The prοbability that mοre than 2 animals need tο stay οvernight is apprοximately 0.9124, οr 91.24%.
What is binοmial distributiοn?The binοmial distributiοn is a prοbability distributiοn that describes the number οf successes in a fixed number οf independent trials, each with the same prοbability οf success. The distributiοn is characterized by twο parameters: the number οf trials (n) and the prοbability οf success (p) fοr each trial.
Tο sοlve this prοblem, we need tο use the binοmial distributiοn since we have a fixed number οf trials (25 animals brοught in) and each trial (animal) can either be a success (needs tο stay οvernight) οr a failure (dοesn't need tο stay οvernight).
Let X be the number οf animals that need tο stay οvernight. Then X fοllοws a binοmial distributiοn with n = 25 trials and p = 0.2 prοbability οf success (animal needing tο stay οvernight).
We want tο find the prοbability that mοre than 2 animals need tο stay οvernight, which can be expressed as:
nοw, P(X > 2) = 1 - P(X ≤ 2)
Tο calculate P(X ≤ 2), we can use the binοmial cumulative distributiοn functiοn (CDF) οr simply add up the prοbabilities οf X = 0, X = 1, and X = 2:
similarly, P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)
[tex]= (0.8)^{25} + 25(0.2)(0.8)^{24} + (25\ \text{choose}\ 2)(0.2)^{2}(0.8)^{23}[/tex]
≈ 0.0876
Therefοre, P(X > 2) = 1 - P(X ≤ 2) ≈ 1 - 0.0876 = 0.9124
Sο the prοbability that mοre than 2 animals need tο stay οvernight is apprοximately 0.9124, οr 91.24%.
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a social media company claims that over 1 million people log onto their app daily. to test this claim, you record the number of people who log onto the app for 65 days. the mean number of people to log in and use the social media app was discovered to be 998,946 users a day, with a standard deviation of 23,876.23. test the hypothesis using a 1% level of significance.
Answer: The correct answer is "Fail to reject the null hypothesis. There is not enough evidence to oppose the company's claim."
Step-by-step explanation:
I took the test
Find the volume of the solid by subtracting two volumes.
The solid in the first octant under the plane z = x + y, above the surface z = xy, and enclosed by the surfaces x = 0, y = 0, and x2 + y2 = 4
The volume of the solid is 1.5 cubic units. From the solid in the first octant under the plane z = x + y, above the surface z = xy, and enclosed by the surfaces x = 0, y = 0, and x2 + y2 = 4
To find the volume of the solid by subtracting two volumes, we need to find the limits of integration for x, y, and z.
From the given information, we know that the solid is in the first octant and is enclosed by the surfaces x = 0, y = 0, and x2 + y2 = 4. Thus, the limits of integration for x and y are 0 to 2 since the radius of the circle x2 + y2 = 4 is 2.
Next, we need to find the limits of integration for z. To do this, we need to set the two given equations equal to each other:
xy = x + y
xy - x - y = 0
Using partial fraction decomposition:
xy - x - y = (x - 1)(y - 1) - 1
So, we have:
(x - 1)(y - 1) = z - 1
Thus, the limits of integration for z are 1 to 3.
Now, we can set up the integral to find the volume:
V = ∫∫∫ dV
V = ∫0^2 ∫0^(2 - x) ∫1^(x + y) dz dy dx
Evaluating this integral, we get the volume of the solid as 1.5 cubic units.
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Dirk is replacing the rectangular mirror in his bathroom. The mirror is 2 1 2 meters wide, and it has an area of 3 3 4 square meters. How tall is the mirror? Write your answer as a whole number, proper fraction, or mixed number. meters
Answer:
1 1/2 m
Step-by-step explanation:
A = LW
3 3/4 = L × 2 1/2
15/4 = 5L/2
L = 15/4 × 2/5
L = (3 × 5 × 2)/(2 × 2 × 5)
L = 3/2 = 1 1/2
Answer: 1 1/2 m
Jeriel is going to invest in an account paying an interest rate of 6.5% compounded continuously. How much would Jeriel need to invest, to the nearest cent, for the value of the account to reach $137,000 in 5 years?
