Answer:
half-life ≈ 2.74
Step-by-step explanation:
One formula we can use for half life is,
N(t) = No * (1/2)^(t / t_1/2), where
N(t) is the amount remaining, No is the initial amount,1/2 is the base t is the time, and t_1/2 is the half lifeWe already know that N(t) = 28, No = 128, the base is 1/2, and t is 6. Thus, we must solve for t_1/2 using the following equation:
28 = 128 * (1/2) ^ (6 / t_1/2)
Step 1: Divide both sides by 128 to clear 128 on the right-hand side of the equation:(28 = 128 * (1/2) ^ (6 / t_1/2) / 128
0.21875 = (1/2) ^ (6 / t_1/2)
Step 2: Take the natural log (ln) of both sides:ln (0.21875) = ln (1/2 ^ (6 / t_1/2))
Step 3: According to the rules of logs, since we're taking the natural log of ln (1/2 ^ 6 / t_1/2, we can bring down the 6 / t_1/2 and it will now act like a coefficient:ln (0.21875) = 6 / t_1/2 * ln (1/2)
Step 4: Divide both sides by ln (1/2) to clear ln (1/2) on the right-hand side of the equation:(ln ( 0.21875) = 6 / t_1/2 * ln (1/2)) / ln (1/2)
ln (0.21875) / ln (1/2) = 6 / t_1/2
Step 5: You can cross multiply, which appears easier when you use the vertical fraction form instead of the horizontal fraction form.[tex]\frac{ln(0.21875)}{ln(1/2)}=\frac{6}{t_{1/2} }\\ \\ t_{1/2}*ln(0.21875)=6*ln(1/2)[/tex]
Step 6: Finally, you can now divide both sides by ln (0.21875) to isolate t_1/2 and to find the half-life. I simply rounded to the nearest hundredth, but I'll provide the entire half-life number so you can round as liberally as much as you need or would like(t_1/2 * ln (0.21875) = 6 * ln (1/2)) / ln (0.21875)
t_1/2 = (6 * ln (1/2) / ln (0.21875)
t_1/2 = 2.736420983 hours
t_1/2 = 2.74 hours
The only real difference between the longer number and the rounded number is that the longer answer gives a more exact answer when you plug it in, but the rounded answer seems to make more sense to write:
Result when plugging in exact answer for t_1/2:
N (2.736420983) = 128 (1/2) ^ (6 / 2.736420983) = 28
Result when plugging in rounded answer for t_1/2:
N (2.74) = 128 (1/2) ^ (6 / 2.74) = 28.05564116
We will first find x − x 2 . In column 2 in the table below we will calculate the deviation between each data value and the mean. Then in column 3 we will square each deviation. x x − x x − x 2 50 50 − 40.545 (9.455)2 = 89.397 28 28 − 40.545 (-12.545)2 = 157.377 37 37 − 40.545 (-3.545)2 = 12.567 30 30 − 40.545 (-10.545)2 = 111.197 58 58 − 40.545 (17.455)2 = 304.677 38 38 − 40.545 (-2.545)2 = 6.477 39 39 − 40.545 (-1.545)2 = 2.387 59 59 − 40.545 (18.455)2 = 340.587 47 47 − 40.545 (6.455)2 = 41.667 34 34 − 40.545 (-6.545)2 = 42.837 26 26 − 40.545 (-14.545)2 = 211.557 The sum of the squared deviations in column 3, rounded to three decimal places, is x − x 2 =
For the deviation between each data value and the mean in column 3, there are around 1320.511 squared deviations in all.
