The probability that exactly none will graduate is [tex]0.003375[/tex].
What is probability?
Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes.
Step-by-step explanation:
Let [tex]X[/tex] be the random variable for the number of students who graduate.
Binomial distribution theorem tells that, [tex]P(X=x)=C(n , x)p^xq^{n-x}[/tex].
Here [tex]p=[/tex]probability of success on a single trial, [tex]q=[/tex]probability of failure on a single trial, [tex]n=[/tex] number of trials.
Given that [tex]p=0.85, q=1-p=1-0.85=0.15[/tex] and [tex]n=3.[/tex]
[tex]P(X=x)=C(3 , x)0.85^x0.15^{3-x}[/tex]
When [tex]3[/tex] students are randomly selected the probability that exactly none will graduate is given by,
[tex]P(X=0)=C(3 , 0)0.85^00.15^{3-0}[/tex]
[tex]P(X=0)=\frac{3!}{0!(3-0)!} 0.15^{3}[/tex]
[tex]P(X=0)=0.15^{3}[/tex]
[tex]P(X=0)=0.003375[/tex]
Hence the probability that exactly none will graduate is [tex]0.003375[/tex].
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A parallelogram with coordinates A (-2,3) , B (3,3) , (4,6) , and D (-1 , 6) is first rotated 90 degrees clockwise and the. Translated 4 units left and 2 units down to form quadrilateral A’B’C’D’. What is the distance , in units, between point C’ and point D’ in the resulting figure.
The distance between the translated points C and D is 5 units
How to determine the distance between the translated points?From the question, the coordinates are given as
A (-2,3) , B (3,3) , C (4,6) , and D (-1 , 6)
The sequence of transformations is given as
First rotated 90 degrees clockwiseTranslated 4 units left and 2 units downThe above sequence of transformations are rigid transformations.
This means that the lengths are preserved
In other words,
CD = C'D'
So, we have the distance to be
Distance = √[(x₁ - x₂)² + (y₁ - y₂)²]
Where
(x, y) = C (4,6) , and D (-1 , 6)
So, we have
Distance = √[(4 + 1)² + (6 - 6)²]
Evaluate
Distance = 5
Hence, the distance is 5 units
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-4, 0, -2/3, 4.11111…, 2, π, √6 which are integers?
Integer Numbers
It can be defined as the number that can be written without a fractional (decimal) component.
Integers can be positive, negative, or 0.
From the numbers on the list only -4, 0, and 2 are integers. The rest of the numbers cannot be written without a decimal component.
For example:
-2/3 = -0.666
π = 3.14
The square root of 6 is 2.45
4.111... has an evident decimal component.
Answer: -4, 0, and 2
I need help ASAP
write an equitation of the line shown
The equations of the lines are:
7. y = 3/2x - 3/2
8. y = -1/3x - 8/3
What is the Equation of a Line?The equation that represents a line, in slope-intercept form is, y = mx + b.
Slope of the line = m = rise/run or change in y / change in x.Y-intercept of the line = b = the point where the line intercepts the y-axis.7. Find the slope (m) between (5, 6) and (1, 0):
Slope (m) = (6 - 0)/(5 - 1) = 6/4
Slope (m) = 3/2
Find the y-intercept of the line, b, by substituting m = 3/2 and (x, y) = (1, 0) into y = mx + b:
0 = 3/2(1) + b
-3/2 = b
b = -3/2
To write the equation, substitute m = 3/2 and b = -3/2 into y = mx + b:
y = 3/2x - 3/2
8. Find the slope (m) between (-5, -1) and (1, -3):
Slope (m) = (-1 -(-3))/(-5 - 1) = 2/-6
Slope (m) = -1/3
Find the y-intercept of the line, b, by substituting m = -1/3 and (x, y) = (1, -3) into y = mx + b:
-3 = -1/3(1) + b
-3 = -1/3 + b
-3 + 1/3 = b
-8/3 = b
b = -8/3
To write the equation, substitute m = -1/3 and b = -8/3 into y = mx + b:
y = -1/3x - 8/3
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I used 999 sheets of toilet paper each day for 777 days. The roll had 969696 sheets when it was new. How many sheets of toilet paper have not been used? please get the answer right
The number of sheets of toilet paper that have not been used is 193473.
What is multiplication?Multiplication simply has to do with the product of numbers.
From the information, the roll had 969696 sheets when it was new and the person used 999 sheets of toilet paper each day for 777 days.
