Consider functions f and g.
f(x)
g(x)
Which expression is equal to f(x) + g(x)?
=
=
-3x² + 4x + 4
x (-7x - 7)
O A. -10x² 3x + 4
OB.
-3x²
3x
3
O C. -10x² + 4x - 3
4x² 3x + 4
O D.
-
-
-
-

The result of the original integral is:

∫15sin3(x)cos2(x)dx = (15/2)(cos(3x + 2x) + cos(3x - 2x)) + 2C

What is the integration?

In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data.

The integral of the product of sine and cosine functions can be evaluated using the identity:

sin(a)cos(b) = (1/2)(sin(a + b) + sin(a - b))

Therefore, we can rewrite the integrand as:

15sin3(x)cos2(x) = (15/2)sin(3x + 2x) + (15/2)sin(3x - 2x)

Now, we can integrate each of the two terms separately:

∫(15/2)sin(3x + 2x)dx = (15/2)cos(3x + 2x) + C

∫(15/2)sin(3x - 2x)dx = (15/2)cos(3x - 2x) + C

Therefore, the result of the original integral is:

∫15sin3(x)cos2(x)dx = (15/2)(cos(3x + 2x) + cos(3x - 2x)) + 2C

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C. The matrix is the augmented matrix of a consistent linear system for every value of h.

What is augmented matrix ?

An augmented matrix is one that is created by joining the columns of two matrices.

The augmented matrix of a consistent linear system can have any value in the last column, as long as it corresponds to a valid solution of the system of linear equations.

The presence of a non-zero value in the last column simply indicates that the system has a unique solution, while a zero value in the last column indicates that the system is either inconsistent or has infinitely many solutions.

In this case, the value of h does not affect the consistency of the system.

Hence,  The matrix is the augmented matrix of a consistent linear system for every value of h.

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Answer:

4.7 miles per day

Step-by-step explanation:

35.8 - 17 = 18.8 miles

So, she needs to ride 18.8 miles in 4days

18.8 divided by 4 = 4.7 miles per day

So, she needs to ride 4.7 miles each day to meet her goal.

The value of investment at maturity is $15094.

what is compound interest?

Interest that is added to a loan or deposit sum is known as compound interest. In our daily lives, it is the notion that is employed the most frequently. Compound interest is calculated for a sum using the principal and interest accrued over time. Compound interest and simple interest differ primarily in this way.

a=9000

r= 0.09

t=6

y=a(1+r)ᵗ

=> y=9000(1+0.09)⁶

=> y= 9000(1.09)⁶

=> y= 15093.900

Rounded to whole number : $15094

The value of investment at maturity is $15094

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The increasing and decreasing behavior of the function f(x) on the given intervals is as follows:

On the interval (-∞, -3), f(x) is increasing.

On the interval (-3, 0), f(x) is decreasing.

On the interval (0, 3), f(x) is increasing.

On the interval (3, ∞), f(x) is decreasing.

We have,

To determine the increasing and decreasing behavior of the function f(x) = x / (x² - 9) on the given intervals, we can evaluate the sign of the derivative of the function.

Taking the derivative of f(x) with respect to x and simplifying, we have:

[tex]f'(x) = (-x^2 + 9 - x(2x)) / (x^2 - 9)^2\\= (-x^2 + 9 - 2x^2) / (x^2 - 9)^2\\= (-3x^2 + 9) / (x^2 - 9)^2[/tex]

To identify the increasing and decreasing behavior, we need to examine the sign of f'(x) on each interval.

For the interval (-∞, -3):

Plugging in a value less than -3, such as -4, into f'(x) yields a positive result.

Plugging in a value between -3 and 0, such as -2, into f'(x) gives a negative result.

Therefore, f'(x) is positive for x < -3 and negative for -3 < x < 0, indicating that f(x) is increasing on the interval (-∞, -3) and decreasing on the interval (-3, 0).

For the interval (-3, 3):

Plugging in a value between -3 and 0, such as -2, into f'(x) yields a negative result.

Plugging in a value between 0 and 3, such as 1, into f'(x) gives a positive result.

Therefore, f'(x) is negative for -3 < x < 0 and positive for 0 < x < 3, indicating that f(x) is decreasing on the interval (-3, 0) and increasing on the interval (0, 3).

For the interval (3, ∞):

Plugging in a value between 3 and 4, such as 3.5, into f'(x) yields a positive result.

