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The summation notation for the given arithmetic series is  [tex]\sum_1^4(4n)[/tex]

An arithmetic series is the sum of the terms in an arithmetic sequence with a definite number of terms.

Given is an arithmetic series, 4+8+12+16, we need to find the summation notation for the given arithmetic series,

To generate the terms of a series given in sigma notation, successively replace the index of summation with consecutive integers from the first value to the last value of the index.

To generate the terms of the series given in sigma notation above, replace n by 1, 2, 3 and 4

[tex]\sum_1^4(4n)[/tex] = 4(1) + 4(2) + 4(3) + 4(4)

= 4 + 8 + 12 + 16

= 40

Therefore, the sum of the series is 40

Hence, the summation notation for the given arithmetic series is  [tex]\sum_1^4(4n)[/tex]

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Let's call the number of candles Roma sold for $5 each "x".

What is the unitary method's formula?

What is the unitary method's formula? The unitary method's formula is to identify the value of a single unit, then multiply that value by the number of units to obtain the required value.

Since she sold 200 candles in total, we know that x + 3y = 200, where y is the number of sets of three candles she sold for $11.

We also know that the total revenue was $788, so we can set up another equation based on the total revenue:

5x + 11y = 788

Now that we have two equations, we can use substitution to solve for x. First, let's solve for y:

y = (200 - x) / 3

Plugging this expression for y into the second equation:

5x + 11((200 - x) / 3) = 788

Expanding and simplifying the equation:

5x + (2200 - 11x) / 3 = 788

Multiplying both sides by 3 to get rid of the fraction:

15x + 2200 - 11x = 2364

Combining like terms:

4x = 164

Finally, dividing both sides by 4 to solve for x:

x = 41

So Roma sold 41 candles for $5 each at the craft fair.

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Applying the secant-secant theorem, the value of x is: 12.

The secant-secant theorem states that if you draw two lines from a point outside a circle that intersect the circle at two different points, then the product of the length of one line segment and the length of the portion of the line outside the circle is equal to the product of the length of the other line segment and the length of its portion outside the circle.

Based on the secant-secant theorem, we have:

EF * ES = ED * EC

Substitute the values:

8(8 + 10) = 9(2x - 17 + 9)

Solve for x:

144 = 18x - 72

144 + 72 = 18x

216 = 18x

216/18 = x

x = 12

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116 years it take  for the account value to reach 26500 dollars

percentage, a relative value indicating hundredth parts of any quantity.

Given that 7700 dollars is placed in an account with an annual interest rate of 5.5%.

We need to find the time it  take for the account value to reach 26500 dollars

[tex]A=P(1+r)^{t}[/tex]

A = final amount=26500

P = initial amount (7700)

r = annual interest rate (5.5%)

n = number of times interest is compounded per year

t = time in years

Solving for t, we get:

[tex]25600=7700(1+5.5/100)^{t}[/tex]

[tex]25600=7700(1.055)^{t}[/tex]

Divide both sides by 7700

[tex]25600/7700=1.055^{t}[/tex]

3.32=tlog1.055

3.32=0.02t

t=116 years

Hence, 116 years it take  for the account value to reach 26500 dollars

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Answer:

8 hours

Step-by-step explanation:

We know that since Lila earns $12/hr and works 6 hr/week, she earned 72 since 12 * 6 = 72.

We can let the amount Patrick earns each week represent 9h, where h is the amount of hours he works.

We can solve for h by setting Patrick's equation equal to 72, which is Lila's earnings:

[tex]9h=72\\h=8\\\\9(8)=72\\12(6)=72[/tex]

Two gardeners can cut a similar field in three hours. A soccer field might be cut in two hours by six grounds-keepers, every one of whom works at a pace of one-6th of the field every hour.

To get the number of grounds-keepers expected to cut the very field in that timeframe, we should initially decide the speed at which the field can be cut in 3 hours, which is 1/3 of the field consistently.

To get the required number of groundskeepers, we partition this rate by the pace of every nursery worker, which is 1/6 of the field every hour, yielding the condition 1/3 / 1/6 = 2.

Subsequently, two nursery workers might cut similar regions in three hours.

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Step-by-step explanation:

What graph are we talking about?

The height of the other tree is 7.25 meters

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

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

Ratio = Height : Shadow

So, we have

Height : Shadow = 4 : 16

Simplify

Height : Shadow = 1 : 4

So, we have

Height : 29 = 1 : 4

This means that

Height = 29 * 1/4

Evaluate

Height = 7.25

Hence the height is 7.25 meters

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Answer:

The height of the other tree is 7.25 meters

Step-by-step explanation:

By AA similarity Triangle PQR and TQS are similar.

Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles. Similar figures are described as items with the same shape but varying sizes, such as two or more figures.

Given:

As, PR || TS then

<RPQ = <TSQ (Alternate Interior Angle)

< <QTS = <QRP (Alternate Interior Angle)

So, Triangle PQR and TQS are similar by AA similarity criteria.

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The greatest number of people that they may invite and still stay within their budget is 126 persons.

An equation is a mathematical statement in symbolic form that indicates that two things are exactly the same. Equations are written with an equal sign (=) as follows:

The statements above are similar. Equations can be used to express the similarity of two expressions composed of one or more variables.

