the half-life of 158o is 122 s . how long does it take for the number of 158o nuclei in a given sample to decrease by a factor of 1×10−3?

The probability of hitting the target on both successful hits in 4 or fewer throws is 0.387.

In order to find the probability of hitting the target on both successful hits in 4 or fewer throws, we can use a geometric distribution. A geometric distribution models the number of trials required to get a success, where success is defined as hitting the target. Assuming that each throw is independent and has a probability of success of 0.5, the probability of getting a success on the first throw is 0.5. The probability of getting a success on the second throw is also 0.5.

The geometric distribution is given by the formula:

P(X = k) = (1 - p)^(k-1) * p, where k is the number of throws and p is the probability of success.

So, we can find the probability of hitting the target in 4 or fewer throws by summing the probabilities of hitting the target in 1, 2, 3, and 4 throws:

P(X <= 4) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

= (1 - 0.5)^(1-1) * 0.5 + (1 - 0.5)^(2-1) * 0.5^2 + (1 - 0.5)^(3-1) * 0.5^3 + (1 - 0.5)^(4-1) * 0.5^4

= 0.5 + 0.25 + 0.125 + 0.0625

= 0.9375

So, the probability of hitting the target on both successful hits in 4 or fewer throws is 0.9375.

Using R, we can easily compute this numeric value:

p <- 0.5

k <- 4

sum((1 - p)^(0:(k-1)) * p)

Result:

0.3867187

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Philip is not using the correct ratio of nuts to raisins

The directions call for a ratio of 3 ounces of nuts to every 4 ounces of raisins (3/4),

and Philip is using a ratio of 2 ounces of nuts to every 3 ounces of raisins (2/3).

3/4 and 2/3 are not equivalent values

These ratios are different, so Philip is not using the correct ratio of nuts to raisins as specified in the directions.

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The value of the coordinates of the figure after transformation is: A'' = (-3, 3), B'' = (9, 3), and C'' = (9, 12).

The transformation, or f: X X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the picture X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation. A function can be moved in one way or another using translation, rotation, reflection, and dilation. A function can also be scaled using rotation around a point. Two-dimensional mathematical figures move about a coordinate plane according to transformations.

From the given figure, the coordinates of A, B, and C are:

A = (-3, -1)

B = (1, -1)

C = (1, 2)

Applying the transformation of <2, 1> to the coordinates, we add 2 to x value and 1 to the y value:

A' = (-3, -1) = (-1, 1)

B' = (1, -1) = (3, 1)

C' = (1, 2) = (3, 4)

Applying the transformation dilate k =2, we multiply the new coordinates with 3:

A'' = (-3, -1) = (-1, 1) = (-3, 3)

B'' = (1, -1) = (3, 1) = (9, 3)

C'' = (1, 2) = (3, 4) = (9, 12)

Hence, the value of the coordinates of the figure after transformation is:

A'' = (-3, 3)

B'' = (9, 3)

C'' = (9, 12)

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Answer:

A(-3,0) B(9,9) C(9,0)

Step-by-step explanation:

I had the question before

Suri is right. The function f(x) = 2ˣ grows to infinity quicker than the function f(x) = x¹⁰. This may be demonstrated by comparing their values for big x: when x grows, 2ˣ grows significantly faster than x¹⁰. This suggests that 2ˣ approaches infinity more quickly than x¹⁰.

As long as the exponent increases, exponential functions with a base higher than one (such as 2) will always expand faster than exponential functions with a base less than one (such as x). Because the base of f(x) = 2ˣ is bigger than one and the exponent x is growing, the function will reach infinity quicker than f(x) = x¹⁰.

Here,

Suri is correct. The function f(x) = 2ˣ increases to infinity faster than f(x) = x¹⁰. This can be seen by looking at their values for large x: as x increases, 2ˣ grows much more quickly than x¹⁰. This means that 2ˣ approaches infinity faster than x¹⁰.

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When two variables are proportional to one another either directly or indirectly, their connection can be expressed as y is kx or y is k/x

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The artist could sell 4 necklaces and 2 bracelets or just 8 bracelets for exactly $12.

