The probability that the equipment will operate for at least 200 hours without failure is [tex](1-e^{-2} )^2[2e^-2+1][/tex].
Given:
mean = 1/100
Let X = the number of components that fail before 200 hours . The X has a binomial distribution n = 3 and p = 1 – e^-2.
probability p = 3/2[tex]p^{2} (1-p)[/tex] + 3/3 [tex]p^{3}[/tex].
= 3([tex]1-e^-2)^2[/tex][tex]e^-2[/tex] + ([tex]1-e^-2)^3[/tex]
= [tex](1-e^-^2)^2[3e^-^2 - e^-^2+1][/tex]
= [tex](1-e^{-2} )^2[2e^-2+1][/tex]
Therefore the probability that the equipment will operate for at least 200 hours without failure is [tex](1-e^{-2} )^2[2e^-2+1][/tex].
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8 points
Megan and Desmond each added the same amount of water to their aquariums. Megan mixed
5 mL of a chemical solution with every gallon of water for her aquarium. Desmond mixed
8 mL of the chemical solution with every 2 gallons of water for his aquarium.
Which of these statements is true?
A Megan used more solution per gallon of water than Desmond, because 5:1 is greater
than 8: 2.
B Megan used more solution per gallon of water than Desmond, because 5 mL is greater
than 2 mL.
C Desmond used more solution per gallon of water than Megan, because 8 mL is greater
than 5 mL.
D Desmond used more solution per gallon of water than Megan, because 8:2 is greater
than 5: 1.
3
What is the area of the composite figure?
12.5cm
20cm
500
490.62
245.31
745.31
25cm
4
27
Answer: 745.31 cm²
Total area of the figure can be obtained by adding area of the semi circle and rectangle.
The radius of the semi circle is given as 12.5cm and it's area is equal to (πr²)/2
I hope you understand It's simple!
A particle moves along the x-axis so that at any time t≥0 its position is given by x(t)=12(a−t)2, where a is a positive constant. For what values of t is the particle moving to the right? responses the particle is moving to the right only if 0
The particle will move to the right for t > a .
In the question ,
it is given that ,
a particle moves along the x axis , such that at any time t ≥ 0 ,
its position is given by the equation
x(t) = 12(a−t)² ,
where a is = positive constant
to find value of the particle moves right ,
we differentiate x(t) , with respect to "x" .
x'(t) = 12×2(a - t)×(-1)
v(t) = -24(a-t) ..... because x'(t) = v(t)
for particle to move right , v(t) > 0 .
-24(a-t) > 0
dividing both sides by "-24" , we get
a - t < 0
a < t
t > a .
Therefore , The particle will move to the right for t > a .
The given question is incomplete , the complete question is
A particle moves along the x-axis so that at any time t ≥ 0 its position is given by x(t)=12(a−t)² , where a is a positive constant. For what values of t is the particle moving to the right ?
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the annual rainfall in a certain region is approximately normally distributed with mean 41.4 inches and standard deviation 5.5 inches. round answers to the nearest tenth of a percent. a) what percentage of years will have an annual rainfall of less than 43 inches?
The probability percentage the year will have an annual rainfall less than 43 inches is 61.41%.
How to calculate the probability?
Given
μ = 41.4
σ = 5.5
First, we need to find the z score when the rainfall 43 inches. So:
z = (x - μ) / σ
z = (43 - 41.4) / 5.5
z = 0.2909
Then, to find out the probability we need to find P(z < 0.2909) in the z score table. So, we get 0.6141 or in percentage is 61.41%.
Thus, the probability percentage the year will have an annual rainfall less than 43 inches is 61.41%.
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This graph shows the height in inches, h, of a bamboo plant t months after it had been planted
4.1 Write an equation that describes the relationship between t and h.
4.2 After how many months will the Bamboo plant be 66 inches tall?
The linear function or equation represents the height of the bamboo h with respect to time t is y = 3x + 12 and the time taken to reach 66 inches is 3 months.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
A linear function is a function that varies linearly with respect to the changing variable.
