They are different because they are inverse expressions.
what is prime factor ?
A positive integer factor that is also a prime number is known as a prime factor in mathematics. Otherwise put, a prime factor is a prime number that may be multiplied by additional prime factors to produce the original integer. For instance, since 24 can be written as the product of the numbers 2, 2, 2, and 3, the prime factors of 24 are 2, 2, 2, and 3. There is only one set of prime factors for every positive integer since a number's prime factors are always unique. Finding a number's prime factors is a technique called prime factorization. It is a fundamental idea in number theory and has lots of real-world uses, including in computer science and cryptography.
given
Due to the way division operates, the quotient of three by one-fifth differs from the quotient of one-fifth by three. You get a greater quotient when you divide a larger number by a smaller number, and a smaller quotient when you divide a smaller number by a larger number.
To demonstrate these two scenarios, consider the following two tales:
The Quotient of Three Divided by One-Fifth is the first story.
There once were three pals named Chris, Ben, and Alex. They made the decision to split the five equally sized slices of pizza. Due to his extreme hunger, Alex chose to grab three of the slices for himself, leaving Ben and Chris with just two pieces each.
We write the expressions first mathematically:
three divided by one-fifth:
(3) / (1/5)
one-fifth divided by three:
(1/5) / (3)
We now use the double c method to find the results:
(3) / (1/5) = (3 * 5) / (1 * 1) = 15/1 = 15
(1/5) / (3) = (1 * 1) / (5 * 3) = 1/15 = 0.066666667
The difference between the two is:
15-0.066666667 = 14.93333333
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evaluate 1/6r+11/24 when r =1/4
how many 1/3s are in three
find exact value in radians
arccos(- square root 3/2)
(1/x-y)-(2/2x+y)+(1/x+y)-(2/2x-y)
Answer:
6xy^2/(x-y)(x+y)(2x+y)(2x-y)
Step-by-step explanation:
1 - 2 + 1 - 2
x-y 2x+y x+y 2x-y
= take LCM
Then simplify.
Answer:
-2x+2/x
Step-by-step explanation:
PART A: A can of cat food measures 1" tall and a diameter of 3.5". What is the volume of cat food in the can? To solve Give your answer in cubic inches. Round to the nearest hundredth.
PART B: Cat food is sold by ounces (weight).
If the can holds 5.8 ounces, write a ratio to show cubic inches (your answer from slide 3) to ounces.
A)The volume of cat food in the can is 9.62 cubic inches .
B) A ratio to show cubic inches to ounces is 4.83.
What is a cylinder?
A cylinder is a three-dimensional geometric shape that has two congruent circular bases connected by a curved surface.
The volume of a cylinder can be calculated using the formula
=> [tex]V = \pi r^2h,[/tex]
where r is the radius of the circular base, h is the height of the cylinder, and π is the mathematical constant pi (approximately equal to 3.14).
To find the volume of the cat food in the can, we need to use the formula for the volume of a cylinder,
Since the diameter is 3.5 inches, the radius is half of that, which is 1.75 inches. The height is 1 inch.
So,[tex]V=3.14\times(1.75)^2\times1[/tex] = 9.62 cubic inches (rounded to the nearest hundredth).
Therefore, the volume of cat food in the can is approximately 9.62 cubic inches.
Now ,To find the ratio of cubic inches to ounces,
Since the can holds 5.8 ounces of cat food, we can find the volume of cat food in cubic inches by dividing the weight by the density:
=> 5.8 ounces / 1.2 ounces per cubic inch
= 4.83 cubic inches (rounded to the nearest hundredth).
Therefore, a ratio to show cubic inches to ounces is 4.83.
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Help with math problems
The answer choice which is not a true statement include the following: C. the solution set of |3k + 3| ≤ -9 is {k|-4 ≥ k ≥ 2}.
What is an inequality?In Mathematics and Geometry, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;
Greater than (>).Less than (<).Greater than or equal to (≥).Less than or equal to (≤).In order to determine the solution set to the given inequality, we would write out the absolute value function (inequality) as shown below.
|3k + 3| ≤ -9
Since |3k + 3| would always be positive and negative nine (-9) is negative, |3k + 3| will always be greater than negative nine (-9), and as such, the inequality cannot be true and has no solution set.
