Jamal measures the round temperature dial on a thermostat and calculates that it has a circumference of 87.92 millimeters. What is the dial's radius?

Answer:

Supplementary angle= two angle that sum upto 180 degrees.

Step-by-step explanation:

[tex]180 - 22 = 158[/tex]

Supplementary angle of 22° is 158°

The given differential equations can be rewritten in matrix-vector form as dX/dt = AX, where X = [x₁, x₂]ᵀ and A = [[2, 1], [1, 2]].

To rewrite the given differential equations in matrix-vector form, follow these steps:

1. Identify the dependent variables, x₁ and x₂, and arrange them into a column vector, X. This gives X = [x₁, x₂]ᵀ.

2. Identify the coefficients of x₁ and x₂ in the given differential equations. For dx₁/dt = 2x₁ + x₂ and dx₂/dt = x₁ + 2x₂, these coefficients are 2, 1, 1, and 2.

3. Arrange the coefficients into a matrix A, with rows corresponding to the order of the dependent variables. This gives A = [[2, 1], [1, 2]].

4. Write the matrix-vector equation dX/dt = AX. This represents the original system of differential equations in matrix-vector form.

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Answer:

f(2) = 24

Step-by-step explanation:

to evaluate f(2) substitute x = 2 into f(x) , that is

f(2) = 15(2) - 6 = 30 - 6 = 24

The formula to find the total number of trees, t, in r rows is [tex]t = 10 \times r[/tex]

Sequence and series - A sequence is a list of items/objects which have been arranged in a sequential way. A series can be highly generalized as the sum of all the terms in a sequence. However, there has to be a definite relationship between all the terms of the sequence.

If there are 10 trees planted in each row, then the total number of trees in one row is 10. To find the total number of trees in r rows, we need to multiply the number of trees in one row (10) by the number of rows (r):

[tex]t = 10 \times r[/tex]

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If the trees are planted in rows of 10, then the total number of trees in r rows can be found using the formula: t = 10r

A sequence is an ordered list of numbers or other mathematical objects, such as functions or geometric figures, that follow a certain pattern or rule. A sequence can be finite or infinite and can be specified using a formula or a recursive rule.

A series is a sum of the terms in a sequence, typically written using the sigma notation Σ

where t is the total number of trees and r is the number of rows. This formula simply multiplies the number of trees in each row (which is 10) by the number of rows, to get the total number of trees.

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The magnitude of the magnetic flux through the circular ring is 3.741×10−4 Tm².

To find the magnitude of the magnetic flux through the circular ring, we can use the formula:

Φ = BA cosθ

where Φ is the magnetic flux, B is the magnetic field strength, A is the area of the ring, and θ is the angle between the magnetic field and the normal to the ring.

Given that the magnetic field strength is 8.5×10−2 T, the radius of the ring is 3.9 cm (or 0.039 m), and the angle between the magnetic field and the normal to the ring is 24∘, we can calculate the area of the ring:

A = πr²
A = π(0.039)²
A = 0.0048 m²

Substituting the values into the formula, we get:

Φ = (8.5×10−2)(0.0048)cos24∘
Φ = 3.741×10−4 Tm^2

Therefore, the magnitude of the magnetic flux through the circular ring is 3.741×10−4 Tm².

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Answer:

Step-by-step explanation:

You are asked for the area and perimeter of a figure comprised of a square and two sectors.

The perimeter of the figure is the sum of the lengths of the outside edges. You recognize vertical edges AD and BC as being the sides of a square that are 4 units long.

The other two sides of the square are AB and CD, but these are not part of the perimeter. The significance of those is that they are radii of the sectors ABE and CDF. The straight segments of AE and CF of those sectors have the same length (4 units) as the side of the square. Those straight segments are part of the perimeter.

In effect, the four straight segments of the perimeter are all 4 units.

The curved edges of the two sectors have a length that is found using the formula ...

  s = rθ

where r is the sector radius, and θ is the central angle in radians.

The angle is shown as 30°, which is 30°(π/180°) = π/6 radians. The radius is the square side length, 4, so each curved line has length ...

  s = (4)(π/6) = 2/3·π

The perimeter of the figure is the sum of the lengths of the straight segments and the curved arcs:

  P = 4(4 units) +2(2/3π units) = 16 +4/3π units ≈ 20.19 units

As with the perimeter, the area is composed of the area of a square and the areas of two sectors.

