(a) Make the subject of the formula t
2(a+t)=5t+7

The term "standard error of the mean" refers to the sample mean's standard deviation. And the formula for the standard deviation is σ/√n.

The square root of a random variable's variance is the standard deviation of a sample, statistical population, data collection, or probability distribution. Compared to the average absolute deviation, it is algebraically easier but less reliable in practice. The standard deviation has the advantage of being represented in the same unit as the data, unlike the variance, which is a desirable characteristic.

The standard error of a statistic (such the sample mean) is related to the standard deviation of a population or sample, however they are very different. Standard deviation of the population divided by the square root of sample size yields the standard deviation of the sampling distribution of means. "Standard error of the mean" is the term for the sampling distribution's standard deviation.

The term "standard error of the mean" refers to the sample mean's standard deviation.

And the formula for the standard deviation is given by σ/√n.

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Answer:

30.34 degree

Step-by-step explanation:

Apply sine formula

\(\frac{sin\left(A\right)}{a}=\frac{sin\left(B\right)}{b}\)

\(\frac{\sin \left(45^{\circ \:}\right)}{7}=\frac{\sin \left(b\right)}{5}\)

->simplify

\(\frac{\sin \left(b\right)}{5}=\frac{\frac{\sqrt{2}}{2}}{7}\)

you will get

\(\sin \left(b\right)=\frac{5\sqrt{2}}{14}\)

which
sin b is about 0.50507

\(sin^{-1}\left(0.50507\right)\)

->arc sine in degree mode

the answer is 30.34

The graph of the inequality, 2x + y ≥ 4, is: option 1.

Given the inequality, 2x + y ≥ 4, rewrite in slope-intercept form:

2x + y ≥ 4

y ≥ -2x + 4

Thus, this means that the slope of the graph will be a declining slope of -2, and it will intercept the y-axis at 4.

Also, since the inequality sign is ≥, the shaded region will be above a solid line.

Option 1 has a slope of -2 and is also a solid line having the shaded part above it.

Therefore, the correct graph is option 1.

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Answer:

Total consumer spending is 160

Step-by-step explanation:

Here , we are interested in calculating the total consumer spending.

In a long run perfect competition market, price interest with MC and minimum point of AC

Hence , P = AC

this means that Q = 40,000/P = 40,000/150 = 266.67 which is approximately 267 potatoes will be consumed

The total consumer spending is thus 267 * 0.6 = 160

Answer:

Step-by-step explanation:

You have a 30-60-90 triangle. The sides of a 30-60-90 are in the ratio 1:√3:2.

The side opposite the 30° angle is 5, so the side opposite the 60° angle is 5√3, and the side opposite the 90° angle is 5×2 = 10.

x = 5√3

y = 10

The given differential equations.

a) Steady states:\(\ (y = 0\) (unstable), \ (y = 4\) (stable)\)

b) Steady states: \(\ (y = 0\) (stable), \ (y = 6\) (unstable)\)

c) Steady states:\(\ (y = 1\) (unstable), \ (y = 5\) (stable)\)

d) Steady states:\(\ (y = 2\) (stable), \ (y = 8\) (unstable)\)

To solve the given differential equations and check the stability at the steady state, we need to find the steady-state solutions (where the derivatives are zero) and then analyze the stability around those steady states.

\(a) \ (y' = 8y - 2y^2\)\)

To find the steady state, set y' = 0:

\(\ (0 = 8y - 2y^2\)\\\ (0 = 2y (4 - y) \)\\\ (y = 0\) or \ (y = 4\)\)

To analyze stability, we take the derivative of y' with respect to y:

y'' = 8 - 4y

For y = 0:

y'' = 8 - 4(0)

   = 8 (positive)

The steady state y = 0 is unstable.

For y = 4:

y'' = 8 - 4(4)

   = -8 (negative)

The steady state y = 4 is stable.

b) \(\ (y' = 3y^2 - 18y\)\)

To find the steady state, set y' = 0:

\(\ (0 = 3y^2 - 18y\)\\\ (0 = 3y (y - 6) \)\\\ (y = 0\) or \ (y = 6\)\)

To analyze stability, we take the derivative of y' with respect to y:

y'' = 6y - 18

For y = 0:

\(\ (y'' = 6(0) - 18 \\= -18\) (negative)\)

The steady state y = 0 is stable.

