If y = y(x), then the derivative with respect to x is dy/dx. Differentiating both sides of the given equation gives
d/dx [4x ² + y ²] = d/dx [36]
8x + 2y dy/dx = 0
2y dy/dx = -8x
dy/dx = -4x/y
The turning points of the curve, taken as a function of x, are those points where the derivative vanishes.
-4x/y = 0 ===> x = 0
This value of x corresponds to two points on the curve,
4×0² + y ² = 36 ===> y ² = 36 ===> y = ±6
So there are two turning points, (0, -6) and (0, 6).
A golf ball is hit from ground level. Its path is modelled by the relation h(t) = -4.9 t2 + 27.2t , where h is the ball’s height above the ground, in meters, and t is the time, in seconds. Determine the time the ball is in the air.
what is the domain of f(x)=3x/x-1
help I was never taught how to do this im confused
Answer:
36
Step-by-step explanation:
Area of a triangle = (bh)/2
Where b = base length and h = height
Given base length: 18ft
Given height: 4ft
This being known let's define the variables
b = 18
h = 4
Now to find the area we simply plug in these values into the formula
Area = (18)(4)/2
Simplify multiplication 18 * 4 = 72
Area = 72/2
Simplify division
Area = 36
A random sample of 49 measurements from a population with population standard deviation σ1 = 4 had a sample mean of x1 = 11. An independent random sample of 64 measurements from a second population with population standard deviation σ2 = 5 had a sample mean of x2 = 14. Test the claim that the population means are different. Use level of significance 0.01. What distribution does the sample test statistic follow? Explain.
Answer:
Reject H0 and conclude that population means are different.
Step-by-step explanation:
H0: μ1 = μ2
H1: μ1 ≠ μ2
x1 = 11 ; σ1 = 4 ; n1 = 49
x2 = 14 ; σ2 = 5 ; n2 = 64
The test statistic :
(x1 - x2) / sqrt[(σ1²/n1 + σ2²/n2)]
Test statistic :
(11 - 14) / sqrt[(4²/49 + 5²/64)]
Test statistic :
-3 / √0.7171556
Test statistic = - 3.542
Using α = 0.01
The critical value Zα/2 ; Z0.01/2 = 2.58
Decison region :
Reject H0 : if Test statistic < Zcritical
Reject H0 : - 3.542 < - 2.58
Solve for x in this equation: 3/4+|5-x|=13/4
In sunlight, a vertical yardstick casts a 1 ft shadow at the same time that a nearby tree casts a 15 ft shadow. How tall is the tree? (Make a sketch to help solve the problem. Hint: 3ft equals one yard.)
A) 45 ft
B) 50 ft
C) 44 ft
D) 48 ft
Answer: A) 45 ft
Step-by-step
The yardstick is 3ft tall since 1 yard = 3ft. It is 3 times as tall as its shadow. The tree has a 15ft long shadow. The tree should also be 3 times as tall as its shadow. The tree is 15*3ft tall, so it is 45ft tall. I attached an image of the diagram I made.
If a 60 year old buys a $1000 life insurance policy at a cost of $50 and has a probability of 0.954 of living to age 61 find the expectation of the policy until the person reaches 61. round your answer to the nearest cent.
Answer:
The expectation of the policy until the person reaches 61 is of -$4.
Step-by-step explanation:
We have these following probabilities:
0.954 probability of a loss of $50.
1 - 0.954 = 0.046 probability of "earning" 1000 - 50 = $950.
Find the expectation of the policy until the person reaches 61.
Each outcome multiplied by it's probability, so:
[tex]E = -0.954*50 + 0.046*950 = -4[/tex]
The expectation of the policy until the person reaches 61 is of -$4.
Use the Wilcoxon matched-pairs signed rank test to determine whether there is a significant difference between the related populations represented by the data below. Assume a 5% level of significance and (differences = before - after).
