Solve the simultaneous equation
2x+3y=13
4x-y=-2

The variable P0 represents the initial amount.

In the exponential growth model, P(t) represents the population at time t, P0 represents the initial population at time t=0, k represents the growth rate, and e is the mathematical constant, approximately equal to 2.71828. Therefore, P0 represents the initial amount or the starting point of the population.

The correct answer is B, the variable P0 represents the initial amount.

B. The variable P0 represents the initial amount.

In the exponential growth model P(t) = P0 * e^(kt), the variables are defined as follows:
- P(t): The population size at time 't'
- P0: The initial population size (i.e., the population size at the beginning, when t=0)
- e: The base of the natural logarithm (approximately 2.71828)
- k: The growth rate constant
- t: Time

In this model, P0 is the population size at the beginning of the observed period (when t=0). Therefore, it represents the initial amount.


The variable P0 in the exponential growth model P(t) = P0 * e^(kt) represents the initial amount of the population or quantity being studied.

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Answer:

4/5

Step-by-step explanation:

If two lines are parallel, then they have the same slope. So, we first need to put the equation in slope intercept form (y = kx + b)

8x - 10y = -60

-10y = -8x - 60

y = 4/5x + 6

So the slope is 4/5.

Answer:

In slope intercept form -5y = -4 - 30

Step-by-step explanation:

Slope intercept form is y=mx + b

Rewrite your equation in this form

-10y = -8x - 60

Find GCF (Greatest Common Factor) in this case it is 2

Divide all by 2

-5y = -4x - 30

Step-by-step explanation:

Notice how both systems have the same slope but different y intercept.

This means these lines are parallel so they have no solutions.

Answer:

\(x<-8\)

Step-by-step explanation:

So we have the inequality:

\(3x-1>4x+7\)

Add 1 to both sides. The left side cancels:

\(3x>4x+8\)

Subtract 4x from both sides. The right side cancels:

\(-x>8\)

Divide both sides by -1. Since we're dividing by a negative, we flip the sign:

\(x<-8\)

And we're done!

Our solution is all numbers less than -8.

Answer:

x = -8

Step-by-step explanation:

I will be the brainliest, its hard to explain on a document, i could make you avideo how to do these problems, im a math teacher.

(a) for all integers a, b, and c, if a | b and a | c, then a | (b c)  is true.(b) for all integers a, b, and c, if a | b or a | c, then a | (b c)  is false (c) for all integers a, b, and c, if a | b and a | c, then a | bc is true. (d) for all integers a, b, and c, if a | b or a | c, then a | bc is false. (e) for all integers a, b, and c, if a | b and a | c, then a2 | bc  is false. (f) for all integers a, b, and c, if a | bc, then a | b or a | c.  is false.

Let's examine each statement one by one:

(a) For all integers a, b, and c, if a | b and a | c, then a | (bc).

To prove this statement, we can use the definition of divisibility. If a divides both b and c, it means that b and c can be written as multiples of a. Let's assume b = ka and c = ma, where k and m are integers.

Now, we can express the product bc as follows:

\(bc = (ka)(ma) = (km)(a^2)\)

Since (km) is an integer and \(a^2\) is also an integer, we can conclude that a | (bc). Therefore, statement (a) is true.

(b) For all integers a, b, and c, if a | b or a | c, then a | (bc).

This statement is false. For example, let's consider a = 2, b = 3, and c = 5. In this case, 2 does not divide 3 or 5 individually. However, the product of b and c (3 * 5 = 15) is divisible by 2. Therefore, statement (b) is false.

(c) For all integers a, b, and c, if a | b and a | c, then a | bc.

This statement is true. If a divides both b and c, we can express b and c as multiples of a: b = ka and c = ma, where k and m are integers. Now, we can express the product bc as follows:

bc = (ka)(ma) = (km)(a)

Since (km) is an integer, we can conclude that a | bc. Therefore, statement (c) is true.

