Looks like the equation is
[tex]x^7y+y^7x=7[/tex]
Differentiate both sides with respect to [tex]x[/tex], taking [tex]y[/tex] to be a function of [tex]x[/tex].
[tex]\dfrac{\mathrm d[x^7y+y^7x]}{\mathrm dx}=\dfrac{\mathrm d[7]}{\mathrm dx}[/tex]
[tex]\dfrac{\mathrm d[x^7]}{\mathrm dx}y+x^7\dfrac{\mathrm dy}{\mathrm dx}+\dfrac{\mathrm d[y^7]}{\mathrm dx}x+y^7\dfrac{\mathrm dx}{\mathrm dx}=0[/tex]
[tex]7x^6y+x^7\dfrac{\mathrm dy}{\mathrm dx}+7y^6x\dfrac{\mathrm dy}{\mathrm dx}+y^7=0[/tex]
Solve for [tex]\frac{\mathrm dy}{\mathrm dx}[/tex]:
[tex](x^7+7y^6)\dfrac{\mathrm dy}{\mathrm dx}=-(7x^6y+y^7)[/tex]
[tex]\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac{7x^6y+y^7}{x^7+7y^6}[/tex]
You are at your work study job in the Department of Mathematics and Statistics. You've been asked to
make copies at the copy center. It will 4 minutes to walk there, and 1 minute to get the copier set up
and running. Then you need to make 836 copies. The copier can print 38 pages per minute. It will then
take 5 minutes to walk back to the department. What time will you get back? Will you have time to get
to your 2 PM dass that is a five-minute walk from the math building?
4 minutes to walk there, 5 minutes to walk back, 4+5 = 9 minutes total walking time. Add this onto the 1 minute to get the copier set up and we have 9+1 = 10 minutes so far.
The copier can print 38 pages per minute. There are 836 copies, so 836/38 = 22 minutes is needed to print out all the pages.
So we have 22+10 = 32 minutes in total so far. Add on the last 5 minute stretch (going from the math department to your 2PM class) to get to 37 minutes. You'll need 37 minutes total.
You didn't provide a starting time, but we can subtract 37 minutes from 2PM to get
02:00 - 00:37 = 01:23
Meaning that if you left the math department at 1:37 PM, then you'd do all those tasks to get to your next class at 2 PM exactly, assuming no other things happen. So it's best to leave before 1:37 PM
A food safety guideline is that the mercury in fish should be below 1 part per million. Listed below are the amounts of mercury (ppm) found in tuna sushi sampled at different stores in a major city. Construct a 98% confidence interval estimate of the mean amount of mercury in the population. Does it appear that there is too much mercury in tuna sushi?
0.59 0.68 0.10 0.98 1.37 0.55 0.97
Required:
What is the confidence interval estimate of the population mean μ ?
Answer:
the confidence interval is 1.2282 and 0.269
Step-by-step explanation:
n = 7
the mean of the sample =
0.59+0.68+0.10+0.98+1.37+0.55+0.97/7
= 5.25/7
= 0.74857= 0.7486
the standard dev!aton of the sample
= √(0.59-0.7486)²+(0.68-0.7486)²+(0.1-0.7486)²+(0.98-0.7486)²+(1.37-0.7486)²+(0.55-0.7486)²+(0.97-0.7486)²/n-1
= √0.02515+0.0047+0.4206+0.0535+0.3861+0.03944+0.0490/6
= √0.9786/6
= √0.163083
= 0.4038
degree of freedom = 7-1= 6
crtcal value at 2% significance and df of 6 = 3.143
confidence interval =
0.7486±3.143(0.4038/√7)
= 0.7486±3.143(0.1526)
0.7486+0.4796 = 1.2282
0.7486-0.4795 = 0.269
=
Match the correct rational number to its equivalent repeating decimal: 27.33333
A. 82/3
B. 100/3
C. 42/4
D. 22/7
Answer:
A. [tex]\frac{82}{3}[/tex]
Step-by-step explanation:
Step 1: We know .3333... is [tex]\frac{1}{3}[/tex], we rewrite the equation as [tex]\frac{1}{3}[/tex]
[tex]27\frac{1}{3}\\ \frac{1+(27)(3)}{3}\\\frac{1+81}{3}\\\frac{82}{3}\\[/tex]
Therefore the answer would be A. [tex]\frac{82}{3}[/tex]
Answer:
A. 82/3
Step-by-step explanation:
[tex]3\overline{|\smallspace82}\space\space\space\space\\\mathrm{Divide}\:8\:\mathrm{by}\:3\:\mathrm{to\:get}\:2\\\begin{matrix}\space\space\space\space\emptyspace2\space\space\space\space\space\space\space\space\space\space\space\space\space\space\\ 3\overline{|\smallspace82}\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}\\[/tex]
