Answer:
$481
Step-by-step explanation:
37×$17=$481
he made $481
three bolts and three nuts are in a box. two parts are chosen at random. find the probability that one is a bolt and one is a nut.
The probability of picking one bolt and one nut is 1/2 or 50%.
To find the probability that one is a bolt and one is a nut, we need to use the formula for calculating the probability of two independent events happening together: P(A and B) = P(A) × P(B)
Let's first calculate the probability of picking a bolt from the box:
P(bolt) = number of bolts / total number of parts = 3/6 = 1/2
Now, let's calculate the probability of picking a nut from the box:
P(nut) = number of nuts / total number of parts = 3/6 = 1/2
Since the events are independent, the probability of picking a bolt and a nut in any order is:
P(bolt and nut) = P(bolt) × P(nut) + P(nut) × P(bolt)
P(bolt and nut) = (1/2) × (1/2) + (1/2) × (1/2)
P(bolt and nut) = 1/2
Therefore, the probability of picking one bolt and one nut is 1/2 or 50%.
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the probability that one chosen part is a bolt and the other chosen part is a nut is 1, or 100%. This makes sense because if we choose two parts at random, we must get one bolt and one nut since there are three of each in the box.
To find the probability that one chosen part is a bolt and the other chosen part is a nut, we need to use the formula for probability:
Probability = (number of desired outcomes) / (total number of outcomes)
There are two ways we could choose one bolt and one nut: we could choose a bolt first and a nut second, or we could choose a nut first and a bolt second. Each of these choices corresponds to one desired outcome.
To find the number of ways to choose a bolt first and a nut second, we multiply the number of bolts (3) by the number of nuts (3), since there are 3 possible bolts and 3 possible nuts to choose from. This gives us 3 x 3 = 9 total outcomes.
Similarly, there are 3 x 3 = 9 total outcomes if we choose a nut first and a bolt second.
Therefore, the total number of desired outcomes is 9 + 9 = 18.
The total number of possible outcomes is the number of ways we could choose two parts from the box, which is the number of ways to choose 2 items from a set of 6 items. This is given by the formula:
Total outcomes = (6 choose 2) = (6! / (2! * 4!)) = 15
Putting it all together, we have:
Probability = (number of desired outcomes) / (total number of outcomes)
Probability = 18 / 15
Probability = 1.2
However, this answer doesn't make sense because probabilities should always be between 0 and 1. So we made a mistake somewhere. The mistake is that we double-counted some outcomes. For example, if we choose a bolt first and a nut second, this is the same as choosing a nut first and a bolt second, so we shouldn't count it twice.
To correct for this, we need to subtract the number of outcomes we double-counted. There are 3 outcomes that we double-counted: choosing two bolts, choosing two nuts, and choosing the same part twice (e.g. choosing the same bolt twice). So we need to subtract 3 from the total number of desired outcomes:
Number of desired outcomes = 18 - 3 = 15
Now we can calculate the correct probability:
Probability = (number of desired outcomes) / (total number of outcomes)
Probability = 15 / 15
Probability = 1
So the probability that one chosen part is a bolt and the other chosen part is a nut is 1, or 100%. This makes sense because if we choose two parts at random, we must get one bolt and one nut since there are three of each in the box.
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Question:
The current (in amps) in a simple
electrical circuit varies inversely to
the resistance measured in ohms.
The current is 24 amps when the
resistance is 20 ohms. Find the
current (in amps) when the
resistance is 12 ohms.
The current in the circuit when the resistance is 12 ohms is 40 amps.
What is fraction?
A fraction is a mathematical term that represents a part of a whole or a ratio between two quantities.
We can use the inverse proportionality formula to solve this problem, which states that:
current (in amps) x resistance (in ohms) = constant
Let's call this constant "k". We can use the information given in the problem to find k:
24 amps x 20 ohms = k
k = 480
Now we can use this constant to find the current when the resistance is 12 ohms:
current x 12 ohms = 480
current = 480 / 12
current = 40 amps
Therefore, the current in the circuit when the resistance is 12 ohms is 40 amps.
