The variance of the number of green voters in the sample is 160.
What is variance?
In statistics, variance is a measure of the spread or variability of a set of data. It measures how much the values in a dataset differ from the mean or average value. Specifically, variance is the average of the squared differences from the mean.
We can use the binomial distribution to model the number of green voters in the sample, where the probability of success (voter being green) is p = 0.2 and the number of trials (voters in the sample) is n = 1000.
The expectation or mean of the number of green voters in the sample is given by the formula:
E(X) = np
where X is the random variable representing the number of green voters in the sample. Substituting the values, we get:
E(X) = 1000 * 0.2 = 200
So we expect to see about 200 green voters in the sample.
The variance of the number of green voters in the sample is given by the formula:
Var(X) = np(1 - p)
Substituting the values, we get:
Var(X) = 1000 * 0.2 * (1 - 0.2) = 160
So the variance of the number of green voters in the sample is 160.
To learn more about variance visit:
https://brainly.com/question/9304306
#SPJ1
The theoretical probability of an albino Galapagos tortoise being born is 0.001%. If 500,000 Galapagos tortoises hatch, how many would you expect to be albino?
So, we would expect about 5 albino Galapagos tortoises to be born out of 500,000 Galapagos tortoises hatched, assuming that the theoretical probability holds true in practice.
What is probability?Probability is a branch of mathematics that deals with the measurement and analysis of random events. It is the study of how likely an event is to occur, expressed as a number between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event. Probability is used in many areas of mathematics, science, and engineering, such as statistics, physics, finance, and computer science. It is a fundamental concept for understanding and predicting the behavior of random events and systems.
Here,
To find the expected number of albino Galapagos tortoises, we can use the formula:
Expected value = Probability of event * Total number of trials
In this case, the probability of an albino Galapagos tortoise being born is 0.001 or 0.001/100 = 0.00001 (as a decimal). The total number of trials is 500,000, since that is the number of Galapagos tortoises that hatched.
Therefore, the expected number of albino Galapagos tortoises is:
Expected value = 0.00001 * 500,000
= 5
To know more about probability,
https://brainly.com/question/30034780
#SPJ1
Choose all of the two-dimensional shapes that result from a vertical, horizontal, or angled cross section of a cone.
A- Rectangle
B- Triangle
C- Circle
D- Parabola
E- Ellipse
The cross section across a conic section would produce:
Triangle, Circle and Parabola
What are the properties of conic sections?Looking at the given options, we can say that ellipse, circle and parabola are all conic sections and as such they are possible figures that can be made if we intersect a plane and a cone.
However, rectangle is not a conic section.
A cylinder which could have a rectangular cross section if the plane is perpendicular to the base or A tetrahedron could have a square cross section, which is a special case of a rectangle.
In forming a conic section , we could also form an ellipse.
Now, when we cut a cross section across a cone, we can get a circle, triangle or parabola
Read more about Conic Sections at: https://brainly.com/question/21098648
#SPJ1
the graph of y=ex is transformed as showed in the graph below. Which equation represents the transformed function?
The transformed function [tex]y =e^x + 3[/tex] by shifting the graph of [tex]y =e^x[/tex] upwards with 3 units as per given graph.
What is a transformation?A transformation in a graph is a function that maps each point in the original graph to a corresponding point in a new graph.
According to the graph it shows that there is transformation to 3 unit upwards.
To transform the equation [tex]y =e^x[/tex] to [tex]y =e^x + 3[/tex] , we can add 3 to both sides of the given equation:
[tex]y+3 =e^x + 3[/tex]
So the equation [tex]y = e^x + 3[/tex] is the transformed version of [tex]y = e^x[/tex] Geometrically, this transformation shifts the graph of [tex]y = e^x[/tex] upwards by 3 units, while maintaining its shape and curvature. This means that it will intersect the y-axis at the point (0, 3) and will never touch the x-axis.
In summary, the transformed function [tex]y = e^x + 3[/tex] by shifting the graph of [tex]y = e^x[/tex] upwards with 3 units.
To know more about transformation, visit:
https://brainly.com/question/28025572
#SPJ1
The formula v=0. 83B^3/2 represent the wind speed, v, in relation to b, the Beaufort scale number Determine the Beaufort scale number when the wind speed is 9. 4 meter per second
Answer:
5.0
Step-by-step explanation:
You want the Beaufort scale number corresponding to 9.4 m/s, given the formula ...
v = 0.83B^(3/2)
SolutionPut the given speed in the formula and solve for B.
