Answer:
It will take 15.029 years for element X to reach mass of 260 grams
Step-by-step explanation:
The half life period of radioactive element X is 26 years
The initial mass of radioactive element X is 260 grams
Elapsed time = half life * log (beginning amount /ending amount)/log 2
Substituting the given values, we get
Elapsed time = 26 * log (390/260)/log 2
= 15.209 years
A company wanted to estimate the mean lifetime of its new model of lightbulbs. They use a method for testing bulbs that accelerates the process so the bulbs burn out relatively quickly, and the company can accurately calculate the corresponding lifetime under regular usage. They took a random sample of 555 of these new bulbs and calculated their lifetimes. Here are the data and summary statistics:
Bulb 1 2 3 4 5
Lifetime 14.2 12.2 13.4 12.6 14.6
Mean= 13.4 years
Standard deviation= sx =1.02 years
Required:
Wrtite a 90% confidence interval for the mean lifetime in years) for this type of bulb.
Answer:
13.4±2.132(1.02/5)
Step-by-step explanation:
Khan Academy
The confidence interval for the mean life time is; CI = 13.4 ± 3.678(1.02/5)
What is the confidence interval?
Formula for confidence interval is;
CI = x' ± z(s/√n)
We are given;
Mean; x' = 13.4
Standard deviation; s = 1.02
Sample size; n = 5
z-score at confidence level of 90% = 1.645
Thus;
CI = 13.4 ± 1.645(1.02/√5)
CI = 13.4 ± 3.678(1.02/5)
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what is 8w+5=4(2w+1)
Answer:
No solution
Step-by-step explanation:
1. Distribute the right side.
8w+5=8w+4
2. This has no solution.
n 2019, approximately 97.4% of all the runners who started the Boston Marathon (in Boston, Massachusetts, USA) were able to complete the 42.2 km (26.2 mile) race. If 100 runners are chosen at random, find the probability that at least 5 of them did not finish the marathon
Answer:
0.1199 = 11.99% probability that at least 5 of them did not finish the marathon
Step-by-step explanation:
For each runner, there are only two possible outcomes. Either they finished the marathon, or they did not. The probability of a runner completing the marathon is independent of any other runner. This means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
97.4% finished:
This means that 100 - 97.4 = 2.6% = 0.026 did not finish, which means that [tex]p = 0.026[/tex]
100 runners are chosen at random
This means that [tex]n = 100[/tex]
Find the probability that at least 5 of them did not finish the marathon
This is:
[tex]P(X \geq 5) = 1 - P(X < 5)[/tex]
In which
[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{100,0}.(0.026)^{0}.(0.974)^{100} = 0.0718[/tex]
[tex]P(X = 1) = C_{100,1}.(0.026)^{1}.(0.974)^{99} = 0.1916[/tex]
[tex]P(X = 2) = C_{100,2}.(0.026)^{2}.(0.974)^{98} = 0.2531[/tex]
[tex]P(X = 3) = C_{100,3}.(0.026)^{3}.(0.974)^{97} = 0.2207[/tex]
[tex]P(X = 4) = C_{100,4}.(0.026)^{4}.(0.974)^{96} = 0.1429[/tex]
[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0718 + 0.1916 + 0.2531 + 0.2207 + 0.1429 = 0.8801[/tex]
[tex]P(X \geq 5) = 1 - P(X < 5) = 1 - 0.8801 = 0.1199[/tex]
0.1199 = 11.99% probability that at least 5 of them did not finish the marathon
Find the minimum value of
C = 2x + 3y subject to the following constraints:
(4x + 3y > 29
X + 2y 11
x20
y > 0
C = [?]
WITH THE STEPS
FOR THE 2 SHAPE
Answer:
70 in
Step-by-step explanation:
7 * 7 = 49 {that's the square}
(7 * 6) * 1/2 = 21 {that's the triangle}
49 + 21 = 70
Answer:
the square SxS= 7x7 = 49
the triangle is hxs÷2=(7×6 )÷2 =42 ÷2 = 21
What’s the correct answer for this question?
Answer:
$16 is correct answer
Hope it helps you
Could someone help me figure this out??
Answer:
180
Step-by-step explanation:
what is the area of the triangle 16, 10, 8
Answer:
480
Step-by-step explanation:
(16x10x8) divided by 2 = 480
A rectangle is 4 times as long as it is wide. If the area is 64 square feet, find its perimeter
Answer:
40 feet
Step-by-step explanation:
long sides are 16
short sides are 4
Perimeter is l + l + w + w
so 16 + 16 + 4 + 4
= 40
The perimeter of the given rectangle is 40 feet.
What is the perimeter of a rectangle?The perimeter of a rectangle is defined as the sum of all the four sides of the rectangle.
