Answer:
2.53%
Step-by-step explanation:
all you have to do is 1 / 39.51 = about 0.0253 = 2.53%
Find the dimensions of the rectangle of maximum area with sides parallel to the coordinate axes that can be inscribed in the ellipse 4x^2 16y^2
Answer:
The answer is below
Step-by-step explanation:
Find the dimensions of the rectangle of maximum area with sides parallel to the coordinate axes that can be inscribed in the ellipse 4x² + 16y² = 16
Solution:
Given that the ellipse has the equation: 4x² + 16y² = 16
let us make x the subject of the formula, hence:
4x² + 16y² = 16
4x² = 16 - 16y²
Dividing through by 4:
x² = (16 - 16y²)/4
x² = 4 - 4y²
Taking square root of both sides:
[tex]x=\sqrt{4-4y^2 }\\[/tex]
The points of the rectangle vertices is at (x,y), (-x,y), (x,-y), (-x,-y). Hence the rectangle has length and width of 2x and 2y.
The area of a rectangle inscribed inside an ellipse is given by:
Area (A) = 4xy
A = 4xy
[tex]A=4(\sqrt{4-4y^2} )y\\\\A=4y\sqrt{4-4y^2}=4\sqrt{4y^2-4y^4} \\\\The\ maximum\ area\ of\ the\ rectangle\ is\ at\ \frac{dA}{dy}=0\\\\ \frac{dA}{dy}=4(\frac{4-8y^2}{\sqrt{4-4y^2} } )\\\\4(\frac{4-8y^2}{\sqrt{4-4y^2} } )=0\\\\4-8y^2=0\\\\8y^2=4\\\\y^2=1/2\\\\y=\frac{1}{\sqrt{2} }\\\\x=\sqrt{4-4(\frac{1}{\sqrt{2} })^2}=\sqrt{2}[/tex]
Therefore the length = 2x = 2√2, the width = 2y = 2/√2
how many HOURS are in d days and h hours?!
Answer:
24
Step-by-step explanation:
because its 24 gkrjkkmn lol
An integer between -1.6 and -0.4
PLEASE HELP!
|−1.25| + |2.5|
Explanation
-1.25+2.5=1.25
Answer:
1.25 is the answer .......
Step-by-step explanation:
hello will u be friend with me
Limit as x approaches 0 of (sin^2x)/x
Answer:
0Step-by-step explanation:
Given the expression
[tex]\lim_{x \to \ 0} \frac{sin^2x}{x}[/tex]
Substitute the value of x in the function
[tex]= \frac{sin ^2(0)}{0}\\= 0/0 (indeterminate) \\[/tex]
Apply l'hospital rule
[tex]\lim_{x \to \ 0} \frac{d/dx(sin^2x)}{d/dx(x)} \\= \lim_{x \to \ 0} \frac{(2sinxcosx)}{1} \\[/tex]
Substitute the value of x
= 2 sin(0)cos(0)
= 2 * 0 * 1
= 0
Hence the limit of the function is 0
Jermaine and Monica will usually both run 4.5 miles each time they go running. This month, Jermaine ran an additional 27 miles. Which answer choice shows an expression that represents the total distance Jermaine and Monica ran this month if j = the number of times that Jermaine ran and m = the number of times that Monica ran?
Answer:
4.5 (j + m) + 27
Step-by-step explanation:
An aircraft seam requires 20 rivets. The seam will have to be reworked if any of these rivets is defective. Suppose rivets are defective independently of one another, each with the same probability. (Round your answers to four decimal places.) (a) If 16% of all seams need reworking, what is the probability that a rivet is defective
Answer:
probability that a rivet is defective is 0.00868
Step-by-step explanation:
given data
rivets = 20
all seam need reworking P = 16% = 0.16
solution
we consider here probability of a defective rivet = p
and 0.16 = P [Seam needs reworking) = P (at least one rivet in the seam is defective)
so that for non-defective = 1 - P [all the rivets are non-defective]
and that will be here as = 1 - P [rivet 1 is non-defective, rivet 2 is non-defective, rivet 3 is non-defective,...............,rivet 20 is non-defective]
= [tex]1 - (p})^{20}[/tex] ....................1
so
1-0.16 = [tex]1 - (p})^{20}[/tex]
0.84 = [tex]1 - (p})^{20}[/tex]
[tex]0.84^{\frac{1}{20}}[/tex] = 1 - p
solve it we get
p = 0.00868
so, probability that a rivet is defective is 0.00868
What is the slope of the line?
