Find the sum of the first 50 positive even integers.

The binomial expansion is solved and the error in Dakota's statement is the incorrect substitution of 36g^2h^2 for the correct expression

Given data ,

Dakota made a mistake because the third term of the expansion of (2g + 3h) should have been 36g2h2. The binomial theorem asserts that the expansion of (2g + 3h) is as follows:

( x + y )ⁿ = ⁿCₐ ( x )ⁿ⁻ᵃ ( y )ᵃ

Here, x = 2g and y = 3h. Since term numbers begin at 0, since we are seeking for the third term, r = 2.

So , on simplifying the equation , we get

= nC2 * (2g)⁽ⁿ⁻²⁾ * (3h)²

= (n! / (2! * (n - 2)!)) * (2g)⁽ⁿ⁻²⁾ * (3h)²

= ((n * (n - 1)) / 2) * (2g)⁽ⁿ⁻²⁾ * (3h)²

Hence , the correct expression for the third term of the expansion of (2g + 3h) is ((n * (n - 1)) / 2) * (2g)^(n - 2) * (3h)², where n is the exponent in the binomial expansion.

To learn more about binomial expansion click :

https://brainly.com/question/3537167

#SPJ1

Answer:

B. Add 5y to both sides in the first equation.

Step-by-step explanation:

When we add 5y to both side in the first equation we will see that x = 22 + 5y

Then we can use this information in second equation like this:

-8(22+5y) + 7y = 22 which is a simpler equation and easier to solve.

So the answer to this question is B.

Answer:

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

Because 63 is a multiple of 7

So.... 63/7

=9

So this shows us 9 is the mean

HOPE IT HELPS YOU!

PLEASE MARK ME AS BRAIN LIST IF MY ANSWER IS HELP FUL

Answer:any number is correct

Step-by-step explanation:

4(3x+1)=12x+4

12x+4=12x+4

12x-12x=4-4

0=0

This equation has no answer.

Actually any number you put in place of x this equation will be true so we can say the answer is

X=infinity

Answer: All

Step-by-step explanation:

Answer: 172 ounces

Step-by-step explanation:

We are given 10 pounds and 12 ounces to convert to ounces.

There are 16 ounces in 1 pound.

We can create a proportion to find out how much ounces 10 pounds is.

10 pounds / x ounces = 1 pound / 16 ounces

We need to solve for x by isolating the variable x.

10/x = 1/16

10 = x/16

10 * 16 = x

160 ounces = x

so 10 pounds is equivalent to 160 ounces. But we are not done yet.

We were asked to convert 10 pounds and 12 ounces.

So add together the ounces to find the total ounces:

160 ounces + 12 ounces = 172 ounces.

Answer:

  (b)  3 units

Step-by-step explanation:

You want to know the length of OB' when OB = 3/4 and ∆ABC is dilated about point O by a factor of 4.

The dilation factor multiplies every length.

If OB is 3/4, then OB' is 4(3/4) = 3.

The length of OB' is 3 units.

<95141404393>

The approximation of the area under the curve f(x) = \(2x^2 + 6\) from x = 2 to x = 4 using left rectangles and a step size of Δx = 0.5 is 60.5 square units to one decimal place.

To approximate the area under the curve f(x) = \(2x^2 + 6\) between x = 2 and x = 4 using left rectangles and a step size of Δx = 0.5, we have to divide the interval [2, 4] into a number of sub-intervals of width 0.5 and evaluate the function at the left endpoint of each sub-interval.

First find the number of steps: (4-2)/0.5 = 4

The x-coordinates for the left endpoints of each sub-interval are: 2, 2.5, 3, 3.5, 4

We evaluate the function f(x) = \(2x^2 + 6\) at each of these left endpoints and multiply the result by the width of the sub-interval (0.5) to find the area of each rectangle.

For \(x = 2\), \(f(x) = 2(2)^2 + 6 = 14\)

Area = 0.5 * 14 = 7

For \(x = 2.5, f(x) = 2(2.5)^2 + 6 = 19.5\)

Area = 0.5 * 19.5 = 9.75

For \(x = 3, f(x) = 2(3)^2 + 6 = 24\)

Area = 0.5 * 24 = 12

For \(x = 3.5, f(x) = 2(3.5)^2 + 6 = 29.5\)

Area = 0.5 * 29.5 = 14.75

For \(x = 4, f(x) = 2(4)^2 + 6 = 34\)

Area = 0.5 * 34 = 17

The sum of the areas of these rectangles is 7 + 9.75 + 12 + 14.75 + 17 = 60.5

Therefore, the approximation of the area under the curve f(x) = \(2x^2 + 6\) from x = 2 to x = 4 using left rectangles and a step size of Δx = 0.5 is 60.5 square units to one decimal place.

