After 38 hours, there will be 43.1 mg of the radioactive substance remaining.This means that the amount of a radioactive substance decreases exponentially over time
Radioactive decay follows an exponential decay curve. This means that the amount of a radioactive substance decreases exponentially over time. The equation for this is: [tex]A(t) = A0*e^(-λ*t\\[/tex])Where A(t) is the amount of substance at time t, A0 is the initial amount of substance, and λ is the decay constant. In this problem, A0 = 100 mg, t = 29 hours, and A(t) = 50 mg. We can use this to solve for λ:50 mg = 100 mg * [tex]e^(-λ*29)λ =[/tex] -0.027Now that we have the decay constant, we can calculate the amount of substance remaining after 38 hours:A(38) = 100 mg * [tex]e^(-0.027*38[/tex]).A(38) = 43.1 mg.Therefore, after 38 hours, there will be 43.1 mg of the radioactive substance remaining.
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what is the minimum value of y=x^2+36/5
Answer:
(36/5)
Step-by-step explanation:
y=x^2+36/5
Since x is squared, the result will always be a positive number, regardless of the actual value of x. Starting with a value of x of zero, the x^2 term will only grow as one moves away from 0. E.g., (-1)^2 = 1, (-2)^2 = 4, etc.
So the minium for this equation will occur when x = 0. It only gets larger from that point. The minimum is (36/5).
See the attached graph.
find the values of the variables for the parallelogram
The value of m is 40 degrees, the value of x is 6 and value of y is 9.
What is Parallelogram?Parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.
To find the value of variable m.
Forming an equation:
3m = 120°
m = 120/3
m = 40
Therefore the value of m is 40.
Finding x:
x is opposite to the side of measure 6.
As per the first property.
x = 6
So, x = 6
Therefore the value of x is 6.
Finding y.
5y is opposite the angle measuring 45°.
Forming an equation.
5y = 45°
y = 45/5
y = 9
Therefore the value of y is 9.
Hence, the value of m is 40 degrees, the value of x is 6 and value of y is 9.
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The complete question is given below and in attachment
Find the value of each variable in the parallelogram. explain step by step
Please help! I don't understand how my teacher does the work, so therefore, I don't understand how to do these word problems. 100-point jackpot for answering.
Answer: 1) 4 $3 and 4 $2; 2) 4 candles; 3) 4 adults and 6 students; 4) Small is 11.67 and Large is 83.75
Step-by-step explanation: 1. Total of $20 and needs 9 donuts. One is $3 and one is $2. Start with 3 $3 that 9 and let's do 3 for $2 which is 6. 9+6 is $15. 20-15 is 5. We have $5 left so we can buy in total 4 $3 donuts and 4 $2 donuts.
2. She has to make at least 4 candles. Booth is $40. And $2 per candle. 4*2 is $8. 40+8 = 48 and 48/12 is 4 candles.
3. They have a total of 120 sold. So let's start with adult tickets: $15 each. So let's start with 4 sold. 15*4 = 60. Students: $10 each. 10*4 is $40. 60+40 is 100 sold! So let's do 2 more student tickets to get 120 sold. 4 adults sold and 6 students sold.
4. Let's work with 6 and 8 you set up the equation 6x+8y=670 you get x = 11.67 and y is 83.75. So the large price is $83.75 and the Small is $11.67
a rectangular piece of cardbord of dimensions
A rectangular piece of cardbord has 3D dimensions.
What is the definition of a rectangle?Rectangles are enclosed 2-D shapes with four sides, four corners, and four right angles.Equal and parallel opposite sides make up a rectangle.
What are the properties of a rectangle ?The rectangle's properties are listed below:
There are four vertices and four sides.Every vertex has a 90-degree angle.The opposing sides have parallel and equal sides.Intersect each other diagonally.The perimeter of an object is equal to twice its combined length and width.Its area is calculated as the product of its length and breadth.It is a parallelogram and has four right angles.All inner angles added together equal 360 degreesTo know more about Rectangular visit;
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There are 15 oranges in a basket. 4 oranges are rotten. Danial takes two oranges at random from the basket without replacement. Find the probability that (a) both oranges are rotten. (b) only one of the oranges is rotten.
who can help me pls
Part (a)
4 rotten15 total4/15 is the probability of getting a rotten orange
After one is taken and not put back, there are
4-1 = 3 rotten 15-1 = 14 totalmeaning 3/14 is the probability of a second rotten orange.