Answer:
2
Step-by-step explanation:
Answer:
First the line is positive so you can eliminate all negative choices for slope
Now start from a random point that lands on the graph
Now it can’t be 1 becuase it has am extra box but that line isn’t on a point
Now 1/2 it can’t be becuase if you rise 1 and go right 2 it’ll not land ona. Point
But for 2, you rise up 2 and right 1 and you land on a point on the graph so the final answer is 2
144 ÷ a = 16
Find the value of a.
Answer:
9
Step-by-step explanation:
Move the variable to the other side of the equation
144 ÷ 16 = a
9 = a
Check:
144 ÷ a = 16 (Correct)
please give me the right answer i’ve been having trouble for an hour now
Answer:
B
Step-by-step explanation:
(x+4)(3x^2-7)
multiply and get 3x^3 +12x^2 -7x -28 which is anwser choice b
Sana bought a dress for $32.99 and two purses. The total cost for the three items was $57.97. What was the cost for one purse?
Answer:
$12.49
Step-by-step explanation:
cost of two purses = $57.97 - cost of dress = $57.97 - $32.99 = $24.98
cost of one purse = $24.98 ÷ 2 = $12.49
4. The ratio of the measures of the three angles in a triangle is 7:8:5, what is the
measure of the smallest angle?
Your answer
Step-by-step explanation:
let the angles be ' 7x, 8x and 5x'
as we know, the sum of all the angles of a triangle is 180 degree, so,
7x + 8x + 5x = 180
20 = 180
x = 180/2
x = 90 degrees
7x = 7 × 90 = 630 degree
8x = 8 × 90 = 720 degrees
5x = 5 × 90 = 540 degrees
therefore, 5x is the smallest degrees
Select the correct answer.
Which equation is true for the value b= 10?
O A. 2(b + 4) = 16
OB.
2(b + 2) = 40
OC. 316 - 2) = 24
OD. 2(8 + b) = 42
O E. 3(b - 4) = 20
Answer:
C. 3(b - 2) = 24Step-by-step explanation:
b = 10
Substitute b in every equation below and compare the results
A. 2(b + 4) = 16
2(10 + 4) = 2(14) = 28 ≠ 16, incorrectB. 2(b + 2) = 40
2(10 + 2) = 2(12) = 24 ≠ 40, incorrectC. 3(b - 2) = 24
3(10 - 2) = 3(8) = 24, correctD. 2(8 + b) = 42
2(8 + 10) = 2(18) = 36 ≠ 42, incorrectE. 3(b - 4) = 20
3(10 - 4) = 3(6) = 18 ≠ 20, incorrectAnswer:
C. 3(b - 2) = 24..
What is the quotient?
-4/5➗2
Can someone please help me write an equation for this graph? This is a different one.
Answer:
The equation of a line passing through points [tex](x_1,y_1)[/tex]and [tex](y_1,y_2)[/tex] is given by:
[tex]y-y_1 = \frac{(y_2-y_1)}{x_2-x_1}(x-x_1)[/tex]
According to question, the passing points of the line are (1,1) and (3,-3). So, its equation is given by:
[tex]y-1 = \frac{-3-1}{3-1} (x-1) \\or, y-1 = \frac{-4}{2}(x-1)\\or, 2y-2 = -4x+4\\or, 4x + 2y = 2+4\\or, 4x+2y = 6\\or, 2x+y = 3 is the required equation.[/tex]
CAN SOMEONE HELP WALLAHI THIS IS SO HARDDDDDD
Answer:
3[tex]\sqrt{5}[/tex]
__+ (-4) = -1 what is the missing number
Answer:
3
Step-by-step explanation:
_+(-4) = -1
_-4 = -1
_ = 3
The mayor of a town has proposed a plan for the construction of a new community. A political study took a sample of 1300 voters in the town and found that 45% of the residents favored construction. Using the data, a political strategist wants to test the claim that the percentage of residents who favor construction is more than 42%. Find the value of the test statistic. Round your answer to two decimal places.