[tex]\begin{matrix}\space\space\space\space\emptyspace2\space\space\space\space\space\space\space\space\space\space\space\space\space\space\\ 3\overline{|\smallspace82}\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\underline{\emptyspace6}\space\space\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}\\\mathrm{Multiply\:the\:quotient\:digit}\:\left(2\right)\:\mathrm{by\:the\:divisor}\:3\\[/tex]
[tex]\begin{matrix}\space\space\space\space\emptyspace2\space\space\space\space\space\space\space\space\space\space\space\space\space\space\\ 3\overline{|\smallspace82}\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\underline{\emptyspace6}\space\space\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}\\\mathrm{Subtract}\:6\:\mathrm{from}\:8\\[/tex]
[tex]\begin{matrix}\space\space\space\space\emptyspace2\space\space\space\space\space\space\space\space\space\space\space\space\space\space\\ 3\overline{|\smallspace82}\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\underline{\emptyspace6}\space\space\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\emptyspace2\space\space\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}\\[/tex]
[tex]\mathrm{Bring\:down\:the\:next\:number\:of\:the\:dividend}\\[/tex]
[tex]\begin{matrix}\space\space\space\space\emptyspace2\space\space\space\space\space\space\space\space\space\space\space\space\space\space\\ 3\overline{|\smallspace82}\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\underline{\emptyspace6}\space\space\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\emptyspace2\emptyspace2\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}[/tex]
Divide 22 by 3 to get 7
[tex]\begin{matrix}\space\space\space\space\emptyspace2\emptyspace7\space\space\space\space\space\space\space\space\space\space\space\space\\ 3\overline{|\smallspace82}\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\underline{\emptyspace6}\space\space\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\emptyspace2\emptyspace2\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}[/tex]
Multiply the quotient digit 7 by the divisor
and sbtract 21 from 22=1
= 27 remainder 1
Seven baseballs are randomly selected from the production line to see if their stitching is straight. Over time, the company has found that 89.4% of all their baseballs have straight stitching. If exactly five of the seven have straight stitching, should the company stop the production line
Answer and Step-by-step explanation:
p= probability of straight stitching = 89.4% = 89.4/100= 0.894
n = the total sample of randomly selected baseballs
x = quantity of baseballs that have straight stitching = 5
x follows a binomial distribution
p(X=x) = nCx * p^x(1-p)^n-x
= 7C5 * 0.894⁵ * (1-0.894)⁷⁻⁵
= 21 * 0.571 * 0.011236
= 0.1347
= 13.47%
the probability is only 13.47% therefore the company has to stop the production line
If a cube has a volume of 4913 feet, then what is the length.
Answer:
length = 17 feetStep-by-step explanation:
Since it's a cube all it's sides are equal
Volume of a cube = l³
where
l is the length of one side
From the question
Volume = 4913 ft³
Substitute the value into the above formula and solve for the length
That's
[tex] {l}^{3} = 4913[/tex]
Find the cube root of both sides
We have
[tex] \sqrt[3]{ {l}^{3} } = \sqrt[3]{4913} [/tex]
We have the final answer as
length = 17 feetHope this helps you
Answer:
17 because 17 x 17 x 17 =4913
Step-by-step explanation:
Choose the number that belongs to the set described. i don’t understand this, someone please help me!