The area of the square is the square of its side length:

  A = s²

  A = (4 units)² = 16 units²

The area of each sector is effectively the area of a triangle with base equal to the arc length (2/3π) and height equal to the radius of the arc (4 units). The sector area is ...

  A = 1/2rs

  A = 1/2(4 units)(2/3π units) = 4/3π units²

The area of the whole figure is the sum of the area of the square and the areas of the two sectors:

  A = square area + 2×(sector area)

  A = 16 units² + 2×(4/3π units²) = (16 +8/3π) units² ≈ 24.38 units²

__

Additional comment

In general, you find the perimeter and/or area of a strange figure by decomposing it into parts whose perimeter and area you can compute. (When you get to calculus, those parts will be infinitesimally small and there will be an infinite number of them.) At this point, you will generally be making use of formulas that should be familiar.

The formula for the area of a sector is usually written ...

  A = 1/2r²θ

Here, we have made use of our previous computation of s=rθ to write the area formula as A = 1/2rs. The similarity to the triangle area formula is not accidental.

Answer:

2.80

Step-by-step explanation:

35p = £0.35

8 × £0.35 = £2.80

The data set is a Population, because it is a collection of salaries for all baseball players in the league.Therefore option D is correct.

To determine whether the data set is a population or a sample:

Population, because it is a collection of salaries for all baseball players in the league.

The data set includes every single baseball player's salary in the league, which makes it a population.

It is not a sample because it includes every individual in the group being studied, rather than just a subset of them.

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The Reverse Polish Notation of the expression A * B )/( C * D is: AB* CD* /

To express the given expression A * B )/( C * D in Reverse Polish Notation (RPN):

You would follow these steps:

STEP 1: Identify the operators and operands in the expression: A * B, /, and C * D
STEP 2: Convert the sub-expressions to RPN:
  - A * B becomes AB*
  - C * D becomes CD*
STEP 3: Combine the RPN sub-expressions with the remaining operator, /:
  - AB* CD* /

So, the Reverse Polish Notation of the expression A * B )/( C * D is: AB* CD* /

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Answer:

Let’s call the width of the rectangle “w”. Since the length of the rectangle is twice its width, we can call the length “2w”. We know that the diagonal of the rectangle is equal to the square root of 45 cm. Using Pythagorean theorem, we can find that:

diagonal^2 = length^2 + width^2 45 = (2w)^2 + w^2 45 = 4w^2 + w^2 45 = 5w^2 w^2 = 9 w = 3

So the width of the rectangle is 3 cm and its length is twice that, or 6 cm.

Step-by-step explanation:

The following parts can be answered by the concept of null hypothesis.

a) The best conclusion if H0 is rejected is (ii) The scale is not in calibration.

b) If the scale is actually in calibration but the conclusion is reached that the scale is not in calibration, it would be a Type I error

a) If H0 is rejected, it means that there is enough evidence to suggest that the population mean reading on the scale is not equal to 10, which indicates that the scale is not in calibration. Therefore, the best conclusion in this case would be (ii) The scale is not in calibration.

b) If the conclusion is reached that the scale is not in calibration, but in reality, it is actually in calibration (i.e., μ=10), it would be a Type I error. This is because the null hypothesis (H0) is rejected incorrectly, leading to a false conclusion. Therefore, the type of error in this case would be a Type I error.

Therefore, the answer is:

a) The best conclusion if H0 is rejected is (ii) The scale is not in calibration.

b) If the scale is actually in calibration but the conclusion is reached that the scale is not in calibration, it would be a Type I error

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The cylindrical coordinates of the point with rectangular coordinates (x, y, z) = (-3, 5, -1) are (ρ, θ, z) ≈ (sqrt(34), -1.03, -1).

Cylindrical coordinates are a type of coordinate system used in three-dimensional space to locate a point using three coordinates: ρ, θ, and z. The cylindrical coordinate system is based on a cylindrical surface that extends infinitely in the z-direction and has a radius of ρ in the xy-plane.

To convert rectangular coordinates (x, y, z) to cylindrical coordinates (ρ, θ, z), we use the following formulas:

ρ =[tex]\sqrt(x^2 + y^2)[/tex]

θ = arctan(y/x)

z = z

Substituting the given values, we get:

ρ = [tex]\sqrt((-3)^2 + 5^2)[/tex]= sqrt(34)

θ = arctan(5/-3) ≈ -1.03 radians or ≈ -58.8 degrees (measured counterclockwise from the positive x-axis)

z = -1

Therefore, the cylindrical coordinates of the point with rectangular coordinates (x, y, z) = (-3, 5, -1) are (ρ, θ, z) ≈ (sqrt(34), -1.03, -1).

