we must have made an incorrect assumption along the way. One possible mistake is to assume that the exterior angle of ∠3 is formed by extending the side opposite to ∠3.
What is Triangle ?
In geometry, a triangle is a 2-dimensional polygon that is formed by connecting three non-collinear points with straight lines.
To find the measure of ∠3, we can use the fact that the sum of angles in a triangle is 180 degrees. Therefore, we can write:
∠3 + ∠4 + ∠5 = 180
However, we don't know the measures of ∠4 and ∠5, so we need to use additional information from the problem to find them.
Since ∠3 is in the same triangle as ∠4 and ∠5, we can use the fact that the exterior angle of a triangle is equal to the sum of its remote interior angles. In other words:
∠4 + ∠5 = exterior angle of ∠3
We don't know the measure of the exterior angle of ∠3 either, but we can use the fact that it is supplementary to ∠3. Therefore:
exterior angle of ∠3 + ∠3 = 180
Combining these equations, we can solve for ∠3:
exterior angle of ∠3 + ∠3 = 180
∠4 + ∠5 = exterior angle of ∠3
∠3 + ∠4 + ∠5 = 180
Substituting ∠4 + ∠5 for the exterior angle of ∠3 in the first equation, we get:
∠3 + (∠4 + ∠5) = 180
∠3 + (exterior angle of ∠3) = 180
Simplifying, we get:
∠3 + (∠4 + ∠5) = 180
2∠3 + (∠4 + ∠5) = 180
2∠3 + exterior angle of ∠3 = 180
Now, we need to know the value of the exterior angle of ∠3. It is formed by extending one of the sides of the triangle containing ∠3, ∠4, and ∠5, and it is equal to the sum of the other two angles in the triangle. We don't have enough information to determine which side is extended, so we will assume that it is the one opposite to ∠3. In this case, we have:
exterior angle of ∠3 = ∠4 + ∠5
Substituting in the equation above, we get:
2∠3 + ∠4 + ∠5 = 180
Now, we can solve for ∠3:
2∠3 + ∠4 + ∠5 = 180
2∠3 = 180 - (∠4 + ∠5)
2∠3 = 180 - (exterior angle of ∠3)
2∠3 = 180 - (∠4 + ∠5)
2∠3 = 180 - (∠3 + ∠4 + ∠5)
2∠3 = 180 - 180
2∠3 = 0
∠3 = 0
However, this result doesn't make sense, because an angle can't have a measure of 0 degrees in a triangle.
Therefore, we must have made an incorrect assumption along the way. One possible mistake is to assume that the exterior angle of ∠3 is formed by extending the side opposite to ∠3.
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A building is constructed using bricks that can be modeled as right rectangular
prisms with a dimension of 7 1/4 in by 21 1/4 in by 3 1/4 in. if the bricks weight 0.06 ounces per cubic inch and cost cost $0.13 per ounce, find the cost of 1800 bricks. round your answer to the nearest cent.
The cost of 1800 bricks is $7,386.76. The cost of 1800 bricks, each measuring 7 1/4 in by 21 1/4 in by 3 1/4 in and weighing 0.06 ounces per cubic inch, can be calculated as follows:
First, we need to find the volume of one brick by multiplying its three dimensions:
Volume of one brick = 7.25 in x 21.25 in x 3.25 in = 526.0156 cubic inches
Next, we can find the weight of one brick by multiplying its volume by its weight per cubic inch:
Weight of one brick = 526.0156 cubic inches x 0.06 ounces/cubic inch = 31.56094 ounces
The total weight of 1800 bricks can be found by multiplying the weight of one brick by 1800:
Total weight of 1800 bricks = 31.56094 ounces/brick x 1800 bricks = 56,809.6928 ounces
Finally, we can find the cost of the bricks by multiplying their total weight by the cost per ounce:
Cost of 1800 bricks = 56,809.6928 ounces x $0.13/ounce = $7,386.76
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Solve for X. Assume that lines which appear are tangent.
According to the figure the value of x is
c) 7How to find the value of xThe value of x is solved using the intersecting secant tangent theorem
The theorem have the formula
12^2 = 9 * (9 + x)
solving for x
144 = 81 + 9x
9x = 63
9x / 9 = 63 / 9
x = 7
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Find the area of the regular pentagon with radius 19 mm.
