How many atoms of carbon are in a single molecule of sugar?
Bromine-82 has a half of about 35 hours. After 140 hour, how many milliliters of an 80 mL sample will remain? A,65mL B.20mL C.10mL D.5mL
Final answer:
After 140 hours, which is equivalent to 4 half-lives, the amount of bromine-82 remaining from an 80 mL sample will be 5 mL, as the amount is halved after each half-life period of 35 hours.
Explanation:
The question involves the half-life of a radioactive isotope, which is a concept in Chemistry specifically related to nuclear chemistry and radioactive decay. Since bromine-82 has a half-life of about 35 hours, after 140 hours, which is equivalent to 4 half-lives, the amount of the element remaining in the sample will be reduced by a factor of two after each half-life. To calculate this, we start with the initial 80 mL and reduce it by half 4 times.
After the first half-life (35 hours), 40 mL remains.
After the second half-life (70 hours), 20 mL remains.
After the third half-life (105 hours), 10 mL remains.
After the fourth half-life (140 hours), 5 mL remains.
Therefore, the correct answer is D. 5mL.
Final answer:
After 140 hours, which is four half-lives of Bromine-82, only 5 mL of an initial 80 mL sample will remain, making the correct answer D. 5mL.
Explanation:
The question is asking how much of a radioactive isotope will remain after a certain amount of time, given its half-life. In this example, the half-life of Bromine-82 is about 35 hours, and we want to know how much of an 80 mL sample will remain after 140 hours. To solve this, we will use the concept of half-life, which is the time it takes for half of the radioactive atoms in a sample to decay.
Since 140 hours is equal to 4 half-lives (140 hours ÷ 35 hours/half-life), we can calculate the remaining amount of Bromine-82 in the sample by halving the initial amount repeatedly, four times:
After the first half-life (35 hours), the remaining amount is ⅓ × 80 mL = 40 mL.
After the second half-life (70 hours in total), the remaining amount is ⅓ of 40 mL = 20 mL.
After the third half-life (105 hours in total), the remaining amount is ⅓ of 20 mL = 10 mL.
After the fourth half-life (140 hours in total), the remaining amount is ⅓ of 10 mL = 5 mL.
The correct answer is D. 5mL.
If a storage tank that measures 12 feet by 9 feet by 8 feet is designed to store gas that costs $1.82 per cubic foot, what does it cost to fill the tank to one-half of its capacity?
Rent-a-car rents compact cars for a fixed amount per day plus a fixed amount for each mile driven Benito rented a car for 6 days drove it 550 miles and spent $337. Lisa rented the same car for 3 days drove it 350 miles and spent $185. What is the charge per day and charge per mile for the compact car?
Please show all work! TYSM! ☺♥♫
The charge per day and charge per mile for the compact car is $36 and $0.22 respectively
let
x = charge per day
y = charge per mile
6x + 550y = 337 (1)
3x + 350y = 185 (2)
multiply (2) by 2
6x + 700y = 370 (3)
6x + 550y = 337 (1)
subtract (1) from (3)
700y - 550y = 370 - 337
150y = 33
y = 33/150
y = 0.22
substitute y = 0.22 into (2)
3x + 350y = 185
3x + 350(0.22) = 185
3x + 77 = 185
3x = 185 - 77
3x = 108
x = 108/3
x = 36
Therefore, charge per day and charge per mile for the compact car is $36 and $0.22 respectively
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Write an equation of the direct variation that includes the point (6, –2). y = –3x
Answer:
-1/3x is the answer
Step-by-step explanation:
Do the problem.
An equation of the direct variation that includes the point (6, –2) is y = -1/3(x).
What is a direct variation?In Mathematics, a direct variation is also referred to as direct proportion and it can be modeled by using the following mathematical expression or function:
y = kx
Where:
y represents the y-variable or dependent variable.x represents the x-variable or independent variable.k represents the constant of proportionality.Under direct variation, the value of x represent an independent variable while the value of y represents the dependent variable. Therefore, the constant of proportionality (variation) can be calculated as follows:
Constant of proportionality (k) = y/x
Constant of proportionality (k) = -2/6
Constant of proportionality (k) = -1/3
Therefore, the required equation is given by;
y = kx
y = -1/3(x)
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The length of a rectangle with length 12 yd and width 11 yd is divided by 6.
what is the value of x in the equation 1,331x^4-216=0?
a) -6/11
b) 11/6
c) 1/6
d) 6/11
Mattie uses the discriminant to determine the number of zeros the quadratic equation 0 = 3x2 – 7x + 4 has. Which best describes the discriminant and the number of zeros?