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The statement "If F and G are vector fields, then curl(F + G) = curl F + curl G" is true.

To explain why, let's consider the curl operation which follows the standard rules of vector calculus. The curl of a vector field is given by the cross product of the del (∇) operator and the vector field. For two vector fields F and G, the statement can be represented mathematically as:

curl(F + G) = curl F + curl G

Now, let's compute the curl of the sum of the vector fields (F + G):

curl(F + G) = ∇ × (F + G)

Using the distributive property of the cross product, we can distribute the del operator across the sum of the vector fields:

∇ × (F + G) = (∇ × F) + (∇ × G)

The left side of the equation represents the curl of the sum of vector fields (F + G), and the right side represents the sum of the individual curls of F and G:

curl(F + G) = curl F + curl G

Therefore, the statement is true, and the curl operation follows the linearity property in vector calculus.

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Number of books - 4

Number of pencils - 7

Now, we can order this as a ratio.

A ratio is two numbers put as a proportion. It's normally written out as first number: second number.

In this case, it's the ratio of number of

books: number of pencils.

Fill in the number of books and number of pencils into each side of the equation.

number of books: number of pencils

4 books: 7 pencils (the unit is normally dropped)

So therefore, 4:7 would be your final answer.

Note

Note you have asked for ratio but option is in fraction

Hope this helped!

please make me brainalist and keep smiling dude I hope you will be satisfied with my answer is updated

Answer: Ratio of the books to pencil is

Step-by-step explanation:

There are:

7 pencils

5 books

So the ratio of books to pencils is 5:7

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The probability that a randomly selected student spends at most 185 hours on the project is 1 (or 100%).

The mean of a gamma distribution with parameters a and ß is a/ß², so in this case, the mean is 50/3 = 16.67 hours.

The variance of a gamma distribution with parameters a and ß is a/ß², so in this case, the variance is 50/9 = 5.56 hours. Therefore, the standard deviation is the square root of the variance, which is approximately 2.36 hours.

We can convert X to a standard normal variable Z using the formula:

Z = (X - μ) / σ

where μ is the mean of X and σ is the standard deviation of X. Substituting in the values we calculated in Step 1, we get:

Z = (X - 16.67) / 2.36

To find the probability that a randomly selected student spends at most 185 hours on the project,

we need to find the corresponding Z-score for X = 185 and then find the area under the standard normal curve to the left of that Z-score.

Z = (185 - 16.67) / 2.36 = 69.53

Using a standard normal table or calculator, we can find that the area to the left of Z = 69.53 is essentially 1. Therefore, the approximate probability that a randomly selected student spends at most 185 hours on the project is 1 (or 100%).

This is because the gamma distribution with a large a is well approximated by a normal distribution, and so the probability of X being more than a few standard deviations away from the mean is extremely small.

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Answer:

(3)

Step-by-step explanation:

the limit lines are the same (and correct) in all 4 pictures.

the difference is the applicable side of the lines.

y <= x + 3

because of the "<=" the valid area is below the line. in our case to the right and below the line.

that eliminates (1) and (4).

y >= -2x - 2

because of the ">=" the valid area is above the line. in our case right and above the line.

so, (3) is correct.

Consider a homogeneous linear system with a 4 by 9 coefficient matrix. The coefficient matrix has rank at most equal to 4 and at least 5 free variable columns.

This is because the rank of a matrix cannot exceed the number of rows or columns it has. In this case, the matrix has 4 rows, so the rank cannot exceed 4.

Additionally, the number of free variable columns can be found by subtracting the rank of the matrix from the number of columns. In this case, there are 9 columns, so subtracting the maximum rank of 4 gives us 5 free variable columns.

Therefore, The coefficient matrix has rank at most equal to 4 and at least 5 free variable columns.

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Answer:

C

Step-by-step explanation:

Sin is opposite divided by hypotenuse, so that would be 21 divided by 35.

The point of intersection is (0, 3). This means that the graphs of g(x) and h(x) intersect at the point where x=0 and y=3.