Answer:
621.09 mm²
Step-by-step explanation:
Area of pentagon = [tex]\frac{(perimeter) (apothem)}{2}[/tex]
Let's solve
[tex]\frac{(5 times 19) times 13.08}{2}[/tex] = 621.09 mm²
So, the answer is 621.09 mm²
Answer: 8.58 cm²
Step-by-step explanation:
The area of the central triangle bounded by each of the sides can be computed as ...
A = (1/2)r²sin(α) . . . . where α is the central angle, 360°/5 = 72°
There are 5 such triangles, so the area of the pentagon is
A = (5/2)(1.9 cm)²sin(72°) ≈ 8.58 cm²
Wnte an equation in slope-intercept form of the line that passes through (-3, 2) and (-2, - 5).
WILL GIVE BRAINLIEST
An equation in slope-intercept form of the line that passes through (-3, 2) and (-2, - 5) is: C. y = -7x - 19.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation:
y - y₁ = m(x - x₁)
Where:
m represent the slope.x and y represent the points.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (-5 - 2)/(-2 + 3)
Slope (m) = -7/1
Slope (m) = -7
At data point (-3, 2), a linear equation in slope-intercept form for this line can be calculated as follows:
y - y₁ = m(x - x₁)
y - 2 = -7(x + 3)
y = -7x - 21 + 2
y = -7x - 19
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HELPPPP DUE SOON!!!!
Answer:
D: Left side
Step-by-step explanation:
a computer in a house uses 0.4 kilowatt for 20.7 hour. if electricity costs $0.08 per kilowatt-hour, how much does it cost (in dollars, to the penny) to use the computer? use exact numbers; do not estimate.
The total amount of energy used by the computer is:
0.4 kW × 20.7 h = 8.28 kWh
The cost of the energy used is:
8.28 kWh × $0.08/kWh = $0.6624
Therefore, it costs $0.66 to use the computer.
A computer in a house uses 0.4 kilowatt for 20.7 hours. If electricity costs $0.08 per kilowatt-hour, how much does it cost (in dollars, to the penny) to use the computer? use exact numbers; do not estimate.
The cost of using the computer for 20.7 hours can be found by multiplying the electricity used per hour by the cost per kilowatt-hour.
That is,Cost = Power (kilowatts) × Time (hours) × Cost per kilowatt-hour (dollars)Given that the power used by the computer is 0.4 kilowatts and the time it was used is 20.7 hours, we can find the total cost of using the computer by substituting the values in the above equation.Cost = 0.4 kilowatts × 20.7 hours × $0.08 per kilowatt-hourCost = 0.4 × 20.7 × 0.08Cost = $0.06624Therefore, it costs $0.06624 to use the computer.
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Simplify the expression 4(32f+1)−7(f+5) .
Answer:
121f + 39
Step-by-step explanation:
Simplify the expression:
[tex]4(32f+1)-7(f+5)[/tex]
Use the distributive property to distribute 4 and 7
[tex]128f+4-7f+35[/tex]
Lets rearrange terms to make it easier
[tex]128f+-7f+4+35[/tex]
Add like terms and integers
[tex]121f+39[/tex]
(co 1) in a normally distributed data set with a mean of 22 and a standard deviation of 4.1, what percentage of the data would be between 13.8 and 30.2? g
The percentage of data between 13.8 and 30.2 in a normally distributed data set with a mean of 22 and a standard deviation of 4.1 is approximately 94.19%.
To solve this problem, we can first standardize the values of interest using the standard normal distribution formula, z = (x - μ) / σ, where x is the value of interest, μ is the mean, and σ is the standard deviation.
For the lower value of 13.8, we have z = (13.8 - 22) / 4.1 = -1.95. For the upper value of 30.2, we have z = (30.2 - 22) / 4.1 = 2.05.
Next, we can use a calculator to find the area between these two z-scores. Alternatively, we can use the complement rule to find the area to the left of -1.95 and the area to the right of 2.05, and subtract their sum from 1.
Using a calculator, we find that the area between -1.95 and 2.05 is approximately 0.9419 or 94.19%. Therefore, approximately 94.19% of the data falls between 13.8 and 30.2 in this normally distributed data set.
