Answer:
ang sentimeter ay ang tamang yunit ng pagsukat para sa pagsukat sa lugar ng isang panyo
Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt.
xy = 2
a. Find dy/dt, when x = 4, given that dx/dt = 13.
b. Find dx/dt, when x = 1, given that dy/dt = -9.
Answer:
a. [tex]\frac{dy}{dt} = -\frac{13}{8}[/tex]
b. [tex]\frac{dx}{dt} = \frac{9}{2}[/tex]
Step-by-step explanation:
To solve this question, we apply implicit differentiation.
xy = 2
Applying the implicit differentiation:
[tex]y\frac{dx}{dt} + x\frac{dy}{dt} = \frac{d}{dt}(2)[/tex]
[tex]y\frac{dx}{dt} + x\frac{dy}{dt} = 0[/tex]
a. Find dy/dt, when x = 4, given that dx/dt = 13.
x = 4
So
[tex]xy = 2[/tex]
[tex]4y = 2[/tex]
[tex]y = \frac{2}{4} = \frac{1}{2}[/tex]
Then
[tex]y\frac{dx}{dt} + x\frac{dy}{dt} = 0[/tex]
[tex]\frac{1}{2}(13) + 4\frac{dy}{dt} = 0[/tex]
[tex]4\frac{dy}{dt} = -\frac{13}{2}[/tex]
[tex]\frac{dy}{dt} = -\frac{13}{8}[/tex]
b. Find dx/dt, when x = 1, given that dy/dt = -9.
x = 1
So
[tex]xy = 2[/tex]
[tex]y = 2[/tex]
Then
[tex]y\frac{dx}{dt} + x\frac{dy}{dt} = 0[/tex]
[tex]2\frac{dx}{dt} - 9 = 0[/tex]
[tex]2\frac{dx}{dt} = 9[/tex]
[tex]\frac{dx}{dt} = \frac{9}{2}[/tex]
Question 11 of 45
Which similarity postulate or theorem can be used to verify that the two
triangles shown below are similar?
12
6 R
X 2 z
O A. Similarity cannot be determined,
B. SSS theorem
O C. AA postulate
D. SAS theorem
Answer:
You are only given a Side, an Angle, and then a side. So that is what I would choose. It can't be AA because you weren't given two angles. It can't be SSS because you weren't given 3 sides.
Step-by-step explanation:
ΔPQR and ΔXYZ are similar due to the SSS theorem.
Option B is the correct answer.
What is triangle congruency?There are ways to prove that two triangles are congruent.
- Side-Side-Side (SSS) Congruence.
The three sides of one triangle are equal to the corresponding three sides of another triangle.
- Side-Angle-Side (SAS) Congruence.
The two sides and the included angle of one triangle are equal to the corresponding two sides and included angle of another triangle.
- Angle-Side-Angle (ASA) Congruence.
The two angles and the included side of one triangle are equal to the corresponding two angles and included side of another triangle.
- Angle-Angle-Side (AAS) Congruence.
We have,
Similar triangles are triangles that have the same shape but may have different sizes.
Two triangles are similar if their corresponding angles are equal, and their corresponding sides are proportional.
When two triangles are similar, they have the same shape, but one may be larger or smaller than the other.
Now,
ΔPQR and ΔXYZ
PQ/XY = 12/4 = 3
PR/XZ = 6/2 = 3
Since the two sides are proportional,
QR/YZ will be proportional.
Now,
PQ/XY = PR/XZ = QR/YZ
ΔPQR and ΔXYZ are similar due to the SSS theorem.
Thus,
ΔPQR and ΔXYZ are similar due to the SSS theorem.
Learn more about triangle congruency here:
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An article claims that 12% of trees are infested by a bark beetle. A random sample of 1,000 trees were tested for traces of the infestation and found that 127 trees were affected. what is the value of the z-test statistic?
Answer:
The value of the z-test statistic is [tex]z = 0.68[/tex]
Step-by-step explanation:
An article claims that 12% of trees are infested by a bark beetle.
At the null hypothesis, we test if the proportion is of 12%, that is:
[tex]H_0: p = 0.12[/tex]
At the alternative hypothesis, we test if the proportion is different of 12%, that is:
[tex]H_1: p \neq 0.12[/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.
