Answers
a) This is a discrete probability distribution because the sum of the probabilities is of 1 and each probability is positive.
b) The distribution is represented by Graph A.
c) The mean is of: 1.559.
d) The standard deviation is of: 1.4
e) The probability that a student is involved in three activities is of 0.151.
f) The probability that a student is involved in three or four activities is of 0.28.
What is the probability distribution?From the table, the distribution is presented as follows:
P(X = 0) = 0.332.P(X = 1) = 0.186.P(X = 2) = 0.202.P(X = 3) = 0.151.P(X = 4) = 0.129.The sum of these probabilities is of:
0.332 + 0.186 + 0.202 + 0.151 + 0.129 = 1.
Since the sum is of one and none of the probabilities is negative, this is a valid discrete distribution shown by Graph A, as it associates each valeu of the input with it's respective probability.
The mean of the distribution is the sum of each outcome multiplied by it's probability, hence:
E(X) = 0 x 0.332 + 1 x 0.186 + 2 x 0.202 + 3 x 0.151 + 4 x 0.129 = 1.559.
The standard deviation is the square root of the sum of the differences squared between each outcome and the mean, multiplied by it's probability, hence:
S(X) = sqrt((0-1.559)² x 0.332 + (1-1.559)² x 0.186 + (2-1.559)² x 0.202 + (3-1.559)² x 0.151 + (4-1.559)² x 0.129) = 1.4.
The probabilities are given as follows:
Three activities: P(X = 3) = 0.151.Three or four activities: P(X = 3) + P(X = 4) = 0.151 + 0.129 = 0.28.A similar problem, also featuring a discrete distribution, is presented at brainly.com/question/27899440
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Related Questions
An inequality _________ always opens to the ______________ number.
Answers
Answer:
symbol
greater
Step-by-step explanation:
An inequality symbol always opens to the larger,greater,bigger number.
Examples:
5 > 1
2 > -1
-4 < 0
2 < 3
Answer: An inequality Sign always opens to the smaller number.
Step-by-step explanation:
16 divided by 20 in decimal form
Answers
Answer:
0.8
Step-by-step explanation:
[tex]\frac{16}{20} =\frac{4(4)}{4(5)}=\frac{4}{5}=0.8[/tex]
Answer: 0.8
Step-by-step explanation:
16/20=4/5, which is the equivalent to 0.8
Se divide una suma de Gs. 1.365.000 en tres capitales. Colocados respectivamente al 2%, 3% y 4%, producen el mismo interés simple anual. Calcula dichos capitales
Answers
Los capitales depositados en las cuentas de 2 %, 3 % y 4 % son 630.000, 420.000 y 315.000, respectivamente.
¿Cuántos capitales se deben ingresar en tres cuentas para obtener ganancias por interés simple?
En este problema tenemos el caso de una suma de dinero distribuida y depositada en tres cuentas con tres tasas de interes simple distintas. Existe una tasa de interés simple cuando el interés generado sobre el capital no es acumulativo en el tiempo. El modelo de interés simple es descrito por la siguiente fórmula:
C' = C · (1 + r / 100)
Donde:
C - Capital inicial.C' - Capital final.r - Tasa de interés, en porcentaje.A continuación, describimos la ganancia registrada en cada cuenta tal que produce la misma ganancia:
Cuenta al 2 %:
z = x · (2 / 100)
z = 0.02 · x
0.02 · x - z = 0
Cuenta al 3 %:
z = y · (3 / 100)
z = 0.03 · y
0.03 · y - z = 0
Cuenta al 4 %:
z = (1.365.000 - x - y) · (4 / 100)
z = 54600 - 0.04 · x - 0.04 · y
0.04 · x + 0.04 · y + z = 54600
La solución de este sistema de ecuaciones lineales se obtiene mediante métodos numéricos:
(x, y, z) = (630.000, 420.000, 12.600)
Finalmente, el capital depositado en la cuenta al 4 % es:
c = 1.365.000 - 630.000 - 420.000
c = 315.000
Se deposita capitales de 630.000, 420.000 y 315.000 en las cuentas de 2 %, 3 % y 4 %, respectivamente.