How to determine deviation?To find the sum of the squared deviations in column 3, add up all the values in that column.
x x − x (x − x)²
50 50 − 40.545 (9.455)² = 89.397
28 28 − 40.545 (-12.545)² = 157.377
37 37 − 40.545 (-3.545)² = 12.567
30 30 − 40.545 (-10.545)² = 111.197
58 58 − 40.545 (17.455)² = 304.677
38 38 − 40.545 (-2.545)² = 6.477
39 39 − 40.545 (-1.545)² = 2.387
59 59 − 40.545 (18.455)² = 340.587
47 47 − 40.545 (6.455)² = 41.667
34 34 − 40.545 (-6.545)² = 42.837
26 26 − 40.545 (-14.545)² = 211.557
To find the sum of the squared deviations, add up the values in column 3:
x − x² = 89.397 + 157.377 + 12.567 + 111.197 + 304.677 + 6.477 + 2.387 + 340.587 + 41.667 + 42.837 + 211.557 = 1320.511
Rounded to three decimal places:
x − x² ≈ 1320.511
Therefore, the sum of the squared deviations in column 3 is approximately 1320.511.
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The triangle shown has a perimeter of 13 units. The variable x has a
positive value.
Jenny says the length of the missing side of the triangle is 5 units, no
matter what the value x is.
2x+1
?
7-2x
Perimeter: 13 units
Do you agree or disagree? Show your work and explain your thinking.
Manny bought a brand new car in 2012 for $28,750. If the car depreciates by 12% each year, write an exponential function to model the situation, then find the value of the car in 2018. please round to two decimal places.
note use formula f(t)=a(1+r)^t
Therefore, the value of the car in 2018 was approximately $13,197.36. Rounded to two decimal places, this is $13,197.36.
What is decimal?A decimal is a way of representing a number that is based on powers of ten. It is a number expressed in the base-ten system, which means that each digit in the number represents a power of 10. The decimal point separates the whole number part of the decimal from the fractional part of the decimal.
To model the depreciation of the car over time, we can use the formula:
f(t) = a(1 - r)^t
where:
After t years, f(t) is the car's worth.
a is the initial value of the car, which is $28,750.
r is the annual depreciation rate, which is 12% or 0.12 (expressed as a decimal).
t represents how long it has been since the car been acquired.
Substituting the given values, we get:
f(t) = 28,750(1 - 0.12)^t
To find the value of the car in 2018, we need to substitute t = 6 (since 2018 is 6 years after 2012) and evaluate the function:
f(6) = 28,750(1 - 0.12)^6
Simplifying,
f(6) = 28,750(0.88)^6
Evaluating using a calculator, we get:
f(6) ≈ 13,197.36
Therefore, the value of the car in 2018 was approximately $13,197.36. Rounded to two decimal places, this is $13,197.36.
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The value of the car in 2018 was approximately $14,303.22.
What is exponential functions?
An exponential function is a mathematical function of the form f(x) = [tex]a^{x}[/tex], where a is a positive constant and x is the input variable. The base a is usually a positive real number, but it can also be a complex number.
The initial value of the car is $28,750, and it depreciates by 12% each year. This means that the value of the car after t years can be modeled by the exponential function:
f(t) = [tex]28750(1 - 0.12)^{t}[/tex]
Simplifying the expression inside the parentheses:
f(t) = [tex]28750(0.88)^{t}[/tex]
To find the value of the car in 2018, we need to substitute t = 6, since 2018 is 6 years after 2012:
f(6) = [tex]28750(0.88)^{6}[/tex]
Using a calculator, we get:
f(6) = [tex]28750(0.497^{1})[/tex]
f(6) = 14,303.22
Therefore, the value of the car in 2018 was approximately $14,303.22.
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If c is the least common multiple of A and B, which must be trye?
A. c b and c>a
D. c≥b and c≥a
The statement that must be true is c is the least common multiple of A and B, is D. c ≥ b and c ≥ a.
Why is this so ?The rationale behind this lies in the fact that finding the least common multiple (LCM) of two numbers necessitates determining a value that is commensurate with both figures, yet simultaneously represents their most diminutive shared multiple.
To expound further, It is the minimal positive integer among all feasible ones that can be divided entirely without any leftover remainder by all supplied integers. Thus, this computation allows you to determine the minimum possible factorization required to obtain each number while preserving its numerical integrity.
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A coffee shop offers an annual "Mug Club Membership" in which customers can purchase a mug for $75, then mug refills cost $1.95 each for the year. Find the total cost for a Mug Club member if they refill their cup 120 times in one year.
the total cost for a Mug Club member who refills their cup 120 times in one year is $309.