To find the point of intersection between the graphs of g(x)=2x+3 and h(x)=5x+3, we need to solve the equation g(x) = h(x) for x:

2x + 3 = 5x + 3

Subtracting 2x from both sides, we get:

3 = 3x + 3

Subtracting 3 from both sides, we get:

0 = 3x

Dividing both sides by 3, we get:

x = 0

So the graphs of g(x) and h(x) intersect at x = 0. To find the y-coordinate of the point of intersection, we can substitute x = 0 into either g(x) or h(x). Using g(x), we get:

g(0) = 2(0) + 3 = 3

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The best descriptiοn and example οf the null hypοthesis in a hypοthesis test is: "A statistical hypοthesis that there is nο difference between a parameter and a specific value, οr between twο parameters. Example: Hοu - 90"

The null hypοthesis is a statistical hypοthesis that states there is nο significant difference between twο grοups οr variables being cοmpared.

It is οften denοted as H₀ and is a statement that researchers assume tο be true until prοven οtherwise by empirical evidence.

Frοm the given οptiοns

The best descriptiοn and example οf the null hypοthesis in a hypοthesis test is: "A statistical hypοthesis that there is nο difference between a parameter and a specific value, οr between twο parameters. Example: Hοu - 90"

In a hypοthesis test, the null hypοthesis represents the default assumptiοn that there is nο significant difference between twο grοups, οr between a sample and a pοpulatiοn.

The example given, "H₀: μ = 90", represents a null hypοthesis where there is nο significant difference between a parameter (represented by the variable "Hοu") and a specific value (90).

This means that if the null hypοthesis is true, the parameter "H₀: μ" is equal tο 90 οr dοes nοt differ significantly frοm 90.

Hence,

The best descriptiοn and example οf the null hypοthesis in a hypοthesis test is: "A statistical hypοthesis that there is nο difference between a parameter and a specific value, οr between twο parameters. Example: Hοu - 90"

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The sample size increases, but the standard deviation may increase, decrease, or stay the same depending on the probability of success.

False.

The mean (or expected value) of a binomial distribution is given by the formula np, where n is the sample size and p is the probability of success. So as the sample size increases, the mean of the distribution increases proportionally, assuming the probability of success remains constant.

However, the standard deviation of a binomial distribution is given by the formula sqrt(np(1-p)). As the sample size increases, the standard deviation does not necessarily increase. In fact, it can decrease if the probability of success is small or large, and increase if the probability of success is close to 0.5. This is because the variance of the binomial distribution is given by np(1-p), which has a maximum value at p = 0.5. When the probability of success is close to 0 or 1, the variance decreases as the sample size increases because the outcome becomes more predictable. Conversely, when the probability of success is close to 0.5, the variance increases as the sample size increases because there is greater variability in the outcomes.

In summary, the mean of a binomial distribution always increases as the sample size increases, but the standard deviation may increase, decrease, or stay the same depending on the probability of success.

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If a and b are both positive integers, then (2a − 1) mod (2b − 1) = 2a mod b − 1, because the left side can be rewritten as (2a mod (2b − 1)) - 1, which equals the right side.

To show that (2a − 1) mod (2b − 1) = 2a mod b − 1, let's break it down step-by-step:

1. Consider (2a − 1) mod (2b − 1). Apply the property of modular arithmetic, which states that (A mod N) = (A mod N) mod N.

2. This gives us (2a mod (2b − 1)) - 1.

3. Observe that 2a mod (2b − 1) can also be written as 2a mod (2(b − 1) + 1), which equals 2a mod 2(b - 1) + 2a mod 1.

4. Since 2a mod 1 = 0, we have 2a mod 2(b - 1) + 0 = 2a mod 2(b - 1).

5. Apply the distributive property of modular arithmetic to get 2(a mod (b - 1)) = 2a mod b.

6. Substitute this back into the expression from step 2: (2a mod b) - 1.

7. Therefore, (2a − 1) mod (2b − 1) = 2a mod b − 1.

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The linear equation in point-slope form is:

y + 6 = (3/4)*(x + 4)

For a linear equation whose slope is m, and we know that it passes through a point (x₁, y₁), the point slope form can be written as follows:

y - y₁ = m*(x - x₁)

Here we know that the slope of the linear equations is (3/4) and the point is (-4, -6)

Then the linear equation in the point slope form can be written as:

y + 6 = (3/4)*(x + 4)

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The number of bacteria in a bacteria culture after following number of hours are: a) After 3 hours, there are 12,800 bacteria. b) After t hours, there are 200 * 2^(2t) bacteria. c) After 40 minutes, there are 400 bacteria.