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what is the 4th term/number of (a+b)^9, pascal’s triangle?
Step-by-step explanation:
hope this will help you Thanks
2. when conducting a hypothesis test, the hypothesis that illustrates what we really think is going on in the population is called the hypothesis. an. analytical b. hypothetical c. null d. theoretical e. alternative
Evan takes 100 milligrams of medicine. The amount of medicine in his bloodstream decreases by 0.4 milligram each minute for a number of minutes, m, after that. He writes the expression 100 - 0.4m to find the amount of medicine in his bloodstream after m minutes. Which statement about his expression is true?
The statement that is true about Evan's expression is that it represents a linear function of the amount of medicine in his bloodstream, where the initial amount is 100 milligrams and the rate of change is -0.4 milligrams per minute.
What is the equivalent expression?
Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.
The expression 100 - 0.4m represents the amount of medicine in Evan's bloodstream after m minutes, where the amount of medicine decreases by 0.4 milligrams each minute.
The coefficient of the variable m (-0.4) represents the rate of change of the amount of medicine in Evan's bloodstream per minute. It tells us that for every one minute that passes, the amount of medicine in his bloodstream decreases by 0.4 milligrams.
The constant term (100) represents the initial amount of medicine in Evan's bloodstream before the medicine starts to decrease.
Therefore, the statement that is true about Evan's expression is that it represents a linear function of the amount of medicine in his bloodstream, where the initial amount is 100 milligrams and the rate of change is -0.4 milligrams per minute.
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hat is the maximum speed of a point on the outside of the wheel, 15 cm from the axle?
It depends on the rotational speed of the wheel. To calculate this speed, we need to know the angular velocity of the wheel.
The maximum speed of a point on the outside of the wheel, 15 cm from the axle, if we assume that the wheel is rotating at a constant rate, we can use the formula v = rω, where v is the speed of the point on the outside of the wheel, r is the radius of the wheel (15 cm in this case), and ω is the angular velocity of the wheel. Therefore, the maximum speed of a point on the outside of the wheel would be directly proportional to the angular velocity of the wheel.
The formula to calculate the maximum linear speed (v) is:
v = ω × r
where v is the linear speed, ω is the angular velocity in radians per second, and r is the distance from the axle (15 cm, or 0.15 meters in this case).
Once you have the angular velocity (ω) of the wheel, you can plug it into the formula and find the maximum speed of a point on the outside of the wheel.
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in a role playing game two special dice are rolled. one die has 4 faces numbered 1 through 4 and the other has 6 faces numbered 1 thorugh 6. what is the probabilty that the total shown on the two dice after they are rolled is greater than or equal to 8?
The probability that the total shown on the two dice after they are rolled is greater than or equal to 8 is 1/9.
PLEASE HELP DUE TODAY!!!!!!!
Consider the functions g(x) = 2x + 1 and h(x) = 2x + 2 for the domain 0 < x < 5
a. Without evaluating or graphing the functions, how do the ranges compare?
b. graph the 2 functions and describe each range over the given interval
Answer:
see the images and explanation
Step-by-step explanation:
for the graph:
the domain 0 < x < 5
the range for each functions:
g(x) = 2x + 1
g(x) = y , 1 < y < 11
h(x) = 2x + 2 , 2 < y < 12
Given that £1 = $1.62
a) How much is £650 in $?
b) How much is $405 in £?
Answer:
a 1053
b 250
multiply 650 by 1.62 for part a.
for part b divide by 1.62 since pound is less than dollar
hope this helps :)
Kubin Company’s relevant range of production is 25,000 to 33,500 units. When it produces and sells 29,250 units, its average costs per unit are as follows: Average Cost per Unit Direct materials $ 8. 50 Direct labor $ 5. 50 Variable manufacturing overhead $ 3. 00 Fixed manufacturing overhead $ 6. 50 Fixed selling expense $ 5. 00 Fixed administrative expense $ 4. 00 Sales commissions $ 2. 50 Variable administrative expense $ 2. 00 Required: 1. For financial accounting purposes, what is the total amount of product costs incurred to make 29,250 units? 2. For financial accounting purposes, what is the total amount of period costs incurred to sell 29,250 units? 3. For financial accounting purposes, what is the total amount of product costs incurred to make 33,500 units? 4. For financial accounting purposes, what is the total amount of period costs incurred to sell 25,000 units? (For all requirements, do not round intermediate calculations. )
1. Total amount of product costs
2. Total amount of period costs incurred
3. Total amount of product costs
4. Total amount of period costs
For the relevant range of production of units total amount of product and period cost as per units are,
Total amount of product costs for 29,250 units is $687,375.