How to solve?
If a customer purchases a Mug Club membership, they pay $75 for the mug and then refill it for $1.95 per refill. If they refill their mug 120 times in one year, the total cost would be:
$75 (for the initial purchase of the mug) + $1.95 x 120 (for the 120 refills)
= $75 + $234
= $309
Therefore, the total cost for a Mug Club member who refills their cup 120 times in one year is $309.
Cost refers to the amount of money or resources that are required to produce or obtain a good or service. It can include expenses such as materials, labor, rent, utilities, and other expenses incurred in the production or acquisition of a product or service.
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HELP WHATS THE ANSWER
The surface area covered with stickers is 169.4 cm².
How to calculate the surface area of the paperweight?
We need to find the area of each face and then add them up for calculate the surface area of the paperweight,
We know,
Area of the rectangular base [tex]= length \times breadth = 17 cm \times 11 cm = 187 \: {cm}^{2} [/tex]
Area of the triangular top = (1/2) x base x height = (1/2) × 15 cm × 8 cm × 7 cm / √((15/2)² - (8/2)²) = 42 cm²
Area of the front and back faces (which are rectangles) [tex]= 2 \times length \times height = 2 \times 17 cm \times 10 cm = 340 \: cm²[/tex]
Area of the left and right faces (which are trapezoids) [tex]= ( \frac{1}{2} )(a+b) \times h \times 2 = ( \frac{1}{2} )(15 cm + 8 cm) \times 7 cm \times 2 = 91 {cm}^{2} [/tex]
Area of the bottom face (which is a rectangle) [tex]= length \times breadth = 17 cm \times 11 cm = 187 cm²[/tex]
Total surface area = 187 cm² + 42 cm² + 340 cm² + 91 cm² + 187 cm² = 847 cm²
To find the surface area covered with stickers, we need to calculate 20% of the total surface area:
Surface area covered with stickers [tex]=20\% \: of \: 874 \: {cm}^{2} = 0.2 \times 847 \: {cm}^{2} = 169.4 \: {cm}^{2} [/tex]
Therefore, the surface area covered with stickers is 169.4 cm² approximately.
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What unit of measurement would you use to weigh an elephant? A Ounce B Ton C Millimeter D Pound
Answer:
B
Step-by-step explanation:
The unit of measurement that would typically be used to weigh an elephant is the ton. Elephants are very large animals, and they can weigh several tons, depending on their species and size. While other units of measurement like pounds, kilograms, or ounces could also be used to measure the weight of an elephant, the ton is the most appropriate unit for such a large animal.
what is the x and y coordinates of the vertex for f(x) = -2x^2 + 12x - 9
Answer:
The vertex of a quadratic function of the form f(x) = ax^2 + bx + c is located at the point (-b/2a, f(-b/2a)).
In this case, the quadratic function is f(x) = -2x^2 + 12x - 9, so we can use the formula above to find the coordinates of the vertex:
x-coordinate of vertex = -b/2a = -12/(2*(-2)) = 3
To find the y-coordinate of the vertex, we can evaluate the function at x = 3:
f(3) = -2(3)^2 + 12(3) - 9 = 9
Therefore, the coordinates of the vertex are (3, 9). The x-coordinate of the vertex is 3, and the y-coordinate of the vertex is 9.
3 The headmaster at a private school wants to
update the student dress code. He wishes to
survey a select group of parents of the students
enrolled at the school to determine their
opinion on the addition of a blazer to the school
uniform. Which method can be used to ensure
an unbiased sample is obtained for the survey?
A All parents attending the next PTO meeting
are surveyed.
B Every fifth person on a list of parent
volunteers is surveyed.
C All parents waiting in the pick-up line after
school are surveyed.
D All parents of students whose birthdays are
on even numbered days are surveyed.
(I will give brainliest if you proof your answer)
The best method to ensure an unbiased sample is to randomly select parents from the entire population of parents with enrolled students at the school.
