How can you create and graph a piecewise function that has restrictions on the domain?
Answer:
Use inequalities.
At certain x values.
Step-by-step explanation:
[tex]3 \leqslant x \leqslant 6[/tex]
[tex] - \infty < x < \infty [/tex]
[tex]x = 6[/tex]
rose says the quantity of four dollars is a terminating decimal. Sharon says it is an integer.Do you agree witheither of them
Answer:
Agree with Sharon
Step-by-step explanation:
A terminating decimal includes numbers beyond the decimal point.
An integer is a whole number.
4 is a whole number so it's an integer which is what Sharon said.
The number of defective circuit boards coming off a soldering machine follows a Poisson distribution. During a specific ten-hour period, one defective circuit board was found. (a) Find the probability that it was produced during the first hour of operation during that period. (Round your answer to four decimal places.) (b) Find the probability that it was produced during the last hour of operation during that period. (Round your answer to four decimal places.) (c) Given that no defective circuit boards were produced during the first five hours of operation, find the probability that the defective board was manufactured during the sixth hour. (Round your answer to four decimal places.)
Answer:
a) the probability that the defective board was produced during the first hour of operation is [tex]\frac{1}{10}[/tex] or 0.1000
b) the probability that the defective board was produced during the last hour of operation is [tex]\frac{1}{10}[/tex] or 0.1000
c) the required probability is 0.2000
Step-by-step explanation:
Given the data in the question;
During a specific ten-hour period, one defective circuit board was found.
Lets X represent the number of defective circuit boards coming out of the machine , following Poisson distribution on a particular 10-hours workday which one defective board was found.
Also let Y represent the event of producing one defective circuit board, Y is uniformly distributed over ( 0, 10 ) intervals.
f(y) = [tex]\left \{ {{\frac{1}{b-a} }\\\ }} \right _0[/tex]; ( a ≤ y ≤ b )[tex]_{elsewhere[/tex]
= [tex]\left \{ {{\frac{1}{10-0} }\\\ }} \right _0[/tex]; ( 0 ≤ y ≤ 10 )[tex]_{elsewhere[/tex]
f(y) = [tex]\left \{ {{\frac{1}{10} }\\\ }} \right _0[/tex]; ( 0 ≤ y ≤ 10 )[tex]_{elsewhere[/tex]
Now,
a) the probability that it was produced during the first hour of operation during that period;
P( Y < 1 ) = [tex]\int\limits^1_0 {f(y)} \, dy[/tex]
we substitute
= [tex]\int\limits^1_0 {\frac{1}{10} } \, dy[/tex]
= [tex]\frac{1}{10} [y]^1_0[/tex]
= [tex]\frac{1}{10} [ 1 - 0 ][/tex]
= [tex]\frac{1}{10}[/tex] or 0.1000
Therefore, the probability that the defective board was produced during the first hour of operation is [tex]\frac{1}{10}[/tex] or 0.1000
b) The probability that it was produced during the last hour of operation during that period.
P( Y > 9 ) = [tex]\int\limits^{10}_9 {f(y)} \, dy[/tex]
we substitute
= [tex]\int\limits^{10}_9 {\frac{1}{10} } \, dy[/tex]
= [tex]\frac{1}{10} [y]^{10}_9[/tex]
= [tex]\frac{1}{10} [ 10 - 9 ][/tex]
= [tex]\frac{1}{10}[/tex] or 0.1000
Therefore, the probability that the defective board was produced during the last hour of operation is [tex]\frac{1}{10}[/tex] or 0.1000
c)
no defective circuit boards were produced during the first five hours of operation.
probability that the defective board was manufactured during the sixth hour will be;
P( 5 < Y < 6 | Y > 5 ) = P[ ( 5 < Y < 6 ) ∩ ( Y > 5 ) ] / P( Y > 5 )
= P( 5 < Y < 6 ) / P( Y > 5 )
we substitute
[tex]= (\int\limits^{6}_5 {\frac{1}{10} } \, dy) / (\int\limits^{10}_5 {\frac{1}{10} } \, dy)[/tex]
[tex]= (\frac{1}{10} [y]^{6}_5) / (\frac{1}{10} [y]^{10}_5)[/tex]
= ( 6-5 ) / ( 10 - 5 )
= 0.2000
Therefore, the required probability is 0.2000
the area of a triangular garden is 200 square feet. If the base is 30 feet more than its height, what is the base of the garden?
