Please help me I cannot do this (BUT it might be easy for u if ur an expert) B]

The error in the measurement is 3.5%.

Percentage error is a measurement of the discrepancy between an observed (measured) and a true (expected, accepted, known etc.) value. Mathematically, we can write -

\($\delta = \left| \frac{v_A - v_E}{v_E} \right| \cdot 100\%\)

Given is that James tries to cut a wooden board 20 inches long. The wooden board ends up being 20.7 inches long.

We can write the percentage error as -

p% = |20.7 - 20|/20 x 100

p% = 0.7 x 5

p% = 3.5%

Therefore, the error in the measurement is 3.5%.

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The probability of randomly selected patient selected for coronary, oncology or both is equal to P( H∪C ) = 0.24.

Let patient admitted with heart disease represented by P(H)

P(H) = 12%

       = 0.12

And patient admitted for cancer disease represented by P(C)

P(H) = 16%

       = 0.16

Percent of patient received both coronary and oncology = 4%

P( H∩C ) = 0.04

Probability of randomly selected patient admitted for coronary, oncology or both is :

P( H∪C ) = P(H) + P(C) - P(H∩C )

⇒P( H∪C ) = 0.12 + 0.16 - 0.04

⇒ P( H∪C ) = 0.24

Therefore, the probability of randomly selected patient getting treatment for coronary, oncology or both is given by  P( H∪C ) = 0.24.

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Answer:

(a) The domain of f(x) is all real numbers, as there are no restrictions or excluded values for the expression x^2 - 16.

(b) There are no vertical asymptotes for f(x). The horizontal asymptote does not exist since the function is not a rational function.

(c) The intervals of increase for f(x) are (-∞, -4) and (4, +∞), while the interval of decrease is (-4, 4).

Step-by-step explanation:

(a) To determine the domain of f(x), we need to consider any potential restrictions on the function. In this case, the expression x^2 - 16 does not have any limitations or excluded values. Therefore, the domain of f(x) is all real numbers.

(b) Vertical asymptotes occur when the function approaches infinity or negative infinity as x approaches a certain value. However, for the function f(x) = x^2 - 16, there are no fractions or denominators involved, which are common sources of vertical asymptotes. Therefore, there are no vertical asymptotes for f(x).

Horizontal asymptotes, on the other hand, are typically found in rational functions. Since f(x) = x^2 - 16 is not a rational function (it is a polynomial), it does not have a horizontal asymptote. The function does not approach a specific y-value as x tends to infinity or negative infinity.

(c) To determine the intervals of increase and decrease, we can look at the behavior of the function f(x) = x^2 - 16. The function is a quadratic polynomial, and its graph is a parabola opening upwards.

Since the coefficient of the x^2 term is positive, the parabola opens upwards, indicating that the function increases on either side of the vertex. The vertex of the parabola occurs at x = 0, where the function reaches its minimum value of -16.

Therefore, the intervals of increase for f(x) are (-∞, -4) and (4, +∞), as the function is increasing to the left of -4 and to the right of 4.

The interval of decrease for f(x) is (-4, 4), as the function decreases from -4 to 4, reaching its minimum value at x = 0.

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Step-by-step explanation:

Based on the cost of the copy paper and the discount on ink cartridges, the cost of the ink cartridge is $15 each.

First find the amount paid for the ink cartridges:

= Total spent - cost of copy paper

= 175 - 45

= $130

He got a discount of $2 per cartridge. For 10 cartridges he got a discount of:

= 2 x 10

= $20

The cost of each ink cartridge is:

= (Amount spent on ink cartridges + Discount) / Number of cartridges

= (130 + 20) / 10

= $15 each

In conclusion, each cartridge cost $15.

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the surface integral is approximately 81.02.

We need to evaluate the surface integral:

∫∫H 8y dA

where H is the helicoid given by the vector parametric equation

r(u, v) = (u cos v, u sin v, v), 0 ≤ u ≤ 1, 0 ≤ v ≤ 7π.