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a control chart that measures variables measures what? group of answer choices characteristic that has a discrete value and can be counted. characteristics that can be measured on a continuum of value like weight and volume. characteristics that are soft and pliable all of the above previousnext
A control chart that measures variables measures characteristics that can be measured on a continuum of value like weight and volume.
Control diagrams are a measurable instrument used to screen and control processes over the long haul. They are utilized to follow factors that can be estimated on a consistent scale, like weight, volume, temperature, or time. These factors are not discrete, yet rather fall along a reach or continuum of values. By plotting information over the long haul on a control graph, a cycle can be observed to guarantee that it stays inside a predetermined scope of OK variety. The control diagram gives a visual portrayal of the cycle information, permitting process proprietors to recognize when the interaction is crazy or when it might require remedial activity. Generally, control outlines that action factors assist with guaranteeing the nature of the cycle yield by empowering process proprietors to distinguish and address issues before they bring about deformities or mistakes.
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In the figure below, find the measure of the indicated arc.
Answer:
109°
Step-by-step explanation:
Given:
arc QS = 65°
∠QRS = 44°
Find: arc PS -
.
∠QRS = arc PS - arc QS
arc PS = ∠QRS + arc QS
arc PS = 44° + 65° = 109°
8.phone calls arrive at a voicemail system at a rate of 16 per hour according to a poisson process. the voicemail system routes calls to appropriate operators based on pushing buttons on the phone. the voicemail system can handle only one call at a time. if a second call arrives while the voicemail system is busy, then the call is lost. the time for the voicemail system to route a call follows an exponential distribution with a mean of 2.5 minutes. once it has routed the call, it is free to take another call. what is the probability that an arriving call will be routed by the voicemail system?
The probability that an arriving call will be routed by the voicemail system is given by[tex]P(Y = 0) = e^(-0.1067) * 0.1067^0 / 0! = 0.8982,[/tex]rounded to four decimal places.
Since phone calls arrive at a rate of 16 per hour, the arrival rate of calls in minutes is 16/60 = 0.2667 calls per minute. We can model the arrival rate of calls as a Poisson distribution with parameter λ = 0.2667.
The time for the voicemail system to route a call follows an exponential distribution with a mean of 2.5 minutes. Let X be the time it takes to route a call. Then X follows an exponential distribution with parameter μ = 1/2.5 = 0.4.
We want to find the probability that an arriving call will be routed by the voicemail system. This is equivalent to finding the probability that there are no calls being routed by the voicemail system when a call arrives. Let Y be the number of calls being routed by the voicemail system. Then Y follows a Poisson distribution with parameter λμ = 0.2667 x 0.4 = 0.1067.
Therefore, the probability that an arriving call will be routed by the voicemail system is given by
[tex]P(Y = 0) = e^(-0.1067) * 0.1067^0 / 0! = 0.8982,[/tex] rounded to four decimal places.
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undergraduate students at a college belong to one of four groups depending on the year they are supposed to graduate. each student must choose one of twenty-one distinct majors. how many students are needed to guarantee that there are two students expected to graduate in the same year who have the same major?
Total 84 students, are needed to guarantee that there are two students expected to graduate in the same year who have the same major.
We have undergraduate students at a college. Students belong to 4 groups (depending on year ) and 21 different majors. Total different majors for choice
= 21
We have to determine number of students needed to guarantee that there are two students expected to graduate in the same year who have the same major. Using the combinations, total different combinations possible for student having a particular major and year = 21× 4 = 84
By Pigeon Hole principle, if there is n boxes and m objects then atleast one box must contain more then one object. Here, we have 84 different Buckets . The 85th object ( 84 + 1 = 85) makes sure
bucket has 2 objects. The 85 is required number of students to that atleast one Year and 21 students in same year and same major.
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Expand using the Product property...In 2xy
As a result, the product property can be used to manipulate and equation statements containing 2xy, as well as to express 2xy in terms of its factors.
What is equation?An equation is a statement that shows the equality between two mathematical expressions. It is a fundamental concept in mathematics and is used to describe relationships between quantities.
The purpose of an equation is to find the value of the unknown variable(s) that make the equation true. This is typically done by applying algebraic operations to manipulate the equation, with the goal of isolating the variable on one side of the equal sign.
