Given:
The function used to compute the probability of x successes in n trials, when the trials are dependent.
Required:
To choose the correct option for the given statement.
Explanation:
The hypergeometric distribution is a discrete probability distribution. It is used when you want to determine the probability of obtaining a certain number of successes without replacement from a specific sample size.
Therefore the option c is correct.
Final Answer:
c ) hypergeometric probability function.
A survey of 100 high school students provided thisfrequency table on how students get to school:Drive toTake theGradeWalkSchoolbusSophomore2253Junior13202Senior2555Find the probability that a randomly selected studenteither takes the bus or walks.[?P(Take the bus U Walk)
Let's call the event of a student taking the bus as event A, and the event of a student walking as event B. The theoretical probability is defined as the ratio of the number of favourable outcomes to the number of possible outcomes. We have a total of 100 students, where 50 of them take the bus and 10 of them walk. This gives to us the following informations:
[tex]\begin{gathered} P(A)=\frac{50}{100} \\ P(B)=\frac{10}{100} \end{gathered}[/tex]The additive property of probability tells us that:
[tex]P(A\:or\:B)=P(A)+P(B)-P(A\:and\:B)[/tex]Since our events are mutually exclusive(the student either walks or takes the bus), we have:
[tex]P(A\:and\:B)=0[/tex]Then, our probability is:
[tex]P(A\cup B)=\frac{50}{100}+\frac{10}{100}-0=\frac{60}{100}=\frac{3}{5}[/tex]The answer is:
[tex]P(Take\:the\:bus\cup Walk)=\frac{3}{5}[/tex]are figures A and B congruent? explain your reason
Instructions: Complete the following table, computing each students' mean, median, mode, and range: Math Test Scores ( picture attached ) What is the mean score for Test 2? What is the mode of Test 7? ________What is the median score of Test 4? ________What is the range of Test 6? ________
The completed worksheet is the following:
This worksheet involves three measures of central tendency: Mean, Median, Mode and Range
Mean: To get the mean of a dataset, add up all the data and divide by the number of datum (or inputs)
Median: To get the median of a dataset, sort the data in ascending order, and choose the central datum.
For example, if you have a dataset with 7 inputs, sort it in ascending order and select the 4th datum, as there would be 3 values above and 3 below (Hence it being the central datum).
Mode: The mode is the most repeated value of a dataset.
Range: The range is the difference between the biggest and smallest values of a dataset.
10 ft to 8 ft The percent of change is
The percent of change is computed as follows:
[tex]\text{percent of change = }\frac{new\text{ value }-previous\text{ value}}{previous\text{ value}}\cdot100[/tex]Substituting with data:
[tex]\begin{gathered} \text{ percent of change = }\frac{8-10}{10}\cdot100 \\ \text{ percent of change =}-20\text{ \%} \end{gathered}[/tex]need help asap look in file attached
Answer:
length: 21 cm
width: 16 cm
Step-by-step explanation:
. A rectangle has two lengths and two widths, or two sides that are vertical (up and down) and two sides that are horizontal (left and right)
. In order to find the perimeter we must add up all four side lengths.
. You can find the perimeter of a rectangle by adding the length and the width then multiplying by 2, because there are two of each side length.
P = 2(l+w)
In the question the perimeter is given, which is 74.
We can divide 74 by 2 so that we can find the sum of the length and width.
74/2 = 37
l + w = 37
In the question is states that the length is 5 inches longer than the width.
l = (5 + w)
There are two widths and two lengths in a rectangle, the measurement of the two lengths is 5 inches longer than the two widths.
5 + w + w = 37
5 + 2w = 37
Now that we have our equation we can solve for w, or the width.
1. Move the term containing the variable to the left
5 + 2w = 37
2w + 5 = 37
2. Subtract 5 from both sides of the equation, the opposite of adding 5
2w + 5 = 37
2w + 5 - 5 = 37 - 5
2w = 32
3. Divide by 2 in both sides of the equation, the opposite of multiplying 2
2w = 32
2w/2 = 32/2
4. Cancel out the 2s on the left, but leave the x
2w/2 = 32/2
w = 16
So, now that w, or the width = 16, we can find the length:
l = 5 + w
l = 5 + 16
l = 21
You can check your answer by plugging in our values into the original perimeter formula:
P = 2(l+w)
P = 2(21 + 16)
P = 2(37)
P = 74, so my answer is correct, because 74 is the perimeter given in the question.
Derek has $20 to spend on used books, but he can not spend all $20.Hardcover books cost $5 each and paperbacks cost $2 each. Create aninequality which determines the number (x) of hardcover books and the number(y) of paperback books he can buy.