Plugging in a value greater than 4, such as 5, into f'(x) gives a negative result.

Therefore, f'(x) is positive for 3 < x < 4 and negative for x > 4, indicating that f(x) is increasing on the interval (3, 4) and decreasing on the interval (4, ∞).

Thus,

The increasing and decreasing behavior of the function f(x) on the given intervals is as follows:

On the interval (-∞, -3), f(x) is increasing.

On the interval (-3, 0), f(x) is decreasing.

On the interval (0, 3), f(x) is increasing.

On the interval (3, ∞), f(x) is decreasing.

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An ellipse is described by this equation. It is a conic section because it has two variables, x and y, that are squared and multiplied together. The conic's shape is fixed because the equation also contains a constant.

An ellipse is described by this equation. It is a conic section because it has two variables, x and y, that are squared and multiplied together. A constant in the equation, 4x2 + 3xy + 5y2 - x - y = 0, shows that the conic's shape is fixed.  The equation is neither a parabola nor a hyperbola because it lacks any x or y terms. The equation therefore describes an ellipse. An oval-shaped closed curve known as an ellipse is produced when a plane and a cone intersect. The foci, or the two places at which the ellipse is symmetric, serve as its two defining points. The standard form of an ellipse, which is centred at the origin and contains the equation A(x2) + B(xy) + C(y2) + D(x) + E(y) + F = 0, is described by the equation provided. In this case, the constants are A=4, B=3, C=5, D=1, and E=1, and F=0. The major axis to minor axis ratio in the equation is 4:5, describing a moderately flattened ellipse. The equation can be used to determine the ellipse's area, circumference, and other parameters because it is symmetrical.

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Jacques' average revenue per basket is $ per basket.

Average revenue (AR) is calculated by dividing total revenue (TR) by total quantity sold (Q).

Therefore, AR = TR/Q

Given that Jacques sells 32,000 baskets and the highest price consumers are willing to pay according to the demand curve, his total revenue (TR) is unknown.

However, we can calculate his average revenue (AR) by dividing his total revenue (TR) by the quantity sold (Q).

AR = TR/32,000

Therefore, Jacques' average revenue per basket is $ per basket.

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Complete question:How much average revenue will Jacques make if he sells 32,000 baskets at the highest price consumers are willing to pay according to the demand curve?

34 questions was answered correctly by the student, while 6 questions were incorrect

An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.

A math test has 40 questions. A student answers 85% of the questions correctly.

Number of questions answered correctly = 85% of total questions = 0.85 * 40 questions = 34 questions

Number of questions not answered correctly = 40 - 34 = 6 questions

34 questions was answered correctly by the student.

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So, when R is rotated along the line y = 4, the volume of the solid formed is roughly 12.57 cubic units. So, when R is rotated about the line y = 5, the volume of the solid formed is roughly 81.34 cubic units.

Every three-dimensional item requires some amount of space. The volume of this space is measured. Volume is defined as the space occupied by an item inside the confines of three-dimensional space. It is also known as the object's capacity.

Here,

The volume of the solid generated when R is rotated about the line y = 4 is given by the formula:

V = π * ∫[a,b] (x² - 4)² dx

where a and b are the x-coordinates of the points where the parabola y = x² intersects the line y = 4. To find these points, we set y = x² and y = 4 and solve for x:

x²= 4

x = ±2

So the points of intersection are (2, 4) and (-2, 4). The region R is the part of the parabola between these points, so a = -2 and b = 2.

Substituting these values into the formula for V, we have:

V = π * ∫[-2,2] (x² - 4)² dx

Evaluating the definite integral, we obtain:

V = π * [x⁵/5 - 4x³/3 + 16x] evaluated from -2 to 2

= π * (16/5 - 16/3 + 16 - (-16/5 + 16/3 - 16))

= π * (32/5)

= 12.57 ≈ 12.57 (rounded to 4 decimal places)

For the volume of the solid generated when R is rotated about the line y = 5, we can use the same formula:

V = π * ∫[a,b] (x² - 5)² dx

where a and b are the x-coordinates of the points where the parabola y = x² intersects the line y = 5. These can be found in the same way as before:

x² = 5

x = ±√5

So the points of intersection are (√5, 5) and (-√5, 5). The region R is the part of the parabola between these points, so a = -√5 and b = √5.

