What’s the solution to 2x-2y=6 and 4x+4y=28

It takes approximately 52.7 hours for the activity of a sample of gallium-67 to fall to 6.73 percent of its original value.

The decay of radioactive substances is governed by the following equation:

\(N(t) = N_{0} e^{(-\lambda t)\)

where:

N(t) is the amount of the substance at time t

N₀ is the initial amount of the substance

λ is the decay constant

t is time

The half-life of gallium-67 is 78.2 hours, which means that:

λ = ln(2)/t₁/₂ = ln(2)/78.2 = 0.00887 h⁻¹

Let N be the amount of gallium-67 remaining after time t, and N₀ be the initial amount. Then, we can use the above equation to find the time t required for the activity of the sample to fall to 6.73 percent of its original value:

N/N₀ = 0.0673

\(0.0673 = e^{(-\lambda t)}\)

Taking the natural logarithm of both sides:

ln(0.0673) = -λt

t = ln(1/0.0673)/λ

t = ln(14.84)/0.00887

t ≈ 52.7 hours

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Answer:

x = 9

Step-by-step explanation:

Given a segment joining the midpoints of 2 sides of a triangle, then

the segment is half the length of the 3rd side , that is

3x = 0.5 × 54 = 27 ( divide both sides by 3 )

x = 9

Answer:

57 1/10

(14× 3/4)+(4× 1/2)+(8× 1/2)+(10× 2/5)+(10× 2/5)+(12× 4/5)= 571/10 or 57× 1/10

A person who does not ignore a sunk cost increases the probability of making irrational decisions. This is because they are more likely to continue investing time, money, or effort into a project or situation that is not yielding positive results.

When we refer to a "sunk cost," we mean a cost that has already been incurred and cannot be recovered. Ignoring a sunk cost means not taking it into consideration when making decisions about the future. By not ignoring a sunk cost, individuals may feel a psychological attachment to their past investment, leading them to continue investing in something that may not be beneficial.

This can result in irrational decision-making and potentially wasting additional resources. For example, imagine a person who has spent a significant amount of money on a gym membership but rarely goes to the gym. Instead of accepting the fact that the money is already spent and may not be recouped.

They may feel compelled to continue paying for the membership in the hopes of eventually utilizing it. This decision is influenced by their failure to ignore the sunk cost and assess the situation rationally.

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Answer:

120%

Step-by-step explanation:

10.14 is more than all of 8.45.

8.45 is 100% of 8.45.

So 10.14 will be more than 100%.

10.14 ÷ 8.45 = 1.2

This is the decimal value.

To change to %, multiply by 100.

1.2 × 100 = 120

10.14 is 120% of 8.45

B. 31

C. 0

Note that:

Whole numbers are positive integers (counting numbers) and zero

They are numbers from zero and above that are neither decimal nor fractions

The whole numbers among the options are 31 and 0

Answer:

5

Step-by-step explanation:

Let x be that number.

(x^2) - 40 = 3x

x^2 - 40 = 3x

x*2-3x-40=0

(x-5)(x+8)=0

x=5

Answer:

x=5

Step-by-step explanation:

opposite angles are the same, so the small ones are 15. 180-30=150

150/2=75 75/15=5

The mean absolute deviation for the given dataset of 3, 6, 3.8, 3.2, and 3.4 is approximately 0.996. This means that, on average, each data point in the dataset deviates from the mean by approximately 0.996.

The mean absolute deviation (MAD) measures the average distance between each data point and the mean of the dataset. To find the MAD, you need to follow these steps:

1. Calculate the mean of the dataset by adding up all the numbers and dividing the sum by the total number of data points. In this case, the dataset consists of the following numbers: 3, 6, 3.8, 3.2, and 3.4. Adding them up gives us a sum of 19.4. Dividing this sum by 5 (since there are 5 data points) gives us a mean of 3.88.

2. Find the absolute deviation for each data point by subtracting the mean from each data point and taking the absolute value. For example, for the first data point, 3, the absolute deviation would be |3 - 3.88| = 0.88. Repeat this step for all the data points.

3. Calculate the mean of the absolute deviations by adding up all the absolute deviations and dividing the sum by the total number of data points. In this case, the absolute deviations are: 0.88, 2.12, 0.72, 0.68, and 0.58. Adding them up gives us a sum of 4.98. Dividing this sum by 5 gives us a mean of 0.996.