Therefore, the sheet left will be:
= Number in the new roll - Sheets used
= 969696 - (777 × 999)
= 969696 - 776223
= 193473
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Which ordered pair is a solution to the system of linear equations?
2x + 3y= 6
–3x + 5y = 10
(0,2)
(2,0)
(3,2)
(2,3)
The solution of the system of linear equations 2x + 3y = 6 and -3x + 5y = 10 is (0, 2).
Linear equation:
Linear equation refers an equation in which the highest power of the variable is always 1. It is also called as a one-degree equation.
Given,
Here we have the following system of linear equations.
2x + 3y = 6
-3x + 5y = 10
Now, we need to find the solution for the equations.
Here we have to use the substitution method to solve this one,
To do the substitution method we have to follow the following steps:
Step 1) Solve anyone of the equations either for the variable x or y
Step 2) Now, substitute the value obtained from step 1 to the other equation
Step 3) Finally, solve the equation to find the value of the remaining variable.
Here we have to take the equation (2), and we have to solve it for the value of y,
For that we have to rewrite the equation as,
5y = 10 + 3x
y = (10 + 3x)/5
Apply the value of y on the equation (1), in order to get the value of x,
So,
2x + 3(10 +3x)/5 = 6
2x + (30 + 9x)/5 = 6
(10x + 9x + 30)/5 = 6
19x + 30 = 30
19x = 0
x = 0
Now, apply the value of x on the equation in order to get the value of y,
y = (10 + 3(0))/5
y = 10/5
y = 2.
Therefore, the resulting ordered pairs for the system of linear equation is (0, 2).
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Find a translation that has the same effect as the composition of translations below. T(5.3) (X,Y) followed by T -3,6) (X,Y) Choose the correct answer below. c A. (x,y)=(x + 2,y - 3) O B. (x,y)=(x + 2 y + 9) o C. (x,y)=(x + 8.y + 9) O D. (x,y)—(X + 8.y-3)
letter D is the answer
In 17.2 seconds, a shopping cart is pushed 15.6 meters towards the west. What is the velocity of the cart? A. 1.6 m/s East B. 0.9 m/s West C. 1.1 m/s West D. 1.6 m/s West c
We have that:
[tex]\text{velocity}=\frac{\text{distance}}{\text{time}}[/tex]then, in this case, we have:
[tex]\begin{gathered} d=15.6m \\ t=17.2s \\ v=\frac{d}{t} \\ \Rightarrow v=\frac{15.6m}{17.2s}=0.90\frac{m}{s} \\ v=0.9\frac{m}{s} \end{gathered}[/tex]therefore, the velocity of the cart is 0.9 meters per second.
In Central city, there are 29,791 registered voters and 93 voting centers. Each voting centers serves about _____ of the city's population, what's the answer?
If in Central city, there are 29791 registered voters and 93 voting centers, then each voting centers serves about 320 of the city population.
Total number of registered voters in Central city = 29791 voters
Total number of voting centers = 93 voting centers
The number of population serves by each center = Total number of registered voters in Central city ÷ Total number of voting centers
Substitute the values in the equation
The number of population serves by each center = 29791/93
= 320.33
≈ 320
Hence, If in Central city, there are 29791 registered voters and 93 voting centers, then each voting centers serves about 320 of the city population.
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60 pointsssssssss
algebra 1
Answer:
-16
Step-by-step explanation:
fog(18)=f(g(18))
g(18)=[tex]\sqrt{18-9} =\sqrt{9} =3[/tex]
f(3)=-8(3)+8
=-16
Simplify the expression: 2v - 7 - 12v + 15
Hey there!
2v - 7 - 12v + 15
COMBINE the LIKE TERMS
= (2v - 12v) + (-7 + 15)
= 2v - 12v - 7 + 15
= -10v + 8
Therefore, your answer should be:
-10v + 8
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
9. Determine whether the following graph is a function or a relation.
Answer: Relation
Step-by-step explanation: it is a relation because if you take any number on the x axis and look at its points there are two points on multiple parts
make k the subject
2A= πK^2 +3t
Answer:
k = ± [tex]\sqrt{\frac{2A-3t\p}{\pi } }[/tex]
Step-by-step explanation:
2A = πk² + 3t ( subtract 3t from both sides )
2A - 3t = πk² ( isolate k² by dividing both sides by π )
[tex]\frac{2A-3t}{\pi }[/tex] = k² ( take square root of both sides )
± [tex]\sqrt{\frac{2A-3t}{\pi } }[/tex] = k
A test is worth 100 pts. Each problem is worth either 2 or 5 pts. The number of 5 pt problems is 22 less than 2pt problems. How many problems of each type are on the test
The number of two pt problems are 30 and 5 pt problems are 8.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let x= one type of question
Let x-22= the other type of questions
100=2x+5(x-22) Distribute
100=2x+5x-110
100=7x-110
100+110=7x
210=7x
Divide both sides by 7
one type 30=x
second type 30-22=8
Hence the number of two pt problems are 30 and 5 pt problems are 8.
