The value of absolute inequality will be given by 0.002 ≥ |x-3|.
Inequality may be defined as the expression which shows unequal behavior between two entities while absolute inequality expression includes inequality along with an absolute value. For example, |x| > 3, |x| <3, |x| ≤3 or |x| ≥3. Now, let us assume the length of the part in the question as x. Since, the desired length is given as 3mm and also the parts are within 0.002 mm of the desired specifications.
Therefore, the maximum length of the part can be = 3 + 0.002
and the minimum length of the part can be = 3 - 0.002
Therefore, we can write the inequality as
3 - 0.002 ≤ x ≤ 3 + 0.002
⇒ 3 - 0.002 ≤ x and x ≤ 3 + 0.002
⇒ -0.002 ≤ x-3 and x-3 ≤ 0.002
⇒ 0.002 ≥ -(x-3) and x-3 ≤ 0.002 (Because a > b ⇒ -a<-b)
⇒ 0.002 ≥ | x - 3 |
Thus, the required absolute inequality is 0.002 ≥ |x-3|.
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Answer:
A: |x - 3| ≤ 0.002
Step-by-step explanation:
If
F(x) = f(xf(xf(x))),
where
f(1) = 2, f(2) = 5, f '(1) = 4, f '(2) = 5,
and
f '(5) = 6,
find
F '(1).
F '(1) =
The composite function F(1) has a value of 2
How to evaluate the composite function?The definition of the composite function is given as
F(x) = f(xf(xf(x)))
Also, we have
f(1) = 2, f(2) = 5, f '(1) = 4, f '(2) = 5, and f '(5) = 6,
Substitute 1 for x in the equation F(x) = f(xf(xf(x)))
So, we have
F(1) = f(xf(xf(1)))
From the question
f(1) = 2
So, we have
F(1) = f(xf(2))
From the question
f(2) = 5
So, we have
F(1) = f(5)
As a general rule
If f '(2) = 5 then f(5) = 2
So, we have
F(1) = 2
Hence, the value of the function F(1) is 2
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It is possible to approximate the outside temperature based on how fast crickets are chirping. Suppose on a 50 degree day, you measure 52 chirps in a minute, and on a 74 degree day, you measure 148 chirps in a minute. A. Based on this data, determine a linear equation that will output the number of chirps in a minute, n, given the temperature in degrees, t.__________B.. Use your equation to predict the temperature if you heard 96 chirps in a minute, to the nearest degree.________ degrees
Step-by-step explanation:
we have to find the equation, that's why we select the data
(t, n) = (50, 52) and (14,148)
we look as follows
n-52 = ((148-52) / (14-50)) * (t-50)
We perform the indicated operations
n-52 = (96/24) * (t-50)
n-52 = 4 (t-50)
finally we get the result
n = 4t-148
Answer:
Linear equation n = 4t-148
B)
[tex]n=96[/tex]Therefore,
[tex]\begin{gathered} 96=4t-148 \\ 4t=96+148 \\ 4t=244 \\ t=\frac{244}{4}=61^0 \end{gathered}[/tex]Hence, the answer is 61degrees.
159,095 rounded to ten thousands place
Answer:
160,000
Step-by-step explanation:
help me please!!!!!!!!
Answer:
First option is correct.
Step-by-step explanation:
Normally, Pete's dad deposits $25 into his bank account every week.
Now, he wants to deposit x extra dollars for 8 weeks. So, the total deposits for these 8 weeks will be:
8*(25 + x)
He wants to keep the total deposits above 500. So
8*(25 + x) > 500
Now we solve the inequality similarly to how we would solve an equality.
8*(25 + x) > 500
200 + 8x > 500
8x > 500 - 200
8x > 300
x > 300/8
x > $37.50
So the first option is correct.
3. The graph of a polynomial function fis
shown. Which statement about the
polynomial is true?
-3
A. The degree of the polynomial is even.
B. The degree of the polynomial is odd.
C. The constant term of the polynomial is even.
D. The constant term of the polynomial is odd.
The degree of the polynomial is even.
