For engineering, it would be very useful to know Pythagorean theorem. You can use it to measure the tension in each ropes.
a test for diabetes results in a positive test in 95% of the cases where the disease is present and a negative test in 07% of the cases where the disease is absent. if 10% of the population has diabetes, what is the probability that a randomly selected person has diabetes, given that his test is positive
Answer:
0.9378 = 93.78% probability that a randomly selected person has diabetes, given that his test is positive.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Positive test
Event B: Person has diabetes.
Probability of a positive test:
0.95 out of 0.1(person has diabetes).
0.007 out of 1 - 0.1 = 0.9(person does not has diabetes). So
[tex]P(A) = 0.95*0.1 + 0.007*0.9 = 0.1013[/tex]
Probability of a positive test and having diabetes:
0.95 out of 0.1. So
[tex]P(A \cap B) = 0.95*0.1 = 0.095[/tex]
What is the probability that a randomly selected person has diabetes, given that his test is positive?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.095}{0.1013} = 0.9378[/tex]
0.9378 = 93.78% probability that a randomly selected person has diabetes, given that his test is positive.
Given the recursive formula shown, what are the first 4 terms of the sequence?
Answer:
5,20,80,320
Step-by-step explanation:
a1 = 5
an = 4 an-1
Let n = 2
a2 = 4 * a1 = 4*5 = 20
Let n = 3
a3 = 4 * a2 = 4*20 = 80
Let n = 4
a4 = 4 * a3 = 4*80 = 320
Mai is kayaking on a river that has a current of 2 miles per hour. If r represents her rate in calm water, then (r + 2) represents her rate with the current, and (r – 2) represents her rate against the current. Mai kayaks 2 miles downstream and then back to her starting point. Use the formula for time,
t
=
d
r
t=
r
d
, where d is the distance, to write a simplified expression for the total time it takes Mai to complete the trip.
4
(
r
+
2
)
(
r
−
2
)
h
o
u
r
s
(r+2)(r−2)
4
hours
4
r
(
r
+
2
)
h
o
u
r
s
(r+2)
4r
hours
4
r
(
r
+
2
)
(
r
−
2
)
h
o
u
r
s
(r+2)(r−2)
4r
hours
4
(
r
−
2
)
h
o
u
r
s
(r−2)
4
hours
Answer:
Plese explain your answer properly
Step-by-step explanation:
Answer:what is the answer
Step-by-step explanation:
sin4x.sin5x+sin4x.sin3x-sin2x.sinx=0
Recall the angle sum identity for cosine:
cos(x + y) = cos(x) cos(y) - sin(x) sin(y)
cos(x - y) = cos(x) cos(y) + sin(x) sin(y)
==> sin(x) sin(y) = 1/2 (cos(x - y) - cos(x + y))
Then rewrite the equation as
sin(4x) sin(5x) + sin(4x) sin(3x) - sin(2x) sin(x) = 0
1/2 (cos(-x) - cos(9x)) + 1/2 (cos(x) - cos(7x)) - 1/2 (cos(x) - cos(3x)) = 0
1/2 (cos(9x) - cos(x)) + 1/2 (cos(7x) - cos(3x)) = 0
sin(5x) sin(-4x) + sin(5x) sin(-2x) = 0
-sin(5x) (sin(4x) + sin(2x)) = 0
sin(5x) (sin(4x) + sin(2x)) = 0
Recall the double angle identity for sine:
sin(2x) = 2 sin(x) cos(x)
Rewrite the equation again as
sin(5x) (2 sin(2x) cos(2x) + sin(2x)) = 0
sin(5x) sin(2x) (2 cos(2x) + 1) = 0
sin(5x) = 0 or sin(2x) = 0 or 2 cos(2x) + 1 = 0
sin(5x) = 0 or sin(2x) = 0 or cos(2x) = -1/2
sin(5x) = 0 ==> 5x = arcsin(0) + 2nπ or 5x = arcsin(0) + π + 2nπ
… … … … … ==> 5x = 2nπ or 5x = (2n + 1)π
… … … … … ==> x = 2nπ/5 or x = (2n + 1)π/5
sin(2x) = 0 ==> 2x = arcsin(0) + 2nπ or 2x = arcsin(0) + π + 2nπ
… … … … … ==> 2x = 2nπ or 2x = (2n + 1)π
… … … … … ==> x = nπ or x = (2n + 1)π/2
cos(2x) = -1/2 ==> 2x = arccos(-1/2) + 2nπ or 2x = -arccos(-1/2) + 2nπ
… … … … … … ==> 2x = 2π/3 + 2nπ or 2x = -2π/3 + 2nπ
… … … … … … ==> x = π/3 + nπ or x = -π/3 + nπ
(where n is any integer)
Dr. Kingston predicted that swearing can help reduce pain. In the study, each participant was asked to plunge a hand into icy water and keep it there as long as the pain would allow. In one condition, the participants repeatedly yelled their favorite curse words while their hands were in the water. In the other condition the participants repeated a neutral word. The table below presents the amount of time that participants kept their hand in the ice in each condition.