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Select all ratios equivalent to 8:4
4:2. 14:7. 5:10
Answer:
4:2 and 14:7
Step-by-step explanation:
The ratios equivalent to 8:4 would be:
4:2
14:7
5:10 wouldn't be equivalent because if you simplify that, it is 1/2 and if you simplify 8/4, it is 2. 1/2 and 2 are not the same.
:D
Answer:
They are all equivalent except for 5:10
Step-by-step explanation:
You can write ratios as fractions
[tex]\frac{8}4}[/tex] [tex]\frac{4}{2}[/tex] [tex]\frac{14}{7}[/tex] [tex]\frac{5}{10}[/tex] If I simplify each fraction, I can see that they all equal 2 expect for the the last one.
2 2 2 1/2
Determine the length of the line segment shown.
graph of line segment from negative 6 comma negative 5 to 0 comma 3
100 units
25 units
10 units
8 units
The length of the line segment will be 10 units.
What is Distance?
The distance between two points (x₁ , y₁) and (x₂, y₂) is defined as;
D = √( y₂ - y₁)² + (x₂ - x₁)²
Given that;
Two endpoints of the line segment are (6, -5) and (0, 3).
Now,
The length of the line segment is distance between two endpoints (6, -5) and (0, 3).
So, The distance between two endpoints (6, -5) and (0, 3) is calculated as;
D = √(0 - 6)² + (3 - (-5))²
D = √36 + 64
D = √100
D = 10 units
Thus, The length of the line segment will be 10 units.
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Jeremiah keeps a record of how many pages he reads each day. He read 40% fewer pages today than yesterday. If he read 90 pages today, how many pages did he read yesterday?
Answer:
126
Step-by-step explanation:
90 ÷ 10 = 9
9 × 4 = 36
90 + 36 = 126
Find y please help me !
Answer:
y = 5
Step-by-step explanation:
since the triangles are congruent then corresponding sides are congruent, so
AB = CD , that is
7y = 3y + 20 ( subtract 3y from both sides )
4y = 20 ( divide both sides by 4 )
y = 5
Please help I will give brainliest
The value of x in the triangle is 3.
How to find the angles in a triangle?The exterior angle of the triangle is VBC.
Using the exterior angle theorem, the value of x can be found in the triangle.
The exterior angle theorem states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.
In other words, an exterior angle of a triangle is equal to the sum of the two opposite interior angles.
Therefore,
m∠D = 9x - 2
m∠C = 40°
m∠VBC = 20x + 5
Hence,
20x + 5 = 9x - 2 + 40
20x + 5 = 9x + 38
20x - 9x = 38 - 5
11x = 33
x = 33 / 11
x = 3
Therefore,
x = 3
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H(x)=-5/6x;h(x)=10
Find the value of x so that the function has the given value
The value of x = -12.
Define Function.
A special relationship where each input has a single output. It is often written as "f(x)" where x is the input value. Example: f(x) = x/2 ("f of x equals x divided by 2")
The given expression is
H(x)=-5/6 x
also, H(x) = 10
so, put H(x) value in given expression,
10 = -5/6 x
Now, solve for 'x'
-5x = 60
x = 60/(-5)
x = -12
Therefore, the value of x = -12
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suppose we want to choose 2 letters without replacement from four letters ABCD. (A)how many ways can the speed on if the order of choices is taken into consideration?(B) how many ways can this be done if the order of choices is not taken into consideration ?
A)
If the order of choice is taken into consideration, we consider four possibilities for the first choice and three for the second. Then the total number of ways is given by:
[tex]4\cdot3=12[/tex]B)
If the order of choices is not taken into consideration, we must divide the the previous result by 2, which is the total number of ways by which we can organize two letters (ex: AB and BA):
[tex]\frac{12}{2}=6[/tex]PLEASE HELP DUE SOON!!!