What is polynomial ?Algebraic expressions called polynomials include indeterminates and constants. Polynomials can be considered a particular type of mathematics. In practically all areas of mathematics, including calculus, they are used to express numbers. They are also regarded as being crucial in several areas of mathematics. Examples of polynomials include 2x + 9 and [tex]x^{2}[/tex] + 3x + 11. The "=" sign is absent from all of these samples, as you may have observed.
The polynomial's degree is even since the final behavior is the same in both directions (for -x and for +x, y→∞).
The y-intercept is the fixed term. Since it is not an integer, evenness and oddness cannot be determined.
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Hope some math whiz is on pls dont answer if u dont know
Match the scenario with the law of reasoning.
Law of Contrapositive
Law of Syllogism
Law of Detachment
Not a valid conclusion
options:
1.
If Alex runs a mile in under 6 minutes, then he will have a new personal record.
Alex ran a mile in 5 minutes and 45 seconds.
Therefore, Alex set a new personal record.
2.
If you go to the water park, then you will need to bring sunscreen.
If you do not bring sun screen, then you will burn.
Therefore, when you go to the water park you will get a sunburn.
3.
If the measures of two angles in a triangle are 30° and 60°, then the third angle is 90°.
If a triangle has a 90° angle, then it is a right triangle.
Therefore, if a triangle has two angles that measure 30° and 60°, then it is a right triangle.
4.
If two lines are parallel, then they never intersect.
Line a and line b intersect.
Therefore, line a and line b are not parallel
1. If Alex runs a mile in under 6 minutes, then he will have a new personal record. Alex ran a mile in 5 minutes and 45 seconds. Therefore, Alex set a new personal record. - law of Detachment
2. If you go to the water park, then you will need to bring sunscreen. If you do not bring sun screen, then you will burn. Therefore, when you go to the water park you will get a sunburn. - law of contrapositive
3. If two lines are parallel, then they never intersect. Line a and line b intersect. Therefore, line a and line b are not parallel - Law of Syllogism
4. If the measures of two angles in a triangle are 30° and 60°, then the third angle is 90°. If a triangle has a 90° angle, then it is a right triangle. Therefore, if a triangle has two angles that measure 30° and 60°, then it is a right triangle. - Not a valid conclusion
How to illustrate the information?According to the law of contrapositive, the initial assertion is accurate if and only if the contrapositive is accurate. The original assertion is untrue if the contrapositive is false. A conditional assertion that may or may not depend on another is a contrapositive.
Using deductive reasoning, a syllogism is a three-part logical argument in which two premises are joined to get a conclusion.
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A soccer ball is kicked in the air. The table shows the heights y (in feet) of the ball after x seconds. Write an equation for the height of the soccer ball. Find the height of the soccer ball after 1.8 seconds.
I got my function as [tex]y=0.06x^2 +17.82x[/tex] and 32.27 feet as the height after 1.8 seconds, I want to make sure though.
The height of the soccer ball after 1.8 seconds will be 372.47 feet.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
An air kick is made with a soccer ball. The table displays the ball's height y (in feet) after x seconds.
The function is given as,
y = 0.06x² + 17.82x + 32.27
The height of the soccer ball after 1.8 seconds will be given as,
y = 0.06(18)² + 17.82(18) + 32.27
y = 19.44 + 302.76 + 32.27
y = 372.47
The height of the soccer ball after 1.8 seconds will be 372.47 feet.
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Determine the value of the trigonometric ratio.
Given,
The measure of side YZ is 21.
The measure of side XY is 20.
The measure of side XZ is 29.
Required:
The value of tanX.
The trigonometric ratio is calculated as,
[tex]tan\theta=\frac{side\text{ opposite to }\theta}{side\text{ adjacent of }\theta}[/tex]Substituting the values,
[tex]\begin{gathered} tanX=\frac{YZ}{XY} \\ tanX=\frac{21}{20} \end{gathered}[/tex]ence, the value of tanX is 21/290.
Find the surface area (in square units) of the polyhedron. i need help!!