0.12 is tested at the null hypothesis:
This means that [tex]\mu = 0.12, \sigma = \sqrt{0.12*0.88}[/tex]
A random sample of 1,000 trees were tested for traces of the infestation and found that 127 trees were affected.
This means that [tex]n = 1000, X = \frac{127}{1000} = 0.127[/tex]
What is the value of the z-test statistic?
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.127 - 0.12}{\frac{\sqrt{0.12*0.88}}{\sqrt{1000}}}[/tex]
[tex]z = 0.68[/tex]
The value of the z-test statistic is [tex]z = 0.68[/tex]
Answer these please!!!
Answer:
(upper left) 3 triangles
(upper right) 5 triangles
(lower left) 9 rectangles
(lower right) next pattern is a grid that is 8 by 8.
The pattern is the previous side multiplied by 2
first block is 1x1
second block is 2x2
third block is 4x4
next block would be 8x8
Step-by-step explanation:
Find the volume of the cylinder pictured below. What is the exact volume in terms of pi?
If this the graph of f(x), then which of the following could be the graph of f-1(x)
The graph (C) represents the inverse function of f(x) if the graph of a function f(x) is given option (C) is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have a graph of f(x) is shown in the picture.
As we know, if f(x) has ordered double (x, y)
Then inverse of function g(x) must have ordered double (y, x)
From the given options graph (C) satisfy the condition.
Thus, the graph (C) represents the inverse function of f(x) if the graph of a function f(x) is given option (C) is correct.
Learn more about the function here:
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Answer:
the answer would be option C
a principios de un mes, el precio de la gasolina de 95 octanos era de 750 el litro. si aunmento en un 12% el dia 10 y luego disminiyo un 5% el dia 24 ¿cual es el precio a fin de mes?
Answer:
750/100*12=90. 640, 37.5 O 32, entonces seria 670.5 o 673, tu decides, porque no se si el aumento o disminuyo del segundo es a base del valor inicial, pero yo diria que si, asi que suerte! espero te ayude
The first five terms of a sequence are 34, 35, 36, 37, 38.
Write down the general term of the sequence
33+n
Hope it helps you...
YA is the angle bisector of ZXYZ. If mZXYZ = 52°, what is mZZYA?
Given:
[tex]YA[/tex] is the angle bisector of [tex]\angle XYZ[/tex].
[tex]m\angle XYZ=52^\circ[/tex]
To find:
The measure of [tex]m\angle ZYA[/tex].
Solution:
It is given that [tex]YA[/tex] is the angle bisector of [tex]\angle XYZ[/tex]. It means
[tex]m\angle XYA=m\angle ZYA[/tex] ...(i)
Now,
[tex]m\angle XYA+m\angle ZYA=m\angle XYZ[/tex]
[tex]m\angle ZYA+m\angle ZYA=52^\circ[/tex] [Using (i)]
[tex]2m\angle ZYA=52^\circ[/tex]
Divide both sides by 2.
[tex]m\angle ZYA=\dfrac{52^\circ}{2}[/tex]
[tex]m\angle ZYA=26^\circ[/tex]
Therefore, the required value is [tex]m\angle ZYA=26^\circ[/tex].
HW HELP ASAP PLZZZZZ
Answer:
ur ans is here...
Find the value of y and show work
Answer:
75
Step-by-step explanation:
∠K and ∠ R are congruent (equal)
Triangle Sum Theory - angles of all triangles add to 180
180 - 79 - 26 = 75
The 11th term of an progression is 25 and the sum of the first 4 terms is 49. The nth term of the progression is 49
1. Find the first term of the progression and the common difference
2. Find the value of n
Step-by-step explanation:
everything can be found in the picture
camila is saving money to buy a 5 piece drum set that costs $360. She already has 80.00 saved and can earn the rest of the money by washing 20 cars. If m represents how much she earns for washing each car, which of the following equations can be solved to find how much Camila is paid for washing each car? Does anyone know
A. 20m -80 = 360
B. m(20+80) = 360
C. 360-80=20m
D. 80 + m= 360
Answer:
c
Step-by-step explanation:
two plus two
the terminal side of 0 passes through the point (8,-7) what is the exact value of cos 0 in simplified form
Answer: [tex]\cos(\theta) = \frac{8\sqrt{113}}{113}\\\\[/tex]
=================================================
Work Shown:
x^2+y^2 = r^2
(8)^2+(-7)^2 = r^2
113 = r^2
r = sqrt(113)
The distance from (0,0) to (8,-7) is exactly sqrt(113) units.
