The extremum of f(x,y) is subject to the given constraint, There is a global minimum (x,y,z.) (4,2,-8).
An instance of a constraint is the fact that there are only so many hours in a day to perform things. Embarrassed reserve or reticence; awkwardness. one which restricts, limits, or regulates; a test.
A constraint is something that limits or controls what you may do. Their decision to abandon the ride turned into made due to economic constraints. Water shortages in the location could be the main constraint on development. Synonyms: limit, drawback, scale back, rein more Synonyms of constraint.
predicament or restriction. repression of herbal emotions and impulses: to exercise constraint. unnatural restraint in manner, communique, and many others.; embarrassment. Something that constrains.
By lagranier multi plur
of = hog
(2x, is, 22>= 25-47
8x=42
10x + 2 = 42
2
28
2x=4, 4= 2
=2
722 (4)
(4.9,2) = (4.2-8)
(4,2-8)= 84
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What is [tex]\frac{3}{4}[/tex] - [tex]\frac{2}{b}[/tex]
The answer is [tex]\boxed {\frac{3b - 8}{4b}}[/tex].
3/4 - 2/b3(b) - 2(4) / 4(b)3b - 8 / 4bif y=mx+b, find m and use the formula for the previous question to find m when the coordinates are (4,7) and b=12
Answer:
m = -5/4
Step-by-step explanation:
In the slope-intercept form formula, y = mx + b, substitute 4 for x, 7 for y, and b for 12 to solve for m.
y = mx + b
7 = 4m + 12
-5 = 4m
m = -5/4
Write 304.9% as a decimal.
Answer:
3.049
Step-by-step explanation:
Move the decimal place in 304.9% to the left two places in order to convert from a percentage to a decimal. 3.049 is the answer.
Brainliest, please :) Hope this helps!
Defective electronics: A team of designers was given the task of reducing the defect rate in the manufacture of a certain printed ole circuit board. The team decided to reconfigure the cooling system. A total of 985 boards were produced the week before the reconfiguration was implemented, and 260 of these were defective. A total of 842 boards were produced the week after reconfiguration, and 194 of these were defective. Part: 0/2 Part 1 of 2 (a) Construct a 99% confidence interval for the decrease in the defective rate after the reconfiguration. Use the TI-84 Plus calculator and round the answers to three decimal places. A 99% confidence interval for the decrease in the defective rate after the reconfiguration is <21-22<0.
The 99% confidence interval for the decrease in the defective rate after the reconfiguration is (-0.018, 0.086).
How to find Confidence Intervals?Let the random variable & parameters be;
x1 : Number of successes from group 1
x2 : Number of successes from group 2
p1: Proportion of successes in group 1
p2: Proportion of successes in group 2
n1 : number of trial in group 1
n2: number of trial in group 2
We are given;
x1 = 260
n1 =985
x2 = 194
n2 = 842
Thus;
p1 = 260/985
p1 =0.2640
p2 = 194/842
p2 = 0.2304
Constructing a (1 - α)100% confidence interval for proportion from the formula;
(p₁ - p₂) - z√[((p₁(1 - p₁)/n₁) + p₂(1 - p₂)/n₂)]
plugging in z = 2.576 and the values of p₁, p₂, n₁ and n₂, we have the confidence interval as;
(-0.0184631, 0.0855743)
Therefore the 99% confidence interval for the decrease in the defective rate after the reconfiguration is (-0.018, 0.086).
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URGENT!!! What happens to the graph of y=−x6−6x5+50x3+45x2−108x−108 as x heads toward ∞ and −∞?
A. as x→∞, y→−∞ as x→−∞, y→−∞
B. as x→∞, y→∞ as x→−∞, y→∞
C. as x→∞, y→∞ as x→−∞, y→−∞
D. as x→∞, y→−∞ as x→−∞, y→∞
Using limits, the correct option regarding the end behavior of the function is given by:
A. as x→∞, y→−∞ as x→−∞, y→−∞.
How to find the end behavior of a function f(x)?The end behavior is found calculating the limit of f(x) as x goes to infinity.
For this problem, the equation is given by:
[tex]f(x) = -x^6 - 6x^5 + 50x^3 + 45x^2 - 108x - 108[/tex]
Since x goes to infinity, we consider only the term with the highest exponent, hence the limits are given as follows:
[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} -x^6 - 6x^5 + 50x^3 + 45x^2 - 108x - 108 = \lim_{x \rightarrow -\infty} -x^6 = -(-\infty)^6 = -\infty[/tex]
[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} -x^6 - 6x^5 + 50x^3 + 45x^2 - 108x - 108 = \lim_{x \rightarrow \infty} -x^6 = -(\infty)^6 = -\infty[/tex]
Hence the correct option is:
A. as x→∞, y→−∞ as x→−∞, y→−∞.
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A variety of two types of snack packs are delivered to a store. The box plots compare the number of calories in each snack pack of crackers to the number of calories in each snack pack of trail mix.
