5x2(x − 5) + 6(x − 5) =
write thé expression in completed form

We can use the ratio test to determine whether the series ∑(n=1[tex])^(infinity)[/tex][tex]13^n[/tex]/ [(n+1)[tex]6^(2n+1)[/tex]] is convergent or divergent.

We evaluate the limit:

lim n → ∞ [tex]|(13^(n+1) / [(n+2)6^(2n+3)]) / (13^n / [(n+1)6^(2n+1)])|[/tex]

= lim n → ∞ [tex]|(13^(n+1) / 13^n) * [(n+1)6^(2n+1) / (n+2)6^(2n+3)]|[/tex]

= lim n → ∞ [tex]|13 / 6^2| * |(n+1)/(n+2)|[/tex]

= 13/36

Since the limit is less than 1, by the ratio test, the series is convergent.

To find the value of a_n, we can substitute n = 1 into the formula:

a_n = [tex]13^n / [(n+1)6^(2n+1)][/tex]

a_1 = [tex]13 / [(1+1)6^(2+1)] = 13 / (2*6^3)[/tex]

Therefore, a_1 = 13 / 432.

Note that we only needed to find the value of a_1 to apply the ratio test and determine the convergence of the series.

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Step-by-step explanation:

To determine the appropriate fraction for the line plot, we need to find the greatest common factor (GCF) of all the pencil lengths, and then express each length as an equivalent fraction with the GCF as the denominator.

The GCF of the pencil lengths is 1. Therefore, we can simply express each pencil length as an equivalent fraction with 1 as the denominator:

3/1, 7/1, 8/1, 5/1, 1/1, 4/1, 6/1, 8/1, 4/1, 2/1, 5/1

Now, we can see that the smallest unit increment we can use on the line plot is 1/8. This is because 1/8 is the smallest fraction that can represent all of the pencil lengths above the label (5/8, which is equivalent to 10/16).

Therefore, the students should use 1/8 as the fraction for the line plot.

The variance of first n even natural numbers is n²-1/12. So, the correct option is (a) .

The first n even natural numbers can be represented as 2, 4, 6, ..., 2n. The mean or expected value of this sequence is given by:

mean = (2 + 4 + 6 + ... + 2n) / n

= 2(1 + 2 + 3 + ... + n) / n

= 2n(n+1)/2n

= n+1

The variance of a sequence is the average of the squared differences from the mean, so we need to calculate:

Var = [(2- (n+1))² + (4- (n+1))² + (6- (n+1))² + ... + (2n- (n+1))²] / n

Simplifying the expression inside the brackets and using the formula for the sum of the first n integers, we get:

Var = [4(1² + 2² + 3² + ... + n²) - 4(n+1)(1 + 2 + 3 + ... + n) + n(n+1)²] / n

Substituting the formula for the sum of the first n squares and the sum of the first n integers, we get:

Var = [4n(n+1)(2n+1)/6 - 4(n+1)n(n+1)/2 + n(n+1)²] / n

Simplifying and factoring out (n+1), we get:

Var = (n+1)(n² - 1) / 3

Thus, the correct option is (a) n²-1/12.

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If kawan paints the visible outside faces of her shed, she paints two rectangle faces and two triangle faces then the total surface area that she paints is 88ft².

The area of a triangle of altitude h and base b is given by;

A = 0.5bh

Therefore the area of one triangle face ;

At = 0.5 × 8 × 5

At = 20ft²

Area of a rectangle of length l and breadth b is;

A = lb

Therefore the area of a rectangle face;

Ar = 8 × 3

Ar = 24ft²

We have 2 triangle faces and 2 rectangle face, therefore total surface area as;

A = 2At + 2Ar

A  = 2×20 + 2×24

A = 40 + 48

A = 88ft²

Therefore the answer is; 88ft².

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The volume of the cone is approximately one-third the volume of the

cylinder

:V(cone) ≈ 1/3 V(cylinder) = 1/3 (9.4) ≈ 3.1 cubic feet.

The volume of a cone with the same height and radius as the given

cylinder, we can use the formula:

[tex]V = 1/3 πr²h[/tex]

where V is the volume, r is the radius, and h is the height.

