Write an inequality
I can work at most 30 hours per week

Answer:

Step-by-step explanation:

The parametric equations of the line are: x = 1 - t, y = 2, z = 3

Given the line passes through the point (1, 2, 3) and is parallel to the xz-plane and the yz-plane.

To find a set of parametric equations of the line, let's follow the steps below:

Step 1: Find the direction vector of the line.

Since the line is parallel to the xz-plane and the yz-plane, the direction vector must be perpendicular to both planes.

Therefore, the direction vector is the cross product of the normal vectors of both planes.

The normal vectors of the xz-plane and the yz-plane are given by i + 0j + k and 0i + j + k respectively.

Hence, the direction vector is given by:

n = i + 0j + k × 0

i + j + k= -i

Then, a point on the line is (1, 2, 3), and the direction vector is -i.

So, the vector equation of the line can be given by:

r(t) = (1, 2, 3) + t(-1, 0, 0) = (1-t, 2, 3)

The parametric equations of the line are: x = 1 - t, y = 2, z = 3

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2005 is 10 years after 1995.

\(392(10)+5400=\boxed{\$8690}\)

It should be noted that points that have the same x-coordinate and opposite y-coordinates will always be the same distance but on opposite sides of the x-axis.

The same x-coordinate indicates that a point will be at the same distance along the x-axis, and the opposite y-coordinate indicates that a point will be on the opposite side of y = 0.

Therefore, points with the same x-coordinate and opposite y-coordinates will always be at the same distance but on opposite sides of the x-axis.

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Two points have the same x-coordinate but opposite y-coordinates. What does this imply?

Answer:

567 minutes each month.

Step-by-step explanation:

Let x be the number of minutes of talk time used each month.

The cost for talk time beyond 500 minutes is $0.08 * (x - 500)

The cost for email is $27.70 * 0.3 = $8.31

The total monthly cost is $27.70 + $0.08 * (x - 500) + $8.31 = $35.99

The total cost for 9 months is $35.99 * 9 = $323.91

So we can set up the equation:

$27.70 + $0.08 * (x - 500) + $8.31 * 9 = $367.29

Solving for x, we get:

x = 567

So the number of minutes of talk time used each month is 567 minutes.

Answer:

0.402, 0.42, 12, 375

the area of the rhombus=32cm; one diagonal (q)=18meters

p=(2×area)/q

p=(2×32)/18=18

therefore the length of the unknown diagonal is 18.

the unknown diagonal can be calculated using the perimeter of the rhombus which is given as 32cm; one diagonal (p)=18 half of this diagonal

=18÷2=9units

Answer:

31 years

Step-by-step explanation:

65000*(1.07) ^31 is around $529000

however, 65000*(1.07) ^30 is around $491000

so you would need 31 years to gain more than $500,000.

It will take approximately 30 years to reach $500,000 in savings with an investment that earns an average of 7% per year.

To determine the number of years it will take to reach $500,000 in savings with an investment that earns an average of 7% per year, we can use the given investment model equation: y = 65000(1.07)ˣ.

We need to find the value of x, which represents the number of years.

Setting y = $500,000, we can solve for x:

500,000 = 65,000(1.07)ˣ

500,000/65,000 = (1.07)ˣ

100/13 = (1.07)ˣ

To solve for x, we take the logarithm of both sides:

ln 100/13 = ln (1.07)ˣ

ln 100/13 = x ln (1.07)

x = (ln 100/13)/(ln (1.07))

x = 30

Therefore, it will take approximately 30 years to reach $500,000 in savings with an investment that earns an average of 7% per year.

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Answer:

The answer is y = 3x + 3.

Step-by-step explanation:

Hope it helped!

Intellectually gifted people score in the top 1 - 2percent on a standard IQ test.

