The probability solved by binomial distribution that all will survive is 0.8154.
What is Binomial distribution?When each trial has the same probability of achieving a given value, the number of trials or observations is summarized using the binomial distribution. The likelihood of observing a specific number of successful outcomes in a specific number of trials is determined by the binomial distribution.
Computation of probability of all survived people from heart attack;
A heart attack patient has a 0.04 percent chance of dying from the attack (i.e., 4 of 100 die of the attack).
What is the likelihood that each of the five patients who experience a heart attack will survive?
We'll refer to a victory in this scenario as a heart attack (p = 0.04). In other words, we are interested in the likelihood that none of our n=5 patients will die (0 successes).
Each attack has a chance of being fatal or not, with a probability of 4 percent for all patients, and each patient's result is independent.
Assume for the purposes of this example that the five individuals being examined are unrelated, of the same age, and free of any concomitant disorders.
By binomial distribution,
[tex]\begin{gathered}P(0 \text { successes })=\frac{5 !}{0 !(5-0) !} 0.04^{0}(1-0.04)^{5-0} \\P(0 \text { successes })=\frac{5 !}{5 !}(1)(0.96)^{5}=(1)(1)(0.8154)=0.8154\end{gathered}[/tex]
Therefore, with a 4 % chance that anyone will die, there is an 81.54% chance that every patient will survive the onslaught. The outcomes in this example could be 0, 1, 2, 3, 4 or 5 successes (fatalities).
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Total area=
Help me please, thankss
The Area of given figure is 341.6 square.
According to the statement
we have to find the total area of given figure.
Here a= 10 and h= 11
So, we use the formula is A = a(a + √((a)^2 + 4(h)^2))
where the a represent the base of given solid or sides of the equilateral triangle
And h represent the slant height of the solid.
So, Substitute the values in above formula then
A = 10(10 + √((10)^2 + 4(11)^2))
A = 10(10 + √((100 + 4(121))
A = 10(10 + √(100 + 484)
A = 10(10 + √(584)
A = 10(10 + 24.16)
A = 10(34.16)
A= 341.6
So, The Area of given figure is 341.6 square.
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Some articles were bought at 6 for rupees 5 and sold at 5 for rupees 6. find the gain percent
44% is the answer
6 Article price at buying =5 Rs
1 Article price at buying = 5/6...(i)
5 Articles sold at Rs. 6
1 Articles cost at sold = 6/5 ....(ii)
% Gain=((6/5 - 5/6)/ 5/6) * 100
= 11/25 * 100 = 44%
Profit is a general increase in an asset or the value of an asset. If the item's current price is higher than the original purchase price, you will make a profit. For accounting and tax purposes, profits can be categorized in several ways: B. Gross profit and net profit, or realized profit and unrealized (paper) profit.
The definition of victory is profit, benefit, or increase. An example of profit is a 5% increase in income over the past year. An example of a win is a 5 point lead over another team.
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solve this pls>>>>>>>there’s a pic
Answer:
x = 5, 1
Step-by-step explanation:
To solve for x, you must factor the equation. The factored equation will be: (x - 1) (x - 5) = 0. After factoring, isolate the two factored equations: (x - 1) = 0 and (x - 5) = 0. Then solve for x for both the equations which should get you to x = 5, 1.
In the given circle the m∠DFB is 41°, mArc EF is 52° what is the m∠C ?
Check the picture below.
The requried measure of the angle m∠C in the given circle is 15°.
In the given circle the m∠DFB is 41°, mArc EF is 52°
To find out the measure of the angle m∠C.
Following the properties of arcs in the circle,
arc BD = 2m∠BFD
arc BD=2*41 = 82
Now we know that,
The angle subtended by two sectants drawn from the single point that lies outside the circle is given by the difference in larger and minor arcs divided by 2.
∠c= BD- EF / 2
∠c = 82°-52°/2
∠c = 15°
Thus, the requried measure of the angle m∠C in the given circle is 15°.
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Joe and Sue were trying to calculate the square inches of paper needed to create a cone for the cotton candy. The radius
was 2 in and the height was 6 inches and there was a 1/2 in of overlap for the glue.
Calculations
Joe
2π√10+ √10
Sue
12π + 3
choose the correct statements below.
select one or more:
Sue was correct.
Joe was correct.
Sue used the correct height and radius and calculated the overlap by adding the area for the strip of glue.
Neither were correct.
Joe used the height and radius to calculate the slant height.
The correct statements are Neither was correct and Joe used the height and radius to calculate the slant height.