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Jeremy and Leslie are each flying their own drones in a flat field with their drones hovering between the two of them. Jeremy's drone is closer to him than to Leslie, and Leslie's drone is closer to her than to Jeremy. Jeremy's drone is 30 meters above the ground, and he is located 50 meters to
the left from the point directly below the drone. The angle of elevation from Leslie's location on the ground to her dronp is 55°, and the distance between her location on the ground and her drone is 70 meters.
1. Calculate whose drone is higher. Show all work.
2. The angle elevation from the lower drone to the higher drone is 25 degrees. Use this information to calculate the distance between Jeremy and Leslie. Show all work.
3. Jeremy now flies his drone vertically so that it is the same height as Leslie’s drone. Draw a new diagram that includes Jeremy, Leslie, and the drones after Jeremy flies his drone to the same height as Leslie’s.
4. Explain why the angle of elevation from Jeremy’s location on the ground to his drone is different from the angle of elevation between Leslie’s location on the ground and her drone, given that both drones are at the same elevation above the ground.
5. Calculate the angle of elevation from Jeremy’s location on the ground to his drone to validate your reasoning. Show all work.
The solutions are explained below.
Given that, Jeremy and Leslie are each flying their own drones in a flat field with their drones hovering between the two of them. The figure is attached.
Height of Jeremy's drone = 30 m
Height of Leslie's drone = x m
h / 70 = sin 53°
h = 70 × sin 53°
h = 57.34
Therefore, Leslie's drone is higher than Jeremy's drone.
Difference of height = 57.34 - 30 = 27.34 m
27.34 / x = tan25°
x = 58.63 m
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please help me solve this
Step-by-step explanation:
what "normal" trigonometric function did this remind us of ?
it starts at "high" for x = 0.
"high" signs mean "1" for the standard functions.
the trigonometric function that starts with 1 at x = 0 is cosine.
so, this is a cosine function that we need to scale properly.
original value : 1
graph : 15
original value : -1
graph : 12
original value : 0
graph : (15+12)/2 = 27/2 = 13.5
so, we need to add this to the cosine function result.
the distance from the 0 level (13.5) to high or low is 1.5 (instead of originally 1).
Du, we need to stretch the cosine function result to go from -1.5 to +1.5 (12 to 15).
and for the x-axis :
12 hours = 180° or pi (the interval for cosine to go from +1 to -1).
1 hour = 180/12 = 15° or pi/12.
so, for cosine to react to the hour value as for the curdling degrees we need to multiply x by 180/12 or by pi/12.
so, our temperature function temp(x) is then
temp(x) = 1.5×cos(x×180/12) + 13.5
or
temp(x) = 1.5×cos(x×pi/12) + 13.5
Use the given information to find the minimum sample size required to estimate an unknown population mean μ.
How many business students must be randomly selected to estimate the mean monthly earnings of business students at one college? We want 95% confidence that the sample mean is within $135 of the population mean, and the population standard deviation is known to be $538.
54
62
43
86
Answer:
the correct answer is option B.
Step-by-step explanation:
We can use the formula for the margin of error for a confidence interval for a population mean with a known population standard deviation:
Margin of error = z*σ/√n
where z is the critical value from the standard normal distribution for the desired confidence level (95% in this case), σ is the population standard deviation, and n is the sample size.
We are given that the margin of error is $135 and σ is $538. We need to find the sample size, n. To do this, we first need to find the appropriate value of z for a 95% confidence level. Using a standard normal distribution table or calculator, we can find that z = 1.96.
Substituting the values into the margin of error formula and solving for n, we have:
$135 = 1.96*($538)/√n
Squaring both sides and solving for n, we get:
n = [1.96*($538)/$135]^2 ≈ 62
Therefore, a sample size of 62 business students must be randomly selected to estimate the mean monthly earnings of business students at one college with 95% confidence that the sample mean is within $135 of the population mean, assuming the population standard deviation is known to be $538.
So the correct answer is option B.
Ten cards numbered 1 thru 10 are placed in a box. If a card is de random from the box, what is the probability of drawing a prime a 10% b 25% c 40% d 50%
The probability of drawing a prime is 40%.
