The probability that all three components fail is 1.756 × 10⁻⁷. The probability of at least one of the components does not fail 0.9999998244.
What is a Probability?Probability is the likelihood for an event to occur. In a given statistical distribution, the probability explains the range of values and probabilities that a randomized variable could have.
From the given information;
Assuming each component's failure/success is independent of the others: the probability that all three components fail is:
P(three components fail) = (0.0056)^3
P(three components fail) = 1.756 × 10⁻⁷
The probability that at least one does not fail is:
P(at least one does not fail) = 1 - P(all three components fail)
P(at least one does not fail) = 1 - 1.756 × 10⁻⁷
P(at least one does not fail) = 0.9999998244
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Use slopes and y-intercepts to determine if the lines 10x+3y=−3 and 5x−4y=−3 are parallel.
Answer:
They are not parallel
Step-by-step explanation:
original equation
10x + 3y = -3
subtract 10x
3y = -10x - 3
divide by 3
y = -10/3x - 1
original equation
5x - 4y = -3
subtract 5x
-4y = -5x-3
divide by -4
y = 5/4x + 3/4
the slopes are not equal to each other (5/4x and -10/3x) so they are not parallel
Donna took out a loan for $17,000 and was charged simple interest at an annual rate of 6.8% .
The total interest she paid on the loan was $867 . Do not round any intermediate computations.
Total amount she paid to repay her loan was $17,687
Amount is the total sum of money paid to the bank.It is basically the sum of interest and principal amount.
Principal is the sum of money taken from the bank
Interest is the sum of money charge by the bank during the period of loan repayment.
Rate of interest is the rate at which interest is charge in the principal sum
Time is the total period of the loan repayment.
Simple interest = (P x Rx T)/100
where, P=principal
R=rate of interest
T= time
Amount= Principal +Interest
As per question,
P=$17000
R=6.8%
I=$687
Amount=P+I
=$17000+687
=$17687
Therefore,Total amount she paid to repay her loan was $17,687
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Please help! Photo is attached. Will give brainliest if correct answer.
0.66 inches of material is needed to be cut off to make the volume maximum.
maximum and minimum points testWhen the second derivative of a function is negative, the function has a maximum point and if the second derivative is positive, the function has a minimum point.
Analysis:
After cut and folded, length = 8-2x
Width = 3-2x
Thickness = x.
Volume of the folded shape = (8-2x)(3-2x)(x)
After expansion, V = 4[tex]x^{3}[/tex]-[tex]22x^{2}[/tex] +24x
for turning point of the function, dv/dx = 0
dv/dx = 12[tex]x^{2}[/tex] -44x + 24
lowest term = 3[tex]x^{2}[/tex] - 11x + 6
3[tex]x^{2}[/tex] - 11x + 6 = 0
3[tex]x^{2}[/tex] - 9x -2x +6 = 0
3x(x-3) -2(x-3) = 0
(3x-2)(x-3) = 0
x = 2/3 or x = 3
To test for maximum point, we differentiate dv/dx again
we have 6x - 11
for x = 3, 6(3) - 11 = 18 - 11 = 7 which is positive x= 3 is a minimum
for x = 2/3 6(2/3) - 11 = 4 - 11 = -7, x = 2/3 is a maximum.
Therefore for maximum volume, the length to be cut out is 2/3 which is 0.66 inches.
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Renate launched an object vertically from a point that is 58.9 meters above ground level with an initial velocity of 21.6 meters per second. This situation can be represented by the equation h=−4.9t2+21.6t+58.9, where h is the height of the object in meters and t
is the time in seconds after the object is launched.
What is the maximum height of the object?
The maximum height of the object is 82.7034 from the ground
What is Velocity ?Velocity is the measure of movement of an object with respect to time.
It is measured in m/sec
h = -4.9t²+21.6t +58.9
dh/dt = -9.8t +21.6
At maximum height , velocity = 0
therefore
-9.8t +21.6 = 0
9.8t = 21.6
t = 2.204 sec
h = -4.9 (2.204)²+ 21.6 * 2.204 +58.9
h = -23.803 +47.606 +58.9
h = 82.7034 from the ground
h = 23.80 from the point it is launched.
The maximum height of the object is 82.7034 from the ground
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The graphs of exponential functions f and g are shown on the coordinate plane below.