To ensure an unbiased sample for the survey, the method used should not favor any particular group or exclude any group from the population.
Option A: Surveying all parents attending the next PTO meeting would not be an unbiased sample as not all parents attend PTO meetings.
Option B: Surveying every fifth person on a list of parent volunteers would also not be an unbiased sample as it may exclude parents who are not on the list.
Option C: Surveying all parents waiting in the pick-up line after school may not be an unbiased sample as it may exclude parents who do not pick up their children from school.
Option D: Surveying all parents of students whose birthdays are on even-numbered days may not be an unbiased sample as it excludes parents whose children's birthdays are on odd-numbered days.
Therefore, the best method to ensure an unbiased sample is to randomly select parents from the entire population of parents with enrolled students at the school.
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The diagram shows the height of a cone that holds ice cream. The cone has a volume of 4.5 π cubic inches. Which measurement is closest to the radius of the cone in inches?
On solving the query we can say that The slant height, along with the function cone's height and radius, makes a right triangle as it measures from the apex to a certain point on the circular base.
what is function?Mathematics is concerned with numbers and their variations, equations and related structures, shapes and their places, and possible placements for them. The relationship between a collection of inputs, each of which has an associated output, is referred to as a "function". An relationship between inputs and outputs, where each input yields a single, distinct output, is called a function. Each function has a domain and a codomain, often known as a scope. The letter f is frequently used to represent functions (x). X is the input. The four main types of functions that are offered are on functions, one-to-one functions, many-to-one functions, within functions, and on functions.
You are informed that the cone in this scenario has a volume of 4.5 cubic inches. Using the aforementioned calculation, you can determine the radius if you know the cone's height.
Alternately, you may use the Pythagorean theorem to calculate for the radius if you know the cone's slant height. The slant height, along with the cone's height and radius, makes a right triangle as it measures from the apex to a certain point on the circular base.
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The Question is below ⬇️
Answer:
63
Step-by-step explanation:
given the sight of the angle it should be 63, correct me if I'm wrong.
What is the volume of a cube 12 inches by 12 inches and 12 inches high?
Answer: 1728 cubic meters
Step-by-step explanation: 12 x 12 x 12 V= LxWxH
A certain three-dimensional figure has one base and
3 faces.
The area of each face is the same.
The area of the base is 5 square centimeters.
The total surface area of the figure, including the base, is 26 square centimeters.
What is the area of one face of the three-dimensional figure?
7 is the area of one face of the three-dimensional figure .
What exactly is a three-dimensional figure?
Objects or shapes with three dimensions—length, breadth, and height—are referred to as three-dimensional objects or solid figures in geometry. The height of a three-dimensional object is the same as its thickness or depth, in contrast to a two-dimensional shape, which lacks height.
area of base = 5 cm²
total surface area = 26 cm²
26 = 3 * area of one face + 5
26 - 5 = 3 * area of one face
21/3 = 3 * area of one face
area of one face = 7
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one face of the three-dimensional figure has a surface area of 16/3 square centimeters.
What is surface area?The area is the space occupied by a two-dimensional flat surface. It is expressed in square units. The surface area of a three-dimensional object is the area occupied by its outer surface. It's also expressed in square units.
Let A represent the area of one of the three-dimensional figure's faces.
The overall surface area of the figure, including the base, is 26 square centimeters, according to the problem description. The total area of the base and the three similar faces is 26 - 5 = 21 square centimeters.
Because the three faces are identical, the total area of the three faces is 3A. As a result, we can write:
3A + 5 = 21
Subtraction of 5 from both sides yields:
3A = 16
By dividing both sides by three, we get:
A is equal to 16/3 square centimeters.
As a result, one face of the three-dimensional figure has a surface area of 16/3 square centimeters.
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If a surgery has a 92% change of being successful, what is the probability that a surgeon does 8 surgeries out of which 5 are successful?
According to probability, the answer to the question is that an average surgeon performs 8 operations, of which 5 are successful. 18.9%.