The perimeter of a rectangle = 2( l + b)
It is given that rectangle is 4 times as long as it is wide. If the area is 64 square feet,
The area is 64 square feet = l x w
So,
The long sides are 16
The short sides are 4
Perimeter = 2 (l + w)
Perimeter = 2( 16 + 4)
Perimeter = 40
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How many moles are present in 4.51x1015 atoms of Aluminum (Al)?
Answer:
divide by avagadro number to get the amount of moles in the atoms you have
What is the slope of the line that passes through (5,4) and (7,10)?
A. 3
B. -3
C. 2
D. -2
Answer:
A. 3
Step-by-step explanation:
I just did it on a calculator and got it correct
Answer plz due in a few min
Answer:
40
Step-by-step explanation:
24^2+32^2=c^2
square root of 1600 is 40
Answer:40
Step-by-step explanation:Because
a^2 + b^2=c^2
What is the perimeter?? Please help!
Step-by-step explanation:
perimeter of the given figure=24cm+24cm+30cm+20cm+20cm+20cm+5cm+5cm
=148cm
Answer:
148mm aka 1.48cm aka 1cm48mm
Step-by-step explanation:
to obtain the small thing between the"24mm" and"20mm":
(30mm-20mm)÷2
=5mm
so add up all those given information:
24mm+24mm+20mm+20mm+20mm+30mm+5mm+5mm
comment below if you still don't get it ;)
Calculate the number of edges of the solid. Given it has 8 faces; 4 hexagons & 4 triangles
Answer:
20 Edges
Step-by-step explanation:
As this figure shows only 10 edges..so to meet the given condition (8 faces; 4 hexagons & 4 triangles) same figure is present at the back making total of 20 Edges.
HELP WILL GIVE BRANLIEST
Answer:
The answer would be B [tex]120ft^{3}[/tex]
Step-by-step explanation:
volume of triangular prism is 30 and volume of the cube is 90 :)
Two imaginary roots
A.144
B.O
D.-4
C.36
Answer:
D) -4 (with imaginary roots ±2i)
Step-by-step explanation:
Since you cannot take the square root of a negative number to produce a real result, the only option that has two imaginary roots is D) -4, where the two imaginary roots are 2i and -2i.
What is the measure of DEF
The calculated measure of the arc DEF is 204 degrees
Calculating the measure of arc DEFFrom the question, we have the following parameters that can be used in our computation:
The circle
The measure of the arc intercepted by the angle DEF is calculated as
Arc DF = 2 * DEF
When the given values are substituted in the above equation, we have the following equation
Arc DF = 2 * 78
So, we have
Arc DF = 156
The measure of arc DEF is then calculated as
Arc DEF = 360 - 156
Evaluate
Arc DEF = 204
Hence, the measure of the arc DEF is 204 degrees
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On a coordinate plane, a line goes through (negative 4, 0) and (4, negative 4). A point is at (2, 3).
What is the equation of the line that is parallel to the given line and passes through the point (2, 3)?
x + 2y = 4
x + 2y = 8
2x + y = 4
2x + y = 8
9514 1404 393
Answer:
(b) x +2y = 8
Step-by-step explanation:
The only offered line that includes the given point is ...
x +2y = 8
__
We can check the other choices:
x + 2y = 2 +2(3) = 2+6 = 8 . . . matches B (not A)
2x +y = 2(2) +3 = 4+3 = 7 . . . . not a choice
_____
Getting there from scratch
The standard form equation for a line can be written from ...
(y2 -y1)x -(x2 -x1)y = constant
(-4 -0)x -(4 -(-4))y = constant . . . . using the given points (-4, 0) and (4, -4)
-4x -8y = constant
For standard form, we need the leading coefficient to be positive, and we need common factors removed. We can get there by dividing by -4.
x +2y = constant
The value of the constant will be whatever it takes for the given point to lie on the line. For (x, y) = (2, 3) to be a solution, we must have ...
x +2y = (2) +2(3) = constant = 8
The desired line has the equation ...
x +2y = 8
Answer:
B on edge
Step-by-step explanation:
The number of mold spores on a piece of bread after a different amount of time or listed in the table below
Which function models the number of mold spores on the bread after X days
Answer:
Option (4)
Step-by-step explanation:
From the table attached,
Ratio of spores in day 2 and day 1 = [tex]\frac{400}{200}[/tex]
= 2
Ratio of spores in day 3 and day 2 = [tex]\frac{800}{400}[/tex]
= 2
There is a common ratio of 2 in each successive to the previous term of the Mold spores.
Therefore, spores are growing exponentially.
Let the function representing exponential function is,
y = a(b)ˣ
Here, y = Number of spores after time 'x'
x = Number of days
a and b are the constants.
On day 1,
x = 1
y = 200
By substituting these values in the exponential function,
200 = a(b)¹
ab = 200 -------(1)
On day 2,
x = 2
y = 400
400 = a(b)² -------(2)
Divide equation 2 by equation 1,
[tex]\frac{400}{200}=\frac{ab^{2} }{ab}[/tex]
b = 2
By substituting the value of b in equation (1),
a(2) = 200
a = 100
Therefore, equation of the function will be,
y = 100(2)ˣ
Option (4) will be the answer.
