Find the limit of the function as x approaches 1 by inspecting the graph.
O 2 O oo O -1 O 5 O 0

We solve this system of equations and we can note that the system don't have a solution, so the vector b is not a linear combination of a1, a2, and a3.

First of all we put the vectors in terms of different variables, such as:

a1(1,-2,0)=(a,-2a,0);

a2(0,1,3)=(0,b,3b);

a3(6,-6,18)=(6c,-6c,18c);

To know that a vector is a linear combination we need to express it like a sum of other different vectors.

(2,-2,6)=(a,-2a,0)+(0,b,3b)+(6c,-6c,18c)

(2,-2,6)=(a+0+6c,-2a+b-6c,0+3b+18c)

We express this sum like a system of equations.

a+6c=2

-2a+b-6c=-2

3b+18c=6

We solve this system of equations and we can note that the system don't have a solution, so the vector b is not a linear combination of a1, a2, and a3.

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Answer:

[tex]\frac{1}{x} ; x > 2[/tex]

Step-by-step explanation:

A fraction less than one half would have to be one out of a larger number than two.

Basically, let's change the denominator to "x"

[tex]\frac{1}{x}[/tex] -> for this fraction to be less than 2, x always has to be greater than two

Answer:

a. To find the factor by which the area decreases in 10 years, we can use the formula for exponential decay: A(t) = A0 * e^(-kt) where A0 is the initial area, k is the decay constant, and t is the time in years.

Given that A(t) = 11 -0.98^t.

so, we can say k =0.98

The area after 10 years will be:

A(10) = 11 - 0.98^10

The decrease factor is:

(A(10)/A(0)) = (11 - 0.98^10)/11

b. To find the factor by which the area decreases each month, we can first convert the annual decay rate to a monthly rate by dividing by 12, since there are 12 months in a year.

So, the monthly decay rate is 0.98/12 = 0.0816

Then we can use the formula for exponential decay again with the new decay rate:

A(t) = A0 * e^(-kt)

The area after 1 month will be:

A(1/12) = 11 - 0.0816^(1/12)

The decrease factor is :

(A(1/12)/A(0)) = (11 - 0.0816^(1/12))/11

if i helped you, can you mark my answer as best?

[tex]\bold{n + (n+1)^{2}}[/tex]

An unknown number can be interpreted with any letter of the alphabet, they will be our unknowns to be able to form an algebraic expression.

Well, in this case, I will use the variable n, to name the unknown number.

Let "n" be the number, the square of it is; n² and the following number results from adding the unit; then (n + 1) will be the next of the number.

(grouping the data the following algebraic expression is obtained):

[tex]\bold{n + (n+1)^{2}}[/tex]

Answer:

(n + 1 )

Let "n" be the number, the square of it is; n² and the following number results from adding the unit; then (n + 1) will be the next of the number.

..

The angle of your initial isosceles triangle was cut in half by drawing the vertical, therefore you multiply by two to determine theta top.

You may determine the base angles by using:

theta_base = arcos(m/2p)

The top angle can be calculated using:

theta_top = 2*arcsin(m/2p)

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Answer:

see below

Step-by-step explanation:

there are 3 points given

diff in y / diff in x = slope

so plug in any 2 points' Y and x and get the slope

because it's downward shaped, you  know the slope MUST be negative.

so diff in Y = 23-29 = -6

diff in X = 3-7 =2

so slope is +3

intercept is given, when x=0 y = 32

it represents what F is when it's 0C°

The equation represents this relationship between the variables 'x' and 'y' will be y = -2x.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

If y varies directly from x. Then the proportionality is given as,

y ∝ x

If the proportionality signature is removed then a constant is introduced. Then the equation is given as,

y ∝ x

y = kx

The constant of variation is -2. Then the equation is given as,

y = - 2x

The equation represents this relationship between the variables 'x' and 'y' will be y = -2x.

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Considering the definition of probability, the probability that the selected student is in none of the clubs listed is 0.375 or 37.5%.

Probability is the greater or lesser chance that a given event will occur.

In other words, the probability establishes a relationship between the number of favorable events (number of cases in which event A may or may not occur)  and the total number of possible events through the Laplace's Law as follow:

P(A)= number of favorable cases÷number of total cases

In this case, you know:

Replacing in the definition of probability:

P(A)= 15÷40

Solving:

P(A)= 0.375

Expressed as a percentage:

P(A)= 37.5%

Finally, the probability is 0.375 or 37.5%.

