Determine an expression for dy/d x = y' if [1+y]²-x+y=4 10.
The integration method you must use here is
Logarithmic q_23 = 1 Implicit q_23 = 2 Product rule q_23 = 3

The simplified expression for y' = 1/q_24y + q_25

Answer:

your answer is 5.............

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The Correct choice is :

Solution is in attachment ~

we have that

Part 1

Remember that breakpoint is when the revenue (R) is equal to the cost (C)

so

C=7x+30,000

R=10x

equate both equations

10x=7x+30,000

solve for x

10x-7x=30,000

3x=30,000

x=10,000 units

Part 2

net profit of $ 21,000

so

R-C=21,000

10x-(7x+30,000)=21,000

10x-7x-30,000=21,000

3x=21,000+30,000

3x=51,000

Part 3

net profit equal to $ 60,000

so

R-C=60,000

10x-(7x+30,000)=60,000

10x-7x-30,000=60,000

3x=60,000+30,000

3x=90,000

The length of the shadow casted by the building is 31.06 meters. The solution has been obtained by using trigonometry.

What is trigonometry?

Trigonometry is a discipline of mathematics that deals with the study of sides, angles, and relationships in triangles.

We are given that at a certain time of day, the angle of elevation of the sun is 44 degrees. The height of the building is given as 30 meters.

Using trigonometry,

We know that tan theta = opposite side/ adjacent side

So,

⇒tan 44° = 30/x

⇒0.9657 = 30/x

⇒x = 31.06

Hence, the length of the shadow casted by the building is 31.06 meters.

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Answer:

\(x = \frac{-15}{2}\)

Step-by-step explanation:

to answer these types of questions, we want to isolate the variable to one side of the equation

\(4x + 9 = 2x - 6\\4x - 2x = -6 - 9\\2x = -15\\x = \frac{-15}{2}\)

Answer:

x = -7.5 :)

Step-by-step explanation:

4x + 9 = 2x - 6

-2x         -2x

----------------------

  2x + 9 =  -6

        -9      -9

-----------------------

     2x = -15

     ---     ----

     2       2

x = -7.5  

Answer:

Step-by-step explanation:

17. Domain is all real numbers because the equation has a y-value for all x-values as far as we can see with the information given.

18. Range is 3< y <8, because the equation only has values for x where y is between those numbers.

19. Range is 3> y >-∞ (negative infinity) because the parabola's vertex has a y-coordinate of 3 and the parabola goes on forever in the negative direction (as seen by the arrows).

20. Domain is -∞ < x < 4 because the parabola's vertex has an x-coordinate of 4 and goes on forever in the negative x direction.

Hope this helps! :)

Given:

Total number of boyfriends = 72

Number of boyfriends who jump off the window  = 9

To find:

The remaining number of boyfriends.

Solution:

We need to subtract the number of boyfriend who jump off the window from the total number of boyfriends to get the remaining number of boyfriends.

\(\text{Remaining boyfriends}=72-9\)

\(\text{Remaining boyfriends}=63\)

Therefore, the number of remining boyfriends is 63.

Answer:

About 79 million

Step-by-step explanation:

Answer:

a lot

89 x 67= 292829

So hence that's the answer

Hope this helps! :)

Let's denote the length of the shorter part as x.

According to the given information, the shorter part is one quarter of the length of the rod. Since the rod is 200 cm long, the length of the shorter part can be expressed as:

x = (1/4) * 200

x = 50 cm

Now, to express the shorter part as a percentage of the longer part, we need to calculate the ratio of the shorter part (50 cm) to the longer part (200 cm) and multiply it by 100 to convert it into a percentage:

Percentage = (Shorter Part / Longer Part) * 100

= (50 / 200) * 100

= 0.25 * 100

= 25%

Therefore, the shorter part is 25% of the longer part.

False. When linearizing exponential data using logarithms, the data will become linear and the r²-value of the regression line will likely increase.

The logarithm transformation of the data will help to better fit the data with a linear regression line, since linear regression is used to fit linear data. Therefore, the use of logarithms can actually increase the r²-value of the regression line, not decrease it.

It is important to note that the r²-value does not necessarily indicate the accuracy of the model, but rather how well the model fits the data.

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Josh should mix 1.2 gallons of dark pink paint and 1.8 gallons of light pink paint to achieve the desired medium pink color.