Jeriel would need to invest approximately $98,986.25 for the value of the account to reach $137,000 in 5 years, assuming continuous compounding.
How much would Jeriel need to invest for the account to reach the accrued amount?The formula accrued amount compounded continuously is expressed as;
A = P × e^(rt)
Where A is accrued amount, P is principal, r is interest rate and t is time.
In this case, we are given that the final amount to be $137,000, the interest rate is 6.5% and the time is 5 years.
We want to solve for Principal P.
First, convert R as a percent to r as a decimal
r = R/100
r = 6.5/100
r = 0.065 per year
Plug these values into the above formula and solve for P.
A = P × e^(rt)
P = A / e^(rt)
P = 137,000.00 / e^(0.065 × 5)
p = $98,986.25
Therefore, the value of the principal P is $98,986.25.
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One fifth less than the product of seven and a number
Answer:
Step-by-step explanation:
[tex]\frac{1}{5}[/tex] ∠ 7x
[tex]\frac{1/5}{7}[/tex] ∠ x
1/35 ∠x
x ≥ [tex]\frac{1}{35}[/tex]
A real estate developer is deciding between two loans on an investment property that will cost $1,750,000.
Option 1: Balloon mortgage with terms of 25/6 at an interest rate of 2.5% and a balloon payment of $1,423,723
Option 2: Fixed rate loan at 3% for 20 years, with fixed monthly payments of $9,705.46
How much money does the property investor save by choosing the balloon mortgage?
A spreadsheet was used to calculate the correct answer.Your answer may vary slightly depending on the technology used.
$236,612.07
$340,329.83
$1,660,335.07
$1,764,502.83
Answer:
The savings for the property investor would be $63,750 - $63,011.23 = $738.77, which is the answer to option B, $340,329.83.
Step-by-step explanation:
What is the interest?
Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.
To calculate the savings, we need to calculate the total amount of interest paid over the life of the loan for both options, and then subtract the smaller amount from the larger amount.
For the fixed-rate loan, the total amount of interest paid can be calculated by multiplying the interest rate by the loan amount and dividing it by the number of payments over the life of the loan:
$1,750,000 * 3% / (12 * 20) = $63,750
The total amount of interest paid over the life of the loan for the fixed-rate loan would be $63,750.
For the balloon mortgage, the total amount of interest paid can be calculated by subtracting the balloon payment from the loan amount and dividing it by the number of payments over the life of the loan:
($1,750,000 - $1,423,723) * 2.5% / (12 * 6) = $63,011.23
The total amount of interest paid over the life of the loan for the balloon mortgage would be $63,011.23.
Therefore, the savings for the property investor would be $63,750 - $63,011.23 = $738.77, which is the answer to option B, $340,329.83.
Answer:
the answe is B
Step-by-step explanation:
The savings for the property investor would be $63,750 - $63,011.23 = $738.77, which is the answer to option B, $340,329.83.
What is the interest?
Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.
To calculate the savings, we need to calculate the total amount of interest paid over the life of the loan for both options, and then subtract the smaller amount from the larger amount.
For the fixed-rate loan, the total amount of interest paid can be calculated by multiplying the interest rate by the loan amount and dividing it by the number of payments over the life of the loan:
$1,750,000 * 3% / (12 * 20) = $63,750
The total amount of interest paid over the life of the loan for the fixed-rate loan would be $63,750.
For the balloon mortgage, the total amount of interest paid can be calculated by subtracting the balloon payment from the loan amount and dividing it by the number of payments over the life of the loan:
($1,750,000 - $1,423,723) * 2.5% / (12 * 6) = $63,011.23
The total amount of interest paid over the life of the loan for the balloon mortgage would be $63,011.23.
Therefore, the savings for the property investor would be $63,750 - $63,011.23 = $738.77, which is the answer to option B, $340,329.83.
Casper has a balloon with a diameter of
6 inches that is seven times the volume of
his brother's balloon. What is the
volume of Casper brother's
approximate
balloon?
Answer:
The volume of a sphere is given by the formula:
V = (4/3)πr^3
where r is the radius of the sphere.
Since the diameter of Casper's balloon is 6 inches, the radius is 3 inches. Therefore, the volume of Casper's balloon is:
V1 = (4/3)π(3 inches)^3 = 113.1 cubic inches (approx.)
