Answer:
Step-by-step explanation:
This is a related rates problem from calculus using implicit differentiation. The main equation is Pythagorean's Theorem. Basically, what we are looking for is [tex]\frac{dx}{dt}[/tex] when y = 6 and [tex]\frac{dy}{dt}=-2[/tex].
The equation for Pythagorean's Theorem is
[tex]x^2+y^2=c^2[/tex] where x and y are the legs and c is the hypotenuse. The length of the hypotenuse is 10, so when we find the derivative of this function with respect to time, and using implicit differentiation, we get:
[tex]2x\frac{dx}{dt}+2y\frac{dy}{dt}=0[/tex] and divide everything by 2 to simplify:
[tex]x\frac{dx}{dt}+y\frac{dy}{dt}=0[/tex]. Looking at that equation, it looks like we need a value for x, y, [tex]\frac{dx}{dt}[/tex] and [tex]\frac{dy}{dt}[/tex].
Since we are looking for [tex]\frac{dx}{dt}[/tex], that can be our only unknown and everything else has to have a value. So what do we know?
If we construct a right triangle with 10 as the hypotenuse and use 6 for y, we can solve for x (which is the only unknown we have, actually). Using Pythagorean's Theorem to solve for x:
[tex]x^2+6^2=10^2[/tex] and
[tex]x^2+36=100[/tex] and
[tex]x^2=64[/tex] so
x = 8.
NOW we can fill in the derivative and solve for [tex]\frac{dx}{dt}[/tex].
Remember the derivative is
[tex]x\frac{dx}{dt}+y\frac{dy}{dt}=0[/tex] so
[tex]8\frac{dx}{dt}+6(-2)=0[/tex] and
[tex]8\frac{dx}{dt}-12=0[/tex] and
[tex]8\frac{dx}{dt}=12[/tex] so
[tex]\frac{dx}{dt}=\frac{12}{8}=\frac{6}{4}=\frac{3}{2}=1.5 m/sec[/tex]
From a set of 5 nickels, 10 dimes and 15 quarters, six coins are removed at random without replacement.
a. Find the probability of not removing 6 quarters.
b. Find the probability of removing exactly 2 nickels, 2 dimes and 2 quarters.
Answer:
(a) 1 - (15 C 6) / (30 C 6)
(b) (5 C 2) x (10 C 2) x (15 C 2) / (30 C 2)
Step-by-step explanation:
Number of nickels = 5
Number of dimes = 10
Number of quarters = 15
(a) The probability of getting 6 quarters
= (15 C 6) / (30 C 6)
So, the probability of not getting 6 quarters = 1 - (15 C 6) / (30 C 6)
(b) Probability of getting 2 nickels , 2 dimes and 2 quarters
= (5 C 2) x (10 C 2) x (15 C 2) / (30 C 2)
2. Commission: A car saleswoman earns a
commission of 7% on each car she sells. How
much did she earn on the sale of a car for
$12,500?
Answer:
Step-by-step explanation:
commission = 0.7% of $12,500
= 0.007×$12,500
= $87.5
Given the points (-7, -1) and (8, 5) find the slope.
Answer:
(-7, -1) =(x1,y1)
(8, 5)=(x2,y2)
now
[tex]slope (m) = \frac{y2 - y1}{x2 - x1} [/tex]
[tex]or = \frac{5 - ( - 1)}{8 - ( - 7)} [/tex]
[tex]or = \frac{5 + 1} {8 + 7} [/tex]
[tex]or = \frac{6}{15} [/tex]
[tex]or = \frac{2}{5} [/tex]
Step-by-step explanation:
Explanation is in the attachmenthope it is helpful to you ☺️
find the degree of polynomial of the following
[tex]3x^{3} - x ^{5} [/tex]
Answer:
the degree is the value of the biggest exponent = 5 (fifth degree)
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
Since the highest power of x is 5, the degree of the polynomial x
3
−9x+3x
5
is 5.
Write the range of the function using interval notation.
Answer:
[-3, -1]
Step-by-step explanation:
The minimum y value is -3.
The maximum y value is -1.
-3 and -1 are included, so we use square brackets.
