Answer
it is 5 : )
Step-by-step explanation:
All current-carrying wires produce electromagnetic (EM) radiation, including the electrical wiring running into, through, and out of our homes. High frequency EM is thought to be a cause of cancer; the lower frequencies associated with household current are generally assumed to be harmless. The following table summarizes the probability distribution for cancer sufferers and their wiring configuration in the Denver area.
Leukemia Lymphoma Other Cancers
High Frequency wiring 0.242 0.047 0.079
Low frequency wiring 0.391 0.098 ???
(a) What is the missing probability (labelled ???) in the above table?
(b) What is the probability of having high frequency wiring among cancer suffers in the Denver area?
(c) Is the event "Having Leukemia" independent of the event "Having high frequency frequency wiring"? Explain.
Answer:
[tex]x = 0.143[/tex]
[tex]P(High\ |\ Cancer) = 0.215[/tex]
Not independent
Step-by-step explanation:
Given
See attachment for proper table
Solving (a): The missing probability
First, we add up the given probabilities
[tex]Sum = 0.242+0.047+0.079+0.391+0.098[/tex]
[tex]Sum = 0.857[/tex]
The total probability must add up to 1.
If the missing probability is x, then:
[tex]x + 0.857 = 1[/tex]
Collect like terms
[tex]x = -0.857 + 1[/tex]
[tex]x = 0.143[/tex]
Solving (b): P(High | Cancer)
This is calculated as:
[tex]P(High\ |\ Cancer) = \frac{n(High\ n\ Cancer)}{n(Cancer)}[/tex]
So, we have:
[tex]P(High\ |\ Cancer) = \frac{0.079}{0.242+0.047+0.079}[/tex]
[tex]P(High\ |\ Cancer) = \frac{0.079}{0.368}[/tex]
[tex]P(High\ |\ Cancer) = 0.215[/tex]
Solving (c): P(Leukemia) independent of P(High Wiring)
From the attached table
[tex]P(Leukemia\ n\ High\ Wiring) = 0.242[/tex]
[tex]P(Leukemia) = 0.242 + 0.391 =0.633[/tex]
[tex]P(High\ Wiring) = 0.242+0.047+0.079=0.368[/tex]
If both events are independent, then:
[tex]P(Leukemia\ n\ High\ Wiring) = P(Leukemia) * P(High\ Wiring)[/tex]
[tex]0.242 = 0.633 * 0.368[/tex]
[tex]0.242 \ne 0.232[/tex]
Since the above is an inequality, then the events are not independent
In a direct variation, the ratio of y -values to x -values is equal to a constant.
True or False?
HELP PLEASE
Answer:
True
Step-by-step explanation:
The equation of direct variation is
y = kx ← k is the constant of variation
To find k divide both sides by x
[tex]\frac{y}{x}[/tex] = k
That is the constant is the ratio of y- values to x- values
Porfavor necesito ayuda en esto.
Es para hoy :(
Answer:
17
Step-by-step explanation:
[tex]factorise : - \\ \\ 4x {}^{2} - 56x + 196 \\ \\ please \: help \: [/tex]
[tex]\large\bold{\underline{\underline{ 4( {x - 7})^{2} }}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex]4x {}^{2} - 56x + 196[/tex]
Take [tex]4[/tex] as the common factor.
[tex] = 4( {x}^{2} - 14x + 49)[/tex]
[tex] = 4( {x}^{2} - 7x - 7x + 49)[/tex]
Taking [tex]x[/tex] as common from first two terms and [tex]7[/tex] from last two terms, we have
[tex] = 4 \: [ x(x - 7) - 7(x - 7) ][/tex]
Taking the factor [tex](x-7)[/tex] as common,
[tex] = 4(x - 7)(x - 7)[/tex]
[tex] = 4( {x - 7})^{2} [/tex]
[tex]\bold{ \green{ \star{ \red{Mystique35}}}}⋆[/tex]
which equation represents a line parallel to the y-axis?