(d) For all integers a, b, and c, if a | b or a | c, then a | bc.

This statement is false. Similar to statement (b), let's consider a = 2, b = 3, and c = 5. In this case, 2 does not divide 3 or 5 individually. However, the product of b and c (3 * 5 = 15) is divisible by 2. Therefore, statement (d) is false.

(e) For all integers a, b, and c, if a | b and a | c, then \(a^2\) | bc.

This statement is false. Let's consider a = 2, b = 4, and c = 6. In this case, 2 divides both b and c, but \(a^2 (2^2 = 4)\) does not divide bc (4 * 6 = 24). Therefore, statement (e) is false.

(f) For all integers a, b, and c, if a | bc, then a | b or a | c.

This statement is false. Let's consider a = 2, b = 4, and c = 3. In this case, 2 divides the product bc (4 * 3 = 12), but 2 does not divide b or c individually. Therefore, statement (f) is false.

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Joy was charged the labor of 11 hours .

Joy was charged a total of $1215 from the landscaper for listed parts and labor.

He was charged $445 for listed parts

He was charged the rest for labor

The hourly rate for labor is $ 70

Let the number of hours worked by labor be x

so, we can form a linear equation here as 445 + 70x = 1215

Now we have to solve this linear equation

445 + 70x = 1215

70x= 1215 - 445

70x = 770

x = 770/ 70

x = 11

Therefore, 11 hours of labor were needed to complete the job.

The correct question is Joy recently hired a landscaper to do some necessary work. On the final bill, Joy was charged a total $1215.  $445 was listed for parts and the rest for labor. If the hourly rate for labor was $70, how many hours of labor were needed to complete the job?

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Answer:

5 - \(\frac{40}{5}\) = 5 - 8 = -3

Step-by-step explanation:

The first mistake made by the student is in Step A where the problem was not copied down correctly.

To draw a less than type ogive for the given weight data and determine the median weight, we can plot the cumulative frequency against the upper class boundaries. Here's a step-by-step approach:

Create a table with two columns: "Weight (in kg)" and "Cumulative Frequency."

Weight (in kg) Cumulative Frequency

Less than 38 0

Less than 40 3

Less than 42 5

Less than 44 9

Less than 46 14

Less than 48 28

Less than 50 32

Less than 52 35

Plot the cumulative frequency against the upper class boundaries on a graph.

The upper class boundaries are: 38, 40, 42, 44, 46, 48, 50, 52.

The corresponding cumulative frequencies are: 0, 3, 5, 9, 14, 28, 32, 35.

Connect the plotted points to form a less than type ogive.

To find the median weight from the graph, draw a horizontal line at the cumulative frequency value of N/2, where N is the total number of students (35 in this case).

The median weight can be determined by the intersection of this horizontal line with the less than type ogive.

To verify the result using the formula, we can use the cumulative frequency distribution.

Median weight = L + ((N/2 - CF) * w) / f

Where:

L = lower class boundary of the median class

N = total number of students

CF = cumulative frequency of the class before the median class

w = width of the median class

f = frequency of the median class

By following these steps and using the graph and formula, you can determine the median weight from the given data and verify the result.

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Based on the perimeter of the square and the area, it is not possible to draw a square that has an area of 14 units² and a perimeter of 18 units.

A square has the same dimensions for all its sides which means that the area of a square can be found as:
= Side x Side

Similarly, the length of one side can be found as:

= √side

The dimensions of the square using the area is:
= √14

= 3.74 units

Yet, the perimeter of this same square is:

= 18 / 4

= 4.5 units

The units do not match so it is not possible to draw such a square.

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The Boolean expression that is not equivalent to the given expression "num * -1 ≥ 10" is option D: "NOT num * -1 < 10."

What is Boolean expression?

A Boolean expression is an expression or equation that evaluates to true or false. It includes the use of logical operators such as AND, OR, and NOT, as well as comparison operators such as equal to (=), greater than (>), less than (<), and more.

