∞∑n=1 (2n!/2^2n) What is the value of r from the ratio test? What does this r value tell you about the series?

First, we need to convert the volume of the juice in the jar from liters to milliliters, since the volume of the glasses is given in milliliters.

1 liter = 1000 milliliters

So, 70 liters = 70 * 1000 = 70,000 milliliters

Next, we'll divide the volume of the juice in the jar by the volume of each glass to find out how many glasses can be filled with the juice.

70,000 milliliters ÷ 150 milliliters/glass = 466.67 glasses (rounded to the nearest whole number)

Therefore, 466 glasses can be filled completely with the juice.

Finally, we can find out how much juice is left in the jar by subtracting the total volume of the juice used to fill the glasses from the volume of the juice in the jar.

70,000 milliliters - (466 glasses x 150 milliliters/glass) = 70,000 milliliters - 69900 milliliters = 800 milliliters

So, 800 milliliters of juice is left in the jar.

Answer:

25°

Step-by-step explanation:

look at the picture, that's the ans

Answer:

x = 25.4

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

139° is an exterior angle of the triangle, then

5x - 25 + 37 = 139

5x + 12 = 139 ( subtract 12 from both sides )

5x = 127 ( divide both sides by 5 )

x = 25.4

The value of k in the exponential function is -3.

Taking the natural logarithm of both sides of the equation, we have:

ln [ (1 + 65/x)^(3x) ] = ln(e^k)

Using the properties of logarithms, we can simplify the left side of the equation:

3x ln(1 + 65/x) = k

Taking the limit as x approaches infinity, we have:

lim (x → ∞) 3x ln(1 + 65/x)

= lim (x → ∞) [ln(1 + 65/x) / (1/x)] × 3

Using L'Hopital's rule, we can evaluate the limit:

lim (x → ∞) [ln(1 + 65/x) / (1/x)]

= lim (x → ∞) [-65 / (x(1+65/x))]

= -65/65

= -1

Therefore, we have:

lim (x → ∞) 3x ln(1 + 65/x)

= lim (x → ∞) [ln(1 + 65/x) / (1/x)] × 3

= -3

Thus, the exponential equation simplifies to:

-3 = k

Learn more about limits here: https://brainly.com/question/23343679

#SPJ1

We have the expression:

[tex]\displaystyle{\lim_{x\to \infty} \left(1+\dfrac{65}{x}\right)^{3x} = e^k} \\[/tex]

As [tex]\displaystyle{x\to \infty} \\[/tex], the term [tex]\displaystyle{\dfrac{65}{x}} \\[/tex] approaches 0. Therefore, we can rewrite the expression as:

[tex]\displaystyle{\lim_{x\to \infty} \left(1+\dfrac{65}{x}\right)^{x \cdot \dfrac{3x}{65}} = e^k} \\[/tex]

Simplifying the exponent, we get:

[tex]\displaystyle{\lim_{x\to \infty} \left(1+\dfrac{65}{x}\right)^{\dfrac{3x^2}{65}} = e^k} \\[/tex]

Now, as [tex]\displaystyle{x\to \infty} \\[/tex], the expression [tex]\displaystyle{\left(1+\dfrac{65}{x}\right)^{\dfrac{3x^2}{65}}} \\[/tex] approaches [tex]\displaystyle{e^{-3}} \\[/tex].

Therefore, we have:

[tex]\displaystyle{e^k = e^{-3}} \\[/tex]

Comparing the exponents, we can conclude that:

[tex]\displaystyle{k = -3} \\[/tex]

Hence, the correct value of k is indeed -3.

Answer:

A large container is a better deal because for a large container the amount of jam per dollar is greater thank that in the three smaller containers.

Step-by-step explanation:

What is the volume of a cylinder?

The volume of a cylinder is given by -

V[c] = πr²h

Given is Terrel who has to buy either one large jar or three small jars of jam. A small jar has a diameter of 6 cm, a height of 7 cm, and costs $4. A large jar has a diameter of 8 cm, a height of 16 cm, and costs $12.

For one large container, its volume will be -

V[L] = πr²h = 22/7 x 4 x 4 x 16 = 804.56 cm³

Amount of jam per dollar = V[1] = 804.56 / 12 = 67.04 cm³

For three small containers, the total volume will be -

V[S] = πr²h = {22/7 x 3 x 3 x 7} x 3 = 594 cm³

Amount of jam per dollar = V[2] = 594 / 12 = 49.5 cm³

It can be seen that for a large container the amount of jam per dollar is greater than that in the three small container. Hence, a big container would be a better deal for Terrell.

Therefore, a large container is a better deal because  for a large container the amount of jam per dollar is greater than that in the three small container.