4.1)
The linear equation is given as y = mx + c
Here, m is the slope while c is the y-intercept.
Given line has a y-intercept of 12.
Slope m = (12 - 24)/(0 - 4) = 3
Thus, h = 3t + 12
4.2)
Time is taken to bamboo to 66 inches tall,
66 = 3t + 12
3t = 54
t = 3 months.
Hence "The linear function or equation represents the height of the bamboo h with respect to time t is y = 3x + 12 and the time taken to reach 66 inches is 3 months".
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Give an example of how u worked it out, please.
a. The value of 9.9² × 1.79 is 175.44.
b. The value of ✓97.5 + 1.96 is 11.83
What is an exponent?An exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.
In this case, the value of 9.9² × 1.79 will be:
= 9.9² × 1.79
= 98.01 × 1.79
= 175.44
The value of ✓97.5 + 1.96 will be:
= ✓97.5 + 1.96
= 9.87 + 1.96
= 11.83
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What is the equation of a parabola that passes through the points (−5, −10), (−3, 2), and (2, −3)?.
The equation of the parabola is y = -x² - 2x + 5
What is a Parabola?
A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line
The equation of the parabola is given by
( x - h )² = 4p ( y - k )
where ( h , k ) is the vertex and ( h , k + p ) is the focus
y is the directrix and y = k - p
The equation of the parabola is also given by the equation
y = ax² + bx + c
where a , b , and c are the three coefficients and the parabola is uniquely identified
Given data ,
The equation of the parabola with the points
A ( -5 , -10 ) , B ( -3 , 2 ) and C ( 2 , -3 )
So , from the equation of parabola ,we get
y = ax² + bx + c
Substituting the values of x and y , in the equation of point A , we get
-10 = a ( -5 )² - 5b + c
-10 = 25a - 5b + c be equation (1)
Substituting the values of x and y , in the equation of point B , we get
2 = a ( -3 )² - 3b + c
2 = 9a - 3b + c be equation (2)
Substituting the values of x and y , in the equation of point C , we get
-3 = a ( 2 )² + 2b + c
-3 = 4a + 2b + c be equation (3)
By the method of brute force , we can solve the equations and derive the equation for the parabola
So , the equation for the parabola will be
y = -x² - 2x + 5
Now , substituting the values of x and y from the points , we get
For point A ( -5, -10 )
-10 = - 25 + 10 + 5
-10 = -10
Therefore , the equation is TRUE
Now , substituting the values of x and y from the points , we get
For point B ( -3, 2 )
2 = -9 + 6 + 5
2 = 2
Therefore , the equation is TRUE
Now , substituting the values of x and y from the points , we get
For point C ( 2 , -3 )
-3 = -4 - 4 + 5
-3 = -3
Therefore , the equation is TRUE
Hence , the equation of the parabola is y = -x² - 2x + 5
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The 3rd term of a a G.P is 18 and the 7th term is 32/9. Find the G.P
The G.P. of a term is 256/243.
To find out the G.P. for the 3rd term:
Let us consider the 1st term to be 'a'.
So, [tex]ar^{2}=18[/tex] ....... Equation (1)
Also [tex]ar^{6} = \frac{32}{9}[/tex] ..... Equation (2)
Dividing (2) by (1), we get,
[tex]\frac{ar^{6}}{ar^{2}} = \frac{32}{162}[/tex]
[tex]r^{4}[/tex] = 16/81.
r = 2/3.
Putting r in equation (1) than we will get
a = 81/2.
So, 10th term = [tex]ar^{9}[/tex]
= (81/2) ×(512/19683)
= 256/243.
Hence the answer is the G.P. of a term is 256/243.
