 0.40) is approximately y = -0.24x + 0.88.
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Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule. A(n) = –3 + (n – 1)(–2.2)
The arithmetic sequence A(n) = –3 + (n – 1)(–2.2) yields the first, fourth, and tenth terms as -3, -9.6, and -22.8 respectively when n is substituted with the corresponding term number.
Explanation:The arithmetic sequence described by the rule A(n) = –3 + (n – 1)(–2.2) can be used to find specific terms of the sequence. To find the first term, plug in n = 1 into the formula to get A(1) = -3 + (1 - 1)(-2.2) = -3. The fourth term can be found by plugging in n = 4 which yields A(4) = -3 + (4 - 1)(-2.2) = -9.6. The tenth term is calculated as A(10) = -3 + (10 - 1)(-2.2) = -22.8. Therefore, the first, fourth, and tenth terms are -3, -9.6, and -22.8 respectively.
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Max is observing the velocity of a runner at different times. After one hour, the velocity of the runner is 5 km/h. After two hours, the velocity of the runner is 3 km/h.
Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the cyclist at different times. Show your work and define the variables used. (5 points)
Part B: How can you graph the equations obtained in Part A for the first 4 hours? (5 points)
Which of the following inequalities matches the graph?
graph of an inequality with a solid vertical line through the point negative 7, 0 and shading to the left of the line
if the lines a and b in the diagram below are parallel why do angles 1 nd 8 measure 120 degree angles
A) Because they are alternate interior angles.
B) Because they are corresponding angles.
C) Because they are alternate exterior angles.
D) Because they are same-side interior angles.
If g is the variable, which mathematical sentence expresses the information below? "The number of gallons of gas in the tank plus 7 more adds up to 12 gallons."
Answer: [tex]g+7=12[/tex]
Step-by-step explanation:
The given statement : The number of gallons of gas in the tank plus 7 more adds up to 12 gallons.
Given variable : 'g'
if g represents the number of gallons of gas in the tank, then for the given statement we have the following expression:-
[tex]g+7=12[/tex]
Hence, the mathematical sentence expresses the given information :-
[tex]g+7=12[/tex]
What is the value of x 20 35 60 70
Answer:
Value of x is:
20
Step-by-step explanation:
Clearly, the two angles are vertically opposite
and vertically opposite angles are always equal
So, x+40=3x
Subtracting both sides by x, we get
x+40-x=3x-x
i.e. 40= 2x
Dividing both sides by 2, we get
x = 20
Hence, Value of x is:
20
For a fixed amount of gas at a constant temperature, the volume of the gas is inversely proportional to its pressure. The function v=18000/p relates the volume in cubic inches and pressure in pounds per square inch of a gas. What is the volume when the pressure is 900 pounds per square inch?
Answer:
Volume of the gas is 20 cubic inches.
Step-by-step explanation:
Inverse proportion: Let x and y be two quantities are said to be inverse proportion or inversely proportional if one quantity increases at the same rate the other decreases.
[tex]x \propto \frac{1}{y}[/tex] or
[tex]x = \frac{k}{y}[/tex] ⇒[tex]k =xy[/tex] where k is constant.
Since, it is given that the volume of gas is inversely propotional to its pressure.
Given the function:
[tex]v = \frac{18000}{p}[/tex] ......[1] ; where volume in cubic inches and pressure in pounds per square.
To find the volume in cubic inches.
The pressure (p) = 900 pounds per square inch.
Substitute the value of p in [1];
[tex]v = \frac{18000}{900}= 20 in^3[/tex]
Therefore, the volume(v) = 20 cubic inches when the pressure is 900 pounds per square inch.
The volume when the pressure is 900 pounds per square inch is [tex]20 in^3.[/tex]
What is proportionality?proportionality can be explained as equality between two ratios, it gives relationship that is always in the same ratio.
We were given the function as[tex]v= \frac{18000}{p}[/tex]
But the pressure is given as pressure (p) = 900 pounds per square inch.
We can get volume, if we substitute "p" as;
[tex]v=\frac{18000}{p}[/tex]
[tex]V= \frac{18000}{900} =20 in^3.[/tex]
Hence, the volume when the pressure is 900 pounds per square inch is [tex]20 in^3.[/tex]
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The table and the graph below each show a different relationship between the same two variables, x and y:
How much more would the value of y be on the graph than its value in the table when x = 12?
Please just help me understand, do not give me the answer! thank you
A regular octagon rotates 360° about its center. How many times does the image of the octagon coincide with the preimage during the rotation?