The surface area and volume of the polyhedron are mathematically given as
SA=160 Sqr UnitsV=105 cubic unitsThis is further explained below.
What is surface area?Generally, The surface area of a three-dimensional object is equal to the total of areas of all of its faces, also known as surfaces. A cuboid has six faces that are rectangular in shape.
Add together the areas of each of the cube's six sides to get the surface area of the cube. To get the surface area of the prism, we may additionally label its length (l), width (w), and height (h), and then use the formula surface area = length (l) times width (w) times height (h).
To refresh your memory, the surface area of an item is the entire area of the exterior surfaces of the three-dimensional object or the total sum of the area of the faces of the object.
In other words, the surface area of an object is its "face area." It is expressed in terms of square units as a measurement.
In conclusion, Generally, the Surface area is mathematically given as
SA= 9+35+35+33+36+12
SA=160 Sqr Units
Generally, the equation for Volume is mathematically given as
V=(11*9)+6
V=99+6
V=105 cubic units
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CQ is attached surface area
Are the triangles scaled copies of each other? True or false?
Answer:
You cannot multiply or divide for 4 and 3 so no false
Step-by-step explanation:
Customer 1 buys 2 hamburgers and 4 drinks, and his total is $13.00. Customer 2 buys 3 hamburgers and 7 drinks, and his total comes out as $21.00. PART A. You want to buy 8 drinks and 9 hamburgers for you and your friends. How much do you expect to pay?PART B. Show your work or explain how you got your answer.
Answer:
[tex]\text{Total= \$43.5}[/tex]Step by step explanation:
To solve this situation we can create a system of linear equations, with the given information for the customers:
Let x be the price for each hamburger
Let y be the price for each drink
[tex]\begin{gathered} 2x+4y=13\text{ (1)} \\ 3x+7y=21\text{ (2)} \end{gathered}[/tex]To solve for x and y. We can use the substitution method, which consists of isolating one variable in one of the equations and substitute it into the other.
Let's isolate y in (1):
[tex]\begin{gathered} 4y=13-2x \\ y=\frac{13}{4}-\frac{2}{4}x \end{gathered}[/tex]Now, substitute it into equation (2).
[tex]3x+7(\frac{13}{4}-\frac{2}{4}x)=21[/tex]Solve for x:
[tex]\begin{gathered} 3x+\frac{91}{4}-\frac{7}{2}x=21 \\ -\frac{1}{2}x+\frac{91}{4}=21 \\ -\frac{1}{2}x=21-\frac{91}{4} \\ -\frac{1}{2}x=-\frac{7}{4} \\ x=\frac{7\cdot2}{4} \\ x=\frac{7}{2}=\text{ \$3.5 } \end{gathered}[/tex]With the x-value, we can substitute it into the equation (1) to find the price for each drink:
[tex]\begin{gathered} y=\frac{13}{4}-\frac{2}{4}(3.5) \\ y=\frac{13}{4}-\frac{7}{4} \\ y=\frac{6}{4}=\text{ \$1.5} \end{gathered}[/tex]Therefore, the price for each hamburger is $3.5 and for each drink is $1.5.
Now, if we want to buy 8 drinks and 9 hamburgers:
[tex]\begin{gathered} \text{Total}=(8\cdot1.5)+(9\cdot3.5) \\ \text{Total}=12+31.5 \\ \text{Total= \$43.5} \end{gathered}[/tex]Not sure how to do this question
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
he detiails of the solution are as follows:
sing the Laws of logarithm which says that:
[tex]\log _bP-\log _bQ=log_b(\frac{P}{Q})[/tex]Hence,
[tex]\log _340_{}-log_310=log_3\text{(}\frac{40}{10})=log_34[/tex]For 15 points, label this:
Source of magnetic force - Nail
Source electric force - battery cell
What is an electromagnet?We know that the electromagnet is a type of magnet whose magnetic property depends on the interaction of the magnetic material with an electric field. We can see in the image that the nail which serves as the magnetic material is connected to a cell which is the source of the given electric current.