A number line goes from 65 to 115. Crackers's whiskers range from 70 to 100, and the box ranges from 75 to 85. A line divides the box at 80. Cookies's whiskers range from 70 to 115, and the box ranges from 90 to 105. A line divides the box at 100.
Which statement is true about the box plots?
The interquartile range of the trail mix data is greater than the range of the cracker data.
The value 70 is an outlier in the trail mix data.
The upper quartile of the trail mix data is equal to the maximum value of the cracker data.
The number of calories in the packs of trail mix have a greater variation than the number of calories in the packs of crackers.
The statement that is true about the box plots is: D. The number of calories in the packs of trail mix have a greater variation than the number of calories in the packs of crackers.
What is a Measure of Variation?For a data distribution that is displayed by a box plot, the measure of variation that can be used to describe the data distribution is the interquartile range.
What is the Interquartile Range of a Data Distribution?Interquartile range, which is a measure of variation can be determined from a box plot by finding the value of the third quartile and first quartile, the finding their difference. The difference is the interquartile range.
Interquartile range = third quartile - first quartile.
Interquartile range for crackers = 85 - 75
Interquartile range for crackers = 10
Interquartile range for trail mix = 105 - 90
Interquartile range for trail mix = 15.
The bigger the value of the interquartile range, the more variation there is that exist in a data distribution.
Interquartile range for trial mix is the largest, therefore, the statement that is true about the box plots is: D. The number of calories in the packs of trail mix have a greater variation than the number of calories in the packs of crackers.
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In need of help for answers
The piecewise equation for the function shown in the diagram is [tex]f(x)=\left \{ {{{[\frac{9}{10}x+5.9\ \ \ -6 \leq x\leq -1 } \atop {[2\ \ \ \ \ \ \ \ \ \ \ -1 < x\leq 2}} \atop {[-\frac{5}{2}x+6\ \ \ 2 < x\leq 6 }} \right.[/tex]
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.
From the diagram using the point (-6, 0.5) and (-1, 5):
y - 0.5 = [(5 - 0.5)/(-1 - (-6))](x - (-6))
y = (9/10)x + 5.9
Also, using the point (2, 1) and (4, -4):
y - 1 = [(-4 - 1)/(4 - 2)](x - 2)
y = -(5/2)x + 6
The piecewise equation for the function shown in the diagram is [tex]f(x)=\left \{ {{{[\frac{9}{10}x+5.9\ \ \ -6 \leq x\leq -1 } \atop {[2\ \ \ \ \ \ \ \ \ \ \ -1 < x\leq 2}} \atop {[-\frac{5}{2}x+6\ \ \ 2 < x\leq 6 }} \right.[/tex]
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Use the wave equation to find the speed of a wave given by y(x,t) = (9. 13 mm) sin[(6. 65 m-1)x - (5. 52 s-1)t]
The speed of the wave is 0.83 m/s.
According to the statement
we have given that the equation and we have to find the speed of the wave.
So, For this purpose, we know that the
The given equation is y(x,t) = (9. 13 mm) sin [(6. 65 m^-1)x - (5. 52 s^-1)t]
Then we have to find the speed of the wave
So, Comparing y(x,t) = (9. 13 mm) sin[(6. 65 m-1)x - (5. 52 s-1)t]
to the general expression y(x,t)=y m sin(kx−ωt),
Because the general expression is y(x,t)=y m sin(kx−ωt)
we see that k= 6.65 m −1 and ω= 5.52 rad/s.
The speed of the wave is
v=ω/k=(5.52 rad/s)/(6.65 m )= 0.83 m/s
So, The speed of the wave is 0.83 m/s.
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Figure 222 is a scaled copy of Figure 111.
PLEASE HELP
Identify the side in Figure 222 that corresponds to side \overline{CD}
CD
start overline, C, D, end overline in Figure 111.
Choose 1 answer:
Choose 1 answer:
A contractor is excavating a ramp into a trench for a construction project. How much dirt will the crew have to remove? To answer, find the volume of the triangular prism in the figure shown. Opening 4 x 6, ramp 8'deep
‼️‼️‼️‼️HELP‼️‼️‼️‼️‼️‼️‼️
Michael took a drive down to the beach and drove at a pace of 45mph on the way there. The trip took him 3 hours. He drives the exact same route on the way back, but takes it slow so he can enjoy the sunset. If Henry's return trip took him 4 hours, how fast was he driving on his return?