The Boolean expression that is not equivalent to the expression "num * -1 ≥ 10" is option D: "NOT num * -1 < 10."

Let's break down each option and evaluate its equivalence to the given expression:

A. (num < 0) AND (num * -1 = 10)

This expression checks if "num" is negative and if the absolute value of "num" is equal to 10. It does not directly represent the condition "num * -1 ≥ 10," so it is not equivalent.

B. (num < -10) OR (num = -10)

This expression checks if "num" is less than -10 or if "num" is exactly equal to -10. It also does not directly represent the condition "num * -1 ≥ 10," so it is not equivalent.

C. (num * -1 > 10) OR (num = -10)

This expression checks if the negative value of "num" is greater than 10 or if "num" is exactly equal to -10. Although it involves the negative value of "num," it represents the condition "num * -1 > 10" when "num" is positive. Therefore, it is equivalent to the given expression.

D. NOT num * -1 < 10

This expression checks if the negative value of "num" is not less than 10. While it involves the negative value of "num," it does not directly represent the condition "num * -1 ≥ 10." Additionally, the use of "NOT" operator flips the condition, which makes it different from the original expression. Hence, it is not equivalent.

Therefore, the Boolean expression that is not equivalent to the given expression "num * -1 ≥ 10" is option D: "NOT num * -1 < 10."

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The value of the curvature κ(x) = 10 sec^2 x tan x /[1+25 sec^4 x]^3/2.

To find the curvature using the formula κ(x)=|f"(x)|/[1+(f’(x))^2]^3/2 with the function y = 5 tan x, we need to differentiate y twice and substitute the values in the formula.

Given function is y = 5 tan x.

The first derivative of y = 5 tan x is: y' = 5 sec^2 x.

The second derivative of y = 5 tan x is: y'' = 10 sec^2 x tan x.

Substitute the value of f"(x) and f'(x) in the formula of curvature κ(x) = |f"(x)|/[1+(f’(x))^2]^3/2 :κ(x) = |10 sec^2 x tan x|/[1+(5 sec^2 x)^2]^3/2κ(x) = 10 sec^2 x tan x /[1+25 sec^4 x]^3/2

Therefore, the value of the curvature κ(x) = 10 sec^2 x tan x /[1+25 sec^4 x]^3/2.

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Answer:

They are all equal sides so divide 180 by 3

Step-by-step explanation:

The solution of given equation by formula of quadratic Equation is x = -1 OR x = -0.5

A quadratic equation is a polynomial equation of the second degree, meaning it contains one or more terms that involve a variable raised to the power of two. The standard form of a quadratic equation is:

ax² + bx + c = 0where a, b, and c are constants, and x is the variable.

The equation is 2x(x+1.5)=-1.

Expanding the left-hand side, we get:

2x² + 3x + 1 = 0

We can solve for x using the quadratic formula:

x = (-b ± √(b²- 4ac)) / 2a

Where a = 2, b = 3, and c = 1.

x = (-3 ± √(3² - 4(2)(1))) / 4

x = (-3 ± √(1)) / 4

x = (-3 ± 1) / 4

So, x can be either:

x = -1 OR x = -0.5

Rounding to the nearest tenth, we have:

x ≈ -1.0 OR x ≈ -0.5

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Answer:

She colored 30 yellow place value disks and 50 disks are left to color.

Step-by-step explanation:

Let total number of disks be x.

It is given that, she colored 2/6 of the disks red. She colored 1/4 of the disks yellow.

\(\text{Red disks}=\dfrac{2}{6}x\)

\(\text{Yellow disks}=\dfrac{1}{4}x\)

She colored 40 red place value disks.

\(\dfrac{2}{6}x=40\)

\(\dfrac{1}{3}x=40\)

\(x=120\)

It means total number of disks is 120.

\(\text{Yellow disks}=\dfrac{1}{4}x=\dfrac{1}{4}(120)=30\)

So, she colored 30 yellow place value disks.

