The exponential decay function to model the amount of Os-182 in a sample over time is given below :Given: A radioactive isotope of the element osmium Os-182 has a half-life of 21.5 hours.
The initial amount is Ag The amount after time t in hours is A We know that if there are 100 grams of Os-182 in a sample, after 21.5 hours, there will only be 50 grams of that isotope remaining .Let's substitute these values in the exponential decay function to find the value of k. We get, The required exponential decay function is[tex]A = Ag × e^(-kt)[/tex]
Note: We are multiplying by 100/100 because the initial amount is given as 100 grams. We can also simplify the function as shown below: [tex]A = 100 × e^(-0.0322t)[/tex]Hence, the exponential decay function to model the amount of Os-182 in a sample over time [tex]is A = Ag × e^(-kt) = 100 × e^(-0.0322t).[/tex]
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How many distinct triangles can be formed for which m∠E = 64°, g = 9, and e = 10?
triangle(s)
Using the law of sines, it is found that 1 triangle can be formed with the given conditions.
What is the law of sines?Suppose we have a triangle in which:
The length of the side opposite to angle A is a.The length of the side opposite to angle B is b.The length of the side opposite to angle C is c.The lengths and the sine of the angles are related as follows:
[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]
Hence, for this problem, we have that the relation is:
[tex]\frac{\sin{64^\circ}}{10} = \frac{\sin{G}}{9}[/tex]
[tex]\sin{G} = 0.9\sin{64^\circ}[/tex]
[tex]\sin{G} = 0.8089[/tex]
[tex]G = \arcsin{0.8089}[/tex]
G = 54º
A triangle can have one angle of 64º and another of 54º, hence 1 triangle can be formed with the given conditions.
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From Andys house to Billys hometown you can travel by 3 roads. And to get from Billys hometown to Willies's house you can travel by 5 roads. How many possible wats are there to travel from andys house to willies house?
Using the Fundamental Counting Theorem, there are 15 ways to travel from Andy's house to Willie's house.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
For this problem, the parameters are:
[tex]n_1 = 3, n_2 = 5[/tex].
Hence the number of ways is:
N = 3 x 5 = 15.
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Solve this system of equations using the substitution method
y = 2x + 17
y = 6x - 3
Step-by-step explanation:
well, as you can witness both of the equations are equal to y, so you're free to reckon that they are equal as well
[tex]6x - 3 = 2x + 17 = = = > \\ 4x = 20 = = = > x = 5 \: and \: \\ y = 6(5) - 3= = = > y = 27[/tex]
Answer:
<3
Step-by-step explanation:
5, 27 is right on acellus
x=5
y=27
Who am I ?
- My thousands digit is 4
- My hundreds digit is 4 less than the digit in the thousands place
- The sum of my tens digit and ones digit is 7
- My tens digit is 3 more than my ones digit
- The digits in the thousands period have a sum of 10
- My first digit is half the digit that immediately follows it.
I am the number_______________
I am the number 4052. It is rather confusing and i cannot promise that it is correct. Hope it helps : )
In a recent poll, 230 people were asked if they liked dogs, and 90% said they did. Find the margin of error of this poll, at the 99% confidence level.
The margin of error of this poll is
Given that 230 people were asked if they liked dogs, and 90% said they did.
In a random sample, a margin of error is a statistical measure that takes into account the discrepancy between actual and expected results.
Sample size (N)=230
Sample proportion [tex](\hat{p})[/tex] = 90% = 0.90 and
confidence interval = 99%
The critical value at 99% confidence interval with α=0.01 is
[tex]\begin{aligned}Z_{c}&=Z_{1-\frac{\alpha}{2}}\\ &=Z_{1-\frac{0.01}{2}}\\ &=Z_{0.995}\\ &=2.576\end[/tex]
This value is taken from the Standard normal distribution table.