For y = 6:

\(\ (y'' = 6(6) - 18 \\= 18\) (positive)\)

The steady state y = 6 is unstable.

c)\(\ (y' = -y^2 + 6y - 5\)\)

To find the steady state, set \ (y' = 0\):

\(\ (0 = -y^2 + 6y - 5\)\\\ (0 = (y - 1) (y - 5) \)\\\ (y = 1\) or \ (y = 5\)\)

To analyze stability, we take the derivative of \(y'\) with respect to \(y\):

\ (y'' = -2y + 6\)

For \ (y = 1\):

y'' = -2(1) + 6

= 4 (positive)

The steady state \ (y = 1\) is unstable.

For \ (y = 5\):

y'' = -2(5) + 6

   = -4 (negative)

The steady state \ (y = 5\) is stable.

d)\(\ (y' = y^2 - 10y + 16\)\)

To find the steady state, set \ (y' = 0\):

\(\ (0 = y^2 - 10y + 16\)\\\ (0 = (y - 2) (y - 8) \)\\\ (y = 2\) or \ (y = 8\)\)

To analyze stability, we take the derivative of \(y'\) with respect to \(y\):

\ (y'' = 2y - 10\)

For \ (y = 2\):

\(\ (y'' = 2(2) - 10 \\= -6\) (negative)\)

The steady state \ (y = 2\) is stable.

For

\(\ (y = 8\):\\\ (y'' = 2(8) - 10 = 6\)\) (positive

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If a driver drives at a constant rate of 32 miles per hour, how long would it take the driver to drive 272 miles? It would take the drive hour(s) to drive 272 miles?​

In this problem

Applying proportion

1 /32=x/272

solve for x

x=272/32

Answer:

the answer is 357

Step-by-step explanation:

350 + 440 + 400 = 1190

30% of 1190 = 357

May I have brainliest please? :)

Answer:

h = \(\frac{2A}{b}\)

Step-by-step explanation:

A = \(\frac{1}{2}\) bh ( multiply both sides by 2 to clear the fraction )

2A = bh ( isolate h by dividing both sides by b )

\(\frac{2A}{b}\) = h

The critical value of t for constructing a 99% confidence interval with a sample size of 30 and a sample standard deviation of 0.05 is 2.7564.

A confidence interval is a range of values within which the population parameter is estimated to lie with a certain level of confidence. In this case, we are constructing a 99% confidence interval for the population mean. The critical value of t is used to determine the width of the confidence interval.

The formula for calculating the confidence interval for the population mean is:

Confidence interval = sample mean ± (critical value) * (standard deviation of the sample / square root of the sample size)

Given that the sample size is 30 (n = 30) and the standard deviation of the sample is 0.05 (S = 0.05), we need to find the critical value of t for a 99% confidence level. The critical value of t depends on the desired confidence level and the degrees of freedom, which is equal to n - 1 in this case (30 - 1 = 29). Looking up the critical value in a t-table or using statistical software, we find that the critical value of t for a 99% confidence level with 29 degrees of freedom is approximately 2.7564.

Therefore, the 99% confidence interval for the population mean would be calculated as follows: sample mean ± (2.7564) * (0.05 / √30). The final result would be a range of values within which we can be 99% confident that the true population mean lies.

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Step-by-step explanation:

\(2xy^2 + 8y\)

2y is the common factor so:

\(2y(xy + 4)\)

Answer:

4. x = 50

5. x = 5

Step-by-step explanation:

For question 4:

For question 5:

Answer:

4) x= -50

5) x= 5

Step-by-step explanation:

Number 5

Simplifying

-3x + -2 = -17

Reorder the terms:

-2 + -3x = -17

Solving

-2 + -3x = -17

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2' to each side of the equation.

-2 + 2 + -3x = -17 + 2

Combine like terms: -2 + 2 = 0

0 + -3x = -17 + 2

-3x = -17 + 2

Combine like terms: -17 + 2 = -15

-3x = -15

Divide each side by '-3'.

x = 5

Simplifying

x = 5

Number 4

x/5+7 = -3 // + 3

x/5+3+7 = 0

1/5*x+10 = 0 // - 10

1/5*x = -10 // : 1/5

x = -10/1/5

x = -50

x = -50

Answer: 3.5

Step-by-step explanation:

y=(10)-6.5

To determine whether the series is absolutely convergent, conditionally convergent, or divergent, we need to evaluate the sum of the series. The given series is:

∞Σk=1 4k/(5k+k)

Simplifying the denominator, we get:

∞Σk=1 4k/(6k)

= ∞Σk=1 2/3

Since the summand is a constant value (2/3) and does not depend on k, the series is a divergent series.

