Answer:
13
Step-by-step explanation:
The biggest number minus the smallest number.
Answer:
13
Step-by-step explanation:
the highest value is 45
the lowest value is 32
subtract them from each other and you get 13
Absolute minimum and maximum values of [tex]f(x)=2cos (x) +sin (2x)[/tex] on the interval [tex][0,pi/2][/tex]
Step-by-step explanation:
f'(x)=-2sin(x)+2cos(2x)=0
as cos(2x)=2sin(x)cos(x),
-2sin(x)+4cos(x)sin(x)=0
sin(x)-2cos(x)sin(x)=0
(sin(x))(1-2cos(x))=0
-> x = 0, pi/3
testing these values along with the end points of the interval,
f(0)=2
f(pi/3)=1+(0.5sqrt(3))
f(pi/2)=0
so the min is 0 and the max is 2.
Here is a rhombus.
Diagram not drawn to scale
80°
A straight line joining the midpoints of two of its sides is drawn.
Answer:
130 degrees
Step-by-step explanation:
The right top triangle is isosceles, so the supplementary angle of angle α is (180 - 80)/2 = 50 degrees.
Therefore, α = 180 - 50 = 130 degrees.
Help! I can't figure this out!
Answer:
57/6 60/6 22/6 26/6
Step-by-step explanation:
So the answers for the blanks are 57, 60, 22, 26.
Let me know if I am incorrect.
Classify the segment in each part below.
Only use the information given in the figure.
Do not assume measures are equal unless the markings indicate they are.
If necessary, you may learn what the markings on a figure indicate.
Answer:
See belowStep-by-step explanation:
(a)
IO is the perpendicular bisector of FH(b)
ZV is the angle bisector of Z#a
Check IO bisects the FH at 90°.
So it's a perpendicular bisector of FH#b
Its altitudeSo the options are
Perpendicular bisector.Angle bisectorAltitudeSuppose a normal distribution has a mean of 62 and a standard deviation of 4. What is the probability that a data value is between 56 and 64? Round your answer to the nearest tenth of a percent. OA. 64.5% B. 63.5% O c. 62.5% O D. 61.5%
Answer:Given a normal distribution with μ = 62 and σ = 4., calculate the 68-95-99.7 rule, or three-sigma rule, or empirical rule ranges
Calculate Range 1:
Range 1, or the 68% range, states that 68% of the normal distribution values lie within 1 standard deviation of the mean
68% of values are within μ ± σ
μ ± σ = 62 ± 4.
62 - 4. <= 68% of values <= 62 + 4.
58 <= 68% of values <= 66
Calculate Range 2:
Range 2, or the 95% range, states that 95% of the normal distribution values lie within 2 standard deviations of the mean
95% of values are within μ ± 2σ
μ ± 2σ = 62 ± 2(4.)
62 - 2 x 4. <= 95% of values <= 62 + 2 x 4.
62 - 8 <= 95% of values <= 62 + 8
54 <= 95% of values <= 70
Calculate Range 3:
Range 3, or the 99.7% range, states that 99.7% (virtually ALL) of the normal distribution values lie within 3 standard deviations of the mean
99.7% of values are within μ ± 3σ
μ ± 3σ = 62 ± 3(4.)
62 - 3 x 4. <= 99.7% of values <= 62 + 3 x 4.
62 - 12 <= 99.7% of values <= 62 + 12
50 <= 99.7% of values <= 74
Step-by-step explanation:
The probability that a data value is between 56 and 64 is,
= 64.7%
What is mean by Probability?The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
Given that :
Mean (m) = 62
Standard deviation (s) = 4
Hence, Probability that a data value is between 56 and 64
P(56 < x < 64)
Using the relation :
(x - m) / s
P(x < 56) : (56 - 62) / 4
= - 1.5
P(Z < - 1.5) = 0.10565
( Z probability calculator)
P(x < 64) :
(64 - 62) / 4 = 0.75
P(Z < 0.75) = 0.77337 (Z probability calculator)
Hence, We get;
P(Z < 0.75) - P(Z < - 1.25)
0.77337 - 0.10565
= 0.64772
= 64.7%
Thus, the probability that a data value is between 56 and 64 is,
= 64.7%
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An 8-year-old boy is half his sister's age. When the boy is 12, how old will his sister be?