A party store sells large plates in packs of 12 and small plates in packs of 8 . In order to have an equal number of both , what is the least amount of large plants that would have to be purchased
The two triangular prisms shown are similar. The dimensions of the larger prism were multiplied by a scale factor of to create the smaller prism.
When the large prism was reduced, the surface area changed by a factor of
A.64/125
B.16/25
C.4/5
D.10/8
Answer: B. [tex]\frac{16}{25}[/tex]
Step-by-step explanation:
We know that if a figure or solid shape is dilated to create a new shape then the new shape is similar to the original shape.
Also, the scale factor of dilation is the ratio of the sides of new shape to the corresponding sides of the original shape .
Let k be the scale factor of dilation, then
Given : Original shape - larger prism
New shape - smaller prism
Surface area of prism with all sides equal (a)=[tex]4a^2[/tex]
Surface area of original prism =[tex]4(10)^2=400[/tex]
Surface area of new prism =[tex]4(8)^2=256[/tex]
[tex]\Rightarrow k=\frac{256}{400}=\frac{16}{25}[/tex]
Hence, the scale factor = [tex]\frac{16}{25}[/tex]
Ten percent of all dynamite mints candies are orange and 45 percent of all holiday mints candies are orange. two independent random samples, each of size 25, are selected⎯one from dynamite mints candies and the other from holiday mints candies. the total number of orange candies in the two samples is observed. what are the expected total number of orange candies and the standard deviation for the total number of orange candies, respectively, in the two samples?
The mean and standard deviation of the sample of orange sweets can be ibtaide using the binomial approximation relation. Hence, the mean and standard deviation are 13.75 and 2.905
Mean = np
Sample size, n = 25 Proportion, pDynamite mints :
25 x 0.1 = 2.5Holiday mints:
25 x 0.45 = 11.25Total orange candies = (2.5 + 11.25) = 13.75
2.)
Standard deviation, σ = √(npq)
q = 1 - pDynamite mints :
√[25 x 0.1 × (1 - 0.1)] = 1.5
Holiday mints :
√[25 x 0.45 (1 - 0.45)] = 2.4874
Combined standard deviation : s²(x + y) = s²(x) + s²(y)
Std = √(1.5²2 + 2.4874²) = 2.905
Therefore, the mean and sample standard deviation are 13.75 and 2.905 respectively.
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How many differnet points could a parabola intersect a ircle?
Yun is making some investments in the stock market. Stock for Company A has a 30% chance of losing $12,000, a 45% chance of breaking even, and a 25% chance of earning Yun $11,000. Assuming Yun would like the odds to be in favor of her gaining money, should she invest in Company A? Explain.
a. no, 7,700 > 3,600
b. yes, 7,700 > 3,600
c. yes, 3,600 > 2,750
d. no, 3,600 > 2,750
We have been given that company A has a 30% chance of losing $12,000.
Let us calculate the amount that Yun can loose.
[tex]\frac{12000\times 30}{100} \\ \\ =\$3600[/tex]
Now, 45% chance of breaking even. It means neither loss nor profit.
Then, 25% chance of earning Yun $11,000.
Let us calculate the amount of profit
[tex]\frac{11000 \times 25}{100} \\ \\ =\$2750[/tex]
Since, 3,600 > 2,750. It means that Yun will be in loss on investing in the company.
Hence, she will not invest in the company A.
d is the correct option.
d. no, 3,600 > 2,750
A and b are independent events. the probability that a will happen is 1/4 and the probability that b will happen is also 1/4. what is the probability they will both happen?
For independent events A and B, the probability of both happening is the product of their individual probabilities. In this case, the probability of both A and B happening is 1/16.
Explanation:In the field of probability in mathematics, when dealing with independent events like A and B in your question, the probability of both A and B happening (denoted as P(A AND B)) is calculated by multiplying the probability of A happening (P(A)) by the probability of B happening (P(B)) This is known as the multiplication rule for independent events.
So, if the probability that A will happen (P(A)) is 1/4, and the probability that B will happen (P(B)) is also 1/4, then the probability that both A and B will happen (P(A AND B)) is (1/4) * (1/4) = 1/16.
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A polygon has 13 sides calculate the sum of the interior angle measure of each polygon
What is the interquartile range of this data? A.6 B.7 C.8 D.9
Why does it take more centimeters than inches to measure the same distance?
You purchase a new desktop computer for $2,200. you put a 6% down payment and $100 per month on a 24 month purchase plan. determine the total finance
does the lateral area in a prism include the base?