Calculating probability:To calculate the probability of drawing a prime number, use the formula
P(E) = Number of favorable outcomes / Total number of outcomes
Where P(E) is the probability of event E, and we determine the number of favorable outcomes and total possible outcomes based on the given conditions.
Here we have
Ten cards numbered 1 to 10 are placed in a box.
The total number of outcomes will get in a random experiment = 10
Here set of prime numbers from 1 to 10 = {2, 3, 5, 7}
Number of favorable outcomes that are getting prime number = 4
Hence, the probability of getting a prime number
= 4/10 = 2/5 = 0.4 = 40% [ Multiplied by 100 ]
Therefore,
The probability of drawing a prime is 40%.
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Can someone help me with this?
Answer: 63,932
Step-by-step explanation:
September: 11,724
October: 14,380 + 11,724 = 26,104
November: 14,380 + 11,724 = 26,104
Combine all 3 months to get your answer= 63,932
sophomores have 26% please help me with math!
Answer: 234 are sophomores
Step-by-step explanation:
You would take 26% of 900 to get 234
It's simple, don't overthink it :)
Have a nice day.
Step-by-step explanation:
Sophomores are 26 % of 900 students
26 % * 900 = the number of sophomores
26% * 900 = .26 * 900 = 234 sophomores
Find an angle in each quadrant with a common reference angle with 319°, from 0°≤θ<360°
The angles with a common reference angle of 319° in each quadrant are:
First quadrant: 319°, Second quadrant: -139°, Third quadrant: 139°, Fourth quadrant: 41°.
To find an angle in each quadrant with a common reference angle of 319°, we can start by subtracting 360° from 319° repeatedly until we get a result between 0° and 360°. This is because angles that differ by a multiple of 360° are coterminal, which means they have the same reference angle.
319° - 360° = -41° (not in the range 0° to 360°)
319° - 2(360°) = -401° (not in the range 0° to 360°)
319° - 3(360°) = -721° (not in the range 0° to 360°)
319° - 4(360°) = -1041° (not in the range 0° to 360°)
319° - 5(360°) = -1361° (not in the range 0° to 360°)
319° - 6(360°) = -1681° (not in the range 0° to 360°)
319° - 7(360°) = -2001° (not in the range 0° to 360°)
Since none of these results are in the range of 0° to 360°, we need to add multiples of 360° instead.
319° - 1(360°) = -41° (not in the range 0° to 360°)
319° - 0(360°) = 319°
319° + 1(360°) = 679° (not in the range 0° to 360°)
319° + 2(360°) = 1039° (not in the range 0° to 360°)
319° + 3(360°) = 1399° (not in the range 0° to 360°)
So, the angle with a common reference angle of 319° in the first quadrant (0° to 90°) is:
θ = 319° - 1(360°) = -41° + 360° = 319°
The angle with a common reference angle of 319° in the second quadrant (90° to 180°) is:
θ = 180° - 319° = -139°
The angle with a common reference angle of 319° in the third quadrant (180° to 270°) is:
θ = 319° - 180° = 139°
The angle with a common reference angle of 319° in the fourth quadrant (270° to 360°) is:
θ = 360° - 319° = 41°
Therefore, the angles with a common reference angle of 319° in each quadrant are:
First quadrant: 319°
Second quadrant: -139°
Third quadrant: 139°
Fourth quadrant: 41°
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Let f(x, y) = x² + xy + y². What is the direction of minimum rate of change at point (5,2)? (Enter a vector, using [,] brackets, such that the first coordinate (x-coordinate) is 1, 0, or -1.) Components of vector of minimum change direction are
Answer:
Step-by-step explanation:
To find the direction of minimum rate of change for the function f(x, y) = x² + xy + y² at the point (5, 2), we need to find the gradient vector (also known as the gradient or the vector of partial derivatives) and then find the direction orthogonal to the gradient vector, as this direction will have the minimum rate of change.