Substituting these values into the formula for V, we have:

V = π * ∫[-√5,√5] (x² - 5)² dx

Evaluating the definite integral, we obtain:

V = π * [x⁵/5 - 5x³/3 + 25x] evaluated from -√5 to √5

= π * (25/5 - 25/3 + 25√5/2 - (-25/5 + 25/3 - 25√5/2))

= π * (50/3 + 25√5)

= 50.97 + 25√5 ≈ 50.97 + 25 * 2.236 = 81.34 (rounded to 2 decimal places)

So the volume of the solid generated when R is rotated about the line y = 4 is approximately 12.57 cubic units. So the volume of the solid generated when R is rotated about the line y = 5 is approximately 81.34 cubic units.

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The values of the composite functions are

From the question, we have the following functions that can be used in our computation:

f(x) = 2x³ - 10x + 3, h(x) = x - 5 and g(x)=2x

Using the above as a guide, we have the following:

a) (f + h)(x) = 2x³ - 10x + 3 + x - 5 = 2x³ - 9x - 2

b) (f - h)(x) = 2x³ - 10x + 3 - x + 5 = 2x³ - 11x + 8

c) (fg)(x) = f(g(x)) = f(2x) = 2(2x)³ - 10(2x) + 3 = 16x³ - 20x + 3

d) (fh)(x) = f(h(x)) = f(x - 5) = 2(x - 5)³ - 10(x - 5) + 3

e) (f/g)(x) = f(x)/g(x) = (2x³ - 10x + 3)/(2x)

The above are the values of the composite functions

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An element around me that has one of the aforementioned shapes is a ball.

One of the geometric shapes around me is a basketball. This has a completely spherical shape that from any perspective looks circular.

This ball is orange in color and due to its circular or sphere shape it can roll on the floor. Additionally, this ball has the property of deforming when it hits the ground and bounces.

Additionally, with this ball we can make parabolic shots to score it on a basketball court.

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Answer:

7.35 million

Step-by-step explanation:

49*0.81^9 =7.35 million

The values mean, variance and standard deviation for Pomona and Anaheim are compared to identify the deviation in the air quality level.

The air quality index values for various area of southern California. Here the random variable (X) represents the air quality index values for Pomona.

From the given information the data values are 28, 42, 58, 48, 45, 55, 60, 49 and 50

Range = max. value - min.value

           = 60 - 28 = 32

mean for air quality index for Pomona = x'

                                            = sum of the values/total no.of samples

                                            = (∑Xi )/ (n)

                                            = 435/9 = 48.33

sample variance , ∑(Xi - x')/ n-1 = 92.75

standard deviation is the sq.root of variance , i.e √92.75

                                            = 11.66

Use mean 48.3, variance 136 and standard deviation 11.66 to compare with the air quality in Pomona and Anaheim.

The air quality index reading for Pomona mean is equal to Anaheim. That is, The Pomona mean (48.3) is equal to the Anaheim mean (48.3).

The variance and sample standard deviation for Anaheim are 136 and 11.66, respectively.

The variance and sample standard deviation for Pomona are 92.75 and 9.63, respectively.

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Answer:

Step-by-step explanation:

18

The absolute maximum value of f is 1.

The function f(x) is defined as the natural logarithm of x (lnx) divided by x. This function is undefined when x is equal to 0, but for positive x values, the maximum value of f(x) is 1. To prove this, we need to take the derivative of f(x) and set it equal to 0. We can calculate the derivative of f(x) by using the quotient rule.

The quotient rule states that for two functions u(x) and v(x), the derivative of their quotient can be calculated by taking the derivative of u(x) times v(x) minus the derivative of v(x) times u(x), all divided by v(x)2. After taking the derivative of f(x) = lnx/x, we get f'(x) = (1/x) – (lnx/x2).

Now we set f'(x) = 0 and solve for x. This gives us x = 1, so when x = 1, we get the maximum value of f(x) = ln1/1 = 1. Therefore, the absolute maximum value of f is 1.

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The graph of y = 3ex ex − 5 has a horizontal asymptote of y = 3 and a vertical asymptote of x = -3/5.

The equation y = 3ex ex − 5 can be rewritten as y = 3x2ex − 5. In order to find the horizontal and vertical asymptotes of this function, we must first find its degree of the numerator and denominator. The numerator is a second degree polynomial while the denominator is a first degree polynomial.