What is Binomial probability?In a fixed number of independent trials, each of which can only have one of two outcomes—success or failure—the number of successes is expressed as a probability distribution known as a binomial probability. Additionally, it is presummated that each trial has an equivalent chance of success.
The binomial probability formula can be used to determine the likelihood that a surgeon will perform 5 successful operations out of 8 given that each operation has a 92% chance of being successful.
You may find the binomial probability formula by using:
[tex]P(X = k) = C(n, k)*p^k*(1 - p)^{(n - k)}[/tex]
Where:
P(X = k) is the likelihood that, out of n surgeries, exactly k will be successful.
The binomial coefficient, C(n, k), is defined as the number of ways to select k successful operations among n surgeries C(n, k) = n! / (k! * (n - k)!), where ! denotes factorial.
p is the likelihood that a single surgery will succeed (92% in this case, or 0.92).
The number of successful operations that interests us is k.
The total number of operations is n, which in this case is 8.
By entering the values, we can determine the probability using the formula below:
P(X = 5) = C(8, 5) * 0.92⁵ * (1 - 0.92)⁽⁸⁻⁵⁾
C(8, 5) = 8! / (5! * (8 - 5)!) = 56
0.92⁵ = 0.659
(1 - 0.92)³ = 0.512
P(X = 5) = 56 * 0.512 * 0.659 = 18.89 or 18.9%
Given a 92% success rate for each surgery, the likelihood that a surgeon will perform 5 successful operations out of 8 is roughly 18.9%.
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Rewrite 5^/4. /2 as a single radical
O 10^/2^9
O10^/20^9
O9^/2^10
The expression can be rewriten as a single radical as:
[tex]\sqrt[5]{4} *\sqrt{2} = \sqrt[10]{2^9}[/tex]
How to rewrite the expression as a single radical?We want to rewrite the expression below as a single radical:
[tex]\sqrt[5]{4} *\sqrt{2}[/tex]
First remember that 4 = 2², then we can replace that to get:
[tex]\sqrt[5]{4} *\sqrt{2} = \sqrt[5]{2^2} *\sqrt{2}[/tex]
Converthing the roots to exponents we will get.
[tex]\sqrt[5]{2^2} *\sqrt{2} = 2^{2/5}*2^{1/2}[/tex]
Now the exponents are just added:
[tex]2^{2/5}*2^{1/2} = 2^{2/5 + 1/2} = 2^{4/10 + 5/10} = 2^{9/10} = \sqrt[10]{2^9}[/tex]
That is the correct option.
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im confused can someone explain step by step please
Which is the function represented by the table? A 2-column table with 4 rows. Column 1 is labeled x with entries negative 2, negative 1, 0, 1. Column 2 is labeled f (x) with entries negative 8, negative 4, 0, 4. f (X) = 4 x f (x) = x minus 6 f (x) = x + 4 f (x) = negative 4 x
The answer is an option (D) f(x) = One-half (one-half) superscript x.
What is the linear function?
A linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to a straight line.
To determine the exponential function represented by the values in the table, we need to look for a function of form f(x) = abˣ that passes through the given points.
Let's plug in the x and f(x) values from the table into the general formula:
When x = -2, f(x) = 16 gives us 16 = ab⁻²
When x = -1, f(x) = 8 gives us 8 = ab⁻¹
When x = 0, f(x) = 4 gives us 4 = ab⁰
When x = 1, f(x) = 2 gives us 2 = ab¹
When x = 2, f(x) = 1 gives us 1 = ab²
We can rewrite the equations as:
16 = a/b²
8 = a/b
4 = a
2 = ab
1 = ab²
We can solve for a and b by using a system of equations:
From the equation 4 = a, we get a = 4.
Substituting a = 4 into the equation 2 = ab, we get b = 2/a = 1/2.
Therefore, the exponential function represented by the values in the table is:
f(x) = 4(1/2)ˣ
Hence, the answer is an option (D) f(x) = One-half (one-half) superscript x.
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A group consists of men and women. people are selected to attend a conference.
a. In how many ways can people be selected from this group of ?
