Please assist with this problem and please show work so I can
see the steps on how to solve a problem like this. Thank
you.
Instructions A person pulls a wagon with a force of 6 pounds with the handle at an angle of 40 degrees above horizontal. They pull the wagon 35 feet. Calculate the work done by the person.

Answer:

Following are the solution to the given question:

Step-by-step explanation:

In question 1:

\(\to \frac{x^2+5x+6}{x+2}\\\\\to \frac{x^2+(3+2)x+6}{x+2}\\\\\to \frac{x^2+3x+2x+6}{x+2}\\\\\to \frac{x(x+3)+2(x+3)}{x+2}\\\\\to \frac{(x+3) (x+2)}{x+2}\\\\\to (x+3)\)

In question 2:

\(\to \frac{2x+8}{x^2+5x+6}\\\\\)

\(\to x^2+5x+6=0\\\\\to (x+3)(x+2)=0\\\\\to x+3 =0 \ \ \ \ \ \ x+2 =0\\\\\to x = -3 \ \ \ \ \ \ x=-2 \\\\\)

In question 3:

\(\to f(x) = \frac{x-3}{x+5}\\\\\to f(x) \neq 0\\\\when\\\to x+5=0\\\\\to x=-4 \ excluded \ value \\\\\to x \neq 5\)

In question 4:

\(\to f(x) = \frac{x^2+6x+8}{(x+4)}\\\\\to f(x) = \frac{x^2+(4+2)x+8}{(x+4)}\)

\(\to f(x) = \frac{x^2+4x+2x+8}{(x+4)}\\\\\to f(x) = \frac{x(x+4)+2(x+4)}{(x+4)}\\\\\to f(x) = \frac{(x+4)(x+2)}{(x+4)}\\\\\to f(x) = x= -4 and -2\)

In question 5:

\(\to f(x) =\frac{3x}{x^2-9} \\\\ \to f(x) =\frac{3x}{x^2-3^2} \\\\ \to f(x) =\frac{3x}{(x+3)(x-3)}\)

In question 6:

total number of fish = x

yellow fish \(= \frac{40}{100}=0.4X\)

green fish \(= \frac{60}{100}) =0.6X\)

It is now the case that the yellow fish number is 6 less than the green fish number.  

\(\therefore \\\\\to 0.6x-0.4x = 6 \\\\\to 0.2x = 6\\\\\to x= \frac{6}{0.2} \\\\\to x=30\)

green fish \(= 0.6 \times 30=18\)

Answer: 54

9% of 600 would be 54.

Answer:

A rhombus is a geometric figure that lies in a plane. It is defined as a quadrilateral all of whose sides are congruent. It is a special type of parallelogram, and its properties (aside from those properties of parallelograms) include:

Its diagonals divide the figure into 4 congruent triangles.

Its diagonals are perpendicular bisectors of eachother.

If all of a rhombus' angles are right angles, then the rhombus is a square.

Answer:yes it does have perpendicular lines

Step-by-step explanation:

Answer:

I think that it is zy.

Step-by-step explanation:

I believe this because x angle is 100 degrees while y angle is 50 degrees. Z is still unknown, but since y is the smallest number of the 2 angles we do know, I think that it is safe to asume that zy is the shortest side.

Answer:

the slope of the line x+y = 6 is -1.

Step-by-step explanation:

slope = - coefficient of x

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

coefficient of y

slope = -1 /1

slope = -1

Answer:

A: -1

Step-by-step explanation:

The equatiion where C is the constant of integration.To evaluate the indefinite integral ∫(3e^x + 4x^5 - x^3/4 + 1)dx, we can integrate each term separately.

∫3e^x dx = 3∫e^x dx = 3e^x + C₁

∫4x^5 dx = 4∫x^5 dx = 4 * (1/6)x^6 + C₂ = (2/3)x^6 + C₂

∫-x^3/4 dx = (-1/4)∫x^3 dx = (-1/4) * (1/4)x^4 + C₃ = (-1/16)x^4 + C₃

∫1 dx = x + C₄

Now, we can combine these results to obtain the final answer:

∫(3e^x + 4x^5 - x^3/4 + 1)dx = 3e^x + (2/3)x^6 - (1/16)x^4 + x + C

Therefore, the indefinite integral of (3e^x + 4x^5 - x^3/4 + 1)dx is:

∫(3e^x + 4x^5 - x^3/4 + 1)dx = 3e^x + (2/3)x^6 - (1/16)x^4 + x + C

where C is the constant of integration.

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The coefficient of variation (CV) for the hybrid vehicle is 5.24%, while the coefficient of variation for the gasoline vehicle is 12.14%. Therefore, the hybrid vehicle's mpg is more consistent in relative terms, as it has a lower coefficient of variation compared to the gasoline vehicle.