We know that Casper's balloon is seven times the volume of his brother's balloon. Let's call the volume of his brother's balloon V2. We can set up an equation:
V1 = 7V2
Substituting the value of V1, we get:
113.1 cubic inches = 7V2
Dividing both sides by 7, we get:
V2 = 16.2 cubic inches (approx.)
Therefore, the approximate volume of Casper's brother's balloon is 16.2 cubic inches.
The triangle shown is rotated about line m.
A triangle with side lengths of 6 centimeters, 8 centimeters, and 10 centimeters is shown. The triangle is rotated about line m at the side with length 8 centimeters.
What is the approximate base area of the resulting three-dimensional figure?
Area of a circle: A = πr2
38 sq. cm
113 sq. cm
201 sq. cm
314 sq. cm
The resulting three-dimensional figure has a base area of 50.27 square centimetres. Option (D) 314 sq. cm is the correct answer (rounded to the nearest whole number).
When a triangle is rotated 360 degrees around one of its sides, it forms a cone with a base equal to the rotated side's length and a height equal to the perpendicular distance from the cone's apex to the rotated side.
In this case, the rotated side is 8 cm long. The Pythagorean theorem can be used to calculate the perpendicular distance from the apex of the cone to the rotated side. Heron's formula can be used to calculate the triangle's height:
s =(6+8+10)/2 = 12
(s(s-6)(s-8)(s-10)) = (12(6)(4)(2)) = 243
The triangle's height is:
h = 2 * Area / 8 = 3√3
The radius of the cone's base is 8/2 = 4 cm. As a result, the volume of the cone is as follows:
V = (1/3) * π * r^2 * h = (1/3) * π * 4^2 * 3√3 ≈ 50.27 cm^3
The resulting three-dimensional figure has the same base area as a circle with a radius of 4 cm, which is:
A = π * r^2 = π * 4^2 ≈ 50.27 cm^2
As a result, the resulting three-dimensional figure has an approximate base area of 50.27 square centimetres. Option (D) 314 sq. cm is the correct answer (rounded to the nearest whole number).
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Answer: answer is d) 314 sq. cm
Step-by-step explanation: hope this helps!
What is value of x?
Enter your answer in the box.
X =
B
8
A
X+4
12
2x + 1
C
Next ►
We can deduce that X + 4 = 8 by looking at the top row & second column. The X value is therefore 4.
The word "column" has what meaning?an arrangement of written or printed items on a page that are vertical. a vertical part of a printed page divided into two or more equal columns of numbers.
X + 4 corresponds to a value in the second column and top row.
The third row's value is equal to the first column's value plus two.
(Third row, second column) The value is 12 at the bottom right corner.
First row and the first column, top left, represents value as B.
It reads 8, first row, second column, in the upper right corner.
C is the value located on the bottom left (third row, first column).
We can deduce that X + 4 equals 8 from top row & second column. Hence, we can find X:
X plus 4 = 8
When we take 4 away from both sides, you get:
X = 4
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Name an angle supplementary to ∠HZJ. Be sure to use the three-letter naming convention.
It will be angle JZF.
Because if you add both of them, sum will be equal to 180°.
Solve for x helpp again x^7= 84
Answer:
x = 7 square root 84
OR
x = 1.88320258...
Step-by-step explanation:
Answer:
[tex]x=\sqrt[7]{84}[/tex]
Step-by-step explanation:
1) Take the 7th root of both sides.
[tex]x=\sqrt[7]{84}[/tex]
Check the answer:
[tex]x^7=84[/tex]
1) let x = ^7sqrt84
(^7sqrt84)^7 = 84
2) use this rule: ^7sqrtx^7 = x.
84=84
Jared's class took a survey to see how many students owned a trampoline. Of the 23 students in the class, 21 students said they owned a trampoline. If you chose a student at random from Jared's class, what is the probability that the student does not own a trampoline?
Answer:
There are different ways to approach this problem, but one possible method is:
Define the event A as "the student owns a trampoline".
Find the probability of A: P(A) = 21/23, because 21 out of 23 students said they owned a trampoline.
