A hot air balloon is 1550 feet off of the ground and it’s altitude is slowly changing at a constant rate of - 7 1/2 feet per second. How many seconds, *s*, will it take for the balloon to drop to below 465 feet?

Answer:

(3,1)

Step-by-step explanation:

When a point is reflected across the y axis, the sign of its x coordinate flips. Since point A is at (-3,-5), when it is reflected across the y axis its new position will be (3,-5). Now, point A is 3 units from the line y=-2, meaning that when it is reflected across it will be 3 units away from the other direction. (-2+(3))=1, meaning that the final coordinates of point A are (3,1). Hope this helps!

Answer:

The hour marks on a clock face are evenly spaced, 30° apart. To find the angle a line from the four o'clock mark to the twelve o'clock mark makes with a horizontal line, we need to count the number of hour marks between the two positions and multiply by 30°.

Starting from the four o'clock mark and moving clockwise to the twelve o'clock mark, we count 8 hour marks, including the one at the twelve o'clock mark. Multiplying 8 by 30°, we get:

8 x 30° = 240°

Therefore, the angle between the line from the four o'clock mark to the twelve o'clock mark and a horizontal line is 240°.

Answer:

Step-by-step explanation:c

The solution to the differential equation is y = ∫cos(x)e^xdx / e^x.

A. To compute the integrating factor for a given differential equation, we use the following steps:

1. Write the given differential equation in the form of y' + P(x)y = Q(x).
2. Identify the coefficient of y as P(x) and the right-hand side of the equation as Q(x).
3. Compute the integrating factor (IF) using the formula IF = e^(∫P(x)dx).

B. To solve the differential equation by hand using the integrating factor, follow these steps:

1. Compute the integrating factor (IF) using the formula IF = e^(∫P(x)dx) from step A.
2. Multiply both sides of the differential equation by the integrating factor.
3. Simplify and rearrange the equation to get it in the form of (IF * y)' = IF * Q(x).
4. Integrate both sides of the equation to solve for y.

C. To use technology to find the solution to the differential equation and compare it with the solution found by hand, follow these steps:

1. Use software or a calculator with an integral function to compute the integrating factor and solve the differential equation.
2. Compare the solution obtained using technology with the one found by hand to check for consistency and accuracy.

D. To draw the slope field for the differential equation and plot the solution on it using technology, follow these steps:

1. Use software or an online tool capable of drawing slope fields to graphically represent the differential equation.
2. Plot the solution obtained in step C on the slope field to visualize how it fits with the slope vectors.

Now let's apply these steps to the given differential equations:

1. For the equation y + 3y = 2 with initial condition

y(0) = 4:
A. The coefficient of y is 1, so P(x) = 1 and

Q(x) = 2.

The integrating factor is IF = e^(∫P(x)dx)

= e^(∫1dx)

= e^x.
B. Multiply both sides of the equation by e^x:

e^xy + 3e^xy = 2e^x.
  Simplify and rearrange: (e^x * y)' = 2e^x.
  Integrate both sides: e^x * y = 2e^x + C.
  Solve for y: y = 2 + Ce^(-x).
  Using the initial condition y(0) = 4, we find

C = 2.
  Conclusion: The solution to the differential equation is y = 2 + 2e^(-x).

2. For the equation y + y = ?

with initial condition y(0) = 1:
A. The coefficient of y is 1, so P(x) = 1 and

Q(x) = ?.

The integrating factor is IF = e^(∫P(x)dx)

= e^(∫1dx)

= e^x.
B. Multiply both sides of the equation by e^x: e^xy + e^xy = ?e^x.
  Simplify and rearrange: (e^x * y)' = ?e^x.
  Integrate both sides: e^x * y = ?e^x + C.
  Solve for y: y = ? + Ce^(-x).
  Using the initial condition y(0) = 1,

we find C = 1 - ?.
  Conclusion: The solution to the differential equation is y = ? + (1 - ?)e^(-x).

3. For the equation y + y = cos(x):
A. The coefficient of y is 1, so P(x) = 1 and

Q(x) = cos(x).

