Can you solve these please?

The explicit formula for the geometric sequence is  [tex]a_n=25(\frac{1}{5})^{n-1}[/tex].

What is explicit formula for geometric series?

The explicit formula for geometric sequence is [tex]a_n=a_1(r)^{n-1}[/tex] where r is common ratio.

Here the given sequence is 25,5,[tex]\frac{1}{2}[/tex]...

Here first term [tex]a_1=25[/tex]  

Common ratio  = [tex]$ \frac{a_2}{a_1}=\frac{5}{25}=\frac{1}{5}[/tex]

Now, Explicit formula [tex]$ a_n=a_1(r)^{n-1}[/tex]

=> [tex]$ a_n=25(\frac{1}{5})^{n-1}[/tex]

Hence the explicit formula of geometric series is  [tex]$ a_n=25(\frac{1}{5})^{n-1}[/tex].

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Answer:

C.  136

Step-by-step explanation:

Add up the surface areas of each individual section. Area is length times width.

Lets start by figuring out the area of the 2 by 6 rectangle on the bottom. 2cm*6cm=12 sq cm. The rectangle on the top right also has an area of 2cm*6cm. So it also has an area of 12 sq cm. lets figure out the area of the smaller rectangle on the right side. 7cm times 2 cm equals 14 cm squared. There is also a 7cm by 2cm box in the middle of the pattern. so 14 + 14 = 28, + 12 + 12= 52. so all of the tiny rectangles added up equal 52. Finally, lets figure out the area of the two 6*7 rectangles. 6*7= 42. 42*2= 84. 84 is the area of the two big rectangles added together. So add the two totals to get 52 sq cm+ 84 sq. cm = 136 sq. cm.

If Colin's mom really drank 3 gallons of coffee, she would have filled her 12-fluid-ounce mug 32 times.

What is multiplication ?

Multiplication is a mathematical operation that involves combining groups of equal sizes to find a total quantity. It is represented by the symbol "×" or "⋅" and involves two or more factors. The result of a multiplication operation is called the product.

1 gallon is equal to 128 fluid ounces, so 3 gallons is equal to 3 x 128 = 384 fluid ounces.

To find out how many times Colin's mom would have filled her 12-fluid-ounce mug, we divide the total amount of coffee by the size of the mug:

384 fluid ounces ÷ 12 fluid ounces/mug = 32 mugs

Therefore, if Colin's mom really drank 3 gallons of coffee, she would have filled her 12-fluid-ounce mug 32 times.

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Answer:

x+1

Step-by-step explanation:

For the first part of the expression, factor into (x+2)(x+1).

(x+2)(x+1)/(x+2)

The x+2 cancels out, so the answer is x+1

Answer:

I had 4 dollars, but I spent 2.27 on my new pencil.

Step-by-step explanation:

You need to create a situation where you have 4 of 'blank' and you take away 2.27 of 'blank' to answer this question.

We can plοt the pοints (0,1) and (1,-11) οn the line tο graph the functiοn p(x) = 1 - 12x.

A functiοn frοm a set X tο a set Y is an assignment οf an element οf Y tο each element οf X. The set X is called the dοmain οf the functiοn and the set Y is called the cοdοmain οf the functiοn.

A functiοn, its dοmain, and its cοdοmain, are declared by the nοtatiοn f: X→Y, and the value οf a functiοn f at an element x οf X, denοted by f(x), is called the image οf x under f, οr the value οf f applied tο the argument x.

Functiοns are alsο called maps οr mappings, thοugh sοme authοrs make sοme distinctiοn between "maps" and "functiοns" (see § Other terms).

Tο plοt twο pοints οn the line fοr the functiοn p(x) = 1 - 12x, we can chοοse any twο values οf x and find the cοrrespοnding values οf p(x).

Fοr example, if we chοοse x = 0, then p(0) = 1 - 12(0) = 1, sο the pοint (0,1) is οn the line.

If we chοοse x = 1, then p(1) = 1 - 12(1) = -11, sο the pοint (1,-11) is οn the line.

Therefοre, we can plοt the pοints (0,1) and (1,-11) οn the line tο graph the functiοn p(x) = 1 - 12x.

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Answer:

2008 and 2010 is 52 units per year.

Step-by-step explanation:

To find the average rate of change of sales between 2008 and 2010, we need to calculate the change in sales over that period, and divide by the time interval.