Swear Words
Neutral Words
98
56
70
61
52
47
87
60
46
32
120
92
72
53
41
31
1. Calculate the mean for the Swear Words condition:_______________
Answer:
Step-by-step explanation:
First, we add them all up.
98+70+52+87+46+120+72+41 = 586
Now, we divide 586 by the number of things there are. 586 / 8 = 73.25.
The mean of the swear words condition is 73.25.
In the figure, triangles ABC and DEF are congruent.
Find the measure of DF.
a. 13m
b. 13m
c. 7m
d. 13.928m
Please show work to help me understand.
since the two triangles are congruent..
AB=ED
AC=FD(side opposite to the right angle)
FD=AC
•°•FD=13m
which of the following are ordered pairs for the given function f(x)=1+x.? (1,2) (3,3) (0,2) (1,0) (0,1)
Answer:
no,
(
1
,
0
)
is not an ordered pair of the function
f
(
x
)
=
1
+
x
.
Step-by-step explanation:
Ordered pairs are usually written in the form
(
x
,
y
)
by tradition.
so usingthe function,
f
(
x
)
=
1
+
x
we can rewrite it as,
y
=
1
+
x
any pair of x and y that satisfy this equation are solutions to the equation.
so subbing in
(
1
,
0
)
,
0
=
1
+
(
1
)
0
=
2
which is not true so the point does not make the function true.
It might be easier to see graphically,
graph{1+x [-10, 10, -5, 5]}
any combination of x and y on this line make the equation true and as such are an ordered pair of the function.
Answer:
Step-by-step explanation:
a grocery store cashier packed 2 carts of groceries equally into 12 paper bags. what fraction of a cart is in each bag?
Answer:
Step-by-step explanation:
(2 carts)/(12 bags) = (⅙ cart)/bag
The table shows a linear function.
Which equation represents the function?
x f(x)
-6 -1
-3 4
0 9
3 14
A. f(x)= -5/3x+9
B. f(x)= -5/3x-9
C. f(x)= 9x+5/3
D. f(x)= 5/3x+9
Answer:
D.
Step-by-step explanation:
Try A:
x = -6, f(x) = -1:-
f(-6) = -5/3(-6) + 9
= 10 + 9 = 19 NOT A.
Try B:
f(-3) = -5/3(-3) - 9
= 5 - 9 = -4 NOT B
Try C:
9(0) + 5/3 = 5/4 NOT C
Try D:
f(3) = 5 + 9 = 14
f(0) = 9, f(-6) = -1 and f(-3) = 4
A survey is conducted to determine the percentage of students at state universities who change their major at least once. In a study of 100 students 78% indicated that they graduated with a major different from the one with which they entered college. Determine a 90% confidence interval for the percentage of students who change their major.
Answer:
Step-by-step explanation:
Confidence Level - "P" values
90% 1.645
Confidence Interval - "P" values
(0.7119 , 0.8481 )
The length of a rectangle is (x+1) cm, and its width is 5 cm less than its length.
a) Express the area of the rectangle, A cm^2 , in terms of x.
b) The area of the rectangle is 24 cm^2. Calculate the length and width of the rectangle.
