Answer:
the production of milk at the Dancing Dairy Farm is increasing by 2158 gallons/year
Step-by-step explanation:
Given the data in the question;
Let us represent the number of cows at the farm with x and
each cow produces y gallons of milk
Total mil production will be T.
so
T = x × y
now, differentiating with respect to t
dT/dt = d( xy )/dt
dT/dt = xdy/dt + ydx/dt
given that;
x = 441
y = 1157
dx/dt = -13
dy/dt = 39
so we substitute
dT/dt = ( 441 )( 39 ) + ( 1157 )( -13 )
dT/dt = 17199 - 15041
dt/dT = 2158
Therefore, the production of milk at the Dancing Dairy Farm is increasing by 2158 gallons/year
In how many ways can the letters in the word 'Illinois' be arranged?
Answer
How to enter your answer
Answer:
The numbers of ways to permute letters of the word Illinois if the two Ls must be consecutive is 7.
The word ILLINOIS contains 7 letters.
How do you find the number of distinguishable permutations of the letters in a word?To estimate the number of different permutations, consider the total number of letters factorial and divide by the frequency of each letter factorial. The little n's exist the frequencies of each various (different) letter.
We will use the formula for the number of permutations with imperceptible objects. Since the two L's must be consecutive, we consider them to be a single letter LL. Then the word ILLINOIS contains n = 7 letters: 3 I's, 1 LL, 1 N, 1 O, and 1S.
Hence the number of methods to permute letters of the word ILLINOIS if the two L's must be consecutive exists:
[tex]$\frac{7 !}{3 ! 1 ! 1 ! 1 ! 1 !}=7 \cdot 6 \cdot 5 \cdot 4=840 \text {. }$$[/tex]
The word ILLINOIS contains 7 letters.
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-6c< -12
what will the answear be
Answer:c>2
Step-by-step explanation:
-6c (divide) (-6) > -12 (divide) (-6)
c>-12 (divide) (-6)
c>12 (divide) 6
c> 2
If you vertically compress the square root parent function by a factor of 1/3, what is the equation of the new function?
9514 1404 393
Answer:
y = (1/3)√x
Step-by-step explanation:
Vertical scaling of a function is accomplished by multiplying the function by the scale factor. If you want to scale the square root function by a factor of 1/3, then the scaled function is ...
y = (1/3)√x
A furniture store donated a percent of every cell to charity the total sales were 7000 and 900 so the store donated $632 what percent of $7900 was donated to the charity
9514 1404 393
Answer:
8%
Step-by-step explanation:
The fraction donated was $632/$7900.
As a percentage, that is ...
632/7900 × 100% = 0.08 × 100% = 8%
The store donated 8% of sales to charity.
what is a bank statement
Answer:
A statement that shows current balance of an account and all transactions that occurred on that account since the last statement.
Transactions such as deposits, withdrawals, checks written, debt card uses...
There are other examples of bank statements for things like home loans, business loans, and investments.
NEED HELP ASAP!!! Giving brainliest!!!!!!!
C.(f-g)(x) = 4x^3 +5x²-7x-1
Step-by-step explanation:
Given information :
[tex]f(x) = 4 {x}^{3} + 5 {x}^{2} - 3x - 6 \\ g(x) = 4x - 5[/tex]
Find :
[tex](f - g)(x) = \\ (4 {x}^{3} + 5 {x}^{2} - 3x - 6) \\ - 4x -5[/tex]
Open bracket and Simplify
[tex]4 {x}^{3} + 5 {x}^{2} - 3x - 6 - 4x + 5 \\ 4 {x}^{3} + 5 {x}^{2} - 7x - 1[/tex]
Please!!!!!! I need whole process
Answer:
This is the whole process I guess
Tìm căn bậc hai của số phức z=1+i√3
Write z in polar form:
z = 1 + √3 i = 2 exp(i π/3)
Taking the square root gives two possible complex numbers,
√z = √2 exp(i (π/3 + 2kπ)/2)
with k = 0 and k = 1, so that
√z = √2 exp(i π/6) = √(3/2) + √(1/2) i
and
√z = √2 exp(i 7π/6) = -√(3/2) - √(1/2) i
6.
