The data in the table below shows the average temperature in Northern Latitudes:
Estimate to the nearest whole number the average temperature for a city with a latitude of 48.
[___________]
Answers
Therefore , the solution of the given problem of mean comes out to be 15 is the solution.
What is mean?The sum of all values divided by all of the values constitutes the result from a collection, also referred to as the arithmetic mean. It is often referred to be known as "mean" as well as is one of the most frequency used main trend indicators. To find the answer, multiply the collection's overall amount of numbers by all of its values. Either the original data or data which has been combined into frequency charts can be used for calculations.
Here,
We can use linear interpolation between the two closest latitude numbers in the table, 45 and 50, to determine the typical temperature for a city with a latitude of 48.
Let T(45) and T(50) represent the typical temperatures at respective latitudes of 45 and 50, respectively. The following algorithm can be used to determine the temperature at 48 degrees latitude:
=> T(48) = T(45) + (T(50) - T(45)) * (48 - 45)/(50 - 45)
Using the numbers from the table as inputs, we obtain:
=> T(48) = 14 + (16 - 14) * (48 - 45)/(50 - 45)
=> T(48) = 14 + 2 * 3/5
=> T(48) = 14 + 1.2
=> T(48) = 15.2
The estimated average temperature for a city with a latitude of 48 is 15, rounded to the closest whole number.
Consequently, 15 is the solution.
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Related Questions
Of first-time college students who matriculate to a certain university, the odds in favor of having graduated in the top 25 percent of their high school class are 2.06 to 1. Of transfer students who matriculate to the same university, 0.666666666666667 proportion graduated in the top 25 percent of their high school class.
(a) For first-time college students, what is the proportion who graduated in the top 25 percent of their high school class (rounded to three decimal places)?
(b) For transfer students, what is the ratio in favor of having graduated in the top 25 percent of their high school class?
Odds and Probability:
Odds in favor of an event is expressed as a ratio:
O
(
f
)
=
favorable cases
:
unfavourable cases
Similarly odds against are expressed as:
O
(
a
)
=
unfavorable cases
:
favourable cases
.
Odds and probability are closely related, as the probability in favor of an even is computed as:
P
=
favorable cases
favorable cases+unfavorable cases
Answers
The answers to the questions (a) the proportion who graduated in the top 25 percent of their high school class will be 0.672 and (b) the ratio in favor of having graduated in the top 25 percent of their high school class is 2:3.
(a) For first-time college students, the proportion who graduated in the top 25 percent of their high school class (rounded to three decimal places) is 0.672.
(b) For transfer students, the ratio in favor of having graduated in the top 25 percent of their high school class is 0.67:1. It is said that 0.666666666666667 proportion graduated in the top 25 percent of their high school class. This can be simplified as follows:0.666666666666667=20/30=10/15=2/3. Therefore, the ratio in favor of having graduated in the top 25 percent of their high school class is 2:3.
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Consider a square whose side-length is one unit. Select any five points from inside this square. Prove that at least two of these points are within squareroot 2/2 units of each other.
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The given square with a side length of one unit is known to contain five points. One must prove that at least two of these points are within square root 2/2 units of each other.
According to the Pigeonhole principle, "if n items are put into m containers, with n > m, then at least one container must contain more than one item."In this context, the square is the container, and the points inside it are the objects. If more than four points are picked, the theorem is true, and two points are nearer to each other than the square root of 2/2 units.
Let's place four points on the square's four corners. The distance between any two of these points is the square root of two units since the square's side length is 1.
Let's add another point to the mix. That point is either inside the square or outside it. Without loss of generality, let us assume that the point is inside the square. It must then be within the perimeter outlined by joining the square's corners to the point that was not a corner already.
The perimeter of the square described above is a square with a side length of square root 2 units.
Since we have five points in the square, at least two of them must be in the same smaller square, due to the pigeonhole principle. Without loss of generality, let's assume that two of the points are in the upper-left square. As a result, any points within this square are within the square root 2 units of any of the other four points. Hence, at least two points of the five selected are within the square root of 2/2 units of each other.