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Willis Rusch recently purchased a 5-lb box of treats for his dog. The total purchase price was $8.87. What was the price per pound?
Answers
Answer:
Willis paid 1.774 dollars a pound
Step-by-step explanation:
Assuming there was no tax in the purchase, you can divide 8.87/5 to get your price per pound.
three means between 2 and 512
Answers
The three geometric mean between 2 and 512 are
When r = 4 , 8,32, 128When r = -4, -8, 32, -128The first term = 2
Consider the common ratio as r
Then the second term = 2r
The third term = [tex]2r^2[/tex]
The fourth term is = [tex]2r^3[/tex]
The fifth term is given that 512
The fifth term = [tex]2r^4[/tex]
Then the equation will be
[tex]2r^4[/tex] = 512
[tex]r^4[/tex] = 512 / 2
[tex]r^4[/tex] = 256
r = ±4
When r = 4
The three geometric mean between 2 and 512 are
2r = 2×4 = 8
[tex]2r^2[/tex] = 2×4×4 = 32
[tex]2r^3[/tex] = 2×4×4×4 = 128
When r = -4
The three geometric mean between 2 and 512 are
2r = 2×-4 = -8
[tex]2r^2[/tex] = 2×-4×-4 = 32
[tex]2r^3[/tex] = 2×-4×-4×-4 = -128
Hence, the three geometric mean between 2 and 512 are
When r = 4 , 8,32, 128When r = -4, -8, 32, -128The complete question is :
Find the three geometric means between 2 and 512.
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Let f(x-3) = x2- 2x+ 7, find f(-1)
Answers
For given function f(x-3) = x^2- 2x+ 7, the value of f(-1) is 10
For given function f(x-3) = x^2- 2x+ 7 we need to find the value of f(-1)
i.e., we get an equation,
x - 3 = -1
x = -1 + 3
x = 2
Substitute x = 2 in given function,
f(-1) = (-1)^2- 2(-1) + 7
f(-1) = 1 - (-2) + 7
f(-1) = 1 + 2 + 7
f(-1) = 10
Therefore, for given function f(x-3) = x^2- 2x+ 7, the value of f(-1) is 10
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graph the linear inequality y≤-2/5x-4
Answers
The graph of the inequality, y ≤ -2/5x - 4, is shown below
Graph of Linear inequalitiesFrom the question, we are to graph the given linear inequalities.
The given linear inequalities is y ≤ -2/5x - 4.
To graph the linear inequality,
First, we will draw the line of the equation y = -2/5x - 4
To draw the line, we will use the x-intercept and y-intercept.
y-intercept
When x = 0
y = -2/5x - 4
y = -2/5(0) - 4
y = 0 - 4
y = -4
Thus, the coordinate of the y-intercept is (0, -4)
x-intercept
When y = 0
y = -2/5x - 4
0 = -2/5x - 4
4 = -2/5x
4 × 5 = -2x
20 = -2x
x = 20/-2
x = -10
Thus, the coordinate of the x-intercept is (-10, 0)
Now, using the coordinates of the x and y-intercepts, the line of the graph is shown.
Since the sign of the inequality is less than or equal to (≤), the line is a solid line and the solution is below the line.
The graph of the inequality is shown below.
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How much should be deposited in an account paying 4.5% interest, compounded semiannually, in order to have a balance of $ 5,000 after 19 years and 6 months?
*Enter the answer in dollars and cents, and round to the nearest cent, if needed. Do not include the dollar sign. For example, if the answer is $0.61, only the number 0.61 should be entered.*
Principal ≈ $ ____________
Answers
The suitable for blank is 2099.43 approximately.
Let the principle be P.
Time (t) = 19 years and 6 months = 19.5 years
Compound is semiannually.
