Sean is conducting an experiment with an isotope of a particular element that has a half-life of 4 hours. He begins with a sample of the isotope with a mass of 92 grams. He then measures the mass of the object every hour. What is the approximate mass of the sample after 20 hours?

A proportional relationship between y and x can be represented by a linear equation of the form:

y = kx

where k is the unit rate of change of y with respect to x. Given that the unit rate of change of y with respect to x is 0.4, we can substitute this value for k in the equation:

y = 0.4x

This equation represents the line that shows the proportional relationship between y and x.

To graph this equation, we can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept. We can rewrite our equation as:

y = 0.4x + b

Since the y-intercept is the point where the line crosses the y-axis, we can substitute any value of x with 0 and solve for b

y = 0.4x + b

y = 0.4*0 + b

y = b

So the y-intercept is b = 0

Therefore, the slope-intercept form of the equation is y = 0.4x + 0

To graph the line, we can take any two x values and substitute them into the equation, and then plot the corresponding y values on the graph. For example, when x = 0, y = 0.40 + 0 = 0 and when x = 1, y = 0.41 + 0 = 0.4.

We can use these points to plot the line on a graph, it will be a straight line passing through the point (0,0) with a slope of 0.4.

Note: This line is also known as the direct variation equation.

Answer:

Y=0.4X

Step-by-step explanation:

when x=1, Y =0.4

when x=2, Y=0.8

Now you have 2 points, draw a line.  voila.

see attached

Answer:

101 Faces

Step-by-step explanation:

Hope it helps + get it right

The English sentences that are translated from single letters, such as P, Q, R, etc., can either be true or false depending on the context in which they are used.

For example, if P is translated as "the sky is blue," then this sentence is true. However, if P is translated as "the sky is orange," then this sentence is false. In order to determine the truth value of the translated sentence, we must first identify the context in which the letter is being used. Then, we can decide whether the translation is true or false by using logic and reasoning. For example, if we know that the sky is not orange, then the translation of P can be determined to be false.

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The inverse matrix of the given matrix is

[tex]\left[\begin{array}{ccc}3/2&-2\\-1/2&1\end{array}\right][/tex]

What is meant by inverse matrix?

If A is a non-singular square matrix, then A^-1, often known as the inverse matrix of A, must exist if it is to satisfy the following property:

AA^-1 = A^-1A = I, Where I is the Identity matrix

Now, we will first find the determinant of the given matrix, whichis as follows:

Determinant = 6-4 = 2

Since, the determinant is not zero, this means that the inverse matrix exists.

Now, let's find the inverse matrix i.e. A^-1

[tex]A^{-1} = \frac{1}{D} \left[\begin{array}{ccc}d&-b\\-c&a\end{array}\right][/tex]

[tex]A^{-1} = \frac{1}{2} \left[\begin{array}{ccc}3&-4\\-1&2\end{array}\right][/tex]

[tex]A^{-1} = \left[\begin{array}{ccc}3/2&-4/2\\-1/2&2/2\end{array}\right][/tex]

[tex]A^{-1} = \left[\begin{array}{ccc}3/2&-2\\-1/2&1\end{array}\right][/tex]

Hence, the inverse matrix of the given matrix is as under

[tex]\left[\begin{array}{ccc}3/2&-2\\-1/2&1\end{array}\right][/tex]

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Answer: A) The decay constant (λ) is a measure of the rate at which a radioactive isotope decays. It is defined as the probability per unit time that an atom of the isotope will decay. The decay constant can be calculated using the formula:

λ = -ln(1 - x) / t

Where x is the fraction of the original activity that has decayed (in this case, 0.40), and t is the time over which the decay occurred (in this case, one week).

B) The half-life (T1/2) is the amount of time it takes for half of the original activity of a radioactive isotope to decay. It can be calculated using the formula:

T1/2 = ln(2) / λ

C) The mean lifetime (τ) is the average amount of time an atom of a radioactive isotope will survive before it decays. It can be calculated using the formula:

τ = 1 / λ

It's important to note that the above formulas are based on the exponential decay model, which assumes that the decay process is random and that the decay constant is constant over time. If the isotope does not decay in this way, these formulas may not give accurate results.

Step-by-step explanation:

The cost of making 60 triangular flags with base 3.5feet and height 2.5 feet with making charges of $0.40per square foot  is equal to $105.

Flag is triangular in shape.

Base of the flag = 3.5 feet

Height of the flag = 2.5feet

Area of the flag = ( 1/2) base × height

                          = ( 1/2 )× ( 3.5 ) × ( 2.5)

                          = 4.375 square feet.