Answer:

Step-by-step explanation:

buy one large jar has which has a diameter of 8 cm, and a height of 16 cm.

The length of the unknown side is 11.2ft

Using the Pythagorean theorem which states that the square of the hypotenuse side is equal to the sum of the squares of the other two sides.

From the image shown,we have the parameters as;

Now, substitute the values, we have;

x² = 10² + 5²

Find the squares

x² = 100 + 25

Add the values

x ² = 125

Find the square root

x = 11.2 ft

Hence, the value is 11.2ft

Learn about Pythagorean theorem at: https://brainly.com/question/231802

#SPJ1

The toothpicks lennon should use in each row is 185.

Algebra is the study of abstract symbols, and logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction also. This approach is used to answer the given problem correctly and completely.

We are given that;

Total number of toothpicks= 3330

Number of rows= 18

Now,

To find the number of toothpicks in each row

=3330/18

=1665/9

=185

Therefore, by algebra the answer will be 185.

To know more about the Algebra visit;

brainly.com/question/953809

#SPJ9

The probability of drawing a black card in a standard deck of 52 cards is 1/2.

Probability of an event is a number that indicates how likely the event is to occur. It is expressed as a number in the range from 0 and 1. There are total 52 cards out of which 26 are black cards and 26 are red cards.

There are 26 black cards (13 spades and 13 clubs) in a standard deck of 52 cards.

Therefore, the probability of drawing a black card from a standard deck of 52 cards is 26/52.

Probability = 26/52 = 1/2

So, the probability of drawing a black card is 1/2.

Learn more about probability here: brainly.com/question/13604758

#SPJ4

Answer:

1.25 laps per minute

Step-by-step explanation:

5 laps in 4 minutes so distance over time is equal to rate so

5/4=1.25

The appropriate measure of variation (spread) for these data is the standard deviation, which is 2.287.

The appropriate measure of variation (spread) for these data is the standard deviation. Standard deviation is a measure of how much the data values vary from the mean (average) of the data set. It is calculated by taking the square root of the variance, which is the average of the squared differences between each data value and the mean.

To calculate the standard deviation for this data set, follow these steps:

1. Find the mean of the data set by adding up all of the data values and dividing by the total number of values. In this case, the mean is (4 + 7 + 2 + 3 + 4 + 2 + 1 + 3 + 9 + 8 + 5 + 1 + 3 + 2 + 3 + 2 + 4 + 3 + 6 + 5) / 20 = 3.65

2. Find the variance by subtracting the mean from each data value, squaring the result, and then finding the average of these squared differences. The variance for this data set is ((4 - 3.65)^2 + (7 - 3.65)^2 + (2 - 3.65)^2 + ... + (6 - 3.65)^2 + (5 - 3.65)^2) / 20 = 5.2275

3. Take the square root of the variance to find the standard deviation. The standard deviation for this data set is sqrt(5.2275) = 2.287

Therefore, the appropriate measure of variation (spread) for these data is the standard deviation, which is 2.287.

To learn more about the appropriate measure of variation, click here: https://brainly.com/question/28502442

#SPJ11

The area of the semi circle is 14.13 units²

a semicircle is a one-dimensional locus of points that forms half of a circle. It is a circular arc that measures 180°. It has only one line of symmetry.

The area of a semicircle is the half of the area of a full circle.

The area of a full circle is πr², therefore the area of a semicircle is ½πr²

r = d/2 = 6/2 = 3

A = ½πr²

= 1/2 × 3.14 × 3²

A = 28.26/2

A = 14.13 units²

therefore the area of the semi circle is 14.13 units²

learn more about area of a semi circle from

https://brainly.com/question/15822332

#SPJ1

Answer: Look below :)

Step-by-step explanation:

I graphed the inequality below:

from that we can see:

a. Points on the line are combinations of US/Mexico minutes he can do where all of his prepaid money will be used, For example, he could do 50 USA minutes and 80 Mexico minutes, and there would be no money left to spend

b. Points above the line are combinations of US/Mexico minutes that will cost him more than the prepaid $50.

c. Points below the line are combinations of US/Mexico minutes that will leave him with money left over from his $50.

I hope this makes sense! ask questions if you have any :)

Answer:

C

Step-by-step explanation:

The spaces go F A C E. The note shown is C.

Answer:

(4-g) X 1.5

Step-by-step explanation:

The number of sides the polygon have 9.

A vertex is a point on a polygon where two rays or line segments meet, the sides, or the edges of the object come together. Vertex is the plural form of vertices.

Given:

We have a polygon can be divided into 5 triangles when the diagonals are drawn from one of its vertices.

As, we know  the number of triangles in a polygon is  = n−2

where n is the number of sides (or vertices)

So, the number of sides the polygon have

n= 5+ 2

n = 7 sides

Thus, the polygon is Heptagon.