Answer:
20 years
Step-by-step explanation:
when the boy is 8 and half his sisters age his sister is 16
four years later the boy will be twelve, so if his sister was 16 four years later she will be 20
Answer:
20 years old
Step-by-step explanation:
Let n represent the age of the boy's sister then...
[tex]8=\frac{1}{2}n[/tex]
Multiply both sides by 2
[tex]n=16[/tex]
When the boy is 12, it will be 4 years from when he is 8 therefore...
16 + 4 = 20 years old
-2(x + 7) simplified expression, please do it I don't understand it for some reason and I'm gonna fail my test which is 50% of my grade :(
Answer:
-2 (x+7)
-2x-14
hope it helps you
have a great day :)
Use the distributive property to write an expression that is equivalent to each expression. If you get stuck, consider drawing boxes to help organize your work.
9(4x−3y−23)
-2(-6x+3y−1)
15(20y−4x−13)
8(-x−12)
-8(-x−34y+72)
Answer:
a) 36x-27y-207
b)12x-6y+2
c)300y-60x-195
d)-8x-96
d)8x+272y-576
Step-by-step explanation:
In all of these equations, you multiply the numbers on the outside of the parentheses to all of the terms inside the parentheses to get each of your different answers.
Hope this helps and please award brainliest if possible!
y = 4.45 = 1.4
y=
Please help (ASAP‼️)
Answer:
y=6.23 hope this Helps!
Step-by-step explanation:
Use the given equation to find the missing coordinates of the points and then find the slope of the line for each equation.
y=-2/3x+1/6 ; A(...,6) ; B(9,...)
Answer:
6
Step-by-step explanation:
the least common denominator of 3 and 6 is 6
THATS how I got six
Hopped this helped <3
The slope of the line will be -2/3. And the coordinates will be A(-35/4, 6) and B(9, -34/6).
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = -2/3 x + 1/6
The slope of the line is - 2/3.
At y = 6, the value of 'x' is calculated as,
6 = -2/3 x + 1/6
35/6 = -2/3 x
x = -35 / 4
At x = 9, the value of 'y' is calculated as,
y = -2/3 (9) + 1/6
y = -6 + 1/6
y = -35/6
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a case of toothpicks has 5,400 toothpicks, there are 9 boxes of toothpicks in the case.how many toothpicks are in each box?
( awnser this untill tmr and u will get 200 points!)
Answer:
divide it, 5400 divided by 9 is 600.
A sine function has an amplitude of 3, a period of pi, and a phase shift of pi/4 What is the y-intercept of the function?
Answer:
(0, -3)
Step-by-step explanation:
It will help to graph it out.
Also is the phase shift negative or is it just to the right? Im assuming its just right pi over 4
Answer: 0
Step-by-step explanation:
2pi/4 does not equal pi, it equals half of pi. 2pi/2 equals pi. Regardless here's my answer, since it also checks out for a similar function that was confirmed to have a phase shift of pi/2:
The formula for this is asin(bx - c) + d, where
|a| = amplitude
period = 2pi/b
and phase shift = c/b
The amplitude is 3
3sin(bx - c) + d
Phase shift is c/b, in this case, pi/4
3sin(4x - pi) + d
d is vertical shift
(phase shift, c, is also known as horizontal shift)
We don't see any d here so graph on Desmos as follows....
Graph 3sin(4x - pi)
Looks like the y-intercept is 0
Check by substituting 0 for x:
3sin(4x - pi)
3sin(4(0) - pi)
3sin(-pi) = 0
The answer is 0, checks out.
What are the domain and range of the function?
f(x) = -5/5x^3
Answer:
Domain: all real numbers
Range: all real numbers
Step-by-step explanation:
Hope that helps!
Find the probability of each event. Write your answer as a fraction and as a percent. Drawing
a diamond from a standard deck of cards.
b. Rolling a number less than five on a standard number cube.
C. a Drawing a blue marble from a bag of 18 marbles, three of which are blue.
Answer: See below
Step-by-step explanation:
Event 1:
There are 13 diamond cards in total
A standard deck of cards has a total of 52 cards
Probability = 13/52
P = 1/4 or 25%
Event 2:
There are a total of 6 sides on a standard dice
Probability = 4/6
P = 2/3 or 66.67%
Event 3:
There are 3 blue marbles in a bag of 18 marbles
Probability = 3/18
P = 1/6 or 16.67%
Answer: a) 1/4 b) 2/3 c) 1/6
Step-by-step explanation:
All of these are probability problems. They have this trick.