Answer: [-3, -1]
What is the perimeter of parallelogram WXYZ? StartRoot 5 EndRoot + StartRoot 17 EndRoot units 2 StartRoot 5 EndRoot + 2 StartRoot 17 EndRoot units 16 units 22 units
Answer:
b
Step-by-step explanation:
im doing it on edge right now
Math algebra 2 show you’re work plz
9514 1404 393
Answer:
(t, u, w) = (1, -2, -2)
Step-by-step explanation:
A graphing calculator makes short work of this, giving the solution as ...
(t, u, w) = (1, -2, -2)
__
There are many ways to solve this "by hand." Here's one of them.
Add the first and third equations. Their sum is ...
-3t +4w = -11 . . . . . [eq4]
Add this to twice the second equation. That sum is ...
(-3t +4w) +2(-4t -2w) = (-11) +2(0)
-11t = -11
t = 1
Substituting this into the second equation gives ...
-4(1) -2w = 0
w +2 = 0 . . . . divide by -2
w = -2 . . . . add -2
Substituting for t in the third equation lets us find u.
2(1) -2u = 6
-1 +u = -3 . . . . . divide by -2
u = -2 . . . . add 1
The solution is (t, u, w) = (1, -2, -2).
How to find the surface area of a cuboid
Answer:
To find the surface area of a cuboid we can also label the length, width and the height of the prism and use the formula SA=2LW+2LH+2HW to find the area of a cuboid
Answer:
202 cm²
Step-by-step explanation:
The opposite faces of a cuboid are congruent , then
SA = top/bottom + front/ back + sides , that is
SA = 2(9 × 4) + 2(9 × 5) + 2(4 × 5)
= 2(36) + 2(45) + 2(20)
= 72 + 90 + 40
= 202 cm²
If a driver averages 50 miles per hour, the number of hours it will take to drive 360 miles is
Divide total miles by speed:
360 / 50 = 7.2 hours
xp-q+1×xq-r+1×xr-p+1
Answer:
Look into the picture
Step-by-step explanation:
Let me know if there's something wrong to my answer
38. The ______ is also not convenient to use because the process of working for it produces large numbers due to squaring. 39. The ______ is the most reliable measure of variability. 40. The lesser the variability, the ______ is the mean.
Answer:
This Question Is From The Novel Of The Fantastic Mr.Fox
Q. Boggis , Bunce and Bean are Offering a reward for Mr.Fox , They are tired of Losing Chickens Geese and Cider , Create a Description And Drawing of Mr.Fox to allow him to be captured , use the word bank....
________________________________
Swift | Slay | Ginger | Rough | Fast
Thief. | Clever | Fur | Tail | Wife | Night
Cunning | Bushy | wiry | bush | Den | trick
________________________________
What angles can you construct using just a pair of compasses and a ruler?
Answer:
By using a pair of compasses and a ruler you can draw all angles
Please help, I’m running out of time. Please.
Answer:
which standard questions is it
Determine the domain and range of the function
Answer:
Domain: -4 ≤ x ≤ -1
Range: -1 ≤ y ≤ 3
Step-by-step explanation:
Hi there!
The domain is the possible x-values of a function.
The lowest x-value the function contains is -4, and the greatest is -1.
Therefore, the domain is -4 ≤ x ≤ -1.
The range is the possible y-values of a function.
The lowest y-value the function contains is -1, and the greatest is 3.
Therefore the range is -1 ≤ y ≤ 3.
I hope this helps!
What is the average rate of increase in enrollment
per
decade between 1950 and 2000?
Given:
The graph that represents the enrollment for college R between 1950 and 2000.
To find:
The average rate of increase in enrollment per decade between 1950 and 2000?
Solution:
The average rate of change of function f(x) over the interval [a,b] is:
[tex]m=\dfrac{f(b)-f(a)}{b-a}[/tex]
So, the average rate of increase in enrollment per year between 1950 and 2000 is:
[tex]m=\dfrac{f(2000)-f(1950)}{2000-1950}[/tex]
[tex]m=\dfrac{7-4}{50}[/tex]
[tex]m=\dfrac{3}{50}[/tex]
[tex]m=0.06[/tex]
It is given average rate of increase in enrollment per year between 1950 and 2000 is 0.06.