There are 715 ways to select four people from a group of six men and seven women to attend a conference.
What are combinations?Combinations in mathematics relate to the various ways that a group of things can be chosen, regardless of the order in which they are chosen. Combinations are a form of counting problem where a smaller subset of the objects in the bigger set are selected.
The combination is given by the formula:
C(n,r) = n!/(r!(n-r)!)
The total number of people = 13.
The number of ways we can choose 4 people from the given 13 people are:
C(13,4) = 13!/(4!9!) = (13x12x11x10)/(4x3x2x1) = 715
Hence, there are 715 ways to select four people from a group of six men and seven women.
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The complete question is:
A rocket is launched in the air. Its height in feet is given by ℎ ( � ) = − 16 � 2 + 144 � h(t)=−16t 2 +144t where � t represents the time in seconds after launch. What is the rocket’s greatest height?
The calculated value of the rocket’s greatest height is 324 feet
Calculating the rocket’s greatest height?From the question, we have the following parameters that can be used in our computation:
h(t) = -16t² + 144t
Differentiate the height function and set the differentiated equation to 0
So, we have
32t = 144
This gives
t = 144/32
So, we have
t = 4.5
Substitute t = 4.5 in the above equation, so, we have the following representation
h(4.5) = -16(4.5)^2 + 144(4.5)
Evaluate
h(4.5) = 324
Hence, the rocket’s greatest height is 324 feet
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Complete question
A rocket is launched in the air. Its height in feet is given by h(t) = −16t² + 144t where t represents the time in seconds after launch.
What is the rocket’s greatest height?
A saving account that earns 3.2% interest compounded bi annually has a balance of $6049.15 after 6 years Determine the total amount of interest earned on the account
O1049.15
O1409.15
O4145.24
O5000.0
The total amount of interest earned on the account is $1049.15.
What is simple and compound interest?Simple interest is interest that is just based on the principal. It does not account for any interest accrued in prior periods and is determined as a percentage of the principal. If your principal is $1,000 and your yearly interest rate is 5%, for instance, you would make $50 in simple interest after a year ($1,000 0.05).
Contrarily, compound interest is calculated on the principal amount in addition to any prior quarters' interest. This means that interest is calculated on the new amount after the principal and interest earned during each period have been added.
The compound interest is given by the formula:
[tex]A = P(1 + r/n)^{(nt)}[/tex]
Rearranging for P we have:
[tex]P = A / (1 + r/n)^{(nt)}[/tex]
Substituting the value of r = 3.2%, n = 2 and t = 6 we have:
[tex]P = 6049.15 / (1 + 0.032/2)^{(2*6)}[/tex]
P = 5000
Here, P is the initial balance.
Now, for interest we have:
I = A - P
Substituting the values:
I = $6049.15 - $5000
I = $1049.15
Hence, the total amount of interest earned on the account is $1049.15.
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Suppose you start with one liter of vinegar and repeatedly remove 0.14 L, replace with water, mix, and repeat. a. Find a formula for the concentration after n steps. b. After how many steps does the mixture contain less than 9% vinegar?
Formula for the concentration after n steps is [tex]C(n) = C(0) * (0.86)^n[/tex] and
after 11 steps, the mixture contains less than 9% vinegar.
What is concentration?
Concentration in science refers to the amount of a particular substance (the solute) that is dissolved in a given amount of a solution. It is typically expressed in units of moles per liter (M or mol/L) or as a percentage or fraction of the total solution.