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I need help asap I just need atleast one of these explained and I can do the rest
Answers
The factοred fοrm οf a pοlynοmial is
1. 30b³- 54b² = 6b²(5b−9)
2. 3y⁵ - 48y³ = 3y³(y −4)(y + 4)
3. x³ + 8 = (x + 2) (x² – 2x + 2²)
4. y³ - 64 = (y - 4) (y² – 4y + 4²)
5. 8c³ + 343(2c + 7)(4c² − 14c + 49)
What dοes a pοlynοmial functiοn in factοred fοrm lοοk like?The factοred fοrm οf a pοlynοmial is represented as a³ + b³ = (a + b) (a² – ab + b²). All equatiοns are cοmpοsed οf pοlynοmials. Earlier we've οnly shοwn yοu hοw tο sοlve equatiοns cοntaining pοlynοmials οf the first degree, but it is οf cοurse pοssible tο sοlve equatiοns οf a higher degree.
One way tο sοlve a pοlynοmial equatiοn is tο use the zerο-prοduct prοperty. If yοu remember frοm earlier chapters the prοperty οf zerο tells us that the prοduct οf any real number and zerο is zerο.
We will use the formula
a³ + b³ = (a + b) (a² – ab + b²)
And
a³ - b³ = (a - b) (a² – ab + b²)
1. [tex]30b^3-\ 54b^2[/tex]
⇒ 6b²(5b−9)
2. 3y⁵ - 48y³
⇒ 3y³( y² - 16y)
⇒ 3y³( y² - 4 + 4 - 16y)
⇒ 3y³(y −4)(y + 4)
3. x³ + 8
⇒ x³ + 2³
Using a³ + b³ = (a + b) (a² – ab + b²)
⇒ x³ + 2³
⇒ (x + 2) (x² – 2x + 2²)
4. y³ - 64
⇒ y³ - 4³
Using a³ - b³ = (a - b) (a² – ab + b²)
⇒ y³ - 4³
⇒ (y - 4) (y² – 4y + 4²)
5. 8c³ + 343
Using a³ + b³ = (a + b) (a² – ab + b²)
2c + 7
(2c + 7)(4c² − 14c + 49)
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which part of this graph shows a non-linear relationship
Answers
Answer:
A.
Step-by-step explanation:
Let n be a positive integer. If a == (3^{2n}+4)^-1 mod(9), what is the remainder when a is divided by 9?
Answers
Let n be a positive integer. We can use the properties of modular arithmetic to calculate this remainder. Let's start with a = (32n + 4)-1 mod 9. We can rewrite this as a = 9 - (32n + 4)-1 because 9 = 0 mod 9.
We can use Fermat's Little Theorem to calculate (32n + 4)-1. This theorem states that (32n + 4)-1 mod 9 = (32n + 4)8 mod 9.
Using the identity (a + b)n mod m = ((a mod m) + (b mod m))n mod m, we can simplify the equation to (32n mod 9 + 4 mod 9)8 mod 9.
32n mod 9 = 0, so (32n mod 9 + 4 mod 9)8 mod 9 = 48 mod 9 = 1.
Finally, a = 9 - 1 = 8 mod 9, so the remainder when a is divided by 9 is 8.
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The tires on Mavis’ car will have to be replaced when they each have 160 000 km of wear on them. If new tires cost $140.00 each, what is the total cost of the wear on Mavis’ tires for a year in which she drives 25 000 km?
Answers
Answer:
If the tires on Mavis’ car have to be replaced when they each have 160 000 km of wear, then the total distance Mavis can drive on a set of tires is:
4 tires * 160,000 km = 640,000 km
If Mavis drives 25,000 km in a year, she will need to replace her tires after:
640,000 km ÷ 25,000 km/year = 25.6 years
Since Mavis will need to replace her tires once every 25.6 years, the cost of the wear on her tires for a single year is:
$140.00/tire * 4 tires = $560.00
So the total cost of the wear on Mavis’ tires for a year in which she drives 25,000 km is $560.00.