Remaining disks = Total disks - Red disks - Yellow disks

               \(=120-30-40\)

               \(=50\)

Therefore, 50 disks are left to color.

Answer:

1.

\(C.\\sin(N)=\frac{\sqrt{3} }{2}\)

2.

\(x=82.1\)

3.

x = 18°

Step-by-step explanation:

1. The sine ratio is sin(θ) = opposite/hypotenuse, where θ is the reference angle.  When N is the reference angle, we see that side OP with a measure of 5√3 units is the opposite side and side NP with a measure of 10 units is the hypotenuse.

Thus, we can find plug everything into the sine ratio and simplify:

\(sin(N)=\frac{5\sqrt{3} }{10} \\\\sin(N)=\frac{\sqrt{3} }{2}\)

2. We can use the tangent ratio to solve for x, which is tan (θ) = opposite/adjacent.  If we allow the 75° to be our reference angle, we see that the side measuring x units is the opposite side and the side measuring 22 units is the adjacent side.  Thus, we can plug everything into the ratio and solve for x or the measure of the opposite side:

\(tan(75)=\frac{x}{22}\\ \\22*tan(75)=x\\\\82.10511777=x\\\\82.1=x\)

3. Since we're now solving for an angle, we must using inverse trigonometry.  We can use the inverse of the tangent ratio, whose equation is tan^-1 (opposite/adjacent) = θ.  We see that when the x° is the reference angle, the side measuring 11 units is the opposite and the side measuring 33 units is the adjacent side.  Now we can do the inverse trig to find the measure of x:

\(tan^-^1(\frac{11}{33})=x\\ 18.43494882=x\\18=x\)

Question is asking about the percentage of buyers who paid certain prices for a certain model of new homes, assuming that the prices are normally distributed with a mean of $150,000. We can use the 68-95-99.7 rule, also known as the empirical rule, to find this percentage.

According to the 68-95-99.7 rule, for a normal distribution:
- Approximately 68% of the data falls within one standard deviation of the mean.
- Approximately 95% of the data falls within two standard deviations of the mean.
- Approximately 99.7% of the data falls within three standard deviations of the mean.

To find the percentage of buyers who paid a certain price, we need to determine how many standard deviations away from the mean that price is.

Let's consider some examples:

1. If a buyer paid $150,000, which is exactly the mean, it falls within one standard deviation of the mean. So, approximately 68% of the buyers paid this price.

2. If a buyer paid $162,000, which is one standard deviation above the mean, it falls within two standard deviations of the mean. So, approximately 95% of the buyers paid this price or less.

3. If a buyer paid $174,000, which is two standard deviations above the mean, it falls within three standard deviations of the mean. So, approximately 99.7% of the buyers paid this price or less.

By using the 68-95-99.7 rule, we can determine the approximate percentages of buyers who paid certain prices for the model of new homes.

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Answer:1,978.2

Step-by-step explanation: we will need to find the circumference (the perimeter of a circle). The formula for the circumference is C=2пr

The diameter is 2r, so we have to divide 42 by two. You get 21 for the radius. We will use 3.14 for the pi.

then you plug it in to the formula

C = 2 (3.14) * 21

The answer is 131.88

Then times that with 3

you get 395.64

but since it has been 5 minutes, then you times it with 5

that's 1,978.2

Answer:

630 ft because 3x5=15 then 15x42

normal curve lies to the left of option c. 0.308.

To find the value of z such that 62.1% of the standard normal curve lies to the left of z, we need to use the standard normal distribution table or a statistical calculator.

Using a standard normal distribution table or a calculator, we can find the z-value associated with the cumulative probability of 62.1%. The closest value in the standard normal distribution table to 62.1% is 0.6116.

The z-value associated with a cumulative probability of 0.6116 is approximately 0.308.

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Using the binomial distribution, it is found that the expected score of the game is of 21.