Two rotten in a row has the probability (4/15)*(3/14) = 2/35. I skipped a few steps so let me know if you need to see in more detail how I got to that result.
Answer: 2/35=====================================================
Part (b)
We want to calculate the probability exactly one of the two oranges selected is rotten.
There are two possible cases here:
Case 1) The first orange is rotten and the second is not rotten.Case 2) The first orange is not rotten and the second is rotten.Let's determine the probability for case 1.
4/15 was mentioned earlier in part (a) as the probability of a rotten orange. There are 15-4 = 11 non-rotten oranges and 15-1 = 14 remaining since we aren't replacing the first selection. That gives 11/14 as the probability the 2nd selection is fresh.
We get (4/15)*(11/14) = 22/105 as the probability for case 1 to happen.
Through similar calculations, the probability for case 2 is (11/15)*(4/14) = 22/105
Cases 1 and 2 are mutually exclusive. Both cannot happen simultaneously. There is no overlap. This fact allows us to add the results to get:
22/105 + 22/105 = 44/105
That fraction cannot be reduced.
Answer: 44/105What are the zeros of this function?
Answer:
B
Step-by-step explanation:
the zeros are the values of x on the x- axis where the graph crosses.
the graph crosses the x- axis at x = 3 and x = 6
then
the zeros are x = 3 and x = 6
What is the light collecting area (aperture), in [m2], of a telescope with the primary mirror diameter: 50 [cm]?
The area of the aperture storing light is 0.196 [tex]m^{2}[/tex].
What are shapes?Mathematical figures which have a set of pre defined properties are known as shapes. For example, Square shape is a mathematical figure who has four sides and all of them are equal in length and all the four corner of square have an angle of 90 degree. Similarly if there a figure who has been formed by the help of four lines of equal length but the corners are not 90 degrees then it will be Rhombus and not Square.
Now for the given question:
Diameter of the mirror=50 cm
we convert dia. unit in meter as area is asked in meter.
Dia.= [tex]\frac{50}{100}[/tex]
= [tex]\frac{1}{2}[/tex]
Area of a circle=π× [tex](\frac{dia}{2} )^{2}[/tex]
=π×[tex](\frac{1}{4} )^{2}[/tex]
Area= π/16
π=3.14
Area=[tex]\frac{3.14}{16}[/tex]
= 0.196 [tex]m^{2}[/tex]
Hence area of the aperture is 0.196 [tex]m^{2}[/tex].
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A bag contains three blue counters and four yellow counters. Two counters are removed without replacement and X is the number of blue counters removed.
This is a probability problem. To find the probability of removing two blue counters, we need to calculate the number of possible outcomes of removing two blue counters out of seven counters (3 blue and 4 yellow).
The number of possible outcomes of removing two blue counters is 3C2 = 3! / (2! * (3-2)!) = 3.
So, the probability of removing two blue counters is 3/7C2 = 3/21.
To find the probability of X being equal to 2, we need to calculate the probability of removing two blue counters.
Therefore, the probability of X being equal to 2 is 3/21.
When you
make a stem-and-leaf plot for the data set
5.6, 5.4, 4.1, 3.2, 4.7, 3.9, which place value
will the stems represent? Which place
value will the leaves represent?
The values on the stem are {5, 5, 4, 3, 4, 3} and the leaf of the data set is represented by {6, 4, 1, 2, 7, 9}.
What is stem and leaf plot?A stem and leaf plot, also known as a stem and leaf diagram, is a way to arrange data so that it is simple to see how frequently various sorts of values occur. It is a graph that displays ordered numerical data. A stem and a leaf are divided into each piece of data.
A stem and leaf plot is shown as a customized table with the first or final digit of each data value divided into a stem and the remaining digit in a leaf.
According to the stem leaf plot the first digit is the stem and the second digit is the leaf.
