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It will take about 225.25 years of time for 15 grams to be present.

The half-life of a radioactive substance is the time it takes for half of the substance to decay.

For this substance with a half-life of 170 years, we can use the following formula to find the value of k:

[tex]0.5 = e^(^-^1^7^0^k^)[/tex]

Taking the natural logarithm of both sides, we get:

ln(0.5) = -170k

Solving for k, we get:

k = ln(0.5) / (-170)

= 0.004085

Now, we can use the model [tex]y = y_0e^(^-^k^t^)[/tex] to find the time t required for the substance to decay from 40 grams to 15 grams.

We have:

[tex]15 = 40e^(^-^0^.^0^0^4^0^8^5^t^)[/tex]

Dividing both sides by 40 and taking the natural logarithm of both sides, we get:

ln(15/40) = -0.004085t

Solving for t, we get:

t = ln(15/40) / (-0.004085)

= 225.25 years

Therefore, it will take about 225.25 years for 15 grams to be present.

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Answer:

Step-by-step explanation:

The common difference between the number of jumping jacks is 50, as you correctly stated. This means that the number of jumping jacks increases by 50 for each additional minute.

The slope of the line that connects any two points on this table represents the rate of change of the number of jumping jacks with respect to time. Since the common difference is constant, the slope of the line that connects any two points on this table will be the same. In this case, the slope is 50.

The slope of the line that connects the first and fourth points is calculated as (200 - 50) / (4 - 1) = 150 / 3 = 50, not 150.

The common difference (aka slope aka rate of change) is constant because the number of jumping jacks increases by the same amount for each additional minute. This means that the relationship between time and the number of jumping jacks is linear.

Answer: 10w + 3 + 4.5w = 90

Step-by-step explanation:

a right angle is 90 degrees, so 10w + 3 and 4.5w have to add up to 90 degrees

Surface area of similar cone is 44π square inches

What does a cone in maths ?

A cone is referred to as a "right cone" when its vertex is higher than the base's centre (i.e., when the angle formed by the vertex, base center, and any base radius is a right angle); otherwise, the word "oblique" is used. A cone is referred to as an elliptic cone when the base is assumed to be an ellipse rather than a circle.

The surface area of a cone is given by:

surface area = πr(r + l)

where r is the radius and l is the slant height.

surface area of original cone = π(3)(3 + 12) = 45π

slant height of similar cone = (6/3)(12) = 24 inches

surface area of similar cone = π(6)(6 + 18) = 144π

ratio of surface areas = surface area of similar cone / surface area of original cone

= (144π) / (45π)

= 3.2

Therefore, The exact surface area of the similar cone is 6 times the surface area of the original cone,

6 × 45π = 144π square inches

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Answer:

  117

Step-by-step explanation:

You want the cross product of vectors u = (12i -3j) and v = (-5i +11j).

The cross product of 2-dimensional vectors is a scalar that is effectively the determinant of the matrix of coefficients.

  u×v = (12)(11) -(-3)(-5) = 132 -15

  u×v = 117

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The expected value for playing roulette if a person bet $16 on red is -$0.84.

b. The statement that best describes what this value means is option b. Over the long run, the player can expect to lose about $1.05 for each game played.

To be able to calculate the expected value, you need to multiply the probability of winning by the amount won hence it will be:

Expected value = (18/38) x  $16 - (20/38) x  $16

= -$0.84

Based on the fact that the expected value has a negative sign, it implies that, on average, the player tend to lose money over the long run.

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See full question below

one option in a roulette game is to bet $16 on red. (there are 18 red compartments, 18 compartments, and two compartments that are neither red nor black) if the ball lands on red, you get to keep the $16 you paid to play the game and you are awarded $16. If the ball lands elsewhere, you are awarded nothing and the $16 that you bet is collected.

a. what is the expected value for playing roulette if you bet $16 on red?

$__________ (round to the nearest cent)

b. chosen the statment below that best describes what this value means???