Answer:
1). Option (H)
2). Option (C)
3). Option (C)
4). Option (G)
5). Option (E)
Step-by-step explanation:
(1). Integers are the ''whole numbers''.
Therefore, negative integer will be a whole number with negative notation =(-8).
Option (H) will be the answer.
(2). "Numbers that can not be written as a fraction are irrational numbers"
Option (C). √7
(3). "Whole numbers are the basic counting numbers starting from 0"
Option (C). 0
(4). A rational number is a number that can be written as a fraction(in the form of [tex]\frac{p}{q}[/tex].
Option (G). [tex]\frac{3}{4}[/tex]
(5). "All positive integers are the natural numbers."
Option (E). 12
The Futurists, a rock group, are planning a concert tour with performances to be
given in five cities: San Francisco, Los Angeles, San Diego, Denver, and Las Vegas.
how many ways can they arrange their itinerary if
a.There are no restrictions?
b.The tree performances in California must be given consecutively?
Answer:
a. 24
b. 12
Step-by-step explanation:
a. You can choose from 4 cities for the first performance, then from 3 cities, then from 2 cities, then the last city.
4 * 3 * 2 * 1 = 24
b. Think of the three performances in California as a unit. Within this unit, you can choose from 3 cities for the first one, then 2 cities for the second one, and finally 1 city for the last one.
3 * 2 * 1 = 6
Now you can have the 3 California performances first, followed by Denver, or Denver first followed by California.
6 * 2 = 12
"Henri has calculated a z-test statistic of -2.73. What is the p-value of the test statistic? Answer choices are rounded to the thousandths place."
Answer:
0.003
Step-by-step explanation:
P-value = The value of probability.
P value can be defined are the probability of a given test statistic ( which could be z score, t score, f score) that is can be less than, equal to or greater than a given null hypothesis.
In the above question, the test statistic we are given = z score.
z score = -2.73
To find the P- value, we can make use of a z table for normal distribution.
Hence, P(z = -2.73) = 0.0031667
Approximately to the nearest thousandth = 0.003
Find the volume of the cube 8cm
Answer:
512 cm^3
Step-by-step explanation:
The side length is 8 cm
V = s^3 where s is the side length
V = 8^3
=512 cm^3
Answer: 512 cm³
Explanation: Since the length, width, and height of a cube are all equal,
we can find the volume of a cube by multiplying side × side × side.
So we can find the volume of a cube using the formula v = s³.
In the cube in this problem, we have a side length of 8 cm.
So plugging into the formula, we have (8 cm)³
or (8 cm)(8 cm)(8 cm), which is 512 cm³.
So the volume of the cube is 512 cm³.
What happens when the two addends have opposite signs and the number with the larger magnitude (size) is positive?
Answer:
The smaller addend is subtracted from the bigger addend
Step-by-step explanation:
Represent the two numbers with a and b such that a > b
So, the mathematical representation will be
[tex]+a + (-b)[/tex]
Open the bracket
[tex]+a -b[/tex]
This implies that the smaller addend (b) is subtracted from the bigger addend (b)
Take for instance; a = 6 and b = 4
This gives
[tex]+6 + (-4)[/tex]
Open the bracket
[tex]= +6 - 4[/tex]
[tex]= 2[/tex]
p(a) = 0.60, p(b) = 0.20, and p(a and b) = 0.15 what is p(a or b) choices: A. 0.12, B. 0.65, C. 0.40, or D. 0.80 (Note- This is on AP3X)
Answer:
[tex]P(a\ or\ b) = 0.65[/tex]
Step-by-step explanation:
Given
P(a) = 0.60
P(b) = 0.20
P(a and b) = 0.15
Required
Determine P(a or b)
In probability;
[tex]P(a\ and\ b) = P(a) + P(b) - P(a\ or\ b)[/tex]
Substitute values for P(a and b), P(a) and P(b)
[tex]0.15 = 0.60 + 0.20 - P(a\ or\ b)[/tex]
Collect Like Terms
[tex]P(a\ or\ b) = 0.60 + 0.20 - 0.15[/tex]
[tex]P(a\ or\ b) = 0.65[/tex]
Hence, option B answers the question
Answer
0.65
Step-by-step explanation:
apeeex
Look at this shape:
Which image shows a rotation?
