Answer:
Step-by-step explanation:
Each gallon of 7% milk contains 0.07 gallon of butterfat.
Each gallon of 4% milk contains 0.04 gallon of butterfat.
291 gallons of 6% milk contain 291×0.06 = 17.46 gallons of butterfat.
Let x be the number of gallons of 7% milk used. 291-x is the number of gallons of 4% milk used.
0.07x + 0.04(291-x) = 17.46
0.03x + 11.64 = 17.46
x = 200
Use 200 gallons of 7% and 91 gallons of 4%.
Find y' for the following.
Answer:
[tex]\displaystyle y' = \frac{\sqrt{y} + y}{4\sqrt{x}y \Big( y^\Big{\frac{3}{2}} + \sqrt{y} + 2y \Big) + \sqrt{x} + x}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Quotient Rule]: [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Implicit Differentiation
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \frac{\sqrt{x} + 1}{\sqrt{y} + 1} = y^2[/tex]
Step 2: Differentiate
Implicit Differentiation: [tex]\displaystyle \frac{dy}{dx} \bigg[ \frac{\sqrt{x} + 1}{\sqrt{y} + 1} \bigg] = \frac{dy}{dx}[ y^2][/tex]Quotient Rule: [tex]\displaystyle \frac{(\sqrt{x} + 1)'(\sqrt{y} + 1) - (\sqrt{y} + 1)'(\sqrt{x} + 1)}{(\sqrt{y} + 1)^2} = \frac{dy}{dx}[ y^2][/tex]Rewrite: [tex]\displaystyle \frac{(x^\Big{\frac{1}{2}} + 1)'(y^\Big{\frac{1}{2}} + 1) - (y^\Big{\frac{1}{2}} + 1)'(x^\Big{\frac{1}{2}} + 1)}{(y^\Big{\frac{1}{2}} + 1)^2} = \frac{dy}{dx}[ y^2][/tex]Basic Power Rule [Addition/Subtraction, Chain Rule]: [tex]\displaystyle \frac{\frac{1}{2}x^\Big{\frac{-1}{2}}(y^\Big{\frac{1}{2}} + 1) - \frac{1}{2}y^\Big{\frac{-1}{2}}y'(x^\Big{\frac{1}{2}} + 1)}{(y^\Big{\frac{1}{2}} + 1)^2} = 2yy'[/tex]Factor: [tex]\displaystyle \frac{\frac{1}{2} \bigg[ x^\Big{\frac{-1}{2}}(y^\Big{\frac{1}{2}} + 1) - y^\Big{\frac{-1}{2}}y'(x^\Big{\frac{1}{2}} + 1) \bigg] }{(y^\Big{\frac{1}{2}} + 1)^2} = 2yy'[/tex]Rewrite: [tex]\displaystyle \frac{x^\Big{\frac{-1}{2}}(y^\Big{\frac{1}{2}} + 1) - y^\Big{\frac{-1}{2}}y'(x^\Big{\frac{1}{2}} + 1)}{2(y^\Big{\frac{1}{2}} + 1)^2} = 2yy'[/tex]Rewrite: [tex]\displaystyle x^\Big{\frac{-1}{2}}(y^\Big{\frac{1}{2}} + 1) - y^\Big{\frac{-1}{2}}y'(x^\Big{\frac{1}{2}} + 1)}= 4yy'(y^\Big{\frac{1}{2}} + 1)^2[/tex]Isolate y' terms: [tex]\displaystyle x^\Big{\frac{-1}{2}}(y^\Big{\frac{1}{2}} + 1) = 4yy'(y^\Big{\frac{1}{2}} + 1)^2 + y^\Big{\frac{-1}{2}}y'(x^\Big{\frac{1}{2}} + 1)}[/tex]Factor: [tex]\displaystyle x^\Big{\frac{-1}{2}}(y^\Big{\frac{1}{2}} + 1) = y' \bigg[ 4y(y^\Big{\frac{1}{2}} + 1)^2 + y^\Big{\frac{-1}{2}}(x^\Big{\frac{1}{2}} + 1)} \bigg][/tex]Isolate y': [tex]\displaystyle \frac{x^\Big{\frac{-1}{2}}(y^\Big{\frac{1}{2}} + 1)}{4y(y^\Big{\frac{1}{2}} + 1)^2 + y^\Big{\frac{-1}{2}}(x^\Big{\frac{1}{2}} + 1)} = y'[/tex]Rewrite/Simplify: [tex]\displaystyle y' = \frac{\sqrt{y} + y}{4\sqrt{x}y \Big( y^\Big{\frac{3}{2}} + \sqrt{y} + 2y \Big) + \sqrt{x} + x}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Book: College Calculus 10e
4 football is kicked with a speed of 18.0 m/s at an angle of 36.9to the horizontal. 8. How long is the football in the air? Neglect air resistance. A ) 1.1 s B C ) 2.2 D) 3.3 E) 4.0
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Answer:
C) 2.2 seconds
Step-by-step explanation:
The initial vertical speed of the football is ...