Cost of one square foot flag = $0.40

Cost of making one flag = $ ( 0.40 ×  4.375 )

                                        = $ 1.75

Cost of making 60 flags =  $ ( 1.75 × 60 )

                                        = $ 105.

Therefore, the cost of making 60 triangular flag is equal to $105.

The given question is incomplete, I answer the question in general according to my knowledge:

You make and sell triangular flags. Each flag has a base of 3.5 feet and a height of 2.5 feet. Fabric for the flags costs $0.40 per square foot. What is the cost to make 60 flags?

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Step-by-step explanation:

A right triangle is a triangle that has one angle that measures 90 degrees. Based on the information provided, the following triangles are right triangles:

Triangle A - OA. 55° and 70° are not right angles

Triangle B - OB. 30° and 60° are not right angles

Triangle C - O C. 45° and 45° form a right angle

Triangle D - OD. 60° and 60° form a right angle.

SAA is a mnemonic for solving the triangle, not a triangle itself

24°, 45°, and 126° are not angles that form a triangle as the sum of all angles in a triangle is 180.

The ratio of their shares is 1:2:3 and amount is 180.5, 3564, 5371.5 respectively.

To find the amount each received:

Atta received 13.5*(51+110) = 1807.5

Abena received 27*(51+110) = 3564

Kojo received 40.5*(51+110) = 5371.5

The total amount shared is 51 + 110 = 161

The ratio of their shares is 1:2:3, meaning Atta receives 1/6 of the total amount, Abena receives 2/6 of the total amount, and Kojo receives 3/6 of the total amount.

To find the amount each received, we multiply their respective share (1/6, 2/6, and 3/6) by the total amount (161)

Kojo received 3 times as much as Atta, and Atta received 1/2 times as much as Abena.

Atta received 1/6 of the total amount, which is (51 + 110)/6 = 81/6 = 13.5

Abena received 2/6 of the total amount, which is (51 + 110)*2/6 = 162/6 = 27

Kojo received 3/6 of the total amount, which is (51 + 110)*3/6 = 243/6 = 40.5

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Answer: No solution

Step-by-step explanation:

x + 1/2 = x - 1/2

Subtract x from both sides:

1/2 = -1/2

This is not true, so there are no solutions to this equation

Answer:

Step-by-step explanation: multiply one and a half by x then thats ur answer

Answer:

what's the question? how many days? 4 day is the breakeven mark.

Step-by-step explanation:

80+60x = 100+55x

5x =20

x=4

for a 4-day rental, it'll be the same.  

if longer than 4 days, go with enterprise.  shorter than 4 days go with hertz.

Answer: The standard algorithm for division is also known as long division, it is a method for solving division problems that involve larger numbers. To solve 66 divided by 7 using the standard algorithm, you can follow these steps:

Step 1: Write the dividend (66) and the divisor (7) in a division problem format, like this:

66 | 7

--- |

Step 2: Divide the first digit of the dividend (6) by the divisor (7). Since 6 is less than 7, write a 0 as the first digit of the quotient.

66 | 7

--- | 0

Step 3: Multiply the divisor (7) by the first digit of the quotient (0) and write the product (0) under the first digit of the dividend (6).

66 | 7

--- | 0

0 |

Step 4: Subtract the product (0) from the first digit of the dividend (6) and write the result (6) under the subtraction.

66 | 7

--- | 0

0 | 6

Step 5: Bring down the next digit of the dividend (6) and append it to the result of the subtraction to form a new 2-digit number (66).

66 | 7

--- | 0

0 | 6

| 66

Step 6: Divide the new 2-digit number (66) by the divisor (7) and write the quotient (9) above the line.

66 | 7

--- | 09

0 | 6

| 66

Step 7: Multiply the divisor (7) by the quotient (9) and write the product (63) under the new 2-digit number (66).

66 | 7

--- | 09

0 | 6

--- | 63

Step 8: Subtract the product (63) from the new 2-digit number (66) and write the result (3) under the subtraction.

66 | 7

--- | 09

0 | 6

--- | 63

| 3

Step 9: Write the final result (9) as the quotient and the remainder (3) of the division problem.

66 | 7

--- | 09

0 | 6

--- | 63

| 3

So, 66 divided by 7 = 9 with a remainder of 3

So the answer is 9 R 3

Step-by-step explanation:

The solution is: 66 divided by 7 is  9 with a remainder of 3.