How to find the square inches of paper needed.The square inches of paper needed A = surface area of cone + area of overlap
Surface area of cone
The surface area of the cone is given by A = πr[r + √(h² + r²)] where
r = radius of cone = 2 in and h = height of cone = 6 in.So, A = πr[r + √(h² + r²)]
A = π × 2 × [2 + √(6² + 2²)]
A = π × 2 × [2 + √(36 + 4)]
A = π × 2 × [2 + √40]
A = π × 2 × [2 + 2√10]
A = 2π[2 + 2√10]
A = 4π + 4π√10
The area of overlap
The area of overlap A' = wL where
w = width of overlap = 1/2 in and L = slant height of cone = √(h² + r²)So, A' = wL
A' = w[√(h² + r²)]
A' = 1/2[√(6² + 2²)]
A' = 1/2[√(36 + 4)]
A' = 1/2[√40]
A' = 1/2 × 2√10
A' = √10
So, the number of square inches of paper needed is A" = A + A'
= 4π + 8π√10 + √10
Since the number of square inches of paper needed is 4π + 4π√10 + √10
So, the correct statements are Neither was correct and Joe used the height and radius to calculate the slant height.
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How many sequences of 0s and 1s of length 19 are there that begin with a 0, end with a 0, contain no two consecutive 0s, and contain no three consecutive 1s
65 sequences.
Lets solve the problem,
The last term is 0.
To form the first 18 terms, we must combine the following two sequences:
0-1 and 0-1-1
Any combination of these two sequences will yield a valid case in which no two 0's and no three 1's are adjacent
So we will combine identical 2-term sequences with identical 3-term sequences to yield a total of 18 terms, we get:
2x + 3y = 18
Case 1: x=9 and y=0
Number of ways to arrange 9 identical 2-term sequences = 1
Case 2: x=6 and y=2
Number of ways to arrange 6 identical 2-term sequences and 2 identical 3-term sequences =8!6!2!=28=8!6!2!=28
Case 3: x=3 and y=4
Number of ways to arrange 3 identical 2-term sequences and 4 identical 3-term sequences =7!3!4!=35=7!3!4!=35
Case 4: x=0 and y=6
Number of ways to arrange 6 identical 3-term sequences = 1
Total ways = Case 1 + Case 2 + Case 3 + Case 4 = 1 + 28 + 35 + 1 = 65
Hence the number of sequences are 65.
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Hi! It’d be really helpful if someone could explain he two questions below, thanks!
Lola bought x pencils that cost $0.25 each and y erasers that cost $0.50. She spent less than $3. Which graph represents lolas purchase
The graph that represents Lola's Purchase is as shown in the attached file.
How to interpret Inequality Graph?Lola bought x pencils that cost $0.25 and Y erasers that cost $0.50.
Total expenditure is less than $3.
Representing expense in the equation form gives us;
Expense on pencils + expense on erasers < 3
Thus;
0.25X + 0.50Y < 3
Dividing through by 0.25, we have;
X + 2Y < 12
This inequality when graphed, line will be plotted in dots and area below the line will be in the shaded form.
From the standard equation of line in slope intercept form, we can deduce that; Slope of this line is = (-1/2)
The correct graph is attached below.
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Factor the greatest common factor: −6m2 18m − 36. −6(m2 − 3m 6) −1(6m2 − 18m 36) −6m(m2 − 3m 6) −6(m2 3m − 6)
Answer:
Step-by-step explanation:
−6m2 18m − 36
= -6(m2 - 3m + 6)
The triangle below is being reduced by a scale factor of two-thirds. What is the base of the new drawing? 15 m
Answer:
10
Step-by-step explanation:
A scale factor of 2/3 means multiplying all side lengths by 2/3
15*2/3=10
If she was vaping every 15 minutes, assuming she was awake from 7 am- 11 pm (16 hours) how many times in a day would she vape?
Answer:
64 times
Step-by-step explanation:
16 hours to minutes: 16*60 = 960 minutes
vaping every 15 minutes: 960/15 = 64
What equation shows that 9 is a factor of 72?
The equation that shows that 9 is a factor of 72 is given as 9 * 8 = 72
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The equation that shows that 9 is a factor of 72 is given as 9 * 8 = 72
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there are five chemistry instructors and six physics instructors at a college. if a committee of four instructors is selected,
The probability of at least one of them being a physics instructor is 120 ways to form the committee.
Probability of Independent Events: The 'At Least One' Rule?Sometimes, simply the occurrence of the event at least once matters when computing independent events. The "At Least One" Rule is used to describe this. The complement of the probability of the event never occurring will be used to calculate the probability of the event occurring at least once.
There are five chemistry instructors and six physics instructors at a college. If a committee of four instructors is selected.