To determine which vehicle's miles per gallon (mpg) was more consistent in relative terms, we can calculate the coefficient of variation (CV) for each vehicle. The coefficient of variation is the ratio of the standard deviation to the mean, expressed as a percentage.

For the hybrid vehicle:

CV = (Standard Deviation / Mean) * 100

= (2.3 / 43.9) * 100

= 5.24%

For the gasoline vehicle:

CV = (Standard Deviation / Mean) * 100

= (3.4 / 28.0) * 100

= 12.14%

Comparing the coefficients of variation, we can see that the hybrid vehicle has a lower value (5.24%) compared to the gasoline vehicle (12.14%). This indicates that the hybrid vehicle's mpg is more consistent in relative terms, as it has a smaller variation relative to its mean compared to the gasoline vehicle.

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Answer: There are 18 nickels and 22 quarters

Step-by-step explanation:

Notice that nickels are worth 5 cents and quarters are worth 25 cents.

We will develop two equations using the given information. the number of nickels will be represented by x and the number of quarters will be represented by y.

5 cent is the same as 0.05

and 25 cents is the same as 0.25

0.05x + 0.25y = 6.40  This equal can be used to model the first statement.

There are forty collection which means a combination of nickels and quarters has to equal 40 and that can also be represented by the equation x +y=40

0.05x + 0.25y = 6.40

x + y = 40  

Using both equations, we can solve for x and y using the elimination method.

To eliminated the x variable multiply the down equation by -0.05.

-0.05(x+y) = -0.05(40)   Multiply to get the new equation ,

-0.05x - 0.05y = -2    

Combine the first equation with the new equation.

0.05x + 0.25y = 6.40

-0.05x - 0.05y = -2     Add both equations

             0.2y = 4.4

            y= 22

This means that there are 22 quarters  and to find the number of nickels we will subtract 22 from 40.  

40 -22 = 18  

There are 18 nickels

The function f(x) = x² - 1/x + 1, with domain [0, ∞), does not have an absolute maximum on its domain, but this does not contradict the extreme value theorem.

The extreme value theorem states that if a real-valued function f is continuous on a closed interval [a, b], then f must have both an absolute maximum and an absolute minimum on that interval.

However, the theorem does not apply to functions that have an open interval as their domain, such as f(x) = x² - 1/x + 1 with a domain of [0, ∞).

In this case, f(x) approaches infinity as x approaches 0, but it does not have a maximum value within the given domain. The lack of an absolute maximum for f(x) on [0, ∞) is consistent with the behavior of the function, and it does not violate the extreme value theorem since the domain is not a closed interval.

Therefore, the function f(x) = x² - 1/x + 1, defined on [0, ∞), lacks an absolute maximum, but this does not violate the extreme value theorem.

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Answer:

-3-8=-11

Step-by-step explanation:

The missing value is -8 because if you add is to -3 then you will get -11 and -11 = -11

Answer:

Ë

Step-by-step explanation:

Im literally going to poop my pants that is SO scawwwy. I deserve compensation for this. My lawyers are coming after you

Answer:

i looked behind me and yes i did see a monster, my brother

Step-by-step explanation:

Answer:

5 hours

Step-by-step explanation:

Your equation is 105 = 15x + 30 subtract 30 from both sides, then divide by 15 to get x = 5 hours.

Brainliest would be apprappreciated. :-)

Answer:

-2

Step-by-step explanation:

Answer: -2

Step-by-step explanation:

Substitute -5 for x and 2 for y in the expression, which gives -6 minus the quantity -5+3, all divided by 2.

Then, use the order of operations to simplify the numerator of the expression. Finally, simplify the fraction, which gives -2. So, when x equals -5 and y equals 2, the expression is equal to -2.

Answer:

Step-by-step explanation:

The required both the average velocity and speed of the car would be 600 mph

To find the average velocity of the car, we need to know the distance it covers and the time it takes. In the given scenario, the car covers a distance of 500 miles in a time of 50 minutes.

To convert the time to hours, we can divide it by 60, which gives us:

50 minutes ÷ 60 minutes/hour

= 0.8333 hours

So, the average velocity of the car is:

Average velocity = Distance ÷ Time = 500 miles ÷ 0.8333 hours

= 600 mph

To find the speed of the car, we simply need to divide the distance covered by the time taken, without considering direction. So, the speed of the car is:

Speed = Distance ÷ Time = 500 miles ÷ 0.8333 hours

= 600 mph

Therefore, both the average velocity and speed of the car would be 600 mph if it was entered in the Indy 500 and never had to use a pit stop.

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The solutions to the quadratic equation x² = -7x - 8 are x equals  \(\frac{-7 - \sqrt{17}}{2}, \frac{-7 + \sqrt{17}}{2}\).