Rate of Interest (r) = 4.5%
Amount will be (A) = $5000
So, suitable equation is given by,
[tex]A=P\left(1+\frac{r}{200}\right)^2t\\5000=P\left(1+\frac{4.5}{200}\right)^{2\times19.5}=P\left(1+\frac{9}{400}\right)^{39}\\\\P\approx2099.43[/tex]
Hence the suitable for the blank is 2099.43.
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The Body for Life gym charges $15 a month membership fee and a $2 per day usage fee. What does the ordered pair (13, 41) mean?
Answers
The ordered pair (13, 41) simply means a daily usage fee of $41 would be charged to use the Body for Life gym for 13 days.
How to calculate the slope-intercept form of the equation?Mathematically, the slope-intercept form of a line can be calculated by using this equation:
y = mx + c
Where:
m represents the slope.x represents the number of days.y represents the daily usage fee.c represents the y-intercept.Based on the information provided, a linear equation which models the situation is given by:
y = 2x + 15
For the ordered pair (13, 41), we have:
y = 2x + 15
y = 2(13) + 15
y = 26 + 15
y = $41.
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The principal P is borrowed at a simple interest rate r for a period of time t. Find the simple interest owed for the use of the money. Assume days in a year.
P = 7000$, r = 7.5%, t =15 months
Answers
Answer:
$656.25
Step-by-step explanation:
The formula for simple interest is:
[tex]A=Prt[/tex]
Where A is the final amount, P is the principal, r is the rate, and t is the time in years.
The question does not specify whether the interest rate is annual or not, but I will assume it is! To convert 15 months to years, divide it by 12 months!
[tex]\frac{15}{12}=\frac{5}{4}=1.25[/tex]
I also need the percent to be a decimal. To convert a percent to a decimal, divide by 100.
[tex]7.5/100 = 0.075[/tex]
Now, plug the values into the formula!
[tex]A=7000*0.075*1.25\\A=656.25[/tex]
The total amount after 15 months is $656.25
Geometry gina Wilson help plsss
Answers
Answer: m<BCA = 57°
Step-by-step explanation:
180-(10x-37)°
180-(10x(16)-37)°
180-123
57°
i’ll mark brainliest!! helppp
Answers
Answer:
T
Step-by-step explanation:
Answer:
T
Step-by-step explanation:
T because it is the same position and Q therefore being congruent to each other, a way visualize it is to flip it and aline the lines together and see which one is the same angle as Q.
What is the value of the
underlined digit?
5,678.321 6# ñame
Answers
The value of the underlined digit is 600.
What is the place value strategy?
The place value strategies are defined as math strategies that use to assist you in resolving your elementary math problems, use your places values, such as tens and hundreds. It is possible to employ enlarged notation or compensation. Using regrouping techniques, you can make the problem easier by compensating for addition.
We must determine the values of each integer in order to calculate the value of the underlined digit (6) in the equation.
In 5,678.321, the first digit, 5, is 1,000 in the thousands of places.
The second digit, 6, is in the hundreds (100) place.
So the value is 600.
Hence the answer is, the value of the underlined digit is 600.
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A line passes through the points (14, 9) and (7, 3). What is its equation in slope-intercept form?
Answers
Answer:
solve 9 = -6/-7(14) + b this is not the answer but when you solve it that will be your answer
Step-by-step explanation:
m = y2 - y1 y = mx + b
x2 - x1 9 = -6/-7(14) + b
m = 3 - 9
7 - 14
3 - 9 = -6
7 - 14 = -7
m = -6/-7
First I found the slope using the formula below. Then I plugged that slope into the equation y=mx+b along with the values of y and x to find the y-intercept.
please help me with this practice question
Answers
Answer:
10u^2 - 2u - 2
Step-by-step explanation:
Combine like terms:
4u^2 + 3 + 6u^2 - 2u - 5
10u^2 - 2u - 2
does a low outlier cause the mean to be lower than the median?
pretty sure it does just making sure :)
Answers
Answer:
yesss
Step-by-step explanation:
Word problem 2: Paula wants to divide 480 tomatoes equally among 40 baskets. How man
will Paula put in each basked?
