The expected number of radiation induced cancers according to the linear no threshold model of cancer induction is 500
Radiation is defined as the energy that comes from a source and travels through space at the speed of light.
Here we have given that 1,000,000 people are exposed to 10 msv and here we need to find the the expected number of radiation induced cancers according to the linear no threshold model of cancer induction.
As we all know that the amount of dose depends on the type of x-ray examination. A CT examination with an effective dose of 10 milli Sieverts
And it may be associated with an increase in the possibility of fatal cancer of approximately 1 chance in 2000.
therefore, here we have the total number as 1,000,000
Then the expected number if calculated as,
=> 1,000,000/2000
=> 500
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nd the local maximum and minimum values and saddle point(s) of the function. you are encouraged to use a calculator or computer to graph the function with a domain and viewpoint that reveals all the important aspects of the function. (enter your answers as comma-separated lists. if an answer does not exist, enter dne.) f(x, y)
Answers : A(-1,0) is a local maximum point, B(-1,2) is saddle point, C(3,0) is also a saddle point, D(3,2) is the minimum point.
saddle point : a point on a curved surface at which the curvatures in two mutually perpendicular planes are of opposite signs
The function :
f(x , y) = x³ = y³ = - 3x² - 3y² - 9x
The first partial derivative with respect to x is:
f' x = 3x²-6x-9
And the partial derivative with respect to y is:
f' y = 3y²-6y
Now equate the above derivatives to zero, to obtain the system of equation:
3x²-6x-9 = 0
3y²-6y = 0
On solving the two equations:
The critical points are : A(-1,0), B(-1,-2), C(3,0) and D(3,2)
Now calculate the discriminant
D = f xx(x , y)f y(x , y)-f xy(x , y)²
Here,
f xx = 6x-6
f yy = 6y-6
f xy = 0
On putting the above values we get:
D = (6x-6)(6y-6)
At, A(-1,0)
D = -18<0
Hence , A(-1,0) is a local maximum point.
At, B(-1,2)
D = -72<0
Hence B(-1,2) is saddle point.
At, C(3,0)
D = -72
Hence C(3,0) is also a saddle point
At, D(3,2)
D = 12>0
Hence , D(3,2) is the minimum point.
Answers : A(-1,0) is a local maximum point, B(-1,2) is saddle point, C(3,0) is also a saddle point, D(3,2) is the minimum point.
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four distinct fair coins are tossed. if it is known that at least one of the coins shows a head, what is the probability that all coins show heads?
Since, Four distinct fair coins are tossed. if it is known that at least one of the coins shows a head . The probability that all coins show heads is 3/4.
Probability:
Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes for an event. In an experiment with 'n' outcomes, the number of favorable outcomes can be denoted by x. The formula for calculating the probability of an event is:
Probability (Event) = Favorable Outcome / Total Outcome = x/n
The probability of an event can be calculated using the probability formula by simply dividing the number of favorable outcomes by the total number of possible outcomes. The value of the probability that an event will occur can range from 0 to 1. This is because the preferred number of outcomes can never exceed the total number of outcomes. Also, the resulting favorable number can never be negative.
Given that:
Four District fair coins are tossed.
So, possible outcomes are
HH,HT,TH,TT
We know that:
Probability= total possible outcomes / favorable outcomes
Now,
Favorable outcomes = HH,HT,TH
And,
Probability = 3/4
Therefore, the probability that all coins show heads is 3/4.
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Find the area of the shaded triangle
The area of shaded triangle is 20 square feet
What is the area?
A two-dimensional figure's area is the amount of space it takes up. In other terms, it is the amount that counts the number of unit squares that span a closed figure's surface.