Pick One!

a. over the long run, the player can expect to win about $1.05 for each game played

b. over the long run, the player can expect to lost about $1.05 for each game player

c. over the lung run, the player can expect to break even

Answer:

All of them have a combined of 2,227 Stamps

Mean: 2014

The correct answer is C: (-0.3,0) and (1.8,0) are zeros of the quadratic function because they are the points where the parabola intersects the x-axis.

The right response is C: (- 0.3,0) and (1.8,0) are zeros of as far as possible since they are the places where the parabola meets the x-turn.

plot the y-get at (0,1),

x = - b/2a

To find the x-heading of the vertex, which is x = 3/4. Substitute this worth into the capacity to find the y-course of the vertex, which is

f(3/4) = 1/8.

Plot the vertex at (3/4, 1/8).

Then, utilize this data to plot the remainder of the parabola. The zeros are the places where the parabola crosses the x-focus, which are close (- 0.3,0) and (1.8,0) obviously following changing in accordance with the closest 10th.

To track down the zeros of the quadratic capacity by illustrating, one ought to at first plot the y-get at (0,1) and a brief time frame later utilize the vertex condition to track down the headings of the vertex. Following plotting the vertex, the remainder of the parabola can be drawn. The zeros of the capacity are the x-gets, which can be found by finding the places where the parabola combines the x-turn. For this current situation, the zeros are close (- 0.3, 0) and (1.8, 0) resulting to adjusting to the closest 10th.

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The probability that an eighth-grade girl will have long hair and be wearing a dress is 3/8 or 0.375, which is the same thing expressed as a decimal.

what is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

To solve the problem, we need to find the intersection of the events "having long hair" and "wearing a dress" and calculate the probability of that intersection.

Let L be the event "having long hair" and D be the event "wearing a dress". Then we know:

P(L) = 3/4, since three-fourths of the girls have long hair.

P(D) = 1/2, since half of the girls are wearing dresses.

To find P(L ∩ D), we need to multiply the probabilities of the two events:

P(L ∩ D) = P(L) × P(D) = (3/4) × (1/2) = 3/8

Therefore, the probability that an eighth grade girl will have long hair and be wearing a dress is 3/8 or 0.375, which is the same thing expressed as a decimal.

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Answer:

Distance that car B travels =1.2× distance that car A travels

=1.2×221.5=265.8 km

Answer:

car B travels a distance of 265.8 km during the same time.

Step-by-step explanation:

Car A travels 221.5 km at a given time.

To find the distance traveled by car B, which is 1.2 times the distance traveled by car A, we can multiply the distance of car A by 1.2:

Distance of Car B = 1.2 * Distance of Car A

Distance of Car B = 1.2 * 221.5 km

Distance of Car B = 265.8 km

Therefore, car B travels a distance of 265.8 km during the same time.

The fraction of the square that is red is 1/6.

A fraction is a number that represents a part or parts of a whole. It consists of two numbers separated by a horizontal or diagonal line, with the number above the line (numerator) representing the part and the number below the line (denominator) representing the whole. For example, the fraction 3/4 represents three parts out of a whole that is divided into four equal parts.

A square divided into six equal parts has six equal sixths.

If Soo colors one of these equal parts red, then she has colored one-sixth of the square red.

Therefore, the fraction of the square that is red is 1/6.

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The simplification of the function is r(x)=10x - 95.

We are given that;

s(x) = -85 and a(x) = 10(x - 1)

Now,

To create a function that combines them, you can substitute these expressions into the formula above:

r(x) = s(x) + a(x) r(x) = (-85) + 10(x - 1)

You can simplify this function by distributing the 10 and combining the constants:

r(x) = -85 + 10x - 10 r(x) = 10x - 95

Therefore, the function will be r(x)=10x - 95.

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the limit expression gives the value of the derivative of a function at a specific point. where f'(x_0) denotes the derivative of f(x) at x = x_0.

what is derivative  ?

The derivative of a function is a measure of how the function changes as its input variable changes. It gives the instantaneous rate of change or slope of the tangent line of the function at a specific point.

In the given question,

The expression you provided represents the limit definition of the derivative of a function f(x) at the point x = x_0. The limit evaluates the instantaneous rate of change or slope of the tangent line of the function f(x) at the point x = x_0.