Answers
Answer:
12
Step-by-step explanation:
480 tomatoes/40 baskets = 12 per basket
the price of an item has been reduced by $6.14. the new price is $73.59. what was the original price?
Answers
Answer:
79.73
Step-by-step explanation:
Answer:79.73
Step-by-step explanation: because if you take 6.14 and add it to 73.59 you get 79.73
Under a 750:1 magnification microscope, a paramecium has a length of
19 mm. What is the actual length of the paramecium?
Answers
Using the scale size, the actual length of the paramecium is 0.253.
In the given question we have to find the actual length of the paramecium.
Under a 750:1 magnification microscope, a paramecium has a length of
19 mm.
Using the microscope length of paramecium = 19 mm
Magnification microscope = 750:1
So the actual length of paramecium = microscope length of paramecium× scale size
The actual length of paramecium = 19× 1/750
The actual length of paramecium = 19/750
The actual length of paramecium = 0.253
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Watch help video
What are the coordinates of the point on the directed line segment from (-10, 2) to
(-3,-5) that partitions the segment into a ratio of 4 to 3?
Answers
The coordinates of the point on the directed line segment from (-10, 2) to (-3,-5) that partitions the segment into a ratio of 4 to 3 is (-6,-2).
Given:
we have two points :
(-10, 2) to (-3,-5)
and the ratio which partitions the segment is:
4:3
we are asked to determine the coordinates of the point.
Let the given points (-10,2) be (x₁, y₁) and (-3,-5) be (x₂, y₂) and the ratio be m:n.
Using section formula to find the coordinates:
x = (mx₂ + nx₁)/(m+n)
= {4(-3) + 3(-10)} /(4+3)
= -12-30/7
= -42/7
= -6
y = (my₂ + ny₁)/(m+n)
= {4(-5) + 3(2)} / (4+3)
= -20+6/7
= -14/7
= -2
Therefore, the required point is (-6,-2)
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can you solve the question that is showed below
5x5=9+3
Answers
The value of x is 1.1913
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
5[tex]x^5[/tex] = 9+3
5[tex]x^5[/tex] =12
[tex]x^5[/tex]=12/5
Take 5th root on both sides
[tex]x=\sqrt[^5]{12/5}[/tex]
x= 1.1913
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A park is planning a rectangle shaped koi pond with an area given by the expression 4d2 + 8d square feet. Draw one possible design for the koi pond and label the dimensions for length and width
Answers
The general rule for the dimensions will be 4d and (d + 2) after taking d = 1, the dimensions are 4 and 3 feet
What is the area of the rectangle?It is defined as the area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
It is defined as two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral.
It is given that:
A park is planning a rectangle-shaped koi pond with an area given by the expression 4d² + 8d square feet.
= 4d(d + 2)
The dimensions could be 4d and (d + 2)
Let d = 1
The dimensions are 4 and 3 feet
Thus, the general rule for the dimensions will be 4d and (d + 2) after taking d = 1, the dimensions are 4 and 3 feet
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A coastline has receded 450 centimeters in 9 years. Each year, the coastline recedes the same distance. One meter is equal to 100 centimeters. How far does the coastline recede each year, in meters?
Answers
We need to determine the length per year, so take the ratio of 450/9 and simplify it.
r = 450cm/9yr
r = 50cm/1yr
r = 50cm
50cm/100cm = 1/2
So, the coastline recedes 1/2 meters every year.
Answer:0.50 meters
Step-by-step explanation:
33) A recipe for pancakes calls for 9 cups of
milk. Nicole has already put in 3 cups.
How many more cups does she need to put
in?
Answers
A(1,3), B(2, 1) and C(5, 3) are points on a coordinate grid.
Show that the line segments AB and BC are perpendicular.
Input note: find the gradient of AB and the gradient of BC.
