Answer: Intenisy = 83.2 milliroentgens per hour
Let the intensity from the radiation = I
Let the distance = d
The intensity is inversely proportional to the square of its distance
[tex]\begin{gathered} I\text{ }\propto\text{ }\frac{1}{d^2} \\ \text{Introducing a proportionality constant} \\ I\text{ = }\frac{k\text{ x 1}}{d^2} \\ I\text{ = }\frac{k}{d^2} \\ \text{When I = 62.5 , d = 3} \\ \text{From the above equation} \\ K=I\cdot d^2 \\ K\text{ = 62.5 }\cdot(3)^2 \\ K\text{ = 62.5 x 9} \\ K\text{ = 562.5 } \\ \text{ Find the intensity wen D = 2.6 meters} \\ I\text{ = }\frac{k}{d^2} \\ I\text{ = }\frac{562.5}{(2.6)^2} \\ I\text{ = }\frac{562.5}{6.76} \\ I\text{ = 83. 2 milliroentgens per our} \end{gathered}[/tex]Set up a proportion and soive for
side TV (y):
ATUV-AXWV
As we Know that, ΔTUV[tex]\sim[/tex] ΔXWV
So, for the given proportion TV(y) = 21.
What is Proportion?
A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls. 0.25 are male (by dividing 1 by 4)
What is Ratio?
The link between two or more things in terms of quantity, amount, or size.
Given that,
ΔTUV[tex]\sim[/tex] ΔXWV
∠T = ∠X
∠U = ∠W
∠TUV = ∠XWV
So, TU/WX = TV/WV
10/10 = TV/21
1 = TV/21
TV = 21
So, for the given proportion the value for the side TV(y) = 21
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Sketch the graph of y= sin x° for 0≤x≤360
Answer:
Step-by-step explanation:
This is a sketch graph of y= sin x° for 0 ≤ x ≤360.
It is called as Sine curve. A mathematical curve described in terms of the sine trigonometric function, of which it is the graph, is known as a sine wave, sinusoidal wave, or simply sinusoid. It is a smooth periodic function and a particular kind of continuous wave.
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help meeeeeeeeeeeeeee pleaseeeeeee
Answer: 2.5, 5.4
Step-by-step explanation:
[tex]-16t^2 +126t=213\\\\16t^2 -126t+213=0\\\\t =\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(213)}}{2(16)}\\\\t \approx 2.5, 5.4[/tex]
√20 - 2√5solve with using adding and subtracting radicals
the initial expression is:
[tex]\sqrt[]{20}-2\cdot\sqrt[]{5}[/tex]so to rest them we want to have the same radical so we can rewrite the root of 20 so:
[tex]\begin{gathered} \sqrt[]{4\cdot5}-2\cdot\sqrt[]{5} \\ 2\cdot\sqrt[]{5}-2\cdot\sqrt[]{5}=0 \end{gathered}[/tex]a board of directors consists of ten men and five women. a four-member search committee is randomly chosen to recommend a new company president. what is the probability that all four members of the search committee will be women?
The probability of all four women being on the search committee as members in it is 1/273.
We have 15 people in total out of which there are 10 men and 5 women. We need four people on the committee out of these 15.
The probability of that happening can be calculated using the formula -
= Probability of all four women getting selected/Probability of all getting selected
= (5!/4!.1!) / (15!/4!11!)
= (5!/4!1!) * (4!11!/15!)
= (5*4*3*2*1) / (15*14*13*12)
= 1/273
From this, we know that if we need to have all four women as members of the search committee, the probability of that happening is 1/273.
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Which equation represents a proportional relationship?
OA. y = 4x
OB. y=3x2
OC. y = 5x+2
OD. y = 7
A is the equation representing proportional relationship .
What is proportional relationship ?Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportionate relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of this constant.
CalculationIf the y intercept is anything but 0, then the linear function is not proportional. So C is not proportional (2 is the y intercept)
B is a quadratic and it will not give proportional results. y/x is not a constant.
D has no x value and is not going to give a proportional result. y/x is undefined.
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What is an equation of the line that passes through the points (6,0) and (3, 4)?
The slope-intercept form of the equation of a straight line is given to be:
[tex]y=mx+b[/tex]where m is the slope and b is the intercept on the y-axis.
The slope is calculated using two points on the line by the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Therefore, for this line, the slope will be:
[tex]m=\frac{4-0}{3-6}=-\frac{4}{3}[/tex]Therefore, this value for the slope is substituted back into the equation for the line:
[tex]y=-\frac{4}{3}x+b[/tex]At the point (6, 0), we can calculate the value of b to be:
[tex]\begin{gathered} 0=-\frac{4}{3}(6)+b \\ b=\frac{4}{3}(6) \\ b=8 \end{gathered}[/tex]Therefore, the equation is:
[tex]y=-\frac{4}{3}x+8[/tex]If point (x, y) is reflected over the line y = x, the resulting point is (y,x).TrueFalse
When we reflect a point over y = x, the x and y coordinates become swapped and switch places, that is why (x,y) results to (y,x).