To evaluate the limit, substitute x = x_0 + h in the expression of the function f(x) and simplify:

[tex]lim h - > 0 [f(x_{0} + h) - f(x_{0})] / h = f'(x_{0})[/tex]

where f'(x_0) denotes the derivative of f(x) at x = x_0.

Therefore, the limit expression gives the value of the derivative of a function at a specific point.

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The information provided by each of the graphs is Sales from July to December and graph A best represents the data

From the question, we have the following parameters that can be used in our computation:

The graphs

On the graphs, we have the information to be

Sales from July to December

The graph that is the best representation of the data is the A

This is because the scale and origin of the graph are defined

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The mixed fraction 1 and 1/4 is equal to 5/4 and the mixed fraction 1 and 1/2 is equal to 3/2.

Given first number = 1 and 1/4.

1 and 1/4 is a mixed fraction so, we can write it in the form as  [tex]1\frac{1}{4}[/tex] .

To find the value of  [tex]1\frac{1}{4}[/tex]  we have to multiply 4 with 1 and add the numerator part of the fraction which is 1 and then divide it by 4 which is the denominator. So,

 [tex]1\frac{1}{4}[/tex]  = ((4x1) + 1 )/4 = 5/4.

Similary, for 1 and 1/2,

[tex]1\frac{1}{2}[/tex] = ((2x1) + 1)/2 = 3/2.

From the above analysis, we can conclude that the value of 1 and 1/4 is 5/4 and the value of 1 and 1/2 is 3/2.

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We can set up the equation :

0.9x = 110 ,

where x is the unknown number. To solve for x, we can divide both sides by 0.9 :

x = 110 ÷ 0.9

x = 122.22 (rounded to two decimal places)

So the unknown number is approximately 122.22.

To find 9% of that number, we can multiply 122.22 by 0.09 :

0.09 × 122.22 = 11.00 (rounded to two decimal places)

Therefore, 9% of the number is approximately 11.

The solutions  of the system of equations are (0, -6) and (7, 8)

Here we have the system of equations:

y=x^2−5x−6

y=2x−6

To solve this, we need to solve the equation:

x^2 - 5x - 6 = 2x - 6

x^2 - 7x = 0

x*(x - 7) = 0

We can see that the two solutions are:

x = 0

x = 7

Evaluating the line in these values we get:

y = 2*0 - 6 = -6

y = 2*7 - 6 = 8

Then the solutions are (0, -6) and (7, 8)

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The strength of the beam is proportional to the width and the square of the depth, so we can express it as Strength = k * width * depth²

where k is the proportionality constant.

In the given figures, the beam is cut from a cylindrical log of diameter d = 24 cm, which means the maximum width and depth of the beam are limited by this diameter. We can see from the figures that the width and depth of the beam change depending on the angle at which it is cut from the log.

In Figure 1, the width and depth of the beam are equal, so we can express the strength of the beam as:

Strength = k * width * depth² = k * x² * (d/2 - x)²

where x is the width and depth of the beam.

In Figure 2, the width and depth of the beam are not equal, so we need to express them separately. Let w be the width and d be the depth, then we can express the strength of the beam as:

Strength = k * width * depth² = k * w * d² = k * ((d/2)sinθ)² * ((d/2)cosθ)²

where θ is the angle at which the beam is cut from the log.

In Figure 3, the width and depth of the beam also vary with the angle θ. We can express the width and depth as follows:

w = d sinθ

d = (d/2)cosθ

Then we can express the strength of the beam as:

Strength = k * width * depth² = k * (d sinθ) * [(d/2)cosθ]²

Therefore, depending on the angle at which the beam is cut from the log, the strength of the beam can be expressed using different equations, but in all cases, the strength is proportional to the width and the square of the depth, with a proportionality constant k.

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Complete question is:

The strength of a beam is proportional to the width and the square of the depth. A beam is cut from a cylindrical log of diameter d = 24 cm. The figures show different ways this can be done. Express the strength of the beam as a function of the angle in the figures. (Use k as your proportionality constant.)