The standard algorithm for division is also known as long division, it is a method for solving division problems that involve larger numbers.

To solve 66 divided by 7 using the standard algorithm, you can follow these steps:

Step 1: Write the dividend (66) and the divisor (7) in a division problem format, like this:

66 | 7

--- |

Step 2: Divide the first digit of the dividend (6) by the divisor (7). Since 6 is less than 7, write a 0 as the first digit of the quotient.

66 | 7

--- | 0

Step 3: Multiply the divisor (7) by the first digit of the quotient (0) and write the product (0) under the first digit of the dividend (6).

66 | 7

--- | 0

0 |

Step 4: Subtract the product (0) from the first digit of the dividend (6) and write the result (6) under the subtraction.

66 | 7

--- | 0

0 | 6

Step 5: Bring down the next digit of the dividend (6) and append it to the result of the subtraction to form a new 2-digit number (66).

66 | 7

--- | 0

0 | 6

| 66

Step 6: Divide the new 2-digit number (66) by the divisor (7) and write the quotient (9) above the line.

66 | 7

--- | 09

0 | 6

| 66

Step 7: Multiply the divisor (7) by the quotient (9) and write the product (63) under the new 2-digit number (66).

66 | 7

--- | 09

0 | 6

--- | 63

Step 8: Subtract the product (63) from the new 2-digit number (66) and write the result (3) under the subtraction.

66 | 7

--- | 09

0 | 6

--- | 63

| 3

Step 9: Write the final result (9) as the quotient and the remainder (3) of the division problem.

66 | 7

--- | 09

0 | 6

--- | 63

| 3

So, 66 divided by 7 = 9 with a remainder of 3

So the answer is 9 R 3.

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Size of x = 102°

In geometry, an angle is formed when two rays are joined at their endpoints. These rays are called the sides or arms of the angle.

Given,

In triangle ABC

Sum of interior angles is 180°

∠CAB + ∠ABC + ∠BCA = 180°

87° + ∠ABC + 36° = 180°

123° + ∠ABC = 180°

∠ABC = 180° - 123°

∠ABC = 57°

In triangle DBG

Exterior angle is equal to sum of two opposite interior angles.

DGF = GDB + DBG

DGF = GDB + ABC

DGF = 45° + 57°

DGF = 102°

DGF and EFC are alternate angles made by EF and DG on BC

∴ EFC = DGF

x = 102°

Hence, 102° is size of x.

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The domain and the range of y = 12x - 35 are the set of all real numbers

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

y = 12x - 25

There is no restriction on the input values, x

So, the domain of y = 12x - 35 is all real numbers, since there is no restriction on the input (x).

The range of y = 12x - 35 is also all real numbers, since the output (y) can be any real value, depending on the input (x).

This can be seen by considering that for any real number x, the output y = 12x - 35 will also be a real number.

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Heath had the longest jump of 6 meters in the competition.

Comparison theory is a psychological theory that proposes that people use social comparisons to better understand their own value and place in society. According to this hypothesis, people compare themselves to others in order to assess themselves, typically focusing on the traits that they have and the qualities that other people have. Individuals utilise the comparison to estimate their own value and how they should conduct in order to achieve approval and acceptance from their peers.

This question requires the use of the Comparison Theory.

This theory states that when presented with two or more items, we can compare them to determine which is larger, smaller, longer, shorter, etc.

In this case, we need to compare the distances of each jump for each teammate in order to determine which one had the longest jump.

Step 1: Look at the distances of each jump for Heath.

Step 2: Look at the distances of each jump for Amari.

Step 3: Compare the distances of each jump for both Heath and Amari.

Step 4: Determine which jump was the longest - Heath's 6 meter jump.

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Using cross multiplication method, a total of 2.7 kilograms of coffee was in the bag.

Cross multiplying is the process of multiplying the denominator of the second fraction on the other side of the equals to symbol by the numerator of the first fraction on one side of the equals to symbol.

Comparably, the numerator of the second fraction is multiplied by the denominator of the first fraction. Cross multiply is another name for the butterfly method of multiplication. The cross-multiply method is used to find one or more variables in a fraction. Cross multiplying can also be used to compare fractions.

The fraction of 3/8 of a bag of coffee = 1.6875kg

Let, The total mass of the bag of coffee be x, i.e.

3/8 = 1.6875/x

Using Cross-multiplication

3x = 1.6875 × 8

3x = 13.5

x = 13.5/5

x = 2.7kg

Thus, Using cross multiplication method, a Total of 2.7 kilograms of coffee was in the bag.