Before After
5.6 6.4
1.3 1.5
4.7 4.6
3.8 4.3
2.4 2.1
5.5 6.0
5.1 5.2
4.6 4.5
3.7 4.5
a. What is the value of T= 36.5 is wrong
b. What is the value of T= 8.5 is wrong
c. What is the test statistic, T= 5 is wrong
Answer:
We fail to reject the null and conclude thattherw is no difference in population means.
Step-by-step explanation:
Before After
5.6 6.4
1.3 1.5
4.7 4.6
3.8 4.3
2.4 2.1
5.5 6.0
5.1 5.2
4.6 4.5
3.7 4.5
H0 : There is no difference in population
H1 : There population are not all equal
Difference, d = (Before - After)
d = -0.8, -0.2, 0.1, -0.5, 0.3, -0.5, -0.1, 0.1, -0.8
The test statistic :
T = dbar / (Sd/√n)
dbar = Σx / n = - 2.4 / 9 = 0.2666
Standard deviation of difference Sd; [√Σ(d - dbar)² / n-1]
Sd = 0.403 (using calculator)
Hence,
T = dbar / (Sd/√n)
-0.266 / (0.403/√9)
-0.266 / 0.1343333
= - 1.980
The Pvalue ;
df = n - 1 ; 9 - 1 = 8
Pvalue(-1.980, 8) = 0.083
α = 0.05
Since Pvalue > α; We fail to reject the null and conclude thattherw is no difference in population means.
I am need help and an explanation on how to read these graphs.
Answer:
i think its b
Step-by-step explanation:
Find the equation of the line that passes through (-1,2) and is perpendicular to 2y=2x−1. Leave your answer in the form y=mx+c
Answer:
y = x + 3
Step-by-step explanation:
given line in slope/intercept form:
y = x -1/2
slope of the perpendicular line = 1
equation of the line
y - 2 = x + 1
y = x + 3
Answer:
y=-x+1
Step-by-step explanation:
since the line is perpendicular to 2y=2x-1, this means that its slope with be the opposite reciprocal of the line 2y=2x-1 's slope.
first, we should find the slope of the line 2y=2x-1:
2y=2x-1
y=x-1/2
therefore, the slope of 2y=2x-1 is 1.
the opposite reciprocal of 1 is -1.
so far, we have this:
y=-x+b
to find b (the y-intercept) we can plug the point (-1,2) into the equation we have so far and solve for b.
y=-x+b
2=-(-1)+b
2=1+b
b=1
so, the equation of the line that passes through (-1,2) and is perpendicular to 2y=2x-1 is:
y=-x+b
If Mateo converts his anxiety score into a z-score, he can both indicate how many standard deviation units his score is from the mean and whether that his score is above or below the mean.
a. True
b. False
Answer:
The answer is "Option a"
Step-by-step explanation:
In the given scenario, the z-score value is used as the score which is used to shows that how many standard deviation units in this score were uses as the from mean and whenever this score is above or below by the mean, therefore the given statement is true.
A spinner is divided into 6 equal parts. These sections are labeled with a number 1, one section has a 2, one section has a 3, and one section has a 4. If the spinner is spun two times, what is the probability it will land on both 2 sides?
Answer:
[tex]\frac{1}{36} = 0.0278[/tex] = 2.78% probability it will land on both 2 sides.
Step-by-step explanation:
For each trial, there are only two possible outcomes. Either it lands on 2, or it does not. The probability of the spinner landing on two in a trial is independent of any other trial, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
One of the six sides is 2:
This means that [tex]p = \frac{1}{6}[/tex]
If the spinner is spun two times, what is the probability it will land on both 2 sides?
This is P(X = 2) when n = 2. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{2,2}.(\frac{1}{6})^{2}.(\frac{5}{6})^{0} = \frac{1}{36} = 0.0278[/tex]
[tex]\frac{1}{36} = 0.0278[/tex] = 2.78% probability it will land on both 2 sides.
The store employee works 35 hours per week. Which inequality can be used to find the dollar value, x, of weekly sales that the employee must make to earn more than $400 per week?
A researcher considers two methods for collecting data to determine if store-brand laundry detergents work as well as name-brand detergents.