Answer:

To solve for z in terms of x and y using the given equations:

x + y = z ........(1)

y - z = x ........(2)

From equation (2), we get:

y - x = z (by adding z on both sides)

Substituting this value of z in equation (1), we get:

x + y = y - x

2x = 0

x = 0

Substituting x = 0 in equation (2), we get:

y - z = 0

y = z

Therefore, the solution is:

z = y

We cannot determine a specific value of z without knowing the values of x and y.

The probability of selecting all defective transistors is 1/560.

The probability of selecting all defective transistors can be calculated as:

P(all defective) = (number of ways to select 3 defective transistors) / (total number of ways to select 3 transistors)

The number of ways to select 3 defective transistors is simply the number of combinations of 3 defective transistors out of the total of 3, which is 1. The total number of ways to select 3 transistors out of 16 is:

total number of ways = number of combinations of 3 transistors out of 16

= (16 choose 3)

= 560

Therefore, the probability of selecting all defective transistors is:

P(all defective) = 1 / 560

To simplify the answer, we can write it as a fraction in lowest terms:

P(all defective) = 1 / 560 = 1/ (161514/321) = 1/560

Therefore, the probability of selecting all defective transistors is 1/560.

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Answer: 14.5 kg

Step-by-step explanation:

Using the ratios, 1 yd/3 feet, 1 mi/5,280 feet, and 200 yards/1 feet, the number of flags required to mark the racecourse with a flag every 200 yards is 22.

Ratios are relative sizes of one quantity or value compared to another.

Ratios are depicted as fractional values using decimals, percentages, or fractions, including the standard ratio form (:).

The total distance of the racecourse = 2.5 miles

The common distance between each flag = 200 yards

1 mile = 1,760 yards

2.5 miles = 4,400 yards

1 yard = 3 feel

The number of flags required to cover the distance = 22 (4,400 ÷ 200)

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Answer: 8.25

Step-by-step explanation:

The two roots of the quadratic equation x² - 5x + 3 = 0 are (5 + √13) / 2 and (5 - √13) / 2.

To find the roots of the quadratic equation x² - 5x + 3 = 0, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation.

Substituting the values of a, b, and c from the given equation, we have:

x = (-(-5) ± √((-5)² - 4(1)(3))) / 2(1)

x = (5 ± √(25 - 12)) / 2

x = (5 ± √13) / 2

Therefore, the roots of the equation are (5 + √13) / 2 and (5 - √13) / 2.

To verify that these are indeed the roots of the equation, we can substitute each of these values for x in the original equation and check if the equation is satisfied. For example, if we substitute (5 + √13) / 2 for x, we get:

(5 + √13)² - 5(5 + √13) + 3 = 0

Simplifying this equation, we get:

13 - 5√13 + 8 + 13 - 5√13 + 3 = 0

This equation is true, which means that (5 + √13) / 2 is a root of the equation x² - 5x + 3 = 0. Similarly, we can verify that (5 - √13) / 2 is also a root of the equation.

These roots can be found using the quadratic formula, which is a useful tool for solving quadratic equations.

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if a student scored a 69 on his first test, predict that his score on the second test will be approximately 64.57.

Students’ test scores on the first two tests in an introductory calculus class.

To make a prediction for the student's score on the second test based on their score of 69 on the first test, we need to find the regression equation for the data set.

The regression equation for these data is

y = 0.6443x + 19.943

Where y is the predicted score on the second test and x is the actual score on the first test.

Substituting x = 69 into this equation, we get

y = 0.6443(69) + 19.943 ≈ 64.57

Therefore, if a student scored a 69 on his first test, we predict that his score on the second test will be approximately 64.57.

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Answer:

{-3, √3, -√3, 13/3}

Step-by-step explanation:

Since the polynomial has rational coefficients, any irrational zeros must come in conjugate pairs. So, if √3 is a zero, then so is its conjugate, -√3.