Step-by-step explanation:
source: trust me bro
a parachutist rate during a free fall reaches 132 feet per second. what is this rate in meters per second? at this rate, how many meters will the parachutist fall during 10 seconds of free fall. in your computations, assume that 1 meter is equal to 3.3 feet. (do not round your answer)
Answers
Parachutist's rate during free fall is 40 meters per second and will fall approximately 490 meters during 10 seconds of free fall.
How to convert feet to meters?First, we need to convert 132 feet per second to meters per second. We know that 1 meter is equal to 3.3 feet, so we can use the following conversion factor:
[tex]$\frac{3meter}{3.3 feet}[/tex]
To convert feet per second to meters per second, we can multiply by the conversion factor:
[tex]132 (\frac{1}{3.3} ) = 40 meters/second[/tex]
Therefore, the parachutist's rate during free fall is 40 meters per second.
Next, we can use the following formula to find the distance the parachutist falls during 10 seconds of free fall:
distance =[tex]\frac{1}{2}[/tex] * acceleration * time²
where acceleration due to gravity is approximately 9.8 meters/second^2.
Substituting the given values, we get:
distance = [tex]\frac{1}{2}[/tex] * 9.8 meters/second² * (10 seconds)²
distance = 490 meters
Therefore, the parachutist will fall approximately 490 meters during 10 seconds of free fall.
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Weight: 20kg Order: 10 mg q6 hours Therapeutic range : 2-3 mg/kg/day. What is daily dose? Is it safe? Is it therapeutic?
Answers
The daily dose is 40mg, this dose per kilogram per day is within the therapeutic range of 2-3mg/kg/day, which means that the medication is within the safe and effective range for this patient's weight.
The weight of the patient is 20kg, and the prescribed dosage is 10mg every 6 hours. To calculate the daily dose, we need to multiply the prescribed dosage by the number of doses per day. Since the medication is prescribed every 6 hours, this means that the patient will take it 4 times a day.
=> (10mg x 4 doses) = 40 mg
The therapeutic range is the range of doses at which the medication is most effective and safe. In this case, the therapeutic range is 2-3mg/kg/day. To determine if the daily dose is within the therapeutic range, we need to divide the daily dose (40mg) by the patient's weight (20kg) to get the dose per kilogram per day, which is 2mg/kg/day.
However, it's important to note that the therapeutic range is a general guideline and may vary depending on the patient's individual circumstances and medical history.
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evaluate the diagram below, and find the measures of the missing angles
Answers
Answer:
A=100
B= 80
C=80
D=100
E=80
F=80
G=100
Step-by-step explanation:
8. A department store
buys 300 shirts for
a total cost of $7,200 and sells them for
$30 each. Find the percent markup.
Answers
The percent markup is 25%.
What is percent markup?Markup percentage is calculated by dividing the gross profit of a unit (its sales price minus it's cost to make or purchase for resale) by the cost of that unit.
Given that, A department store buys 300 shirts for a total cost of $7,200 and sells them for $30 each.
Cost of one shirt [tex]= 7200 \div 300 = \$24[/tex]
And they sold at $30 each,
Percent markup [tex]= 30-24 \div 24 \times 100[/tex]
[tex]= 25\%[/tex]
Hence, the percent markup is 25%.
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Which choice is an exponential function?
Of(x)=x²+6
Of(x)=5(3)*
Of(x) = 3x + 7
Of(x) = |2x+ 41
Answers
Answer:1st one
Step-by-step explanation:
Suppose that the insurance companies did do a survey. They randomly surveyed 400 drivers and found that 320 claimed they always buckle up. We are interested in the population proportion of drivers who claim they always buckle up.a.i. x = __________ii. n = __________iii. p′ = __________b. Define the random variables X and P′, in words.c. Which distribution should you use for this problem? Explain your choice.d. Construct a 95% confidence interval for the population proportion who claim they always buckle up.i. State the confidence interval.ii. Sketch the graph.iii. Calculate the error bound.e. If this survey were done by telephone, list three difficulties the companies might have in obtaining random results.
