Evaluate the definite integral. (Assume a > 0.) a2/5 x4 a2 − x5 dx 0

Answer:

to find domain just take the first values of each ordered pairs.

to find range take the second values of the ordered pairs.

The total earnings in commission is $93.50

The given parameters are:

Commission = $5.50

Items = 17

The total commission is:

Total = $5.5 0 * 17

Evaluate

Total = $93.50

Hence, the total earnings in commission is $93.50

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Answer:

Simplified = 5

Classification = Monomial

Step-by-step explanation:

Given expression:

 3x² + 6x + 5 - 3x (2 + x)

Expand parenthesis by distributive property:

= 3x² + 6x + 5 - 3x (2) - 3x (x)

= 3x² +6x + 5 - 6x - 3x²

Put like terms together:

= 3x² - 3x² + 6x - 6x + 5

= 0 + 0 + 5

= [tex]\boxed{5}[/tex]

Concept:

Polynomial is classified by the number of terms a polynomial has.

Classify the given expression:

Original = 3x² + 6x + 5 - 3x (2 + x)

Simplified = 5

5 is a constant and it has only one term

Therefore, it is a monomial.

Hope this helps!! :)

Please let me know if you have any questions

The answer is 5, which is a monomial.

Let's simplify using the distributive property.

If the resulting expression has only one term, it is classified as a monomial.

there are two correct options:

We know that:

f(x) = 3x + 1

Now, if we look at the graph of f(x), we can see that the y-intercept is at y = -5, and for each increase in one unit in the x-variable, there is an increase of 3 units in the y-variable.

Then the equation of g(x) is:

g(x) = 3*x - 5

Then g(x) is a translation downwards of 6 units, such that:

g(x) = f(x) - 6 = (3x + 1) - 6 = 3x - 5

And we also could write it as a horizontal translation of 2 units to the right:

g(x) = f(x - 2) = 3*(x - 2) + 1 = 3*x - 3*2 + 1 = 3x - 5

So there are two correct options:

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The volume of the cone based on the figure illustrated wil be 196cm³.

The information is incomplete and the complete question wast found online. An overview will be given.

Let's assume that the height is 4cm and the radius of the cone is 7cm. The volume of the cone will be:

= 1/3πr²h

= 1/3 × 3.14 × 7² × 4

= 196cm³

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Answer:

33600 m²

Step-by-step explanation:

The top and bottom horizontal sides are parallel, so this is a trapezoid with bases DC and AB. The height is BC.

area of trapezoid = (a + b)h/2

where a and b are the lengths of the bases, and h is the height.

We need to find the height, BC.

Drop a perpendicular from point A to segment DC. Call the point of intersection E. E is a point on segment DC.

DE + EC = DC

EC = AB = 360 m

DC = 600 m

DE + 360 m = 600 m

DE = 240 m

Use right triangle ADE to find AE. Then BC = AE.

DE² + AE² = AD²

DE² + 240² = 250²

DE² = 62500 - 57600

DE² = 4900

DE = √4900

DE = 70

BC = 70 = h

area = (a + b)h/2

area = (600 m + 360 m)(70 m)/2

area = 33600 m²

Answer:

33,600 m^2.

Step-by-step explanation:

This is a trapezium, so

Area = (h/2)(a + b)

=  (h/2) ( 360 + 600)

= 960h / 2

= 480h,

We find the value of h using Pythagoras:

250^2 = h^2  + (600-360)^2

h^2 =  250^2 - 240^2 = 4900

h = 70.

So the Area = 70 * 480

= 33,600 m^2

The type of correlation relationship that exists between the number of fire stations in a city and the number of parks is: accidental correlation relationship.

Accidental relationship is a type of correlation relationship whereby there is a strong correlation between two variables without a logical explanation for such relationship. It is often regarded as coincidental.

Therefore, the type of correlation relationship that exists between the number of fire stations in a city and the number of parks is: accidental correlation relationship.

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The equation that describes how the parent function, y = x³, is vertically stretched by a factor of 4 is y = 4x³.

When an equation is vertically stretched, it means that the parent equation has been multiplied by a number that is more than one.

This means that the equation is multiplied by some factor.

It is given that we should describe how the parent function is vertically stretched by a factor of 4.

The parent function is given as y = x³.

Since the equation is said to be vertically stretched by a factor of 4, we must multiply the parent equation by 4 to stretch it.