v = (18.0 m/s)sin(36.9°) ≈ 10.807 m/s
Since the ball starts and ends at ground level, its speed when it hits the ground is the same as its launch speed. That is, the acceleration due to gravity causes the velocity to change from +v to -v. The time required to do that is ...
t = 2v/g = 2(10.807 m/s)/(9.8 m/s^2) = 21.614/9.8 s ≈ 2.206 s
The football is in the air about 2.2 seconds.
The ratio of the volumes of two similar solid polyhedra is equal to the square root of the ratio between their edges. True or False? HELP QUICK PLSSSSS
Answer:
FALSE.The ratio of the volumes of two similar solid polyhedra is equal to the square of the ratio between their edges. This statement is false. A polyhedron is a shape that has no gaps between their edges or vertices.
Answer:
it's false
~~~~~~~~~~~
Help once again thanks! !!!!!!!
Find r given: (4,-7) and (-2, r) with a slope of 8/3
Answer:
r = -23
Step-by-step explanation:
slope = (y1-y2)/(x1-x2)
(r--7)/(-2-4) = 8/3
(r+7)/-6 = 8/3
3(r+7)=8 x -6
3r + 21 = -48
3r = -69
r = -23
Find the length of AC
Answer:
377.19 (rounded off to 2dp)
Step-by-step explanation:
since its a right angled triangle, we can use tangent
tan(x) =opp/adj
tan(5) =33/AC
AC =33/tan(5)
SOMEONE PLS HELP ME!!!
Answer:
No
Step-by-step explanation: Bye
express the following in standard form (0.000000045)^4
0.00000004 to the power of 4
Your answer would be 0
The time it takes me to wash the dishes is uniformly distributed between 8 minutes and 17 minutes.
What is the probability that washing dishes tonight will take me between 14 and 16 minutes?
Give your answer accurate to two decimal places.
The time it takes to wash has the probability density function,
[tex]P(X=x) = \begin{cases}\frac1{17-8}=\frac19&\text{for }8\le x\le 17\\0&\text{otherewise}\end{cases}[/tex]
The probability that it takes between 14 and 16 minutes to wash the dishes is given by the integral,
[tex]\displaystyle\int_{14}^{16}P(X=x)\,\mathrm dx = \frac19\int_{14}^{16}\mathrm dx = \frac{16-14}9 = \frac29 \approx \boxed{0.22}[/tex]
If you're not familiar with calculus, the probability is equal to the area under the graph of P(X = x), which is a rectangle with height 1/9 and length 16 - 14 = 2, so the area and hence probability is 2/9 ≈ 0.22.
A distribution of values is normal with a mean of 1986.1 and a standard deviation of 27.2.
Find the probability that a randomly selected value is greater than 1914.8.
P(X> 1914.8) =
Enter your answer as a number accurate to 4 decimal places. *Note: all z-scores must be rounded to
the nearest hundredth.
Answer:
I used the function normCdf(lower bound, upper bound, mean, standard deviation) on the graphing calculator to solve this.
Lower bound = 1914.8Upper bound = 999999Mean = 1986.1Standard deviation = 27.2Input in these values and it will result in:
normCdf(1914.8,9999999,1986.1,27.2) = 0.995621
So the probability that the value is greater than 1914.8 is about 99.5621%
I'm not sure if this is correct 0_o
15.8 Use multiple linear regression to fit x1 0 1 1 2 2 3 3 4 4 x2 0 1 2 1 2 1 2 1 2 y 15.1 17.9 12.7 25.6 20.5 35.1 29.7 45.4 40.2 Compute the coefficients, the standard error of the estimate, and the correlation coefficient.