It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.

The expected number of trials until q successes is:

\(E_s(X) = \frac{q}{p}\)

In this problem, a die has a p = 1/6 probability of resulting in a 1, hence the expected number of trials is:

\(E_s(X) = \frac{1}{\frac{1}{6}} = 6\)

In each trial, each outcome from 1 to 6 is equally as likely, hence the expected score of a single trial is given by:

\(E = \frac{1 + 6}{2} = 3.5\)

Then, the expected score of the six trials is:

6 x 3.5 = 21.

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Answer:

yea

Step-by-step explanation:

u need more details

Answer:

x = 30

y = 14

Step-by-step explanation:

If the linear pairs are equal, then we can conclude that the angle on each of the sides is 90

Thus 3x = 90

and x = 90/3 = 30

Also;

9y - 36 = 90

9y = 90 + 36

9y = 126

y = 126/9

y = 14

Answer:

21

Step-by-step explanation:

prim factors: 2, 3, 5, and 11

The sum of the prime factors of the number 330 is 21.

A natural number other than 1 whose only factors are 1 and itself is said to have a prime factor. In actuality, the first few prime numbers are 2, 3, 5, 7, 11, and so forth.

Given:

The number is 330

Factorize the above number,

330 = 1 × 2 × 3 × 5 × 11

Prime factors are = 2, 3, 5, 11

Calculate the sum of the prime factor

2 + 3 + 5 + 11 = 21

Therefore, the sum of the prime factors of the number 330 is 21.

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Answer:

y intercept

Step-by-step explanation:

The [y-intercept] is the point where the line crosses the y-axis. Notice that the y-intercept occurs where x = 0, and the x-intercept occurs where y = 0.

Answer:

Y-intercept

Step-by-step explanation:

That is another name for it

Answer: The lowest possible product would be -6724 given the numbers 82 and -82.

We can find this by setting the first number as x + 164. The other number would have to be simply x since it has to have a 164 difference.

Next we'll multiply the numbers together.

x(x+164)

x^2 + 164x

Now we want to minimize this as much as possible, so we'll find the vertex of this quadratic graph. You can do this by finding the x value as -b/2a, where b is the number attached to x and a is the number attached to x^2

-b/2a = -164/2(1) = -164/2 = -82

So we know one of the values is -82. We can plug that into the equation to find the second.

x + 164

-82 + 164

82

Step-by-step explanation: Hope this helps.

Answer:

c = 13

Step-by-step explanation:

1. Pythagorean theorem states that c^2 = a^2 + b^2

2. In this case, a = 5, b = 12. Therefore, the equation is:

c^2 = 5^2 + 12^2

3. c^2 = 25+144 = 169

4. square root both sides

5. c = 13, c = -13

6. c = 13 since a length cannot be negative.

7. Final answer: C = 13

Answer: c. When a > 0 and b > 1, the function models exponential growth.

You have exponential decay when a > 0 and 0 < b < 1.

Step-by-step explanation:

Answer:

25% of the sweets in the jar are jelly beans.

Answer:

25% of sweets are jelly bean

Step-by-step explanation:

Yes , SAS (Side-Angle-Side) is a second Congruence postulate to prove triangle congruence by showing that two sides and their included angles are congruent.

Side-Angle-Side is the rule used to prove whether a given set of triangles are congruent. The SAS rule states: Triangles are congruent if two sides and an included angle of a triangle are equal to two sides and an included angle of another triangle. An included angle is the angle formed by two given sides.. For example : let's us consider two triangles ∆SQR and ∆TSR ,

In above given figure, sides

RS = RS ( common side)

QS = ST ( S divides QT in two equal parts) and angle between QS and SR equal to angle between SR and ST i.e. ∠QSR = ∠RST = 90° (right angle ) and it is included angle . So, by SAS Congruence rule, both of triangles are congruent. Hence, Δ ABC ≅ Δ PQR.

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