Therefore, the answer is true.
prime or composite
number 1
67
67 is a prime number and 1 is neither prime nor composite number.
What is prime number and composite number?
A prime number is a number which has exactly two factors i.e. '1' and the number itself. A composite number has more than two factors, which means apart from getting divided by 1 and the number itself, it can also be divided by at least one positive integer.
The given two numbers are 1 and 67.
Since, the prime numbers from 1 to 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
67 has exactly two factors i.e. 1 and the number 67 itself.
Therefore, 67 is a prime number.
Due to the fact that it only has one factor, 1, number is not a prime.
Hence, 67 is a prime number and 1 is neither prime number nor composite number.
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A store that sells cell phones has cell-phone covers in a variety of 6 colors and 6 designs. An employee will randomly choose a cell-phone cover to give to each customer who purchases a new cell
phone. Which simulation best models the outcomes of the possible cell-phone covers?
rolling two number cubes at the same time and recording the results
flipping a coin twice and recording the results
rolling a number cube and recording the results
rolling a number cube, flipping a coin, and recording the results
Answer: I am pretty sure that the answer is flipping a coin twice and recording the result
Step-by-step explanation: my reasoning is you can compare the results unlike the rest
What values of c and d would make
the following expression represent a real number?
i(2 + 3i)(c + di)
c = 2, d = 3
c = –2, d = 3
c = 3, d = –2
c = –3, d = –2
The values of c and d that would make that the given expression represent a real number are c = –3, d = –2.
What is meant by the term real number?In mathematics, a real number is a quantity that may be articulated as just an infinite decimal expansion. In comparison to the natural numbers 1, 2, 3,..., which are derived from counting, real numbers are employed in measurements of varying different quantities including such size and time.For the given question;
The expression is given as;
= i(2 + 3i)(c + di)
Simplify the expression;
= i(2c + 2di + 3ci + 3di²)
= 2ci + 2di² + 2ci² + 3di³
= (2c - 3d)i - 2d - 3c
In order is for expression to yield a real number, the coefficient of must now be zero.
Check the values from option;
2c - 3d = 2 x 2 - 3x 3 = -5
2c - 3d = 2 x -2 - 3 x -3 = -13
2c - 3d = 2 x 3 + 3 x -2 = -1
2c - 3d = 2 x -3 -3 x - 2 = 0
Thus, the correct values for the expression to becomes real number is
c = –3, d = –2.
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Jennifer's family is going to see the Atlanta Symphony Orchestra. Tickets cost $79 each, and there is a $14.95 convenience fee for each ticket. If Jennifer's mom buys tickets for 6 people, how much money does she spend in all?
Answer:
563.7
Step-by-step explanation:
add 79 + 14.95 and multiply that by 6
What number will complete the point-slope equation that models this scenario?
y−50,000=[_______](x−10)
−3,000
−2,000
2,000
3,000
A Point-Slope equation of a straight line models this scenario: y -50,000 = -3,000(x -10).
What is the Point-slope form?The equation of the straight line has its slope and given point.
If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation
y-y₁ = m(x-x₁)
We can recognize any points of the graph.
(0,80000) ; (10,50000)
Given that;
y -50,000 =______(x -10)
We need to find the slope.
Slope = Change in y / Change in x
Slope = 80,000 - 50,000 / 0 - 10 = 30,000 / -10
= -3,000
The slope is equal to -3000 that is Choice A; y -50,000 = -3,000(x -10)
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The complete question is;
The newspaper in Haventown had a circulation of 80,000 papers in the year 2000. In 2010, the circulation was 50,000. With x = 0 representing the year 2000, the graph below models this scenario.
Do 5 + 3 and 3 + 5 represent the same express? Explain.
5 + 3 = 8
3 + 5 = 8
The represent the same expression
|x - 7| ≥ 1?
what is the solution?
Answer: Inequality form: x is less then or equal to 6 or xis greater then or equal to 8
Interval Notation: (-infinity,6] u [8,infinity)
Answer:
x ≤ 6 ∨ x ≥ 8
Step-by-step explanation:
x-7 ≥ 0
when
x≥7
if x≥7
x-7≥ 1
x ≥ 7 + 1
x ≥ 8
if x < 7
-x + 7 ≥ 1
-x ≥ -7 + 1
-x ≥ -6
x ≤ 6
Final solution
x≤ 6 ∨ x ≥ 8
write the new coordinates after a glide reflection described by. (x,y) (x, y-2) reflection in x=0.