Answer:
a) x^2-3x-4(you also can express it as (x+1)(x-4))
b)The length is 8 cm, the width is 3 cm
Step-by-step explanation:
a) The length is x+1
The width is (x+1-5)= x-4
The area is the product of the length and the width
(x+1)(x-4)= x^2-3x-4
b) The formula for counting the area is x^2-3x-4
It is equal to 24
S0 x^2-3x-4=24
x^2-3x-28=0
a=1 b=-3 c=-28
D= b^2-4ac= 3^2-4*(-28)= 9+112= 121
sqrtD= 11
x1= (-b-sqrtD)/2a=(3-11)/2=-4 The length is -4+1=-3<0, but the length must be positive, this root isn't suitable.
x2= (-b+sqrtD)/2a=(3+11)/2=7 The length is 7+1=8 (it is suitable)
8-5=3 - The width
(52+2)-3x -6
help me with thanks
Answer:
48 - 3X
Step-by-step explanation:
( 52+2) - 3x - 6
54 - 3x - 6 So first we deal with the numbers in brackets and that is 52 + 2 giving us 54.
54 - 6 - 3x Then you simplify the expression that is collecting like terms so then we subtract 6 from 54
48 - 3x This is the final expression after simplifying
HOPE THIS HELPED
Need help please due in 1 hour and 30 mins
Answer:
the answer of that is number C
Find the length of the segment indicated.
A. 16.4
B. 11.4
C. 12.1
D. 13.3
using Pythagorean triplet
[tex]\\ \sf\longmapsto P^2=H^2-B^2[/tex]
[tex]\\ \sf\longmapsto x^2=19.6^2-15.4^2[/tex]
[tex]\\ \sf\longmapsto x^2=384.16-237.16[/tex]
[tex]\\ \sf\longmapsto x^2=147[/tex]
[tex]\\ \sf\longmapsto x=\sqrt{147}[/tex]
[tex]\\ \sf\longmapsto x=12.1[/tex]
Answer:
C.) 12.1
Step-by-step explanation:
I got it correct on founders edtell
Need the help thanks guys
Answer:
x=−5+√29 or x=−5−√29
Step
Let's solve your equation step-by-step.
x2+10x+10=14
Step 1: Subtract 14 from both sides.
x2+10x+10−14=14−14
x2+10x−4=0
For this equation: a=1, b=10, c=-4
1x2+10x+−4=0
Step 2: Use quadratic formula with a=1, b=10, c=-4.
x=
−b±√b2−4ac
2a
x=
−(10)±√(10)2−4(1)(−4)
2(1)
x=
−10±√116
2
x=−5+√29 or x=−5−√29
Write the equation of the line in fully simplified slope-intercept form.
From the graph, we can write that
The equatuon of line passes through (0,4) and
(-8,0) points.
So
[tex] \sf \: slope \: \: m = \frac{4 - 0}{0 - ( - 8)} = \frac{4}{8} = \frac{1}{2} \\ \therefore \green{\sf \: m = \frac{1}{2} }[/tex]
Intercept of Y-axis c = 4
So equation is :
[tex] \bf \: y = mx + c \\ \bf = > y = \frac{1}{2} x + 4 \\ \bf = > 2y = x + 4 \\ \bf= > \orange{ \boxed{ \bf \: x - 2y + 4 = 0}}[/tex]
a. Which number is greater? 1/4 or 5/4 -3/4 or 5/8
b. Which number is farther from 0? 1/4 or 5/4 -3/4 or 5/8
c. Is the number that is farther from 0 always the greater number?
Answer:
a. Which number is greater? 1/4 or 5/4 -3/4 or 5/8:
answer: 5/4
b. Which number is farther from 0? 1/4 or 5/4 -3/4 or 5/8:
answer: 5/4
c. Is the number that is farther from 0 always the greater number?:
answer: nah really.
A number can be further from zero but when it's a negative or positive. But negative value is less than zero.
[tex] {}^{ - } \infin \leqslant 0 \leqslant {}^{ + } \infin[/tex]
(a) answer is 5/4
(b) answer is 5/4
(c) No , when dealing with negative numbers , the number closer to zero is the bigger number . zero has the unique distinction of being neither positive nor negative . zero separates the positive number from the negative ones .
hope this will help you
mrk above ans braniliest
A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 55% salt and Solution B is 70% salt. She wants to obtain 30 ounces of a mixture that is 60% salt. How many ounces of each solution should she use?