Answers
As gradients multiplied we get [tex]\frac{-4}{3}[/tex] the line segments AB and BC are not perpendicular
How to find lines are perpendicular?
Perpendicular lines are those that cross at a right angle when two non-vertical lines in the same plane. Vertical and horizontal lines, or the axes of the coordinate plane, are perpendicular to one another. Two parallel lines' slopes have negative reciprocal slopes.
To find whether the line segments are perpendicular we have to first find the gradient of AB and BC
Finding the gradient of AB
A(1,3) and B(2,1)
[tex]m_{AB}[/tex]=(1-3)/(2-1)
= [tex]\frac{-2}{1}[/tex]
=-2
Finding the gradient of BC
B(2,1) and C(5,3)
[tex]m_{BC}[/tex]=(3-1)/(5-2)
=[tex]\frac{2}{3}[/tex]
When we multiply the two gradients if we get -1 then the two line segments are perpendicular.
[tex]m_{AB}X m_{BC} = -2X\frac{2}{3}[/tex]
= [tex]\frac{-4}{3}[/tex]
As the gradient is not equal to -1 the line segments AB and BC are not perpendicular
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Hey can someone please help me out on this question and explain?It’s below. Thanks so much I appreciate it:) I’ll give brainly
Answers
Answer:
153.86
Step-by-step explanation:
to get the area of the circle you take the radius to the power of 2 and then multiply with π
when the radius of circle S is half the radius of circle L and circle L has radius 14 inch, then the radius of S is 7.
area = radius² * π = 7² * π = 49 * π
π is approximately 3.14
so 49*3.14 = 153.86
Part 2: The xy-Plane
Use these two graphs to answer questions 4 and 5.
4. Do these graphs represent functions? Explain.
Answers
Answer:
Answer and explanation in image
Step-by-step explanation:
Use your calculator to find the angle, to the nearest hundredth of a degree, whose cosine value is 1/7
Answers
The angle with cosine value of 1/7 is 81.79°
How to determine the angle?Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles
Given that: the cosine value of the angle is 1/7
Let the angle be θ. Then we can write that:
cos θ = 1/7
θ = cos⁻¹ (1/7) (Take the inverse of cosine on both sides)
θ = 81.79°
Note: To get cos⁻¹ on your calculator, press the shift button followed by the cos button
Therefore, the angle is 81.79°
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For a project in his Geometry class, Anand uses a mirror on the ground to measure the height of his school’s football goalpost. He walks a distance of 14.75 meters from the goalpost, then places a mirror on flat on the ground, marked with an X at the center. He then steps 1.3 meters to the other side of the mirror, until he can see the top of the goalpost clearly marked in the X. His partner measures the distance from his eyes to the ground to be 1.45 meters. How tall is the goalpost? Round your answer to the nearest hundredth of a meter.
Answers
The height of the goalpost is 16.45 m.
Given, Anand uses a mirror on the ground to measure the height of his school’s football goalpost.
He walks a distance of 14.75 meters from the goalpost, then places a mirror on flat on the ground, marked with an X at the center.
He then steps 1.3 meters to the other side of the mirror, until he can see the top of the goalpost clearly marked in the X.
His partner measures the distance from his eyes to the ground to be 1.45 meters.
we are asked to determine the height of the goalpost = ?
As per the rule of reflection in physics,
Angle of incidence = Angle of reflection
As we can see in the picture attached, both the angles (θ) are equal.
m∠ACB = m∠ECD = 90° - θ
m∠ABC = m∠ADC = 90°
Therefore, both the triangles ΔABC and ΔEDC will be similar.
And by the property of similar triangles, their corresponding sides will be proportional.
AB/ED = CB/CD
1.45/ED = 1.3/14.75
ED = 14.75×1.45/1.3
ED = 16.45 m
Hence the height of the goal post is 16.45 m
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Alton estimated that 240 people attended the band concert. The actual count for attendance was 200 people. Find the percent of error.
8%
17%
20%
40%
it's not 17% so