To find the new coordinates, we just have to use the given rule
[tex](x,y)\rightarrow(x,y-2)[/tex]Let's apply it to each vertex
[tex]\begin{gathered} A(2,10)\rightarrow A^{\prime}(2,10-2)\rightarrow A^{\prime}(2,8) \\ B(3,-4)\rightarrow B^{\prime}(3,-4-2)\rightarrow B^{\prime}(3,-6) \\ C(-3,1)\rightarrow C^{\prime}(-3,1-2)\rightarrow C^{\prime}(-3,-1) \end{gathered}[/tex]Therefore, the new coordinates are A'(2,8), B'(3,-6), and C'(-3,-1).Solve for u.
-2|3u| +5 > -5
The value of u is -5/3 < u < 5/3
We need to calculate the value of u
-2|3u| +5 > -5
-2(3u) + 5 > -5
-6u + 5 > -5
-6u > -10
6u < 10
3u < 5
u < 5/3
-2(-3u) + 5 > -5
6u + 5 > -5
6u > -10
3u > -5
u > -5/3
Therefore, the value of u is -5/3 < u < 5/3
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PAINTINGS Julio is selling paintings that he made. He sells each painting for $25, and he spent $200 on supplies to make the paintings. The function m=25p−200 represents the profit m that Julio earns after selling p paintings. Find the zero of the function. Describe what this value means in the context of the situation.
The zero of the function m = 25p - 200 is, p = 8 represents her break even.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, He sells each painting for $25, and he spent $200 on supplies to make the paintings.
The function m = 25p - 200 represents the profit m that Julio earns after selling p paintings.
The zeroes of the function is when she break even,
At p = 8 means after selling 8 paintings she will have break even as,
m = 25(8) - 200.
m = 200 - 200.
m = 0.
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true or false? The sun of an even whole number and an odd whole number is always odd.
Answer:
the sum of an even whole number and odd whole number is always odd ,
True
help me solve this
-7+3=?
-4Answer:
Step-by-step explanation:
Answer:
-7 + 3 = -4
Step-by-step explanation:
May I have Brainliest please? I am so close to getting my next ranking! I just need 2 more for it! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
suppose that there are two types of tickets: advanced and same day. advance tickets cost $25 and same day tickets are $30.for one performance there were 65 tickets sold in all. and the total amount paid for them was $1800.how many tickect of each were sold
The number of advance and same day tickets sold are 25 and 35 respectively.
How many tickect of each were sold?let
number of advance tickets sold = xNumber of same day tickets sold = yx + y = 65
25x + 30y = 1800
From (1)
x = 65 - y
Substitute x = 65 - y into (2)
25x + 30y = 1800
25(65 - y) + 30y = 1800
1625 - 25y + 30y = 1800
5y = 1800 - 1625
5y = 175
y = 175/5
y = 35
Substitute y = 35 into (1)
x + y = 65
x + 35 = 65
x = 65 - 35
x = 25
Therefore, Simultaneous equation is used to determine the number of advance and same day tickets sold.
25 advance tickets and 35 same day tickets were sold.
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Describe how a drywaller might use a formula to estimate the
number of sheets of drywall needed for a room.
Answer:
Square footage
Step-by-step explanation:
Four times a number is less than 56. Find the largest integer that satisfies the inequality
13.
13x4 is 52 which is the largest integer that's less than 56.
14 x 4 is 56 which is equal or less than.
You and your best friend have $10,000 each, which you would like to keep in a savings account. 5/3rd bank offers 4.23% continuous interest and bank of america will give 4.4% interest compounded quarterly. what would be the difference between the two investments after 35yrs? (round to the nearest dollar (whole number))
The difference between the two investments after 35yrs is $4700 and Bank of America is offering higher interest than 5/3rd banks.
Explain compound interest and continuous interest.Most interest is compounded semiannually, quarterly, or monthly. Continuous compounding assumes that interest is compounded indefinitely and reentered on the balance sheet. The continuous compounding formula takes into account four variables.
For the given question,
5/3rd bank offers continuous interest:
For continuous interest, A = P[tex]e^{rt}[/tex]
where,
P = the initial amount
A = the final amount
r = the rate of interest
t = time
e is a mathematical constant where e ≈ 2.7183.