The base of the triangular garden is calculated as 40 ft
The given parameters include:
the area of the triangular garden, A₁ = 200 ft²let the height of the triangular garden = hthe base of the triangular garden, b = 30 ft + hThe area of a triangle is given as;
[tex]Area \ = \frac{1}{2} \times \ base \times \ height\\\\A = \frac{1}{2} bh\\\\2A = bh\\\\b = \frac{2A}{h} \\\\Recall, \ b= 30 + h\ \ \ and \ A = 200\\\\30+ h = \frac{2(200)}{h} \\\\30 \ + h = \frac{400}{h} \\\\30h + h^2 = 400\\\\h^2 + 30h - 400= 0\\\\Factorize \ the \ above \ expression\\\\h^2 + 40h- 10h- 400 = 0\\\\h(h + 40) - 10(h + 40) = 0\\\\(h- 10)(h+40)= 0\\\\h = 10 \ \ or \ \ -40\\\\since\ the \ height \ can't \ b e\ negative\\\\h = 10 \ ft\\\\[/tex]
Now solve for 'b' = 30 ft + 10 ft = 40 ft
Therefore, the base of the garden is 40 ft
To learn more about area of a triangle visit: https://brainly.com/question/2391510
All of my friends like fruit. 9 friends like bananas, 8 friends like oranges, and 7 friends like plums. 5 friends like both bananas and oranges, 3 friends like both bananas and plums, 4 friends like both oranges and plums, and 2 friends like bananas, oranges and plums. How many friends do I have?
Answer:
you have 38 friends
Step-by-step explanation:
because you have to add I think so
Answer:
38 friends
Step-by-step explanation:
How many of each coin does he have?
_____nickels
_____quarters
Use the order of operations to evaluate this expression (-2+1)
Answer:
12
Step-by-step explanation:
2²×3
I hope its correct
Answer:
4
[tex] {( - 2 + 1)}^{2} + 5(12 \div 3) - 9 \\ 2 + 1 + 5 \times 4 - 9 \\ 3 + 20 - 9 \\ 23 - 9 \\ 14[/tex]
Write the greatest and smallest number of 8 suing following digits. 1,2,3,4,5,6,7,8
Answer:
Not very sure what you mean,
But in the provided set, 8 is the greatest number, and 1 is the smallest.
Hope this helps!!
Please help im new and i need help!
Please help me if you onlw the answers please!!
9514 1404 393
Answer:
a) 2.038 seconds
b) 5.918 meters
c) 1.076 seconds
Step-by-step explanation:
For the purpose of answering these questions, it is convenient to put the given equation into vertex form.
h = -4.9t² +9.2t +1.6
= -4.9(t² -(9.2/4.9)t) +1.6
= -4.9(t² -(9.2/4.9)t +(4.6/4.9)²) +1.6 +4.9(4.6/4.9)²
= -4.9(t -46/49)² +290/49
__
a) To find h = 0, we solve ...
0 = -4.9(t -46/49)² +290/49
290/240.1 = (t -46/49)² . . . . subtract 290/49 and divide by -4.9
√(2900/2401) +46/49 = t ≈ 2.0378 . . . . seconds
The ball takes about 2.038 seconds to fall to the ground.
__
b) The maximum height is the h value at the vertex of the function. It is the value of h when the squared term is zero:
290/49 m ≈ 5.918 m
The maximum height of the ball is about 5.918 m.
__
c) We want to find t for h ≥ 4.5.
h ≥ 4.5
-4.9(t -46/49)² +290/49 ≥ 4.5
Subtracting 290/49 and dividing by -4.9, we have ...
(t -46/49)² ≥ 695/2401
Taking the square root, and adding 46/49, we find the time interval to be ...
-√(695/2401) +46/49 ≤ t ≤ √(695/2401) +46/49
The difference between the interval end points is the time above 4.5 meters. That difference is ...
2√(695/2401) ≈ 1.076 . . . . seconds
The ball is at or above 4.5 meters for about 1.076 seconds.
__
I like a graphing calculator for its ability to answer these questions quickly and easily. The essentials for answering this question involve typing a couple of equations and highlighting a few points on the graph.
_____
Additional comment
I have a preference for "exact" answers where possible, so have used fractions, rather than their rounded decimal equivalents. The calculator I use deals with these fairly nicely. Unfortunately, the mess of numbers can tend to obscure the working.
"Vertex form" for a quadratic is ...
y = a(x -h)² +k . . . . where the vertex is (h, k) and 'a' is a vertical scale factor.
In the above, we have 'a' = -4.9, and (h, k) = (46/49, 290/49) ≈ (0.939, 5.918)
Which equation shows a slope of 3 and a y-intercept of (0,7)?
y = 7x + 3
y = −7x + 3
y = 3x
y = 3x + 7
Answer:
[tex]{ \tt{y = 3x + 7}}[/tex]
Step-by-step explanation:
General equation of a line:
[tex]{ \boxed{ \bf{y = mx + c}}}[/tex]
m is the slope, and c is the y-intercept:
m = 3, and c = 7
Translate sentence into inequality
A number c increased by 8 is greater than 30.
