Answer:
0.0618
Step-by-step explanation:
z = (x - μ)/σ, where
x is the raw score = 69
μ is the sample mean = population mean = 65
σ is the sample standard deviation
This is calculated as:
= Population standard deviation/√n
Where n = number of samples = 25
σ = 13/√25
σ = 13/5 = 2.6
Sample standard deviation = 2.6
z = (69 - 65) / 2.6
z = 4/2.6
z = 1.53846
Approximately to 2 decimal places = 1.54
Using the z score table to determine the probability,
P(x = 69) = P(z = 1.54)
= 0.93822.
The probability that the sample mean is greater than 69 is
P(x>Z) = 1 - 0.93822
P(x>Z) = 0.06178
Approximately to 4 decimal places = 0.0618
x/5=-2 . And how did you get it?
[tex]\dfrac{x}{5}=-2\\\\x=-10[/tex]
Answer:
[tex]\huge \boxed{{x=-10}}[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{x}{5} =-2[/tex]
We need the x variable to be isolated on one side of the equation, so we can find the value of x.
Multiply both sides of the equation by 5.
[tex]\displaystyle \frac{x}{5}(5) =-2(5)[/tex]
Simplify the equation.
[tex]x=-10[/tex]
The value of x that makes the equation true is -10.
If you randomly select a letter from the phrase "Sean wants to eat at Olive Garden," what is the probability that a vowel is randomly selected
Answer:
12/27
Step-by-step explanation:
Count all letters and all vowels then divide vowels by letters
The probability that a vowel is randomly selected in the experiment of selecting a letter from the phrase "Sean wants to eat at Olive Garden", is 4/9.
What is the probability of an event in an experiment?The probability of any event suppose A, in an experiment is given as:
P(A) = n/S,
where P(A) is the probability of event A, n is the number of favorable outcomes to event A in the experiment, and S is the total number of outcomes in the experiment.
How to solve the given question?In the question, we are given an experiment of selecting a letter from the phrase "Sean wants to eat at Olive Garden".
We are asked to find the probability that the selected letter is a vowel.
Let the event of selecting a vowel from the experiment of selecting a letter from the phrase "Sean wants to eat at Olive Garden" be A.
We can calculate the probability of event A by the formula:
P(A) = n/S,
where P(A) is the probability of event A, n is the number of favorable outcomes to event A in the experiment, and S is the total number of outcomes in the experiment.
The number of outcomes favorable to event A (n) = 12 (Number of vowels in the phrase)
The total number of outcomes in the experiment (S) = 27 (Number of letters in the phrase).
Now, we can find the probability of event A as:
P(A) = 12/27 = 4/9
∴ The probability that a vowel is randomly selected in the experiment of selecting a letter from the phrase "Sean wants to eat at Olive Garden", is 4/9.
Learn more about the probability of an event at
https://brainly.com/question/7965468
#SPJ2
change 4 5/9 from a mixed number to an improper fraction
Step-by-step explanation:
Hello, there!!
The answer would be 41/9.
The reason for above answer is to change any mixed fraction into improper fraction we should follow a simple step:
multiply the denominator with whole number.Add the answer (after mutiplied ).look here,
=[tex] \frac{4 \times 9 + 5}{9} [/tex]
we get 41/9.
Hope it helps...
The given fraction into the improper fraction should be [tex]\frac{41}{9}[/tex]
Given that,
The mixed number fraction is [tex]4 \frac{5}{9}[/tex]Computation:[tex]= 4\frac{5}{9}\\\\ = \frac{41}{9}[/tex]
Here we multiply the 9 with the 4 it gives 36 and then add 5 so that 41 arrives.
learn more about the fraction here: https://brainly.com/question/1301963?referrer=searchResults
A company has 8 mechanics and 6 electricians. If an employee is selected at random, what is the probability that they are an electrician
Answer:
[tex]Probability = \frac{3}{7}[/tex]
Step-by-step explanation:
Given
Electrician = 6
Mechanic = 8
Required
Determine the probability of selecting an electrician
First, we need the total number of employees;
[tex]Total = n(Electrician) + n(Mechanic)[/tex]
[tex]Total = 6 + 8[/tex]
[tex]Total = 14[/tex]
Next, is to determine the required probability using the following formula;
[tex]Probability = \frac{n(Electrician)}{Total}[/tex]
[tex]Probability = \frac{6}{14}[/tex]
Divide numerator and denominator by 2
[tex]Probability = \frac{3}{7}[/tex]
Hence, the probability of selecting an electrician is 3/7
Find the distance between the points. Give an exact answer and an approximation to three decimal places.