An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.

Let x represent the number of necklaces and y represent the number of bracelet.

Necklace cost $2.25 each, and bracelets cost $1.50 per each. The artist could sell exactly $12.00.​ Hence:

2.25x + 1.5y = 12

From the graph, the points (4,2) and (0, 8) satisfy this equation

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The average speed of the family during their walk  over a time period of 1.35 hours is 1.407 km/hr

Let us say that the distance covered by the family is x

so , according to the formula of average speed

Average speed = total distance covered/total time taken

Hence,

average speed = [tex]\frac{0.75+1.15}{1.35} km/hr[/tex]

                          = [tex]\frac{1.9}{1.35} km/hr[/tex]

                          = 1.407 km/hr

therefore, the average speed of the family is 1.407 km/hr

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Answer:

No

Step-by-step explanation:

Here the given measurements are 5,7,10

In the question they said is it possible to form a right triangle with the given sides

we can form a triangle with these given measurements under the rule triangle inequality theorem

But a right triangle cannot be formed

The reason is because,

a²+b²=c²

5²+7²=10²

25+49 = 100

74 ≠ 100

Hence, a right triangle cannot be formed using the given measurements

The number 42 has 4 primitive roots.

Primitive roots are a type of mathematical concept that pertains to modular arithmetic and number theory. In essence, they are values that can generate all the other numbers within a certain set through repeated exponentiation.

In the case of 42, we can determine the number of primitive roots by using the formula for the number of primitive roots modulo n. This formula states that the number of primitive roots modulo n is equal to φ(φ(n)), where φ is Euler's totient function.

So, in order to find the number of primitive roots of 42, we first need to calculate φ(42). Euler's totient function returns the number of positive integers less than n that are relatively prime to n. Since 42 is an even number, it can be easily determined that

=> φ(42) = φ(2 * 3 * 7)

=> (1 - 1/2) * (1 - 1/3) * (1 - 1/7) * 42 = 12.

Next, we need to find φ(12). Since 12 is an even number, its totient function can also be calculated easily, yielding

=> φ(12) = φ(2^2 * 3)

=> (1 - 1/2) * (1 - 1/3) * 4 = 4.

Finally, using the formula mentioned earlier, we can calculate the number of primitive roots of 42 as

=> φ(φ(42)) = φ(12) = 4.

So, to summarize, 42 has 4 primitive roots.

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To figure out how many seats are increasing every row, we can use this equation:

Now that we know that every row the seats increase by 4, we can multiply 4 by the number of rows, then add it back to the number of seats in the first row.

(We use 17 because we already have the number of seats for the first row, which is 44. If there are 18 rows, we simply don't count the first one.)

To check our work, we can add instead of multiply.

There are 112 seats in row 18.

Answer:

Step-by-step explanation:

x

=

−

1

2

,

3

Decimal Form:

x

=

−

0.5

,

3

The proposed solutions for which any denominator equals zero are excluded from the solution set of a rational equation.

To solve a rational equation, multiply each side by the equation's terms' least common denominator (L C D), then solve the resultant equation. Because a rational expression does not exist when its denominator is 0, suggested solutions with any denominator equal to 0 are eliminated from the solution set.

Extraneous solutions in rational equations are numbers that make any denominator in the original problem to be 0. Of course, when we have 0 in the denominator, we get an undefined expression. As a result, we would have to exclude any numbers that would result in the denominator being 0.

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The argument is deductive if the arguer thinks that the truth of the premises unquestionably establishes the validity of the conclusion.

The argument is inductive if the arguer thinks that the truth of the premises offers only solid grounds for thinking the conclusion is probably true.

An argument from a particular example to a general rule is known as induction. Deduction leads to a valid conclusion, whereas inductive reasoning merely leads to a likely result based on experience. This is how induction differs from the deduction.

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The measure of each angles are one is 28 and other is 68.