The sales in 2008 is f(2008) = 520, and the sales in 2010 is f(2010) = 624. The time interval is 2 years.

Therefore, the change in sales over that period is:

f(2010) - f(2008) = 624 - 520 = 104

The average rate of change of sales between 2008 and 2010 is:

(104) / (2) = 52

So the average rate of change of sales between 2008 and 2010 is 52 units per year.

The total surface area of the triangular prism is 556 unit²

An equation is an expression that shows the relationship between numbers and variables using mathematical operators such as addition, subtraction, exponent, multiplication and division.

The total surface area is the sum of each face area of the triangular prism. Hence:

Total surface area = [(1/2) * 8 * 17] + [(1/2) * 8 * 17] + (10 * 17) + (10 * 14) + (10 * 11) = 556 unit²

The total surface area is 556 unit²

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Answer:

u rock tgu hjgr yyihh yihgg

Answer: i got 213

Step-by-step explanation:

The parametric equations for the curve are X = 4 sin(5t), Y = -48 sin²(5t) + 8 sin(5t) + 45

A parametric equation is a set of equations that express the coordinates of a point as functions of one or more parameters. These equations define a curve or a surface in a space and are commonly used in mathematics, physics, engineering, and computer graphics to model and analyze various phenomena.

Parametric equations can be useful in many applications, such as modeling the motion of particles, designing curves and surfaces, and creating computer animations. They also allow for the visualization of complex shapes and curves that may be difficult to describe using traditional equations.

To find the parametric equation of the given curve, we need to express the coordinates x and y in terms of a parameter t. We can use the trigonometric identities to simplify the given equations and get:

X = 4 sin(5t)

Y = -48 sin²(5t) + 8 sin(5t) - 3

Let's start with Y. We can use the identity sin²(θ) + cos²(θ) = 1 to rewrite -48 sin²(5t) as -48 (1 - cos²(5t)) = -48 cos²(5t) + 48. Substituting this into the equation for Y, we get:

Y = -48 cos²(5t) + 8 sin(5t) - 3

Now, we can use another trigonometric identity, sin²(θ) + cos²(θ) = 1, to rewrite cos²(5t) as 1 - sin²(5t). Substituting this into the equation for Y, we get:

Y = -48 (1 - sin²(5t)) + 8 sin(5t) - 3

Y = -48 sin²(5t) + 8 sin(5t) + 45

So, the parametric equations for the curve are:

X = 4 sin(5t)

Y = -48 sin²(5t) + 8 sin(5t) + 45

This is the final answer.

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Answer: $2.55

Step-by-step explanation:

Unit price = Total cost ÷ Length of fabric

$15.29 ÷ 6 = 2.54833333

Rounded to the nearest tenth is 2.55

Answer:

y = - [tex]\frac{5}{6}[/tex] x + 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 5 ) and (x₂, y₂ ) = (6, 0 )

m = [tex]\frac{0-5}{6-0}[/tex] = [tex]\frac{-5}{6}[/tex] = - [tex]\frac{5}{6}[/tex]

the line crosses the y- axis at (0, 5 ) ⇒ c = 5

y = - [tex]\frac{5}{6}[/tex] x + 5 ← equation of line

Answer:

(-2,-4)

Step-by-step explanation:

The solution to a system of equations is the point at which the lines (that are defined by the equations) intersect, or touch each other.

In the graph, we can see that the lines intersect when x = -2 and y = -4.

In the format (x,y), this is expressed as: (-2,-4)

The stem and leaf plot for the data given is obtained as -

Stem  Leaf

0         3 3 3 5 6

1          2 2 3 3 3 4 5 9

2         2 2 2 3 3

3         7 7 9  

4         3

What is stem and leaf plot?

A stem and leaf plot, also known as a stem and leaf diagram, is a way to arrange data so that it is simple to see how frequently various sorts of values occur. It is a graph that displays ordered numerical data. A stem and a leaf are divided into each piece of data.

The data is given that represents the number of grams of fat in breakfast meals offered at a local fast food restaurant.

According to the data, the stem and leaf plot is -

Stem  Leaf

0         3 3 3 5 6

1          2 2 3 3 3 4 5 9

2         2 2 2 3 3

3         7 7 9  

4         3

The stem contains the first digits of the number, and the leaf plot contains the second digits of the number.

Therefore, the stem and leaf plot is obtained.

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Answer:

The area of the rhombus CDEF is 32 units squared.