The integrating factor is IF = e^(∫P(x)dx)

= e^(∫1dx)

= e^x.
B. Multiply both sides of the equation by e^x: e^xy + e^xy = cos(x)e^x.
  Simplify and rearrange: (e^x * y)' = cos(x)e^x.
  Integrate both sides: e^x * y = ∫cos(x)e^xdx.
  Solve for y: y = ∫cos(x)e^xdx / e^x.
  Use technology or a table of integrals to evaluate the integral.
  Conclusion: The solution to the differential equation is y = ∫cos(x)e^xdx / e^x.

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The expected value to pick a package is $.1125.

To find the expected value, you need to multiply the value of each package by the probability of selecting it and then add up all of these values.

The probability of selecting one of the $.70 packages is 20/40 = 1/2, since there are a total of 40 packages and 20 of them are worth $.70. The expected value of selecting one of these packages is $.70 * (1/2) = $.35

The probability of selecting one of the $.60 packages is 15/40 = 3/8, since there are a total of 40 packages and 15 of them are worth $.60. The expected value of selecting one of these packages is $.60 * (3/8) = $.22.5

The probability of selecting one of the $.30 packages is 5/40 = 1/8, since there are a total of 40 packages and 5 of them are worth $.30. The expected value of selecting one of these packages is $.30 * (1/8) = $.0375

The expected value of selecting one package at random is therefore $.35 + $.22.5 + $.0375 = $.61.25. However, you have to pay $.50 to pick a package, so the net expected value is $.61.25 - $.50 = $.1125.

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Picking a bundle is anticipated to be worth $.1125.

You must multiply the value of each package by the likelihood that it will be chosen before adding up all of these values to arrive at the expected value.

Given that there are a total of 40 packages and 20 of them are valued at $.70 each, the likelihood of choosing one of the $.70 packages is 20/40 = 1/2. Selecting one of these packages has an expected value of $.70 * (1/2) = $.35.

Given that there are 40 products in total and 15 of them are worth $.60 each, the probability of choosing one of the $.60 packages is 15/40 = 3/8. Choosing one of these packages will result in a value of $.60 * (3/8) = $.22.5.

There are a total of 40 packets, and 5 of them are worth $.30, hence the likelihood of choosing one of the $.30 packages is 5/40 = 1/8. By choosing one of these packages, the predicted value is $.30 * (1/8) = $.0375.

Therefore, $.35 + $.22.5 + $.0375 = $.61.25 is the expected value of choosing one package at random. The net expected value is $.61.25 - $.50 = $.1125 due to the fact that you must pay $.50 to choose a bundle.

If angle b is five times the size of angle c, the equation can be used to find the measure of angle is 5x+x=90°.

because complementary angles complete each other to 90 degrees.

These angles b and c add up to 90° because they are complementary.

Let's say angle C is named x.

angle b is five times the size of angle c, this can be written: 5x

Complementary angles add up 90°, so angle B add angle C equal 90°

the equation to find the measure of angle C is 5x+x = 90°.

Types of angles are one of the materials in mathematics that you always encounter at every level of education. Learning about angles is very important, because angles are always present in everyday life and need to be identified.

An angle is a shape formed by two rays having an endpoint at one point. In angles, terms such as the leg of the angle, vertex, and area of the angle are also found.

The legs of the angle are the lines forming the angle. The vertex is the point where the two legs of the angle intersect, and the area of the angle is the area bounded by the two legs of the angle.

Your question is incomplete but most probably your full question was:

Only Interaction Angle B and angle C are complementary: If angle B is five times the size of angle C which equation can be used to find the measure of angle C?

5x+x=180

5x = 180

5x+x=9

5x = 90

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Velocity vector in terms of and acceleration vector in terms of and can be found from the given information: r = a(3 - sinθ), and dθ/dt = 5Velocity

vector can be found by differentiating the position vector r with respect to time t:

Velocity vector, v = dr/dt Here, r = a(3 - sinθ) and θ is a function of time t.