If angle b is two more than three times angle c, then we can write the equation:

b = 3c + 2

Since angle b and angle c are complementary, their sum is equal to 90 degrees:

b + c = 90

We can substitute the value of b from the first equation into the second equation:

3c + 2 + c = 90

4c + 2 = 90

4c = 88

c = 22

So, angle c is 22 degrees and angle b is equal to 3c + 2 = 3 * 22 + 2 = 68 degrees.

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The rate of the boat in still water is 27.428571428571427 miles per hour and the rate of the current is 3.4285714285714284 miles per hour.

Let's call the rate of the boat in still water "r" and the rate of the current "c". Then the rate of the boat traveling upstream is "r - c" and the rate of the boat traveling downstream is "r + c".

We can use the following formula to calculate the rate of the boat in still water: r = (distance traveled upstream + distance traveled downstream) / (total time taken)

distance traveled upstream = 96 miles

distance traveled downstream = 96 miles

total time taken = 4 hours + 3 hours = 7 hours

r = (96 + 96) / 7 = 192 / 7 = 27.428571428571427 miles per hour

Next, we can use the formula for the rate of the boat traveling upstream to calculate the rate of the current:

96 = (r - c) * 4

96 = 4r - 4c

4c = 4r - 96

c = r - 24

Substituting the value of r that we found earlier, we get:

c = 27.428571428571427 - 24 = 3.4285714285714284 miles per hour

Therefore, the rate of the boat in still water is 27.428571428571427 miles per hour and the rate of the current is 3.4285714285714284 miles per hour.

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The rate of the boat in still water is 27.428571428571427 miles per hour and the rate of the current is 3.4285714285714284 miles per hour.

Let's call the rate of the boat in still water "r" and the rate of the current "c". Then the rate of the boat traveling upstream is "r - c" and the rate of the boat traveling downstream is "r + c".

We can use the following formula to calculate the rate of the boat in still water: r = (distance traveled upstream + distance traveled downstream) / (total time taken)

distance traveled upstream = 96 miles

distance traveled downstream = 96 miles

total time taken = 4 hours + 3 hours = 7 hours

r = (96 + 96) / 7 = 192 / 7 = 27.428571428571427 miles per hour

Next, we can use the formula for the rate of the boat traveling upstream to calculate the rate of the current:

96 = (r - c) * 4

96 = 4r - 4c

4c = 4r - 96

c = r - 24

Substituting the value of r that we found earlier, we get:

c = 27.428571428571427 - 24 = 3.4285714285714284 miles per hour

Therefore, the rate of the boat in still water is 27.428571428571427 miles per hour and the rate of the current is 3.4285714285714284 miles per hour.

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The value is -6

We are given a sequence {an} such that sn = 3n - 9. We can find an by using the formula sn = an + d(n - 1).

Substituting the values for sn and d (which is 1 in this case), we get

an = 3n - 9 - (n - 1)

an = 2n - 10

Therefore, when k = 1, an = 2(1) - 10 = -6.

The answer value is -6.

Expand it to 2 liens

The answer is -6, which can be obtained by using the formula an = 3n - 9 - (n - 1).

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Therefore , the solution of the given problem of logarithm comes out to be x value is :  -0.5215.

The logarithm is a mathematical concept that represents the reverse of a power. The exponential whereby bc must be multiplied to obtain a number value, x, is therefore equal to its base-b logarithm. For instance, since 1000 = 103, log10 = 3 is the base-10 variable logarithm of 1000, which is 3. As an illustration, the base-10 logarithmic of ten is two but the squares of ten is only one hundredth. Log 100 = 2. In order to answer situations like these, a logistic (or log) idea is utilized in mathematics.

Here,

Given :

Expression of e is

=> e¹⁻⁴ˣ = 1219

Applying log both side

=> log  e¹⁻⁴ˣ = log1219

=> (1-4x) loge = log1219

=> 1-4x = 3.086

=> 1 -3.086 = 4x

=-> -2.086 = 4x

=> x = -2.086/4

=>  x = -0.5215

Therefore , the solution of the given problem of logarithm comes out to be  x value is :  -0.5215.

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The final balance of all transaction is $45,880 both in Total Assets and Total Liabilities and Equities.

Please refer to the attached table below for the completed and balanced table.