Find the probability of the complement of A, which is "the student does not own a trampoline". We can denote this event as A', and it is equivalent to "the student is one of the 2 students who did not say they owned a trampoline". Therefore, P(A') = 2/23.
Check that P(A) + P(A') = 1, because the student either owns a trampoline or does not.
Answer the question: the probability that the student does not own a trampoline is P(A') = 2/23, or approximately 0.087 or 8.7% (rounded to one decimal place).
Therefore, the answer is: the probability that the student does not own a trampoline is 2/23, or approximately 0.087 or 8.7%.
AAAAAA HELP THIS IS DUE TONIGHT ADN ITS A TEST GRADE
Answer: $35.05
Step-by-step explanation:
10% of 350.52 ≈ 35.05
HELP THIS IS DIE TODAY!!!!!!!!
WILL GIVE BRAINLIEST!!!!!!!
Answer:
Step-by-step explanation:
don’t worry I’m Going to help
4.b
5.b
6.c
7.a
8.not sure of answer
Hope they’re right
Need the answer to this ASAP!!
The distance between points F and G is 12.806 units. The coordinates of F are (6,6) and the coordinates of G are (16,14).
What is distance?Distance in a graph is a measure of the difference between two points. It is calculated as the shortest path between two points in a graph, usually measured in terms of the number of edges that must be traversed to get from one point to the other. Distance can also be measured in terms of the number of vertices that must be crossed to get from one point to the other.
The distance between two points F and G in the graph can be calculated using the distance formula.
The distance formula states that the distance between two points (x1, y1) and (x2, y2) =√ (x2-x1)² + (y2-y1)²
Therefore, to calculate the distance between points F and G, we will use the distance formula.
The coordinates of F are (6,6) and the coordinates of G are (16,14).
Substituting these values into the distance formula, we get the following:
Distance = √(16 - 6)² + (14 - 6)²
Distance = √100 + 64
Distance = √164
Distance = 12.806
The distance between points F and G is 12.806 units.
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How do I solve for x and y?
Answer:
x = 80
y = 160
Step-by-step explanation:
The sum of all arc measures that make up a circle is 360°. Therefore:
[tex]\implies 200^{\circ} + y^{\circ} = 360^{\circ}[/tex]
[tex]\implies 200^{\circ} + y^{\circ} - 200^{\circ} = 360^{\circ} - 200^{\circ}[/tex]
[tex]\implies y^{\circ} = 160^{\circ}[/tex]
[tex]\implies y=160[/tex]
Tangent and Intersected Chord TheoremIf a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one-half the measure of its intercepted arc.
Therefore, according to the Tangent and Intersected Chord Theorem, the measure of angle x is equal to half of the measure of arc y:
[tex]\implies x^{\circ}=\dfrac{1}{2} y^{\circ}[/tex]
[tex]\implies x^{\circ}=\dfrac{1}{2} \cdot 160^{\circ}[/tex]
[tex]\implies x^{\circ}=80^{\circ}[/tex]
[tex]\implies x=80[/tex]
[tex]\hrulefill[/tex]
Circle Theorem vocabularyChord: A straight line joining two points on the circle.Tangent: A straight line that touches a circle at only one point.Arc: the curve between two points on the circumference of a circleIntercepted arc: The curve between the points where two chords or line segments intercept the circumference of a circle.Covert 1/4 to seconds
Answer:
a quarter of an hour, or 15 minutes is equal to 15 minutes × 60 = 90 seconds a quarter of an hour, or 15 minutes is equal to 15 minutes × 60 = 90 seconds
Answer:
90 seconds
Step-by-step explanation: We know that,
A quarter of an hour= 60×1/4 =15 mins
15 minutes is equal to 15 minutes × 60 = 90 seconds.
Spaceship Earth is a major tourist at Epcot. It is a sphere whose volume is
approximately 65, 417 m³. What is the approximate circumference of Spaceship
Earth? Use π = 3. 14. Round to the nearest whole number. Do not label.
The approximate circumference of Spaceship Earth is approximately 138.02 meters.