Method 1: The researcher surveys shoppers as they enter a grocery store. The shoppers are asked which type of detergent they use and then rate the cleanliness of their laundry on a scale from 1 to 10 (with 10 being the cleanest). The ratings of the name-brand detergents are compared to the ratings of the store-brand detergent.
Method 2: The researcher creates 10 loads of soiled fabrics and washes 5 of the loads with name-brand detergent and the other 5 with store-brand detergent. Volunteers are asked to assess the cleanliness of the fabrics using a scale from 1 to 10 (with 10 being the cleanest), and the ratings of the name-brand detergents are compared to the ratings of the store-brand detergent.
Which method describes an observational study?
Method 2 is an observational study because volunteers assess the fabrics.
Method 1 is an observational study because many people can be surveyed.
Method 1 is an observational study because no attempt is made to influence results.
Both methods are observational studies because information on both types of detergent can be collected.
Not A.
Answer:
C. Method 1 is an observational study because no attempt is made to influence results.
Step-by-step explanation:
Based on the descriptions provided: Method 1 is an observational study because no attempt is made to influence the results. Option 3 is the correct answer.
An observational study is a type of study where researchers observe and collect data without actively intervening or manipulating any variables.
Method 1 involves surveying shoppers and asking them about their detergent use and laundry cleanliness ratings. The researcher is merely collecting data without intervening or manipulating any variables. The study relies on the natural behavior of shoppers and their responses.
Method 2, on the other hand, involves actively creating soiled fabrics and washing them with different detergents. This intervention introduces an element of manipulation, making it more of an experimental study than an observational one.
To know more about observational study :
https://brainly.com/question/29141360
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A small manufacturing company recently instituted Six Sigma training for its employees. Two methods of training were offered: online and traditional classroom. Management was interested in whether the division in which employees worked affected their choice of method. Below is a table summarizing the data.
Sales Quality Operations Total
Traditional 16 10 8 34
Online 35 23 44 102
Total 51 33 52 136
Required:
a. What is the probability that an employee chose online training?
b. What is the probability that an employee is in the Quality division and chose online training?
c. What is the probability that an employee chose online training given that he/she is in the Sales division?
Answer:
(a) [tex]P(Online\ Training) = 0.750[/tex]
(b) [tex]Pr = 0.169[/tex] --- Quality Division and Online Training
(c) [tex]P(A\ |\ B) = 0.686[/tex] --- Online Training given Sales Division
Step-by-step explanation:
Given
The two-way table
Solving (a): P(Online Training)
The total employee is:
[tex]Total = 136[/tex]
The employees for online training is:
[tex]Online\ Training = 102[/tex]
So, the probability is:
[tex]P(Online\ Training) = \frac{102}{136}[/tex]
[tex]P(Online\ Training) = 0.750[/tex]
Solving (b): P(Quality Division and Online Training)
The number of employees that choose quality Division and online training is 23
So, the probability is:
[tex]Pr = \frac{23}{136}[/tex]
[tex]Pr = 0.169[/tex]
Solving (c): P(Online Training | Sales Division)
This is calculated as:
Let:
[tex]A \to[/tex] Online training
[tex]B \to[/tex] Sales division
So, we have:
[tex]P(A\ |\ B) = \frac{n(A\ n\ B)}{n(B)}[/tex]
From the table:
[tex]n(A\ n\ B) =35[/tex]
[tex]n(B) = 16 + 35 = 51[/tex]
So, the probability is:
[tex]P(A\ |\ B) = \frac{35}{51}[/tex]
[tex]P(A\ |\ B) = 0.686[/tex]
If x+y=6 and xy =2find x³+y³(please help me fast with explanation also please) T^T
Answer: x³+y³=180
Step-by-step explain: let's remember the formula x³+y³=(x+y)(x²-xy+y²) and also x³+y³=(x+y)³-3xy(x+y) then [tex]\displaystyle\boldsymbol{ x^3+y^3=\underbrace{(x+y)^3}_{6}-3\underbrace{xy}_{2}\underbrace{(x+y)}_6}=\\\\6^3-3\cdot 2\cdot 6=216-36=180[/tex]
A ship sailed 30 kilometers in 1 1/2 hours. What is was its rate in kilometers per hour?