Therefore, we have found the equation that describes how the parent function, y = x³, is vertically stretched by a factor of 4 to be y = 4x³.

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Answer: C

Step-by-step explanation:

Just C

The 41th term of the arithmetic sequence is 66.

Arithmetic sequences are those that contain these patterns. The difference between successive terms in an arithmetic series is constant. Because the difference between consecutive words is always two, the sequence 3, 5, 7, and 9 is an example of arithmetic.

[tex]a_{n}=a_{1}+(n-1)d[/tex]

[tex]a_n[/tex] =   the nᵗʰ term in the sequence.

[tex]a_1[/tex] =  the first term in the sequence.

d    =   the common difference between terms.

Finding arithmetic sequence for the nth term:

aₙ = a₁ + (n-1)d

d = the common difference

a₇ = a₁ + (7-1)d

34 = 5 + 6d

29 = 6d

d = 29/6

Now ,

Finding the  41st term of the arithmetic sequence.

a₄₁ = a₁ + (n-1)d

   = 5 + (41-1)d

   = 5 + 40d

   = 5 + 40(29/6)

   = (198)* 1/3

  =  66

The 41th term of the arithmetic sequence is 66.

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The reason that completes the proof for step 6 is (a) Definition of median

From the graph, point R' to be the midpoint of points M' and O'

Also, points P' and Q' are the midpoints of lines M'N' and N'O', respectively

This means that the three points are the median of the sides of the triangle

The line drawn through the three medians meet at point S

Hence, the reason that completes the proof for step 6 is (a) Definition of median

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Answer: median

Step-by-step explanation:

A system equations that can be used to determine after how many months the boys will owe the same amount is

60 x = $ 1000

20 y = $ 600

In mathematics, a system of equations, also known as a system of simultaneous or systems of equations, is a finite system of equations for which we have sought common solutions. A system of equations can be classified in a similar way to simple equations. A system of equations finds application in our everyday life in modeling problems where unknown values can be represented in the form of variables.

In algebra, a system of equations contains two or more equations and looks for common solutions to the equations. "A system of linear equations is a set of equations that are satisfied by the same set of variables."

We need to find a system equations that can be used to determine after how many months the boys will owe the same amount

Let lan take x months to pay $ 1000 to his parents

In 1 month Ian pays $60

In x months Ian pays =

60 x= $ 1000

Let Ken take y months to pay $ 600 to his parents

In 1 month Ian pays $20

In y months Ian pays =

20 y= $ 600

Hence 60 x= $ 1000 and 20 y= $ 600 are the system of equations

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Direct Variation; k=3 best describes the function on the graph

Option A)

Direct variation is a linear function defined by an equation of the form y = kx when x is not equal to zero. Inverse variation is a nonlinear function defined by an equation of the form xy = k when x is not equal to zero and k is a nonzero real number constant. In direct variation, as one number increases, so does the other. This is also called direct proportion: they're the same thing. An example of this is relationship between age and height. As the age in years of a child increases, the height will also increase. In inverse variation, it's exactly the opposite: as one number increases, the other decreases. This is also called inverse proportion. An example would be the relationship between time spent goofing off in class and your grade on the midterm. The more you goof off, the lower your score on the test

The given equation is a Straight line with equation y = 3x.

Thus the given graph is direct Variation graph with k=3.

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The ratio of the area of the smaller rectangle to the area of the larger rectangle is 1:16

Area of a rectangle

The formula for calculating the area of a rectangle is expressed as:

A = length * width

For the large triangle

Area = 16 * 12

Area of large triangle = 192 square units

For the smaller rectangle

Area = 4 * 3

Area. of small rectangle = 12 square units

Ratio = 12/192 = 1:16

Hence the ratio of the area of the smaller rectangle to the area of the larger rectangle is 1:16

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Using the binomial distribution, the probabilities are given as follows:

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

The values of the parameters for this problem are:

n = 10, p = 0.4.