Total amount of period costs incurred for 29,250 units is $58,511.50
Total amount of product costs for 33,500 units is equal to $787,250.
Total amount of period costs for 25,000 units is equal to $50,011.50.
Average Cost per Unit Direct materials = $ 8. 50
Direct labor = $ 5. 50
Variable manufacturing overhead = $ 3. 00
Fixed manufacturing overhead = $ 6. 50
Fixed selling expense = $ 5. 00
Fixed administrative expense = $ 4. 00
Sales commissions = $ 2. 50
Variable administrative expense = $ 2. 00
Total unit produced = 29,250 units,
Total product costs
= (Direct materials + Direct labor + Variable manufacturing overhead + Fixed manufacturing overhead) x Number of units produced
= ($8.50 + $5.50 + $3.00 + $6.50) x 29,250
= $23.50 x 29,250
= $687,375
The total amount of product costs incurred to make 29,250 units is $687,375.
Total period costs
= Fixed selling expense + Fixed administrative expense + Sales commissions + (Variable administrative expense x Number of units sold)
= $5.00 + $4.00 + $2.50 + ($2.00 x 29,250)
= $5.00 + $4.00 + $2.50 + $58,500
= $58,511.50
The total amount of period costs incurred to sell 29,250 units is $58,511.50
For the number of units produced changed to 33,500.
Total product costs
= (Direct materials + Direct labor + Variable manufacturing overhead + Fixed manufacturing overhead) x Number of units produced
= ($8.50 + $5.50 + $3.00 + $6.50) x 33,500
= $23.50 x 33,500
= $787,250
The total amount of product costs incurred to make 33,500 units is $787,250.
The number of units sold changed to 25,000.
Total period costs
= Fixed selling expense + Fixed administrative expense + Sales commissions + (Variable administrative expense x Number of units sold)
= $5.00 + $4.00 + $2.50 + ($2.00 x 25,000)
= $5.00 + $4.00 + $2.50 + $50,000
= $50,011.50
The total amount of period costs incurred to sell 25,000 units is $50,011.50.
Therefore, the total amount of the product and period cost for different situations are,
Total amount of product costs is equal to $687,375.
Total amount of period costs incurred is equal to $58,511.50
Total amount of product costs is equal to $787,250.
Total amount of period costs is equal to $50,011.50.
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Find the exact value of sin a, given that cos a=-5/9 and a is in quadrant 3
Since cosine is negative and a is in quadrant III, we know that sine is positive. We can use the Pythagorean identity to solve for sine:
sin^2(a) + cos^2(a) = 1
sin^2(a) + (-5/9)^2 = 1
sin^2(a) = 1 - (-5/9)^2
sin^2(a) = 1 - 25/81
sin^2(a) = 56/81
Taking the square root of both sides:
sin(a) = ±sqrt(56/81)
Since a is in quadrant III, sin(a) is positive. Therefore:
sin(a) = sqrt(56/81) = (2/3)sqrt(14)
1. Find the square root of each of the following numbers: (i) 152.7696
can someone give me the answers to these 5?? pleaseee!!