Hence, the values on the stem are {5, 5, 4, 3, 4, 3} and the leaf of the data set is represented by {6, 4, 1, 2, 7, 9}.
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geometric: you vs serena williams* you are playing serena williams (who has one hand tied behind her back) in tennis. your probability of losing is 98% and thus probability of winning is 2%. you will stop playing after you beat her. what is the probability you win on the 20th game played?
Probability determines the likelihood of an event occurring: P(A) = f / N. Odds and probability are related but odds depend on the probability. You first need probability before determining the odds of an event occurring.
P(A) = f / N.
probability = 2%/100=0.0002
One of the areas of probability theory is the estimation of the chance of experiments occurring. Using a probability, we can calculate everything from the likelihood of getting heads or tails when flipping a coin to the likelihood of making a research error, for example. It is essential to appreciate the most basic definitions of this branch, such as the formula for computing probabilities in equiprobable sample spaces, the likelihood of two events joining together, the probability of the complementary event, etc., in order to properly understand it .Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. Mathematics has incorporated probability to forecast the likelihood of various events.
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question 4
help me asap
The unknown angle in the cyclic quadrilateral is as follows:
m∠B = 121 degrees.
How to find angles in a cyclic quadrilateral?In a cyclic quadrilateral, the sum of a pair of opposite angles is 180° (supplementary). The sum of angles in a cyclic quadrilateral is 360 degrees.
Therefore, let's find the angle m∠B in the cyclic quadrilateral.
m∠D = 59 degrees
m∠A = 33 degrees
Therefore,
m∠B = 180 - m∠D
This is because the angle m∠B is opposite to the angle m∠D.
Hence,
m∠B = 180 - 59
m∠B = 121 degrees.
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if a =5 and A = 50° find c
The length of the side c of the right-angled triangle is equal to 6.5 to the nearest tenth using the trigonometric ratio of sine of angle 50°.
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.
The basic trigonometric ratios includes;
sine, cosine and tangent.
Considering the right-angled triangle ABC, we shall calculate for the length c by application of the trigonometric ratio of sine for the angle 50°.
sin 50° = 5/c {opposite/hypotenuse}
by cross multiplication
c = 5/sin 50°
c = 6.5270
Therefore, the length of the side c of the right-angled triangle is equal to 6.5 to the nearest tenth using the trigonometric ratio of sine of angle 50°.
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10 The number of students who brought
their own lunch to school on Tuesday was"
57 fewer than the number of students
who ate the school lunch. There were
more than 485 students who brought
their lunch.
Part A
Write an inequality to find the possible
number of students, n, who ate the
school lunch.
Part B
How many students could have possibly
eaten the school lunch?
Part A: The inequality to find the possible number of students, n, who ate the school lunch n > 542 students
Part B: The number of students, that possibly eat lunch at school is 542 or more students
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
Part A; The number of students who bring lunch, B > 485 students
The number of students who eat lunch in school, E = B + 57
∴ E > 485 + 57
The number of students who can possibly eat lunch in school;
E > 542 students
Part B;
The number of students, n, that possibly eat lunch at school, are;
n = 542 or more students.
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a force of 192 lb is required to hold a spring stretched 3 ft beyond its natural length. how much work w is done in stretching it from its natural length to 9 inches beyond its natural length?
The work required to stretch the spring from its natural length to a distance of 9 inches beyond its natural length is 2.25 lb-ft.
The problem involves calculating the work required to stretch a spring from its natural length to a distance of 9 inches beyond its natural length, given that a force of 192 lb is required to hold the spring stretched 3 ft beyond its natural length.
To solve the problem, we use the formula for the work done by a force that varies with distance, which is given by:
W = (1/2) k (x2^2 - x1^2)
where W is the work done, k is the spring constant, x1 is the initial distance, and x2 is the final distance.
In this case, the initial distance is the natural length of the spring, which is 0 ft, and the final distance is 9/12 ft. To find the spring constant, we use the fact that a force of 192 lb is required to hold the spring stretched 3 ft beyond its natural length, which gives us:
192 = k * 3
Solving for k, we get k = 64 lb/ft.
