Answer:
[tex]3 + \frac{1}{2\sqrt{3} } + \frac{1}{5\sqrt[5]{81} }[/tex]
Step-by-step explanation:
Just to make it easier to see, [tex]\sqrt{x} = x^{\frac{1}{2} }[/tex] and [tex]\sqrt[5]{x} = x^{\frac{1}{5} }[/tex] This way we could more easily use the power rule of derivatives.
So if f(x) = [tex]x^{2} +x^{\frac{1}{2} } +x^{\frac{1}{5} }[/tex] then f'(x) will be as follows.
f'(x) = [tex]x^{1} +\frac{1}{2} x^{-\frac{1}{2} } +\frac{1}{5} x^{-\frac{4}{5} } = x +\frac{1}{2x^{\frac{1}{2} }} +\frac{1}{ 5x^{\frac{4}{5} }} = x +\frac{1}{2\sqrt{x}} +\frac{1}{ 5\sqrt[5]{x^4} }[/tex]
to find f'(3) just plug 3 into f'(x) so [tex]3 + \frac{1}{2\sqrt{3} } + \frac{1}{5\sqrt[5]{81} }[/tex]
In the year 2000, the average car had a fuel economy of 22.6 MPG. You are curious as to whether the average in the present day is less than the historical value. What are the appropriate hypotheses for this test
Answer:
The appropriate null hypothesis is [tex]H_0: \mu = 22.6[/tex]
The appropriate alternative hypothesis is [tex]H_1: \mu < 22.6[/tex]
Step-by-step explanation:
The average car had a fuel economy of 22.6 MPG. Test if the current average is less than this.
At the null hypothesis, we test if the current average is still of 22.6 MPG, that is:
[tex]H_0: \mu = 22.6[/tex]
At the alternative hypothesis, we test if the current mean has decreased, that is, if it is less than 22.6 MPG. So
[tex]H_1: \mu < 22.6[/tex]
What is the area??!??
Answer:
142.7 m²
Step-by-step explanation:
but sure, what you know about triangles and trigonometry (simplified, the relationship of angles and sides of shapes based on circles enclosing them)
so, here a quick summary of important facts and angle/side relationships in triangles :
the sum of all angles in a triangle is always and for every triangle 180 degrees.
sin(angle) is vertically up or down from the horizontal diameter of the encircling circle to the point on the circle hit by a line from the center of the circle with the described angle from the horizontal diameter.
cos(angle) is horizontally left or right from the center of the encircling circle to the point, where the sine-line hits the horizontal diameter.
the sides are named in relation to their opposing corners and their angles. so, for example, side a is opposing the corner point A and the angle at this point (also called A).
here it is also important to know :
a/sin(A) = b/sin(B) = c/sin(C)
and the area of a general triangle is
area = 1/2 × b × c × sin(A) or
1/2 × a × c × sin(B) or
1/2 × a × b × sin(C)
so, if we want to use the first option, we need to calculate b first. for this we use
b/sin(B) = c/sin(C)
b = (c × sin(B)) / sin(C)
for this we need to calculate C first. and we use
A + B + C = 180
C = 180 - A - B = 180 - 54.3 - 30.4 = 95.3 degrees
=>
b = (26.3 × sin(30.4)) / sin(95.3) = 13.36583...
=> area = 1/2 × 13.36583... × 26.3 × sin(54.3) = 142.7324...
= 142.7 (rounded)
Create a table to represent the function y=1/3x+4
Answer:
this is a linear equation. whatever value you set for x, you substitute and make a table that would probably look like this.
x | y
-------------|-----------
5 | 17/3 <------- what would y be if x is 5?
3 | 5 lets substitute x with 5
| y=1/3*5+4
| y=5/3+4
| y=17/3
wHAT IS THE REFERENCE ANGLE -935°
The sum of 10x + 6 and -x + 8
9x +14
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Some help figuring out the answer?? Also explain a little how you got there
9514 1404 393
Answer:
x = 10·cos(θ) -4·cot(θ)
Step-by-step explanation:
Apparently, we are to assume that the horizontal lines are parallel to each other.
The relevant trig relations are ...
Sin = Opposite/Hypotenuse
Cos = Adjacent/Hypotenuse
If the junction point in the middle of AB is labeled X, then we have ...
sin(θ) = 4/BX ⇒ BX = 4/sin(θ)
cos(θ) = x/XA ⇒ XA = x/cos(θ)
Then ...
BX +XA = AB = 10
Substituting for BX and XA using the above relations, we get
4/sin(θ) +x/cos(θ) = 10
Solving for x gives ...
x = (10 -4/sin(θ))·cos(θ)
x = 10·cos(θ) -4·cot(θ) . . . . . simplify
_____
We used the identity ...
cot(θ) = cos(θ)/sin(θ)
You damage your car and it will cost $7,200 to repair. You have a $1,000 deductible. How much will the insurance company pay?