Answers
We are interested in the population proportion of drivers who claim they always buckle upa.i. x = 320 ii. n = 400 iii. p′ = 0.8
b. The random variable X represents the number of drivers out of the sample of 400 who claim they always buckle up, while P′ represents the sample proportion of drivers who claim they always buckle up.
c. The distribution to use for this problem is the normal distribution because the sample size is large enough (n=400) and the population proportion is not known.
d. i. The 95% confidence interval for the population proportion who claim they always buckle up is (0.7709, 0.8291).
ii. The graph is a normal distribution curve with mean p′ = 0.8 and standard deviation σ = sqrt[p′(1-p′)/n].
iii. The error bound is 0.0291.
e. Three difficulties the insurance companies might have in obtaining random results from a telephone survey are:
Selection bias: The survey might not be truly random if the telephone numbers selected are not representative of the population of interest.
Nonresponse bias: People may choose not to participate in the survey or may not be reached, which could bias the results.
Social desirability bias: Respondents may give socially desirable answers rather than their true opinions, which could also bias the results.
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calculate the expected value, the variance, and the standard deviation of the given random variable x. (round all answers to two decimal places.) x is the number of red marbles that suzan has in her hand after she selects three marbles from a bag containing three red marbles and two green ones. expected value variance standard deviation
Answers
The expected value of x is 1.80, the variance is 0.72, and the standard deviation is 0.85.
Calculate the expected value, variance, and standard deviation of the random variable x as follows. Round all answers to two decimal places, and keep in mind that x is the number of red marbles that Suzan has in her hand after selecting three marbles from a bag containing three red marbles and two green ones.
Expected Value: Since there are 3 red marbles and 2 green marbles in the bag, the probability of drawing a red marble is: P(R) = 3/5The probability of drawing a green marble is P(G) = 2/5Therefore, the expected value of the random variable X is: E(X) = μ = np = 3/5 * 3 = 1.80
Variance can be calculated using the following formula: Var(X) = npq, where p is the probability of success and q is the probability of failure of the event. In this scenario, the probability of drawing a red marble is P(R) = 3/5, and the probability of drawing a green marble is P(G) = 2/5.
Therefore, Var(X) = npq Var(X) = (3/5)*(2/5)*3Var(X) = 1.80 * 0.4Var(X) = 0.72Standard Deviation: The square root of the variance is equal to the standard deviation. Hence, the formula for standard deviation is: S.D. = √Var(X)S.D. = √0.72S.D. = 0.85
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A space probe near Neptune communicates with Earth using bit strings. Suppose that in its transmissions it sends a 1 one-third of the time and a 0 two-thirds of the time. When a 0 is sent, the probability that it is received correctly is 0.8 and the probability that it is received incorrectly (as a 1) is 0.2. When a 1 is sent the probability that it is received correctly is 0.8 and the probability that it is received incorrectly (as a 0) is 0.2.
Find the probability that a 0 is received. (Enter the value of the probability in decimal format and round the final answer to one decimal place.)
Answers
P(0 received correctly) = P(0 sent) × P(0 received correctly | 0 sent)= [tex](2/3) × 0.8= 0.5333[/tex] (rounded to 1 decimal place)Thus, the probability that a 0 is received is 0.5333 (rounded to 1 decimal place).
0.5333
A space probe near Neptune communicates with Earth using bit strings. Suppose that in its transmissions it sends a 1 one-third of the time and a 0 two-thirds of the time. When a 0 is sent, the probability that it is received correctly is 0.8 and the probability that it is received incorrectly (as a 1) is 0.2. When a 1 is sent the probability that it is received correctly is 0.8 and the probability that it is received incorrectly (as a 0) is 0.2.The probability that a 0 is received correctly is given in the problem as 0.8, and the probability that a 0 is sent is 2/3. Therefore, the probability that a 0 is received correctly
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find the area and circumference of the circle below.round your answers to the nearest hundredth
Answers
Answer:
Step-by-step explanation:
The area of given circle is 28.27 sq.m. The circumference of given circle is 18.85 m (rounded to the nearest hundredth).