1) 20
2)30
3)45
4)90
5)Not enough information is given.
Answer:
20km/hr
Step-by-step explanation:
Given that a ship sailed 30km in one and a half hours. We need to find out the rate of ship in kilometres/hour . The rate is also called Speed.
Speed:- Distance travelled per unit time is called Speed .
Here , according to Question,
Distance = 30 km
Time = 1½ hrs .
We know that ,
[tex]\rm\implies Distance = Speed \times Time [/tex]
Subsequently ,
[tex]\rm\implies Time = \dfrac{Distance}{Time} [/tex]
Substitute the respective values ,
[tex]\rm\implies Rate =\dfrac{ 30km}{ 1.5 hrs } [/tex]
We can write 1.5 as 3/2 , therefore ,
[tex]\rm\implies Rate = \dfrac{ 2\times 30}{3} km/hr[/tex]
Simplify the RHS ,
[tex]\rm\implies\boxed{\blue{\rm Rate = 20\ km/hr}} [/tex]
Hence the Rate/Speed of the ship is 20km/hr .
5.For the function define by :
Please help
Answer:
Step-by-step explanation:
The breaking point for the graph (if there was one), is one. That means at one the function you use changes.
It goes from x^2 to 2x + 1
Answer A
Here's the catch. Where is 0? Zero is less than one. So what do you use? The answer is that f(x) = x^2
Answer B
if f(x) = x^2 then wherever you see an x, you put in 0.
f(x) = x^2
f(0) = 0^2
You could multiply 0 by itself a million times and it would still get 0.
f(0) = 0
Given C(4, 3) and D(-4, -3) are two points on a circle, centered at the origin. Given
that CD is a diameter of the circle?
a) Find the radius of the circle.
b) State the equation of the circle
Based on the information in table 3, how many females from a randomly selected population of 100,000 females live to the age of 38?
Answer:
According to the table, 97,825 females from a randomly selected population of 100,000 females live to the age of 38.
Step-by-step explanation:
Answer:
See image
Step-by-step explanation:
Plato
A game is played using one die. If the dio is rolled and shows 5, the player wins $35. If the die shows any number other than 5, the player wins nothing
a. If there is a charge of $7 to play the game, what is the game's expected value
Answer:
Let random variable "x" be a count of player gain.
X-values are: 4, -1
P(x=4) = 1/6; P(x= -1) = 5/6
---------------------------------
E(x) = (1/6)(4) + (5/6)(-1)
E(x) = [4-5]/6
E(x) = -1/6 = -17 cents
=============================
Cheers,
Stan H.
I need help with this
Answer:
A.
Step-by-step explanation:
A for apple....
Dwuhhhhhhhhhhhhh
Isss ezeewer dan anytwing
If there is a song that is 2 minutes and 58 seconds long and it plays 40 times how long does it play convert answer into seconds.
Answer: I got 7120 seconds
Step-by-step explanation:
There's 178 seconds in the song (for more context, I just converted the 2 minutes into seconds and added it with 58) then I multiplied it by the total amount of times it played (in this case, 40)
Hope this helps
a baceball team won 11 on its first 18 games at this rate how many games will the team win in a 162 game season
Answer:
Step-by-step explanation:
Set up the following proportion. x is the number of games you should win.
11/18 = x / 162
11*162 / 18 = x
x = 99 You likely would be out of the playoffs with a number like this.
A ladder is leaning against a building so that the distance from the ground to the top of the latter is 1 foot less than the length of the latter find the length of the latter is the distance from the bottom of the ladder to the building is 7 feet
Answer:
[tex]25\text{ feet}[/tex]
Step-by-step explanation:
The ladder, ground, and building form a right triangle where the vertical distance between the top of the ladder and the bottom of the ground is one leg, the horizontal distance between the bottom of the ladder and the building is another leg, and the length of the ladder is the hypotenuse.