Answer:
Amount paid by insurance company = $6,200
Step-by-step explanation:
Given:
Total cost of car damage = $7,200
Amount deductible = $1,000
Find:
Amount paid by insurance company for total damage
Computation:
Amount paid by insurance company = Total cost of car damage - Amount deductible
Amount paid by insurance company = $7,200 - $1,000
Amount paid by insurance company for total damage = $6,200
Please help me with this question
Answer:
B
Step-by-step explanation:
In a boxplot, when the median is in the middle of the box, or when there are equal proportions around the median, the distribution is symmetric. As is shown here, the median is closer to the left side of the box, making it positively skewed (the mean is greater than the median) and not symmetric.
The manager of The Cheesecake Factory in Boston reports that on six randomly selected weekdays, the number of customers served was 175, 125, 180, 220, 240, and 245. She believes that the number of customers served on weekdays follows a normal distribution. Construct the 99% confidence interval for the average number of customers served on weekdays.
Answer:
(121.576 ; 273.424)
Step-by-step explanation:
Given the data:
175, 125, 180, 220, 240, 245
We can calculate the mean and standard deviation
Mean = Σx/ n = 1185 / 6 = 197.5
Standard deviation = 46.125 (calculator)
The confidence interval :
Mean ± margin of error
Margin of Error = Tcritical * s/sqrt(n)
Tcritical at 99%, df = n - 1 ; 6 - 1 = 5
Tcritical = 4.032
Margin of Error = 4.032 * 46.125/√6
Margin of error = 75.924
Confidence interval :
197.5 ± 75.924
Lower boundary = 197.5 - 75.924 = 121.576
Upper boundary = 197.5 + 75.924 = 273.424
(121.576 ; 273.424)
If 80 persons can perform a piece of work in 16 days of 10 hours each, how
many men will perform a piece of work twice as great in tenth part of the time
working 8 hours a day supposing that three of the second set can do as much
work as four of the first set?
Answer:
The number of men needed to perform a piece of work twice as great in tenth part of the time working 8 hours a day supposing that three of the second set can do as much work as four of the first set is:
1200 men.Step-by-step explanation:
To find the answer, first, we're gonna find how many hours take to make the piece of work in 16 days, taking into account each day just has 10 hours:
Number of hours to make a piece of work = 16 * 10 hoursNumber of hours to make a piece of work = 160 hours.Now, we divide the total hours among the number of persons:
Equivalence of hours per person = 160 hours / 80 persons.Equivalence of hours per person = 2 hours /personThis equivalence isn't the real work of each person, we only need this value to make the next calculations. Now, we have a piece of work twice as great as the first, then, we can calculate the hours the piece of work needs to perform it (twice!):
Number of hours to make the second piece of work = 160 hours * 2Number of hours to make the second piece of work = 320 hoursWe need to make this work in tenth part of the time working 8 hours a day, it means:
Time used to the second work = 320 hours / 10Time used to the second work = 32 hours Time used to the second work = 32 hours / 8 hours (as each day has 8 hours)Time used to the second work = 4 daysNow, we know three of the second set can do as much work as four of the first set, taking into account the calculated equivalence, we have:
Work of four workers of first set = Work of three workers of second setWork of four workers of first set = Equivalence * 4 persons.Work of four workers of first set = 2 hours /person * 4 personsWork of four workers of first set = 8 hours.So, three persons of the second set can make a equivalence of 8 hours. At last, we calculate all the number of workers we need in a regular time:
Number of needed workers in a regular time = (320 hours / 8 hours) * 3 persons.Number of needed workers in a regular time = 40 * 3 personsNumber of needed workers in a regular time = 120 personsRemember we need to perform the job not in a regular time, we need to perform it in tenth part of the time, by this reason, we need 10 times the number of people:
Number of needed workers in tenth part of the time = 120 persons * 10Number of needed workers in tenth part of the time = 1200 personsWith this calculations, you can find the number of men needed to perform a piece of work twice as great in tenth part of the time working 8 hours a day supposing that three of the second set can do as much work as four of the first set is 1200 persons.
Find the value of x in the given figure
Answer:
20 degrees
Step-by-step explanation:
Angles on a line equal 180 degrees.
180–140=40
40=2x
x=20
20 degrees
Help me out thankssssss !!!!!!
Answer:
78/2=39°
Step-by-step explanation:
thx for the points
PLSSSSSS HELP ASAP !!!
Answer:
m4+m5=180
answer is second option
Circle the answer choice below that does not equal the following:
– 80/10
1) - 8
2) 80/-10
3) - (80/10)
4) 8
Answer: 4) 8
Step-by-step explanation:
-80/10=-8
-8 = - 8. - No
80/-10= - 8. - 8=-8 - No
-(80/10)=-(8)=-8. - 8=-8 - No
8 - Yes.