$8000 at 3% annually for 4 years
Evan graphs the function h(x)=x^2+4. Victor graphs the function g(x)=(x+4)^2. Which statments are true regarding the two graphs? Check all that apply.
A professional golfer gets a hole-in-one 0.003% of the time they try on a hole. If the golfer plays 32,000 holes over the course of their professional career, about how many hole-in-ones should they expect over their career?
96 holes I think is the correct answer
what is the 14 letter word with the definition of an example showing a statement is not true. it is c--n-e-t--m-l-
The equation for a projectile's height versus time is h(t)=-16t^2+Vt+h. A tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an initial speed of 130 feet per second. Which equation correctly models the ball's height as a function of time?
The maximum height at the moment is 266.0625 ft.
Projectile's heightThe equation for a projectile's height versus time is
[tex]&h(t)=-16 t^{2}+V t+h \\[/tex]
h = 2
V = 130
Substitute these values into the function
[tex]$h(t)=-16 t^{2}+130 t+2$[/tex]
Take the first derivative
[tex]$h^{\prime}(t)=-16* 2 t+130[/tex]
[tex]=-32 t+130$[/tex]
Equate the derivative with zero [tex]$h^{\prime}(t)=0$[/tex].
Solve the equation -32 t + 130=0
32 t = -130
t = -130 /(-32)
= 4.0625(s) .
Find the maximum height at the moment
t = 4.0625 (s)
h(4.0625) [tex]= -16(4.0625)^{2}+130 * 4.0625+2[/tex]
= - 264.0625+528.125+2
= 266.0625 ft.
Therefore, the maximum height at the moment is 266.0625 ft.
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Can Someone PLEASE help me
And if you can show your work.
This image shows a square pyramid. What is the surface area of this square pyramid? 36 ft² 72 ft² 78 ft² 84 ft² Note: Image not drawn to scale. The figure shows a square pyramid. The slant height is shown as a dashed line perpendicular to the base edge. The length of the base edge is 6 feet. The lateral edge makes a 45 degree angle with the base edge.
The square's area is relatively simple:
A=b²
A=6²=36 ft²
But now let's observe the triangles, a triangle's area is:
A=(1/2)*b*h
the base is equal to 6 ft
b=6 ft
AC=BC----------> because the angle is 45°
AC=6 ft/2----> 3 ft
so
BC=3 ft
A=(1/2)*6*3----> 9 ft²
Multiply the triangle's area by four to account for all four triangular faces and add the squares area for your answer
Surface area=36 +4*9-----> 72 ft²
the answer is
72 ft²
Answer:
72
Step-by-step explanation:
just took quiz
What is the value of x
find the base of a parallelogram with an area of 18 square inches and a height of 2 inches
Which correlation coefficient obtained from modeling advertising and sales data of tutti frutti ice cream expresses the strongest correlation of the data?
a.r = .10
b.r = .50
c.r = .75
d.r = .90
Answer:
d) r=0.90
Step-by-step explanation:
When the r value is closer to +1 or -1, it indicates that there is a stronger linear relationship between the two variables. A correlation nearerto -1 is a strong negative correlation while a correlation of 0.10 would be a weak positive correlation.
Correlation coefficient measures the strength of association between two variables.
It may be positive or negative.
If nearer to 1 or - there is strong correlation
Since here is it 0.90 positive and nearer to 1 out of all 4 options
option d is correct
A scatter plot is shown:
A scatter plot is shown. Data points are located at 0 and 0, 1 and 0.25, 2 and 1, 3 and 2, 4 and 3, 5 and 4, 5.5 and 5, 6 and 6, 6.4 and 7, 6.7 and 7.8, 7 and 9.
What type of association does the graph show between x and y?
Linear positive association
Nonlinear positive association
Linear negative association
Nonlinear negative association
Answer:
The correct option is 2.
Step-by-step explanation:
From the given graph it is noticed that the data points are located at (0,0), (1,0.25), (2,1), (3,2), (4,3), (5,4), (5.5,5), (6,6), (6.4,7), (6.7,7.8) and (7,9).
The rate of change from first two data points is
[tex]m_1=\frac{y_2-y_1}{x_2-x_1}=\frac{0.25-0}{1-0}=0.25[/tex]
The rate of change from next two data points is
[tex]m_2=\frac{2-1}{3-2}=1[/tex]
[tex]m_1\neq m_2[/tex]
The rate of change it not constant, therefore the given data points are non linear.
The value of y increases as the value of x-increases. It means there is a positive relation between x and y.
Therefore the graph represent a Nonlinear positive association between x and y. Option 2 is correct.
Answer:
The correct answer is 2.