Starting with 6, choose two because we require at least two professors. Let's move on to the remaining 8 individuals (there were initially 10, but now there are just 8): and select 3.
6 select 2; 8 select 3
15×56 =840
We then chose 5 individuals from a group of 10, at least 2 of whom were lecturers.
(9) = 20 options for selecting the professors. 3
(3) = 6 options for selecting the professors.
(9) (¹) = 20 × 6 = 120 ways.
Therefore, 120 ways to form the committee.
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Complete question:
There are five chemistry instructors and six physics instructors at a college. If a committee of four instructors is selected, find the probability of at least one of them being a physics instructor?
What is the measure of arc QR?
Answer:
answer is the third choice : 104
Step-by-step explanation:
Inscribed Angle Theorem
If an angle is inscribed in a circle, then the measure of the angle equals one half the measure of its intercepted arc.
so the intercepted arc is TWICE the measure of an angle inscribed in a circle
1. A central angle is an angle with endpoints located on a circle's circumference and vertex located at the circle's center. A central angle in a circle determines an arc.
2. An inscribed angle is an angle formed by three points on the circle's circumference.
Angle at the Center Theorem: An inscribed angle is half of the central angle (if they determine the same arc).
In your case angles:
1. ∠QSR is insribed (determines the arc QR);
2. ∠QTR is central (determines the arc QR).
Then by Angle at the Center Theorem, m∠QTR=2m∠QSR=2·52°=104°. Arc QR has the same measure as central angle QSR.
gathmath
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The circumference of a circular field is 222.94 yards. What is the radius of the field? Use 3.14 for π and do not round your answer.
Answer:
35.5
Step-by-step explanation:
→ Write down the formula
2 × π × r = 222.94
→ Simplify
6.28 × r = 222.94
→ Divide both sides by 6.28
r = 35.5
Answer:
35.5 = r
Step-by-step explanation:
The circumference of a circle is given by
C = 2 * pi *r where r is the radius
222.94 = 2 * 3.14 * r
222.94 = 6.28 r
Divide each side by 6.28
222.94/6.28 = r
35.5 = r
PR=
Help me please thanks so much
Formula: U*V=R*T
3*1=4*x
3=4x
x=3/4
Hope it helps!
Answer:
[tex]\sf PR =\dfrac{3}{4}[/tex]
Step-by-step explanation:
Intersecting chords theorem:It two chords or secants intersect inside the circle, then the product of the length of the segments of one chord is equal to the product of the lengths of the segments of the other chords.
TP * PR = UP * PV
4 * PR = 3 * 1
[tex]\sf PR = \dfrac{3}{4}[/tex]
Suppose that you are interested in determining the average height of a person in a large city. You begin by collecting the heights of a random sample of 256 people from the city. The average height of your sample is 64 inches, while the standard deviation of the heights in your sample is 4 inches.The standard error of your estimate of the average height in the city is .
The standard error of the estimate of average height in the city is 0.25.
Given average height 64 inches, sample mean and sample standard deviation of 4 inches.
We have to determine the standard error of the estimate of the average height in the city.
Standard error is the error which is predicted before research to happen in research. It is calculated by dividing the standard deviation of the sample by the square root of the sample size.
n=256
μ=mean
s = sample standard deviation
Standard error=s/[tex]\sqrt{n}[/tex]
=4/[tex]\sqrt{256}[/tex]
=4/16
=0.25
Hence the standard error of the estimate of the average height is 0.25.
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Which equation represents exponential decay? * a y=3^x-4 b y=2(4)^x c y=1/2(3)^x d: y=6(1/3)^x
The equation which represents exponential decay is y=[tex]6(1/3)^{x}[/tex]
Given four equations : 1)y=[tex]3^{x} -4[/tex], 2) y=[tex]2(4)^{x}[/tex], 3) y=[tex]3^{x}/2[/tex], 4) y=[tex]6(1/3)^{x}[/tex].
Equation is relationship between two or more variables expressed in equal to form. Equations of two variables look like ax+by=c. Exponential equation look like [tex]a^{x}[/tex].
Decay means when x value increases ,the y value decreases.
We haveto put 3 values for x in the equations to check.
1)y=[tex]3^{x} -4[/tex]
put x=0,y=-3
put x=1, y=-1
put x=2, y=5
No,itdoes not represents exponential decay.
2) y=2[tex]4^{x}[/tex]
put x=0,y=2
put x=1, y=8
put x=2, y=32
No,it does not represents exponential decay.
3) y=[tex]3^{x}/2[/tex]
put x=0,y=0.5
put x=1, y=1.5
put x=2, y=4.5
No,it does not represents exponential decay.