40 x 6+ (9+21)
I need help ASAP please due tomorrow show work
Find a power series for the function, centered at c, and determine the interval of convergence. f(x) = 9 3x + 2 , c = 6
Answer:
[tex]\frac{9}{3x + 2} = 1 - \frac{1}{3}(x - \frac{7}{3}) + \frac{1}{9}(x - \frac{7}{3})^2 - \frac{1}{27}(x - \frac{7}{3})^3 ........[/tex]
The interval of convergence is:[tex](-\frac{2}{3},\frac{16}{3})[/tex]
Step-by-step explanation:
Given
[tex]f(x)= \frac{9}{3x+ 2}[/tex]
[tex]c = 6[/tex]
The geometric series centered at c is of the form:
[tex]\frac{a}{1 - (r - c)} = \sum\limits^{\infty}_{n=0}a(r - c)^n, |r - c| < 1.[/tex]
Where:
[tex]a \to[/tex] first term
[tex]r - c \to[/tex] common ratio
We have to write
[tex]f(x)= \frac{9}{3x+ 2}[/tex]
In the following form:
[tex]\frac{a}{1 - r}[/tex]
So, we have:
[tex]f(x)= \frac{9}{3x+ 2}[/tex]
Rewrite as:
[tex]f(x) = \frac{9}{3x - 18 + 18 +2}[/tex]
[tex]f(x) = \frac{9}{3x - 18 + 20}[/tex]
Factorize
[tex]f(x) = \frac{1}{\frac{1}{9}(3x + 2)}[/tex]
Open bracket
[tex]f(x) = \frac{1}{\frac{1}{3}x + \frac{2}{9}}[/tex]
Rewrite as:
[tex]f(x) = \frac{1}{1- 1 + \frac{1}{3}x + \frac{2}{9}}[/tex]
Collect like terms
[tex]f(x) = \frac{1}{1 + \frac{1}{3}x + \frac{2}{9}- 1}[/tex]
Take LCM
[tex]f(x) = \frac{1}{1 + \frac{1}{3}x + \frac{2-9}{9}}[/tex]
[tex]f(x) = \frac{1}{1 + \frac{1}{3}x - \frac{7}{9}}[/tex]
So, we have:
[tex]f(x) = \frac{1}{1 -(- \frac{1}{3}x + \frac{7}{9})}[/tex]
By comparison with: [tex]\frac{a}{1 - r}[/tex]
[tex]a = 1[/tex]
[tex]r = -\frac{1}{3}x + \frac{7}{9}[/tex]
[tex]r = -\frac{1}{3}(x - \frac{7}{3})[/tex]
At c = 6, we have:
[tex]r = -\frac{1}{3}(x - \frac{7}{3}+6-6)[/tex]
Take LCM
[tex]r = -\frac{1}{3}(x + \frac{-7+18}{3}+6-6)[/tex]
r = -\frac{1}{3}(x + \frac{11}{3}+6-6)
So, the power series becomes:
[tex]\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}ar^n[/tex]
Substitute 1 for a
[tex]\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}1*r^n[/tex]
[tex]\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}r^n[/tex]
Substitute the expression for r
[tex]\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}(-\frac{1}{3}(x - \frac{7}{3}))^n[/tex]
Expand
[tex]\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}[(-\frac{1}{3})^n* (x - \frac{7}{3})^n][/tex]
Further expand:
[tex]\frac{9}{3x + 2} = 1 - \frac{1}{3}(x - \frac{7}{3}) + \frac{1}{9}(x - \frac{7}{3})^2 - \frac{1}{27}(x - \frac{7}{3})^3 ................[/tex]
The power series converges when:
[tex]\frac{1}{3}|x - \frac{7}{3}| < 1[/tex]
Multiply both sides by 3
[tex]|x - \frac{7}{3}| <3[/tex]
Expand the absolute inequality
[tex]-3 < x - \frac{7}{3} <3[/tex]
Solve for x
[tex]\frac{7}{3} -3 < x <3+\frac{7}{3}[/tex]
Take LCM
[tex]\frac{7-9}{3} < x <\frac{9+7}{3}[/tex]
[tex]-\frac{2}{3} < x <\frac{16}{3}[/tex]
The interval of convergence is:[tex](-\frac{2}{3},\frac{16}{3})[/tex]
Calculate the interest rate with a deposit $27,580.00 in an interest-bearing account. After one year, your accrued interest is $1,442.43.
Answer:
5.23%
Step-by-step explanation:
See Image below:)
Which answer describes the pattern in this sequence?
2, 1, 12, 14, ...
multiply by 2
subtract 1
add 12
multiply by 12
What is sin(C)? Please explain.
Answer:
sin(C) = opposite side / hypotenuse
= 15/17
Answer:
[tex] \small \sf \: Sin ( C ) = \blue{ \frac{15}{17}} \\ [/tex]
Step-by-step explanation:
[tex] \small \sf \: Sin ( C ) = \frac {Opposite \: side }{Hypotenuse} \\ [/tex]
Where we have given :-
Opposite side = 15Hypotenuse = 17substitute the values, we get
[tex] \small \sf \: Sin ( C ) = \blue{ \frac{15}{17}} \\ [/tex]
what is the square root of 15
Step-by-step explanation:
[tex] \sqrt{15} = 3.872983346 = 3.88[/tex]
The number of visits to public libraries increased from 1.3 billion in 1993 to 1.7 billion in 1997. Find the average rate of change in the number of public library visits from 1993 to 1997.