We need to find the average rate of increase in enrollment per decade between 1950 and 2000, So, multiply the average rate of increase in enrollment per year by 10.
[tex]0.06\times 10=0.6[/tex]
Therefore, the average rate of increase in enrollment per decade between 1950 and 2000 is 0.6.
I don’t understand these problems
Both E and F are sets.
E = {w | w ≤ 2}
means that E is the set of all numbers w satisfying the condition that w ≤ 2. In other words, E contains all real numbers less than and including 2.
Similarly,
F = {w | w > 9}
is the set of all real numbers strictly greater than 9.
The intersection of E and F, denoted E ∩ F, is the set that contains the overlap of the two sets, or all the numbers that are common to both sets. In this case, E ∩ F is the empty set; this is because all numbers small than 2 cannot be larger than 9, so E ∩ F = ∅.
The union of E and F, written as E ∪ F, is the set containing all elements from both sets. In interval notation, E = (-∞, 2] and F = (9, ∞), so E ∪ F = (-∞, 2] ∪ (9, ∞).
what is the measure of angle X in degrees
Answer:
If you are working with equilateral triangles, divide 180 by three to find the value of X. All of the angles of an equilateral triangle are equal. Solve for X in interesting lines by finding the value of one adjacent angle and subtracting it from 180 degrees.
Step-by-step explanation:
Expand (2x - 4)2 using the square of a binomial formula.
(x)2 + 2(x)(4) + 42
O (2x)2 + 2(2x)(4) - 42
O(x2 - 2(x)(4) - 42
(2x)2 - 2(2x)(4) + 42
Step-by-step explanation:
We have to expand,
[tex]\longrightarrow [/tex] (2x — 4)²
(a ― b)² = a² + b² ― 2ab[tex]\longrightarrow [/tex] (2x)² + (4)² ― 2(2x × 4)
[tex]\longrightarrow [/tex] 4x² + 16 ― 2(8x)
[tex]\longrightarrow [/tex] 4x² + 16 ― 16x
[tex]\longrightarrow [/tex] 4x² ― 16x + 16
Hence, solved!
Answer:
D is the correct answer (2x)2 – 2(2x)(4) + 42
Step-by-step explanation:
Convert the following to a simplified fraction. Show all your work.
Answer:
11/6
Step-by-step explanation:
What is the product of
(5^-4)(5^-3)
Answer:
option one is the correct answer
Answer:
1/625
Step-by-step explanation:
Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 144 millimeters, and a variance of 49 . If a random sample of 46 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by more than 2 millimeters? Round your answer to four decimal places.
Answer:
0.0524 = 5.24% probability that the sample mean would differ from the population mean by more than 2 millimeters.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
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.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean diameter of 144 millimeters, and a variance of 49.
This means that [tex]\mu = 144, \sigma = \sqrt{49} = 7[/tex]
Sample of 46:
This means that [tex]n = 46, s = \frac{7}{\sqrt{46}}[/tex]
Wat is the probability that the sample mean would differ from the population mean by more than 2 millimeters?
Above 144 + 2 = 146 or below 144 - 2 = 142. Since the normal distribution is symmetric, these probabilities are equal, which means that we find one of them and multiply by two.
Probability the sample mean is below 142:
p-value of Z when X = 142, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{142 - 144}{\frac{7}{\sqrt{46}}}[/tex]
[tex]Z = -1.94[/tex]
[tex]Z = -1.94[/tex] has a p-value of 0.0262
2*0.0262 = 0.0524
0.0524 = 5.24% probability that the sample mean would differ from the population mean by more than 2 millimeters.
)
Gos
1. Select all the relations that represent a
function.
(3,2), (2,1), (3,9) (4,7)
(1,7), (2,2), (3,5) (4,8)
(2,6), (6,5), (3,2) (5,3)
(4,3), (3,3), (2,3) (1,3)
(2,2), (2,5), (2,1) (2,3)
Answer:
(1,7), (2,2), (3,5) (4,8)
(2,6), (6,5), (3,2) (5,3)
(4,3), (3,3), (2,3) (1,3)
Step-by-step explanation:
those represent functions b/c the domain of the relation is not written twice
Hope that'll help!