To find out how much of each leftover paint Josh should mix to achieve a medium pink color (50% red), we can set up a system of equations based on the percentages of red in the paints.

Let's assume that Josh needs x gallons of dark pink paint and y gallons of light pink paint to achieve the desired color.

The total amount of paint needed is 3 gallons, so we have the equation:

x + y = 3

The percentage of red in the dark pink paint is 80%, which means 80% of x gallons is red. Similarly, the percentage of red in the light pink paint is 30%, which means 30% of y gallons is red. Since Josh wants a 50% red mixture, we have the equation:

(80/100)x + (30/100)y = (50/100)(x + y)

Simplifying this equation, we get:

0.8x + 0.3y = 0.5(x + y)

Now, we can solve this system of equations to find the values of x and y.

Let's multiply both sides of the first equation by 0.3 to eliminate decimals:

0.3x + 0.3y = 0.3(3)

0.3x + 0.3y = 0.9

Now we can subtract the second equation from this equation:

(0.3x + 0.3y) - (0.8x + 0.3y) = 0.9 - 0.5(x + y)

-0.5x = 0.9 - 0.5x - 0.5y

Simplifying further, we have:

-0.5x = 0.9 - 0.5x - 0.5y

Now, rearrange the equation to isolate y:

0.5x - 0.5y = 0.9 - 0.5x

Next, divide through by -0.5:

x - y = -1.8 + x

Canceling out the x terms, we get:

-y = -1.8

Finally, solve for y:

y = 1.8

Substitute this value of y back into the first equation to solve for x:

x + 1.8 = 3

x = 3 - 1.8

x = 1.2

Therefore, Josh should mix 1.2 gallons of dark pink paint and 1.8 gallons of light pink paint to achieve the desired medium pink color.

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Answer:

B

Step-by-step explanation:

x*3/7=42

divide 42 by 3/7: 42*7/3=98

x=98

Answer:

B) 98

Step-by-step explanation:

3/7 = 42/x

3x = 294

x = 98

Answer:

DC like the DC superheroes

Step-by-step explanation:

We need to sum at least one term to ensure that the remainder is less than\(10^{-6\).

We know that the alternating series test states that if a series is alternating and its terms are decreasing in absolute value, then the series converges. We can see that the series ∑[infinity]k=1(−1)kk4 is an alternating series because the signs of the terms alternate, and the terms decrease in absolute value because \(k_4\) > (k+1)4 for all k.

Now, we can use the remainder formula for an alternating series, which tells us that the remainder Rn of an alternating series ∑[infinity]k=1(−1)ka_k after n terms is less than or equal to the absolute value of the next term \(a_{n+1\):

|Rn| ≤ |\(a_{n+1\)|

So, we want to find the smallest value of n such that |a_n+1| < 10^(-6). We have:

\(a_k = (-1)^k \times k^4\)

\(a_{n+1} = (-1)^{(n+1)} \times(n+1)^4\)

We want to find n such that:

\(|(n+1)^4| < 10^{(-6)\)

Taking the fourth root of both sides, we get:

\(|n+1| < (10^(-6))^(1/4)\)

|n+1| < 0.1

n+1 < 0.1 or -(n+1) < 0.1

n < 0.1 - 1 or n > -0.1 - 1

n < -0.9 or n > -1.1

Since n must be a positive integer, the smallest possible value of n that satisfies this inequality is n = 1. Therefore, we need to sum at least one term to ensure that the remainder is less than \(10^{(-6)\).

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The probability of completing the project in 27 months using PERT is approximately 0.8413 (or 84.13%). PERT assumes a normal distribution with a mean of 24 months and a variance of 9.

To calculate the probability that the project will be completed in 27 months using PERT (Program Evaluation and Review Technique), we need to use the concept of normal distribution.

PERT assumes that the completion time of a project follows a normal distribution with a mean (expected completion time) and variance. In this case, the expected completion time is 24 months and the variance is 9.

To find the probability of completing the project in 27 months, we can use the standard normal distribution table or a statistical calculator to find the area under the normal curve.

First, we need to calculate the standard deviation (σ) using the variance (σ^2):

σ = \(\sqrt{\text{variance}} = \sqrt{9} = 3\)

Next, we can calculate the z-score, which represents the number of standard deviations away from the mean:

\(z = \frac{x - \mu}{\sigma}\)

where x is the desired completion time and μ is the mean.