A = 10000 × [tex]2.71^{0.042*35}[/tex]
A = 10000 × 4.04
A = $40400 approximately
Interest = Amount - Principle
Interest = 40400 - 10,000
Interest = $30400
Bank of America offers compound interest:
For compound interest:
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
A = 10000 × 4.51
A = $45100
Interest = Amount - Principle
Interest = 45100 - 10,000
Interest = $35100
The above calculation explains Bank of America is offering higher interest than 5/3rd bank by $35100 - $30400 = $4700
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a line that passes through the point (2,1) and is parallel to the line y = -2x + 5
A line in slope-intercept form is represented by the following equation:
[tex]\begin{gathered} y=mx+b \\ \text{where,} \\ m=\text{slope} \\ b=y-\text{intercept} \end{gathered}[/tex]Parallel lines have the same slope, then if the line is parallel to the line y=-2x+5, the slope of the parallel line would be -2 too.
Now, by the given point (2,1) and knowing the slope of the line, we can use the slope-point form of the line equation to get the slope-intercept form:
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ \text{where,} \\ (x_0,y_0)\text{ is the given point} \\ m\text{ is the slope} \end{gathered}[/tex]Substituting:
[tex]\begin{gathered} y-1=-2(x-2) \\ y=-2x+4+1 \\ y=-2x+5 \end{gathered}[/tex]Notice that the parallel line would be the same original line, y=-2x+5.
help meeeeeeeeeeeeeee pleaseeeeeee
Answer: Width = 4.7 meters, Length = 6.7 meters
Step-by-step explanation:
Let the width be w. Then, the length is w+2.
[tex]w(w+2)=32\\\\w^2 +2w=32\\\\w^2 +2w-32=0\\ \\ w=\frac{-2 \pm \sqrt{2^2 -4(1)(-32)}}{2(1)}\\\\w \approx 4.7\\\\\implies w+2 \approx 6.7[/tex]
Given 3 and one-tenth times negative 6 times seven-twelfths, determine the product.
eighteen and one sixtieth
negative eighteen and 7 over 120
ten and 17 over 20
negative 10 and 17 over 20
The given statement expression is equivalent to -2 [tex]\frac{1}{10}[/tex].
What is a expression? What is a mathematical equation? What is Equation Modelling? What are complex numbers?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted [i], called the imaginary unit and satisfying the equation -
[tex]{\displaystyle i^{2}=-1}[/tex]
Every complex number can be expressed in the form a + bi, where [a] and [b] are real numbers
We have the following statement -
3 and one-tenth times negative 6 times seven-twelfths
We can write -
3 (1/10 x - 6) × 7/12
- 3 [tex]\frac{3}{5}[/tex] × 7/12
-18/5 × 7/12
-3/5 x 7/2
- 21/10
- 2 [tex]\frac{1}{10}[/tex]
Therefore, the given statement expression is equivalent to -2 [tex]\frac{1}{10}[/tex].
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BRAINLIST PLEASE HELP!
(a) Angle B = Angle C = 65 degree.
(b) Angle x and Angle y is 70 degree .
Given,
In the question:
9. Write a sequence of rigid motion to take figure ABC to figure DEF.
Now According to the question:
Take a figure ABC to figure DEF
So, CB = FE
BA = ED
Angle B = Angle E
10.(a) To find the unknown measure:
In triangle ABC
Angle A = 90 degree
To find the Angle B and C
Let the angle B and C be x
We know that :
Sum of angle triangle is 180 degree
50 + x + x = 180
50 + 2x = 180
2x = 180 - 50
2x = 130
x = 65°
Hence, Angle B = Angle C = 65 degree.
10. (b) Given,
Angle ABC = Angle BAC
If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
Substitute Angle ABC = y and Angle BAC = x into Angle ABC = Angle BAC .
Angle (ABC + ACB + BAC) = 180 degree (Angle sum theorem)
=> y + 40 + x = 180
=> x + 40 + x = 180
=> 2x = 180 - 40
=> 2x = 140
x = 70°
Hence, Angle x and Angle y is 70 degree .
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What percent of 120 is 180%
What percent of 120 is 180
we know that
120 represent the 100%
so
Applying proportion
100/120=x/180
solve for x
x=(100/120)*180
x=150%
the answer is 150%In a video game, Shar has to build a pen shaped like a right triangle for her animals. If she needs 6 feet of fence for the shortest side and 10 feet of fence for the longest side, how many feet of fencing is needed for the entire animal pen?
If in a video game, Shar has to build a pen shaped like a right triangle for her animals. The feet of fencing that is needed for the entire animal pen is : 24 feet.
How to find the feet of fencing needed?First step is to make use of Pythagorean theorem formula to find the other side of the triangle
c= √a²+b²
Where:
a=Side of right triangle
b=Side of right triangle
c=hypotenuse
= √(10² - 6²)
=√(100 - 36)
= √62
= 8 feet
Now let find the perimeter of the triangle
Perimeter of the triangle = 6 feet + 8 feet + 10 feet
Perimeter of the triangle = 24 feet
Therefore the feet needed is 24 feet.
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Answer:24 feet
Step-by-step explanation:i took a test