If x - 2 ≥ 5; then
a. x can be 7 or more
b. x = 5
c. x = 7
d. x = 5

Answer:

added in picture

Step-by-step explanation:

added in picture

Answer:

3:1

Step-by-step explanation:

The squirrel tore up 3 of the sleeping bags and one was left untouched.

Answer:

Rational

Step-by-step explanation:

Pi 9/25 = 1.131

Decimals are usually rational

Answer:

sure

Step-by-step explanation:

Answer:

-8

the way you meant to write it was -4^2 x 2^-1

Step-by-step explanation:

Answer:

it is 8 but it's not negative 8

I tried negative 8 and it said it was wrong so it must be 8

The Pythagorean Theorem states the following:

Where "c" represents the hypotenuse of the Right triangle (which is a triangle that has an angle that measures 90 degrees), and "b" and "c" are the legs of the triangle.

To rewrite the formula solving for "b", you can follow the steps shown below:

1. Apply the Subtraction property of Equality by subtracting a^2 from both sides of the equation:

2. Now you must apply square root to both sides of the equation:

Because remember that:

Therefore, the formula solved for "b", is:

Answer:

It is the third one.

Step-by-step explanation:

The area of the room is 168 square feet, obtained by multiplying the length (3.5 yards converted to 10.5 feet) by the width (4 yards converted to 12 feet).

To calculate the area of the room, we first need to convert the measurements from yards to feet. Since 1 yard is equal to 3 feet, the length of the room is 3.5 yards × 3 feet/yard = 10.5 feet, and the width is 4 yards × 3 feet/yard = 12 feet.

To find the area, we multiply the length by the width: 10.5 feet × 12 feet = 126 square feet.

Therefore, the area of the room is 126 square feet.

It's important to include units in our calculations to ensure accurate measurements and conversions. In this case, we converted the measurements from yards to feet to maintain consistency. By multiplying the length and width, we obtained the total area of the room in square feet, which is 126 square feet.

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Answer:

Angle:

When two lines/rays intersect at a point, they form an angle.

=> Angles may be in radians and degrees.

See the attached file in which two rays intersect to form an angle.

Answer:

\(\boxed{\mathrm{view \: explanation \: and \: attachment}}\)

Step-by-step explanation:

Two lines (arms/rays) intersect at one point (vertex) creating an angle.

A statistic is a numerical summary of a sample.

A sample statistic is explained as any number computed from a sample of data.

Examples include the sample average, median, sample standard deviation, and percentiles. A statistic is a random variable because it is based on data obtained by sampling technique in which each sample has an equal probability of being chosen.

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a) It is a continuous random variable.

b) It is a discrete random variable.

c) It is not a random variable nor discrete.

d) It is a continuous random variable

e)  It is a discrete random variable

f) It is a discrete random variable

A continuous variable has an uncountable range of possible values.

Any value falling inside an interval is acceptable.

They cannot be stated as decimal numbers and can only accept a discrete value. Counting is used to obtain them rather than measuring.

a). The height of a randomly selected giraffe is a continuous random variable.

b). The random variable is discrete. You can count how many people are sitting at a computer.

c). The gender of college students ⇒ Gender is categorical data. It is neither continuous nor discrete.

d). The number of people in a restaurant that has a capacity of 300 is a continuous random variable

e). The number of bald eagles in a country Since the number of people cannot be expressed as decimals, thus it is a discrete random variable

f). it is a discrete random variable as a number of people is a discrete count, which takes values such as 0 or 1 or 2.

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Answer:

=d+6c

Step-by-step explanation:

I hope this is the right answer

For the first sample {2.038 2.054 2.053 2.055 2.059 2.059 2.009 2.042 2.053 2.047}, the process is still "in order," while for the second sample {2.022 1.997 2.044 2.044 2.032 2.045 2.045 2.047 2.030 2.044}, the process might be "out of order."

To determine whether the process is still "in order" or "out of order," we can compare the current sample of output to the known mean and standard deviation of the process.

For the first sample {2.038 2.054 2.053 2.055 2.059 2.059 2.009 2.042 2.053 2.047}:

Calculate the sample mean by summing up all the values in the sample and dividing by the number of values (n = 10):

Sample mean = (2.038 + 2.054 + 2.053 + 2.055 + 2.059 + 2.059 + 2.009 + 2.042 + 2.053 + 2.047) / 10 = 2.048.