First, the trick. The chance of taking an x amount of blue marbles out of a bag of y marbles is x/y. Now using this…
a) there are 13 diamonds and 52 total. 13 is x, and 52 is y. It is 13/52 = 1/4
b) There are 4 numbers you need to get, and 6 in total. Therefore; there is a 4/6 chance which simplifies to 2/3.
c) There are 3 marbles you need, and 18 of them in total. It is 3/18 which is 1/6.
I once struggled on these problems, for they can be difficult.
Convert 24 feet to inches.
Answer:
288 inches
Step-by-step explanation:
24x12 = 288
each foot has 12 inches
in order for students to have a club at school they need a minimum of 26 students. If there are 19
students signed up for the club, how many more students does the club need?
What are the solutions? Select the correct choice below and fill in the answer box to complete your
choice
Answer:
7 more students.Basic subtraction:
needed students: minimum required students - students signed up
needed students: 26 - 19
needed students: 7 students, the club needs.
Solution:
We know that the inequality form is x ≥ 26. If we subtract the number of students required by the number of students joined, we will obtain the required students to start the club.
=> Required students - Students joined = Students remained to join=> 26 - 19 = Students remained to join=> 7 studentsHence, the club needs 7 more students to have a club.
tori has to place one more x on the line plot for the eighth month then the total length in hours of all the calls for the eighth month will be 6 hours what is the length in hours of tori's phone calls for just eight months.
Talks 1hr month 9
Talks 1 1/2 hrs 10 and. 11th month
Ta;ks. 3/4 hr 12th month
Line plots are used to express variables using markers
The total phone call for eight months is [tex]10\frac 34[/tex] hours
How to determine the total phone callsFrom the line plot, we have the following summation
[tex]Total = 1hr + 1\frac 12 hr * 2 + \frac 34 hr[/tex]
When the total hours of phone call for the 8th month is added, the summation equation becomes
[tex]Total = 1hr + 1\frac 12 hr * 2+ \frac 34 hr + 6 hr[/tex]
Add the expressions
[tex]Total = 10\frac 34[/tex]
Hence, the total phone call for eight months is [tex]10\frac 34[/tex] hours
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1. Think of two things that you can measure. Give one that requires high precision, or a low level of uncertainty. Give another that can have lower precision, or a higher level of uncertainty.
2. Explain why you made your choices. Why does one measurement need to be more precise than the other
1. We can measure the following two things:
(i) a person's height
(ii) the velocity required to reach Mars.
2. Everything involving a rocket launch needs to be extremely precise; otherwise, it could result in tragedy. However, anything involving a person's height won't result in disaster.
This can be solved using the concept of precision and uncertainty concept.
What is precision and uncertainty?The accuracy of a material or substance is the distance or degree to which two or more measurements are near to one another. Every time a measurement is performed, a new result is obtained that falls within the uncertainty interval that surrounds the measured value.
1. We don't need to be very precise because we can measure a person's height with a modest degree of accuracy. The person hearing would get a notion of their height if we said, "That individual is roughly 5 feet tall."
On the other hand, if we estimate the rocket speed to Mars incorrectly, it would lead to tragedy in the future, hence we require great precision. In order to ensure that we strike the necessary objective in space, we apply intricate mathematics.
2. Like we stated in problem 1, everything involving space travel needs extreme accuracy. The spaceship might crash and calamity could ensue if our estimates are incorrect. Engineers utilized the incorrect settings in the one instance where anything went wrong, causing the Mars lander to smash into the planet rather than securely land there.
Due to the enormous expense of these space exploration missions, it is imperative to obtain as many exact and accurate values as possible. Now, details like a person's height don't necessarily need to be accurate because we can just guesstimate a person's height depending on who we're speaking to.
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Paul had 84 fliers to post around town. Last week, he posted 1/4 of them. This week, he posted 4/7 of the remaining fliers. How many fliers has he still not posted?