Answer:
-5
Step-by-step explanation:
Since g(x) is f(x) shifted 5 units down, g(x) = f(x) -5. Therefore k = -5
6. Using the discriminant, determine the value of k that will give 1 solution (i.e. discriminant equals zero) y = kx²-4x + 4
Answer:
k = 1
Step-by-step explanation:
Discriminant
[tex]b^2-4ac\quad\textsf{when }\:ax^2+bx+c=0[/tex]
[tex]\textsf{when }\:b^2-4ac > 0 \implies \textsf{two real roots}[/tex]
[tex]\textsf{when }\:b^2-4ac=0 \implies \textsf{one real root}[/tex]
[tex]\textsf{when }\:b^2-4ac < 0 \implies \textsf{no real roots}[/tex]
As we need to determine the value of k that will give one solution, set the discriminant to zero.
Given equation:
[tex]y=kx^2-4x+4[/tex]
Therefore:
a = kb = -4c = 4Substitute these values into the discriminant and solve for k:
[tex]\begin{aligned}b^2-4ac & = 0\\\implies (-4)^2-4(k)(4) & = 0\\16-16k & = 0\\16k & = 16\\\implies k & = 1\end{aligned}[/tex]
answer a-d please!!!!!!!!!!!!!!!!
a) Intercepts are the points on the x and y axis
In the graph:
x-int: (-2,0), (2,0)
y-int: (0,1)
b) Domain is the list of x-values and Range is the list of y-values that make this graph true
Interval notations of domain and range
(Square brackets because the circles are closed)
Domain: [3,3]
Range: [0,3]
c) Intervals of increase and decrease: where the graph is increasing and decreasing
Increasing: -2 to 0 & 2 to 3
Decreasing: -3 to -2 & 0 to 2
d)Even, odd or neither
It is an even degree as both of its hands are facing upwards
Hope it helps!
6/64 reduce to lowest terms
Answer:
[tex]\frac{3}{32}[/tex]
Step-by-step explanation:
-> Simplify
[tex]\frac{6}{64} =\frac{6/2}{64/2} =\frac{3}{32}[/tex]
6/64 simplified.
If 22% of high school students say they eat out 3 times a week, how many students of the 2346 students who attend WHS would you expect eat out 3 times a week?
Answer:
516 students eat out 3 times a week
Step-by-step explanation:
22% of 2346 is 516.12 and a person can't be a decimal so it's 516
22 x 2346 = 51612
and 51612÷100 = 516.12
We would expect about 516 WHS students to eat out 3 time
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that 22% of high school students say they eat out 3 times a week
We need to find the number of students of the 2346 students who attend WHS would you expect eat out 3 times a week
We can start by using the proportion:
(22/100) = (x/2346)
where x is the number of students we would expect to eat out 3 times a week.
To solve for x, we can cross-multiply:
100x = 22 × 2346
100x = 51612
Divide both sides by 100
x = 516.12
Hence, we would expect about 516 WHS students to eat out 3 time
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Maria expanded the following square as follows: (x+3)² =x²+9, is this correct?
Answer:
x² + 6x + 9
Explanation:
[tex]\sf = \left(x+3\right)^2[/tex]
Use perfect square formula: (a + b)² = a² + 2ab + b²
[tex]= \sf x^2 + 2(x) (3) + 3^2[/tex]
simplify the following
[tex]= \sf x^2 + 6x +9[/tex]
Hence Maria is not correct. The correct answer is x² + 6x + 9.
The following table shows how far a bus has gone in t hours. Which of the following equations represents this information?
Step-by-step explanation:
You need to attach the table in order to get an answer.
Suppose that
f
(
x
,
y
)
=
x
+
5
y
f
(
x
,
y
)
=
x
+
5
y
at which
−
1
≤
x
≤
1
,
−
1
≤
y
≤
1
-
1
≤
x
≤
1
,
-
1
≤
y
≤
1
.
Absolute minimum of
f
(
x
,
y
)
f
(
x
,
y
)
is
Absolute maximum of
f
(
x
,
y
)
f
(
x
,
y
)
is
========================================================
Explanation:
The range of x values is [tex]-1 \le x \le 1[/tex] which means x = -1 is the smallest and x = 1 is the largest possible.
Similarly the smallest y value is y = -1 and the largest is y = 1.
----------
Plug in the smallest x and y value to get
f(x,y) = x+5y
f(-1,-1) = -1+5(-1)
f(-1,-1) = -6
Therefore, the absolute min is -6
----------
Now plug in the largest x and y values
f(x,y) = x+5y
f(1,1) = 1+5(1)
f(1,1) = 6
The absolute max is 6
The line whose equation is y=4x+2 has a y-intercept with coordinates
Answer: 2xy
Step-by-step explanation: 2xy is the answer bra
Multiply (Make sure to show work on a separate sheet of paper)
Please use the equation writer that is on top. Look for this sign √ and click on it. That will allow you to write an exponent.