For example, for real x members, the following equation is always true:

x(x - 1) = x² − x.

The above equation is an example of identity.

An equation that is always true regardless of the values of the variables in it. 

According to the question:

Oscar and Julie Ashton have a budgeted $4,500 for their reception.

The reception hall charges a $90 cleanup fee plus $35 per person.

Let the total number of persons be = p

Clean up is a one time charge.

So, the inequality forms:

90+ 35p= < $4500

90 + 35p =< $4500

35p =< $4500 - 90

35p=< 4410

p=< 4410 : 35

p =< 126 persons

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Answer:

Step-by-step explanation:

The most precise term for the quadrilateral ABCD with vertices A(4, 7), B(6, 5), C(4, 1), and D(2, 5) is a trapezoid. A trapezoid is a quadrilateral with exactly one pair of parallel sides.

Maxine paid total amount of $10800 on the loan.

The percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given,

Maxine took loan of $9000

Interest she paid = 20%

Total interest = (20/100) × 9000

                      = $1800

Total amount = $9000 + $1800 = $10800.

Hence, $10800 is total amount Maxine paid at end of the loan.

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Answer:

She should walk at a rate of 16 km/hr

Step-by-step explanation:

At a rate of 12 km/hr, she would have traveled 4 km in 20 minutes. This can be calculated by finding the ratio of 20 minutes to 1 hour which is 1/3. We then multiply this ratio by the rate to find the distance Shalu needs to walk to school.

We then need to find the necessary km/hr in order for Shalu to travel 4 km in 15 minutes. 15 minutes is a quarter of 1 hr. Therefore a rate of 4 km/15 minutes is equal to a rate of 16 km/hr. This means that the average speed Shalu would have to walk is 16 km/hr.

One way we can check this is to simply multiply 15 by 12 to get 180.

Or you could even switch the numbers around.

But if we wanted to check it further, we can take the total and divide that by one of the multiplican or multipliers (15 or 12) to get the correct product.

Therefore, these are some ways to use the numbers 180, 15 and 12 in expressions.

Answer:

16

Step-by-step explanation:

(fog)x=f{g(x)}

=f(x-2)

=(x-2)^2

So,

(fog)(-2)=(-2-2)^2

=-4^2

=16

Answer:

Step-by-step explanation:

KE = (1/2) * m * v^2

where KE is the kinetic energy, m is the mass of the object, and v is the velocity of the object.

We are given the mass of the bumblebee as 0.015 kg and its velocity as 21.0 m/sec. We can plug these values into the formula to calculate its kinetic energy:

KE = (1/2) * m * v^2

= (1/2) * 0.015 kg * (21.0 m/sec)^2

= (1/2) * 0.015 kg * 441.0 m^2/sec^2

= 2.92625 J

Therefore, the bumblebee has 2.92625 Joules of kinetic energy as it hits the windshield.

Answer:

The kinetic energy of the bumblebee as it hits the windshield is given by the equation KE = 0.5 x 0.015 kg x (21.0 m/s) squared. This gives us a total of 945 J of kinetic energy.

Answer: a. To create the graph, we need to find the speed (in km/min) of Lin and Andre. The speed is calculated as distance divided by time.

For Lin: speed = 1.5 km / 5 min = 0.3 km/min

For Andre: speed = 2 km / 8 min = 0.25 km/min

We can plot these speeds as points on a graph with time on the x-axis and speed on the y-axis.

b. The point for Lin is (5, 0.3) and for Andre is (8, 0.25).

c. From the graph, we can see that Lin was biking faster, with a speed of 0.3 km/min compared to Andre's speed of 0.25 km/min.

Step-by-step explanation:

Bethany says, Using these exchange rates, £1 is worth 1.17 euros.

Step-by-step explanation

1 euro = 1.07 dollars

£1 = 1.25 dollars

Now ,

⇒ £1 = 1.25 dollars

⇒ £1 =

⇒ £1 =

⇒ £1 =

⇒ £1 =

⇒ £1 =1.17 euros

Therefore , Bethany says, Using these exchange rates, £1 is worth 1.17 euros.

Answer:

B

Step-by-step explanation:

it says why

Answer:

-3, 4

Step-by-step explanation:

First, we can simplify this expression by diving both sides by 6. Thus, we get x² - x - 12 = 0. Solving this, we get (x-4)(x+3). Thus, the solutions for x are 4 and -3. So, the answer is x = -3, 4

The two numbers that can be true for the equations are 5 and 12

From the information given, we have the equations;

x+y=17

x-y=7

From equation (1), make 'x' the subject of formula

x = 17 - y

Now, substitute the value into the formula, we have;

17 - y - y= 7

collect like terms

-y-y = 7 - 17

Subtract the iike terms

-2y = -10

Make 'y' the subject

y = 5

Substitute the value

x = 17 -5

x = 12

Hence, the values are 12 and 5

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For rectangle ABCD, the value of x is 6.44 inches

Consider the following diagram.