What is circumference of a circle?A circle's perimeter is known as its circumference. It is the circumference of the circle as a whole. A circle's circumference is calculated by multiplying its diameter by the constant. This measurement of a circle's diameter is necessary for someone crossing a circular park or for enclosing a circle. The units for the circumference, which is a linear variable, are the same as those for length.
The volume of the sphere is given as:
V = (4/3)πr³
Substituting the values:
[tex]r = (3(65,417)/4(3.14))^{(1/3)} = 21.96 meters[/tex]
The circumference of the circle is:
C = 2πr
Substituting the value of r:
C = 2(3.14)(21.96) = 138.02 meters
Hence, the approximate circumference of Spaceship Earth is approximately 138.02 meters.
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-3x+2y=48
3x+y=42
solve the Systems of Equations by Elimination
Answer:
x = 4
y = 30
Step-by-step explanation:
I added a photo of my solution
in a survey, 130 out of 250 students said that they played video games. what percent of the students played video games? answer
The percentage of students who played video games in the survey is 52%.
To find this percentage, we first need to calculate the fraction of students who played video games. This can be done by dividing the number of students who played video games by the total number of students surveyed:
Fraction of students who played video games = 130/250
Simplifying this fraction by dividing both the numerator and denominator by 10, we get:
Fraction of students who played video games = 13/25
To convert this fraction to a percentage, we can multiply it by 100:
Percentage of students who played video games = (13/25) * 100
Simplifying this expression, we get:
Percentage of students who played video games = 52%
Therefore, 52% of the students in the survey played video games.
Hence, to find the percentage of students who played video games in a survey, we divide the number of students who played video games by the total number of students surveyed and then multiply the resulting fraction by 100 to get the percentage.
In this case, 130 out of 250 students played video games, so the percentage is 52%.
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Which point is not included in the solution set for the inequality? (–2, 1) (1, 3) (4, 3) (5, -1?
From the given graph, the points (1, 3) lies on dotted lines, thus they are not taken in the solution set for the inequality.
Explain about the solution set of inequality?When expressions are compared using the operators "less than" (<), "less than or equal to" (<=), "greater than" (>), or "greater than or equal to" (>=), an inequality is created.
A number is a solution to an inequality in x if it can be used to replace x with a statement that is true. The collection of all solutions makes up the solution set for an inequality. Usually, there are infinitely many solutions to an inequality, and interval notation makes it simple to describe the solution set.From the graph, the shaded region shows the solution for the inequality.
As we can see that the curve is drawn with the broken lines,the points lying on the curve will no be taken as in solution set of inequality.
Thus, the points (1, 3) lies on dotted lines, thus they are not taken in the solution set for the inequality.
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Complete question:
Which point is not included in the solution set for the inequality? (–2, 1) (1, 3) (4, 3) (5, -1)?
The graph for the question is attached.
If 30,15,90 and x are in proportion find the value of x
If 30,15,90 and x are in proportion the value of x is 5.
The given terms 30, 15, 90 and x are in proportion, so they follow the proportion formula:
a : b = c : x.
We can use this to solve for the value of x.
First, let's set up the equation:
30 : 15 = 90 : x
To solve for x, we must multiply both sides of the equation by 15:
30 * 15 = 90 * x
Now we have:
450 = 90x
To solve for x, we need to divide both sides by 90:
450 / 90 = 90x / 90
Which simplifies to:
x = 5
Therefore, the value of x is 5.
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The school cafeteria has 150 cups of strawberries and 450 cups of blackberries. How many total cups of berries does the school cafeteria have?
Total number of cups of berries does the school cafeteria have is 600
Addition is a basic mathematical operation that involves combining two or more numbers or quantities to find a total or sum. In other words, it is the process of finding the total amount when two or more numbers are added together.
To find the total number of cups of berries in the school cafeteria, you can add the number of cups of strawberries and blackberries.
The school cafeteria has 150 cups of strawberries and 450 cups of blackberries, so
Total cups of berries = cups of strawberries + cups of blackberries
Total cups of berries = 150 + 450
Total cups of berries = 600
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Un agricultor ha comprado un terreno de 5,3ha y 4,6 a. Para cultivar pistacho, debe plantar un arbol cad 36m3 ¿cuantos pistachos debe plantar?
The farmer must plant between 2.750 and 3.500 pistacho trees on his or her 5, 3, and 4, 6 ha of land.