TI
(S.
(3.1, 0.3) and (2.7, -4.9)
Th
(Rd
Answer:
5.215 units (rounded up to three decimal places)
Step-by-step explanation:
To find the distance between points (3.1 , 0.3) and (2.7, -4.9)
We use the Pythagoras Theorem which states that for a right triangle of sides a,b and c then;
a² + b² = c² , Where c is the hypotenuse.
In our case, the distance between the two points is the hypotenuse of triangle formed by change in y-axis and change in x-axis.
The distance (hypotenuse) squared = (-4.9 - 0.3)² + (2.7 - 3.1)² = 27.04 + 0.16 = 27.2
Hypotenuse (the distance between) = [tex]\sqrt{27.2}[/tex] = 5.215 units (rounded up to three decimal places)
Factor this trinomial completely. -6x^2 +26x+20
Answer:
Step-by-step explanation:
-6x²+26x+20
=-2(3x²-13x-10)
=-2(3x²-15x+2x-10)
=-2[3x(x-5)+2(x-5)]
=-2(x-5)(3x+2)
The end of a hose was resting on the ground, pointing up an angle. Sal measured the path of the water coming out of the hose and found that it could be modeled using the equation f(x) = –0.3x2 + 2x, where f(x) is the height of the path of the water above the ground, in feet, and x is the horizontal distance of the path of the water from the end of the hose, in feet. When the water was 4 feet from the end of the hose, what was its height above the ground? 3.2 feet 4.8 feet 5.6 feet 6.8 feet
Answer: 3.2 feet.
Step-by-step explanation:
Given: The end of a hose was resting on the ground, pointing up an angle. Sal measured the path of the water coming out of the hose and found that it could be modeled using the equation[tex]f(x) = -0.3x^2 + 2x[/tex], where [tex]f(x)[/tex] is the height of the path of the water above the ground, in feet, and [tex]x[/tex] is the horizontal distance of the path of the water from the end of the hose, in feet.
At x= 4 , we get
[tex]f(x) = -0.3(4)^2 + 2(4)=-0.3(16)+8 =-4.8+8=3.2[/tex]
Hence, when the water was 4 feet from the end of the hose, its height above the ground is 3.2 feet.
Answer:
3.2 feet.
Step-by-step explanation:
The radius of a right circular cylinder is increasing at the rate of 7 in./sec, while the height is decreasing at the rate of 6 in./sec. At what rate is the volume of the cylinder changing when the radius is 20 in. and the height is 16 in.
Answer:
[tex]\approx \bold{6544\ in^3/sec}[/tex]
Step-by-step explanation:
Given:
Rate of change of radius of cylinder:
[tex]\dfrac{dr}{dt} = +7\ in/sec[/tex]
(This is increasing rate so positive)
Rate of change of height of cylinder:
[tex]\dfrac{dh}{dt} = -6\ in/sec[/tex]
(This is decreasing rate so negative)
To find:
Rate of change of volume when r = 20 inches and h = 16 inches.