Using product rule of differentiation:

dr/dt = a(-cosθ)(dθ/dt) + a(3 - sinθ)(dθ/dt)dr/dt = a[dθ/dt (3 - sinθ) - (cosθ)dθ/dt]

Velocity vector is: v = a[dθ/dt (3 - sinθ) - (cosθ)dθ/dt]

Acceleration vector can be found by differentiating.

the velocity vector with respect to time t: Acceleration vector, a = dv/dt Using the product rule of differentiation:

dv/dt = a[d²θ/dt² (3 - sinθ) - 2(dθ/dt)cosθ]

Acceleration vector is:

a = a[d²θ/dt² (3 - sinθ) - 2(dθ/dt)cosθ]

Therefore, the velocity vector in terms of θ and a is:

v = a[dθ/dt (3 - sinθ) - (cosθ)dθ/dt]

The acceleration vector in terms of θ and a is:

a = a[d²θ/dt² (3 - sinθ) - 2(dθ/dt)cosθ]

therefore, r = a(3 - sinθ), and dθ/dt = 5Velocity

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Answer:

15/34

Step-by-step explanation:

add 15+19=34

then make it a fraction

Answer:

7.) (m+4)(m-16)

8.) Area= 3x^3-5x^2+7x+3

Step-by-step explanation:

7.) m^2-12m-64

=(m^2+4m)+(-16m-64)

=m(m+4)-16(m+4)

=(m+4)(m-16)

8.) Area = L(W)

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

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

=3x^3+x^2-6x^2-2x+9x+3

=3x^3-5x^2-2x+9x+3

=3x^3-5x^2+7x+3

Answer:

18.3

Step-by-step explanation:

384.3 divided by 21

Answer:

Step-by-step explanation:

Sum of interior angles of any triangle is 180°:

Answer:

150\(\geq\) 2.50x + 10

Step-by-step explanation:

It's 10 dollars for shipping. Then it is 2.50 times the amount of paper she chooses to by but it cannot be more 150.

Answer:

(7n-4n) ×6 = 42-24n

Step-by-step explanation:

Happy to help

Answer:

42-24 the other guy is correct to

Step-by-step explanation:

hope this helped luis!

Answer:

\(b^{4}\)

Step-by-step explanation:

Step 1:

\(\frac{b^{10} }{b^{6} }\)              Equation

Step 2:

\(b^{10-6}\)         Subtract

Answer:

\(b^{4}\)    

Hope This Helps :)

Answer:

huh looks simple....it's unreactive because it's already stable

Step-by-step explanation:

it has eight electrons in the outer most energy level making it stable so it doesn't need to loose or gain electrons

The vertices of the parallelogram are (0,0), (5,2), (6,4), and (11,6). We can use the distance formula to find the lengths of the sides of the parallelogram:

The distance between (0,0) and (5,2) is √(5^2 + 2^2) = √29.

The distance between (5,2) and (6,4) is √(1^2 + 2^2) = √5.

The distance between (6,4) and (11,6) is √(5^2 + 2^2) = √29.

The distance between (11,6) and (0,0) is √(11^2 + 6^2) = √157.

Since opposite sides of a parallelogram are congruent, the lengths of the opposite sides are equal. So the area of the parallelogram is the product of the length of one pair of opposite sides and the height, which is the perpendicular distance between the parallel sides. We can find the height by drawing a line perpendicular to one of the parallel sides and finding its length using the Pythagorean theorem. For example, we can draw a line from (0,0) perpendicular to the side connecting (5,2) and (6,4):

The slope of the side connecting (5,2) and (6,4) is (4-2)/(6-5) = 2.

The slope of a line perpendicular to this side is -1/2.

The equation of the line perpendicular to this side passing through (0,0) is y = (-1/2)x.

The x-coordinate of the point where this line intersects the side connecting (5,2) and (6,4) can be found by setting y = 2 in the equation y = (-1/2)x. Solving for x, we get x = -4.

The length of the line from (0,0) to the point (-4,2) is √((-4-0)^2 + (2-0)^2) = 2√5.