Answer:
Let x = the number of ounces of Solution A
Let y = the number of ounces of Solution B
x + y = 180 y = 180 - x
.60x + .85y = .75(180)
.60x + .85y = 135 Multiply both sides of the equation by 100 to remove the decimal points.
60x + 85y = 13500
60x + 85(180 - x) = 13500
60x + 15300 - 85x = 13500
-25x = -1800
x = 72ounces
y = 180 - 72
y = 108 ounces
Step-by-step explanation:
Wyzant (ask an expert) solution on their website.
find the probability of being dealt 5 cards from a standard 52 card deck, and the cards are 6,7,8,9, and 10, all of the same suit. What is the probability of being dealt this hand is
Answer: 20/52 x 4/51 x 3/50 x 2/49 x 1/48 = .00000153908
Step-by-step explanation:
The probability of being dealt 5 cards from a standard 52 card deck, and the cards are 6,7,8,9, and 10 of the same suit is 0.00000153908
What is Probability?
The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible
The value of probability lies between 0 and 1
Given data ,
Let the number of cards in deck be = 52 cards
Total number of cards selected = 5
The number of ways of choosing 5 cards = ⁵²C₅
The cards selected are of the same suit
So , there are 4 ways to select them , Hearts , Clubs , Spades and Diamonds = ⁴C₁
And there is only one way to select the cards 6 , 7 , 8 , 9 , 10 = 1
Now , we use combination to select the cards in a deck,
So,
The probability of being dealt 5 cards from a standard 52 card deck, and the cards are 6,7,8,9, and 10, all of the same suit is calculated by,
P ( x ) = 1 / ⁵²C₅ x ⁴C₁ x 1
P ( x ) = 1 / 52! / ( 47! x 5! ) x 4! / 3! x 1
P ( x ) = 1 / ( 52 x 51 x 50 x 49 x 48 ) / ( 2 x 3 x 4 x 5 ) x 4
P ( x ) = 1 / ( 2598966 ) x 4
P ( x ) = 4 / 2598966
P ( x ) = 0.00000153908
Hence , The probability of being dealt 5 cards from a standard 52 card deck, and the cards are 6,7,8,9, and 10 of the same suit is 0.00000153908
To learn more about probability click :
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Verizon charges a $40 sign-up fee and the $60 a month for their new hotspot. T-Mobile
charges $100 sign-up fee and then $45 per month for their new hotspot. After how many
months of service will the two company's fees be the same?
Step-by-step explanation:
Start Unlimited:
$70 for one line
$60 for two lines
$45 for three lines
$35 for four lines
Play More Unlimited:
$80 for one line
$70 for two lines
$55 for three lines
$45 for four lines
Do More Unlimited:
$80 for one line
$70 for two lines
$55 for three lines
$45 for four lines
Get More Unlimited:
$90 for one line
$80 for two lines
$65 for three lines
$55 for four lines
Answer:
4 months
As we show that ;
40 + (60x * 4) = 280
100 + (45x * 4) = 280
but in simultaneous equations Verizon must be set equal to 240 being 80 x 3
and T mobile must be equal to 45 x 4 = 180
so that 240+ 180 = 420 to find 4
This would be a method on distribution as "60 sign up is 1/3 more than 1st equation.
Step-by-step explanation:
This is a simultaneous equation but trial and error is below to prove all is true.
step 1 make all equations same
40s + (60x) * 3 = 180x LCM = 80 x 3 = 1 1/3 of 60
100s + (45x) * 4 = 180x LCM = 45 x 4 = 1 of 45 as verizon charges 1/3 more sign up.
100s- 40s + 180x = (180x) = 240 + 180
60s + 180x = 420
s = 60
so our equations must each end with 420
when we get 60s + 180x = 420 then
420 - 180 = 240
240/60 = 4
x = 4 months
Verizon = 1st and T mobile = 2nd
40 + (60x * 5) = 340
100 + 45x * 5 = 325
with $15 out after 5 months so we try 6 months
40 + (60x * 6) = 400
100 + 45x * 6 = 370
and see this is increasing in difference, so try a smaller value of months..