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Three sisters have ages that are consecutive even integers. Find their ages If the sum of twice the youngest and three times the oldest is Pourteen more than four times the middle sister's age
Answer:
12 ; 13 ; 14
Step-by-step explanation:
x = sister one
x+ 1 = sister two
x+2 = sister three
2x + 3(x+2) = 4(x+1) + 14
2x + 3x + 6 = 4x + 4 + 14
5x + 6 = 4x + 18
5x - 4x = 18 - 6
x = 12 (sister one)
12 + 1 = 13 (sister two)
12 + 2 = 14 (sister three)
the garden table and a bench cost $582 combined. the garden table costs $68 less than the bench. what is the cost of the bench?
Answer:
$325
Step-by-step explanation:
t +b = 582
t = b - 68
b - 68 + b = 582
2b = 582 + 68
2b = 650
2/2 b = 650 / 2
b = 325
Label each point on the number line with the correct value.
Click each dot on the image to select an answer. Choices:
Answer:B= 7/9 C=10/9 A=0.62
Step-by-step explanation:
i know this because i multiplyed by 1/3 by 3 to get 3/9 6/9 9/9 for the number line
can you substitute y=2x+4 and 6x-3y=-12
Answer: x=0 y=4
Step-by-step explanation:
6x - 3(2x + 4) = 12
6x - 6x - 12 = 12
0 = 0
therefore, x = 0
substitute x=0 into y = 2x + 4
y = 2(0) + 4 = 4
s: Practice
Question 3 of 5
Type the correct answer in each box. Use numerals Instead of words. If necessary, use / for the fraction bar(s).
A group of friends are ordering food. The total amount that they can spend on their food bill is $41, including the delivery charge of $6.
The equation below represents the situation, where x is the cost of each friend's meal.
6 + az = 41
The cost of each friend's meal in terms of a is
The cost of each friend's meal when the number of friends is 5 is $
Submit
Reset
Answer:
$7
Step-by-step explanation:
You want to know the cost of each friend's meal if 5 friends spend $41 on their food, which includes a $6 delivery charge.
CostFor 'a' friends spending 'x' on each meal, the total cost is ...
6 + ax = 41
Solving for x, we have ...
ax = 41 -6 = 35
x = 35/a
5 FriendsWhen the number of friends is a = 5, the cost of a meal is ...
x = 35/5 = 7
The cost of each friend's mean when the number of friends is 5 is $7.
<95141404393>
what is the reciprocal of 5 1/3
Answer:
Step-by-step explanation:
reciprocal of 51/3 is 3/16
Hi you need to change 5 1/3 from mixed number to improper fraction 51/3=(5x3)+1 /3 =16/3
The reciprocal of 16/3 is 3/16
you send e-mails to tell your four friends about the school fair.Then those people send e-mails to four more people. Which formula can be used in this situation
The formula used in the situation of sending the emails is distributive property of multiplication and simple addition formula
How to determine the formula to be usedinformation gotten from the question
you send e-mails to tell your four friends about the school fair
Then those people send e-mails to four more people
From the first statement the number of emails sent is 4
The second statement says that the 4 persons sent to 4 more people hence each person sent one email
The total number of email sent is solved by
= 4 emails sent by you + 1 email sent by each friend * 4 (distributive property)
= 4 emails sent by you + 4 emails sent by friends
= 8 emails
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8. Consider a $2 principal investment with a 10% annual simple interest rate.
a. Write and graph the simple interest equation that represents the situation.
b. What does the y-intercept represent?
c. What does the slope of the graph represent?
d. What does the point (5, 3) represent on the graph?
9. AMORTIZATION Car loans are often spread into multiple regular payments over
in collod amortization. Each payment reduces the remaining
Answer:
Step-by-step explanation: 0.2
PLEASE HELP, NEEDED ASAP
Answer:
a) x=5
b) x=4
Step-by-step explanation:
4x-3=2x+7
-2x. -2x
2x-3=7
+3. +3
2x=10
x=5
2x+6=7x-14
-2x. -2x
6=5x-14
+14. +14
20=5x
/5. /5
4=x
Hopes this helps please mark brainliest
Two similar bottles are shown. The smaller bottle can hold 500 ml of water. How much water can the larger bottle hold?