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English Full question

An employee of a cafeteria took 3/8 of a bag of coffee, which corresponds to 1.6875kg. How many kilograms was the bag of coffee?

The real world scenario that would represent a causal relationship in causation:

Example 1: Shark attacks and sales of ice cream

Example 2: Box Office Income and Master's Degrees

Example 3: Nuclear Energy Production vs. Pool Drownings

Example 4: Marriage Rate versus. Measles Cases

The concept of causation states that one occurrence results in another event. Just a test with a correct engineering can demonstrate correlation. Similar groups are given various treatments in these trials, and the results of each group are examined. Only when there is a discernible difference between the groups' results can we say that a treatment had an impact.

People frequently misunderstand and misuse the concept of causality in statistics because they believe that just because data reveals a correlation, there must definitely be an underlying causal relationship.

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Answer:

12 inches

Step-by-step explanation:

Use a proportion.

1 inch is to 8 yards as x inches is to 96 yards

1/8 = x/96

Cross multiply.

8x = 96

x = 12

Answer: 12 inches

Nelson hourly wage is $11.8

Nelson earned $379.25 in net pay for working 40 hours

He paid $56.64 in federal and state taxes

He also paid $36.11 in FICA tax

Therefore Nelson hourly wage can be calculated as follows

The first step is to calculate the total earnings

= 379.25 + 56.64 + 36.11

= 472

The next step is to calculate the hourly wage

472/40

= 11.8

Hence Nelson hourly wage is $11.8

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By using the equation of the trend line, the​ hiker's elevation after 145 minutes is equal to 2,077.3 feet.

In order to determine the​ hiker's elevation after 145 minutes, we would have to substitute the value representing the number of minutes (x) into the linear equation that models the​ hiker's elevation in feet and then evaluate as follows;

y = 9.54x + 694

When the value of x = 145 minutes, the hiker's elevation (y) in feet is given by;

Hiker's elevation (y) = 9.54x + 694

Hiker's elevation (y) = 9.54(145) + 694

Hiker's elevation (y) = 1,383.3 + 694

Hiker's elevation (y) = 2,077.3 feet.

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Answer: To find the smallest non-zero whole number h for which 528h is a multiple of 540, we need to find the smallest positive whole number h such that 528h is divisible by 540.

First, we can simplify the prime factorization of 540:

540 = 22 x 3³ x 5

To make 528h a multiple of 540, we need to ensure that the prime factors of 528h are the same as the prime factors of 540.

528 = 24 x 3 x 11

So, 528h = (24 x 3 x 11)h = 24h x 3h x 11h

We can see that 24h and 11h are not factors of 540.

So, the only way to make 528h a multiple of 540 is to make 3h a factor of 3³.

3h = 3³ = 27

So, h = 27/3 = 9

So, the smallest non-zero whole number h for which 528h is a multiple of 540 is 9.

For (ii)

The smallest whole number k for which a factor of 540

540 = 22 x 3³ x 5

The smallest whole number k that is a factor of 540 is 5.

Step-by-step explanation:

Answer:

200,000 times

Step-by-step explanation:

80 km × (1000 m)/(1 km) × (100 cm)/(1 m) = 8,000,000 cm

8,000,000 cm / 40 cm = 200,000

Answer: 200,000 times

The circumference of a circle with diameter 8 units is equal to 25.14 units.

Circumference is the perimeter of a circle, circles are featured solely by diameter. The formula for circumference is described below:

s = π · D

Where D is the diameter, in units.

If we know that D = 8 units, then the circumference of the circle is:

s = π · 8

s = 8π

s = 25.14

The circle (diameter: 8 units) has a circumference of 25.14 units.

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The triangle △FUN is congruent to the triangles △CAR.  And the diagram is given below.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

In triangles △FUN and △CAR, then we have

∠FUN = ∠CAR = 90°    

∠UFN = ∠ACR    

FN = CR

Then the triangles △FUN and △CAR are congruent triangles. And the diagram is given below.

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The surface area of the rectangular prism is 100m²

The formula for calculating the surface area of a rectangular prism is expressed as;

Surface area = 2(wl + hw + lh)

Given that;

From the diagram shown, let's substitute the values, we have;

Surface area = 2(2× 7 + 4× 2 + 7 × 4)

multiply the values, we get;

Surface area = 2(14 + 8 + 28)

Add the values

Surface area = 2(50)

Expand the bracket

Surface area = 100m²

Hence, the value is  100m²

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Answer: 6 2/3

Step-by-step explanation: 2 5/12 + 4 1/4  29/12 + 4 1/4 29/12 + 17/4 (3/3) 29/12 + 51/12 80/12/4/4 20/3 6 2/3

An equation system's solution is a collection of values for the variable that concurrently fulfill each equation.