Michael took the return trip at a velocity 33.75 miles per hour.
How fast did Michael drive in his return trip?
Let suppose that Michael drove in straight line road and at constant velocity. Therefore, the speed of the vehicle (v), in miles per hour, can be defined as distance traveled by the vehicle (d), in miles, divided by travel time (t), in hours.
First trip
45 = s / 3 (1)
Second trip
v = s / 4 (2)
By (1) and (2):
45 · 3 = 4 · v
v = 33.75 mi / h
Michael took the return trip at a velocity 33.75 miles per hour.
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I need help on how to solve for Z
Answer:
[tex]z=\frac{t^{2}(m-3) }{4}[/tex] or [tex]z=\frac{1}{4}t^{2} (m-3)[/tex]
Step-by-step explanation:
[tex]t=\sqrt{\frac{4z}{m-3} }[/tex]
[tex]t^{2} =\frac{4z}{m-3}[/tex]
[tex]4z=t^{2} (m-3)[/tex]
[tex]z=\frac{t^{2}(m-3) }{4}[/tex]
Hope this helps
There is 1 pint of liquid in this container. if another pint were added, how much liquid would there be? a) 2 cups b) 1 pint c) 1 quart d) 2 gallons
Answer:
C: 1 Quart
Step-by-step explanation:
2 pints are the equivalent of 1 quart
Answer:1 Quart
Step-by-step explanation: Because 2 pints equals=1 quart
Write an expression containing x2-terms, x-terms and constants. The
x2-terms should combine to −2x2 the x-terms should sum to 3x,
and the constants should sum to 3.
[tex]7x^{2} - 9x^{2} +8x-5x + 10-7[/tex] is the given expression
Like terms are terms whose variables (and their exponents such as the 2 in [tex]x^{2}[/tex]) are the same. Like terms can easily be added and substracted. Such questions just need like terms to be bought together and simplified
Infinite number of equations or expressions can be written for the given question. So writing one possibility for the given question,
= [tex]7x^{2} - 9x^{2} +8x-5x + 10-7[/tex]
which sums up to
= [tex]-2x^{2} +3x+3[/tex]
Thus [tex]7x^{2} - 9x^{2} +8x-5x + 10-7[/tex] is the given expression
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What is the slop of the line?
Solve x2 − 24x = −80 by completing the square. what is the solution set of the equation?
Answer:
Solve x2 − 24x = −80 by completing the square. what is the solution set of the equation?
The Answer Is X = 20 or x = 4
Find the quotient.
18.)97.2
Answer:
540
Step-by-step explanation:
540 =18% of 97.2
Done please
it's quotient it's a synthax error..
What is the independent variable in the following function?
The independent variable of f(c) = -3c + 9 is c
What are variables?Variables in an equation are the unknown parameters of the equation that change in values
There are two types of variables
Dependent variableIndependent variableHow to determine the independent variable?The equation of the function is given as
f(c) = -3c + 9
The dependent variable is the output of the function, while the independent variable is the input of the function
For the function, f(c) = -3c + 9
The input variable is c
Hence, the independent variable of f(c) = -3c + 9 is c
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number 7 please and don t care abt others lol
Answer:
The question does not make a lot of sense to me but I think this is how its supposed to be done
so there are 15 shirts
2 are sold at 3.90, 2 x 3.90 = 7.8
15-2= 13 t shirts
13 sold at 4.70, 13 x 4.70 = 61.1
amount of money made is = 7.8 + 61.1
= 68.9
Select the correct answer. which of these organizations provides help to the friends and families of an alcoholic? a. national clearing house for alcohol and drug information b. american council on alcoholism c. alateen
Answer: C
Step-by-step explanation:
Solve the equation in the image (yr 8 maths, 50pts)
Answer: x = 4
Step-by-step explanation:
Given equation
4x - 20 = -x
Add x on both sides
4x - 20 + x = -x + x
5x - 20 = 0
Add 20 on both sides
5x - 20 + 20 = 0 + 20
5x = 20
Divide 5 on both sides
5x / 5 = 20 / 5
[tex]\Large\boxed{x=4}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
In your own words, define the unit rate in an equation of proportional relationship y= kx.
Answer:
hdchyf
Step-by-step explanation:
fhyrb ufgfyg hchybgvtct ugh
PLEASE HELP ME QUICKLY!! IM BEING TIMED
The sum of 2 numbers is 36. The first number is twice the second number. Find the second number
Answer: 24+12=36
Step-by-step explanation:
36= _+_
2x(2 times)
x
X+2x=36
3x=36
12
12+2(12)=36
12+24=36
Answer:
The value of the second number is 24 and the first no 12.Step-by-step explanation:
Greetings !From, the given word explanation try to create your own equation like
x + y = 36... (1) let the two numbers be x and y respectively.2x = y ....(2) let x be the first no and it's twice that of the second number.From, equation (1) solve for x
x + y = 36x = 36-y... (3)Substitute, equation (3) to equation (2).
2(36-y) =y72 - 2y =y72 = y + 2y.... solve for y72 = 3y.... divide both sides by 372/3 = y..y=24 ...simplified
Which of the following linear equations corresponds to the table above?
O A. y = 4x - 3
O B. y=¹/4 x-3
OC. y=1/4x+3
OD. y = 4x + 3
The linear equations that corresponds to the table is y = 4x + 3
How to determine the linear equation?The missing table of values in the complete question is given as:
x y
0 3
3 15
7 31
10 43
Start by calculating the slope of the equation using
m = (y2 - y1)(x2 - x1)
Substitute the values on the table in the above equation
m = (15 - 3)/(3 - 0)
Evaluate the difference
m = 12/3
Evaluate the quotient
m = 4
The linear equation is then calculated as:
y = m(x - x1) + y1
This gives
y = 4(x - 0) + 3
Evaluate the expression
y = 4x + 3
Hence, the linear equations that corresponds to the table is y = 4x + 3
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! What are modern numbers? and how are they used?
Modern numbers are the ten numerical digits used in constructing other numbers.
What are modern numbers?Modern numbers are also called Arabic numerals. They are the ten numerical digits:
0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
Uses of modern numbers;
They are used as symbols to write decimal numbers.They are used in writing numbers in other systems like the octal, and for writing identifiers such as computer symbols, trademarks, or license plates.They are used in constructing other numbers.Hence, modern numbers are the ten numerical digits used in constructing other numbers.
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Morgan is designing a rectangular quilt. The quilt will be 1 3/5 meters wide and will have an area of 6m 2 (To the power). How long is the quilt?
Answer:3 3/4 meters
Step-by-step explanation:
6/(1 3/5)=3.75 meters or 3 3/4 meters
How many lattice points (points with integer coordinates) are on the line segment whose endpoints are $(3,17)$ and $(48,281)
Any line through the points [tex](a,b)[/tex] and [tex](c,d)[/tex] has
[tex]\gcd(c-a,d-b)+1[/tex]
lattice points. In this case, the count is GCD(45, 264) + 1.
Using Euclid's algorithm, we have
264 = 5•45 + 39
45 = 1•39 + 6
39 = 6•6 + 3
6 = 2•3 + 0
so that GCD(45, 264) = 3. Then there are 3 + 1 = 4 lattice points.
A friend of mine believes that the average GPA at KSU is equal to 3.0. In order to test whether he/she is right, I collect some information from the data. Specifically, I use 100 KSU students to form a sample and find that their sample average GPA is equal to 3.3. In addition, suppose that I also know the population standard deviation of GPA at KSU is 1.5. I decide to use 0.05 as the level of significance for my hypothesis testing. Could you help me with Q1-Q10 below? Q1: What should be my null hypothesis? What should be my alternative hypothesis? Q2: Is this a lower-tailed, upper-tailed or two-tailed case? Q3: Show me how to calculate my test statistic.
Q4: If I use the critical value approach, explain how to derive my critical value(s). Q5: If I use the p-value approach, explain how to derive my p-value. Q6: If I use the confidence interval approach, show me how to derive the confidence interval. Q7: How to make my decision, if I use the critical value approach? Q8: How to make my decision, if I use the p-value approach? Q9: How to make my decision, if I use the confidence interval approach? Q10: Are the decisions in Q7, Q8, and Q9 the same?
The solution of the questions is given as
a)
The alternative hypothesis is that mu is equal to 3.0. ( the average GPA at KSU is not equal to 3.0)
b)
This is a case with two separate arguments. (This is a two-tailed case)
c)
Test Statistic is given by:
z= 2.00
d)
Critical values of Z come from the table and equal [tex]\pm[/tex]1.96.
e)
, p-value = 0.0455
f)
CI= (3.006, 3.594)
g)
Conclusion: The evidence does not back up the assertion that KSU students have a cumulative grade point average of 3.0.
h)
Conclusion: The evidence does not back up the assertion that KSU students have a cumulative grade point average of 3.0.
i) Conclusion: The evidence does not lend credence to the assertion that KSU's typical grade point average is equivalent to 3.0.
j)
The choices you choose in Questions 7, 8, and 9 are identical.