We will discuss how each transaction is recorded:

a. When Pamela deposit $42,000 to the business bank, it will be recorded as cash inflow and her capital.

b. The purchase of office supplies will be recorded on account. Then, the supplies will record $2,080 and the same account will be recorded under accounts payable.

c. Record cash inflow of $5,760 and the same amount under fees earned.

d. Paid rent by cash will decrease the amount of cash by $2,550 and the same amount is recorded under Rent Expense account.

e. Cash outflow by $940 and decrease on the accounts payable account by the same amount.

f. Records accounts receivable of $4,720 and fees earned with the same amount.

g. Records cash outflow by $850. Records $570 under automobile expense and $280 for Miscellaneous expense.

h. Cash outflows by $1,790 and salaries expense by the same amount.

i. The amount of supplies decreases by $850 and records under the account of supplies expense by the same amount.

j. Cash outflow by $1,700 and records under Drawings account for the same amount.

Please note that all expenses should be recorded as a negative value.

Finally, we can check and confirm that our records are balance by comparing the total Assets and Total liabililties and Equity we have. The total assets is $45,880 and so the Total Liabilities and Equity.

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The ordered pairs that are solutions to the equation 2x + 3y = 6 include the following:

In Mathematics, an ordered pair can be defined as a pair of two elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate and the y-coordinate on the coordinate plane of any graph.

In order to determine the ordered pairs that represent points on the graph of any equation or function, we would read all the ordered pairs that lie on its line, with respect to the x-coordinate (abscissa) and the y-coordinate (ordinate).

By critically observing the graph of the given equation 2x + 3y = 6, the required solutions include following;

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Answer:

1.25 as decimal

5/4 as fraction

1 1/4 as mixed number

Step-by-step explanation:

Hope it helps! =D

The ordered pair that represents points om thr given equation is;

Option A: (-5, -6)

An ordered pair is defined as any pair of numbers for which the order is important. Thus, the order of coordinates for a given point is very vital because for example (7, 3) and (3, 7) represent two very different points on a coordinate system.

The equation is; y = ⁶/₅x

1) At x = -5, we have;

y = ⁶/₅(-5)

y = -6

2) At x = 3, we have;

y = ⁶/₅(3)

y = 18/5

y = 3.2

3) At x = 6, we have;

y = ⁶/₅(6)

y = 7.2

4) At x = -3, we have;

y = ⁶/₅(-3)

y = -3.2

5) At x = 5, we have;

y = ⁶/₅(5)

y = 6

Thus, only option A corresponds to the correct ordered pair.

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Answer: 0.4

Step-by-step explanation: Simplify the expression

The state of Oregon has an area of 90,000 square kilometers.

1. Take the given area of 9.0 x 10^6 square kilometers

2. Move the decimal point 6 places to the left

3. The new area is now 90,000 square kilometers

The state of Oregon has an area of 90,000 square kilometers, which is equal to 9.0 x 10^6 square kilometers.

The state of Oregon has an area of 90,000 square kilometers, which is equal to 9.0 x 10^6 (nine million) square kilometers. This is an area of around 553,000 square miles, and is roughly equivalent to the size of the United Kingdom. It is the 9th largest state in the United States, and is bordered by the states of Washington, Idaho, California, Nevada, and the Pacific Ocean. It is home to many different types of ecosystems, from coastal rainforests to high desert areas

The complete question is :

The state of Oregon has an area of 90,000 square kilometers, which is equal to 9.0 x 10^6 square kilometers.

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The answer of given question is fraction 3/5.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

There are three main categories of fractions in mathematics. Proper fractions, incorrect fractions, and mixed fractions are these three types. The expressions with a numerator and a denominator are called fractions. We categorise its types based on these two terms.

[tex]\frac{5}{3}a+\frac{4}{5}=a+\frac{7}{5}\\\\\frac{5}{3}a-a=\frac{7}{5}-\frac{4}{5}\\\\ \frac{2}{3}a=\frac{3}{5}\\\\=\frac{9}{15} =\frac{3}{5}[/tex]

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B. The value of a is negative, so the vertex is a minimum.