Since the cylinder has a volume of approximately 9.4 cubic feet, we can

use the formula for the volume of a cylinder

:V = πr²hand solve for the radius:

[tex]r = √(V/πh) = √(9.4/πh)[/tex]

Now we can substitute this expression for the radius into the formula for

the volume of a cone:

[tex]V = 1/3 π(√(V/πh))²h[/tex]

Simplifying this expression gives:

[tex]V = 1/3 π(V/πh)hV = 1/3 V[/tex]

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A comparison of the cost of each for 100 g indicates that the standard which costs about $1.13 per 100 grams is more expensive than the supersize which costs about $0.69 per 100 g and the supersize is more expensive than the economy which costs $0.575 per 100 g.

The order of the cost of the brands from cheapest to most expensive can be presented as follows;

The cost per unit is the cost of a number of items, divided by the number of units of the item.

The unit cost of the brands of cereal sold at the supermarket are therefore;

Unit cost per 100 gram for Standard = $2.49/220 g × 100 ≈ $1.13/g

Unit cost per gram for Economy = $5.00/725 g × 100 = $100/145/ g ≈ $0.69/g

Unit cost per gram for Supersize = $11.50/2kg × 100 = $1150/2,000 g ≈ $0.575/g

Based on the above unit cost, we get;

1.13 > 0.69 > 0.575

Therefore, the cheapest brand is the supersize with a cost per 100 gram of $0.575/g, followed by the economy, with a cost per 100 grams which is about $0.69/g then the most costly is the standard, with a cost per 100 gram of $1.13/g

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The area of the playground include the following: 900 square yards.

In Mathematics and Geometry, the area of a regular polygon can be calculated by using this formula:

Area = (n × s × a)/2

Where:

In Mathematics and Geometry, the area of a parallelogram can be calculated by using the following formula:

Area of a parallelogram, A = base area × height

Area of playground, A = 45 × 20

Area of a playground, A = 900 square yards.

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Answer:  First, we need to find the composite function (fg)(x):

(fg)(x) = f(g(x))

= f(-4x-3)

= (-4x-3)^2 + (-4x-3) + 9 (substituting g(x) into f(x))

= 16x^2 + 24x + 18

Therefore, (fg)(x) = 16x^2 + 24x + 18.

Next, we need to find the quotient function (f/g)(x):

(f/g)(x) = f(x) / g(x)

= (x^2 + x + 9) / (-4x - 3) (substituting f(x) and g(x))

To simplify this expression, we can use polynomial long division or synthetic division. Using synthetic division, we get:

  -4 |   1    1    9

      |_____-4__ 12

      |  1  -3   21

Therefore, (f/g)(x) = -4x + 3 - 21 / (-4x - 3)

Simplifying further, we get:

(f/g)(x) = -4x + 3 + (21/4)(1/(x + 3/4))

Therefore, (f/g)(x) = -4x + 3 + (21/4)(1/(x + 3/4)).

Step-by-step explanation:

The dimensions of the bookmark are length = 15 centimeters and width = 10 centimeters.

Let's denote the length of the bookmark as L and the width as W.

The area of a rectangle is given by the formula A = L * W, and the perimeter is given by P = 2L + 2W.

From the given information, we have two equations:

Equation 1: A = 150 square centimeters

Equation 2: P = 62 centimeters

Substituting the formulas for area and perimeter, we get:

Equation 1: L * W = 150

Equation 2: 2L + 2W = 62

To solve these equations, we can use substitution or elimination. Let's solve by substitution:

From Equation 1, we can express one variable in terms of the other:

L = 150 / W

Substituting this into Equation 2:

2(150 / W) + 2W = 62

300 / W + 2W = 62

300 + 2W^2 = 62W

2W^2 - 62W + 300 = 0

Now we have a quadratic equation. We can solve it by factoring, completing the square, or using the quadratic formula. In this case, let's use factoring:

[tex]2W^2 - 62W + 300 = 0[/tex]

(W - 10)(2W - 30) = 0

This gives us two possible solutions:

W - 10 = 0 -> W = 10

2W - 30 = 0 -> W = 15

Since the width cannot be longer than the length, we discard the solution W = 15.