a. Let C(n) be the concentration of vinegar after n steps. At each step, we remove 0.14 L of the mixture, which contains C(n) liters of vinegar. So we are left with (1 - C(n)) liters of water. We then add back 0.14 L of water, giving us a total volume of 1 liter. Therefore, the concentration after one step is:
[tex]C(1) = C(0) * \frac{1 - 0.14}{1}[/tex]
where C(0) is the initial concentration of vinegar, which is 1 liter per liter or 100%. After two steps, we repeat the process:
C(2) = C(1) * [tex]\frac{1 - 0.14}{1}[/tex]
Substituting the formula for C(1), we get:
C(2) = C(0) * [tex](\frac{1 - 0.14}{1}) * (\frac{1 - 0.14}{1})[/tex]
or, more generally:
[tex]C(n) = C(0) * (0.86)^n[/tex]
b. We want to find the smallest integer n such that C(n) < 0.09 or 9%. Substituting the formula from part (a), we get:
[tex]C(0) * (0.86)^n < 0.09[/tex]
Dividing both sides by C(0), we get:
[tex](0.86)^n < 0.09[/tex]
Taking the natural logarithm of both sides, we get:
n * ln(0.86) < ln(0.09)
Dividing both sides by ln(0.86), we get:
n > ln(0.09) / ln(0.86)
Using a calculator, we get:
n > 10.7
Since n must be an integer, the smallest possible value of n is 11. Therefore, after 11 steps, the mixture contains less than 9% vinegar.
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Which choice is equivalent to the product below? √3 times √5 times √6
An answer choice that is equivalent to the product below include the following: B. 3√10.
How to determine the equivalent product?In this scenario and exercise, you are required to determine the correct and most accurate answer choice that is equivalent to the product of the given mathematical expression.
In this scenario and exercise, the simplest form of the given expression √3 × √5 × √6 can be determined or calculated by simplifying it as follows;
Expression = √3 × √5 × √6
Expression = √3 × √5 × √(3 ×2)
Expression = √3 × √5 × √3 × √2
Expression = 3 × √(5 × 2)
Expression = 3 × √10
Expression = 3√10.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
what is angle NSR equal to?
The measure of the angle NSR is equal to 113 degrees
Calculating what is angle NSR equal to?From the question, we have the following parameters that can be used in our computation:
The circle
Using the angle of intersecting chords theorem, we have following equation
NSR = 1/2(Sum of major and minor arcs NS)
So, we have
NSR = 1/2 * (176 + 50)
Evaluate
NSR = 113
Hence, the angle is 113 degrees
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Given the circle below with secants JKL and NML, find the length of JK. Round to the nearest tenth if necessary.
The length of JK is 42 units, which can be calculated using the theorem that states JK × JL = ML × JN, with the given lengths of KL, LM, and MN.
What is length?Length is a measurement of how long or extended an object or distance is, typically measured in units such as meters, centimeters, feet, or inches.
What is Theorem?A theorem is a statement or proposition that has been proven to be true through deductive reasoning or a mathematical proof, and is often used as a basis for further reasoning and conclusions.
According to the given information:
To find the length of JK, we can use the theorem which states that the product of the lengths of the segments of a secant is equal. In other words, JK × JL = ML × JN. We are given the lengths of KL, LM, and MN, and we know that KL + LM + MN = JL + JN.
We can use this information to solve for JK. First, we need to find JL and JN. We can do this by subtracting KL and MN from LM to get JL = LM - KL and JN = LM - MN. Substituting these values into the equation JK x (LM - KL) = KL × (LM - MN), we can solve for JK.
JK = (KL × (LM - MN)) / (LM - KL) = (14 × (17 - 14)) / (17 - 14) = 14 × 3 = 42.
Therefore, the length of JK is 42.
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-10-9-8-7-6-5-4-3-2-1 0 1 2 3 4 5 6 7 8 9 10
Which of the following inequalities is represented by the number line?
A) x > 4.5
B) x ≥ 4.5
OC) x < 4.5
D) x ≤ 4.5
Answer:
The Correct answer is B
x≥4.5
Select all the true statements about
the function h(x) = x/3 + 7 .
A. When x = 3, h(x) = 16.
B. When x = 4, h(x) = 8 1/3.
C. When x = 9, h(x) = 10.
D. When x = 10, h(x) = 10 1/3.
E. When x = 12, h(x) = 12.
Answer:
A. When x = 3, h(x) = 16 is false.
B. When x = 4, h(x) = 8 1/3 is true.
C. When x = 9, h(x) = 10 is true.
D. When x = 10, h(x) = 10 1/3 is true.
E. When x = 12, h(x) = 12 is false.Therefore, the true statements are B, C, and D.
If the length and width of a rectangle are 11 cm and 10 cm, then find its perimeter. OA. 420 cm OB. 21 cm OC. 42 cm OD. 110 cm
Answer:
Perimeter = 42 cmStep-by-step explanation:
It is given that length and width of a rectangle is 11 cm and 10 cm.