Area of triangle = 0.5*base*height
Area of whole triangle = 0.5*8*10 = 40 square feet
Area of unshaded triangle = 0.5*4*10 = 20 square feet
Area of shaded triangle
= Area of whole triangle - Area of unshaded triangle
= 40 - 20
= 20 square feet
Thus, the area of shaded triangle is 20 square feet
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Find the sum of the geometric sequence if the first term is -8, the common ratio is -3 and there are 10 terms
Answer:
Step-by-step explanation:
The formula for the sum of a geometric sequence is: S = a(1 - r^n) / (1 - r)
In this case, our a = -8, r = -3, and n = 10.
S = -8(1 - (-3)^10) / (1 - (-3))
S = -8(1 - (-59049)) / 4
S = -8(59049) / 4
S = -2362196
Select the expressions that are equivalent to 5(4u).
20u - u+20 - u+9 - 5(u+3u)
The expressions that are equivalent to 5(4u) will be 20 u and 5(u + 3u).
How to calculate the expression?It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.
Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc. The expression that is equivalent to 5(4u) will be:
= 20 u
and
5(u + 3u)
= 20u
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What is a 3 regular graph?
A 3-regular graph is called a cubic graph. A strongly regular graph is a regular graph where every adjacent pair of vertices has an equal number of neighbors in common, and every non-adjacent pair of vertices has an equal number of neighbors in common.
In the mathematical field of graph postulate, a cubic graph is a graph in which all vertices have a degree of three. In other terms, a cubic graph is a 3-regular graph. Cubic graphs are also known as trivalent graphs.
A bicubic graph is called a cubic bipartite graph.
In graph theory, a regular graph is a graph where each vertex has an equal number of neighbors; i.e. every vertex has an equal degree or valency.
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If the age of a person and three-fourth of his áge are added, the result becomes 70 years. Find the age of the person.
A farmer has sixty three goats and twenty times as many sheeps. if the number of sheep he has is thirty times the number of his chickens , find the number of legs of the animals
Answer:
I would really like to help but I have no idea
Construct a confidence interval of the population proportion at the given level of confidence.
x=120 n =1200 95% confidence
The upper bound of the confidence interval is ____ (round to the nearest thousandth as needed)
The lower bound of the confidence intervals is ____ (round to the nearest thousandth as needed)
The confidence interval's upper and lower bounds, respectively, are 0.117 for the higher and 0.083 for the lower.
What is proportion's subject?The interaction between two or much more quantities is the focus of the branch of mathematics known as ratio and proportion. A key component of GCSE mathematics, ratio and proportion comprehension has connections to several subjects in number, algebra, geometry, probability, and statistics. An equilibrium for two ratios is a percentage. We use proportions to construct comparable ratios and find solutions to problems involving unknown numbers.
[tex]\begin{aligned}\bar{p} & =\frac{x}{n}=\frac{120}{1200}=0.10 \\\frac{\alpha}{2} & =\frac{1-\text { Confidence } \%}{2}=\frac{1-0.95}{2}=0.025 \\z_{1-\alpha / 2} & =z_{0.975}=1.960 \Rightarrow \text { Use the Excel formula "=NORMSINV(0.975)" }\end{aligned}[/tex]
[tex]S . E .=z_{1-\alpha / 2} \sqrt{\frac{\bar{p}(1-\bar{p})}{n}}=1.960 \sqrt{\frac{0.1(1-0.1)}{1200}}=0.017[/tex]
The confidence interval's top bound: [tex]\bar{p}[/tex] + S.E = 0.10 + 0.017 = 0.117
The confidence interval's lowest bound: [tex]\bar{p}[/tex] - S.E. = 0.10 - 0.017 = 0.083
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A boy ha 35 paperback book and 20 hardback book. What fraction of the book are hardback
The fraction of the books are hardback is 4 / 11.
In Mathematics, a fraction defined as the part of the whole thing. For example, a pizza is divided into four equal pieces, then each piece is represented by ¼. Fractions help to distribute and judge the numbers easily and make the calculation faster.
from given conditions, a boy ha 35 paperback book and 20 hardback book.
so, the total books are 35 paperback book + 20 hardback book = 55 books
fraction of books which are hardback book are,
20 / 55
= 4 / 11
Therefore, the fraction of the books are hardback is 4 / 11.