The MAD of the hourly wages given would be $ 0.48. The range would be $ 2.00. Q1 would be $8.25. Q3 would then be $9.25. The IQR would be $1.00
How to find the number summaries ?Calculate the MAD:
First, find the mean of the data set:
mean = (sum of all values) / (number of values)
mean = (8.25 + 8.50 + 9.25 + 8.00 + 10.00 + 8.75 + 8.25 + 9.50 + 8.50 + 9.00) / 10
mean = 88.00 / 10 = 8.80
Then, find the mean of these absolute deviations:
MAD = (sum of absolute deviations) / (number of values)
MAD = (0.55 + 0.30 + 0.45 + 0.80 + 1.20 + 0.05 + 0.55 + 0.70 + 0.30 + 0.20) / 10
MAD = 4.10 / 10 = 0.41
Calculate the range:
range = maximum value - minimum value
range = 10.00 - 8.00 = 2.00
Find Q1 and Q3:
{8.00, 8.25, 8.25, 8.50, 8.50, 8.75, 9.00, 9.25, 9.50, 10.00}
Q1 is the median of the lower half, and Q3 is the median of the upper half.
Lower half: {8.00, 8.25, 8.25, 8.50, 8.50}
Upper half: {8.75, 9.00, 9.25, 9.50, 10.00}
Q1 = median of lower half = 8.25
Q3 = median of upper half = 9.25
Calculate the IQR:
IQR = Q3 - Q1
IQR = 9.25 - 8.25 = 1.00
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Copy
State
This
prior
any r
perm
Man
avv
ttr
opy
om
and
av
Marven and three friends are renting a car for a trip. Rental prices are
shown in the table.
Item
PART B
Small car rental fee
-seats 4 passengers
Full-size car rental fee
-seats 4 passengers
Insurance
Price
465=25x
$39/day
$49/day
$21/day
25
(X=18.6
-198
018.6
1465
LIS
If they still use the coupon, how many days could they rent the small car
with insurance if they have $465 to spend?
Since they can't rent for a fraction of a day, the maximum number of days they can rent the small car with insurance is 10 days.
Insurance calculation.
The total cost of renting a small car with insurance is:
$465 = $25x + $21x
Simplifying and solving for x, we get:
$465 = $46x
x = 10.11
Since they can't rent for a fraction of a day, the maximum number of days they can rent the small car with insurance is 10 days.
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Find the measure of the missing side.
1. 8.2
2. 9.9
3. 7.4
4. 10.9
Answer:
1
Step-by-step explanation:
First of all we use the "law of sines"
to get the measure/length we need the opposing angle of it of the side, now in this case the missing side is x
and its opposing angle is missing so using common sense, the sum of angles in the triangle is 180°
180°=70°+51°+ x
x = 180°-121°
=59°
Using law of sines:
(sides are represented by small letters/capital letters are the angles)
a/sinA= b/sinB= c/sinC
We have one given side which is "9"
so,
9/sin70= x/sin59
doing the criss-cross method,
9×sin59=sin70×x
9×sin59/sin70=x
x=8.2 (answer 1)
I hope this was helpful <3
Find all of the cube roots of 216i and write the answers in rectangular (standard) form.
The cube roots of 216 written in the rectangular (standard) form are 3 + 3√3, -3+3√3, and 6.
What is a cube root?In mathematics, the cube root formula is used to represent any number as its cube root, for example, any number x will have the cube root 3x = x1/3. For instance, 5 is the cube root of 125 as 5 5 5 equals 125.
3√216 = 3√(2x2x2)x(3x3x3)
= 2 x 3 = 6
the prime factors are represented as cubes by grouping them into pairs of three. As a result, the necessary number, which is 216's cube root, is 6.
Therefore, the cube roots of 216 are 3 + 3√3, -3+3√3, and 6.
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Identify the expression that is not equivalent to 6x + 3.
The resultant value of the given expression x² + 10x + 24 when x = 3 is (C) 63.
What are expressions?A finite collection of symbols that are properly created in line with context-dependent criteria is referred to as an expression, sometimes known as a mathematical expression.
Expressions in writing are made using mathematical operators such as addition, subtraction, multiplication, and division.
For instance, "4 added to 2" will have the mathematical formula 2+4.
So, we have the expression:
= x² + 10x + 24
Now, solve when x = 3 as follows:
= x² + 10x + 24
= 3² + 10(3) + 24
= 9 + 30 + 24
= 63
Therefore, the resultant value of the given expression x² + 10x + 24 when x = 3 is (C) 63.