To learn more about the area under the curve:

https://brainly.com/question/15122151

#SPJ4

Distance from A to B = 3 - (-4) = 7

The price of the couch after the markup gotten during a sale, a store offered a 30% discount on a couch that originally sold for $870 is $791.70.

The concept that will be used here is the discounted price . The discount is represented in the advertisement as a percentage off the list price. As a result, a sale price of $70 will be achieved with a 30% discount on a $100 list price. Another way to understand the phrase is to say that it simply refers to the selling price of an item.

The  price of the couch after the markup can be determine as :

$870 * (1 + 30% ) *  (1 - 30% )

Then this can be simplifIed as :

= $870  *1.3 * 0.7

=$ 791.7

Then Rounding up to the nearest cent will give $ 791.70

Learn more about discount at:

https://brainly.com/question/7459025

#SPJ1

Measure of the arc or angle indicated is 150.9 degrees.

In geometry, an arc is a portion of the circumference of a circle or any other curved shape. It is defined by two endpoints and all the points on the curve that lie between them. An arc is usually named by its two endpoints, with a small arc symbol above them to indicate that it is an arc.

The length of an arc can be calculated using the formula:

Arc length = (central angle/360) x 2πr

where r is the radius of the circle, and the central angle is the angle subtended by the arc at the center of the circle, measured in degrees.

The measure of an arc is the degree measure of the central angle subtended by the arc. A semicircle is an arc that subtends a central angle of 180 degrees, and a full circle is an arc that subtends a central angle of 360 degrees.

Since DE and PE are chords of the circle, and they intersect at point P, we can use the intersecting chords theorem to find the length of DP. Let x be the length of DP. Then:

DP * PE = DE * PC

x * (x + PE) = (\(\frac{CE}{2}\)) * (\(\frac{CE}{2}\))

x² + x(PE) - \(\frac{CE}{2}^{\frac{2}{4} }\) = 0

Since angle DPE is 60 degrees, we can use the law of cosines to find PE. Let y be the length of PE. Then:

y² = DE² + DP² - 2 * DE * DP * cos(60)

y² = (\(\frac{CE}{2}\))² + x^2 - (\(\frac{CE}{2}\)) * x

Substitute this expression for y^2 into the equation for x and simplify:

\(x^{2} +x((\frac{CE}{2})^{2} + x^{2} -\frac{CE}{2} *x)^{0.5} -(\frac{CE}{2} ^{\frac{2}{4} } )=0\)

Solve for x:

x = \(\frac{CE^{2} -4*(CE^{2} -3*\frac{CE}{2} ^{2} )^{0.5} }{4}\)

x = \(\frac{3}{4} *\frac{CE^{2} }{CE^{2} -12}\)

Now we can find the measure of the CD arc by using the formula for the central angle:

CD arc = \(2*arctan(\frac{DP}{CE})\)

CD arc = \(2*arctan(\frac{x}{\frac{CE}{2} } )\)

CD arc = \(2* arctan(CE^{2} -4*(CE^{2} -3*\frac{(\frac{CE}{2} ^{2})^{0.5}}{CE^{2}-12 } ))\)

Simplifying this expression, we get:

\(CD arc=2*arctan(2*3^{\frac{1}{2} } -1)\)

CD arc ≈ 150.9 degrees.

To know more about expression visit:

https://brainly.com/question/10063670

#SPJ1

Measure of the arc or angle indicated in the given figure is 150.9 degrees.

In geometry, an arc is a portion of the circumference of a circle or other curved shape. It is defined by his two endpoints and all midpoints of the curve. Arcs are usually named after their two endpoints, with a small arc symbol above them to indicate that they are arcs.

Arc Length = (Center Angle/360) x 2πr

where r is the radius of the circle and the central angle is the angle the arc makes at the center of the circle, measured in degrees.

The arc measurement is the angle of the central angle defined by the arc. A half circle is an arc that spans a central angle of 180 degrees, and a full circle is an arc that spans a central angle of 360 degrees.