Answer:
The average rate of change in the number of public library visits from 1993 to 1997 was of 0.1 billion an year.
Step-by-step explanation:
Average rate of change:
Division of the subtraction of the final value by the initial value, divided by the length of time.
The number of visits to public libraries increased from 1.3 billion in 1993 to 1.7 billion in 1997.
Initial value: 1.3 billion
Final value: 1.7 billion
1997 - 1993 = 4 years.
Thus:
[tex]A = \frac{1.7 - 1.3}{4} = \frac{0.4}{4} = 0.1[/tex]
The average rate of change in the number of public library visits from 1993 to 1997 was of 0.1 billion an year.
which expression is it please help
Answer:
first option is the correct answer.
Step-by-step explanation:
PLSSSSS
cos36 * cos72=???
I need procedure
cos 36 × cos 72 = 0.25
cos 36 × cos 72 =
0.309 x 0.809 = 0.249 = 0.25
please step by step with formula.
Suppose that you deposit $3,850 in an account paying 4.65% simple interest. How long will it take to earn $150 in interest?
Answer:
0.837
Step-by-step explanation:
3850*4.65%=179.025
150/179.025=0.837
0.837
There are 14 books on a shelf. 9 of these books are new. The rest of them are used. (GIVING POINTS AND BRAINLEST TO BEST ANSWER) what is the ratio?
Answer:
A: 9:5 B: 5:14
Step-by-step explanation:
At an assembly plant for light trucks, routine monitoring of the quality of welds yields the following data:
Number of Welds
High Moderate Low
Quality Quality Quality
Day Shift
Evening Shift
Night Shift 467 191 42
445 171 34
254 129 17
Can you conclude that the quality varies among shifts?
a. State the appropriate null hypothesis.
b. Compute the expected values under the null hypothesis.
c. Compute the value of the chi-square statistic.
d. Find the P-value. What do you conclude?
Answer:
Kindly check explanation
Step-by-step explanation:
H0 : quality does not vary among shift
H1 : quality varies among shift
The expected values :
(Row * column) / grand total
Given the data:
Observed values :
_________________total
_______467 191 42 __700
_______445 171 34 __650
_______254 129 17 _ 400
Total __ 1166 491 93 _ 1750
Expected value count using the formula :.
Expected Values:
466.4 ____196.4 ______37.2
433.086 _182.371___ 34.5429
266.514_ 112.229____ 21.2571
The Chisquare statistic (χ²) :
χ² = (observed - Expected)²/ observed
χ² = 5.76045
The degree of freedom = (row - 1) * (column - 1)
Degree of freedom = (3-1)*(3-1) = 2*2 = 4
Pvalue = 0.2178
Pvalue > α ; We foal to reject H0 ; Hence, we conclude that quality does not vary among shift
how do you find contribution margin %?
Answer:
Contribution margin = Revenue − Variable costs
Step-by-Step Explanation
For example, if the price of your product is $20 and the unit variable cost is $4, then the unit contribution margin is $16.
The first step in doing the calculation is to take a traditional income statement and recategorize all costs as fixed or variable. This is not as straightforward as it sounds, because it’s not always clear which costs fall into each category.
Hope this helps and if it does, don't be afraid to rate my answer as well as maybe give it a "Thanks"? (Or even better a "Brainliest"). And if it’s not correct, I am sorry for wasting your time, and good luck finding the correct answer :)
A, B, and C are collinear points:
C is between A and B.
If AC = 2x + 1, CB = 3x - 1, and AB = 35, findX.
Answer:
X = 7
Step-by-step explanation:
Which parent function is represented by the graph?
Which parent function is represented by the graph?
A . The quadratic parent function
B . The linear parent function
C . The absolute value parent function
D . An exponential parent function
Answer:
D. An exponential parent function
Step-by-step explanation:
The basic parent function of any exponential function is f(x) = bx, where b is the base. Using the x and y values from this table, you simply plot the coordinates to get the graphs. The parent graph of any exponential function crosses the y-axis at (0, 1), because anything raised to the 0 power is always 1.
The parent function that represents the graph is exponential.
What is function?A function is a relation between a dependent and independent variable. We can write the examples of function as -
y = f(x) = ax + b
y = f(x, y, z) = ax + by + cz
Given is a function as shown in the image. It is asked to identify the parent function of this graph.