9.4 = 0.83B^(3/2)
9.4/0.83 = B^(3/2)
B = (9.4/0.83)^(2/3) ≈ 5.043
The wind speed is about 5.0 on the Beaufort scale.
If y=5/3+4 what’s Y and what slope would that make?
Answer: 5/3
Step-by-step explanation:
y = mx +b
m is equal to the slope
b is the y intercept
therefore, m or 5/3 is the slope.
given the vertex at (-4, 5) and a-value of 5, write the vertex form of the quadratic equation.
The vertex form of a quadratic equation is y = a(x-h)^2 + k, where (h,k) is the vertex.
To write the vertex form of a quadratic equation given the vertex (-4, 5) and a-value of 5, you can use the vertex form equation:
y = a(x - h)² + k
where (h, k) is the vertex and a is the a-value.
In this case, h = -4, k = 5, and a = 5. Substitute these values into the equation:
y = 5(x - (-4))² + 5
Simplify the equation:
y = 5(x + 4)² + 5
So, the vertex form of the quadratic equation is:
y = 5(x + 4)² + 5
Learn more about quadratic equation here: brainly.com/question/30098550
#SPJ11
The vertex form of the quadratic equation is: y = 5[tex](x + 4 )^2[/tex] + 5
A quadratic equation's vertex form is provided by:
y = a[tex](x - h)^2[/tex] + k
where "a" is the coefficient of the parabola and "(h, k)" is its vertex [tex]x^2.[/tex]
Given that the vertex is (-4, 5) and a-value is 5, we can substitute the values into the vertex form equation:
h = -4
k = 5
a = 5
When we enter these numbers into the equation, we obtain:
y = 5(x -[tex](-4) ^2[/tex] + 5
Simplifying the equation, we get:
y = 5[tex](x + 4)^2[/tex] + 5
So, the vertex form of the quadratic equation is:
y = 5[tex](x + 4 )^2[/tex] + 5
Learn more about “ quadratic equation “ visit here;
https://brainly.com/question/30098550
#SPJ4
HELP ME AND I'LL GIVE YOU 100 POINTS!!! ANSWER IT HONESTLY PLS!!!
Find the area, in square inches, of the composite figure.
12 in.
2 in.
3 in.
3 in.
25 in.
looks somewhat like what my problem looks like but with the numbers I listed
URGENT - Will also give brainliest to simple answer
The area of the sector in terms of pi is: 75π cm²
The Length of arc = 15π cm
What is the Area of a Sector and Length of an Arc of a Circle?Area of a sector = ∅/360 * πr²
Length of arc = ∅/360 * 2πr, where r is the radius and ∅ is the reference angle.
Given the following:
Reference angle (∅) = 270°
Radius of circle (r) = 10 cm
Area of the sector = 270/360 * π * 10²
Area of the sector = 75π cm²
Length of arc = 15π cm
Learn more about the area of sector on:
https://brainly.com/question/9790386
#SPJ1
Given a reduced echelon matrix in R3 is 1--1 iff the homogeneous system Ax = 0 has only the trivial solution iff there are no free variables.
A. True B. False
A reduced echelon matrix in R3 is 1--1 if and only if the homogeneous system Ax = 0 has only the trivial solution if and only if there are no free variables.
The statement is true.
A reduced echelon matrix in R3 represents a linear system of equations that can be solved using Gaussian elimination.
The reduced echelon form of a matrix is obtained by performing row operations that reduce the matrix to a triangular form, with ones on the main diagonal and zeros below it.
If the homogeneous system Ax = 0 has only the trivial solution, it means that the only solution to the system is the zero vector.
In other words, there are no non-zero vectors that satisfy the system.
This is equivalent to saying that the rank of the matrix is equal to the number of columns, or in other words, there are no free variables in the system.
If the system has no free variables, it means that each variable can be expressed as a unique function of the other variables.
This implies that the system has a unique solution, or in other words, the mapping from the system of equations to the solution vector is one-to-one.
If the system is one-to-one, it means that each solution vector corresponds to a unique system of equations.
This implies that there are no redundant equations or variables, and therefore no free variables.
Hence, the homogeneous system Ax = 0 has only the trivial solution.
The statement is true.
A reduced echelon matrix in R3 is 1--1 if and only if the homogeneous system Ax = 0 has only the trivial solution if and only if there are no free variables.
For similar questions matrix
https://brainly.com/question/2456804
#SPJ11
3-1 The roof area of a fable roof is made up of two rectangles. (True or False)
Given statement "The roof area of a gable roof is made up of two rectangles"
The given statement is True.