The probability that more than 4 weigh more than 20 pounds is:

[tex]P(X > 4) = 1 - P(X \leq 4)[/tex]

In which:

[tex]P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]

Then:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{10,0}.(0.4)^{0}.(0.6)^{10} = 0.0061[/tex]

[tex]P(X = 1) = C_{10,1}.(0.4)^{1}.(0.6)^{9} = 0.0403[/tex]

[tex]P(X = 2) = C_{10,2}.(0.4)^{2}.(0.6)^{8} = 0.1209[/tex]

[tex]P(X = 3) = C_{10,3}.(0.4)^{3}.(0.6)^{7} = 0.2150[/tex]

[tex]P(X = 4) = C_{10,4}.(0.4)^{4}.(0.6)^{6} = 0.2502[/tex]

Hence:

[tex]P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0061 + 0.0403 + 0.1209 + 0.2150 + 0.2502 = 0.6325[/tex]

[tex]P(X > 4) = 1 - P(X \leq 4) = 1 - 0.6325 = 0.3675[/tex]

0.3675 = 36.75% probability that more than 4 weigh more than 20 pounds.

The probability that fewer than 3 weigh more than 20 pounds is:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0061 + 0.0403 + 0.1209 = 0.1673

0.1673 = 16.73% probability that fewer than 3 weigh more than 20 pounds.

For more than 7, the probability is:

[tex]P(X > 7) = P(X = 8) + P(X = 9) + P(X = 10)[/tex]

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 8) = C_{10,8}.(0.4)^{8}.(0.6)^{2} = 0.0106[/tex]

[tex]P(X = 9) = C_{10,9}.(0.4)^{9}.(0.6)^{1} = 0.0016[/tex]

[tex]P(X = 10) = C_{10,10}.(0.4)^{10}.(0.6)^{0} = 0.0001[/tex]

Since P(X > 7) < 0.05, it would be unusual if more than 7 of them weigh more than 20 pounds.

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The width of the deck is 6.5 feet.

The perimeter of a two-dimensional shape is the total length of the outline. To find the perimeter of a rectangle, we add the lengths of all four sides. Since opposite sides of a rectangle are always equal, we need to find the dimensions of length and width to find the perimeter of a rectangle. We can write the perimeter of the rectangle as twice the sum of its length and width. The perimeter is a linear measure and has units as meters, centimeters, inches, feet, etc.

Assuming the deck is rectangle

Perimeter = 2(length + width)

33ft = 2 (10 + width)

16.5 = 10 + width

width = 6.5 ft

Thus the width of the deck is 6.5 feet.

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Answer:

Below in bold.

Step-by-step explanation:

(a) Using the Pythagoras theorem:

30^2 = 21^2 + p^2

p^2 = 30^2 - 21^2 = 459

p = √459

  = 21.4 cm to nearest tenth.

(b) cos P = 21/30 = 0.70

   m < P = 45.57 degrees to nearest hundredth.

Answer:

a)  p = 21.4 cm (nearest tenth)

B)  P = 45.6° (nearest tenth)

Step-by-step explanation:

As triangle PQR is a right triangle, we can use Pythagoras Theorem to find the length of p.

Pythagoras Theorem

[tex]a^2+b^2=c^2[/tex]

where:

From inspection of the triangle:

Substitute the given values into the formula and solve for p:

[tex]\implies 21^2+p^2=30^2[/tex]

[tex]\implies 441+p^2=900[/tex]

[tex]\implies 441+p^2-441=900-441[/tex]

[tex]\implies p^2=459[/tex]

[tex]\implies \sqrt{p^2}=\sqrt{459}[/tex]

[tex]\implies p=\pm 3\sqrt{51}[/tex]

As p is the length, p can be positive only.

Therefore, p = 21.4 cm (nearest tenth)

To find the angle P, use the cosine trigonometric ratio.

Cosine trigonometric ratio

[tex]\sf \cos(\theta)=\dfrac{A}{H}[/tex]

where:

From inspection of the triangle:

Substitute the given values into the formula and solve for P:

[tex]\implies \sf \cos P=\dfrac{21}{30}[/tex]

[tex]\implies \sf P=\cos^{-1}\left(\dfrac{21}{30}\right)[/tex]

[tex]\implies \sf P=45.572996^{\circ}[/tex]

Therefore, the measure of angle P is 45.6° (nearest tenth).

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Answer:

Step-by-step explanation:

hello :

The graph of y =-3x+4 is the line

Step-by-step explanation:

3x° + 2x° = 180° ( supplementary angle )

5x° = 180°

x = 180° / 5

x = 36°

[tex]...[/tex]

The standard form of the given equation is: y = -3(x-6)²+35.

In mathematics, the most typical way to represent a specific element is called standard form.

A standard form is a way to express a particular mathematical idea, such as an equation, number, or expression, in prose that adheres to a set of criteria.