Compare the sample mean to the known process mean (2.050):

The sample mean (2.048) is very close to the process mean (2.050), indicating that the process is still "in order."

Calculate the sample standard deviation using the formula:

Sample standard deviation = sqrt(sum((x - mean)^2) / (n - 1))

Using the formula with the sample values, we find the sample standard deviation to be approximately 0.019 liters.

Compare the sample standard deviation to the known process standard deviation (0.020):

The sample standard deviation (0.019) is very close to the process standard deviation (0.020), further supporting that the process is still "in order."

For the second sample {2.022 1.997 2.044 2.044 2.032 2.045 2.045 2.047 2.030 2.044}:

Calculate the sample mean:

Sample mean = (2.022 + 1.997 + 2.044 + 2.044 + 2.032 + 2.045 + 2.045 + 2.047 + 2.030 + 2.044) / 10 ≈ 2.034

Compare the sample mean to the process mean (2.050):

The sample mean (2.034) is noticeably different from the process mean (2.050), indicating that the process might be "out of order."

Calculate the sample standard deviation:

The sample standard deviation is approximately 0.019 liters.

Compare the sample standard deviation to the process standard deviation (0.020):

The sample standard deviation (0.019) is similar to the process standard deviation (0.020), suggesting that the process is still "in order" in terms of variation.

In summary, for the first sample, the process is still "in order" as both the sample mean and sample standard deviation are close to the known process values.

However, for the second sample, the difference in the sample mean suggests that the process might be "out of order," even though the sample standard deviation remains within an acceptable range.

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Answer: A.)

Step-by-step explanation: if you start at 7 and take 8 away your left with a negative

A is correct purple line to 7 and red line to -1

Hope this helps

The given unity feedback system is the type-1 system, which can be observed from the given open-loop transfer function G(s).

Steady state error is the difference between the input and the output as time approaches infinity. It is also the difference between the desired value and the actual output at steady-state.

The steady-state error is calculated using the error coefficient, which depends on the type of the system.Find the steady-state error if the input is 80u(t):The transfer function of the given system can be written as follows;G(s) = 80(8²)/(s+4)(8+6)(8+17)The type of the given system is the type-1 system.

As the input to the system is u(t), the error coefficient is given as,Kp = lims→0sG(s) = 80/4(6)(17) = 5/153The steady-state error can be found out by the following formula;

ess = 1/Kp = 153/5.

Therefore, the steady-state error of the given system if the input is 80u(t) is 153/5.Find the steady-state error if the input is 80tu(t):As the input to the system is tu(t), the error coefficient is given as,Kv = lims→0s²G(s) = 0The steady-state error can be found out by the following formula;ess = 1/Kv = ∞.

Therefore, the steady-state error of the given system if the input is 80tu(t) is infinity.Find the steady-state error if the input is 80t²u(t):As the input to the system is t²u(t), the error coefficient is given as,Ka = lims→0s³G(s) = ∞The steady-state error can be found out by the following formula;

ess = 1/Ka = ∞.

Therefore, the steady-state error of the given system if the input is 80t²u(t) is infinity.

By using the error coefficient formula, we have found that the steady-state error of the given system if the input is 80u(t) is 153/5, steady-state error of the given system if the input is 80tu(t) is infinity and steady-state error of the given system if the input is 80t²u(t) is infinity.

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Answer:

A , B , D , F

Step-by-step explanation:

Answer:

a. Replace "a number" with the variable, n.

b. The two operations are multiplication and addition.

d. The constants are 6 and 9.

f. The expression is written as 6(9 + n).

Step-by-step explanation:

The measure of angle A in a right triangle with base 5 cm and hypotenuse 10 cm is approximately 38.21 degrees.

We can use the inverse cosine function (cos⁻¹) to find the measure of angle A, using the cosine rule for triangles.

According to the cosine rule, we have:

cos(A) = (b² + c² - a²) / (2bc)

where a, b, and c are the lengths of the sides of the triangle opposite to the angles A, B, and C, respectively. In this case, we have b = 5 cm and c = 10 cm (the hypotenuse), and we need to find A.

Applying the cosine rule, we get:

cos(A) = (5² + 10² - a²) / (2 * 5 * 10)

cos(A) = (25 + 100 - a²) / 100

cos(A) = (125 - a²) / 100

To solve for A, we need to take the inverse cosine of both sides:

A = cos⁻¹((125 - a²) / 100)

Since this is a right triangle, we know that A must be acute, meaning it is less than 90 degrees. Therefore, we can conclude that A is the smaller of the two acute angles opposite the shorter leg of the triangle.