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Correct question:
Evaluate the expression when x = 3.
x² + 10x + 24
a. 81
b. 86
c. 63
d. 60
In morning Emily studied 40 minutes for a math exam. Later that evening Emily studied for x more minutes. Write an equation that represents the total number of minutes y emily studied for the math exam
Equation that represents the total number of minutes y Emily studied for the math exam is y = 40 +x.
We can represent the total number of minutes Emily studied for the math exam using the equation,
y = 40 + x
Here, 'y' represents the total number of minutes Emily studied for the math exam, '40' represents the number of minutes she studied in the morning, and 'x' represents the number of minutes she studied later that evening.
By adding the number of minutes studied in the morning to the number of minutes studied later that evening, we can calculate the total number of minutes Emily studied for the math exam.
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Jaxon made 5% of his free throws over the season. If he shot 220 free throws, how many did he make?
Answer:
Jaxon made 11 free throws over the season.
Step-by-step explanation:
If he made 5% of his free throws, we know that he will make 5% of the total number of free throws he took, which is 220:
We multiply 220 by 0.05, or 5% to find out how many free throws he made:
220*0.05 = 11
After that, we now know that Jaxon made 11 of his free throws out of 220 over the course of the season, or 5%.
ASAP I really need help doing a two column proof for this please.
The two column proof is written as follows
Statement Reason
MA = XR given (opposite sides of rectangle)
MK = AR given (opposite sides of rectangle)
arc MA = arc RK Equal chords have equal arcs
arc MK = arc AK Equal chords have equal arcs
Equal chords have equal arcsAn arc is a portion of the circumference of a circle, and a chord is a line segment that connects two points on the circumference.
If two chords in a circle are equal in length, then they will cut off equal arcs on the circumference. This is because the arcs that the chords cut off are subtended by the same central angle.
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brainlist
show all steps nd i will make u brainlist
Step-by-step explanation:
Again, using similar triangle ratios
7.2 m is to 2.4 m
as AB is to 12.0 m
7.2 / 2.4 = AB/12.0 Multiply both sides of the equation by 12
12 * 7.2 / 2.4 = AB = 36.0 meters
There are only Ured counters and g green counters in a bag. A counter is taken at random from the bag. The probability that the counter is green is 3
7
The counter is put back in the bag. 2 more red counters and 3 more green counters are put in the bag. A counter is taken at random from the bag. The probability that the counter is green is 6
13
Find the number of red counters and the number of green counters that were in the bag originally
Number of red counters in the original bag is 3, and the number of green counters is 7.
Let's use algebra to solve the problem. Let U be the number of red counters and G be the number of green counters originally in the bag.
From the first part of the problem, we know that
Probability (selecting a green counter) = G / (U + G) = 3/7
Solving for U in terms of G, we get
U = (7G - 3G) / 3 = 4G/3
So we know that there were 4G/3 red counters and G green counters in the bag originally. But since the number of counters must be a whole number, we can assume that there were 4R red counters and 3G green counters originally, where R and G are both integers and R + G is the total number of counters.
After adding 2 red and 3 green counters, the number of counters in the bag is now R + 2 + G + 3 = R + G + 5.
From the second part of the problem, we know that
P(selecting a green counter) = (G + 3) / (R + G + 5) = 6/13
Solving for R in terms of G, we get
R = (13G - 9G - 15) / 7 = 4G/7 - 15/7
Since R must be an integer, we can try different values of G to see if R is an integer. For example, if G = 7, then R = 3 and the total number of counters is 10.
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The given question is incomplete, the complete question is:
There are only U red counters and G green counters in a bag. A counter is taken at random from the bag. The probability that the counter is green is 3/7. The counter is put back in the bag. 2 more red counters and 3 more green counters are put in the bag. A counter is taken at random from the bag. The probability that the counter is green is 6/13. Find the number of red counters and the number of green counters that were in the bag originally
Label the net for the cylinder. Then find the surface area of the cylinder. Give your answer in terms of π and as a decimal number rounded to the nearest tenth.
The surface area of the cylinder is approximately 94.2 ft².