A
B
с
A
B
с
X 2
Practice with our app
Answer:
A
Step-by-step explanation:
Image A shows a rotation. B is a translation. C is a reflection.
An algebraic relationship of that quantity is greater than or less then another quantity ?
Answer:
Inequality
Step-by-step explanation:
13. – 5x – 10 = 2-2(x – 4)
Answer:
[tex] \boxed{ \boxed{ \bold{ \purple{ - 6.67}}}}[/tex]Step-by-step explanation:
[tex] \sf{ - 5x - 10 = 2 - 2(x - 4)}[/tex]
Distribute 2 through the parentheses
⇒[tex] \sf{ - 5x - 10 = 2 - 2x + 8}[/tex]
Move constant to right hand side and change it's sign
Similarly , Move variable to left hand side and change it's sign
⇒[tex] \sf{ - 5x + 2x = 2 + 8 + 10}[/tex]
Collect like terms
⇒[tex] \sf{ - 3x = 2 + 8 + 10}[/tex]
Add the numbers
⇒[tex] \sf{ - 3x = 20}[/tex]
Divide both sides of the equation by -3
⇒[tex] \sf{ \frac{ - 3x}{ - 3} = \frac{20}{ - 3} }[/tex]
Calculate
⇒[tex] \sf{x = - 6.67}[/tex]
Hope I helped !
best regards!!
Brenda bought a coat for $20. She also paid $1.50 in tax. What kind of tax did Brenda pay on the coat?
Answer:
Sales Tax
Step-by-step explanation:
there are 8 girls and 5. boys on the math team which ratio correctly describes the relationship between boys and girls on the math team
Answer:
8:5
Step-by-step explanation:
I'm honestly not sure how to explain this because it's just a ratio, but good luck!
SOMEONE HELP ME!! THIS IS DUE IN 11:45 TODAY‼️ 33 POINTS‼️
Answer:
1: 1/2
2: 1
3: Assuming 2 medium triangles = 1 large triangle, then 2
Step-by-step explanation:
1: 2 small triangle makes 1 square. So, if we divide the area of the square (1 square unit) by 2 because 2 small triangles make 1 square, we get 1/2.
2: 2 small triangles makes 1 medium triangle, so using the above logic, 1/2 X 2 = 1.
3: Assuming 2 medium triangles = 1 large triangle, then the same thing applies. medium * 2 = 2
Jan is constructing an inscribed regular hexagon for the circle shown. Point A will be one vertex of the hexagon. What step should be completed next?
Answer:
D) set the width of the compass to equal AP
Step-by-step explanation:
Regular hexagon has a property that its side is equal to radius. The step which should be taken is to set the length of compass equal to radius which is the distance AP.Correct answer option is D)
Answer options:
A) draw a ray from point P through A B) construct a diameter of the circle C) place a second point on the circle D) set the width of the compass to equal APSuppose coffee is initially brewed at 205 F and the room temperature is 70 F. Determine the value of kk if the temperature of the coffee drops from 205 F to 200 F in the first two minutes after brewing. Round answer to 4 decimal places.
Answer:
0.0189
Step-by-step explanation:
We solve for this using Newton's Law of cooling.
The formula for Newton's Law of cooling =
T −Ts = (To−Ts)e^-kt
T = Temperature after cooling
To = Initial temperature
Ts = Room temperature
k = constant
t = time = 2 mins
(200 - 70) = (205 - 70)e^-2k
130 = 135e^-2t
e^-2k= 130/135
k = In(130/135)/-2
k = 0.018870164
Approximately to 4 decimal places = 0.0189
Therefore, the value of k = 0.0189
The Polleys want to put in a swimming pool next summer. They need to save $7,000 over 12 months in order to achieve this goal. They set aside the same amount each month and after 6 months discovered they have saved $3,200. The Polleys know that they must adjust their plan in order to meet their goal, so they come up with the following options Option A: Save the original amount each month but put the pool in one month later than originally planned. Option B: Increase savings each month by $125 from their original plan. Which plan, if any, will work for the Polleys?