[tex]2xy = 2 * x * y[/tex]
[tex]2xy = 2x * y = 2y * x = x * 2y = y * 2x = x * y * 2[/tex]
[tex]4x^2y * 3xy^2 = (4 * x * x * y) * (3 * x * y * y)[/tex]
[tex]= 12 * x^3 * y^3[/tex]
As a result, the product property can be used to manipulate and simplify statements containing 2xy, as well as to express 2xy in terms of its factors.
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Which formula would be used to find the measure of angle 1? one-half(a° b°). one-half(a° â€"" c°). one-half(b° c°). one-half(a° â€"" b°).
The formula one-half(a° - b°) is derived from the fact that the exterior angle of a triangle is equal to one-half the difference between the measures of the two remote interior angles.
The formula that would be used to find the measure of angle 1 is one-half(a° - b°). This formula applies to a situation where angle 1 is an exterior angle of a triangle, and a° and b° are the measures of the two remote interior angles of the triangle that are adjacent to angle 1. The exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. Mathematically, this can be expressed as:
angle 1 = a° - b°
To find the measure of angle 1 using the formula one-half(a° - b°), we would simply plug in the known values of a° and b°, and perform the necessary arithmetic operations.
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Carson's favorite store is having a sale. All clothing is 40% off, and Carson has a coupon for another $10 off his purchase. He buys a sweater for $65.99. How much does Carson pay for the sweater after the discounts?
Answer:
First, we can calculate the discount from the sale. The sweater costs $65.99, and with a 40% discount, the price is reduced by:
$65.99 x 0.40 = $26.40
So the sale price of the sweater is:
$65.99 - $26.40 = $39.59
Next, we can apply Carson's $10 coupon to the sale price:
$39.59 - $10 = $29.59
Therefore, Carson pays $29.59 for the sweater after the discounts.
To calculate the total discount that Carson receives, we can first find the amount of the 40% discount on the sweater, which is:
40% of $65.99 = 0.4 x $65.99 = $26.40
Then, we can add the additional $10 coupon discount to get the total discount:
$26.40 + $10 = $36.40
Therefore, the total discount that Carson receives on the sweater is $36.40.
To find the final price that Carson pays after the discounts, we can subtract the total discount from the original price:
$65.99 - $36.40 = $29.59
Therefore, Carson pays $29.59 for the sweater after the discounts.
Whats the best anime of all time?
According to the anime history, the best anime of all time with no haters is fullmetal alchemist brotherhood.
What is anime?Anime is a style of animation that originated in Japan and has become popular worldwide. It is characterized by distinctive visual styles, such as colorful graphics, exaggerated features of characters, and expressive facial expressions. Anime covers a wide range of genres, including action, adventure, drama, comedy, romance, b fiction, fantasy.
There are numerous anime series that are widely popular and have received critical acclaim, such as "Fullmetal Alchemist: Brotherhood," "Attack on Titan," "Death Note," "Cowboy Bebop," "Dragon Ball Z," "Naruto," "One Piece," "Spirited Away," "Akira," "Ghost in the Shell," and many more.
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Can someone tell me where and how I graph this?
Assuming the coordinates of point A are (3, 5): we would have the following results.
1. To reflect over the x-axis: the x-coordinate remains the same and the y-coordinate changes sign. So point B will have the same x-coordinate as point A (3), but the y-coordinate will be -5. Therefore, the coordinates of point B are (3, -5).
2. To reflect over the y-axis: the y-coordinate remains the same and the x-coordinate changes sign. So point C will have the same y-coordinate as point A (5), but the x-coordinate will be -3. Therefore, the coordinates of point C are (-3, 5).
3. To translate: add the given values to the x and y coordinates. So point D will have an x-coordinate of 3 + 3 = 6, and a y-coordinate of 5 + 4 = 9. Therefore, the coordinates of point D are (6, 9).
4. To rotate 180 degrees clockwise: flip the signs of both the x and y coordinates and then swap them. So point E will have an x-coordinate of -5 and a y-coordinate of -3. Therefore, the coordinates of point E are (-5, -3).