The horizontal asymptote will be the line y = b/a, where b and a are the coefficients of the highest degree terms in the numerator and denominator, respectively. In this case, b = 3 and a = 1, so the horizontal asymptote is y = 3.

The vertical asymptote of a function is the line x = a/b, where a and b are the coefficients of the highest degree terms in the numerator and denominator, respectively. In this case, a = 3 and b = -5, so the vertical asymptote is x = -3/5.

Therefore, the graph of y = 3ex ex − 5 has a horizontal asymptote of y = 3 and a vertical asymptote of x = -3/5.

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There is sufficient evidence to support the claim of a greater variance for machine 1

Given two data sets, n1=25 and n2=22, their means are calculated as x1=3.3284 and x2=3.2782 respectively. The variance for each data set is calculated as s1=0.2211 and s2=0.0768 respectively.

The null hypothesis is that the variance of data set 1 (s1) is less than or equal to the variance of data set 2 (s2), while the alternative hypothesis is that the variance of data set 1 is greater than the variance of data set 2.

The test statistic F is calculated as the ratio of the variance of data set 1 squared to the variance of data set 2 squared, resulting in a value of 8.288.

The P-value is calculated as the probability of obtaining the value of the test statistic, or a more extreme value, which is less than 0.01.

Therefore, based on the significance level, the null hypothesis is rejected and the alternative hypothesis is accepted.
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There is sufficient evidence to support the claim of a greater variance for machine 1

Given two data sets, n1=25 and n2=22, their means are calculated as x1=3.3284 and x2=3.2782 respectively. The variance for each data set is calculated as s1=0.2211 and s2=0.0768 respectively.

The null hypothesis is that the variance of data set 1 (s1) is less than or equal to the variance of data set 2 (s2), while the alternative hypothesis is that the variance of data set 1 is greater than the variance of data set 2.

The test statistic F is calculated as the ratio of the variance of data set 1 squared to the variance of data set 2 squared, resulting in a value of 8.288.

The P-value is calculated as the probability of obtaining the value of the test statistic, or a more extreme value, which is less than 0.01.

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In the exponential function y = 3 × q⁵ the starting value is 3.

The formula for an exponential function is f(x) = aˣ, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

Given is an exponential function is -

y = 3 × q⁵

The exponential function is written in the form abˣ.

Here, a is considered to be the initial value, b is considered to be the base and x represents the growth factor.

So, the initial or starting value in function y = 3 × q⁵ is -

a = 3

Hence, the starting value is 3.

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Three different types of discontinuity exist.

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Answer: the meaning of the variable m is Meagan, M is a shortened version to show that 3 is how much money she has.

Step-by-step explanation:

hope this helps ^^

To the nearest hundred, Tony rounded the figures 1183 and 1145.

Our entire number system is built on place value. In this system, a digit's position within a number affects its value. The placements of the digits make the numbers 42,316 and 61,432 distinct from one another.

Place value is the value that a digit in a number represents based on where it appears in the number.

In order to round the number to the nearest hundred, look at the digit after the tens place.

In the hundreds place, we add one if the number in the tens place is greater than or equal to 5.

We replace the remaining digits with 0 if the number in the tens place is less than 5.

1200 is the result of rounding 1183 to the nearest tenth (8 in this case).

1145 is rounded to 1100 because there are four tens places in it.

The complete question is;

Tony rounded each of the numbers 1183 and 1145 to the nearest hundred. Which choice correctly compares the rounded numbers

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The amount of money una earns in a week she serves $355 worth of meals including her base earnings is $177.25

Amount una makes in a week= $64

Additional amount una earn = 15% of x

Cost of meal she serves = x

Total amount she makes= y

y = 0.15x + 64

If she serves $355 worth of meals.

y = 0.15x + 64

y = 0.15(355) + 64

= 53.25 + 64

y = $177.25

In conclusion, una makes a total of $177.25 in a week.

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Answer:

5 cents each

Step-by-step explanation:

to find out how much each pen costs, you would divide the total price(7.50) by the number of pens(150) to get to the price for each pen ($0.05)

Answer:

To find this, you just want to divide 7.50 by 150.

Take note that since were looking for how much each individual pen costs, 7.50 with come first in the equation, as shown:

7.50/150 = 0.05

Each Pen Costs 5 cents each!

Step-by-step explanation:

Hope it helps! =D

Answer: False

Step-by-step explanation:

7 is not an even number, and it never will be.

