The amount of the 12 grams sample of gold-195m having a half-life of 30.5 s that would remain after 41 s is 4.726 g
How to determine the number of half-lives Half-life (t½) = 30.5 sTime (t) = 41 sNumber of half-lives (n) =?n = t / t½
n = 41 / 30.5
n = 82/61
How to determine the amount remaining Original amount (N₀) = 12 gNumber of half-lives (n) = 82/61Amount remaining (N) =?N = N₀ / 2ⁿ
N = 12 / 2^(82/61)
N = 4.726 g
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A frame around a rectangular family portrait has a perimeter of 138 inches. The length is nine more than three times the width. Find the length and width of the frame.
Given :
Perimeter of the frame is 138 inches.The length is nine more than three times the width⠀
To Find :
The Length and width of the frame .⠀
Solution :
We know that,
[tex]\qquad{ \bold{ \pmb{2(Length + Breadth ) = Perimeter_{(rectangle)}}}}[/tex]
Let's assume the width of the rectangle as x inches. Then the length will become (3x + 9).
⠀
Now, Substituting the given values in the formula :
[tex]\qquad \dashrightarrow{ \sf{2(3x + 9 + x )= 138}}[/tex]
[tex]\qquad \dashrightarrow{ \sf{2(4x + 9 )= 138}}[/tex]
[tex]\qquad \dashrightarrow{ \sf{8x + 18= 138}}[/tex]
[tex]\qquad \dashrightarrow{ \sf{8x = 138 - 18}}[/tex]
[tex]\qquad \dashrightarrow{ \sf{8x = 120}}[/tex]
[tex]\qquad \dashrightarrow{ \sf{x = \dfrac{120}{8} }}[/tex]
[tex]\qquad \dashrightarrow{ \bf \: x = 15}[/tex]
⠀
Therefore,
[tex]\qquad { \pmb{ \bf{ Width _{(frame)} = x = 15 \: inches}}}\:[/tex]
[tex]\qquad { \pmb{ \bf{ Length _{(frame)} = (3x + 9) \: = 3(15) + 9 = 54 \: inches}}}\:[/tex]
Kiara has already written 37 pages, and she expects to write 1 page for every additional hour spent writing. How many hours will Kiara have to spend writing this week in order to have written a total of 50 pages?
Answer:
13 hours
Step-by-step explanation:
Since Kiara has already written 37 pages she only needs 13 more to get to 50 pages. If she takes one hour per page then it will take her 13 hours to write 13 pages.
I need help on it pls pls
Answer:
b,d
Step-by-step explanation:
find the equation of a line passes through a point (0,4) and has a gradient of 2. leave your answer in the form y=mx+c
Answer:
y = 2x + 4
Step-by-step explanation:
the equation of a line in point- slope form is
y = mx + c ( m is the slope and c the y- intercept )
here m = 2 and passes through point (0, 4 ) ⇒ c = 4
y = 2x + 4 ← equation of line
Answer:
y = 2x + 4
Step-by-step explanation:
General form of linear equation: y = mx + c
where m is the gradient and c is the y-intercept
Given gradient = 2
⇒ m = 2
⇒ y = 2x + c
y-intercept is when x = 0
Given (0, 4), so y = 4 when x = 0
⇒ c = 4
⇒ y = 2x + 4
I need help with B find the roots
Answer:
-1 and 3
Step-by-step explanation:
The roots of the quadratic function can be determined by [tex]f(x')=0[/tex] where x' is the roots of the quadratic function. In that graph, x = -1 and x = 3 makes the value of f(-1) = 0 and f(3) = 0. So, x = -1 and x = 3 are the roots of the f(x).
What is the area of this trapezoid?
Enter your answer in the box.
__ft²
Answer:
468 ft²
Step-by-step explanation:
Area= (sum of the 2 parallel sides÷2)×perpendicular height
=(15+37)÷2×18
=52÷2×18
=468
Angle 1 and Angle 2 are complimentary angles. Find x and the measure of Angle 1.
Angle 1 = (3x+2)°
Angle 2 = (4x +4)º
x = ?
The measure of Angle 1 = ?
degrees
Answer:
x=12 pls give brainliest
Step-by-step explanation:
Answer: x = 12, Angle 1 = 38°
Step-by-step explanation: Complimentary angles add up to 90°.
Add the two angles and set them equal to 90°:
(3x + 2) + (4x + 4) = 90
Add like terms:
7x + 6 = 90
Subtract 6 from both sides:
7x = 84
Divide both sides by 7:
x = 12
Now, to get Angle 1, plug x in:
Angle 1 = 3(12) + 2
Angle 1 = 38°
Hope this helps!