Now, we will calculate the margin of error (E) by using the formula
[tex]E=Z_{c}\sqrt{\frac{\hat{p}(1-\hat{p})}{N}}[/tex]
Substituting the values in the formula, we get
[tex]\begin{aligned}E &=2.576\times \sqrt{\frac{0.90(1-0.90)}{230}}\\ &=2.576\times \sqrt{\frac{0.09}{230}}\\ &=2.576\times\sqrt{0.00039}\\ &=2.576\times 0.0197\\ &=0.0507\end[/tex]
Hence, the margin of error when 230 people were asked if they liked dogs, and 90% said they did is 0.0507.
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Determine the area of the figure.
Answer: 3x - 6 (in^2)
Step-by-step explanation:
base * height / 2
=
3 ( 2x - 4) / 2 (in^2)
= 3x - 6 (in^2)
Answer: 3x-6 in^2
Step-by-step explanation:
There is no way to figure out what x is without additional information, so you have to leave the answer in this form
A worker at a shoe factory is required to box at least
8
pairs of shoes per minute, but is not allowed to box more than
12
pairs of shoes per minute. According to this information, what is a possible amount of time, in minutes, that it could take the worker to box
168
pairs of shoes?
The possible amount of time, in minutes, that it could take the worker to box 168 pairs of shoes is between 14 minutes to 21 minutes.
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.
A worker at a shoe factory is required to box at least 8 pairs of shoes per minute, and not more than 12 pairs of shoes per minute.
For 168 pairs of shoe:
Maximum time = 168 pair / 8 pairs per minute = 21 minutes
Minimum time = 168 pair / 12 pairs per minute = 14 minutes
The possible amount of time, in minutes, that it could take the worker to box 168 pairs of shoes is between 14 minutes to 21 minutes.
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A zoologist researched the feeding habits of lemurs. she collected data by studying the lemurs in a zoo exhibit for a one-month period and drew conclusions based on her data. what kind of statistical study did the zoologist conduct?
The kind of statistical study the zoologist conducted was D. observational study.
What is observational study in research?An observational study serves as a study whereby the researcher simply observes the subjects without interfering with it.
This is different from carrying out experiment on them or just a theoretical approach.
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CHECK THE COMPLETE QUESTION BELOW:
A zoologist researched the feeding habits of lemurs. She collected data by studying the lemurs in a zoo exhibit for a one-month period and drew conclusions based on her data. What kind of statistical study did the zoologist conduct? A. survey B. theoretical study C. experiment D. observational study
Calculate the mean and standard deviation for the average yards rushed by
each player. Then graph the data (use the mean for each player and SD for error bars).
Compare and contrast the mean rushing yards Dillon and Corey.
What does the SD indicate about the mean rushing yards for each player?
Question:
A sample of cans of peaches was taken from a warehouse, and the content of each can mearsed for weight. the sample means was 486g with stand deviation 6g. state the weight percentage of cans with weight:
Draw normal curve to help - split into 8 section ( i can't draw it here)
a) 34.13% of cans will be between 480g and 486g.
b) 13.59 + 2.15 + 0.13= 15.87% of cans greater than 492g.
Look at the Stand Dev Graph where the give you the number
Step-by-step explanation:
Let me give you a different question and i will answer it, which you help you answer your question.
Tara has 4 and 4 over 5 feet of rope.
part a: how many 2 over 5 foot pieces can tara cut from the 4 and 4 over 5 feet of rope? show your work. (5 points)
part b: using the information in part a, interpret the meaning of the quotient in terms of the two fractions given. (5 points)
the answer box is a writing thing so might have to explain it differently
Part A - Tara cuts [tex]12[/tex] pieces of [tex]2/5[/tex] from [tex]4\frac{4}{5}[/tex] feet of rope.
Part B - The quotient means the amount of foot pieces so it is [tex]12[/tex] foot pieces.
How can we find the foot pieces of [tex]2/5[/tex] from [tex]4\frac{4}{5}[/tex] rope. ?
from part A
we solve the fraction
[tex]4\frac{4}{5} =24/5[/tex] rope
And Tara needs to pieces of [tex]2/5[/tex] foot
So we need to divide
[tex]\frac{24/5}{2/5} \\=\frac{24}{5} *\frac{5}{2} \\=\frac{24}{2} \\=12[/tex]
For part B
When we using the information from part A we decide that the quotient means the amount of foot pieces Tara can cut from the [tex]4\frac{4}{5}[/tex] feet of rope.