The volume of blocks = 27n³cm3.
volume of the cube box = 216n⁹ cm3.
Solution:Here given,
6n³cm is the length of the cube-shaped box's side.
3n cm is the side length of the cube-shaped blocks.
We must calculate the volume of the box and the blocks.
The formula for cube volume is,
S³ = V
where s is the cube's side length
by substituting the values,
(6n³)³ cm3 box volume
= 216 n⁹ cm³
(3n)³ cm3 is the volume of the blocks.
= 27n³ cm³
As a result, the volume of the blocks is 27n³cm3 and the volume of the box is 216 n⁹ cm³.
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Answer:
A) Volume of one block = 27n³ cm³
Volume of the box = 216n⁹ cm³
B) 8n⁶ blocks will fit in one box.
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{4 cm}\underline{Volume of a cube}\\\\$V=s^3$\\\\where:\\ \phantom{ww}$\bullet$ $V$ is the volume. \\\phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}[/tex]
Part AThe side length of the cube-shaped block is 3n cm.
Substitute the given side length into the formula to find the volume of the block:
[tex]\begin{aligned}\implies \textsf{Volume of one block}&=(3n)^3\\&=3^3 \cdot n^3\\&=27n^3\;\sf cm^3\end{aligned}[/tex]
The side length of the cube-shaped box is 6n³ cm.
Substitute the given side length into the formula to find the volume of the box:
[tex]\begin{aligned}\implies \textsf{Volume of one box}&=(6n^3)^3\\&=6^3 \cdot (n^3)^3\\&=216n^9\; \sf cm^3\end{aligned}[/tex]
Part BTo find the number of blocks that will fit in the box, divide the volume of the box by the volume of one block:
[tex]\begin{aligned}\implies \textsf{Number of blocks}&=\dfrac{\textsf{Volume of box}}{\textsf{Volume of block}}\\\\& = \dfrac{216n^9}{27n^3}\\\\&=\dfrac{216}{27} \cdot \dfrac{n^9}{n^3}\\\\&=8 \cdot n^{9-3}\\\\&=8n^6\end{aligned}[/tex]
*IMAGE ATTACHED* (What’s the perimeter of the shaded figure below?
Answer:
The perimeter is 12 units.
Step-by-step explanation:
The answer would be 12 units because each side is 1 unit. If you count all the sides together, you get 12 units.
Answer: 12 units
Step-by-step explanation:
The perimeter is the length around a 2D shape. We will count the units that make up this shape's outline. See attached. Please note that as long as you count every side for this shape, it doesn't matter the order you count.
The perimeter is 12 units, the last option.
The length of a piece of paper is 11 inches. What is the length of the paper in
centimeters?
(1 inch = 2.5 centimeters).
Answer:
Length in inches → 11
1 inch = 2.5 centimeters
Length in Centimetres → 11 × 2.5 → 27.5 cm
Solve the following system of equations by graphing. If this system is inconsis
identify the type of constraint.
y = 4x + 4
-12x + 3y = 3
Answer:
Inconsistent: parallel lines.
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}y=4x+4\\-12x+3y=3\end{cases}[/tex]
Use arithmetic operations to isolate y in the second equation:
[tex]\implies -12x+3y+12x=3+12x[/tex]
[tex]\implies 3y=12x+3[/tex]
[tex]\implies\dfrac{3y}{3}=\dfrac{12x}{3}+\dfrac{3}{3}[/tex]
[tex]\implies y=4x+1[/tex]
Therefore, we can see that both equations have the same slope and so the graphs of these equations are parallel.
The solution to a system of linear equations is the point of intersection.
As parallel lines never intersect, there are no solutions to this system and the system is said to be inconsistent.
Which equation does not represent a linear function?
a. y = 8x
by = ½x+2
c. y=0.5x - 1
d. y = 2x³
Answer:
d. y= 2x³
Step-by-step explanation:
All of the other equations represent linear functions, and are in the form y = mx + b. D on the other hand contains an exponent, making it a non-linear (in this case cubic) function.
Number One in the photo provided
a. np = 8.91 and nq = 18.09 where n = 27 and p = 0.33
b. np = 3.75 and nq = 21.25 where n = 25 and p = 0.15
c. np = 9.68 and nq = 34.32 where n = 44 and p = .22
Solution:a. Given n = 27
p = 0.33
np = 27 x 0.33
= 8.91
nq = 27 x (1 - 0.33)
= 18.09
For the approximation of binomial distribution, the sample size must be greater than 10 for both the products np and n(1-p) to approximate the binomial distribution by a normal distribution.