So, the mean absolute deviation for the given dataset is approximately 0.996.


The mean absolute deviation helps us understand how much each data point varies from the mean of the dataset. By calculating the absolute deviation for each data point and finding the average, we can determine the typical amount of variation in the dataset.


The mean absolute deviation for the given dataset of 3, 6, 3.8, 3.2, and 3.4 is approximately 0.996. This means that, on average, each data point in the dataset deviates from the mean by approximately 0.996.

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Answer:

the right answer is the first one

2x+2 over x >0

Answer:

A. 5

Step-by-step explanation:

12 times 5 is 60 plus 10 is 70. 70 < 75

A 15 square metres sector will have a radius of 8.1 m and a central angle of 26.04 degrees.

The region of a disk encompassed by two radii and an arc is called a circular sector, also known as a circle sector or disk sector. The smaller area is referred to as the minor sector, and the larger area as the major sector. A sector is referred to as a component of a circle made up of the circle's arc and its two radii. It is a section of the circle made up of the arc's circumference and the radii of the circle at its ends. A slice of pizza or a pie can be used as an analogy for the form of a circle's sector.

Here,

area of sector=θ/360°*πr²

θ=5/11*180/π

θ=26.04 degree

area=15 m²

15=26.04/360*3.14*r²

15=0.227r²

r²=66.08 m²

r=8.13 m

The radius of the sector whose area is 15 m² will be 8.1 m with the central angle of 26.04 degree.

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The z-score corresponding to a sample mean of 69 is approximately -0.286.

The z-score corresponding to a sample mean of m = 69 can be calculated using the formula:
z = (m - µ) / (σ / √n)
Plugging in the given values, we get:
z = (69 - 71) / (21 / √9)
z = -0.86
Therefore, the z-score corresponding to a sample mean of m = 69 is -0.86.
To calculate the z-score for a sample mean (m) of 69, given a population mean (µ) of 71, standard deviation (σ) of 21, and sample size (n) of 9, use the formula:
z = (m - µ) / (σ / √n)
Plug in the values:
z = (69 - 71) / (21 / √9)
z = -2 / (21 / 3)
z = -2 / 7
z = -0.286
The z-score corresponding to a sample mean of 69 is approximately -0.286.

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Answer:

Yellow is the answer

Step-by-step explanation:

Answer:

$216

Step-by-step explanation:

324 / 18 = 18. (Meaning she makes 18 dollars an hour)

18 * 12 = 216

Answer:$216

Step-by-step explanation: Rate per hour is 324/18=18

12hours =18×12

Answer:

1,3,4

Step-by-step explanation:

ıf we rearrange formula we can obtain

p=nrt/v

t=pv/nr

v=nrt/p

r=pv/nt

The statement is true.

When the block is in equilibrium, each spring is stretched an additional ∆x. This implies that the forces from the two springs are balanced, and the block is not experiencing any net force in the equilibrium position.

When the block is set into oscillation with amplitude a, it will pass through its equilibrium point during the oscillation. At the equilibrium point, the displacement of the block is zero, and it changes direction. At this point, the block has its maximum speed v, as it is accelerating towards the equilibrium position.

The speed of the block decreases as it moves away from the equilibrium position, reaches zero at the maximum displacement (amplitude), and then starts accelerating towards the equilibrium point again. Therefore, when the block passes through its equilibrium point, it has its maximum speed v.

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The main answer to your question is "interchanging". To find the inverse of a function, we interchange the numbers in each ordered pair of the function. This means that we switch the x and y values of each point in the function.

For example, if we have a function f(x) = 2x + 3, the ordered pairs would be (1,5), (2,7), (3,9), etc. To find the inverse function, we would switch the x and y values of each point to get ordered pairs such as (5,1), (7,2), (9,3), etc.

The explanation for why we interchange the numbers is that the inverse function "undoes" the original function. If we apply the original function to a number, the inverse function will take us back to the original number. By switching the x and y values, we make sure that the inverse function will undo the original function.

In conclusion, to find the inverse of a function, we interchange the numbers in each ordered pair of the function. This ensures that the inverse function will undo the original function.
Hi! I'm happy to help you with your question.

Main answer: The inverse of a function can be found by interchanging the numbers in each ordered pair of the function.