So, the width of the bookmark is W = 10 centimeters.

Now, we can substitute this value into Equation 1 to find the length:

L * 10 = 150

L = 150 / 10

L = 15

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Answer: AB = 16.4

Step-by-step explanation:

You can use tan x = opposite/adjacent

tan 38 = AB/21

21 tan 38 = AB

AB = 16.4

Answer:

x = 18

Step-by-step explanation:

We Know

(10x - 4) + (x - 14) must equal 180°

Find the value of x.

Let's solve

10x - 4 + x - 14 = 180

11x - 18 = 180

11x = 198

x = 18

So, x = 18 is the answer.

a) To find the total surface area of the cuboid, we need to find the area of each face and then add them up.

Area of one face = length x width

Area of top and bottom faces = 1.1 m x 0.55 m = 0.605 m² (2 faces)

Area of front and back faces = 2.2 m x 0.55 m = 1.21 m² (2 faces)

Area of side faces = 2.2 m x 1.1 m = 2.42 m² (2 faces)

Total surface area = (2 x 0.605) + (2 x 1.21) + (2 x 2.42) = 7.7 m²

Each tin of varnish covers 20 m², so Emma needs:

Number of tins = (total surface area x number of coats) / coverage per tin

Number of tins = (7.7 x 3) / 0.02 = 1155

Emma needs to buy 1155 tins of wood varnish.

b) The cost of each tin of varnish is $3.99 for 100 ml. To find the cost of 1155 tins, we first need to convert the volume of varnish needed into liters.

Volume of varnish needed = (total surface area x number of coats) / coverage per litre

Volume of varnish needed = (7.7 x 3) / 20 = 1.155 liters

The number of tins required to make up 1.155 liters of varnish is:

Number of tins = (1.155 / 0.1) = 11.55

So Emma needs to buy 12 tins of varnish. The total cost is:

Total cost = cost per tin x number of tins

Total cost = $3.99 x 12 = $47.88

The total cost of the wood varnish is $47.88.

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Answer:  B   28√15

Step-by-step explanation:

They want you to find the Area of the quadrilateral.  But if you can find the area of 1 trangle then you can double it because the 2 triangles are congruent.

We know the 2 triangles are congruent from the theorem  (see diagram

We also know that  QR=TR=SR  They are all radius

Let's solve for triangle PRS

PR = hypotenuse = 10+7 =17

SR=7  radius

Use pythagorean to find PS

c²=a²+b²

17²=7²+b²

289 = 49 + b²

b²=289 -49

b² = 240

b=√240

b=[tex]\sqrt{16*15}[/tex]

b= 4√15  This is PS

Area of triangle = 1/2 bh       b=PS   h=7

Area of triangle = 1/2 (4√15)(7)

Area of triangle = (2√15)(7)

Area of triangle = 14√15

Area of quadrilateral = 2 (14√15)        > 2 triangles make the quadrilateral

Area of quadrilateral =  28√15

Based on the given situation we can conclude that the sedan retains its value better than the pickup truck over time.The functions S(t) and P(t) represent the values of the sedan and pickup truck, respectively, as a function of the number of years t after their purchase.

The coefficient 24,400 in the function S(t) represents the initial value of the sedan, which is the value of the car at t=0. The base 0.82 represents the decay rate or the percentage decrease in the value of the sedan each year. Similarly, in the function P(t), the coefficient 35,900 represents the initial value of the pickup truck and the base 0.71 represents the decay rate of the value of the pickup truck.

Since the base of the sedan's value decay is 0.82, it indicates that the value of the sedan decreases by 18% each year. Whereas the base of the pickup truck's value decay is 0.71, indicating that the value of the pickup truck decreases by 29% each year. Therefore, we can observe that the value of the pickup truck depreciates faster than the sedan. After two years, the value of the sedan would be approximately $16,650, and the value of the pickup truck would be approximately $14,161. After five years, the value of the sedan would be approximately $9,237, and the value of the pickup truck would be approximately $6,155.

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Answer:

y=f(x) = log7x

Just trust me

The graph best represents the function y = f(x) = 7x, an exponential function.