Using the Pythagorean theorem, we can find the length of the missing side at

a² = c² - b² = 10² - 5² = 75

a = √75 = 5√3

Substituting this into the formula for A, we get:

A = cos⁻¹((125 - (5√3)²) / 100) ≈ 38.21 degrees

Therefore, the measure of angle A is approximately 38.21 degrees.

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The ratio of the area of the first circle to the second circle is 4:1.

To find the ratio of the areas of two circles, where the circumference of the first circle is double the circumference of the second circle, we can use the formula for the circumference of a circle:

Circumference = 2 * π * radius

Let's assume that the radius of the second circle is 'r'. Since the circumference of the second circle is half of the first circle, we can write:
C2 = 2 * C1
2 * π * r = 2 * π * (2 * r)
2 * π * r = 4 * π * r

Now, let's find the ratio of the areas. The formula for the area of a circle is:

\(Area = π * radius^2\)

For the first circle, with radius '2r', the area is:

\(A1 = π * (2r)^2\)

\(A1 = π * (4r^2)\)

For the second circle, with radius 'r', the area is:

\(A2 = π * r^2\)

Now, let's find the ratio of the areas:

Ratio of areas = A1 / A2

\(Ratio of areas = (π * (4r^2)) / (π * r^2)\)

\(Ratio of areas = 4r^2 / r^2\)

Ratio of areas = 4

Therefore, the ratio of the area of the first circle to the second circle is 4:1.

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Answer:

130°

Step-by-step explanation:

angle TFM + angle MFD = 180° (being a linear pair)

or, 4m + 142° +2m + 56°= 180°

or, 6m= 180°- 198°

or, m= -18°/6

so, m= -3°

now, angle TFM = 4m +142°= -12°+142°= 130°

Answer: C

Step-by-step explanation: C

2 divided into 9 parts is 2/9.

Let's' explain this visually

Take this pizza, (image below)

Let's say we have two pizzas for 8 friends (including ourselves), so naturally, we'll cut the pizza's each into 9 slices, 1 for each, now everyone gets 1/9 of a pizza, but there are two pizzas, so if we add 1/9+1/9, we'll get two ninths.

Now 2/9=0.2 repeating!

This is how I got my answer sorry for the vague  explanation

The total change in the number of bushels has for sold after 6 days is 120.4.

A farmer has 220 bushels of wheat to sell at her roadside stand. She sells an average of 16 1/5 bushels each day.

To Represent the total change in the number of bushels she has for sale after 6 days.

The answer provided below has been developed in a clear step by step manner.

Step: 1

The given parameters are:

The initial number of bushels the farmer has = 220

The amount of bushels the farmer sells each day

\(16\frac{1}{5} = \frac{(16*5)+1}{5} = \frac{81}{5}\)

First we need to find the total number of bushels the farmer has for sell after 6 days.

First we simplify use the mixed fraction. Now we have to find the total number of bushels the farmer has for sell after 6 days.

Step: 2

The number of bushels sold after 6 days is:

\(= 6 * \frac{81}{5}\)

= \(\frac{486}{5}\)

Hence the total change in the number of bushels has for sale after 6 days is

\(= 220 - \frac{486}{5}\)

\(= \frac{614}{5}\)

= 122.8

First we find the total number of bushels sold after 6 days. Then substract it from the initial number of bushels.

Hence the answer is, the total change in the number of bushels has for sold after 6 days is 120.4.

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Answer:

\(a_{37}=249\)

Step-by-step explanation:

A sequence that has a common difference is an arithmetic sequence:

\(a_n=a_1+(n-1)d\)

where aₙ is the nth term, n is the index, and d is the common difference.

In your question:

Plug those into the formula:

\(a_{37}=-39+(37-1)8\)

Then solve:

\(a_{37}=-39+(36)8\\a_{37}=-39+288\\a_{37}=249\)

The drop in the price of peanut butter would result in an increase in the demand for bread. In other words, the decrease in the price of peanut butter would result in an increase in the demand for bread.

