Answer:
40
Step-by-step explanation:
84 runners to start a race
in the first half of the race 1/3 of them dropped out = 84/3 = 28 dropped out
so 56 left
in the second half of the race 2/7 of the remaining runners dropped out
2/7 *56 =16 dropped out
so 56-16 = 40 left
how many runners finish
40
When a plant or animal dies, it stops acquiring carbon-14 from the atmosphere. The amount y (in grams) of carbon-14 in the body of an organism after
t years is-y = a(0. 5)*/3730, where a is the initial amount grams). What percent of the carbon-14 is released each year? Round your answer to the
nearest hlindredth
At 0.0175% of the carbon-14 is released each year, rounded to the nearest hundredth.
The amount of carbon-14 released each year can be represented as the rate of change of the amount of carbon-14 in the body of an organism with respect to time.
Carbon-14, the longest-lived radioactive isotope of carbon, whose decay allows the accurate dating of archaeological artifacts. The carbon-14 nucleus has six protons and eight neutrons, for an atomic mass of 14.[tex]\frac{d(y)}{dt}=\frac{-y}{tau}[/tex]Where
d(y)/dt represents the rate of change of the amount of carbon-14 in the body. y represents the amount of carbon-14 in the body, and tau (τ) represents the half-life of carbon-14 (5730 years).To find the percent of the carbon-14 that is released each year, we can divide the rate of change by the initial amount of carbon-14 and multiply by 100 to express it as a percentage:
⇒percent released/year =[tex]=100*\frac{ d(y)}{dt}[/tex]/a
[tex]=\frac{-100*y}{a* tau}[/tex] = [tex]-100 * (0.5)^(t / tau) / tau[/tex]
At t = tau, the percent released/year will be[tex]-100 * (0.5)^\frac{(1) }{tau}[/tex],
which is approximately -0.0175 per year.
So,
Therefore, each year approximately 0.0175 percent of the carbon-14 is released, rounded to the nearest hundredth.
For more such questions on carbon-14 is released
https://brainly.com/question/29183250
#SPJ4
the diameter of a manufactured widget is normally distributed with a mean of 65 and a standard deviation of 9. what is the probability a widget sampled at random will be less than or equal to 56? use excel and carry your answer to at least five decimal places.
Considering all the given information, the probability of a widget being less than or equal to 56 is approximately 0.1587
The formula for converting a value to a standard score, also known as a z-score, is:
z = (x - μ) / σ
Where x is the value of interest, μ is the mean, and σ is the standard deviation.
To find the probability of a widget being less than or equal to 56, we first find the corresponding z-score:
z = (56 - 65) / 9 = -1
We can then use the cumulative distribution function (CDF) of the standard normal distribution to find the probability of a z-score being less than or equal to -1:
P(z ≤ -1) = 0.1587
So the probability of a widget being less than or equal to 56 is approximately 0.1587, or 15.87%.
To learn more about standard deviation Click here:
brainly.com/question/23907081
#SPJ4
The function f(x) = 5x + 2,500 models the number of computer chips produced by a manufacturing plant each month during its first year. How many computer chips was the plant able to produce in month 3?
The number of computer chips produced in 3 months will be 2515.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the function f(x) = 5x + 2,500 models the number of computer chips produced by a manufacturing plant each month during its first year.
The number of chips will be calculated as:-
f(x) = 5x + 2,500
f(3) = 5 x 3 + 2500
f(3) = 15 + 2500
f(3) = 2515
Therefore, the number of chips will be 2515.
To know more about an expression follow
https://brainly.com/question/25870863
#SPJ1
The growth in visitors to a community website from 2006 to 2007 was 117%. The number of visitors was 8.9 million in 2006. How many visitors were there in 2007?
Answer:
10413000 visitors
Step-by-step explanation:
117% = 1.17
8900000 times 1.17 = 10413000 visitors
So, there were 10413000 visitors in 2007.
A quantity with an initial value of 8500 grows exponentially at a rate such that the quantity doubles every 9 years. What is the value of the quantity after 23 years, to the nearest hundredth?