Answer:
B. x=4
Step-by-step explanation:
I hope this helps!
the question please i need help
Answer:
90g strawberry jelly
6 sponge fingers
315ml custard
135g tinned fruit
Step-by-step explanation:
----------------------------------------
Since those ingredients that are in the question say making a trifle for four people, let's divide each ingredient by four to find the ingredients for one person, and multiply by 3 to find the ingredients for 3 people.
So,
[tex]120/4=30[/tex]g strawberry jelly
[tex]8/4=2[/tex] sponge fingers
[tex]420/4=105[/tex]ml custard
[tex]180/4=45[/tex]g tinned fruit
There are the ingredients to make a trifle for one person.
-------------------->>>>
Now, let's multiply each of the ingredients for one person and multiply that by three to find the ingredients needed to make a trifle for four people.
[tex]30*3=90[/tex]g strawberry jelly
[tex]2*3=6[/tex] sponge fingers
[tex]105*3=315[/tex]ml custard
[tex]45*3=135[/tex]g tinned fruit
These are the ingredients needed to make a trifle for three people.
----------------------------------------
Hope this is helpful.
X,Y and Z from a business with capitals Rs 5000,Rs.4500 and Rs.6500 respectively,after 6 month,X doubles has capital and after next 3 months Y trebles his capital .If the profit at the end of the year amount to RS.8300,find the profit obtained by each X,Y and Z.
Answer:
Profit obtained by X = Rs. 2,976.64
Profit obtained by Y = Rs. 2,545.58
Profit obtained by Z = Rs. 2,777.78
Step-by-step explanation:
Total capital for the first 6 months = Rs 5000 + Rs.4500 + Rs.6500 = Rs. 16,000
Total capital for the next 3 months = Rs. 16,000+ Rs 5000 = Rs. 21,000
Total capital for the last 3 months of the year = Rs. 21,000 + (Rs 4500 * 2) = Rs. 30,000
Share of profit of each partner is the sum of all the ratios of his capital to total capital of the business at each point in time multiply by the ratio of the numbers of months covered by each capital to 12 months and then multiply by RS.8300.
Profit obtained by X = ((Rs 5000 / 16,000) * (6 / 12) * Rs. 8300) + ((Rs 10,000 / 21,000) * (3 / 12) * Rs. 8300) + ((Rs 10,000 / 30,000) * (3 / 12) * Rs. 8300) = Rs. 2,976.64
Profit obtained by Y = ((Rs 4500 / 16,000) * (6 / 12) * Rs. 8300) + ((Rs 4500 / 21,000) * (3 / 12) * Rs. 8300) + ((Rs 13,500 / 30,000) * (3 / 12) * Rs. 8300) = Rs. 2,545.58
Profit obtained by Z = ((Rs 6500 / 16,000) * (6 / 12) * Rs. 8300) + ((Rs 6500 / 21,000) * (3 / 12) * Rs. 8300) + ((Rs 6,500 / 30,000) * (3 / 12) * Rs. 8300) = Rs. 2,777.78
Confirmation of total profit shared = Rs. 2,976.64 + = Rs. 2,545.58 + Rs. 2,777.78 = Rs. 8,300
Please help me with this one
Answer:
240
Step-by-step explanation:
well do *
so 8x6x5 = 240 there's your answer
Answer:
[tex]S.A=1/2(8+8)(9^{2})+8\times 6+8\times 5[/tex]
[tex]=26\times2+48+40[/tex]
[tex]=140 ~cm^{2}[/tex]
-------------------------
HOPE IT HELPS
HAVE A GREAT DAY!!
Write 8 as the ratio of two integer
Answer:
Step-by-step explanation: 7 1 16 37
8/1 8 divided by 1
16/2 16 divided by 2
24/3 24 divided by 3 I could go on, but won't
Ed buys a box of eggs costing £2.40, two packs of bacon for £2.60 each and two tins of baked beans.
He pays with a £10 note and gets 80p change.
How much does a tin of beans cost in pounds, £?