Answer:
a.) because one month isn't very long
Step-by-step explanation:
In a state's Pick 3 lottery game, you pay $1.15 to select a sequence of three digits (from 0 to 9), such as 966. If you select the same sequence of three digits that are drawn, you win and collect $258.35. Complete parts (a) through (e).
a. How many different selections are possible?
b. What is the probability of winning? (Type an integer or adecimal.)
c. If you win, what is your net profit? (Type an integer or a decimal.)
d. Find the expected value. $ (Round to the nearest hundredth as needed.)
e. If you bet $ 1.15 in a certain state's Pick 4 game, the expected value is negative −$0.89. Which bet is better, a $1.15 bet in the Pick 3 game or a $ 1.15$ bet in the Pick 4 game?
Explain.
A. Neither bet is better because both games have the same expected value.
B. The Pick 4 game is a better bet because it has a larger expected value.
C. The Pick 3 game is a better bet because it has a larger expected value.
Answer:
A) 1000 different selections
B) probability of winning = 0.001
C) Net profit on winning = $257.20
D) E(y) = -0. 89165
E) Option B - The Pick 4 game is a better bet because it has a larger expected value.
Step-by-step explanation:
A) For the different selections possible, since each of the digits from 0 - 9 can take a total of 10 digits, then the different selections possible will be = 10³ = 1000 different selections
B) To find the probability of winning, since only one pick can be a winning one. Thus probability of winning = 1/1000 = 0.001
C) Net profit on winning = Amount won - Amount staked
Amount won = $258.35
Amount staked = $1.15
Thus;
Net profit on winning = $258.35 - $1.15
Net profit on winning = $257.20
D) If we call the net profit "y", then Expected value is:
E(y) = 257.2(0.001) - 1.15(1 - 0.001)
E(y) = 0.2572 - 1.14885
E(y) = -0. 89165
E) We are told that:If you bet $ 1.15 in a certain state's Pick 4 game, the expected value is negative −$0.89
The expected value of -0.89 in pick 4 is better than that in pick 3 because it's larger.
Does the table describe x as a function of y?
х
у
-3
-2
Does the table describe x as a function of y?
O A. Yes, each output y is assigned to exactly one input x.
O B. No, more than one output value y is assigned to the input x-value
OC. No, more than one output value x is assigned to the input y-value
OD. Yes, exactly one output x is assigned to each input y.
-
3
6
0
7
1
7
2
4
3
- 1
Click to select and enter your answer(s) and then click Check Answer.
Answer:
C. No, more than one output value x is assigned to the input y-value
Step-by-step explanation:
Given
х у
-3 -2
3 6
0 7
1 7
2 4
3 - 1
Required
State if the table shows x as a function of y
x being a function of y means
[tex]x = f(y)[/tex]
i.e. x represents the output while y represents the input of the function
Note that each value of y (input) must be assigned to separate values of x (output) for a function to be established
Having said;
Next step: We have to examine the x and y column
In the y column, the value 7 occurred twice (as shown below)
х у
0 7
1 7
This implies that;
Input 7 gives output of 0 and 1.
Hence, this is not a function.
Option C answers the question.
7^1 in expanded form
Step-by-step explanation:
[tex] {7}^{1} = 7 \times 1 \\ = 7[/tex]
multiply and simplify (3-5i)(-2+4i)
Answer:
14+22i
Step-by-step explanation:
We multiply and simplify (3-5i)(-2+4i) to get:
14 + 22i
How to multiply and simplify (3-5i)(-2+4i)?A complex number is a number of the form a + bi, where a and b are real numbers, and i is an imaginary unit satisfying i² = -1. For example, 2 + 3i is a complex number.