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x is an int variable and y is a double variable and the input is: 10 20.7.The output will be x = 10, y = 20.7

given that

x is an int variable

y is a double variable

The C++ double should have a floating-point precision of up to 15 digits as it contains a precision that is twice the precision of the float data type.

When you declare a variable as double, you should initialize it with a decimal value. For example, 3.0 is a decimal number. However, if you initialize it with 3, it will also work fine because although 3 and 3.0 seem to be identical i.e., an integer, there is a big difference in their internal representation.

the input is: 10, 20.7

after execution of the statement

cin >> x >> y

The output will be x = 10, y = 20.7

because x is declared as integer variable so it will print the same

y is declared as double integer variable so it will print same as given input , if it is declared as integer variable then it will be printed as 20

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The product of the two polynomials is 16x^4 + 36x^3 - 4x^2 - 26x + 8. The solution is obtained by the method of polynomial multiplication.

What is polynomial multiplication?

The process of multiplying two or more polynomials together is known as polynomial multiplication. To obtain the final polynomial, the terms of the first and second polynomials are multiplied. We can multiply polynomials in a variety of ways depending on the kinds we are using. Each form of polynomial has a different set of guidelines for multiplication. Polynomials are multiplied by multiplying the coefficient by another coefficient and the variable by another variable.

We are given two polynomials

Polynomial 1: 4x^2 + 5x − 4

Polynomial 2: 4x^2 + 4x − 2

Multiplying both, we get

⇒(4x^2 + 5x − 4)*(4x^2 + 4x − 2)

⇒16x^4 + 16x^3 - 8x^2 + 20x^3 + 20x^2 - 10x - 16x^2 - 16x + 8

⇒16x^4 + 36x^3 - 4x^2 - 26x + 8

Hence, the product of the two polynomials is

16x^4 + 36x^3 - 4x^2 - 26x + 8.

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The total amount of money that the phone will cost including tax would be = $31.03

Cost price is the amount of money that a seller tags a particular product which is usually after the tax fees and other service fees has been added apart from the actual price of the product.

The price of the phone = $29

The percentage of tax = 7% of 29

= 7/100 × 29

= 203/100 = $2.03

Therefore, the total amount of money that the phone will cost including tax would be = 29 + 2.03 = $31.03

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Given the following histogram (image now attached), for a set of data, the number of values in the data set that are greater than 6.5 and less than 9.5 is: 14 (Option D)

A histogram is a rough depiction of the numerical data distribution. Karl Pearson was the first to coin the phrase.

A histogram is a graph that depicts the frequency distribution of a few data points from a single variable. Histograms frequently divide data into "bins" or "range groups" and count the number of data points that belong to each of those bins.

Between 6.5 and 9.5 there are 3 bars. Their heights are:

3, 6, 5, 4, and 3. Adding the values, we have:

3 + 6 + 5 = 14

Thus, the values in the data set are greater than 6.5 and less than 9.5 are 14.

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Full Question:

See attached image.

Answer:

x = 3000

Step-by-step explanation:

Answer:

x=3000

Step-by-step explanation:

Given that, 12% of x=360

 or, (x)× (12÷100)=360

 or, (12x ÷100)=360

 or, 12x=36000

 or, x=36000÷12

 or, x=3000

The angular momentum of the flywheel is equal to the product of the applied torque, the time interval, and the moment of inertia. Therefore, the angular momentum of the flywheel will be 2.5 Nm × 10.0 s × 2.0 kg m2 = 50 kg m2/s.

1. Determine the angular momentum of the flywheel:

Angular momentum = Torque × Time × Moment of Inertia

= 2.5 Nm × 10.0 s × 2.0 kg m2

= 50 kg m2/s

The angular momentum of an object can be determined from the product of the applied torque, the time interval, and the moment of inertia. The moment of inertia is the rotational inertia of an object, which is the resistance to changes in its angular velocity. The angular momentum of the flywheel in this question is equal to the product of the applied torque, the time interval, and the moment of inertia. Therefore, the angular momentum of the flywheel will be 2.5 Nm × 10.0 s × 2.0 kg m2 = 50 kg m2/s. This means that the flywheel will have an angular momentum of 50 kg m2/s after the 10-second interval when the torque is applied. The angular momentum of the flywheel will remain constant until another torque is applied to change it.