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

IQ of intellectual gifted people

The general rule is that

People with intellectuals are usually ranked high and the range is usually small

Next, we test the options

A. 10

The top 10% has a high range

B. 5-10

The top 10% omits people in top 5%

C. 5

The top 5% has a high range

D. 1-2

This has a small range and it is the highest

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The range of the number of benefits is 38.8 million to 41.2 million

The given parameters are

Number of students, n = 30 million

Margin of error, E = 3%

The range of the number of benefits is then calculated as

Range = Number of students * (1 ± Margin of Error)

This gives

Range = n * (1 ± E)

So, we have

Range = 40 million * (1 ± 3%)

Expand the expression in the bracket

Range = 40 million * (1 - 3%, 1 + 3%)

Evaluate the sum and the differences

So, we have

Range = 40 million * (0.97, 1.03)

Evaluate the products

So, we have

Range = (38.8 million, 41.2 million)

Hence, the range of the number of benefits is 38.8 million to 41.2 million

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Complete question

The graph shows the results of a survey that asked 4300 students ages 7 to 18 what they thought would be the most important benefit of air travel in the future. There are about 40 million students in the United States. If the margin of error is \pm3\%±3%, what is the range of the number of students ages 7 to 18 who would likely say that "finding new resources for Earth" is the most important benefits

The area of the parallelogram LMNO is equal to 18 square units.

Since Parallelograms are quadrilaterals formed by two pairs of parallel sides, the area of a parallelogram (A), in square units, is the following formula:

A = b · h

Where, b - Length of the base and h - Length of the height.

Now, to determine the area of the parallelogram. First, the lengths for the base and the height of the parallelogram:

b = 6, h = 3

A = 6 · 3

A = 18

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Answer:

2/3

Step-by-step explanation:

Answer:

y=13

Step-by-step explanation:

y=-x+6

x=-7

substitute

y=-(-7)+6

y=13

Answer:

y = 13

Step-by-step explanation:

y = -x + 6 if x = -7

since x = -7, -x = 7:

y = 7 + 6

7 + 6 = 13:

y = 13

hope dis helps ^-^

Answer:

3/10 liters more

Step-by-step explanation:

8/10 - 5/10 = 3/10

Answer:

  A dilation with a scale factor of 2

Step-by-step explanation:

Each image coordinate is double the corresponding pre-image coordinate. That means the figure was dilated by a factor of 2.

Step-by-step explanation:

a:

g(10) = -3(10)+1

g(10) = -29

b:

g(x) = 16

-3x + 1 = 16

-3x = 15

x = -5

CHECK:

g(-5) = -3(-5) + 1

g(-5) = 15 + 1

g(-5) = 16

Hope that helps

For the given equations, the inverse of V(r) is r = ∛(V/π), and the inverse of \(y = e^{(22-3)\)is y = ln(y)/ln(\(e^{(22-3)\)). In the logarithmic scale equation D = 10log₁₀(I) + 120, the expression \(I = 10^{((D - 120)/10)\) represents the intensity as a function of D. When D increases by 20, the intensity increases by a factor of 100 because the intensity is proportional to \(10^{(D/10)\), and an increase of 20 in D corresponds to an increase of \(10^{(20/10) }= 100\) in the intensity.

To find the inverse of V(r) = (1/3)πr³, we need to solve for r in terms of V. Rearranging the equation, we have r³ = 3V/π, and taking the cube root of both sides, we get r = ∛(V/π). This gives us the inverse function of V(r) where r is expressed as a function of V.

For the equation y = \(e^{(22-3)\), the inverse can be found by taking the natural logarithm (ln) of both sides. This gives ln(y) = 22–3. To isolate y, we can divide both sides by ln(\(e^{(22-3)\)), which simplifies to ln(y)/ln(\(e^{(22-3)\)). Therefore, the inverse of y is expressed as y = ln(y)/ln(\(e^{(22-3)\)).

In the equation D = 10log₁₀(I) + 120, we can express I as a function of D by rearranging the equation. Subtracting 120 from both sides gives 10log₁₀(I) = D - 120. Dividing both sides by 10 and using the logarithmic property log₁₀(a^b) = b*log₁₀(a), we get log₁₀(I) = (D - 120)/10. To isolate I, we can rewrite the equation as I = 10^((D - 120)/10). This expression represents the intensity as a function of D.