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If
\[x^2 - 7x + c = (x + a)^2\]for some constants $a$ and $c,$ then find $c.$
Answer:
Step-by-step explanation:
[tex]x^{2} -7x+c=(x+a)^{2}[/tex]
[tex]x^{2} -7x+c=x^{2} +2ax+a^{2}[/tex]
[tex]-7x=2ax\\a=-7/2[/tex]
[tex]a^{2} =c\\c=(-7/2)^{2} =49/4[/tex]
What is the volume of a hemisphere with a radius of 44. 9 m, rounded to the nearest tenth of a cubic meter?.
The volume of a hemisphere with a radius of 44.9 m is approximately 189582.2 cubic meters, rounded to the nearest tenth.
To calculate the volume of a hemisphere, you can use the formula
V = (2/3)πr^3
where V is the volume, π is pi (approximately 3.14), and r is the radius. In this case, r = 44.9 m.
So, (2/3)π(44.9)^3 = 189582.234 cubic meters.
This is the exact volume, but since the question asked for the volume rounded to the nearest tenth, the final answer would be 189582.234 cubic meters. It's worth mentioning that a hemisphere is half of a sphere, thus, the volume of a full sphere with a radius of 44.9 m would be double of this value.
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explain how to use arrays or area models to find factor pairs
Answer: An array is a visual representation of a multiplication problem, and an area model is a way to represent a multiplication problem using rectangles. Both arrays and area models can be used to find factor pairs of a number.
Here's an example of how to use an array to find the factor pairs of 12:
Draw a rectangle that represents 12.
Divide the rectangle into smaller rectangles by drawing rows and columns.
Fill in the rectangles with the numbers 1 through 12.
Find the factor pairs by looking for the rectangles that have the same area as the original rectangle, 12.
The factor pairs of 12 are 1 and 12, 2 and 6, and 3 and 4.
Here's an example of how to use an area model to find the factor pairs of 12:
Draw a rectangle that represents 12.
Divide the rectangle into smaller rectangles by drawing rows and columns.
Label the rectangles with the factors of 12, which are 1, 2, 3, 4, 6 and 12.
Find the factor pairs by looking for the rectangles that have the same area as the original rectangle, 12.
The factor pairs of 12 are 1 and 12, 2 and 6, and 3 and 4.
Both arrays and area models are an effective way of finding the factor pairs of a number because they help you to visualize the multiplication problem and to see the relationship between the factors and the product.
Step-by-step explanation:
How do I do this step by step
Answer:
84
Step-by-step explanation:
this is an isosceles triangle so the base angles are equal meaning <BAC= <BCA =48°
48° +48° =96°
180°- 96° = 84°
<ABC = 84°
The volleyball team at West View High School is comparing T-shirt companies where they can purchase their practice shirts. The two companies, Shirt Box and Just Tees, are represented by this system of equations where x is the number of T-shirts and y is the total cost of the T-shirts. y
Therefore , the solution of the given problem of linear equation comes out to be $105 is the total cost
The definition of a linear equation.A linear regression model is one that uses the equation y=mx+b. The slope is B, and the y-intercept is m. The preceding sentence is commonly referred to as a "math equation with two variables," despite the fact that both y and x are separate factors. The only variables in bivariate linear equations are two. In all circumstances, the solutions to linear equations' application domains are zero. Y=mx+b is the formula for a single linear equation.
Here,
The first company's equation is y = 10.5x.
Additionally, the second company's equation is y = 7.5x + 30.
Where
number of T-shirts equals x.
y = overall cost
For the overall cost to be the same for both businesses, we have to:
=> 10.5x = 7.5x + 30
=> 10.5 x - 7.5 x = 30
=> 3 x = 30
=> x = 30/3
=> x = 10
To make the T-shirts' prices equal, the volleyball team must purchase 10 from each vendor.