Smaller bottle length=15cm
Larger bottle length=21cm
The larger bottle will be able to hold a volume of 1372ml
What is Volume of similar object?If two solids are similar, then the ratio of their volumes is equal to the cube of the ratio of their corresponding linear measures.
This shows that the ratio of the cube of length of the bottle is equal to the the ratio of their volumes
the length of the smaller bottle = 15, the cube of the length= 15^3= 3375
the length of the larger volume = 21, the cube of the length is 21^3=9261
therefore 3375/9261= 500/x
x is the volume of the larger bottle
therefore x= 500×9261/3375
x= 1372ml.
therefore the volume of the larger bottle is 1372ml
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PLEASE HELP 50 POINTS!! NO LINKS
The solution for the intersection point of a triangle is given below.
What is a triangle?A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.
The sum of angle of a triangle is always 180°
Perpendicular bisectors of the sides is circum center.
The bisector of angles of a triangle is in center.
Intersection point of medians is centroid
The intersection point of altitudes is ortho center.
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Simplify
1-(cos^2)theta/(sin^2 )theta
A. 1
B. sin^2 theta
C. cos^2 theta
D. tan^2 theta
The shapes below are mathematically similar.
X
9 cm
Calculate the length of side x.
8 cm
12 cm
Not drawn
to scale
The length of side x is 6cm
We need to find the scale factor of the shapes below are mathematically similar.
it can be found using the two bases given.
The base of the smaller triangle is 9 and that of large triangle is 12
9/12 = 3/4
The smaller triangle is 3/4 of the larger one.
Multiply the known side by 3/4
X = 8 x 3/4 = 6
X= 6
Therefore, the length of side x is 6cm
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a 2013 study by pediatricians investigates whether it is better to give children the diphtheria, tetanus and pertussis (dtap) vaccine in the thigh or the arm. the pediatricians collected the data from two different random samples. the first random sample was collected from children who were given the vaccine in the thigh. the second random sample was collected from children who were given the vaccine in the arm. pediatricians recorded whether the children had a severe reaction or not. no severe reaction severe reaction thigh observed expected 4758 4750.9 30 37.1 arm observed expected 8840 8853.1 76 68.9 reference: jackson, l.a., peterson, d., nelson, j.c., et al. (13 co-authors). 2013. vaccination site and risk of local reactions in children one through six years of age. pediatrics 131: 283-289. pediatricians conducted a chi-square test of independence. the chi-square test statistic for this datais 2.0609 with a p-value of 0.1511. what can the pediatricians conclude? group of answer choices there is a statistically significant association between vaccine location and severe reaction. pediatricians have strong evidence that the severe reactions to vaccine depend on location of the vaccine. there is not enough evidence to conclude that there is an association between vaccine location and severe reaction. the pediatricians cannot make a conclusion. the conditions for use of the chi-square test are not met.
Ther right option is that there is not enough evidence to conclude that there is enough association between vaccine location and severe reaction.
Given that,
Children who received the vaccine in the thigh received the first random sample. Children who received the immunization in the arm provided the second random sample.
The chi-square test yields a chi square is 2.0609 with a P value of 0.1511 meaning, the chi square test is not statistically significant.
A,B is therefore out.
C is not also right.
D is what we get when we cannot reject null hypothesis.
Therefore, We cannot conclude that there is dependence.
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8. Angles x and y are located in the first quadrant
such that sin x=5/3 and cos y=5/13
a) Determine an exact value for cosx.
b) Determine an exact value for siny.
sin y =12/13 but can't find cos x as sin x can't exceed from 1.
It can be solved by using identities of trigonometry.
What are the trigonometric identities?
These are the equivalent ways to define trigonometric functions.