Given:
The amount to spend on books, T=$20.
The cost of a handcoverbook, m=$5.
The cost of a paperback, n=$2.
Let x be the number of handcover books and y be the number of paperback books.
It is said that the complete amount of $20 cannot be spend.
So, the inequality to determine x and y can be written as,
[tex]\begin{gathered} T>mx+ny \\ 20>5x+2y \end{gathered}[/tex]So, the inequality is 20>5x+2y.
A group of 38 people are going to an amusement park together. They decide to carpool to save fuel. If seven people can fit in each car, how many cars do they need to take on the outing? [?] cars 3
So, the number of people = 38
7 people can fit in a one car
so, to find the number of cars divide 38 by 7
So, the number of cars = 38/7 = 5.4
But the number of cars must be integer
so, the number of cars = 6 cars
The answer is 6 cars
the ratio of the length to the width of a rectangular hall is 5:3. if the width is 1500cm, find the lenght.
Step-by-step explanation:
The ratio of the length to the width that is- length:width = 5:3
Take x as a common value,
5x= length
3x= width
Width of the rectangle= 1500 cm
3x= 1500 cm
x= 1500/3
x= 500 cm
Length of the rectangle= 5x
x=500 cm
Length= 5*500
=2500 cm
Length of the rectangle= 2500 cm
Find all the powers of four in the range of 4 and 1000
[tex]4(3w-2)=8(2w+3)[/tex]
The most appropriate choice for linear equation will be given by -
w = -8 is the required answer
What is linear equation?
At first it is important to know about equation
Equation shows the equality between two algebraic expressions by connecting the two algerbraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Here
[tex]4(3w - 2) = 8(2w+3)\\12w - 8 = 16w+24\\16w - 12w = -8-24\\4w = -32\\w = -\frac{32}{4}\\w = -8[/tex]
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In an arithmetic sequence with a1=-5 and d=-3, which term is -24?The term -24 is the ___th term of the sequence
Given:
[tex]\begin{gathered} a_1=-15 \\ d=-3 \\ a_n=-24 \end{gathered}[/tex]To find:
The value of n.
Explanation:
The nth term formula for the arithmetic sequence is,
[tex]a_n=a_1+(n-1)d[/tex]Substituting the given values we get,
[tex]\begin{gathered} -24=-15+(n-1)(-3) \\ -24=-15-3n+3 \\ -24=-3n-12 \\ -3n=-24+12 \\ -3n=-12 \\ n=4 \end{gathered}[/tex]Thus, -24 is the 4th term of the sequence.
Final answer:
The term -24 is the 4th term of the sequence.
heyy could you help me out with this problem I'm stuck
Since congruent angles are equal
Therefore the two figures are similar
we have
9 / 9 = 2x / x + 4
introduce cross multiplication
9 (2x) = 9(x + 4)
18x = 9*x + 9*4
18x = 9x + 36
collect the like terms
18x - 9x = 36
9x = 36
divide boths sides by 9
9x / 9 = 36/9
x = 4
The first missing variable is 2x
2 x 4
= 8
The second is x + 4
we have 4 + 4
= 8
m
Alan is putting money into a savings account. He starts with $550 in the savings account, and each week he had $70. Let S represent the total amount of money in the savings account in dollars, and let W represent the number of weeks Allen has been adding money. Write an equation relating S to W. Then use this equation to find the total amount of money in the savings account after 18 weeks.
Equation: S = $70·W + $550
Amount of manoey after 18 weeks: $1810
To solve this, we have two variables, the amount of weeks (W) and savings (S)
Each week, $70 dolars are added to the account. Then we can write this as: $70·W.
Now there is an initial amount of $550. Then we must add that mount to the previous calculation: $70·W + $550
This give us the savings on each week. THen THe complete equation is S = $70·W + $550
Now, to know the savings after 18 weeks, we can replace W = 18 and solve:
[tex]\begin{gathered} S=$70\cdot W+$550 \\ S=70\cdot18+550 \\ S=1260+550=1810 \end{gathered}[/tex]Thus, the savings after 18 weeks is $1810
A-32-10A. 20-C?LBDIn the similaritytransformation of AABCEto AEDF, AABC was dilated bya scale factor of [?], reflectedacross the [ ], and movedthrough the translation [ ].B. 1/23 4F 5 Find the answer to all three missing boxes
To find the scale factor use the next formula:
[tex]sf=\frac{dimension\text{ }new\text{ }shape}{dimension\text{ }original\text{ }shape}[/tex]Use dimension of corresponding sides AB and ED:
[tex]sf=\frac{2}{4}=\frac{1}{2}[/tex]Then, the scale factor is 1/2___________After the dilation the figure is reflected across the y-axis_____________
Then, the triangle is translated one unit to the right and 3 units up [+1,+3] or [1,3]Determine the value of b.
b3 = 343
b = ±114.3
b = ±7
b = 114.3
b = 7
Answer:
(d) b = 7
Step-by-step explanation:
You want the solution to b³ = 343.
