A group of 40 students from your school is part of the audience for a TV game show. The total number of people in the audience is 120 . What is the theoretical probability of 5 students from your school being selected as contestants out of 10 possible contestant spots?
Using the hypergeometric distribution, it is found that there is a 0.1363 = 13.63% theoretical probability of 5 students from your school being selected as contestants out of 10 possible contestant spots.
What is the hypergeometric distribution formula?The formula is:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.The values of the parameters are given as follows:
N = 130, k = 40, n = 10.
The theoretical probability of 5 students from your school being selected is P(X = 5), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 5) = h(5,120,10,40) = \frac{C_{40,5}C_{80,5}}{C_{120,10}} = 0.1363[/tex]
0.1363 = 13.63% theoretical probability of 5 students from your school being selected as contestants out of 10 possible contestant spots.
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Jose wants to find the perimeter of triangle ABC. He uses the distance formula to determine the length of AC. Finish Jose’s calculations to find the length of AC.
What is the perimeter of triangle ABC? Round the answer to the nearest tenth, if necessary.
12.0 units
12.4 units
15.0 units
15.4 units
Answer:
15 units
Step-by-step explanation:
15.0
make r the subject and find the value
[tex]~~~~~~~~\dfrac{1}{R} = \dfrac{1}{R_1} + \dfrac 1{R_2}\\\\\\\implies \dfrac 1{R_2} = \dfrac{1}{R } - \dfrac 1{R_1}\\\\\\\implies \dfrac 1{R_2} = \dfrac{R_1 -R}{RR_1}\\\\\\\implies R_2 = \dfrac{RR_1}{R_1-R}\\\\\\\text{When}~ R= 24~ \Omega ~ \text{and}~ R_1 = 30~ \Omega,\\\\R_2 = \dfrac{24 \times 30}{30-24}~\Omega\\\\\\~~~~~=\dfrac{720}{6}~ \Omega\\\\\\~~~~= 120~ \Omega[/tex]
How to find the sum of these terms. 1. 5x,12x,9x
2. -5x,19x,-7x
Answer:
just solve normally as if theres no x,
1. 26x
2. -7x
There are square tiles arranged in a pattern. the pattern has rows that are 5 tiles wide and an unknown number of rows. if you take these tiles and add one additional tile, you can create a pattern that has rows that are 3 tiles wide, with 3 more total rows than the original pattern. how many are in the original pattern?
An equation is formed of two equal expressions. The number of rows in the original pattern will be 4.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let the number of rows be represented by x. Now, the pattern has rows that are 5 tiles wide and an unknown number of rows. if you take these tiles and add one additional tile, you can create a pattern that has rows that are 3 tiles wide, with 3 more total rows than the original pattern. Therefore, we can write,
(Number of Tiles before) + 1 tile = (Number of Tiles afterward)
5x + 1 = 3(x+3)
5x + 1 = 3x + 9
5x - 3x = 9 - 1
2x = 8
x = 4
Hence, the number of rows in the original pattern will be 4.
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Use the following triangles to determine the trig ratios below simplify all fractions rationalize and simplify all radicals and convert all decimals answers to fractions
STATISTICS in a recent year the mean score on the mathematics section of the SAT test was 515 and the standard deviation was 114. This means that people within one deviation of the mean have SAT math scores that are no more than 114 points higher or 114 points lower than the mean A. write an absolute value inequality to find the range of SAT mathematics test scores within one standard deviation of the mean B. what is the range of SAT mathematics test scores 12 standard deviation from the mean?
An absolute value inequality to find the range of SAT mathematics test scores within one standard deviation of the mean is; |x – 515| ≤ 114
How to Write Inequalities?
A) We are told that;
Mean score = 515
Standard deviation = 114
We are now given that people within one deviation of the mean have SAT math scores that are no more than 114 points higher or 114 points lower than the mean. Thus, the absolute value inequality is;
|x – 515| ≤ 114
B) The range of scores to within ±2 standard deviations of the mean is;
Range = 515 ± 2(114)
Range = 287 to 743
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what is the median of this data set
Answer:
8
Step-by-step explanation:
The median is the number right in the middle. Eight is in the middle of the number line making it the median.