Equation 1) 2x - 3y = 6 Equation 2) 4y - x = 12 *
Answer:
2x - 3y = 6
[tex]x = 3 + \frac{3y}{2}[/tex]
[tex]y = 2 + \frac{2x}{3}[/tex]
4y - x = 12
[tex]x = 12 + 4y\\y = 3 + \frac{x}{4}[/tex]
Step-by-step explanation:
Divide both sides of the equation to "solve for x and y."
Hope it helps!!!Brainliest pls!!!pahelp pooo, thank u
Answer:
1. 25 cm^2
2. 9 m
3. 4.8x5=24 m^2
4. 56/6=9.33 cm
5. 8x7.2=57.6 m^2
If a 40 ft tall flagpole casts a 256 ft long shadow then how long is the shadow that a 6 ft tall woman casts?
feet
Answer:
38.4 ft
Step-by-step explanation:
Basically, draw out your two Situations like I have did.
Then find the scale factor by doing 6/40.
Multiply the SF by 256 to get X, or the shadow of the woman.
The screenshot provided shows the drawings.
which number line expression show how to find distance from 2 to -5?
the last one is the line expression who shows the distance from 2 to negative 5
Option D is the correct answer.
We need to identify which number line expression shows how to find the distance from 2 to -5.
What is a number line?A line on which numbers are marked at intervals is used to illustrate simple numerical operations.
If we see option D, it has been marked correctly at 2 and -5.
Therefore, option D is the correct answer.
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#SPJ5
how do you write 13. 085 in words
ANSWER
thirteen point zero eight five
Juanita walks 3 hours and burns 750 calories
Answer:
And............ What?
HELLLLLP ILL GIVE BRAINLIEST!!!!
Given that each package contains 9 trading cards.
Packages Trading cards
2 18
4 36
7 63
The question is in the picture, please help.
Answer:
how to understand the problem is picture the shape as a house and try to figure out what to do next
Step-by-step explanation:
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. Match each pair of points A and B to point C such that ∠ABC = 90°. A(3, 3) and B(12, 6) C(6, 52) A(-10, 5) and B(12, 16) C(16, -6) A(-8, 3) and B(12, 8) C(18, 4) A(12, -14) and B(-16, 21)
9514 1404 393
Answer:
A(3, 3) and B(12, 6), C(16, -6)A(-10, 5) and B(12, 16), C(18, 4)Step-by-step explanation:
As the attached diagram shows, a perpendicular line from B intersects a choice of C only for B1(12, 6) and B2(12, 16). We note that there are only 3 choices of point C shown, instead of 4, so the question may be incomplete.
__
It seems easiest to graph the points and use a square (right-angle tool) to identify points C that may be appropriate.
It can also work to use a spreadsheet to do the slope calculations. You want to find a point C such that BC ⊥ AB, for a given AB pair. That is, the slope of BC is the negative reciprocal of the slope of AB.
The 2nd and 3rd C points listed make right angles with the 1st and 2nd AB pairs listed, respectively.
Pieter wrote the equation 7h – 5(3h – 8) = –72 to model the number of hours it takes to dig a well to a level of 72 feet below sea level. How many hours will it take to dig the well?
4
10
14
17
Answer:14
Step-by-step explanation:
Answer:
14
Step-by-step explanation: Correct
HEY GUYS HELP ME ON THIS ONE PLS DO IT FAST
Answer:
The answer is 72
Step-by-step explanation:
The formula to find the area of a trapezoid
[tex]A= \frac{1}{2}h(b_{1} + b_2{} )[/tex]
First, we can add the bottom base together
5 + 8 + 3 = [tex]16_{2}[/tex]
We know that the height of the trapezoid is 6 and base1 is 8
[tex]A= \frac{1}{2}6(16 + 8)[/tex]
[tex]A=\frac{1}{2}6(24)[/tex]
[tex]A=3(24)[/tex]
[tex]A=72[/tex]
OR
Find the area of the two triangles
[tex]A=\frac{1}{2}5(6)\\\\A=5(3)\\\\A=15\\\\[/tex][tex]A=\frac{1}{2}3(6)\\\\A=3(3)\\\\A=9\\[/tex]
15 + 9 = 24
For the area of the rectangle
6 x 8 = 48
48 + 24 = 72
Solve for p: 5p+1/8 =3p-5/4 *Make sure you show all your work.
HELPP PLS!!!
Step-by-step explanation:
I think this is the answers. hope it helps you
The figure has line(s) of symmetry. What type(s) of symmetry does the figure have?
Answer:
i domisa
Step-by-step explanation:
If 5000 is borrowed with an interest of 12.3% compounded semi-anually
Answer:
312.5
Step-by-step explanation:
P=5000
r=12.5%=0.125
t=6month=0.5years
I=P•r•t
I=(5000)(0.125)(0.5)
I =$312.5
when a cannonball is fired, the equation of its pathway can be modeled by h=-16t^2+128t
Answer:
there is no way to further simplify the equation
Step-by-step explanation:
Mike spent half of his allowance going to the movies. He washed the family
car and earned 9 dollars. What is his weekly allowance if he ended with 16
dollars ? HELP
Answer: Mike's weekly allowance is 20 dollars
Step-by-step explanation:
1 and 3 fourths - 7/10
Answer:
1.05
There you go!