Solution:
First of all, let us have a look at the formula for Volume:
[tex]V = \pi r^2h[/tex]
Differentiating it w.r.to 't':
[tex]\dfrac{dV}{dt} = \dfrac{d}{dt}(\pi r^2h)[/tex]
Let us have a look at the formula:
[tex]1.\ \dfrac{d}{dx} (C.f(x)) = C\dfrac{d(f(x))}{dx} \ \ \ (\text{C is a constant})\\2.\ \dfrac{d}{dx} (f(x).g(x)) = f(x)\dfrac{d}{dx} (g(x))+g(x)\dfrac{d}{dx} (f(x))[/tex]
[tex]3.\ \dfrac{dx^n}{dx} = nx^{n-1}[/tex]
Applying the two formula for the above differentiation:
[tex]\Rightarrow \dfrac{dV}{dt} = \pi\dfrac{d}{dt}( r^2h)\\\Rightarrow \dfrac{dV}{dt} = \pi h\dfrac{d }{dt}( r^2)+\pi r^2\dfrac{dh }{dt}\\\Rightarrow \dfrac{dV}{dt} = \pi h\times 2r \dfrac{dr }{dt}+\pi r^2\dfrac{dh }{dt}[/tex]
Now, putting the values:
[tex]\Rightarrow \dfrac{dV}{dt} = \pi \times 16\times 2\times 20 \times 7+\pi\times 20^2\times (-6)\\\Rightarrow \dfrac{dV}{dt} = 22 \times 16\times 2\times 20 +3.14\times 400\times (-6)\\\Rightarrow \dfrac{dV}{dt} = 14080 -7536\\\Rightarrow \dfrac{dV}{dt} \approx \bold{6544\ in^3/sec}[/tex]
So, the answer is: [tex]\approx \bold{6544\ in^3/sec}[/tex]
PLEASE HELP FAST!! The cone and the cylinder below have equal surface area. True or False??
Answer:
B. FALSE
Step-by-step explanation:
Surface area of cone = πr(r + l)
Where,
r = r
l = 3r
S.A of cone = πr(r + 3r)
= πr² + 3πr²
S.A of cone = 4πr²
Surface area of cylinder = 2πrh + 2πr² = 2πr(h + r)
Where,
r = r
h = 2r
S.A of cylinder = 2πr(2r + r)
= 4πr² + 2πr²
S.A of cylinder = 6πr²
The surface are of the cone and that of the cylinder are not the same. The answer is false.
Answer:false
Step-by-step explanation:
False
A population has a mean and a standard deviation . Find the mean and standard deviation of a sampling distribution of sample means with sample size n. nothing (Simplify your answer.) nothing (Type an integer or decimal rounded to three decimal places as needed.)
Complete Question
A population has a mean mu μ equals = 77 and a standard deviation σ = 14. Find the mean and standard deviation of a sampling distribution of sample means with sample size n equals = 26
Answer:
The mean of sampling distribution of the sample mean ( [tex]\= x[/tex]) is [tex]\mu_{\= x } = 77[/tex]
The standard deviation of sampling distribution of the sample mean ( [tex]\= x[/tex]) is
[tex]\sigma _{\= x} = 2.746[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 77[/tex]
The standard deviation is [tex]\sigma = 14[/tex]
The sample size is [tex]n = 26[/tex]
Generally the standard deviation of sampling distribution of the sample mean ( [tex]\= x[/tex]) is mathematically represented as
[tex]\sigma _{\= x} = \frac{ \sigma }{ \sqrt{n} }[/tex]
substituting values
[tex]\sigma _{\= x} = \frac{ 14}{ \sqrt{26} }[/tex]
[tex]\sigma _{\= x} = 2.746[/tex]
Generally the mean of sampling distribution of the sample mean ( [tex]\= x[/tex]) is equivalent to the population mean i.e
[tex]\mu_{\= x } = \mu[/tex]
[tex]\mu_{\= x } = 77[/tex]
How many dimensions does an angle have?
Answer:
the length has dimension 1, the area has the dimension 2, the volume has dimension 3, etc. And the angle has dimension 0.
Step-by-step explanation:
if 2500 amounted to 3500 in 4 years at simple interest. Find the rate at which interest was charged
Answer:
35%
Step-by-step explanation:
[tex]Principal = 2500\\\\Simple\:Interest = 3500\\\\Time = 4 \:years\\\\Rate = ?\\\\Rate = \frac{100 \times Simple \: Interest }{Principal \times Time}\\\\Rate = \frac{100 \times 3500}{2500 \times 4} \\\\Rate = \frac{350000}{10000}\\\\ Rate = 35 \%[/tex]
[tex]S.I = \frac{PRT}{100}\\\\ 100S.I = PRT\\\\\frac{100S.I}{PT} = \frac{PRT}{PT} \\\\\frac{100S.I}{PT} = R[/tex]
Answer:
35%
Step-by-step explanation:
I REALLY HOPE I HELPED
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
JUST A RANDOM GIRL WANTING TO HELP PEOPLE!