Given the graph of the function below, which of the following is the graph of it's inverse?
The inverse of the graph is (b)
How to determine the inverse?To determine the inverse of the graph, we have to swap the x and the y axes.
This means that we plot the y coordinates on the x coordinates and vice versa.
The interpretation of this on the given curve is that:
The vertical curve becomes an horizontal curve (as seen in graph b)
Hence, the inverse of the graph is (b)
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Part B
What is the area of the target that earns at least 30 points on a throw?
Select the correct from the drop-down menu.
the area is ____ square inches.
a) 16
b) 49
c) 121
d) 144
The area of the target which earns 30 points on a throw.
Solution:[tex]\huge\boxed{Formula: a= \pi{r}^{2}}[/tex]
[tex]4+3[/tex]
[tex]=7[/tex]
Let's solve
We have to find the answer in terms of π so, we'll just have to multiply the radius by itself.
[tex]a={7}^{2}[/tex]
[tex]\large\boxed{a= 49 \pi\: {in}^{2}}[/tex]
Hence, the area of the target which earns 30 points on a throw is 49π square inches.
Answer= Option B
Which of the following is the solution of 5x - 6 = 44?
O x= -10
38
Ox=
x = -5
O x=
Ox-10
Work Shown:
5x-6 = 44
5x-6+6 = 44+6 ... see note 1
5x = 50
5x/5 = 50/5 ... see note 2
x = 10
note1: We add 6 to both sides to undo the -6note2: Divide both sides by 5 to undo the multiplication. Think of 5x as 5*x or "5 times x".The value of a car decreases by 7.2% each year.
When bought the car cost £6200.
Work out how much the car will be worth after one year.
The car will be worth after one year is £ 5753.6.
What is exponential function?An exponential function is defined by the formula f(x) = [tex]a^{x}[/tex], where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.
The exponential function is an important mathematical function which is of the form
f(x) = [tex]a^{x}[/tex]
Where a > 0 and a is not equal to 1.
x is any real number.
Given
Car cost when bought A = £ 6200
Value of a car decreases by 7.2% each year.
n = 1
r = 7.2% or 0.072
The car will be worth after one year
[tex]y= A (1-r)^{n}[/tex]
⇒ [tex]y =6200(1-0.072)^{1}[/tex]
⇒ [tex]y = 6200(0.928)[/tex]
⇒ y = £ 5753.6
Hence, the car will be worth after one year is £ 5753.6.
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What is this function written in vertex form? f(x) = (x –1)2 – 7 f(x) = (x 1)2 – 7 f(x) = (x –1)2 – 5 f(x) = (x 1)2 – 5
The vertex form of all expressions is given below.
We have given that the expressions
We have to write the function in vertex form.
What is the vertex form of the equation?
The vertex form of a quadratic function is given by f (x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.
Therefore the first equation
[tex]f(x)=(x-1)^2-7[/tex]
it can be written as
[tex]f(x)=1(x-1)^2+(-7)[/tex]
The second equation can be written as
[tex]f(x) = (x+1)^2 -7[/tex]
vertex for is,
[tex]f(x)=1(x-(-1))^2+(-7)[/tex]
The third equation is,
[tex]f(x) = (x -1)^2 - 5[/tex]
Vertex form is,
[tex]f(x)=1(x-1)^2+(-5)[/tex]
Forth equation is,
[tex]f(x) = (x +1)^2 +(- 5)[/tex]
Vertex form is,
[tex]f(x) =1 (x -(-1))^2 +(- 5)[/tex]
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PLEASE HELP!!! Use the vertical line to test to determine if the relation whose graph is provided is a function
Answer:
This graph does not represent a function.
Step-by-step explanation:
The vertical line test describes how, in order to be a function, there must be only one output for every input. Remember, the input of a function is the "x" value and the output is the "y" value.
Because of the circular nature, this graph does not represent a function. As you can see, there are "x" values which could correspond with mutliple "y" values. For example, when x = 2, there are two "y" values: y = -1 and y = -5.
Can someone please help me figure out these 10th grade geometry arc problems? ANY help appreciated, but please explain how you got your answer! Will reward brainly and 5 stars + thanks!