Because, A gable roof consists of two sloping roof surfaces that meet at the top, forming a triangle shape on both ends of the building.
Each of these sloping surfaces can be represented as a rectangle, and the combined area of these two rectangles represents the total roof area.
Area is a measure of the amount of space inside a two-dimensional (2D) or three-dimensional (3D) shape.
It is typically measured in square units, such as square meters, square feet, or square inches.
For similar question on area.
https://brainly.com/question/27950508
#SPJ11
retail price $24.50; discount rate 15%
Evaluate the expression when a = 3 and x = -7 .
-a + 9x
Find the volume of the cone. Use 3. 14 for π. Round to the nearest tenth.
A. 18,324. 8 cm3
B. 1,271. 7 cm3
C. 1,527. 1 cm3
D. 4,581. 2 cm3
The volume of the cone is1527.1 cm³
And the correct answer is an option (c)
We know that he formula for the volume of the cone is:
V = 1/3(π × r² × h)
Here, the diameter of the base of the cone is 15 cm
so, the radius of the cone would be,
r = 15/2 cm
r = 7.5 cm
And the slant heihgt of the cone is l = 27 cm
Using Pythagoras theorem the height h of the cone would be,
h = √(l² - r²)
h = √(27² - 7.5²)
h = √(672.75)
h = 25.94 cm
Using above formula, the volume of the cone would be,
V = 1/3(π × r² × h)
V = 1/3(π × (7.5)² × 25.94)
V = 1527.99 cm³
V = 1527.1 cm³
Therefore, the correct answer is an option (c)
Learn more about the volume of cone here:
https://brainly.com/question/29767724
#SPJ4
Find the complete question below.
What are all values of x for which the function f is defined by f(x)= x^3 +3x^2 -9x +7 is increasing?a) -31d) x <-1 or x > 3e) all real numbers
The values of x for which the function f(x) = x³ + 3x² - 9x + 7 is increasing are (-∞, -3) and (1, +∞).
To find the values of x for which the function f(x) = x³ + 3x² - 9x + 7 is increasing, we need to take the derivative of the function and determine where the derivative is positive.
f(x) = x³ + 3x² - 9x + 7
f'(x) = 3x² + 6x - 9
To find where f(x) is increasing, we need to find the values of x where f'(x) > 0.
3x² + 6x - 9 > 0
Simplifying this inequality, we get
x² + 2x - 3 > 0
Factoring the left side of the inequality, we get
(x + 3)(x - 1) > 0
The critical points of f(x) occur when f'(x) = 0 or when the denominator of f'(x) is undefined. The denominator of f'(x) is always defined, so we only need to find where f'(x) = 0
3x² + 6x - 9 = 0
Dividing both sides by 3, we get
x² + 2x - 3 = 0
Factoring the left side of the equation, we get
(x + 3)(x - 1) = 0
So the critical points of f(x) are x = -3 and x = 1.
Now we can use a sign chart to determine the intervals where f'(x) > 0.
Learn more about critical points here
brainly.com/question/30325317
#SPJ4
The given question is incomplete, the complete question is:
What are all values of x for which the function f is defined by f(x)= x³ +3x² -9x +7 is increasing?
A random sample of 130 purchases from a particular pharmacy was taken. The type of item purchased was recorded, and a table of the data was created.
Item Purchased Health & Medicine Beauty Household Grocery
Number of Purchases 55 23 22 30
Which graphical representation would be best to display the data?
Box plot
Histogram
Stem-and-leaf plot
Bar graph
Answer:
Bar Graph
Step-by-step explanation:
A bar graph would be the best graphical representation to display the data.
A bar graph is a good choice for displaying categorical data, where each category is represented by a separate bar. In this case, the categories are the different types of items purchased (Health & Medicine, Beauty, Household, and Grocery), and the number of purchases for each category is represented by the height of the corresponding bar.
A box plot is generally used to display numerical data, while a histogram is used to display the distribution of continuous data. A stem-and-leaf plot can also be used to display numerical data, but it is generally used for smaller datasets.
Therefore, in this case, a bar graph is the most appropriate choice to display the data.
The best graphical representation for the given dataset would be a Bar Graph. The categories of items purchased can be shown on one axis and the number of purchases on the other. Other plots such as Box plots, Histograms, and Stem-and-leaf plots are not suitable for this kind of categorical data.
Explanation:To represent this data graphically, the best option would be a Bar Graph. A bar graph is a graph that uses either horizontal or vertical bars to show comparisons between categories of data. In this case, you have four categories (Item Purchased: Health & Medicine, Beauty, Household, Grocery) and the Number of Purchases associated with each category.