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The equation -2x − y = -4 shows the budget for spending on supplies over the next few weeks. If the total money (y) decreases every week (x), how many weeks will it take for the budget money to run out?
The number of weeks it will take for the budget money to run out is; 2 weeks.
How many weeks will it take for the money to run out?The number of weeks it would take for the budget money to decrease till it runs out as required in the task can be interpreted as the x-value which corresponds to a Y-value of zero.
Hence, by setting y=0; we have;
-2x -0 = -4
-2x = -4
Divide both sides of the equation by; -2.
x = 2
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Find a linear and an exponential equation that matches f(2)=12 and f(4)=48.
please help :))
The linear and exponential equation that matches f(2) = 12 and f(4) = 48 are y = 18x - 24 and f(x) = 3(2)ˣ respectively
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
For the exponential function, when f(2) = 12:
12 = ab² (1)
Also, at f(4) = 48:
48 = ab⁴ (2)
Hence:
a = 3, b = 2
f(x) = 3(2)ˣ
For the linear function using the points (2, 12) and (4, 48):
y - 12 = [(48 - 12) / (4 - 2)](x - 2)
y = 18x - 24
The linear and exponential equation that matches f(2) = 12 and f(4) = 48 are y = 18x - 24 and f(x) = 3(2)ˣ respectively
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Scott counted 23 beats in 10 seconds. What is his approximate heart rate?
123 bpm
130 bpm
138 bpm
230 bpm
Anyone is here
Answer:
138
Step-by-step explanation:
There is 60 seconds in a minute, so if the heart beats 23 times in 10 seconds, it is 138 bpm.
23 * 6 = 138
1.rani was selling flowers. each day she made 7 bouquets by arranging 8 roses and 6 marigolds in each bouquet. each bouquet was sold for rs.85. a) find the number of marigolds used in a day. b) find the total number of flowers used by using suitable property of whole numbers. c) if she sold 42 bouquets in a whole week, find the amount she earned. 2. by suitable rearrangement, find the value of a) 819 + 364 + 181 + 436 b) 20 x 348 x 50 3. using suitable property find the value of 492 x 13 + 492 x 37 4. a) name the property 86 + 65 = 65 + 83 b) the multiplicative identity of whole numbers is ______ 5. find the next two numbers in the pattern 1,1,2, 3,5,8, ______, ________
1.(a) The number of marigolds used in a day is 42.
(b) The total number of flowers used by using suitable property of whole numbers is 98.
(c) She earned Rs. 3570
2.(a) The value of [tex]819 + 364 + 181 + 436[/tex] is 1800.
(b) The value of [tex]20 \times 348 \times 50[/tex] is 348000.
3. The value of [tex]492 \times 13 + 492 \times 37[/tex] is 24600.
4.(a) Name the property 86 + 65 = 65 + 86 is commutative property.
(b) The multiplicative identity of whole numbers is 1.
5. The next two numbers in the pattern 1,1,2, 3,5,8 are 13 and 21.
1. (a) The number of marigolds used in a day is 42.
Rani made 7 bouquets on each day by arranging 8 roses and 6 marigolds in each bouquet. So number of marigolds used in a day is 7×6 = 42.
(b) The total number of flowers used by using suitable property of whole numbers is 98 flowers used by using distributive property.
What is distributive property of whole numbers?
The distributive property of multiplication states that when multiplying a number by the sum/difference of 2 numbers, the final value is equal to the sum/difference of each addend multiplied by the third number.
Distributive property = a×(b+c) = a×b+a×c
Total number of flowers = 7×(8+6) = 7×14 = 98.
(c) If she sold 42 bouquets in a whole week, find the amount she earned is rs.3570.