We can write the polynomial with these zeros as:

p(x) = a(x + 3)(x - √3)(x + √3)(x - 13/3)

where a is some constant coefficient. Multiplying out the factors, we get:

p(x) = a(x + 3)(x^2 - 3)(x - 13/3)

To find the remaining zeros, we need to solve for x in the expression p(x) = 0. So we set up the equation:

a(x + 3)(x^2 - 3)(x - 13/3) = 0

This equation is true when any of the factors is equal to zero. We already know three of the zeros, so we need to solve for the fourth:

(x + 3)(x^2 - 3)(x - 13/3) = 0

Expanding the quadratic factor, we get:

(x + 3)(x - √3)(x + √3)(x - 13/3) = 0

Canceling out the (x - √3) and (x + √3) factors, we get:

(x + 3)(x - 13/3) = 0

Solving for x, we get:

x = -3 or x = 13/3

Therefore, the other zeros are -3 and 13/3.

The complete set of zeros is {-3, √3, -√3, 13/3}.

Hope it helps^^

The preparation of the journal entry to record the sale and the settlement of the account receivable is as follows:

January 10, 2022:

Debit Accounts Receivable $16,600

Credit Sales Revenue $16,600

(To record the sale of merchandise on account to Robertsen Co, n/30.)

February 9, 2022:

Debit Notes Receivable $16,600

Credit Accounts Receivable $16,600

(To record the receipt of a 11% promissory note in settlement of account receivable.)

Journal entries refer to the initial records maintained about business transactions.

Journal entries show how the transactions will be posted in the general ledger.

January 10, 2022: Accounts Receivable $16,600 Sales Revenue $16,600

Terms n/30

February 9, 2022: Notes Receivable $16,600 Accounts Receivable $16,600

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Prepare the journal entry to record the sale and the settlement of the account receivable.

Option (b), 62% is correct.

By the given condition,

B/A = A/(A + B) ..... (1)

Now to find the percentage of A = B, we consider B = Ax. From (1), we get

Ax/A = A/(A + Ax)

or, x = 1/(1 + x)

or, x² + x - 1 = 0

Using the quadratic formula, we get

x = {- 1 ± √(1 + 4)}/2

= (- 1 ± √5)/2

Since x cannot be negative, we take

x = (- 1 + √5)/2

≈ 0.62

Therefore the required percentage is

= 0.62 × 100%

= 62%

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B as a percentage ofAis equal to Aas a

percentage of(A+B). How much percent

of A is B?

(a) 60%

(b) 62%

(C) 64%

(d) 66%

Answer: [tex]\frac{2}{5}[/tex] x [tex]\frac{4}{5}[/tex] = [tex]\frac{8}{25}[/tex]

Step-by-step explanation:

We can do this by counting the boxes for both the Width and the Length.

If we look at the width of these boxes (horizontally) then we see that there are 5 boxes all together, with 2 shaded green.

this means that 2 out of 5 of the boxes are shaded for the width, giving us the fraction: [tex]\frac{2}{5}[/tex]

Then for the Length (vertically) we see that there are also 5 boxes, but this time 4 are shaded. This gives us the fraction:  [tex]\frac{4}{5}[/tex].

Then, to fill the equation in, we do: [tex]\frac{2}{5}[/tex] x [tex]\frac{4}{5}[/tex] , which gives us          [tex]\frac{8}{25}[/tex]

2 x 4 = 8

5 x 5 = 25

To double check this answer, we can count how many boxes are shaded green.

We see that 8 are shaded green, out of the 25 boxes that are there.

Therefore, giving us a complete answer of:  [tex]\frac{2}{5}[/tex] x [tex]\frac{4}{5}[/tex] = [tex]\frac{8}{25}[/tex]

(a) The value of the row operation of -2(row1) + row (2) is [-10     4    -12].

(b) The interchange of row 1 and row 2 is  [0     6    -3]

                                                                       [5    -2     6]

The value of the row operation of -2(row1) + row (2) is calculated as follows;

-2 (row 1) = 2 [5   -2    6]

-2 (row 1) = [-10     4    -12]

The addition of -2(row1) to row (2) is calculated as follows;

[-10     4    -12] + [0    6    -3]

= [-10   10  - 15]

The interchange of row 1 and row 2 is calculated as follows;

R₁ ↔ R₂

= [5    -2     6]    =   [0     6    -3]

  [0     6    -3]         [5    -2     6]

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