SOMEONE HELP PLEASE! So for this problem the answer I got is $4000. Is that the correct or incorrect answer? Can someone please help me if it is the incorrect answer. Thank you for your time.
Answer:
You're correct
Step-by-step explanation:
Suppose a large shipment of televisions contained 9% defectives. If a sample of size 393 is selected, what is the probability that the sample proportion will differ from the population proportion by less than 3%
Answer:
0.9624 = 96.24% probability that the sample proportion will differ from the population proportion by less than 3%
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
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.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
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]
Suppose a large shipment of televisions contained 9% defectives
This means that [tex]p = 0.09[/tex]
Sample of size 393
This means that [tex]n = 393[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.09[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.09*0.91}{393}} = 0.0144[/tex]
What is the probability that the sample proportion will differ from the population proportion by less than 3%?
Proportion between 0.09 - 0.03 = 0.06 and 0.09 + 0.03 = 0.12, which is the p-value of Z when X = 0.12 subtracted by the p-value of Z when X = 0.06.
X = 0.12
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.12 - 0.09}{0.0144}[/tex]
[tex]Z = 2.08[/tex]
[tex]Z = 2.08[/tex] has a p-value of 0.9812
X = 0.06
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.06 - 0.09}{0.0144}[/tex]
[tex]Z = -2.08[/tex]
[tex]Z = -2.08[/tex] has a p-value of 0.0188
0.9812 - 0.0188 = 0.9624
0.9624 = 96.24% probability that the sample proportion will differ from the population proportion by less than 3%
What is y=-2(x+3)^2+2
Answer:
y = -2(x + 3)² + 2
y = 2{ -(x + 3)²+ 1}
y = 2{ -(x² + 6x + 9) + 1}
y = 2{ -x² - 6x - 9 + 1}
y = 2{ -x² - 6x - 8 }
y = -2 { x² + 6x + 8}
OR
y = -2{(x + 4)(x + 2)}
Choose the system of inequalities that best matches the graph below.
Answer:
"D" is the correct answer
Step-by-step explanation:
Find the measure of ∠C in the image below. 60+55+m∠C=180
Answer:
angle C= 65 degree
Step-by-step explanation:
60+55+x= 180
115+x= 180
x= 180-115
x= 65
angle C= 65 degree
Please mark me as brainliest.
Is the point (-3,2) part of the solution set to the system y < -4x - 3, x + 8y > 7
Answer:
Yes
Step-by-step explanation:
If you replace each x with -3 and each y with 2 you get:
1) 2<-4*(-3)
2<12
True
2) -3+8*2>7
13>7
True
Therefore the point is part of the solution set
I will mark you brainliest if you provide evidence you know what your doing
Work out the problem and make the answer clear
Option C
SOLUTION:
We need to find the value of B - CF
First find the value CF:
[tex]CF=\left[\begin{array}{ccc}12&0&1.5\\1&-6&7\\\end{array}\right] \left[\begin{array}{ccc}-2&0\\0&8\\2&1\end{array}\right][/tex]
[tex]CF=\left[\begin{array}{ccc}12(-2)+0 *0+1.5*2&12*0+0.8+1.5*1\\1*(-2)+(-6)*0+7.2&1*0+(-6)*8+7.1\\\end{array}\right][/tex]
[tex]CF=\left[\begin{array}{ccc}-21&1.5\\12&-41\\\end{array}\right][/tex]
Now find value of B - CF:
[tex]B-CF=\left[\begin{array}{ccc}2&8\\6&3\\\end{array}\right] -\left[\begin{array}{ccc}-21&1.5\\12&-41\\\end{array}\right][/tex]
[tex]B-CF=\left[\begin{array}{ccc}23&6.5\\-6&44\\\end{array}\right][/tex]
∴ the value of B - CF is [tex]\left[\begin{array}{ccc}23&6.5\\-6&44\\\end{array}\right][/tex]
I hope this helps....
If the rectangle were translated three units down, then reflected across the y-axis, what would be the coordinates of point D ?
Answer
all y values change sign that is reflection over x axis SKETCH IT !!!!
More