The sum of 75 and 45 is divided by 5 and the difference of quotient and 10 is multiplied by 2. (Ans: 28) (Hint:- Make mathematical expressions, then simplify) (Please solve my question)
Answer:
28
Step-by-step explanation:
(((75+45) ÷5) - 10 )2 -> first add 75 and 45
((120 ÷ 5) - 10)2 -> Divide 120 by 5
(24 - 10)2 -> Subtract 24 by 10
(14)2 - > 28
Ans: 28
Three workers are digging a ditch. They take turns working, and every one of them works for as long as it would take the other two to dig half of the ditch. They finished digging the ditch working in this manner. How many times faster would the three workers have finished digging the ditch if they had all been working at the same time?
The work would be finished 2.25 times faster if they had been doing the work at the same time.
Rate of doing workAssumption;
Provided each one of the workers works for an hour which is equivalent to the time it takes to finish half of the ditch.In essence, the total time required to finish the ditch by 2 workers is; 2 hours.
Hence, for 3 workers working simultaneously, the time required is 1hour 20 minutes. = 80 minutesHowever, since they took 1 hour turns on the job, it follows that; The total time used is;
Total time = 3 × 1hr = 3 hours = 180 hoursHence they could have finished the work in;
R = 180/80 times faster = 2.25 times faster.Read more on rate of work;
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Evaluate −4|x+2| when x=−5.
−28
−12
12
28
Answer:
Step-by-step explanation:
Please help me I really need this
Answer:
56
Step-by-step explanation:
8C5 = 56
Answer:
8C5 = 56
Step-by-step explanation:
The formula for nCk is ...
nCk = n!/(k!(n-k)!)
Then the value of 8C5 is ...
8!/(5!(8-5)!) = 8·7·6/(3·2·1) = 8·7
8C5 = 56
_____
Additional comment
The larger of the denominator factorials will cancel most of the factors of the numerator. The remaining denominator factors can be factored from the remaining numerator values to simplify the problem of doing the math by hand. Most graphing calculators and all spreadsheets can compute this function for you.
[tex]\dfrac{8!}{5!\cdot3!}=\dfrac{8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}{(5\cdot4\cdot3\cdot2\cdot1)(3\cdot2\cdot1)}=\dfrac{8\cdot7\cdot6}{3\cdot2\cdot1}=\dfrac{8\cdot7\cdot6}{6}=8\cdot7[/tex]
If you were in charge of the money, how would you recommend your friends spend it? Explain why you chose the solution you did. Why do you think it's the most fair? (3 points: 1 point for stating your recommendation and 2 points for explaining your reasoning)
Prioritize meeting basic needs and invest in education and skill development, while supporting community projects for a fair distribution of funds.
Prioritize basic needs: I would recommend ensuring that everyone's basic needs are met first, such as food, shelter, and healthcare. This promotes fairness by addressing essential requirements for survival and well-being.
Invest in education and skill development: Allocating funds towards education and skill development programs can empower individuals to improve their future prospects and contribute to society. It promotes fairness by providing equal opportunities for personal growth and advancement.
Support community projects: Encouraging investments in community projects, infrastructure development, and social initiatives can benefit a broader range of people. It promotes fairness by aiming to uplift the community as a whole, rather than focusing solely on individual interests.
By following these principles, the recommended approach for spending money can ensure fairness by addressing basic needs, fostering personal development, and benefiting the community at large. Ultimately, the specific allocation of funds would depend on the context, priorities, and values of the individuals involved.
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Help please I am lost
HELPP MEEE WITH MY HOMEWORK PLEASEEEE
Answer:
Letter a is 6:38 and letter b is 2:17
Hope this helps!
(x + 4)2 – 3(x + 4) – 3 = 0 Select the solution(s) of the original equation.
Answer:
x=−7
Step-by-step explanation:
(x+4)(2)−3(x+4)−3=0
(x)(2)+(4)(2)+(−3)(x)+(−3)(4)+−3=0(Distribute)
2x+8+−3x+−12+−3=0
(2x+−3x)+(8+−12+−3)=0(Combine Like Terms)
−x+−7=0
Use the figure to solve the inequality
Answer:
c hope this hrlpe
Step-by-step explanation:
Help math math ASAP
Answer:
y = 2x - 3
Step-by-step explanation:
y - 9 = 2 ( x - 6 )
y - 9 = 2x - 12
Hi! I can help you with a smile! :)
Perpendicular lines have slopes that are opposite reciprocals.In order to find the opposite reciprocal of a number, flop it over, and change its sign:-1/2-22 (slope of the line that's perpendicular to the given line)Use Point-Slope:y-y1=m(x-x1)y-9=2(x-6)y-9=2x-12y=2x-12+9y=2x-3Answer:
y=2x-3
Hope it helps!