The surface integral of a scalar function f(x, y, z) over a surface S is given by:

∫∫S f(x, y, z) dA = ∫∫D f(x, y, g(x, y)) √(fx^2 + fy^2 + 1) dA

where D is the projection of the surface S onto the xy-plane, and g(x, y) is the z-coordinate of the surface S as a function of x and y.

In this case, we have:

f(x, y, z) = 8y

x = u cos v

y = u sin v

z = v

So, we need to find the partial derivatives:

fx = -u sin v

fy = u cos v

fz = 0

and evaluate the expression under the square root:

fx^2 + fy^2 + 1 = u^2 + 1

The projection of the helicoid H onto the xy-plane is the unit circle centered at the origin, since for any value of v, the values of x and y trace out a circle of radius u. So, we have:

D: x^2 + y^2 ≤ 1

The z-coordinate of the helicoid is simply z = v, so we have:

g(x, y) = z = arctan(y/x)

Putting it all together, we get:

∫∫H 8y dA = ∫∫D 8u sin v √(u^2 + 1) dA

= ∫0^1 ∫0^2π 8u sin v √(u^2 + 1) dudv (converting to polar coordinates)

Performing the u-integration first, we get:

∫0^1 8√(u^2 + 1) [ -cos v ]_0^2π du

= 16∫0^1 √(u^2 + 1) du

= 16(0.5[e^2π - 1] + 0.5 sinh^-1(1))

≈ 81.02

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Answer:

Look below

Step-by-step explanation:

The equation is y=mx+b where m is the slope and b is the y-intercept.

We can find this by first calculating the slope by using any two x and y values

\(Slope = \frac{rise}{run} = \frac{y_{2}-y_{1}}{x_{2}-x_{1} } = \frac{-12+2}{3-1} =\frac{-10}{2} =-5\)

Now we can plug the slope back into the equation to solve for the y-intercept

y=-5x+b

-12=-5(3)+b

-12=-15+b

b=3

Therefore the equation is y=-5x+3

Now we plug in the values for x/y to complete the table

y=-5(0)+3=0+3=3

y=-5(2)+3=-10+3=-7

68=-5x+3

65=-5x

x=-13

y=-5(25)+3=-125+3=-122

So the missing values (in order from left to right) are:

3, -7, -13, and -122

The percentage of people who do not like to listen to radio as well as watch the television is 65%.

It is important to note that a percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

From the information, 36% like to listen to radio as well as watch the television.

Therefore, the percentage of the people who do not like to listen to radio as well as watch the television will be:

= 1 - 35%

= 65%

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In a survey of a community. 55% of the people like to listen the radio, 65% like to watch the television and 35% like to listen the radio as well as watch the television

Find the percentage of the people who do not like to listen radio as well as watch the television.

The true statements about the linear equation are:

"The y-intercept means the initial cost is $60."

"The slope means the cost increases $40 each hour."

Remember that the general linear equation in the slope-intercept form is:

y = a*x + b

Where a is the slope and b is the y-intercept.

Here the linear equation is:

y = 40x + 60

Where y is the cost for hiring an electrician for x hours.

We can se that the slope is 40, so that is what the electrician charges per hour, and the y-intercept is 60, so that is the initial cost.

Then the true statements are:

"The y-intercept means the initial cost is $60."

"The slope means the cost increases $40 each hour."

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Answer:B and C

Step-by-step explanation:

Answer:

1,000*31 = 31,000

Step-by-step explanation:

since the first 1000 fans get a ball and each ball costs $31 then u multiply

Answer:

132 m

Step-by-step explanation:

Refer to attachment for figure.