Answer:
Kindly check explanation
Step-by-step explanation:
regression to fit
x1 0 1 1 2 2 3 3 4 4
x2 0 1 2 1 2 1 2 1 2
y 15.1 17.9 12.7 25.6 20.5 35.1 29.7 45.4 40.2
Using technology ;
The multiple linear regression fit for the data is :
y = 9.025x1 - 5.704x2 + 14.461
Where 9.025 and - 5.704 are the slope values of x1 and x2 respectively.
14.461 = intercept.
The Correlation Coefficient, R from the output is 0.998 ; this depicts a strong positive relationship between the independent variables and dependent variable.
Which of the following is a quadratic function
A quadratic a function has a form of,
[tex]f(x)=ax^2+bx+c,a\neq0[/tex]
The first function has a term [tex]x^3[/tex] which doesn't fit the profile of a quadratic function. The highest exponent on x inside a quadratic function can be 2, but here we have 3 so this is not a quadratic function, but rather a cubic function.
The second function fits the form of a quadratic function perfectly.
The third function is a bit tricky. While technically the third function could be considered quadratic if the leading term would be something like [tex]0x^2[/tex] and we did't even see it written out because multiplying with 0. But when we specified the form of a quadratic function, we strictly said that the number before [tex]x^2[/tex] aka [tex]a[/tex] cannot equal to zero. So the last function is not a quadratic function but rather a linear function.
Hope this helps :)
Step-by-step explanation:
f(x) = 4x² + x - 3
[tex]f(x) = 4x {}^{2} + 3 - 2[/tex]
r3t40 is correct
Days before a presidential election, a nationwide random sample of registered voters was taken. Based on this random sample, it was reported that "52% of registered voters plan on voting for Robert Smith with a margin of error of ±3%." The margin of error was based on a 95% confidence level. Fill in the blanks to obtain a correct interpretation of this confidence interval. We are ___________ confident that the ___________ of registered voters ___________ planning on voting for Robert Smith is between ___________ and ___________.
Answer:
We are 95% confident that the percentage of registered voters in the nation planning on voting for Robert Smith is between 49% and 55%.
Step-by-step explanation:
Given that :
Margin of Error = ±3%
Sample Proportion = 52%
Confidence level = 95%
The 95% confidence interval is :
Sample proportion ± margin of error
52% ± 3%
Lower boundary = 52% - 3% = 49%
Upper boundary = 52% + 3% = 55%
The interpretation is that at a given confidence level ; the popukation proportion based on the sample proportion and margin of error is in the confidence interval.
which of the following is the formula in solving for the area of a circle?
A.A=2πr
B.A=πr²
C.A=πd
D.A=2πr²
The area of circle is πr²
Answer:
πr²
Step-by-step explanation:
The answer is πr² where,
π = pi, 3.14...
r = radius
This is the most common way of solving for the area of the circle.
Evaluate the functions
Answer:
Step-by-step explanation:
Which statement best applies to the slope of the line below?
A.
the slope is negative
B.
the slope is zero
C.
the slope is positive
D.
the line has no slope
Answer:
D
Step-by-step explanation:
fro the diagram below there line has no slope
Answer: B) The slope is zero
============================================================
Explanation:
Any horizontal line will always have a slope of 0. This is because there is no change in y (aka the rise is 0).
So we could say something like
slope = rise/run = 0/1 = 0
The run can be anything we want, and we'd still get 0 every time.
------------
Another way to see this is to pick two points from this line. Whichever points are selected, they are plugged into the slope formula
m = (y2-y1)/(x2-x1)
You'll find that the y2-y1 expression turns into 0. Why? Because y1 and y2 are the same, so they subtract to 0. It doesn't matter what x2-x1 turns into.
Using traditional methods it takes 92 hours to receive an advanced flying license. A new training technique using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique on 70 students and observed that they had a mean of 93 hours. Assume the population variance is known to be 36. Is there evidence at the 0.05 level that the technique lengthens the training time?
Find the value of the test statistic. Round your answer to two decimal places.
Answer:
The value of the test statistic is z = 1.39.