When D increases by 20, we need to examine the relationship between D and the corresponding increase in intensity. Since intensity is proportional to 10^(D/10), an increase of 20 in D corresponds to an increase of 10^(20/10) = 100 in the intensity. This means that the intensity increases by a factor of 100 when D increases by 20 in the logarithmic scale.

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The solution to the initial value problem is:

y(t) = (-3/4) * e^(-4t+4) + (3/8) * e^(2t+8)

To solve a second-order linear homogeneous differential equation the equation is y′′ 2y′-8y = 0.

Given initial conditions: y(102) = 3 and y′(102) = -12.

To solve this differential equation, we can use the characteristic equation: r^2 + 2r - 8 = 0

Factoring this equation, we get: (r + 4)(r - 2) = 0

So the roots of the characteristic equation are r = -4 and r = 2.

The general solution to the differential equation is:

y(t) = c1 * e^-4t + c2 * e^2t

To find the values of c1 and c2, we can use the initial conditions.

We know that y(102) = 3, so we can substitute t = 2 into the general solution:

3 = c1 * e^-8 + c2 * e^4

We also know that y′(102) = -12, so we can take the derivative of the general solution and substitute t = 2:

y′(t) = -4c1 * e^-4t + 2c2 * e^2t

y′(102) = -4c1 * e^-8 + 2c2 * e^4 = -12

Solving for c1, we get:

c1 = (-3/4) * e^4 + (3/4) * e^-8

Solving for c2, we get:

c2 = (3/8) * e^8 - (3/8) * e^-4

Therefore, the solution to the initial value problem is:

y(t) = (-3/4) * e^(-4t+4) + (3/8) * e^(2t+8)

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Answer:

Go down to -4 and make a 1/1 graph

Step-by-step explanation:

Answer:

7 Quarters

Step-by-step explanation:

Let's assume Zachary has x quarters.The total value of the quarters is 25x cents.

The total value of the dimes is 11*10 = 110 cents.Together, the total value of the coins is 25x + 110 cents. We know that this total value is at least $2.75, which is equal to 275 cents.So we can set up the following inequality:25x + 110 >= 275Solving for x, we get:25x >= 165

x >= 6.6Since x must be a whole number, the smallest possible value for x is 7.Therefore, Zachary must have at least 7 quarters.

Zachary has 11 dimes worth $1.10 and needs to make up $1.65 for a total of $2.75. He would need 7 quarters to do this, giving him a total of 18 coins.

To find out the minimum amount of quarters, one would need to understand that he only has 20 coins and $2.75 minimum. Considering a dime is worth 10 cents and Zachary has 11 dimes, they collectively amount to $1.10.

This leaves $1.65 to reach the minimum of $2.75. We know a quarter is worth 25 cents. To find the number of quarters needed to reach $1.65, we would divide 165 (representing $1.65) by 25 (a quarter's worth), which equals 6.6. However, you can't have 0.6 of a quarter, so we would round up to 7 quarters.

To check this answer, the total count of coins which is dimes and quarters should not exceed 20. Indeed, 7 quarters and 11 dimes equals 18 coins, which is less than or equal to 20. Therefore, the minimum number of quarters Zachary could have is 7.

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A provision that ensures performance fees are not earned until the value of a fund exceeds its previous highest level is referred to as High-water mark

A high-water mark is the highest peak in value that an investment fund or account has reached. This term is often used in the context of fund manager compensation, which is performance-based.

The high-water mark ensures the manager does not get paid large sums for poor performance. If the manager loses money over a period, he must get the fund above the high-water mark before receiving a performance bonus

With a high-water mark, the investor pays a fee that only covers the amount the fund earned between the point of entry and its highest level.

The high-water mark prevents this "double fee" from occurring.

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Answer:

$405.60

Step-by-step explanation:

40x13=520

520x.22= 114.4

520-114.4=405.60

Answer:

80,023,904

Step-by-step explanation:

Just add all the numbers together.