Answer:
£0.80
Step-by-step explanation:
1 box of eggs: £2.40
2 packs of bacon: 2 * £2.60
2 tins of baked beans: 2x
Change: 80p
Total = 2x + £2.40 + £5.20 + £0.80
Total = 2x + £8.40
2x + £8.40 = £10
2x = £1.60
x = £0.80
Answer: £0.80
A bottling company marks a 0 for every bottle that comes out correct and a 1 for every defective bottle. Estimate the probability that the next bottle is defective
Answer:
See Explanation
Step-by-step explanation:
Given
[tex]0 \to[/tex] Correct
[tex]1 \to[/tex] Defective
Required
The probability that the next is defective
The question is incomplete because the list of bottles that came out is not given.
However, the formula to use is:
[tex]Pr = Num ber\ o f\ d e f e c t i v e \div T o t a l\ b o t t l e s[/tex]
Take for instance, the following outcomes:
[tex]0\ 1\ 0\ 0\ 0\ 1\ 0\ 0\ 1\ 1\ 0\ 0\ 0\ 1[/tex]
We have:
[tex]Total = 14[/tex]
[tex]D e f e ctive = 9[/tex] --- i.e. the number of 0's
So, the probability is:
[tex]Pr = 9 \div 14[/tex]
[tex]Pr = 0.643[/tex]
Answer:
1/20
Step-by-step explanation:
000000000000100000
It is asking the probability of a defective bottle
there is one defective bottle out of 20
Solve for x. PLZ HELP ASAP!!!
X is a vertical angle to the angle marked as 100 degrees.
Vertical angles are the same so x = 100 degrees
Answer: 100 degrees
Someone please help me with this algebra problem
Answer:
90
Step-by-step explanation:
A quadratic equation is shown below:
6x2 + 17x + 9 = 0
Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points)
Part B: Solve 4x2 − 4x + 1 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)
(10 points)
Answer:
x = -0.70,-2.212.
Step-by-step explanation:
(a) The quadratic equation is :
[tex]6x^2 + 17x + 9 = 0[/tex]
Here,
a = 6, b = 17, c = 9
Put all the values in the quadratic formula.
[tex]x=\dfrac{-17+\sqrt{17^2-4\times 6\times 9}}{2(6)},\dfrac{-17-\sqrt{17^2-4\times 6\times 9}}{2(6)}\\\\x=-0.70,-2.12[/tex]
So, the solution of the given equation are -0.70,-2.212.
(b) Equation is : [tex]4x^2 -4x + 1 = 0[/tex].
Here, a = 4, b = -4 and c = 1
So,
[tex]x=\dfrac{-(-4)+\sqrt{(-4)^2-4\times 4\times 1}}{2(4)},\dfrac{-(-4)-\sqrt{(-4)^2-4\times 4\times 1}}{2(4)}\\\\x=0.5,0.5[/tex]
Hence, this is the required solution.
A rectangle has an area of 18 cm2
The lengths of the sides are whole numbers.
How long could the sides of the rectangle be?
Give all the examples you can think of
Answer:
9 possible values of length and breadth.
Step-by-step explanation:
Given that the area of the rectangle is 18cm² . And the lengths of the sides are whole numbers. We need to tell the possible dimensions of the rectangle .
Let :-
[tex]\rm\implies Length = x [/tex]
[tex]\rm\implies Breadth = y [/tex]
We know that :-
[tex]\rm\implies Area = length \times breadth [/tex]
Put in the assumed variables[tex]\rm\implies Area = x y \\\\\rm\implies xy = 18cm^2 [/tex]
Now look out for the possible factors of 18 . That is , ( 1 × 18 ) , ( 2 × 9) , ( 3 × 6 ) , ( 6 × 3 ) , ( 9 × 2 ) , (18 × 1 ) . That is total 9 possible values .
Need help on this question asap pleasee
Answer:
I believe its the 1st answer.
There are 35 times as many students at Wow University as teachers. When all the students and
teachers are seated in the 8544 seat auditorium, 12 seats are empty. How many students attend
Wow University?
Given:
There are 35 times as many students at Wow University as teachers.
When all the students and teachers are seated in the 8544 seat auditorium, 12 seats are empty.
To find:
The total number of students.