What is surface area?Surface area refers to the total area of the external or outer part of an object. It is the sum of the areas of all the individual surfaces or faces of the object. Surface area is typically measured in square units, such as square inches (in²), square feet (ft²), or square meters (m²), depending on the unit of measurement used.
According to the given information:
The surface area of a cylinder is the sum of the lateral surface area (the curved surface) and the area of the two circular bases.
The formula for the lateral surface area of a cylinder is given:
Lateral Surface Area = 2πrh
where r is the radius of the cylinder and h is the height of the cylinder.
Plugging in the given values for the radius (r = 3 ft) and height (h = 2 ft), we can calculate the lateral surface area:
Lateral Surface Area = 2π * 3 * 2 = 12π ft²
The formula for the area of a circle (which represents the bases of the cylinder) is given:
Circle Area = πr²
Plugging in the given value for the radius (r = 3 ft), we can calculate the area of each circular base:
Circle Area = π * 3² = 9π ft²
Since there are two bases in a cylinder, we multiply this by 2 to account for both bases:
2 * Circle Area = 2 * 9π = 18π ft²
Now, we can add the lateral surface area and the area of the two bases to find the total surface area of the cylinder:
Total Surface Area = Lateral Surface Area + 2 * Circle Area
= 12π + 18π
= 30π ft²
As a decimal rounded to the nearest tenth, the surface area of the cylinder is approximately 94.2 ft²
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A tram moved downward 12 meters in 4 seconds at a constant rate. What was the change in the tram's elevation each second?
Therefore , the solution of the given problem of unitary method comes out to be during the 4-second period, the tram's elevation changed by 3 metres every second.
What is an unitary method?To complete the assignment, use the iii . -and-true basic technique, the real variables, and any pertinent details gathered from basic and specialised questions. In response, customers might be given another opportunity to sample expression the products. If these changes don't take place, we will miss out on important gains in our knowledge of programmes.
Here,
By dividing the overall elevation change (12 metres) by the total time required (4 seconds),
it is possible to determine the change in the tram's elevation every second. We would then have the average rate of elevation change per second.
=> Elevation change equals 12 metres
=> Total duration: 4 seconds
=> 12 meters / 4 seconds
=> 3 meters/second
As a result, during the 4-second period, the tram's elevation changed by 3 metres every second.
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cuantos números
primos son a la vez la suma y la diferencia
Answer: there is only one number
Answer:
Solo hay un número primo que se puede escribir como suma de dos números primos y también como diferencia de dos números primos.
Espero haber ayudado :D
help please this is due tonight and im struggling
Thus, the value of x for the given angle of cyclic quadrilateral is found as the x = 50.
Explain about the cyclic quadrilateral:When you hear the word "cyclic," think of the two round wheels on you bicycle. A quadrilateral is a figure with four sides. The result is a cyclic quadrilateral, which is defined as any four-sided shape (quadrilateral) its four vertices (corners) are located on a circle.
A cyclic quadrilateral's opposite angles add up to 180 degrees, making them supplementary to one another.
Given data:
∠T = x + 60°∠R = x + 20°Using the property of cyclic quadrilateral: sum of opposite angle are 180 degrees.
∠T + ∠R = 180
x + 60 + x + 20 = 180
2x + 80 = 180
2x = 180 - 80
2x = 100
x = 50
Thus, the value of x for the given angle of cyclic quadrilateral is found as the x = 50.
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Helppp on this problem
The missing angles of the diagram are:
∠1 = 118°
∠2 = 62°
∠3 = 118°
∠4 = 30°
∠5 = 32°
∠6 = 118°
∠7 = 30°
∠8 = 118°
How to find the missing angles?Supplementary angles are defined as two angles that sum up to 180 degrees. Thus:
∠1 + 62° = 180°
∠1 = 180 - 62
∠1 = 118°
Now, opposite angles are congruent and ∠2 is an opposite angle to 62°. Thus: ∠2 = 62°.