Cells use the hydrolysis of adenosine triphosphate, abbreviated as ATP, as a source of energy. Symbolically, this reaction can be written asATP(aq)+H2O(l)⟶ADP(aq)+H2PO−4 (aq)where ADP represents adenosine diphosphate. For this reaction, ΔG∘=−30.5kJ/mol.a. Calculate K at 25∘C .b. If all the free energy from the metabolism of glucoseC6H12O6(s)+6O2(g)⟶6CO2(g)+6H2O(l)goes into forming ATP from ADP, how many ATP molecules can be produced for every molecule of glucose?
Answer:
Step-by-step explanation:
From the given information:
ΔG° = -30.5 kJ/mol
By applying the following equation to calculate the value of K.
ΔG° =-RT㏑K
making ㏑ K the subject of the formula:
[tex]\mathtt{ In \ K} = \dfrac{\Delta G^0}{-RT}[/tex]
where;
Temperature at 25° C = (25 + 273)K
= 298K
R = 8.3145 J/mol.K (gas cosntant)
[tex]\mathtt{ In \ K} = \dfrac{-30.5 \times 10^{3}\ J /mol} {-(8.3145 \ J/mol. K \times 298 \ K}[/tex]
[tex]\mathtt{ In \ K} = \dfrac{-30.5 \times 10^{3}\ J /mol} {-2477.721 J/mol }[/tex]
㏑K = 12.309
[tex]K = e^{12.309}[/tex]
K = 221682.17
K = 2.22 × 10⁵
b) The reaction for the metabolism of glucose is given as:
[tex]C_6H_{12} O_6 + 6O_{2(g)} \to + 6CO_{2(g)} + 6H_2O_{(l)}[/tex]
From the above expression, let calculate the Gibbs free energy by using the formula:
[tex]\Delta G^0_{rx n }= \Delta G^0_{product}- \Delta G^0_{reactant}[/tex]
[tex]\Delta G^0_{rx n }= [6 \times \Delta G^0_{f}(CO_2) + 6 \times \Delta G^0_{f}(H_2O)] - [1 \times \Delta G^0_{f}(C_6H_{12}O_6) + 6 \times \Delta G^0_{f}(O_2)][/tex]
At standard conditions;
The values of corresponding compounds are substituted into the equation above:
Thus,
[tex]\Delta G^0_{rx n }= [6 \times (-394) + 6 \times (-237)] - [1 \times (-911) + 6 \times (0)] \ kJ/mol[/tex]
[tex]\Delta G^0_{rx n }= [-2364-1422] - [-911+0] \ kJ/mol[/tex]
[tex]\Delta G^0_{rx n }= -3786 +911 \ kJ/mol[/tex]
[tex]\Delta G^0_{rx n }= -2875 \ kJ/mol[/tex]
[tex]\Delta G^0_{rx n }= -2875000 \ J/mol[/tex]
Now, the no of ATP molecules generated = [tex]\dfrac{\Delta G^0 \text{of metabolism for glucose}}{\Delta G^0 \text{of hydrolysis for ATP}}[/tex]
= (-2875000 J/mol ) / -30500 J/mol
= 94.26
≅ 94 ATP molecules generated
When a number is decreased by 40% of itself the result is 96. What is the number?
Answer:
160
Step-by-step explanation:
96 / (100%-40%) = 96/ (60%)
= 96/0.6 = 160
Q) 96/(100% - 40%)
→ 96/ 60%
→ 96/ 0.6
→ 160 is the number.
WILL MARK BRAINLIEST PLEASE HELP
What are the roots of the polynomial x2 - 4x + 1 ?
Work out your answer on our whiteboard. Then, click the buttons below to
see the step-by-step solution.
Answer:
x = (2 + √3) , (2 - √3)
Step-by-step explanation:
GIVEN :-
A quadratic polynomial x² - 4x + 1TO FIND :-
Roots of the quadratic polynomialGENERAL FORMULAE TO BE USED IN THIS QUESTION :-
Quadratic formulae -
For a polynomial ax² + bx + c , its roots are :-
[tex]x = \frac{-b + \sqrt{b^2 - 4ac} }{2a} \; ; \frac{-b - \sqrt{b^2 - 4ac} }{2a}[/tex]
SOLUTION :-
Use the quadratic formulae to find the roots of the polynomial.