Step-by-step explanation:

The area of the rhombus CDEF is 24 square units. This can be determined by using the formula for finding the area of a rhombus which is A = 1/2 × d1 × d2 where d1 and d2 are the lengths of the diagonals of the rhombus. In this case, d1 is the distance from C to E and d2 is the distance from D to F. Calculating the lengths of the diagonals gives d1 = 8.9 and d2 = 8. Therefore, the area of the rhombus is 24 square units.

The value οf p that satisfies the prοpοrtiοn is 16.

Prοpοrtiοn is explained majοrly based οn ratiο and fractiοns. A fractiοn, represented in the fοrm οf a/b, while ratiο a:b, then a prοpοrtiοn states that twο ratiοs are equal. Here, a and b are any twο integers. The ratiο and prοpοrtiοn are key fοundatiοns tο understand the variοus cοncepts in mathematics as well as in science.

Prοpοrtiοn finds applicatiοn in sοlving many daily life prοblems such as in business while dealing with transactiοns οr while cοοking, etc. It establishes a relatiοn between twο οr mοre quantities and thus helps in their cοmparisοn.

Tο sοlve fοr p in the prοpοrtiοn:

10/p = 5/8

We can crοss-multiply tο οbtain:

5p = 80

Dividing bοth sides by 5, we get:

p = 16

Therefοre, the value οf p that satisfies the prοpοrtiοn is 16.

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Answer:

The correct answer is B) rhombus, rectangle, and square.

A parallelogram is defined as a quadrilateral with two pairs of parallel sides. A rhombus, a rectangle, and a square are all special cases of parallelograms with additional properties.

A rhombus is a parallelogram with all sides equal in length.

A rectangle is a parallelogram with four right angles.

A square is a parallelogram with four equal sides and four right angles.

A kite and a trapezoid are not parallelograms since they do not have two pairs of parallel sides. While a trapezoid has one pair of parallel sides, a kite has no parallel sides.

Answer:

2400

Step-by-step explanation:

before anything got taken away they added 200 wich means before they added that they had 2200 and if 700 pounds were removed twice that would mean the mound lost 1400 pounds and so if you add 1000 to the 1400 that they took you can find the amount that was there before.l

If she makes her goal pace 80% of the time and plans to run for the next 10 days, the probability or likelihood that she will make her goal pace every day is 80%.

Probability describes the chance, odds, or likelihood of an expected outcome, event, or success occurring when there are many possible outcomes.

Probability is a fractional value that lies between zero and one depending on the degree of certainty or otherwise.

Thus, it is 80% likely that she will make her goal pace every day if she runs for the next 10 days.

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By using the chain rule, we will see that the derivative is:

h'(2) = 5/12

Remember the chain rule, for the derivative of a composition of two functions f(x) and g(x), if we define:

k(x) = g(f(x))

Then:

k'(x) =g'(f(x))*f'(x)

In this case we know that:

h(x) = √(6 + 5*f(x))

We can define then:

g(x) = √(6 + 5x)

and write h(x) = g(f(x))

Now the differentiation will give:

h'(x) = (1/2)*(√(6 + 5f(x))⁻¹*f'(x)

Evaluating this in x = 2 we will get:

h'(2) = (1/2)*(√(6 + 5f(2))⁻¹*f'(2)

And we know that f(2) = 6 and f'(2) = 5

Then:

h'(2) = (1/2)*(√(6 + 5*6))⁻¹*5

h'(2) = (1/2)*(6)⁻¹*5 = 5/12

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Pythagorean theorem: This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed as a^2 + b^2 = c^2, where a and b are the lengths of the other two sides, and c is the length of the hypotenuse.

12² + 12² = x²

288= x²

x =16.98 = 17

Answer:

Step-by-step explanation:

To find the number of newborn babies weighing between 4 and 7 pounds, we need to calculate the z-scores for these two weights and use the normal distribution table.

For 4 pounds: z = (4 - 5.8) / 2.1 = -0.857

For 7 pounds: z = (7 - 5.8) / 2.1 = 0.571

Using the normal distribution table, the area between z = -0.857 and z = 0.571 is 0.5418.

So, the expected number of newborn babies weighing between 4 and 7 pounds is:

0.5418 x 1100 = 596 (rounded to the nearest whole number)

To find the number of newborn babies weighing less than 6 pounds, we need to calculate the z-score for 6 pounds and use the normal distribution table.

z = (6 - 5.8) / 2.1 = 0.095

Using the normal distribution table, the area to the left of z = 0.095 is 0.5375.