Step-by-step explanation:
the inequality is
[tex]c + 8 > 30[/tex]
Building A is 170 feet shorter than building B. The total height of the two buildings is 1520 feet. what is the height of each building?
Answer:
Step-by-step explanation:
If A is 170 less than B, than the equation for that is:
A = B - 170 (1) where the word "is" means equals and less than is subtraction.
If the total of A + B is 1520, then
A + B = 1520 (2). Sub equation (1) into equation (2):
(B - 170) + B = 1520 and
2B - 170 = 1520 and
2B = 1690 so
B = 845. Building B is 845 feet tall and Building A is
A = 845 - 170 (this is equation (1) with the height of B subbed in) so
A = 675 feet
675 + 845 should equal 1520 according to our equation. And of course it does.
Answer: 675 + 845 should equal 1520 according to our equation. And of course it does.
juan compra 12 dulces por 30 pesos, si al dia siguien el precio del dulce se incremento a 3.5 pesos cuanto se ahorro juan por cada dulce al comprarlos con el precio anterior
Need help ASAP
A) -3/2
B)-1/2
C) 3/2
D) Undefined
Answer:
A) -3/2
Step-by-step explanation:
You pick the difference between the two points and divide them.
y-axis: 2-(-1)= 3
x-axis: -3-(-1) = -2
So slope is -3/2
help i need help with math help if u can
Factorise: 25x^2 - 1/49
Answer:
[tex] (5x + \frac{1}{7} )(5x - \frac{1}{7} )[/tex]Step-by-step explanation:
Given,
[tex] {25x}^{2} - \frac{1}{49} [/tex]
[tex] = {(5x)}^{2} - {( \frac{1}{7}) }^{2} [/tex]
Since,
[tex] {x}^{2} - {y}^{2} = (x + y)(x - y)[/tex]
Then,
[tex] = (5x + \frac{1}{7} )(5x - \frac{1}{7} )(ans)[/tex]
Solve the following system of equations using the elimination method
8x + 2y= 30
7x+2y= 24
A) (3.-12)
B) (-53)
C) 1-6,-5)
D) 16,9)
Answer:
(6, -9)
Step-by-step explanation:
let: 8x + 2y = 30 be equation (a).
7x + 2y = 24 be equation (b).
[tex]{ \bf{equation \: (a) - equation \: (b) : }}[/tex]
[tex] (8 - 7)x + (2 - 2)y = (30 - 24) \\ x + 0y = 6 \\ x = 6[/tex]
substitute for x in equation (a):
[tex] (8 \times 6) + 2y = 30 \\ 48 + 2y = 30 \\ y = - 9[/tex]
If a rope 36 feet long is cut into two pieces in such a way that one piece is twice as long as the other piece, how long must the long piece be? If a rope 36 feet long is cut into two pieces in such a way that one piece is twice as long as the other piece, how long must the long piece be
Answer:
24feet
Step-by-step explanation:
the first rope well give it letter X and the longer rope we'll give it 2x since it's twice then we add the two unknown numbers which must lead to a total of 36feet when we add the unknown digits we'll get 3x then simply the unknown digit with the total and u'll get 12 replace the X from the first letters with 12by multiplying
Kayla made two paper chains. The paper links on one represented the number of days until her birthday, and the other showed the days until summer vacation. Altogether, she made 135 links for her chains. The birthday chain had twice as many links as the vacation chain. How many links are on Kayla's birthday chain?
Answer:
90 days
Step-by-step explanation:
b= number of days til her birthday
s = number of days til summer
b+s =135
b = 2s
2s+s = 135
3s = 135
Divide by 3
3s/3 =135/3
s =45
b = 2s = 2(45) = 90
Calculate the volume pyramid whose height de Priangular by of a 20cm, and has base of 8cm by 12cm by 150mm
Answer:
see it
Step-by-step explanation:
A lady wearing a McDonalds t-shirt with a delicious-looking Big Mac on it asks which fast food restaurant is your favourite. This leads to which type of bias?
a) Response Bias
b) Sampling Bias
c) Measurement Bias
d) Non-response Bias
11
Select the correct answer.
Which expression is equivalent to the given expression?