Solution:
Let x be the number of teachers at Wow University. So, the number of student is :
[tex]35\times x=35x[/tex]
When all the students and teachers are seated in the 8544 seat auditorium, 12 seats are empty.
[tex]x+35x=8544-12[/tex]
[tex]36x=8532[/tex]
[tex]x=\dfrac{8532}{36}[/tex]
[tex]x=237[/tex]
The number of total students is:
[tex]35x=35(237)[/tex]
[tex]35x=8295[/tex]
Therefore, the total number of students is 8295.
which eqation represents the line that passes through (-6, 7) and (-3, 6)
Answer:
The answer is y= - ⅓x + 5 in slope intercept form and y-7 = - ⅓ (x + 6) in point slope form.
HELP HELP HELPPPP PLEASEEE
Directions: Determine if segments AB and CD are parallel, perpendicular, or neither.
AB formed by (-2, 13) and (0, 3)
CD formed by (-5, 0) and (10, 3)
Given:
AB formed by (-2,13) and (0,3).
CD formed by (-5,0) and (10,3).
To find:
Whether the segments AB and CD are parallel, perpendicular, or neither.
Solution:
Slope formula:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
AB formed by (-2,13) and (0,3). So, the slope of AB is:
[tex]m_1=\dfrac{3-13}{0-(-2)}[/tex]
[tex]m_1=\dfrac{-10}{2}[/tex]
[tex]m_1=-5[/tex]
CD formed by (-5,0) and (10,3). So, slope of CD is:
[tex]m_2=\dfrac{3-0}{10-(-5)}[/tex]
[tex]m_2=\dfrac{3}{10+5}[/tex]
[tex]m_2=\dfrac{3}{15}[/tex]
[tex]m_2=\dfrac{1}{5}[/tex]
Since [tex]m_1\neq m_2[/tex], therefore the segments AB and CD are not parallel.
[tex]m_1\times m_2=-5\times \dfrac{1}{5}[/tex]
[tex]m_1\times m_2=-1[/tex]
Since [tex]m_1\times m_2=-1[/tex], therefore the segments AB and CD are perpendicular because product of slopes of two perpendicular lines is always -1.
Hence, the segments AB and CD are perpendicular.
Answer:
AB is perpendicular to CD.
Step-by-step explanation:
AB formed by (-2, 13) and (0, 3)
CD formed by (-5, 0) and (10, 3)
Slope of a line passing through two points is
[tex]m= \frac{y''-y'}{x''- x'}[/tex]
The slope of line AB is
[tex]m= \frac{3- 13}{0+2} = -5[/tex]
The slope of line CD is
[tex]m'= \frac{3 -0 }{10+5} = \frac{1}{5}[/tex]
As the product of m and m' is -1 so the lines AB and CD are perpendicular to each other.
Pls solve last question pls pls
Answer:
i don't know how to work this
Answer:
x = [tex]\frac{3}{4}[/tex] , x = 20
Step-by-step explanation:
2([tex]\frac{3x-5}{x+2}[/tex] ) - 5 ([tex]\frac{x+2}{3x-5}[/tex] ) = 3
Multiply through by (x + 2)(3x - 5) to eliminate the fractions
2(3x - 5)² - 5(x + 2)² = 3(x + 2)(3x - 5) ← expand factors on both sides
2(9x² - 30x + 25) - 5(x² + 4x + 4) = 3(3x² + x - 10) ← distribute parenthesis
18x² - 60x + 50 - 5x² - 20x - 20 = 9x² + 3x - 30 ← simplify left side
13x² - 80x + 30 = 9x² + 3x - 30 ( subtract 9x² + 3x - 30 from both sides )
4x² - 83x + 60 = 0 factor by splitting the x- term
4x² - 80x - 3x + 60 = 0
4x(x - 20) - 3(x - 20) = 0
(4x - 3)(x - 20) = 0
Equate each factor to zero and solve for x
4x - 3 = 0 ⇒ 4x = 3 ⇒ x = [tex]\frac{3}{4}[/tex]
x - 20 = 0 ⇒ x = 20
Which arc is a minor arc?