Therefore, the given series is divergent.
Hi! To determine whether the series is absolutely convergent, conditionally convergent, or divergent, we will consider the given series:

Σ (4 / (5k)), where k = 1 to ∞

First, we'll examine absolute convergence by taking the absolute value of the series terms:

Σ |4 / (5k)| = Σ (4 / (5k))

Since the absolute value does not change the terms in this case, the series is the same. Now we'll apply the Ratio Test:

lim (n → ∞) |(4 / (5(k+1))) / (4 / (5k))|

= lim (n → ∞) (4 / (5(k+1))) * (5k / 4)

= lim (n → ∞) (5k / (5(k+1)))

= lim (n → ∞) (5k / (5k + 5))

= lim (n → ∞) (k / (k + 1))

= 1

The result of the Ratio Test is 1, which means the test is inconclusive. However, we can apply the Comparison Test with the harmonic series Σ (1 / k), which is known to be divergent. Since 4 / (5k) ≤ 1 / k for all k, and the harmonic series is divergent, the given series is also divergent by the Comparison Test.

So, the given series is divergent.

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Answer:

C

Step-by-step explanation:

sinθ=\(\frac{2}{5}\)

θ=sin⁻¹ ( \(\frac{2}{5}\) )

θ=23.57817848

2θ=47.15635696

sin2θ=sin(47.15635696)=0.7332121112°≈ ((4\(\sqrt{21}\))/25)

Answer: When students register online, the question appears in a pop-up window that must be answered in order to proceed with registering. If students register in person, make them answer the question before their registration is processed.

Step-by-step explanation:

Answer:

A. 1 7/10x+2 1/2y+6

B. 7/10x+2 1/2y+6

C. 7/10x+8 1/2y+6

D. 1 7/10x+4 1/4y+3

The 99.5% confidence interval for the mean weight of all one-year-old baby boys in the United States is (24.8, 26.2) pounds.

We are given a sample of 360 one-year-old baby boys in the United States with a mean weight of 25.5 pounds and a population standard deviation of σ=5.1 pounds. We need to construct a 99.5% confidence interval for the mean weight of all one-year-old baby boys in the United States.

To construct the confidence interval, we can use the formula:

Confidence interval = sample mean ± (z-score)(standard error)

where the z-score is based on the confidence level and the standard error is calculated as:

standard error = σ/√n

Plugging in the given values, we get:

standard error = 5.1/√360 = 0.27 pounds

Since we want a 99.5% confidence interval, the corresponding z-score is 2.807. Therefore, the confidence interval is:

Confidence interval = 25.5 ± (2.807)(0.27) = (24.8, 26.2) pounds

We can be 99.5% confident that the mean weight of all one-year-old baby boys in the United States falls within the range of 24.8 to 26.2 pounds.

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The volume of the cube that is above the surface of the fluid is approximately 2.67 cubic meters.

When an object is submerged in a fluid, it experiences an upward buoyant force equal to the weight of the fluid it displaces. To determine the volume of the cube above the fluid's surface, we need to find the volume of the cube and subtract the volume of the cube that is submerged in the fluid.

Calculate the volume of the cube.

Given that the sides of the cube have a length of 1.77 m, we can calculate the volume using the formula: V = s^3, where s is the length of the side.

V = \((1.77 m)^3\)

V ≈ 5.859 cubic meters

Calculate the volume of the cube submerged in the fluid.

The density of the fluid is given as 1,008 \(kg/m^3\), and the density of the cube is given as 522 \(kg/m^3\). Since the cube is denser than the fluid, it will sink until it displaces an amount of fluid with a weight equal to its own weight. The volume of the submerged cube can be calculated using the formula: V_submerged = (m_cube / ρ_fluid), where m_cube is the mass of the cube and ρ_fluid is the density of the fluid.

Given that density = mass / volume, we can rearrange the formula to find the mass of the cube: m_cube = density_cube * V_cube.

m_cube = 522 kg/\(m^3\) * 5.859 cubic meters

m_cube ≈ 3,056.098 kg

Now we can calculate the volume of the submerged cube using the formula: V_submerged = m_cube / ρ_fluid.