Each bouquet was sold for Rs.85. Then she earned a whole week off = 42×85 = rs.3570.
2. (a) By suitable rearrangement, the value of 819 + 364 + 181 + 436 is 1800.
Rearrangement of the given numbers = (819+181)+(364+436)
= 1000+800
= 1800
(b) By suitable rearrangement, the value of 20 x 348 x 50 is 348000.
Rearrangement of the given numbers = 348×(50×20)
= 348×1000
= 348000
3. Using suitable property find the value of 492 x 13 + 492 x 37 is 24600 by using distributive property.
By using distributive property = 492 x 13 + 492 x 37
= 492×(13+37)
= 492×50
= 24600
4. (a) Name the property 86 + 65 = 65 + 86 is commutative property.
What is commutative property?
This law simply states that with addition and multiplication of numbers, you can change the order of the numbers in the problem and it will not affect the answer.
By using commutative property, a+b = b+a
86 + 65 = 65 + 86
151 = 151
(b) The multiplicative identity of whole numbers is 1.
Multiplying a whole number by 1 equals that identical number, the whole number 1 is called the multiplicative identity.
5. The next two numbers in the pattern 1,1,2, 3,5,8,?,? are 13 and 21.
Just add the no before the given no then you will get the pattern. example first no=1 and no before it is 0
1+0=1
1+1=2
2+1=3
3+2=5
5+3=8
8+5=13
Hence, The next two numbers for the given series are 13 and 21.
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One of the reasons to use the bootstrap method is because the formula for the confidence interval is too hard to derive. Group of answer choices True False
The confidence interval formula is extremely complicated to derive, which is one of the justifications for using the bootstrap approach. this statement is true.
What purposes serve the bootstrap method?A resampling technology named the bootstrap can be used to sample a dataset using replacement to calculate statistics on a group. Estimating summary statistics like the mean or standard deviation may be done using it.
The advantages of the bootstrap methodThe benefits of bootstrapping include its simplicity in estimating standard errors and confidence intervals as well as its cost-effectiveness in avoiding the need to conduct the operation to get additional groups of sampled data.
Therefore it can be concluded that the said query statement is true.
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Can someone please help
Solving the given equation, the value of v that makes the statement true is:
A. v = 8.
What is the given equation?The equation is:
[tex]12 = 12 + \frac{v - 8}{2}[/tex]
Hence:
[tex]\frac{v - 8}{2} = 0[/tex]
Applying cross multiplication:
v - 8 = 0
v = 8.
Hence option A is correct.
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The ratio of boys and girls in a class with 40 students = 3:2. If 4 new boys are added, what will be the new ratio?
Answer: 7:4
Step-by-step explanation:
40 boys and girls 3:2 = 24 boys + 16 girls
4 boys are added 28 boys + 16 girls /4 = 7:4
Answer:
7:11
Step-by-step explanation:
We know the total number of students and the ratio of boys to girls. The total for the ratio of boys and girls would be 5 (3+2). Now we can set up proportions knowing these numbers.
b = 3
g =2
t =5
Let's find out how many actual boys there are by setting up a proportion
3/5 = b/40
I will look at the denominators to find x. 5 times what gives me 40? (8). So, I will multiple the top number (numerators). Since I need to multiple the bottom number by 8 to get the number 40, I will now multiple the top number by 8 and get 24.
Now, I know how many actual boys and girls were in the original class. There were 24 boys, 16 girls (40 - 24) and 40 total students.
Now I will take this new information and apply it to the new situation. Now I have 28 boys (24 + 4) and a new total 44.
The ratio of boys to girls would not be 28: 16 or 7:4
A card is randomly chosen from the cards in the image. Find the probability of choosing the cards with either Q or R on them.
P(Q or R) = ________
The probability of choosing cards either Q or R when a card is drawn from a deck of 8 cards is 0.25.
Given that a card is randomly chosen from 8 cards shown in figure.
We have to calculate the probability of choosing either Q or R when a card is drawn from those 8 cards.