Since DE and PE are chords of the circle and intersect at P, we can use the chord rule to find the length of DP. Let x be the length of DP.  Then:

DP × PE = DE × PC

x × (x + PE) = (CE/2) × (CE/2)

x² + x(PE) - \(\frac{CE}{2} ^{\frac{2}{4} }\) = 0

Since angle DPE is 60 degrees, we can use the law of cosines to find PE. Let y be the length of PE. Then:

y² = DE² + DP² - 2 × DE × DP × cos(60)

y² = (\(\frac{CE}{2}\))² + x² -  (\(\frac{CE}{2}\)) × x

Substitute this expression for y² into the equation for x and simplify:

\(x^{2} +x((\frac{CE}{2} ^{2}) + x^{2} - \frac{CE}{2}*x)^{0.5} -\) \(\frac{CE}{2} ^{\frac{2}{4} }\) = 0

Solve for x:

x = \(\frac{CE^{2} - 4*(CE^{2}-3*\frac{CE}{2} ^{2})^{0.5} }{4}\)

x = (3/4) × (CE²/CE²-12)

Now we can find the measure of the CD arc by using the formula for the central angle:

CD arc = 2arc tan(DP/CE)

CD arc = 2arc tan [x/(CE/2)]

CD arc = 2arc tan (CE² - 4 × (CE² - 3 × \(\frac{(\frac{CE}{2} ^{2}) ^{0.5} }{CE^{2}-12 }\) )

Simplifying this expression, we get:

CD arc ≈ 150.9 degrees.

To know more about arc, visit:

https://brainly.com/question/16930503

#SPJ1

Answer:

9x - 6

Hope this helps! <3

(If you need a step by step lmk)

Answer:

6x+3(x-2)

6x+3x-6

9x-6

Inequalities help us to compare two unequal expressions. The correct representations of the inequality –3(2x – 5) < 5(2 – x) are A and C.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.

It is mostly denoted by the symbol <, >, ≤, and ≥.

The given inequality can be written as,

-3(2x - 5) < 5(2 - x)

-6x + 15 < 10 - 5x (It is the third option)

-6x + 5x < 10 - 15

-x < -5

x > 5 (First option)

Hence, the correct representations of the inequality –3(2x – 5) < 5(2 – x) are A and C.

Learn more about Inequality:

https://brainly.com/question/19491153

#SPJ1

Answer:

x ≥ 3

Step-by-step explanation:

- 3(2x - 1) ≤ x - 18 ← distribute parenthesis on left side

- 6x + 3 ≤ x - 18 ( subtract x from both sides )

- 7x + 3 ≤ - 18 ( subtract 3 from both sides )

- 7x ≤ - 21

divide both sides by - 7, reversing the symbol as a result of dividing by a negative quantity.

x ≥ 3

Answer:

A. x=32

B. x=55

C. y=-18

D. m=-70

E. p=3

F. t=7

G= x=-11

H. n=-25

I. u=16

J. v=27

Answer:

A) x = 32

B) x=55

C) y = -18

D) m = -70

E) p = 3

F) t = 7

G) x = -11

Step-by-step explanation:

\(A) \ \dfrac18x=4\implies x=4\times8\implies x=32\)

\(B) \ \dfrac15x=11\implies x=11\times5\implies x=55\)

\(C) \ \dfrac19y=-2\implies y=-2\times9\implies y=-18\)

\(D) \ \dfrac12m=-35\implies m=-35\times2\implies m=-70\)

\(E) \ 6p=18\implies p=\dfrac{18}6\implies p=3\)

\(F) \ 12t=84\implies t=\dfrac{84}{12}\implies t=7\)

\(G) \ 3x=-33\implies x=\dfrac{-33}3\implies x=-11\)

Yes, an acute triangle less than 90 degrees

what is acute triangle?

An acute angled triangle is one in which all of the angles are fewer than 90 degrees. One such illustration of an acute angled triangle is the one below.

Hence the triangle less than 90 degrees is acute angle

To learn more about acute angle from the given link  

https://brainly.com/question/6979153

#SPJ4

Answer:

35

Step-by-step explanation:

*I'm just gonna answer this*

When you are 70, your brother will be 67.

If you were six, and he was half of that, he was three, meaning he was 3 years younger than you.

At x = 0 and x = 7, the function g(x) is undefined.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression of the function is,

⇒ g (x) = 6 / x (x - 7)

Now, We know that;

The function f(x) = a(x) /b (x) is not defined at b (x) ≠ 0

Here, The expression of the function is,

⇒ g (x) = 6 / x (x - 7)

So, Function g (x) is not defined when,

x (x - 7) = 0

⇒ x = 0

or, x - 7 = 0

⇒ x = 7

Thus, At x = 0 and x = 7, the function g(x) is undefined.