V_submerged = 3,056.098 kg / 1,008 kg/\(m^3\)

V_submerged ≈ 3.034 cubic meters

Calculate the volume above the surface.

The volume above the surface is the difference between the volume of the cube and the volume of the submerged cube.

V_above_surface = V_cube - V_submerged

V_above_surface ≈ 5.859 cubic meters - 3.034 cubic meters

V_above_surface ≈ 2.825 cubic meters

Therefore, the volume of the cube that is above the surface of the fluid is approximately 2.67 cubic meters.

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The temperature of the soda after 20 minutes is approximately -18 degrees Celsius. To find the initial temperature of the soda, we can evaluate the function T(x) at x = 0.

Substitute x = 0 into the function T(x):

T(0) = -19 + 39e^(-0.45*0).

Simplify the expression:

T(0) = -19 + 39e^0.

Since e^0 equals 1, the expression simplifies to:

T(0) = -19 + 39.

Calculate the sum:

T(0) = 20.

Therefore, the initial temperature of the soda is 20 degrees Celsius.

To find the temperature of the soda after 20 minutes, we substitute x = 20 into the function T(x):

Substitute x = 20 into the function T(x):

T(20) = -19 + 39e^(-0.45*20).

Simplify the expression:

T(20) = -19 + 39e^(-9).

Use a calculator to evaluate the exponential term:

T(20) = -19 + 39 * 0.00012341.

Calculate the sum:

T(20) ≈ -19 + 0.00480599.

Round the answer to the nearest degree:

T(20) ≈ -19 + 1.

Therefore, the temperature of the soda after 20 minutes is approximately -18 degrees Celsius.

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INCOMPLETE QUESTION

A can of soda is placed inside a cooler. As the soda cools, its temperature Tx in degrees Celsius is given by the following function, where x is the number of minutes since the can was placed in the cooler. T(x)= -19 +39e-0.45x. Find the initial temperature of the soda and its temperature after 20 minutes. Round your answers to the nearest degree as necessary.

Answer:

- 6

Step-by-step explanation:

Step 1:

2x - 9 = - 21       Equation

Step 2:

2x = - 12       Add 9 on both sides

Step 3:

- 12 ÷ 2     Divide

Answer:

x = - 6

Hope This Helps :)

Answer:

x = -6

Step-by-step explanation:

Let x = unknown number

2x -9 = -21

Add 9 to each side

2x -9+9 = -21+9

2x = -12

Divide by 2

2x/2= -12/2

x = -6

========================================================

Explanation:

Let's say there are 100 students total. You can start with any number you want, but I'm picking a large round number to work with.

3/5 of the total voted, so (3/5)*100 = 0.6*100 = 60 people voted

Of the 60 who voted, 3/4 of those went to the winning candidate.

3/4 of 60 = (3/4)*60 = 0.75*60 = 45

We have 45 people who voted for the winning candidate out of 100 total students, so,

45/100 = (9*5)/(20*5) = 9/20

Meaning that 9/20 of the student body voted for the winning candidate.

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

You could also multiply the two given fractions to get the same answer

(3/5)*(3/4) = (3*3)/(5*4) = 9/20

When multiplying, you multiply the numerators together and the denominators together. Reduce the fraction if possible.

The expression is solved to \(2^2^x^+^y\)

Index forms are simply defined as mathematical forms that are used as representatives of variables or numbers that are too large or too small to be written.

These index forms are also referred to as scientific notation or standard forms.

Some of the rules of index forms are;

From the information given, we have that;

4ˣ ×  \(2^y\)

Put forms in like bases format, we get;

2²ˣ × \(2^y\)

Now, add the exponents, we get;

\(2^2^x^+^y\)

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Answer:

she goes through 29 rooms

Step-by-step explanation:

116/4= 29

The spot on the shoreline is moving at a rate of about 1.764 feet per minute when it is 13 feet from the point on the shoreline closest to the lighthouse.

What is differentiation?

Differentiation is a mathematical operation that is used to find the rate at which a function changes. More specifically, it is the process of finding the derivative of a function.

The derivative of a function at a given point is a measure of how quickly the function is changing at that point. It gives the slope of the tangent line to the graph of the function at that point. The derivative can be thought of as the instantaneous rate of change of the function at that point.