Basic identities are:
sin²x + cos²x = 1
1 + tan²x = sec²x
1 + cot²x = cosec²x
For cos x:
cos²x = 1 - sin²x
= 1 - (5/3)²
= 1- (25/9)
= -16/9
i.e. not possible
For sin y:
sin²y = 1 - cos²y
= 1 - (5/13)²
= 1 - 25/169
= 144/169
So, sin y = ±(12/13)
but as mentioned x and y are in 1st quadrant ,
so, sin y = 12/13.
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Graph equations that represent the growth rates of hamburgers sold
and wraps sold in the same coordinate plane. Compare the steepness
of the graphs. What does this mean in the context of the problem?
(a) Hamburgers sells faster than Wraps ,
(b) The graph of the equations that represents the Hamburgers and Wraps sold are shown below .
In the question ,
it is given that
the rate at which the hamburgers are selling = 160 hamburgers per hour ,
we need to find the rate at which the wraps are selling
From the table ,
we can see that the wraps are sold in an Arithmetic Progression ,
So , at 60 minutes the wraps sold = 2.5 + (n-1)d
= 2.5 + 59×2.5
= 2.5 + 147.5
= 150
So , after one hour , number of wraps sold is 150 and the number of hamburgers sold is 160 .
Similarly , after 2 hours , the number of wraps sold will be 300 and number of hamburgers sold will be 320 .
So, the hamburgers sells faster than wraps .
the slope(steepness) of the hamburgers = (number of hamburgers sold)/60
= 160/60
= 2.667
the slope(steepness) of the wraps = (number of wraps sold)/60
= 150/60
= 2.5
from the above data , we can see that the steepness of hamburgers is more ,
which means that the hamburgers sells faster than wraps .
the equation that denotes the number of hamburgers sold is y = 2.667x
the equation that denotes the number of wraps sold is y = 2.5x
where x is time in minutes .
The graph that represents the growth rate of hamburger and wraps is shown below .
Therefore , (a) Hamburgers sells faster than Wraps ,
(b) The graph of the equations that represents the Hamburgers and Wraps sold are shown below .
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The sum 691 + 208 is closest to the sum
A. 600 + 200
B. 700 + 200
C. 700 + 300
D. 900 + 200
Answer:
B. 700+200
Step-by-step explanation:
691+208=899
A. 600+200=700
B.700+200=900
C.700+300=1000
D.900+200=1100
B is closest to 899
Answer:
700+200
Step-by-step explanation:
we round these numbers to the closest hundreds by looking at the tenth place
5 or more we round up
4 or less we let it rest and round down
691 since it is 9 in the tenths place we round up to 700
208 since the tenths place is 0 we round down to get 200
700+200 is the answer hopes this helps please mark brainliest
Rosario paid $2.50 for 3 pounds of apples. Select all of the rates that are equivalent to the rate Rosario paid. 6.RP.3, 6.RP.3b $0.80 for 1 pound 14.50 for 5 pounds $7.50 for 9 pounds $9.60 for 11 pounds $10.00 for 12 pounds
The rates that are equivalent to the rate Rosario paid are $0.80 for 1 pound, $7.50 for 9 pounds, and $10.00 for 12 pounds.
What are the rates?
A rate is a unique ratio where the two words are expressed in several units.
Rate formula
r = d/t
Here, we calculate different rates
a. Per pound price of apples = Total cost / total weights of apples
= 0.80 / 1 = $0.80
Cost of 3 pounds of apples = 3 × 0.80 = $2.4
b. Per pound cost of apples = Total cost / total weights of apples
= 14.50 / 5 = $2.9
Cost of 3 pounds of apples = 3 × 2.9 = $8.7
c. Per pound cost of apples = Total cost / total weights of apples
= 7.50 / 9 = $0.833
Cost of 3 pounds of apples = 3 × 0.833 = $2.49
d. Per pound cost of apples = Total cost / total weights of apples
= 9.60 / 11 = $0.872
Cost of 3 pounds of apples = 3 × 0.872 = $2.61
e. Per pound cost of apples = Total cost / total weights of apples
= 10 / 12 = $0.833
Cost of 3 pounds of apples = 3 × 0.833 = $2.49
Hence, The rates that are equivalent to the rate Rosario paid are $0.80 for 1 pound, $7.50 for 9 pounds, and $10.00 for 12 pounds.