Answer:
The value of the test statistic is t = 2.19.
Step-by-step explanation:
Central Limit Theorem
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Our test statistic is:
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the expected mean, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
Sample of 1300 voters:
This means that [tex]n = 1300[/tex]
Found that 45% of the residents favored construction.
This means that [tex]X = 0.45[/tex]
A political strategist wants to test the claim that the percentage of residents who favor construction is more than 42%.
This means that [tex]\mu = 0.42[/tex], and by the Central Limit Theorem:
[tex]\frac{\sigma}{\sqrt{n}} = s = \sqrt{\frac{0.42*0.58}{1300}} = 0.0137[/tex]
So, the test statistic is:
[tex]t = \frac{X - \mu}{s}[/tex]
[tex]t = \frac{0.45 - 0.42}{0.0137}[/tex]
[tex]t = 2.19[/tex]
The value of the test statistic is t = 2.19.
A pound of apples cost $1.35 a pound of cherries cost $3.62. How much will it cost to by 1.6 pounds of apples and 2.5 pounds of cherries?
Answer:
apples cost a total of 2.16
cherrys cost a total of 9.05
Step-by-step explanation:
1.35*1.6=2.16
3.62*2.5=9.05
Please help me answer this with the correct answer :)
Explain your answer
I will give braisnlt :)
Answer:
Hey
Step-by-step explanation:
Where is the question
Find the indicated term of each sequence by repeatedly multiplying the first term by the common ratio.
Enter your answer to 5 decimal places if necessary. Use a calculator.
A
-50, 35, -24.5,..;5th term
The 5th term of the sequence is 70
Answer:
Step-by-step explanation:
The first term here is -50 and the common ratio is 0.70. Note that the second term is 0.70(50) = 35.
The formula a(n) = a(0)*r^(n -1) becomes a(n) = -50*0.70^(n -1), and so
the 5th term is a(5) = -50*0.70^4 = -12.005
Sketch and shade the region in the xy-plane defined by the equation or inequalities.
|x| < 7 and |y| < 3 g
Answer:
attached below is the solution
Step-by-step explanation:
|x| < 7
= -7 < x < 7
| y | < 3
= -3< y < 3
attached below is the shaded region in the xy-plane
Question Help
9
s shown by the formula F= C+32. At what temperature will a Fahrenheit thermometer read the same as a Celsius thermometer
X
Answer:
It will read the same at F = -40.
Step-by-step explanation:
The relation between fahrenheit and celsius is given by the following equation:
[tex]C = \frac{5(F-32)}{9}[/tex]
At what temperature will a Fahrenheit thermometer read the same as a Celsius thermometer?
This is F for C = F. So
[tex]C = \frac{5(F-32)}{9}[/tex]
[tex]F = \frac{5(F-32)}{9}[/tex]
[tex]9F = 5F - 160[/tex]
[tex]4F = -160[/tex]
[tex]F = -\frac{160}{4}[/tex]
[tex]F = -40[/tex]
It will read the same at F = -40.
In a class of 26 students, 11 are female and 10 have an A in the class. There are 2 students who are female and have an A in the class. What is the probability that a student is a female given that they have an A?
The probability that a student is a female given that they have an A is 0.2
How to determine the probability?The given parameters are:
Female = 11
A= 10
Female and A = 2
The probability is calculated using:
P(Female given A) = P(female and A)/P(A)
This gives
P(Female given A) = 2/10
Simplify
P(Female given A) = 0.2
Hence, the probability that a student is a female given that they have an A is 0.2
Read more about probability at:
https://brainly.com/question/251701
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what is the answer? ;3
Can someone Help me please ?