We try 4 months;
40 + (60x * 4) = 280
100 + (45x * 4) = 280
How many times greater is
3.8 X 10^5 than
1.9 X 10^2
2
20
200
2000
Answer:
2 * 10^3 = 2000.
Step-by-step explanation:
3.8/1.9 * 10^5/10^2
= 2 * 10^3
Pls if anyone knows the answer that will be greatly appreciated :)
Answer:
For octagon =1080.......
Explanation:
180(8-2)
180×6
1080°
A store spends $10 for each pair of Brand X jeans and adds a 120% markup to the cost. What is the selling price of the jeans? (circle one)
Answer:
12
Step-by-step explanation:
120 divided by 100 =1.2 x 10
Help 50 point question
Answer:
1/3
Step-by-step explanation:
.444444444(repeating)- .111111111111(repeating)
.44444444......
-.11111111........
--------------------
.33333333........
Let x = .3333333.....
10x = 3.3333333.....
Subtract the first equation from the second
10x = 3.33333.....
-x = .33333.....
--------------------------
9x = 3
x = 3/9
x = 1/3
---------------------------
write down the length of the diameter of the circle
Answer:
Diameter = 2 × Radius
Step-by-step explanation:
Answer:
Step-by-step explanation:
The diameter of a circle is the length of the line through the center and touching two points on its edge. In the figure above, drag the orange dots around and see that the diameter never changes. The diameter is also a chord.
Jim is designing a seesaw for a children's park. The seesaw should make an angle of 30° with the ground, and the maximum height to which it should rise is 2 meters, as shown below:
A seesaw is shown with one end on the ground and the other in the air. The seesaw makes an angle of 30 degrees with the ground. The height of the seesaw from the ground, at the other end, is labeled 2 meters.
What is the maximum length of the seesaw?
3 meters
3.5 meter
4 meters
4.5 meters
You are giving the angle and opposite leg.
Using the law of sines:
Sin(angle) = opposite leg / hypotenuse
Sin(30) = 2/ hypotenuse
Hypotenuse = 2/sin(30)
Hypotenuse = 4 meters
The maximum length of the seesaw is : (C). 4 meters
Meaning of Maximum lengthMaximum length can be defined as the total distance between two point in consideration.
Maximum length can also be said to be the total sum of all the length along a distance.
In the case above, the hypotenuse side is the maximum length.
In conclusion, The maximum length of the seesaw is : 4 meters
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find out the area of the following composite figures
Help meee I’ll give 10 pts and brainliest!!!
Step-by-step explanation:
i) [tex]\overline{AB} = \sqrt{(x_A - x_B)^2 + (y_A - y_B)^2}[/tex]
[tex]\:\:\:\:\:\:\:=\sqrt{(2)^2 + (12)^2} = 12.3[/tex]
ii) [tex]m = \dfrac{y_A - y_B}{x_A - x_B} = \dfrac{-12}{2} = -6[/tex]
iii) [tex](\overline{x},\:\overline{y}) = \left(\dfrac{x_A + x_B}{2},\:\dfrac{y_A + y_B}{2}\right)[/tex]
[tex]\:\:\:\:\:\:\:=(3,\:-2)[/tex]
what is the lub of 0.2,0.23,0.234,0.2343,0.23434,0.234343
Answer:
The lub is 0.2343, while the glb is 0.2
Step-by-step explanation:
btw the 43 seems to be repeating for the lub.
Have a good day!
This answer was confusing for sure
Explanation:
Normally, y = cos(x) has a period of 2pi. This means that every 2pi horizontal units, the graph repeats itself. However, we can see that the period here is pi units instead.
One way to see this is to start at (0,1). This is a local max point. Move to its neighboring local max at (pi,1). We have moved pi units along the x axis and the cycle is finished, after which point the cycle repeats itself.
Since T = pi is the period, we then can say B = 2pi/T = 2pi/pi = 2
This is then plugged into y = A*cos(B(x-C))+D where
A = 1
C = 0
D = 0
That leads us to y = cos(2x)
Since the period is often connected to time values, it might help to think of this wave's oscillations occurring twice as often compared to y = cos(x). So that might help see why we replace the x with 2x.