Probability means calculating the likeliness of happening an event among all the events possible. It lies between 0 and 1. It cannot be negative.
Number of cards=8
Number of repeated cards=0
Number of cards showing Q and R =1 each.
Probability of getting Q or R is P(X=Q)+P(X=R)
= 1/8+1/8
=2/8
=1/4
=0.25
Hence the probability of getting either P or Q when a card is drawn from 8 cards is 0.25.
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Solve F=gm1*m2/d2 for g
The expression for g in terms of other variables is g = Fd^2/m1m2
Subject of formulaGiven the expression below as shown
F=gm1*m2/d2
We are to make g the subject of the formula
F=gm1*m2/d2
Cross multiply
Fd2 = gm1m2
Divide both sides by m1m2
Fd^2/m1m2 = g
g = Fd^2/m1m2
Hence the expression for g in terms of other variables is g = Fd^2/m1m2
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Which expression could help you find the distance between –1 and 3 on the number line?
Answer:
|-1| + |3|
Step-by-step explanation:
We can use absolute values to find the distance between positive and negative numbers on a number line.
|-1| + |3| =
Keep in mind that
- the absolute value of a positive number is positive and
- the absolute value of a negative number is positive
1 + 3 =
4 units
If you substitute 12 2x for y in the second equation, how is the resulting equation written in standard form?
The resulting equation written in standard form is 16x² - 22x + 6 = 0.
What is equation in standard form?Quadratic Equation in Standard Form: ax² + bx + c = 0
a, b and c are known values. a can't be 0.
"x" is the variable or unknown (we don't know it yet).
The "solutions" to the Quadratic Equation are where it is equal to zero.
They are also called "roots", or sometimes "zeros"
We can Factor the Quadratic (find what to multiply to make the Quadratic Equation)
Or we can Complete the SquareOr we can use the special Quadratic Formula:Quadratic Formula: x = [ -b (+-) √(b² - 4ac) ] / 2a, Just plug in the values of a, b and c, and do the calculations.Calculation for the given equation-
Now, y=-16x²+24x+6
Substitute, y = 12+2x in y = -16x²+24x+6.
=> 12+2x = -16x²+24x+6
=> 16x²-24x-6+12+2x = 0
=> 16x²-22x+6 = 0
Therefore, the quadratic equation given in the standard form is 16x²-22x+6 = 0.
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The complete question is-
The two equations are given below;
Y = 12 + 2x linear equation
Y = -16x² + 24x + 6 quadratic equation
If you substitute 12 + 2x for y in the second equation how is the resulting equation written in standard form?
How much does a $5.40 lunch cost if it is discounted by 10%
Answer:
$4.86
Step-by-step explanation:
Original price: $5.40
Discount: 10%
Discount amount:
10% of $5.40 = 0.1 × $5.40 = $0.54
Discounted price:
$5.40 - $0.54 = $4.86
Answer:
$4.86
Step-by-step explanation:
There are two approaches to this problem.
1:
You can multiply the original value by 10% and subtract it from the original value. In this case, $5.40-(5.40×10%). This becomes $5.40-$0.54. This is $4.86.
2:
You can simply multiply the original value by 90%. In this case, $5.40×90%. This also becomes $4.86.
4.10.1 checkup, answer questions about the unit circle
Using the unit circle, the correct answer regarding the comparison of angles w and t is given by:
a. t > w.
What is the unit circle?For an angle [tex]\theta[/tex] the unit circle is a circle with radius 1 containing the following set of points: [tex](\cos{\theta}, \sin{\theta})[/tex].
From this, we get that the sine is represented by the vertical axis. As we advance into the second quadrant, as the angle increases, sine decreases. Hence, since sin w > sin t, we have that t > w and option a is correct.