9514 1404 393
Answer:
1) c, f
2) a, e
3) b, d
Step-by-step explanation:
If you think about the units associated with a coordinate (feet, for example), then you may recognize the following
a) each difference is of "feet", so each difference will have units of "feet". The ratio of "feet" to "feet" cancels the units, leaving a pure number. In this case, it is called "steepness" in selection e. Steepness is given by the slope formula (2).
__
b) The difference in parentheses has units of "feet" (as in (a)), so the square will be "square feet". The sum of two of those will still be "square feet" and the square root of that will be "feet". The units of the formula are those of distance, or length, matching selection d. Distance is given by the distance formula (3).
__
c) The form shown is an ordered pair. That is the same as the representation of a coordinate point, selection f. Coordinates of a point are given by the midpoint formula (1).
Select the correct answer from each drop-down menu.
Cameron is a member of a national gardening club. She asked 200 of her fellow members whether they use compost to fertilize their plants, and
45% responded favorably.
What is the 90% confidence interval for the true proportion of club members who use compost?
Answer:
0.45 and 0.5
Step-by-step explanation:
plato/edmentum
The 90% confidence interval for the true proportion of club members who use compost is given as (0.4, 0.507)
What is Confidence Interval?
This refers to the probability of a parameter falling across a set of values around the mean.
To find the 90% confidence interval,
Probability= 45%= 0.45
Level of significance= 90%
1-0.90
= 0.10
[tex]z\alpha /2 = z(0.1/2) = 0.05[/tex]
The value of 0.05
P0.05= 1.645
P ± 1.645 x [tex]\sqrt{P0-p/n}[/tex]
0.45 ± 1.645 * [tex]\sqrt{0.48 (1-0.45)/200}[/tex]
0.45 ± 1.645 * 0.035178
0.45 ± 0.0578
0.45 - 0.0578, 0.45 + 0.0578
(0.4, 0.507)
Read more about confidence intervals here:
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PLEASE HELP FOR 20 POINTS, Yesterday, Chang planted 6 trees that were each 8 feet tall in his yard. Chang projects the trees to grow at the following annual rates over the next 5 years. Assume that x represents the amount of years from when Chang planted the trees. Which of the following equations represent the height of each of the trees in 5 years? Select all that apply.
Answer:
Its oka linden
Step-by-step explanation:
Just cause
13-6=3x-14 whats the value of x
Answer:
x=9
Step-by-step explanation:
13+14=3x
27=3x
27/3=x
9=x
2+5xi-3y=14+3x-5yi.Find x and y
Question:
[tex]5x-3y=14[/tex]
[tex]3x-5y=2[/tex]
Find x and y
Answer:
[tex]x = 4[/tex]
[tex]y =2[/tex]
Step-by-step explanation:
Given
[tex]5x-3y=14[/tex] -- (1)
[tex]3x-5y=2[/tex] -- (2)
Required
Find x and y
We'll solve this using elimination method.
Multiply (1) by 3 and (2) by 5 to eliminate x
([tex]5x-3y=14[/tex]) * 3
([tex]3x-5y=2[/tex]) * 5
-------------------------------
[tex]15x - 9y = 42[/tex]
[tex]15x - 25y =10[/tex]
Subtract
[tex]15x - 9y = 42[/tex]
- ([tex]15x - 25y =10[/tex])
-----------------------
[tex]15x - 15x - 9y + 25y = 42 - 10[/tex]
[tex]- 9y + 25y = 42 - 10[/tex]
[tex]16y = 32[/tex]
Make y the subject
[tex]y = \frac{32}{16}[/tex]
[tex]y =2[/tex]
Substitute 2 for y in [tex]5x-3y=14[/tex]
[tex]5x - 3 * 2 = 14[/tex]
[tex]5x - 6 = 14[/tex]
Collect Like Terms
[tex]5x = 14+6[/tex]
[tex]5x = 20[/tex]
Make x the subject
[tex]x = \frac{20}{5}[/tex]
[tex]x = 4[/tex]