We know the formula of Perimeter of rectangle
[tex]:\implies \: [/tex] Perimeter = 2(L + B)
Where 'L' denote the length of the rectangle and 'B' denotes the breadth of the Rectangle.
Now Let's substitute the value of Length= 11 cm and Breadth = 10 cm in the above formula .
[tex]:\implies \: [/tex] 2(11 + 10)
[tex]:\implies \: [/tex] 2 × 21
[tex]:\implies \: [/tex] 42 cm
Henceforth The perimeter of the rectangle is 42 cm
The perimeter of a rectangle is calculated by multiplying by 2 the sum of its length and width. So, in this case, the rectangle's perimeter is 42 cm.
Explanation:The subject of this question is on calculating the perimeter of a rectangle. The formula for finding the perimeter of a rectangle is 2*(length + width). Applying the values given, that is length = 11 cm and width = 10 cm.
So, the perimeter of a rectangle = 2*(11 + 10) cm = 2*21 cm = 42 cm
Therefore, the correct option is OC. 42 cm.
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Drag each tile to the correct location on the table. Each tile can be used more than once but not all tiles will be used. Choose the justification for each step in the solution to the given equation.
The value of x from the given equation is 8/15.
The given equation is 17/3 - 3/4 x= 1/2 x+5
17/3 - 3/4 x= 1/2 x+5 (Given)
17/3 - 3/4 x -17/3= 1/2 x+5 -17/3 (Subtraction property of equality)
-3/4 x = 1/2 x -2/3
-3/4 x -1/2 x = 1/2 x -2/3 -1/2 x (Subtraction property of equality)
-5/4 x=-2/3
-5/4 x × 4/5=-2/3 × 4/5 (Multiplication property of equality)
x= 8/15
Therefore, the value of x from the given equation is 8/15.
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Question 2 of 5
The dance committee at Northeast Middle School is
choosing the theme for the spring dance. Members of the
committee conduct a poll to ask students about their
choices. They ask every 10th student entering the cafeteria
to complete a survey.
What is the sample in this study?
A. All students at Northeast Middle School
B. The students in the cafeteria
C. The students on the dance committee
D. The students who complete the survey
The sample in this study is D. The students who complete the survey.
This is because the dance committee is only collecting data from those students who are surveyed, which represents a smaller group within the entire population of the school.
The sample in this study refers to the specific group of individuals who are selected to participate in the survey or study.
In this case, the dance committee at Northeast Middle School is choosing the theme for the spring dance and conducts a poll to ask students about their choices.
They ask every 10th student entering the cafeteria to complete a survey.
Therefore, the sample in this study is the students who complete the survey.
They are the specific group of individuals who are selected to participate in the survey and provide information about their preferences for the spring dance theme.
D. The students who complete the survey.
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Answer:
The students who complete the survey
Step-by-step explanation:
Which of the following components should you look for when editing in speech rhetorical strategies main? Idea and supporting detail grammar and spelling errors level of formality
When editing a speech, you should look for these components:
rhetorical strategieslevel of formalitygrammar and spelling errorsmain idea and supporting details.What does editing a speech involves?The act of editing speech involves more than just correcting grammar and spelling errors as its also involves analyzing the rhetorical strategies used, ensuring that the level of formality is appropriate for the audience and occasion and making sure that the main idea and supporting details are clearly presented and organized.
An effective editing can help to strengthen the message of the speech and increase its impact on the audience. Therefore, it is important to consider all of these components when editing a speech.
Full question "Which of the following components should you look for when editing in speech rhetorical strategies main? Idea and supporting detail grammar and spelling errors level of formality"
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