(2x−4)(x−6)
Answer:
[tex]2x^{2}[/tex] - 16x + 14
Step-by-step explanation:
(2x - 4)(x - 6)
= (2x + −4)(x + −6)
= (2x)(x) + (2x)(−6) + (−4)(x) + (−4)(−6)
= [tex]2x^{2}[/tex] − 12x − 4x + 24
= [tex]2x^{2}[/tex] - 16x + 14
A circle has a radius of 5 ft, and an arc of length 7 ft is made by the intersection of the circle with a central angle. Which equation gives the measure of the central angle, q? 08- 5 O 0-7+5 O e-7-5
The equation gives the measure of the central angle 7/5 times 3 60/2 π.
What is Central angle?An angle with its vertex at the center of a circle and with sides that are radii of the circle.
radius= 5 feet.
Circumference of circle,
= 2πr
=2*3.14*5
= 31.4 feet.
Arc length = 7.
Then, the part of circle 7 feet arc have
=7/31.4
=0.2229
Also, 0.2229 * 360 = 80.244°
In radian,
80.244° = 1.4 radians
Hence, 7/5 times 360/2 π.
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-2/9u=12
Solve for u
u=-54
you have -54 because
-54(-2)=108/9=12
Answer:
u =-54
Step-by-step explanation:
-2/9u=12
To solve for u multiply each side by -9/2 to isolate u
-9/2 * -2/9 u= 12 * -9/2
u =-54
Which graph shows the greatest integer function?
By critically observing the given graphs, we can logically deduce that "graph C" returns greatest integer that is less than or equal (≤) to x.
What is a greatest integer function?A greatest integer function can be defined as a type of function which returns the greatest integer that is less than or equal (≤) to the number.
Mathematically, the greatest integer that is less than or equal (≤) to a number (x) is represented as follows:
y = [x].
By critically observing the given graphs, we can logically deduce that y in "graph C" returns greatest integer that is less than or equal (≤) to x.
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Which of the following slopes of a line pass through points (1, -3) and (0, 2)?
m=5
m = -5
m = undefined
None of these choices are correct.
The slope of the line that passes through (1, -3) and (0, 2) is: B. m = -5.
What is the Slope of a Line?Slope (m) = rise / run = change in y / change in x.
Given the points, (1, -3) and (0, 2):
Slope (m) = (-3 - 2)/(1 - 0)
Slope (m) = -5/1
Slope (m) = -5
Therefore, the slope of the line is: B. m = -5.
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What is the surface area of a sphere with radius 3?
Answer:
A≈113.1
Step-by-step explanation:
A=4πr2=4·π·32≈113.09734
If a patient is given 3 tablespoons of medication for me for 150 ML bottle how many millimeters of medication remain in the bottle
Answer:
105.6397
ROUNDED ANSWER:
105
Help please asap I’m desperate!
Answer:
f(x)=x-2x+3; f(x)=-bx
x-2x=3=-bx
x+4x+3=0
(x+3) (x+1) = 0
x=-3 or x=-1
when x+-3. f(x)=b x(-3)=18
x=-1. f(x) = - b x (-1) = b
so system of equations : ( -3, -18)
; (-),b
Step-by-step explanation:
hope it helps
Need help!!!!!!!!!!!!!!!!!
One number is 6 more than twice another. If their sum is 51, find the numbers.
Which of the following systems of equations represents the word problem?
y = 2x + 6 and y = x + 51
y = 2x + 6 and x + y = 51
y = 2(x + 6) and x + y = 51
Answer:
y = 2x + 6 and y + x = 51
Step-by-step explanation:
the first number is y
the second number is X
" 6 is more than" implying +
"6 is more than twice another" implying y = 6 + 2 multiples by the second number "X"
their sum is equal to 51
add first and the second number
that is
y+x = 51
so we have
y = 6+2x and y +x = 51
A car travels 18 mile in 213 minutes. What is its speed in terms of miles per minute?
Answer:
[tex]\textsf {0.08 miles per minute}[/tex]
Step-by-step explanation:
[tex]\textsf {Speed = Distance (Miles) / Time (Minute) }[/tex]
[tex]\textsf {Speed = 18 miles / 213 minutes }[/tex]
[tex]\textsf {Speed = 0.08 miles per minute }[/tex]
Answer:
The speed in miles per minute is 0.0845 mpm.
Step-by-step explanation:
The explanation above clearly states that a car travel a distance of 18 miles in a time of 213 minutes . And it is asking for speed in miles per minute. Keep this in mind that the symbol for miles per minute is mpm. Speed formula is distance ÷ time.