Plotting these points on a graph,
A (3, 5)
B (3, -5)
C (-3, 5)
D (6, 9)
E (-5, -3)
we get the attached graph.
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I think I got it but can someone explain it
The coordinates of the image is at
(-3, -2)(-3, 0)(-1, 0)(1, -2)How to find the coordinates of the imageThe coordinates of the image is solved by applying the translation rule which is
(x, y) → (x + 6, y - 4)
This is applied as follows
preimage coordinates translation image coordinates
(-9, 2) → (-9 + 6, 2 - 4) → (-3, -2)
(-9, 4) → (-9 + 6, 4 - 4) → (-3, 0)
(-7, 4) → (-7 + 6, 4 - 4) → (-1, 0)
(-5, 2) → (-5 + 6, 2 - 4) → (1, -2)
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Eva has a collection of 180 coins. How many coins represent 20% of her collection?
Answer:
36 coins
Step-by-step explanation:
10 percent is 18 coins. so just double that.
Answer:
Step-by-step explanation:
Total coin Eva has = 180
20% of her coins are represented by 20% of the 180
= 20/100 * 180
=0.2 * 180= 36
36 coins represent 20% of Eva's coins.
A percentage is a number or ratio that represents a fraction of 100. It is used to describe numbers. It is a dimensionless quantity. A percentage is denoted by the % symbol.
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What is the interquartile range (IQ) of the data set represented by this box plot?
A. 23
B. 56
C.10
D. 33
Answer: D. 33
Step-by-step explanation:
A right triangle with an angle of approximately 53.1° is inscribed in the first quadrant of the unit circle, with a horizontal length of 3/5 and a vertical length of 4/5.
The length 53.1°, 90°, and 39.9°,vertical length: 3/5 ,length of vertical: 4/5 1 hypotenuse.
What is angle?Angle is a geometric concept that describes the relative difference between two straight lines or planes that meet at a common point. It is measured in degrees, radians or grads, and is often represented by the symbol θ. An angle can be acute, right, obtuse, straight, reflex, or full. Angles can be used to measure the size of a triangle, to calculate the area of a figure, and to determine the position of a point in a coordinate system.
We possess that
Angle = 53.1°
Vertical length = 3/5 (this is the adjacent cathetus)
Vertical length equals 4/5 (this is the opposite cathetus)
We can use it to check this.
tg(angle) = adjacent/opposite:
tg(53.1) = 1.33
and
(4/5)/(3/5) = 4/3 = 1.33
This makes sense, then.
Using the relationship, we can now identify the hypotenuse:
Sin(angle) = the antipode or hypotenuse
sin(53.1) = (4/5)/H
H = (4/5)/sin(53.1) = 1
Hence, there is always a 90° angle in a triangle or rectangle.
We may get the final angle using the fact that the sum of a triangle rectangle's three interior angles is always 180 degrees.
A + 53.1° + 90° = 180°
A = 90° - 53.1° = 36.9°
Now that we have located every missing part of the triangle.
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What is the equation of the line that passes through the point (-6, -7) and has a
slope of 1/3?
Answer:
y = 1/3x - 5
Step-by-step explanation:
The equation is y = mx + b
m = the slope
b = y-intercept
m = 1/3
Y-intercept is located at (0, -5)
So, the equation of the line is y = 1/3x - 5
Jamal is buying lunch for his family. He buys 4 drinks that each cost $1.75 and 4 sandwiches that each cost $7.50. If the prices include tax and he also leaves a $7 tip, how much does he spend in all?
Jamal spends a total of $44 on lunch for his family, including tax and tip.
What is Algebraic expression?Algebraic expression can be defined as combination of variables and constants.
The total cost of the drinks is 4 x $1.75 = $7.
The total cost of the sandwiches is 4 x $7.50 = $30.
So, the subtotal before the tip is $7 + $30 = $37.
Since the prices include tax, we can directly add the tip to the subtotal to get the total amount Jamal spends:
Total cost = Subtotal + Tip = $37 + $7 = $44.
Therefore, Jamal spends a total of $44 on lunch for his family, including tax and tip.
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After walking 8 km at a speed of 4 km/h, Ann starts to run at a speed of 8 km/h. For how many minutes will she have to run in order to have an average speed of 5 km/h over her complete journey?