Substituting the values into the formula, we get:
W = (1/2) * 64 * (9/12)^2
Simplifying, we get:
W = 2.25 lb-ft
This calculation shows how the work done by a force that varies with distance can be calculated using the spring constant and the distances involved.
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Find the 92nd term of the arithmetic sequence 8, 25, 42, ...8,25,42,
The 92nd term of the arithmetic sequence 8, 25, 42, ..... is equal to 1,555.
How to calculate an arithmetic sequence?Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:
aₙ = a₁ + (n - 1)d
Where:
d represents the common difference.a₁ represents the first term of an arithmetic sequence.n represents the total number of terms.Next, we would determine the common difference as follows.
Common difference, d = a₂ - a₁
Common difference, d = 25 - 8
Common difference, d = 17
Substituting the given parameters into the formula, the 92nd term of this arithmetic sequence is given by;
a₉₂ = a₁ + (92 - 1)d
a₉₂ = 8 + (91)(17)
a₉₂ = 8 + 1,547
a₉₂ = 1,555.
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among 8 electrical components exactly one is known not to function properly. if 2 components are randomly selected, find the probability that at least one does not function properly.
The probability that at least one component does not function properly when 2 components are randomly selected from 8 is 1/4, or 0.25.
The total number of ways to select 2 components from 8 is:
C(8,2) = 8! / (2! (8-2)!) = 28
Now, let's find the probability that at least one component does not function properly. We can find this probability by subtracting the probability that both components function properly from 1.
The probability that the first component functions properly is 7/8, since there are 7 working components out of 8. The probability that the second component also functions properly, given that the first component does, is 6/7, since there are 6 working components left out of 7. Therefore, the probability that both components function properly is:
(7/8) * (6/7) = 6/8 = 3/4
So the probability that at least one component does not function properly is:
1 - 3/4 = 1/4
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Sam bought six pens for an unknown price plus a backpack. If he spent a total of $28.50, write an equation to find the cost of each pen.
Answer: $4.75 for each pen
Step-by-step explanation:
$28.50/6= 4.75$
Which pairs of rectangles are similar polygons?
Select each correct answer.
Answer:
The corrects answers are B and D
Since you divide the same side for both the the rectangles on both parts and if the division statements are equaled, then they are similar.
Step-by-step explanation:
have a nice day.
The table below shows the cost of mailing a postcard in different years. During
which time interval did the cost increase at the greatest average rate?
Answer: 1898-1971
Step-by-step explanation: find the difference between the years and divide it over the change in cost
1. difference of yrs. : 1971-1898 = 73
2. difference of cost : 6-1 = 5
3. divide : 73/5 = 14.6 (avg)
avg for #1) 14.6
avg of #2) 1
avg of #3) 2.1
avg of #4) approx. 0.55
10+3s≥19 Need help pls
Answer: s≥3
Step-by-step explanation: fist you need to get the variable by itself on one side. So subtract the 10 from each side and you have 3s≥9. Then you divide each side ny 3 to get s by itself, divide 9 by 3. Then your answer is s≥3
write 70a-84b+20ab-24b^2 as a product
Answer:
2 • (10ab + 35a - 12b2 - 42b)
Step-by-step explanation:
(20ab + 70a - 84b) - (23•3b2)
20ab + 70a - 24b2 - 84b =
2 • (10ab + 35a - 12b2 - 42b)
graphing systems of equations
graph equation and state the solution (the point where they intersect)
pls pls pls help i’m ripping my hair off trying to solve this
The system of linear equations represented in the graph have (b) ne solution at (-3, 1)
How to determine the number of solutionsFrom the question, we have the following parameters that can be used in our computation:
0 = y - x - 4
3y + 9 = -4x
The above system represents two linear functions
The point of intersection of the linear functions represent the solution
In this case, the linear functions intersect at (-3, 1)
See attachment for graph
Hence, it has one solution at (-3, 1)
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An aeroplane flies 1400km in 1h 45mins.how far will it fly in 2h 30min at the same avarage speed?
Answer:
The aeroplane will fly 2000 km if travelling at the same average speed.
Step-by-step explanation:
To calculate the distance an aeroplane will fly in 2 h 30 min if it flies 1400 km in 1 h 45 mins, use the Speed Distance Time formula.