PLEASE ANSWER ILL GIVE BRIA LIEST
Answer:B
Step-by-step explanation:
Find the volume of the figure. Round to the nearest hundredth if necessary. (Figure is not to scale)
Answer:
360 mi^3
Step-by-step explanation:
The figure is composed by two parallelepipeds. For find the volume we have to find the volume of both the solids and the added up the two values
solid 1
length = 11 - 4 = 7 mi
base area = length x width = 7 x 4 = 28 mi^2
V = base area x height = 28 x 6 = 168 mi^3
solid 2
base area = 8 x 4 = 32 mi^2
V = 32 x 6 = 192 mi^3
total volume: 168 + 192 = 360 mi^3
The volume of the figure is 360 mi³.
What is Volume?Volume of a three dimensional shape is the space occupied by the shape.
Given is a figure where two rectangular boxes are put on top of each other.
Volume of a rectangular prism = L × W × H
Here L is the length, W is the width and H is the height.
The dimensions of the rectangular prism are :
Larger one having L = 11 mi, W = 6 mi and H = 4 mi
Smaller one on top having L = 4 mi, W = 6 mi and H = 8 - 4 = 4 mi.
Volume of the figure = volume of larger box + Volume of smaller box
= (11 × 6 × 4) + (4 × 6 × 4)
= 264 + 96
= 360 mi³
Hence the volume of the figure is 360 mi³.
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Which is bigger? 2^4 or 4^2?
Answer:
Both are equal
Step-by-step explanation:
[tex]2^4 = 16 \\ \\ {4}^{2} = 16 \\ \\ \implies \: {2}^{4} = {4}^{2} [/tex]
Answer:
Step-by-step explanation:
2^4=16 and 4^2=16
They both equal the same thing so im guessing neither. They are both the same value.
Hope this helped!
PLS let me know if i'm wrong so i can correct my mistake!!
A die is rolled. What is the probability of getting an even number?
A. 1/6
B. 1/2
C. 1/3
D. 1/4
Answer:
I wanna say 1/3 because there 3 even numbers on a dice
Step-by-step explanation:
Find the height of ABD
Answer:
[tex]Height=\boxed{10\sqrt{2}} [/tex]
[tex] Area =\boxed{165\sqrt{2}} [/tex]
Step-by-step explanation:
By geometric mean theorem:
[tex] AC=\sqrt{25\times 8}[/tex]
[tex] AC=\sqrt{5^2 \times 2^2 \times 2}[/tex]
[tex] AC=5\times 2\sqrt{2}[/tex]
[tex] AC=10\sqrt{2}[/tex]
So,
[tex]Height=\boxed{10\sqrt{2}} [/tex]
[tex] Area = \frac{1}{2} \times base\times height [/tex]
[tex] \therefore Area = \frac{1}{2} \times (25+8)\times 10\sqrt{2} [/tex]
[tex] \therefore Area =33\times 5\sqrt{2} [/tex]
[tex] Area =\boxed{165\sqrt{2}} [/tex]
Solve for x using
cross multiplication.
X + 8
-
3x – 2
8
3
x = [?]
Answer:
x=70
Step-by-step explanation:
(x+8)*8=(3x-2)*3
8x+64=9x-6
x=70
Find the value of x in the diagram below( HELP PLEASE)
9514 1404 393
Answer:
x = 30
Step-by-step explanation:
The sum of exterior angles of a convex polygon is 360°. Here, that means ...
3x° +x° +2x° +2x° +4x° = 360°
12x = 360
x = 360/12 = 30
The value of x is 30.
Answer:
Solution :-Sum of all angles = 360⁰
[tex] \to \sf \: 2x + 2x + x + 4x + 3x = 360[/tex]
[tex] \to \: 12x = 360[/tex]
[tex] \to \: x = \dfrac{360}{12} [/tex]
[tex] \sf \: x = 30[/tex]
How do we solve this in factor form? X^2-11x+24=0
Answer:
x=8, 3
Step-by-step explanation:
24 has 8 factors: 1,2,3,4,6,8,12,24
8 and 3 make 11
If you factor it out, the equation is (x-8)(x-3)=0
to get 0, only one of the expressions has to equal 0
so x can have 2 different values
I need help fast!!!
Please
Answer:
B
Step-by-step explanation:
Please help me with this ASAP ASAP please please help please please
Answer:
Step-by-step explanation:
Base perimeter: 5 x 2 x π = 10π
LA = 10π x 2 = 20π
Base area : 5^2π = 25π
SA = 25π x 2 + 20π = 70π
V : 25π x 2 = 50π
Which of the following equations will produce the graph shown below?
Answer:
x-1/8y^2=0
Step-by-step explanation:
just took the test