Let's call the point on the shoreline closest to the lighthouse "P". We know that the distance from the spotlight to P is 130 feet, and we want to find the rate at which the distance from the spotlight to P changes when the spotlight is 13 feet from P.

To do this, we can use the chain rule to differentiate the distance formula with respect to time. Let's call the distance between the spotlight and P "d". Then:

                           d²= 130² + x²

Taking the derivative of both sides with respect to time gives:

                   2d * dd/dt = 0 + 2x * dx/dt

We can solve for dd/dt by plugging in the values we know:

130² + 13² = d²

d = \(\sqrt{(130^2 + 13^2)}\) = 130.325 ft

2(130.325) * dd/dt = 2(13) * dx/dt

dd/dt = (13/130.325) * dx/dt

We know that the spotlight revolves at a rate of 281 rad/min, or 281/2π ≈ 44.7 revolutions per minute. Each revolution of the spotlight covers a distance of 2π * 130 feet, so its speed is:

(2π * 130 ft/rev) * (44.7 rev/min) = 18410.8 ft/min

To find dx/dt when x = 13, we need to find the angular velocity of the spotlight at that point. The spotlight makes one full revolution every 60/14 ≈ 4.29 seconds, so its angular velocity is:

2π radians/rev ÷ 4.29 s/rev = 1.47 radians/s

At any given moment, the angle between the spotlight and the line connecting the lighthouse and P is equal to the arctangent of x/130. When x = 13, this angle is:

arctan(13/130) ≈ 5.71°

The rate at which the angle is changing is equal to the angular velocity of the spotlight, so we can use the formula for the derivative of the arctangent to find dx/dt:

dx/dt = 130 * tan(5.71°) * (1.47 radians/s)

dx/dt ≈ 17.602 ft/min

Finally, we can substitute this value into the expression we found for dd/dt:

dd/dt = (13/130.325) * 17.602

dd/dt ≈ 1.764 ft/min

So the spot on the shoreline is moving at a rate of about 1.764 feet per minute when it is 13 feet from the point on the shoreline closest to the

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Answer:

x = 8

Step-by-step explanation:

The measure of an arc is equal to the angle at the centre subtended by the arc.

The sum of the 3 arcs = 180° , then

5x + 6 + 83 + 51 = 180

5x + 140 = 180 ( subtract 140 from both sides )

5x = 40 ( divide both sides by 5 )

x = 8

Answer:

f(x - 2) = - x + 8

Step-by-step explanation:

Substitute x = x - 2 into f(x)

f(x - 2) = - (x - 2) + 6 = - x + 2 + 6 = - x + 8

The raster data model is commonly used to represent field features, but it is not suitable for representing point, line, and polygon features.

The raster data model is a grid-based representation where each cell or pixel contains a value representing a specific attribute or characteristic. It is well-suited for representing continuous spatial phenomena such as elevation, temperature, or vegetation density. Raster data is organized into a regular grid structure, with each cell having a consistent size and shape.

However, the raster data model has limitations when it comes to representing discrete features like points, lines, and polygons. Since raster data is based on a grid, it cannot precisely represent the exact shape and location of these features. Instead, they are approximated by the cells that cover their extent.

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The coordinates of the specified vertex after the given sequence of transformations is given by;

Q' = (3, -3).

In Mathematics, the translation of a geometric figure to the right simply means adding a digit to the value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure that is translated up simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image or parent function.

Mathematically, a horizontal translation to the right is modeled by this mathematical expression g(x) = f(x + N) while a vertical translation to the positive y-direction (upward) is modeled by this mathematical expression g(x) = f(x) + N.

Where:

By translating the coordinate Q (1, 3) two (2) units to the right, we have the following:

Coordinate Q (1, 3) → Coordinate Q' (1 + 2, 3) = Q (3, 3)

In Mathematics, a reflection across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate would change from positive to negative. Therefore, a reflection over the x-axis is given by this transformation rule:

(x, y)      →       (x, -y)

Coordinate Q' (3, 3) → (3, -3).

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Answer:

8

Step-by-step explanation:

Let's call the unknown side \(c\).

The Pythagorean Theorem states that in any right triangle, \(a^{2} + b^2 = c^2\)

Now plug in the known values.

\(6^2 + (2\sqrt 7)^2 = c^2\\36 + 4(7) = c^2\\36 + 28 = c^2\\64 = c^2\\c = \sqrt{64} = 8\)