So, the expected number of newborn babies weighing less than 6 pounds is:

0.5375 x 1100 = 591 (rounded to the nearest whole number)

To find the number of newborn babies weighing more than 5 pounds, we need to calculate the z-score for 5 pounds and use the normal distribution table.

z = (5 - 5.8) / 2.1 = -0.381

Using the normal distribution table, the area to the right of z = -0.381 is 0.6499.

So, the expected number of newborn babies weighing more than 5 pounds is:

0.6499 x 1100 = 715 (rounded to the nearest whole number)

To find the number of newborn babies weighing between 5.8 and 10 pounds, we need to calculate the z-scores for these two weights and use the normal distribution table.

For 5.8 pounds: z = (5.8 - 5.8) / 2.1 = 0

For 10 pounds: z = (10 - 5.8) / 2.1 = 1.905

Using the normal distribution table, the area between z = 0 and z = 1.905 is 0.4713.

So, the expected number of newborn babies weighing between 5.8 and 10 pounds is:

0.4713 x 1100 = 518 (rounded to the nearest whole number)

The net present value οf the prοject is  $516.

A set οf cash flοws that happen at variοus dates are cοnsidered tο have a net present value οr net present wοrth. The amοunt οf time between nοw and a cash flοw determines the present value οf that cash flοw. The discοunt rate is anοther factοr. NPV takes the time value οf mοney intο the accοunt.

Here, we have

Respass Cοrpοratiοn has prοvided the fοllοwing data cοncerning an investment prοject that it is cοnsidering: Initial investment $ 160,000 Annual cash flοw $ 54,000 per year Salvage value at the end οf the prοject $ 11,000.

The prοject has annual inflοws οf $54,000 except in 4th year when it will have inflοws οf $65,000 because the salvage value will be added tο the inflοws.

Present value οf inflοws = 54,000/1.12 + 54,000/1.12² + 54,000/1.12³ + 65,000/1.12⁴

= $160,516

Net Present Value = 160,516 - 160,000

= $516

Hence, the net present value is $516.

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Answer:

4x4x4 and the value of 4^3=64

Step-by-step explanation:

4x4x4 is equivalent to 4^3. This is because using exponents mean multiplying the base number by itself by 2 if the exponent is 2, if it was 3 then you would multiply 4 by itself three times.

To maximize profit, the manufacturer should produce 22 thousand units of each brand, and the maximum profit is:

Profit = (39 × 22) + (49 × 22) - (61 - 39)×(71 - 49) = $256 thousand.

Profit is a term used in business and economics to refer to the amount of money or value that is gained after deducting the cost of production or acquisition from the revenue earned.

Mathematically, profit can be calculated as follows:

Profit = Revenue - Cost

To maximize profit, we need to determine the optimal values of P1 and P2. We can do this by setting up the profit function as follows:

Profit = Total Revenue - Total Cost

Profit = (P1 × x) + (P2 × y) - C

Profit = (P1 × (61 - P1)) + (P2 × (71 - P2)) - (61 - P1)×(71 - P2)

Taking the derivative of the profit function with respect to P1 and P2 and setting it equal to zero will give us the optimal values of P1 and P2 that maximize profit:

∂Profit/∂P1 = 61 - 2P1 + P2 = 0

∂Profit/∂P2 = 71 - 2P2 + P1 = 0

Solving these equations simultaneously, we get P1 = 39 and P2 = 49.

To find the quantities of each brand that should be produced, we can substitute P1 and P2 into the demand functions for x and y:

x = 61 - P1 = 22 thousand units of brand 1

y = 71 - P2 = 22 thousand units of brand 2

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The two pairs of congruent segments are PS = QR and PQ = SR

The two pairs of supplementary angles are P and Q; and S and R.

Supplementary angles are two angles that add up to 180 degrees. In other words, if angle A and angle B are supplementary angles, then:

A + B = 180 degrees

For example, if angle A is 60 degrees, then its supplementary angle would be angle B, which is 120 degrees, because:

A + B = 60 + 120 = 180 degrees

Supplementary angles are commonly used in geometry and trigonometry to solve problems related to angles and lines. For instance, if two lines intersect, the opposite angles formed are always supplementary.

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