In(2e/x)
O A. In 2 – In x
OB. 1 + In 2 - In x
Oc. In 2 + In x
OD. In 1 + In 2 - In
Reset
Next
Answer:
B. 1 + ln 2 - ln x
General Formulas and Concepts:
Algebra II
Natural logarithms ln and Euler's number eLogarithmic Property [Multiplying]: [tex]\displaystyle log(ab) = log(a) + log(b)[/tex] Logarithmic Property [Dividing]: [tex]\displaystyle log(\frac{a}{b}) = log(a) - log(b)[/tex]Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle ln(\frac{2e}{x})[/tex]
Step 2: Simplify
Expand [Logarithmic Property - Dividing]: [tex]\displaystyle ln(\frac{2e}{x}) = ln(2e) - ln(x)[/tex]Expand [Logarithmic Property - Multiplying]: [tex]\displaystyle ln(\frac{2e}{x}) = ln(2) + ln(e) - ln(x)[/tex]Simplify: [tex]\displaystyle ln(\frac{2e}{x}) = ln(2) + 1 - ln(x)[/tex]Rewrite: [tex]\displaystyle ln(\frac{2e}{x}) = 1 + ln(2) - ln(x)[/tex]Write an equation that represents the line.
Use exact numbers.
Answer: y=2/3X- 4/3
Step-by-step explanation:
Slope = (4-2)/(4-1)=2/3
Y-2=2/3(x-1)
Y-2=2/3x-2/3
Y=2/3X-2/3+2
Y=2/3X-4/3
Which statement is true about this quadratic equation?
y=x^(2)-11x+7
Answer: This quadratic equation has two real solutions.
Step-by-step explanation:
[tex]y=x^{2} -11x+7\\\\D=(-11)^{2} -4 \cdot 7=121-28=93 \: > 0\\\\x=\dfrac{11 \pm \sqrt{93} }{2}[/tex]
i need help!!! due by 12
Answer:
1. $11747.083
2. $29,253
3. $24222.04
4. $1542.23
Step-by-step explanation:
Message for explanation if you want.
find the missing side lengths
Answer:
x=2
y=1.732
Step-by-step explanation:
we use the formulae.....
SOHCAHTOA
where..Cos 60°=1/x
cos60=0.5
0.5=1/1
X=2
0.8660=y/2
y= 1.732
You are studying 112 returning combat veterans with deployment related injuries. You are testing a cognitive impairment screen to detect traumatic brain injuries (TBI). There are six veterans with confirmed TBI and five of them screen positive. There are 93 veterans who do not have TBI and screen negative. There are a total 18 veterans who screen positive. One of the veterans has a negative screen and wants to know the probability that he does not have a TBI. You tell him:_________
Answer:
0.9894 = 98.94% probability that he does not have a TBI.
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: Negative screen
Event B: Does not have a TBI.
Probability of a negative screen:
93 are negative and do not have a TBI.
1 is negative and has a TBI.
Out of 112.
So
[tex]P(A) = \frac{93+1}{112} = \frac{94}{112}[/tex]
Probability of a negative screen and not having a TBI:
93 are negative and do not have a TBI, out of 112, so:
[tex]P(A \cap B) = \frac{93}{112}[/tex]
One of the veterans has a negative screen and wants to know the probability that he does not have a TBI.
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{\frac{93}{112}}{\frac{94}{112}} = \frac{93}{94} = 0.9894[/tex]
0.9894 = 98.94% probability that he does not have a TBI.
PLEASE HELP ME !!!!
How many solutions does the system of equations below have?
y = x - 3
3y-3x = -9
A. Exactly 1 solution
B. At least 1 solution
C. More than 1 solution
D. No solution
9514 1404 393
Answer:
C. More than 1 solution
Step-by-step explanation:
Divide the second equation by 3.
y -x = -3
Add x.
y = x -3
This matches the first equation exactly, meaning that any solution to the first equation is also a solution to the second equation. There are an infinite number of possibilities. There is "More than 1 solution."
Given the triangle below, what is the length of the third side, rounded to the nearest whole number?
Answer:
Step-by-step explanation:
You need the Law of Cosines for this, namely:
[tex]x^2=21^2+14^2-2(21)(14)cos58[/tex] where x is the missing side.
[tex]x^2=441+196-311.5925[/tex] and
[tex]x^2=325.4075[/tex] so
x = 18.0 or just 18
mJWL=87 degrees. Find the value of x.
JWL = JWI + IWL
87 = (2x + 24) + (3x - 12)
87 = 5x + 12
5x = 75
x = 15
Hope this helps!
The value of the variable x will be 15. Then the correct option is A.
What is an angle?The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.
Linear angle - If the total of two angles is 180 degrees, they are said to be linear angles.
The measure of the angle ∠JWL will be 87°.
The angle ∠JWI and angle ∠IWL will be the linear angle.
Then the sum of the angle ∠JWI and angle ∠IWL is equal to the angle ∠JWI.
∠JWI + ∠IWL = 87°
(2x + 24) + (3x – 12) = 87
5x + 12 = 87
5x = 87 – 12
5x = 75
x = 75 / 5
x = 15
Thus, the value of the variable x will be 15.
Then the correct option is A.
More about the angled link is given below.
https://brainly.com/question/15767203
#SPJ5