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PLEASE HELP NOW
Which formula can be used to find the volume of the cylinder? Check all that apply. A = ( d )( h ) V = B( h ) V = ( l )( w )( h ) V = 2( r )( h ) V = (pi) (r squared) (h)
Answer:
V= (pi) (r squared) (h)
Step-by-step explanation:
solve this pls>>>>>>>there’s a pic
Answer:
x = 5, 1
Step-by-step explanation:
To solve for x, you must factor the equation. The factored equation will be: (x - 1) (x - 5) = 0. After factoring, isolate the two factored equations: (x - 1) = 0 and (x - 5) = 0. Then solve for x for both the equations which should get you to x = 5, 1.
Use the drop-down menus to complete each equation so the statement about its solution is true. CLEAR CHECK No Solutions 3x 9 4x x
The complete equation so that the statement is true is 3x+9+4x+x= 8x + 1
How to complete the equation?The equation is given as:
3x+9+4x+x=
Represent the blank with y
So, we have:
3x + 9 + 4x + x = y
Evaluate the like terms
8x + 9 = y
For the equation to have no solution the value of y and 8x + 9 must not be equal.
Take for instance
y = 8x + 1
So, we have:
8x + 9 = 8x + 1
Subtract 8x from both sides
9 = 1
The above equation is false because 1 and 9 are not equal
Hence, the complete equation so that the statement is true is 3x+9+4x+x= 8x + 1
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Complete question
Use the drop-down menus to complete each equation so the statement about its solution is true.
No Solutions
3x+9+4x+x=
Sketch the curve y = \sqrt{x+3} .
Find the area bounded by the curve, X-axis and Y-axis.
I get the first part but not the second part.
The area bounded by the curve, x-axis and y-axis of the function y = √(x + 3) is 2√3
How to determine the area bounded by the curve, x-axis and y-axis?The curve is given as:
y = √(x + 3)
The area bounded by the curve, x-axis and y-axis is when x = 0 and y = 0
When y = 0, we have:
0 = √(x + 3)
This gives
x = -3
So, we set up the following integral
A = ∫ f(x) d(x) (Interval a to b)
This gives
A = ∫ √(x + 3) d(x) (Interval -3 to 0)
When the above is integrated, we have:
A = 1/3 * [2(x + 3)^(3/2)] (Interval -3 to 0)
Expand
A = 1/3 * [2(0 + 3)^3/2 - 2(-3 + 3)^3/2]
This gives
A = 1/3 * 2(3)^3/2
Apply the law of indices
A = 2(3)^1/2
Rewrite as:
A = 2√3 or 3.46
Hence, the area bounded by the curve, x-axis and y-axis of the function y = √(x + 3) is 2√3
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which unit of measure would be appropriate for the volume of a sphere with aradius of 2 meters?
Answer:
The unit of measuring volume of the sphere is cubic meters.
One student can paint a wall in 12 minutes. Another student can paint the same wall in 24minutes. Working together, how long will it take for them to paint the wall?
Answer:
8 minutes.
Step-by-step explanation:
We work in fractions of the wall they can paint in 1 minute, so
1/12 + 1/24 = 1/x where x is the time it takes when working together.
Multiplying through by 24x:
2x + 1x = 24
3x = 24
x = 8 minutes.
By the definition of complementary angles, since
∠
1
is complementary to
∠
2
,
m
∠
1
+
m
∠
2
=
90
∘
. By the vertical angles theorem,
∠
4
≃
_
∠
1
, and
m
∠
4
=
m
∠
1
by the definition of congruence. Combined with the given equation,
m
∠
4
=
40
∘
, the substitution property of equality means that
40
∘
=
m
∠
1
. Using the ,
40
∘
+
m
∠
2
=
. Finally, using the ,
m
∠
2
=
50
∘
.
Blank 1: Substitution property of equality
Blank 2: 50
Blank 3: Subtraction property of equality
The blank spaces in the task content can be filled with; Substitution property, 90° and subtraction property.
What are the missing statements in the proof?Since it follows from the vertical angles theorem that angle 1 = angle 4 as they are congruent.
Additionally, angles 1 and 2 are said to be complementary and hence, the sum of their measures is equal to 90°.
Finally, by virtue of the subtraction property of equality, the measure of angle 2 is; 90° - 40° = 50°.
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