Answer:
Step-by-step explanation:
Modeling an Equation
Use the algebra tiles to model the equation
2x + 4 = 3x + (−1). Then complete the sentences.
To model 2x + 4, you need:
positive x-tiles to represent 2x.
positive unit tiles to represent 4.
To model 3x + (−1) you’ll need:
3
x-tiles to represent 3x.
1
unit tile to represent –1.
Yes all your used tiles are correct.
Let's solve the equation too
2x+4=3x+(-1)2x+4=3x-14+1=3x-2xx=5The value of variable x in the equation 2x+4=3x+(-1) is 5.
What is equation?Equation is a relationship between two or more variables that are expressed in equal to form. Equation of twwo variable looks like ax+y=c. It cab be linear equation, quadratic equation and cubic equation. linear equation has a straight line curve.
How to solve equation?We have been given equation 2x4=3x+(-1) and we have to solve the equation. Our equation has only one variable, so we have to solve for that variable only.
2x+4=3x+(-1)
2x+4=3x-1
5=x
Hence the value of x in the equation 2x+4=x+(-1) is 5.
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Wren is at the grocery store buying fruit. She buys x pounds of apples for $1.68 per pound. She buys 2 fewer pounds of grapes for $2.48 per pound. The cost of the fruit, before tax, is $13.76. How many pounds of each fruit is she buying?
A.
2.8 pounds of apples and 4.8 pounds of grapes
B.
3.3 pounds of apples and 1.3 pounds of grapes
C.
3.8 pounds of apples and 1.8 pounds of grapes
D.
4.5 pounds of apples and 2.5 pounds of grapes
Answer:
A.
Step-by-step explanation:
Wren is at the grocery store buying fruit. She buys x pounds of apples for $1.68 per pound. She buys 2 fewer pounds of grapes for $2.48 per pound. The cost of the fruit, before tax, is $13.76. How many pounds of each fruit is she buying?
A.
2.8 pounds of apples and 4.8 pounds of grapes
B.
3.3 pounds of apples and 1.3 pounds of grapes
C.
3.8 pounds of apples and 1.8 pounds of grapes
D.
4.5 pounds of apples and 2.5 pounds of grapes
A six-sided die is rolled seven times. What is the probability that the die will show an even number at least six times?
Answer:
Step-by-step explanation:
Explanation
On a 6 sided die, there are three even numbers (2,4,6)
That's 1/2 the number on the die.
So getting 6 even numbers is
P(6) = 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 0.00781
Where did that extra 1/2 come from? Well one of the numbers thrown was an odd number, and it has to be counted.
P(7) = the same answer. 0.00781
Total 0.0156
As seen in the picture. Any help is appreciated :)
Suppose that g(x) = f(x-4). Which statement best compares the grap
g(x) with the graph of f(x)?
The transformation of a function may involve any change. The graph of g(x) is the graph of f(x) shifted 4 units to the right.
How does the transformation of a function happen?The transformation of a function may involve any change.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units, y=f(x+c) (same output, but c units earlier)
Right shift by c units, y=f(x-c)(same output, but c units late)
Vertical shift
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
As per the transformation of the function, if the function g(x) = f(x-4), then the graph of g(x) will be 4 units in the right of f(x).
Hence, the graph of g(x) is the graph of f(x) shifted 4 units to the right.
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Kellie thinks of a number, then doubles the number, and then multiplies the result by 3. If her final number is 65 more than her original number, then what was her original number I will give 70 points pls
Kellie's original number given the analogy and corresponding equation is 13
How to write and solve equation?let
the unknown number = x(x × 2) × 3 = x + 65
2x × 3 = 65 + x
6x = 65 + x
6x - x = 65
5x = 65
divide both sides by 5x = 65/5
x = 13
check:
6x = 65 + x
6(13) = 65 + 13
78 = 78
Therefore, the unknown number, x is 13
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What might the area of the rectangle be?
Answer:
Not enough information to determine the area.
Step-by-step explanation:
Mo buys a house for £120 000
He sells the house for £150 000
Work out the percentage profit that Mo makes.