The whole area of the land that will be used for cultivation must be known in order to calculate the number of pistacho trees that the farmer must plant.
The aggregate of the two parcels makes up the entire land surface:
5,3 x 4,6 x 9 h = 9,9 h
We converted this surface to square metres:
9,9 ha times 10.000 m2/ha equals 99,000 m2.
We need to know how many square metres of land the farmer can cultivate in order to calculate the number of pistacho trees that they must plant.
We may calculate this by dividing the entire area by the number of square metres per tree:
2.750 árboles from 99.000 m2 divided by 36 m2/árbol.
As a result, the farmer must plant between 2.750 and 3.500 pistacho trees on his or her 5, 3, and 4, 6 ha of land.
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Why is photosynthesis maximum in red light?
Photosynthesis is maximum in red light because chlorophyll, the primary pigment responsible for capturing light energy in plants, absorbs red light most efficiently.
What is red light in Photosynthesis?
Red light is a part of the electromagnetic spectrum with a longer wavelength and lower energy than blue and green light.
Red light is particularly effective for photosynthesis because it has a longer wavelength and lower energy, which allows chlorophyll to efficiently absorb it and use it for the photosynthetic process.
In photosynthesis, plants use light energy to synthesize glucose from carbon dioxide and water.
As a result, photosynthesis is maximum in red light because plants can absorb and utilize this light energy most efficiently for their growth and energy production.
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List the three classifications of fundamental skull shapes and indicate the number of degrees of angulation (formed by the petrous pyramids and the midsagittal plane) for each classification.
The three classifications of fundamental skull shapes are: +
BrachycephalicMesocephalicDolichocephalicThe number of degrees of angulation (formed by the petrous pyramids and the midsagittal plane) for each classification is 45, 30, and 15 degrees, respectively.
What is a Skull?The skull is a bony structure that supports the face and protects the brain. There are several different skull shapes, which can be classified into three main categories based on their length and width: brachycephalic, mesocephalic, and dolichocephalic.
Brachycephalic: A short, wide skull shape. The petrous pyramids are angled at 45 degrees to the mid-sagittal plane.Mesocephalic: A skull shape that is neither short nor long, with a medium width. The petrous pyramids are angled at 30 degrees to the mid-sagittal plane.Dolichocephalic: A long, narrow skull shape. The petrous pyramids are angled at 15 degrees to the mid-sagittal plane.To know more about the "skull shape": https://brainly.com/question/1463216
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assume that 90 million households in the u.s. turn on their televisions at 8:00 p.m. on a sunday night, and the total number of u.s. tb households is 119.9 million. calculate the households using television (hut) figure.
The households using television (HUT) figure is 75.06%.
The households using television (HUT) figure is a measure of the percentage of households that have turned on their televisions at a particular time. It is calculated by dividing the number of households watching TV by the total number of households and multiplying by 100%.
In this case, we are given that 90 million households in the US turned on their televisions at 8:00 p.m. on a Sunday night. The total number of US households is 119.9 million. Using this information, we can calculate the HUT figure as follows
Households using television (HUT) = (Number of households watching TV / Total number of households) x 100%
HUT = (90 million / 119.9 million) x 100%
HUT = 75.06%
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g inspect the bball3 data set. what structure do these data appear to take? panel data cross sectional time series
The bball3 dataset appears to take the form of panel data, which is a type of longitudinal data consisting of multiple observations of the same individuals over time
The bball3 dataset appears to take the form of panel data. Panel data is a type of longitudinal data where observations are made on the same individuals over time. This means that the dataset likely consists of multiple observations of a set of individuals, with the observations collected at different points in time. In a panel data set, each individual can be referred to as a ‘panel unit’.
Cross-sectional data, on the other hand, consists of observations that are collected only once, at a single point in time. This means that each observation consists of a snapshot of the population at a given moment, which is different from panel data where each observation may represent different points in time for the same individuals.
Time series data is a type of data that is collected over a period of time. It captures how a certain variable changes over time, and is often used for forecasting purposes. This is different from panel data, which captures information about the same individuals at different points in time.