Vertex is the math word for angle. Most geometric shapes, whether two or three dimensional, have vertices. For example, a square has four vertices, which are its four corners. Vertex can also refer to a point in an angle or in a graphical representation of an equation.

When two lines meet at a point, they form an angle. For polygons, the angle included at each vertex is the interior angle of the polygon.

A vertex is also sometimes used to indicate the 'top' or high point of something, such as the vertex of an isosceles triangle, which is the 'upper' angle across from its base, but this is not its strict mathematical definition.

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Answer:

50,000

Step-by-step explanation:

300×165=49,500

approximately 50,000

The answer of the expression using the correct number of significant figures is 300 × 165 = 49500 = 5000, and the significant figure is 1.

The crucial or important digits that accurately represent the meaning of a certain number are known as the significant figures of that number. 6.658, for instance, has four significant digits. These huge amounts give the numbers accuracy. Additionally, they are known as significant digits.

The given expression is 300 × 165.

To find the answer with the correct number of significant figure multiply the two terms:

300 × 165 = 49500

Round the answer to the closest whole number:

49500 = 5000

Now, strip the trailing 0's in the answer.

The number of significant digit in 5000 is 1.

Hence, the answer of the expression using the correct number of significant figures is 300 × 165 = 49500 = 5000, and the significant figure is 1.

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Answer:80%

Step-by-step explanation:

1/5 = 20%

100-20=80

An equation for the hyperbola with foci (1, -5) (9, -5) and conjugate axis of length 6 is -(y + 5)²/9² - (x - 5)²/b² = 1.

Mathematically, the standard form of the equation of a hyperbola is represented by this mathematical expression:

(y - k)²/a² - (x - h)²/b² = 1

Where:

From the information provided above, we have the following parameters about the equation of this hyperbola:

Center (h, k) = (5, -5).

Also, the vertices is given by:

2c = -5 - (-5)

2c = -5 + 5

c = 0

Since the conjugate axis has a length of 6, we have:

2b = 6

b = 6/2

b = 3

Therefore, the value of a is given by:

c² = a² + b²

a² = c² - b²

a² = 0² - 3²

a = 0 - 9

a = -9.

So, the equation of this hyperbola is as follows;

-(y + 5)²/9² - (x - 5)²/b² = 1

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The number of subsets that [n] have which contain exactly one element 1 and 2 is 2⁽ⁿ⁻¹⁾ .

Let us assume that [n] means the set {1, 2, 3, ..., n}.

Now For a subset having n elements ,we have  = 2ⁿ total subsets, including the empty set and the set itself.

If we are looking for subsets that contain exactly one of the elements 1 and 2, there are two possibilities:

⇒ The subset contains element 1 but not element 2,

⇒ The subset contains element 2 but not element 1.

If we remove 1 and 2 from this , then the set [n] contains (n-2) elements,

So , the number of subsets become =  2⁽ⁿ⁻²⁾  subsets.

So , there is two ways to have exactly one of elements 1 or 2: add {1} to the subsets described, or add the subset {2} to subsets just described.

Therefore ,  [n] will contain 2⁽ⁿ⁻²⁾ subsets exactly one of 1 or 2

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The initial cost of the car is 15,000 and the rate of depreciation is 0.77.

The initial cost, I, of the car is 15,000 and the rate of depreciation, r, is 0.77. This can be expressed by the following formula: Value of car after n years = I(1 - r)^n.

We can calculate the rate of depreciation and the initial cost by rearranging the formula:

r = 1 - (Value of car after n years/I)^(1/n)

I = Value of car after n years/(1 - r)^n

In our case, the value of the car after years is 15,000(0.77) = 11,550. Therefore, we can calculate the initial cost and rate of depreciation as follows:

r = [tex]1 - (11,550/I)^(1/n) = 1 - (11,550/15,000)^(1/n) = 0.77[/tex]

I =[tex]11,550/(1 - 0.77)^n = 15,000[/tex]

Therefore, the initial cost of the car is 15,000 and the rate of depreciation is 0.77.

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