So, each category would be represented by a bar, and the length or height of the bar would represent the Number of Purchases.
Box plots, Histograms, and Stem-and-leaf plots are not appropriate because they are typically used for continuous data or to examine ranges of data, and the data listed here is categorical and discrete (it's countable).
Learn more about Bar Graph here:https://brainly.com/question/32166542
#SPJ2
(T/F) If the size of a sample is at leastâ 30, then you can useâ z-scores to determine the probability that a sample mean falls in a given interval of the sampling distribution.
The statement "If the size of a sample is at least 30, then you can use a z-scores to determine the probability that a sample mean falls in a given interval of the sampling distribution." is true because when the sample size is at least 30, the Central Limit Theorem applies and the sampling distribution of the sample mean can be approximated by a normal distribution.
If the size of a sample is at least 30, the Central Limit Theorem (CLT) applies, which states that the distribution of sample means is approximately normal, regardless of the underlying distribution of the population, as long as the sample size is sufficiently large.
When the sample size is at least 30, the sampling distribution of the sample mean can be approximated by a normal distribution, and z-scores can be used to calculate probabilities of sample means falling in a given interval.
Learn more about Central Limit Theorem here
brainly.com/question/18403552
#SPJ4
(8x10) +(4x1)+(5x1/100
The value of solution of the expressions are,
⇒ 84.05
We have to given that;
The expression is,
⇒ (8 × 10) + (4 × 1) + (5 × 1/00)
Now, We can simplify as;
⇒ (8 × 10) + (4 × 1) + (5 × 1/100)
⇒ 80 + 4 + (5 × 0.01)
⇒ 84 + 0.05
⇒ 84.05
Thus, the value of solution of the expressions are,
⇒ 84.05
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ1
Which of the following options have the same value as 72%, percent of 50?
Malia drinks 2 pints of milk each day. How many days does it take her to drink 1 gallon of milk?
0.305 in word form??
help me please
Answer:
three hundred five thousanths
Step-by-step explanation:
what proportion of the poplation has a favorite social network
Answer:
Step-by-step explanation:
Social media usage is one of the most popular online activities and in 2021, 82 percent of the population in the United States had a social networking profile, representing a two percent increase from the 80 percent usage reach in the previous year.
Social media usage is one of the most popular online activities, and in 2021, 82 percent of the population in the United States had a social networking profile, marking a two percent rise over the previous year's usage reach of 80 percent.
Brainlist?
You have $910 in your checking account. You have paid $185 in bill's online, which were immediately deducted from your checking account. The following day you withdrew $30 for lunch, bought pants for $43, and purchased a gift card for $15 using your debit card. After, you returned the pants for a full refund. How much is in your checking account?
Answer:
Therefore, the answer to how much is in the checking account is $677.
Step-by-step explanation:
The amount in the checking account after all the transactions would be $677.
Here's the breakdown of the transactions:
Starting balance: $910
Bill payment: -$185
Withdrawal for lunch: -$30
Purchase of pants: -$43
Purchase of gift card: -$15
Refund for pants: +$43
Total = $910 - $185 - $30 - $43 - $15 + $43 = $677
Solve for x. Round your answer to the nearest tenth, and type it in the blank without units.
The value of x in the triangle is 17.6 m.
How to solve for the value of x in the triangle?
Trigonometry deals with the relationships between the sides and angles of triangles.
The three primary trigonometric functions are sine, cosine, and tangent, which are ratios of the sides of a right triangle. These functions are often abbreviated as sin, cos, and tan.
Using the given triangle:
cos 54° = x/30 (cos = adjacent/hypotenuse)
x = 30 * cos 54°
x = 17.6 m
Learn more about Trigonometry on:
https://brainly.com/question/24349828
#SPJ1
A coin tossed what is the theoretical probability of the coin landing on heads
Answer: 50%
Step-by-step explanation: each side has a 1 in 2 chance of landing on it
sin^2x = (power reducing formula)
[tex]sin^2(x)[/tex] can be expressed as [tex](1 - cos(2x)) / 2[/tex] using the power reducing formula.
To express [tex]sin^2(x)[/tex]using the power reducing formula,
we need to recall the following trigonometric identity:
[tex]sin^2(x) = (1 - cos(2x)) / 2[/tex]
Recognize that the question asks for the power reducing formula for sin^2(x).