It the follows that the nail above is the source of the magnetic force because the coils of wire while the battery cell is the source of the electrical force.
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Please help me solve this
(a) 291/2020
Divide the total for the 10-14 year column by the total.(b) 77/465
There are 465 people from the east, 77 of which were loyal for 10 to 14 years(c) 437/1010
There are 291+583=874 people who were loyal for at least 10 years. Divide this by the total of 2020 people.(d) 145/376
376 people are from the West, (45+100)=145 of which are at least 10.(e) 32/157
157 people were loyal for less than a year, 32 of which were from the East.(f) 53/157
157 people were loyal for less than a year, 53 of which were from the South.(g) 433/465
465-32=433 people were loyal for at least 1 year out of the 465 people from the East.(h) 335/376
376-41=355 people were loyal for at least 1 year out of the 376 people from the West.The lines intersect. Parallel lines never intersect. What must be true?
A) The lines are not parallel.
B) The lines do not intersect.
C) The lines are perpendicular.
D) The lines are parallel.
To make Citrus Orange paint, a paint store mixes yellow, white, and red paint in the ratio of 5 to 3 to 1. How many gallons of yellow, white, and red paint does the store need to mix to make 135 gallons of Citrus Orange paint?
Answer:
yellow 75 gallons
white 45 gallons
red 15 gallons
Step-by-step explanation:
yellow (5) + white (3) + red (1) equal 9 total parts.
5/9 is yellow
3/9 is white
1/9 is read
5/9 x 135 = 75
3/9 of 135 = 45
1/9 of 135 = 15
A rectangle has a length six inches less than its width. If the perimiter of the rectangle is 54 inches, find the dimensions
Answer:
l=10.5 in , w=16.5 in
Step-by-step explanation:
p=2l+2w
54=2(w-6)+2(w)
54=2w-12+2w
54=4w-12
66=4w
w= 16.5
l=w-6
l=16.5-6
l=10.5 in
w=16.5 in
hope this helps
Peaches Water (cups)
40
30
400
300
How many peaches are needed for every 1 cup of water? Note: Your answer may be exact or rounded to the nearest hundredth
The table below shows the number of peaches and cups of water used to make fruit punch according to a certain recipe.
The peaches required for every cup of water is 4/3
what is unitary method?
The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
so;
A.T.Q:-
Is there two columns of data and two data points? Like this:
peaches Water
40 30
400 300
If so, then there are two ways to do it.
1) You can set up a ratio like this
40/30 = x
:-Where x is the number of peaches for every cups of water .
So;
x = 40/30 peaches
x = 4/3 peaches
2) Look at the increase from one to the other.
3 cups of water requires 4 peaches.
∵ Hence by unitary method
1 cup of water requires 4 /3 peaches.
:- so; 4/3 peaches are required for every cup of water.
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factor and find all roots
Answer: x = 3
x = ± √3 = ± 1.7321
Step-by-step explanation:
those are 2 solutions
A monument in the form of a marble cylinder has a circular base with a radius 1.5 meters. The altitude of the monument is 3.5 meters. How many cubic meters of marble does this monument contain?
A. 24.74 M 3
B. 6.19 M 3
C. 21.21 M 3
D. 7.07 M 3
If a monument in the form of a marble cylinder has a circular base with a radius 1.5 meters and the altitude of the monument is 3.5 meters. then the quantity of marbles contains in the monument is 24.74 meter cube
The shape of the monument is cylinder
The base radius of the cylinder = 1.5 meter
The altitude of the monument = 3.5 meters
The volume of the cylinder = [tex]\pi r^{2}h[/tex]
Where r is the radius of the cylinder
h is the height of the cylinder
Substitute the values in the equation
The volume of the cylinder = [tex]\pi (1.5)^{2}(3.5)[/tex]
= 24.74 meter cube
Hence, If a monument in the form of a marble cylinder has a circular base with a radius 1.5 meters and the altitude of the monument is 3.5 meters. then the quantity of marbles contains in the monument is 24.74 meter cube
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The weekly repair cost Y for a machine has a probability density function given by f(y)=3(1−y)^2, 0
Using integrals, the 90th percentile of the given probability distribution is of $53.58.