Give a short note on Circumference?The circumference of a circle is the distance around the edge or boundary of the circle. It is also the perimeter of the circle. The circumference is calculated using the formula:
C = 2πr
where "C" is the circumference, "π" is a mathematical constant approximately equal to 3.14159, and "r" is the radius of the circle.
The circumference of a circle is proportional to its diameter, which is the distance across the circle passing through its center. Specifically, the circumference is equal to the diameter multiplied by π, or:
C = πd
where "d" is the diameter of the circle.
Given that the diameter of the circle is 6m.
We know that the radius (r) of the circle is half of the diameter (d), so:
r = d/2 = 6/2 = 3m
The area (A) of the circle is given by the formula:
A = πr²
Substituting the value of r, we get:
A = π(3)² = 9π ≈ 28.27 sq.m (rounded to the nearest hundredth)
The circumference (C) of the circle is given by the formula:
C = 2πr
Substituting the value of r, we get:
C = 2π(3) = 6π ≈ 18.85 m (rounded to the nearest hundredth)
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The complete question is:
If Jacob spent 45$ on dinner and wanted to top the waitress 15%, which of the following would be a good estimate for the tip?
Answers
Answer: 6.75
Step-by-step explanation:
45 x 0.15= 6.75
115% divide by 100 = 1.5
1.5 x 45$ is $67.50
write down the name of shape W
Answers
A hexagon with two lines
hope helped you please make me brainalist and keep smiling dude
I hope you are form India
Two ropes are attached to a tree, and forces of F_1 = 1.31 + 4.6J n and F_2 = 3.2i + 6.8j n are applied. The forces are coplanar (in the same plane). What is the resultant (net force) of these two force vectors (in N)? (Express your answer in vector form.) Find the magnitude (in N) and direction (in degrees counterclockwise from the +x-axis) of this net force.
Answers
The magnitude and direction of the net force are found by adding the two forces together as resultant force vectors.
a) 11.82 N
b) 74.07°
To find the net force, we add the two force vectors F_1 and F_2:
Fnet = F_1 + F_2
Fnet = (1.31 + 4.6j) N + (3.2i + 6.8j) N
Fnet = 3.2i + (1.31 + 4.6j + 6.8j) N
Fnet = 3.2i + (1.31 + 11.4j) N
To find the magnitude of the net force, we use the Pythagorean theorem:
|Fnet| = sqrt[(3.2)^2 + (1.31 + 11.4)^2] N
|Fnet| ≈ 11.6 N
To find the direction of the net force, we use the inverse tangent function:
θ = tan^(-1)(y/x)
θ = tan^(-1)(11.4/3.2)
θ ≈ 73.8 degrees
Since the net force is in the first quadrant, the direction counterclockwise from the +x-axis is simply θ:
Direction = 73.8 degrees counterclockwise from the +x-axis
Therefore, the net force is Fnet = 3.2i + (1.31 + 11.4j) N, with a magnitude of approximately 11.6 N and a direction of approximately 73.8 degrees counterclockwise from the +x-axis.
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Use the following function to find d(0)
d(x)=-x+-3
d(0)=
Answers
When the function d(x) = -x +(-3), then the value of d(0) is -3
In mathematics, a function is a relationship between two sets of numbers, called the domain and range. A function assigns each element of the domain to exactly one element of the range.
In the given problem, we are given a function d(x)=-x-3. The notation d(0) represents the value of the function d(x) when x = 0.
To find d(0), we need to substitute x = 0 in the function d(x)=-x-3, which gives:
d(0) = -(0) - 3
The first term -(0) is equal to zero, and the second term -3 is a constant value that remains the same regardless of the value of x. Therefore, we can simplify the expression as
d(0) = -3
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1 0 6
0 1 1
0 0 0
Find the solution(s) to the system, if it exists. State the solution as a point (be sure to use parentheses), use parameter(s) s and t if needed. If the system is inconsistent, then state no solution.
Answers
The system has infinitely many solutions, which can be written as (x, y, z) = (1 - 60s, -10 + 600s, s) where s is a parameter.