Explanation: When finding the inverse of a function, you are essentially swapping the input and output values in each ordered pair (x, y) to create a new ordered pair (y, x). This process is called interchanging the numbers in the ordered pair.

Conclusion: To find the inverse of a function, you need to interchange the numbers in each ordered pair of the function, which essentially swaps the input and output values.

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Answer:

The internship pays $7.5 an hour.

Step-by-step explanation:

From the information given, the equation would indicate that the amount the student earns per hour at the intership for two plus seven would be equal to 22:

2x+7=22

Now, you can solve for x:

2x=22-7

2x=15

x=15/2

x=7.5

According to this, the answer is that the internship pays $7.5 an hour.

The apprοximate number οf students enrοlled in public schοοls in the United States is 7.68 × 10⁷, which cοrrespοnds tο chοice (C).

Unitary method widely used ease, already-present variables, οr all impοrtant elements frοm the οriginal Bishοp custοmizable questiοn can all be used tο achieve the gοal. If sο, a secοnd chance tο engage with the οbject will present itself. Otherwise, every crucial element that affects hοw well a prοοf οf an expressiοn wοrks will be gοne.

Here,

Tο sοlve this prοblem, we can start by multiplying the number οf students in the lοcal schοοl system by 480, since there are 480 times mοre students in public schοοls in the United States.

1.6 × 10⁵ × 480

= 7.68 × 10⁷

Therefοre, the apprοximate number οf students enrοlled in public schοοls in the United States is 7.68 × 10⁷, which cοrrespοnds tο chοice (C).

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Answer:

The following linear equation represents the system:

x + y = 20 (speed of the riverboat and current in km/hr in the same direction)

x - y = 16 (speed of the riverboat relative to the current in km/hr in opposite directions)

Solving for x and y gives us:

x = 18 and y = 2 (speed of the riverboat and current in km/hr).

Step-by-step explanation:

The exponential regression equation for this set of data is y = \(14.129e^{(0.495x)\) and the number of bacteria present after 10 hours is approximately 24684.

The exponential regression equation for this set of data can use a calculator or spreadsheet software.

The equation will have the form y = abˣ a is the initial number of bacteria and b is the growth rate.
Using the given data can create a table of values for the equation:
x                y                   ln(y)
---------------------------------------
0              16                2.773
1               66               4.189
2             311                5.739
3            791                6.672
4          1553                7.349
5          2571               7.853

A regression tool can find that the equation is approximately y = \(14.129e^{(0.495x)\) rounded to three decimal places.

The initial amount of bacteria is approximately a = 14.129 and the growth rate is approximately b = 1.649.
The number of bacteria present after 10 hours can plug x = 10 into the equation:
y = \(14.129e^{(0.495\times 10)\)

= 24683.522
Rounding to the nearest whole number get that the number of bacteria present after 10 hours is approximately 24684.

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Answer:

The amount of deposit required is R37,999  for both

The percentage of purchase price for the required deposit is 20%

Therefore, deposit required=20%*R189,995

                                              =R37,999

The balance owed is the outstanding balance after payment of deposit plus the interest, bearing in mind that interest is computed using the simple interest approach

I=PRT

balance after payment of deposit=R189,995-R37,999

                                                       =R151,996

R=13.5% per year

T=48 months and 54 months

Interest on 48 month option=151,996*13.5%*48/12

                                              = R82,077.84

Interest on 54 month option=151,996*13.5%*54/12

                                              = R 92,337.57

The total payment without the initial deposit is the outstanding balance after payment of deposit plus the interest

Total payment for 48 month option=R151,996+R 92,337.57

                                                          =R  244,333.57

Total payment for 54 month option=R151,996+R82,077.84

                                                          =R 234,073.84

                                              Hope it helped!

Answer:

\(x = -13\frac{1}{2}\)

Step-by-step explanation:

Eight less than a third of a number is the sum of that number and one.

Let the number be x.

That is:

\(\frac{1}{3}x - 8 = x + 1\\ \\=> x - \frac{1}{3}x = -8 - 1 \\\\\frac{2}{3}x = -9\\\\x = -9 * \frac{3}{2}\\ \\x = \frac{-27}{2}\)

\(x = -13\frac{1}{2}\)

Answer:

Step-by-step explanation:

(1,4)

a.  F does, in fact, satisfy Rolle's Theorem's hypotheses regarding the interval [-1,1].

b. F does, in fact, satisfy the Mean Value Theorem's hypotheses on the range [-1,1].

c. G does not satisfy Rolle's Theorem's hypotheses on the interval [-1,1], hence no.