Find the area of the following figure. Explain how you got your answer.
Answer:
26.5
Step-by-step explanation:
cut the shape into 3 shapes
area of a retangle is = L*W= 5*4 = 20
Area of a triangle = a= h*b/2 = 3*3/2 = 4.5
Area of a triangle = a= h*b/2 = 2*2/2 =2
can someone answer this question plsss now now
Answer:
Abe I would estimate 20 and actual time would be 21
Lane I would estimate 15 and the actual time would be 17
Norma I would estimate 15 and actual time would be 13
Amado I would estimate 40 and actual time would be 40
Cesar I would estimate 25 and actual time would be 25
Step-by-step explanation:
Hope this helps a bit!
Sketch a graph of x−y=−4
Answer:
x-intercept(s):
(
4
,
0
)
y-intercept(s):
(
0
,
−
4
)
Step-by-step explanation:
What is the value of x?
3
4
5
6
Answer:
x = 6
Step-by-step explanation:
Using the relationships between the entries in the table, you can find x two different ways.
1.The numbers down the Total column add to give the one at the bottom:
0.1 + 0.09x = 0.64
0.09x = 0.54 . . . . . . . subtract 0.1
x = 6 . . . . . . . . . . . . divide by 0.9
__
2.The product of the numbers in the first two columns is the number in the third. On the bottom row, this means ...
(2 +x)(0.08) = 0.64
2 +x = 8 . . . . . . . . . . . divide by 0.08
x = 6 . . . . . . . . . . . subtract 2
Consider Nibbles, a very specialized brand of parakeet chow.
When its price is $16 per package, it sells 40,000 units. When its price rises to $20, it sells 30,000
units. Calculate its price elasticity of demand, carefully following all numeric directions. You will
interpret this result in the next question.
The price elasticity of demand for the parakeet chow is 1.33.
What is price elasticity of demand?Price elasticity of demand is the change in product quantity demanded to change in price.
From the question:
[tex]\%\ Change\ in \ quantity=\frac{30000-40000}{30000}= -33.3\%\\\\\%\ Change\ in \ price=\frac{20-16}{16}= 25\%\\\\PED=|\frac{\%\ Change\ in \ quantity}{\%\ Change\ in \ price} |=|\frac{-33.3\%}{25\%}|=1.33[/tex]
The price elasticity of demand for the parakeet chow is 1.33.
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In an accelerated failure test, components are operated under extreme conditions so that a substantial number will fail in a rather short time. In such a test involving two types of microchips, 620 chips manufactured by an existing process were tested, and 125 of them failed. Then, 820 chips manufactured by a new process were tested, and 130 of them failed. Find a 90% confidence interval for the difference between the proportions of failures for chips manufactured by the two processes. (Round the final answers to four decimal places.) The 90% confidence interval is ( . , ).
Answer:
The 90% confidence interval is [tex] 0.0097 < p_1 -p_2 < 0.0773 [/tex]
Step-by-step explanation:
From the question we are told that
The first sample size is [tex]n_1 = 620[/tex]
The number of chips that failed is k = 125
The second sample size is [tex]n_2 = 820[/tex]
The number of chips that fail is [tex]u = 130[/tex]
Generally the confidence level is 90% , hence the level of significance is
[tex]\alpha = (100 - 90)\% [/tex]
=> [tex]\alpha = 0.10 [/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]
Generally the first sample proportion is
[tex]\r p _1 = \frac{125}{620}[/tex]
=> [tex]\r p _1 = 0.202[/tex]
Generally the second sample proportion is
[tex]\r p _1 = \frac{130}{820}[/tex]
=> [tex]\r p _1 = 0.1585[/tex]
Generally the standard error is mathematically represented as
[tex]SE = \sqrt{\frac{\r p_1 (1 - \r p_1)}{n_1} +\frac{\r p_2 (1 - \r p_2)}{n_2} }[/tex]
=> [tex]SE = \sqrt{\frac{0.202(1 - 0.202)}{620} +\frac{0.1585 (1 - 0.1585)}{820} }[/tex]
=> [tex]SE = 0.0206[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * SE[/tex]
=> [tex]E = 1.645 * 0.0206[/tex]
=> [tex]E =0.0338[/tex]
Generally 95% confidence interval is mathematically represented as
[tex](\r p_1 -\r p_2) -E < p_1 - p_2 < (\r p_1 -\r p_2) +E [/tex]
=> [tex](0.202 -0.1585) -0.0338 < p_1 - p_2 < (0.202 -0.1585) +0.0338 [/tex]
=> [tex] 0.0097 < p_1 - p_2 < 0.0773 [/tex]