Even though january has 31 days, 7 is an odd number.

False. 7 is an odd number. This is because an even number is a number which can be divided by 2 without a remainder. 7 cannot be divided by 2 without a remainder, so it is an odd number.

To calculate this, we can use the remainder operator. This operator is represented by the percentage sign (%). When using this operator, the result is the remainder of a division operation. For example, if we divide 7 by 2, the result is 3 with a remainder of 1. If we write this as an equation, it will be 7 % 2 = 1. This means that 7 is not evenly divisible by 2, and is thus an odd number.

Therefore, even though january has 31 days, 7 is an odd number.

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The bond would pay back its face value of $1000 at the end of the 10 years.

The face value of the bond is the amount the bond will be worth when it matures, and it is also known as the "par value" or the "principal amount."

In this case, the face value of the bond is $1000, so at the end of the 10 years, the bond will pay back $1000 in principal to the bondholder.

The coupon rate, which is 4% in this case, determines the amount of the annual interest payment that the bondholder will receive.

Therefore, regardless of the changes in interest rates, the bond will pay back its face value of $1000 at the end of the 10 years.

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Work the dollar amount d that Julia earns varies directly as the number of hours is 23 hours is the solution.

According to the information provided, Julia's earnings correspond closely to the amount of hours she puts in at work.

Also, at t = 15 h, d equals $116.25.

The direct variation's formula is d = kt.

where k is the variational constant.

Find k and replace the known values:

116.25 = k * 15

k = 116.25/15 k = 7.75

Find t now that d is equal to 178.25. In the direct variation equation, swap out d and k, then figure out t:

23 hours are equal to 178.25 = 7.75t t.

t = 23 hours is the solution.

Work the dollar amount d that Julia earns varies directly as the number of hours is 23 hours is the solution.

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The values using Law of Sines are:

∠ B = 62∘; b = 11.58 and c = 16.40.

The relationship between a triangle's sides and angles is demonstrated using the sine rule. It is specified as:

A/Sin(A) = B/Sin(B) = C/Sin(C)

Where A, B, and C are indeed the angles and A, B, and C are the angles' opposing sides.

∠ A = 43 ∘ , ∠ C = 75 ∘ , b = 15 ;

Part a:

∠ B = 180 -  ∠ A  -  ∠ C

∠ B = 180 - 43 ∘  - 75∘

∠ B = 62∘

Part b: the value of a.

a/Sin(A) = b/Sin(B)

a =  b/Sin(B) * Sin(A)

a = 15/Sin(62) * Sin(43)

b = 11.58

Part c: the value of c

b/Sin(B) = c/Sin(C)

c = b/Sin(B) * Sin(C)

c = 15/Sin(62) * Sin(75)

c = 16.40

Thus, the values using Law of Sines are obtained.

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The area under the curve y = |x + 3| above the x-axis and between x = -6 and x = 0 is 9 units^2.

What is the area under the curve?

The area under a curve refers to the area between a curve and the -axis. This area could be entirely above the -axis, entirely below the -axis, or a combination of above and below the -axis. In calculus, the area under a curve is a visual representation of an integral.

The graph of y = |x + 3| is a piecewise linear function that starts at (3,0), increases linearly as x decreases to -3, reaches a maximum value of 3 at x = -3, and then decreases linearly as x decreases further to -6. The area under the curve y = |x + 3| above the x-axis and between x = -6 and x = 0 can be calculated by finding the area of two triangular regions. One triangular region is formed by the line y = x + 3 from x = -6 to x = -3 and the x-axis, and the other triangular region is formed by the line y = -(x + 3) from x = -3 to x = 0 and the x-axis. The area of each triangular region can be calculated using the formula 1/2 * base * height, and the total area is the sum of the areas of the two triangular regions.

So, The area under the curve y = |x + 3| above the x-axis and between x = -6 and x = 0 is 9 units^2.

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[tex]\huge\begin{array}{ccc}x=1;&y=\frac{\sqrt3}{2}\end{array}[/tex]

Look at the picture.

We have:

[tex]a=\dfrac{1}{2}\\\\2a=x\\\\a\sqrt3=y[/tex]

Therefore:

[tex]x=2\cdot\dfrac{1}{2}\to\boxed{x=1}\\\\y=\dfrac{1}{2}\cdot\sqrt3\to\boxed{y=\dfrac{\sqrt3}{2}}[/tex]