SolutionThe equation can be written in standard form and factored according to the factoring of the difference of cubes:
b³ -343 = 0
(b -7)(b² +7b +49) = 0
The solutions to this are the values of b that make the factors 0.
b -7 = 0 ⇒ b = 7
b² +7b +49 = 0 ⇒ b = -3.5 ± i√36.75 . . . . . complex solutions
The one real solution to the equation is b = 7.
__
Additional comment
Every cubic has 3 solutions. Here, two of them are complex. When the only terms in the equation are the cubic term and the constant, there will always be only one real root.
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The equation b^3 = 343 has two valid real solutions: b = 7 and b = -7. Both values satisfy the equation and meet the given condition. Option B.
To determine the value of b, we can solve the equation b^3 = 343.
Taking the cube root of both sides, we get:
b = ∛343
The cube root of 343 is 7, since 7 * 7 * 7 = 343. Therefore, one solution to the equation is b = 7.
However, it's important to note that the cube root function has a real and complex solution. In this case, b = 7 is the real solution, but there are two additional complex solutions.
Using complex numbers, we can express the other two solutions as follows:
b = -∛343
b = -7
So the complete set of solutions for b is b = 7, -7.
In summary, the equation b^3 = 343 has two real solutions: b = 7 and b = -7. These solutions satisfy the equation and fulfill the condition. So Option B is correct.
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Write the equation of a line containing (3,-7) that is parallel to the line given by the equation -4x+8y=3
Two lines are parallel is they have the same slope. In this case:
[tex]-4x\text{ + 8y = 3}[/tex]Solving the equation for y, and obtaining the slope-intercept equation for the line equation, we have:
[tex]8y\text{ = 3 + 4x}[/tex][tex]y\text{ = }\frac{3}{8}\text{ + }\frac{4}{8}x[/tex]Then,
Select the three expressions that are equivalent to 410
Answer:
A, C, E
Step-by-step explanation:
4^10 = 1048576
A: (4^5)^2 = 1048576
C: 4^20 / 4^10 = 1048576
E: (4^2 x 4^3)^2 = 1048576
help meee pleaseeee pleasee
Answer:
f(x) = (-1/4)x - 5
Step-by-step explanation:
(-8, -3), (-12, -2)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ -2 - (-3) -2 + 3 1 -1
m = ------------ = ------------- = ----------- = --------- = -------
x₂ - x₁ -12 - (-8) -12 + 8 -4 4
y - y₁ = m(x - x₁)
y - (-3) = (-1/4)(x - (-8)
y + 3 = (-1/4)(x + 8)
y + 3 = (-1/4)x - 2
-3 -3
-------------------------------
y = (-1/4)x - 5
I hope this helps!
Find the average value of the following numbers 87, 79, 84, 70, 90
82
Explanation
the average is calculated by dividing the sum of the values in the set by their number.
Step 1
Let
[tex]\begin{gathered} \text{set}=\lbrace87,79,84,70,90\rbrace \\ the\text{ sum of the values is=87+79+84+70+90}=410 \\ n\text{umber of values= 5} \end{gathered}[/tex]Step 2
apply the equation
[tex]\text{Average}=\text{ }\frac{the\text{ sum of the values}}{\nu mber\text{ of values}}=\frac{410}{5}=82[/tex]so, the answer is 82
Find the absolute change and the percentage change for the given situation 150 increased to 861
Given that 150 is increased to 861
The absolute change formula is
[tex]\text{Absolute Change}=New\text{ value - Old value}[/tex]Where
The new value = 861
The old value = 150
The absolute change is
[tex]\text{Absolute Change}=861-150=711[/tex]Hence, the absolute change is 711
The formula for percentage is
[tex]Percentage\text{ change}=\frac{New\text{ value-Old value}}{Old\text{ value}}\times100\text{\%}[/tex]Substitute the values into the percentage change formula
[tex]\begin{gathered} Percentage\text{ change}=\frac{New\text{ value-Old value}}{Old\text{ value}}\times100\text{\%} \\ Percentage\text{ change}=\frac{861-150}{150}\times100\text{\%} \\ Percentage\text{ change}=\frac{711}{150}\times100\text{\%}=4.74\times100\times=474\text{\%} \\ Percentage\text{ change}=474\text{\%} \end{gathered}[/tex]Hence, the percentage change is 474% increase
There are 9,321 leaves on a tree. Explain why the digit 3 stays the same when9,321 is rounded to the nearest hundred.