Answer: We can use the formula for exponential growth to find the value of the quantity after 23 years:
Q(t) = 8500 * 2^(t/9)
Where Q(t) is the value of the quantity after t years, and t/9 is the number of doublings that have occurred.
Substituting t = 23 into the formula:
Q(23) = 8500 * 2^(23/9) = 8500 * 2^2.56 = 8500 * 12.90 = 109350
So, after 23 years, the quantity has a value of approximately 109,350, rounded to the nearest hundredth.
Step-by-step explanation:
Select strong association moderate assossiation or weak association for each correlation 0.8, .25 ,0.9, 0.65coeffcient
The correlation coefficient measures the strength of the linear relationship between two variables. A coefficient of 0.8 implies a strong linear relationship between two variables, a coefficient of 0.25 implies a weak linear relationship between two variables.
0.8: Strong Association
0.25: Weak Association
0.9: Strong Association
0.65: Moderate Association
The correlation coefficient is a numerical measure of the strength of the linear relationship between two variables. Values of the correlation coefficient fall between -1 and +1. A coefficient of 0 implies that there is no linear relationship between two variables. The closer the coefficient is to either -1 or +1, the stronger the correlation. A coefficient of 0.8 implies a strong linear relationship between two variables, a coefficient of 0.25 implies a weak linear relationship between two variables, a coefficient of 0.9 implies a very strong linear relationship between two variables, and a coefficient of 0.65 implies a moderate linear relationship between two variables.
The correlation coefficient measures the strength of the linear relationship between two variables. A coefficient of 0.8 implies a strong linear relationship between two variables, a coefficient of 0.25 implies a weak linear relationship between two variables, a coefficient of 0.9 implies a very strong linear relationship between two variables, and a coefficient of 0.65 implies a moderate linear relationship between two variables.
Learn more about correlation here
https://brainly.com/question/28898177
#SPJ4
What is the relationship between DE and AC? There are two properties to state, be sure to state both.
Anna compra helado y naranjas en la tienda.
• Ella paga un total de $59.53.
• Ella paga un total de $6.49 por el helado.
• Ella compra 8 bolsas de naranjas que cuestan la misma cantidad cada una.
Escribe y resuelve una ecuación que se pueda usar para determinar X, cuánto cuesta
cada bolsa de naranjas.
Ecuación:
Respuesta: X=
Answer:
Podemos utilizar la información proporcionada para escribir la siguiente fórmula y resolverla para encontrar el valor de X, que representa el costo de cada bolsa de naranjas:
6,49 + 8X = 59,53
Para resolver la fórmula, primero debemos despejar la variable X. Restamos 6.49 de ambos lados:
8X = 53,04
Luego, dividimos ambos lados por 8:
X = 6,63
Por lo tanto, cada bolsa de naranjas cuesta $6.63.
Why in arithmetic sequence does the graph of Tn vs n need to be a straight line
Answer:
It's because the graph of arithmetic sequence forms a set of discrete points lying on a straight line.
Madison starts with a population of 1,000 1 , 000 amoebas that triples in size every hour for a number of hours, ℎ h . She writes the expression 1,000(3ℎ) 1,000 ( 3 h ) to find the number of amoeba after ℎ h hours. Tyler starts with a population of 1 1 amoeba that increases 30% 30 % in size every hour for a number of hours, ℎ h . He writes the expression (1+0.3)ℎ 1 + 0 . 3 h to find the number of amoeba after ℎ h hours. Use the drop-down menus to explain what each part of Madison’s and Tyler’s expressions mean.
Here we get 1.3 is the growth factor, 0.3 is the growth rate, and 1 is the initial population of amoebas.
Since Madison's population of 1,000 amoebas begins by doubling every hour for a certain number of hours, h.
In other words, the total number of amoebas after one hour is
3*1000=[tex]3^{1}[/tex]*1000.
Total number of amoebas after two hours is equal to 3*3000=[tex]3^{2}[/tex]*1000. The total number of amoebas after three hours is 3*9000=[tex]3^{3}[/tex]*1000.
In a similar manner, the total number of amoebas,
f(h) = [tex](1+0.3)^{h}[/tex]
where the starting amoeba population is 1000. 3 is the population growth factor, and f(h) is the amoeba population after h hours.