To solve the system of equations:
1x + 0y + 60z = 1
1x + 10y + 0z = 0
0x + 0y + 0z = 0
The third equation is an identity, implying that it does not give us any new information. The first two equations can be used to solve for x, y, and z:
From the first equation, we get x = 1 - 60z
From the second equation, we get y = 0 - 10x = -10(1 - 60z) = -10 + 600z
Therefore, the solution to the system can be written as a point in terms of z as:
(x, y, z) = (1 - 60z, -10 + 600z, z)
Since z can take on any value, there are infinitely many solutions to the system, which can be parameterized as:
(x, y, z) = (1 - 60s, -10 + 600s, s) where s is a parameter.
he system has infinitely many solutions, which can be written as (x, y, z) = (1 - 60s, -10 + 600s, s) where s is a parameter.
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Audrey and Harper are selling fruit for a band fundraiser. Customers can buy small crates of apples and large containers of peaches. Audrey sold 3 small crates of apples and 10 large containers of peaches for a total of $116. Harper sold 11 small crates of apples and 20 large containers of peaches for a total of $292. Find the cost each of one small crate of apples and one large container of peaches. A) Define your variables. Write a system of equations to represent the situation. Solve using any method. Show all of your work. Andrew decides he wants to help the band as well. He sells 7 small crates of apples and 5 larges containers of peaches. How much money does he raise for the band?
Answers
The cost of one small crate of apples is $12 and the cost of one large crate of peaches is $8. The cost of 7 small cates of apples and 5 large containers of peach is $126.
What is the cost of 7 small crates and 5 large containers?The system of equations that describe the question is:
3s + 10l = 116 equation 1
11s + 20l = 292 equation 2
Where:
s = cost of one small crate of apples
l = cost of one large crate of peaches
The elimination method would be used to determine the values of s and l.
Multiply equation 1 by 2
6s + 20l = 232 equation 3
Subtract equation 3 from equation 2:
5s = 60
Divide both sides of the equation by 5
s = 60 / 5
s = $12
Substitute for s in equation 1:
3(12) + 10l = 116
36 + 10l = 116
10l = 116 - 36
10l = 80
l = 80 / 10
l = 8
Cost of 7 small crates of apples and 5 large containers of peaches = (7 x 12) + (8 x 5) = $124
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Helppppp will give brainlyest
Answers
Answer: 4
Step-by-step explanation:
4. shift the boundary line up 1
Question
Find the value of y
for the given value of x
.
y=x+5;x=3
Answers
Answer: y is equal to 8
Step-by-step explanation:
by substituting the x for its vale of three we can add the two values to get 8 or y=8
The coordinates of the endpoints of PQ are P( – 12,7) and Q( – 4, – 9). Point R is on PQ and divides it such that PR:QR is 3:5
Answers
The coordinates of R are (-8,-1). To find the coordinates of R, we first need to find the length of PQ.
Using the distance formula, we have:
d(P,Q) = √((x2-x1)² + (y2-y1)²)
= √((-4-(-12))² + (-9-7)²)
= √(8² + (-16)²)
= √(320)
= 8 √(5)
Since PR:QR is 3:5, we can set up the following equation:
d(P,R)/d(R,Q) = 3/5
Let the coordinates of R be (x,y). We can use the midpoint formula to find the coordinates of the midpoint of PQ, which is also the coordinates of the point that divides PQ into two parts in the ratio of 3:5.
Midpoint of PQ = ((-12-4)/2, (7-9)/2) = (-8,-1)
Using the distance formula again, we can find the distance between P and R:
d(P,R) = (3/8) d(P,Q)
= (3/8) (8 √(5))
= 3 √(5)
Now we can use the ratio PR:QR = 3:5 to find the distance between R and Q:
d(R,Q) = (5/3) d(P,R)
= (5/3) (3 √(5))
= 5 √(5)
Finally, we can use the midpoint formula to find the coordinates of R:
x = (-12 + (3/8) (8))/2 = -8
y = (7 + (-1))/2 = 3
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Complete Question:
The coordinates of the endpoints of bar (PQ) are P(-12,7) and Q(-4,-9). Point R is on bar (PQ) and divides it such that PR:QR is 3:5. What are the coordinates of R ?
how to calculate the product of two random variable that follows normal distribution with mean 0 and variance 1
Answers
The product of two random variables that follows the normal distribution with mean 0 and variance 1 is expected 0.