PEACE!
Which given answer is correct and how do you solve for it?
Answer:
b
Step-by-step explanation:
Answer the question :)
Answer:
A. -11
Step-by-step explanation:
In the function, replace x with -2
R(x) = x^2 - 3x - 1 ➡ R(-2) = (-2)^2 - 3 × 2 -1 = -11
The net of a triangular prism is shown below. What is the surface area of the prism? A. 128 cm^2 B. 152 cm^2 C. 176 cm^2 D. 304 cm^2
Answer:
B. 152 cm²
Step-by-step explanation:
To find the surface area using a net, do this:
Take apart the figure. We see that there are three rectangles and two triangles. Find the area of each ([tex]A=l*w[/tex]) and then add the values together:
The first rectangle on the left is the same as the one on the right.
[tex]5*8=40[/tex]
Two measures are 40 cm².
The middle rectangle is:
[tex]6*8=48[/tex]
48 cm²
The formula for the area of a triangle is [tex]A=\frac{1}{2}*b*h[/tex]:
[tex]A=\frac{1}{2}*6*4\\\\A=\frac{1*6*4}{2}\\\\A=\frac{24}{2}\\\\ A=12[/tex]
The area of the two triangles is 12 cm².
Now add the values:
[tex]40+40+48+12+12=152[/tex]
The area of the figure is 152 cm².
:Done
In training to run a half marathon, Jenny ran 2/5 hours on Tuesday, 11/6 hours on
Thursday, and 21/15 hours on Saturday. What is the total amount of hours that Jenny
ran this week? (Simplify your answer and state it as a mixed number.)
I
Answer:
Total hours that Jenny ran = 3.63 hours.
Step-by-step explanation:
Jenny ran on Tuesday for = 2/5 hours or 0.4 hours.
Time consumed to run on Thursday = 11/6 hours or 1.83 hours.
Time consumed to run on Saturday = 21/ 15 hours or 1.4 hours.
Here, the total hours can be calculated by just adding all the running hours. So the running hours of Tuesday, Thursday, and Saturday will be added to find the total hours.
Total hours that Jenny ran = 0.4 + 1.83 + 1.4 = 3.63 hours.
Simplify the following expression. (75x - 67y) - (47x + 15y)
Hi there! :)
Answer:
[tex]\huge\boxed{2(14x - 41y)}[/tex]
(75x - 67y) - (47x + 15y)
Distribute the '-' sign with the terms inside of the parenthesis:
75x - 67y - (47x - (15y))
75x - 67y - 47x - 15y
Combine like terms:
28x - 82y
Distribute out the greatest common factor:
2(14x - 41y)
[PLEASE HELP] Consider this function, f(x) = 2X - 6.
Match each transformation of f (x) with its descriptions..
Answer:
Find answer below
Step-by-step explanation:
f(x)=2x-6
Domain of 2x-6: {solution:-∞<x<∞, interval notation: -∞, ∞}
Range of 2x-6: {solution:-∞<f(x)<∞, interval notation: -∞, ∞}
Parity of 2x-6: Neither even nor odd
Axis interception points of 2x-6: x intercepts : (3, 0) y intercepts (0, -6)
inverse of 2x-6: x/2+6/2
slope of 2x-6: m=2
Plotting : y=2x-6
A triangle has sides with lengths of 5x - 7, 3x -4 and 2x - 6. What is the perimeter of the triangle?
Answer:
Step-by-step explanation:
perimeter of triangle=sum of lengths of sides=5x-7+3x-4+2x-6=10x-17
Answer:
10x - 17
Step-by-step explanation:
To find the perimeter of a triangle, add up all three sides
( 5x-7) + ( 3x-4) + ( 2x-6)
Combine like terms
10x - 17
can someone help me answer this??
Answer:
hkkr
need school the long said
Answer:
That would indicate 20.0 ml
id appreciate a rating thanks XP
What are the Links of two sides of a special right triangle with a 306090° and a Hypotenuse of 10
Answer:
Step-by-step explanation:
60°=2×30°
one angle is double the angle of the same right angled triangle.
so hypotenuse is double the smallest side.