Answer:

"8023904

Step-by-step explanation:

20 000 + 8 000 000=8020000

4+3000=3004

3004+900=3904

3904+ "8023904"

For f (t) = teat for t ≥ 0, the Laplace transform of f (t) is 1 / (s+a)^2.

The Laplace transform of f(t) is defined as:

Lf(t) = ∫[0,∞) f(t) e^(-st) dt

Substituting f(t) into the above equation, we get:

Lf(t) = ∫[0,∞) t e^(-at) e^(-st) dt

We can simplify this by factoring out e^(-at) from the integral, giving:

Lf(t) = ∫[0,∞) t e^(-(a+s)t) dt

We can now integrate by parts, using u = t and dv = e^(-(a+s)t) dt:

Lf(t) = [-t e^(-(a+s)t) / (a+s)] [0,∞) + ∫[0,∞) e^(-(a+s)t) dt/(a+s)

The first term evaluates to 0, since t e^(-(a+s)t) approaches 0 as t approaches infinity. The second term simplifies to:

Lf(t) = [1 / (a+s)] ∫[0,∞) e^(-(a+s)t) dt

This integral is a standard Laplace transform, so we can substitute in its value from the Laplace transform table:

Lf(t) = [1 / (a+s)] * [1 / (a+s)]

Lf(t) = 1 / (s+a)^2

Therefore, the Laplace transform of f(t) is 1 / (s+a)^2.

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Answer:

find the x in my bag ;D

Answer:

x = 5

Step-by-step explanation:

3 = x/ 3 + 4

This is same as

3/1 = x/ 3 + 4

Then cross multiply

1(x + 4) = 3× 3

x + 4 = 9

x = 9 - 4

x = 5

The probability is 0.091125.

To calculate the probability of not flipping a head until the fourth flip, we need to consider the probability of flipping tails in each of the first three flips.

Given that the coin comes up tails 55% of the time, the probability of flipping tails on any given flip is 0.55. The probability of not flipping a head on a single flip is therefore 1 - 0.55 = 0.45.

Since we want to find the probability of not flipping a head until the fourth flip, we need to calculate the probability of flipping tails on each of the first three flips and then multiplying them together.

P(not flipping a head on the first flip) = 0.45

P(not flipping a head on the second flip) = 0.45

P(not flipping a head on the third flip) = 0.45

To find the probability of all three events occurring, we multiply the individual probabilities together:

P(not flipping a head until the fourth flip) = 0.45 * 0.45 * 0.45 = 0.091125

Therefore, the probability of not flipping a head until the fourth flip is approximately 0.091125, or 9.11%.

Correct Question :

A coin is unbalanced such that it comes up tails 55% of the time. What is the probability that you don't flip a head until the fourth flip?

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Answer:

\(\huge\boxed{\bf\:2\left(3x-1\right)\left(3x+2\right) }\)

Step-by-step explanation:

\(18x^{2} + 6x - 4\\\\Factor \: out \: the \: common \: factor = 2\\\\= 2\left(9x^{2}+3x-2\right) \\\\Split\:the\:quadraric\:equation\:inside\:the\:parentheses \\\:using\:the\:splitting-the-middle-term \:method.\\\\= 2\left(9x^{2}-3x\right)+\left(6x-2\right) \\= 2 (3x\left(3x-1\right)+2\left(3x-1\right) )\\= \boxed{\bf\:2 \left(3x-1\right)\left(3x+2\right) }\)

\(\rule{150pt}{2pt}\)

Answer:

2(3x - 1)(3x + 2)

Step-by-step explanation:

18x² + 6x - 4 ← factor out 2 from each term

= 2(9x² + 3x - 2) ← factor the quadratic

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 9 × - 2 = - 18 and sum = + 3

the factors are - 3 and + 6

use these factors to split the x- term

9x² - 3x + 6x - 2 ( factor first/second and third/fourth terms )

= 3x(3x - 1) + 2(3x - 1) ← factor out (3x - 1) from each term

= (3x - 1)(3x + 2) ← in factored form

then

18x² + 6x - 4

= 2(3x - 1)(3x + 2)