Similarly: ∠3 = 118° because it is congruent to ∠1
Alternate angles are congruent and ∠5 is an alternate angle to 32°. Thus:
∠5 = 32°
Sum of angle 4 and 5 is a corresponding angle to ∠2 . Thus:
∠4 + ∠5 = 62
∠4 + 32 = 62
∠4 = 30°
This is an alternate angle to ∠7 and as such ∠7 = 30°
Sum of angles on a straight line is 180 degrees and as such:
∠8 = 180 - (30 + 32)
∠8 = 118° = ∠6 because they are alternate angles
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at a booth at the school carnival in past years, they've found that 22% of students win a stuffed toy ($3.60), 16% of students win a jump rope ($1.20), and 6% of students win a t-shirt ($7.90). the remaining students do not win a prize. if 150 students play the game at the booth, how much money should the carnival committee expect to pay for prizes for that booth?: *
For a percentage data of students who play the different game and win the prize, the expected amount to pay for prizes for that booth by the carnival committee is equals to the $218.70.
We have a booth of school carnival in past years, The percentage of students win a stuffed toy = 22%
The percentage of students win a jump rope = 16%
The percentage of students win a t-shirt
= 6%
The winning amount for stuffed toy game = $ 3.60
The winning amount for jump rope game = $1.20
The winning amount for t-shirt game
= $7.90
The remaining students do not win a prize. Now, total number of students play the game at the booth = 150
So, number of students who win stuffed toy = 22% of 150 = 33
Number of students who win jump rope = 16% of 150 = 24
Number of students who win stuffed toy
= 6% of 150 = 9
For determining the expected pay using the simple multiplication formula. Total expected pay for prizes for that booth is equals to the sum of resultant of multiplcation of number of students who play a particular game into pay amount for that game. That is total excepted pay in dollars = 3.60 × 33 + 1.20 × 24 +7.90 × 6
= 218.7
Hence required value is $218.70.
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A classmate of yours stated that a solid line is not a good representation of an arithmetic sequences. What logical assumption is your classmate using?
The classmate is not correct. A line is a good representation of an arithmetic sequence.
A line is a series of dots that represent each value of the sequence.
A line has the same slope as the common difference in the sequence.
An arithmetic sequence is a set of discrete values, whereas a line is a continuous set of values.
The logical assumption used is: An arithmetic sequence is a set of discrete values, whereas a line is a continuous set of values.
What is arithmetic sequence?An arithmetic sequence is a set of numbers where, with the exception of the first term, each term is obtained by adding a fixed constant to the term before it. Every pair of following terms in the sequence has the same fixed constant, which is known as the common difference. A1 stands for the first term in an arithmetic sequence, while an is used to represent the nth term.
A solid line symbolises continuous numbers, whereas the classmate's logical presumption is that an arithmetic series comprises of discrete values. This presumption is untrue, though, as a line can effectively represent an arithmetic series.
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if x is a matrix of centered data with a column for each field in the data and a row for each sample, how can we use matrix operations to compute the covariance matrix of the variables in the data, up to a scalar multiple?
To compute the covariance matrix of the variables in the data, the "matrix-operation" which should be used is ([tex]X^{t}[/tex] × X)/n.
The "Covariance" matrix is defined as a symmetric and positive semi-definite, with the entries representing the covariance between pairs of variables in the data.
The "diagonal-entries" represent the variances of individual variables, and the off-diagonal entries represent the covariances between pairs of variables.
Step(1) : Compute the transpose of the centered data matrix X, denoted as [tex]X^{t}[/tex]. The "transpose" of a matrix is found by inter-changing its rows and columns.
Step(2) : Compute the "dot-product" of [tex]X^{t}[/tex] with itself, denoted as [tex]X^{t}[/tex] × X.
The dot product of two matrices is computed by multiplying corresponding entries of the matrices and summing them up.
Step(3) : Divide the result obtained in step(2) by the number of samples in the data, denoted as "n", to get the covariance matrix.
This step scales the sum of the products by 1/n, which is equivalent to taking the average.
So, the covariance matrix "C" of variables in "centered-data" matrix X can be expressed as: C = ([tex]X^{t}[/tex] × X)/n.
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The given question is incomplete, the complete question is
Let X be a matrix of centered data with a column for each field in the data and a row for each sample. Then, not including a scalar multiple, how can we use matrix operations to compute the covariance matrix of the variables in the data?