A)SQ
B)PSR
C)PS
D)SO
Answer:
Answer: The arc PS would be a minor arc · Step-by-step explanation: As a minor arc is one that is less that 180 degrees, it would be the only viable ...
In a county containing a large number of rural homes, 60% of the homes are insured against fire. Four rural homeowners are chosen at random from this county, and x are found to be insured against fire. Find the probability distribution for x.
Answer:
[tex]\begin{array}{cccccc}x & {0} & {1} & {2} & {3} & {4} \ \\ P(x) & {0.0256} & {0.1536} & {0.3456} & {0.3456} & {0.1296} \ \end{array}[/tex]
Step-by-step explanation:
Given
[tex]p = 60\%[/tex]
[tex]n = 4[/tex]
Required
The distribution of x
The above is an illustration of binomial theorem where:
[tex]P(x) = ^nC_x * p^x *(1 - p)^{n-x}[/tex]
This gives:
[tex]P(x) = ^4C_x * (60\%)^x *(1 - 60\%)^{n-x}[/tex]
Express percentage as decimal
[tex]P(x) = ^4C_x * (0.60)^x *(1 - 0.60)^{n-x}[/tex]
[tex]P(x) = ^4C_x * (0.60)^x *(0.40)^{4-x}[/tex]
When x = 0, we have:
[tex]P(x=0) = ^4C_0 * (0.60)^0 *(0.40)^{4-0}[/tex]
[tex]P(x=0) = 1 * 1 *(0.40)^4[/tex]
[tex]P(x=0) = 0.0256[/tex]
When x = 1
[tex]P(x=1) = ^4C_1 * (0.60)^1 *(0.40)^{4-1}[/tex]
[tex]P(x=1) = 4 * (0.60) *(0.40)^3[/tex]
[tex]P(x=1) = 0.1536[/tex]
When x = 2
[tex]P(x=2) = ^4C_2 * (0.60)^2 *(0.40)^{4-2}[/tex]
[tex]P(x=2) = 6 * (0.60)^2 *(0.40)^2[/tex]
[tex]P(x=2) = 0.3456[/tex]
When x = 3
[tex]P(x=3) = ^4C_3 * (0.60)^3 *(0.40)^{4-3}[/tex]
[tex]P(x=3) = 4 * (0.60)^3 *(0.40)[/tex]
[tex]P(x=3) = 0.3456[/tex]
When x = 4
[tex]P(x=4) = ^4C_4 * (0.60)^4 *(0.40)^{4-4}[/tex]
[tex]P(x=4) = 1 * (0.60)^4 *(0.40)^0[/tex]
[tex]P(x=4) = 0.1296[/tex]
So, the probability distribution is:
[tex]\begin{array}{cccccc}x & {0} & {1} & {2} & {3} & {4} \ \\ P(x) & {0.0256} & {0.1536} & {0.3456} & {0.3456} & {0.1296} \ \end{array}[/tex]
20 Points- Which of the following is true for f of x equals the quotient of the quantity x squared plus 9 and the quantity x minus 3?
There is a removable discontinuity at x = 3.
There is a non-removable discontinuity at x = 3.
The function is continuous for all real numbers.
Answer:
There is a non-removable discontinuity at x = 3
Step-by-step explanation:
We are given that
[tex]f(x)=\frac{x^2+9}{x-3}[/tex]
We have to find true statement about given function.
[tex]\lim_{x\rightarrow 3}f(x)=\lim_{x\rightarrow 3}\frac{x^2+9}{x-3}[/tex]
=[tex]\infty[/tex]
It is not removable discontinuity.
x-3=0
x=3
The function f(x) is not define at x=3. Therefore, the function f(x) is continuous for all real numbers except x=3.
Therefore, x=3 is non- removable discontinuity of function f(x).
Hence, option B is correct.
A number ending in ___ is never a perfect square.
Answer:
2, 3, 7 or 8
Step-by-step explanation:
Can some help with this problem
[tex]solve : - \\ \\ (4 {}^{2} + 5 {}^{2} ) = {?}[/tex]
Step-by-step explanation:
4² = 16
5² = 25
16+25 = 41
41 is the answer.