The parent function will be quadratic if the plotted graph is a parabola.
The parent function will be linear if the plotted graph is a straight line.
The parent function will be an absolute function if it is V - shaped.
So, none of the options other than the exponential parent function represents the graph.
Therefore, the parent function that represents the graph is exponential.
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Adam tabulated the values for the average speeds on each day of his road trip as 60.5, 63.2, 54.7, 51.6, 72.3, 70.7, 67.2, and 65.4 mph. The sample standard deviation is 7.309.Select the 98% confidence interval for Adam’s set of data.a. 46.94 to 71.33b. 46.94 to 79.46c. 55.45 to 79.46d. 55.45 to 70.95
Answer:
Option D, 55.45 to 70.95
Step-by-step explanation:
Alpha = 1 – confidence interval
Alpha = 1 – 0.98 = 0.02
Sample size = n = 8
t (alpha/2) ; (n-1) = t (0.02/2) ; (8-1) = t 0.01, 7 = 2.998
Mean = sum of all frequencies /total number of frequency = 505.6/8 = 63.2
s = 7.309
E = t (0.01;7) * s/sqrt n
Substituting the given values, we get –
E = 2.998 * 7.309 /sqrt (8)
E = 7.75
98% confidence interval
Mean – E and Mean + E
63.2 – 7.75 and 63.2 + 7.75
(55.45, 70.95)
Answer: 55.45 to 70.95
Step-by-step explanation:
To solve the equation 6x + 3 = 9 for x, what operations must be
performed on both sides of the equation in order to isolate the variable
x?
Answer:
Subtraction, and then division.
Step-by-step explanation:
We would subtract 3 on each side to undo the '3', and then divide by 6 on both sides to isolate 'x'.
[tex]6x+3 = 9\\\\6x + 3 - 3 = 9 - 3\\\\ 6x = 6\\\\\frac{6x=6}{6}\\\\\boxed{x=1}[/tex]
Hope this helps.
To solve the equation 6x + 3 = 9 for x, the operations that must be performed on both sides of the equation in order to isolate the variable x are subtraction and then division.
What is a linear equation?A linear equation in one variable has the standard form Px + Q = 0. In this equation, x is a variable, P is a coefficient, and Q is constant.
How to solve this problem?Given that 6x + 3 = 9.
First, we have to separate variable and constants. So, we have to subtract 3 from both sides.
6x + 3 - 3 = 9 - 3
i.e. 6x = 6
Now, to solve this equation, we use division.
x = 6/6 = 1
i.e. x = 1
Therefore, to solve the equation 6x + 3 = 9 for x, the operations that must be performed on both sides of the equation in order to isolate the variable x are subtraction and then division.
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Find the distance from (4,2) to the line defined
by y = -2x + 5. Express as a radical or a number
rounded to the nearest hundredth.
Answer:
The desired distance is √5
Step-by-step explanation:
Recall that the distance from a point to a line is measured along a path perpendicular to the line. Thus, given the line y = -2x + 5, the slope of any line perpendicular to it is the negative reciprocal of -2: +1/2.
The line perpendicular to y = -2x + 5 and passing through (4, 2) is
y - 2 = (1/2)(x - 4), or
2y - 4 = x - 4, or 2y = x, or y = (1/2)x.
Now our problem becomes "find the length of the line connecting (4, 2) and the intersection of y = -2x + 5 and y = (1/2)x."
Equating these, we get (1/2)x = -2x + 5, which, if multiplied through by 2, becomes x = -4x + 10, or 5x = 10, or x = 2. If x = 2, then y = (1/2)(2) = 1.
Finally, find the distance between (2, 1) and (4, 2):
Using the Pythagorean Theorem, d = √(2^2 + 1^2) = √5
The distance from (4, 2) to the line y = -2x + 5 is √5
this image may be the result of the ___. if mRQS is 75, then mTPU is ____.
Answer:
B for first one.
75 for second.
Hope this helps !
Step-by-step explanation:
Helppppppp
Which choice is equivalent to the product below
Step-by-step explanation:
jkkkkkkkkkkkkkkkkkkkkk
Answer:
[tex]2 \sqrt{35} [/tex]
Help pls ASAP this need to be done
D
Because slope of section D is greater than the others and hence speed is highest.
∫▒〖e^2x dx〗= ???? thanks
Answer:
Step-by-step explanation:
I=∫e^2x dx
put 2x=t
2dx=dt
dx=dt/2
I=1/2∫e^t dt
=1/2 e^t+c
=1/2 e^{2x}+c