Total for each business:
=> 10.5x = 10.5 (10) = $ 105
OR
Totals for each company are calculated as follows:
=> 7.5x + 30 = 7.5(10) + 30 = 75 + 30
=> $105
Therefore , the solution of the given problem of linear equation comes out to be $105 is the total cost.
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A grocery store sells a bag of 6 oranges for $5.22. What is the cost of oranges, in dollars per orange?
The graph shows the depth in feet of snow after each two-hour period during a snowstorm. Find the slope of the line. Enter your answer an an integer or decimal.
Answer:
.5 or 1/2
Step-by-step explanation:
1-.5 .5
------=------- simplify= .5 slope is in fractions 1/2
2-1 1
Can someone please please help mke i was suppose to finnish this at least 2 weeks ago please can someone answer these 3 question for at leat 150 or 200 points.
The ratios are 80 : 2/3, 10 : 1/12 and 90 : 3/4 for the equivalent ratio 20 : 1/6.
What is equivalent ratio?By dividing both the antecedent and consequent values by a similar fraction, equivalent ratios can be reduced to the same value. In other words, two ratios are deemed equivalent if the bigger one in value can be expressed as a multiple of the other.
Therefore, we only need to multiply the two amounts by the same number to obtain the equivalent ratio of another ratio. Equivalent ratios and equivalent fractions both have similar ideas. Examples of equivalent ratios include 1:2 and 4:8, 3:5 and 12:20, 9:4 and 18:8, etc.
20 : 1/6
Multiply both by 6
120 : 1
Thus, 120 × 2/3 : 1 × 2/3
80 : 2/3
multiply by 3
80 × 3 : 2/3 × 3
240 : 2
120 : 2
When ratio is 120 : 1
divide both by 120
120/120 : 1/120
1 : 1/120
1 × 10 : 1/120 × 10
10 : 1/12
multiply by 12
120 : 1
1 × 90 : 1/120 × 90
90 : 3/4
multiply by 4
90 × 4 : 3/4 × 4
360 : 3
120 : 1
Thus, the ratios are 80 : 2/3, 10 : 1/12 and 90 : 3/4 for the proportion 20 : 1/6.
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291 is the same as 359 increased by the product of 125 and m
The equation 291 = 359 + 125m represents the given phrase, and the required value of m is 2.33
What is Algebra?Algebra is a discipline of mathematics that deals with symbols and the rules that govern their use. These symbols, known as variables in elementary algebra, indicate quantities with no set values. Equations in mathematics express relationships between variables in the same way that sentences indicate relationships between specific words.
The equation 291 = 359 + 125m can be solved for m by subtracting 359 from both sides, resulting in:
291 - 359 = 125m - 359
-68 = 125m - 359
Adding 359 to both sides gives:
-68 + 359 = 125m
291 = 125m
Dividing both sides by 125 gives the solution for m:
291 / 125 = 125m / 125
2.33 = m
So, m is equal to 2.33.
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The question seems incomplete, the completed question would be as:
If 291 is the same as 359 increased by the product of 125 and m. what is the value of f?
I need help with the following questions please!!!!!!
Step-by-step explanation:
f(-1) = (1/8)^-1 = 1/(1/8) = 8
f(0) = (1/8)⁰ = 1 (a⁰ = 1 for any a)
f(1) = (1/8)¹ = 1/8 = 0.125
f(2) = (1/8)² = 1/64 = 0.015625
f(3) = (1/8)³ = 1/512 = 0.001953125
remember
(a/b)ⁿ = aⁿ / bⁿ
in the same way as
(a×b)ⁿ = aⁿ×bⁿ
Help me I need help on how to do this I will upload 13 questions this is number 1
The value of x is 85°
What is angle of a sector?A circular sector, also known as circle sector or disk sector is the portion of a disk enclosed by two radii and an arc, where the smaller area is known as the minor sector and the larger being the major sector
A sector is a region bounded by two radii of a circle and the intercepted arc of the circle. The angle formed by the two radii is called a central angle. A sector with a central angle less than 180° is called a minor sector. A sector with a central angle greater than 180° is called a major sector.