So the area of the parallelogram is (length of one pair of opposite sides) x (height) = √29 x 2√5 = 2√145.

Therefore, the area of the parallelogram is 2√145 square units.

The vertices of the parallelogram are (0,0), (-2,4), (6,-5), and (4,-1). We can use the distance formula to find the lengths of the sides of the parallelogram:

The distance between (0,0) and (-2,4) is √((-2-0)^2 + (4-0)^2) = √20.

The distance between (-2,4) and (6,-5) is √((6-(-2))^2 + (-5-4)^2) = √185.

The distance between (6,-5) and (4,-1) is √((4-6)^2 + (-1-(-5))^2) = √20.

The distance between (4,-1) and (0,0) is √((0-4)^2 + (-1-0)^2) = 2√17.

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Answer:

12

Step-by-step explanation:

75 * 0.16 = 12

Answer:

12 cars

Step-by-step explanation:

Answer:

6.125

Step-by-step explanation:

49 divided by 8

49÷8=6.125

Answer:

6

Step-by-step explanation:

49 / 8 = 6.125

Rounding = 6

Explanation:

For every problem, plug in the number where the variable is.

For example:

Evaluate the following expression by substituting 8 for x.

x + 9

You would take the x and turn it into 8, then you would do 8 + 9.

Answer:

1)  

a= 17

b= 7

c= 56

d= 4

e= 29

f= 10

g= 18

h= 4

2)

a= -1

b= 2/3

c= -4/3

d= -5/3

e= -2

f= -8/3

g= -14/9

h= -17/9

3)

a= 1/2

b= 5/6

c= 1/6

d= -1/3

e= 1/3

f= 5/12

g= 7/18

h= 0.75

Step-by-step explanation:

Answer:

all real numbers

Step-by-step explanation:

f(x)=(1/3)^x

The domain is the values that x can take

X can take any value

Answer:

all real numbers

Step-by-step explanation:

Answer:

y = x-2

Step-by-step explanation:

find the slope. 0,-2 and 2,0

0- -2 / 2-0 = 1

y-0 = 1(x-2)

y = x - 2

Answer:

70

Step-by-step explanation:

When we have a normal model for the sampling distribution, we cannot say that a sample mean or sample proportion is approximately 2 standard errors (ses) away from the population mean or the true proportion.

Instead, we can say that 95% of the sample proportions fall within two standard errors of the population proportion. Similar to this, the percentage of sample proportions decreases as the standard error distance decreases and increases as the standard error distance increases.

Therefore, the standard error distance will be greater than 2 standard errors (ses) if 99% of the sample proportions are within a given standard error distance of the population proportion.

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The end behaviour of the graph of the Polynomial as required to be determined in the task content is; As x tends negative infinity, y tends to negative infinity and As x tend to infinity, y tends to infinity.

By observation of the polynomial equation; the degree is 3 which is odd and the leading coefficient is; positive.

Therefore, it follows that the end behaviour is; As x tends negative infinity, y tends to negative infinity and As x tend to infinity, y tends to infinity.

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The end behavior of the polynomial y = 2x³ + x² - 45 is:

As x approaches negative infinity, y approaches negative infinity. As x approaches positive infinity, y approaches positive infinity.

The degree of the polynomial and the sign of the leading coefficient  describe the end behavior.

Below are rules for determining the end behavior of a function:

a. Even and Positive: As x approaches negative infinity, y approaches positive infinity. Also, as x approaches positive infinity, y approaches positive infinity

b. Even and Negative: As x approaches negative infinity, y approaches negative infinity. Also, as x approaches positive infinity, y approaches negative infinity

c. Odd and Positive: As x approaches negative infinity, y approaches negative infinity. Also, as x approaches positive infinity, y approaches positive infinity.

d. Odd and Negative: As x approaches negative infinity, y approaches positive infinity. Also, as x approaches positive infinity, y approaches negative infinity.

Given: y = 2x³ + x² – 45

The degree (largest exponent) of the polynomial = 3 (odd)

Leading coefficient (coefficient of largest exponent) = 2 (positive)

Since the degree and leading coefficient are positive and negative respectively.