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1

9514 1404 393

Answer:

  (x, y) = (3, 12)

Step-by-step explanation:

Using the given variable definitions, we can write the equations ...

  y = x + 9

  2(x +y) = 30

__

Solving the second equation for y, we have ...

  y = 15 -x

Substituting this into the first equation gives ...

  15 -x = x +9

  6 = 2x . . . . . . . . . add x-9

  3 = x . . . . . . . . . . divide by 2

  y = 3+9 = 12 . . . . substitute into the first equation

The numbers are (x, y) = (3, 12).

Answer:

A i think

Step-by-step explanation:

Answer:

x=7

Step-by-step explanation:

9x-9=5x+19

Combine like terms

9x-5x=19+9

4x=19+9

4x=28

x=7

Answer:

$2.60

Step-by-step explanation:

40 x 0.065 = $2.60

Answer:

the tax would be 2.60$

Step-by-step explanation:

6.5% of 40 is 2.6

(6.5 x .40=2.6)

Answer:

154×5×100=770×100=77000

look at the picture above for the answer with process

Answer:

The correct answer is B, also may be Brain??

Step-by-step explanation:

The perimeter of a rectangle can be calculated using the formula P = 2l + 2w, where l is the length and w is the width. If the length of the rectangle is 25 cm and we want the perimeter to be greater than 90 cm, we can set up an inequality to solve for the width: 2l + 2w > 90.

Substituting the value for the length gives 2 * 25 + 2w > 90, which simplifies to 50 + 2w > 90. Subtracting 50 from both sides gives 2w > 40, and dividing by 2 gives w > 20.

So the width of the rectangle must be greater than 20 cm to make the perimeter greater than 90 cm. The correct answer is B: width > 20 cm.

Answer:

i'm guessing this but not 100% sure

Step-by-step explanation:

Let w = the width

P = 2l + 2w

2w + 2(25) > 90

2w + 50 > 90

2w > 40

w > 20 cm

A randomized experiment with order, replacement, and no repetition is one in which the order of the outcomes matters, the same outcome can occur multiple times, and no outcome can occur more than once.

For example, drawing a card from a deck and then flipping a coin would be a random experiment with order, replacement, and no repetition. The order of the results is important because the outcome of the coin toss will depend on the outcome of the card draw.

The same result can occur multiple times because the same card can be drawn twice, and no result can occur more than once because the coin can only land heads or tails once.

Learn more about the experiments at

brainly.com/question/17274244

#SPJ1

Random experiment with order, replacement and without repetition

Answer: 156.38 m

Step-by-step explanation:

Using the arc length formula, the answer is \(2\pi(8^2) \cdot \frac{140}{360} \approx 156.38\)

Answer:

$1.65

Step-by-step explanation:

Given that:

Batch mixture :

Cinnamon - 200 ounces

Nutmeg - 100 ounces

Cloves - 100 ounces

Cost of Seasoning mix :

Cinnamon - 1.80 per ounce

Nutmeg - 1.60 per ounce

Cloves - 1.40 per ounce

Price per ounce of mixture :

Let the price per ounce of mixture = x

Total ounce of mixture = (100 + 100 + 200) = 400 ounces

Σ(ounce * cost) = total ounce * cost of mixture

(200*1.80)+(100*1.60)+(100*1.40) = 400 * x

$360 * $160 * $140 = 400x

$660 = 400x

x = $660 / 400

x = $1.65

Price per ounce of mixture = $1.65

Answer:

63

Step-by-step explanation:

180 -  143 = 37

80 + 37 + x = 180

117 + x = 180

x = 63

The range, in centimetres (cm), of the following lengths is 20.5 cm

What is the range?

The difference between the lowest and highest numbers is referred to as the range. For instance, the range will be 10 - 2 = 8 if the given data set is 2, 5, 8, 10, and 3.

As a result, the range may alternatively be thought of as the distance between the highest and lowest observation. The range of observation is the name given to the outcome. Statistics' range reflects the variety of observations.

Given, 15 cm, 0.5 cm, 10.3 cm, 16.7 cm, 21 cm, 8.6 cm

So, the highest value of length = 21 cm

the lowest value of length = 0.5 cm

Then, range = the highest value - the lowest value

                    = 21 - 0.5 = 20.5 cm

Hence, the range, in centimetres (cm), of the following lengths is 20.5 cm

To learn more about range

https://brainly.com/question/29794774

#SPJ1

Answer:

Step-by-step explanation:

x-intercept is where the line cuts the x-axis. That is, when y=0.

Substitute y=0 and we get:

       \(0=\frac{1}{3} x-1\)

       \(1=\frac{1}{3} x\)

       \(x=3\)

So x-intercept is the point (3,0).