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What is the y-intercept of g(x) = -|x +6|+ 4
Answer: -2
Step-by-step explanation:
since g(x) is a function, x needs to be 0 in order to find the y-intercept. so we plug in 0 to the function. -|0+6|+4=-2 so the y-intercept is -2
what is 10 + 10 i need some help
Answer:20
Step-by-step explanation: my man
Answer:
20
Step-by-step explanation:
1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 10
+ 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 10
= 20
8. You are selling concessions at a local swim meet. Hot dogs are being sold for
$1.00 and soda is being sold for $0.50. At the end of the day you made $150.
Let x represent the number of hotdogs sold and y represent the number of
sodas sold. Write an equation that can be used to find the number of hotdogs
and sodas sold at the swim meet.
a. Standard Form:
b. Slope-Intercept Form:
c. If you sold 40 hot dogs how many sodas did you sell?
d. Using the Standard Form, identify the x-intercept of the graph and explain
how the x-intercept relates to the number of hot dogs and sodas sold.
e. Using the Standard Form, identify the y-intercept of the graph and explain
how the y-intercept relates to the number of hot dogs and sodas sold.
The equation that can be used to find the number of hotdogs
and sodas sold at the swim meet.
a)x+0.50y=150
b) y=-2x+300
c)Number of soda sold y =220 if hot dog is 40.
d) x intercept=150. It is related to the total earnings of soda and hot dogs sold.
f) y intercept = 300 . It is related to the 2 times of the total earnings of soda and hot dogs sold.
What is x-intercept and y-intercept?
An equation's or a function's graph that contacts the x axis is said to have a "X intercept." This is comparable to a point having a value of zero. Given that it is located on the horizontal axis, this is sometimes referred to as the horizontal intercept. The y value at the point where the line meets the y axis is known as the y intercept. By examining the graph and identifying the point that crosses the y axis, we may determine the y intercept. This point's x coordinate will always be 0. It will be recorded as (0,y). Given that it is on the vertical axis, this is also referred to as a vertical intercept.
Let us take number of hot dogs sold as x and number of soda sold as y.
Cost of one hot dog = $1.00
Cost of one soda = $0.50
Then , cost of x number of hot dogs sold = 1x
cost of y number of soda sold = 0.50y
Then, . At the end of the day you made $150.
=> 1x+0.50y= 150
a) standard form of the equation is ,
=> x+0.50y=150 ------->1
b) x+0.50y=150
=> x+[tex]\frac{1}{2}[/tex]y=150
=>2x+y=150*2
=>2x+y=300
Then slope intercept form is y=-2x+300------->2
c) Number of hot dogs sold x=40 and put into 2 ,
then , y=-2(40)+300
=> y=-80+300
=>y=220
Number of soda sold y =220
d) To find x intercept put y=0 into 1 , then
=> x+0=150
=>x=150
Here x intercept=150. It is related to the total earnings of soda and hot dogs sold.
e)To find y intercept put x=0 into 1,
=> 0+0.50y=150
=> y = 150/0.50
=> y =300
Here y intercept = 300 . It is related to the 2 times of the total earnings of soda and hot dogs sold.
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Complete by solving the square!(need help asap!)
Explain step by step!
3x^2+x-2=0
Answer: x = -2/3 , 1
Step-by-step explanation:
step 1 (hardest step!) factor by grouping:
(3x + 2)(x-1) = 0
the rest is easy:
3x + 2 = 0 or (x-1) = 0
Solve each for x:
3x + 2 = 0
x = -2/3
x-1 = 0
x = 1
So your 2 solutions for x are -2/3 and 1