Solve for x.

−1.5x−3.1<5.5

Drag and drop a number or symbol into each box to correctly complete the solution.

Answer:

30/4

Step-by-step explanation:

7 times 4 = 28

28+2=30

Answer:

Since the Airbus A300 model airplane was made to scale, measuring 36 centimeters, while the real airplane measures 54 meters, to determine the scale ratio between both planes, the following calculation must be performed:

36cm = 0.36m

0.36 = 1

54 = X

54 x 1 / 0.36 = X

150 = X

Therefore, the scale ratio between the model and the real plane is 150:1.

The solution is Option C.

The L'Hopital's rule is applied to the equation lim x approaches 0 (1-cosx)/x

L'Hopital's rule then states that the slope of the curve when t = c is the limit of the slope of the tangent to the curve as the curve approaches the origin, provided that this is defined. The limit of a quotient of functions (i.e., an algebraic fraction) is equal to the limit of their derivatives.The tangent to the curve at the point [g(t), f(t)] is given by [g′(t), f′(t)]

And , lim x approches c  [ f ( x ) / g ( x ) ] = lim x approches c [ f' ( x ) / g' ( x ) ]

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

The equation is A = lim x approaches 0 (1/x)

On simplifying the equation , we get

The limit diverges as the function diverges and limit does not exist

And ,  lim x approaches 0₊ (1/x) ≠ lim x approaches 0₋ (1/x) = ∞

b)

The equation is A = lim x approaches 0 ( 2x² - 1 ) / ( 3x - 1 )

On simplifying the equation , we get

when x = 0 ,

Substitute the value of x = 0 in the limit , we get

A = ( 2 ( 0 )² - 1 ) / ( 3 ( 0 ) - 1 )

A = ( 0 - 1 ) / ( 0 - 1 )

A = 1

c)

The equation is A = lim x approaches 0 ( 1 - cosx ) / x

On simplifying the equation , we get

Applying L'Hopital's rule , we get

lim x approches c  [ f ( x ) / g ( x ) ] = lim x approches c [ f' ( x ) / g' ( x ) ]

f ( x ) = ( 1 - cos x )

g ( x ) = x

f' ( x ) = sin x

g' ( x ) = 1

So ,

lim x approches 0 [ f' ( x ) / g' ( x ) ] = lim x approches 0 ( sin x / 1 )

when x = 0

sin ( 0 ) = 0

Therefore , the value of lim x approaches 0 (1-cosx)/x = 0

d)

The equation is A = lim x approaches 0 ( cos 2x ) / 2

On simplifying the equation , we get

when x = 0 ,

A = cos ( 2 ( 0 ) / 2

A = cos ( 0 ) / 2

A = 1/2

Hence , the L'Hopital's rule is applied to lim x approaches 0 ( 1 - cosx ) / x

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Answer:

45-4=41 square units

Step-by-step explanation:

full shape area = 9x5=45

cut rectangle area = 4x1=4

blue shape area = 45-4=41

Answer:

the answer is B on ed2020

Step-by-step explanation:

for answer b, if you subtract 330 from 510 you get soda = 180 cal. then if you subtract 110 from 370 you get 260, and 260 divided by two (he consumed 2 juice) equals 130.

so you have soda = 180 cal and juice = 130 cal

if you plug it into joe's calorie intake you do 130 (1 serving of juice) + 180 (1 serving of soda) and + 220 (two servings of milk) you get 530 which is joe's total calorie intake in liquids, so B (110) is correct

Using matrices to solve, the number of calories that are in 1 serving of milk is; 110 Calories

Let the calories in one serving of milk be x

Let the calories in one serving of juice be y

Let the calories in one serving of soda be z

Thus, for Joe, equation to show amount of calories is;;

2x + y + z = 530    -----(1)

For Darius, equation to show amount of calories is; ;

x + 2y = 370     ------(2)

For Marian, equation to show amount of calories is;

3x + z = 510    ------(3)

Using matrix calculator online to calculate this 3 equations, we have;

x = 110 calories.

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To meet the given requirements, the account would need to have around $4,378 at time t=3/5.

To solve this problem, let's break it down into different parts and calculate the required amount in the account at time t=3/5.

1. Calculate the dollar-weighted rate of return:

The dollar-weighted rate of return can be calculated by dividing the total gain or loss by the total investment.