In smaller triangle with angle theta , we have ,

⇒ tanθ = p/b

⇒ tanθ = h/121m

⇒ tanθ = h/121 m

In triangle with angle 90-∅

⇒ tan(90-θ) = p/b

⇒ cot θ = h/144 m

Multiplying these two ,

=> tanθ . cotθ = h/121 m × h/144m

=> 1 = h²/ (121 m × 144m )

=> h² = 121m × 144m

=> h= √ ( 121m × 144m)

=> h = 11m × 12m

=> h = 132 m

Step-by-step explanation:

priorities of operations :

1. brackets

2. exponents

3. multiplications and divisions

4. additions and subtractions

[(18 + 3×2) + 8 + 5×3] + 6

18 + 3×2 = 18 + 6 = 24

24 + 8 + 5×3 = 24 + 8 + 15 = 47

47 + 6 = 53

[(18 + 3×2) + 8 + 5×3] + 6 =

= 18 + 6 + 8 + 15 + 6 = 53

Answer: 200% increase

Step-by-step explanation:

Being an increase from 12inches to 36inches, we will calculate the percentage increase.

%increase = final length -initial length/initial length × 100%

Initial length = 12inches

Final length = 36inches

%increase = 36-12/12 × 100%

%increase = 24/12 × 100%

%increase = 200%

Answer:

200% increase

Step-by-step explanation:

percent change = [(difference between initial and final value) ÷ initial value] x 100

⇒ percent change = [(36 - 12) ÷ 12] x 100 = 200% increase

The equation of tangent plane is -x + 2x - 1 = 0

Given,

r = < u² , 8usinv , ucosv >

Here,

r = < u² , 8usinv , ucosv >

Differentiate partially with respect to u and v,

\(r_{u}\) = < 2u , 8sinv , cosv >

\(r_{v}\) = < 0, 8ucosv , -4sinv >

Substitute u = 1 and v = 0

\(r_{u}\) = < 2, 0 , 0 >

\(r_{v}\) = < 0 , 8 , 0 >

Now,

N = \(r_{u}\) × \(r_{v}\)

N = \(\left[\begin{array}{ccc}i&j&k\\2&0&1\\0&8&0\end{array}\right]\)

N = -8i -j(0) +16k

N = < -8 , 0 , 16 >

Tangent plane

-8x + 16z + d = 0

Coordinates of tangent plane : <1, 0 ,1>

Substitute the values in the equation,

-8(1) + 16 (1) + d = 0

d = -8

Substitute in the tangent plane equation,

-8x + 16z - 8 = 0

-x + 2x - 1 = 0

Thus equation of tangent plane: -x + 2x - 1 = 0

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The value of cos A in the triangle is 1 / 9.

The triangle is given as ABC. The side lengths are a, b and c. Therefore, cos A of the triangle can be found using cosine rule as follows:

a² = b² + c² - 2bc cos A

a = 4

b = 3

c = 3

Therefore,

4² = 3² + 3² - 2(3)(3) cos A

16  = 9 + 9 - 18 cos A

16 - 18 = - 18 cos A

-2 = - 18 cos A

divide both sides by - 18

cos A = - 2 / - 18

cos A = 1 / 9

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True. Time series data refers to a collection of observations gathered over time, where the time dimension is a critical component of the data.

Each data point is linked to a specific point in time. In contrast, cross-sectional data is collected at a single point in time and does not have a time dimension. Therefore, the timing of each observation is crucial in time series data but not as important in cross-sectional data.

Time series data is a sequence of data points indexed in time order. It is used to track change over time.

Cross-sectional data is a snapshot of data at a specific point in time. It is used to compare different groups or variables .

Think about how the time at which each observation is made affects the analysis of time series data and cross-sectional data.