Learn more about Vertices here:

https://brainly.in/question/21792809

#SPJ9

[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{9}}}{\underset{\textit{\large run}} {\underset{x_2}{8}-\underset{x_1}{1}}} \implies \cfrac{ -1 }{ 7 } \implies - \cfrac{1 }{ 7 }[/tex]

On solving the provided question, we can say that the inequality is  y+2> -3x-3, Graph the points (0,-5) and (-2,1)

An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.

the inequality is

y+2> -3x-3

y > -3x-5

y = -3x-5

x   y = -3x-5

0   -5

-1   -2

-2   1

Graph the points (0,-5) and (-2,1)

To know more about inequality visit:

https://brainly.com/question/29914203

#SPJ1

The probability of receiving two heads and one tail is 3/8, or 0.375.

One of the areas of probability theory is the estimation of the chance of experiments occurring. Using a probability, we can calculate everything from the likelihood of getting heads or tails when flipping a coin to the likelihood of making a research error, for example. It is essential to appreciate the most basic definitions of this branch, such as the formula for computing probabilities in equiprobable sample spaces, the likelihood of two events joining together, the probability of the complementary event, etc., in order to properly understand it .Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. Mathematics has incorporated probability to forecast the likelihood of various events.

Learn more about probability from

brainly.com/question/13604758

#SPJ4

The ratio of pencils to pens can be calculated by dividing the number of pencils by the number of pens. In this case, the ratio of pencils to pens is 10/14.

A ratio is a way to compare two or more values or quantities. It is expressed as a fraction or as a colon-separated pair of numbers. The first number in the ratio represents the number of units of the first quantity, and the second number represents the number of units of the second quantity.

In the case of the ratio of pencils to pens, the first quantity is the number of pencils and the second quantity is the number of pens. To calculate the ratio, you divide the number of pencils by the number of pens. In this case, you would divide 10 by 14, which is equal to 10/14 or 5/7.

The ratio can be expressed as either a fraction or as a colon-separated pair of numbers. In this case, the ratio of pencils to pens is either 5/7 or 5:7.

To learn more about ratio please click on below link        

https://brainly.com/question/1504221

#SPJ4

Type A: 5.45 per pound, Type B: 4.35 per pound. This month's mixture: We know that an is 5.45 per pound, so we divide  total cost  401.65 by 5.45 to get a result of 73.69 LB of Type A. 2B + A = 410.35 2(4.35) = 8.70 A + 8.70 = 410.35 A = 401.65.

Total cost is a term used in economics to describe the least expensive way to produce a specific amount of a good (TC). Fixed costs, which are unaffected by the quantity of a good produced and include inputs like buildings and machinery, possibly including sunk costs, and variable costs, which change with the quantity of a good produced and include inputs like labor and raw materials, make up the total economic cost of production. Economics considers the total potential cost of each manufacturing item as one of the total cost's fixed or variable costs.

Learn more about costs  from

brainly.com/question/25109150

#SPJ4

a) (f ∘ g)(4) = 2

b) (g ∘ f)(4) = √2 + 5

c) (h ∘ g ∘ g)(-5) = 2 - 1/ (√(2√5) + 5)

d) (g ∘ f)(x) = √(x + 5) + 5.

e) (f ∘ g)(x) = √(√x + 5) + 5

f) (h ∘ f)(x) = 2 - 1/ (√x + 5)

What is Function?

A function is an expression or relationship that involves one or more variables. It has several inputs and outputs.

a) (f ∘ g)(4) means plugging in the value of 4 into g(x) and then plugging the result into f(x). So we have:

g(4) = √4 + 5 = √9 = 3

f(g(4)) = f(3) = √3 + 5 = 2

Therefore, (f ∘ g)(4) = 2.

b) b) (g ∘ f)(4) means plugging in the value of 4 into f(x) and then plugging the result into g(x). So we have:

f(4) = √4 = 2

g(f(4)) = g(2) = √2 + 5

Therefore, (g ∘ f)(4) = √2 + 5.

c) (h ∘ g ∘ g)(-5) means plugging in the value of -5 into g(x) twice, and then plugging the result into h(x). So we have:

g(-5) = √(-5) + 5 = √(20) = 2√5

g(g(-5)) = g(2√5) = √(2√5) + 5

h(g(g(-5))) = h(√(2√5) + 5) = 2 - 1/ (√(2√5) + 5)

Therefore, (h ∘ g ∘ g)(-5) = 2 - 1/ (√(2√5) + 5).

d) (g ∘ f)(x) means plugging in the function f(x) into g(x), which gives:

g(f(x)) = √(x + 5) + 5

Therefore, (g ∘ f)(x) = √(x + 5) + 5.

e) (f ∘ g)(x) means plugging in the function g(x) into f(x), which gives:

f(g(x)) = √(√x + 5) + 5

Therefore, (f ∘ g)(x) = √(√x + 5) + 5.

f) (h ∘ f)(x) means plugging in the function f(x) into h(x), which gives:

h(f(x)) = 2 - 1/ (√x + 5)

Therefore, (h ∘ f)(x) = 2 - 1/ (√x + 5).