First, let's find the gradient vector by computing the partial derivatives of f(x, y) with respect to x and y:
∂f/∂x = 2x + y
∂f/∂y = x + 2y
Now, evaluate the gradient vector at the point (5, 2):
∇f(5, 2) = (2(5) + 2, 5 + 2(2)) = (12, 9)
The gradient vector is (12, 9). To find the direction orthogonal to the gradient vector, we can swap the x and y components and negate one of them. Since the question asks for a vector with an x-component of 1, 0, or -1, we'll negate the x-component:
Orthogonal vector = (-1, 12)
So, the direction of minimum rate of change at point (5, 2) is given by the vector [-1, 12].
HELP ASP 20 POINTS PLSp
Answer:
Step-by-step explanation:
$499.99 - 15% will give your answers
Answer:
424.99
Step-by-step explanation:
Let f(x)=2x-1, h(x) = -x-5.
Find (f o h)(-3).
(foh)(-3)=
So, (f o h)(-3) = 3. This is the value of the composite function (f o h) at -3. Please note that (f o h)(-3) is equivalent to f(h(-3))
What is function?An input and an output are connected by a function. It functions similarly to a machine with an input and an output. Additionally, the input and output are somehow connected. The traditional format for writing a function is f(x) "f(x) =... "
To find (f o h)(-3), we need to first evaluate h(-3), and then plug that result into the function f(x).
Given:
f(x) = -2x - 1
h(x) = -x - 5
First, we evaluate h(-3):
h(-3) = -(-3) - 5
h(-3) = 3 - 5
h(-3) = -2
Now, we plug the result of h(-3) into the function f(x):
f(h(-3)) = f(-2)
f(h(-3)) = -2(-2) - 1
f(h(-3)) = 4 - 1
f(h(-3)) = 3
So, (f o h)(-3) = 3. This is the value of the composite function (f o h) at -3. Please note that (f o h)(-3) is equivalent to f(h(-3)), which means we first evaluate h(-3) and then plug that result into f(x). I hope this helps! Let me know if you have any further questions. :)
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Which represents the solution(s) of the system of equations, y + 4 = x² and y - x = 2?
graphing.
O (-2, 0)
O (-2, 0) and (2, 0)
O (-2, 0) and (3, 5)
Ono solutions
Answer(-2,0) and (3,5)
Step-by-step explanation:
trust me bro
What is the value of
3
0 1000
27
0 1000
9
10
27
0 10
3
10
?
Answer:
27/1000 is your answer
Step-by-step explanation:
A small cube's edges are 2.5 inches long. A large cube's edges are 5 inches long. How many small cubes would it take to fill the large cube?
It would take 64 small cubes to fill the large cube. This is because the volume of a cube is equal to the length of its edges.
What is volume?The amount of space occupied by an object or the amount of space an object can fill. It is usually expressed in cubic units, such as cubic centimeters or cubic meters.
This is because the volume of a cube is equal to the length of its edges cubed, or V = s³, where s is the length of the edge.
We can calculate the volume of the large cube by replacing the length of its edges with 5 inches, or V = 53 = 125 in³.
To find the number of small cubes, we must first figure out the volume of a single small cube.
We can do this by replacing the length of the small cube's edges with 2.5 inches, or V = 2.53 = 15.625 in³
We can then divide the volume of the large cube (125 in³) by the volume of the small cube (15.625 in³) to get the number of small cubes needed to fill the large cube, which is equal to
125 / 15.625 = 8 * 8 = 64.
Therefore, it would take 64 small cubes to fill the large cube.
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Need some help
50 points!!
Answer:
145°
Step-by-step explanation:
The exterior angle 3 is equal to the sum of angle 1 and 2.
Using substitution we can say that:
5x + 4x + 10 = 10x -5
9x + 10 = 10x -5
10x-9x=10+5
x= 15
We have just found that the value of x is equal to 15.
By substituting this back to the angle 3 expression, 10x-5, we get
10(15) - 5
150 - 5
145°
1 1/9 x 2 2/5 as a mixed number in simplest form
Answer:
2 [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
1 1/9 x 2 2/5 = ?
1 1/9 = 10/9
2 2/5 = 12/5
[tex]\frac{10}{9}[/tex] x [tex]\frac{12}{5}[/tex] = [tex]\frac{120}{45}[/tex] = [tex]\frac{8}{3}[/tex] = 2 [tex]\frac{2}{3}[/tex]
So, the answer is 2 [tex]\frac{2}{3}[/tex]
each question answered correctly is worth 2 points. The first paper scored 30 points and the second scored 5o points. How many questions did the students answere correctly altogether?
The students answered 150 questions correctly in total based on proportions concept if points are given.
If the first paper scored 30 points and the second scored 50 points, then the total score is 30 + 50 = 80 points. Since each question answered correctly is worth 2 points, we can divide the total score by 2 to find the number of questions answered correctly altogether.
80 / 2 = 40
Therefore, the students answered 40 questions correctly in total.
Another way to approach this problem is to use proportions. Let's say that the number of questions answered correctly on the first paper is x, and the number of questions answered correctly on the second paper is y. Then we can set up a proportion:
x/15 + y/25 = 1
where 15 and 25 are the total number of questions on each paper, and 1 represents the total proportion of questions answered correctly.
Multiplying LHS and RHS by least common multiple of 15 and 25, which is 75:
5x + 3y = 75
If we know that x = 30 and y = 50, we substitute these values into equation and check that if its true:
5(30) + 3(50) = 150 + 150 = 300
Dividing sides by 2 to get:
300 / 2 = 150
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A bag contains 8 red marbles, 3 blue marbles, and 1 green marble. Find P(not blue). a. 9 c. One-fourth b. Four-thirds d. three-fourths Please select the best answer from the choices provided A B C D
Answer:
The probability of not getting a blue marble is the probability of getting either a red or a green marble. P(not blue) = P(red or green) P(red or green) = P(red) + P(green) P(red or green) = 8/12 + 1/12 P(red or green) = 9/12 P(not blue) = 3/4 Therefore, the answer is D. three-fourths.
At one college, GPAs are normally distributed with a mean of 2.9 and a standard deviation of 0.6. Find the 70th percentile.
The GPA corresponding to the 70th percentile at the college is approximately 3.246 based on standard deviation.
We can use the conventional normal distribution table or a calculator with a normal distribution function to determine the 70th percentile of GPAs at a college, which are normally distributed with a mean of 2.9 and a standard deviation of 0.6.
The inverse normal distribution function with a mean of 2.9, a standard deviation of 0.6, and a percentile of 70 can be used on a calculator. This results in:
[tex]3.246 for invNorm(0.7, 2.9, 0.6).[/tex]
As a result, the GPA that represents the 70th percentile is roughly 3.246.
We can determine the z-score corresponding to the 70th percentile, which is 0.5244, by using a common normal distribution table. Thus, we may apply the equation z = (x - ) /, where x is the GPA that corresponds to the 70%ile, is the mean, and is the standard deviation, and all three variables have values of 2.9. After finding x, we obtain:
0.5244 = (x - 2.9) / 0.6
x = 3.246
Once more, doing so yields the same outcome as using a calculator.
In conclusion, the GPA at the college that represents the 70th percentile is roughly 3.246.
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The number of students who ride the school bus is 110%of the number of students who walk.How many students ride the school bus
If the number of students who walk is represented by x, then the number of students who ride the school bus is 110% of x, which can be written as:
1.10x
This is because 110% can be written as 1.10 (since 110% means 110 out of 100).
So, if we know the value of x, we can multiply it by 1.10 to find the number of students who ride the school bus.
However, we don't know the value of x in this problem. Therefore, we cannot find the exact number of students who ride the school bus.
Answer:If the number of students who walk is represented by x, then the number of students who ride the school bus is 110% of x, which can be written as:
1.10x
This is because 110% can be written as 1.10 (since 110% means 110 out of 100).
So, if we know the value of x, we can multiply it by 1.10 to find the number of students who ride the school bus.
However, we don't know the value of x in this problem. Therefore, we cannot find the exact number of students who ride the school bus.
Step-by-step explanation:
Can someone please help ASAP!
The correct answer for this would be: Triangles BCA and DAC are congruent according to the Angle-Side-Angle (ASA) Theorem.
What is a Parallelogram?
A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.
According to the ASA theorem, if the included side of one triangle and its two angles are comparable to the parts of another triangle, then the triangles are said to be congruent.
Check the attached file for the image of this problem.