Since Tyler begins with a colony of a single amoeba that grows by 30% per hour for a certain length of hours.
In other words, after one hour, there were =[tex](1+0.3)^{1}[/tex]
After two hours, there were a total of =[tex](1+0.3)^{2}[/tex]
After three hours, there were a total of =[tex](1+0.3)^{3}[/tex]
In a similar manner, the total number of amoebas,
f(h) =[tex](1+0.3)^{h}[/tex]
where 1.3 is the growth factor, 1 is the initial population of amoebas and 0.3 is the growth rate.
Learn more about expressions:
https://brainly.com/question/11702440
#SPJ4
You can use the equation A = HW 1/2 to approximate a person's body surface area A (in 3600 square meters), where His height (in centimeters), and Wis weight (in kilograms). Approximate the body surface area to the nearest tenth of a person with a height of 160 centimeters and a weight of 64 kilograms. m²
The body surface area is 1.7 m²
How to determine the body surface areaFrom the question, we have the following parameters that can be used in our computation:
A = (HW/3600)^(1/2)
Where H is the height in cm and W is the weight in kg.
Substitute the known values in the above equation, so, we have the following representation
A = (160 * 64 / 3600)^(1/2)
Evaluate
A ≈ 1.69 m²
Rounding to the nearest tenth:
A ≈ 1.7 m²
Read more about equation at
https://brainly.com/question/2972832
#SPJ1
during basketball practice mai attempted 40 free trows and was successful on 25% of them how many successful free trows did she make
Answer:
10
Step-by-step explanation:
25% of 40 1/4*40=40/4=10
Casey buys a bracelet. She pays for the bracelet and pays
$
0.72
$0.72dollar sign, 0, point, 72 in sales tax. The sales tax rate is
6
%
6%6, percent.
What is the original price of the bracelet, before tax?
Answer: The original price of the bracelet before tax can be found using the following formula:
original price = (total price) / (1 + sales tax rate as decimal)
In this case, the total price is 0.72 dollars, and the sales tax rate as a decimal is 0.06. Plugging these values into the formula, we get:
original price = 0.72 / (1 + 0.06)
original price = 0.72 / 1.06
Step-by-step explanation:
Ned made the design at the right. Use a protractor. Find and write the measure of each of the 3 angles
The measures of the three angles are 60 degrees, 75 degrees and 45 degrees.
A semi-circle has a total angle measure of 180 degrees. The sum of the angles formed by the two arcs must equal the total angle measure of the semi-circle.
Let's call the angle formed by the first arc "angle A" and the angle formed by the second arc "angle B".
From the given information, we know that:
angle A = 60 degrees
angle B = 75 degrees
So, angle A + angle B = 60 degrees + 75 degrees = 135 degrees
Since the total angle measure of the semi-circle is 180 degrees, the measure of the remaining angle is:
180 degrees - 135 degrees = 45 degrees
Therefore, the measures of the three angles are:
angle A = 60 degrees
angle B = 75 degrees
angle C = 45 degrees
Learn more about Semi-circle here https://brainly.com/question/14429410
#SPJ4
Question: Ned made the design at the right. Use a protractor. Find and write the measure of the 3rd angle with given 60 and 75 degrees.
Which three statements describe the expression 8 + 3n?
Responses
A The expression represents 8 plus n times n times n.The expression represents 8 plus n times n times n .
B The expression represents the sum of 3n and 8.The expression represents the sum of 3 n and 8.
C The expression represents 8 plus n plus n plus n.The expression represents 8 plus n plus n plus n .
D The expression represents 8 plus the product of 3 and n.The expression represents 8 plus the product of 3 and n .
E The expression represents the product of 8 and 3n.The expression represents the product of 8 and 3 n .
42. Solve for y: 2(y - 4) > 0
Answer:
Step-by-step explanation:
if we divide each side with 2,
(2(y-4))/2>0/2
y-4>0
y>4
Answer:
y > 4
Step-by-step explanation:
2(y - 4) > 0
Solving the inequality:
Divide each side by 2.