[tex]\boxed{\sf Speed=\dfrac{Distance}{Time}}[/tex]
There are 60 minutes in one hour. Therefore:
1 h 45 mins = 1.75 hours2 h 30 mins = 2.5 hoursTo calculate the speed of the aeroplane, divide the distance by the time it takes to travel that distance. Therefore, if an aeroplane flies 1400 km in 1.75 hours then its average speed is:
[tex]\sf Speed=\dfrac{1400\;km}{1.75\;h}=800\;km/h[/tex]
To determine the distance the aeroplane will travel in 2.5 hours, multiply the found speed of 800 km/h by the time:
[tex]\sf Distance=800\;km/h \times 2.5\;h=2000\;km[/tex]
Therefore, the aeroplane will fly 2000 km in 2 h 30 min if travelling at the same average speed.
Use the graph of the number of gallons of lemonade in a container, y, after drinking x glasses of lemonade.
The graph states that there are 2 number of gallons of lemonade in a container, y, after drinking 12 glasses of lemonade.
How to interpret a graph?
The horizontal scale across the bottom and the vertical scale along the side tell us how much or how many. The points or dots on the graph show us the facts. The lines connecting the points give estimates of the values between the points.
since , it is a decreasing graph because it has a negative slope . Therefore , as no of glasses increases the gallons numbers decreases.
Hence , the graph states that there are 2 number of gallons of lemonade in a container, y, after drinking 12 glasses of lemonade.
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Answer:
no run hide
Step-by-step explanation:
hide run boo
Bryanna's younger sister is stacking her toy blocks on top of each other to build a tall tower. If each block is 2.4 inches long, how many blocks will she have stacked if the tower reaches a height of 4 fe
Solve the equation for x (0 ≤ x ≤ 2π)
cos²x + sin x = 1
To solve the equation cos²x + sin x = 1, we can use the trigonometric identity cos²x = 1 - sin²x. By substituting this identity into the equation, we get:
1 - sin²x + sin x = 1
Combining like terms, we get:
1 - sin²x = 0
Solving for sin x, we get:
sin x = 1
However, the sine function has a range of [-1, 1], so the only solution in the interval [0, 2π] is sin x = 1, which corresponds to x = π/2. So the solution to the equation cos²x + sin x = 1 in the interval [0, 2π] is x = π/2.
What information does the source supply?
The information provided by a source in a graph is C. Who put the data together.
How does a source contribute to a graph ?The information provided by a source in a graph can include various aspects such as the data being displayed, the method used to collect the data, and who put the data together (also known as the data source).
The data source is important because it provides context and credibility to the data being presented. It helps to understand the reliability and accuracy of the data, as well as any potential biases that may be present. In this case, the source is the Human Resources Department.
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Evaluate 4t + 8 if t = 3.
=4t + 8
=4×3 + 8
= 12 +8
= 20
[tex]...[/tex]
What is the slope of the line that passes
through the points (-4, 4) and (-1, 3)?
Write your answer in simplest form.
Answer:
the answer is : m= -1/3
Step-by-step explanation:
you need the steps?
The annual profits for a company are given
in the following table, where x represents
the number of years since 2006, and y
represents the profit in thousands of
dollars. Write the linear regression
equation that represents this set of data,
rounding all coefficients to the nearest
hundredth. Using this equation, estimate
the calendar year in which the profits
would reach 482 thousand dollars.
Years since 2006 (x)
0
1
2
3
4
5
Profits (y)
(in thousands of dollars)
147
167
209
239
250
267
The linear regression of the data is given as follows:
y = 25.1x + 150.4.
The estimate for the year in which the profit would reach $482,000 is of:
2019.
How to find the equation of linear regression?To find the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator.
The points for this problem are given as follows:
(0, 147), (1, 167), (2, 209), (3, 239), (4, 250), (5, 267).
Hence the equation is of:
y = 25.1x + 150.4.
The estimate for the year in which the profit would reach $482,000 is x years after 2006, when y = 482, hence:
482 = 25.1x + 150.4.
x = (482 - 150.4)/25.1
x = 13.
2006 + 13 = 2019 -> year.
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