The p-value of the test is 0.0823 > 0.05, which means that there is not evidence at the 0.05 level that the technique lengthens the training time.
Step-by-step explanation:
Using traditional methods it takes 92 hours to receive an advanced flying license.
This means that at the null hypothesis, it is tested if the mean is of 92, that is:
[tex]H_0: \mu = 92[/tex]
Test if there is evidence that the technique lengthens the training time
At the alternative hypothesis, it is tested if the mean is more than 92, that is:
[tex]H_1: \mu > 92[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
92 is tested at the null hypothesis:
This means that [tex]\mu = 92[/tex]
A researcher used the technique on 70 students and observed that they had a mean of 93 hours. Assume the population variance is known to be 36.
This means that [tex]n = 70, X = 93, \sigma = \sqrt{36} = 6[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{93 - 92}{\frac{6}{\sqrt{70}}}[/tex]
[tex]z = 1.39[/tex]
The value of the test statistic is z = 1.39.
P-value of the test and decision:
The p-value of the test is the probability of finding a sample mean above 93, which is 1 subtracted by the p-value of z = 1.39.
Looking at the z-table, z = 1.39 has a p-value of 0.9177.
1 - 0.9177 = 0.0823.
The p-value of the test is 0.0823 > 0.05, which means that there is not evidence at the 0.05 level that the technique lengthens the training time.
Solve the following equation for n. Be sure to take into account whether a letter is capitalized or not.
t=n-r
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]n = t + r[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Solving for 'n'...}}\\\\t = n - r\\----------\\\rightarrow t + r = n -r + r\\\\\rightarrow t+r = n\\\\\rightarrow \boxed{n=t+r}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Consider points a, b, and c in the graph. Determine which of these points is relative maxima on the interval x = –1 and x = 2 in the graph.
Given:
The graph of a function is given.
To find:
The point that is the relative maxima on the interval x = –1 and x = 2 in the graph.
Solution:
Relative maxima: It is the maximum point of a function over a short interval.
From the given graph it is clear that the graph of the function over the interval x = –1 and x = 2 has a relative maxima at (0,0).
Clearly, (0,0) is represented by point a.
So, the point a is the relative maxima on the interval x = –1 and x = 2 in the graph.
Therefore, the correct option is A.
The point (3,-4) is on the terminal side of an angle 0. What is cos 0?
А. 3/4
В. -3/4
C. 3/5
D. -3/5 E. 3
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Answer:
C. 3/5
Step-by-step explanation:
The distance from the origin to the given point is ...
d = √(3² +(-4)²) = √(9+16) = 5
The cosine of the angle is the ratio of the x-coordinate to this value:
cos(θ) = x/d
cos(θ) = 3/5
1 poir
Question 1. Jessica has $1,625.00 to purchase a five-year Certificate of
Deposit (CD). In the chart, there are CD rates frombankrate.com. What
would the account ending balance be at Synchrony Bank if it is
compounded quarterly? *
Use the Compound Interest Formula to calculate the ending balance. A = P(1 + 5)nt
Nationwide
Bank
Nationwide
2.01%
No
Synchrony Bank
all synchrony
1.95%
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Answer:
$1790.99
Step-by-step explanation:
Given:
$1625 is invested at an annual rate of 1.95% compounded quarterly for 5 years
Find:
the ending balance
Solution:
The compound interest formula applies.
FV = P(1 +r/n)^(nt) . . . Principal P at rate r for t years, compounded n per year
FV = $1625(1 +0.0195/4)^(4·5) = $1625(1.004875^20) ≈ $1790.99
The account ending balance would be $1790.99.
Prove: Quadrilateral ABCD is a parallelogram.
m∠AEB = m∠CED
Answer:
m∠ AEB = m∠ CED ......... By Vertical Angles Theorem.
Step-by-step explanation:
Vertical Angles Theorem: Vertical angle theorem states that vertical angles, angles that are opposite each other and formed by two intersecting lines, are congruent. If two lines intersect each other, we have the two pair of vertical opposite angles. As shown in the figure. Here, ∠ 1 and ∠ 2 are vertical opposite angles, and also they are equal. ∠ 3 and ∠ 4 are also vertical opposite angles, and also they are equal. For, step 3. m∠ AEB = m∠ CED Therefore, the reason for this proof is Vertical Angles Theorem.