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The isosceles trapezoid has rotational symmetry about the marked point. This means that when the trapezoid is rotated by an angle of 360°, it will look the same as it did before. Since the trapezoid has 4 sides, the rotational symmetry is 4-fold, or 4 magnitude. Therefore, the answer is b) 4.

The correct answer is b) 4, as the isosceles trapezoid has 4-fold rotational symmetry about the marked point.The answer is b) 4, as the isosceles trapezoid has 4-fold rotational symmetry about the marked point.

The isosceles trapezoid has rotational symmetry about the marked point. This means that when the trapezoid is rotated by an angle of 360°, it will look the same as it did before. Since the trapezoid has 4 sides, the rotational symmetry is 4-fold, or 4 magnitude. Therefore, the answer is b) 4.

The correct answer is b) 4, as the isosceles trapezoid has 4-fold rotational symmetry about the marked point.The answer is b) 4, as the isosceles trapezoid has 4-fold rotational symmetry about the marked point.

The complete question is :

Which of the following are magnitudes for rotational symmetry of the isosceles trapezoid below about the marked point?

a) 2

b) 4

c) 6

d) 8

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There is 99% confidence that the population mean number of books read is between 1.51 and 26.69. This confidence interval indicates that there is a 99% probability that the true mean number of books read by people in the past year falls between 1.51 and 26.69.

Confidence interval for the mean = (x - z(s/√n), x + z(s/√n))

Where x is the sample mean, s is the sample standard deviation, n is the sample size, and z is the critical value for the given confidence level (in this case, 99%).

Therefore, the confidence interval for the mean number of books read is:

(14.1 - 2.58(16.6/√1018), 14.1 + 2.58(16.6/√1018))

= (1.51, 26.69)

This confidence interval indicates that there is a 99% probability that the true mean number of books read by people in the past year falls between 1.51 and 26.69. In other words, it is likely that the average number of books read by people in the past year is between these values. This interval is an estimate of the population mean and the confidence level indicates how confident we can be that the true mean falls within this range.

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The percentile for a redwood tree that is 375 feet tall would be 93rd percentile. This is because the z-score of 1.5 (375-360/10) corresponds to a percentile of 93.

Step 1: Find z-score

z-score = (375-360)/10 = 1.5

Step 2: Find percentile

Using a z-score table, the percentile corresponding to a z-score of 1.5 is 93.

Therefore, the percentile for a redwood tree that is 375 feet tall is 93rd percentile.

The percentile of a redwood tree that is 375 feet tall can be determined using a z-score table. The z-score of a data point is the difference between the data point and the mean, divided by the standard deviation. In this case, the z-score is (375-360)/10 = 1.5. This z-score corresponds to a percentile of 93 on a z-score table. Therefore, the percentile for a redwood tree that is 375 feet tall is 93rd percentile. This means that 93% of redwood trees are shorter than 375 feet tall. It also means that only 7% of redwood trees are taller than 375 feet tall. This information can be used to compare the size of a particular redwood tree to other redwood trees.

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The simplified form of the given expression is 1073741824x¹⁵.

Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.

The given expression is ((4x)³)⁵

= (4x)¹⁵

= 1073741824x¹⁵

Therefore, the simplified form of the given expression is 1073741824x¹⁵.

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Step-by-step explanation:

g(f(x)) means that we first take x and calculate f(x).

then we take that result and use as input value for g(x).

x = -5

f(-5) = (-5)² + -5 - 12 = 25 - 5 - 12 = 8

and now

g(8) = -2×8 - 15 = -16 - 15 = -31

g(f(-5)) = -31

It would take 12 minute for them to mow their lawn if they work together

An equation is an expression showing the relationship between numbers and variables.

John can mow his lawn in 3 hours and his sister, Julie, can mow it in 2 hours.

Let t represent the time it would take them to mow their lawn if they work together, hence:

(1/3hours) * t + (1/2hours) * 2 = 1

t(1/3 + 1/2) = 1

(5/6)t = 1

t = 6/5 hours = 1 hour 12 minutes

It would take 12 minutes

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The Line chart should be used by the data analyst.

Option (A) is correct.

What is a line chart?

A line chart is a type of chart that is used to display a series of data points over time. It shows how a variable changes over time by connecting data points with lines. The line chart is commonly used to display trends, patterns and changes over time in continuous data.