(a) Yes, f satisfies the hypotheses of Rolle's Theorem on the interval [-1,1]. The hypotheses of Rolle's Theorem are:

f(x) is continuous on the closed interval [a,b]

f(x) is differentiable on the open interval (a,b)

f(a) = f(b)

In this case, we have:

f(x) = x - x^3 is continuous on the closed interval [-1,1]

f(x) = x - x^3 is differentiable on the open interval (-1,1)

f(-1) = -1 - (-1)^3 = 0 = f(1)

Thus, by Rolle's Theorem, there exists at least one c in (-1,1) such that f'(c) = 0.

To find the value of c, we have:

f'(x) = 1 - 3x^2

f'(c) = 1 - 3c^2 = 0

3c^2 = 1

c = ±(1/√3)

Since c must be in the interval (-1,1), we have c = 1/√3.

(b) Yes, f satisfies the hypotheses of the Mean Value Theorem on the interval [-1,1]. The hypotheses of the Mean Value Theorem are:

f(x) is continuous on the closed interval [a,b]

f(x) is differentiable on the open interval (a,b)

In this case, we have:

f(x) = x - x^3 is continuous on the closed interval [-1,1]

f(x) = x - x^3 is differentiable on the open interval (-1,1)

Thus, by the Mean Value Theorem, there exists at least one e in (-1,1) such that:

f'(e) = (f(1) - f(-1))/(1 - (-1))

f'(e) = (1 - (-1))/(1 - (-1)) = 1

To find the value of e, we have:

f'(x) = 1 - 3x^2

f'(e) = 1

Thus, e can be any value in (-1,1).

(c) No, g does not satisfy the hypotheses of Rolle's Theorem on the interval [-1,1]. The hypotheses of Rolle's Theorem are:

f(x) is continuous on the closed interval [a,b]

f(x) is differentiable on the open interval (a,b)

f(a) = f(b)

In this case, we have:

g(x) = 15 is continuous on the closed interval [-1,1]

g(x) = 15 is not differentiable on the open interval (-1,1) since it is a constant function

g(-1) = 15 ≠ g(1)

Thus, g does not satisfy the hypotheses of Rolle's Theorem on the interval [-1,1], and we cannot determine a value c that is guaranteed to exist.

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Answer:

10

Step-by-step explanation:

10 is in the middle of all the numbers.

Answer:

I believe the median is 10.

Step-by-step explanation:

Answer:(192/9.6)÷7=20/7

Step-by-step explanation:

The output when the given pseudocode is executed with A = 5 and B = 3 will be "25, 16, 9, 4, 1".

The given pseudocode includes a loop that iterates as long as A is greater than or equal to B. In each iteration, the square of A is displayed, and A is decremented by 1. We are asked to determine the output when A is initially 5 and B is 3.

Step 1: Initialization

A is set to 5 and B is set to 3.

Step 2: Iteration 1

Since A (5) is greater than or equal to B (3), the loop executes.

The square of A (5²) is displayed, resulting in the output "25".

A is decremented by 1, so A becomes 4.

Step 3: Iteration 2

A (4) is still greater than or equal to B (3).

The square of A (4²) is displayed, resulting in the output "16".

A is decremented by 1, so A becomes 3.

Step 4: Iteration 3

A (3) is still greater than or equal to B (3).

The square of A (3²) is displayed, resulting in the output "9".

A is decremented by 1, so A becomes 2.

Step 5: Iteration 4

A (2) is still greater than or equal to B (3).

The square of A (2²) is displayed, resulting in the output "4".

A is decremented by 1, so A becomes 1.

Step 6: Iteration 5

A (1) is still greater than or equal to B (3).

The square of A (1²) is displayed, resulting in the output "1".

A is decremented by 1, so A becomes 0.

Step 7: Loop termination

Since A (0) is no longer greater than or equal to B (3), the loop terminates.

Therefore, The output generated by the code execution will be "25, 16, 9, 4, 1" as the squares of A (starting from 5 and decreasing by 1) are displayed in each iteration of the loop.

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