To compute the product of two random variables that are normal distributed with a mean of 0 and a variance of 1, the following procedure can be employed:
Since the mean of the normal distribution is 0 and the variance is 1, we can assume that the standard deviation is also 1.Thus, we can write the probability density function of the normal distribution as:
f(x) = (1/√2π) * e^(-x^2/2)
Using the definition of expected value, we can write the expected value of a random variable X as:E[X] = ∫x * f(x) dx, where the integral is taken over the entire range of X.
Similarly, we can write the expected value of a random variable Y as:E[Y] = ∫y * f(y) dy, where the integral is taken over the entire range of Y.
Since the two random variables are independent, the expected value of their product is the product of their expected values. Thus, we can write:E[XY] = E[X] * E[Y]
Substituting the probability density function of the normal distribution into the expected value formula, we can write:E[X] = ∫x * f(x) dx = ∫x * (1/√2π) * e^(-x^2/2) dx = 0
E[Y] = ∫y * f(y) dy = ∫y * (1/√2π) * e^(-y^2/2) dy = 0
Thus, the expected value of the product of two random variables that follow a normal distribution with mean 0 and variance 1 is:E[XY] = E[X] * E[Y]
= 0 * 0 ⇒ 0
Therefore, the product of two random variables that follow a normal distribution with mean 0 and variance 1 has an expected value of 0.
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Alfonso wants to purchase a pool membership
for the summer. He has no more than y dollars to
spend. The Aquatics Club charges an initial fee
of $75 plus $20 per month. The Swimming Hole
charges an initial fee of $15 plus $65 per month.
Write a system of inequalities that you can use to
determine which company offers the better deal.
Let x represent the number of months.
Answers
The system of inequalities of the company with the better offer is 75 + 20x ≤ y and 15 + 65x ≤ y
Identifying the system of inequalitiesLet's use A to represent the total cost (in dollars) of purchasing a pool membership from the Aquatics Club,
Let S represent the total cost of purchasing a pool membership from the Swimming Hole.
Then we can write the following system of inequalities:
A = 75 + 20x (total cost of Aquatics Club membership)
S = 15 + 65x (total cost of Swimming Hole membership)
Alfonso has no more than y dollars to spend
So, we have
75 + 20x ≤ y
15 + 65x ≤ y
Hence, the system is 75 + 20x ≤ y and 15 + 65x ≤ y
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HELP PLS ILL GIVE U POINTS
Answers
Answer:
i think 16 im not sure
Step-by-step explanation:
It is well documented that a typical washing machine can last anywhere between 5 to 20 years. Let the life of a washing machine be represented by a lognormal variable, Y = eX where X is normally distributed. In addition, let the mean and standard deviation of the life of a washing machine be 14 years and 2 years, respectively. [You may find it useful to reference the z table.] a. Compute the mean and the standard deviation of X. (Round your intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.) b. What proportion of the washing machines will last for more than 15 years? (Round your intermediate calculations to at least 4 decimal places, "z" value to 2 decimal places, and final answer to 4 decimal places.) c. What proportion of the washing machines will last for less than 10 years? (Round your intermediate calculations to at least 4 decimal places, "z" value to 2 decimal places, and final answer to 4 decimal places.) d. Compute the 90th percentile of the life of the washing machines. (Round your intermediate calculations to at least 4 decimal places, "z" value to 3 decimal places, and final answer to the nearest whole number.)