What is the 90th percentile of the distribution?The amount exceeded only 10% of the time is the 90th percentile of the distribution, which is the value of p for which:
[tex]\int_0^p f(y) dy = 0.9[/tex]
The integral represents the cumulative density function of the distribution, which is the reason why we use it to find the 90th percentile of the distribution.
The function is given by:
f(y) = 3(1 - y)²
Hence the integral is calculated as follows:
[tex]\int_0^p 3(1 - y)^2 dy[/tex]
Applying the integral of the power of y rule, along with the substitution, it is found that:
[tex]\int 3(1 - y)^2 dy = -(1 - y)^3[/tex]
Hence:
[tex]\int_0^p 3(1 - y)^2 dy = -(1 - y)^3|_{y = 0}^{y = p}[/tex]
Applying the Fundamental Theorem of Calculus, considering the value of the definite integral, it is found that:
-(1 - p)³ + 1 = 0.9
-(1 - p)³ = -0.1
(1 - p)³ = 0.1
Applying the cube root to both sides:
1 - p = 0.4642.
p = 1 - 0.4642
p = 0.5358.
This amount is in hundredths of dollars, hence the 90th percentile of the given probability distribution is of $53.58, as 0.5358 x 100 = $53.58.
What is the missing information?The problem is missing, and is given by the image at the end of the answer.
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find the mean median and mode 85,91,76,85,93
Answer:
mean: 86 median: 85 mode: 85
Step-by-step explanation:
The Hike 4 Life company manufactures hiking boots. The production facility has foxed costs of $400 a day and the cost of making 1 pair of boots is $4.75. Which of the following equations
represents the daily production cost based on the number of pairs of boots manufactured each day?
The equation that represents the daily production cost based on the number of pairs of boots manufactured each day is C(x) = 4.75x + 400.
What are linear equations?
Linear equations are a subset of first order equations. Linear equations are defined for lines in the coordinate system. One homogeneous variable of degree one constitutes a linear equation in one variable (i.e., only one variable). A linear equation could contain multiple variables. When a linear equation comprises two variables, for instance, linear equations in two variables are utilized. A mathematical statement known as an equation contains an algebraic expression and the equal symbol (=). It is the equation for a straight line. The equation is shown to be valid when values are substituted for the unknown values in the solutions of linear equations. When there is just one variable, there is just one answer.
Given, the daily production cost (in $) = C(x)
The number of pairs of boots manufactured = x
The cost of making a pair of boots = $ 4.75
The fixed cost of production each day = $ 400
Thus, net cost of making 'x' boots added to the daily fixed production cost will give the daily production cost.
Therefore, C(x) = 4.75x + 400, is the correct equation.
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Please help it’s geometry and it’s hard
Measure of the angle m ∠ RQS = 58 ° for the given circle with arc RS subtending m ∠RPS=14 x + 46 ° at the center P and m ∠ RQS = 3 x + 43 ° at Q, on the circumference.
As given in the question,
Measure of the angle is given by :
m ∠ RPS=14 x + 46 °
m ∠ RQS=3 x + 43 °
m ∠ RPS = twice m ∠RQS (angle subtended at center of the circle)
14 x +46 =2(3 x + 43)
⇒ 14x + 46 = 6x +86
⇒ 14x-6x=86-46
⇒8x=40
⇒ x=5°
m ∠ RQS = (3 x + 43) °
=[3(5) + 43 ]°
= 58°
Therefore, measure of the angle in the given circle m ∠RQS is equal to the 58 °
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Find the average value of the following numbers: -7,-4.2,-1,0,2,6,10,12
Answer:2.225
Step-by-step explanation:
If you add all the numbers and then divide by the number of numbers given you get the average.
280Joules of work is done pushing a bike 35m. How much force was used to push the bike?