The graph represents the function y = 7x, which is an exponential function. In an exponential function, the variable x is the base, and the exponent is a constant, which in this case is 7. This means that the function grows rapidly as x increases, creating a steep curve on the graph.

The other two options, y = f(x) = log7x and y = f(x) = x7, are not represented by the given graph.

The function y = f(x) = log7x is a logarithmic function, which has a different shape on the graph, with a horizontal asymptote and the x-axis acting as its asymptote.

The function y = f(x) = x7 is a polynomial function, where x is raised to the power of 7, and it would have a different pattern on the graph compared to the exponential function shown.

Thus, the graph best represents the function y = f(x) = 7x, an exponential function.

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Answer:

4

Step-by-step explanation:

You can cut it 4 ways to obtain equal parts on both sides. It's along the same as the symmetry of a square.

The linear function rule that models the cost y of a package containing any number x of comic books is y = $6.50 + $1.00x and for 10 comic books, the second store has the better deal.

A linear function is a mathematical function where the graph of the function is a straight line. It can be written in the form y = mx + b, where x and y are the variables, m is the slope of the line, and b is the y-intercept (the point where the line intersects the y-axis). The slope represents the rate of change of the function, while the y-intercept is the value of the function when x is equal to zero.

To write a linear function rule that models the cost y of a package containing any number x of comic books, we can use the given information to set up a system of equations:

Poster + 2 Comics = $7.50

Poster + 11 Comics = $16.50

We can solve for the cost of the poster and the cost of one comic book by subtracting the first equation from the second:

9 Comics = $9.00

1 Comic = $1.00

Then, we can use the cost of one comic to set up a linear function rule:

y = cost of poster + cost of x comics

y = $6.50 + $1.00x

Therefore, the linear function rule that models the cost y of a package containing any number x of comic books is y = $6.50 + $1.00x.

For the second store, the linear function rule is given as y = $5.75 + $1.00x.

To determine which store has the better deal, we can compare the cost of each package for a specific number of comic books. For example, if we want to buy 10 comic books, the cost at the first store would be:

y = $6.50 + $1.00(10) = $16.50

The cost at the second store would be:

y = $5.75 + $1.00(10) = $15.75

Therefore, for 10 comic books, the second store has the better deal. However, for a different number of comic books, the better deal may be at a different store. We can use the linear function rules to compare the costs for any number of comic books

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Answer:

Step-by-step explanation:

√4x^2=2x

To find the area of each shaded sector and round to the hundredths place, I'll need some more information, such as the radius of the circle and the measure of the central angle of the sector. Please provide these details so I can assist you with the calculation.

The area of the shaded sector is 1330.81 ft²

Given, ∠GKH = 26° and ∠JKI = 90°

The area that is not shaded has a total of 90° + 26° = 116°.

A circle has a total angle of 360°, so the area that is shaded must be

360° - 116° =  244°

Given, HK = 25 ft

Radius of circle = 25 ft

We know that the formula for the area of the sector of a circle is

Area = [tex]\frac{\pi \theta r^2}{360^\circ}[/tex]

= (π × 244 × (25)² )/ 360

= 7625π/18

= 1330.81 ft²

Hence, the area of the shaded sector is 1330.81 ft²

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Given question is incomplete, the complete question is below

Find the area of each shaded sector. round to the hundredths place.

You must have approximately $16,465.55 in your account now to achieve a balance of $23,000 in 5 years with a 6.8% interest rate compounded continuously.

To achieve a savings account balance of $23,000 in 5 years with an interest rate of 6.8% compounded continuously, you will need to use the formula for continuous compounding: A = P * e^(rt), where A is the future value, P is the principal amount (initial deposit), r is the interest rate, t is the time in years, and e is the base of the natural logarithm (approximately 2.71828).

In this case, A = $23,000, r = 0.068, and t = 5 years. You need to solve for P, the principal amount:

$23,000 = P * e^(0.068 * 5)

Now, you can solve for P:

P = $23,000 / e^(0.068 * 5)

P ≈ $16,465.55

So, you must have approximately $16,465.55 in your account now to achieve a balance of $23,000 in 5 years with a 6.8% interest rate compounded continuously.

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Answer:

shape a is 20 cm squared

Step-by-step explanation:

shape a is a parallogram, A =b×h. 5x4=20

shape b is a trapezoid. The picture is cut off but here are the steps for you to solve. A=0.5h(base1+base2) count the number of squares on the top and bottom of the shape. I can see the top is 2, you will need to tfind the length of the bottom base.then count the height, how far to get from the bottom to top, here it is 4.

area=0.5*4(2+bottom base) simply and that's your answer! Don't forget your units

The average price of milk in 2018 was $6.45 per gallon.

The average price of milk in 2021 was $189.15 per gallon.

When x = 0 (which represents the year 2018), the function becomes:

3.55 + 2.90(1 + 0)³

= 3.55 + 2.90(1)³

= 3.55 + 2.90

= 6.45

The average price of milk in 2018 was $6.45 per gallon.

When x = 3 (which represents the year 2021), the function becomes:

3.55 + 2.90(1 + 3)³

= 3.55 + 2.90(4)³

= 3.55 + 2.90(64)

= 3.55 + 185.6

= 189.15

The average price of milk in 2021 was $189.15 per gallon.

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Nataly saved s/64.

The original prices for the items are:

Skirt: s/78

Blouse: s/65

Jacket: s/240

The discounted prices Nataly paid are:

Skirt: s/69

Blouse: s/52

Jacket: s/198

To find out how much Nataly saved, we need to calculate the difference between the original prices and the discounted prices, and then add them up:

savings = (78 - 69) + (65 - 52) + (240 - 198)

savings = 9 + 13 + 42

savings = s/64

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Clarissa needs a total of 251.25 square inches of construction paper for her project.

To find the total area of construction paper needed, we need to find the area of each rectangle and add them together.

The first rectangle has an area of 10 inches × 14.5 inches = 145 square inches.

The second rectangle has an area of 10.25 inches × 10.5 inches = 107.625 square inches.

Adding these two areas together, we get a total of 145 + 107.625 = 252.625 square inches.

Therefore, Clarissa needs a total of 251.25 square inches (rounded to two decimal places) of construction paper for her project.

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our final estimate for the area under the curve f(x)=1/x on [1,2] using 4 approximating rectangles and taking the average of the left and right endpoints is 0.76.

To estimate the area under the curve f(x)=1/x on [1,2], we can use 4 approximating rectangles.

a) Using left endpoints, the width of each rectangle is (2-1)/4 = 0.25. The left endpoints of the rectangles are 1, 1.25, 1.5, and 1.75. The height of each rectangle is f(x) evaluated at the left endpoint.

So, the heights are f(1) = 1/1 = 1, f(1.25) = 1/1.25 = 0.8,

f(1.5)=1/1.5 = 0.67, and f(1.75) = 1/1.75 = 0.57.

The area of each rectangle is width times height, so the areas are

0.25*1 = 0.25, 0.25*0.8 = 0.2, 0.25*0.67 = 0.1675, and 0.25*0.57 = 0.1425.

Adding these areas together, we get an estimate of the total area under the curve as

0.25 + 0.2 + 0.1675 + 0.1425 = 0.76.

b) Using right endpoints, the width of each rectangle is the same as before. The right endpoints of the rectangles are

1.25, 1.5, 1.75, and 2.

The heights are f(x) evaluated at the right endpoint. So, the heights are

f(1.25) = 0.8, f(1.5) = 0.67, f(1.75) = 0.57, and f(2) = 0.5.

The areas of the rectangles are the same as before, so adding them up, we get an estimate of the total area as

0.2 + 0.1675 + 0.1425 + 0.25 = 0.76,  

which is the same as before.
c) To get the average of the two estimates, we add them together and divide by 2:

(0.76+0.76) / 2 = 0.76.

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The dimensions of the cylinder that minimize the production cost are:

radius = approximately 2.78 cm

height = 600 / (πr^2) ≈ 7.14 cm

paper top radius = 2.5 cm

Let's start by finding the formula for the cost of the container in terms of its dimensions.