Line chart

This type of chart is called a line chart. A line chart is a type of chart that is used to display a series of data points over time. It shows how a variable changes over time by connecting data points with lines. The line chart is commonly used to display trends, patterns and changes over time in continuous data.

It uses a horizontal x-axis and a vertical y-axis, with the data points connected by a line. It is great for visualizing trends and changes in data over a period of time, and it can be used to compare multiple variables at once.

Hence, the Line chart should be used by the data analyst.

Option (A) is correct.

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The parameterization equation for (0,0,0) and (5,3,7/2) is[tex]\frac{x}{5}=\frac{y}{3}=\frac{z}{3.5}[/tex]. Equation of parameterization is what it is.

mathematical formulas

[tex]$$\begin{aligned}& x=0+5 t \\& y=0+3 t \\& z=0+3.5 t\end{aligned}$$[/tex]

Equations with symmetry

[tex]\frac{x}{5}=\frac{y}{3}=\frac{z}{3.5}[/tex]

A straight line is the most straightforward curve to parametrize. It is possible to parametrize a line that passes through the origin along the vectors a, b. X is equal to AT and Y is BT. Two vectors parallel to the plane and a point on the plane must be located in order to find a parametrization. On the plane, finding a location is simple. We may use any number for x and y to determine z using the plane's equation. In the event when x and y are both 0, equation (1) states that

z= 18 x + 2 y 3 = 180 + 2 (0) 3= 6.

The process of locating parametric equations of a curve, a surface, or, more generally, a manifold or a variety, described by an implicit equation, is known as in mathematics, and is most commonly used in geometry.

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Answer:

6(45 + 25)

Step-by-step explanation:

Answer:

Solution in attached photo.

Step-by-step explanation:

Steps are in the attached photo, do note for this question, the units for vectors are called 'units'. Also do note that square roots and squared will cancel out each other (Power 2 x Power Half = Power 1).

Edit: I have included solutions for both scenarios for reference.

Answer:

21°

Step-by-step explanation:

Let smaller angle be x

Bigger angle = 2x + 27

Since they are complementary they all sum up to 90°

Therefore 2x + 27 + x = 90

3x = 90 - 27

3x = 63

x = 21, therefore the smaller angle is 21°

The measure of angle 1 is 92 and the measure of angle 2 is 83.

Lines are straight with little depth or width. Perpendicular lines, intersecting lines, transversal lines, and other types of lines will be covered. An angle is a shape formed by two rays emerging from a common point. In this field, you may also come across alternate and corresponding angles.

Given that ABCD is given, the interior angle at vertex B is 97 degrees and the exterior angle at vertex A is 88 degrees. Lines AB and CD are parallel.

The measure of angle 1 is,

∠1 = 180 - 92 = 88

The measure of angle 2 is,

∠2 = 180 - 97 = 83

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The measure of CD and CE in the centroid are 22 and 33 respectively.

What is Centroid?

Centroid is a term used in mathematics to refer to the center of mass of a geometric object. It is typically represented by a point, which is the average of all points in the object. The centroid is often used as a reference point for other calculations or for the positioning of objects.

From the given diagram, the following are true:

CD = 2DE

Given that DE = 11

CD = 2(11)

CD =22

Similarly;

CE = CD + DE

CE = 22 + 11

CE = 33

Hence the measure of CD and CE are 22 and 33 respectively.

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The length of the remaining candle is equal to the total length of the candle minus the length of the candle that has been burned, or (total length - b).

The length of the remaining candle can be calculated by subtracting the length of the candle that has been burned (b) from the total length of the candle. This is because when a candle is burned, the length of the candle decreases. To calculate the remaining length of the candle, start by determining the total length of the candle. Then, subtract the length of the candle that has been burned (b). The result is the length of the remaining candle. The formula for this calculation is (total length - b).  The length of the candle remaining is (b - 2). For example, if the total length of the candle is 6 inches and 2 inches of the candle have been burned, the remaining length of the candle would be 4 inches (6 - 2 = 4).

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A complete question: Based on your answer(s) to part (a), complete the following statement to represent the length of candle remaining in terms of the burned length bb.

Answer: there would be 8 men

Step-by-step explanation:

can you give me brainliest

Answer: I believe there would be 25 men

Step-by-step explanation: We can see there are 40 women and the ration is 5 (men) to 8 (women)

If we take 40 and divide it by 8 we get 5

so for every 8 women there are 5 men and we do that 5 times

we get: 40 women and 25 men.