This is the exact length of the hypotenuse of the right triangle.
Next, we do the following steps:
[tex]\cos(\text{angle}) = \frac{\text{adjacent}}{\text{hypotenuse}}\\\\\cos(\theta) = \frac{x}{r}\\\\\cos(\theta) = \frac{8}{\sqrt{113}}\\\\\cos(\theta) = \frac{8\sqrt{113}}{\sqrt{113}*\sqrt{113}}\\\\\cos(\theta) = \frac{8\sqrt{113}}{\sqrt{113*113}}\\\\\cos(\theta) = \frac{8\sqrt{113}}{\sqrt{113^2}}\\\\\cos(\theta) = \frac{8\sqrt{113}}{113}\\\\[/tex]
Side note: cosine is positive in quadrant Q4.
What is the value of 6 / x + 2x squared when x = 3
Answer:
8
Step-by-step explanation:
The equation will become 6/3+2(3)
-->6/3=2
-->Because of Order of Operation we will multiply the 2 and 3 before adding so 2(3) = 6
--> 6+2=8
Answer:
x=6
Step-by-step explanation:
when its squared you multiply by 2
(X+2)(X+3)(X+4)=990
I know that x=7 but how do i solve it without substitution?
ie. i don't want to use y=x+3 where 990=(y-1)(y)(y+1)
Step-by-step explanation:
foctorized 990 = 9×10×11
so, (X+2)(X+3)(X+4)=9×10×11
we can choose one of the factors, and get the answer with the same x values
x+2 = 9 , => x =7
x+3 = 10, => x = 7
x+4 = 11, => x = 7
You intend to estimate a population proportion with a confidence interval. The data suggests that the normal distribution is a reasonable approximation for the binomial distribution in this case. While it is an uncommon confidence level, find the critical value that corresponds to a confidence level of 97.1%.
Answer:
The critical value that corresponds to a confidence level of 97.1% is [tex]Z = 2.18[/tex].
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
97.1% confidence level
So [tex]\alpha = 0.029[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.029}{2} = 0.9855[/tex], so [tex]Z = 2.18[/tex].
The critical value that corresponds to a confidence level of 97.1% is [tex]Z = 2.18[/tex].
Use the exact values of the ratios and find the value of tan 45° + sin 30°
Answer:
1.5
tan45=1
sin30=1/2
so 1+1/2=1.5 or 3/2
At Western University the historical mean of scholarship examination scores for freshman applications is 900. Ahistorical population standard deviation \sigmaσ= 180 is assumed known.
Each year, the assistant dean uses a sample of applications to determine whether the mean examination score for the new freshman applications has changed.
a. State the hypotheses.
b. What is the 95% confidence interval estimate of the population mean examination
score if a sample of 200 applications provided a sample mean \overline x
x
= 935?
c. Use the confidence interval to conduct a hypothesis test. Using \alphaα= .05, what is your
conclusion?
d. What is the p-value?
Answer:
(910.053 ; 959.947)
Pvalue = 0.00596
Step-by-step explanation:
Given :
Population mean, μ = 900
Sample size, n = 200
Population standard deviation, σ = 180
The hypothesis :
H0 : μ = 900
H0 : μ ≠ 900
The 95% confidence interval:
Xbar ± Margin of error
Margin of Error = Zcritical * σ/√n
Since the σ is known, we use the z- distribution
Zcritical at 95% confidence = 1.96
Hence,
Margin of Error = 1.96 * 180/√200
Margin of Error = 24.947
95% confidence interval is :
935 ± 24.947
Lower boundary = 935 - 24.947 = 910.053
Upper boundary = 935 + 24.947 = 959.947
(910.053 ; 959.947)
Hypothesis test :
Test statistic
(935- 900) ÷ (180/√(200))
Test statistic = 2.750
Pvalue from Test statistic ;
Pvalue = 0.00596
Pvalue < α ; Reject H0 and conclude that score has changed
Hence, we can conclude that the score has changed
Create a system of equations whose solution is (2,-4).