The sector where x is the minor sector
The angular distance is x and it is measured in degrees (°)
Therefore the value of x is 85°
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The diameter of the Sun is 1.4 x 10 9 m and that of the Earth is 1.2756 x 10 7
m. Approximately how many times is the diameter of the sun greater as compared
to that of the earth ?
Answer:
The Sun has 1.0975 x 10^2 times the diameter of Earth
Step-by-step explanation:
Diameter of Sun = 1.4 x 10^9 m
Diameter of Earth = 1.2756 x 10^7 m
ratio between Diameter of Sun and Earth :-
Diameter of Sun/Diameter of Earth = 1.4 x 10^9/ 1.2756 x 10^7
= 1.0975 x 10^2
points r, s and t are vertices of an equilateral triangle, and points x, y and z are midpoints of its sides. how many noncongruent triangles can be drawn using any three of these six points as vertices?
2 congruent triangle can be drawn using any three of these six points as vertices.
What is triangle?A triangle in geometry is a three-sided polygon with three edges and three vertices.
The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic.
This characteristic is known as the triangle's angle sum property.
If ABC is a triangle, it is written as ABC, where A, B, and C represent the triangle's vertices.
In Euclidean geometry, a triangle is a two-dimensional shape represented by three non-collinear points in a single plane.
Hence, 2 congruent triangle can be drawn using any three of these six points as vertices.
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please help me.
What is
Answer:
90
Step-by-step explanation:
The symbol represented in the angle is the right angle symbol ∟
This means that the angle would be 90
Have a lovely day :)
Answer:
There's no m so I'm assuming you meant b.
The angle of b is 121
Step-by-step explanation:
The shape here is a heptagon. The formula for calculating the sum of interior angles is ( n − 2 ) × 180. *n represents the number of sides.
(7-2) × 180 There are 7 sides so plug that in.
(5) × 180 = 900 This means the shape's interior angles add up to 900.
Now, all we have to do is add up all the sides known and set it equal to 900.
c + d + e + f + g + a = 900
148 + 90 + 142 + 130 + 139 + 130 + b = 900
779 + b = 900
now subtract 779 from both sides to isolate b.
b = 121
Convert the following degree measure to radian measure 98
98 degrees is approximately equal to 5.48 radians.
How to convert degree measure to radian measure?
To convert a degree measure to a radian measure, you can use the conversion factor of 180/π.
98 degrees is equal to (98*π)/180 radians
So, 98 degrees is approximately equal to 5.48 radians.
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What is the product? help
Answer:
C. 14x^7-56x^6-126x^5+35x^4-140x^3-315x^2
I'm only providing an answer but if you need an explanation you can ask me because I did it in my journal.
Pls mark as brainliest ;)
Indicate if each equation in the table has no solutions, one solution, or
infinitely many solutions.
Questions
} (8 – 24x) =12
6x
OA
O C
-
Answer
Choices
A. No Solution
B. One Solution
C. Infinitely many
solutions
The correct option is A, the linear equation has no solutions.
How many solutions does the equation has?Here we want to see how many solutions do the equation below has:
(1/4)*(8 - 24x) = 12 - 6x
Now let's try to solve that linear equation, we can start by simplifying the left side:
(1/4)*(8 - 24x) = 12 - 6x
8/4 - 24x/4 = 12 - 6x
2 - 6x = 12 - 6x
Now we can add 6x in both sides, so we will get:
2 - 6x + 6x = 12 - 6x + 6x
2 = 12
That is a false equation, thus, the equation has no solutions.