Hypotenuse=10
smallest side=10/2=5
third side =√(10²-5²)=5√(2²-1)=5√3
Find the mean of the data summarized in the given frequency distribution. Compare the computed mean to the actual mean of 51.1 degrees. Low Temperature (◦F) 40−44 45−49 50−54 55−59 60−64 Frequency 3 6 13 7
Answer:
[tex]Mean = 53.25[/tex]
Step-by-step explanation:
Given
Low Temperature : 40−44 || 45−49 || 50−54 || 55−59 || 60−64
Frequency: --------------- 3 -----------6----------- 1-----------3--- -----7
Required
Determine the mean
The first step is to determine the midpoints of the given temperatures
40 - 44:
[tex]Midpoint = \frac{40+44}{2}[/tex]
[tex]Midpoint = \frac{84}{2}[/tex]
[tex]Midpoint = 42[/tex]
45 - 49
[tex]Midpoint = \frac{45+49}{2}[/tex]
[tex]Midpoint = \frac{94}{2}[/tex]
[tex]Midpoint = 47[/tex]
50 - 54:
[tex]Midpoint = \frac{50+54}{2}[/tex]
[tex]Midpoint = \frac{104}{2}[/tex]
[tex]Midpoint = 52[/tex]
55- 59
[tex]Midpoint = \frac{55+59}{2}[/tex]
[tex]Midpoint = \frac{114}{2}[/tex]
[tex]Midpoint = 57[/tex]
60 - 64:
[tex]Midpoint = \frac{60+64}{2}[/tex]
[tex]Midpoint = \frac{124}{2}[/tex]
[tex]Midpoint = 62[/tex]
So, the new frequency table is as thus:
Low Temperature : 42 || 47 || 52 || 57 || 62
Frequency: ----------- 3 --||- -6-||- 1-||- --3- ||--7
Next, is to calculate mean by
[tex]Mean = \frac{\sum fx}{\sum x}[/tex]
[tex]Mean = \frac{42 * 3 + 47 * 6 + 52 * 1 + 57 * 3 + 62 * 7}{3+6+1+3+7}[/tex]
[tex]Mean = \frac{1065}{20}[/tex]
[tex]Mean = 53.25[/tex]
The computed mean is greater than the actual mean
Suppose P( A) = 0.60, P( B) = 0.85, and A and B are independent. The probability of the complement of the event ( A and B) is: a. .4 × .15 = .060 b. 0.40 + .15 = .55 c. 1 − (.40 + .15) = .45 d. 1 − (.6 × .85) = .490
Answer: a. 0.4 × 0.15 = 0.060
Step-by-step explanation: Probability of the complement of an event is the one that is not part of the event.
For P(A):
P(A') = 1 - 0.6
P(A') = 0.4
For P(B):
P(B') = 1 - 0.85
P(B') = 0.15
To determine probability of A' and B':
P(A' and B') = P(A')*P(B')
P(A' and B') = 0.4*0.15
P(A' and B') = 0.06
Probability of the complement of the event is 0.060
The X- and y-coordinates of point P are each to be chosen at random from the set of integers 1 through 10.
What is the probability that P will be in quadrant II ?
О
1/10
1/4
1/2
Answer:
Ok, as i understand it:
for a point P = (x, y)
The values of x and y can be randomly chosen from the set {1, 2, ..., 10}
We want to find the probability that the point P lies on the second quadrant:
First, what type of points are located in the second quadrant?
We should have a value negative for x, and positive for y.
But in our set; {1, 2, ..., 10}, we have only positive values.
So x can not be negative, this means that the point can never be on the second quadrant.
So the probability is 0.
A patio 20 feet wide has a slanted roof, as shown in the figure. Find the length of the roof if there is an 8-inch overhang. Show all work and round the answer to the nearest foot. Be sure to label your answer appropriately. Then write a sentence explaining your answer in the context of the problem.