~Nature~
Enjoy your day!
Find the inverse of the matrix [6, 7] [-6, 7] if it exists
For any square matrix A, if it is invertible, its inverse is given by
[tex]A^{-1} = \dfrac1{\det(A)} \mathrm{adj}(A)[/tex]
where adj(A) is the so-called adjugate matrix, which is the transpose of the cofactor matrix of A. If you don't know what that is, that's not terribly important. What is important is that the inverse does not exist if the determinant, det(A), is zero.
We have
[tex]A=\begin{bmatrix}6&7\\-6&7\end{bmatrix} \implies \det(A) = 6\times7-7\times(-6)=84 \neq 0[/tex]
so the inverse does indeed exist. (And we eliminate D as an answer.)
From the given choices, it's quite clear that C must the correct answer, since we know det(A) = 84, and we can easily confirm that
[tex]\begin{bmatrix}7&-7\\6&6\end{bmatrix} \begin{bmatrix}6&7\\-6&7\end{bmatrix} = \begin{bmatrix}84&0\\0&84\end{bmatrix}[/tex]
so that multiplying by 1/84 recovers the identity matrix.
We are given with a square matrix and we are asked to find it's inverse if it exists . So , let's recall some important points first :-
Inverse can only be found of square matrices.If [tex]{\bf A}[/tex] is a square matrix than , it's inverse is denoted by [tex]{\bf A^{-1}}[/tex] , and is given by [tex]{\bf{A^{-1}=\dfrac{1}{adj(A)}det(A)}}[/tex] , where adj(A) is the adjoint of the matrix A and det(A) is the determinant of the matrix AInverse of a matrix exist if A is non-singular Non-Singular means that det(A) ≠ 0 Adjoint of a matrix is the matrix of transpose of cofactors Transpose of a matrix is founded by exchanging it's rows by columns and columns by rows and is denoted by [tex]{\bf{A^{T}}}[/tex]Now , in this question let's assume that [tex]{\sf A=\begin{bmatrix}6 & 7 \\ -6 & 7\end{bmatrix}}[/tex]
Now , Calculating det(A) :-
[tex]{:\implies \quad \sf det(A)=\begin{vmatrix}6 & 7 \\ -6 & 7 \end{vmatrix}}[/tex]
[tex]{:\implies \quad \sf det(A)=42-(-42)}[/tex]
[tex]{:\implies \quad \sf det(A)=42+42}[/tex]
[tex]{:\implies \quad \sf det(A)=84}[/tex]
As , det(A) ≠ 0 . So , [tex]{\bf A^{-1}}[/tex] exists . Now , we need to find the matrix of cofactors first , but let's find cofactors first , so here ;
[tex]{\blacktriangleright \sf C_{11}=7,\: C_{12}=6,\: C_{21}=-7,\: C_{22}=6}[/tex]
Now , let's assume that matrix of cofactors is C , so putting the cofactors as elements of the matrix , C will be ;
[tex]{:\implies \quad \sf C=\begin{bmatrix}7 & 6 \\ -7 & 6\end{bmatrix}}[/tex]
Now , adj(A) will be found by interchanging it's rows by columns and vice versa.
[tex]{:\implies \quad \sf adj(A)=\begin{bmatrix}7 & -7 \\ 6 & 6\end{bmatrix}}[/tex]
Now as [tex]{\sf A^{-1}}[/tex] is given by [tex]{\bf{A^{-1}=\dfrac{1}{adj(A)}det(A)}}[/tex]
[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{A^{-1}=\dfrac{1}{84}\begin{bmatrix}7 & -7 \\ 6 & 6\end{bmatrix}}}}[/tex]
Hence , Option C) [tex]{\sf \dfrac{1}{84}\begin{bmatrix}7 & -7 \\ 6 & 6\end{bmatrix}}[/tex] is correct :D