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The cost of a battling token is $1.5 and the cost of a miniature golf game is $2.

The set of values for the variable that simultaneously satisfy all of the equations in an equation system is called the solution. In order to solve an equation system, all sets of variable values that could possibly exist must be found. The second equation, however, is initially without a solution (5, 4).

The set of values for the variable that simultaneously satisfy all of the equations in an equation system is called the solution.

If both variables are eliminated and you are left with a true statement, there are an infinite number of ordered pairs that satisfy both equations. In reality, the equations' lines are the same.

Let cost token be x and golf games be y, i.e.

16x + 3y = 30

22x + 5y = 43

Lets Solve by using Elimination method both the expression in equal terms

 80x + 15y = 150

- 66x + 15y = 129

14x = 21

x = 21/14

x = 1.5

Then, for y

16(1.5) + 3y = 30

y = 2

Thus, The cost of a battling token is $1.5 and the cost of a miniature golf game is $2.

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According the diagram, Alyssa trying to solve the problem 4 5/8 - 1 7/8. So the option C is correct.

Alyssa draws the following model to solve a problem.

We can see on the diagram that there have lock of two colors red and black. Some block are cut in both colors.

The total block of red color = 3

The total block of black color = 13/8

So the total block = 3 + 13/8

The total block = (24 + 13)/8

The total block = 37/8

The total block = 4 5/8

The block cut in color red = 1

The block cut in color black = 7/8

Total cut block = 1 + 7/8

Total cut block = (8 + 7)/8

Total cut block = 15/8

Total cut block = 1 7/8

So the problem should be

= The total block - Total cut block

= 4 5/8 - 1 7/8

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The complete question is given below:

(x^4+10x^3+10x^2-15x-6)/(x+2) Synthetic Division

The synthetic division for the polynomial (x^4+10x^3+10x^2-15x-6) divided by (x+2) would be:

x^3 + 8x^2 - 19x - 12 + (R)

Where R is the remainder.

The quotient is x^3 + 8x^2 - 19x - 12

A synthetic division, also known as long division of polynomials or polynomial synthetic division, is a method of dividing polynomials that is faster and simpler than the traditional polynomial long division method. It is particularly useful for dividing a polynomial by a linear factor of the form (x - a), where a is a real number.

Synthetic division allows you to divide a polynomial by a linear factor without having to perform the traditional long division algorithm, by using the polynomial's coefficients instead of the polynomial itself. Synthetic division is also useful for finding the remainder of a polynomial division. The quotient and the remainder are written in a form of simplified polynomials.

Therefore, the correct answer is as given above

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a. The amount of minutes it will take for the two pools to have thesame amount of water is 24 minutes

b. The amount of water in each pool is 1098liters

Simultaneous equations are two or more algebraic equations with the same unknown variables and the same value of the variables satisfies all such equations. This implies that the simultaneous equations have a common solution. Some of the examples of simultaneous equations are: 2x - 4y = 4, 5x + 8y = 3.

Represent the number of minutes it will take the two pool to have thesame amount y be x

therefore ;

y = 654+ 18.5x equation 1

y = 0+ 45.75x equation 2

from equation 2, y = 45.75x

substitute 45.75x for y in equation 1

45.75x = 654+ 18.5x

collect like terms

654 = 45.75x - 18.5x

654 = 27.25x

x = 654/27.25

x= 24minutes

from equation 2,

y = 0 + 45.75 × 24

y = 1098 litres

therefore at 24minutes the first and second pool will have the same volume of water of 1098litres

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The water in each pool when they have the same amount will be 1098 liters.

An equation simply has to do with the statement that illustrates the variables given.

In this case, two pools are being filled with water. To start, the first pool contains 654 liters of water and the second pool is empty. Water is being added to the first pool at arate of 18.5 liters per minute.

Water is being added to the second pool at a rate of 45.75 liters per minute.

Let the minute be represented by m. The equation will be:

653 + 18.5m = 45.75m

Collect the like terms

45.75m - 18.5 m = 654

27.25m = 654

Divide

m = 654 / 27.25

m = 24 minutes

The water in each pool when they have the same amount will be:

= 45.75 × 24

= 1098 liters

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