Total Gain/Loss = Account Value at t=1 - Total Investment

             = $3,300 - ($2,000 + $1,000)

             = $3,300 - $3,000

             = $300

Dollar-weighted Rate of Return = Total Gain/Loss / Total Investment

                             = $300 / $3,000

                             = 0.10 or 10% (in decimal form)

2. Calculate the time-weighted rate of return:

The time-weighted rate of return is given as 0.0175 higher than the dollar-weighted rate of return.

Time-weighted Rate of Return = Dollar-weighted Rate of Return + 0.0175

                           = 0.10 + 0.0175

                           = 0.1175 or 11.75% (in decimal form)

3. Calculate the additional investment at time t=3/5:

Let's assume the required amount to be in the account at time t=3/5 is X.

To calculate the additional investment needed at t=3/5, we need to consider the dollar-weighted rate of return and the time period between t=1 and t=3/5.

Account Value at t=1 = Total Investment + Gain/Loss

$3,300 = ($2,000 + $1,000) + ($2,000 + $1,000) × Dollar-weighted Rate of Return

Simplifying the equation:

$3,300 = $3,000 + $3,000 × 0.10

$3,300 = $3,000 + $300

At t=3/5, the additional investment would be:

X = $3,000 × (1 + 0.10) + $1,000 × (1 + 0.10)^(3/5)

Calculating the expression:

X = $3,000 × 1.10 + $1,000 × 1.10^(3/5)

X ≈ $3,300 + $1,000 × 1.078

X ≈ $3,300 + $1,078

X ≈ $4,378

Therefore, the amount that would have to be in your account at time t=3/5 is approximately $4,378.

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Answer:

\(5(n + 4)^{\frac{3}{2} }\)  

I hope this helps!

Answer:

Step-by-step explanation:

y = e^((1/2)(tan(x) + C)) is the solution to the given differential equation.

To solve the given differential equation (y^2 + 2) dx = y sec^2(x) dy, follow these steps:

Step 1: Rewrite the equation as a separable differential equation.
To do this, divide both sides by y(y^2 + 2) to isolate dx and dy:

(dy/y) = (sec^2(x) dx) / (y^2 + 2)

Step 2: Integrate both sides of the equation.
Integrate the left side with respect to y, and the right side with respect to x:

∫(1/y) dy = ∫(sec^2(x) / (y^2 + 2)) dx

Step 3: Evaluate the integrals.
For the left side, the integral of 1/y with respect to y is ln|y| + C₁ (where C₁ is a constant).
For the right side, let u = y^2 + 2, then du = 2y dy, so the integral becomes:

∫(sec^2(x) / u) (1/2) du = (1/2) ∫(sec^2(x) du)

Now, the integral of sec^2(x) with respect to u is tan(x) + C₂ (where C₂ is another constant).

Step 4: Combine the constants and express the solution.
The general solution is given by:

ln|y| = (1/2)(tan(x) + C), where C = 2(C₁ - C₂).

To express y in terms of x, take the exponential of both sides:

y = e^((1/2)(tan(x) + C))

This is the solution to the given differential equation.

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Let  p be the function that gives the cost , in dollars, of producing 1 watt of solar energy years after 1977. Here is a table showing the values of  from 1977 to 1987.

t         p(t)                       p(10)-p(0)

0 80                          p(10)

1 60                          p(10)- p(0)/10-0

2 45                            p(10-0)

3 33.75

4 25.31

5 18.98

6 14.24

7 10.68

8 8.01

9 6.01

10 4.51

Which phrase best captures the average rate of change in the price of solar energy between 1977 and 1987?

Which phrase best captures the average rate of change in the price of solar energy between 1977 and 1987?

Which equation best captures the yearly average increase rate of solar prices between 1977 and 1987?

This discussion aims to help students remember what average rate of change for a function means and how it is computed. Select students to explain what each expression's value in this context means. For instance, the cost difference for a solar cell between 1977 and 1987 is represented by the formula p(10)- p(0), whereas the percent change between 1977 and 1987 may be calculated as p(10)/p(0). The fact that the real phrase for the average rate of change, p(10)-p(0)/10-0=-7.55, reveals that the price declined by -$7.55 on average per year since the expression considers the whole difference in price between the 1977 and 1987 divided by the total number of years that passed.

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Answer:

8/100 = 2/25 = .08

Step-by-step explanation:

If a factory machine bends wire at rate of 2 units of curvature per  second, then the time required to bend the "straight-wire" into a circle of radius of 4 is 12.56 seconds.