For completing the project in 27 months:

\(z = \frac{27 - 24}{3} = 1\)

Using the standard normal distribution table or a statistical calculator, we can find the area to the left of the z-score of 1. This represents the probability that the project will be completed in 27 months or earlier.

The probability that the project will be completed in 27 months is approximately 0.8413 (or 84.13% when expressed as a percentage).

Therefore, the probability that the project will be completed in 27 months is approximately 0.8413.

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Therefore , the solution of the given problem of unitary method comes out to be music video cost =  $1.99.

After establishing the size of a little slice, multiply the quantity by two to complete a task utilizing unitary technique. Simply expression the unit technique serves to isolate a programmed thing from a certain set or sets of sets. For example, the price of 40 pens is 400 pounds ($1.01) or Rs. It's possible that one country will have total control over the method employed to do this. Almost every living creature has a distinctive quality. It can equally integrate and reciprocate (mathematics, algebra).

Here,

Given :

2  music videos , a TV series and a movie worth $42.95

Let x be the cost of  movie

From given information,

we can say

Cost of TV series  = 2x

So ,

equation comes out to be x = 12.99 for movie

So TV series cost = 2 * 12.99 = 25.98

So ,

=> 2 music videos + 25.98 + 12.99 = 42.95

=> 2 music videos + 38.97 = 42.95

=>  2 music videos = 42.95 - 38.97

=> music video cost = 3.98 /2

=> music video cost =  $1.99

Therefore , the solution of the given problem of unitary method comes out to be music video cost =  $1.99.

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The student can only work a whole number of hours, the student should work 8 hours at the doctor's office each week. The student should then tutor for 12 hours each week in order to earn at least $375.

Let x represent the number of hours the student works at the doctor's office each week, and let y represent the number of hours the student tutors each week. The system of inequalities that represents the given constraints can be written as:

x + y ≤ 20

15x + 25y ≥ 375

To maximize the number of hours the student works at the doctor's office while still earning at least $375, we must solve this system of inequalities. To do this, we can subtract 15x from both sides of the second inequality to isolate y:

25y ≥ 375 - 15x

We can then divide both sides of this equation by 25 to solve for y:

y ≥ (375 - 15x) / 25

We can then substitute this expression for y in the first inequality to solve for x:

x + (375 - 15x) / 25 ≤ 20

We can then rearrange and solve this equation for x:

15x + 375 ≤ 500

15x ≤ 125

x ≤ 8.33.

Since the student can only work a whole number of hours, the student should work 8 hours at the doctor's office each week. The student should then tutor for 12 hours each week in order to earn at least $375.

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All logic connectives can be expressed in terms of ¬ and ∨.

The logic connectives ¬ (negation) and ∨ (disjunction) are sufficient to express all other logical connectives. Here is how each connective can be expressed:

Conjunction (∧): The conjunction of two propositions, p and q, can be expressed as ¬(p ∨ q), which means "not (p or q)." This is equivalent to saying "neither p nor q is true."

Implication (→): The implication of propositions p and q can be expressed as ¬p ∨ q, which means "not p or q." This states that if p is false or q is true, then the implication is true.

Biconditional (↔): The biconditional of propositions p and q can be expressed as (p ∧ q) ∨ (¬p ∧ ¬q), which means "either both p and q are true or both p and q are false." This captures the idea that p and q have the same truth value.

Exclusive OR (⊕): The exclusive OR of propositions p and q can be expressed as (p ∨ q) ∧ ¬(p ∧ q), which means "either p or q is true, but not both." This ensures that the propositions have different truth values.

By combining negation and disjunction, we can express all logic connectives. This shows the expressive power and versatility of these two fundamental connectives in logic.

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Answer:

A. start absolute value negative 4 commas negative 1 end absolute value

Step-by-step explanation:

Expression could be used to find the distance between point A and point B.

The chain rule is a formula used in calculus to find the derivative of a composition of functions. It is an important tool for solving problems in many areas of mathematics and science.

The chain rule formula can be stated as follows:

If y = f(g(x)), then the derivative of y with respect to x is given by:

dy/dx = (df/dg) * (dg/dx)

In other words, the derivative of y with respect to x is equal to the derivative of f with respect to g, multiplied by the derivative of g with respect to x.