From this figure we can observe that the dimansions of the rectangle: length is given by expression (7x + 1) and width is given by expression 'x'

We know that tha formula for the perimeter of the rectangle,

P = 2 × (length + width)

Here, the perimeter of rectangle ABCD is 105 inches.

Using above formula of perimeter we get an expression,

P = 2 × ((7x + 1)+ x)

105 = 2 × (8x + 1)

We solve above equation for x.

105/2 = 8x + 1

52.5 - 1 = 8x

8x = 51.5

x = (51.5)/8

x = 6.44 inches

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Note that the line of reflection that reflects quadrilateral ABCD onto quadrilateral A'B'C'D' is given as attached. Note that when a shape is reflected, it must be reflected over a line. In this case, the line of reflection is y = -3.

A line of reflection is a line that acts as a mirror, reflecting a figure across the line so that the image is a mirror image of the original.

When a shape is reflected, it must be reflected over a line. The line of reflection of quadrilateral ABCD onto quadrilateral A'B'C'D is

From the given graph, we have the following observations

ABCD was flipped over to form A'B'C'D'

The line of reflection is between both shapes.

Using points C and C' as references;

We have:

C = (-3, -1)

C" = (-3, -5)

Notice that both points have the same x-coordinate

This means that the line of reflection is parallel to the x-axis and passes through the y-axis.

The point at which it passes through the y-axis is calculated using the mid-point formula.

Therefore, we have:

y = (y1+y2)/2

y = (-1-5)/2

y = -6/2

y = -3

Hence, the line of reflection is y = -3
See the attachment for the line of reflection.

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Answer:

Step-by-step explanation:

The horizontal line of length 7cm is added as an attachment

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

Line = 7 cm

The following steps would create the perpendicular bisector

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Answer:

tsa=6a^2

=6x(6.5x6.5)

=235.3cm sq.

Step-by-step explanation:

i hope it will help u

The equation of line is y = 12x and the number of boxes the shipping company can pack in 18 hour period is 216 boxes

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the number of hours be x

Let the number of boxes be y

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 5 , 60 )

Now , the slope of the line m = y/x

Substituting the values in the equation , we get

Slope m = 60 / 5 = 12

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 60 = 12 ( x - 5 )

y - 60 = 12x - 60

y = 12x

Now , when x = 18 hours

y = 12 ( 18 ) boxes

y = 216 boxes

Hence , the number of boxes is 216 boxes

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By standard deviation, 3.4 defects per million that a six sigma program has. Whereas the remaining ones are not appropriate in this context.

What does standard deviation mean ?

The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean.

                               Data are said to be more closely grouped around the mean when the standard deviation is low and more dispersed when the standard deviation is high.

Describe standard deviation using an example?

The dispersion of the data around the mean value is measured by the standard deviation. It might be helpful when comparing data sets that may have the same mean but a different range.

                         The means of the two numbers 15, 15, 15, 14, 16, and 2, 7, 14, 22, 30 are the same, for instance. The second is, however, obviously more dispersed.

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The measure of the angle ∠PSR will be equal to 25 degrees.

One of the earliest areas of mathematics is geometry, along with arithmetic. It is concerned with spatial characteristics like the separation, shape, size, and relative placement of objects.

Given that In quadrilateral PQRS, the exterior angle at Q when PQ is extended measures 155 and PS = QR.

The measure of the angle PSR will be calculated as:-

∠Q exterior  = 155

∠PQR = 180 - 155

∠PQR = 25

∠PQR = ∠PSR = 25°

Therefore, the value of the angle ∠PSR is 25°.

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Answer: To find the highest common factor (HCF) of two polynomials, we can use the Euclidean algorithm for polynomials. The Euclidean algorithm involves dividing the larger polynomial by the smaller polynomial and continuing the division process until the remainder is zero. The last non-zero remainder is the HCF of the two polynomials.

In this case, we have:

2x^3 + x^2 - 3x = (2x^3 - x^3) + x^2 - 3x

= x^3 + x^2 - 3x

Now, we divide x^3 + x^2 - 3x by x^3 - x

x^3 + x^2 - 3x = x^3 - x * (1 + x - 3)

= x^3 - x * (x^2 - 2x + 3)

We cannot simplify this expression further, so the HCF of 2x^3 + x^2 - 3x and x^3 - x is x^3 - x.

Step-by-step explanation:

Answer:

[tex]\frac{1}{4}[/tex]

Step-by-step explanation:

Originally our equation looks like [tex]x^{2}[/tex] + 2y

First, we want to substitute x = [tex]\frac{1}{2}[/tex]  & y= 0 into the equation.

The equation now looks like [tex]([/tex][tex]\frac{1}{2}[/tex][tex])^{2}[/tex] + 2 x 0

The brackets are added to the fraction as we are squaring the WHOLE fraction, and the 2y has a hidden multiplication sign, with it being 2 x y, so it is 2 x 0.

Now that we have our values substituted into the equation, we can solve it!

 [tex]([/tex][tex]\frac{1}{2}[/tex][tex])^{2}[/tex] = [tex]\frac{1}{4}[/tex]  

therefore,

[tex]\frac{1}{4}[/tex]  + 2 x 0

= [tex]\frac{1}{4}[/tex]