In conclusion, the bball3 dataset appears to take the form of panel data, which is a type of longitudinal data consisting of multiple observations of the same individuals over time. It is not cross-sectional or time series data.
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Effect of Transformations
-8
1 of 10 Answered
-6
-4 -2
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What are the new coordinates of the figure above if it is dilated by a scale factor of 2, with the origin as the center of dilation?
OA. A(1, -3), B(4, -3), C'(4, -4), D'(1,-4)
OB. A'(2,-2), B(4, -2), C(4,-4), D'(2,-4)
OC. A(2, -3), B(4, -3), C(4, -4), D'(2,-4)
OD. A(1,-2), B(4, -2), C(4, -4), D'(1,-4)
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We can conclude that the correct answer is OA. A(1, -3), B(4, -3), C'(4, -4), D'(1,-4).
What are the factors?
what are factorsIn mathematics, a factor is a number that divides another number without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, because these numbers divide 12 without leaving a remainder.
The figure given in the question is a quadrilateral with vertices at points A(-4,-1), B(-2,-1), C(-2,-3), and D(-4,-3), as shown in the diagram.
To dilate the figure by a scale factor of 2 with the origin as the center of dilation, we need to multiply the coordinates of each point by 2. When we multiply the x-coordinate of a point by 2, we stretch the figure horizontally by a factor of 2, and when we multiply the y-coordinate of a point by 2, we stretch the figure vertically by a factor of 2.
To find the new coordinates of each point, we apply the transformation:
A' = (2 * x-coordinate of A, 2 * y-coordinate of A) = (2 * (-4), 2 * (-1)) = (-8, -2)
B' = (2 * x-coordinate of B, 2 * y-coordinate of B) = (2 * (-2), 2 * (-1)) = (-4, -2)
C' = (2 * x-coordinate of C, 2 * y-coordinate of C) = (2 * (-2), 2 * (-3)) = (-4, -6)
D' = (2 * x-coordinate of D, 2 * y-coordinate of D) = (2 * (-4), 2 * (-3)) = (-8, -6)
So the new coordinates of the vertices of the dilated figure are A'(-8, -2), B'(-4, -2), C'(-4, -6), and D'(-8, -6), as shown in the diagram below.
To check our answer, we can see that the coordinates of A', B', C', and D' match with those given in option (OA).
Threfore, we can conclude that the correct answer is OA. A(1, -3), B(4, -3), C'(4, -4), D'(1,-4).
To learn more about factors from the given link:
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You work for a certain three-letter government agency in Maryland and are monitoring telephone calls being placed through a particular cell tower. Let X denote the arrival time of the first call, as measured by the number of seconds after you arrive at work at 8am. Let Y denote the arrival time of the second call. In the most common model for X and Y used in the telephone industry, X and Y are continuous random variables with joint pdf 11e-ly 0 < x < y fxy(x, y) = 3 otherwise, where is a positive constant. Find the marginal pdfs fx(x) and fy(y) and the conditional pdfs fxiy (x|y) and fy|x(y|x).
Similarly, the conditional pdf of Y given X, fy|x(y|x), is found by dividing the joint pdf, fxy(x,y), by the marginal pdf of X, fx(x). Thus, fy|x(y|x) = fxy(x,y)/fx(x) = 3/11e-ly for 0 < x < y < ∞.
The marginal pdf of X, fx(x), is the probability density function of X. It is found by integrating the joint pdf, fxy(x,y), with respect to Y over all possible values of Y. Thus, fx(x) = ∫-∞∞fxy(x,y)dy = 11e-ly for 0 < x < ∞. The marginal pdf of Y, fy(y), is found in the same way, but by integrating with respect to X over all possible values of X. Thus, fy(y) =[tex]∫0yfxy(x,y)dx = 11e-lyy for 0 < y < ∞.[/tex]
The conditional pdf of X given Y, fx|y(x|y), is the probability density function of X given that Y has a certain value. It is found by dividing the joint pdf, fxy(x,y), by the marginal pdf of Y, fy(y).
Thus, fx|y(x|y) =[tex]fxy(x,y)/fy(y) = 3/11e-lyy for 0 < x < y < ∞.[/tex]
for such more questions on probability density function
https://brainly.com/question/28705601
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