Speed = Distance ÷ Time
Speed = 18 m / 213 min
18 divided by 213 = 0.0845
speed = 0.0845 mpm
Therefore the speed in miles per minute is 0.0845 mpm.
Suppose that A ∩ C = B ∩ C. Is it true that A=B? Justify your answer.
Answer:
No
Step-by-step explanation:
If these two individual statements are true, it means they share the same elements of set C. In addition to this, sets A and B could have additional elements, hence this cannot be true.
Assume that a procedure yeilds a binomial with n trial and the probability of success for one trial is p. Use the given values of n and p to find the mean and standard deviation. Also, use the range rule of thumb to find the minimum usual value mean -2standard deviation and the maximum usual value mean + 2 standard deviation n=1490,p=2/5
The value of minimum usual value is, [tex]\mu-2\sigma=-119.2[/tex]
The value of maximum usual value is, [tex]\mu+2\sigma=1311.2[/tex]
Given the values of the parameters of Binomial Distribution are,
Total number of trials (n) = 1490
probability of success in one trial is (p) = 2/5
The probability of failure in on trial is given by,
[tex]q=1-p=1-\frac{2}{5}=\frac{5-2}{5}=\frac{3}{5}[/tex]
For Binomial distribution we know that,
Mean [tex](\mu)=np=1490\times\frac{2}{5}=596[/tex]
and Standard Deviation [tex](\sigma)=\sqrt{npq}=\sqrt{1490\times\frac{2}{5}\times\frac{3}{5}}=357.6[/tex]
Now, calculating the required measurement we get,
The minimum usual value is given by,
Mean -2 Standard Deviation [tex]=\mu-2\sigma=596-2\times357.6=-119.2[/tex]
The maximum usual value is given by,
Mean + 2 Standard Deviation [tex]=\mu+2\sigma=596+2\times357.6=1311.2[/tex]
Hence the minimum and maximum usual values are -119.2 and 1311.2 respectively.
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Could use some help! Brainliest to who answers :)
Answer:
N. The number of people purchasing coffee each day in a coffee shop
Step-by-step explanation:
A fraction of a person could not buy coffee because every person is a whole person. If something is not a person, it's not a person. Therefore, the only numbers you could add to this value are 0 and 1.
evaluate question 4 only
Substitute [tex]y = \sqrt x[/tex], so that [tex]y^2 = x[/tex] and [tex]2y\,dy = dx[/tex]. Then the integral becomes
[tex]\displaystyle \int \frac{dx}{\sqrt{1 + \sqrt x}} = 2 \int \frac y{\sqrt{1+y}} \, dy[/tex]
Now substitute [tex]z=1+y[/tex], so [tex]dz=dy[/tex]. The integral transforms to
[tex]\displaystyle 2 \int \frac y{\sqrt{1+y}} \, dy = 2 \int \frac{z-1}{\sqrt z} \, dz = 2 \int \left(\sqrt z - \frac1{\sqrt z}\right) \, dz[/tex]
The rest is trivial. By the power rule,
[tex]\displaystyle \int \left(\sqrt z - \frac1{\sqrt z}\right) \, dz = \frac23 z^{3/2} - 2z^{1/2} + C = \frac23 \sqrt z (z - 3) + C[/tex]
Put everything back in terms of [tex]y[/tex], then [tex]x[/tex] :
[tex]\displaystyle 2 \int \frac y{\sqrt{1+y}} \, dy = \frac43 \sqrt{1+y} (y - 2) + C[/tex]
[tex]\displaystyle \int \frac{dx}{\sqrt{1+\sqrt x}} = \boxed{\frac43 \sqrt{1+\sqrt x} (\sqrt x - 2) + C}[/tex]
DO NOT PUT A WRONG ANSWER OR ELSE I WILL START TO REPORT YOU!!! MAKE SURE THAT YOU SHOW ALL THE STEPS OR SOLUTIONS AND EXPLAIN THE PROBLEM.
Consider a ‘Witch of Agnesi’ curve, defined:
x^2 y + 4y = 8
Find:
a) dy/dx as a function of x, using implicit differentiation. Then, verify your result by finding y explicitly and differentiating.
b) The equation of the tangent line to the graph when x = 2.
The answers are as follow:
a) y'= -2x/y
b) y' = -4/y
Why do we use implicit differentiation?
The technique of implicit differentiation allows you to find the derivative of y with respect to x without having to solve the given equation for y.
Given:
x²y+4y=8
On differentiation
applying product rule
2xy+ x²y' = 0
2xy = - x²y'
2y = -xy'
y'= -2x/y
b) equation of the tangent line to the graph when x = 2.
y' = -4/y
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What is the area of a circle with 20cm diameter
Answer:
area of the circle
area=7.54