Given equation is: y = − 3x² + 36x - 73

In order to convert to the standard form,

y+73 = −3x² +36x

Subtract 108 from both the sides,

y+73-108 = −3x² +36x-108

y-35 = -3(x² -12x+36)

y-35 = -3(x-6)²

y = -3(x-6)²+35

This is the required standard form, corresponding to the given equation.

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1) [tex]\overline{AB} \cong \overline{CD}[/tex], [tex]\overline{AD} \cong \overline{CB}[/tex], [tex]\overline{AX} \perp \overline{BD}[/tex], [tex]\overline{CY} \perp\overline{BD}[/tex] (given)

2) [tex]\overline{BD} \cong \overline{BD}[/tex] (reflexive property)

3) [tex]\triangle ABD \cong \triangle ACDB[/tex] (SSS)

4) [tex]\angle ADB \cong \angle CBY[/tex] (CPCTC)

5) [tex]\angle CYB[/tex] and [tex]\angle AXD[/tex] are right angles (perpendicular lines form right angles)

6) [tex]\triangle CYB[/tex] and [tex]\triangle AXD[/tex] are right triangles (a triangle with a right angle is a right triangle)

7) [tex]\triangle AXD \cong \triangle CYB[/tex] (HA)

8) [tex]\overline{AX} \cong \overline{CY}[/tex] (CPCTC)

Answer:

[tex]0 = {x}^{2} + 14x + 46[/tex]

[tex] \boxed{ {x}^{2} - 14x - 46 = 0}[/tex]

[tex]x1.2 = \frac{ - b ±  \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]

[tex]x1.2 = \frac{ - 14  ± \sqrt{ { - 14}^{2} - 4(1 \times 46) } }{2 (1)} [/tex]

[tex]x1.2 = \frac{ - 14 ±  \sqrt{196 - 184} }{2} [/tex]

[tex]x1.2 = \frac{ - 14 ± \sqrt{12}  }{2} [/tex]

[tex]x1.2 = \frac{ \cancel{ - 14} ±  \sqrt{12} }{ \cancel{2} } [/tex]

[tex]x1.2 = - 7 ±  \sqrt{12} [/tex]

[tex]x1.2 = - 7 ±  \sqrt{4 \times 3} [/tex]

[tex] \boxed{ \bold{ - 7 ± 2 \sqrt{3}}} [/tex]

Answer:

its a I hope it's helps you

Answer:

By 3.

Step-by-step explanation:

-12-3=-15

Hope this helps!

Answer:

-12 exceeds -15 by 3

Step-by-step explanation:

To find out by how much a exceeds b, subtract a - b.

For example, by how much does 8 exceed 6?

Here, a = 8 and b = 6.

a - b = 8 - 6 = 2

2 is correct since we know that 8 is 2 greater than 6.

Now we do this problem.

By how much does -12 exceed -15?

a = -12; b = -15

a - b = -12 - (-15) = -12 + 15 = 3

Answer: -12 exceeds -15 by 3

Answer:

[tex]\sf 1\dfrac{2}{5} \ cm[/tex]

Step-by-step explanation:

    If two sides of the triangle are equal, then the triangle is called isosceles triangle.

Let the two equal sides = x cm

Perimeter of the triangle = [tex]\sf 4\dfrac{2}{15}[/tex] cm

[tex]\sf x + x + \dfrac{4}{3}=4\dfrac{2}{15}\\\\[/tex]

      [tex]\sf 2x +\dfrac{4}{3}=\dfrac{62}{15}[/tex]

             [tex]\sf 2x = \dfrac{62}{15}-\dfrac{4}{3} \ [\text{\bf LCM of 15 , 3 = 15}]\\\\2x = \dfrac{62}{15}-\dfrac{4*5}{3*5}\\\\2x = \dfrac{62}{15}-\dfrac{20}{15}\\\\2x = \dfrac{42}{15} \ [\text{\bf Divide both sides by 2}]\\\\ x = \dfrac{42}{15*2}\\\\ x = \dfrac{7}{5}\\\\ x = 1\dfrac{2}{5}[/tex]

[tex]\sf \boxed{\text{Equal sides of isosceles triangle = $1\dfrac{2}{5}$ cm}}[/tex]

The best description of the geometric construction of the quotient z/w on the complex plane is; Option A; z is scaled by a factor of One-fifth and rotated 90 degrees clockwise

We are given;

z = 3(cos(15°) + i sin(15°))

w = 5(cos(90°) + i sin(90°))

Now, if we want to find the quotient z/w, it is clear that in geometric construction, the procedure will be to scale z by a factor of 1/5 and thereafter we will rotate by 90° clockwise.