4)y=6[tex](1/3)^{x}[/tex]
put x=0,y=6
put x=1, y=2
put x=2, y=0.67
Yes ,it represents exponential decay.
Hence the equation which represents exponential decay is y=6[tex](1/3)^{x}[/tex].
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100 POINTS OKK!!!!
1. If y varies directly as x and y=5, when x=3, find the equation that relates x and y.
2. If v varies directly as w and v=21, when w=8. find the equation that relates v and w.
3. If p varies inversely with q and p=5 when q=6, find the equation that relates p and q.
4. If y varies inversely with x and y=11 when x=3 find the equation that relates x and y.
5. The force needed to break a board varies inversely with its length. If Tom uses 20 pounds of pressure to break a 1.5-foot-long board, how many pounds of pressure would he need to use to break a 6-foot-long board?
Variation is a topic that describes the relationship between or among given variables. So that the expected answers to the questions are;
y = [tex]\frac{5}{3}[/tex] xv = [tex]\frac{21}{8}[/tex]wp = [tex]\frac{30}{q}[/tex]y = [tex]\frac{33}{x}[/tex]F = 5 poundsVariation is a topic that can be used to show the relationship between or among a given number of variables. The types are direct variation, inverse variation, constant variation, and joint variation.
The required answers to the given questions are:
1. y [tex]\alpha[/tex] x
⇒ y = kx
where k is the constant of proportionality.
Given that, y = 5 and x =3, then;
5 = 3x
x = [tex]\frac{5}{3}[/tex]
Thus,
y = [tex]\frac{5}{3}[/tex] x
2. v [tex]\alpha[/tex] w
v = kw
Given: v = 21, w = 8
Then,
21 = 8k
k = [tex]\frac{21}{8}[/tex]
Thus,
v = [tex]\frac{21}{8}[/tex]w
3. q [tex]\alpha[/tex] [tex]\frac{1}{q}[/tex]
y = [tex]\frac{k}{q}[/tex]
Given: q = 5, q = 6
Then,
5 = [tex]\frac{k}{6}[/tex]
k = 5 x 6
k = 30
Thus,
p = [tex]\frac{30}{q}[/tex]
4. y [tex]\alpha[/tex] [tex]\frac{1}{x}[/tex]
y = [tex]\frac{k}{x}[/tex]
Given: y = 11, x = 3
Then,
11 = [tex]\frac{k}{3}[/tex]
k = 11 x 3
k = 33
Thus,
y = [tex]\frac{33}{x}[/tex]
5. F [tex]\alpha[/tex] [tex]\frac{1}{l}[/tex]
F = [tex]\frac{k}{l}[/tex]
Given; F = 20 pounds, l = 1.5 ft
20 = [tex]\frac{k}{1.5}[/tex]
k = 20 x 1.5
k = 30
F = [tex]\frac{30}{l}[/tex]
When l = 6 ft, then;
F = [tex]\frac{30}{6}[/tex]
F = 5 pounds
The amount of force required is 5 pounds.
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Find the difference. express the answer in scientific notation. (8.64 times 10 superscript 20 baseline) minus (7.83 times 10 superscript 20 baseline) 8.1 times 10 superscript 19 0.81 times 10 superscript 20 8.1 times 10 superscript 21 0.81 times 10 superscript 40
Answer:
Its A or B
Step-by-step explanation:
One number is 4 more than another and their sum is 60.
If x = the larger number and y = the smaller number, then which of the following is the value of the smaller number?
The larger number is 32 and the smaller number is 28 given that one number is 4 more than another and their sum is 60. This can be obtained by forming algebraic equation and finding
Calculate the value of the numbers:Given that one number is 4 more than another,
⇒x = y + 4 (equation (1))
Their sum is 60,
⇒x + y = 60
y + 4 + y = 60 (From (1))
2y + 4 = 60
2y = 56 ⇒ y = 28
x = y + 4 = 28 + 4 = 32
Hence the larger number is 32 and the smaller number is 28 given that one number is 4 more than another and their sum is 60.
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See photo for problem, please help
Considering the given functions in the graph, we have that:
(f + g)(3) = 4.(f - g)(1) = -2.How to find (f + g)(3) looking at the graph?We look at the graph, and find f(3) and g(3), then add them. Hence:
g(3) = 4.f(3) = 0.Then the addition is:
(f + g)(3) = f(3) + g(3) = 0 + 4 = 4.
As for (f - g)(1):Same logic, at the graph we have that:
f(1) = -1.g(1) = 1.Hence:
(f - g)(1) = f(1) - g(1) = -1 - 1 = -2.