To know more about function visit,

https://brainly.com/question/22340031

#SPJ1

A process in which a number is changed, such as by adding, subtracting, dividing or multiplying is called arithmetic process.

The four basic operations of mathematics are addition, subtraction, multiplication and division. We call this group of four operations "arithmetic". Arithmetic is defined by the four most basic operations in mathematics. These four operations are the most basic, but that doesn't mean they're always easy to perform. In other words, arithmetic ranges from very simple things like 1 + 1 to very complex and complex things. It all depends on the context in which a person is working, but when we are dealing with one of the four operations of addition, subtraction, multiplication or division we are dealing with so-called arithmetic operations in mathematics.

To learn more arithmetic operations, visit :

https://brainly.com/question/22650153

#SPJ4

Complete question:

A process in which a number is changed, such as by adding, subtracting, dividing or multiplying is called:________.

For given geometrical shape, The angles which we need to find are  ∠z=115° and y=21.

What are geometric shapes, exactly?

Geometric shapes are mathematical figures that reflect the shape of objects we see in our daily lives. Shapes are geometric shapes that have boundary lines, angles, and surfaces. There are several types of 2d and 3d shapes.

Shapes are also classified according to their regularity or homogeneity. A symmetrical regular form, such as a square or circle, is common. Asymmetry can take on irregular shapes. They're also referred to as organic forms or freeform shapes. A tree, for example, has an irregular or organic shape.

In plane geometry, two-dimensional forms are flat shapes and closed figures such as circles, squares, rectangles, rhombuses, and so on. In solid geometry, the three-dimensional shapes are the cube, cuboid, and sphere.

Now,

In given figure ∠z+65°=180°    (Sum of two interior angles)

then ∠z=115°

and ∠z=∠6y-11   (vertically opposite angles)

6y-11=115

6y=126

y=21

Hence,

           For given geometrical shape, ∠z=115° and y=21.

To know more about geometric shapes visit the link

https://brainly.com/question/10059415?referrer=searchResults

#SPJ1

Answer: 90 miles in 180 minutes

Step-by-step explanation: Since 90 minutes is two times 45, there would be 2 miles in one minute. Then, you multiply 2 times 45 so therefore you get 90 miles in 180 minutes.

The total volume of lemonade held by 24 bottles would be 18,000 mL (750 mL x 24) or 24x 0.75 liters = 18 liters.

And it would be to express the total volume in terms of the volume of one bottle. You can say that 24 bottles of lemonade is equal to 18 times the volume of one bottle, or 18 x 750 mL = 18,000 mL. This can also be written as 24 x 0.75 liters = 18 liters. This can also be expressed as 18 liters, since 1 liter is equal to 1000 mL.

Regardless of how you choose to express the answer, both methods give us the same result: 24 bottles of lemonade hold a total of 18,000 mL or 18 liters of the beverage. This information can be useful in various contexts, such as for planning a party or for ordering supplies for a lemonade stand. It's important to note that while both answers give the same result, they present the information in different ways. The first answer provides the total volume of lemonade held by all 24 bottles, while the second answer provides the number of times the volume of one bottle is contained within the total volume. Both answers provide useful information and the choice of which one to use may depend on the specific context in which the question is being asked.

To know more about volume of lemonade click here:

brainly.com/question/27860133

#SPJ4

====================================================

Work Shown:

n = number of nickels

22-n = number of dimes

5n = value of the nickels in cents

10(22-n) = value of the dimes in cents

5n+10(22-n) = total value in cents

5n+10(22-n) = 180

5n+220-10n = 180

-5n+220 = 180

-5n = 180-220

-5n = -40

n = -40/(-5)

n = 8 is the number of nickels

22-n = 22-8 = 14 is the number of dimes

-----------------

Check:

8 nickels = 8*5 = 40 cents

14 dimes = 14*10 = 140 cents

8 nickels + 14 dimes = 40 cents + 140 cents = 180 cents = $1.80

8 nickels + 14 dimes = 22 coins total

The answers are confirmed.

Answer:

Step-by-step explanation:

make the inequality y=3x-7 to get the linear line then find x=0 with is -7 and anything below that line or on the line is not part of the inequality therefore remember to graph with a dotted line instead of a solid.