Here, f and g are functions of x, and y is a function of g. The chain rule formula tells us how to find the derivative of y with respect to x, by taking into account the effect of both f and g on the function y.

The chain rule can be extended to more complex compositions of functions, by applying the formula repeatedly. For example, if y = f(g(h(x))), then the chain rule can be applied twice, as follows:

dy/dx = (df/dg) * (dg/dh) * (dh/dx)

This formula tells us how to find the derivative of y with respect to x, by taking into account the effects of all three functions f, g, and h on the function y.

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The curve given by the parametric equations x = 4t/7 and y = 1 represents a line in the Cartesian coordinate system. The slope of the line is 4/7, and the y-coordinate is always equal to 1. This line passes through the point (0, 1) and has a positive slope.

The parametric equations x = 4t/7 and y = 1 describe the relationship between the parameter t and the coordinates (x, y) of points on the curve. In this case, the x-coordinate is determined by the expression 4t/7, while the y-coordinate is always equal to 1.

The equation x = 4t/7 represents a line in the Cartesian coordinate system. The slope of this line is 4/7, indicating that for every increase of 7 units in the x-coordinate, the corresponding increase in the y-coordinate is 4 units. This means that the line has a positive slope, slanting upward as we move from left to right.

The y-coordinate being constantly equal to 1 means that every point on the line has the same y-value, regardless of the value of t. This implies that the line is parallel to the x-axis and intersects the y-axis at the point (0, 1).

In conclusion, the parametric equations x = 4t/7 and y = 1 describe a line with a positive slope of 4/7. This line is parallel to the x-axis and passes through the point (0, 1).

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Answer

27^0.5+0.25 or 3^0.5+0.25

3^2t + 1/4 expression is equivalent to 81^0.5t+0.25​.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given an expression  81^0.5t+0.25​

Simplifying the given expression:

=> 81^0.5t+0.25​

Simplify using the exponent power rule: (a^m)^n = (a)^mn

Convert decimal to fraction:

=> (3⁴ )^0.5t + 25/100

Cross out the common factor:

=> 3^2t + 1/4

therefore, 3^2t + 1/4 expression is equivalent to 81^0.5t+0.25​.

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First three days;

5L 400 ML;

Next two days 3 L each = a total of 6 L

Remaining 4 days; 1.5 L each which is a total of 4 * 1.5 = 6 L

Total amount drank will be;

6 + 6 + 5L 400 ML

= 17L 400 ML

Therefore, she drank 17L 400 ML that week.

Answer:

Step-by-step explanation:

Total in one week is:

Step-by-step explanation:

To find the longest time that Ian has to wait to fill the tank, we need to find the total time it takes to fill the tank from its current level of 20 gallons to its maximum level of 125 gallons.

First, we need to find the amount of water that needs to be added to the tank by subtracting the current water level from the maximum water level:

125 gallons - 20 gallons = 105 gallons

Next, we need to divide the amount of water that needs to be added by the rate at which Ian is filling the tank to find the time it will take:

105 gallons / 8 gallons per minute = 13.125 minutes

So the longest time that Ian has to wait to fill the tank is 13.125 minutes.

Answer:

100cm, 1m are equal to 0.001km

Step-by-step explanation:

0.001 is 1 thousandths and a kilometer is 1,000 meters so it would be 1m/1000m, 100 centimeter because one meter is one hundred centimeters.

The cost of a one-mile taxi ride is equal to $6.

The slope-intercept definition of a linear function is

y = mx + b.

We are given that taxi driver charges a $2 fee plus an additional $4 per mile, hence the slope and the intercept are given as follows:

m = 4, b = 2.

Thus the function  gives the cost for a x mile ride is:

y = 4x + 2.

The cost for a one mile ride is;

y = 4(1) + 2 = $6.

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The required probability that their scores differ by more than 15 points is 0.99807.

As stated in the question, a specific country administers an exam to students with scores that are regularly distributed with a mean of 41 points and a standard deviation of 9 points. Assume we randomly select two of these testers and define the random variable d as the difference in their scores.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,
Z = x - μ / σ
Z = 15 - 41 / 9
Z = -2.88
Now,
P(x > 15) = P (z > -2.88)
            = 0.99807

Thus, the needed chance is 0.99807 and their scores differ by more than 15 points.

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Answer:

I'll help with whatever it is.

Step-by-step explanation:

I'll try my best, just let me know.