Since here np < 10 approximation is not applicable.
μp = np = 27 x 0.33
= 8.91
σp = √npq = √(27)x (.33) x (1 - 0.33)
= 2.443
b. n = 25 and p = 0.15
np = 25 x 0.15
= 3.75
nq = 25 x (1 - 0.15)
= 21.25
Approximation is not possible because np < 10.
c. n = 44 and p = .22
np = 44 x 0.22
= 9.68
nq = 44 x (1 - 0.22)
= 34.32
Since here np< 10 approximation is not possible.
μp = np = 44 x 0.22
= 9.68
σp =√npq = √(44)x (.22) x (1 - 0.22)
= 2.747
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Question
Evaluate the expression when k = 3 and j = 10.
(5k−j)2+2k
Responses
80
80
45
45
31
31
20
Answer:
31Step-by-step explanation:
Given Expression (5k − j)² + 2kEvaluateWhen k = 3, j = 10SolutionSubstitute and calculate:
(5k − j)² + 2k = (5*3 - 10)² + 2*3 = (15 - 10)² + 6 = 5² + 6 = 25 + 6 = 31
Loule and Nicky were asked to find point P that divides the directed line segment FG so that the ratio of FP to PG is 4 to 1. Loule says the coordinate of point P is (-4,-4), while Nicky says the coordinate of point P is (2, 5). Who is correct? Describe the mistake that was made by the student who was incorrect
Using ratio and proportion, Louie is correct.
Ratio is defined as the relationship between two quantities. On the other hand, proportion is defined as the equality between two or more ratios.
From the given graph (see attached photo), the coordinates of Point F and Point G is (4, 8) and (-6, -7).
If the ratio of FP to PG is 4 to 1, then the ratio of the horizontal distance and vertical distance between the two endpoints is also 4 to 1.
FP : PG = 4 : 1
FP/PG = 4/1 = 4
x-coordinate of P
(4 - x)/(x - -6) = 4
(4 - x) = 4(x + 6)
4 - x = 4x + 24
-5x = 20
x = -4
y-coordinate of P
(8 - y)/(y - -7) = 4
(8 - y) = 4(y + 7)
8 - y = 4y + 28
-5y = 20
y = -4
Hence, the coordinates of Point P is (-4, -4).
Therefore, Louie is correct, while Nicky is mistaken probably while setting up the proportion and solving for the coordinates.
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Write an equation in point-slope form for the line through the two points. Then change it toslope-intercept form. Rewrite the equation in standard form.10. (1, 2) and (3, 12)11. (6, 2) and (-2,-2) 12. (4,1) and (1,4)Please help I have sooo many assignments (:
For the point 13. we have that the line passes through the points (-1,-2) and (0,1) then the slope is
[tex]m=\frac{-2-1}{-1-0}=\frac{-3}{-1}=3[/tex]and the line equation will be:
[tex]y-1=3x\Rightarrow y=3x+1[/tex]For the point 14: we have that the line passes through the points (-1,0) and (0,-1) then the sslope is:
[tex]m=\frac{-1-0}{0-(-1)}=\frac{-1}{1}=-1[/tex]and the line equation will be:
[tex]y=-1(x-(-1))\Rightarrow y=-x-1[/tex]For the point 15: the line equation is y=-3 because the y coordinate will be always the same (-3) and the slope of the line will be equal to zero
when the proper fraction $\frac{n}{37}$ is written as a repeating decimal, the sum of the first $40$ digits to the right of the decimal point is $236$. what is $n$?
A decimal is a number that is divided into two parts: a whole and a fraction. Between integers, decimal numbers are used to express the numerical value of complete and partially whole quantities.
n/37=236n=1111 /37 =0.2972972972972972972972972972972972972972
What is decimal?The accepted method for representing both integer and non-integer numbers is the decimal numeral system. It is the expansion of the Hindu-Arabic numeral system to non-integer values. Decimal notation is the term used to describe the method of representing numbers in the decimal system.
A decimal is a number that is divided into two parts: a whole and a fraction. Between integers, decimal numbers are used to express the numerical value of complete and partially whole quantities.
A fraction expressed in a particular way is called a decimal. As an alternative to expressing 1/2, you might write 0.5 instead, with the zero in the ones place and the five in the tenths position.
n/37=236n=1111 /37 =0.2972972972972972972972972972972972972972
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