To complete her journey Ann needs to run for (120/3) = 40 minutes in order to travel at an average speed of 5 km/h.
We can start by using the formula:
average speed = total distance ÷ total time
Let's first calculate the total distance Ann covers:
distance walked = speed x time = 4 km/h x (8 km / 4 km/h) = 8 km
distance run = speed x time
Let's call the time Ann runs for "t". Then:
distance run = 8 km/h x (t/60) h = (8t/60) km
Total distance = distance walked + distance run = 8 km + (8t/60) km = (480 + 8t) / 60 km
Now, let's find the total time:
total time = time walked + time run
time walked = distance ÷ speed = 8 km ÷ 4 km/h = 2 h
time run = t/60 h
total time = 2 h + t/60 h = (120 + t)/60 h
Now we can substitute the values we have found into the formula for average speed:
5 km/h = [(480 + 8t)/60 km] ÷ [(120 + t)/60 h]
Simplifying the right-hand side, we get:
5 km/h = (480 + 8t) / (120 + t)
Multiplying both sides by (120 + t), we get:
600 + 5t = 480 + 8t
Subtracting 480 and 5t from both sides, we get:
120 = 3t
Therefore, Ann has to run for (120/3) = 40 minutes to have an average speed of 5 km/h over her complete journey.
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How much does 3.25 m of lace cost if 0.8 m costs 5.60
The cost of 3.25m lace would be $22.75
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
we are given 0.8m of lace costs $5.60
now, we can find cost of 1m of lace
so, we have to divide both sides by 0.8
1 m of lace cost [tex]=5.60\div0.8[/tex]
1 m of lace cost [tex]=7[/tex]
so, we will also get
[tex]3.25\div0.8 = 4.0625[/tex]
Now multiply that by 3.25
[tex]3.25 \times 7 = 22.75[/tex]
So, the cost of 3.25m lace is $22.75
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Find the sum of the arithmetic series : 28 + 28.4 ... + 42.
The sum of the arithmetic series of 28 + 28.4 ...+ 42 is 1260.
What is arithmetic series?An arithmetic series is a sequence of numbers in which each term is obtained by adding a constant difference, called the common difference, to the preceding term.
According to question:To resolve this issue, we can utilise the following formula for the sum of an arithmetic series:
S = (n/2) * (a₁ + aₙ)
When n is the number of terms, a1 is the first term, and an is the nth term, S is the series total.
To find the number of terms, we need to figure out the pattern of the series. The common difference (d) is expressed as follows:
d = 28.4 - 28 = 0.4
To get from 28 to 42, we need to add (42 - 28)/0.4 = 35 terms.
So the number of terms is:
n = 35 + 1 = 36
The first term is a₁ = 28, and the last term is aₙ = 42.
Now we can plug these values into the formula:
S = (n/2) * (a₁ + aₙ)
= (36/2) * (28 + 42)
= 18 * 70
= 1260
Therefore, the sum of the arithmetic series is 1260.
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F=2(3+5x)+8(7-x)+4(x-1)
After simplifying the given functiοn F=2(3+5x)+8(7-x)+4(x-1) the answer is F = 2x + 58.
What is functiοn?In mathematics, a functiοn frοm a set X tο a set Y assigns each element οf X exactly οne element οf Y. The sets X and Y are referred tο as the functiοn's dοmain and cοdοmain, respectively.
Initially, functiοns represented the idealized relatiοnship between varied quantities and οther variables. Fοr instance, time affects a planet's pοsitiοn. In the past, the idea was develοped with the infinitesimal calculus at the end οf the 17th century, and until the 19th century, the functiοns that were taken intο cοnsideratiοn were differentiable (that is, they had a high degree οf regularity).
Expanding and simplifying the expressiοn F:
F = 2(3) + 2(5x) + 8(7) - 8(x) + 4(x) - 4(1)
F = 6 + 10x + 56 - 8x + 4x - 4
F = 2x + 58
Therefοre, F = 2x + 58.