2/2(y - 4) > 0/2
y - 4 > 0
Add 4 to each side.
y - 4+4 > 0+4
y > 4
HELP ASAP, WILL GIVE BRAINLIEST,
In a repeated experiment, Kim rolled a fair die twice. The theoretical probability of both rolls equaling a sum greater than 9 is 6 over 36. Predict how many times the rolls will result in a sum greater than 9 if the experiment is repeated 144 times.
24
12
9
6
Answer: We can predict that the rolls will result in a sum greater than 9 approximately 24 times.
Step-by-step explanation: The theoretical probability of both rolls equaling a sum greater than 9 is given as 6/36. To predict how many times the rolls will result in a sum greater than 9 if the experiment is repeated 144 times, we can use the concept of probability.
The probability of an event occurring is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
In this case, the probability of both rolls resulting in a sum greater than 9 is 6/36, which simplifies to 1/6. This means that out of every 6 possible outcomes, 1 will result in a sum greater than 9.
To predict the number of times this will occur in 144 repetitions, we can multiply the probability by the number of repetitions:
(1/6) * 144 = 144/6 = 24
Therefore, we can predict that the rolls will result in a sum greater than 9 approximately 24 times if the experiment is repeated 144 times.
In 2010, the population of a city was 87,000. From 2010 to 2015, the population grew by 7.7%. From 2015 to 2020, it fell by 4.5%. To the nearest 100 people, what was the population in 2020?
Answer:
The population of the city in 2020 was 89,500 to the nearest 100 people.
Step-by-step explanation:
The original population in 2010 is 100%.
If the population is increased by 7.7% from 2010 to 2015, the total percentage in 2015 is 107.7% of the population in 2010.
Convert this to a decimal and multiply by the original population of 87,000 to find the population of the city in 2015.
[tex]\begin{aligned}\implies \sf 107.7\%\;of\;87000&=\sf 1.077 \times 87000\\&=\sf 93699\end{aligned}[/tex]
Therefore, the population of the city in 2015 was 93,699.
The population in 2015 is 100%.
If the population is decreased by 4.5% from 2015 to 2020, the total percentage in 2020 is 95.5% of the population in 2015.
Convert this to a decimal and multiply by the population in 2015 to find the population of the city in 2020.
[tex]\begin{aligned}\implies \sf 95.5\%\;of\;93699&=\sf 0.955 \times 93699\\&=\sf89482.545 \end{aligned}[/tex]
Therefore, the population of the city in 2020 was 89,500 to the nearest 100 people.
please answer all these for crown and separate them from each other ty ill give u a crown
The values of x for the different diagrams are given below.
What are parallel lines?Lines in a plane that are consistently spaced apart are known as parallel lines. Parallel lines don't cross each other.
Given:
There are four diagrams.
Diagram 1:
By the alternate exterior angles,
8x + 19 = 139
8x = 120
x = 15
Diagram 2:
By the corresponding angles,
17x - 45 = 108
17x = 153
x = 9
Diagram 3:
By the alternate interior angles,
7x -1 = 13x - 43
6x = 42
x = 7
Diagram 4:
By the consecutive interior angles,
8x + 19 = 139
8x = 120
x = 15
Hence, the solutions for all the values are given above.
To learn more about the parallel lines;
brainly.com/question/16701300
#SPJ1
A parabola can be drawn given a focus of
(5, -4) and a directrix of y=2. Write the equation of the parabola in any form.
Therefore , the solution of the given problem of equation comes out to be the equation of the parabola in standard form is x² - 10x - 12y + 13 = 0
Define equation.In arithmetic equations, the identical figure (=) is used to denote the equivalence of two assertions. It is demonstrated that mathematical methods, which have acted as manifestations of reality, can be used to assess a variety of numerical factors. The equal sign actually splits the number 12 into two separate pieces, despite the fact that the result is y + 6 = 12.
Here,
The distance between the focus and vertex is the same as the distance between the vertex and directrix, which is |-4 - (-1)| = 3. This distance is also equal to the absolute value of the coefficient "a" in the equation of the parabola.