Answer:
x=-4 and y=2 Those 2 equations when graphed give a vertical line and a horizontal line that intersect at the point (-4,2)
x+4=0 and y-2=0 are the same two lines.
or if you want more complicated systems of equations, with the same solution:
x+y=-2 and x-y=-6
in standard form, that's y=-x-2 and y=x+6 Graph those two lines and they intersect at (-4,2)
Those 2 lines are with slopes of -1 and +1. Those 2 equations are a system of equations
whose solution is x=-4 and y=2.
Rotate two perpendicular lines around the point (-4,2) and you get more systems of
equations with the same solution.
They don't have to be perpendicular though. x+y=-2 and x=-4 are two lines forming
a 45 degree angle, with the same solution (-4,2)
They don't have to be linear either. Take a parabola with the vertex (-4,2) and the line x=-4.
They intersect at the point (-4,2). That parabola could be the simple y=x2 shifted up and
to the left, to y-2 = (x+4)2 or y=x2+8x+18 or it could be any one of a family of parabolas with
the same vertex.
You could have 2 circles tangent at the point (-4,2) Endless circles could have that point
as a tangent and their equations having that same solution (-4,2)
Step-by-step explanation:
Hope this helps <3
A square-based tent covers an area of 64 square feet. What is the length of one side of the tent?
Answer:
8 feet
Step-by-step explanation:
A square's area can be expressed as l², with l representing one side of the tent. Therefore, as our area is 64, we can say that 64 = l². Taking the square root of both sides, we get that √64 = l, and l = 8 feet
((X + 2) + (y - 5) =1
Answer:
on like term
Step-by-step explanation:
x+2)=(y-5)=2+5=7
x-y{x-y]=7x-y
by Emmanuel okorie
CAN SOMEONE HELP WITH THE STEPS THXX
Write a recursive formula for the following sequence:10, 5, 0, -5,... *
Answer:
decrease by 5
Step-by-step explanation:
n= 10
then in sequence,
n= n-5
Need help on this question been stuck on it
Answer:
Exponential Function
Step-by-step explanation:
y values increase by x4
Answer:
exponential function
the ans is b
The Arizona Department of Transportation wishes to survey state residents to determine what proportion of the population would like to increase statewide highway speed to 75 from 65 mph. At least how many residents do they need to survey if they want to be at least 99% confident that the sample proportion is within 0.02 of the true proportion?
Answer:
They need to survey 4145 residents.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
At least how many residents do they need to survey if they want to be at least 99% confident that the sample proportion is within 0.02 of the true proportion?
This is n for which [tex]M = 0.02[/tex]. As we have no estimate for the proportion, we use [tex]\pi = 0.5[/tex]. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.02 = 2.575\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.02\sqrt{n} = 2.575*0.5[/tex]
[tex]\sqrt{n} = \frac{2.575*0.5}{0.02}[/tex]
[tex](\sqrt{n})^2 = (\frac{2.575*0.5}{0.02})^2[/tex]
[tex]n = 4144.1[/tex]
Rounding up:
They need to survey 4145 residents.
[3⋅5]7=
help pls anyone pls help me
What is the area of each semicircle of the following composite figure?
12 ft x 4 ft rectangle and a 4 ft circle
12.56 ft 2
6.28 ft 2
50.24 ft 2
25.12 ft 2
Estimate the unit selling price of an item for which the following data is available. Labor 15 hours at $26/hr Overhead 150% of labor Material Costs $89 each Packing Costs 10% of labor Subcontract Cost $11 each Sales Commission 5% of selling price Profit 10% of selling price
Answer:
$1281.1
Explanation:
Unit selling price is total cost plus markup(percentage profit on total cost price)
Assuming overhead is already apportioned to each product at $585 each
Total cost:
Labor 15hrs at $26/hr=15×26=$390
Overhead 150% of labor=150%×390=$585
Material Costs= $89
Packing Costs= 10%×390= $39
Subcontract Cost= $11
Sales Commission= 5% of selling price=$55.7
Total cost = $1169.7
Profit =10% of selling price= $111.4
Selling price =total cost + profit
= $1281.1
anyone help me, let's prove
Answer:
In my opinion the limit is equal to 1 not 0, sorry.
Step-by-step explanation: 6 25 13 43
lim n ⇒∞ ((2n - 1)/2n)
lim n ⇒∞ (2n/2n) - 1)/2n) 2n/2n = 1 1/∞ = 0
= 1 - 0
= 1
when I graphed the function I also got 1