Given that the bacteria culture starts with 200 bacteria and doubles in size every half hour.

a) To find this, we first need to determine how many half-hour intervals are in 3 hours. Since there are 2 half-hours in an hour, we have 3 hours * 2 = 6 half-hour intervals. The bacteria doubles in size every half hour, so we have:
200 bacteria * 2^6 = 200 * 64 = 12,800 bacteria

b) To generalize this for any number of hours (t), we need to find how many half-hour intervals are in t hours. That's 2t half-hour intervals. Then we have:
200 bacteria * 2^(2t)

c) First, we need to convert 40 minutes to hours. Since there are 60 minutes in an hour, we have 40/60 = 2/3 hours. We then find how many half-hour intervals are in 2/3 hours: (2/3) * 2 = 4/3 intervals. Since we can't have a fraction of an interval, we'll round down to 1 interval (since the bacteria doubles every half-hour). Then we have:
200 bacteria * 2^1 = 200 * 2 = 400 bacteria

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The Set corresponding to (AUB)nc is Option C. (3, 4, 5, 7, 9).

(AUB)nc represents the complement of the union of sets A and B. To find this set, we first need to find the union of sets A and B, which is the set of all elements that are in either A or B or both.

Set A contains all prime numbers, so A = (2, 3, 5, 7, 11, ...). Set B contains (4, 7, 9, 11, 13, 14). Taking the union of sets A and B gives us:

AUB = (2, 3, 4, 5, 7, 9, 11, 13, 14)

The complement of this set (denoted by nc) contains all elements that are not in this set. Therefore, (AUB)nc contains all elements that are not in the union of sets A and B.

Option A contains 13, which is in AUB. Option B contains 4 and 7, which are also in AUB. Option D contains all elements in AUB. Therefore, the correct answer is option C, which contains (3, 4, 5, 7, 9) and does not contain any elements that are in A or B.

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To write this distance in scientific notation, we can express it as:

[tex]1.08[/tex] × [tex]10^8 km[/tex]

Distance refers to the physical length or space between two objects or points, measured typically in units such as meters, kilometers, miles, etc.

Light travels at a constant speed of approximately 299,792,458 meters per second (m/s) in a vacuum. To convert this speed to kilometers per minute, we can use the following steps:

Multiply the speed of light in meters per second by the number of seconds in one minute:

299,792,458 m/s × 60 seconds/minute = 17,987,547,480 m/minute

Convert this distance from meters to kilometers by dividing by 1,000:

17,987,547,480 m/minute ÷ 1,000 = 17,987,547.48 km/minute

Therefore, light travels approximately 17.99 million kilometers per minute.

To find out how far light travels in 6 minutes, we can multiply the distance it travels in one minute by 6:

17,987,547.48 km/minute × 6 minutes = 107,925,284.88 km

To write this distance in scientific notation, we can express it as a number between 1 and 10 multiplied by a power of 10:

107,925,284.88 km = 1.0792528488 × [tex]10^8 km[/tex]

Rounding this to two significant figures gives:

[tex]1.08[/tex] × [tex]10^8 km[/tex]

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The tangential component of acceleration is c. aT = 4t/√4t²+5.

We need to follow these steps:

1. Calculate the first derivative of r(t) to get the velocity vector v(t).
2. Calculate the second derivative of r(t) to get the acceleration vector a(t).
3. Calculate the magnitude of the velocity vector |v(t)|.
4. Calculate the tangential component of acceleration aT by finding the dot product of a(t) and v(t), and then dividing by the magnitude of the velocity vector |v(t)|.

Let's go through these steps:

1. r(t) = ti + t²j + 2tk
  v(t) = dr(t)/dt = (1)i + (2t)j + (2)k

2. a(t) = dv(t)/dt = (0)i + (2)j + (0)k

3. |v(t)| = √(1² + (2t)² + 2²) = √(1 + 4t² + 4) = √(4t² + 5)

4. aT = (a(t) • v(t)) / |v(t)| = ((0)(1) + (2)(2t) + (0)(2)) / √(4t² + 5) = (4t) / √(4t² + 5)

So, the tangential component of acceleration is:

aT = 4t / √(4t² + 5)

This corresponds to option c. aT = 4t/√4t²+5.

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Answer:

0+8=8

8+0=8

8-0=8

8-8=0