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A utility company in a western city of the United States expects the consumption of electricity to increase by 11%/year during the next decade, due mainly to the expected increase in population. If consumption does increase at this rate, find the amount by which the utility company will have to increase its generating capacity in order to meet the needs of the area at the end of the decade.
The utility company will have to increase its generating capacity by approximately 185.3% to meet the expected increase in electricity consumption over the next decade.
Exponential growth:The problem involves the use of the exponential growth formula in mathematics, where we are given the current consumption of electricity in a city and we are asked to find the expected consumption of electricity after a certain period of time, assuming a fixed annual growth rate.
We can use the formula:
C = C₀ × (1 + r)ⁿHere we have
A utility company in a western city in the United States expects the consumption of electricity to increase by 11%/year during the next decade, due mainly to the expected increase in population.
Let C₀ be the current consumption of electricity in the western city of the United States, and let C₁₀ be the expected consumption of electricity at the end of the decade.
We can use the following formula to calculate C₁₀:
C₁₀ = C₀ × (1 + r)ⁿ
Where r is the annual growth rate, n is the number of years
The amount by which the utility company will have to increase its generating capacity in order to meet the needs of the area at the end of the decade is given by the difference between C₁₀ and C₀
That is:
Amount of increase = C₁₀ - C₀
Substituting the values given in the problem, we get:
C₁₀ = C₀ (1 + 0.11)¹⁰
C₁₀/C₀ = (1.11)¹⁰
C₁₀/C₀ = (1.11)¹⁰
C₁₀ = C₀ × 2.84
Therefore, the amount by which the utility company will have to increase its generating capacity in order to meet the needs of the area at the end of the decade is:
Amount of increase =C₁₀ - C₀ = 2.853 × C₀ - C₀ = 1.853 × C₀
Therefore,
The utility company will have to increase its generating capacity by approximately 185.3% to meet the expected increase in electricity consumption over the next decade.
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What would the family have done if they
had opted out of paying the $210
monthly premium for health insurance?
If a family chose to opt out of paying the $210 monthly premium for health insurance, they would not have coverage under the health insurance plan. This means that they would be responsible for paying for any medical expenses out of pocket.
Without health insurance, the cost of medical care can be quite high, and a family could potentially face financial ruin if they experienced a serious illness or injury. They may also be unable to afford routine check-ups or preventative care, which could lead to undiagnosed health issues.
It's important for individuals and families to carefully consider the costs and benefits of health insurance coverage, and to choose a plan that best fits their needs and budget. While the monthly premium may seem like a significant expense, the cost of not having coverage can be much higher in the long run.
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The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.74
5.74
millimeters and a standard deviation of 0.07
0.07
millimeters. Find the two diameters that separate the top 5%
5
%
and the bottom 5%
5
%
.
The diameter that separates the bottom 5% of bolt diameters produced in the machine shop is approximately 5.62985 millimeters.
We can use the Z-score formula to find the diameters that separate the top 5% and bottom 5% of the bolt diameters produced in the machine shop.
For the top 5%, we want to find the diameter such that 5% of the bolts have a larger diameter. Using a standard normal distribution table or calculator, we find that the Z-score corresponding to the top 5% is 1.645.
So, the Z-score formula gives us:
1.645 = (x - 5.74) / 0.07
Solving for x, we get:
x = 5.74 + 1.645 * 0.07
x = 5.85015
Therefore, the diameter that separates the top 5% of bolt diameters produced in the machine shop is approximately 5.85015 millimeters.
For the bottom 5%, we want to find the diameter such that 5% of the bolts have a smaller diameter. Using the same Z-score of 1.645, but with a negative sign, we get:
-1.645 = (x - 5.74) / 0.07
Solving for x, we get:
x = 5.74 - 1.645 * 0.07
x = 5.62985
Therefore, the diameter that separates the bottom 5% of bolt diameters produced in the machine shop is approximately 5.62985 millimeters.
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Graph the equation in
Desmos: -2x² + 8x + 10
List the key features: x-
intercepts, y-intercept, and
vertex.
Answer:
[tex] - 2(x - 5)(x + 1)[/tex]
Step-by-step explanation:
[tex]1. \: - 2(x {}^{2} - 4x - 5) \\ 2. \: - 2(x - 5)(x + 1)[/tex]