Therefore, the equation of the parabola in vertex form is:
(x - 5)² = 4p(y + 1)
where "p" is the distance between the vertex and the focus, which is 3. Substituting this value into the equation gives:
(x - 5)² = 4(3)(y + 1)
Simplifying:
(x - 5)² = 12y + 12
Expanding the left side:
x² - 10x + 25 = 12y + 12
Moving all the terms to one side:
x² - 10x - 12y + 13 = 0
So the equation of the parabola in standard form is:
x^2 - 10x - 12y + 13 = 0
To know more about equation visit:
https://brainly.com/question/649785
#SPJ1
If A(-9, 4) and B(3, -2), find the midpoint of AB.
Answer:
(-3,1)
Step-by-step explanation:
The value of x [tex]\frac{-9+3}{2}[/tex] = -3
The value of y [tex]\frac{4-2}{2}[/tex] = 1
Answer:
Mid point is (-3, 1)
Step-by-step explanation:
Let mid point be M
[tex] { \boxed{ \sf{m = ( \frac{x _{1} + x _{2} }{2}} , \: \frac{y _{1} + y _{2}}{2}) }} \\ \\ { \tt{m = ( \frac{ - 9 + 3}{2} , \: \frac{4 - 2}{2} )}} \\ \\ { \tt{m = ( \frac{ - 6}{2}, \: \frac{2}{2} ) }} \\ \\ { \tt{m = ( - 3, \: 1)}}[/tex]
on a blueprint, a rectangular kitchen has a length of 4 inches and a width of 3 inches. if the length of the kitchen is 6 feet, what is the perimeter of the kitchen?
21 feet is the perimeter of the kitchen .
In arithmetic, what is a perimeter?
The perimeter is the space surrounding a shape's edge. Discover how to calculate the perimeter of various forms by multiplying their side lengths. The whole distance that the sides or limits of a rectangle cover is known as its perimeter.
The perimeter of a rectangle will be equal to the sum of its four sides because rectangles have four sides.
on a blueprint, a rectangular kitchen has a length = 4 inches
a width = 3 inches
So it's width is equal to = 6/4 * 3
= 4.5 feet
the perimeter of this kitchen is = 2(6 + 4.5 )
= 2 * 10.5 = 21 feet
Learn more about the perimeter
brainly.com/question/9369181
#SPJ4
HELP PLEASEEEEEEEEEEE
Answer:
y intercept = -3
the slope of the line is 1
Step-by-step explanation:
y intercept is the value of y when x = 0
x = 0 when y = -3
The points (4,2) and (5,r) fall on a line with a slope of
–7. What is the value of r?
Answer:
r = -5
Step-by-step explanation:
To find the value of 'r', use the slope formula.
(4, 2) ; x₁ = 4 and y₁ = 2
(5 , r ) ; x₂ = 5 and y₂= r
[tex]\boxed{slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\dfrac{r -2}{5 - 4 }= -7\\\\\dfrac{r -2}{1}=-7[/tex]
r - 2 = -7
r = -7 + 2
r = -5
Probability: The answer i got was 0.2
this is my work:
Non-negativity: f(x) ≥ 0 for all x in the support of X.
normalization: The sum of f(x) over all x in the support of X must be equal to 1.
In this case, the support of X is {0, 1, 2, 3, 4}. So, for f(x) to be a valid probability distribution function, i should have:
0 ≤ f(x) for all x in {0, 1, 2, 3, 4}
and
f(0) + f(1) + f(2) + f(3) + f(4) = 1
so find the value of k such that:
0 ≤ k ≤ 1
and
f(x) = k for all x in {0, 1, 2, 3, 4}
since f(x) must be equal to k for all x in the support of X, we have:
k = f(0) = f(1) = f(2) = f(3) = f(4)
and
k * 5 = 1 so, k = 1/5
so,
f(x) = 1/5 for all x in {0, 1, 2, 3, 4}
is a valid probability distribution function for a discrete random variable X which can take on the values 0, 1, 2, 3, or 4.
so the answer is 0.2
The required [tex]f(x) = x/10[/tex] is a valid probability distribution function for a discrete random variable X which can take on the values 0, 1, 2, 3, or 4.
What is probability?Probability can be defined as the ratio of favorable outcomes to the total number of events.