Answer:
[tex]Slanted\ Roof = 20.77\ ft[/tex]
Step-by-step explanation:
The question has missing attachment (See attachment 1 for complete figure)
Given
Width, W = 20ft
Let the taller height be represented with H and the shorter height with h
H = 10ft
h = 8ft
Overhang = 8 inch
Required
Determine the length of the slanted roof
FIrst, we have to determine the distance between the tip of the roof and the shorter height;
Represent this with
This is calculated by
[tex]D = H - h[/tex]
Substitute 10 for H and 8 for h
[tex]D = 10 - 8[/tex]
[tex]D = 2ft[/tex]
Next, is to calculate the length of the slant height before the overhang;
See Attachment 2
Distance L can be calculated using Pythagoras theorem
[tex]L^2 = 2^2 + 20^2[/tex]
[tex]L^2 = 4 + 400[/tex]
[tex]L^2 = 404[/tex]
Take Square root of both sides
[tex]\sqrt{L^2} = \sqrt{404}[/tex]
[tex]L = \sqrt{404}[/tex]
[tex]L = 20.0997512422[/tex]
[tex]L = 20.10\ ft[/tex] -------Approximated
The full length of the slanted roof is the sum of L (calculated above) and the overhang
[tex]Slanted\ Roof = L + 8\ inch[/tex]
Substitute 20.10 ft for L
[tex]Slanted\ Roof = 20.10\ ft + 8\ inch[/tex]
Convert inch to feet to get the slanted roof in feet
[tex]Slanted\ Roof = 20.1\ ft + 8/12\ ft[/tex]
[tex]Slanted\ Roof = 20.10\ ft + 0.67\ ft[/tex]
[tex]Slanted\ Roof = 20.77\ ft[/tex]
Hence, the total length of the slanted roof in feet is approximately 20.77 feet
The radius of a sphere is measured as 7 centimeters, with a possible error of 0.025 centimeter.
Required:
a. Use differentials to approximate the possible propagated error, in cm3, in computing the volume of the sphere.
b. Use differentials to approximate the possible propagated error in computing the surface area of the sphere.
c. Approximate the percent errors in parts (a) and (b).
Answer:
a) dV(s) = 15,386 cm³
b) dS(s) = 4,396 cm²
c) dV(s)/V(s) = 1,07 % and dS(s)/ S(s) = 0,71 %
Step-by-step explanation:
a) The volume of the sphere is
V(s) = (4/3)*π*x³ where x is the radius
Taking derivatives on both sides of the equation we get:
dV(s)/ dr = 4*π*x² or
dV(s) = 4*π*x² *dr
the possible propagated error in cm³ in computing the volume of the sphere is:
dV(s) = 4*3,14*(7)²*(0,025)
dV(s) = 15,386 cm³
b) Surface area of the sphere is:
V(s) = (4/3)*π*x³
dV(s) /dx = S(s) = 4*π*x³
And
dS(s) /dx = 8*π*x
dS(s) = 8*π*x*dx
dS(s) = 8*3,14*7*(0,025)
dS(s) = 4,396 cm²
c) The approximates errors in a and b are:
V(s) = (4/3)*π*x³ then
V(s) = (4/3)*3,14*(7)³
V(s) = 1436,03 cm³
And the possible propagated error in volume is from a) is
dV(s) = 15,386 cm³
dV(s)/V(s) = [15,386 cm³/1436,03 cm³]* 100
dV(s)/V(s) = 1,07 %
And for case b)
dS(s) = 4,396 cm²
And the surface area of the sphere is:
S(s) = 4*π*x³ ⇒ S(s) = 4*3,14*(7)² ⇒ S(s) = 615,44 cm²
dS(s) = 4,396 cm²
dS(s)/ S(s) = [ 4,396 cm²/615,44 cm² ] * 100
dS(s)/ S(s) = 0,71
Solve for y.
-1 = 8+3y
Simplify you answer as much as possible.
Answer:
-3
Step-by-step explanation:
[tex]8+3y = -1\\3y = -9\\y = -3[/tex]
Answer:
y = -3
Step-by-step explanation:
-1=3y+8
3y+8=-1
3y=-9
y=-3
solve for x: 5x+3+8x-4=90
Answer:
[tex]x = 7[/tex]
Step-by-step explanation:
We can solve the equation [tex]5x+3+8x-4=90[/tex] by isolating the variable x on one side. To do this, we must simplify the equation.