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Identify each expression that represents the slope of a tangent to the curve y = 1/x+1 at any point (x,y)
The expressions that represent the slope of a tangent to the curve [tex]y = \frac{1}{x+1}[/tex] are [tex]m = \lim_{h \to 0}\frac{\frac{1}{x + h + 1} - \frac{1}{x + 1} }{h}[/tex] and [tex]m = -\frac{1}{(x + 1)^{2}}[/tex], respectively.
How to find an expression for the slope at any point of a function
The slope at any point of the function can be found by definition of derivative following algebraic handling:
[tex]m = \lim_{h \to 0}\frac{\frac{1}{x + h + 1} - \frac{1}{x + 1} }{h}[/tex]
[tex]m = \lim_{h \to 0} \frac{\frac{x+1 - x - h - 1}{(x + h + 1)\cdot (x + 1)} }{h}[/tex]
[tex]m = -\lim_{h\to 0} \frac{1}{(x + h + 1)\cdot (x + 1)}[/tex]
[tex]m = -\frac{1}{(x + 1)^{2}}[/tex]
Thus, the expressions that represent the slope of a tangent to the curve [tex]y = \frac{1}{x+1}[/tex] are [tex]m = \lim_{h \to 0}\frac{\frac{1}{x + h + 1} - \frac{1}{x + 1} }{h}[/tex] and [tex]m = -\frac{1}{(x + 1)^{2}}[/tex], respectively.
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I need help with cancelling units please
Answer:
D
Step-by-step explanation:
You are looking for what you would need to cancel the yards in 800 yards.
800 yards (1 mile/ 1760 yards). You have yards in the numerator of your original measurement. You will cross cancel out the yard on the the top and the yards on the bottom.
When you roll two number cubes, what are the odds, in simplest form, in favor of getting two numbers less than 4?
A. 1:3
B. 3:1
C. 1:4
D. 4:1
Answer:
c 1:4
Step-by-step explanation:
A machine manufactuers 300 nails a day. how many did it produce in the month of april 2007
The machine produces 3000 nails in the month of April 2007.
Production of Nails in the Month of April
According to the given information,
Number of nails manufactured per day by the machine, x = 300
And, we know that April is the fourth month of a year which has total 30 days.
Hence, number of days the machine is manufacturing nails in the month of April, y = 30
So, the number of nails that will be produced by the machine in the month of April is given by,
N = Number of nails produced per day × Number of days in April
N = xy
N = 300 × 30
N = 9000
Therefore, the machine produces 9000 nails in the April month of year 2007.
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Which of the following parabolas has its vertex the furthest away from the x-axis
Oy
x² - 1
y = 3x² + 4
Oy
=
Y =
1/2x²
Oy = x² - 10
Question 12 (1 point)
Answer:
y=x^2-10
Step-by-step explanation:
can someone please help me
Answer:
[tex]\frac{13\pi }{9}[/tex] radians
Step-by-step explanation:
to convert degrees to radians
degrees × [tex]\frac{\pi }{180}[/tex]
= 260 × [tex]\frac{\pi }{180}[/tex]
= 26 × [tex]\frac{\pi }{18}[/tex]
= 13 × [tex]\frac{\pi }{9}[/tex]
= [tex]\frac{13\pi }{9}[/tex]
The vectors are linearly independent if and only if?
The vectors are linearly independent if and only if k ≠ -11
How to solve the vectorIn mathematics, the definition of a vector is a quantity that is made up of both magnitude and also have direction. This type of quantity is not one that is considered based on its position. A very good example of such a quantity with magnitude and direction is acceleration.
Vectors are used to represent items such as position, velocity, physical quantities and others in mathematics and in physics.
In this question,
We have 2v - 3w
We have to multiply 2 by the values of v and multiply 3 with the values of w
this would produce
[2,6,8]-[6,6,12]
subtract w from v
= [-4, 0, -4]
We u as -1, 0 and 10+k
It is not possible to -1 = 10 + k
-11 = k
Hence we have to conclude that they are linearly independent if and only if k ≠ -11
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y≤1/2x-3
y + 2x > 6
I need help solving this problem shjsdjjsjdndjskdjdkkdndnsjsjmsmskdndnd
Answer:
6-2x < y < ½x-3Step-by-step explanation:
The first part tells us that y is, or is anywhere below ½x-3
The second part tells us that above 6-2x
Since we don't know what x is, we cannot actually find y.
The best answer to this question is:
6-2x < y < ½x-3
Which reads, in words, as: six minus two-x is below y; and y is below one-half-x minus three.
Hopefully, this is what your teacher or math program is looking for. There is hardly another way to solve it, other than graphing it. The graphed version will be attached, but I highly doubt you'll need it.