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the sequence always multiplies itself by 5 so since we have 625 multiply that by 5 and we get 3125 multiply that by 5 and we get 15625 as our last number

Answer:

Step-by-step explanation:

18 - 7m > 0 ⇒ 7m < 18 ⇒ m < 18/7

Answer:

\( \displaystyle m_{1} = 2 \quad \text{and} \quad \displaystyle m _{2} = - 9\)

Step-by-step explanation:

we are given a logarithm equation

\( \displaystyle \log_{4}( {m}^{2} ) = \log_{4}(18 - 7m) \)

notice that, we have \(\log_4\) both sides therefore we can get rid of it

\( \displaystyle {m}^{2} = 18 - 7m\)

in order to solve it we should make it standard form we know that

\( \displaystyle a {x}^{2} + bx + c = 0\)

so right hand side expression to left hand side and change its sign:

\( \displaystyle {m}^{2} + 7m- 18=0\)

now we can solve it by using factoring method

to do so rewrite the middle term as sum or subtraction of two different terms

in that case -2m+9m is good to use

\( \displaystyle {m}^{2} - 2m + 9m - 18 = 0\)

factor out m:

\( \displaystyle m({m}^{} - 2 )+ 9m - 18 = 0\)

factor out 9:

\( \displaystyle m({m}^{} - 2 )+ 9(m - 2)= 0\)

group:

\( \displaystyle (m - 2)(m + 9) = 0\)

hence,

\( \displaystyle m_{1} = 2 \quad \text{and} \quad \displaystyle m _{2} = - 9\)

remember that,

when we deal with logarithm equation we should always check the roots

let's check the root 1:

\( \displaystyle \log_{4}( {2}^{2} ) \stackrel{?}{=} \log_{4}(18 - 7.2) \)

simplify square:

\( \displaystyle \log_{4}( 4) \stackrel{?}{=} \log_{4}(18 - 7.2) \)

simplify multiplication:

\( \displaystyle \log_{4}( 4) \stackrel{?}{=} \log_{4}(18 - 14) \)

simplify substraction:

\( \displaystyle \log_{4}( 4) \stackrel{?}{=} \log_{4}(4) \)

simplify logarithm:

\( \displaystyle 1 \stackrel{ \checkmark}{=} 1\)

let's check root 2:

\( \displaystyle \rm \log_{4}( { - 9}^{2} ) \stackrel{?}{=} \log_{4}(18 - 7.( - 9)) \)

simplify square:

\( \displaystyle \rm \log_{4}( 81 ) \stackrel{?}{=} \log_{4}(18 + 63) \)

simplify addition:

\( \displaystyle \rm \log_{4}( 81 ) \stackrel{ \checkmark}{=} \log_{4}(81) \)

therefore,

\( \displaystyle m_{1} = 2 \quad \text{and} \quad \displaystyle m _{2} = - 9\)

Answer:

x = \(7\sqrt{2}\)

Step-by-step explanation:

a is the hypotenuse of the right angled triangle ehereas the other two sides are legs of a right angle triangle .

since the other two sides are equal both should be denoted as x.

now the value of a is given i.e 14 m

using pythagoras theorem,

pythagoras theorem states that sum of square of two smaller sides of a right triangle is equal to the sum of square of hypotenuse. so,

a^2 + b^2 = c^2

x^2 + x^2 = 14^2

2x^2 = 196

x^2 = 196/2

x^2 = 98

x = \(\sqrt{98}\)

x = \(7\sqrt{2}\)

Answer:

\(x=7\sqrt{2}\)

Step-by-step explanation:

The given triangle is a right isosceles triangle. This means that it is a triangle with two congruent sides and a right angle (indicated by the box around one of the angles). One of the properties of a right isosceles triangle is that it follows the following sides-ratio,

\(x-x-x\sqrt{2}\)

Where (x) represents the legs (sides adjacent to the right angle of a right triangle) or the congruent sides in this case. (\(x\sqrt{2}\)) represents the hypotenuse or the side opposite the right angle. Form a proportion based on the given information and solve for the unknown value (x).