What is the null hypothesis?a)
The null hypothesis states that mu equals 3.0. ( the average GPA at KSU is equal to 3.0) (Claim)
The alternative hypothesis is that mu is equal to 3.0. ( the average GPA at KSU is not equal to 3.0)
b)
This is a case with two separate arguments.
c)
Test Statistic is given by:
[tex]z=\frac{\barx-u^0}{σ/Vn}\\\\z=33 - 3.0/1.5/V100[/tex]
z= 2.00
d)
[tex]\alpha = 0.05[/tex]
Critical values of Z come from the table and equal [tex]\pm[/tex]1.96.
e)
Z Score = 2.00
reading from table, p-value = 0.0455
f)
Confidence Interval:
[tex]CI= \barx \pm \frac{ZX\sigma }{\sqrt((n)}[/tex]
[tex]CI =3.3 \pm 1.96 x 1.5 / \sqrt{100}[/tex]
CI= (3.006, 3.594)
g)
The disparity is noteworthy given that the computed value of Z = 2.00 is higher than the crucial value of z = 1.96. Cast doubt on the null hypothesis.
Conclusion: The evidence does not back up the assertion that KSU students have a cumulative grade point average of 3.0.
h)
The difference may be considered statistically significant since the p-value of 0.0455 is lower than the alpha threshold of 0.05. Cast doubt on the null hypothesis.
Conclusion: The evidence does not back up the assertion that KSU students have a cumulative grade point average of 3.0.
i)
The difference is statistically significant since the value of 3.0 is not included in the confidence range (3.006 - 3.594). Cast doubt on the null hypothesis.
Conclusion: The evidence does not lend credence to the assertion that KSU's typical grade point average is equivalent to 3.0.
j)
The choices you choose in Questions 7, 8, and 9 are identical.
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the selling price of a mobile after discount is 10000.if the discount is 10% find the mp
Answer:
Rs.11,111.11 (2 d.p.)
Step-by-step explanation:
The original price of the mobile is 100% of the price.
Therefore, the price of the mobile after a discount of 10% is 90% of the original price.
Let x be the original price.
If the price of the mobile after the discount is Rs.10000 then:
⇒ 90% of x = Rs.10000
⇒ 0.9x = 10000
⇒ x = 10000 ÷ 0.9
⇒ x = 11111.11 (2 d.p.)
M.P. =Rs 11111.1111
Answer:
Solution Given:
Selling price (S.P.) = Rs 10,000.
Discount =10%
Marked Price (M.P.)=?
we have
M.P. = S.P. + discount% of M.P.
keeping M.P. on same side
M.P. - discount% of M.P=S.P.
substituting value
M.P. - 10% of M.P.= Rs 10,000
taking common M.P.
M.P.(1-10%)=Rs. 10,000
we know that %=1/100
M.P.(1-10/100)=Rs 10,000
(9/10)M.P.= Rs 10,000
M.P.= Rs 10,000*10/9
M.P.=Rs11111.1111
Please answer quickly!
19) The sum of the arithmetic series is - 397. (Correct choice: E)
33) The sum of the geometric series is 1700. (Correct choice: E)
How to determine the sum of a given series
19) Arithmetic series are sets of elements generated by a linear expression of the form:
aₙ = a₁ + (n - 1) · d (1)
Where:
aₙ - n-th term of the seriesa₁ - First term of the series n - Index of the n-th term of the series.d - Change between two consecutive elements of the series.If we know that a₁ = 27, n = 20 and d = - 5, then sum of the first 20 terms of the series is:
x = 27 + 22 + 17 + 12 + 7 + 2 + (- 3) + (- 8) + (- 13) + (- 18) + (- 23) + (- 28) + (- 33) + (- 38) + (- 43) + (- 48) + (- 53) + (- 58) + (- 63) + (- 68)
x = - 397
The sum of the arithmetic series is - 397. (Correct choice: E)
33) Geometric series are sets of elements generated by a exponential expression of the form:
aₙ = a₁ · rⁿ (2)
Where:
aₙ - n-th term of the seriesa₁ - First term of the seriesr - Ratio between two consecutive elements of the series.If we know that a₁ = 1458 and r = 1 / 3, then the sum of the first 6 terms of the geometric series is:
x = 1458 + 162 + 54 + 18 + 6 + 2
x = 1700
The sum of the geometric series is 1700. (Correct choice: E)
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