By definition, the work is given by:
[tex]W=F\cdot d\text{.}[/tex]Where W is the work in Joules (J), F is the force in Newtons (N) and d is the distance in meters (m).
In this problem we have:
• W = 280J,
,• d = 35m.
We can find the force F in terms of W and d:
[tex]F=\frac{W}{d}\text{.}[/tex]Replacing the values of W and d, we find that the force F is:
[tex]F=\frac{280J}{35m}=8\frac{J}{m}=8N\text{.}[/tex]In the last step, we used that J = N m.
Answer: The force is F = 8N.
Hello, help me please )
Find the inverse of:
[tex]f(x)=(x+3)^2[/tex]a. To sketch f(x), we use the graph of the parent function
[tex]g(x)=x^2[/tex]Translated 3 units to the left:
b. The part of the function f(x) that is one-to-one and non-decreasing is in the domain [-3, ∞). Expressing in inequality notation: x ≥ -3.
c. The function f(x) can be written as:
[tex]y=(x+3)^2[/tex]Applying square root on both sides:
[tex]\pm\sqrt{y}=x+3[/tex]Solving for x:
[tex]x=\pm\sqrt{y}-3[/tex]Swapping letters:
[tex]y=\pm\sqrt{x}-3[/tex]Since we have chosen only the non-negative part of the domain for f(x), we use only the positive sign:
[tex]f^{-1}(x)=\sqrt{x}-3[/tex]Both functions, f(x) and its inverse are shown below:
Types of Posts Cost of Each Post Base Price Posts with Words Only S5 $5 Posts with Pictures Only $10 $25 Posts with Words and Pictures $10 $35 Samuel ordered 2 posts with words only and 2 posts with pictures only. After placing his order, Samuel realized he could have saved money if he, instead, ordered 2 posts with words and pictures. Let y represent Samuel's savings, in dollars, and let x represent the number of posts. Which equation could be used to determine the amount of money Samuel could have saved if he ordered 2 posts with words and pictures, instead of his original order? A y = 5x – 5B. y = 5.r + 65C y = -5r + 25D y = 2
x = Number of posts
y = samuel's savings
If he order 2 posts with words and pictures:
y = 2(10) + 35 = 55
If he order 2 posts with words only and 2 posts with pictures only.
y = 2(5) + 2(10) + 5 + 25 = 10 + 20 + 5 + 25 = 60
Therefore, he could have save 5 dollars
Therefore the equation is:
y = 5x - 5
A random sample of n = 50 teachers was selected from a Local Government and it has been established that 30% of the entire teachers are ghost workers and 70% are real workers. Determine the expected number of the real workers in any sample of size 50. Select one: O 35 O 15 O 50 O 20 <
The expected number of the real workers in any sample of size 50 is 35
What is basic algebra ?Algebra is a branch of mathematics that facilitates the description of problems or situations into mathematical statements. It involves variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division to generate a valid mathematical statement. All branches of mathematics, such as coordinate geometry, calculus, and trigonometry, employ algebra. An elementary algebraic formula is 2x + 4 = 8. Algebraic expressions serve as the mathematical statement when operations on variables and constants, such as addition, subtraction, multiplication, division, etc., are done. Assume James and Natalie had the notion to arrange the matchsticks into numerical patterns while they were fiddling with them.
Given that : A random sample of n = 50 teachers was selected from a Local Government and it has been established that 30% of the entire teachers are ghost workers and 70% are real workers.
n= 50
30 % are ghost workers
= 30% 0f 50
= 0.3×50
= 15 are ghost workers
50 - 15 = 35 are real workers
The expected number of the real workers in any sample of size 50 is 35
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Find the perimeter of the figure to the right.
The perimeter is
(Simplify your answer.)
4y
meters.
2y meters
7y meters
6 meters
18 meters
6y meters
Answer:
72 m
Step-by-step explanation:
We observe that 7y+6=18, and thus y=12/7.
So, the perimeter is:
[tex]2(18+7y+6) \\ \\ =14y+48 \\ \\ =14(12/7)+48 \\ \\ =72[/tex]