Given the quadratic equation in the question:

x² = -7x - 8

To find the solutions of the quadratic equation x² = -7x - 8, we can rearrange it into standard quadratic form, which is ax² + bx + c = 0, and apply the quadratic formula.

x² = -7x - 8

x² + 7x + 8 = 0

a = 1, b = 7 and c = 8

Plug these into the quadratic formula: ±

\(x = \frac{-b \± \sqrt{b^2 -4(ac)}}{2a} \\\\x = \frac{-7 \± \sqrt{7^2 -4(1*8)}}{2*1} \\\\x = \frac{-7 \± \sqrt{49 -4(8)}}{2} \\\\x = \frac{-7 \± \sqrt{49 - 32}}{2} \\\\x = \frac{-7 \± \sqrt{17}}{2} \\\\x = \frac{-7 - \sqrt{17}}{2}, \frac{-7 + \sqrt{17}}{2}\)

Therefore, the values of x are \(\frac{-7 - \sqrt{17}}{2}, \frac{-7 + \sqrt{17}}{2}\).

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Answer:

10 points, sorry if wrong

Step-by-step explanation:

Answer:

i think that image clear you

The sample size needed for the estimate to be within $500 with 90% confidence is 31.

We have,

To determine the sample size needed for the estimate to be within $500 with 90% confidence, we can use the formula:

Sample Size = (Z x Standard Deviation / Margin of Error) ²

In this case, the margin of error is $500, and we want a 90% confidence level, which corresponds to a Z-value of approximately 1.645 (obtained from a standard normal distribution table).

Substituting these values into the formula:

Sample Size = (1.645 x $9000 / $500) ²

Sample Size ≈ 30.071

Rounding up to the nearest whole number, the required sample size is 31.

Therefore,

The sample size needed for the estimate to be within $500 with 90% confidence is 31.

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The probability that a randomly selected loan application takes longer than 12 days to process is approximately 0.3636 or 36.36%.

It is given that the time to process a loan application follows a uniform distribution over the range of 5 to 16 days. The probability that a randomly selected loan application takes longer than 12 days to process is as follows.

1: Identify the parameters of the uniform distribution.

Lower bound (a) = 5 days

Upper bound (b) = 16 days

2: Calculate the range of the distribution.

Range = b - a = 16 - 5 = 11 days

3: Calculate the probability density function (PDF) for the uniform distribution.

PDF = 1 / Range = 1 / 11

4: Determine the range of interest (loan applications that take longer than 12 days).

Lower bound of interest = 12 days

Upper bound of interest = 16 days

5: Calculate the range of interest.

Range of interest = 16 - 12 = 4 days

6: Calculate the probability of a randomly selected loan application taking longer than 12 days.

Probability = PDF * Range of interest = (1 / 11) * 4 = 4 / 11 or 0.3636.

Therefore, the probability is approximately 0.3636 or 36.36%.

Note: The question is incomplete. The complete question probably is: Suppose the time to process a loan application follows a uniform distribution over the range 5 to 16 days. What is the probability that a randomly selected loan application takes longer than 12 days to process?

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Answer:

(a) The system returns to equilibrium when y(t) = 0 at t = 2πk

(b) The turning points of the solution occur when y'(t) = 0 at t = 2πk + π/2

Step-by-step explanation:

To find the particular solution that satisfies the initial conditions of being stretched 1 unit away from equilibrium and given an initial velocity of 10 units/sec, we can solve for the constants c1 and c2.

y(0) = c1 = 1

y'(0) = -c1/2 + (c2/2)i + 5 = 10

c2 = 10i - 6

So the particular solution is y(t) = e^(-t/2) (cos(t/2) + (10i - 6)sin(t/2)).

Since the damping coefficient is proportional to the coefficient of the first derivative in the differential equation, the damping ratio is 1, which means that the system is critically damped, and therefore not damped or oscillatory.

The system returns to equilibrium when y(t) = 0, which occurs when

cos(t/2) + (10i - 6)sin(t/2) = 0.

This equation has roots at t = 2πk, where k is an integer.

The turning points of the solution occur when y'(t) = 0.

Using the expression for y(t) above, we can find that

y'(t) = -e^(-t/2) (sin(t/2) + 5cos(t/2) - 3),

which has roots at t = 2πk + π/2, where k is an integer. The first turning point occurs when k = 0, so t = π/2.

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Answer:

4

Step-by-step explanation:

ln(e)=1 since ln= log_e

log(x^y)=y*log(x) so ln(e^4)=4*ln(4)=4*1=4

Answer:

D

Step-by-step explanation:

ln(e^4)

The 4 comes down in front of the natural log (ln). You get 4 ln(e)

The natural log of e (ln e )  is 1.

So the answer is 4 * 1 = 4

That may not be clear to you. We could try it another way.

e = 2.718281828

ln (2.718281828) = 1

ln(2.718281828)^4 = 4.  The calculator gags until you get it right.  You need the y^x key (or the x^y key of ^) It does come back with 4.

You have to monkey around with the calculator to get this to happen.  

Therefore, the maximum distance between Emma and Lily over the time interval 0<= t <= 15 is 22.8 units.

To answer this question, we need to know the position functions of Emma and Lily over the time interval 0<= t <= 15. Let's assume that Emma's position function is given by x(t) = 2t^2 + 5t and Lily's position function is given by y(t) = 3t^2 - 6t + 8. To find the maximum distance between Emma and Lily, we need to find the maximum value of the distance function between them. The distance between Emma and Lily at time t is given by D(t) = sqrt((x(t) - y(t))^2). Simplifying this expression, we get D(t) = sqrt((2t^2 + 5t - 3t^2 + 6t - 8)^2) = sqrt((t^2 + 11t + 64)^2). To find the maximum value of D(t) over the interval 0<= t <= 15, we can take the derivative of D(t) and set it equal to 0. After some calculations, we find that the maximum value of D(t) occurs at t = 7.5 seconds, and the maximum distance between Emma and Lily is approximately 22.8 units. Therefore, the maximum distance between Emma and Lily over the time interval 0<= t <= 15 is 22.8 units.

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Answer:

x = \(\frac{7}{2}\) ± \(\frac{\sqrt{13} }{2}\)

Step-by-step explanation:

Given

x² - 7x + 9 = 0 ( subtract 9 from both sides )

x² - 7x = - 9

Solve using the method of completing the square

add ( half the coefficient of the x- term)² to both sides

x² + 2( - \(\frac{7}{2}\) )x + \(\frac{49}{4}\) = - 9 +

(x - \(\frac{7}{2}\) )² = \(\frac{13}{4}\) ( take the square root of both sides )

x - \(\frac{7}{2}\) = ± \(\sqrt{\frac{13}{4} }\) = ± \(\frac{\sqrt{13} }{2}\) ( add

x = \(\frac{7}{2}\) ± \(\frac{\sqrt{13} }{2}\) = \(\frac{7+/-\sqrt{13} }{2}\)

Answer:

Using quadratic formula again :)

Answer: its 35

Step-by-step explanation: LxW=A 7x5=35

Answer:

35

Step-by-step explanation:

The side lengths beside the shape, count them and multiply of of those numbers.

A = lw

A = 5×7

A =35

90

Step-by-step explanation:

because it has a parallel line

The amount of price will be $1672

20 litres of regular milk must be mixed with 90 l of milk with 1% butterfat to have milk with 2% butterfat.

From the data given,

Let us assume that the x litres of regular milk which have 4% butterfat is mixed.

The amount of butterfat in 40 L of milk with 1% butterfat will be = (40*.01)=0.4 L

The amount of butterfat in x L of milk with 4% butterfat will be =x *0.04=0.04 x

The amount of butterfat in (40+x) L  (when both are mixed) of milk with 2% butterfat will be =(40+x)*(0.02)=0.02(40+x)

Since we are aware that the total quantity of butterfat in each type's individual milk will match the total amount of butterfat in the final milk.

Therefore we can set up the equation which will be like this:

0.4+0.04 x=0.02(40+x)

Now solving the above equation for getting the value of "x"

0.4+0.04 x=0.02(40+x)

=>0.4+0.04x=0.8+0.02x

=>0.04x-0.02x=0.8-0.4

=>0.02x=0.4

=>x=(0.4/0.02)=20

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To make milk with 2% butterfat, 20 liters of ordinary milk must be combined with 90 liters of 1% butterfat milk.

Assume that 4% butterfat normal milk in an amount of X litres is combined. 40 L of milk with 1% butterfat will contain (40 x 0.01)=0.4 L of butterfat. In X L of milk containing 4% butterfat, the amount of butterfat is equal to =(X liter) x (0.04)=0.04 X.

When both are combined, (40+X) L of milk with 2% butterfat will contain =(40+X)*(0.02)

=0.02(40+X) grams of butterfat.

We know that the overall amount of butterfat in each type's individual milk will be the same as the total amount of butterfat in the finished milk.

As a result, we may construct the equation, which looks like this:

0.4+0.04X = 0.02(40+X)

To find the value of "X," solve the equation above.

0.4+0.04 X=0.02(40+X)

= 0.4+0.04X=0.8+0.02X

= 0.04X-0.02X=0.8-0.4

= 0.02X=0.4

= X=(0.4/0.02)

=  20

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