Answer:
25%Step-by-step explanation:
The profit = 150 000 - 120 000 = 30 000
………………………………………………………
The profit percentage is :
[tex]=\frac{30000}{120000} \times 100=0.25 \times 100 = 25 \%[/tex]
[tex]\huge\fbox\green{question}[/tex]
#Combine the members of the following sets to from new sets.Show the members in diagrams
a)A={Mine,Shine,Hari} and B={Ram,Sita,Dolma}
b)M={3,6,9,12>and N={5,10,15,20}
c)A={Mari,Rahlm,Bishnu}and B={Bishnu, Kishan,Dorge}
d)C={4,8,12,16,20} and F={8,16,24,32}
Refer to the attachment
Can someone else explain how to do problems like this?
The answer is A , for determining range look at Y-axis only from down to up .For this question we can also say
range: [1,7] , if both ends of the line are arrows it means the line goes from negative infinity to positive infinity (which means range is all real numbers) , but if the point is include just like this graph the points will be also include in range , but if the points are an empty circle the points won't be include for writing range
hope it helps
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Find the midpoint of the line segment. (Giving 25 points please hurry)
Answer:
(-4,-3)
Step-by-step explanation:
Answer:
(-4, -3)
Step-by-step explanation:
well, the only points possible are 3 points, a first, 2nd, and 3rd point. And the 2nd point is the mid-point.
an athlete covers a distance of 0.4 km in completing one round . how many rounds does he make if he runs a total of 8.4 km distance ?
Answer:
21 rounds
Step-by-step explanation:
[tex]1[/tex] [tex]round = 0.4km[/tex]
[tex]Total[/tex] [tex]distance = 8.4km[/tex]
[tex]8.4/0.4[/tex]
[tex]=21[/tex]
The number of rounds he makes, if he runs a total of 8.4 km distance.
Solution:[tex]\large\boxed{R=\frac{Total \: distance}{Distance \: covered \: in \: 1 \: round}}[/tex]
So, we'll have to divide the total distance covered by distance covered in 1 round.
Let's substitute according to the formula.
[tex]R= \frac{8.4}{0.4}[/tex]
= 21 rounds
Hence, the number of rounds he makes, if he runs a total of 8.4 km distance is 21
When h is one-half and j is one-third, g is 4. if g varies jointly with h and j, what is the value of g when h is 2 and j is 3? 4 6 24 144
Answer:
D) 144Giveng varies jointly with h and jg = 4 when h = 1/2, j = 1/3To findValue of g when h = 2 and j = 3Joint variation:g = khj, where k- coefficient
Use given values of h and j, and find the value of k:
4 = k*(1/2)(1/3)4 = (1/6)kk = 4*6k = 24The equation is now:
g = 24hjFind the value of g when h is 2 and j is 3:
g = 24*2*3 = 144Correct choice is D
Answer:
D. 144
Step-by-step explanation:
What is the area of a regular hexagon with an apothem 18.5 inches long and a side 21 inches
long? Round the answer to the nearest tenth.
2,331.0 in.²
1,554.0 in.²
1,165.5 in.²
194.3 in.²
The area of a regular hexagon with an apothem 18.5 inches long and a side 21 inches is 1, 165. 5 In²
How to calculate the area of a regular hexagon
The formula is given thus;
Area of hexagon = (1/2) × a × P
where a = the length of the apothem
P = perimeter of the hexagon
Given a = 18. 5 inches
Note that Perimeter, p = 6a with 'a' as side
p = 6 × 21 = 126 inches
Substitute values into the formula
Area, A = 1 ÷2 × 18. 5 × 126 = 1 ÷2 × 2331 = 1, 165. 5 In²
Thus, the area of the regular hexagon is 1, 165. 5 In²
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The Ratio of two numbers is 3/5, and their sum is 104. What are the 2 numbers?
Answer:
39 and 65
Step-by-step explanation:
the ratio of the two numbers is 3 : 5
sum the parts of the ratio, 3 + 5 = 8 parts
divide the sum by 8 to find the value of one part of the ratio
104 ÷ 8 = 13 ← value of 1 part of the ratio , then
3 parts = 3 × 13 = 39
5 parts = 5 × 13 = 65
the two numbers are 39 and 65