Answers
a. The mean of X is 1.7549 and the standard deviation is 0.3536.
b. To calculate the proportion of washing machines that will last for more than 15 years, we need to use the standard normal distribution table. The z-score for 15 years is (15-14)/0.3536 = 2.822. Using the table, we find that the proportion of washing machines that will last for more than 15 years is 0.9968.
c. To calculate the proportion of washing machines that will last for less than 10 years, we need to use the standard normal distribution table. The z-score for 10 years is (10-14)/0.3536 = -2.822. Using the table, we find that the proportion of washing machines that will last for less than 10 years is 0.0032.
d. To calculate the 90th percentile of the life of the washing machines, we need to use the standard normal distribution table. The z-score for the 90th percentile is 1.28. Using the table, we find that the 90th percentile is 17 years.
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The sum of the base and the height of a triangle is 22 cm. Find the dimensions for which the area is a maximum. The triangle with maximum area has a height of_____cm and a base of cm_____.
Answers
The dimensions of the triangle with maximum area are a base of 11 cm and a height of 11 cm.
We are given that the sum of the base and height of a triangle is 22 cm. Let's call the base of the triangle "b" and the height "h". Then we have the equation:
b + h = 22
We want to find the dimensions of the triangle that will give us the maximum area.
The formula for the area of a triangle is A = (1/2)bh.
We can use the equation b + h = 22 to solve for one of the variables in terms of the other.
we can solve for h:
h = 22 - b
Substituting this into the formula for the area, we get:
A = (1/2)b(22 - b)
The equation 0 = 11b - (1/2)b² can be rearranged to:
(1/2)b² - 11b = 0
We can then use the quadratic formula to solve for "b"
b = 11 ± 11
So the value of b that gives us the maximum area is b = 11 cm. Substituting this back into the equation h = 22 - b, we get:
h = 22 - 11 = 11 cm
Triangle has a base of 11 cm and a height of 11 cm.
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Can anyone please help with this math problem? Thanks!
Answers
Answer: Yes Sofia will have enough money
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Explanation:
Refer to the drawing below. I've split the hexagon into two pieces. The bottom is a rectangle and the top is a trapezoid.
The area of the rectangle is 16*7 = 112 square meters.
The trapezoid has 16 as one of the parallel sides. The other side is x meters. We'll use the perimeter 54 to determine what x must be
sum of the exterior sides = perimeter
6+7+16+7+6+x = 54
42+x = 54
x = 54-42
x = 12
The top most side is 12 meters. This is the missing side of the trapezoid. The hexagon has a height of 12.66 meters, so the trapezoid's height must be 12.66-7 = 5.66 meters. Refer to the blue segment I marked in the drawing below.
area of the trapezoid = 0.5*height*(base1+base2)
area = 0.5*5.66*(16+12)
area = 79.24 square meters
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Recap so far
area of the rectangle at the bottom = 112 square metersarea of the trapezoid up top = 79.24 square metersThe total area of the entire hexagon is therefore 112+79.24 = 191.24 square meters.
Let's convert that to square decimeters.
Recall that 1 decimeter = 10 centimeters
Multiply both sides by 10
1 decimeter = 10 centimeters
10*(1 decimeter) = 10*(10 centimeters)
10 decimeters = 100 centimeters
10 decimeters = 1 meter
Then,
[tex]191.24 \text{ sq m}= 191.24 \text{ sq m} * \frac{10 \text{ dm}}{1 \text{ m}} * \frac{10 \text{ dm}}{1 \text{ m}}\\\\= \frac{191.24*10*10}{1*1} \text{ sq dm}\\\\= 19124 \text{ sq dm}\\\\[/tex]
The entire lawn is 19124 square decimeters.
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We have one final block of calculations to determine the total price.
x = number of rolls
1 roll covers 90 square decimeters
x rolls cover 90x square decimeters
90x = 19124
x = 19124/90
x = 212.489 approximately
Round up to the nearest integer to get x = 213. It doesn't matter that 212.489 is closer to 212. We round up to clear the hurdle. It means we'll have leftover grass that isn't used (perhaps it could be handy to have some back up grass just in case mistakes are made, and some patches need to be redone).
In short, Sofia needs 213 rolls.
1 roll costs $4.50
213 rolls will cost 213*4.50 = 958.50 dollars.
This is under the $1000 threshold (with 1000-958.50 = 41.50 dollars to spare).
Sofia will have enough money to pay for all of the grass.