[tex]5x+3+8x-4=90[/tex]
Combine like terms:
[tex]13x - 1 = 90[/tex]
Add 1 to both sides:
[tex]13x = 91[/tex]
Divide both sides by 13:
[tex]x = 7[/tex]
Hope this helped!
Answer:
x = 7
Step-by-step exxplanation:
5x + 3 + 8x - 4 = 90
5x + 8x = 90 - 3 + 4
13x = 91
x = 91/13
x = 7
probe:
5*7 + 3 + 8*7 - 4 = 90
35 + 3 + 56 - 4 = 90
In this diagram, bac~edf. if the area of bac= 6 in.², what is the area of edf? PLZ HELP PLZ PLZ PLZ
Answer:
2.7 in²
Step-by-step explanation:
Since ∆BAC and ∆EDF are similar, therefore, the ratio of their area = square of the ratio of their corresponding side lengths.
Thus, if area of ∆EDF = x, area of ∆BAC = 6 in², EF = 2 in, BC = 3 in, therefore:
[tex] \frac{6}{x} = (\frac{3}{2})^2 [/tex]
[tex] \frac{6}{x} = (1.5)^2 [/tex]
[tex] \frac{6}{x} = 2.25 [/tex]
[tex] \frac{6}{x}*x = 2.25*x [/tex]
[tex] 6 = 2.25x [/tex]
[tex] \frac{6}{2.25} = \frac{2.25x}{2.25} [/tex]
[tex] 2.67 = x [/tex]
[tex] x = 2.7 in^2 [/tex] (nearest tenth)
Find the point(s) on the ellipse x = 3 cost, y = sin t, 0 less than or equal to t less than or equal to 2pi closest to the point(4/3,0) (Hint: Minimize the square of the distance as a function of t.) The point(s) on the ellipse closest to the given point is(are) . (Type ordered pairs. Use a comma to separate answers as needed.)
Answer and Step-by-step explanation:
The computation of points on the ellipse is shown below:-
Distance between any point on the ellipse
[tex](3 cos t, sin t) and (\frac{4}{3},0) is\\\\ d = \sqrt{(3 cos\ t - \frac{4}{3}^2) } + (sin\ t - 0)^2\\\\ d^2 = (3 cos\ t - \frac{4}{3})^2 + sin^2 t[/tex]
To minimize
[tex]d^2, set\ f' (t) = 0\\\\2(3cos\ t - \frac{x=4}{3} ).3(-sin\ t) + 2sin\ t\ cos\ t = 0\\\\ 8 sin\ t - 16 sin\ t\ cos\ t = 0\\\\ 8 sin\ t (1 - 2 cos\ t) = 0\\\\ sin\ t = 0, cos\ t = \frac{1}{2} \\\\ t= 0, \ 0, \pi,2\pi,\frac{\pi}{3} , \frac{5\pi}{3}[/tex]
Now we create a table by applying the critical points which are shown below:
t [tex]d^{2} = (3\ cos t - \frac{4}{3})^{2} + sin^{2}t[/tex]
0 [tex]\frac{25}{9}[/tex]
[tex]\pi[/tex] [tex]\frac{169}{9}[/tex]
[tex]2\pi[/tex] [tex]\frac{25}{9}[/tex]
[tex]\frac{\pi}{3}[/tex] [tex]\frac{7}{9}[/tex]
[tex]\frac{5\pi}{3}[/tex] [tex]\frac{7}{9}[/tex]
When t = [tex]\frac{\pi}{3}[/tex], x is [tex]\frac{3}{2}[/tex] and y is [tex]\frac{\sqrt{3} }{2}[/tex]. So, the required points are [tex](\frac{3}{2},\frac{\sqrt{3} }{2})[/tex]
When t = [tex]\frac{5\pi}{3}[/tex], x is [tex]\frac{3}{2}[/tex] and y is [tex]\frac{-\sqrt{3} }{2}[/tex]. So, the required points are [tex](\frac{3}{2},\frac{-\sqrt{3} }{2})[/tex]