The surface areas of two similar solids are 16m2 and 100 m2. The volume of the larger one is 750m3. What is the volume of the smaller one?
Answer:
48 m^3
Step-by-step explanation:
If the scale factor of linear dimensions between two solids is k, then the scale factor for areas is k^2, and the scale factor of volumes is k^3.
Let's call the solid with 16 m^2 of area solid A, and the other one solid B.
The scale factor of areas from, A to B is (100 m^2)/(16 m^2) = 25/4
In other words, multiply the area of the solid A by 25/4 to get the area of solid B.
Let's check: 16 m^2 * 25/4 = 16 * 25/4 m^2 = 4 * 25 m^2 = 100 m^2
We do get 100 m^2 for solid B, so the area scale factor of 25/4 is correct.
The area scale factor is k^2, so we have:
k^2 = 25/4
We solve for k:
k = 5/2
Now we cube both sides to get k^3, the scale factor of volumes.
k^3 = 5^3/2^3
k^3 = 125/8
Let V = volume of smaller solid, solid A.
V * 125/8 = 750 m^3
V = 750 * 8/125 m^3
V = 48 m^3
If there are12 books on a rack,a person has to choose 5books.
In how many ways can he choose if one particular book is always selected?
Answer:
330
11 choose 4
[tex]=\frac{11!}{4!\left(11-4\right)!}\\= 330[/tex]
Step-by-step explanation:
Use the graph to complete the statement. O is the origin.
T<2,1> ο r(90°,O) : (4,-1)
Answer:
(3,5)
Step-by-step explanation:
After transformation the point will be (3, 5).
What is a rotation in a transformation ?A rotational transformation can be done clockwise or anticlockwise to certain number of degrees. Rotational transformation does not alter the size and shape of the figure.
Rotating (4,-1) 90° anticlockwise centred at the origin yields the point (1, 4).
Then transforming the point (1, 4) two units to the right and 1 unit up results in the point (3, 5).
We can also rotate 90° clockwise that would result in some different point on this coordinate system.
Instead on a straight line we can also have some 2D figures like a triangle a rectangle etc.
Learns more about Rotational transformation here :
https://brainly.com/question/12865301
#SPJ5
A baseball is thrown into the air from the top of a 224-foot tall building. The baseball's approximate height over time can be represented by the quadratic equation
MO-167 +800+ 224, where t represents the time in seconds that the baseball has been in the air and represents the baseball's height in feet. When factored, this
equation is -16(-7)(t+ 2).
What is a reasonable time for it to take the baseball to land on the ground?
OA 2 seconds
ОВ
7 seconds
C. 5 seconds
D.
9 seconds
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Answer:
A. 7 seconds
Step-by-step explanation:
We assume your factored equation is something like ...
h(t) = -16t(t -7)(t +2)
The time it takes the ball to reach the ground is the positive value of t that makes a factor zero:
t -7 = 0 ⇒ t = 7
The ball will land on the ground in 7 seconds.
by selling a purse for rupees 250 Rajan loses one sixth of what cost should find the cost price of the first her loss percentage
Answer:
300, 16.67%
Step-by-step explanation:
Let x be the cost price. x-(1/6)x=250. 5x/6=250. x=300. Losss percentage is 16.67%
write your answer as an integer or as a decimal rounded to the nearest tenth
Answer:
VW ≈ 4.0
Step-by-step explanation:
Using the sine ratio in the right triangle
sin35° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{VW}{VX}[/tex] = [tex]\frac{VW}{7}[/tex] ( multiply both sides by 7 )
7 × sin35° = VW , then
VW ≈ 4.0 ( to the nearest tenth )
Please help explanation if possible
Answer:
Step-by-step explanation:
so d = 2r which means r = 5cm.
A = πr^2 = π(5)^2 = 25π = (25)(3.14) = 78.5 cm^2.
So input 78.5
Answer:
see below
Step-by-step explanation:
so d = 2r which means r = 5cm.
A = πr^2 = π(5)^2 = 25π = (25)(3.14) = 78.5 cm^2.
So input 78.5
HOPE IT HELPS YOU
the value of 5/121^1/2
Answer:
√5/121
Step-by-step explanation:
formula: a^½=√a
(⁵/¹²¹)^½=√⁵/¹²¹