For a function f(x) to be a valid probability distribution function (pdf) for a discrete random variable X, it must satisfy the following conditions:
Non-negativity: [tex]f(x) = x/k[/tex] is non-negative for all x when k > 0.
Normalization: We need to find the value of k such that the sum of the probabilities for x = 0, 1, 2, 3, 4 is equal to 1.
[tex]f(x) = x/k[/tex] for x = 0, 1, 2, 3, 4.
The sum of the probabilities is given by:
[tex](0/k) + (1/k) + (2/k) + (3/k) + (4/k) = 1[/tex]
[tex]10/k = 1[/tex]
So, k = 10.
Thus,[tex]f(x) = x/10[/tex] is a valid probability distribution function for a discrete random variable X which can take on the values 0, 1, 2, 3, or 4.
Learn more about probability here:
brainly.com/question/14290572
#SPJ1
A quilter created the following shape to use in a block for a new quilt.
What is the area of the shape for the quilt block?
Answer: 166.5 inch.
Explanation:
There are a lot of steps to this. First of all, as seen in the picture below, we split the shape into a triangle and a rectangle. We can first find the area of the triangle first, which would be:
[tex]\frac{45}{2}[/tex] = 22.5 inch.
Next, using the pythagoras theorem, we can find the missing side of the triangle. So, we do:
[tex]\sqrt{7.5^2+6^2} = x\\\\\frac{3\sqrt{41} }{2} = x = 9.6[/tex]
Now we have that side, we can calculate the area of the rectangle, which would be 16 x 9 = 144 inch.
So now we can add both areas:
144 + 22.5 = 166.5 inch.
How does Huck feel in the adventures of huckleberry finn
In Adventures of Huckleberry Finn, at first, Huck feels good about writing to Jim's owner.
What is adventures?Adventure is an exciting experience or undertaking that is usually daring, sometimes risky. Adventures can be dangerous activities such as travel, exploration, skydiving, mountain climbing, diving, rafting or other extreme sports.
here, we have,
Adventures are often undertaken for psychological excitement or to achieve a greater goal, such as the pursuit of knowledge that can only be obtained through such activities.
Adventure not only expands your mind, increasing courage, but also gives you the opportunity to grow and learn. New environments and cultures are full of meaningful lessons that you may not encounter in your everyday life. Adventures expand the way we see and interact with the world.
To learn more about adventures, refer;
brainly.com/question/24468179
#SPJ1
which of these data sets represent continuous data? a.) number of questions answered correctly in a multiple-choice quiz b.) numbers of tickets sold for a football game c.) heights of members of a baseball team d.) population of towns within a state
All four data which is number of questions answered correctly in a multiple-choice quiz and numbers of tickets sold for a football game and heights of members of a baseball team and population of towns within a state are continuous data.
Countable data is referred to as continuous data. The values in this data are not constant and can take on an endless number of different forms. You can also divide these measures up into smaller, independent components. Examples of continuous data include the following: A person's height or weight
in a) number of questions answered correctly in a multiple-choice quiz can be count
b.) numbers of tickets sold for a football game can be count and c.) heights of members of a baseball team can be measure and d.) population of towns within a state can be count .
For more about continuous data click here ;
https://brainly.com/question/14533512
#SPJ4
3/4 (1/6x + 16) = 3/7 (35/8 - 21)
Answer:
x=-153
Step-by-step explanation
3/4(1/6x) + 3/4(16) = 3/7(35/8)-3/7(21)
1/8x+12=15/8-9
8(1/8x+12=15/8-9)
1x+96=15-72
1x+96=-57
x=-153
Identify the letter that represents the following numbers on the number line.
Letters which represent negative integers on a number line are present on the left side of zero and you can also identify them with the minus sign they carry.
What is number lines ?
Integers are arranged at equal intervals along horizontal, straight lines known as number lines. A number line can be used to visualize all the numbers in a succession. Both endpoints of this line continue indefinitely.
The number line is a straightforward straight line with divisions indicated at regular intervals, much like a scale. Any point can be selected as "0," and all positive and negative numbers are arranged to the right and left of the "0" respectively.
Learn more about number line
brainly.com/question/13425491
#SPJ1
The complete question is -
Identify the letter that represents the following number negative integers on a number line .