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Complete question is:
Simplify F=2(3+5x)+8(7-x)+4(x-1).
an acme bearings manager wants to compare the average ball bearing sizes from two different machines. she suspects the mean diameter for bearings from machine 2 exceeds that of bearings from machine 1. she takes two independent, random samples of size 50, one from each machine. the mean and standard deviation of bearings taken from machine 1 are 3.302 mm and 0.051 mm. the mean and standard deviation of bearings taken from machine 2 are 3.355 mm and 0.050 mm. run a hypothesis test consistent with her suspicions. be sure to a. check all necessary assumptions; b. state the null and alternative hypotheses; c. decide whether or not to pool and explain why; d. calculate the test statistic and p-value; e. state your conclusion in a complete sentence based on the p-value.
a. The necessary assumptions are the population variances are equal and combine the two sample variances into one.
b. The null and alternative hypotheses are defined.
c. The sample sizes are equal, and the sample standard deviations are approximately equal, we can safely assume equal variances and pool the sample variances.
d. The value of test statistic is 3.15 and p value is 0.05.
e. The mean diameter of bearings from machine 2 is greater than that of machine 1 at a 5% level of significance.
To begin the hypothesis test, the manager needs to state the null and alternative hypotheses. The null hypothesis (H0) is the statement of "no difference" between the mean diameters of bearings from the two machines. The alternative hypothesis (Ha) is the statement that the mean diameter of bearings from machine 2 is greater than that of machine 1.
In symbols,
H0: μ1 = μ2 (where μ1 is the mean diameter of machine 1 and μ2 is the mean diameter of machine 2) and
Ha: μ2 > μ1.
Before conducting the hypothesis test, we need to check some assumptions.
The next step is to calculate the test statistic and p-value. We use a t-test to compare the means of two independent samples. The test statistic is calculated as:
t = (x₁ - x₂) / [s_p x √(2/n)]
where x₁ and x₂ are the sample means, s_p is the pooled standard deviation, and n is the sample size.
Plugging in the numbers, we get:
t = (3.355 - 3.302) / [0.050 x √(2/50)] = 3.15
Using a t-distribution table with 98 degrees of freedom (n₁ + n₂-2), we find that the p-value associated with a t-value of 3.15 is less than 0.01.
Finally, we need to state our conclusion based on the p-value. Since the p-value is less than our significance level of 0.05, we reject the null hypothesis.
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A machine makes 50 parts. Out of 50 parts, 3 are defective. Using a number or a number range, describe the probability that a randomly selected part is not defective.
The probability that a randomly selected part is not defective is 47/50.
What is probability?Probability is a way of calculating how likely something is to happen. It is difficult to provide a complete prediction for many events. Using it, we can only forecast the probability, or likelihood, of an event occurring. The probability might be between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty.
Here Total number of parts machine makes = 50
Number of parts defective out of 50 = 3
Then number of parts not defective out of 50 = 50-3 = 47.
Now using probability formula:
Probability = No of favorable item/ Total no of item
Now probability that a randomly selected part is not defective is,
= 47/50.
Hence the probability that a randomly selected part is not defective is 47/50.
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Daily BER (kl/day) = 5.4 x 24 hours x body mass (kg) Mihir has a body mass of 65 kg. Calculate Mihir's daily basic energy requirement.
Mihir's daily basic energy requirement is 8424 (kl/day).
How to find BMI body mass index or BER from body mass?
As the formula to find daily BER is given below,
[tex]Daily\ BER\ = 5.4 \times 24 \times body\ mass[/tex]
body mass = 65 kg
Therefore, put body mass, to find BER,
[tex]Daily\ BER\ = 5.4 \times 24 \times 65\\Daily\ BER\ = 8424\ (kl/day)[/tex]
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Mihir's daily basic energy requirement is 7,776 kJ/day.
what is meaning of body mass?A person's BMI is calculated by dividing their weight in kilograms (or pounds) by their square of height in meters (or feet). A high BMI may indicate excessive body fat. BMI measures weight categories that could lead to health issues, but it does not assess a person's health or body fat percentage.
to calculate Mihir's daily basic energy requirement using the formula:
Daily BER (kl/day) = 5.4 x 24 hours x body mass (kg)
We can substitute the given values to get:
Daily BER (kl/day) = 5.4 x 24 hours x 65 kg
Daily BER (kl/day) = 7,776 kJ/day
Therefore, Mihir's daily basic energy requirement is 7,776 kJ/day.
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