\(x=\frac{a}{\sqrt{2}}\)

Substitute,

\(x=\frac{14}{\sqrt{2}}\)

Simplify,

\(x=\frac{14}{\sqrt{2}}\\\\x=\frac{14*\sqrt{2}}{\sqrt{2}*\sqrt{2}}\)

\(x=\frac{14\sqrt{2}}{2}\)

\(x=7\sqrt{2}\)

The addition of two numbers is 410+210 is 620.

From the given numbers,

First number is 410

Second number is 210.

One of the arithmetic operations is addition. The total of the numbers is provided. In other words, addition refers to the operation of adding the numbers together. "+" is the symbol used to denote addition. The outcome of the adding procedure is referred to as the sum. Addends are the numbers that are added together.

The following are the rules of addition operation:

Now,

⇒410+210=620

Therefore, the value is 620.

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(a) \(3u - 3v = 3i + 6j - (9i - 3j) = -6i + 9j\)

(b)\(|u| = √(1^2 + 2^2) = √5\)

(c)\(|v| = √(3^2 + (-1)^2) = √10\)

(d) \(u⋅v = (1)(3) + (2)(-1) = 1\)

(e) The angle between u and v is approximately 45 degrees.

(a) To find 3u - 3v, we distribute the scalar 3 to both vectors and subtract component-wise. This results in -6i + 9j.

(b) To find |u|, we use the Pythagorean theorem. The magnitude of a vector is calculated by taking the square root of the sum of the squares of its components. In this case, \(|u| = √(1^2 + 2^2) = √5.\)

(c) Similarly, to find |v|, we use the Pythagorean theorem.\(|v| = √(3^2 + (-1)^2) = √10.\)

(d) The dot product of two vectors u and v is calculated by multiplying their corresponding components and summing them. In this case, \(u⋅v = (1)(3) + (2)(-1) = 1.\)

(e) To find the angle between u and v, we can use the dot product formula: u⋅v = |u||v|cosθ. Rearranging the formula, we have cosθ = (u⋅v) / (|u||v|). Substituting the values, we get cos\(θ = 1 / (√5 √10)\). Taking the inverse cosine (arccos) of this value, we find the angle to be approximately 45 degrees.

Vectors are quantities that have magnitude and direction and are widely used in mathematics, physics, and engineering. Understanding vector operations, such as scalar multiplication, addition, dot product, and magnitude, is essential for solving various problems involving vectors. Additionally, the angle between vectors provides insights into the relationship and orientation between them. Exploring vector concepts and operations can enhance your problem-solving skills and help you analyze physical phenomena and mathematical structures.

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The sum S12 for the given geometric series 7 + (-7) + 7 + ... can be found using the formula for the sum of a geometric series. A geometric series is a series in which each term is obtained by multiplying the previous term by a fixed, non-zero number called the common ratio (r).

In this case, the series alternates between 7 and -7, so the common ratio is -1. The formula for the sum of a geometric series is S = a * (1 - r^n) / (1 - r), where S is the sum, a is the first term, r is the common ratio, and n is the number of terms.

In this case, a = 7 (the first term), r = -1 (the common ratio), and n = 12 (the number of terms). Plugging these values into the formula, we have:

S12 = 7 * (1 - (-1)^12) / (1 - (-1))

Simplifying further:

S12 = 7 * (1 - 1) / (1 + 1)

Since 1 - 1 = 0, the numerator becomes 0, and the sum S12 is equal to 0 divided by 2, which is 0.Therefore, the sum S12 for the given geometric series 7 + (-7) + 7 + ... is 0.

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Answer:(1,8)

Step-by-step explanation:

Answer: It is 35

Step-by-step explanation: if you go over to the 5 days and go up you will see a dot now if you go all the way to the left on the same middle the dot is on it will land on 35

The Fundamental Theorem of Calculus cannot be used to find s3x2√x³+1dx directly because the function does not have an antiderivative that can be expressed in terms of elementary functions.