The "Circumference" of a circle is defined as the total length of the curve which makes up the circle's outer boundary,

The formula for "circumference" of a circle is ⇒ C = 2 × π × r,

where "C" = circumference, "π" ≈ 3.14159, and "r" = radius,

In this case, the radius of circle is = 4 units,

So, we substitute "r" = 4,

We get,

⇒ Circumference = 2 × π × 4,

⇒ Circumference = 8π

The machine bends wire at a rate of 2 units of curvature per second, we  use the circumference of circle to calculate how long it takes to bend the wire into a complete circle.

The machine bends 2 units of curvature per second, and the circumference of the circle is 8π units,

So, the time taken to bend wire into a complete circle is :

⇒ Time = (Circumference)/(Rate of bending),

⇒ Time = 8π/2,

⇒ Time = 4π ≈ 12.56 seconds.

Therefore, it would take approximately 12.56 seconds to bend a "straight-wire" into a circle.

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The probability that the sample mean exceeds 45 is approximately 0.

By the central limit theorem, the sample mean of a large sample size from any distribution with a finite mean and variance is approximately normally distributed.

Since the exponential distribution has a mean of 4 and a variance of 16, we can approximate the distribution of the sample mean as a normal distribution with mean 4 and standard deviation 4/sqrt(225) = 4/15.

To find the probability that the sample mean exceeds 45, we can standardize the distribution using the z-score formula:

z = (45 - 4) / (4/15) = 10.625

Using a standard normal distribution table or a calculator, we can find the probability that a standard normal random variable exceeds 10.625:

P(Z > 10.625) ≈ 0

Therefore, the probability that the sample mean exceeds 45 is approximately 0.

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To determine which set of data most likely has a mean closest to 29.5, we need to analyze the shape and position of the histograms in relation to the value 29.5.

Looking at the histograms described:

The first histogram ranges from 9 to 48, and the upward trend starts from 1 and ends at 33, followed by a downward trend. This histogram suggests that there may be values lower than 29.5, which would bring the mean below 29.5.

The second histogram ranges from 15 to 48, with an upward trend from 1 to 30 and then a downward trend. Similar to the first histogram, it suggests the possibility of values lower than 29.5, indicating a mean below 29.5.

The third histogram ranges from 12 to 56, and the upward trend starts from 1 and ends at 32, followed by a downward trend. This histogram covers a wider range but still suggests the possibility of values below 29.5, indicating a mean below 29.5.

The fourth histogram ranges from 15 to 54 and exhibits multiple trends. While it has fluctuations, it covers a wider range and includes both upward and downward trends. This histogram suggests the possibility of values above and below 29.5, potentially resulting in a mean closer to 29.5.

Based on the descriptions, the fourth histogram, with its more varied trends and wider range, is most likely to have a mean closest to 29.5.

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Answer:

Area = 84 cm^2

Perimeter = 38 cm

Step-by-step explanation:

The shape is a rectangle.

Area of the rectangle:

The formula for the area of a rectangle is given by:

A = lw, where

Thus, we can plug in 7 for l and 12 for w to find A, the area of the rectangle in cm^2:

A = 7 * 12

A = 84

Thus, the area of the rectangle is 84 cm^2.

Perimeter of the rectangle:

The formula for the perimeter of a rectangle is given by:

P = 2l + 2w, where

Thus, we can plug in 7 for l and 12 for w to find P, the perimeter of the rectangle in cm:

P = 2(7) + 2(12)

P = 14 + 24

P = 38

Thus, the perimeter of the rectangle is 38 cm.

Answer:

1508527.582 cm³/min

Step-by-step explanation:

The net rate of flow dV/dt = flow rate in - flow rate out

Let flow rate in = k. Since flow rate out = 6800 cm³/min,

dV/dt = k - 6800

Now, the volume of a cone V = πr²h/3 where r = radius of cone and h = height of cone

dV/dt = d(πr²h/3)/dt = (πr²dh/dt)/3 + 2πrhdr/dt (since dr/dt is not given we assume it is zero)

So, dV/dt = (πr²dh/dt)/3

Let h = height of tank = 12 m, r = radius of tank = diameter/2 = 3/2 = 1.5 m, h' = height when water level is rising at a rate of 21 cm/min = 3.5 m and r' = radius when water level is rising at a rate of 21 cm/min

Now, by similar triangles, h/r = h'/r'

r' = h'r/h = 3.5 m × 1.5 m/12 m = 5.25 m²/12 m = 2.625 m = 262.5 cm

Since the rate at which the water level is rising is dh/dt = 21 cm/min, and the radius at that point is r' = 262.5 cm.

The net rate of increase of water is dV/dt = (πr'²dh/dt)/3

dV/dt = (π(262.5 cm)² × 21 cm/min)/3

dV/dt = (π(68906.25 cm²) × 21 cm/min)/3

dV/dt = 1447031.25π/3 cm³

dV/dt = 4545982.745/3 cm³

dV/dt = 1515327.582 cm³/min

Since dV/dt = k - 6800 cm³/min

k = dV/dt - 6800 cm³/min

k = 1515327.582 cm³/min - 6800 cm³/min

k = 1508527.582 cm³/min

So, the rate at which water is pumped in is 1508527.582 cm³/min

Note that the absolute value of the difference in the two estimates of Q with an uncertainty range at a 95% confidence interval is 1.052.

To find the average value of Q, we simply add up all the values and divide by the number of trials:

Average value of Q = (41.314 + 40.087 + 41.248 + 40.196 + 40.284 + 41.152 + 38.852 + 36.401 + 37.941 + 39.221 + 39.035 + 38.404 + 40.683 + 41.568 + 42.175 + 42.319)/16

= 39.976

Next, to find the uncertainty range where we can be 95% sure that the true value of Q lies within, we need to find the standard error of the mean. The formula gives this:

Standard error of the mean = standard deviation / √(n)

where n is the number of trials. We can find the standard deviation using the formula:

Standard deviation = √(Σ(Qi - Q_avg)² / (n-1))

where Qi is the value of Q for the ith trial.

Using these formulas, we find:

Standard deviation = 1.549

Standard error of the mean = 0.387

To find the uncertainty range, we say:

Uncertainty range = t-value * standard error of the mean

= 2.131 * 0.387

= 0.826

Therefore, we can be 95% sure that the true value of Q lies within the range:

39.976 ± 0.826

Now, to calculate the absolute value of the difference in the two estimates of Q with an uncertainty range at a 95% confidence interval, we can simply add the uncertainty ranges of the two estimates and take the absolute value of the difference:

|Q1 - Q2| = |39.976 ± 0.826 - 40| + |39.976 ± 0.826 - 39.8|

= 0.826 + 0.226

= 1.052

Therefore, the absolute value of the difference in the two estimates of Q with an uncertainty range at a 95% confidence interval is 1.052.

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Answer:

10

Step-by-step explanation:

\(2(x + y)^{2} = 116 \\ {(x + y)}^{2} = \frac{116}{2} \\ {(x + y)}^{2} = 58....(1) \\ xy = 24.....(2) \\ \because \: {(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy \\ \therefore \: 58 = {x}^{2} + {y}^{2} + 2 \times 24 \\ \therefore \: 58 = {x}^{2} + {y}^{2} + 48 \\ \therefore \: {x}^{2} + {y}^{2} = 58 - 48 \\ \huge \purple{ \boxed{\therefore \: {x}^{2} + {y}^{2} = 10}}\)

Answer:

10

Step-by-step explanation:

2(x+y)^2=116

xy= 24

x^2+y^2 =?

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

x^2+y^2= (x+y)^2- 2xy

Answer:

correlation

Step-by-step explanation:

I took the quiz

The ball traveled approximately \(26.27\) units in total.

To calculate the distance the ball traveled, we can use the distance formula between two points in a Cartesian coordinate system.

Distance = \(\sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1} )^{2} }\)

Let's calculate the distance between Player A and Player B first:

Distance_AB =

\(\sqrt{((16-2)^{2}+(9-4)^{2}) }\)

\(= \sqrt{(14^{2}+5^{2} ) } \\= \sqrt{(196 +25)} \\= \sqrt{221} \\= 14.87\)

Now, let's calculate the distance between Player B and Player C:

Distance_BC =

\(\sqrt{ ((25 - 16)^2 + (16 - 9)^2)}\\= \sqrt{ (9^2 + 7^2)}\\= \sqrt{(81 + 49)}\\= \sqrt{130}\\=11.40\)

Finally, we can calculate the total distance traveled by adding the distances AB and BC:

Total distance = Distance_AB + Distance_BC

\(= 14.87 + 11.40 \\= 26.27\)

Starting from Player A at \((2, 4),\) it was thrown to Player B at \((16, 9),\) covering a distance of about \(14.87\) units. From Player B, the ball was then thrown to Player C at \((25, 16),\) covering an additional distance of approximately \(11.40\) units.

Combining these distances, the total distance the ball traveled was approximately \(26.27\) units.

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The point-slope form of the line is y - (3/4) = 5(x - (3/4)).

The point-slope form of a line is written as y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line. To find the point-slope form of a line that has a slope of 5 and passes through the point (3/4, 3/4), we can plug in the values for the slope and the point into the point-slope formula. This gives us y - (3/4) = 5(x - (3/4)). This is the point-slope form of the line.

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To find the minimum score required for an A grade, we need to determine the cutoff point that corresponds to the top 13% of scores.

Given that the scores on the test are normally distributed with a mean of 69.5 and a standard deviation of 9.5, we can use the standard normal distribution to calculate the cutoff point. Using a standard normal distribution table or a statistical calculator, we find that the z-score corresponding to the top 13% is approximately 1.04. To find the corresponding raw score, we can use the formula:

x = μ + (z * σ)

where x is the raw score, μ is the mean, z is the z-score, and σ is the standard deviation. Plugging in the values, we have:

x = 69.5 + (1.04 * 9.5) ≈ 79.58

Rounding this to the nearest whole number, the minimum score required for an A grade would be 80. Therefore, a student would need to score at least 80 on the test to achieve an A grade according to the professor's grading scheme.

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Answer: 26 Gallons of water

Step-by-step explanation:

First, take 18 divided by 4.5 = 4 gallons per minute

Let y be the number of gallons and x be the number of minutes

So our equation is

y= 4x

Then put 6.5 in for x and you will get

26 Gallons of water

the mode is $6.00

thats the number there is the most of

\(answer \\ (3x - 5)(2x + 2) \\ solution \\ {6x}^{2} - 4x - 10 \\ = {6x}^{2} - (10 - 6)x - 10 \\ = {6x}^{2} - 10x + 6x - 10 \\ = 2x(3x - 5) + 2(3x - 5) \\ = (3x - 5)(2x + 2) \\ hope \: it \: helps\)

Answer:

x = 1⅔ or -1

Step-by-step explanation:

6x² -4x - 10

a=6, b=-4, c=-10, ac= -60

factors -10 & 6

6x² + 6x - 10x -10 =0

(6x² + 6x) - (10x - 10) =0

6x(x +1) - 10(x+1) =0

(6x-10)(x+1)=0

6x-10=0 or. x+1=0

6x= 10 or x= -1

x= 10/6 or. x= -1

x=1⅔ or x= -1

Joule per meter second is the unit of measurement for momentum flux or power per unit area. It is commonly used in physics and engineering to quantify the rate of energy transfer or momentum flow per unit area.

Joule per meter second (J/m^2s) is not the correct unit for momentum flux or power per unit area. The correct unit for momentum flux is Newton per square meter (N/m^2), also known as Pascal (Pa), while the correct unit for power per unit area is watt per square meter (W/m^2). The joule per meter second (J/m^2s) is actually the unit for volumetric energy dissipation rate, which measures the rate at which energy is being dissipated within a fluid volume per unit volume. It is used in the study of fluid dynamics and turbulence.

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Answer:

tan(sin^-1(-1)) is undefined.

The inverse sine function returns a value between -pi/2 and pi/2, and since sin(-pi/2) = -1, sin^-1(-1) = -pi/2. However, at -pi/2, the tangent function is undefined since it results in a vertical asymptote.

Therefore, the answer is option C: theta = pi/2 and theta = 3pi/2.

To determine when tan(theta) is undefined on the unit circle, we need to remember the definition of the tangent function.
Tangent is defined as the ratio of the sine and cosine of an angle. Specifically, tan(theta) = sin(theta)/cos(theta).

Now, we know that cosine can never be equal to zero on the unit circle, since it represents the x-coordinate of a point on the circle and the circle never crosses the x-axis. Therefore, the only way for tan(theta) to be undefined is if the cosine of theta is equal to zero.
There are two values of theta on the unit circle where cosine is equal to zero: pi/2 and 3pi/2.

At theta = pi/2, we have cos(pi/2) = 0, which means that tan(pi/2) = sin(pi/2)/cos(pi/2) is undefined.
Similarly, at theta = 3pi/2, we have cos(3pi/2) = 0, which means that tan(3pi/2) = sin(3pi/2)/cos(3pi/2) is also undefined.
Therefore, the answer is option C: theta = pi/2 and theta = 3pi/2.

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Answer:

-3

Step-by-step explanation:

You need to substract 6 to get the next term.

I HOPE THIS HELPS :)

Answer:

-3

Step-by-step explanation:

21 - 6 = 15

15 - 6 = 9

9 - 6 = 3

3 - 6 = -3