[tex]=> x = \frac{-(-4) + \sqrt{(-4)^2 - 4 \times 1 \times 1c} }{2 \times 1} \; ; \frac{-(-4) - \sqrt{(-4)^2 - 4 \times 1 \times 1} }{2 \times 1}[/tex]
[tex]= \frac{4 + \sqrt{16 - 4} }{2} \; ; \frac{4- \sqrt{16 - 4}}{2}[/tex]
[tex]= \frac{4 + \sqrt{12} }{2} \; ; \frac{4- \sqrt{12}}{2}[/tex]
[tex]= \frac{4 + 2\sqrt{3} }{2} \; ; \frac{4- 2\sqrt{3}}{2}[/tex]
[tex]= \frac{2(2 + \sqrt{3})}{2} \; ; \frac{2(2- \sqrt{3})}{2}[/tex]
[tex]= (2 + \sqrt{3} ) \; ; (2 - \sqrt{3} )[/tex]
PLEASE HELP ME FAST I WILL GIVE BRAINLYEST
7.)
cbrt(1200)
10.63
8.)
sqrt(112)
10.58
Answer:
1.) because 10^3=1000 and 11^3 = around 1330 we know that the answer must fall between 10 and 11. Because they're pretty much equal distance I would estimate it to be around 10.5 (if you need an exact answer it's 2∛150)
2.) because 11^2=121 and 10^2= 100 we know that it must fall between 10 and 11. Because these are pretty much equal distance as well I would estimate it to be around 10.5 as well (if you need an exact answer it's 4√7)
Step-by-step explanation:
HELP ME PLS!!!!
a circle has been divided into 36 equal angles what is the measure of each angle?
Answer:
10°
Step-by-step explanation:
360/36 = 10
The volume of a particular die is 6000 mm. Use the fact that 10 mm equals 1 cm to convert this
volume to cm.
Answer:
600 cm³
Step-by-step explanation:
6000 mm/10 mm = 600 cm
If the weight (in grams) of cereal in a box of Lucky Charms is N(489,6), what is the probability that the box will contain less than the advertised weight of 466 g
Answer:
0.000064 = 0.0064% probability that the box will contain less than the advertised weight of 466 g.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
N(489,6)
This means that [tex]\mu = 489, \sigma = 6[/tex]
What is the probability that the box will contain less than the advertised weight of 466 g?
This is the p-value of Z when X = 466. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{466 - 489}{6}[/tex]
[tex]Z = -3.83[/tex]
[tex]Z = -3.83[/tex] has a p-value of 0.000064
0.000064 = 0.0064% probability that the box will contain less than the advertised weight of 466 g.
14+6×(9-6)
please answer
Answer:
32
Step-by-step explanation:
14+6(9-6)
[9-6=3]
14+6x3
[6x3=18]
14+18
32
---
hope it helps
Answer:
14+6×(9-6)=32
Someone please answer yes I give brainliest
which of these tables represents a function
Answer: choice D
Step-by-step explanation:
In order for something to be a function for every x input there must be exactly 1 y output. This means that if x is a number then y must always be 1 number and that 1 number only.
I will love and rate 5.0 if done correctly with no images and no trolling for answer.
A hardware store receives shipments containing 600 light bulbs each. A sample of 75 light bulbs in a given shipment contains 3 that are defective. What is the sample ratio of defective light bulbs to total light bulbs in the shipment written as a percent?
A - 4%
B - 10%
C - 20%
D - 76%
Find the least number by which 1323 must be multiplied so that the product is a perfect cube
Answer:
Step-by-step explanation:
So, to solve this, lets just break down 1323.
Just looking at it, I am going to take a 3:
1323/3
=
441
So now we have:
3*441=1323
Can we break down 441 any more?
Yup, I can see that 3 goes into 450, 150 times and 441 is 9 less than 450, which means it 3 times less than 150 times, which is 147.
So now we have:
3*3*147=1323
Again, we can take something from 147.
7*20 is 140, and 147 is 7 more than that. So 7*21=147.
This further means:
3*3*7*21=1323
Now it probably isnt too difficult now.
21 can be broken down into 3*7.
So we can rewrite it as:
3*3*7*3*7=1323
And we can use exponents for the extra 3's and 7's we have, so we can simplfy it as:
3^3*7^2=1323
The perfect cube here is 3, since we cube 3(3^3), and then multiply it by 2 7s to make 1323.
The perfect square here is 7, since we square 7(7^2), and then multiply it by 3 3s.
So the PERFECT CUBE for your answer is 3.
The PERFECT SQUARE is 7.
Hope this helps!
What is the answer for this question?
Answer:
The answer is A 1 4/5
Work:
7 1/5- 6 2/5
turn 7 1/5 into 6 6/5 and now subtract the two fractions
6/5-2/5= 4/5
now subtract the whole numbers:
6-6=1
So, your answer should be 4/5 (A)
For a statistics project, Lauren distributed a questionnaire and asked her classmates to fill it out. 2 of them did.
Is this sample of the students in the class likely to be representative? Yes or no
HELP PLSSS I WILL GIVE THE FIRST PERSON TO ANSWER BRAINLYIST IF THERE RIGHT
i suck at math its easy
Option B and D are the correct answers
Answer:
A and B I guess so