Thus, option A is the correct answer.

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The rate of change of area when radius = 4feet is 75.36 feet²/min.

Area definition, any particular extent of space or surface.

Area of circle = πr²

Let the area of the circle be πr²

dr/dt = 3feet/min (GIVEN)

Differentiating both sides with respect to time:

A = πr²

dA/dt =  π(2r).(dr/dt)

dA/dt = (2 * 3.14 * r).(dr/dt)

The rate of change of area when radius = 4feet

dA/dt  = (2 * 3.14 * 4).(3)

dA/dt = 75.36

Hence, the rate of change of area is 75.36feet²/min.

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Answer:

You add the numerator

multiply the denominator and substract

then you can divide the expression.

Step-by-step explanation:

According to BODMAS

division comes before multiplication, addition and subtraction.

but in some cases like this, it's difficult to follow that procedure

Answer: D

Step-by-step explanation:

As the circumference of a circle is 360 degrees, this means arc BC is 64 degrees.

So, we can conclude that arc AB measures 180-64=116 degrees.

Thus, angle AOB is also 116 degrees.

Answer:

D) 116°

Step-by-step explanation:

If arcBAC measure 296°,

And arcAC measure 180°,

You can get arcAB measure 116°,

Because the arc equals the measure of the central angle,

<AOB=116°

Hope this helps <3

The new loan amount is $113,797

What is compound interest?

Compound interest is the interest imposed on a loan or deposit amount. It is the most commonly used concept in our daily existence. The compound interest for an amount depends on both Principal and interest gained over periods. This is the main difference between compound and simple interest.

We can find new loan amount as shown below:

Total amount of loan=4*6,970+4*11,320

=27,880+45,280

=$73,160

Now, we will find new loan amount using compound interest formula.

Amount=[tex]P(1+\frac{r}{n})^{nt}[/tex]

P=$73,160

n=12

t=1 year

r=4.5%=0.045

Putting in formula

Amount[tex]=73,160(1+\frac{0.045}{12})^{12}[/tex]

=$113,797.039

Rounding to nearest dollar

=$ 113,797

Hence, new loan amount after one-year grace period is $113.797.

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The coordinates of the focus and the equation of the directrix is option B: focus: (0, one-half); directrix: y = negative one-half.

Since we were given Parabola x² = 2 y

Then one has to compare and and so it will be  x² = 4 a y

                                                                               4 a = 2

Make a the subject of the formula:

a = 2/4

= 1/2

Therefore,   Focus ( 0,a) = (0, 1/2 )

To solve for directrix:

Note that the equation of the directrix is:

y = -a or y +a=0

Then the equation of the directrix is:

y = - 1/2 or

y = + 1/2 = 0

Then the equation of the directrix will be 2 y +1 =0.

Therefore, The coordinates of the focus and the equation of the directrix is option B: focus: (0, one-half); directrix: y = negative one-half.

See full question below

A parabola can be represented by the equation x2 = 2y. What are the coordinates of the focus and the equation of the directrix? focus: (0,8); directrix: y = –8 focus: (0, one-half); directrix: y = negative one-half focus: (8,0); directrix: x = –8 focus: (one-half, 0); directrix: x = negative one-half

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The total volume of the cubes in factored form is  (4p + 2q^2)(16p^2 -  8pq^2 + 4q^4)

The volume of a figure or a three dimensional shape is the amount of space inside the figure or the three dimensional shape

The two cubes are stacked upon one another, so they form a composite figure.

The side lengths of the cubes are given as

Cube 1 = 4p

Cube 2 = 2q^2

The volume of each cube is calculated as:

Volume = Side length^3

So, the total volume is

Total = (4p)^3 + (2q^2)^3

Evaluate the exponents

Total = 64p^3 + 8q^6

Using the sum of cubes, we have the factored form to be

Total = (4p + 2q^2)(16p^2 -  8pq^2 + 4q^4)

Hence, the total volume of the cubes in factored form is  (4p + 2q^2)(16p^2 -  8pq^2 + 4q^4)

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Complete question

A cube with side length 4p is stacked on another cube with side length 2q^2. What is the total volume of the cubes in factored form?