Therefore, the end behavior of the graph of the polynomial is:

As x approaches negative infinity, y approaches negative infinity. Also, as x approaches positive infinity, y approaches positive infinity.

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Answer:

It will be 40

Step-by-step explanation:

Hope this helped have an amazing day!

The given statement is,

→ if u have 10 and add 20 and add 10.

In mathematical expression,

→ (10 + 20) + 10

→ 30 + 10

→ 40 is the answer.

The probability that the sample mean will be between $10 and $10.2 is approximately 0.3144 or 31.44%.

To calculate the probability that the sample mean will be between $10 and $10.2, we need to use the properties of the sampling distribution of the sample mean. Under certain assumptions (e.g., a large sample size or normality of the population distribution), the sampling distribution of the sample mean follows a normal distribution.

Given that the population mean is $10.2 and the population standard deviation is $1.4, we can use the Central Limit Theorem to approximate the distribution of the sample mean. The Central Limit Theorem states that for a sufficiently large sample size, the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution.

In this case, the sample size is 39, which is considered reasonably large. Therefore, we can approximate the distribution of the sample mean as a normal distribution with a mean of $10.2 and a standard deviation of σ/√n, where σ is the population standard deviation and n is the sample size.

The standard deviation of the sample mean is calculated as follows:

Standard deviation of the sample mean = σ/√n = 1.4/√39 ≈ 0.224

To find the probability that the sample mean will be between $10 and $10.2, we need to calculate the z-scores for both values and then use the standard normal distribution (z-distribution) to find the probability.

The z-score for $10 is calculated as follows:

z1 = (10 - 10.2) / (0.224) ≈ -0.893

The z-score for $10.2 is calculated as follows:

z2 = (10.2 - 10.2) / (0.224) = 0

Now, we can use a standard normal distribution table, calculator, or software to find the probabilities associated with these z-scores.

The probability that the sample mean will be between $10 and $10.2 is equal to the probability of having a z-score between -0.893 and 0.

Using a standard normal distribution table or calculator, the probability can be calculated as follows:

P(-0.893 ≤ Z ≤ 0) ≈ P(Z ≤ 0) - P(Z ≤ -0.893)

Looking up the values in a standard normal distribution table or using a calculator, we find:

P(Z ≤ 0) ≈ 0.5 (probability of being less than or equal to the mean)
P(Z ≤ -0.893) ≈ 0.1856

Therefore,

P(-0.893 ≤ Z ≤ 0) ≈ 0.5 - 0.1856 ≈ 0.3144

Hence, the probability that the sample mean will be between $10 and $10.2 is approximately 0.3144 or 31.44%.

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Answer:

If the pattern is to continue, the next value would be a decrease of 7 from the previous value because 20-13=7. Therefore, the value for this week would be:

13 - 7 = 6

So, if you were to continue the pattern, you would have bought 6 cupcakes this week.

The molar quantity by the Avocado number:

\(\frac{1*10^3g}{3.95*10^{22} g} = 2.53*10^{24}\)  = 2.6 uranium atoms

The Avogadro's number, Nₐ uranium atoms have a mass of 238.03g.

We now calculate of the molar mass of uranium as 238.03⋅g⋅ mol⁻¹.

And thus moles of uranium

= 1000⋅ g / 238.03⋅g⋅mol⁻¹

= 4.20⋅mol.

And then multiply this molar quantity by the Avocado number:

4.20⋅mol × 6.022× 10²³⋅mol⁻¹

canceling out mol and mol⁻¹, we get:

= 4.20 × 6.022× 10²³

=  2.52924 ≈ 2.6 uranium atom.

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Answer: y = -1/2x -4

Step-by-step explanation:

To solve for y, subtract 2x on both sides

2x-2x + 4y = -16 - 2x

Simplify

4y = -16 - 2x

Divide by 4 on both sides to get y by itself

4y/4 = -16 - 2x/4

Simplify

y = -4 - 1/2x

Switch the right-side terms to write them in slope-intercept form

y = -1/2x -4