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Can someone help me with this? I need an equation and the cup of nuts. It’s due tmr
Answer:
Step-by-step explanation:
I assume that the amount of peanut butter chips in original recipe is [tex]1\frac{1}{2}[/tex] c (the picture isn't clear!)
2( [tex]1\frac{1}{2}[/tex] + x ) = [tex]4\frac{1}{2}[/tex]
[tex]1\frac{1}{2}[/tex] + x = [tex]4\frac{1}{2}[/tex] ÷ 2
[tex]1\frac{1}{2}[/tex] + x = [tex]2\frac{1}{4}[/tex]
x = [tex]2\frac{1}{4}[/tex] - [tex]1\frac{1}{2}[/tex] = [tex]1\frac{5}{4}[/tex] - [tex]1\frac{2}{4}[/tex] = [tex]\frac{3}{4}[/tex]
There is [tex]\frac{3}{4}[/tex] of a cup of nuts in original recipe.
PLEEEEESSSSEEEEEEEE HALPPPPPPPP
Answer:
0.75 is less than 1, so the portrait will be smaller than the actual head.
Step-by-step explanation:
The art teacher has said that the portrait will be 0.75 times as tall as the actual head.
0.75 is less than 1, so the portrait will be smaller than the actual head.
A ratio of 0.75 means that the portrait will be 3/4 the size of the actual head. So, if the actual head is 8 inches tall, the portrait will be 6 inches tall (8*0.75 = 6). Therefore, the portrait will be smaller than the actual head.
Which graph shows the solution to the system of linear equations? y equals one half times x x + 2y = 8 coordinate plane with one line that passes through the points 0 comma 4 and 2 comma 5 and another line that passes through the points 0 comma 0 and 2 comma 1 coordinate plane with one line that passes through the points 0 comma 4 and 2 comma 3 and another line that passes through the points 0 comma 0 and 2 comma 1 coordinate plane with one line that passes through the points negative 1 comma 2 and 0 comma 4 and another line that passes through the points 0 comma 0 and 1 comma 2 coordinate plane with one line that passes through the points 0 comma 4 and 2 comma 0 and another line that passes through the points 0 comma 0 and 1 comma 2
Answer:
a line
Step-by-step explanation:
y equals one half times x x + 2y = 8 coordinate plane with one line that passes through the points 0 comma 4 and 2 comma 5 and another line that passes through the points 0 comma 0 and 2 comma 1 coordinate plane with one line that passes through the points 0 comma 4 and 2 comma 3 and another line that passes through the points 0 comma 0 and 2 comma 1 coordinate plane with one line that passes through the points negative 1 comma 2 and 0 comma 4 and another line that passes through the points 0 comma 0 and 1 comma 2 coordinate plane with one line that passes through the points 0 comma 4 and 2 comma 0 and another line that passes through the points 0 comma 0 and 1 comma 2
Answer:
B) A coordinate plane with one line that passes through the points (0, 4) and (2, 3) and another line that passes through the points (0, 0) and (2, 1)
Step-by-step explanation:
Given system of linear equations:
[tex]\begin{cases}y=\frac{1}{2}x\\x+2y=8\end{cases}[/tex]
Substitute the first equation into the second equation and solve for x:
[tex]\implies x+2\left(\dfrac{1}{2}x\right)=8[/tex]
[tex]\implies x+x=8[/tex]
[tex]\implies 2x=8[/tex]
[tex]\implies x=4[/tex]
Substitute the found value of x into the first equation and solve for y:
[tex]\implies y=\dfrac{1}{2}(4)[/tex]
[tex]\implies y=2[/tex]
Therefore, the solution to the given system of linear equations is:
(4, 2)The point of intersection is the solution to a graphed system of linear equations.
Therefore, the graph that shows the solution to the given system of linear equations is the graph where the point of intersection of the two lines is (4, 2).