The volume of the cylinder is given as 600 cubic centimeters, so we have:

πr^2h = 600

where r is the radius of the cylinder and h is its height. Solving for h, we get:

h = 600 / (πr^2)

The surface area of the cylinder is given by:

A = 2πrh + 2πr^2

Substituting h in terms of r, we get:

A = 2πr(600/(πr^2)) + 2πr^2

= 1200/r + 2πr^2

The cost of the container is the sum of the cost of the styrofoam sides and bottom and the cost of the paper top. Let's call the radius of the paper top R, and assume that the height of the cylinder is greater than or equal to the radius of the paper top, so that the top can be completely covered with paper. Then the cost of the container is:

C = 0.04(2πrh + πr^2) + 0.05(πR^2)

Substituting h in terms of r, we get:

C = 0.08πr(600/(πr^2)) + 0.04πr^2 + 0.05πR^2

= 4.8/r + 0.04πr^2 + 0.05πR^2

To minimize the cost, we need to find the values of r and R that minimize the cost function C. To do this, we take the partial derivatives of C with respect to r and R, and set them equal to zero:

dC/dr = -4.8/r^2 + 0.08πr = 0

dC/dR = 0.1πR = 0

Solving for r and R, we get:

r = ∛(60/π) ≈ 2.78 cm

R = 2.5 cm

We can check that these values give us a minimum by checking the second derivatives:

d^2C/dr^2 = 9.6/r^3 + 0.08π > 0 (minimum)

d^2C/dR^2 = 0.1π > 0 (minimum)

Therefore, the dimensions of the cylinder that minimize the production cost are:

radius = approximately 2.78 cm

height = 600 / (πr^2) ≈ 7.14 cm

paper top radius = 2.5 cm

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Kimo should make 5 loads in the small truck and 4 loads in the large truck per day to minimize the total cost while meeting the delivery and union requirements.

What is the equivalent expression?

Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.

the total cost will be minimized when the loads are distributed in the following way:

5 loads in the small truck (total capacity of 5 * 50 = 250 cubic yards)

4 loads in the large truck (total capacity of 4 * 70 = 280 cubic yards)

This will result in a total of 9 loads and a total capacity of 530 cubic yards, which meets both the daily minimum delivery requirement of 350 cubic yards and the union contract requirement of 9 loads per day.

The total cost can be calculated as follows:

Cost of 5 loads in small truck = 5 * $87 = $435

Cost of 4 loads in large truck = 4 * $73 = $292

Total cost per day = $435 + $292 = $727

Therefore, Kimo should make 5 loads in the small truck and 4 loads in the large truck per day to minimize the total cost while meeting the delivery and union requirements.

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Answer:

b

Step-by-step explanation:

point B has coordinates (0, 0 ) which is the origin

Jorge's older brother's watering can holds approximately 165.33 cups of water. And since Jorge's watering can holds half as much water as his older brother's watering can, Jorge's watering can holds approximately (1/2) × 165.33 = 82.67 cups of water, which we can round to 4 cups.

Let's represent the amount of water that Jorge's older brother's watering can holds by x. According to the problem, Jorge's watering can holds half as much water as his older brother's watering can. Therefore, Jorge's watering can holds (1/2)x cups of water.

We also know that Jorge's younger brother's watering can holds 8 cups of water. Altogether, the watering cans hold 2 gallons, which is equal to 2 × 128 = 256 fluid ounces (since there are 128 fluid ounces in a gallon).

We can write an equation based on the given information:

x + (1/2)x + 8 = 256

Simplifying the equation, we get:

(3/2)x = 248

x = 248 × 2/3 = 165.33

Therefore, jorge's watering can holds 4 cups of water.

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1. This is not an example of a quasi-experimental design because the researcher randomly assigned participants to the two groups. In a quasi-experimental design, the researcher does not have full control over the assignment of participants to groups.

2. The dependent variable in this study is the word recall. It is the variable that the researcher is interested in measuring and is expected to be affected by the independent variable.

3. The independent variable in this study is sugar consumption. It is the variable that the researcher manipulated by assigning participants to one of two groups, sugar vs. no sugar.

The purpose of manipulating the independent variable is to examine its effect on the dependent variable, word recall.

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