Complementary goods are items that are frequently consumed together. As a result, when the cost of one of them changes, it affects the consumption of the other. When bread and peanut butter are complementary goods, a price reduction of peanut butter results in an increase in its demand. The demand for bread will increase as a result of the decrease in the price of peanut butter. As a result, if the price of peanut butter is reduced, its consumption will rise. As a result, the demand for bread would increase because of the complementary relationship between the two. Bread and peanut butter are complementary goods that are frequently purchased together.

When the price of peanut butter decreases, people would buy more peanut butter, causing them to purchase more bread to go with it. The drop in the price of peanut butter would result in an increase in the demand for bread. In other words, the decrease in the price of peanut butter would result in an increase in the demand for bread. The relationship between complementary goods is, therefore, inverse.

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Answer:

(8x-7)<9

Use 1 to open the bracket

8x - 7 < 9

Add 7 to both sides

8x < 16

Divide both sides by 8

x < 2

The pH is calculated using the formula:

The question gives the pH of lemon juice to be 2.2.

Hence, the formula is written to be:

Multiply both sides by -1:

Since the log is in base 10, we have:

Apply the law of log

\(1=1+p \\ \\ 1-1=1+p-1 \\ \\ \boxed{p=0}\)

The correct answer is B

Answer:

Step-by-step explanation: Simple plug x in.

x=1

(Square root) 4 -1=1

x=6

(square root) 9 -1=2

x=13

(square root ) 16-1=3

x=1 Y=1

x=6  Y=2

x=13  Y=3

The area inside the curve r = 3 + sin(θ) is (5π)/2 square units.

Double integration is an important tool in calculus that allow us to calculate the area of irregular shapes in the Cartesian coordinate system. In particular, they are useful when we are dealing with shapes that are defined in polar coordinates.

To find the area inside this curve, we can use a double integral in polar coordinates. The general form of a double integral over a region R in the xy-plane is given by:

∬R f(x,y) dA

where dA represents the infinitesimal area element, and f(x,y) is the function that we want to integrate over the region R.

In polar coordinates, we can express dA as r dr dθ, where r is the distance from the origin to a point in the region R, and θ is the angle that this point makes with the positive x-axis. Using this expression, we can write the double integral in polar coordinates as:

∬R f(x,y) dA = ∫θ₁θ₂ ∫r₁r₂ f(r,θ) r dr dθ

where r₁ and r₂ are the minimum and maximum values of r over the region R, and θ₁ and θ₂ are the minimum and maximum values of θ.

To find the area inside the curve r = 3 + sin(θ), we can set f(r,θ) = 1, since we are interested in calculating the area and not some other function. The limits of integration can be determined by finding the values of r and θ that define the region enclosed by the curve.

To do this, we first note that the curve r = 3 + sin(θ) represents a cardioid, which is a type of curve that is symmetric about the x-axis. Therefore, we only need to consider the region in the first quadrant, where 0 ≤ θ ≤ π/2.

To find the limits of integration for r, we note that the curve intersects the x-axis when r = 0. Therefore, the minimum value of r is 0. The maximum value of r can be found by setting θ = π/2 and solving for r:

r = 3 + sin(π/2) = 4

Therefore, the limits of integration for r are r₁ = 0 and r₂ = 4.

The limits of integration for θ are simply θ₁ = 0 and θ₂ = π/2, since we are only considering the region in the first quadrant.

Putting it all together, we have:

Area = ∬R 1 dA

        = ∫\(0^{\pi /2}\) ∫0⁴ 1 r dr dθ

Evaluating this integral gives us:

Area = π(3² - 2²)/2 = (5π)/2

Therefore, the area inside the curve r = 3 + sin(θ) is (5π)/2 square units.

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Using double integrals, the area inside the curve r = 3 + sin(θ) is 0 units².

For the area inside the curve r = 3 + sin(θ), we can use a double integral in polar coordinates. The area can be expressed as:

A = ∬R r dr dθ

where R represents the region enclosed by the curve.

In this case, the curve r = 3 + sin(θ) represents a cardioid shape. To determine the limits of integration for r and θ, we need to find the bounds where the curve intersects.

To find the bounds for θ, we set the expression inside sin(θ) equal to zero:

3 + sin(θ) = 0

sin(θ) = -3

However, sin(θ) cannot be less than -1 or greater than 1. Therefore, there are no solutions for θ in this case.

Since there are no intersections, the region R is empty, and the area inside the curve r = 3 + sin(θ) is zero.

Hence, the area inside the curve r = 3 + sin(θ) is 0 units².

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