Hope it helps! :)
Answer:
[tex]( {4}^{2} + {5}^{2} ) \\ (16 + 25) \\ = 41[/tex]
Find the length of side xx in simplest radical form with a rational denominator.
Answer:
[tex]\frac{\sqrt{10} }{2}[/tex]
Step-by-step explanation:
on a 45 - 45 - 90 triangle if the sides are x then the hypotenuse is x[tex]\sqrt{2}[/tex]
so,
[tex]\sqrt{5}[/tex] = x[tex]\sqrt{2}[/tex] (Divide by [tex]\sqrt{2}[/tex] )
[tex]\frac{\sqrt{5} }{\sqrt{2} }[/tex] = x (rationalize the denominator)
[tex]\frac{\sqrt{5} }{\sqrt{2} }[/tex] · [tex]\frac{\sqrt{2} }{\sqrt{2} }[/tex] = [tex]\frac{\sqrt{10} }{\sqrt{4} }[/tex] = [tex]\frac{\sqrt{10} }{2}[/tex]
The length of side is √10/2
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The given triangle is a 45-90-45 so if the sides are x then the hypotenuse will be x√2
From the figure the hypotenuse of triangle is √5
SO equation it to x√2
We get √5=x√2
Divide both sides by √2
√5/√2=x
As the denominator should be a whole number we have to rationalize the denominator.
Multiply numerator and denominator with √2
√5/√2×√√2/√2
√10/2
Hence, the length of side is √10/2
To learn more on trigonometry click:
https://brainly.com/question/25122835
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Determine the area of an obtuse triangle with a height
of 11 cm and a base of 22 cm
Step-by-step explanation:
A
=
h
b
b
2
=
11
·
22
2
=
121
cm²
The area of the obtuse triangle with a height of 11 cm and a base of 22 cm is 121 cm².
To determine the area of an obtuse triangle, we can use the formula for the area of a triangle, which is given by:
Area = (1/2) * base * height
In this case, the height of the triangle is given as 11 cm and the base is given as 22 cm.
Substituting these values into the formula, we have:
Area = (1/2) * 22 cm * 11 cm
Calculating this expression, we get:
Area = (1/2) * 242 cm²
Simplifying further, we have:
Area = 121 cm²
The area of a triangle is calculated by multiplying half of the base by the height. In this case, the given height is 11 cm and the base is 22 cm. Substituting these values into the formula, the area of the obtuse triangle is calculated to be 121 cm².
To learn more about area click on,
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someone please please help me!
Answer:
[tex]mDE=90[/tex]°
Step-by-step explanation:
In this problem, one is asked to find the measure of the arc in degrees. This problem provides one with a diagram since the center is unnamed, call the center point (O). One is given the information that angle (<DOE) has a measure of (90) degrees. One is asked to find the degree measure of the surrounding arc (DE).
The central angles theorem states that if an angle has its vertex on the center of a circle, the degree measure of the angle is equal to the degree measure of the surrounding arc. One can apply this here by stating the following:
[tex]m<DOE = mDE\\[/tex]
Substitute,
[tex]90=mDE[/tex]
There are 36 pencils in 6 packs. Igor wants to know how many pencils are in 1 pack. Elsa wants to know how many pencils are in 3 packs. please help me I did not bring pencil and paper to Herman park
Answer:
18 pencils in 3 packs.
Step-by-step explanation:
Assuming that each pack will have the same amount of pencils. It is given that there are 36 pencils in all when one has 6 packs. Find the amount in each pack by dividing (total amount of pencils)/(amount of packs) = Amount of pencils per pack:
36/6 = 6
There are 6 pencils in each pack.
Now, Elsa wants to know how much pencils are in 3 packs. Multiply the amount of packs with the amount of pencils in each pack:
Total amount of pencils = amount of packs (3) x amount of pencils per pack (6)
= 3 x 6
= 18
There are 18 pencils in 3 packs.
~