For any right triangle, the Pythagorean Theorem states that the sum of the squares of both legs is equal to the hypotenuse squared ([tex]a^2+b^2=c^2[/tex]), where [tex]c[/tex] is the hypotenuse.
Let the length of the ladder be [tex]\ell[/tex] (hypotenuse of right triangle). The distance between the top of the ladder and the ground (vertical distance) can be represented as [tex]\ell -1[/tex].
From the Pythagorean Theorem, we then have:
[tex]7^2+(\ell-1)^2=\ell^2[/tex]
Expand using [tex](a-b)^2=a^2-2ab+b^2[/tex]:
[tex]49+\ell^2-2\ell+1=\ell^2[/tex]
Subtract [tex]\ell[/tex] from both sides and add [tex]2\ell[/tex] to both sides:
[tex]49+1=2\ell[/tex]
Combine like terms:
[tex]50=2\ell, \\2\ell =50[/tex]
Divide both sides by 2:
[tex]\ell=\frac{50}{2}=\boxed{25\text{ feet}}[/tex]
Therefore, the length of the ladder is 25 feet.
in the given figure poq is a line. if x=30 then find qor and ros
Answer:
[tex]2y + 3y + x = 180 \\ 5y + 30 = 180 \\ 5y = 180 - 30 \\ 5y = 150 \\ y = 30[/tex]
QOR =3Y
=3×30
=90°
ROS = 2Y
=2×30
=60°
Find the volume of the cylinder in terms of [tex]\pi[/tex].
h = 6 and r = 3.
a. 27[tex]\pi[/tex] in.³
b. 108[tex]\pi[/tex] in.³
c. 54[tex]\pi[/tex] in.³
d. 324[tex]\pi[/tex] in.³
Answer:
c. 54[tex]\pi[/tex] in.³
The volume of cylinder is 54[tex]\pi[/tex] in.³
Step-by-step explanation:
Given that :-
Height of cylinder , h = 6.Radius of cylinder, r = 3.To Find :-
Volume of cylinder.Solution:-
We use formula
Volume of cylinder = π × (radius)² × h
Substitute the value of radius and height.Volume of cylinder = π × ( 3)² × 6.
Evaluate the exponent.Volume of cylinder = π × 9 × 6.
Multiply we get ,Volume of cylinder = 54[tex]\pi[/tex] in.³
The formula we use,
→ Volume of cylinder = π × r² × h
It is given that,
→ Height (h) = 6 and radius (r) = 3.
Then we have to,
find the volume of the cylinder,
→ π × r² × h
→ π × 3² × 6
→ π × 9 × 6
→ 54π in.³
Thus, option (c) is the answer.
¿COMO PUTAS SE HACE i¹⁰⁰²?
Answer:
nose
Step-by-step explanation:
The composition of a US dollar bill is 3/4 cotton and 1/4 linen. What percent of a dollar bill is cotton?
Answer:
75% cotton
Step-by-step explanation:
3/4=75%
1/4=25%
total 100%
Determine the x- and y- intercepts for the graph defined by the given equation. y = 7x + 3 a. x-intercept is ( 3, 0) y-intercept is (0, negative StartFraction 3 Over 7 EndFraction) c. x-intercept is (0, negative StartFraction 3 Over 7 EndFraction) y-intercept is ( 3, 0) b. x-intercept is (negative StartFraction 3 Over 7 EndFraction, 0) y-intercept is (0, 3) d. x-intercept is (3, 0) y-intercept is (negative StartFraction 3 Over 7 EndFraction, 0)
Answer:
x-intercept is (-3/7, 0) and the y-intercept is at (0, 3)
Step-by-step explanation:
Given the function y = 7x + 3
The x-intercept occurs at y = 0. Substituting y = 0 into the expression, we will have:
0 = 7x + 3
7x + 3 = 0
7x = -3
x = -3/7
Similarly, the y-intercept occurs at x = 0. Substituting x = 0 into the expression, we will have:
y = 7(0) + 3
y = 0 + 3
y = 3
Hence the x-intercept is (-3/7, 0) and the y-intercept is at (0, 3)