Recall the trigonometric identity:[tex]sin^2(x) = (1 - cos(2x)) / 2[/tex]
The power reducing formula for [tex]sin^2(x)[/tex] is:[tex](1 - cos(2x)) / 2.[/tex]
The power reducing formula is a trigonometric identity that allows you to express a trigonometric function of a higher power in terms of a trigonometric function of a lower power.
It is most commonly used for reducing the power of the sine and cosine functions.
The power reducing formula for cosine is:
[tex]cos^2(x) = (1 + cos(2x))/2[/tex]
The power reducing formula for sine is:
[tex]sin^2(x) = (1 - cos(2x))/2[/tex]
These formulas can be derived using the Pythagorean identity, which states that [tex]sin^2(x) + cos^2(x) = 1.[/tex]
By solving for either[tex]sin^2(x) or cos^2(x)[/tex] in terms of the other, and then using the double angle formula for cosine[tex](cos(2x) = cos^2(x) - sin^2(x)),[/tex] we can arrive at the power reducing formulas.
For similar question on power.
https://brainly.com/question/29257047
#SPJ11
a manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 441 gram setting. is there sufficient evidence at the 0.02 level that the bags are overfilled? assume the population is normally distributed. state the null and alternative hypotheses for the above scenario.
Null hypothesis: Bags are filled correctly at 441 grams. Alternative hypothesis: Bags are overfilled (mean weight > 441 grams).
The null hypothesis (H0) is that the bags are filled correctly at the 441 gram setting, meaning the mean weight of the bags is 441 grams. The alternative hypothesis (Ha) is that the bags are overfilled, meaning the mean weight of the bags is greater than 441 grams. Thus, the hypotheses can be written as:
H0: μ = 441
Ha: μ > 441
To test these hypotheses, we can use a one-sample t-test with a significance level of 0.02. We will compare the sample mean weight of a random sample of bags to the population mean of 441 grams, using the t-test statistic and the corresponding p-value. If the p-value is less than 0.02, we can reject the null hypothesis and conclude that the bags are overfilled
Learn more about Null hypothesis
https://brainly.com/question/28920252
#SPJ4
The radius of a circle is 9 millimeters. What is the circle's circumference?
Use 3.14 for л.
Answer:
56.55
Step-by-step explanation:
C=2πr=2·π·9≈56.54867
Which question would the equation b = 12 - (-3) help to answer?
A. The temperature dropped 12 degrees over 3 hours. How much did it change each hour?
B. The temperature dropped 12 degrees each hour for 3 hours. How much did the temperature change in total?
C. The temperature was -3 degrees and rose to 12 degrees. How much did the temperature change?
Explain your thinking.
The equation b = 12 - (-3) would help to answer question C, "The temperature was -3 degrees and rose to 12 degrees. How much did the temperature change?"
How to find the equation ?This is because the equation b = 12 - (-3) simplifies to b = 12 + 3, which gives us the value of b (the temperature change) when the starting temperature was -3 degrees and the final temperature was 12 degrees.
The subtraction of a negative number (i.e., -3) is the same as adding its absolute value (i.e., 3), so the equation can be rewritten as b = 12 + 3. Therefore, the value of b is 15, which represents the temperature change from -3 degrees to 12 degrees.
Find out more on equations at https://brainly.com/question/26656563
#SPJ1
A ran a 20-mile race that she completed in 2.5 hours.
If A ran at a constant speed for the entire race,what was her speed in miles per hour?
SHOW YOUR WORK
Answer:
The answer for speed is 8 miles/hr
Step-by-step explanation:
speed =distance/time
s=20/2.6
s=8miles/hr
I need help with at least one of these questions (maybe all ) *geometry tangents in circles*
Using Pythagoras Theorem, we have the solutions as:
3) Length of AB = 32 in
4) x = 24
5) Perimeter of PRQ = 35
How to use Pythagoras Theorem?Pythagoras Theorem is the way in which you can find the missing length of a right angled triangle.
3) Using Pythagoras theorem, we can say that:
Radius = √(16² - 5²)
Radius = √231
Radius = 15.2
Thus, AB will be twice the measurement of 16 as the perpendicular distance to bth chords are the same. Thus:
AB = 16 * 2 = 32 in
4) Using Pythagoras theorem,
x = √((18 + 7)² - 7²)
x = √(625 - 49)
x = 24
5) Using Pythagoras theorem, we can say that:
PC = 8.66
RC = √((14² - 8.66²)
RC = 11
Thus:
Perimeter of PRQ = 14 + 10 + 11 = 35
Read more about Pythagoras Theorem at:
#SPJ1