Complex numbers can be multiplied using the following rules:
(a + bi)(c + di) = (ac - bd) + (ad + bc)i
Thus, the two complex numbers can be multiplied and simplified as follow:
(3-5i)(-2+4i) = 3(-2+4i) -5i(-2+4i)
= 3(-2) + 3(4i) -5i(-2) -5i(4i)
= -6 + 12i + 10i -20i²
= -6 + 22i + 20 (Note: i² = -1)
= -6 + 20 + 22i
= 14 + 22i
Learn more about complex numbers on:
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can anyone help me on this??
Answer: about 78 mL
Step-by-step explanation:
When you see the liquid in a curved shape, you want to look at the very bottom of the curve. The bottom shows that our answer will be in the 70 mL, but close to 80. If you look at the lines in between, we can see that there are 5 lines, meaning each line represents 2 mL. Now, we count up and reach 78 mL.
Find the equation of the line that contains the points (2,1) and (6,3). Write the equation in the form y=mx+b and identify m and b
Answer:
y=1/2x+0 m=1/2 b=0
Step-by-step explanation:
You first need to find the slope of this line, the equation for this is.
(y2-y1)/(x2-x1)
In this case it is (3-1)/6-2)
This simplifies to 1/2.
This graph also does not have a +b as when you graph y=1/2x, it already passes through the 2 points shown.
2(3 - x) = 16(x + 1)*
Answer:
x = -5/9
Step-by-step explanation:
Order of Operations: BPEMDAS
Step 1: Write out equation
2(3 - x) = 16(x + 1)
Step 2: Distribute
6 - 2x = 16x + 16
Step 3: Add 2x on both sides
6 = 18x + 16
Step 4: Subtract 16 on both sides
-10 = 18x
Step 5: Divide both sides by 18
-10/18 = x
Step 6: Simplify
-5/9 = x
Step 7: Rewrite
x = -5/9
which of the following represents the factorization of the trinomial below x^2-17x+30
Hello, if [tex]x_1[/tex] and [tex]x_2[/tex] are two zeroes, we can write
[tex]x^2-17x+30=(x-x_1)(x-x_2)=x^2-(x_1+x_2)x+x_1\cdot x_2[/tex]
It means that the coefficients in x must be equal, meaning
[tex]x_1+x_2=17=2+15[/tex]
and the constant terms must be equal, meaning
[tex]x_1\cdot x_2=30 = 2 * 15[/tex]
So the zeroes are 2 and 15.
[tex]x^2-17x+30=x^2-15x-2x+30\\\\=x(x-15)-2(x-15)\\\\\boxed{=(x-2)(x-15)}[/tex]
Thank you
Point T is on line segment SU. Given SU = 5x, TU = 2x, and ST = 4x – 3,
determine the numerical length of TU.
Answer:
the length of TU is 6......
The numeric length of TU for the given line segment will be 3 units.
What is a line segment?A line section that can connect two places is referred to as a segment.
In other words, a line segment is just part of a big line that is straight and going unlimited in both directions.
The line is here! It extends endlessly in both directions and has no beginning or conclusion.
Given a line segment SU in between a point T
Now,
SU = ST + TU
5x = 4x - 3 + 2x
5x = 6x - 3
6x - 5x = 3
x = 3
Now,
TU = 2x = 2(3) = 6 units.
Hence "The numeric length of TU for the given line segment will be 3 units".
For more about line segment,
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CORRECT ANSWER GETS BRAINLIEST!!
Answer:
Step-by-step explanation:
To have Distance proportional to time, the person or object must keep a steady or constant rate like speed.
Let's first look at A runner sprinting in the 100 meter dash, since it tells you nothing about time it goes to not enough information.
Now look at An airplane starting at the end of the runway and taking off, it tells you nothing about time so, not enough information.
Now on to A marathon runner jogging at a constant speed for 45 minutes, this is distance proportional to time, because the runner has a constant rate.
The graph is distance proportional to time because, a straight slanted line indicates a constant speed. If it were curved it would not be constant.
The table with the number is distance not proportional to time because if you find the slopes of (25-5)/(10-5) and (50-25)/(15-10), they are 4 and 5 respectively which means there will not be a straight line on the graph.
Lastly, an airplane traveling at a constant speed across the country is distance directly proportional to time because it has a constant rate which is speed.