To round the nearest hundred the digit in the hundred column and test digit in the tens column.
To round the nearest hundred the digit in the hundred column is rounding digit and the digit in the tens column is test digit.
We find the rounding digit in hundred column is 3. Then we look out the test digit 2 to the right of the 3 in the tens column. Because 2<5 we round down and leave the 3 in the hundred column. Then replace the two rightmost digits with 0's.
The 9,321 rounded to the nearest hundred is 9,300.
how do you find the domain in a range of number 2?
The domain is all the x values included in the function, while the range are all the y values included in the function.
Based on the graph:
Answer:
• Domain:
[tex](-\infty,\text{ }\infty)[/tex]• Range:
[tex](0,\infty)[/tex]The shaded triangle has an area of 4 cm?Find the area of the entire rectangleBe sure to include the correct unit in your answer.
Given:
Area of a shaded region of a rectangle is given.
[tex]\text{Area of the triangle=}4cm^2[/tex]Area of the rectangle is twice the area of the triangle given.
[tex]\begin{gathered} \text{Area of a rectangle=2}\times Area\text{ of a triangle} \\ =2\times4 \\ =8cm^2 \end{gathered}[/tex]Jordan wants to use the Starz princess hall, the Dynamic DJ's as his music And Roscoe's for his equipment. If Jordan has a total of $800 and wants the music to play for 4 hours, how many people can Jordan party?
The number of people that can attend Jordan's party would be; 50 people.
What is equation?The equation that represents the total amount that would be spent at the party would be a linear equation. A linear equation increases at a constant rate.
The form of the linear equation will be;
The Total amount = rental fee + (charge per hour of the Dynamic DJ x number of hours he plays) + (cost per person of Roscoe's rentals x number of people)
Now substitute;
$800 = $400 + ($50 x 4) + ($4 x p)
$800 = $400 + $200 + 4p
$800 = $600 + 4p
$800 - $600 = 4p
$200 = 4p
p = $200 / $4
p = 50 people
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I have an image can I show it to you?
Answer:
Rhombus
Explanation:
Looking at the given figure, the correct option is a Rhombus because the figure is a quadrilateral and all of its sides have the same length, opposites sides are parallel and opposite angles are equal.
Which equation represents a line that passes through the two points in thetable?O A. y+3= (x+3)OB. y-3-(x-3)O G. y+3=(x+3)C.OD.y-3-(x-3)X36y35
The first step is to choose one option and rewrite it in the explicit form
I will choose the second option:
[tex]y-3=\frac{2}{3}(x-3)[/tex][tex]y=\frac{2}{3}(x-3)+3[/tex][tex]y=\frac{2}{3}x-2+3[/tex][tex]y=\frac{2}{3}x+1[/tex]Now replace the x points in the equation to verify if it satisfies their respective value in y
For x=3
[tex]y=\frac{2}{3}(3)+1=\frac{6}{3}+1=2+1=3[/tex]For x=3 satisfy y=3
Now x=6
[tex]y=\frac{2}{3}(6)+1=\frac{12}{3}+1=4+1=5[/tex]For x=6 satisfy y=5
So the answer is b.
What it 3 1/8 + 3/4?
The given expression is:
[tex]\begin{gathered} 3\frac{1}{8}+\frac{3}{4}=3\frac{1+6}{8} \\ =3\frac{7}{8} \end{gathered}[/tex]Therefore, the value of the expression is:
3 7/8
.
Please help. I've been trying to answer this question but I haven't been successful.
Equations
It's required to find the value of x that satisfies the conditions of the figure.
We have an equilateral triangle. We know it's equilateral because all of its interior angles have the same measure (look at the tick mark on each angle).
Recall the sum of the interior angles of any triangle is 180°.
If all the interior angles have the same measure, then each angle measures 180/3 = 60°.
One of the angles is assigned an expression of x. We can equate it to 60:
5x - 18 = 60
Adding 18:
5x = 78
Dividing by 5:
x = 78/5
x = 15.6
Answer: I do believe the answer is 15.6. Hope this helps! ^w^
There are 152 students at a small school and 45 of them are freshmen. What fraction of the students are freshmen? Use "/" for the
fraction bar. Do not use spaces in your answer.
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!
Answer:
To find the perimeter of the triangle, you would add p + m + n. To find the area of the triangle you would use (p x m) /2. To find a missing side of the triangle, given that it is a right triangle, you would use p^2 + m^2 = n^2