However, we can still use other methods to compute the integral and the theorem to find the derivative of related functions. The Fundamental Theorem of Calculus is a theorem that explains the relationship between differentiation and integration. It comprises two different parts, with the first saying that integration is the opposite of differentiation. In other words, it states that if

f(x) is a function, then its integral from a to b is F(b) − F(a), where F(x) is the antiderivative of f(x).

The second part of the Fundamental Theorem of Calculus explains how to compute integrals using antiderivatives. It can be used to evaluate the integral ∫a^b f(x) dx by finding an antiderivative F(x) of f(x) and then computing F(b) − F(a).To determine whether the Fundamental Theorem of Calculus can be used to find s3x2√x³+1dx, we first need to determine whether this function has an antiderivative. Unfortunately, the function does not have an antiderivative that can be expressed in elementary functions. Therefore, the Fundamental Theorem of Calculus cannot be used to evaluate this integral.

We can, however, use other methods to compute this integral. For example, we could use numerical integration methods, such as the trapezoidal rule or Simpson's rule, to approximate the value of the integral. We could also use other techniques, such as substitution or integration by parts, to find a simpler expression for the integral.

Although we cannot use the Fundamental Theorem of Calculus to evaluate the integral s3x2√x³+1dx directly, we can use the theorem to find the derivative of the function

F(x) = ∫a^x 3t^2√t³+1dt.

By the first part of the Fundamental Theorem of Calculus, we know that

F'(x) = 3x^2√x³+1.

Therefore, we have

F'(3) = 3(3)^2√(3³+1)

= 27√28.

This is not the same as the value of the integral s3x2√x³+1dx, but it is still a useful result that can be used in other contexts.

The Fundamental Theorem of Calculus cannot be used to find s3x2√x³+1dx directly because the function does not have an antiderivative that can be expressed in terms of elementary functions. However, we can still use other methods to compute the integral and the theorem to find the derivative of related functions.

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There are 220 triples of values of the form (i,j,k) where each of i, j, and k is in the set {1,2,3,4,5,6,7,8,9,10} where i i + 1).

Therefore, the number of good triples of the form (i, j, k) where i < j < k is given by:693 − 3 x 9 = 666.

Hence, there are 666 good triples of the form (i, j, k) where each of i, j, and k belong to the set S and i < j < k.

Summary:Therefore, there are 220 triples of values of the form (i,j,k) where each of i, j, and k is in the set {1,2,3,4,5,6,7,8,9,10} where i < j < k.

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The dimension of the solution space for 3 linearly independent equations in 5 unknowns is 2.

The dimension of the solution space for 3 linearly independent equations in 5 unknowns is 2. This is because, when solving a system of equations, the number of equations must match the number of unknowns; otherwise, it is impossible to solve. In this case, the number of equations (3) is less than the number of unknowns (5), meaning that the system is underdetermined. This means that there are infinite solutions, and the dimension of the solution space is 2 (the number of free variables).

In other words, the solution space is a two-dimensional plane where each point represents a possible solution to the system of equations. As the equations are linear, the solution space forms a linear subspace, which means that it is a flat surface.

It is also important to note that the linear independence of the equations is crucial to this solution. If the equations are dependent, then the solution space can have a dimension of 1, 0, or even a negative number. So, the dimension of the solution space for 3 linearly independent equations in 5 unknowns is 2.

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We multiply the top numbers with each other and the bottom numbers with each other.

\( \bf \frac{5}{9} \times \frac{2}{3} = \\ \\ \bf = \frac{5 \times 2}{9 \times 3} = \\ \\ \bf = \red{ \frac{10}{27} } \)

The fraction is irreducible, so 10/27 is the result.

Good luck! :)

Answer:

10/27

Step-by-step explanation:

5/9 x 2/3 = 5 x 2/9 x 3 = 10/27

Pay the 8% tax Imao...,..

Initial price of the TV = $899

discount in % = 25 % = 0.25

First, we will find the amount discounted:

sales price after the discount was removed: